B. M. E. Van Der Hoff

A General Model for Prediction of Molecular Weight Distributions of Degraded Polymers. Development and Comparison with Ultrasonic Degradation Experiments

Abstract A general model has been developed for the process of polymer chain breakage. The molecular weight distributions (MWDs) of the degraded polymer, after a specified number of chain ruptures, can be calculated from the model, given the MWD of the initial material. The calculations can easily be handled numerically on a digital computer. The model is applicable to any process in which polymer chains break, e.g., ultrasonation and high shear mechanical action. The course of degradation is described in terms of the probability that a molecule of a given length will break and the probability that a molecule of a particular length will result from this rupture. Any form of both these probability distributions and the initial MWD can be used in the model.

Transient Changes in Topology and Energy on Extension of Polybutadiene Networks

Abstract The theory of elasticity of polymer networks has been developed along two lines. The phenomenological approach leads to the Mooney-Rivlin relation between stress and extension ratio for uniaxial extension. The statistical theory of elasticity, based on a model for polymer molecules, predicts a similar relation with one of the constants zero. Actual elastic properties of rubbers do not agree fully with either theory. Experimental results are reported obtained with quantitatively cured polybutadiene and polyisoprene vulcanizates. These data are near-equilibrium results through the use of a cyclic stress sequence which largely eliminates the influence of long-time creep. The dependence of the initial modulus and the parameters of the Mooney-Rivlin relation on the chemical nature and the degree of branching of the polymer, the type of cross-links, and temperature has been investigated. A possible relation between the energy component of the elastic force and one of the parameters is discussed. These ...

Degradation of Polystyrene in Solution by Ultrasonation - A Molecular Weight Distribution Study

Abstract Ultrasonically induced degradation of polystyrene in tetrahydrofuran solutions has been studied. Four narrow molecular weight distribution (MWD) samples, a material with a wide MWD, and a bimodal MWD sample were degraded at various concentrations, temperatures, and ultrasonic intensities. The MWDs after a number of ultrasonation time periods were obtained from gel permeation chromatograms corrected for instrumental spreading. Degradation index DI, defined as the number of bonds broken per original number of molecules, has been used to describe the extent of degradation. The results of the experiments were used to determine the values of two parameters occurring in the degradation model developed previously. It was found that the course of the changes in MWDs predicted by the model are in good agreement with those observed experimentally when the following values of the model parameters are used. The probability of scission of a molecule with molecular weight M is proportional to the product of it...

A Method for Following Changes in Molecular Weight Distributions of Polymers on Degradation: Development and Comparison with Ultrasonic Degradation Experiments

Abstract When polymers are degraded by submitting them to shearing action, neither the probability of scission of a macromolecule, as a function of molecular weight (MW), nor the probability distribution of the lengths of the resulting fragments is known a priori. Information about these probabilities can be obtained by comparing observed changes in the molecular weight distributions (MWD) of degrading polymer with changes calculated from models. These models are based on assumed functions relating the probabilities mentioned to the MW of the polymer and that of the fragments. In order to make this comparison, equations are derived for various moments of the MWDs in terms of arbitrary initial MWDs and probability functions. Some simplified forms of these equations arising from chosen simple functions for the probabilities are also given. Data are presented to show that the precision of the weight-average MW calculated from gel-permeation chromatography (GPC) is about twice that of the number-average and z...

The Rate of Degradation by Ultrasonation of Polystyrene in Solution

Abstract The rate of degradation by ultrasonation of polystyrene in tetrahydrofuran solutions has been measured at various concentrations, temperatures, and irradiation intensities. As reported earlier, the course of the changes in molecular weight distributions is independent of the molecular weight (MW) of the initial polymer and of the degradation conditions. Therefore, the time dependence of the extent of the degradation can be meaningfully compared for various reaction conditions and for polymers with different original MWs. The extent of the scission process was expressed in terms of the degradation index (DI), the ratio of the number of chain bonds broken to those initially present. The problem of the existence of a minimum MW required for sonic scission is considered and arguments are advanced in favor of the assumption of a minimum degradable chain length for the purpose of evaluation of degradation data. This minimum MW was found to be about 30,000. DI values were corrected for the “unbreakable”...

Relation between Energy Contribution to Elastic Force and Strain Dependence of Modulus for Polybutadiene Vulcanizates

Abstract It is well known that the modulus G = r/(λ - λ−2) varies with deformation, thus deviating from the predictions of statistical theories of rubber elasticity which require it to be constant. It has also been found that there is a nonnegligible energy contribution to the elastic force. It is postulated that these two phenomena are related because both arise from energetic interaction between chains. Based on the lateral order of chains indicated by x-ray fiber diagrams of elongated noncrystallizable elastomers, it is suggested that energetic interaction of chains is induced by strain orientation. Proportionality between these two is assumed. The orientation distribution functions of end-to-end vectors and of statistical chain segments are considered. The proportionality constants are determined from the energy contribution to the strain dependence of the coefficient of thermal expansion. With the aid of these constants the modulus, corrected for energy contribution, is calculated. The observed and c...

Comparison of Stress-Strain Relations of Polybutadiene Vulcanizates in Compression and in Extension

Abstract According to elementary statistical theory of rubber elasticity, the modulus of rigidity τ/(λ - λ−2) is constant. The phenomenological theory predicts that this modulus is in first approximation equal to the sum of a constant (2C1) and a deformation-dependent term, 2C2. The dependence on elongation of experimental modulus data of many elastomers agrees more or less with the C2 term. Several attempts have been made to explain this dependence on the basis of molecular phenomena or by refinements of the statistical theory of elasticity. At present there is no consensus of opinion on the origin or interpretation of the deformation-dependent term. Almost all of the data on this dependence have been generated in extension experiments.

Cylindrical Approximation of Constrained Chain Model for Rubber Elasticity. I. Constant Volume Deformations

Abstract This paper reports a new model for rubber elasticity based on the geometric constraints imposed on a network chain and the chain segments by the crosslinks at each end. Through consideration of these constraints, the number of conformations available to a network chain can be calculated directly assuming the chain is on a lattice. By simplifying the model and by assuming affine deformation, the rigorous equations for the conformational entropy are reduced to an analytic expression for the strain-energy function. From this function, equations describing extension, compression and pure shear are derived. The model is tested against literature data for natural rubber and polybutadiene and is found to reproduce quantitatively all the salient features of the experimental stress-strain curves In the three modes of deformation. It is shown that the decrease in the Gaussian modulus with extension, often characterized by the C2 term in the Mooney-Rivlin theory, arises naturally from the conformational ent...