Polymer-diluent mixtures

The fusion of polymers with low molecular weight diluents will be discussed in this chapter. When considering phase equilibria of multicomponent systems several a priori assumptions have to be made. These assumptions are universal and are applicable to all types of molecular systems and are not unique to polymers. It is necessary to specify whether the disordered, or liquid, state is homogeneous or heterogeneous, i.e. does liquid-liquid phase separation occur. The composition of the crystalline phase and in particular whether it remains pure, also needs to be specified. If the crystalline phase is not pure it is necessary to know whether the diluent enters the crystal lattice as a result of equilibrium considerations and if compound formation occurs. Also to be considered is whether the diluent enters the lattice as a defect. All of these possibilities need to be considered separately. The appropriate expression for the free energy of mixing that apphes in each specific case has to be known. All of these factors will be considered in the following. 

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Berry, G.C. The viscosity of polymer-diluent mixtures. J. Phys. Chem. 70, 1194-1198 (1966). 

It has long been a mystery why diffusion coefficients of polymer-diluent systems, especially when the diluent is a good solvent for a given polymer, exhibit so pronounced a concentration dependence that it looks extraordinary. Several proposals have been made for the interpretation of this dependence. Thus Park (1950) attempted to explain it in terms of the thermodynamic non-ideality of polymer-diluent mixtures, but it was found that such an effect was too small to account for the actual data. Fujita (1953) suggested immobilization of penetrant molecules in the polymer network, which, however, was not accepted by subsequent workers. Recently, Barrer and Fergusson (1958) reported that their diffusion coefficient data for benzene in rubber could be analyzed in terms of the zone theory of diffusion due to Barrer (1957). Examination shows, however, that their conclusion is never definitive, since it resorted to a less plausible choice of the value for a certain basic parameter. 

Here (DJp is the polymer-fixed diffusion coefficient of the penetrant component (see section 1.1) and at is the activity of the penetrant in the given polymer-diluent mixture. Combining Eqs. (2) and (31) and noticing that the product c, , is equal to the volume fraction vt of the penetrant component in the mixture, one obtains... 

Mandelkern, L. Crystallization kinetics in high polymers. II. Polymer-diluent mixtures. J. Appl. Phys. 26, 443—451 (1955). 

Studies on the mechanical properties of glassy polymer-solvent or, more generally, polymer-diluent mixtures have been primarily concerned with the deformation behavior at small strains which is governed by the viscoelastic properties of the material. From these studies it is well known that diluents significantly affect relaxation processes in glassy polymers, as clearly evidenced by phenomena such as plasticization and antiplasticization... 

Glassy polymer-diluent mixtures deformed in a temperature range close to are susceptible to exhibit a cavitational mode of plasticity at hi stresses and strains. Activation of this mechanism in mixtures of polycarbonate with esters of the phthalic acid results in extensive fibrillation and stress whitening of the material. There is strong evidence that the diluent plays an important role in enhancing chain slippage, which is required for the formation of craze fibrils. One of the most fundamental problems which is still unsolved is the elucidation of the molecular mechanism by which diluents become active. 

The molecular weight between entanglements of a homogeneous polymer-diluent mixture in which the concentration of diluent is 0.15 g/cm is 20,000 g/mol. Make a rough estimation of the solvent that should be added to 100 cm of the mixture to give a molecular weight between entanglements of 25,000 g/mol. 

Vi- Vt volmne fraction polymer and solvent in a polymer-diluent mixture,... 

The phase diagram of polyolefins and hydrocarbon diluents is exemplified for high-density polyethylene in Figure 1. When the polymer-diluent mixture is heated, dissolution of the semicrystalline polymer takes place along the borderline 1 (turbidity curve) [43, 44], This line depends on the polymer (e. g., polyethylene, isotactic polypropylene), average chain length, and copolymer composition. 

Empirically Tg of a polymer-diluent mixture could be expressed in terras of the glass transition temperature of the pure polymer 9V and that of the pure diluent Tgd by... 

A relation between Tg and composition of a polymer-diluent mixture can be derived [47] in a relatively straightforward manner from the free-volume concept by postulating that the free volumes of the polymer and diluent are additive in the mixture, and that the free volume fraction has a critical value fg, which is the same for the pure polymer, the diluent and their mixtures at their respective glass temperatures. The composition of polymer-diluent mixtures is conveniently expressed in terms of the volume fractions of polymer cj)p and diluent (f>d. 

Since (an — ac) is roughly constant for many polymers — a value of 2.2x10 being re rted by Sharma et al [37J — Eq. (2.54) can be used to predict the ig value of a polymer-diluent mixture of given composition, provided Tg values of the polymer and the diluent and of the diluent are known. 

The results of viscosity measurements made at 220°C on these polymer-diluent mixtures are shown in Figure 3, where the viscosity measured at a constant shear stress is plotted against the weight fraction... 

In equation (5-7) the subscripts p and d refer to polymer and diluent, respectively, and (j) is the volume fraction. At the Tg of the polymer-diluent mixture,/ becomes 0.025. Using this fact and substituting -P for //, we have... 

Dettenmaier, M. and Leberger, D. (1990) Crazing of polymer-diluent mixtures, in Advances in Polymer Science vols. 91/92, edited by, Kausch, H. H. Berlin Springer-Verlag pp. 119-135. 

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