Solutions dilute, configurational dimensions

A comprehensive investigation of solution properties in various solvents and with a multitude of electrolytes has yielded an important result. Distance parameters can be obtained for all property equations from chemical evidence R = a + ns, where a is the center-to-center distance of closest approach of cation and anion in the solution, s the dimension of an oriented solvent molecule, and n = 0, 1, or 2. An example is given in Table HI, where f exp is the distance parameter from heat of dilution measurements and f caic the quantity calculated from a configuration M +(H20)2S04. ... 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

For polystyrene fractions in diethyl phthalate solution (30000average value of 1.6 x 10 18 ( 50%). In dilute solution e/36M is 1.27 x 10 18 for polystyrene (21). No systematic variations with concentration, molecular weight or temperature were apparent, the scatter of the data being mainly attributable to the experimental difficulties of the diffusion measurements. The value of Drj/cRT for an undiluted tagged fraction of polyfn-butyl acrylate) m pure polymer was found to be 2.8 x 10 18. The value of dilute solution data for other acrylate polymers (34). Thus, transport behavior, like the scattering experiments, supports random coil configuration in concentrated systems, with perhaps some small expansion beyond 6-dimensions. 

More quantitative chemical evidence for random coil configuration comes from cyclization equilibria in chain molecules (49). According to the random coil model there must be a very definite relationship among the concentrations of x-mer rings in an equilibrated system, since the cyclization equilibrium constant Kx should depend on configurational entropy and therefore on equilibrium chain and ring dimensions. Values of /Af deduced from experimental values on Kx for polydimethylsiloxane, both in bulk and in concentrated solution, agree very well with unperturbed dimensions deduced from dilute solution measurements(49). 

The above calculations assume that the gross chain conformations are those of a random walk, which is the case in the melt. However, for an isolated polymer molecule in a dilute solution, the average conformation is affected by excluded-volume interactions between one part of the chain and another. Because the chain must avoid self-intersection, the conformation of the chain will be that of a self-avoiding walk, rather than a random walk, if the solution is athermal—that is, if all interactions are negligible except excluded volume. Self-avoiding walks lead, on average, to more expanded coil dimensions, since expanded configurations are less likely than contracted ones to lead to self-intersection of the chain. Thus, in an athermal solution, the mean-square end-to-end dimension of a polymer molecule scales as... 

Studies of the dilute solution behavior of polymers with a specific stereostructure have revealed that the unperturbed dimensions may depend on the chain configuration. 

The behaviour of diluted solutions is related to the relation between the viscosity and the chain characteristics (structure, configuration, conformation, etc). Usually, the polymer solutions are treated as two-phase systems, consisting from mechanical elements, the macromolecules, immersed into a continuous media, the solvent. For long time, it was considered that the solvent acts to the polymer macromolecules in the same manner in which a fluid exerts forces about a small particle suspended in it. However, the extension of this model to the polymer solution is not adequate since, the ratio between the dimensions of macromolecules and those of solvent molecules essentially differs by that between the dimensions of a solid immersed particle and solvent molecules. On the other side, the flexible macromolecules, randomly coiled, can not be assimilated with the solid particles and therefore the typical relations applied to solid suspensions in liquids can not be used in this case. 

Equations (83) and (84) provide a molecular interpretation of the thermoelastic data through equation (89). This equation establishes the relationship between the purely thermodynamic quantity f /f and its molecular counterpart of dlno/dT, which can be interpreted in terms of the rotational isomeric state theory of chain configurations. It permits comparison of the change of the unperturbed dimensions o obtained by thermoelastic measurements on polymer chains in the bulk (in network structures) with that obtained by viscosity measurements on chains of the same polymer, essentially isolated in dilute solution. 

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