Mechanical properties of discrete polymer molecules

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Abstract
A frequency‐dependent stiffness μB was found from the action of high frequency shear waves on dilute solutions of polyisobutylene, polypropylene, polyethylene, polystyrene, hevea rubber, and polybutadiene microgel. A dynamic viscosity associated with streaming of solvent through the molecular coil, ηB, dropped far more rapidly with rising temperature than solvent viscosity, denoting that it, too, reflected configurational changes. (The μB for polyisobutylene in solution declined moderately with rising temperature, corresponding to an exponential coefficient of 2.3 kcal.) This behavior suggested three chief mechanisms for deformation of isolated chains: (1) viscoelastic configuration changes (W. Kuhn's “macroconstellation changes”) with contribution to rigidity per average molecule per cubic centimeter of solution of 〈 μ2 〉 or force constant 〈 f2 〉; (2) temporary entanglements of interpenetrating segments in the chain coil (like the interchain entanglements in concentrated solutions of J. D. Ferry), with contribution to rigidity 〈 μ3 〉; and (3) restrictions to rotational flexibility around chain linkages, with rigidity contribution 〈 μ4 〉. Arrangement of these processes in parallel with solvent viscosity yielded frequency‐independent constants in agreement with the limited data so far obtained in the 103 to 108 cycle range.Such a model gave molecular mechanical constants correlating roughly with chemical structures. For polyisobutylene, force constants per average molecule were 〈 f2 〉 = 17.1 × 10−13 dyne cm., 〈 f3 〉 = 6.3 × 10−12 and 〈 f4 〉 = 1.6 × 10−10. Lower molecular weight (1.2 × 106 vs. 3.9 × 106) gave slightly lower values. 〈 f4 〉 represents restrictions to rotation per isobutylene residue in the chain of 2.3 × 10−15, or about 104 less than valence bond infrared vibrational or twisting force constants for hydrocarbons. The combined average chain rigidities expressed by the force constant 〈 fB 〉, at 20 kc. and 25°C. were, for polyisobutylene of M̄V ∼ 106, 1.8 × 10−12; hevea rubber of M̄V = 2.3 × 105, 1.5 × 10−15; polystyrene of M̄V = 2.3 × 105, 4.5 × 10−16. Hence, single polystyrene chains are quite flexible, but polybutadiene microgel has 〈 fB 〉 = 5.2 × 10−11, for M̄W ∼ 18 × 106, showing effect of internal cross‐linking.“Poor” solvents (“solvent power” μ > 0) caused chain rigidity of polyisobutylene and polystyrene to decrease, compared to good solvents (“solvent power” μ ∼ 0), and viscosity decreased also. Apparent decrease in 〈 fB 〉 apparently means external (solvent) “compression” of chain, and agrees with technological efficiency of poorly compatible plasticizers.Complete theory of effects has been outlined by Kirkwood, for a rod model. Great range of rigidities shown even by hydrocarbon chains (intrinsic rigidity of polyethylene soln., [μ] = 906 dynes/cm.2, of polypropylene soln., [μ] = 92 dynes/cm.2) has not yet been treated, however.