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In thermogravimetric analysis (TGA), a sample is continually weighted while heating, as an inert gas atmosphere is passed over it. Many solids undergo reactions that evolve gaseous byproducts. In TGA, these gaseous byproducts are removed and changes in the remaining mass of the sample are recorded. Three variations are commonly employed:

• Dynamic TGA – Temperature continues to increase over time as mass is recorded. This allows simulataneous identification of how much gas is removed and the temperature at which it occurs.
• Static TGA – Temperature is held constant as the mass is measured. This can be used to gain more information on a decomposition that happens at a certain temperature or to investigate a material’s ability to withstand a given temperature.
• Quasistatic TGA – Sample is heated in multiple temperature intervals, and held at those intervals for a time, often until the mass stabilizes. This is ideal for investigating substances that are known to decompose in various ways at different temperatures, and better characterizing the way in which they decompose.

How to interpret the data

Figure 1 shows a TGA curve in green. Figure from Physical Methods in Chemistry and Nanoscience by Pavan M.V. Raja and Andrew R. Barron (chemlibretext link).

Data from thermogravimetric analysis is often shown by a graph representing mass as a function of temperature for dynamic TGA. For static TGA, mass is instead plotted as a function of time at a given temperature. Quasistatic TGA produces multiple mass vs. time plots for various temperatures. The derivative of the mass change with temperature is often plotted on the same graph to improve ease of identifying the points at which different mass changes occur; especially helpful in cases where multiple decomposition reactions happen in close proximity to one another.

Examples of some characteristic TGA curves for dynamic TGA

Figure 1. Classification of the different observable TGA Curves. Image source

In general, mass fluctuations correspond to chemical reactions, with some exceptions. A common example is drying, which can easily be seen as a quick initial drop at the beginning of heating that isn’t known to correspond to any chemical reactions. Evaporation/sublimation may also appear on the plot depending on the material to be analyzed. Multistage decomposition is also common, and shows as a step-like pattern. In some cases, these steps may blend together during dynamic TGA, necessitating either far slower heating rates, or step-wise methods like quasistatic TGA. Note that TGA itself may not be sufficient to identify the decomposition products; chemical testing of the sample after TGA analysis is often required to ascertain the identities of suspected decomposition products. TGA itself does not identify substances; other methods such as chemical testing or differential calorimetry must performed alongside TGA to verify the identity of products. 

Good literature examples 

TGA is vital when designing materials that are intended to withstand high temperatures, as if there is even slight decomposition of the material at a temperature that the material would be expected to encounter, devices made of the material may fail over repeated use. The carefully controlled environment of the TGA analyzer also allows for measuring decomposition reaction kinetics. Differential scanning calorimetry can be incorporated into the TGA analyzer to allow for monitoring potential phase changes. Phase changes generally require addition of heat, yet do not increase the temperature of the sample undergoing a phase change. Furthermore, different phases of a material have different heat capacity, and the temperature change per joule of heat applied will vary with phase. By adding a reference pan to the TGA analyzer, changes in the heat capacity in addition to mass changes can be monitored. In this way, both phase changes and thermal decomposition reactions can be simultaneously measured by TGA.

TGA used for decomposition reaction:

Figure S6. Thermogravimetric analysis (TGA) under pure nitrogen flow at 100 mL/min to show a) clean decomposition of 3DP-HKUST-1gel and b) decomposition of 3DP-HKUST-1gelTEA showing that it has several side products during decomposition. (Lim et al. 2019)

Figure 2b. Thermogravimetric analysis (TGA) under simulated ambient conditions (SI section 5), showing desolvation followed by oxidation of 3DP-HKUST-1gel to CuO.

The authors are looking to use colloidal gels containing only ethanol and Cu3(BTC)2 (BTC = 1,3,5-benzenetricarboxylate) (HKUST-1) nanoparticles as ink for the direct ink writing (DIW) of pure densely packed and self-standing Metal-organic frameworks (MOF) monoliths. Traditionally they are synthesized in powder form. The authors are observing the decomposition behavior of the 3DP-HKUST-1gel (made using DIW) and 3DP-HKUST-1gel-TEA (made by triethylamine-induced HKUST-1 gels). It can be observed in the sudden change in weight over the 100-200 °C for Figure S6b that several side products have formed as oppsed to Figure S6a which shows a much cleaner decomposition. The Figure seen in the paper was Figure 2b, the authors attibute the first weight change (16.2 mg) to residual molecules such as H2O, acetate from the copper (II) acetate monohydrate precursor, and excess ethanolic solvent that is trapped inside the 3DP-HKUST-1gel structure. The second weight change (6.2 mg) was observed at 300 °C and is caused by the decomposition of the organic linkers and network. 

In-depth reading and works cited

1. Physical Methods in Chemistry and Nanoscience by Pavan M.V. Raja and Andrew R. Barron (chemlibretext link).
2. A Beginners Guide Thermogravimetric Analysis (TGA): A Beginners Guide to TGA that has FAQ and basic information.
3. Thermogravimetry Analysis (TGA) – online training course: Youtube training course that as good explanation about how the TGA works. Also has good examples of plots and how to understand them.
4. Thermogravimetric Analysis (TGA) & Differential Scanning Calorimetry (DSC): Slideshow with information about the TGA. Includes figures on classification of curves, how balance works, analyis of curves, effects of heat rate, shifts caused by heat rate, etc.
5. THERMAL ANALYSIS OF POLYMERS – Fundamentals and Applications: (WARNING!: This link will download a whole 388 pg. book!) Has a whole chapter dedicated to TGA.

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Dynamic Mechanical Analysis or DMA for short, is an extremely versatile and flexible analytical technique for measuring the physical properties (incl: storage modulus, glass transition temperature, etc..) of a range of materials. Although initial attempts to perform this type of testing started in the early 20th century, commercial machines were not available until the 1950s and these were extremely limited in what they could do. It was not until the 1980s, when the processing power of computers were combined with the mechanics of the DMA, that the technique acquired wider appeal among scientists. During this time many commercial instrument suppliers began to sell DMA machines and gave the technique various different names, some of which are still in use today such as as dynamic mechanical thermal analysis (DMTA), dynamic mechanical spectroscopy or dynamic thermomechanical analysis.

As the technique developed more and more features were added such as the ability to test samples in different forms (solids, liquids, pastes, etc..), in different mode (tension, shear, bending, torsion, etc) and in different environments (air, liquid, range of humidities, etc.).

More powerful machines allowed larger, more representative samples, to be tested. This is particularly important for composites, where different layups can influence the results. As the power of computers increased the DMA technique became more user-friendly, which led to the instruments being used in quality control environments, as well as in the development of new materials.

DMA is now firmly established within the thermal analysis family of techniques, including Differential Scanning Calorimetry (DSC), ThermoGravimetric Analysis (TGA) and ThermoMechanical Analysis (TMA).

Although DMA can be used to investigate many physical properties of a material, its key strength is the evaluation of the glass transition temperature (Tg) of a polymer. The DMA’s sensitivity for Tg makes it the preferred tool for scientists around the world. Not only can DMA accurately measure Tg it can also successful identify secondary transitions, which have a significant impact on the performance of a polymeric material.

In standard use the basic operation of the DMA involves the application of a sinusoidally varying stress to a sample and the monitoring of the resulting deformation. In typical DMA experiments the stress is applied at a constant frequency (usually 1 Hz), the strain is kept constant and the temperature is increased at a constant heating rate (typically between 1 & 5°C/min). As previously mentioned various modes are available to hold a sample, which allows a full range of material types to be measured. The output from a DMA unit is in the form of key mechanical properties (storage modulus E’, loss modulus E” and a measure of “damping” or loss tangent) versus temperature or time. On some DMA machines the coefficient of thermal expansion (CTE) can be measured, as the expansion or contraction of a sample is measured.

Although DMA is a very versatile technique, it has its drawbacks. For example DMA can measure the storage modulus (E’) of a polymeric material, but to achieve an accurate value is very challenging, especially if the operator is performing a thermal scan of the material. In order to allow for the significant changes, which occur in mechanical properties (when a polymeric material is heated) the sample size used for such a test is a compromise in order to keep it within the measuring range of the equipment. To obtain accurate storage modulus (E’) data of a polymeric material, the test is best performed isothermally and significant care must be taken to ensure that the most suitable sample size and clamping geometry is used.

Although it can sometimes be challenging to obtain accurate mechanical data using a DMA, the main purpose of the technique has always been to compare a series of tests using the same sample size and test conditions. Aspects of a material’s formulation or processing conditions can then be varied and the impact on the physical performance of a material studied. This is perfectly acceptable OK if you use the same instrument is used from the same manufacturer, but comparison between different machines do not show a particularly good alignment of the results. This is not surprising as the chambers, which hold the samples from different manufacturers are of significantly different design and sizes. This leads to varying thermal profiles within the chambers and this can lead to subtle, but important variations in the results. Clearly this has to be taken into account when performing DMA experiments and steps have been taken in recent years to attempt to standardise some of the test procedures in order to address this type of issue.

As well as the more standard uses of the DMA to measure polymeric samples, they have been employed to directly measure the physical changes of materials in some unusual environments. For example, the flexibility of some DMA machines allows the mechanical measuring part of the unit to be immersed in liquids, which allow for some interesting applications, these include:

• the measurement of samples of human hair immersed in shampoo in order to monitor the storage modulus. This is particularly important when new chemicals are used, which could potentially have an adverse effect on the properties
• The measurement of food products, such as the direct measurement of the melting of chocolate or the frying of potato chips at different temperatures and in different environments (such as cooking oil). Optimising food products to meet customer expectations is an ongoing challenge and the DMA’s unique ability to provide useful mechanical data in challenging environments is particularly useful.

Coventive Composites has significant experience in the use of the DMA technique, which we employ in both the development our our own materials, as well as providing a service to external customers. All modes of operation are available, as well as some of the more unusual set-ups of the equipment. Please feel free to contact us to discuss your testing requirements or visit our website for further details.

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Dynamic mechanical analysis (DMA), also known as forced oscillatory measurements and dynamic rheology, is a basic tool used to measure the viscoelastic properties of materials (particularly polymers). To do so, DMA instrument applies an oscillating force to a material and measures its response; from such experiments, the viscosity (the tendency to flow) and stiffness of the sample can be calculated.

These viscoelastic properties can be related to temperature, time, or frequency. As a result, DMA can also provide information on the transitions of materials and characterize bulk properties that are important to material performance. DMA can be applied to determine the glass transition of polymers or the response of a material to application and removal of a load, as a few common examples. The usefulness of DMA comes from its ability to mimic operating conditions of the material, which allows researchers to predict how the material will perform.

A Brief History

Oscillatory experiments have appeared in published literature since the early 1900s and began with rudimentary experimental setups to analyze the deformation of metals. In an initial study, the material in question was hung from a support, and torsional strain was applied using a turntable. Early instruments of the 1950s from manufacturers Weissenberg and Rheovibron exclusively measured torsional stress, where force is applied in a twisting motion.

Due to its usefulness in determining polymer molecular structure and stiffness, DMA became more popular in parallel with the increasing research on polymers. The method became integral in the analysis of polymer properties by 1961. In 1966, the revolutionary torsional braid analysis was developed; because this technique used a fine glass substrate imbued with the material of analysis, scientists were no longer limited to materials that could provide their own support. Using torsional braid analysis, the transition temperatures of polymers could be determined through temperature programming. Within two decades, commercial instruments became more accessible, and the technique became less specialized. In the early 1980s, one of the first DMAs using axial geometries (linear rather than torsional force) was introduced.

Since the 1980s, DMA has become much more user-friendly, faster, and less costly due to competition between vendors. Additionally, the developments in computer technology have allowed easier and more efficient data processing. Today, DMA is offered by most vendors, and the modern instrument is detailed in the Instrumentationsection.

Basic Principles of DMA

DMA is based on two important concepts of stress and strain. Stress (σ) provides a measure of force (F) applied to area (A), 2.10.12.10.1 .σ = F/A(2.10.1)(2.10.1)σ = F/A

Stress to a material causes strain (γ), the deformation of the sample. Strain can be calculated by dividing the change in sample dimensions (∆Y) by the sample’s original dimensions (Y) (2.10.22.10.2 ). This value is often given as a percentage of strain.γ = ΔY/Y(2.10.2)(2.10.2)γ = ΔY/Y

The modulus (E), a measure of stiffness, can be calculated from the slope of the stress-strain plot, Figure 2.10.12.10.1 , as displayed in \label{3} . This modulus is dependent on temperature and applied stress. The change of this modulus as a function of a specified variable is key to DMA and determination of viscoelastic properties. Viscoelastic materials such as polymers display both elastic properties characteristic of solid materials and viscous properties characteristic of liquids; as a result, the viscoelastic properties are often a compromise between the two extremes. Ideal elastic properties can be related to Hooke’s spring, while viscous behavior is often modeled using a dashpot, or a motion-resisting damper.E = σ/y(2.10.3)(2.10.3)E = σ/y

Creep-recovery

Creep-recovery testing is not a true dynamic analysis because the applied stress or strain is held constant; however, most modern DMA instruments have the ability to run this analysis. Creep-recovery tests the deformation of a material that occurs when load applied and removed. In the “creep” portion of this analysis, the material is placed under immediate, constant stress until the sample equilibrates. “Recovery” then measures the stress relaxation after the stress is removed. The stress and strain are measured as functions of time. From this method of analysis, equilibrium values for viscosity, modulus, and compliance (willingness of materials to deform; inverse of modulus) can be determined; however, such calculations are beyond the scope of this review.

Creep-recovery tests are useful in testing materials under anticipated operation conditions and long test times. As an example, multiple creep-recovery cycles can be applied to a sample to determine the behavior and change in properties of a material after several cycles of stress.

Dynamic Testing

DMA instruments apply sinusoidally oscillating stress to samples and causes sinusoidal deformation. The relationship between the oscillating stress and strain becomes important in determining viscoelastic properties of the material. To begin, the stress applied can be described by a sine function where σ_o is the maximum stress applied, ω is the frequency of applied stress, and t is time. Stress and strain can be expressed with the following 2.10.42.10.4 .σ = σ0sin(ωt+δ); y=y0cos(ωt)(2.10.4)(2.10.4)σ = σ0sin(ωt+δ); y=y0cos(ωt)

The strain of a system undergoing sinusoidally oscillating stress is also sinuisoidal, but the phase difference between strain and stress is entirely dependent on the balance between viscous and elastic properties of the material in question. For ideal elastic systems, the strain and stress are completely in phase, and the phase angle (δ) is equal to 0. For viscous systems, the applied stress leads the strain by 90^o. The phase angle of viscoelastic materials is somewhere in between (Figure 2.10.22.10.2 ).

In essence, the phase angle between the stress and strain tells us a great deal about the viscoelasticity of the material. For one, a small phase angle indicates that the material is highly elastic; a large phase angle indicates the material is highly viscous. Furthermore, separating the properties of modulus, viscosity, compliance, or strain into two separate terms allows the analysis of the elasticity or the viscosity of a material. The elastic response of the material is analogous to storage of energy in a spring, while the viscosity of material can be thought of as the source of energy loss.

A few key viscoelastic terms can be calculated from dynamic analysis; their equations and significance are detailed in Table 2.10.12.10.1 .

Types of Dynamic Experiments

A temperature sweep is the most common DMA test used on solid materials. In this experiment, the frequency and amplitude of oscillating stress is held constant while the temperature is increased. The temperature can be raised in a stepwise fashion, where the sample temperature is increased by larger intervals (e.g., 5 ^oC) and allowed to equilibrate before measurements are taken. Continuous heating routines can also be used (1-2 ^oC/minute). Typically, the results of temperature sweeps are displayed as storage and loss moduli as well as tan delta as a function of temperature. For polymers, these results are highly indicative of polymer structure. An example of a thermal sweep of a polymer is detailed later in this module.

In time scans, the temperature of the sample is held constant, and properties are measured as functions of time, gas changes, or other parameters. This experiment is commonly used when studying curing of thermosets, materials that change chemically upon heating. Data is presented graphically using modulus as a function of time; curing profiles can be derived from this information.

Frequency scans test a range of frequencies at a constant temperature to analyze the effect of change in frequency on temperature-driven changes in material. This type of experiment is typically run on fluids or polymer melts. The results of frequency scans are displayed as modulus and viscosity as functions of log frequency.

Instrumentation

The most common instrument for DMA is the forced resonance analyzer, which is ideal for measuring material response to temperature sweeps. The analyzer controls deformation, temperature, sample geometry, and sample environment.

Figure 2.10.32.10.3 displays the important components of the DMA, including the motor and driveshaft used to apply torsional stress as well as the linear variable differential transformer (LVDT) used to measure linear displacement. The carriage contains the sample and is typically enveloped by a furnace and heat sink.

The DMA should be ideally selected to analyze the material at hand. The DMA can be either stress or strain controlled: strain-controlled analyzers move the probe a certain distance and measure the stress applied; strain-controlled analyzers provide a constant deformation of the sample (Figure 2.10.42.10.4 ) Although the two techniques are nearly equivalent when the stress-strain plot (Figure 2.10.12.10.1 ) is linear, stress-controlled analyzers provide more accurate results.

DMA analyzers can also apply stress or strain in two manners—axial and torsional deformation (Figure 2.10.52.10.5 ) Axial deformation applies a linear force to the sample and is typically used for solid and semisolid materials to test flex, tensile strength, and compression. Torsional analyzers apply force in a twisting motion; this type of analysis is used for liquids and polymer melts but can also be applied to solids. Although both types of analyzers have wide analysis range and can be used for similar samples, the axial instrument should not be used for fluid samples with viscosities below 500 Pa-s, and torsional analyzers cannot handle materials with high modulus.

Different fixtures can be used to hold the samples in place and should be chosen according to the type of samples analyzed. The sample geometry affects both stress and strain and must be factored into the modulus calculations through a geometry factor. The fixture systems are specific to the type of stress application. Axial analyzers have a greater number of fixture options; one of the most commonly used fixtures is extension/tensile geometry used for thin films or fibers. In this method, the sample is held both vertically and lengthwise by top and bottom clamps, and stress is applied upwards

For torsional analyzers, the simplest geometry is the use of parallel plates. The plates are separated by a distance determined by the viscosity of the sample. Because the movement of the sample depends on its radius from the center of the plate, the stress applied is uneven; the measured strain is an average value.

DMA of the glass transition polymers

As the temperature of a polymer increases, the material goes through a number of minor transitions (Tγ and T_β) due to expansion; at these transitions, the modulus also undergoes changes. The glass transition of polymers (T_g) occurs with the abrupt change of physical properties within 140-160 ^oC; at some temperature within this range, the storage (elastic) modulus of the polymer drops dramatically. As the temperature rises above the glass transition point, the material loses its structure and becomes rubbery before finally melting. The idealized modulus transition is pictured in Figure 2.10.62.10.6 .

The glass transition temperature can be determined using either the storage modulus, complex modulus, or tan δ (vs temperature) depending on context and instrument; because these methods result in such a range of values (Figure 2.10.62.10.6 ), the method of calculation should be noted. When using the storage modulus, the temperature at which E’ begins to decline is used as the T_g. Tan δ and loss modulus E” show peaks at the glass transition; either onset or peak values can be used in determining Tg. These different methods of measurement are depicted graphically in Figure 2.10.72.10.7 .

Advantages and limitations of DMA

Dynamic mechanical analysis is an essential analytical technique for determining the viscoelastic properties of polymers. Unlike many comparable methods, DMA can provide information on major and minor transitions of materials; it is also more sensitive to changes after the glass transition temperature of polymers. Due to its use of oscillating stress, this method is able to quickly scan and calculate the modulus for a range of temperatures. As a result, it is the only technique that can determine the basic structure of a polymer system while providing data on the modulus as a function of temperature. Finally, the environment of DMA tests can be controlled to mimic real-world operating conditions, so this analytical method is able to accurately predict the performance of materials in use.

DMA does possess limitations that lead to calculation inaccuracies. The modulus value is very dependent on sample dimensions, which means large inaccuracies are introduced if dimensional measurements of samples are slightly inaccurate. Additionally, overcoming the inertia of the instrument used to apply oscillating stress converts mechanical energy to heat and changes the temperature of the sample. Since maintaining exact temperatures is important in temperature scans, this also introduces inaccuracies. Because data processing of DMA is largely automated, the final source of measurement uncertainty comes from computer error.

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TGA is a powerful and robust technique to explore the thermal stability of a material. By accurately monitoring the weight of a sample while heating at a constant rate, we can measure changes in a sample’s weight and attribute this to a specific material response to a thermal stress (Figure 1). This is perfect for exploring, in detail, decomposition temperatures and ensuring a material performs adequately in a given temperature range.

During a test, a carrier gas flows over the sample and the weighing mechanism.  This carrier gas serves two purposes: protecting the internals from corrosion/oxidation above 500 °C, and to interact with the sample through gas-solid or gas-liquid reactions. By providing an inert atmosphere, we can test the thermal stability of a material. Reducing environments can explore gas-solid phase reduction reactions or protect specific samples from being oxidized. By the nature of the sensitivity of the TGA balance, we also can observe the absorption of gas onto a porous material at various temperatures. This is an ideal technique for exploring metal organic frameworks, or catalytic porous materials. Owing to the sensitivity of the balance on our SETARAM Labsys Evo instrument, we have ideal sensitivity for running thermokinetic experiments. This experiment has applications towards thermal stability of a given material at elevated temperatures.

The SETARAM Labsys offers the ability to perform TGA analysis up to 1600 °C and additionally under a variety of gas mixtures due to our gas-mixing option.

Differential Scanning Calorimetry (DSC)

DSC is a flexible technique to explore thermal transitions within a given sample. By heating a sample and measuring the heat flow as compared to a reference standard, we can access thermoanalytical information on a given material. DSC curves are generated by plotting heat flow (mW) vs sample temperature (°C), and an example plot is found in Figure 2, and demonstrates the melting and fusion of Indium Corp. Indalloy 80Au/20Sn solder. In this case, we observe a phase change (solid-liquid followed by liquid-solid); however, we can also observe other thermal transitions within a material, such as evaporation, thermal transitions between polymorphs, and determination of key thermal constants. One of these key thermal constants is heat capacity (Cp), which an be difficult to acquire due to the demanding experiment required to gain access to this information. Heat capacity requires precise and very specific sensitivity of the DSC sensor, as it is a very small and difficult thermal effect to capture effectively. Owing to our 3D Calvet type sensor on our µDSC 7, we have the capability to measure such small thermal effects (0.02 µW) requiring the upmost sensitivity and precision from 0 – 120 °C. For higher temperatures, our SETARAM Labsys Evo instrument has a specifically designed 3D-psuedo-Calvet sensor, which allows TAL to perform C_p testing with better than 2% accuracy from ambient temperatures to 1600 °C. This very sensitive and difficult to determine thermal effects also include the glass transition point (T_g), water state in materials and other thermodynamic and thermokinetic effects.

Differential Thermal Analysis (DTA)

DTA is a similar technique to DSC, however instead of measuring the heat flow between the furnace temperature and the sample, you measure the temperature difference between a sample and a standard reference using thermocouples. This is particularly useful for phase-change materials and the study of organic and polymeric materials using analytical precision. Owing to the more sensitive detector within typical DTA sensors, DTA testing is particularly useful for running thermokinetic experiments due to the lower thermal inertial barrier. TAL offers DTA testing from ambient to 1200 °C, allowing us to explore thermal effects at elevated temperature, capabilities which we have newly acquired.

While each of these techniques may be used to probe into a single physical characteristic of a material, the real power we provide is simultaneous thermal analysis techniques for niche applications on a single sample. With TAL’s Labsys Evo 1600 and DSC 131, we offer capabilities to include high temperature ranges with mixtures of gases. For example, TAL offers TGA, DSC and DTA experiments from ambient temperatures up to 1600 °C. Figure 3 shows a TGA-DSC decomposition experiment captured on our Setaram Labsys Evo apparatus, where CuSO₄•5H₂O decomposition can be measured by TGA (water, SO₂ and O₂) and DSC. In addition to these coupled thermal experiments, we offer the capacity to provide gas mixtures for high precision control over the exact atmospheric exposure during thermal analysis runs. TAL also offers the capacity to run samples under vacuum (10^-3 Bar) using our Labsys Evo system, which is useful for isolating gas-sample interactions. TAL also offers pressurized DSC experimentation, allowing for the study of various samples under 200 psi. This can provide insight into thermal transitions under pressure, such as those in the oil and fuel industry or in the case of high-pressure lubricants.