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Storage modulus and loss modulus: What are the two core secrets of dynamic mechanical analysis?
Dynamic Mechanical Analysis (DMA) is a technique for studying and characterizing materials, especially the viscoelastic behavior of polymers. This analysis method involves applying a sinusoidal stress and measuring the strain in the material, in this way, the complex modulus of the material can be determined. By varying the temperature or frequency of the stress on a sample, changes in the complex modulus can be observed, allowing researchers to find the material's glass transition temperature and identify other transitions corresponding to molecular motions.
Properties of viscoelastic materials
Polymers, which consist of long molecular chains, possess unique viscoelastic properties that combine features of elastic solids and Newtonian fluids. Conventional elastic theory describes the mechanical properties of elastic solids in which stress and strain are proportional at small deformations and this response to stress is independent of the strain rate. The rheological theory of fluids describes the properties of viscous fluids, where the response to stress depends on the strain rate. Since polymers possess properties of both solid and liquid behavior, these behaviors can be modeled mechanically through a combination of springs and dampers, which allows viscoelastic materials like asphalt to exhibit both elastic and viscous behavior.
Dynamic modulus of polymers
DMA studies the viscoelastic properties of polymers by applying a sinusoidal force (stress σ) to the material and measuring the resulting displacement (strain). For a perfectly elastic solid, the resulting strain and stress are exactly in phase; for a purely viscous fluid, the strain is delayed by 90 degrees relative to the stress. The viscoelastic properties of polymers show properties in between the two, so a certain phase delay will appear in the DMA test.
The storage modulus is a measure of the energy stored and represents the elastic portion, while the loss modulus is a measure of the energy converted into heat and represents the viscous portion.
Derivation of dynamic modulus
When performing strain measurements, the relationship between stress and strain is described as: stress σ(t) and strain ε(t), which varies with time. The situation can be expressed as follows:
These mathematical expressions introduce temporal randomness and phase difference of strain into the changes of complex modulus, storage modulus and loss modulus. Ultimately, this expression helps scientists understand the performance of materials under different stresses and temperatures, providing data support for many industrial applications.
Applications
Measurement of glass transition temperature
An important application of DMA is the measurement of the glass transition temperature of polymers. Amorphous polymers have different glass transition temperatures, above which the material exhibits rubbery properties rather than glassy behavior and has a significant decrease in stiffness and viscosity. At the glass transition point, the storage modulus decreases significantly, while the loss modulus reaches its maximum. DMA with temperature sweeps is often used to characterize the glass transition temperature of a material.
Polymer composition
Altering the monomer and cross-linking components can increase or change the functionality of the polymer, thus affecting the results obtained with DMA. For example, when mixing ethylene propylene diene monomer (EPDM) with styrene butadiene rubber (SBR), different cross-linking or curing systems will show different physical properties. DMA is an effective method for evaluating the blending properties of polymers, thereby helping to optimize the performance of the material.
Instruments and their types
DMA instruments consist of displacement sensors, temperature control systems, drive motors, and sample fixtures. Sample preparation and handling will vary depending on what is being measured. There are two main types of DMA analyzers: forced resonance analyzers and free resonance analyzers. Forced resonance analyzers are more commonly used. These instruments force the sample to oscillate at a specific frequency and are suitable for performing temperature sweeps.
These techniques have a wide range of applications in industry and research. In the process of understanding material properties and performance, have you ever thought about what other potential areas can benefit from the application of these dynamic mechanical analysis techniques?
