Polymer Molecules in Dilute Solution

B. Zimm. Dynamics of polymer molecules in dilute solutions viscoelasticity, low birefringence and dielectric loss. J Chem Phys 24 269-278, 1956. 

Zimm, BH, Dynamics of Polymer Molecules in Dilute Solution Viscoelasticity, Flow Birefringence and Dielectric Loss, Journal of Chemical Physics 24, 269, 1956. 

Fig. 34.—Schematic representation of polymer molecules in dilute solution.

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. 

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

As is well known, dynamic properties of polymer molecules in dilute solution are usually treated theoretically by Brownian motion methods. Tn particular, the standard approach is to use a Fokker-Planck (or Smoluchowski) equation for diffusion of the distribution function of the polymer molecule in its configuration space. 

We will also deal with sohm features of the behaviour of rigid-chain polymer molecules in dilute solutions with emphasis on their dinamooptical and electroop-tical properties. 

The still faster ( nsec) dynamics of local motions of polymer molecules in dilute solutions have been investigated by Ediger and coworkers (Zhu and Ediger 1995, 1997). They find that the rates of these local motions of a few bonds are not proportional to the solvent viscosity, unless the solvent reorientation rate is fast compared to the polymer local motion. Thus, for local motions (such as bond reorientations) of polymer molecules, Stokes law of drag does not always hold. 

The viscosity method makes use of the fact that the exponent, a, in the Mark-Houwink equation (see Frictional Properties of Polymer Molecules in Dilute Solution), rj = KM° , is equal to 0.5 for a random coil in a theta-solvent. A series of polymers of the same type with widely different known molecular weights is used to determine intrinsic viscosities [t ] at different temperatures and hence a at different temperatures. The theta-temperature can thus be determined either by direct experiment or, if it is not in the measurable range, by calculation. 

FRICTIONAL PROPERTIES OF POLYMER MOLECULES IN DILUTE SOLUTION... 

Figure 3-13. Bead-and-spring representation of a real polymer molecule in dilute solution.

Assuming that the RMS end-to-end distance is an approximate measure of the diameter of the spherical, coiled polymer molecule in dilute solution, compare the volume occupied by one molecule of polyisobutylene of molecular weight 10 ... 

Frictional Properties of Polymer Molecules in Dilute Solution... 

The process [1] goes to the right in the dissolution of the pure polymer, in the dilution of a polymer solution fran above the critical concentration v ere the molecules are in contact, and in the expansion of an essentially isolated polymer molecule in dilute solution. Conversely, the contraction of an essentially isolated polymer molecule, or the precipitation of the polymer from dilute solution (where the "precipitate" is a more concentrated solution of the polymer) involves the process [1] goir to the left. Thus anythir that favors an increase in the number of M M contacts causes molecular contraction and then (possibly) precipitation. Because of this parallel between solubility and conformation, measurements of molecular dimensions, or equivalently (and more simply) of the intrinsic viscosity [yj], can be used to distinguish those effects which may eventually le to the precipitation of the polymer from those which enhance the solubility of the polymer. Such conformational studies are particularly useful because solubility for polymers is very much an "all-or-none" phenomenon, so that superficially one cannot distinguish a system which is on the verge of precipitation from one well removed from this condition. 

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