Viscoelasticity, linear molecular response

It appears that the formal theories are not sufficiently sensitive to structure to be of much help in dealing with linear viscoelastic response Williams analysis is the most complete theory available, and yet even here a dimensional analysis is required to find a form for the pair correlation function. Moreover, molecular weight dependence in the resulting viscosity expression [Eq. (6.11)] is much too weak to represent behavior even at moderate concentrations. Williams suggests that the combination of variables in Eq. (6.11) may furnish theoretical support correlations of the form tj0 = f c rjj) at moderate concentrations (cf. Section 5). However the weakness of the predicted dependence compared to experiment and the somewhat arbitrary nature of the dimensional analysis makes the suggestion rather questionable. 

The reduced expressions of Table 4 form a set of universal viscoelastic functions. Given the polymer molecular weight, material constants [Jg, Je, etc.), and one extremal relaxation/retardation time, one should be able to predict, roughly, the nature of the system response (within the framework of the linear models) from Eqs. (T 1)—(T 6) and Fig. 2—5. 

The stress-strain relations for viscoelastic materials are reviewed. The simplest case of intrinsic absorption in polymers is a molecular relaxation mechanism with a single relaxation time. However, the relaxation mechanisms which lead to absorption of sound are usually more complicated, and are characterized by a distribution of relaxation times. Under causal linear response conditions the attenuation and dispersion of sound in a... 

Many materials, particularly polymers, exhibit both the capacity to store energy (typical of an elastic material) and the capacity to dissipate energy (typical of a viscous material). When a sudden stress is applied, the response of these materials is an instantaneous elastic deformation followed by a delayed deformation. The delayed deformation is due to various molecular relaxation processes (particularly structural relaxation), which take a finite time to come to equilibrium. Very general stress-strain relations for viscoelastic response were proposed by Boltzmann, who assumed that at low strain amplitudes the effects of prior strains can be superposed linearly. Therefore, the stress at time t at a given point in the material depends both on the strain at time t, and on the previous strain history at that point. The stress-strain relations proposed by Boltzmann are [4,39] ... 

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

It is commonplace for rheologists to investigate the linear viscoelastic properties of materials and, indeed, this is certainly the case in the pharmaceutical and related sciences. Bird et al. (24) and Barnes et al. (2) have suggested several reasons for this, including the ability to derive speculative molecular structures of materials from their rheological response in the linear viscoelastic region and, additionally, the ability to relate the parameters derived from the linear viscoelastic response to quality control procedures and, in some instances, to clinical response (7,9,19,25-27). Furthermore, the mathematical principles associated with the linear viscoelastic response are less complex than those for nonlinear viscoelasticity, thus ensuring relatively simple interpretations of results. 

The linear viscoelastic properties in the melt state of highly grafted polymers on spherical silica nanoparticles are probed using linear dynamic oscillatory measurements and linear stress relaxation measurements. While the pure silica tethered polymer nanocomposite exhibits solid-like response, the addition of a matched molecular weight free matrix homopolymer chains to this hybrid material, initially lowers the modulus and later changes the viscoelastic response to that of a liquid. These results are consistent with the breakdown of the ordered mesoscale structure, characteristic of the pure hybrid and the high hybrid concentration blends, by the addition of homopolymers with matched molecular weights. 

The four-parameter model provides a crude quahtative representation of the phenomena generally observed with viscoelastie materials instantaneous elastie strain, retarded elastic strain, viscous flow, instantaneous elastie reeovery, retarded elastie reeovery, and plastic deformation (permanent set). Also, the model parameters ean be assoeiated with various molecular mechanisms responsible for the viscoelastic behavior of linear amorphous polymers under creep conditions. The analogies to the moleeular mechanism can be made as follows. 

Entanglements of flexible polymer chains contribute to non-linear viscoelastic response. Motions hindered by entanglements are a contributor to dielectric and diffusion properties since they constrain chain dynamics. Macromolecular dynamics are theoretically described by the reptation model. Reptation includes fluctuations in chain contour length, entanglement release, tube dilation, and retraction of side chains as the molecules translate using segmental motions, through a theoretical tube. The reptation model shows favourable comparison with experimental data from viscoelastic and dielectric measurements. The model reveals much about chain dynamics, relaxation times and molecular structures of individual macromolecules. 

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