Coil concept, random

This model quantitatively accounts for all the features in the siCs) curve for molten polyethylene, and supports the random coil concept. 

The intrinsic viscosity of polymer solutions can be readily measured. Hence, it is apparent from equation (2.31) that it is possible to obtain a measure of molecular weight provided F can be measured. It is more convenient to replace F, making use of the random coil concept to give an equation of the form... 

Equation (8.97) shows that the second virial coefficient is a measure of the excluded volume of the solute according to the model we have considered. From the assumption that solute molecules come into surface contact in defining the excluded volume, it is apparent that this concept is easier to apply to, say, compact protein molecules in which hydrogen bonding and disulfide bridges maintain the tertiary structure (see Sec. 1.4) than to random coils. We shall return to the latter presently, but for now let us consider the application of Eq. (8.97) to a globular protein. This is the objective of the following example. 

We saw in Chap. 1 that the random coil is characterized by a spherical domain for which the radius of gyration is a convenient size measure. As a tentative approach to extending the excluded volume concept to random coils, therefore, we write for the volume of the coil domain (subscript d) = (4/3) n r, and combining this result with Eq. (8.90), we obtain... 

The above argument shows that complete overlap of coil domains is improbable for large n and hence gives plausibility to the excluded volume concept as applied to random coils. More importantly, however, it introduces the notion that coil interpenetration must be discussed in terms of probability. For hard spheres the probability of interpenetration is zero, but for random coils the boundaries of the domain are softer and the probability for interpenetration must be analyzed in more detail. One method for doing this will be discussed in the next section. Before turning to this, however, we note that the Flory-Huggins theory can also be used to yield a value for the second virial coefficient. 

M molar mass), where I and III are the tricritical or -regions. Here, the chain molecules exhibit an unperturbed random coil confirmation. In contrast, I and II are the critical or good solvent regimes, which are characterized by structural fluctuations in direction of an expanded coil conformation. According to the underlying concept of critical phenomena, the phase boundaries have to be considered as a continuous crossover and not as discontinuous transitions. 

For now, we restrict our discussion to the 0 point, where the poly-mers in solution have a random coil distribution. Therefore, it is reasonable to say that in the semidilute regime at the 6 point the distribution of the segments in the solution is spherical. With this concept, the velocity of the diffusing segments at the 6 condition can be expressed as... 

Abstract. The synthesis and study of dendrimers has been truly dramatic in the last ten years. This review gives a brief introduction to some of the key concepts and main synthetic strategies in dendrimer chemistry. The focus of the chapter is a survey of modern analytical techniques and physical characterization of dendrimers. Results of model calculations and experiments probing the dimensions and conformation of dendrimers are reviewed. In the final sections the experimental work on dendrimer-polymer hybrids is highlighted. The dense spherical conformation of dendrimers has been combined with the loose random-coil conformation of ordinary polymers to form new hybrids with potentially interesting new properties. 

The concept of polymer chains consisting of a freely jointed backbone which could occupy space as a random coil dated from 1933 when Kuhn defined a polymer chain as having n links of length I and the properties defined by a random flight in three-dimensions (Strobl, 1996). This is shown schematically in Figure 1.2. 

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. 

It should be pointed out here that the aforementioned argument about the two types of a-helice, the a, and an forms, based on their conformation-dependent displacement of l3C NMR signals, is restricted to an assumed static picture of these forms. However, a view of the dynamic equilibrium is implicitly taken into account for the interpretation of the l3C chemical shifts of the loop and random coil forms. It seems, therefore, to be more realistic to discuss the conformation and dynamics of more flexible membrane proteins in terms of the new concept of the dynamics-dependent displacement of 13C NMR peaks, to be discussed in Section 6.1. 

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