Solutions chain dimensions

In the limit that the number of effective particles along the polymer diverges but the contour length and chain dimensions are held constant, one obtains the Edwards model of a polymer solution [9, 30]. Polymers are represented by random walks that interact via zero-ranged binary interactions of strength v. The partition frmction of an isolated chain is given by... 

Figure 5.8 presents typical spectra taken on both polymer solutions at 300 K (a) and 378 K (b). The PDMS data are represented by open symbols, while the PIB data are shown by full symbols. Let us first look at the data at 378 K. At Q=0.04 A"i (QR =0.S) we are in the regime of translational diffusion, where the contributions of the intrachain modes amount to only 1%. There the spectra from both polymers are identical. Since both polymers are characterized by equal chain dimensions, the equality of the translational diffusion coefficients implies that the draining properties are also equal. In going to larger Q-values, gradually the spectra from the PlB-solutions commences to decay at later times. This effect increases with increasing Q and is maximal at Q=0.4 A" (see Fig. 5.8a). 

Little is known about the chain dimensions of PPC in solution. Recently, a comparison of the hydrodynamic volume of polystyrene (PS) and PPC has been reported for tetrahydrofuran (THF) as solvent in connection with a size exclusion chromatography (SEC) analysis [78, 79]. The basis for the calculation was the assumption of an immortal PO/CO2 alternating copolymerization, and thus that absolute values of Mn relate to starter and PO/CO2 ratios. Narrow molecular weight distributed PPCs with various molecular weights were prepared from adipic acid as starter. The absolute molecular weight has a relationship of K = K(ps)... 

In some specific cases, dissolved macromolecules take up the shape predicted by the above theories of isolated chain molecules. In general, however, the interaction between solvent molecules and macromolecules has significant effects on the chain dimensions. In poor solvents, the interactions between polymer segments and solvent molecules are not that much different from those between different chain segments. Hence, the coil dimensions tend towards those of an unperturbed chain if the dimension of the unperturbed coil is identical to that in solution, the solution conditions are called conditions (ff solvent, temper-... 

Table 2. Size parameters a0 and at characterizing the chain dimensions of polypeptides in solution derived from light-scattering measurements...

Bueche et al. (33) determined chain dimensions indirectly, through measurements of the diffusion coefficient of C1 Magged polymers in concentrated solutions and melts.The self-diffusion coefficient is related to the molar frictional coefficient JVa 0 through the Einstein equation ... 

This treatment assumes that the forces between molecules in relative motion are related directly to the thermodynamic properties of the solution. The excluded volume does indeed exert an indirect effect on transport properties in dilute solutions through its influence on chain dimensions. Also, there is probably a close relationship between such thermodynamic properties as isothermal compressibility and the free volume parameters which control segmental friction. However, there is no evidence to support a direct connection between solution thermodynamics and the frictional forces associated with large scale molecular structure at any level of polymer concentration. 

As pointed out in Chapter III, Section 1 some specific diluent effects, or even remnants of the excluded volume effect on chain dimensions, may be present in swollen networks. Flory and Hoeve (88, 89) have stated never to have found such effects, but especially Rijke s experiments on highly swollen poly(methyl methacrylates) do point in this direction. Fig. 15 shows the relation between q0 in a series of diluents (Rijke assumed A = 1) and the second virial coefficient of the uncrosslinked polymer in those solvents. Apparently a relation, which could be interpreted as pointing to an excluded volume effect in q0, exists. A criticism which could be raised against Rijke s work lies in the fact that he determined % in a separate osmotic experiment on the polymer solutions. This introduces an uncertainty because % in the network may be different. More fundamentally incorrect is the use of the Flory-Huggins free enthalpy expression because it implies constant segment density in the swollen network. We have seen that this means that the reference dimensions excluded volume effect. 

It is well known that addition of neutral salts to polymer solutions reduces the overall dimensions of polymer chains (the salting-out effect) [43, 44]. In general, the reduction in chain dimensions is reflected in the polymer viscosity. An example of salt effects on water soluble polymer with non-ionic characters has been reported in the literature where the precipitation temperature and the viscosity of polyethylene oxide (PEO) were measured to interpret the unusual... 

In summarizing the intrinsic viscosity relations presented in this section, it must be admitted that they represent nothing more than rather small semi-empirical refinements of the Flory excluded volume theory and the Flory-Fox viscosity theory. For a large fraction of the existing body of experimental data, they offer merely a slight improvement in curve-fitting. But for polymers in good solvents it is believed that a more transcendental result has been achieved. The new equations permit more reliable assessment of unperturbed chain dimensions in such cases, and in some instances (e. g., certain cellulose derivatives see Section III B) they offer possible explanations of heretofore paradoxical solution behavior. 

These polymer chain models find their application not so much in the calculation of chain dimensions as in the application of calculated chain conformations for the prediction of other properties of polymer solutions, of which the solution viscosity is the most important. 

Edwards and co-workers (Edwards and Jeffers, 1979 Edwards and Singh, 1979) adapted these techniques to determine chain dimensions in semidilute solutions. Subsequently, Muthukumar and Edwards (1982) formulated RG expressions for the solution free-energy and derived IT explicitly in the low and high concentration limits. The general expression for the free-energy density relative to that of an infinitely dilute solution is... 

Two conflicting theoretical views concerning the flexibility of polymer chains and the role of the volume effect and the draining effect on fry] are discussed in the literature polymer chains of typical flexibility such as vinyl polymer chains, and a large value of Ip] can be interpreted in terms of the excluded volume effect (view point A) polymer chains are semi- or inflexible and their large unperturbed chain dimension is mainly responsible for a large [ry] (view point B). The former has its foundation on the two parameter theory 110. Untill 1977 these inconsistencies constituted one of the most outstanding problems yet unsolved in the science of polymer solutions. 

Table 13. The unperturbed chain dimension A estimated by various methods for solutions of cellulose and its derivatives 7-119)... 

Discuss the Flory 9 temperature by going to the literature and finding out more than what is written in the text Include in your answer a discussion of how chain dimensions change in dilute solutions. 

Another interesting result is obtained from the comparison of the scattering of the sheared samples in the z direction to that of an isotropic sample. Fig. 30 shows the Zimm plot of sample C in the directions x and z for a specimen cut in the x-z plane. The corresponding curve for an isotropic sample, which has also been plotted in the same figure, is found to be identical to within experimental error to the curve in the z direction. This result indicates that the position correlations within the chain in the neutral direction of the shear flow are not affected by the flow, at least up to the values of stress and strain used in the present study. In particular. Table 7 shows that the mean square chain dimension in that direction, Rg 2> which has been determined either in the x-z or in the y-z planes for the various samples, is round to be equal to the radius of gyration of an isotropic sample to within experimental error (Rg 2=82 lA). The same result has been found by Lindner in dilute solutions [31]. 

Figure 15b shows a solid-state spectrum recorded under conditions such that only the mobile portions of the solid PDHS sample are observed. In this polymer (as previously indicated), the mobile portion of the sample consists of the locally disordered phase II and any amorphous material to the extent that it exists. The chemical-shift pattern for the carbons agrees very well with the solution spectrum (Figure 15a). Because carbon resonances are very sensitive to bond conformation (22), this result demonstrates that the phase II portion of the sample has the same average chain conformation as the polymer chains in solution. Although these NMR data permit a comparison of local bond conformations, they do not provide an indication of the more global chain dimensions. Figure 15b shows increased line widths for the carbons near the silicon backbone, with the C-1 resonance almost broadened into the baseline. This broadening reflects the severe restriction of motion near the backbone.

It is weU known that the dimensions of a pol3mer coil in dilute solution are influenced by two factors the polymer solvent interaction and the intramolecular excluded volume effect. The energy of interaction between polymer segments and the molecules of a good solvent tends to increase the chain dimensions, because expansion creates more polymer-solvent contacts. The intramolecular excluded volume effect also increases the dimensions. 

The radius of gyration has the advantage that it also can be used to characterize the dimensions of branched macromolecules (which have more than two chain ends) and cyclic macromolecules (which have no chain ends). Moreover, properties of dilute polymer solutions that are dependent on chain dimensions are controlled by (S rather than r Y. ... 

When a polymer molecule moves in a dilute solution it undergoes frictional interactions with solvent molecules. The nature and effect of these frictional interactions depend upon the size and shape of the polymer molecule. Thus, the chain dimensions of polymer molecules can be evaluated from measurements of their frictional properties [25]. 

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