Polymer solutions general

Staverman, A. J., "The Entropy of High Polymer Solutions. Generalization of Formulae," Rec. Trav. Chim. Pays-Bas., 69, 163 (1950). 

Polymer solutions generally exhibit viscous behavior when flowing in capillary tubes with constant diameters. However, in porous media where capillary diameters change rapidly, polymer chains are pulled or contracted to exhibit elastic behavior. The elastic behavior leads to a higher apparent viscosity, as described by Eq. 6.8. 

The bulk state, sometimes called the condensed or solid state, includes both amorphous and crystalline polymers. As opposed to polymer solutions, generally there is no solvent present. This state comprises polymers as ordinarily observed, such as plastics, elastomers, fibers, adhesives, and coatings. 

The liquid crystal-forming polymer solutions generally exhibit the anomalous viscometric behavior as a function of polymer concentration or temperature, which is due to the phase transformation of the solutions. 

Probes in small-M polymer solutions generally show Stokes-Einsteinian behavior with r]p, r], including 160 nm spheres(16) in 101 145 kDa PMMArCHCls for rj/rjs up to 10, 20, and 230 nm probes in aqueous 20 kDa dextran(12), and 20-1500 nm spheres in aqueous 50 kDa polyacrylic acid(lO). On the other hand, 49 and 80 nm probes in aqueous 90 kDa poly-L-lysine show small c-independent deviations from Stokes-Einsteinian behavior(14). Stokes-Einsteinian behavior is also found in some large-M systems. Onyenemezu, et al.(l9) find Stokes-Einsteinian behavior within experimental accuracy for 1100 kDa polystyrene solutions having rj/rjs as large as 100. Turner and Hallett(l) and Phillies, et a/. (12) reveal 1... 

Two of the most important functions in the application of neutron scattering are the use of deuterium labelling for the study of molecular confomiation in the bulk state and the use of deuterium solvent in polymer solutions. In the following, we will consider several different applications of die general fomuda to deuteration. 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

For preparative purposes batch fractionation is often employed. Although fractional crystallization may be included in a list of batch fractionation methods, we shall consider only those methods based on the phase separation of polymer solutions fractional precipitation and coacervate extraction. The general principles for these methods were presented in the last section. In this section we shall develop these ideas more fully with the objective of obtaining a more narrow distribution of molecular weights from a polydisperse system. Note that the final product of fractionation still contains a distribution of chain lengths however, the ratio M /M is smaller than for the unfractionated sample. 

We shall be interested in determining the effect of electrolytes of low molecular weight on the osmotic properties of these polymer solutions. To further simplify the discussion, we shall not attempt to formulate the relationships of this section in general terms for electrolytes of different charge types-2 l, 2 2, 3 1, 3 2, and so on-but shall consider the added electrolyte to be of the 1 1 type. We also assume that these electrolytes have no effect on the state of charge of the polymer itself that is, for a polymer such as, say, poly (vinyl pyridine) in aqueous HCl or NaOH, the state of charge would depend on the pH through the water equilibrium and the reaction... 

The scattering of visible light by polymer solutions is our primary interest in this chapter. However, since is a function of the ratio R/X, as we saw in the last section, the phenomena we discuss are applicable to the entire range of the electromagnetic spectrum. Accordingly, a general review of the properties of this radiation and its interactions with matter is worthwhile before a specific consideration of scattering. 

HoUow-fiber fabrication methods can be divided into two classes (61). The most common is solution spinning, in which a 20—30% polymer solution is extmded and precipitated into a bath of a nonsolvent, generally water. Solution spinning allows fibers with the asymmetric Loeb-Soufirajan stmcture to be made. An alternative technique is melt spinning, in which a hot polymer melt is extmded from an appropriate die and is then cooled and sohdified in air or a quench tank. Melt-spun fibers are usually relatively dense and have lower fluxes than solution-spun fibers, but because the fiber can be stretched after it leaves the die, very fine fibers can be made. Melt spinning can also be used with polymers such as poly(trimethylpentene), which are not soluble in convenient solvents and are difficult to form by wet spinning. 

The choice of initiator system depends on the polymerization temperature, which is an important factor in determining final product properties. Cold polymers are generally easier to process than hot polymers and in conventional cured mbber parts have superior properties. The hot polymers are more highly branched and have some advantages in solution appHcations such as adhesives, where the branching results in lower solution viscosity and better cohesion in the final adhesive bond. 

In a number of works (e.g. [339-341]) the authors sought to superimpose graphically the flow curves of filled melts and polymer solutions with different filler concentrations however, it was only possible to do so at high shear stresses (rates). More often than not it was impossible to obtain a generalized viscosity characteristic at low shear rates, the obvious reason being the structurization of the system. 

The following qualitative picture emerges from these considerations in weak flow where the molecular coils are essentially undeformed, the polymer solution should behave approximately as a Newtonian fluid. In strong flow of a highly dilute polymer solution where the macroscopic velocity field can still be approximated by the Navier-Stokes equation, it should be expected, nevertheless, that in the immediate proximity of a chain, the fluid will be slowed down because of the energy intake to stretch the molecular coil thus, the local velocity field may deviate from the macroscopic description. In the general case of polymer flow,... 

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... 

In order to begin this presentation in a logical manner, we review in the next few paragraphs some of the general features of polymer solution phase equilibrium thermodynamics. Figure 1 shows perhaps the simplest liquid/liquid phase equilibrium situation which can occur in a solvent(l)/polymer(2) phase equilibrium. In Figure 1, we have assumed for simplicity that the polymer involved is monodisperse. We will discuss later the consequences of polymer polydispersity. 

Polymer solutions always exhibit large deviations from Raoult s law, though at extreme dilutions they do approach ideality. Generally however, deviation from ideal behaviour is too great to make Raoult s law of any use for describing the thermodynamic properties of polymer solutions. 

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