A simple model is proposed to describe crazing in a very thin polymer film. It is argued that if the thickness of the film is below a certain critical value, the craze microstructure becomes similar to the deformation zone (two-dimensional neck) with the superimposed fibril structure. Deformation zone profile, characteristic fibril size, draw ratio, and critical film thickness are calculated as functions of material parameters and imposed strain rate. The results obtained are in good agreement with experimental values. The predictions of the model can also be used to verify the model of crazing in thick films and bulk polymers, which is described in Part 2 of the present series.

Crazing in thick polymer glass films and bulk glassy polymers is theoretically investigated. A simple microscopic model that treats an amorphous polymer at stresses above the yield stress as a viscous fluid with the scale-dependent surface tension is developed. Craze microstructural parameters including fibril diameter, spacing, and draw ratio are calculated. Crazing stress and critical thickness are determined as functions of material parameters and conditions of testing. The obtained results are in good quantitative agreement with experimental data.

The statistical-mechanical problem of chain pullout from an amorphous polymer under the influence of a constant force has been investigated. A simple microscopic model is proposed to describe the pullout process in both polymer glasses and elastomeric materials from a single point of view. A mean-field approximation for the interchain potential is used to account for the entanglements with the polymer network of the chain being pulled out. The chain mobility and the pullout rate were calculated as a function of pullout force, length of the chain, and other model parameters. In glassy polymers the pullout force was found to be almost rate independent at low pullout rates and linear in rate at high pullout rates. For polymer glasses the model also predicts the existence of some characteristic degree of polymerization Ne of the chain being pulled out, such that the pullout force scales as N for N « Ne but as N3 for N »• Ne. In elastomeric materials the pullout force was found to have a nonlinear dependence on both chain length and rate of pullout.

We study the statistical-mechanical problem of chain pullout during the fracture of a fiber of main-chain liquid-crystalline polymer. A simple model is used in which only longitudinal motion of the polymer chains is permitted and in which a mean-6eld approximation is used for the interchain potential. The dependence of the chain pullout velocity and energy dissipation on the temperature and applied force is obtained. It is shown that in order for the pullout process to start, the applied force should exceed some critical value. The pullout velocity was found to have a nonlinear dependence on the magnitude of the applied force. The work involved in chain pullout is calculated as a function of chain length and pullout velocity. I. INTKODU CTIONOver the past decade the process of chain pullout &om the bulk of polymeric material under the influence of a constant force has been intensively studied &om both theoretical and experimental points of view. ' ' It has been shown to give an important contribution to the toughness of interfaces between immiscible polymers, especially those reinforced by diblock copolymers, crazing and crack propagation in bulk polymers, ' ' as well as to the stiKness and strength of liquid crystalline polymer fibers.A number of models have been proposed to describe the process of chain pullout and the relation between chain pullout and the mechanical properties of bulk polymers and their interfaces.Almost all of these models, however, are phenomenological in nature, and do not consider the microscopic processes involved in chain pullout. Although rather successful in describing general features of the phenomena, these models are unable to explain a number of important experimental facts, including the saturation of the interface toughness at high pullout velocities.In this study we investigate the problem of chain pullout from a microscopic point of view. We restrict ourselves to the treatment of main-chain liquid crystalline homopolymers in order to avoid the additional complications that arise from the disordered structure of random copolymers or amorphous polymers. However, the method applied can, at least in principle, be generalized to the case of disordered materials. Moreover, it turns out that the results obtained in the liquid crystalline case exhibit a remarkable similarity to those found in experiments on glassy polymers.Before we introduce our model we outline the fundamental basis for the methodology we use, and point out the ways in which it divers &om those used previously. As in all theories of the approach to equilibrium, we shall be concerned with both the dissipative and the equilibrium aspects of the system behavior. These are generally connected by relations derived from the Huctuationdissipation theorem. In some previous studies of this problem it has been customary to work in the overdamped limit, where the efFects of the inertial terms in the Hamiltonian are ignored in favor of the dissipative terms. We choose to retain the inertial terms in addition to the damping t...