Polymer molecule

Otlier expressions for tire diffusion coefficient are based on tire concept of free volume [57], i.e. tire amount of volume in tire sample tliat is not occupied by tire polymer molecules. Computer simulations have also been used to quantify tire mobility of small molecules in polymers [58]. In a first approach, tire partition functions of tire ground... 

The depletion picture also applies to otlier systems, such as mixtures of colloidal particles. Flowever, whereas neglecting tire interactions between polymer molecules may be reasonable, tliis cannot be done in tire general case. 

Fluorinated Ethylene-Propylene Resin. Polymer molecules of fiuorinated ethylene-propylene consist of predominantly linear chains with this structure ... 

The term polymer is derived from the Greek words poly and meros, meaning many parts. We noted in the last section that the existence of these parts was acknowledged before the nature of the interaction which held them together was known. Today we realize that ordinary covalent bonds are the intramolecular forces which keep the polymer molecule intact. In addition, the usual type of intermolecular forces—hydrogen bonds, dipole-dipole interactions, and London forces—hold assemblies of these molecules together in the bulk state. The only thing that is remarkable about these molecules is their size, but that feature is remarkable indeed. 

We began this section with an inquiry into how to define the size of a polymer molecule. In addition to the molecular weight or the degree of polymerization, some linear dimension which characterizes the molecule could also be used for this purpose. For purposes of orientation, let us again consider a hydrocarbon molecule stretched out to its full length but without any bond distortion. There are several features to note about this situation ... 

The fully extended molecular length is not representative of the spatial extension that a molecule actually displays. The latter is sensitive to environmental factors, however, so the extended length is convenient for our present purposes to provide an idea of the spatial size of polymer molecules. 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

Since the preparation of the specimen began with such a dilute solution, there seems to be little doubt that the particles are individual polymer molecules rather than clusters thereof. The diameters of the blobs are of the right order of magnitude for random structures, although this comparison must be used cautiously in view of item (1). 

If the concentration of junction points is high enough, even branches will contain branches. Eventually a point is reached at which the amount of branching is so extensive that the polymer molecule becomes a giant three-dimensional network. When this condition is achieved, the molecule is said to be cross-linked. In this case, an entire macroscopic object may be considered to consist of essentially one molecule. The forces which give cohesiveness to such a body are covalent bonds, not intermolecular forces. Accordingly, the mechanical behavior of cross-linked bodies is much different from those without cross-linking. 

Just as it is not necessary for polymer chains to be linear, it is also not necessary for all repeat units to be the same. We have already mentioned molecules like proteins where a wide variety of different repeat units are present. Among synthetic polymers, those in which a single kind of repeat unit are involved are called homopolymers, and those containing more than one kind of repeat unit are copolymers. Note that these definitions are based on the repeat unit, not the monomer. An ordinary polyester is not a copolymer, even though two different monomers, acids and alcohols, are its monomers. By contrast, copolymers result when different monomers bond together in the same way to produce a chain in which each kind of monomer retains its respective substituents in the polymer molecule. The unmodified term copolymer is generally used to designate the case where two different repeat units are involved. Where three kinds of repeat units are present, the system is called a terpolymer where there are more than three, the system is called a multicomponent copolymer. The copolymers we discuss in this book will be primarily two-component molecules. We shall discuss copolymers in Chap. 7, so the present remarks are simply for purposes of orientation. 

The product molecules have the functional groups formed by the condensation reactions interspersed regularly along the backbone of the polymer molecule ... 

Begin by recognizing that a molecule containing x of the head-to-head links will be cleaved into x + 1 molecules upon reaction. Hence if N is the number of polymer molecules in a sample of mass w, the following relations apply before and after cleavage = (x l)Nj, or w/M = (x + l)(w/Mj,). Solving for x and... 

The high molecular weight of a polymer is one of the most immediate consequences of the chain structure of these molecules. As indicated in Sec. 1.2, it is also the basis for describing the size of the polymer molecule, either directly or through the degree of polymerization. Most methods for the determination... 

Next let us apply random walk statistics to three-dimensional chains. We begin by assuming isolated polymer molecules which consist of perfectly flexible chains. 

To isolate polymer chains from one another, we consider a solution which is sufficiently dilute that the domains of the individual polymer molecules are well separated from each other. For the present, we assume the solvent has no influence on the polymer but merely supports the molecule. In fact, this is not generally the case, although it can be achieved by proper choice of solvent or temperature. 

This kind of perfect flexibility means that C3 may lie anywhere on the surface of the sphere. According to the model, it is not even excluded from Cj. This model of a perfectly flexible chain is not a realistic representation of an actual polymer molecule. The latter is subject to fixed bond angles and experiences some degree of hindrance to rotation around bonds. We shall consider the effect of these constraints, as well as the effect of solvent-polymer interactions, after we explore the properties of the perfectly flexible chain. Even in this revised model, we shall not correct for the volume excluded by the polymer chain itself. 

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

Figure 1.9 The spherical domain of a polymer molecule either expanding by imbibing solvent or contracting by excluding solvent.

Figure 1.10 Helical conformations in polymer molecules, (a) A vinyl polymer with R substituents has three repeat units per turn, (b) The a helix of the protein molecule is stabilized by hydrogen bonding. [From R. B. Corey and L. Pauling,/ end. Inst. Lombardo Sci. 89 10 (1955).]...

In this chapter we have focused attention on various aspects of individual polymer molecules. In the next three chapters we shall examine some properties of assemblies of polymer molecules. Our interest in these chapters will be mostly directed toward samples of pure polymer assemblies of high and low molecular weight molecules-polymer solutions—will be discussed in Part III of this book. 

Use the Simha equation and these data to criticize or defend the following proposition These polymer molecules behave like rods whose diameter is 16 A and whose length is 1.5 A per repeat unit. The molecule apparently exists in fully extended form in this solvent rather than as random coils. 

Next, suppose we consider the tangential velocity v of segment i in a polymer molecule. The segment is located a distance r from the center of mass of the molecule and possesses an average angular velocity co. The situation is sketched in Fig. 2.12a. Since v = rco, it follows that the x and y components of the velocity are given by... 

Figure 2.12 (a) Description of segment i in a polymer molecule relative to the... 

For a polymer molecule consisting of n segments, this result must be summed over all the segments in the molecule to give the energy dissipated per second per polymer molecule (AW/At)p ... 

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