Coil expansion factor

Although the emphasis in these last chapters is certainly on the polymeric solute, the experimental methods described herein also measure the interactions of these solutes with various solvents. Such interactions include the hydration of proteins at one extreme and the exclusion of poor solvents from random coils at the other. In between, good solvents are imbibed into the polymer domain to various degrees to expand coil dimensions. Such quantities as the Flory-Huggins interaction parameter, the 0 temperature, and the coil expansion factor are among the ways such interactions are quantified in the following chapters. 

We saw in Sec. 1.11 that coil dimensions are affected by interactions between chain segments and solvent. Both the coil expansion factor a defined by Eq. (1.63) and the interaction parameter x are pertinent to describing this situation. 

Next we consider the situation of a coil which is unperturbed in the hydro-dynamic sense of being effectively nondraining, yet having dimensions which are perturbed away from those under 0 conditions. As far as the hydrodynamics are concerned, a polymer coil can be expanded above its random flight dimensions and still be nondraining. In this case, what is needed is to correct the coil dimension parameters by multiplying with the coil expansion factor a, defined by Eq. (1.63). Under non-0 conditions (no subscript), = a(rg)Q therefore under these conditions we write... 

Next we shall examine the molecular weight dependence of the coil expansion factor a to see if the latter can explain the observations of a s greater than 0.5. 

Our primary objective in undertaking this examination of the coil expansion factor was to see whether the molecular weight dependence of a could account for the fact that the Mark-Houwink a coefficient is generally greater than 0.5 for T 0. More precisely, it is generally observed that 0.5 < a < 0.8. This objective is met by combining Eqs. (9.55) and (9.68) ... 

What is especially significant about Eq. (9.68) is the observation that the coil expansion factor a definitely increases with M for good solvents, meaning that-all other things being equal longer polymer chains expand above their 0 dimensions more than shorter chains. Even though the dependence of a on... 

The radius of gyration is expected to be different under theta and nontheta conditions since the extent of coil swelling due to imbibed solvent changes with solvent goodness. We define a coil expansion factor a as follows ... 

It follows from the theory that the q-dependence of the coil expansion factor or =... 

Figure 2.7 Random coils in solvents of different solvent power a is the linear coil expansion factor which according to the definition is equal to 1 in a theta solvent.

The ellipsoid polymer model upon which Eq. 15 is based [65] has been abandoned because it predicts a molecular weight dependence of the coil expansion factor that does not agree with experimental data. Thus, Eq. 15 may be regarded as purely empirical and rewritten as... 

There is a relationship between kh and the coil expansion factor or coefficient of expansion, a, which is a measure of the extent of the expansion of the polymer coil in a particular solvent. In good solvents, the coil is more extended than in poor solvents and a is correspondingly larger. The Huggins constant seems to vary with (3,14,22,23). One expression for this is (Ref. 23)... 

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