Macromolecules 1990,23, 3975-3982 3975 A New Mechanism of Toughening Glassy Polymers. 2. Theoretical Approach A. S. Argon,' R. E. Cohen, and 0. S. Gebizlioglut Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 H. R. Brown IBM Almaden Research Center, San Jose, California 95120 E. J. Kramer Cornell University, Ithaca, New York 14853 Received November 13, 1989; Revised Manuscript Received February 20, 1990 ABSTRACT: A theoretical model is presented for the toughening of brittle glassy polymers by the controlled solvent crazing action of precipitated low molecular weight rubber diluents existing in the form of randomly dispersed small spherical pools. In this mechanism the central process is the increased sorption of the dil- uent under the deformation-inducednegative pressure existing in a boundary layer on the craze periphery where the sorbed diluent produces substantial plasticization that significantly lowers the craze flow stress to prevent premature craze fracture. The resulting expressions for the reduction of the craze flow stress with increasing volume fraction of diluent are in excellent agreement with experimental measurements. I. Introduction The well-known problem of brittleness of flexible- chain glassy polymers in tension has in the past been dealt with in a number of ways, which have included uniaxial and biaxial orientation;' blending a component of an inflexible-chain polymer with greater craze resistance into a more brittle polymer;2 and introducing compliant composite particles into the brittle polymer to enhance craze pla~ticity.~ While all of these approaches are effective to some degree, they have drawbacks, in the limited shapes of the products to which they can be applied, in requiring substantial volume fractions of craze-resistant polymer or in compromising stiffness and optical properties, not to mention increasing the cost of the product. Recent studies of blending brittle homopolystyrene with very small concentrations of low molecular weight elastomeric components4* have pointed to another very effective and hitherto unappreciated possibility of toughening a brittle polymer by controlled solvent crazing. In such studies Ge- bizlioglu et al.44 have succeeded in substantially lowering the craze yield strength of high molecular weight PS by incorporation of a few percent of low molecular weight PB, which precipitates out in the form of tiny pools of diameters less than 0.2 pm. There is now overwhelming evidence that the liquid PB in these pools acts as a plasticizing agent under the prevailing negative pressures of the craze tip and craze borders to result in a greatly increased propensity for crazing at low stresses to avoid early craze fracture from extrinsic flaws.' The experimental evidence for this phenomenon has been presented in detail in an accompanying papera6 Here we provide the theoretical details of the mechanism of this novel process of toughening. 11. Theoretical Model 11.1. Toughening by Controlled Solvent Crazing. It is now well established that crazes in glassy polymers + Present address: Bell Communications Research, Red Bank, NJ 07701. grow by an interface convolution process both ahead*sQ and in thicknessxo and that the rate of growth is governed, under the prevailing stresses, by the strain rate dependent plastic resistance of the polymer.8 A reduction of this plastic resistance by plasticization results in an increased velocity of craze growth. Consider a volume fraction f of pools of a phase- separated plasticizing liquid phase in a brittle glassy polymer, in the form of randomly dispersed spherical "particles" of diameter a. Assume furthermore that a is sufficiently small so that when incorporated into a craze as a drained cavity, it constitutes a subcritical size flaw in the spongy craze matter. We now postulate that when a craze goes through a randomly distributed field of spherical pools of potential plasticizing agent, it will int sect these pools as a sampling plane, and the contents of & pools will drain onto the already produced surfaces of craze matter and solid polymer. This occurs preferentially along the tip of the craze where the advancing craze front samples the field of particles. If the plasticizing liquid is a low molecular weight PB with low viscosity and good wetting characteristics, it should effectively coat the multiple-convoluted concave surfaces of the craze matter and solid polymer at the craze tip. We assume that this occurs at a rate much faster than the rate of production of a new craze surface in a reference polymer under dry conditions (see Appendix I). Since the PB as a possible diluent of the PS is already in equilibrium with the latter as a separate phase, it should also be in equilibrium with the free surfaces of the craze that it coats, if these surfaces were stress free. (The PB wetting the concave surfaces of the craze must actually be under a mild capillary negative pressure, which, however, should be much less than the initial negative pressure due to thermal expansion misfit in the P B existing in the spherical cavities11 prior to its drainage onto the craze surfaces.) Both at the tip as well as at the borders of a craze where the craze tufts are drawn out of the solid polymer, however, substantial levels of negative pressures exist in a narrow fringing layer. Under these conditions the equilibrium solubility of the PB in the stressed border regions of the craze must increase 0024-9297/90/2223-3975$02.50/0 0 1990 American Chemical Society