The size and shape of polymer molecules

It is found that i7sp varies linearly with c, and its value, extrapolated to zero concentration, is known as the intrinsic viscosity inf long-chain molecules in neutral solvents  

The flexibility of a long-chain polymer leads to problems in specifying the shape in a useful way. One approach is to treat the polymer as infinitely thin and assume that the orientation of each flexible segment has a random orientation unaffected by the orientations of its neighbours. The problem is then that of the Einstein random walk so that, if one end of a molecule has a position vector Rq and the other end has a position vector R, a measure of the space occupied by the molecule is 1 Ro R v I-For the problem specified  

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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 ability to measure the size and shape of polymer molecules has been a key factor in the transformation of polymer technology into a science. The techniques used to measure molecular weight share the common characteristic, with few exceptions, that the polymer must be soluble. The polymer molecular weight is calculated by multiplying the molecular weight of the monomer unit by the number of monomer units or alternatively by the degree of polymerization (DP). 

Diffusion selectivity is based on the ability of the polymer matrix to transmit molecules of a certain shape and size. This ability is determined by the structure of the polymer and the rigidity of the macromolecular ensemble as well as by the properties of the penetrant, the size and shape of its molecules. 

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. 

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. 

Therefore, the diffusion proeess is a kinetic parameter depending on the free volume within the permeable material, segmental mobility of polymer chains, polymer structure, the size and shape of penetrant molecule and crystallinity. The diffusion coefficient D is described by the following equation ... 

The solubility is relatively unaffected except at very high degrees of cross-linking or when the penetrant significantly swells the polymer. The constraint of crosslinking on segmental mobility of the polymer makes the diffusion process more dependent on the size and shape of penetrant molecules. The decreases in inherent segmental mobility makes the diffusion process more concentration dependent. 

Prior to a discussion of the theory of rubber elasticity, it is important to review how isolated polymer chains behave as this will provide a picture of the size and shape of a polymer. Clearly a polymer chain in a vacuum will collapse into a dense unit, but when in a solution the molecule will take on a conformation which is a function of the interaction with the surrounding molecules and the balance between the entropically driven tendency to maximise the spatial configuration and the connectivity of the monomer units. This is the case whether the chain is surrounded by small molecules (solvent) or other macromolecules that may or may not act like a solvent. 

The chemistry of fibers is the same as chat for resins. The important difference is the mechanics. For polymers to be suitable for fibers, you must be able to draw them into a fibrous form, normally by extrusion. Second, the size and shape of the molecules that make up the fiber must be correct. To have acceptable fiber properties, the molecules must be long, so they can be oriented tO lie parallel to the axis of the fiber. Normally, thats done (or enhanced) by drawing or stretching the fiber to several times its original length. The essential differences then between resins and fibers are the shape and the orientation of the molecules. 

The diffusion of larger organic vapor molecules is related to absorption. The rate of diffusion is dependent on the size and shape of the diffusate molecules, their interaction with the polymer molecules, and the size, shape, and stiffness of the polymer chains. The rate of diffusion is directly related to the polymer chain flexibility and inversely related to the size of the diffusate molecules. 

Recent theoretical developments have related the turbidity of polymer solutions to the size and shape of the dissolved molecules. The light scattered by a solution in excess of that scattered by pure solvent (r) can be shown12 to be related to the molecular weight by the continued series equation... 

In lattice models each molecule (or segment of a molecule in the case of polymers) is assumed to occupy a cell in the lattice. The arrangement of the molecules or segments is assumed to depend upon only the composition and the size and shape of the molecules. In this case, the combinatorial (athermal) contribution is calculated from the number of arrangements statistically possible in the lattice. This contribution is also referred to as the entropic term. 

Data obtained from light scattering measurements can give information about the weight average molecular weight Mw, about the size and shape of macromolecules in solution, and about parameters which characterize the interaction between the solvent and polymer molecules. 

Portions of polymer molecules which are in crystalline regions have overall dimensions and space-filling characteristics that arc determined by the particular crystal habit which the macromoleculc adopts. Here, however, we are concerned with the sizes and shapes of flexible polymers in the amorphous (uncrystallized) condition. It will be seen that the computation of such quantities provides valuable insights into the molecular nature of rubber elasticity. 

For gas solutes in large-molecule solvents, Chappelow and Prausnitz (C9), have recently proposed a modified equaticm for in which both the size and shape of the molecules are taken into consideration. They provide accurate gas solubility data for 26 hydrocarbon gas-liquid systems in the temperature range 25°-200 C in the vicinity of 1 atm pressure. Complementary information on the solubility of organic solutes in polymers has also been given recently by Maloney and Prausnitz (M6) and by Stiel and Harnish (S39). 

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