A. V. Tobolsky

A New Approach to the Theory of Relaxing Polymeric Media

A molecular theory of relaxing media is presented which gives an expression for the stress in terms of the strain history. At any given time the strain history produces a distribution in internal strains which for mechanical properties can be characterized by a limited number of internal strain parameters. The second law of thermodynamics is used to define dissipation of energy at constant temperature and explicit expressions for dissipation of energy for any strain history are obtained. Inasmuch as relaxation during straining causes an essential reorganization of structure which is in fact the cause of dissipation, the kinetic theory of elasticity is extended to non‐isotropic polymeric networks. A tensor expression for the stress‐strain‐time relations is thereby developed.

Mechanical Properties of Polymeric Materials

A molecular model in terms of which the elastic viscous properties of rubber‐like substances can be interpreted is presented. Experiments on stress relaxation at constant extension, creep under constant load, extrusion, vibration, and breaking are discussed in terms of a mathematical formulation of this molecular model.

Systems Manifesting Superposed Elastic and Viscous Behavior

Actual substances exhibit a very complicated behavior under mechanical stresses which cannot be described by classical elasticity theory nor by the classical theory of the hydrodynamics of viscous fluids. A general molecular theory describing the behavior of matter under stress is discussed and related to previous investigations and to experimental observations. Particular attention is devoted to rubberlike substances for which the classical theories are definitely inadequate. Experimental results on relaxation and creep of rubbers are interpreted in terms of modern structural concepts. It is found that these substances exhibit three regions of stress‐temperature‐time dependence. At intermediate temperatures there exists a region of relative stability in which the statistical‐thermodynamic theory of rubber elasticity is valid. At elevated temperatures relaxation and creep are caused by chemical changes involving the rupture and formation of primary valence bonds. These chemical changes, which are responsi...

Stress Relaxation Studies of the Viscoelastic Properties of Polymers

Extensive studies of the viscoelastic properties of polymers undertaken in the authors laboratory by means of the method of stress relaxation are here reviewed. The discussion is divided into four parts: chemical stress relaxation, stress relaxation in amorphous polymers, stress relaxation in crystalline polymers, and stress relaxation in certain natural polymers and polyelectrolytes. Mathematical description of the phenomena are presented in simple form. The relation between structure and viscoelastic properties of polymers are discussed and a rather complete over‐all picture of these phenomena seems to be emerging.

The Theory of Permanent Set at Elevated Temperatures in Natural and Synthetic Rubber Vulcanizates

A molecular theory is developed to describe quantitatively the permanent set taking place in thin samples of vulcanized natural and synthetic rubbers held at constant extension at elevated temperatures. Permanent set is considered to be the result of the formation, through the action of molecular scission and cross‐linking reactions, of a dual molecular network in the rubber sample, in which the network chains are of two types: chains which are at equilibrium when the sample is at its unstretched length, and chains which are at equilibrium when the sample is at its stretched length. According to the theory the amount of permanent set in a rubber sample is a function of only two quantities: the relative ratio of the number of chains of the two types, and the elongation at which the sample was held. Experimental data on permanent set for various rubber types and under different conditions are presented and are shown to be in good agreement with the theory.

Stress-relaxation of polyisobutylene in the transition region (1, 2)

Abstract New data are reported on the stress-relaxation of the National Bureau of Standards sample of polyisobutylene at temperatures from −40°C. to −83°C. When properly adjusted, the data agree very well with dynamic-property data at temperatures above −45°C. The data do not agree with the reduced equation for viscoelastic behavior applicable for butadiene-styrene copolymers. A new approach to this problem appears to be fruitful.

The viscoelastic behavior of polymethyl methacrylate

Abstract Complete stress relaxation data for polymethyl methacrylate are presented covering behavior of this linear amorphous polymer from the rubbery state to the glassy state. The effect of water on stress relaxation rates in the glassy state and in the transition region is shown. Fast cooling is shown to increase subsequent stress relaxation rates in the glassy state. The complete pattern of viscoelastic behavior may be represented by a master stress relaxation curve holding for all temperatures, but shifting along the logarithmic time scale with temperature change. The master stress relaxation curve can be represented by a distribution of relaxation times. This distribution has been derived from the master stress relaxation curve, and the master curve recalculated from the distribution has been shown to agree with the experimental master curve. The method used in calculating the distribution of relaxation times is described and can be applied generally.

Viscoelastic Properties of Monodisperse Polystyrene

The viscoelastic properties of five monodisperse polymer samples of polystyrene ranging in molecular weight between 80 000 and 270 000 were studied and accurate values of ηt, Je, τm, and Em were obtained. It is shown that the dependence on molecular weight of these quantities is very different from that predicted by the Rouse—Bueche theory or by the Ferry—Landel—Williams modification of this theory.

Stress‐Time‐Temperature Relations in Polysulfide Rubbers

Polysulfide rubbers of various internal structures have been investigated by measurements of continuous and intermittent relaxation of stress and by creep under constant load at temperatures between 35°C and 120°C. Continuous stress relaxation measurements indicate that these rubbers approximately obey the simple Maxwellian law of relaxation of stress, which indicates that one definite type of bond in the network structure is responsible for stress decay. The activation energy for the relaxation process in each of the polysulfide rubbers is nearly the same, indicating that the same type of bond is responsible for the relaxation behavior of all the polysulfides investigated. In contrast to the hydrocarbon rubbers, oxygen is not the cause of high temperature relaxation in polysulfide rubbers, nor does heating in air at moderate temperatures for times comparable to the relaxation time produce changes in physical properties as determined by modulus or by appearance of the samples. Several possibilities regard...

Solid Solutions of the Alkali Halides

X‐ray studies of solid solutions of alkali halide pairs with a common ion at room temperature and at 550°C show that these pairs can be divided into three groups depending on the percent deviation δ of their lattice parameters. For values of δ less than 6 percent miscibility is complete at room temperature. For values of δ between 6 and 13 percent miscibility is complete at 550°C. For values of δ larger than about 13 percent miscibility is not complete at 550°C. In terms of the Born theory of ionic lattices, the free energy of mixing, and Vegards law, an approximate theory for the phase curve of these solid solutions is derived. For a typical alkali halide with an electrostatic energy of 180 kcal. at the absolute zero of temperature the equation of the phase curve is 9δ2/T(1–2x)+ln x−ln (1−x)=0, where x is the mole fraction of one component dissolved in the other. The temperature above which miscibility is complete is given by T=4.5δ2. The heat of mixing is approximately −9δ2 cal. The predictions of this...