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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.

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1. XPST

XPST is a program package for the analysis of X-ray Photoelectron Spectroscopy (XPS) data. It includes various graphical interfaces as well as commandline functions to facilitate the workup of XPS data.

When a XPST fit project is started, a corresponding subfolder with all required data is generated and saved within the Igor experiment. You can generate fit templates and you can export entire fit projects to share them with your co-workers. As a special feature, a flexible multiplet function was implemented to facilitate a convenient analysis of complex spectra. XPST can handle any number of peaks.

There is also a youtube channel with tutorials.

Several changes in the newest version of XPST were made according to this book about programming Igor.

Installation

XPST was initially developed with Igor 5, but a major revision was made with Igor 7. XPST works also nicely with Igor 8. The Igor 7/8 version is not compatible with Igor 6. If you still run Igor 6, you have to download a previous release.

• Unpack the .zip file
• Copy/Move the folder ‘XPST’ to the folder ‘Igor Procedures’ in Igor’s main folder
• Copy/Move the folder ‘XPSTHelp’ to the folder ‘Igor Help Files’ in Igor’s main folder
• Restart Igor

Before you upgrade to a newer version of XPST, please remove all files associated with your old version from Igor’s folders.
 

Stay in touch …

If you want to stay informed about updates or other issues, just send a blank mail to: xpst_update@freenet.de
This is not a support contact – it only serves to keep you informed about changes.
You can sign off anytime you want using the same address.
 

More functions …

Besides the graphical interfaces, XPST comes with several commandline functions. For example:

• WhereIs() …. returns the absolute path of a selected wave (so it can be easily found)
• WaveOverlap() …. computes the overlap of two selected waves and saves it to a new wave
• CursorCut() …. cuts out regions from a selected wave

Limitations

• Data with ‘kinetic energy’ as x-axis (in waveform format or not) can not be analyzed with the Fit Assistant. Only a positive ‘binding energy’ scale works – however, this should be the most common case. If there is a strong demand for kinetic energies, it could be implemented in future versions.

See: https://www.wavemetrics.com/project/XPStools

2. CasaXPS

CasaXPS processing software offers powerful analysis techniques for both spectral and imaging data. The system originally designed for XPS and Auger data now offers features covering a wide range of analytical techniques including ToF SIMS, dynamic SIMS and many more.

Features in CasaXPS include:

·         Full quantification including transmission correction.

·         Configurable quantification reports.

·         Background type ranging from the standard Linear, Shirley and Tougaard to user-defined cubic-spline approximations.

·         Asymmetric and symmetric line-shapes: Doniach-Sunjic, Voigt, Gaussian-Lorentzian and line-shapes defined from data.

·         Easy-to-use propagation of processing, annotation and peak models to other data.

·         Batch processing for repetitive tasks, including configurable processing, display layout with automatic printing and report generation.

·         State-of-the-art image processing for XPS spectromicroscopy offering quantified chemical-state XPS images.

See: http://www.casaxps.com/

3. Originlab

Origin provides powerful and versatile tools such as Peak Analyzer, Quick Peaks Gadget, Integration Gadget, etc. for baseline correction, peak detection, peak integration and peak fitting.

Origin provides baseline detection and subtraction. Key features include:

• Create baseline with many baseline modes
  • Commonly used baseline types such as Constant, Straight line, Use Existing Dataset, End Points Weighted, Min&Max
  • Automatically find anchor points for baseline, modify the points, create baseline by interpolation or fitting
  • Create baseline for XPS using Shirley or Tougaard method and adjust corresponding parameters to optimize
  • Create baseline using Asymmetric Least Squares (ALS) Smoothing method and adjust corresponding parameters to optimize
• Subtract baseline

Origin allows you to search for peaks including hidden (“convoluted”) peaks and filter out unwanted peaks or manually add or remove peaks.

• Savitzky-Golay smoothing on the spectrum before peak finding

In Origin, you can integrate data with multiple peaks, to obtain peak areas, FWHM and other peak characteristics. Baseline subtraction is supported before peak integration. 

Available options include: 

• Directly select desired data range on graph
• Instantly view results of peak area and FWHM
• Subtract baseline from peak data
• Auto detect peak positions
• Auto determine peak widths for overlapped peaks
• Individually set peak widths
• Fit peaks and obtain fitted peak areas

Origin provides many tools to perform peak fitting: 

• Quick Peaks Gadget  : Visually correct baseline, find and fit peaks
• Multiple Peak Fit: Manually pick peak positions and fit peaks with same function. No baseline correction
• Peak Analyzer: Correct baseline, find peaks and fit by Peak Analyzer wizard
• Nonlinear Curve Fit Dialog: Fit multiple peaks with replicas in the nonlinear curve fit dialog

Available options for peak fitting include:

• Fit peaks with built-in or user-defined functions
• Fit multiple peaks with different functions
• Control fitting process using bounds and constraints
• Fix or share peak parameters
• Vary baseline parameters along with peak fitting

See: https://www.originlab.com/index.aspx?go=Products/Origin/DataAnalysis/PeakAnalysis#Peak_Fitting_PRO

4. XPSPEAK

Free, fully featured, software for the analysis of XPS spectra written by Raymund Kwok.XPSPeak is a XPS Peak Fitting Program.The portable app creates a sandbox folder in its current location, where it stores all its settings and temporary files. Can be downloaded from the US, UK or Hong Kong.

See: https://xpspeak.software.informer.com/4.1/

5. Unifit

See: https://home.uni-leipzig.de/unifit/downloads.htm

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What is XPS?

XPS is a surface-sensitive technique based on the photoelectric effect, which occurs when atoms or molecules are irradiated by photons of suitable energy, resulting in the ejection of electrons. The kinetic energy of the ejected electrons depends upon the elemental core level from which they originated.

Using this information, XPS data can be used to determine the elemental composition of the surface and, in most cases, the bonding environment of the elements.

The schematic figure shown to the right, illustrates the XPS procedure, where x-rays are used to excite and eject photoelectrons from a sodium chloride molecule on a substrate.

XPS detects and quantifies the ejected photoelectrons, which are proportional to the amount present in the uppermost layers of the surface.

To understand more about these uppermost layers, further details on the XPS penetration depth and attenuation length of the X-ray photons are required.

Normal XPS can provide information from the top 10nm (approximately) layer of the surface.

Schematic diagram of photoelectron emission from a sodium atom under x-ray exposure, and (right) example of XPS survey scan spectra of sodium chloride with the Na1s electron XPS peak highlighted in the spectra.

Image provided courtesy of Thermo Fisher Scientific.

Theoretically, XPS should be able to detect all elements. However, helium (He) does not readily form solid compounds and its 1s orbital has a tiny cross-section for photoemission.

Hydrogen (H) also has a tiny cross-section and suffers from having to share its only electron in forming compounds, which then resides in a valence-like orbital, the energy of which varies from compound to compound.

Features of the Thermo Fisher ESCALAB 250Xi XPS instrument

The Thermo Fisher Scientific ESCALAB 250Xi is the most recent advancement in the ESCALAB series.

The instrument is an optimised multi-method platform that is expandable and comes with excellent flexibility and configurability. Its cutting edge technology is driven by smart software and hardware.

Equipped with a micro-focusing X-ray monochromator designed to deliver optimum XPS performance, the instrument ensures maximum sample throughput.

The multi-technique capability and availability of a range of preparation chambers and devices provides the solution to any surface analytical problem.

ESCALAB 250Xi XPS instrumentESCALAB standard sample loading chamber

Some notable features of the instrument include:

• High sensitivity spectroscopy
• Small area XPS
• Depth profiling capability with MAGCIS (Monatomic & Gas Cluster Ion Source)
• Ion scattering spectroscopy (ISS)
• Reflected electron energy loss spectroscopy (REELS)
• Micro-focused X-ray spot
• Efficient Charge Neutralisation
• Angle Resolved Spectroscopy
• Ultra-high sensitivity and energy resolution

XPS analysis sample requirement

XPS is a surface analytical technique that can be used to study the surface properties of a range of sample types. This includes both inorganic and organic (ex-situ and samples suitable to be placed under ultra-high vacuum) materials, polymers, semiconductors, metals, composite materials, geological and archaeological samples, ceramics, and glasses amongst others.

• The ideal dimension for an XPS analysis sample is 1cm X 1cm, with a maximum of 0.5cm thickness. Samples with lengths up to 5cm and widths up to 2.2cm can also be analysed. Samples below 0.5cm x 0.5cm dimension are difficult to mount on the sample stage. XPS analysis depends on the spot size. Ideally we can measure surface areas (spots) greater than 300µm X 300µm, as the smallest X-ray spot/exposure area is 200µm X 200µm for general analysis in our instrument. Please let us know your sample size and type in advance.
• Powder samples can also be measured using XPS. However, please discuss this with us in advance.
• Sample handling is crucial for XPS analysis. As XPS measures the top few atomic layers on the surface (different for depth profiling), it is very easy to contaminate samples with fingerprints. Ideally, XPS samples should be shipped and transferred inside a Wafer Carrier Box used in the semiconductor industry. However, any sealed container that doesn’t alter surface chemistry should be sufficient. Samples stored in zip-lock polymer bags are not ideal.

XPS Instrument Analysis Chamber view.

Image provided courtesy of Thermo Fisher Scientific.

Applications of XPS

XPS surface analysis can provide answers to a wide range of research problems. The following are examples of research questions addressed using XPS by researchers at the University of Brighton and elsewhere.

What material did we make / purchase?

XPS can provide data about the elemental distribution on the surface of a sample.

The limit of detection is 0.1 atomic per cent or better. In the figure (right), two XPS survey scans of gold coated QCM crystals are shown – the inset is a zoomed-in version of the Ti2p area of the spectra.

The two crystals are from two separate purchased batches. As can be seen, batch one (red) contains around 23 atomic per cent of titanium, making the crystal not fit for purpose, while batch two (green) is ‘pure’ as claimed by the manufacturer.

Survey scan spectra of two different batch QCM crystals. (S. Ray, unpublished data)

How thick is the coating/contamination on a surface?

XPS can measure precisely the thickness (below 10nm) of the surface adsorbed layer. This is useful in understanding the nature of surface contamination, and also in studying biomolecular adsorption on implants.

The spectra (right) is a comparison of XPS and Ellipsometric Thickness measurements of three different proteins adsorbed on hydrophobic surfaces, showing extremely close agreement.

XPS and Ellipsometric Thickness measurement comparison of three different proteins adsorbed on hydrophobic surfaces.

What chemical states are present on my surface?

XPS can identify and quantify the nature of the chemical states on a surface, and can help in visualising the surface functionalisation, essential for applications including bio-chemical sensors and chemical conjugations.

In the example (below left image), the experimental verification of graphene oxide reduction is shown, while the right image illustrates the success of a pluoronics (triblock copolymer) coating on reduced graphene oxide.

XPS C1s narrow scan spectra of (left) reduced graphene oxide and (right) pluronics coated reduced graphene oxide (S. Ray, unpublished data)

How can we analyse and quantify contamination or doping in our sample?

XPS can reveal surface or just below-surface contamination, and can successfully quantify any organic and inorganic contaminants and/or doping.

One example of doping quantification would be analysing the nitrogen doping effect on the properties of graphene. From the XPS spectra (right), the amount and bonding nature of nitrogen with graphene could be quantified.

Image on left: Nitrogen (N1s) narrow scan spectra and peak deconvolution to find the nature of nitrogen bonded to graphene (S. Ray, unpublished data).

Can XPS measure the thickness of coatings on nanoparticles?

In his 2017 publication, Professor David Castner (University of Washington) states, “Single particle information from electron microscopy combined with XPS sensitivity in determining composition make a powerful combination for nanoparticle analysis” ( Powell et al., 2017, J. Physical. Chemistry C).

XPS can measure precisely the thickness of single layer or multiple layers of coatings on nano-micro particles. Currently there are numerous situations where nanoparticles are used (e.g. in targeted drug delivery, sunscreens, and antimicrobial socks).

To functionalise these particles according to their target use, a proper understanding of the coating on the nanoparticles is required. In the case of multifunction nanoparticle use for targeted drug delivery, quantification of the single, double or triple layers is necessary.

XPS can help in understanding many other questions, including:

• What is the effect of heat, aging, chemical treatment, or real world use on my samples?
• What coating is on the surface?
• What is wrong inside my thick film?
• Are the thicknesses of film layers correct?
• Is the surface chemistry of a sample uniform?

Accessing the Surface Analysis Laboratory

If you have queries about how XPS can help in your research and/or industrial project, please do not hesitate to get in touch by telephone or email. We are happy to discuss your research requirements and provide quotations as necessary.

We particularly welcome proposals for joint research funding applications.

We also offer an analysis-only service, but can also provide full interpretation of results on request. XPS analysis costs can be charged per sample, per day/half-day or according to your needs.

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Introduction

X-Ray photoelectron spectroscopy (XPS), also known as electron spectroscopy for chemical analysis (ESCA), is one of the most widely used surface techniques in materials science and chemistry. It allows the determination of atomic composition of the sample in a non-destructive manner, as well as other chemical information, such as binding constants, oxidation states and speciation. The sample under study is subjected to irradiation by a high energy X-ray source. The X-rays penetrate only 5 – 20 Å into the sample, allowing for surface specific, rather than bulk chemical, analysis. As an atom absorbs the X-rays, the energy of the X-ray will cause a K-shell electron to be ejected, as illustrated by Figure 1.13.11.13.1. The K-shell is the lowest energy shell of the atom. The ejected electron has a kinetic energy (KE) that is related to the energy of the incident beam (hν), the electron binding energy (BE), and the work function of the spectrometer (φ) (1.13.11.13.1). Thus, the binding energy of the electron can be calculated.

BE = hν − KE − ψs(1.13.1)(1.13.1)BE = hν − KE − ψs

Table 1.13.11.13.1 shows the binding energy of the ejected electron, and the orbital from which the electron is ejected, which is characteristic of each element. The number of electrons detected with a specific binding energy is proportional to the number of corresponding atoms in the sample. This then provides the percent of each atom in the sample.

The chemical environment and oxidation state of the atom can be determined through the shifts of the peaks within the range expected (Table 1.13.21.13.2). If the electrons are shielded then it is easier, or requires less energy, to remove them from the atom, i.e., the binding energy is low. The corresponding peaks will shift to a lower energy in the expected range. If the core electrons are not shielded as much, such as the atom being in a high oxidation state, then just the opposite occurs. Similar effects occur with electronegative or electropositive elements in the chemical environment of the atom in question. By synthesizing compounds with known structures, patterns can be formed by using XPS and structures of unknown compounds can be determined.

Sample preparation is important for XPS. Although the technique was originally developed for use with thin, flat films, XPS can be used with powders. In order to use XPS with powders, a different method of sample preparation is required. One of the more common methods is to press the powder into a high purity indium foil. A different approach is to dissolve the powder in a quickly evaporating solvent, if possible, which can then be drop-casted onto a substrate. Using sticky carbon tape to adhere the powder to a disc or pressing the sample into a tablet are an option as well. Each of these sample preparations are designed to make the powder compact, as powder not attached to the substrate will contaminate the vacuum chamber. The sample also needs to be completely dry. If it is not, solvent present in the sample can destroy the necessary high vacuum and contaminate the machine, affecting the data of the current and future samples.

Analyzing Functionalized Surfaces

Depth Profiling

When analyzing a sample (Figure 1.13.21.13.2 a) by XPS, questions often arise that deal with layers of the sample. For example, is the sample homogenous, with a consistent composition throughout, or layered, with certain elements or components residing in specific places in the sample? (Figure 1.13.21.13.2 b,c). A simple way to determine the answer to this question is to perform a depth analysis. By sputtering away the sample, data can be collected at different depths within the sample. It should be noted that sputtering is a destructive process. Within the XPS instrument, the sample is subjected to an Ar⁺ ion beam that etches the surface. This creates a hole in the surface, allowing the X-rays to hit layers that would not have otherwise been analyzed. However, it should be realized that different surfaces and layers may be etched at different rates, meaning the same amount of etching does not occur during the same amount of time, depending on the element or compound currently being sputtered.

It is important to note that hydrocarbons sputter very easily and can contaminate the high vacuum of the XPS instrument and thus later samples. They can also migrate to a recently sputtered (and hence unfunctionalized) surface after a short amount of time, so it is imperative to sputter and take a measurement quickly, otherwise the sputtering may appear to have had no effect.

Functionalized Films

When running XPS, it is important that the sample is prepared correctly. If it is not, there is a high chance of ruining not only data acquisition, but the instrument as well. With organic functionalization, it is very important to ensure the surface functional group (or as is the case with many functionalized nanoparticles, the surfactant) is immobile on the surface of the substrate. If it is removed easily in the vacuum chamber, it not only will give erroneous data, but it will contaminate the machine, which may then contaminate future samples. This is particularly important when studying thiol functionalization of gold samples, as thiol groups bond strongly with the gold. If there is any loose thiol group contaminating the machine, the thiol will attach itself to any gold sample subsequently placed in the instrument, providing erroneous data. Fortunately, with the above exception, preparing samples that have been functionalized is not much different than standard preparation procedures. However, methods for analysis may have to be modified in order to obtain good, consistent data.

A common method for the analysis of surface modified material is angle resolved X-ray photoelectron spectroscopy (ARXPS). ARXPS is a non-destructive alternative to sputtering, as it relies upon using a series of small angles to analyze the top layer of the sample, giving a better picture of the surface than standard XPS. ARXPS allows for the analysis of the topmost layer of atoms to be analyzed, as opposed to standard XPS, which will analyze a few layers of atoms into the sample, as illustrated in Figure 1.13.31.13.3. ARXPS is often used to analyze surface contaminations, such as oxidation, and surface modification or passivation. Though the methodology and limitations are beyond the scope of this module, it is important to remember that, like normal XPS, ARXPS assumes homogeneous layers are present in samples, which can give erroneous data, should the layers be heterogeneous.

Limitations of XPS

There are many limitations to XPS that are not based on the samples or preparation, but on the machine itself. One such limitation is that XPS cannot detect hydrogen or helium. This, of course, leads to a ratio of elements in the sample that is not entirely accurate, as there is always some amount of hydrogen. It is a common fallacy to assume the percent of atoms obtained from XPS data are completely accurate due to this presence of undetected hydrogen (Table 1.13.11.13.1).

It is possible to indirectly measure the amount of hydrogen in a sample using XPS, but it is not very accurate and has to be done in a roundabout, often time consuming manner. If the sample contains hydrogen with a partial positive charge (i.e. OH), the sample can be washed in sodium naphthalenide (C₁₀H₈Na). This replaces this hydrogen with sodium, which can then be measured. The sodium to oxygen ratio that is obtained infers the hydrogen to oxygen ratio, assuming that all the hydrogen atoms have reacted.

XPS can only give an average measurement, as the electrons lower down in the sample will lose more energy as they pass other atoms while the electrons on the surface retain their original kinetic energy. The electrons from lower layers can also undergo inelastic or elastic scattering, seen in Figure 1.13.41.13.4. This scattering may have a significant impact on data at higher angles of emission. The beam itself is also relatively wide, with the smallest width ranging from 10 – 200 μm, lending to the observed average composition inside the beam area. Due to this, XPS cannot differentiate sections of elements if the sections are smaller than the size of the beam.

Sample reaction or degredation are important considerations. Caution should be exercised when analyzing polymers, as they are often chemically active and X-rays will provide energy to start degrading the polymer, altering the properties of the sample. One method found to help overcome this particular limitation is to use angle-resolved X-ray photoelectron spectroscopy (ARXPS). XPS can often reduce certain metal salts, such as Cu²⁺. This reduction will give peaks that indicate a certain set of properties or chemical environments when it could be completely different. It needs to be understood that charges can build up on the surface of the sample due to a number of reasons, specifically due to the loss of electrons during the XPS experiment. The charge on the surface will interact with the electrons escaping from the sample, affecting the data obtained. If the charge collecting is positive, the electrons that have been knocked off will be attracted to the charge, slowing the electrons. The detector will pick up a lower kinetic energy of the electrons, and thus calculate a different binding energy than the one expected, giving peaks which could be labeled with an incorrect oxidation state or chemical environment. To overcome this, the spectra must be charge referenced by one of the following methods: using the naturally occurring graphite peak as a reference, sputtering with gold and using the gold peak as a reference or flooding the sample with the ion gun and waiting until the desired peak stops shifting.

Limitations with Surfactants and Sputtering

While it is known that sputtering is destructive, there are a few other limitations that are not often considered. As mentioned above, the beam of X-rays is relatively large, giving an average composition in the analysis. Sputtering has the same limitation. If the surfactant or layers are not homogeneous, then when the sputtering is finished and detection begins, the analysis will show a homogeneous section, due to the size of both the beam and sputtered area, while it is actually separate sections of elements.

The chemistry of the compounds can be changed with sputtering, as it removes atoms that were bonded, changing the oxidation state of a metal or the hybridization of a non-metal. It can also introduce charges if the sample is non-conducting or supported on a non-conducting surface.

Using XPS to Analyze Metal Nanoparticles

Introduction

X-ray photoelectron spectroscopy (XPS) is a surface technique developed for use with thin films. More recently, however, it has been used to analyze the chemical and elemental composition of nanoparticles. The complication of nanoparticles is that they are neither flat nor larger than the diameter of the beam, creating issues when using the data obtained at face value. Samples of nanoparticles will often be large aggregates of particles. This creates problems with the analysis acquisition, as there can be a variety of cross-sections, as seen in Figure 1.13.51.13.5. This acquisition problem is also compounded by the fact that the surfactant may not be completely covering the particle, as the curvature of the particle creates defects and divots. Even if it is possible to create a monolayer of particles on a support, other issues are still present. The background support will be analyzed with the particle, due to their small size and the size of the beam and the depth at which it can penetrate.

Many other factors can introduce changes in nanoparticles and their properties. There can be probe, environmental, proximity, and sample preparation effects. The dynamics of particles can wildly vary depending on the reactivity of the particle itself. Sputtering can also be a problem. The beam used to sputter will be roughly the same size or larger than the particles. This means that what appears in the data is not a section of particle, but an average composition of several particles.

Each of these issues needs to be taken into account and preventative measures need to be used so the data is the best representation possible.

Sample Preparation

Sample preparation of nanoparticles is very important when using XPS. Certain particles, such as iron oxides without surfactants, will interact readily with oxygen in the air. This causes the particles to gain a layer of oxygen contamination. When the particles are then analyzed, oxygen appears where it should not and the oxidation state of the metal may be changed. As shown by these particles, which call for handling, mounting and analysis without exposure to air, knowing the reactivity of the nanoparticles in the sample is very important even before starting analysis. If the reactivity of the nanoparticle is known, such as the reactivity of oxygen and iron, then preventative steps can be taken in sample preparation in order to obtain the best analysis possible.

When preparing a sample for XPS, a powder form is often used. This preparation, however, will lead to aggregation of nanoparticles. If analysis is performed on such a sample, the data obtained will be an average of composition of each nanoparticle. If composition of a single particle is what is desired, then this average composition will not be sufficient. Fortunately, there are other methods of sample preparation. Samples can be supported on a substrate, which will allow for analysis of single particles. A pictorial representation in Figure 1.13.61.13.6 shows the different types of samples that can occur with nanoparticles.

Analysis Limitations

Nanoparticles are dynamic; their properties can change when exposed to new chemical environments, leading to a new set of applications. It is the dynamics of nanoparticles that makes them so useful and is one of the reasons why scientists strive to understand their properties. However, it is this dynamic ability that makes analysis difficult to do properly. Nanoparticles are easily damaged and can change properties over time or with exposure to air, light or any other environment, chemical or otherwise. Surface analysis is often difficult because of the high rate of contamination. Once the particles are inserted into XPS, even more limitations appear.

Probe Effects

There are often artifacts introduced from the simple mechanism of conducting the analysis. When XPS is used to analyze the relatively large surface of thin films, there is small change in temperature as energy is transferred. The thin films, however, are large enough that this small change in energy has to significant change to its properties. A nanoparticle is much smaller. Even a small amount of energy can drastically change the shape of particles, in turn changing the properties, giving a much different set of data than expected.

The electron beam itself can affect how the particles are supported on a substrate. Theoretically, nanoparticles would be considered separate from each other and any other chemical environments, such as solvents or substrates. This, however, is not possible, as the particles must be suspended in a solution or placed on a substrate when attempting analysis. The chemical environment around the particle will have some amount of interaction with the particle. This interaction will change characteristics of the nanoparticles, such as oxidation states or partial charges, which will then shift the peaks observed. If particles can be separated and suspended on a substrate, the supporting material will also be analyzed due to the fact that the X-ray beam is larger than the size of each individual particle. If the substrate is made of porous materials, it can adsorb gases and those will be detected along with the substrate and the particle, giving erroneous data.

Environmental Effects

Nanoparticles will often react, or at least interact, with their environments. If the particles are highly reactive, there will often be induced charges in the near environment of the particle. Gold nanoparticles have a well-documented ability to undergo plasmon interactions with each other. When XPS is performed on these particles, the charges will change the kinetic energy of the electrons, shifting the apparent binding energy. When working with nanoparticles that are well known for creating charges, it is often best to use an ion gun or a coating of gold. The purpose of the ion gun or gold coating is to try to move peaks back to their appropriate energies. If the peaks do not move, then the chance of there being no induced charge is high and thus the obtained data is fairly reliable.

Proximity Effects

The proximity of the particles to each other will cause interactions between the particles. If there is a charge accumulation near one particle, and that particle is in close proximity with other particles, the charge will become enhanced as it spreads, affecting the signal strength and the binding energies of the electrons. While the knowledge of charge enhancement could be useful to potential applications, it is not beneficial if knowledge of the various properties of individual particles is sought.

Less isolated (i.e., less crowded) particles will have different properties as compared to more isolated particles. A good example of this is the plasmon effect in gold nanoparticles. The closer gold nanoparticles are to each other, the more likely they will induce the plasmon effect. This can change the properties of the particles, such as oxidation states and partial charges. These changes will then shift peaks seen in XPS spectra. These proximity effects are often introduced in the sample preparation. This, of course, shows why it is important to prepare samples correctly to get desired results.

Conclusions

Unfortunately there is no good general procedure for all nanoparticles samples. There are too many variables within each sample to create a basic procedure. A scientist wanting to use XPS to analyze nanoparticles must first understand the drawbacks and limitations of using their sample as well as how to counteract the artifacts that will be introduced in order to properly use XPS.

One must never make the assumption that nanoparticles are flat. This assumption will only lead to a misrepresentation of the particles. Once the curvature and stacking of the particles, as well as their interactions with each other are taken into account, XPS can be run.

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Principle

X-ray Photoelectron Spectroscopy (XPS) or Electron Spectroscopy for Chemical Analysis (ESCA) is a technique which analyzes the elements constituting the sample surface, its composition, and chemical bonding state by irradiating x-rays on the sample surface, and measuring the kinetic energy of the photoelectrons emitted from the sample surface. XPS instrument using Al Kα rays can generally obtain information on elements within a few nms of the sample surface.

Additionally, the change in bond energy (chemical shift) caused by the electron state surrounding the atoms to be analyzed, such as atomic valence charges and interatomic distances, tend to be greater than the chemical shift observed in AES, which makes the relative ease with which the state of chemical bonds can be identified another advantage of XPS.

Charge compensation mechanism (dual beam charge neutralization)

XPS is used for element/chemical state analysis for a wide range of solid samples from conductive to insulating materials. However, with insulating material samples, a positive charge occurs in the x-ray irradiated area due to the generation of photoelectrons. A spectrum measured in a positively charged state shifts to the high bond energy side (low kinetic energy side) compared to its actual position, making it difficult to grasp the correct energy position. Thus, with insulating material samples, charge neutralization is necessary during measurement. The dual beam technique, which irradiates a low energy electron beam and an ion beam simultaneously, is a neutralization method which stabilizes uneven charges on the surface in a self-repairing way, and is capable of stable charge neutralization for a wide range of insulating materials. It is also an essential feature for microscopic area analysis.

X-ray photoelectron spectroscopy (XPS Analysis) also called Electron
Spectroscopy for Chemical Analysis (ESCA) is a chemical surface
analysis method. XPS measures the chemical composition of the outermost
100 Å of a sample. Measurements can be made at greater depths by
ion sputter etching to remove surface layers.

All elements except for H and He can be detected at concentrations above 0.05 to 1.0 atom %, depending on the element. In addition, chemical bonding information can be determined from detailed analysis. Conductive and nonconductive samples can be measured and the technique is well suited for polymeric materials. The sampled area varies from 1 mm down to 30 µm in diameter.

X-ray Photoelectron Spectroscopy Analysis (XPS)

In XPS, also known as Electron Spectroscopy for Chemical Analysis (ESCA), X-rays bombard a sample creating ionized atoms and ejecting free electrons. The energies of these free electrons are related to their binding energies in the original atom. By measuring these characteristic energies, XPS Analysis identifies the chemical elements present in the sample. XPS provides both elemental and, to a certain extent, chemical information in the top 3-30 atomic layers (10-100Å) in solid samples. The sensitivity varies between 0.01-1 atom% dependent upon the element. It can do nondestructive depth profiling to 100 Å and detect all elements except H and He. Ion sputtering combined with XPS is used to accomplish deeper profiling. XPS is especially good for obtaining elemental surface composition of unknown materials, including conductors and insulators.

Critical problem solving with surface analysis is enhanced by reducing the probe area when using XPS Analysis. Small-spot XPS instruments probe for composition, chemistry, and contamination in 0.01 mm2 areas. It also makes XPS sputter depth profiles a reality.

One of the primary reasons for using XPS Surface Analysis to analyze samples is its inherent high surface sensitivity. This results from the fact that nearly all of the electrons which are used for analysis escape from only the outermost four to five atomic layers of the material. This high surface sensitivity permits the easy detection of most surface concentrated elements that would be undetectable by bulk or quasi-bulk techniques, e.g. XRD, XRF, EDS or Electron Microprobe. Remember, chemistry begins at the surface.

Imagine that a sample surface is contaminated by 20% coverage of Si from a silicone lubricant. Using XPS Analysis, the Si atoms represent ~6% of the atoms present in the 4-atom deep sampling volume. However, by using one of the bulk or quasi-bulk techniques, the Si atoms now represent ~0.03% or less of the >1 µm deep sampling volume. Given that surface Si concentrations as low as 0.10.% can be detected, the advantage of XPS over bulk techniques is readily apparent.

One very important reason for using XPS Surface Aanlysis is that it is nondestructive. XPS uses very soft (low energy) x-rays that produce minimum energy input to the sample during analysis. Electron beam analysis techniques concentrate a high amount of energy in a small region and can be very destructive toward organic materials or other thermally sensitive compounds. Bulk analysis techniques often require that the sample be powdered and placed in a matrix material introducing a high probability of altering or entirely losing some surface species.

In addition to providing a detailed elemental surface composition, XPS Analysis provides even more information about the detected elements. Changes in the chemical environment or oxidation state of an atom can cause corresponding changes in the energies of the electrons that are ejected and analyzed. These energy shifts or “chemical shifts” have been well studied and tabulated for many different compounds. By measuring these shifts, it is possible in most cases to accurately assign the chemical environment of a given element.

Another important advantage of XPS over electron beam techniques, i.e. AES, Electron Microprobe, etc., is its ability to analyze insulating specimens with relative ease. Since the analysis beam (x-rays) does not consist of charged particles, the insulating specimen is not required to conduct away any charge buildup due to incidence of the analysis beam itself. The specimen is only required to conduct away enough charge to compensate for the small number of electrons which were ejected from the sample. This small positive charge buildup is easily compensated for by use of a “flood gun”, which directs low energy electrons to the sample surface.

In addition to the inherent advantages of using XPS generally, the small-spot instrument that Rocky Mountain Laboratories’ employs has a number of special features that give an enormous edge over other instruments. The sample transfer and sample chamber configuration allows the analysis of samples a s large as 3.75″ diameter x 0.375″ high. Or, many specimens may be mounted and measured by software automation, if they are of uniform size and shape. The minimum size is limited only by the size of the smallest x-ray beam (50 µm), which has been used to analyze a single 10 µm organic fiber.

The largest x-ray spot (image of the x-ray beam on the sample) is 1-2 mm and is used primarily for rapid data acquisition during survey scans. The smallest x-ray spot is most often used for analysis of small heterogeneous features on a larger sample or simply for analysis of a very small sample. Because the x-ray spot is smaller than in other XPS instruments, remarkably rapid and precise depth profiles are now routine, since both raster size and beam voltage of the ion etching gun can be greatly reduced.

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X-Ray photoelectron spectroscopy (XPS), also known as electron spectroscopy for chemical analysis (ESCA) is a non-destructive technique used to analyze the surface of a material. The XPS will measure the elemental composition, chemical state as well as the electronic state, thickness measurements of overlayers (up to 8nm), and will give you the empirical formula of the material that is being analyzed. This instrument will only detect elements with an atomic number higher of 3 and higher since hydrogen and helium atoms are very small and the probability of detecting them is almost zero. Also, it can only analyze depths ranging from 1 to 10nm, for this reason it only gives analysis of the surface. Preparation of the samples is minimal if any; you can analyze samples “as receive” or can clean the surface to eliminate any contaminates that might be present. Some examples that can be analyzed using the XPS are elements, metal alloys, semiconductors polymers, ceramics, and inorganic compounds. Other examples include paints, inks, viscous oils, wood and papers.

Physics of XPS

The XPS functions by irradiating a surface with a beam of x-rays which are usually monochromatic Al Ka (1486.6eV) or non-monochromatic Mg Ka (1253.6eV) in an ultra-high vacuum. When the x-ray photons hit the sample, they transfer this energy to core electrons and are emitted from the initial state with a kinetic energy which is being measured (Figure 1). It will also count the number of photoelectrons that are being ejected from the surface with the cylindrical mirror detector analyzer. With this information you can obtain an XPS spectrum which plots the number of electrons detected vs. the binding energy of the electrons detected (Figure 2). Since each element will produce a characteristic peak at characteristic binding energies, the element at the surface can be identified and because the number of electrons in each peak is directly related to the amount of the element, the elemental composition within the area that is being analyzed can be calculated. There are tables with the kinetic energies as well as binding energies already in the system that will help identify the elements present in the surface of the material. 
The binding energy of each emitted electron can be calculated using the equation below since the energy of the x-rays being emitted is known. 
E_binding = E_photon– (E_kinetic + F)
E_binding is the binding energy of the electron, E_photon is the energy of the x-ray photons, E_kinetic is the kinetic energy that is measured by the XPS, and F is the work function of the spectrometer. 
Figure 1. XPS, sample is being irradiated by x-rays which will then emit core electrons which are then detected and data is collected to obtain a spectrum. 

References

• X-Ray Photoelectron Spectroscopy, In National Physical Laboratory, Retrieved October 29, 2012 form http://www.npl.co.uk/science-technology/surface-and-nanoanalysis/surface-and-nanoanalysis-basics/introduction-to-xps-x-ray-photoelectron-spectroscopy
• XPS Works, Actinide Research Quarterly, Retrieved October 29, 2012 form http://arq.lanl.gov/source/orgs/nmt/nmtdo/AQarchive/04summer/XPS.html
• X-Ray Photoelectron Spectroscopy, In Wikipedia, Retrieved October 29, 2012 from http://en.wikipedia.org/wiki/X-ray_photoelectron_spectroscopy
  Torres, D., X-Ray Photoelectron Spectroscopy (XPS),The University of Texas at El Paso, Retrieved October 29, 2012 
  

Example Of XPS

XPS depth profiling study on the passive oxide film of carbon steel in saturated calcium hydroxide solution and the effect of the chloride on the film properties

By: P.Ghods, O.B. Isgor, J.R. Brown, F. Benseabaa, D. Kingston

Introduction

The purpose of the paper presented was to use XPS in order to characterize the passive oxide layer that forms on carbon steel rebar in concrete pore solutions when it is passivated in calcium hydroxide solutions. Since there is very few information on the compositional characteristics of the passive oxide film before and after it has been exposed to this high alkaline environments, they decided to use XPS since it will give the depth profiling of the surface.

Preparation of Specimens

An analysis was conducted on the cross-sections of four carbon steel rebar specimens, which were 8-mm long each. The size designation for the rebar was #10M. The specimens where then hot-mounted and polished to 0.05µm and used isopropyl alcohol in order to prevent oxidation. The epoxy was then removed and three samples were submerged into saturate calcium hydroxide (CH) solution (99.6% CH in distilled water). The first sample (CH-2) was taken out after 2 days and the second one, CH-9, after 9 days. The third sample (CH-Cl) after 9 days, was then submerged in to a 0.05M chloride solution for 14 more days. This was done in order for the chlorides to react with the passivation film. The three specimens after they were taken out of the solution were placed in a jar containing isopropyl alcohol until the use of XPS was needed. The final specimen, AE, was exposed to indoor air at room temperature for 10 minutes to allow oxidation of the steel surface.

XPS Procedures

In this experiment, they used a PerkinElmer PHI-5700-2 XPS spectrometer that used an achromatic Al Ka x-ray source. It contained an electronic ultra-high vacuum chamber with pressure of 10-6 Pa and was operated at 15kV. The work function was calibrated using ultra-pure gold metal. The information was obtained by using a spherical capacitor analyzer, which was at an angle of 54? with the x-ray source, and the x-ray source was at an angle of 90? with the specimen surface. The analyzed area was 800µm.
In order to collect low-energy spectra, they did a survey scan which had the following conditions: energy range=1400eV, analyzer pass energy= 187.8eV, step size= 0.25 and a sweep time of 180s. In order to obtain high-resolution spectra, they used 10 or 20eV spectral windows at an analyzer pass energy of 29.3eV and 0.1eV steps. The spectra was for oxygen (O 1s), carbon (C1s), iron (Fe 2p), chlorine (Cl 2P), calcium (Ca 2p), and sodium (Na 1s). They collected and processed all survey and high-resolution spectra using PHI Access XPS operating software.

XPS Data Analysis

To figure out the sampling depth (d) which is the thickness of the layer, they used the equation below,
d= 3?cos?
where ? is the decreasing length and ? is the take -off angle with respect to the surface normal, which would be zero for this case. To find the kinetic energy the equation below was used,
Ek=hv- Eb
Where Ek is the kinetic energy, h is Planck’s constant, v is frequency, and Eb is the binding energy. Table 2 below shows the calculation of the sampling depth for iron oxide. The average sampling depth was of 8.5nm. 

Curve fitting had to be done to the high-resolution spectra in order to get the minimum number of peaks that will result in an optimum fit. This was done using Casa XPS software and setting a few constraints in order to get the optimal fitting. Constrains included, setting peak positions to the average reported data in literature, peak positions were set constant for all depths, the full width at half maximum (FHWM) were set to the FHWM of the photoelectron core level of each element, Sheirley background corrections algorithms were used, peaks were calibrated to hydrocarbon signal set at 285eV, and semi-quantitative composition data was collected by using XPS elemental sensitivity factors. The curves that were fitted were for Fe 2p, O 1s, C 1s, and Ca 2p spectra. The curve parameters used are shown below in Table 3.

Results and Discussions

The XPS depth profiles for all four elements and for the four specimens analyzed are shown in Fig. 5 below. The graph for iron shows that as depth increases, so does the concentration, as for the oxygen curve, there will be an increase in concentration and around 2.5nm in depth it will decrease. In the carbon curves, the concentration is high at the surface which is most likely due to contamination during preparation, but then remains constant throughout the rest of the analysis. For the calcium curves, most of the samples had a constant concentration as the depth increased except for the sample which was only exposed to air which did not contain large amounts of calcium. The reason for small amounts of calcium present in the AE specimen was because there were particles embedded on the surface during polishing. As for the constant concentrations of calcium in the rest of the sample, SEM and EDS was used and showed that it was due to CH and CaCl precipitates at the surface. It was concluded that because the precipitates contained the same elements (C,O, Ca) that were analyzed by the XPS, their spectra would not be used to study the atomic structure of the oxide film. Only the Fe 2p spectrum would be used to characterize the oxide film.

Analyzing the Fe 2p spectra at different depths for the CH-2 sample, a few observations were made. First, the five components were identified to be, iron (Fe), cementite (Fe3C), magnetite (Fe3O4), hematite/ferrihydrite (Fe2O3/ FeOOH), and Fe2O3 satellite structure; their peak position were also identified as seen in the image (Fig.8). Another observation made was that the Fe peak increased in intensity with ion sputtering which means that the Fe component comes from the substrate. Also, the sputtering shifted the Fe 2P signal to the left which indicates that the oxide film is thin no matter what the exposure time was. 
The effect of exposure conditions on the thickness of the oxide film was also analyzed. Results showed that the AE specimen had a thicker iron oxide layer than the other samples and that the CH-Cl spectrum was the one with the thinnest oxide layers (See spectra below). The reason for the AE sample having a thicker layer can be due to porosity and also because the oxide layer of the CH specimens might have dissolved in the solution. The conclusion made for the CH-Cl curve was that chloride reduces the thickness of the oxide film. It was also concluded that since the spectrum for the different exposure times were almost the same, the exposure time does not affect the thickness as much. The ratio of the iron oxide to the metallic iron concentration at different sputtering depth was analyzed and results showed that above a sputtering depth of 5nm, the ratio remained constant. This meant that the iron oxide film was about 5nm in thickness. To confirm this, they used several equations and the thickness of the oxide layers to be 5.7, 4.1, 4.1, 3.6nm for AE, CH-2, CH-9, CH-Cl respectively. Other observations made where that the concentration of Fe3+ relative to Fe2+ decreased with depth in the oxide film and that longer exposure times will increase the concentration of Fe2+ relative to Fe3+.

Conclusion

In this experiment, they used the XPS depth profiling in order to characterize the oxide film of carbon steel when it was saturated in calcium hydroxide (CH) solutions and also what the effect of chloride (CH-Cl) could be on the film. Samples where carefully prepared and placed in CH and CH-Cl solutions for different amounts of time. Then they were analyzed using the XPS. 
After obtaining the spectra of the specimens studied and analyzing them, they were able to make valuable conclusions. The first finding was that the carbon steel contained precipitates of calcium hydroxide and calcium carbonate so several spectra were not used for analysis. The study was only done for the Fe 2p spectrum. With the XPS depth profiles, they were able to determine the thickness of the iron oxide film to be about 4nm. The spectra for the four different specimens studies also showed that there was almost no difference between them meaning that there was no effect on exposure time to the CH solutions. Analyzing the spectra also showed that the exposure to chloride reduced the thickness of the oxide film. Another conclusion made was that there were higher concentrations of Fe2+ at the substrate and at the surface it was mostly composite of Fe3+. The longer the specimens were exposed to the CH solution, the larger the Fe2+ concentration. As seen with this experiment, the XPS is a valuable instrument that can tell us a lot about a material.

References

• Mark C. Biesinger, Brian R. Hart, Russell Polack, Brad A. Kobe, Roger St.C. Smart, Analysis of mineral surface chemistry in flotation separation using imaging XPS, Minerals Engineering, Volume 20, Issue 2, February 2007, Pages 152-162, ISSN 0892-6875, 10.1016/j.mineng.2006.08.006.
  (http://www.sciencedirect.com/science/article/pii/S0892687506002093)