Coiled polymer molecules

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 ... 

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... 

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. 

B 17 Bxjeche, A. M. Dimensions of coiling polymer molecules from viscosity and light scattering. J. Am. Chem. Soc. 71, 1452 (1949). 

The methods of conformational statistics, discussed so far, had as starting point the real polymer chain. The aim was to relate the dimensions of the coiled polymer molecule statistically to the mutual displaceability of the chain atoms. Nearly exact relationships are obtained for a large number of freely jointed or freely rotating elements. Under conditions of restricted movability, however, the statistical equations can generally not be solved and empirical factors like s, a and a are introduced. 

As was mentioned in Chap. 15, the strong effect of M on r/ for M > Mcr is attributed to entanglements between coil polymer molecules. Obviously, the conditions become less favourable for entanglements as the polymer concentration decreases. So Mcr increases with decreasing concentration, and vice versa. 

Figure 2.13 Schematic representation of a coiled polymer molecule showing the end-to-end distance.

Figure A2.1 (a) Schematic representation of a coiled polymer molecule showing the end-to-end distance, (b) Diagram showing a coiled polymer molecule of end-to-end distance r in a rectangular coordinate system with one chain end fixed at the origin.

Swelling. Figure 5.3 schematically depicts a coiled polymer molecule and illustrates that such a particle encloses a lot of solvent (although the enclosed solvent is not completely immobilized see Section 6.2.2). This is comparable to the entrapment of solvent in aggregates mentioned above. Protein molecules always contain some water, i.e., are swollen. ... 

Consideration of another major modification that has been applied to the flexible chain model seems pertinent at this point. It has long been appreciated that the velocity field of the solvent would be perturbed deep inside a coiled polymer molecule. It is clear that this effect is not considered in the above treatment because the viscous drag is given as psXi in equation (3-51) irrespective of whether Xi happens to be inside the coiled molecule or on its surface. Thus one might expect the Rouse formulation to be most applicable to polymer-solvent systems in which the elongated conformations of polymer chains predominate. For such conformations, there would be little shielding of one part of a molecule by another part of the same molecule. This is the case in... 

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. 

For random-coil polymer molecules, should be taken as the radius of gyration, which is generally two to three times the radius calculated from the molar volume. 

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 ... 

We now consider the intensity of independent scattering from a random coil polymer molecule, consisting of (N + 1) beads connected by N bonds and obeying the Gaussian approximation (5.12). We assume that the volume of a bead is uu and the volume of the chain is v = (N + l)uu. Each bead thus contributes po u to the... 

The intensity I(q) of scattering from a single random-coil polymer molecule in solution, obeying Gaussian statistics, can be written (see Section 5.2.3.1) as... 

Now consider a coiled polymer molecule as being impenetrable to solvent in the first approximation. A hydrodynamic sphere of equivalent radius Re will be used to approximate the coil dimensions (see Figure 3.13). In shear flow, it exhibits a frictional coefficient of /o. Then according to Stokes law. 

Another method of reducing sedimentation is to employ the principle of depletion flocculation (described in Chapter 7). The addition of free (non-adsorbing) polymer can induce weak flocculation of the suspension, when the concentration or volume fraction of the free polymer ( p) exceeds a critical value denoted by p. Asakura and Oosawa reported the first quantitative analysis of the phenomenon [96]. They showed that when two particles approach to a separation that is smaller than the diameter of the free coil, polymer molecules are excluded from the interstices between the particles, leading to the formation a polymer-free zone (depletion zone). Figure 14.16 shows this for the situation below and above. ... 

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