Random-coil model

In addition to an array of experimental methods, we also consider a more diverse assortment of polymeric systems than has been true in other chapters. Besides synthetic polymer solutions, we also consider aqueous protein solutions. The former polymers are well represented by the random coil model the latter are approximated by rigid ellipsoids or spheres. For random coils changes in the goodness of the solvent affects coil dimensions. For aqueous proteins the solvent-solute interaction results in various degrees of hydration, which also changes the size of the molecules. Hence the methods we discuss are all potential sources of information about these interactions between polymers and their solvent environments. 

Peterlin168 has shown that the viscometric data for potato amylose acetate in chloroform solution can be readily interpreted in terms of a random-coil model for the molecule, in which there is hindered rotation at the oxygen atom of the glucosidic linkage. 

Polymeric solids such as polystyrene are most often noncrystalline. The random coil model would be most appropriate to describe such solids. In many polymers, both crystalline and amorphous regions are present in such materials, well-defined coiled regions are embedded in a randomly coiled matrix. 

Current investigations on dilute polymer solutions are still largely limited to the class of macromolecular solutes that assume randomly coiled conformation. It is therefore natural that there should be a growing interest in expanding the scope of polymer solution study to macromolecular solutes whose conformations cannot be described by the conventional random-coil model. The present paper aims at describing one of the recent studies made under such impetus. It deals with a nonrandom-coil conformation usually referred to as interrupted helix or partial helix. This conformation is a hybrid of random-coil and helix precisely, a linear alternation of randomly coiled and helical sequences of repeat units. It has become available for experimental studies through the discovery of helix-coil transition phenomena in synthetic polypeptides. 

Hoffman (37) has offered a variety of circumstantial evidence supporting the random coil model. In A-B block copolymers of styrene and butadiene, for instance, the characteristic dimension of the dispersed phase particles depends on the molecular weight of blocks in the dispersed phase according to ... 

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). 

In Fig. 23, d is plotted against MB, the molecular weight of dimethylsiloxane blocks, for various dispersions. As can be seen, above MB = 10 x 103 d falls between the two limiting lines corresponding to the fully stretched chain model and the random coil model, while below MB = 10 x 103, 6 is closer to the former model than to the latter. 

Fig. 9.— Double Log Plots of (a) Intrinsic Viscosity, (b) the Reciprocal of the Diffiision Coefficient, and (c) Sedimentation Coefficient Data versus Molecular Weight for Human Cervical Mucins. [Key and O, whole mucins and , subunits and A, T-domains. Molecular weights determined from Zimm plots (filled symbols) or the Svedbeig equation using QLS (open symbols). Values for the slopes are in all cases consistent with a random-coil model and not with a rigid sphere or a rod.]...

Figure 3.22. "Random coil" model of humic substances in soil, showing the flocculated (low pH) and dispersed (high pH) forms of the organic polymers.

The main quantitative developments of the random coil model of flexible polymers began in 1934 with the work of E. Guth and H. E Mark [12] and W. Kuhn [13]. Using the concept of free rotation of the carbon-carbon bond, Guth and Mark developed the idea of the random walk or random flight of the polymer chain, which led to the familiar Gaussian statistics of today, and eventually to the famous relationship between the end-to-end distance of the main chain and the square root of the molecular weight, described below. 

The random coil model ignores the role of the solvent a poor solvent will tend to cause the coil to tighten a good solvent does the opposite. Therefore, calculations based on this model are best regarded as lower bounds to the dimensions of a polymer in a good solvent and as an upper bound for a polymer in a poor solvent, The model is most reliable for a polymer in a bulk solid sample, where the coil is likely to have its natural dimensions. 

The development of the random coil by H. F. Mark and many further developments by P. J. Flory led to a description of the conformation of chains in the bulk amorphous state. Neutron scattering studies revealed that the conformation in the bulk is close to that found in solution in 0-solvent (see Chapter 3), thus strengthening the random coil model. On the other hand, some workers suggested that the chains have various degrees of either local or long range order. 

An a helix-random coil model in which the surfactant binding enhances the a-helical content of the protein and disrupts the (3 structure. 

Yamakawa (38) and Imai (83) have published an alternative description based on a random coil model and the Kirkwood-Riseman theory (62) and obtained for theta-solvent conditions an equation equivalent to ... 

In the range of y where the helical and wormlike models display their absolute maxima in Figure 1, the presumably more realistic random coil model R has a much lower and broader... 

Figure 1. F(ii) = NiJP(ii) vi. ii = (4t/ K) sin (e/2) for helical amylosic chain nwdels A, B, and C, wormlike amylosic chain model W, jointed helical model J, and realistic random coil model R. Details of the models are described in the text.

Fig. 5.10 Proposed structures for the noncrystalline regions of polymers (a) the bundle model, (b) the meander model and (c) the random-coil model, ((a) and (c) reprinted by permission of Kluwer Academic Publishers (b) reprinted by permission of John Wiley Sons, Inc.)...

Yang et al. [27], using small-angle neutron scattering (SANS), reported the formation of supermolecular structures in polystyrene latex particles prepared by the seeded emulsion polymerization of styrene onto deuterated polystyrene particles. The recorded scattering intensities, which were much higher than those expected on the basis of the Debye random coil model, indicate the presence... 

The molecular structure of PFOA is indicated in fig. (1) and polymer chain dimensions were derived using both Zimm plots [fig. (la)] and also by fitting the data to a Debye random coil model [9], with good agreement between the two approaches. As the pressure is reduced, the solubility decreases and the PFOA falls out of solution at the critical, "neutron cloud point" (T = 65 300 bar), as indicated [fig. (lb)] by a zero intercept... 

Fig. 24 Schematic pictures of flow-induced crystallization from the polymer melt (a) for the random coil model (b) using the folded-chain fringed-micellar grain model...

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