Conformation excluded volume effects

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. 

Cifra, P. and Bleha, T. Conformer populations and the excluded volume effect in lattice simulations of flexible chains in solutions, Polymer, 34 (1993). 3716-3722... 

If the backbone as well as the side chains consist of flexible units, the molecular conformation arises out of the competition of the entropic elasticity of the confined side chains and the backbone [ 153 -155]. In this case, coiling of the side chains can occur only at the expense of the stretching of the backbone. In addition to the excluded volume effects, short range enthalpic interactions may become important. This is particularly the case for densely substituted monoden-dron jacketed polymers, where the molecular conformation can be controlled by the optimum assembly of the dendrons [22-26,156]. If the brush contains io-nizable groups, the conformation and flexibility may be additionally affected by Coulomb forces depending on the ionic strength of the solvent [79,80]. 

It is generally recognized that the average dimensions of a macromolecule are dependent on two factors one related to short distance interactions, those to which conformational analysis is applied, and one concerned with long distance interactions that are often considered in terms of excluded volume effects or covolume effects. One may, therefore, put ... 

As a result of the branched chain architecture, TASP molecules exhibit some unique conformational properties)5 12-14 47 75 76 148 For example, the folding to a compact state proceeds via two distinct steps the onset of secondary structure in the attached peptide blocks followed by their template-directed self-assembly to a three-dimensional packing topology. Due to its characteristic branched chain connectivity, the conformational space accessible in the unfolded state is considerably reduced compared to a linear chain of similar size (excluded volume effect), resulting in a smaller chain entropy. Thus, folded TASP molecules are expected to show higher thermodynamic stability compared to unbranched polypeptides of comparable size. 

The term excluded - volume effect is used or described any effect arising from intrachain or interchain segment - segment interactions. This interaction, which Flory referred to as a long - range interference of monomer units, decidedly affects the number of conformations that the chain can take up for example, those in which two monomers occupy the same point in space are not realizable. Flory s recognition of this effect triggered the development of polymer solution studies for the last four or five decades. 

The incompatibility phenomenon relates to both the occupation of a volume of the solution by macromolecules and the weak repulsion between unlike macromolecules. Phase separation in mixed solutions of a large number of biopolymers studied is sensitive to entropy factors given by the excluded volume of the macromolecules. Phase behaviour strongly depends, therefore, on the molecular weight and the conformation of the macromolecules. The excluded volume effect that depends on the size and shape of the macromolecules determines the phase separation threshold, water partition between the phases of WIW emulsions and biopolymer activity in mixed solution (Tolstoguzov 1986, 1991, 1992). 

The mean-squared, end-to-end distance in Equation [9] is the simplest average property of interest for a polymer chain. Among other physical properties, this quantity appears in the equations of statistical mechanical theories of rubber-like elasticity. In Equation [9], the angle brackets denote the ensemble (or time) average over all possible conformations. The subscript 0 indicates that the average pertains to an unperturbed chain (theta conditions no excluded volume effects are present). (See Figure... 

Firstly, for rigid-chain polymas the excluded volume effects in thermodynamically good solvents (mainly determining the conformation and size of a flexible-chain molecule in solution are negligible. This has been confirmed both experimentally and theoretically ... 

Ideal behaviour for chain conformation is represented by a Gaussian distribution W(r) of end-to-end distances. Excluded volume effects give a much different end distance distribution function. Figure 1, with the biggest differences operating on chains which happen to have their chain ends in proximity (4). 

The chain conformation is determined by the interaction between neighboring segments and the interaction between distant segments along a polymer which, via chain flexibility, are located in each other s vicinity. The former effect determines the local chain stiffness. The latter is referred to as the excluded volume effect and influences the overall conformation. Both types of interaction can be of electrostatic and nonelectrostatic origin. In the absence of excluded volume effects (flexible polyions in a theta state or... 

---