Linear viscoelasticity concentrated solutions

Non-linear viscoelastic flow phenomena are one of the most characteristic features of polymeric liquids. A matter of very emphasised interest is the first normal stress difference. It is a well-accepted fact that the first normal stress difference Nj is similar to G, a measure of the amount of energy which can be stored reversibly in a viscoelastic fluid, whereas t12 is considered as the portion that is dissipated as viscous flow [49-51]. For concentrated solutions Lodge s theory [52] of an elastic network also predicts normal stresses, which should be associated with the entanglement density. 

For shear strains greater than approximately 2 the ratio cr(r)/> 0 for a concentrated polystyrene solution was reduced at all observable times. For the large strains, relaxation proceeded more rapidly at short times, but at longer times the residua] stress decayed with about the same time dependence as that in the linear viscoelastic region. 

Abstract The discussion of relaxation and diffusion of macromolecules in very concentrated solutions and melts of polymers showed that the basic equations of macromolecular dynamics reflect the linear behaviour of a macromolecule among the other macromolecules, so that one can proceed further. Considering the non-linear effects of viscoelasticity, one have to take into account the local anisotropy of mobility of every particle of the chains, introduced in the basic dynamic equations of a macromolecule in Chapter 3, and induced anisotropy of the surrounding, which will be introduced in this chapter. In the spirit of mesoscopic theory we assume that the anisotropy is connected with the averaged orientation of segments of macromolecules, so that the equation of dynamics of the macromolecule retains its form. Eventually, the non-linear relaxation equations for two sets of internal variables are formulated. The first set of variables describes the form of the macromolecular coil - the conformational variables, the second one describes the internal stresses connected mainly with the orientation of segments. 

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 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). 

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. 

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... 

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. 

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 ... 

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 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. ... 

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