Mechanisms Associated with Viscoelastic Response

Molecular Mechanisms Associated with Viscoelastic Response 

It is descriptive here to quote from Aklonis and McKnight, (1983). It is impossible to describe quantitatively the time ranges that give each type of behavior, since the temperature variable causes all these ranges to be relative. Accordingly. .. a plastic (a polymer in the glassy state) would have a modulus of a rubber on a time scale of perhaps a thousand years while a rubber might behave like a plastic on a nanosecond time scale.  

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Molecular Mechanisms Associated with Viscoelastic Response... 

Describe the molecular mechanisms associated with viscoelastic response in the glassy, transition and rubbery regions of behavior. 

The use of the term glassy-like for this zone arises from the fact that the viscoelastic mechanisms associated with the response are believed to involve local motions, such as occurs in the glassy state. The response in this region is independent of molecular weight, and the creep comphance function obeys Andrade s equation (18,19)... 

This result provides a general definition of the relaxation time of a polymer and allows the relaxation time to be found easily from experimental data without recourse to a mechanical model. It can be used as a material property to give an indication of the time scale associated with viscoelastic response in a polymer and is indicative of the intrinsic viscosity of the polymer. It should again be noted that the relaxation time for a Maxwell model is related to the viscosity through the equation, x = ji/E. In a sense, the Maxwell model provides a defining relationship for the viscosity of a material. It will be shown later that a polymer possesses a distribution of relaxation times and that an individual chain can be thought of as having various relaxation times. 

VISCOELASTICITY. Mechanical behavior of material which exhibits viscous and delayed clastic response to stress in addition to instantaneous elasticity. Such properries can be considered to be associated with rate effects—time derivatives of arbitrary order of both stress and strain appearing in the constitutive equation—or hereditary or memory influences which include the history of the stress and strain variation from the undisturbed state. See also Rheology. 

Real (viscoelastic) materials give an intermediate response that is an exponential curve. The exponential time constants associated with the curve are used to approximate the relaxation times of the material itself. Thus, the shape of the output curve is analyzed to give viscoelastic information, although this model fitting is only strictly legitimate in the linear viscoelastic region. Workers have shown that the mechanical parts of the models (springs and dashpots) can be associated with specific parts of a food s makeup. 

The formalism outlined above will be applied to determine equivalent-circuit models for a TSM resonator with (1) an ideal mass layer, (2) a contacting semiinfinite liquid, and (3) a viscoelastic film. By determining the mechanical impedance Zj associated with each perturbation, the equivalent-circuit model arising from each can be obtained. In cases where the perturbation cannot be easily modeled, the procedure can be reversed the resonator response is used to determine Zg and thereby characterize the perturbation. 

Having discussed the viscoelastic responses of simple mechanical models, we may now consider molecular theories. In this treatment it will be shown that the results of molecular theories can, in fact, be couched in terms of the mechanical models already presented. The molecular theories predict the distribution of relaxation times and partial moduli associated with each relaxation time (r/s and Els for all z s), which we treated as unknowns or parameters in the previous discussion. Thus, although molecular theories are not based on mechanical models, the results of these treatments may be presented in terms of the parameters of these models. Since, as we have already shown, it is possible to develop expressions giving the viscoelastic responses of the models to various types of deformations, the predictions of the molecular theories are obtainable through the known responses of these models. 

Uny et also reported the chemical synthesis of protein polymers based on the (Val-Pro- Ala-Val-Gly) repeat sequence in which glycine is replaced by the D-alanine residue. The hetero-chiral Pro- Ala diad would be erqrected on the basis of stereochemical considerations to adopt a type-II p-tum conformation. Stmctural analyses of small-molecule "Pro- Ala turn models support the formation of the type-II p-mm conformation in solution and the solid state. Polymers based on the (Val-Pro- Ala-Val-Gly) repeat sequence display a thermo-reversible phase transition similar to the corresponding polypeptides derived from the parent (Val-Pro-Gly-Val-Gly) sequence, albeit with a shift of the Tt to approximately 5-10 ° G below the latter due to a slight inaease in hydrophobic character due to the presence of the alanine residue. NMR spectroscopic analyses of the (Val-Pro- Ala-Val-Gly) polymer suggest that the repeat unit retains the p-tum stmcture on the basis of comparison to the corresponding behavior of the (Val-Pro-Gly-Val-Gly) polymer. Stress-strain measurements on cross-linked matrices of the (Val-Pro- Ala-Val-Gly) polymer indicate an elastomeric mechanical response in which the elastic modulus does value in comparison to the (Val-Pro-Gly-Val-Gly) polymer. These smdies of glycine suhstitution support the hypothesis that type-II p-tum formation can he associated with the development of elastomeric behavior with native elastins and elastin-derived polypeptide sequences. Several investigators have proposed that the (Val-Pro-Gly-Val-Gly) pentapeptide represents the minimal viscoelastic unit... 

The QCM-D response to mass uptake on the crystal oscillator is reflected in the changes in both the resonant frequency (Afi and dissipation factor (AD) at different overtones. In contrast to OWLS, the QCM-D approach is sensitive to viscoelastic properties and the density of any mass coupled to the mechanical oscillation of the quartz crystal. In this case, the adsorbed mass consists of the PLL- -PEG copolymer along with solvent molecules associated with it. A Voigt-based model was therefore used in the analysis (software Q-tools, version 2.0.1), where the adsorbed layer was represented as a homogeneous, viscoelastic film characterized by shear viscosity ((/shear), shear modulus (Eshear), and film thickness (htum) (20—22). 

To illustrate this linear combination, various analogical models with no relationship with the molecular nature of the phenomena were proposed, identifying a polymer with a combination of springs and dashpots. The spring can be stfained without inertia and thus reflects a purely elastic mechanical behavior whereas dash-pots, which are pistons moving in cylinders filled with a viscous liquid, cannot respond instantaneously to a stress. These two elements were thus associated under various combinations to simulate the response of a viscoelastic body to a mechanical stress. 

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