Conformations of a Polymer Molecule

As discussed earlier, solid polymers can be distinguished into amorphous and the semicrystalline categories. Amorphous solid polymers are either in the glassy state, or - with chain cross linking - in the rubbery state. The usual model of the macromolecule in the amorphous state is the "random coil". Also in polymer melts the "random coil" is the usual model. The fact, however, that melts of semi-crystalline molecules, although very viscous, show rapid crystallisation when cooled, might be an indication that the conformation of a polymer molecule in such a melt is more nearly an irregularly folded molecule than it is a completely random coil. 

The restrictions imposed by short range steric interactions upon the conformations of a polymer molecule occur at a local level in short sequences of chain segments. There is, however, an interdependence of local chain conformations, that is, the conformation about a given chain segment is dependent upon the conformations about the segments to which it is directly connected (see Problem 2.1). Such interdependent steric restrictions affect the local chain conformations all along a polymer chain and have a significant effect upon chain dimensions. 

The deficiencies of the Flory-Huggins theory result from the limitations both of the model and of the assumptions employed in its derivation. Thus, the use of a single type of lattice for pure solvent, pure polymer and their mixtures is clearly unrealistic since it requires that there is no volume change upon mixing. The method used in the model to calculate the total number of possible conformations of a polymer molecule in the lattice is also unrealistic since it does not exclude self-intersections of the chain. Moreover, the use of a mean-field approximation to facilitate this calculation, whereby it is assumed that the segments of the previously added polymer molecules are distributed uniformly in the lattice, is satisfactory only when the volume fraction (f>2 of polymer is high, as in relatively concentrated polymer solutions. 

In this Section, the general characteristics of the conformation of a polymer molecule in solution are considered. The general model for a linear polymer molecule in solution is based on a randomly coiled, flexible chain, the average form of which possesses spherical symmetry. The distribution of chain ends about the center of this sphere is further supposed to be Gaussian. Since the total number of conformations which the macromolecule may adopt is exceedingly large, only an average dimension can... 

Figure 3.36 Random coil conformation of a polymer molecule and effect of shear...

The other example, shown in Figure 9.4, illustrates how the conformation of a polymer molecule is affected by its interaction with solvent molecules. When heat does not change on introduction of the polymer into the solvent (AH = 0), the polymer molecule adopts the configuration of highest entropy, a random coil. If AH is positive (i.e., enthalpy of the system increases when polymer and solvent are mixed), the polymer molecule will try to minimize interactions with solvent molecules by adopting a folded configuration. 

The quasi-lattice model was developed by Roe (13) and Scheutjens and Fleer (14) (SF theory) The basic analysis considered all chain conformations as step-weighted random walks on a quasi-crystalline lattice that extends in parallel layers from the surface. This is illustrated in Figure 16.2 which shows a possible conformation of a polymer molecule at a flat surface. The partition function was written in terms of the number of chain configurations that were treated as connected sequences of segments. In each layer parallel to the surface, random mixing between the segments and solvent molecules was assumed, i.e. by using... 

Figure 16.2. Possible conformation of a polymer molecule at an interface...

Conformation Conformation of a polymer molecule describes the geometrical arrangements of the atoms in the polymer chain achieved through rotations about or stretching of its chemical bonds and bending of its valence angles. 

The freely jointed chain is a model that treats the conformation of a polymer molecule as a mathematical random walk. This is a simple model for chain conformahon in which... 

Again, depending on the temperature, many changes from one state to another may occur per second. In the glassy or solid state few will take place, while in the liquid state many rotations will occur. Further, which state is preferred will depend upon whether the molecule is in a crystalline close packed state or in the more loosely packed amorphous state. As a result, it is clear that many factors tend to determine the conformations of a polymer molecule. Effects of orientation and temperature will be discussed in later Sections and Chapters. 

The simplest polymers have linear chain-like molecules, which can take on a large number of possible conformations. The principal piece of information about the conformation of a polymer molecule is the end-to-end distance. Even if we had a monodis-perse sample of a polymer (one in which all molecules had the same molecular mass) there would be a distribution of end-to-end distances, because each molecule would coil up differently from the others. 

In contrast to previous treatments [12,13], Eq. (13) emphasizes the effect of the degree of coverage on the overall resistance by a separate factor 1 - 9.) For a rigid object (such as, c.g., a colloidal particle), U z) can simply be taken to be the (Helmholtz) energy of interaction at separation z. However, a polymer is flexible and can adjust its shape to the local field. We should, therefore, average over all allowed conformations of a polymer molecule that has an arbitrary segment at the distance of closest approach z. In other words, one has to evaluate the partition function Q(z) of a chain at a distance z fi-om the surface, in the imposed field of the surface ... 

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