Solutions and Melts

Portions of the literature on viscoelasticity in concentrated polymer systems of narrow distribution have been reviewed recently (15, 16, 152, 153). The following discussion concerns three principal characteristics, the viscosity-molecular weight relation, the plateau modulus, and the steady-state compliance. 

A new set of flow characteristics gradually emerges as the concentration of polymer becomes large. The solution viscosity loses its direct dependence on solvent viscosity and comes to depend on the product of two parameters a friction factor C which is controlled solely by local features such as the free volume (or alternatively the segmental jump frequency), and a structure factor F which is controlled by the large scale structure and configuration of the chains (16)  

The Rouse expression for the viscosity [Eq.(4.25)] is of this form. The frictional coefficient per main chain atom Co is the friction factor in this case the remainder of the expression is the structure factor. 

The friction factor depends upon the same features that govern the viscosity of small-molecule liquids. At low temperatures f0 depends on T — T% (Tg T Tg+ 4-100° C), and at higher temperatures it depends on an activation energy for flow. The value of 3 for a solution depends on the properties of both components and their concentrations, but it is independent of the large scale structure of the polymer as long as its molecular weight is large (Mn 104 for most linear polymers). 

For longer chains the form of the structure factor changes, becoming a much stronger function of molecular weight. At high molecular weights the well known 3.4 power dependence results  

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W. Paul, K. Binder, D. Heermann, K. Kremer. Dynamics of polymer solutions and melts. Reptation prediction and scaling of relaxation times. J Chem Phys 95 7726-7740, 1991. 

This monograph compiles the latest research on the chemistry of complex fluorides and oxyfluorides of tantalum and niobium, and covers synthesis and fluorination processes, crystal structure peculiarities and crystal chemical classification, as well as the behavior of complex ions in fluorine solutions and melts. 

Maklakov AI, Skirde VD, Fatkullin NF (1987) Self-diffusion in polymer solutions and melts (in Russian). University Publ, Kazan... 

Main Features of Crystallization from Oriented Solutions and Melts. 214... 

Two approaches to the attainment of the oriented states of polymer solutions and melts can be distinguished. The first one consists in the orientational crystallization of flexible-chain polymers based on the fixation by subsequent crystallization of the chains obtained as a result of melt extension. This procedure ensures the formation of a highly oriented supramolecular structure in the crystallized material. The second approach is based on the use of solutions of rigid-chain polymers in which the transition to the liquid crystalline state occurs, due to a high anisometry of the macromolecules. This state is characterized by high one-dimensional chain orientation and, as a result, by the anisotropy of the main physical properties of the material. Only slight extensions are required to obtain highly oriented films and fibers from such solutions. 

Usually, crystallization of flexible-chain polymers from undeformed solutions and melts involves chain folding. Spherulite structures without a preferred orientation are generally formed. The structure of the sample as a whole is isotropic it is a system with a large number of folded-chain crystals distributed in an amorphous matrix and connected by a small number of tie chains (and an even smaller number of strained chains called loaded chains). In this case, the mechanical properties of polymer materials are determined by the small number of these ties and, hence, the tensile strength and elastic moduli of these polymers are not high. 

The formation of fibrillar structures during the crystallization of deformed solutions and melts under various conditions of mechanical treatment was observed by many authors22,24,25 who studied the crystallization in stirred or flowing solutions. In all cases... 

The Zimm model predicts correctly the experimental scaling exponent xx ss M3/2 determined in dilute solutions under 0-conditions. In concentrated solution and melts, the hydrodynamic interaction between the polymer segments of the same chain is screened by the host molecules (Eq. 28) and a flexible polymer coil behaves much like a free-draining chain with a Rouse spectrum in the relaxation times. 

Liquids of complex structure, such a polymer solutions and melts, and pseudo-homogeneous suspensions of fine particles, will generally exhibit non-Newtonian behaviour, with their apparent viscosities depending on the rate at which they are sheared, and the time for which they have been subjected to shear. They may also exhibit significant elastic... 

Many materials of practical interest (such as polymer solutions and melts, foodstuffs, and biological fluids) exhibit viscoelastic characteristics they have some ability to store and recover shear energy and therefore show some of the properties of both a solid and a liquid. Thus a solid may be subject to creep and a fluid may exhibit elastic properties. Several phenomena ascribed to fluid elasticity including die swell, rod climbing (Weissenberg effect), the tubeless siphon, bouncing of a sphere, and the development of secondary flow patterns at low Reynolds numbers, have recently been illustrated in an excellent photographic study(18). Two common and easily observable examples of viscoelastic behaviour in a liquid are ... 

In this review, we have described the synthesis of hyperbranched (meth)acry-lates. We have shown that the solution and melt properties are considerably different from their Unear analogs, due to their compact, nonentangled structure. SCV(C)P has become a valuable tool in synthesis of hyperbranched polymers from vinyl monomers. Theoretical investigations help to obtain information on the molecular parameters of the resulting hyperbranched polymers which often could not be obtained experimentally. Studies on the solution and melt properties help one to understand the relationship between the properties and molecular parameters (DB,MW, distribution of branching points), which are extremely valuable from both industrial and scientific viewpoints. 

A comparison of the solution behaviour of PS in both solvents, toluene and frans-decalin, reveals that the limiting power of the molar mass dependence of r 0 (3.35 and 3.28, respectively) is very close to the value of 3.4 observed in highly concentrated solutions and melts. The concentration dependence of r 0, however, is clearly different in each of the solvents ... 

Factorizability has also been found to apply to polymer solutions and melts in that both constant rate of shear and dynamic shear results can be analyzed in terms of the linear viscoelastic response and a strain function. The latter has been called a damping function (67,68). 

Low level wastes (LLW), 23 592. See also Low-level radioactive waste (LLW) from reactors, 77 598 Low-melting lead alloys, 14 779 Low-melting-point indium alloys, 14 196 Low-melting thiodiols, DBTDL-catalyzed step-growth solution and melt polymerization reaction of, 23 744 Low-methoxyl pectins (LM pectins), 4 728 13 69... 

Equation of State of Thermal Polymer Solutions and Melts. 

Conformation and Deformation of Linear Macromolecules in Concentrated Solutions and Melts in the Self-Avoiding Random Walks Statistics... 

Polymeric chains in the concentrated solutions and melts at molar-volumetric concentration c of the chains more than critical one c = (NaR/) ] are intertwined. As a result, from the author s point of view [3] the chains are squeezed decreasing their conformational volume. Accordingly to the Flory theorem [4] polymeric chains in the melts behave as the single ones with the size R = aN112, which is the root-main quadratic radius in the random walks (RW) Gaussian statistics. 

Medvedevskikh Yu. G. Conformation and deformation of linear macromolecules in concentrated solutions and melts in the self-avoiding random walks statistics (see paper in presented book)... 

The size of particles may be increased from molecular dimensions by growing them by crystallisation from both solutions and melts as discussed in Chapter 15. Here, dissolving and recrystallising may provide a mechanism for controlling both particle size and shape. It may be noted, as also discussed in Chapter 15, that fine particles may also be condensed out from both vapours and gases. 

AIChESymp. Ser. (a) 65 (1969) no. 95, Crystallization from solutions and melts (b) 67 (1971) no. 110, Factors affecting size distribution (c) 68 (1972) no. 121, Crystallization from solutions Nucleation phenomena in growing crystal systems (d) 72 (1976) no. 153, Analysis and design of crystallisation processes (e) 76 (1980) no. 193, Design, control and analysis of crystallisation processes (f) 78 (1982) no. 215, Nucleation, growth and impurity effects in crystallisation process engineering (g) 80 (1984) no. 240, Advances in crystallisation from solutions. 

The behaviour of the Q-tensor in shear gives directly the damping function from its definition in Eq. (42) so that h(y)=(l5l4 )Q (Y)ly. This function is plotted in the usual convention in Fig. 17. It is very close to results on monodisperse entangled solutions and melts [64]. 

Often times concentrated polymeric solutions cannot be treated as Newtonian fluids, however, and this tends to offset the simplifications which result from the creeping flow approximation and the fact that the boundaries are well defined. The complex rheological behavior of polymeric solutions and melts requires that nonlinear constitutive equations, such as Eqs. (l)-(5), be used (White and Metzner, 1963) ... 

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