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WERNER BRANDT Du ,Pont Radiation Physics Laboratory, Wilmington, Del.
Theory of Molecular Chain Crystuls and Its Application to High Polymers In high polymer research, the interpretation of macroscopic properties in terms of atomic or molecular parameters is a primary objective. Such interpretation is not only of much fundamental interest, but instrumental toward a systematic development of technologically important materials. Most of the properties characteristic of high-polymeric substances can be attributed to an interplay of the valence forces between the atoms within molecules and the cohesive forces between molecules. These intra- and intermolecular forces must be understood separately before quantitative statements about their interaction can be made
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IS a unique feature of high polymer substances that they are viscoelasticin response to external disturbances they exhibit at once the properties of viscous liquids and elastic solids. T h e relative preponderance of high polymer behavior depends on the experiment performed (2). Viewed microscopically, high polymer molecules respond to disturbances not only by lattice deformations and by gliding past one another, as d o the molecules of ordinary solids and liquids, but also by changing their configuration. As a consequence, elastic restoring forces are set up by the molecules to regain the accompanying loss of configurational entropy. These entropy- or rubberelastic forces, in turn, cause the molecules to diffuse back toward molecular configurations of maximum entropy. Therefore, if a n experiment is performed rapidly compared to the rates of molecular diffusion (adiabatic condition), high polymer substances behave like elastic solids or rubbers. I n comparatively slow experiments (steady-state condition), they behave like viscous liquids. Even though chemically no distinction in kind exists between a polymer and a high polymer, such distinction exists, in fact, physically. Properties charac-
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teristic of high polymers can be observed only if the intermolecular interaction per molecule is large enough to overcome intramolecular restraints against configurational changes. Naively put, a polymer is a high polymer with regard to a propertyp, if H (inte.) > H (intra) P P (1) where Hp(inter) and HP(i”traj refer to the inter- and intramolecular interactions per polymer chain group pertinent to p , respectively, and np to the pertinent number of chain groups. Most high polymer properties are found in compounds with n,, 1000. Because of Equation 1 high polymers should be called plastics only if reference is made to specific industrial products; plastics of the same polymer vary in molecular structure and often contain additives or impurities, depending on their place of origin. O n the whole, the differences between the properties of high polymers of different chemical composition originate in the intramolecular interactions ; differences between plastics of the same polymer stem mainly from differences in the intermolecular force fields. I f H P ( i n t r a ) / n H (inter) < < 1, the molecules ~
can be thought of as consisting of several arbitrarily chosen statistical segments, which must meet only the requirement that the chain configuration a t one end of a segment shows no correlation with the configuration a t the other end. T h e statistical theory of high polymers is very successful in deriving macroscopic properties from the behavior of assemblies of molecules composed of such statistica! segments, and their mutual friction. Clearly, neither the length of statistical segments nor their coefficients of friction are material constants, but functions, as well, of the experimental conditions under which they are measured. I t is the objective of the molecular physics of high polymers to define statistical segments and their mutual friction in terms of molecular constants. As this goal is approached, the development of new and the improvement of known high polymers can make systematic use of the profound knowledge accumulated in molecular and atomic physics to a much larger extent than has yet been possible.
INDUSTRIAL AND ENGINEERING CHEMISTRY
T h e quantitative details of the interplay of intra- and intermolecular forces pose problems of formidable difficulties. Before they can be tackled, however, both force components must be understood separately. Considering the former first, the interaction between chain groups is well knoivn to depend only on the valence bonding between the atoms along the molecular backbones. and the steric effects introduced by the chain groups as a whole. Both are independent of the length of polymer molecules, except where the molecules are held together by conjugated double bonds. Intermolecular interactions between polymer molecules can be described to a good approximation by assuming each chain group to act as a point center of van der Waals forces upon all the chain groups of the neighboring molecules (7) T h e theory of molecular chain crystals rests on such assumptions. I t permits the accurate prediction, from molecular constants. of properties which depend on changes of the distances between and the mutual orientation of chain groups, but not on changes of molecular configurations. Therefore, such properties agree with the principle of corresponding intermolecular states. As the condition of unchanged configurations is relaxed to include high polymer behavior, the problem becomes one of describing the interdependence of lattice structure and intermolecular chain group interaction, because changes in lattice structure employ intramolecular degrees of freedom. This problem is, in fact, so difficult that no general solution can be expected in the near future. However. it is a problem of so far-reaching scientific and practical importance that even partial success fully warrants the perseverance currently given to its solution. literature Cited (1) Brandt, W.: J . Chem. Phys. 26, 262-70 (1957). ( 2 ) Pao, Y. H., Brandt, W., A @ [ . Mech. Revs. 9, 233-6 (1956).
RECEIVED for review January 23, 1958 ACCEPTED February 14, 1958 Division of Industrial and Engineering Chemistry, ,4CS, Christmas Symposium, Cleveland, Ohio, January 1958.
