Viscoelasticity concentrated solutions

Graessley W W 1993 Viscoelasticity and flow in polymer melts and concentrated solutions Physical Properties of Polymers ed J E Mark et al (Washington, DC ACS) pp 97- 143... 

Telechelic Ionomers. Low molecular weight polymers terminated by acid groups have been treated with metal bases to give ionomers in which the cations can be considered as connecting links in the backbones (67—71). The viscoelastic behavior of concentrated solutions has been linked to the neutralizing cation. 

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. 

The viscoelastic response of the UHMWPE pseudo-gels depends also on the solution concentration. As shown in Figure 10, the G increased with concentration at frequency 50 sec"l over the temperature range from -20 C to 100 C. This is probably due to the higher entanglement density and/or higher crystallinity in the higher concentration solution. 

Rheo-optical and rheological strudies of concentrated solutions of UHMWPE/paraffin oil (2-5% w/w concentration) systems indicate that these are pseudo-gels unlike the covalent bonded molecular networks which exhibit a true gel behavior. The viscoelastic properties of the UHMWPE/paraffin oil pseudo-gels,... 

This document gives definitions of terms related to the non-ultimate mechanical behaviour or mechanical behaviour prior to failure of polymeric materials, in particular of bulk polymers and concentrated solutions and their elastic and viscoelastic properties. 

Masuda,T., Toda,N., Aoto,Y, Onogi,S. Viscoelastic properties of concentrated solutions of poly(methyl methacrylate) in diethyl phthalate. Polymer J. (Japan) 3, 315-321... 

Graessley, W.W. Viscoelasticity and Flow in Polymer Melts and Concentrated Solutions. In Physical Properties of Polymers. American Chemical Society, Symposium Series n° 84, Washington DC, 1984, pp 97-153. 

J. O. Park and G. C. Berry, Moderately concentrated solutions of polystyrene. III. Viscoelastic properties at the Flory theta temperature , Macromolecules, 22, 3022 (1989). 

In equation (6.33), the stresses in the moving viscoelastic liquid (6.31) are added to the stresses in the continuum of Brownian particles. When the equations of motion are formulated, we have to take into account the presence of the two interacting and interpenetrating continuous media formed by the viscoelastic liquid carrier and the interacting Brownian particles that model the macromolecules. However, the contribution of the carrier in the case of a concentrated solution is slight, and we shall ignore it henceforth. 

Now, we can try to relate the above results to the experimental data on the viscoelasticity of concentrated solutions of polymers. For the systems of long macromolecules, the estimated values of parameter are small. Having used expressions (6.40) for this case, one can evaluate the terminal relaxation time of the system... 

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. 

The set of internal variables is usually determined when considering a particular system in more detail. For concentrated solutions and melts of polymers, for example, a set of relaxation equation for internal variables were determined in the previous chapter. One can see that all the internal variables for the entangled systems are tensors of the second rank, while, to describe viscoelasticity of weakly entangled systems, one needs in a set of conformational variables xfk which characterise the deviations of the form and size of macromolecular coils from the equilibrium values. To describe behaviour of strongly entangled systems, one needs both in the set of conformational variables and in the other set of orientational variables w fc which are connected with the mean orientation of the segments of the macromolecules. 

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... 

Finally it may be remarked that the dynamic viscoelastic properties of plasticized cellulose derivatives seem to give no evidence of any unusual temperature dependence of the chain conformations. Thus, Landel and Ferry (162, 163, 164) successfully applied the method of reduced variables [see, for example, Ferry (6)] to various concentrated solutions of cellulosic polymers, and found that the temperature reduction factors were quite similar to those for other flexible polymers such as poly(isobutylene). 

Fig. 16.9 shows the low frequency slopes of 2 and 1, respectively, as expected for viscoelastic liquids and the high frequency slopes Vi and 2/3 for Rouse s and Zimm s models, respectively. Experimentally it appears that in general Zimm s model is in agreement with very dilute polymer solutions, and Rouse s model at moderately concentrated polymer solutions to polymer melts. An example is presented in Fig. 16.10. The solution of the high molecular weight polystyrene (III) behaves Rouse-like (free-draining), whereas the low molecular weight polystyrene with approximately the same concentration behaves Zimm-like (non-draining). The higher concentrated solution of this polymer illustrates a transition from Zimm-like to Rouse-like behaviour (non-draining nor free-draining, hence with intermediate hydrodynamic interaction).

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 above phenomenological description of the viscoelastic behaviour of polymer melts and concentrated solutions leads to the following important conclusions if one focuses on the behavioiu- in the terminal region of relaxation, what is usually done for temperature (time-temperature equivalence) may also be done for the concentration effects and the effects of chain length one may define a "time-chain length equivalence" and "time-concentration equivalence"[4]. For monodisperse species, the various shifts along the vertical (modulus) axis and horizontal (time or frequency axis) are contained in two reducing parameters the... 

The Rouse model is the earliest and simplest molecular model that predicts a nontrivial distribution of polymer relaxation times. As described below, real polymeric liquids do in fact show many relaxation modes. However, in most polymer liquids, the relaxation modes observed do not correspond very well to the mode distribution predicted by the Rouse theory. For polymer solutions that are dilute, there are hydrodynamic interactions that affect the viscoelastic properties of the solution and that are unaccounted for in the Rouse theory. These are discussed below in Section 3.6.1.2. In most concentrated solutions or melts, entanglements between long polymer molecules greatly slow polymer relaxation, and, again, this is not accounted for in the Rouse theory. Reptation theories for entangled... 

Forced oscillations in torsion are used in the most versatile and accurate technique for measuring the viscoelastic functions, in the frequency domain, of melts and concentration solutions (12). In this case, the second-order differential equation governing the motion is given by... 

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... 

A major goal in the physics of polymer melts and concentrated solutions is to relate measurable viscoelastic constants, such as the zero shear viscosity, to molecular parameters, such as the dimensions of the polymer coil and the intermolecular friction constant. The results of investigations to this end on the viscosity were reviewed in 1955 (5). This review wiU be principaUy concerned with advances made since in both empirical correlation (Section 2) and theory of melt flow (Section 3). We shall avoid data confined to shear rates so high that the zero shear viscosity cannot be reliably obtained. The shear dq endent behavior would require an extensive review in itself. 

J. R. Richards, and J. D. Frbry Viscoelastic prc erties of concentrated solutions of polyisobutene in cetane. II. Creep and viscous flow. J. Ph5rs. Chem. 67, 327 (1963). 

Concentrated solutions of HA possess extraordinary rheological properties HA solutions exhibit viscoelastic properties, i.e. their viscosities are strongly dependent on the applied shear-stress. Accordingly, rotational viscometers are the instruments of choice to characterize the macroscopic properties of HA solutions [72]. The shock absorbing properties of synovial fluids are based primarily on the viscoelasticity of its main constituent, HA. 

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