The shapes of polymer molecules

In this section consideration is given to the factors that determine the possible shapes and sizes of individual polymer molecules. Fundamentally, these are controlled by the nature of the covalent bonds that bind the atoms of the molecule together and by the particular groupings of atoms that occur within a particular type of polymer chain. 

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The notion that molecules at a surface are in a two-dimensional state of matter is reminiscent of E. A. Abbott s science fiction classic, Flatland.Perusal of this book for quotations suitable for Chapters 6, 7, and 8 revealed other parallels also the color revolt and light scattering, "Attend to Your Configuration" and the shape of polymer molecules, and so on. Eventually, the objective of beginning each chapter with a quote from Flatland replaced the requirement that the passage cited have some actual connection with the contents of the chapter. As it ends up, the quotes are merely for fun Perhaps those who are not captivated by colloids and surfaces will at least enjoy this glimpse of Flatland. 

By collecting the integrated intensities of diffraction peaks and subjecting them to a sequence of analyses, it is possible to determine the positions of the atoms packed in the crystalline unit cell. Such an endeavor constitutes the traditional process of crystal structure analysis, and much of the information that is available today about the shape of polymer molecules and their arrangement in crystals was derived by this method. 

The consequences of directional covalent bonding on the shape of polymer molecules will be explored, to generate the typical polymer shapes that exist in each of the microstructural states. The four covalent single bonds from a carbon atom, point towards the corners of a tetrahedron, with the carbon atom at the centre. The angle between any two of the bonds is 109.5°, and the C—C inter-atomic distance is 0.154 nm. In a polymer chain, every C—C bond can potentially rotate on its axis whether it does or not depends on the temperature. Figure 3.2 defines the rotation angle of bond C2—C3 from the relative positions of bonds Ci—C2 and C3—C4. 

In the spirit of dumbbell models [9], we mimic the dynamics and the shape of polymer molecule by that of a particle at position r where r = 0 corresponds to its center of mass. A force F acting on this particle can be chosen such that the time average of coincides with the mean square radius of gyration of the polymer coil in equilibrium. Furthermore, the effect of the flow of the background fluid is taken into account via a friction force proportional to the difference between the velocity of the particle and the flow velocity v(r). For this model, reduced (dimensionless) variables are used, but they are denoted by the same symbols as the corresponding physical quantities. The reduced mass is put equal to 1. Then the equation of motion reads... 

The parameter a is predominantly dependent on the shape of polymer molecules and the quality of the solvent it is a = 0.5 in a theta solvent and can rise up to 0.8 in better than theta conditions. When a = 1, then the average weight determined from this method is exactly the weight average. 

J. D. Honeycutt, D. Thirumalai. Influence of optimal cavity shapes on the size of polymer molecules in random media. J Chem Phys 92 6851-6858, 1990. 

In addition to the lengths of polymer molecules, the cross-sectional shapes have a major effect on their hardness and thermal stability. Aliphatics (paraffins, polyethylene, etc.) have the most simple cross-sectional shapes. Their simple and relatively symmetric shapes allow them to slide past on another readily via a process called reptation (de Gennes, 1990). As a result, linear polyethylene is relatively soft (Figure 13.1). 

The foregoing characteristics also are found with solutions of small molecules. But properties of solutions, one of whose components is macromolecular. differ from those having only small molecular components in quite understandable ways. For example, where small molecules are involved, molecular distortion is minor. Quite generally, the shapes of small molecules are little affected by environment unless the small molecules react chemically. In contrast with small molecules, there is a considerable variation in polymer conformation with environment. See also Molecule and Polymers. 

Modern hairspray consists of a solution of long, chainlike molecules (called polymers) in a highly volatile solvent. Some brands may also contain oils such as resins and lanolin. In general, a volatile substance is one whose state is unstable at room temperature and may readily change from liquid to gas form. Thus, hairspray is in liquid form within the can, as air pressure has been removed. The can is frequently composed of compounds (e.g., aluminum monobloc or tri-layered steel) that allow for a decreased likeliness of puncturing. Spraying the product results in the deposit of a polymer layer around each hair afrer evaporation of the volatile solvent. The web of polymer molecules on the hairs yields a stiff texture and allows the hairs to resist changing shape. 

Before discussing the detailed chemistry, kinetics, and mechanisms of the various pathways of polymer synthesis, it is necessary to introduce some of the fundamental concepts of polymer science in order to provide essential background to such a development. We need to know what a polymer is and how it is named and classified. It is also necessary to obtain an appreciation of the molecular size and shape of polymer molecules, the molar mass characteristics, the important transition temperatures of polymers, and their distinctive behavior both in solid state and in solution. These concerns are addressed in the first four chapters of the book while the remaining six chapters deal with the important categories of polymerization processes and their mechanisms and kinetic aspects. Throughout this journey the narrative in the text is illuminated with thoughtfully worked out examples which not only complement but also supplement, where necessary, the theoretical development in the text. 

Polymers can be classified in many ways, such as by source, method of synthesis, structural shape, thermal processing behavior, and end use of polymers. Some of these classifications have already been considered in earlier sections. Thus, polymers have been classified as natural and synthetic according to source, as condensation and addition (or step and chain) according to the method of synthesis or polymerization mechanism, and as linear, branched, and network according to the structural shape of polymer molecules. According to the thermal processing behavior, polymers are classified as thermoplastics and thermosets, while according to the end use it is convenient to classify polymers as plastics, fibers, and elastomers (Rudin, 1982). 

Before trying to answer questions about the dimension and shape of polymer molecules, we should first consider a simple molecule such as butane and examine the behavior when the molecule is rotated about the bond joining two adjacent carbons. This rotation produces different conformational states of the molecule. 

The thermal energy of the molecular environment provides the energy required to overcome the rotational energy barrier. Consequently, the shape (flexibility) of a polymer molecule is temperature dependent. At sufficiently high temperatures, the polymer chain constantly wiggles, assuming a myriad of random coil conformations. As we shall see later, the flexibility of polymer molecules, which is a function of substituents on the backbone, has a strong influence on polymer properties. 

As may be expected, polymers behave differently toward solvents than do low-molecular-weight compounds. Studies of the solution properties of polymers provide useful information about the size and shape of polymer molecules. In this section we discuss how some of the molecular parameters discussed in the previous sections are related to and can be calculated from thermodynamic quantities. We start with a discussion of the simplest case of an ideal solution. This is followed by a treatment of deviations from ideal behavior. 

The difference in behavior between ordinary organic compounds and polymeric materials is due mainly to the large size and shape of polymer molecules. Common organic materials such as alcohol, ether, chloroform, sugar, and so on, consist of small molecules having molecular weights usually less than 1,000. The molecular weights of polymers, on the other hand, vary from 20,000 to hundreds of thousands. 

The chemical structures of the repeat units of some common polymers are shown in fig. 1.2, where for simplicity of drawing the backbone bonds are shown as if they were collinear. The real shapes of polymer molecules are considered in section 3.3. Many polymers do not consist of simple linear chains of the type so far considered more complicated structures are introduced in the following section. 

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