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Adsorption is a process where a solid or liquid substance is attracted and held onto the surface of another material. It is an essential process in many industries, including water treatment, food processing, and pharmaceuticals. The effectiveness of adsorption depends on the properties of the adsorbent material, such as its surface area, pore size distribution, and chemical composition. Therefore, finding an optimum adsorbent material is crucial to achieving efficient and cost-effective adsorption processes.

One of the most powerful tools for determining the properties of an adsorbent material is the BET analysis. The BET (Brunauer-Emmett-Teller) analysis is a technique used to measure the specific surface area of a material by measuring the amount of gas adsorbed onto its surface at different pressures. The data obtained from BET analysis can be used to calculate the pore size distribution and other critical parameters that determine the adsorption capacity and efficiency of the material.

BET analysis can be used to evaluate various types of materials, including activated carbon, zeolites, silica gels, and metal-organic frameworks. By using BET analysis, researchers can determine the optimum conditions for preparing and using these materials as adsorbents. Here are some ways BET analysis can help in finding an optimum material for using as an adsorbate:

1. Determining the Specific Surface Area

The specific surface area of an adsorbent material is one of the most critical parameters that affect its adsorption capacity. BET analysis can accurately measure the specific surface area of a material by analyzing the amount of gas adsorbed onto its surface at different pressures. The higher the specific surface area, the more adsorption sites are available for attracting and holding onto target molecules.

2. Calculating Pore Size Distribution

The pore size distribution of an adsorbent material is another crucial factor that affects its adsorption capacity. BET analysis can provide information about the pore size distribution of a material by analyzing the adsorption isotherm data. The pore size distribution can be used to determine the optimum pore size range for the target molecules to be adsorbed.

3. Evaluating Adsorption Capacity

BET analysis can also be used to evaluate the adsorption capacity of an adsorbent material. By measuring the amount of gas adsorbed onto the material at different pressures, researchers can determine the maximum amount of target molecules that can be adsorbed onto the material. This information can be used to optimize the adsorption process and determine the most effective operating conditions.

4. Comparing Different Materials

BET analysis can also be used to compare the properties of different adsorbent materials. By analyzing the specific surface area, pore size distribution, and other parameters, researchers can determine which material is most suitable for a specific application. This information can help in selecting the best material for a particular adsorption process and improve its efficiency and cost-effectiveness.

In conclusion, BET analysis is a powerful tool for evaluating the properties of adsorbent materials and finding an optimum material for using as an adsorbate. By analyzing the specific surface area, pore size distribution, and other parameters, researchers can determine the most effective operating conditions and select the best material for a specific application. BET analysis can help in improving the efficiency and cost-effectiveness of adsorption processes in various industries, making it an essential technique for researchers and engineers working in this field.

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1. Introduction

Today several instruments for fast spectra recording are available. In most cases the difficulty
is to process and analyze the data quickly in a reliable way. The Maud program, in one of its
many undocumented features, can be used to process a list of analyses in batch mode from the
console without requiring the interface. This is useful to process quickly similar spectra or launch
a slow/time consuming refinement in a remote computer without recurring to the interface that
would need to open a session involving the remote display setting.

The overall procedure is to prepare the analysis locally using the interface or to prepare a starting point for a series of spectra
(one common starting point) also using the interface, then to prepare an instruction file in CIF like
format to specify the analyses, the spectra and the kind of refinement to conduct and finally to run
Maud in batch mode providing the instruction file previously prepared. The program will run and
process one analysis at time and prepare an output file extracting some key information (either the
default or some to be specified) in a format suitable to be imported in spreadsheet or graphical
programs to analyze the results.
As an example we will show the procedure to analyze a series of ball milled Cu-Fe mixed powders
in which two different phases may form with a different composition. By an automatic Rietveld
analysis performed in batch mode we will extract information about phase content [2, 1], crystallite
and microstrain for each sample/spectrum. The analysis is further complicated from the fact that
the powders milled at higher energy show the presence of planar defects [5] and texture arising
from sample preparation and the platelet like shape of the grains [3].

2 Analysis and procedure
In this section we will present the procedure to analyze 25 spectra of Cu-Fe different samples. The
spectra has been collected by a Philips X-pert system in Le Mans at the LPEC laboratory of the
1
University du Maine, thanks to A. Gibaud.
2.1 Analysis preparation through the interface
We start the Maud program and load all the datafiles together to check their integrity and to prepare
a common starting analysis file. A plot of all spectra and their differences is available in Figure 1.

We load the two possible phases, bcc iron and fcc copper, from the Maud database. By computing
the spectra once and comparing them visually with the experimental spectra we may notice that
for some samples, milled at longer time, an alloyed fcc phase form (out of equilibrium) and the
bcc iron disappears. Unluckily we could not use the copper rich phase cell parameter to monitor
the Fe content in it as the cell parameter tends to growth as a result probably of oxygen entrapping.
In a first attempt we discovered the spectra were affected by texture, anisotropic crystallite sizes
and microstrain as well as planar defects (especially on the Cu like phase). So we decide here
to include also texture and anisotropic/planar defects effects in the analysis. For both the bcc
and fcc phases we select in the proper panel the Popa model for anisotropic broadening [4], the
Warren model for planar defects and the harmonic model for texture (specifying cylindrical sample
symmetry and Lmax = 6 in the options; it is required by the experiment geometry).
Next step was to adjust the cell parameters for both bcc and fcc phases in order to get a mean
starting value good for all spectra (especially for the fcc); and to adjust the crystallite value to a
good starting point (around 200 angstrom) obtaining peak shapes a little sharper than in the less
broadened spectrum. The background constant parameter was also adjusted to the value of the
spectrum with the lower background. Actually only the cell parameter adjustment is critical, the
background one is even not necessary.
Finally we remove all the spectra (we will specify which datafile to use for each analysis later in an
instruction file) and save the analysis containing everything except the spectrum/a. For the purpose
of this article we save the analysis with the name: FeCustart.par.
2.2 Preparation of the instruction file and batch processing
To run Maud in batch we need to write an instruction file containing the list of analyses to execute
one at time. The file is in CIF format but containing some terms not available in the official CIF
dictionary, but that Maud recognize. All the analyses to be performed are specified through the
loop CIF instruction. The first term of the loop must be the one specifying the starting analysis
file to be loaded (full path in unix convention) and then the others to instruct Maud for the kind
of analysis to perform, iterations and eventually datafile to load and name of the file were to save
the analysis. Additional keywords can be used to append specific results to a file for spreadsheet
analysis. The simplest instruction file is something containing the following:
First example (paths for windows):
loop
riet analysis file
riet analysis iteration number
2
´//C:/mypathfortheanalysis/analysis1.par´ 5
´//C:/mypathfortheanalysis/analysis2.par´ 3
´//C:/mypathfortheanalysis/analysis3.par´ 7
The analysis1.par (or 2 or 3) are some analyses files prepared with Maud, containing also
the datafile/spectrum, already set for the parameters to be refined and saved just ready for the refinement step. Maud will load each analysis, starts the refinement with the number of iterations
specified and save the analysis with the refined parameters under the same name. The analyses can
be loaded at end in Maud (with the interface) to see the result of the refinement.
In the case of the Cu-Fe we need to perform some more steps: first we start from one common analysis point (the FeCustart.par analysis file) but we want to specify different datafiles; second
we want to perform a full automatic analysis in which Maud performs different cycles deciding
which parameters to refine at each step and third we will specify the name of each analysis for the
saving process and a file name were to append some selected results in a tab/column format for
subsequent easy loading in a spreadsheet program.
Cu-Fe example:
loop
riet analysis file
riet analysis iteration number
riet analysis wizard index
riet analysis fileToSave
riet meas datafile name
riet append simple result to
´//mypath/FeCustart.par´ 7 13 ´//mypath/FECU1010.par´ ´//mypath/FECU1010.UDF´
´//mypath/FECUresults.txt´
´//mypath/FeCustart.par´ 7 13 ´//mypath/FECU1011.par´ ´//mypath/FECU1011.UDF´
´//mypath/FECUresults.txt´
…………(lines with all the other 23 datafiles omitted for brevity)
´//mypath/FeCustart.par´ 7 13 ´//mypath/FECU1038.par´ ´//mypath/FECU1038.UDF´
´//mypath/FECUresults.txt´
With this instruction file (that we save under the name: fecu.ins) we specify for example that
as a first analysis, Maud has to load the FeCustart.par file, then to load in the analysis the
FECU1010.UDF datafile, to perform the automatic analysis number 13 (in the wizard panel of
Maud the automatic analysis number 13 is the texture analysis; we need to refine also the texture
parameters along with phase analysis and microstructure) and to use 7 iterations for each cycle (the
texture automatic analysis is composed by 4 cycles) to ensure sufficient convergence. At the end
the analysis is saved with the name FECU1010.par and simple selected results will be appended
in the file FECUresults.txt. The simple results saved in the spreadsheet like file are some of
the most used parameters and results. It is possible to specify the parameters we want in output
using the CIF word riet append result to (in addition or as an alternative), but in the
preparation of the starting analysis file in the Maud interface, the parameters to be added to the
results must be specified by turning to true the switch in the output column of the parameter list
window or panel.
Now to run Maud in batch in the console (
where the Maud.jar is located the following:
DOS (everything in the same line): java -mx512M -cp
“Maud.jar;lib\miscLib.jar;lib\JSgInfo.jar;lib\jgaec.jar;lib\ij.jar”
it.unitn.ing.rista.MaudText -f fecu.ins
Unix (everything in the same line): java -mx512M -cp
Maud.jar:lib/miscLib.jar:lib/JSgInfo.jar:lib/jgaec.jar:lib/ij.jar
it.unitn.ing.rista.MaudText -f fecu.ins
For Mac OS X, it is advised to use the generic Unix Maud installation (or to change the path to
the jar files). Before to run Maud in batch mode it is important to run Maud interactive (with the
interface) at least once to create and extract the databases, examples and preferences folder.

2.3 Analysis of results
After running Maud in batch mode, we can check quickly the results by loading the results file
FECUresults.txt in a spreadsheet program. The results are arranged in rows and separated
by tabs. The first row contains the column titles, each subsequent row a different analysis. The
Rwp value for each analysis is reported in the second column and the biggest value found was
5.6% as an indication of the success of the analysis. As an example we report in Figure 2 the
graphical correlation of the copper-rich phase percentage and its mean crystallite value as found
in the analysis versus the sample number. The files and examples used in this articles will be
uploaded in a tutorial in the Maud web page along with some additional files with the batch mode
commands for an easier use.

3 How to get Maud 2.0 and further informations
For this analysis we need Maud version 2.037 or later and it can be freely downloaded from the
Maud web page at http://www.ing.unitn.it/ maud for the preferred platform. There are two archives
for Windows and Mac OS X plus a generic unix version that can be used for Linux, Solaris or
every unix based system with a Java 2 virtual machine installed. The new version 2.0 has a new
interface focused on reducing the effort of a new user and simplifying the most common tasks.
Some particularity of the new version respect to the previous one are (most of them to provide
some useful routines for ab-initio structure solution):
• Different minimization/search algorithms selectable: Marquardt least squares, Evolutionary
algorithm, Simulated annealing, Metadynamic search algorithm. As an example the evolutionary algorithm can be used in the early steps of the refinement to select the proper starting
solution and the Marquardt to drive it to convergence.
4
• Possibility to use crystallites and microstrain distributions for peak shape description instead
of analytical fixed shape functions.
• Maximum Entropy Electron Map full pattern fitting. An electron map can be used for fitting
instead of atoms.
• Full pattern fitting by a list of peaks. Either an arbitrary list of peaks (each one with its own
position, intensity and shape), or simply a list of structure factors to be imported, instead of
a list of atoms.
• Indexing directly on the pattern, selecting the Le Bail fit and the evolutionary algorithm for
the cell search. This may be used to improve a difficult indexing or a partly done one.
• Introduction of fragments. So fragment search can be done directly on the pattern or on a
list of extracted structure factors.
• Energy minimization. At the moment only the simple repulsion energy is completed. Other
energy principles are under completition.
• Spectra integration from image plate or CCD transmission/reflection 2D images. Center,
tilting errors and distance from sample can be refined in the spectra fitting.
Bugs and errors should be reported to the author through the bug reporter web page; questions in
the Maud forum accessible from the Maud web page.
In a future article we will report the instructions on how to modify/extend the program by little Java programming or provide a new alternative model/plugin for the instrument or the structure/microstructure or datafiles importing.
References
[1] D. L. Bish and S. A. Howard. J. Appl. Cryst., 21, 86–91, 1988.
[2] R. J. Hill and C. J. Howard. J. Appl. Cryst., 20, 467–474, 1987.
[3] L. Lutterotti and S. Gialanella. Acta Mater., 46(1), 101–110, 1998.
[4] N. C. Popa. J. Appl. Cryst., 31, 176–180, 1998.
[5] B. E. Warren. X-ray Diffraction. Addison-Wesley, Reading, MA, 1969

Author: Luca Lutterotti
Dipartimento di Ingegneria dei Materiali e delle Tecnologie Industriali
Universita di Trento, 38050 Trento, Italy `
E-mail: Luca.Lutterotti@ing.unitn.it
WWW: http://www.ing.unitn.it/ maud

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The Scanning Electron Microscope (SEM) produces images by probing the specimen with a focused electron beam that is scanned across a rectangular area of the specimen (raster scanning).

There are two families of electron guns:

• Conventional thermionic emitters such as Tungsten (W) or Lanthanum hexaboride (LaB6) tipped filaments.
• Tungsten field emission gun (FEG) , warm or Cold FEG. A pointed emitter is held at several kilovolts (2000-7000 V) so that there is sufficient potential at the emitter surface to cause field electron emission.

Field emission gun (FEG) is used to produce an electron beam that is smaller in diameter, more coherent and up to three orders of magnitude greater current density or brightness.

scrollable

Energy of electrons is depending of Voltage: 1 Kev to 50KeV

Current (A): Number of electrons /unit of time

1 amp = 1 coulomb/sec 1 coulomb ~ 6 x10¹⁸ electrons

Example if the current measured at sample is around 10^-9A to 10^-12 A then the number of electrons is around 6X10⁶ to 6X10⁹ electrons/sec.

Environmental Scanning Electron Microscope (ESEM)

ESEM is a variety of SEM called environmental scanning electron microscope. It can produce images of sufficient quality and resolution with the samples being wet or contained in low vacuum or gas. This greatly facilitates imaging biological samples that are unstable in the high vacuum of conventional electron microscopes. The major disadvantage of transmission electron microscope is the need for extremely thin sections of the specimens, typically about 100 nanometers. Biological specimens are typically required to be chemically fixed, dehydrated and embedded in a polymer resin to stabilize them sufficiently to allow ultrathin sectioning. Sections of biological specimens, organic polymers and similar materials may require special treatment with heavy atom labels in order to achieve the required image contrast.

ESEM is especially useful for non-metallic, uncoated and biological materials. The presence of gas, mainly Argon, around a sample permits to work with pressure greater than 500 Pa compared to conventional SEM requirements samples under vacuum about 10-3 to 10-4 Pa. This vacuum level creates the possibility to operate on non-conductive samples without any preparation or hydrated specimens without charging.

Transmission Electron Microscope (TEM)

In a Transmission Electron Microscope (TEM), the electron beam is accelerated by an anode typically at +100 keV (40 to 400 keV) with respect to the cathode, focused by electrostatic and electromagnetic lenses, and transmitted through the specimen that is in part transparent to electrons and in part scatters them out of the beam. When it emerges from the specimen, the electron beam carries information about the structure of the specimen that is magnified by the objective lens system of the microscope.

The spatial variation in this information (the “image”) may be viewed by projecting the magnified electron image onto a fluorescent viewing screen coated with a phosphor or scintillator material such as zinc sulfide. Alternatively, the image can be photographically recorded by exposing a photographic film or plate directly to the electron beam, or a high-resolution phosphor may be coupled by means of a lens optical system or a fiber optic light-guide to the sensor of a digital camera. The image detected by the digital camera may be displayed on a monitor or computer.

A transmission electron microscope can achieve better than 50 pm resolution and magnifications of up to about 10,000,000x whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000x. Generally, the image resolution of an SEM is at least an order of magnitude poorer than that of a TEM. However, because the SEM image relies on surface processes rather than transmission, it is able to image bulk samples up to many centimeters in size and (depending on instrument design and settings) has a great depth of field, and so can produce images that are good representations of the three dimensional shape of the sample.

The Scanning Transmission Electron Microscope (STEM) rasters a focused incident probe across a specimen that (as with the TEM) has been thinned to facilitate detection of electrons scattered through the specimen. The high resolution of the TEM is thus possible in STEM. The focusing action (and aberrations) occurs before the electrons hit the specimen in the STEM, but afterward in the TEM.

Focused ion beam (FIB)

Focused ion beam, also known as FIB, is a technique used particularly in the semiconductor industry, materials science and increasingly in the biological field for site-specific analysis, deposition, and ablation of materials. A FIB setup is a scientific instrument that resembles a scanning electron microscope (SEM). However, while the SEM uses a focused beam of electrons to image the sample in the chamber, a FIB setup uses a focused beam of ions instead. Unlike an electron microscope, FIB is inherently destructive to the specimen.

When the high-energy gallium ions strike the sample, they will sputter atoms from the surface. Gallium atoms will also be implanted into the top few nanometers of the surface, and the surface will be made amorphous. A FIB-SEM consists in a system with both electron and ion beam columns, allowing the same feature to be investigated using either of the beams. A FIB-SEM system uses a beam of Ga+ ion to mill into the surface to locate a feature or defect of interest. The integrated SEM then uses a focused beam of electrons to image the sample in the chamber.

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Atomic force microscopy (AFM) is a technique with multiple applications in biology. This method is a member of the broad family of scanning probe microscopy and was initially developed in 1986 by Binnig et al to overcome the disadvantages of the scanning tunneling microscopy (STM) [1]. In the case of STM, only conductive materials can be studied as the resolution is obtained by using a tunneling current between a sharp probe and the sample surface[1]. In contrast, AFM uses small forces on the surface by a probe, thus do not damage samples and can provide information of surface topography of biological materials. AFM soon attracted the attention of the biophysical scientists in biomembrane as well as synthetic membrane research due to its capability of observing biological molecular system with resolution on nanometer scale and its possibility of three dimensional imaging [2].

Fundamental Elements of AFM

An atomic force microscope consists of a flexible cantilever containing a sharp probe, laser, photodiode detector, piezoelectric scanner and feedback electronics [3]. The microscope obtains the surface topography by scanning the tip in gentle touch with the sample. The tip motion is monitored by the piezoelectric scanner. As the tip scans the sample, the forces between the tip and the sample surface cause the cantilever to bend. A photodiode detector detects the deflection of a laser beam reflected off the back of the cantilever onto a two- segment photodiode. In most operating modes, a feedback circuit connected to the cantilever deflection sensor keeps the interaction between the tip and the sample at a fixed value and controls the tip-sample distance. The feedback signal is recorded by a computer to reconstruct a 3D image of the surface topography.

The force between the probe and the sample surface depends on the spring constant (stiffness of the cantilever) and the tip-sample distance). The amount of force is calculated based on Hooke’s law:F=−kx(6.1.1)(6.1.1)F=−kx

• FF: Force
• kk: spring constant
• xx: cantilever deflection.

Imaging modes

There are three primary imaging modes in AFM: contact, non-contact and intermittent (tapping) mode [4]. During contact mode, the probe is in contact with the sample and repulsive Van der Waals forces prevail, whilst attractive Van der Waals forces are dominant when the tip moves further away from the sample surface [5].

Contact Mode

In contact mode, the tip is constantly in touch with the sample surface. The applied force is kept constant while the tip scans the surface, creating the surface image [4]. This imaging mode is good for samples with rough and rigid surfaces as it provides fast scanning with high resolution. One disadvantage of this imaging mode is that soft samples like tissues can be deformed or damaged due to the applied force. This drawback can be solved by measuring the sample in aqueous environments to reduce the interaction force between the tip and the sample.

Tapping Mode

In tapping mode, the tip is not in constant contact with the sample surface. Instead, the cantilever is oscillated at its resonant frequency, which makes the tip lightly tap on the surface during scanning. A constant tip-sample interaction is maintained by monitoring the oscillation amplitude and an image is obtained [4]. Several parameters that affect the image contrast are the height, phase signals and amplitude [6]. Phase signals are influenced by material properties of the sample, for example viscoelasticity [6]. The force during scanning is greatly reduced, therefore this mode is useful for biological samples, where the samples are easily damageable or loosely bound to their surface. However, this imaging mode requires a slower scanning speed and is more challenging to measure in liquids.

Non-contact mode

There is no contact between the sample surface and the probe in non-contact mode. The probe oscillates above the sample surface, forming a weak attractive force between the tip apex atom and the sample surface atom. Feedback signals are obtained by measuring a frequency shift in the mechanical oscillation of the cantilever [6].

The force exerted on the surface sample is very low in this case. Moreover, as there is no contact between the probe and the surface, the probe lifetime can be extended. Another advantage of this operating mode is the possibility to observe an atomic defect if the very weak attractive force can be detected. The drawback of this mode is the reduction of resolution, and the oscillation of the cantilever is affected in case there are contaminants on the sample surface. Usually this operation mode requires a careful control of the environment (in UHV) to carry out [7].

Cantilever and Tips

The scanning probe is an important component of the AFM. The dimensions of the cantilever are in micrometer range, while its tip has a radius of a few nanometers [4]. Different cantilever lengths, shapes and materials lead to various spring constants and resonant frequencies. The most common materials of the probes are silicon nitride (Si₃N₄) or silicon (Si) [5]. Figure 6.1.46.1.4 shows a scanning electron microscope (SEM) image of a silicon nitride (4a, 4b) and silicon (4c, 4d) cantilever chip, where a tiny tip having a pyramid shape is integrated at the end. The silicon nitride probe is often used in static contact mode, where the stiffness of the cantilever should be as low as possible [4]. The silicon probe is usually used in dynamic operation mode, which requires higher values for the spring constant to reduce noise and instabilities [4].

Typically, spring constants of AFM cantilevers vary between 0.01 Nm^-1 and 100 Nm^-1, enabling a force sensitivity of 10-11N [4]. The force sensitivity is influenced by thermal, electrical and optical noise. [5] For biological samples, cantilevers in contact mode often have resonance frequencies between 5 and 50 kHz in vacuum [8]. Figure 6.1.56.1.5 reports an AFM tip made of carbon nanotubes (CNTs), which was a breakthrough in terms of resolution. CNTs tips have a high aspect ratio, small diameter, and a well-defined surface chemistry, therefore appearing to be the ideal probe for biological applications [4].

AFM on membranes

Native membranes studied by AFM

Biomembrane sample preparation

In order to study membranes using AFM, the membranes need to be fixed on a flat solid support [8]. Several solid supports such as mica, highly ordered pyrolitic graphite (HOPG), template stripped gold and molybdenum disulfide have proved to give high resolution images [6, 8]. While mica is an insulator and exposes a hydrophilic surface, HOPG is a good conductor and hydrophobic [8]. The similarity between these two substrates is an atomically flat surface [8]. Based on chemical adsorption mechanism, membranes are attached onto the solid support by adjusting pH and ionic strength. As the gap between membrane and the support is very small (0.5-2nm), this may cause impaired mobility for membrane proteins that are directly attached to the support [6]. Furthermore, the adsorption force may affect the conformation of the membrane proteins. To sum up, current sample preparation methods still need further consideration in order to study dynamics and structure of native membrane proteins.

AFM images of native membrane

AFM can obtain the images of native membranes at submolecular resolution, which is a great advantage comparing to other methods [6]. It is effective in providing information of the native organization of membrane proteins and their complexes. Figure 6.1.66.1.6 shows an example of the study of native membrane using AFM. Disk membranes were prepared from mouse retina and then attached on mica support [6]. The AFM image revealed tight rows of dimers packed in the structure arrangement of rhodopsin [6]. This provides a platform for interaction with arrestin and transducin.

Model lipid membranes studied by AFM

Preparation of supported lipid bilayers.

Supported lipid bilayers (SLBs) have been used as a biomimetic model for biomembranes in numerous studies [3, 9]. This system consists of two lipid leaflets spread on a solid support [3]. Although this model lacks some features of the real membranes, it still provides an insight of the structural organization and characteristics of cell membranes. The first method to prepare SLBs is the fusion of lipid vesicles on solid supports [9]. The vesicles are prepared via sonication or extrusion, then adsorbed on the surface of the solid support. The adsorbed vesicles either form larger vesicles by fusing together, or directly rupture and form SLBs.

Another method is to use a hydrophilic substrate on which two consecutive lipid monolayers are deposited by Langmuir-Blodgett transfer [3]. A Teflon-coated trough contains the aqueous solution, with two movable Teflon barriers used to control the area for lipid spread and form a monolayer at the air-water interface. There is also a balance to measure the surface pressure, controlling lipid packing. The solid support is then pulled vertically through the lipid monolayer, depositing the first lipid layer on the substrate. The transference of the second lipid layer can be completed by dipping the lipid support either horizontally or vertically. This technique can be applied to fabricate SLBs having two different lipid composition.

AFM studies of SLBs formation.

SLBs formation process by fusing lipid vesicles on solid supports can be studied in situ by AFM technique, as illustrated in Figure 6.1.76.1.7. The vesicles spread from the edge towards the center, then stacked on top of each other. The edges of the top and bottom bilayers are joined together to form bigger patches.

Different protocols to prepare multi-component and phase-separated SLBs can affect the asymmetry of the resulting SLBs. In Figure 6.1.86.1.8, the extruded small unilamellar vesicles (SUVs) composed of DLPC/DSPC are heated at 65⁰C, then fused on mica at 20⁰C. The resulting SLB are fully symmetric fluid/gel membranes. On the other hand, using sonicated SUVs heated at 20⁰C prior to fusion results in a completely asymmetric SLBs.

Summary

AFM is a powerful technique for scientists to have an insight in membrane biophysics. Advantages of this method including:

• The ability to image cell surfaces, molecular assemblies in their native aqueous environment at a very high resolution.
• No requirement of a conductive sample.
• Provide 3-D surface profiles.
• The ability to operate in liquid environment and ambient air.

Disadvantages of AFM are limited scanning area and the scanning speed.

Recently there have been some progress in improving AFM scanning speed and resolution, for example high speed AFM (HS-AFM) or high resolution AFM (HR-AFM) [10, 11]. HF-AFM consists of modified components in order to maximize scanning seed, for example soft small cantilevers having high resonance frequencies, high resonance frequency scanners and fast data acquisition devices [10]. AFM is also combined with several techniques such as fluorescence microscopy to acquire more efficient data [9]. The potential improvement of AFM will enhance the possibility to apply this technique in a wider range of biological fields.

References

1. Binnig, G., C. F. Quate, and C. Gerber, Atomic force microscope. Phys. Rev. Lett, 1986(56): p. 930–933.
2. D.J.Muller, Y.F.D., Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology. Nat.Nanotechnol, 2008. 3: p. 261-269.
3. Morandat, S., et al., Atomic force microscopy of model lipid membranes. Anal Bioanal Chem, 2013. 405(5): p. 1445-61.
4. Alessandrini, A. and P. Facci, AFM: a versatile tool in biophysics. Measurement Science and Technology, 2005. 16(6): p. R65- R92.
5. Bullen, R.A.W.a.H.A., Lecture notes: Introduction to Scanning Probe Microscopy
6. Frederix, P.L., P.D. Bosshart, and A. Engel, Atomic force microscopy of biological membranes. Biophys J, 2009. 96(2): p. ​329- ​38.
7. S. Morita, R.W., E. Meyer, Noncontact Atomic Force Microscopy. Springer, 2002. 1.
8. Muller, D.J. and A. Engel, Atomic force microscopy and spectroscopy of native membrane proteins. Nat Protoc, 2007. 2(9): p. ​2191-7.
9. Goksu, E.I., et al., AFM for structure and dynamics of biomembranes. Biochim Biophys Acta, 2009. 1788(1): p. 254-66.
10. Ando, T., T. Uchihashi, and N. Kodera, High-speed AFM and applications to biomolecular systems. Annu Rev Biophys, 2013. ​42: p. 393-414.
11. Bippes, C.A. and D.J. Muller, High-resolution atomic force microscopy and spectroscopy of native membrane proteins. Reports on Progress in Physics, 2011. 74(8): p. 086601.

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Introduction

The physical properties of colloids (nanoparticles) and suspensions are strongly dependent on the nature and extent of the particle-liquid interface. The behavior of aqueous dispersions between particles and liquid is especially sensitive to the ionic and electrical structure of the interface.

Zeta potential is a parameter that measures the electrochemical equilibrium at the particle-liquid interface. It measures the magnitude of electrostatic repulsion/attraction between particles and thus, it has become one of the fundamental parameters known to affect stability of colloidal particles. It should be noted that that term stability, when applied to colloidal dispersions, generally means the resistance to change of the dispersion with time. Figure 2.5.12.5.1 illustrates the basic concept of zeta potential.

From the fundamental theory’s perspective, zeta potential is the electrical potential in the interfacial double layer (DL) at the location of the slipping plane (shown in Figure 2.5.12.5.1 ). We can regard zeta potential as the potential difference between the dispersion medium and the stationary layer of the fluid attached to the particle layer. Therefore, in experimental concerns, zeta potential is key factor in processes such as the preparation of colloidal dispersions, utilization of colloidal phenomena and the destruction of unwanted colloidal dispersions. Moreover, zeta potential analysis and measurements nowadays have a lot of real-world applications. In the field of biomedical research, zeta potential measurement, in contrast to chemical methods of analysis which can disrupt the organism, has the particular merit of providing information referring to the outermost regions of an organism. It is also largely utilized in water purification and treatment. Zeta potential analysis has established optimum coagulation conditions for removal of particulate matter and organic dyestuffs from aqueous waste products.

Brief History and Development of Zeta Potential

Zeta potential is a scientific term for electrokinetic potential in colloidal dispersions. In prior literature, it is usually denoted using the Greek letter zeta, Ζ, hence it has obtained the name zeta potential as Ζ-potential. The earliest theory for calculating Zeta potential from experimental data was developed by Marian Smoluchowski in 1903 (Figure 2.5.22.5.2 ). Even till today, this theory is still the most well-known and widely used method for calculating zeta potential.

Interestingly, this theory was originally developed for electrophoresis. Later on, people started to apply his theory in calculation of zeta potential. The main reason that this theory is powerful is because of its universality and validity for dispersed particles of any shape and any concentration. However, there still some limitations to this early theory as it was mainly determined experimentally. The main limitations are that Smoluchowski’s theory neglects the contribution of surface conductivity and only works for particles which have sizes much larger than the interface layer, denoted as κ_a (1/κ is called Debye length and a is the particle radius).

Overbeek and Booth as early pioneers in this direction started to develop more theoretical and rigorous electrokinetic theories that were able to incorporate surface conductivity for electrokinetic applications. Modern rigorous electrokinetic theories that are valid almost any κa mostly are generated from Ukrainian (Dukhin) and Australian (O’Brien) scientists.

Principle of Zeta Potential Analysis

Electrokinetic Phenomena

Because an electric double-layer (EDL) exists between a surface and solution, then any relative motion between the rigid and mobile parts of the EDL will result in the generation of an electrokinetic potential. As described above, zeta potential is essentially a electrokinetic potential which rises from electrokinetic phenomena. So it is important to understand different situations where electrokinetic potential can be produced. There are generally four fundamental ways which zeta potential can be produced, via electrophoresis, electro-osmosis, streaming potential, and sedimentation potential as shown from Figure 2.5.32.5.3 .

Calculations of Zeta Potential

There are many different ways of calculating zeta potential . In this section, the methods of calculating zeta potential in electrophoresis and electroosmosis will be introduced.

Zeta Potential in Electrophoresis

Electrophoresis is the movement of charged colloidal particles or polyelectrolytes, immersed in a liquid, under the influence of an external electric field. In such case, the electrophoretic velocity, v_e (ms^-1) is the velocity during electrophoresis and the electrophoretic mobility, u­­_e (m ² V ^-1 s ^-1 ) is the magnitude of the velocity divided by the magnitude of the electric field strength. The mobility is counted positive if the particles move toward lower potential and negative in the opposite case. And therefore, we have the relationship v_e­= u_eE, where E is the externally applied field.

Thus, the formula accounted for zeta potential in electrophoresis case is given in EQ, where ε_rs is the relative permittivity of the electrolyte solution, ε₀ is the electric permittivity of vacuum and η is the viscosity.ue =εrsε0ζη(2.5.1)(2.5.1)ue =εrsε0ζηve =εrsε0ζηE(2.5.2)(2.5.2)ve =εrsε0ζηE

There are two cases regarding the size of κa:

1. κa < 1: the formula is similar, 2.5.32.5.3 .
2. κa > 1: the formula is rather complicated and we need to solve equation for zeta potential, 2.5.42.5.4 , where yeζ= eζ/kTyeζ= eζ/kT , m is about 0.15 for aqueous solution.

ue=23εrsε0ζη(2.5.3)(2.5.3)ue=23εrsε0ζη32ηeεrsε0kTue=32yek−6[yek2−ln 2ζ{1−e−ζyek}]2+ka1+3m/ζ2e−ζyek2(2.5.4)(2.5.4)32ηeεrsε0kTue=32yek−6[yek2−ln 2ζ{1−e−ζyek}]2+ka1+3m/ζ2e−ζyek2

Zeta Potential in Electroosmosis

Electroosmosis is the motion of a liquid through an immobilized set of particles, a porous plug, a capillary, or a membrane, in response to an applied electric field. Similar to electrophoresis, it has the electroosmotic velocity, v_eo (ms ^-1 ) as the uniform velocity of the liquid far from the charged interface. Usually, the measured quantity is the volume flow rate of liquid divided by electric field strength, Q_eo,E (m ⁴ V ^-1 s ^-1 ) or diveided by the electric current, Q_eo,I (m ³ C ^-1 ). Therefore, the relationship is given by 2.5.52.5.5 .Qeo= ∫∫veodS(2.5.5)(2.5.5)Qeo= ∫∫veodS

Thus the formula accounted for Zeta potential in electroosmosis is given in EQ.

As with electrophoresis there are two cases regarding the size of κa:

• κa >>1 and there is no surface conduction, where Ac is the cross-section area and KL is the bulk conductivity of particle.
• κa < 1, 2.5.82.5.8 , where Δu =KσKLΔu =KσKL is the Dukhin number account for surface conductivity, KσKσ is the surface conductivity of the particle.

Qeo,E=−εrsε0ζηAc(2.5.6)(2.5.6)Qeo,E=−εrsε0ζηAcQeo,I=−εrsε0ζη1KL(2.5.7)(2.5.7)Qeo,I=−εrsε0ζη1KLQeo,I=−εrsε0ζη1KL(1+2Δu)(2.5.8)(2.5.8)Qeo,I=−εrsε0ζη1KL(1+2Δu)

Relationship Between Zeta Potential and Particle Stability in Electrophoresis

Using the above theoretical methods, we can calculate zeta potential for particles in electrophoresis. The following table summarizes the stability behavior of the colloid particles with respect to zeta potential. Thus, we can use zeta potential to predict the stability of colloidal particles in the electrokinetic phenomena of electrophoresis.

Instrumentation

In this section, a market-available zeta potential analyzer will be used as an example of how experimentally zeta potential is analyzed. Figure 2.5.42.5.4 shows an example of a typical zeta potential analyzer for electrophoresis.

The inside measuring principle is described in the following diagram, which shows the detailed mechanism of zeta potential analyzer (Figure 2.5.52.5.5 ).

When a voltage is applied to the solution in which particles are dispersed, particles are attracted to the electrode of the opposite polarity, accompanied by the fixed layer and part of the diffuse double layer, or internal side of the “sliding surface”. Using the following formula below of this specific Analyzer and the computer program, we can obtain the zeta potential for electrophoresis using this typical zeta potential analyzer (Figure 2.5.62.5.6 .

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Dynamic light scattering (DLS), which is also known as photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QLS), is a spectroscopy method used in the fields of chemistry, biochemistry, and physics to determine the size distribution of particles (polymers, proteins, colloids, etc.) in solution or suspension. In the DLS experiment, normally a laser provides the monochromatic incident light, which impinges onto a solution with small particles in Brownian motion.

And then through the Rayleigh scattering process, particles whose sizes are sufficiently small compared to the wavelength of the incident light will diffract the incident light in all direction with different wavelengths and intensities as a function of time. Since the scattering pattern of the light is highly correlated to the size distribution of the analyzed particles, the size-related information of the sample could be then acquired by mathematically processing the spectral characteristics of the scattered light.

Herein a brief introduction of basic theories of DLS will be demonstrated, followed by descriptions and guidance on the instrument itself and the sample preparation and measurement process. Finally, data analysis of the DLS measurement, and the applications of DLS as well as the comparison against other size-determine techniques will be shown and summarized.

DLS Theory

The theory of DLS can be introduced utilizing a model system of spherical particles in solution. According to the Rayleigh scattering (Figure 2.4.12.4.1), when a sample of particles with diameter smaller than the wavelength of the incident light, each particle will diffract the incident light in all directions, while the intensity II is determined by 2.4.12.4.1 , where I0I0 and λλ is the intensity and wavelength of the unpolarized incident light, RR is the distance to the particle, θθ is the scattering angel, nnis the refractive index of the particle, and rr is the radius of the particle.

I = I01 +cos2θ2R2(2πλ)4(n2 − 1n2 + 2)2r6(2.4.1)(2.4.1)I = I01 +cos2⁡θ2R2(2πλ)4(n2 − 1n2 + 2)2r6

If that diffracted light is projected as an image onto a screen, it will generate a “speckle” pattern (Figure 2.4.22.4.2 ); the dark areas represent regions where the diffracted light from the particles arrives out of phase interfering destructively and the bright area represent regions where the diffracted light arrives in phase interfering constructively.

In practice, particle samples are normally not stationary but moving randomly due to collisions with solvent molecules as described by the Brownian motion, 2.4.22.4.2, where (Δx)2¯¯¯¯¯¯¯¯¯¯¯¯¯(Δx)2¯ is the mean squared displacement in time t, and D is the diffusion constant, which is related to the hydrodynamic radius a of the particle according to the Stokes-Einstein equation, 2.4.32.4.3 , where kB is Boltzmann constant, T is the temperature, and μ is viscosity of the solution. Importantly, for a system undergoing Brownian motion, small particles should diffuse faster than large ones.(Δx)2¯¯¯¯¯¯¯¯¯¯¯¯¯ = 2Δt(2.4.2)(2.4.2)(Δx)2¯ = 2ΔtD =kBT6πμa(2.4.3)(2.4.3)D =kBT6πμa

As a result of the Brownian motion, the distance between particles is constantly changing and this results in a Doppler shift between the frequency of the incident light and the frequency of the scattered light. Since the distance between particles also affects the phase overlap/interfering of the diffracted light, the brightness and darkness of the spots in the “speckle” pattern will in turn fluctuate in intensity as a function of time when the particles change position with respect to each other. Then, as the rate of these intensity fluctuations depends on how fast the particles are moving (smaller particles diffuse faster), information about the size distribution of particles in the solution could be acquired by processing the fluctuations of the intensity of scattered light. Figure 2.4.32.4.3 shows the hypothetical fluctuation of scattering intensity of larger particles and smaller particles.

In order to mathematically process the fluctuation of intensity, there are several principles/terms to be understood. First, the intensity correlation function is used to describe the rate of change in scattering intensity by comparing the intensity I(t) at time t to the intensity I(t + τ) at a later time (t + τ), and is quantified and normalized by 2.4.42.4.4 and 2.4.52.4.5 , where braces indicate averaging over t.G2(τ)= ⟨I(t)I(t + τ)⟩(2.4.4)(2.4.4)G2(τ)= ⟨I(t)I(t + τ)⟩g2(τ)=⟨I(t)I(t + τ)⟩⟨I(t)⟩2(2.4.5)(2.4.5)g2(τ)=⟨I(t)I(t + τ)⟩⟨I(t)⟩2

Second, since it is not possible to know how each particle moves from the fluctuation, the electric field correlation function is instead used to correlate the motion of the particles relative to each other, and is defined by 2.4.62.4.6 and 2.4.72.4.7 , where E(t) and E(t + τ) are the scattered electric fields at times t and t+ τ.G1(τ)= ⟨E(t)E(t + τ)⟩(2.4.6)(2.4.6)G1(τ)= ⟨E(t)E(t + τ)⟩g1(τ)=⟨E(t)E(t + τ)⟩⟨E(t)E(t)⟩(2.4.7)(2.4.7)g1(τ)=⟨E(t)E(t + τ)⟩⟨E(t)E(t)⟩

For a monodisperse system undergoing Brownian motion, g₁(τ) will decay exponentially with a decay rate Γ which is related by Brownian motion to the diffusivity by 2.4.82.4.8 , 2.4.92.4.9 , and 2.4.102.4.10 , where q is the magnitude of the scattering wave vector and q² reflects the distance the particle travels, n is the refraction index of the solution and θ is angle at which the detector is located.g1(τ)= e−Γτ(2.4.8)(2.4.8)g1(τ)= e−ΓτΓ = −Dq2(2.4.9)(2.4.9)Γ = −Dq2q=4πnλsinΘ2(2.4.10)(2.4.10)q=4πnλsinΘ2

For a polydisperse system however, g₁(τ) can no longer be represented as a single exponential decay and must be represented as a intensity-weighed integral over a distribution of decay rates G(Γ) by 2.4.112.4.11 where G(Γ) is normalized, 2.4.122.4.12 .g1(τ)=∫∞0G(Γ)e−ΓτdΓ(2.4.11)(2.4.11)g1(τ)=∫0∞G(Γ)e−ΓτdΓ∫∞0G(Γ)dΓ = 1(2.4.12)(2.4.12)∫0∞G(Γ)dΓ = 1

Third, the two correlation functions above can be equated using the Seigert relationship based on the principles of Gaussian random processes (which the scattering light usually is), and can be expressed as 2.4.132.4.13 , where β is a factor that depends on the experimental geometry, and B is the long-time value of g₂(τ), which is referred to as the baseline and is normally equal to 1. Figure 2.4.42.4.4 shows the decay of g₂(τ) for small size sample and large size sample.g2(τ)= B + β[g1(τ)]2(2.4.13)(2.4.13)g2(τ)= B + β[g1(τ)]2

When determining the size of particles in solution using DLS, g₂(τ) is calculated based on the time-dependent scattering intensity, and is converted through the Seigert relationship to g₁(τ) which usually is an exponential decay or a sum of exponential decays. The decay rate Γ is then mathematically determined (will be discussed in section ) from the g₁(τ) curve, and the value of diffusion constant D and hydrodynamic radius a can be easily calculated afterwards.

Experimental

Instrument of DLS

In a typical DLS experiment, light from a laser passes through a polarizer to define the polarization of the incident beam and then shines on the scattering medium. When the sizes of the analyzed particles are sufficiently small compared to the wavelength of the incident light, the incident light will scatters in all directions known as the Rayleigh scattering. The scattered light then passes through an analyzer, which selects a given polarization and finally enters a detector, where the position of the detector defines the scattering angle θ. In addition, the intersection of the incident beam and the beam intercepted by the detector defines a scattering region of volume V. As for the detector used in these experiments, a phototube is normally used whose dc output is proportional to the intensity of the scattered light beam. Figure 2.4.52.4.5 shows a schematic representation of the light-scattering experiment.

In modern DLS experiments, the scattered light spectral distribution is also measured. In these cases, a photomultiplier is the main detector, but the pre- and postphotomultiplier systems differ depending on the frequency change of the scattered light. The three different methods used are filter (f > 1 MHz), homodyne (f > 10 GHz), and heterodyne methods (f < 1 MHz), as schematically illustrated in Figure 2.4.62.4.6 . Note that that homodyne and heterodyne methods use no monochromator of “filter” between the scattering cell and the photomultiplier, and optical mixing techniques are used for heterodyne method. shows the schematic illustration of the various techniques used in light-scattering experiments.

As for an actual DLS instrument, take the Zetasizer Nano (Malvern Instruments Ltd.) as an example (Figure 2.4.72.4.7), it actually looks like nothing other than a big box, with components of power supply, optical unit (light source and detector), computer connection, sample holder, and accessories. The detailed procedure of how to use the DLS instrument will be introduced afterwards.

Sample Preparation

Although different DLS instruments may have different analysis ranges, we are usually looking at particles with a size range of nm to μm in solution. For several kinds of samples, DLS can give results with rather high confidence, such as monodisperse suspensions of unaggregated nanoparticles that have radius > 20 nm, or polydisperse nanoparticle solutions or stable solutions of aggregated nanoparticles that have radius in the 100 – 300 nm range with a polydispersity index of 0.3 or below. For other more challenging samples such as solutions containing large aggregates, bimodal solutions, very dilute samples, very small nanoparticles, heterogeneous samples, or unknown samples, the results given by DLS could not be really reliable, and one must be aware of the strengths and weaknesses of this analytical technique.

Then, for the sample preparation procedure, one important question is how much materials should be submit, or what is the optimal concentration of the solution. Generally, when doing the DLS measurement, it is important to submit enough amount of material in order to obtain sufficient signal, but if the sample is overly concentrated, then light scattered by one particle might be again scattered by another (known as multiple scattering), and make the data processing less accurate. An ideal sample submission for DLS analysis has a volume of 1 – 2 mL and is sufficiently concentrated as to have strong color hues, or opaqueness/turbidity in the case of a white or black sample. Alternatively, 100 – 200 μL of highly concentrated sample can be diluted to 1 mL or analyzed in a low-volume microcuvette.

In order to get high quality DLS data, there are also other issues to be concerned with. First is to minimize particulate contaminants, as it is common for a single particle contaminant to scatter a million times more than a suspended nanoparticle, by using ultra high purity water or solvents, extensively rinsing pipettes and containers, and sealing sample tightly. Second is to filter the sample through a 0.2 or 0.45 μm filter to get away of the visible particulates within the sample solution. Third is to avoid probe sonication to prevent the particulates ejected from the sonication tip, and use the bath sonication in stead.

Measurement

Now that the sample is readily prepared and put into the sample holder of the instrument, the next step is to actually do the DLS measurement. Generally the DLS instrument will be provided with software that can help you to do the measurement rather easily, but it is still worthwhile to understand the important parameters used during the measurement.

Firstly, the laser light source with an appropriate wavelength should be selected. As for the Zetasizer Nano series (Malvern Instruments Ltd.), either a 633 nm “red” laser or a 532 nm “green” laser is available. One should keep in mind that the 633 nm laser is least suitable for blue samples, while the 532 nm laser is least suitable for red samples, since otherwise the sample will just absorb a large portion of the incident light.

Then, for the measurement itself, one has to select the appropriate stabilization time and the duration time. Normally, longer striation/duration time can results in more stable signal with less noises, but the time cost should also be considered. Another important parameter is the temperature of the sample, as many DLS instruments are equipped with the temperature-controllable sample holders, one can actually measure the size distribution of the data at different temperature, and get extra information about the thermal stability of the sample analyzed.

Next, as is used in the calculation of particle size from the light scattering data, the viscosity and refraction index of the solution are also needed. Normally, for solutions with low concentration, the viscosity and refraction index of the solvent/water could be used as an approximation.

Finally, to get data with better reliability, the DLS measurement on the same sample will normally be conducted multiple times, which can help eliminate unexpected results and also provide additional error bar of the size distribution data.

Data Analysis

Although size distribution data could be readily acquired from the software of the DLS instrument, it is still worthwhile to know about the details about the data analysis process.

Cumulant method

As is mentioned in the Theory portion above, the decay rate Γ is mathematically determined from the g₁(τ) curve; if the sample solution is monodispersed, g₁(τ) could be regard as a single exponential decay function e^-Γτ, and the decay rate Γ can be in turn easily calculated. However, in most of the practical cases, the sample solution is always polydispersed, g₁(τ) will be the sum of many single exponential decay functions with different decay rates, and then it becomes significantly difficult to conduct the fitting process.

There are however, a few methods developed to meet this mathematical challenge: linear fit and cumulant expansion for mono-modal distribution, exponential sampling and CONTIN regularization for non-monomodal distribution. Among all these approaches, cumulant expansion is most common method and will be illustrated in detail in this section.

Generally, the cumulant expansion method is based on two relations: one between g₁(τ) and the moment-generating function of the distribution, and one between the logarithm of g₁(τ) and the cumulant-generating function of the distribution.

To start with, the form of g₁(τ) is equivalent to the definition of the moment-generating function M(-τ, Γ) of the distribution G(Γ), 2.4.142.4.14 .g1(τ)= ∫∞0G(Γ)e−ΓτdΓ = M(−τ,Γ)(2.4.14)(2.4.14)g1(τ)= ∫0∞G(Γ)e−ΓτdΓ = M(−τ,Γ)

The mth moment of the distribution mm(Γ)mm(Γ) is given by the mth derivative of M(-τ, Γ) with respect to τ, 2.4.152.4.15 .mm(Γ)= ∫∞0G(Γ)Γme−ΓτdΓ∣−τ=0(2.4.15)(2.4.15)mm(Γ)= ∫0∞G(Γ)Γme−ΓτdΓ∣−τ=0

Similarly, the logarithm of g₁(τ) is equivalent to the definition of the cumulant-generating function K(-τ, Γ), EQ, and the mth cumulant of the distribution km(Γ) is given by the mth derivative of K(-τ, Γ) with respect to τ, 2.4.162.4.16 and 2.4.172.4.17 .ln g1(τ)=ln M(−τ,Γ) = K(−τ,Γ)(2.4.16)(2.4.16)ln g1(τ)=ln M(−τ,Γ) = K(−τ,Γ)km(Γ)=dmK(−τ,Γ)d(−τ)m∣−τ=0(2.4.17)(2.4.17)km(Γ)=dmK(−τ,Γ)d(−τ)m∣−τ=0

By making use of that the cumulants, except for the first, are invariant under a change of origin, the km(Γ) could be rewritten in terms of the moments about the mean as 2.4.182.4.18 , 2.4.192.4.19 , 2.4.202.4.20 , and 2.4.212.4.21 where here μm are the moments about the mean, defined as given in 2.4.222.4.22 .k1(τ)k2(τ)k3(τ)k4(τ)= ∫∞0G(Γ)ΓdΓ=Γ¯= μ2= μ3= μ4−3μ22⋯(2.4.18)(2.4.19)(2.4.20)(2.4.21)(2.4.18)k1(τ)= ∫0∞G(Γ)ΓdΓ=Γ¯(2.4.19)k2(τ)= μ2(2.4.20)k3(τ)= μ3(2.4.21)k4(τ)= μ4−3μ22⋯μm = ∫∞0G(Γ)(Γ − Γ¯)mdΓ(2.4.22)(2.4.22)μm = ∫0∞G(Γ)(Γ − Γ¯)mdΓ

Based on the Taylor expansion of K(-τ, Γ) about τ = 0, the logarithm of g₁(τ) is given as 2.4.232.4.23 .ln g1(τ)= K(−τ,Γ)= −Γ¯τ +k22!τ2 −k33!τ3 +k44!τ4⋯(2.4.23)(2.4.23)ln g1(τ)= K(−τ,Γ)= −Γ¯τ +k22!τ2 −k33!τ3 +k44!τ4⋯

Importantly, if look back at the Seigert relationship in the logarithmic form, 2.4.242.4.24 .ln(g2(τ)−B)=lnβ + 2ln g1(τ)(2.4.24)(2.4.24)ln(g2(τ)−B)=lnβ + 2ln g1(τ)

The measured data of g₂(τ) could be fitted with the parameters of km using the relationship of 2.4.252.4.25 , where Γ¯Γ¯ (k₁), k₂, and k₃ describes the average, variance, and skewness (or asymmetry) of the decay rates of the distribution, and polydispersity index γ = k2Γ¯2γ = k2Γ¯2 is used to indicate the width of the distribution. And parameters beyond k₃ are seldom used to prevent overfitting the data. Finally, the size distribution can be easily calculated from the decay rate distribution as described in theory section previously. Figure 2.4.62.4.6 shows an example of data fitting using the cumulant method.ln(g2(τ)−B)=]lnβ + 2(−Γ¯τ +k22!τ2 −k33!τ3⋯)(2.4.25)(2.4.25)ln(g2(τ)−B)=]lnβ + 2(−Γ¯τ +k22!τ2 −k33!τ3⋯)

When using the cumulant expansion method however, one should keep in mind that it is only suitable for monomodal distributions (Gaussian-like distribution centered about the mean), and for non-monomodal distributions, other methods like exponential sampling and CONTIN regularization should be applied instead.

Three Index of Size Distribution

Now that the size distribution is able to be acquired from the fluctuation data of the scattered light using cumulant expansion or other methods, it is worthwhile to understand the three kinds of distribution index usually used in size analysis: number weighted distribution, volume weighted distribution, and intensity weighted distribution.

First of all, based on all the theories discussed above, it should be clear that the size distribution given by DLS experiments is the intensity weighted distribution, as it is always the intensity of the scattering that is being analyzed. So for intensity weighted distribution, the contribution of each particle is related to the intensity of light scattered by that particle. For example, using Rayleigh approximation, the relative contribution for very small particles will be proportional to a⁶.

For number weighted distribution, given by image analysis as an example, each particle is given equal weighting irrespective of its size, which means proportional to a⁰. This index is most useful where the absolute number of particles is important, or where high resolution (particle by particle) is required.

For volume weighted distribution, given by laser diffraction as an example, the contribution of each particle is related to the volume of that particle, which is proportional to a³. This is often extremely useful from a commercial perspective as the distribution represents the composition of the sample in terms of its volume/mass, and therefore its potential money value.

When comparing particle size data for the same sample represented using different distribution index, it is important to know that the results could be very different from number weighted distribution to intensity weighted distribution. This is clearly illustrated in the example below (Figure 2.4.92.4.9 ), for a sample consisting of equal numbers of particles with diameters of 5 nm and 50 nm. The number weighted distribution gives equal weighting to both types of particles, emphasizing the presence of the finer 5 nm particles, whereas the intensity weighted distribution has a signal one million times higher for the coarser 50 nm particles. The volume weighted distribution is intermediate between the two.

Furthermore, based on the different orders of correlation between the particle contribution and the particle size a, it is possible to convert particle size data from one type of distribution to another type of distribution, and that is also why the DLS software can also give size distributions in three different forms (number, volume, and intensity), where the first two kinds are actually deducted from the raw data of intensity weighted distribution.

An Example of an Application

As the DLS method could be used in many areas towards size distribution such as polymers, proteins, metal nanoparticles, or carbon nanomaterials, here gives an example about the application of DLS in size-controlled synthesis of monodisperse gold nanoparticles.

The size and size distribution of gold particles are controlled by subtle variation of the structure of the polymer, which is used to stabilize the gold nanoparticles during the reaction. These variations include monomer type, polymer molecular weight, end-group hydrophobicity, end-group denticity, and polymer concentration; a total number of 88 different trials have been conducted based on these variations. By using the DLS method, the authors are able to determine the gold particle size distribution for all these trials rather easily, and the correlation between polymer structure and particle size can also be plotted without further processing the data. Although other sizing techniques such as UV-V spectroscopy and TEM are also used in this paper, it is the DLS measurement that provides a much easier and reliable approach towards the size distribution analysis.

Comparison with TEM and AFM

Since DLS is not the only method available to determine the size distribution of particles, it is also necessary to compare DLS with the other common-used general sizing techniques, especially TEM and AFM.

First of all, it has to be made clear that both TEM and AFM measure particles that are deposited on a substrate (Cu grid for TEM, mica for AFM), while DLS measures particles that are dispersed in a solution. In this way, DLS will be measuring the bulk phase properties and give a more comprehensive information about the size distribution of the sample. And for AFM or TEM, it is very common that a relatively small sampling area is analyzed, and the size distribution on the sampling area may not be the same as the size distribution of the original sample depending on how the particles are deposited.

On the other hand however, for DLS, the calculating process is highly dependent on the mathematical and physical assumptions and models, which is, monomodal distribution (cumulant method) and spherical shape for the particles, the results could be inaccurate when analyzing non-monomodal distributions or non-spherical particles. Yet, since the size determining process for AFM or TEM is nothing more than measuring the size from the image and then using the statistic, these two methods can provide much more reliable data when dealing with “irregular” samples.

Another important issue to consider is the time cost and complication of size measurement. Generally speaking, the DLS measurement should be a much easier technique, which requires less operation time and also cheaper equipment. And it could be really troublesome to analysis the size distribution data coming out from TEM or AFM images without specially programmed software.

In addition, there are some special issues to consider when choosing size analysis techniques. For example, if the originally sample is already on a substrate (synthesized by the CVD method), or the particles could not be stably dispersed within solution, apparently the DLS method is not suitable. Also, when the particles tend to have a similar imaging contrast against the substrate (carbon nanomaterials on TEM grid), or tend to self-assemble and aggregate on the surface of the substrate, the DLS approach might be a better choice.

In general research work however, the best way to do size distribution analysis is to combine these analyzing methods, and get complimentary information from different aspects. One thing to keep in mind, since the DLS actually measures the hydrodynamic radius of the particles, the size from DLS measurement is always larger than the size from AFM or TEM measurement. As a conclusion, the comparison between DLS and AFM/TEM is shown in Table 2.4.12.4.1 .

Conclusion

In general, relying on the fluctuating Rayleigh scattering of small particles that randomly moves in solution, DLS is a very useful and rapid technique used in the size distribution of particles in the fields of physics, chemistry, and bio-chemistry, especially for monomodally dispersed spherical particles, and by combining with other techniques such as AFM and TEM, a comprehensive understanding of the size distribution of the analyte can be readily acquired.

Our XRD interpretation includes:
1. Phase determination
2. Determination of diffracted planes
3- Calculation of crystalline size and microstrain
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1. Profex

What is Profex?

Profex is a graphical user interface for Rietveld refinement of powder X-ray diffraction data with the program BGMN. It provides a large number of convenience features and facilitates the use of the BGMN Rietveld backend in many ways.

• Various options and output formats to create publication-quality graphs
• Main window
• Display hkl line positions from the internal reference structure database
• Powerful text editors support syntax highlighting and various convenience features
• A context help provides descriptions of all refinement parameters
• After the refinement, results are summarized (bottom right)
• Show the refined chemical composition (bottom right)
• A powerful search-match module for phase identification
• CIF / XML import editor to convert CIF or ICDD XML structure files to the native STR format
• Compute electron density maps (Fobs, Fcalc, or difference fourier maps)
• Graphical instrument editor to edit the fundamental parameters
• Generic non-linear curve fitting module
• Various options and output formats to create publication-quality graphs
• Main window

Key features

• Support for a variety of raw data formats, including all major instrument manufacturers (Bruker / Siemens, PANalytical / Philips, Rigaku, Seifert / GE, and generic text formats)
• Export of diffraction patterns to various text formats (ASCII, Gnuplot scripts, Fityk scripts), pixel graphics (PNG), and vector graphics (SVG)
• Batch conversion of raw data scans
• Automatic control file creation and output file name management
• Conversion of CIF and ICDD PDF-4+ XML structure files to BGMN structure files
• Export of refined crystal structures to CIF and Castep CELL format
• Internal database for crystal structure files, instrument configuration files, and predefined refinement presets
• Computation of chemical composition from refined crystal structures
• Batch refinement
• Export of refinement results to spreadsheet files (CSV format)
• Context help for BGMN variables
• Syntax highlighting
• Enhanced text editors for structure and control file management and editing
• Generic support for FullProf.2k as an alternative Rietveld backend to BGMN
• And many more…

Profex runs on Windows, Linux, and Mac OS X operating systems and is available as free software licensed under the GNU General Public License (GPL) version 2 or any later version.

Video tutorials

August 12, 2020. Check out our brand new YouTube channel Profex Tutorials. We will periodically publish new tutorials for selected topics. The first episode explains installation and setup of Profex on three different platforms:https://www.youtube.com/embed/vaWBjTNWG7U?feature=oembed

Profex 4.2 released

August 05, 2020. Profex, our software for Rietveld refinement of powder X-ray diffraction data (XRD), continues to gain popularity and is now established worldwide in the material and earth sciences communities. With the new version 4.2, it has received some long-awaited features that make it easier to use for new and experienced users. As always, Profex remains available as open-source software and is free for academic and commercial use. Visit the What’s new page for an overview of the new features, and download the latest version for Windows, Mac OS or Linux from the Download page.

Feature highlights in version 4.2

Import of CIF structure files has further been improved. Most CIF files require no user input anymore. Wyckoff symbols are determined automatically.

Creating instrument configurations has always been a major obstacle for new users. A brand new graphical instrument editor is easier and more attractive to use. It guides users through the process of creating configuration files for their own devices.

The search-match module for phase identification was introduced with Profex 4.0. With version 4.2, it supports chemical restrictions, which gives more control over the search process and improves the match rate and processing speed

See https://www.profex-xrd.org/

2. OpenXRD

OpenXRD is a program for the analysis of X-ray diffraction data.It will comprise scan treatment (background substraction, peak hunting) as well as mineral identification. OpenXRD will read almost any available data format. OpenXRD is free software and published under the GPL.

We will try to establish a free file with mineral data, fed by scientists and given back to scientists. OpenXRD will be available for Linux/Unix, Windows, and, perhaps Macintosh computers.

Released under GNU General Public License version 2.0 (GPLv2) 

OpenXRD is a free software application from the Other subcategory, part of the Graphic Apps category. The app is currently available in English and it was last updated on 2001-12-27. The program can be installed on All 32-bit MS Windows (95/98/NT/2000/XP) All POSIX (Linux/BSD/UNIX-like OSes) OS X Linux.
OpenXRD (version ) is available for download from our website. Just click the green Download button above to start. Until now the program was downloaded 13911 times. We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.

See: https://openxrd.soft112.com/

3. FullProf

What is FullProf?

The FullProf program has been mainly developed for Rietveld analysis (structure profile refinement) of neutron (constant wavelength, time of flight, nuclear and magnetic scattering) or X-ray powder diffraction data collected at constant or variable step in scattering angle 2theta. The program can be also used as a Profile Matching (or pattern decomposition using Le Bail method) tool, without the knowledge of the structure. Single crystal refinement can also be performed alone or in combination with powder data. Time of flight (TOF) neutron data analysis is also available. Energy dispersive X-ray data can also be treated but only for profile matching.

Features:

• X-ray diffraction data: laboratory and synchrotron sources
• X-ray diffraction data: laboratory and synchrotron sources
• One or two wavelengths (eventually with different profile parameters)
• Scattering variables: 2theta (in degrees), TOF (in microseconds), energy (in KeV)
• Background: fixed, refinable points or polynomial coefficients, Fourier filtering
• Choice of peak shape for each phase: Gaussian, Lorentzian, modified Lorentzian, pseudo-Voigt, Pearson-VII, Thompson-Cox-Hastings (TCH) pseudo-Voigt, numerical, split pseudo-Voigt, convolution of a double exponential with a TCH pseudo-Voigt for TOF
• Multi-phase (up to 16 phases)
• Preferred orientation: two functions available
• Absorption correction for different geometries. Micro-absorption for Bragg-Brentano set-up
• Choice between three weighting scheme: standard least-square, maximum likelihood and unit weights
• Choice between automatic generation of hkl and/or symmetry operators and file given by user
• Magnetic structure refinement (crystallographic and spherical representation of the magnetic moment). Two methods: describing the magnetic structure in the magnetic unit cell or making use of the propagation vectors using the crystallographic unit cell. This second method is necessary for incommensurate magnetic structures
• Automatic generation of reflections for an incommensurate structure with up to 24 propagation vectors. Refinement of propagation vectors components in reciprocal lattice units
• hkl-dependence of FWHM for strain and size effects
• hkl-dependence of the position shifts of Bragg reflections for special kinds of defects
• Profile Matching: the full profile can be adjusted without prior knowledge of the structure (needs only good starting cell parameters and profile parameters)
• Quantitative analysis withour need of structure factor calculations
• Chemical (distances and angles) and magnetic (magnetic moments) slack constraints. They can be generated automatically by the program
• The instrumental resolution function (Voigt function) may be supplied in a file. A microstructural analysis is then performed
• Form factor refinement of complex objects (plastic crystals)
• Structural or magnetic model could be supplied by an external subroutine for special purposes (rigid bodies TLS is the default, polymers, small angle scattering of amphifilic crystals, description of incommensurate structure in real direct space, etc)
• Single crystal data or integrated intensities can be used as observations (alone or in combination with a powder profile)
• Neutron (or X-ray) powder patterns can be mixed with integrated intensities of X-ray (or neutron) for single crystal or powder data
• Full multi-pattern capabilities. The user may mix several powder diffraction patterns (eventually heterogeneous: X-rays, TOF neutrons, etc.) with total control of the weighting scheme
• Montecarlo/Simulated Annealing algorithms have been introduced to search the starting parameters of a structural problem using integrated intensity data

See: https://www.ill.eu/sites/fullprof/php/programs.html

4. PowDLL

PowDLL is a .NET dynamic link library used for the interconversion procedure between variable formats of Powder X-Ray files. The DLL is capable of handling the most common file formats (binary and ASCII). The library can be used as a reusable component with any .NET language or as a standalone utility.

See: http://users.uoi.gr/nkourkou/powdll/

5. Software Ic

The software packages currently developed at IC are:

• Sir: a widely used package for the solution and refinement of macro and small  molecules using either X-ray or electron diffraction single-crystal data.
• EXPO2014/EXPO2013: an integrated package for the indexation of a powder diffraction pattern, the extraction of integrated intensities, the space group determination, the crystal structure solution viaDirect Methods and/or by a direct-space approach, and the structure refinement by the Rietveld technique.
• QualX2.0/QualX: a computer program for phase identification using powder diffraction data.
• Quanto: a Rietveld program for quantitative phase analysis of polycrystalline mixtures from powder diffraction data.
• SunBIM: a suite of programs for the supra- and sub-molecular X-ray imaging of nano and bio materials with SAXS, WAXS, GISAXS and GIWAXS techniques
• RootProf: An interactive, general purpose tool for processing unidimensional profiles with specific applications to X-ray diffraction measurements
• OChemdb: an on-line portal, using an appropriately designed database of already solved crystal structures, for searching and analysing crystal-chemical information of organic, metal-organic and inorganic structures, and providing statistics on desired bond distances, bond angles, torsion angles, and space groups.

The software is free for academic and non-profit research institutions, while it requires the payment of a license fee to commercial users.

To download the software packages, academic and no-profit users must first register to the web site, choosing the software packages of their interest and accepting all the terms and conditions of the on-line Academic License Agreement. After completing the registration, users will receive a confirmation e-mail and will be allowed tologin to download the selected packages.

Registered users can download freely the previous versions of our packages (such as Sir97, Sir2004, EXPO2004, EXPO2009, EXPO2013 and QualX) for non-commercial use from the Old Software section of the web site.

Commercial users must fill the Order Form and send it by email or fax to our office, together with a signed copy of the Commercial License Agreement.

The license covers the use of all the requested programs under all the supported operating systems for an unlimited time on an unlimited number of computers.

See: http://www.ba.ic.cnr.it/softwareic/

X-ray diffraction, abbreviated as XRD, is an old and well-known technique for studying the structure and properties of crystals. The basis of the XRD method is single-color X-ray diffraction by atoms of a substance. Diffraction generally occurs when light strikes an obstacle. When it hits an obstacle, the light beam either bends and propagates or passes through tiny pores on the obstacle. The diffraction phenomenon is visible for all electromagnetic rays, including X-rays. Interference between the X-ray electric vector and the electrons of the material through which the beam passes can be constructive or destructive. In constructive interference, the X-ray diffraction pattern is characterized by a pattern of atomic arrangement in a regular crystal structure. In fact, when an X-ray is shone on a crystal, its diffraction occurs according to the structural characteristic pattern of the crystal.

Bragg’s Law

Due to the regular structure in a crystal, it can be assumed to be regular plates with specified intervals. Diffraction occurs because the distance between the regular layers of a crystal is close to the X-ray wavelength. The X-ray strikes the angle θ with the surface, causing part of the initial beam to propagate at the same angle θ and the other part to enter the inner plates of the crystal. This process is repeated for many pages of a crystal. The distance traveled by X-rays in contact with surface atoms is less than the distance traveled in contact with the inner layer of the crystal. The distance traveled depends on the distance between the two layers and the angle of X-ray radiation.

X-ray diffraction – XRD – analium
Figure 1 X-ray collision and its diffraction method in XRD method

Figure 1 shows that the difference in path traveled between the first and second layers is equal to:

BG = BC = dSinθ (1)

Constructive diffraction occurs when the difference in the length of the X-ray path is an exact multiple of the wavelength. Therefore, for the total distance traveled, it is equal to:

(2) nλ = 2dSinθ

This equation is known as the Bragg relation. In this relation λ the wavelength of the source d is the distance between the crystal plates and θ is the angle of incidence and n is an integer. Note that based on this equation, the X-ray will only be reflected at specific angles obtained from the rearrangement of Equation 1:

   (3) Sinθ = nλ / 2d

An XRD spectrum is obtained by plotting the intensity in θ. By changing θ and knowing the wavelength of the source λ, d is obtained at any moment.

XRD device
Similar to many XRD component analyzers, they include a source, a wavelength selector, a sample location, a detector, and a signal converter. Figure 2 shows an overview of an X-ray diffraction device (XRD).

X-ray diffraction device (XRD) – analium
Figure 2 Overview of an X-ray diffraction device (XRD)

X-ray tubes with tungsten filament are commonly used as sources. Source intensity can be adjusted by adjusting the current flowing through it. The beam wavelength can also be controlled by applying applied voltage control.

A monochromator or filter is used to create a monochromatic beam. A variety of scintillation and semiconductor gas-filled detectors are used in XRD devices.

Preparation of XRD samples
The sample must be well ground to obtain a homogeneous powder from the crystalline sample. In this case, it is possible to place a large number of crystalline particles in the desired direction and in accordance with the Bragg equation. The samples are mixed with a suitable adhesive and then molded.

Crystallization is a very important step in the preparation of XRD samples and requires special skills and expertise.

In powder X-ray diffraction, the diffraction pattern is obtained from the powder form of the sample. XRD powder is usually lighter and simpler than crystalline diffraction. Because in powder form, there is no need to prepare single crystal. In the powder method, the mass pattern (bulk) of the sample is also obtained.

XRD Analysis Tips
The sample must have a crystalline structure.
Has little accuracy in quantifying phases (phases with values ​​less than 5% are not detected).
In qualitative analysis, the element does not perform well.
The method is fast and powerful and with convenient access.
XRD Application Background
Determining the crystal structure and accurate measurement of lattice parameters
Determining fuzzy diagrams
Chemical identification and analysis
Determining the quality and direction of plates in single crystals

Only 10 $ for interpretation of your SEM/TEM/AFM micrograph
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Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction-limit.

Atomic force microscopy is a type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit. The information is gathered by “feeling” or “touching” the surface with a mechanical probe. Piezoelectric elements that facilitate tiny but accurate and precise movements on (electronic) command enable precise scanning.

Abilities

Atomic Force Microscope

The AFM has three major abilities: force measurement, topographic imaging, and manipulation.

In force measurement, AFMs can be used to measure the forces between the probe and the sample as a function of their mutual separation. This can be applied to perform force spectroscopy, to measure the mechanical properties of the sample, such as the sample’s Young’s modulus, a measure of stiffness.

For imaging, the reaction of the probe to the forces that the sample imposes on it can be used to form an image of the three-dimensional shape (topography) of a sample surface at a high resolution. This is achieved by raster scanning the position of the sample with respect to the tip and recording the height of the probe that corresponds to a constant probe-sample interaction (see section topographic imaging in AFM for more details). The surface topography is commonly displayed as a pseudocolor plot. Although the initial publication about the atomic force microscopy by Binnig, Quate and Gerber in 1986 speculated about the possibility of achieving atomic resolution, profound experimental challenges needed to be overcome before atomic resolution of defects and step edges in ambient (liquid) conditions was demonstrated in 1993 by Ohnesorge and Binnig. True atomic resolution of the silicon 7×7 surface – the atomic images of this surface obtained by STM had convinced the scientific community of the spectacular spatial resolution of scanning tunneling microscopy – had to wait a little longer before it was shown by Giessibl,

In manipulation, the forces between tip and sample can also be used to change the properties of the sample in a controlled way. Examples of this include atomic manipulation, scanning probe lithography and local stimulation of cells.

Simultaneous with the acquisition of topographical images, other properties of the sample can be measured locally and displayed as an image, often with similarly high resolution. Examples of such properties are mechanical properties like stiffness or adhesion strength and electrical properties such as conductivity or surface potential. In fact, the majority of SPM techniques are extensions of AFM that use this modality.

Other microscopy technologies

The major difference between atomic force microscopy and competing technologies such as optical microscopy and electron microscopy is that AFM does not use lenses or beam irradiation. Therefore, it does not suffer from a limitation in spatial resolution due to diffraction and aberration, and preparing a space for guiding the beam (by creating a vacuum) and staining the sample are not necessary.

There are several types of scanning microscopy including scanning probe microscopy (which includes AFM, scanning tunneling microscopy (STM) and near-field scanning optical microscope (SNOM/NSOM), STED microscopy (STED), and scanning electron microscopy and electrochemical AFM, EC-AFM). Although SNOM and STED use visible, infrared or even terahertz light to illuminate the sample, their resolution is not constrained by the diffraction limit.

Configuration

Fig. 3 shows an AFM, which typically consists of the following features. Numbers in parentheses correspond to numbered features in Fig. 3. Coordinate directions are defined by the coordinate system (0).Fig. 3: Typical configuration of an AFM.
(1): Cantilever, (2): Support for cantilever, (3): Piezoelectric element (to oscillate cantilever at its eigen frequency), (4): Tip (Fixed to open end of a cantilever, acts as the probe), (5): Detector of deflection and motion of the cantilever, (6): Sample to be measured by AFM, (7): xyz drive, (moves sample (6) and stage (8) in x, y, and z directions with respect to a tip apex (4)), and (8): Stage.

The small spring-like cantilever (1) is carried by the support (2). Optionally, a piezoelectric element (typically made of a ceramic material) (3) oscillates the cantilever (1). The sharp tip (4) is fixed to the free end of the cantilever (1). The detector (5) records the deflection and motion of the cantilever (1). The sample (6) is mounted on the sample stage (8). An xyz drive (7) permits to displace the sample (6) and the sample stage (8) in x, y, and z directions with respect to the tip apex (4). Although Fig. 3 shows the drive attached to the sample, the drive can also be attached to the tip, or independent drives can be attached to both, since it is the relative displacement of the sample and tip that needs to be controlled. Controllers and plotter are not shown in Fig. 3.

According to the configuration described above, the interaction between tip and sample, which can be an atomic scale phenomenon, is transduced into changes of the motion of cantilever which is a macro scale phenomenon. Several different aspects of the cantilever motion can be used to quantify the interaction between the tip and sample, most commonly the value of the deflection, the amplitude of an imposed oscillation of the cantilever, or the shift in resonance frequency of the cantilever (see section Imaging Modes).

Detector

The detector (5) of AFM measures the deflection (displacement with respect to the equilibrium position) of the cantilever and converts it into an electrical signal. The intensity of this signal will be proportional to the displacement of the cantilever.

Various methods of detection can be used, e.g. interferometry, optical levers, the piezoresistive method, the piezoelectric method, and STM-based detectors (see section “AFM cantilever deflection measurement”.).

Image formation

Note: The following paragraphs assume that ‘contact mode’ is used (see section Imaging Modes). For other imaging modes, the process is similar, except that ‘deflection’ should be replaced by the appropriate feedback variable.

When using the AFM to image a sample, the tip is brought into contact with the sample, and the sample is raster scanned along an x–y grid (fig 4). Most commonly, an electronic feedback loop is employed to keep the probe-sample force constant during scanning. This feedback loop has the cantilever deflection as input, and its output controls the distance along the z axis between the probe support (2 in fig. 3) and the sample support (8 in fig 3). As long as the tip remains in contact with the sample, and the sample is scanned in the x–y plane, height variations in the sample will change the deflection of the cantilever. The feedback then adjusts the height of the probe support so that the deflection is restored to a user-defined value (the setpoint). A properly adjusted feedback loop adjusts the support-sample separation continuously during the scanning motion, such that the deflection remains approximately constant. In this situation, the feedback output equals the sample surface topography to within a small error.

Historically, a different operation method has been used, in which the sample-probe support distance is kept constant and not controlled by a feedback (servo mechanism). In this mode, usually referred to as ‘constant height mode’, the deflection of the cantilever is recorded as a function of the sample x–y position. As long as the tip is in contact with the sample, the deflection then corresponds to surface topography. The main reason this method is not very popular anymore, is that the forces between tip and sample are not controlled, which can lead to forces high enough to damage the tip or the sample. It is however common practice to record the deflection even when scanning in ‘constant force mode’, with feedback. This reveals the small tracking error of the feedback, and can sometimes reveal features that the feedback was not able to adjust for.

The AFM signals, such as sample height or cantilever deflection, are recorded on a computer during the x–y scan. They are plotted in a pseudocolor image, in which each pixel represents an x–y position on the sample, and the color represents the recorded signal.Fig. 5: Topographic image forming by AFM.
(1): Tip apex, (2): Sample surface, (3): Z-orbit of Tip apex, (4): Cantilever.

History

The AFM was invented by IBM scientists in 1985, The precursor to the AFM, the scanning tunneling microscope (STM), was developed by Gerd Binnig and Heinrich Rohrer in the early 1980s at IBM Research – Zurich, a development that earned them the 1986 Nobel Prize for Physics. Binnig invented the atomic force microscope and the first experimental implementation was made by Binnig, Quate and Gerber in 1986.

The first commercially available atomic force microscope was introduced in 1989. The AFM is one of the foremost tools for imaging, measuring, and manipulating matter at the nanoscale.

Applications

The AFM has been applied to problems in a wide range of disciplines of the natural sciences, including solid-state physics, semiconductor science and technology, molecular engineering, polymer chemistry and physics, surface chemistry, molecular biology, cell biology, and medicine.

Applications in the field of solid state physics include (a) the identification of atoms at a surface, (b) the evaluation of interactions between a specific atom and its neighboring atoms, and (c) the study of changes in physical properties arising from changes in an atomic arrangement through atomic manipulation.

In molecular biology, AFM can be used to study the structure and mechanical properties of protein complexes and assemblies. For example, AFM has been used to image microtubules and measure their stiffness.

In cellular biology, AFM can be used to attempt to distinguish cancer cells and normal cells based on a hardness of cells, and to evaluate interactions between a specific cell and its neighboring cells in a competitive culture system. AFM can also be used to indent cells, to study how they regulate the stiffness or shape of the cell membrane or wall.

In some variations, electric potentials can also be scanned using conducting cantilevers. In more advanced versions, currents can be passed through the tip to probe the electrical conductivity or transport of the underlying surface, but this is a challenging task with few research groups reporting consistent data (as of 2004).

Principles

Electron micrograph of a used AFM cantilever. Image width ~100 micrometers

Electron micrograph of a used AFM cantilever. Image width ~30 micrometers

The AFM consists of a cantilever with a sharp tip (probe) at its end that is used to scan the specimen surface. The cantilever is typically silicon or silicon nitridewith a tip radius of curvature on the order of nanometers. When the tip is brought into proximity of a sample surface, forces between the tip and the sample lead to a deflection of the cantilever according to Hooke’s law. Depending on the situation, forces that are measured in AFM include mechanical contact force, van der Waals forces, capillary forces, chemical bonding, electrostatic forces, magnetic forces (see magnetic force microscope, MFM), Casimir forces, solvation forces, etc. Along with force, additional quantities may simultaneously be measured through the use of specialized types of probes. Atomic force microscope topographical scan of a glass surface. The micro and nano-scale features of the glass can be observed, portraying the roughness of the material. The image space is (x,y,z) = (20 µm × 20 µm × 420 nm).

The AFM can be operated in a number of modes, depending on the application. In general, possible imaging modes are divided into static (also called contact) modes and a variety of dynamic (non-contact or “tapping”) modes where the cantilever is vibrated or oscillated at a given frequency.^[7]

Imaging modes

AFM operation is usually described as one of three modes, according to the nature of the tip motion: contact mode, also called static mode (as opposed to the other two modes, which are called dynamic modes); tapping mode, also called intermittent contact, AC mode, or vibrating mode, or, after the detection mechanism, amplitude modulation AFM; non-contact mode, or, again after the detection mechanism, frequency modulation AFM.

Despite the nomenclature, repulsive contact can occur or be avoided both in amplitude modulation AFM and frequency modulation AFM, depending on the settings.

Contact mode

In contact mode, the tip is “dragged” across the surface of the sample and the contours of the surface are measured either using the deflection of the cantilever directly or, more commonly, using the feedback signal required to keep the cantilever at a constant position. Because the measurement of a static signal is prone to noise and drift, low stiffness cantilevers (i.e. cantilevers with a low spring constant, k) are used to achieve a large enough deflection signal while keeping the interaction force low. Close to the surface of the sample, attractive forces can be quite strong, causing the tip to “snap-in” to the surface. Thus, contact mode AFM is almost always done at a depth where the overall force is repulsive, that is, in firm “contact” with the solid surface.

Tapping mode

Single polymer chains (0.4 nm thick) recorded in a tapping mode under aqueous media with different pH.

In ambient conditions, most samples develop a liquid meniscus layer. Because of this, keeping the probe tip close enough to the sample for short-range forces to become detectable while preventing the tip from sticking to the surface presents a major problem for contact mode in ambient conditions. Dynamic contact mode (also called intermittent contact, AC mode or tapping mode) was developed to bypass this problem. Nowadays, tapping mode is the most frequently used AFM mode when operating in ambient conditions or in liquids.

In tapping mode, the cantilever is driven to oscillate up and down at or near its resonance frequency. This oscillation is commonly achieved with a small piezo element in the cantilever holder, but other possibilities include an AC magnetic field (with magnetic cantilevers), piezoelectric cantilevers, or periodic heating with a modulated laser beam. The amplitude of this oscillation usually varies from several nm to 200 nm. In tapping mode, the frequency and amplitude of the driving signal are kept constant, leading to a constant amplitude of the cantilever oscillation as long as there is no drift or interaction with the surface. The interaction of forces acting on the cantilever when the tip comes close to the surface, Van der Waals forces, dipole-dipole interactions, electrostatic forces, etc. cause the amplitude of the cantilever’s oscillation to change (usually decrease) as the tip gets closer to the sample. This amplitude is used as the parameter that goes into the electronic servo that controls the height of the cantilever above the sample. The servo adjusts the height to maintain a set cantilever oscillation amplitude as the cantilever is scanned over the sample. A tapping AFM image is therefore produced by imaging the force of the intermittent contacts of the tip with the sample surface.

Although the peak forces applied during the contacting part of the oscillation can be much higher than typically used in contact mode, tapping mode generally lessens the damage done to the surface and the tip compared to the amount done in contact mode. This can be explained by the short duration of the applied force, and because the lateral forces between tip and sample are significantly lower in tapping mode over contact mode. Tapping mode imaging is gentle enough even for the visualization of supported lipid bilayers or adsorbed single polymer molecules (for instance, 0.4 nm thick chains of synthetic polyelectrolytes) under liquid medium. With proper scanning parameters, the conformation of single molecules can remain unchanged for hours, and even single molecular motors can be imaged while moving.

When operating in tapping mode, the phase of the cantilever’s oscillation with respect to the driving signal can be recorded as well. This signal channel contains information about the energy dissipated by the cantilever in each oscillation cycle. Samples that contain regions of varying stiffness or with different adhesion properties can give a contrast in this channel that is not visible in the topographic image. Extracting the sample’s material properties in a quantitative manner from phase images, however, is often not feasible.

Non-contact mode

In non-contact atomic force microscopy mode, the tip of the cantilever does not contact the sample surface. The cantilever is instead oscillated at either its resonant frequency(frequency modulation) or just above (amplitude modulation) where the amplitude of oscillation is typically a few nanometers (<10 nm) down to a few picometers. The van der Waals forces, which are strongest from 1 nm to 10 nm above the surface, or any other long-range force that extends above the surface acts to decrease the resonance frequency of the cantilever. This decrease in resonant frequency combined with the feedback loop system maintains a constant oscillation amplitude or frequency by adjusting the average tip-to-sample distance. Measuring the tip-to-sample distance at each (x,y) data point allows the scanning software to construct a topographic image of the sample surface.

Non-contact mode AFM does not suffer from tip or sample degradation effects that are sometimes observed after taking numerous scans with contact AFM. This makes non-contact AFM preferable to contact AFM for measuring soft samples, e.g. biological samples and organic thin film. In the case of rigid samples, contact and non-contact images may look the same. However, if a few monolayers of adsorbed fluid are lying on the surface of a rigid sample, the images may look quite different. An AFM operating in contact mode will penetrate the liquid layer to image the underlying surface, whereas in non-contact mode an AFM will oscillate above the adsorbed fluid layer to image both the liquid and surface.

Schemes for dynamic mode operation include frequency modulation where a phase-locked loop is used to track the cantilever’s resonance frequency and the more common amplitude modulation with a servo loop in place to keep the cantilever excitation to a defined amplitude. In frequency modulation, changes in the oscillation frequency provide information about tip-sample interactions. Frequency can be measured with very high sensitivity and thus the frequency modulation mode allows for the use of very stiff cantilevers. Stiff cantilevers provide stability very close to the surface and, as a result, this technique was the first AFM technique to provide true atomic resolution in ultra-high vacuumconditions.

In amplitude modulation, changes in the oscillation amplitude or phase provide the feedback signal for imaging. In amplitude modulation, changes in the phase of oscillation can be used to discriminate between different types of materials on the surface. Amplitude modulation can be operated either in the non-contact or in the intermittent contact regime. In dynamic contact mode, the cantilever is oscillated such that the separation distance between the cantilever tip and the sample surface is modulated.

Amplitude modulation has also been used in the non-contact regime to image with atomic resolution by using very stiff cantilevers and small amplitudes in an ultra-high vacuum environment.

Topographic image

Image formation is a plotting method that produces a color mapping through changing the x–y position of the tip while scanning and recording the measured variable, i.e. the intensity of control signal, to each x–y coordinate. The color mapping shows the measured value corresponding to each coordinate. The image expresses the intensity of a value as a hue. Usually, the correspondence between the intensity of a value and a hue is shown as a color scale in the explanatory notes accompanying the image.

What is the topographic image of atomic force microscope?

Operation mode of image forming of the AFM are generally classified into two groups from the viewpoint whether it uses z-Feedback loop (not shown) to maintain the tip-sample distance to keep signal intensity exported by the detector. The first one (using z-Feedback loop), said to be “constant XX mode” (XX is something which kept by z-Feedback loop).

Topographic image formation mode is based on abovementioned “constant XX mode”, z-Feedback loop controls the relative distance between the probe and the sample through outputting control signals to keep constant one of frequency, vibration and phase which typically corresponds to the motion of cantilever (for instance, voltage is applied to the Z-piezoelectric element and it moves the sample up and down towards the Z direction.

Details will be explained in the case that especially “constant df mode”(FM-AFM) among AFM as an instance in next section.

Topographic image of FM-AFM

When the distance between the probe and the sample is brought to the range where atomic force may be detected, while a cantilever is excited in its natural eigen frequency (f₀), a phenomenon occurs that the resonance frequency (f) of the cantilever shifts from its original resonance frequency (natural eigen frequency). In other words, in the range where atomic force may be detected, the frequency shift (df=f-f₀) will be observed. So, when the distance between the probe and the sample is in the non-contact region, the frequency shift increases in negative direction as the distance between the probe and the sample gets smaller.

When the sample has concavity and convexity, the distance between the tip-apex and the sample varies in accordance with the concavity and convexity accompanied with a scan of the sample along x–y direction (without height regulation in z-direction). As a result, the frequency shift arises. The image in which the values of the frequency obtained by a raster scan along the x–y direction of the sample surface are plotted against the x–y coordination of each measurement point is called a constant-height image.

On the other hand, the df may be kept constant by moving the probe upward and downward (See (3) of FIG.5) in z-direction using a negative feedback (by using z-feedback loop) while the raster scan of the sample surface along the x–y direction. The image in which the amounts of the negative feedback (the moving distance of the probe upward and downward in z-direction) are plotted against the x–y coordination of each measurement point is a topographic image. In other words, the topographic image is a trace of the tip of the probe regulated so that the df is constant and it may also be considered to be a plot of a constant-height surface of the df.

Therefore, the topographic image of the AFM is not the exact surface morphology itself, but actually the image influenced by the bond-order between the probe and the sample, however, the topographic image of the AFM is considered to reflect the geographical shape of the surface more than the topographic image of a scanning tunnel microscope.

Force spectroscopy

Another major application of AFM (besides imaging) is force spectroscopy, the direct measurement of tip-sample interaction forces as a function of the gap between the tip and sample (the result of this measurement is called a force-distance curve). For this method, the AFM tip is extended towards and retracted from the surface as the deflection of the cantilever is monitored as a function of piezoelectric displacement. These measurements have been used to measure nanoscale contacts, atomic bonding, Van der Waals forces, and Casimir forces, dissolution forces in liquids and single molecule stretching and rupture forces. Furthermore, AFM was used to measure, in an aqueous environment, the dispersion force due to polymer adsorbed on the substrate. Forces of the order of a few piconewtons can now be routinely measured with a vertical distance resolution of better than 0.1 nanometers. Force spectroscopy can be performed with either static or dynamic modes. In dynamic modes, information about the cantilever vibration is monitored in addition to the static deflection.

Problems with the technique include no direct measurement of the tip-sample separation and the common need for low-stiffness cantilevers, which tend to ‘snap’ to the surface. These problems are not insurmountable. An AFM that directly measures the tip-sample separation has been developed. The snap-in can be reduced by measuring in liquids or by using stiffer cantilevers, but in the latter case a more sensitive deflection sensor is needed. By applying a small dither to the tip, the stiffness (force gradient) of the bond can be measured as well.

Biological applications and other

Force spectroscopy is used in biophysics to measure the mechanical properties of living material (such as tissue or cells) or detect structures of different stiffness buried into the bulk of the sample using the stiffness tomography. Another application was to measure the interaction forces between from one hand a material stuck on the tip of the cantilever, and from another hand the surface of particles either free or occupied by the same material. From the adhesion force distribution curve, a mean value of the forces has been derived. It allowed to make a cartography of the surface of the particles, covered or not by the material. AFM have been also used for mechanically unfolding proteins. In such experiments, the analyzes of the mean unfolding forces with the appropriate model leads to the obtainment of the information about the unfolding rate and free energy profile parameters of the protein.

Identification of individual surface atoms

The AFM can be used to image and manipulate atoms and structures on a variety of surfaces. The atom at the apex of the tip “senses” individual atoms on the underlying surface when it forms incipient chemical bonds with each atom. Because these chemical interactions subtly alter the tip’s vibration frequency, they can be detected and mapped. This principle was used to distinguish between atoms of silicon, tin and lead on an alloy surface, by comparing these ‘atomic fingerprints’ to values obtained from large-scale density functional theory (DFT) simulations.

The trick is to first measure these forces precisely for each type of atom expected in the sample, and then to compare with forces given by DFT simulations. The team found that the tip interacted most strongly with silicon atoms, and interacted 24% and 41% less strongly with tin and lead atoms, respectively. Thus, each different type of atom can be identified in the matrix as the tip is moved across the surface.

Probe

An AFM probe has a sharp tip on the free-swinging end of a cantilever that is protruding from a holder. The dimensions of the cantilever are in the scale of micrometers. The radius of the tip is usually on the scale of a few nanometers to a few tens of nanometers. (Specialized probes exist with much larger end radii, for example probes for indentation of soft materials.) The cantilever holder, also called holder chip – often 1.6 mm by 3.4 mm in size – allows the operator to hold the AFM cantilever/probe assembly with tweezers and fit it into the corresponding holder clips on the scanning head of the atomic force microscope.

This device is most commonly called an “AFM probe”, but other names include “AFM tip” and “cantilever” (employing the name of a single part as the name of the whole device). An AFM probe is a particular type of SPM (scanning probe microscopy) probe.

AFM probes are manufactured with MEMS technology. Most AFM probes used are made from silicon (Si), but borosilicate glass and silicon nitride are also in use. AFM probes are considered consumables as they are often replaced when the tip apex becomes dull or contaminated or when the cantilever is broken. They can cost from a couple of tens of dollars up to hundreds of dollars per cantilever for the most specialized cantilever/probe combinations.

Just the tip is brought very close to the surface of the object under investigation, the cantilever is deflected by the interaction between the tip and the surface, which is what the AFM is designed to measure. A spatial map of the interaction can be made by measuring the deflection at many points on a 2D surface.

Several types of interaction can be detected. Depending on the interaction under investigation, the surface of the tip of the AFM probe needs to be modified with a coating. Among the coatings used are gold – for covalent bonding of biological molecules and the detection of their interaction with a surface, diamond for increased wear resistance and magnetic coatings for detecting the magnetic properties of the investigated surface. Another solution exists to achieve high resolution magnetic imaging : having the probe equip with a microSQUID. The AFM tips is fabricated using silicon micro machining and the precise positioning of the microSQUID loop is done by electron beam lithography.

The surface of the cantilevers can also be modified. These coatings are mostly applied in order to increase the reflectance of the cantilever and to improve the deflection signal.

Forces vs tip geometry

The forces between the tip and the sample strongly depend on the geometry of the tip. Various studies were exploited in the past years to write the forces as a function of the tip parameters.

Among the different forces between the tip and the sample, the water meniscus forces are highly interesting, both in air and liquid environment. Other forces must be considered, like the Coulomb force, van der Waals forces, double layer interactions, solvation forces, hydration and hydrophobic forces.

Water meniscus

Water meniscus forces are highly interesting for AFM measurements in air. Due to the ambient humidity, a thin layer of water is formed between the tip and the sample during air measurements. The resulting capillary force gives rise to a strong attractive force that pulls the tip onto the surface. In fact, the adhesion force measured between tip and sample in ambient air of finite humidity is usually dominated by capillary forces. As a consequence, it is difficult to pull the tip away from the surface. For soft samples including many polymers and in particular biological materials, the strong adhesive capillary force gives rise to sample degradation and destruction upon imaging in contact mode. Historically, these problems were an important motivation for the development of dynamic imaging in air (e.g. ‘tapping mode’). During tapping mode imaging in air, capillary bridges still form. Yet, for suitable imaging conditions, the capillary bridges are formed and broken in every oscillation cycle of the cantilever normal to the surface, as can be inferred from an analysis of cantilever amplitude and phase vs. distance curves. As a consequence, destructive shear forces are largely reduced and soft samples can be investigated.

In order to quantify the equilibrium capillary force, it is necessary to start from the Laplace equation for pressure:Model for AFM water meniscus

{\displaystyle P=\gamma _{L}({\frac {1}{r}}_{1}+{\frac {1}{r}}_{0})\simeq {\frac {\gamma _{L}}{r_{eff}}}}

where γ_L is the surface energy and r₀ and r₁ are defined in the figure.

The pressure is applied on an area of

{\displaystyle A\simeq 2\pi R\simeq [r_{eff}(1+\cos \theta )+h]}

where d, θ, and h are defined in the figure.

The force which pulles together the two surfaces is

{\displaystyle F=2\pi R\gamma _{L}(1+\cos \theta +{\frac {h}{r_{eff}}})}

The same formula could also be calculated as a function of relative humidity.

Gao calculated formulas for different tip geometries. As an example, the forse decreases by 20% for a conical tip with respect to a spherical tip.

When these forces are calculated, a difference must be made between the wet on dry situation and the wet on wet situation.

For a spherical tip, the force is:

{\displaystyle f_{m}=-2\pi R\gamma _{L}(\cos \theta +\cos \phi )(1-{\frac {dh}{dD}})} for dry on wet

{\displaystyle f_{m}=-2\pi R\gamma _{L}{\frac {dr_{0}}{dD}}}for wet on wet

where θ is the contact angle of the dry sphere and φ is the immersed angle, as shown in the figure Also R,h and D are illustrated in the same figure.

For a conical tip, the formula becomes:

{\displaystyle f_{m}=-2\pi R\gamma _{L}{\frac {\tan \delta }{\cos \delta }}(\cos \theta +\sin \delta )(hD)(1-{\frac {dh}{dD}})} for dry on wet

{\displaystyle f_{m}=-2\pi R\gamma _{L}({\frac {1}{\cos \delta }}+\sin \delta )(r_{0})({\frac {dr_{0}}{dD}})} for wet on wet

where δ is the half cone angle and r₀ and h are parameters of the meniscus profile.

AFM cantilever-deflection measurement

Beam-deflection measurement

AFM beam-deflection detection

The most common method for cantilever-deflection measurements is the beam-deflection method. In this method, laser light from a solid-state diode is reflected off the back of the cantilever and collected by a position-sensitive detector (PSD) consisting of two closely spaced photodiodes, whose output signal is collected by a differential amplifier. Angular displacement of the cantilever results in one photodiode collecting more light than the other photodiode, producing an output signal (the difference between the photodiode signals normalized by their sum), which is proportional to the deflection of the cantilever. The sensitivity of the beam-deflection method is very high, a noise floor on the order of 10 fm Hz^{−​1⁄₂} can be obtained routinely in a well-designed system. Although this method is sometimes called the ‘optical lever’ method, the signal is not amplified if the beam path is made longer. A longer beam path increases the motion of the reflected spot on the photodiodes, but also widens the spot by the same amount due to diffraction, so that the same amount of optical power is moved from one photodiode to the other. The ‘optical leverage’ (output signal of the detector divided by deflection of the cantilever) is inversely proportional to the numerical aperture of the beam focusing optics, as long as the focused laser spot is small enough to fall completely on the cantilever. It is also inversely proportional to the length of the cantilever.

The relative popularity of the beam-deflection method can be explained by its high sensitivity and simple operation, and by the fact that cantilevers do not require electrical contacts or other special treatments, and can therefore be fabricated relatively cheaply with sharp integrated tips.

Other deflection-measurement methods

Many other methods for beam-deflection measurements exist.

• Piezoelectric detection – Cantilevers made from quartz (such as the qPlus configuration), or other piezoelectric materials can directly detect deflection as an electrical signal. Cantilever oscillations down to 10pm have been detected with this method.
• Laser Doppler vibrometry – A laser Doppler vibrometer can be used to produce very accurate deflection measurements for an oscillating cantilever (thus is only used in non-contact mode). This method is expensive and is only used by relatively few groups.
• Scanning tunneling microscope (STM) — The first atomic microscope used an STM complete with its own feedback mechanism to measure deflection. This method is very difficult to implement, and is slow to react to deflection changes compared to modern methods.
• Optical interferometry – Optical interferometry can be used to measure cantilever deflection. Due to the nanometre scale deflections measured in AFM, the interferometer is running in the sub-fringe regime, thus, any drift in laser power or wavelength has strong effects on the measurement. For these reasons optical interferometer measurements must be done with great care (for example using index matching fluids between optical fibre junctions), with very stable lasers. For these reasons optical interferometry is rarely used.
• Capacitive detection – Metal coated cantilevers can form a capacitor with another contact located behind the cantilever. Deflection changes the distance between the contacts and can be measured as a change in capacitance.
• Piezoresistive detection – Cantilevers can be fabricated with piezoresistive elements that act as a strain gauge. Using a Wheatstone bridge, strain in the AFM cantilever due to deflection can be measured. This is not commonly used in vacuum applications, as the piezoresistive detection dissipates energy from the system affecting Q of the resonance.

Piezoelectric scanners

AFM scanners are made from piezoelectric material, which expands and contracts proportionally to an applied voltage. Whether they elongate or contract depends upon the polarity of the voltage applied. Traditionally the tip or sample is mounted on a ‘tripod’ of three piezo crystals, with each responsible for scanning in the x,y and z directions. In 1986, the same year as the AFM was invented, a new piezoelectric scanner, the tube scanner, was developed for use in STM. Later tube scanners were incorporated into AFMs. The tube scanner can move the sample in the x, y, and z directions using a single tube piezo with a single interior contact and four external contacts. An advantage of the tube scanner compared to the original tripod design, is better vibrational isolation, resulting from the higher resonant frequency of the single element construction, in combination with a low resonant frequency isolation stage. A disadvantage is that the x–y motion can cause unwanted z motion resulting in distortion. Another popular design for AFM scanners is the flexurestage, which uses separate piezos for each axis, and couples them through a flexure mechanism.

Scanners are characterized by their sensitivity, which is the ratio of piezo movement to piezo voltage, i.e., by how much the piezo material extends or contracts per applied volt. Because of differences in material or size, the sensitivity varies from scanner to scanner. Sensitivity varies non-linearly with respect to scan size. Piezo scanners exhibit more sensitivity at the end than at the beginning of a scan. This causes the forward and reverse scans to behave differently and display hysteresis between the two scan directions.This can be corrected by applying a non-linear voltage to the piezo electrodes to cause linear scanner movement and calibrating the scanner accordingly. One disadvantage of this approach is that it requires re-calibration because the precise non-linear voltage needed to correct non-linear movement will change as the piezo ages (see below). This problem can be circumvented by adding a linear sensor to the sample stage or piezo stage to detect the true movement of the piezo. Deviations from ideal movement can be detected by the sensor and corrections applied to the piezo drive signal to correct for non-linear piezo movement. This design is known as a ‘closed loop’ AFM. Non-sensored piezo AFMs are referred to as ‘open loop’ AFMs.

The sensitivity of piezoelectric materials decreases exponentially with time. This causes most of the change in sensitivity to occur in the initial stages of the scanner’s life. Piezoelectric scanners are run for approximately 48 hours before they are shipped from the factory so that they are past the point where they may have large changes in sensitivity. As the scanner ages, the sensitivity will change less with time and the scanner would seldom require recalibration, though various manufacturer manuals recommend monthly to semi-monthly calibration of open loop AFMs.

Advantages and disadvantages

The first atomic force microscope

Advantages

AFM has several advantages over the scanning electron microscope (SEM). Unlike the electron microscope, which provides a two-dimensional projection or a two-dimensional image of a sample, the AFM provides a three-dimensional surface profile. In addition, samples viewed by AFM do not require any special treatments (such as metal/carbon coatings) that would irreversibly change or damage the sample, and does not typically suffer from charging artifacts in the final image. While an electron microscope needs an expensive vacuum environment for proper operation, most AFM modes can work perfectly well in ambient air or even a liquid environment. This makes it possible to study biological macromolecules and even living organisms. In principle, AFM can provide higher resolution than SEM. It has been shown to give true atomic resolution in ultra-high vacuum (UHV) and, more recently, in liquid environments. High resolution AFM is comparable in resolution to scanning tunneling microscopy and transmission electron microscopy. AFM can also be combined with a variety of optical microscopy and spectroscopy techniques such as fluorescent microscopy of infrared spectroscopy, giving rise to scanning near-field optical microscopy, nano-FTIR and further expanding its applicability. Combined AFM-optical instruments have been applied primarily in the biological sciences but have recently attracted strong interest in photovoltaics and energy-storage research, polymer sciences, nanotechnology and even medical research.

Disadvantages

A disadvantage of AFM compared with the scanning electron microscope (SEM) is the single scan image size. In one pass, the SEM can image an area on the order of square millimeters with a depth of field on the order of millimeters, whereas the AFM can only image a maximum scanning area of about 150×150 micrometers and a maximum height on the order of 10–20 micrometers. One method of improving the scanned area size for AFM is by using parallel probes in a fashion similar to that of millipede data storage.

The scanning speed of an AFM is also a limitation. Traditionally, an AFM cannot scan images as fast as an SEM, requiring several minutes for a typical scan, while an SEM is capable of scanning at near real-time, although at relatively low quality. The relatively slow rate of scanning during AFM imaging often leads to thermal drift in the imagemaking the AFM less suited for measuring accurate distances between topographical features on the image. However, several fast-acting designs were suggested to increase microscope scanning productivity including what is being termed videoAFM (reasonable quality images are being obtained with videoAFM at video rate: faster than the average SEM). To eliminate image distortions induced by thermal drift, several methods have been introduced.Showing an AFM artifact arising from a tip with a high radius of curvature with respect to the feature that is to be visualizedAFM artifact, steep sample topography

AFM images can also be affected by nonlinearity, hysteresis, and creep of the piezoelectric material and cross-talk between the x, y, zaxes that may require software enhancement and filtering. Such filtering could “flatten” out real topographical features. However, newer AFMs utilize real-time correction software (for example, feature-oriented scanning) or closed-loop scanners, which practically eliminate these problems. Some AFMs also use separated orthogonal scanners (as opposed to a single tube), which also serve to eliminate part of the cross-talk problems.

As with any other imaging technique, there is the possibility of image artifacts, which could be induced by an unsuitable tip, a poor operating environment, or even by the sample itself, as depicted on the right. These image artifacts are unavoidable; however, their occurrence and effect on results can be reduced through various methods. Artifacts resulting from a too-coarse tip can be caused for example by inappropriate handling or de facto collisions with the sample by either scanning too fast or having an unreasonably rough surface, causing actual wearing of the tip.

Due to the nature of AFM probes, they cannot normally measure steep walls or overhangs. Specially made cantilevers and AFMs can be used to modulate the probe sideways as well as up and down (as with dynamic contact and non-contact modes) to measure sidewalls, at the cost of more expensive cantilevers, lower lateral resolution and additional artifacts.

Other applications in various fields of study

AFM image of part of a Golgi apparatus isolated from HeLa cells

The latest efforts in integrating nanotechnology and biological research have been successful and show much promise for the future. Since nanoparticles are a potential vehicle of drug delivery, the biological responses of cells to these nanoparticles are continuously being explored to optimize their efficacy and how their design could be improved. Pyrgiotakis et al. were able to study the interaction between CeO₂ and Fe₂O₃ engineered nanoparticles and cells by attaching the engineered nanoparticles to the AFM tip. Studies have taken advantage of AFM to obtain further information on the behavior of live cells in biological media. Real-time atomic force spectroscopy (or nanoscopy) and dynamic atomic force spectroscopy have been used to study live cells and membrane proteins and their dynamic behavior at high resolution, on the nanoscale. Imaging and obtaining information on the topography and the properties of the cells has also given insight into chemical processes and mechanisms that occur through cell-cell interaction and interactions with other signaling molecules (ex. ligands). Evans and Calderwood used single cell force microscopy to study cell adhesion forces, bond kinetics/dynamic bond strength and its role in chemical processes such as cell signaling. Scheuring, Lévy, and Rigaud reviewed studies in which AFM to explore the crystal structure of membrane proteins of photosynthetic bacteria. Alsteen et al. have used AFM-based nanoscopy to perform a real-time analysis of the interaction between live mycobacteria and antimycobacterial drugs (specifically isoniazid, ethionamide, ethambutol, and streptomycine),^[58]which serves as an example of the more in-depth analysis of pathogen-drug interactions that can be done through AFM.

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To satisfy this curiosity, many inventions have been devised. One of them is the optical microscope. The human eye can distinguish objects down to about 0.2 mm. Optical microscopes reveal small objects, which would be otherwise invisible to the human eye, by magnifying them with the help of a combination of glass lenses. If we raise the amplification rate (magnification) of an optical microscope higher and higher, can we see an atom?

Electron microscopes enable clear observation of micro-structures, which is not possible with optical microscopes. Moreover, they also make it possible to analyze substance structures and obtain atomic level information by using an electron beam. The electron microscope is an epoch-making invention used throughout the world to investigate an atomic world that we could hardly imagine.

The difference between Electron Beam and Light

fig1. Ripples caused by the difference in the magnitude of the wave

As explained above, the ability to distinguish a small structure, that is resolution, largely depends on the wavelength of the “wave” used to illuminate the specimen.

The nature of this “wave” may be easily understood by comparing it to the wave pattern arising when a small stone is thrown into a lake. Assume the waves on the water surface come into contact with a rock protruding above the surface. If the rock is larger than the length between the crests of the waves (wavelength), then the wave pattern does not continue behind the rock (Fig,1). This creates a shadow. If the rock is smaller than the wavelength, however, the wave pattern will not be interrupted behind the rock and there is no shadow. In this case, the existence of the rock cannot be detected.

Whereas the wavelength of visible light is 400 to 800 nm (1 nanometer is one 100,000th of 0.1mm), the wavelength of the electron beam, which is used as a light source in the electron microscope, varies depending on the accelerating voltage. The accelerating voltages commonly used are 100 to 200 kV (corresponding to wavelengths of 0.0037nm to 0.0025nm).

This wavelength is far shorter than that of light, and sufficient to distinguish the arrangements of atoms (several nanometers). For the optical microscope the combination of the lens is varied to alter the magnification. In contrast, for the electron microscope, the intensity of the electric current passed to the electromagnets is varied to change the intensity of the magnetic field. This corresponds to the changing the thickness of a convex lens. In fact, by manipulating the electric current, the magnification can be freely controlled.

Another characteristic “electron diffraction”

TEMs employ a high voltage electron beam in order to create an image. An electron gun at the top of a TEM emits electrons that travel through the microscope’s vacuum tube. Rather than having a glass lens focusing the light (as in the case of light microscopes), the TEM employs an electromagnetic lens which focuses the electrons into a very fine beam. This beam then passes through the specimen, which is very thin, and the electrons either scatter or hit a fluorescent screen at the bottom of the microscope. An image of the specimen with its assorted parts shown in different shades according to its density appears on the screen. This image can be then studied directly within the TEM or photographed.  Figure 1 shows a diagram of a TEM and its basic parts. 

Fig. 1 Simplified diagram of a transmission electron microscope.  Drawing by Graham Colm, courtesy of Wikimedia Commons.

What Are the Differences Between a TEM and a Light Microscope?

Although TEMs and light microscopes operate on the same basic principles, there are several differences between the two. The main difference is that TEMs use electrons rather than light in order to magnify images. The power of the light microscope is limited by the wavelength of light and can magnify something up to 2,000 times. Electron microscopes, on the other hand, can produce much more highly magnified images because the beam of electrons has a smaller wavelength which creates images of higher resolution. (Resolution is the degree of sharpness of an image.) Figure 2 compares the magnification of a light microscope to that of a TEM. 

Fig. 2 [left] Cotton stem; area in the circle is the phloem tissue. Light microscope x250. Photo by K. Esau.  [right] Enlarged image of cotton phloem tissue showing a sieve element (top cell) and a companion cell (bottom cell), TEM x8,000. Photo by J. Thorsch.

How Are TEM Specimens Prepared?

Specimens must be very thin so that electrons are able to pass through the tissue. This may be done by cutting very thin slices of a specimen’s tissue using an ultramicrotome.  The tissue must first be put in a chemical solution to preserve the cell structure.  The tissue must also be completely dehydrated (all water removed). 

                                 Fig. 3 Ultramicrotome.  Photo by J. Thorsch.                                                             Fig. 4 Microtome grid.  Image by Laurie Hannah

Once preserved and dehydrated, tissue samples are placed in hard, clean plastic.  The plastic supports the tissue while it is being thinly cut with the ultramicrotome (Fig. 3).

After sections are cut and mounted on grids, (tiny circular disks with openings,) a solution of lead is used to stain the tissue (Fig. 4).  The lead provides contrast to the tissue by staining certain cell parts.  When placed in the electron microscope, the electrons are scattered by the lead.  They do not penetrate the tissue or hit the fluorescent screen, leaving those areas dark. 

Esau’s Work With the TEM

Esau started using the TEM in her research in the early 1960s.  When she moved to UC Santa Barbara in 1963, the campus purchased a Siemens electron microscope for her. She then received a grant from the National Science Foundation in 1969 for another new microscope which she used for the remainder of her career in Santa Barbara. The TEM significantly improved her understanding of the relationship between plants and viruses. Electron microscopy also aided in clarifying the functioning of sieve elements, the food conducting cells in plants. Without the TEM, much of this research would not have been possible. 

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The scanning electron microscope (SEM) uses a focused beam of high-energy electrons to generate a variety of signals at the surface of solid specimens. The signals that derive from electron-sample interactions reveal information about the sample including external morphology (texture), chemical composition, and crystalline structure and orientation of materials making up the sample.

In most applications, data are collected over a selected area of the surface of the sample, and a 2-dimensional image is generated that displays spatial variations in these properties. Areas ranging from approximately 1 cm to 5 microns in width can be imaged in a scanning mode using conventional SEM techniques (magnification ranging from 20X to approximately 30,000X, spatial resolution of 50 to 100 nm). The SEM is also capable of performing analyses of selected point locations on the sample; this approach is especially useful in qualitatively or semi-quantitatively determining chemical compositions (using EDS), crystalline structure, and crystal orientations (using EBSD). The design and function of the SEM is very similar to the EPMA and considerable overlap in capabilities exists between the two instruments.

Fundamental Principles of Scanning Electron Microscopy (SEM)

Accelerated electrons in an SEM carry significant amounts of kinetic energy, and this energy is dissipated as a variety of signals produced by electron-sample interactions when the incident electrons are decelerated in the solid sample. These signals include secondary electrons (that produce SEM images), backscattered electrons (BSE), diffracted backscattered electrons (EBSD that are used to determine crystal structures and orientations of minerals), photons (characteristic X-rays that are used for elemental analysis and continuum X-rays), visible light (cathodoluminescence–CL), and heat. Secondary electrons and backscattered electrons are commonly used for imaging samples: secondary electrons are most valuable for showing morphology and topography on samples and backscattered electrons are most valuable for illustrating contrasts in composition in multiphase samples (i.e. for rapid phase discrimination). X-ray generation is produced by inelastic collisions of the incident electrons with electrons in discrete ortitals (shells) of atoms in the sample. As the excited electrons return to lower energy states, they yield X-rays that are of a fixed wavelength (that is related to the difference in energy levels of electrons in different shells for a given element). Thus, characteristic X-rays are produced for each element in a mineral that is “excited” by the electron beam. SEM analysis is considered to be “non-destructive”; that is, x-rays generated by electron interactions do not lead to volume loss of the sample, so it is possible to analyze the same materials repeatedly.

Scanning Electron Microscopy (SEM) Instrumentation – How Does It Work?

Essential components of all SEMs include the following:

• Electron Source (“Gun”)
• Electron Lenses
• Sample Stage
• Detectors for all signals of interest
• Display / Data output devices
• Infrastructure Requirements:
  • Power Supply
  • Vacuum System
  • Cooling system
  • Vibration-free floor
  • Room free of ambient magnetic and electric fields

SEMs always have at least one detector (usually a secondary electron detector), and most have additional detectors. The specific capabilities of a particular instrument are critically dependent on which detectors it accommodates.

Applications

The SEM is routinely used to generate high-resolution images of shapes of objects (SEI) and to show spatial variations in chemical compositions: 1) acquiring elemental maps or spot chemical analyses using EDS, 2)discrimination of phases based on mean atomic number (commonly related to relative density) using BSE, and 3) compositional maps based on differences in trace element “activitors” (typically transition metal and Rare Earth elements) using CL. The SEM is also widely used to identify phases based on qualitative chemical analysis and/or crystalline structure. Precise measurement of very small features and objects down to 50 nm in size is also accomplished using the SEM. Backescattered electron images (BSE) can be used for rapid discrimination of phases in multiphase samples. SEMs equipped with diffracted backscattered electron detectors (EBSD) can be used to examine microfabric and crystallographic orientation in many materials.

Strengths and Limitations of Scanning Electron Microscopy (SEM)?

Strengths

There is arguably no other instrument with the breadth of applications in the study of solid materials that compares with the SEM. The SEM is critical in all fields that require characterization of solid materials. While this contribution is most concerned with geological applications, it is important to note that these applications are a very small subset of the scientific and industrial applications that exist for this instrumentation. Most SEM’s are comparatively easy to operate, with user-friendly “intuitive” interfaces. Many applications require minimal sample preparation. For many applications, data acquisition is rapid (less than 5 minutes/image for SEI, BSE, spot EDS analyses.) Modern SEMs generate data in digital formats, which are highly portable.

Limitations

Samples must be solid and they must fit into the microscope chamber. Maximum size in horizontal dimensions is usually on the order of 10 cm, vertical dimensions are generally much more limited and rarely exceed 40 mm. For most instruments samples must be stable in a vacuum on the order of 10^-5 – 10^-6 torr. Samples likely to outgas at low pressures (rocks saturated with hydrocarbons, “wet” samples such as coal, organic materials or swelling clays, and samples likely to decrepitate at low pressure) are unsuitable for examination in conventional SEM’s. However, “low vacuum” and “environmental” SEMs also exist, and many of these types of samples can be successfully examined in these specialized instruments. EDS detectors on SEM’s cannot detect very light elements (H, He, and Li), and many instruments cannot detect elements with atomic numbers less than 11 (Na). Most SEMs use a solid state x-ray detector (EDS), and while these detectors are very fast and easy to utilize, they have relatively poor energy resolution and sensitivity to elements present in low abundances when compared to wavelength dispersive x-ray detectors (WDS) on most electron probe microanalyzers (EPMA). An electrically conductive coating must be applied to electrically insulating samples for study in conventional SEM’s, unless the instrument is capable of operation in a low vacuum mode.

User’s Guide – Sample Collection and Preparation

Sample preparation can be minimal or elaborate for SEM analysis, depending on the nature of the samples and the data required. Minimal preparation includes acquisition of a sample that will fit into the SEM chamber and some accommodation to prevent charge build-up on electrically insulating samples. Most electrically insulating samples are coated with a thin layer of conducting material, commonly carbon, gold, or some other metal or alloy. The choice of material for conductive coatings depends on the data to be acquired: carbon is most desirable if elemental analysis is a priority, while metal coatings are most effective for high resolution electron imaging applications. Alternatively, an electrically insulating sample can be examined without a conductive coating in an instrument capable of “low vacuum” operation.