Random coil polymer diffusion

The fluid resistance experienced by a macromolecular solute moving in dilute solution depends on the shape and size of the molecule. A number of physical quantities have been introduced to express this. Typical ones are intrinsic viscosity [ry], limiting sedimentation coefficient s0, and limiting diffusion coefficient D0. The first is related to the rotation of the solute, while the last two are concerned with the translational motion of the solute. A wealth of theoretical and experimental information about these hydrodynamic quantities is already available for randomly coiled chains (40, 60). However, the corresponding information on non-randomly coiled polymers is as yet rather limited in number and in variety. 

The dimensions of a randomly coiled polymer molecule are a topic that appears to bear no relationship to diffusion however, both the coil dimensions and diffusion can be analyzed in terms of random walk statistics. Therefore we may take advantage of the statistical argument we have developed to consider this problem. 

Based on properties in solution such as intrinsic viscosity and sedimentation and diffusion rates, conclusions can be drawn concerning the polymer configuration. Like most of the synthetic polymers, such as polystyrene, cellulose in solution belongs to a group of linear, randomly coiling polymers. This means that the molecules have no preferred structure in solution in contrast to amylose and some protein molecules which can adopt helical conformations. Cellulose differs distinctly from synthetic polymers and from lignin in some of its polymer properties. Typical of its solutions are the comparatively high viscosities and low sedimentation and diffusion coefficients (Tables 3-2 and 3-3). 

Yasuda et a .25 have developed die concept of a homogeneous solvent-swollen membrane in which thermally induced movement of segments of randomly coiled polymer molecules leaves an interstitial free volume available for solute transport. They concluded that the permeability characteristics of highly swollen systems cannot he represented try a single coefficient. Values of solute ned solvent permeabilities depend ou the conditions of mnesurement, in particular, the magnitude of diffusive flux relative to convnetive flux. 

First, the above summarized the published literature on self-diffusion and probe diffusion of random-coil polymers in solution. The concentration dependences of > and Dp are essentially always described well by a stretched exponential (eq. 15) in the matrix concentration c. On a log-log plot of D, against c, stretched exponentials appear as smooth curves, while scaling ( power-law) behavior leads to straight lines. Almost without exception, log-log plots of measured D,(c) give smooth curves, not straight lines. Correspondingly, the hypothesis that the concentration dependence of D, c) shows scaling ( power-law) behavior is uniformly rejected by the published literature. 

Fig. 3. The ramified fractal nature of diffuse interfaces is shown for (top) a computer simulated 2-d monomer-monomer interface where the heavy region represents the connected monomers on one side, (middle) a simulated 2-d random coil polymer interface at the reptation time, and (bottom) electrochemically deposited Silver diffusing in polyimide with the unconnected metal atoms removed to show the fractal diffusion front of the connected metal atoms. (Wool and Long)...

R. Cush, P. S. Russo, Z. Kucukyavuz, et al. Rotational and translational diffusion of a rodlike virus in random coil polymer solutions. Macromolecules, 30 (1997), 4920-4926. 

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. 

For macromolecules, it is important to distinguish between random coils (most synthetic polymers) and globular molecules (most proteins). For the former, the molecular volume is approximately proportional to the square root of the molecular weight. The diffusion coefficient of polyst n ene in toluene was estimated by Giddings et al. [19]... 

Equation (44) relates the diffusion coefficient to gel properties. From scaling laws applied to the conditions for overlap of random coils it is concluded that K and G as well as the friction coefficient/depend on the polymer concentration. In case of a swollen polymer, K, G, and/depend on the degree of swelling,... 

Figure 4. Flory-Mandelkern correlation of intrinsic viscosity, molecular weight, and translational diffusion coefficient for a variety of polymer solvent systems, demonstrating the insensitivity of these data to the structure of the macromolecule ( X PS/tetrahydrofuran (37) (O), protein random coils in 6M guanidine hydrochloride-0,IM mercaptoethanol (26) (X), tobacco mosaic virus in aqueous solution (11) ( ), bovine serum albumen in aqueous solution (37).

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