Polymer molecule dimensions

A method that has won general favor is gel permeation chromatography. Basically, polymer samples are separated by size of molecule. The separation is accomplished by using beads of a rigid, porous gel whose pores are about the same size as polymer molecule dimensions (see Fig. 1-21). 

An apparent negative inaccessible displaceable volume was obtained for several cores when the brine-flush portion of the flow test was evaluated using Eq. 1. The three cores exhibiting this behavior (Cores 42, 48, and 73, Table 2) ate of sufficiently low permeability that a substantial fraction of the pores could have diameters smaller than nominal polymer-molecule dimensions in solution.This could cause plugging of the tighter pores, with trapping of subsequent flowing polymer. Release of... 

We began this section with an inquiry into how to define the size of a polymer molecule. In addition to the molecular weight or the degree of polymerization, some linear dimension which characterizes the molecule could also be used for this purpose. For purposes of orientation, let us again consider a hydrocarbon molecule stretched out to its full length but without any bond distortion. There are several features to note about this situation ... 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

In addition to the size of the molecules and their distribution, the shapes or structures of individual polymer molecules also play an important role in determining the properties and processability of plastics. There are those that are formed by aligning themselves into long chains of molecules and others with branches or lateral connections to form complex structures. All these forms exist in either two or three dimensions. 

Although R2 is the easiest quantity to be obtained theoretically, there is no straigthforward experimental method for its determination. For this reason, two other quantities are widely in use to characterize the dimensions of a randomly coiled polymer molecule ... 

If we consider the size of a polymer molecule, assuming that it consists of a freely rotating chain, with no constraints on either angle or rotation or of which regions of space may be occupied, we arrive at the so-called unperturbed dimension, written (r)o Such an approach fails to take account of... 

Deb P.C., Chatterjee S.R. Unperturbed dimension of polymer molecules from viscosity measurements. Die Makromolekulare Chemie 120,1 (1968) 49-57. 

Apart from their utility in determining the correction factor 1/P( ), light-scattering dissymmetry measurements afford a measure of the dimensions of the randomly coiled polymer molecule in dilute solution. Thus the above analysis of measurements made at different angles yields the important ratio from which the root-mean-square... 

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. 

If the contribution of a polymer molecule to the viscosity of the solution is in reality proportional to the cube of its linear dimension, the intrinsic viscosity in a -solvent should be proportional to the square root of the molecular weight. The influence of intramolecular interactions on the configuration having been neutralized by this choice of solvent medium, it becomes possible to examine separately the hydro-dynamic aspects of the problem. 

Theory presented earlier in this chapter led to the expectation that the frictional coefficient /o for a polymer molecule at infinite dilution should be proportional to its linear dimension. This result, embodied in Eq. (18) where P is regarded as a universal parameter which is the analog of of the viscosity treatment, is reminiscent of Stokes law for spheres. Recasting this equation by analogy with the formulation of Eqs. (26) and (27) for the intrinsic viscosity, we obtain ... 

It has been shown, by theories of the frictional properties of polymer molecules in solution, that the intrinsic viscosity is proportional to the effective hydrodynamic volume of the molecule in solution divided by its Molecular weight. The effective volume is proportional to the cube of a linear dimension... 

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