Concentrated polymer solutions linear viscoelasticity

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... 

The transient net work model is an adaptation of the network theory of rubber elasticity. In concentrated polymer solutions and polymer melts, the network junctions are temporary and not permanent as in chemically crosslinked rubber, so that existing junctions can be destroyed to form new junctions. It can predict many of the linear viscoelastic phenomena and to predict shear-thinning behavior, the rates of creation and loss of segments can be considered to be functions of shear rate. 

The zero-shear viscoelastic properties of concentrated polymer solutions or polymer melts are typically defined by two parameters the zero-shear viscosity (f]o) and the zero-shear recovery compliance (/ ). The former is a measure of the dissipation of energy, while the latter is a measure of energy storage. For model polymers, the infiuence of branching is best established for the zero-shear viscosity. When the branch length is short or the concentration of polymer is low (i.e., for solution rheology), it is found that the zero-shear viscosity of the branched polymer is lower than that of the linear. This has been attributed to the smaller mean-square radius of the branched chains and has led to the following relation... 

For moderately concentrated polymer solutions, we have found that Ni depends on the average molecular weight, the concentration (c.f. Fig. 10) and the solvent power.(7,21) in order to minimize non-linear viscoelastic effects, it is important to know whether the concentration or My< has more influence on Ni. With increasing energy costs, the elastic behavior of polymer solutions must be taken more into consideration in the future. 

Most concentrated structured liquids shown strong viscoelastic effects at small deformations, and their measurement is very useful as a physical probe of the microstructure. However at large deformations such as steady-state flow, the manifestation of viscoelastic effects—even from those systems that show a large linear effects—can be quite different. Polymer melts show strong non-linear viscoelastic effects (see chap. 14), as do concentrated polymer solutions of linear coils, but other liquids ranging from a highly branched polymer such as Carbopol, through to flocculated suspensions, show no overt elastic effects such as normal forces, extrudate swell or an increase in extensional viscosity with extension rate [1]. 

In this chapter, we present currently held molecular theories for the viscoelasticity of linear, flexible macromolecular chains. We begin with a presentation of the static properties of macromolecules and the stochastic processes in the motion of macromolecular chains, as much as they will be necessary to present the molecular aspects of viscoelasticity in this and later chapters. We first present the molecular theories of Rouse (1953) and Zimm (1956), which are basically applicable to dilute polymer solutions and unentangled polymer melts, and then present the molecular theory of Doi and Edwards (1978a, 1978b, 1978c, 1979), which is applicable to concentrated polymer solutions and entangled polymer melts. 

The purpose of this study was to give an insight into molecular properties which imderlie the linear viscoelastic behaviour of molten polymers. Properties were probed from proton magnetic dipoles attached to polymeric chains or to smadl molecules in concentrated polymeric solutions. 

We will begin with a brief survey of linear viscoelasticity (section 2.1) we will define the various material functions and the mathematical theory of linear viscoelasticity will give us the mathematical bridges which relate these functions. We will then describe the main features of the linear viscoelastic behaviour of polymer melts and concentrated solutions in a purely rational and phenomenological way (section 2.2) the simple and important conclusions drawn from this analysis will give us the support for the molecular models described below (sections 3 to 6). 

Figure 3.13 Linear viscoelastic data (symbols) for polystyrene in two theta solvents, decalin and diocty Iphthalate, compared to the predictions (lines) of the Zimm theory with dominant hydrodynamic interaction, h = oo. The reduced storage and loss moduli and G are defined by = [G ]M/NAksT and G s [G"]M/A /cbT, where the brackets denote intrinsic values extrapolated to zero concentration, [G jj] = limc o(G /c) and [G j ] = limc +o[(G" — cor)s]/c), and c is the mass of polymer per unit volume of solution. The characteristic relaxation time to is given by to = [rj]oMrjs/NAkBT. For frequencies ro

It is expected that the same picture that gives a good account of the linear viscoelastic behavior of polymer melts should also hold for semidilute and concentrated solutions. In the case of semidilute solutions some conclusions can be drawn from sealing arguments (19,3, p. 235). In this way, concentration dependence of the maximum relaxation time tmax the zero shear rate viscosity r Q, and the plateau modulus G% can be obtained, where t is the viscosity of the solvent. The relevant parameters needed to obtain Xmax as a function of concentration are b, c, N, kgT, and Dimensional analysis shows that... 

Shear Wave Propagation. A pulse shearometer (Rank Bros.) was used to measure the propagation velocity of a shear wave through the weak gels formed by the solutions of HMHEC in dilute NaCl. The polymer concentration range studied was 0.5-2.0%. With this apparatus, the frequency of the shear wave is approximately 1200 rad s" and the strain is <10 . At this strain, n pst systems behave in a linear viscoelastic fashion, and the wave-rigidity modulus, G is... 

It is well known that the linear viscoelastic properties of polymer melts and concentrated solutions are strong function of molecular structure, average molecular mass and molecular mass distribution (MWD). The relaxation time spectrum is a characteristic quantity describing the viscoelastic properties of polymer melts. Given this spectrum, it is easy to determine a series of rheological parameters. The relaxation time spectrum is not directly accessible by experiments. It is only possible to obtain the spectrum from noisy data. 

Although stress-relaxation and creep measurements are used extensively, measuring oscillatory shear is the most commonly used method for characterizing the linear viscoelastic properties of polymer melts and concentrated solutions. As indicated in Fig. 3.10, the liquid is strained sinusoidally at some frequency co, and in the linear region (small-enough strain amplitude yo)- The stress response at steady state is also sinusoidal, but usually out of phase with the strain by some phase angle steady-state stress signal is resolved into in-phase and out-of-phase components, and these are recorded as functions of frequency ... 

In concentrated solution blends of two polymer components of different molecular weight at a constant total polymer concentration, i/o is determined by M of the polymer blend, while y is in general higher than that of either of the components. The dependence of y on blend proportions, and to some extent the time or frequency dependence of viscoelastic functions, can be described by a cubic blending law cf. Section C5 of Chapter 13). At considerably lower concentrations, however, a linear blending law is fairly satisfactory. ... 

Song MS, Wen Z, Hu GX (1999) Rheological behavior of polymer melts and concentrated solutions, part V a new molecular theory of non-linear viscoelasticity for polymeric suspensions. J Mater Sci Technol 15(2) 169-177... 

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