Coil expansion

In a good solvent, the end-to-end distance is greater than the 1q value owing to the coil expansion resulting from solvent imbibed into the domain of the polymer. The effect is quantitatively expressed in terms of an expansion factor a defined by the relationship... 

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... 

In elongational flow, the entanglement regime was observed at much lower concentrations, even below [r ] c = 0.1 [169], The effect was initially thought to be the result of coil expansion in flow, but was later discarded in favor of the lifetime for entanglement formation, under dynamic conditions of flow. 

The behaviour in solution of the first type of polyions compared with that of uncharged molecules is more involved in that the coil expansion is affected not only by the solvent but also by the electric field formed by the polyion itself, by the counterions and by the ions of other low-molecular-weight electrolytes, if present in the solution. Infinite charge dilution cannot be achieved by diluting the poly electrolyte solution, as a local high-intensity... 

On macroscopic length scales, as probed for example by dynamic mechanical relaxation experiments, the crossover from 0- to good solvent conditions in dilute solutions is accompanied by a gradual variation from Zimm to Rouse behavior [1,126]. As has been pointed out earlier, this effect is completely due to the coil expansion, resulting from the presence of excluded volume interactions. 

Since the degree of expansion of the polymer coils is directly dependent on the solvating power of the solvent, under otherwise comparable conditions, both a and [q] provide a measure of the goodness of a solvent high values of a and [q] (at constant molecular weight and temperature) indicate remarkable coil expansion and therefore a good solvent. Low values of a and [q] indicate a bad solvent. For example, the values a for poly(vinyl acetate) in methanol and acetone are 0.60 and 0.72, respectively. 

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 ... 

For high molecular weight polymers in good solvents, fo] exceeds fo]0 because of coil expansion under nondraining conditions that is, as more solvent enters the coil domain than would be present under 0 conditions, Equation (92) continues to apply, with R replacing R2gfi. Using Equation (90) to quantify this expansion effect, we obtain... 

As a consequence, the given proof for the validity of the stress-optical law remains formally true. The same holds for the relation between the diagonal components of the macroscopic stress tensor and the stored free energy per unit of volume. In fact, it does not make any difference, whether this energy is thought to be built up of the contributions of all complete chains or all subchains contained in the unit of volume. Only one statement will be revized, viz. that with respect to the coil expansion of the entire chain. A detailed discussion of this point will be given in Section 3.3. 

This expression is by the factor (rf/i/rf) smaller than the one originally given by Peterlin (76). However, since the coil expansion is a qualitative measure of the state of deformation of coil molecules in laminar shear flow and, moreover, the first relaxation time is, in general, by far the largest one, the original equation of Peterlin can be used unchanged, if desired. 

This means that the only effect of the q factor on the [77]-M relationship is that of the excluded volume due to coil expansion in a good solvent. It follows from Equations 8 and 16 that... 

The properties of cellulosic graft copolymers have been studied to a considerable extent but mainly in the form of grafted fibers or films of ill-defined composition. However, a few properties have been measured on well defined grafts (147). It was found that solutions of cellulose acetate-polystyrene grafts in dimethyl formamide are less tolerant to the addition of polystyrene than cellulose acetate itself. This result was attributed to the greater coil expansion in the case of the graft copolymer. On the other hand, the tolerance of the grafts to each homo-... 

Stockmayer and Casassa163 realized that for flexible coils this factor varies with the coil expansion but still the more general equation... 

Fig. IS. Molecular-weight dependence of sedimentation constant (rc) and intrinsic viscosity ( ), for various degrees of draining and coil expansion. Full line is for coiled polymers without draining. Dotted curve is for rigid ellipsoids of revolntion at various axial ratios p. Experimental points a, cellulose nitrate in ethyl acetate 729) b, cellulose nitrate in acetone (181) c, cellulose acetate in acetone (125) d., ethyl cellulose in ethyl acetate 223 ) e, ethyl bydroxyethyl cellulose in water (772)...

This scheme implies that the compact conformation having tram azobenzene residues is a constrained form capable of storing a certain amount of strain energy. The strain energy causes coil expansion, and it is released during the unfolding process. 

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