Viscoelasticity molecular theory

Different molecular theories have been established [27-32] to describe the viscoelasticity of polymeric liquids. Due to their importance, a brief survey of the different theories will be given below. 

First approaches at modeling the viscoelasticity of polymer solutions on the basis of a molecular theory can be traced back to Rouse [33], who derived the so-called bead-spring model for flexible coiled polymers. It is assumed that the macromolecules can be treated as threads consisting of N beads freely jointed by (N-l) springs. Furthermore, it is considered that the solution is ideally dilute, so that intermolecular interactions can be neglected. 

The methods described above give continuous distributions of relaxation times. However, the molecular theories of Viscoelasticity of polymers as... 

The mean times t and tw will be called the number-average and weight-average relaxation times of the terminal region, and tw/t can be regarded as a measure of the breadth of the terminal relaxation time distribution. It should be emphasized that these relationships are merely consequences of linear viscoelastic behavior and depend in no way on assumptions about molecular behavior. The observed relationships between properties such as rj0, J°, and G and molecular parameters provides the primary evidence for judging molecular theories of the long relaxation times in concentrated systems. 

Chompff and Duiser (232) analyzed the viscoelastic properties of an entanglement network somewhat similar to that envisioned by Parry et al. Theirs is the only molecular theory which predicts a spectrum for the plateau as well as the transition and terminal regions. Earlier Duiser and Staverman (233) had examined a system of four identical Rouse chains, each fixed in space at one end and joined together at the other. They showed that the relaxation times of this system are the same as if two of the chains were fixed in space at both ends and the remaining two were joined to form a single chain with fixed ends of twice the original size. 

Molecular theories, utilizing physically reasonable but approximate molecular models, can be used to specify the stress tensor expressions in nonlinear viscoelastic constitutive equations for polymer melts. These theories, called kinetic theories of polymers, are, of course, much more complex than, say, the kinetic theory of gases. Nevertheless, like the latter, they simplify the complicated physical realities of the substances involved, and we use approximate cartoon representations of macromolecular dynamics to describe the real response of these substances. Because of the relative simplicity of the models, a number of response parameters have to be chosen by trial and error to represent the real response. Unfortunately, such parameters are material specific, and we are unable to predict or specify from them the specific values of the corresponding parameters of other... 

Pokrovskii VN, Pyshnograi GV (1990) Non-linear effects in the dynamics of concentrated polymer solutions and melts. Fluid Dyn 25 568-576 Pokrovskii VN, Pyshnograi GV (1991) The simple forms of constitutive equation of polymer concentrated solution and melts as consequence of molecular theory of viscoelasticity. Fluid Dyn 26 58-64... 

Pyshnograi GV (1996) An initial approximation in the theory of viscoelasticity of linear polymers and non-linear effects. J Appl Mech Techn Phys 37(1) 123—128 Pyshnograi GV (1997) The structure approach in the theory of flow of solutions and melts of linear polymers. J Appl Mech Techn Phys 38(3) 122—130 Pyshnograi GV, Pokrovskii VN (1988) Stress dependence of stationary shear viscosity of linear polymers in the molecular field theory. Polym Sci USSR 30 2624—2629 Pyshnograi GV, Pokrovskii VN, Yanovsky YuG, Karnet YuN, Obraztsov IF (1994) Constitutive equation on non-linear viscoelastic (polymer) media in zeroth approximation by parameter of molecular theory and conclusions for shear and extension. Phys — Doklady 39(12) 889-892... 

Few examples of the homogeneous diblock-incompatible homo-polymer behavior have been reported. One that has received considerable attention is the system polystyrene-poly-a-methylstyrene (2). Block copolymers of styrene and a-methylstyrene exhibit a single loss peak in dynamic experiments (2,3) and have been shown to be thermorheologi-cally simple (4) hence they are considered to be homogeneous. Mechanical properties data on these copolymers also has been used to validate interesting extensions of the molecular theories of polymer viscoelasticity (2,3,4). 

Time constants are related to the relaxation times and can be found in equations based on mechanical models (phenomenological approaches), in constitutive equations (empirical or semiempirical) for viscoelastic fluids that are based on either molecular theories or continuum mechanics. Equations based on mechanical models are covered in later sections, particularly in the treatment of creep-compliance studies while the Bird-Leider relationship is an example of an empirical relationship for viscoelastic fluids. 

For noninteracting particles D b is + D, but as the particles approach each other, the relative diffusion coefficient becomes dependent on their spatial separation. In liquids for large particles this arises from hydrodynamic interactions ( bow waves ), while in the gas phase the particles screen each other from the bath collisions. For small particles the viscoelastic projjerties of the fluid will become important near contact. The solution of Eq. (2.23) applies only for sufficiently large friction where the relative motion on all length scales is diffusive. In the other limit of very low friction, the general result obtained from molecular theory is of the form... 

Doi molecular theory adds a probability density function of molecular orientation to model rigid rodlike polymer molecules. This model is capable of describing the local molecular orientation distribution and nonlinear viscoelastic phenomena. Doi theory successfully predicts director tumbling in the linear regime and two sign changes in the first normal stress difference,as will be discussed later. However, because this theory assumes a uniform spatial structure, it is unable to describe textured LCPs. 

As alluded to in the introduction to this entry, the LE theory was conceived for small molecule LCs while molecular theories are intended for LCPs. LC molecules retain their equilibrium orientation distribution. LCPs are susceptible to disturbances to their distribution function T (m) its temporal relaxation gives rise to molecular viscoelasticity, while its spatial gradient produces distortional elasticity. A natural question is whether the molecular theories reduce properly to the continuum LE theory in the limiting case of an undisturbed orientation distribution. This situation arises in the weak flow limit where the flow is weak De < . 1) and spatial distortions are small ([V l [Pg.2962]

As indicated above, such an agreement is perhaps expected. On the other hand, it is remarkable that a rather complex phenomenological theory postulated for an LC continuum can be reconciled with an even more complex molecular theory built on the concept of intermolecular potential. Perhaps the only other such happy instance is the agreement between the continuum Oldroyd-B model for viscoelastic liquids and the molecular model based on a dilute suspension of linear Hookean dumbbells in a Newtonian solvent. ... 

For viscoelastic properties of flexible polymers at infinite dilution, several molecular theories had been constructed before successful measurements were obtained. Some of the theories which can be examined by comparing with experimental results will be introduced in this paper. Since the configurational changes of a polymer molecule are extremely complicated even at infinite dilution or in an isolated state, such theories may include many assumptions which must be clarified theoretically. However, these problems, which were treated extensively by Fixman and Stockmayer (4) and by Yamakawa (5), will not be discussed in this paper. 

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. 

Overall, the regime of linear viscoelasticity is characterized by reasonable success in establishing structure-property relationships. The properties themselves are unambiguously and simply specifiable. The relevant structural features are largely recognizable aspects of molecular structure. Molecular theories exist that provide a bridge between the molecular structure and the macroscopic viscoelastic properties. 

The purpose of our study was a rheological evaluation of the effect of composition on the properties of ABS resins in the molten state. Steady-state viscosity was determined over a wide range of temperatures and shear rates. The shear modulus in the molten state was determined by measurement of the diameter of the extrudate. ABS resins in the molten state behaved as an amorphous homophase polymer. The effect of the elastomer phase on the viscoelastic properties which characterize the behavior of the continuous matrix, i.e. monomer friction coefficient and molecular weight between entanglements (Me), was calculated by the application of the molecular theories. The significance of these properties in heterophase systems is discussed. 

A molecular theory of viscoelasticity of molten, high molecular weight polymers that makes use of the reptation concept has been developed by... 

Ferry suggested on the basis of a molecular theory of viscoelasticity that there should be a small vertical shift factor ro/0o/(T/0),where p is the density at T and is the density at the reference temperature T. These shifts have been made in fig. 7.14, but they are usually small and are often neglected.)... 

Molecular Theory of Polymer Viscoelasticity — Elastic Dumbbell Model... 

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