Polymer solution behavior excluded - volume effect

Equation (23) predicts a dependence of xR on M2. Experimentally, it was found that the relaxation time for flexible polymer chains in dilute solutions obeys a different scaling law, i.e. t M3/2. The Rouse model does not consider excluded volume effects or polymer-solvent interactions, it assumes a Gaussian behavior for the chain conformation even when distorted by the flow. Its domain of validity is therefore limited to modest deformations under 0-conditions. The weakest point, however, was neglecting hydrodynamic interaction which will now be discussed. 

In a blend solution, the interaction parameter x of the Flory-Huggins theory is zero (the chain end effect is negligible) and independent of temperature. Otherwise, a temperature-dependent x can lead to a thermorhe-ologically complex behavior of the polymer solution sj tem, which would disallow the apphcation of the time-temperature superposition principle. A theoretical analysis indicates that if M M2, the system is free of the excluded volume effect that will cause the component-two chain to expand in other words, the chain coil remains Gaussian. Here, we consider polystyrene blend solutions with Mi slightly smaller than Mg (= 13,500 for polystyrene). In such a system, the condition M > M2 can be easily satisfied. Furthermore, the solvent, being chains of more than ten Rouse... 

In solution, we have considered the scaling behavior of a single PE (Sect. 2.7.3.1). The importance of the electrostatic persistence length was stressed. The Manning condensation of counterions leads to a reduction of the effective linear charge density (Sect. 2.7.3.1.1). Excluded volume effects are typically less important than for neutral polymers (Sect. 2.7.3.1.2). Dilute PE solutions are typically dominated by the behavior of the counterions. So is the large osmotic pressure of dilute PE solutions due to the entropic contribution of the counterions (Sect. 2.7.3.2). Semidilute PE solutions can be described by the RPA, which in particular yields the characteristic peak of the structure factor. 

The Monte Carlo sample then reflects the number of conformations of polymer molecules. This means that observable parameters describing the solution behavior of polysaccharides are averages of the properties of individual conformations. This approach yields properties corresponding to the equilibrium state of the chain. Results refer to a model for an unperturbed chain that ignores the consequences of the long range excluded volume effect, because only nearest-neighbor interactions are accounted for in the computation of the, 4 surfaces. 

Eq. (9.64) consists of three terms. The first describes the Donnan effect, which states that in osmosis the small ions are not distributed equally on the two sides of the membrane. The Donnan effect always causes an increase in osmotic pressure. To minimize this effect, the protein solution should have high ionic strength or should be near the isoelectric pH. The second term represents the excluded volume effect and the interaction between charges on different macro ions. It is basically similar to the parameter Xi in the properties of synthetic polymer solutions but is a little more complicated because of the charges involved. The third term involves the interaction between macro inons and the actual binding of small ions. This term is particularly important to the study of the behavior of proteins in dilute salt solutions. 

As with flexible chains, most studies of conformational behavior of stiff chains have involved light scattering and intrinsic viscosity studies of dilute polymer solutions. Excluded volume effects are of much diminished significance for stififer chains, so measured persistence lengths usually show only a mild dependence on the nature of the solvent. In fact, Norisuye and Fujita [72] have shown that excluded volume effects become measurable only when chains are very long (L 100 q). Thus, the choice of solvent is normally of less importance in studying the conformation of stiff chains than it is for flexible ones. Temperature, however, frequently has a pronounced impact on the value of q for stiff chain polymers [73]. 

Decreasing the degree of crosslinking will increase the water uptake for a mass of dry gel, though compromises in the efficiency will result. The effect of crosslinks on the separation of vitamin B-12, a nonionic solute of molecular weight 1355, is shown in Fig. 4 [16]. As the crosslink density decreases, the polymer chain length between crosslinks increases, yielding a looser structure which vitamin B-12 can more easily penetrate. The behavior fits well with the prediction from Flory excluded volume theory [16] ... 

Summary The classical treatment of the physicochemical behavior of polymers is presented in such a way that the chapter will meet the requirements of a beginner in the study of polymeric systems in solution. This chapter is an introduction to the classical conformational and thermodynamic analysis of polymeric solutions where the different theories that describe these behaviors of polymers are analyzed. Owing to the importance of the basic knowledge of the solution properties of polymers, the description of the conformational and thermodynamic behavior of polymers is presented in a classical way. The basic concepts like theta condition, excluded volume, good and poor solvents, critical phenomena, concentration regime, cosolvent effect of polymers in binary solvents, preferential adsorption are analyzed in an intelligible way. The thermodynamic theory of association equilibria which is capable to describe quantitatively the preferential adsorption of polymers by polar binary solvents is also analyzed. 

We have introduced three characteristic lengths 1, i e> and to describe the effects of chain overlap on the density fluctuation correlation, the intrachain excluded-volume interaction, and the intrachain hydrodynamic interaction, respectively. In the following chapters, we will illustrate the important roles played by them in understanding the static and dynamic behavior of polymer solutions. 

Abstract This introductory chapter provides a brief (textbook-like) survey of important facts concerning the conformational and dynamic behavior of polymer chains in dilute solutions. The effect of polymer-solvent interactions on the behavior of polymer solutions is reviewed. The physical meanings of the terms good, 9-, and poor thermodynamic quality of the solvent are discussed in detail. Basic assumptions of the Kuhn model, which describes the conformational behavior of ideal flexible chains, are outlined first. Then, the correction terms due to finite bond angles and excluded volume of structural units are introduced, and their role is discussed. Special attention is paid to the conformational behavior of polyelectrolytes. The pearl necklace model, which predicts the cascade of conformational transitions of quenched polymer chains (i.e., of those with fixed position of charges on the chain) in solvents with deteriorating solvent quality, is described and discussed in detail. The incomplete (up-to-date) knowledge of the behavior of annealed (i.e., weak) polyelectrolytes and some characteristics of semiflexible chains are addressed at the end of the chapter. 

---