Characteristics of the intrinsic modulus as applied to particulate composites with both soft and hard particulates utilizing the generalized viscosity/modulus equation

Recently, four significantly different particulate composite modulus deriva tions from the literature were found to yield the same theoretical "intrins ic modulus" for a particulate composite. In this article, this new intrinsi c modulus was successfully combined with the generalized viscosity/modulus equation to yield a good fit of the shear modulus-particulate concentration data of both Smallwood and Nielsen using a variable intrinsic modulus. Som e fillers yielded an intrinsic modulus that was close to the Einstein limit ing value ([G] = [eta] = 2.5), while other fillers yielded intrinsic moduli that were either somewhat larger or somewhat smaller than this value. The intrinsic modulus for carbon black in rubber was much larger than was Einst ein's predicted value. However, intrinsic modulus values for Nielsen's data for particulate composites were smaller than were Einstein's prediction at temperatures below the glass transition temperature of the matrix. The exp lanation for this phenomenon can easily be understood from a review of the properties of the intrinsic modulus. Likewise, the generalized viscosity/mo dulus equation was also successfully applied to available modulus literatur e for ceramics where voids were the particulate phase. When applied to Wang 's data, the intrinsic modulus was found to be negative when describing the compaction of voids in the hot isostatic pressing of a ceramic. For this a pplication, the modulus of a particulate composite as a function of the vol ume fraction of particles was modified to describe the modulus as a functio n of porosity. For the sets of data analyzed, values of the interaction coe fficient and the packing fraction were not necessarily unique if the data s ets were limited to the lower particulate volume fractions. For application s where a minimum amount of data was found to be available, a new approach was introduced to address a relative measure of the compatibility of the pa rticle and the matrix using a new definition for Kraemer's constant. (C) 20 00 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1954-1963, 2000.