Excluded-volume effect onset

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 present chapter aims to describe some typical contributions from recent studies on stiff polymers in dilute solution. We will be mainly interested in (1) applicability of the wormlike chain model to actual polymers, (ii) validity of the hydrodynamic theories [2-4] recently developed for this model, and (iii) the onset of the excluded-volume effect on the dimensions of semi-flexible polymers. Yamakawa [5, 6] has generalized the wormlike chain model to one that he named the helical wormlike chain. In a series of papers he and his collaborators have made a great many efforts to formulate its static and dynamic properties in dilute solution. In fact, the theoretical information obtained is now comparable in both breadth and depth to that of the wotmlike chain (see Ref. [6] for an overview). Unfortunately, however, most of the derived expressions are too complex to be of use for quantitative anal) sis and interpretation of experimental data. Thus, we only have a few to be considered with reference to the practical aspects of the helical wormlike chain, and have to be content with mentioning the definition and some basic features of this novel model. 

Since A"(ni<) begins to depart from zero at ni< near unity, it follows from eq 4.6 that the theoretical critical contour length Lc for the onset of the excluded-volume effect on chain dimensions is approximately given by... 

Transport coefficients of actual polymers should also show die onset of the excluded-volume effect at certain critical contour lengths. It is interesting to study how such lengths can be estimated experimentally and what relations exist between them and Lc or Lc. However, these problems remain almost unexplored. 

As mentioned above, the excluded-volume effect on (S ) of PS in toluene begins to appear when XL exceeds 3. On the other hand, as was early found by Norisuye and Fujita, typical stiff chains in good solvents remain unperturbed up to AL - 50. This difference in the onset of volume effect between flexible and... 

It is pertinent to consider separately the enhancement effect of salt on two steps the initiation step (onset of the flow) and the structured flow. The transport rates are related to the properties of the final structured flow and are contributed from the effects on both steps. The effect on the initiation step is clearly noticed since the critical PVP concentrations for the occurrence of the structured flow depended on the kind of salt. Effects of a salt on the cross diffusion constants of the two polymer components will be examined on both excluded volume and frictional effect. The effect on the excluded volume interaction between the two polymer components is expected to be small. This expectation is partly supported by the result that coil dimension of PVP was not influenced by the addition of a salt at 2 M in the cases of three salts LiCl, NaCl and CsCI, while these salts showed quite diverse effects on the trrmsport rates of PVP. Since viscosities vary with the kind and the concentration of salt, frictional coefficients are influenced by the presence of a salt. In this respect cross diffusion constants may be affected by salt through a change in viscosity of the medium. 

The nematic phase being the liquid crystal of highest symmetry, its condensation from the isotropic liquid should be the simplest to describe. Indeed, molecular theories convincingly explain the natural onset of nematic ordering in a population of anisotropic molecules with excluded volume interaction (Onsager) or in mean field theory (Maier-Saupe). Regarding the effect of symmetry on the isotropic to nematic (I-N) phase transition, the phenomenological approach is useful too. 

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