Theory of Filler Reënforcement. II

Abstract

Abstract Modulus-type properties of loaded rubber depend mainly on the shape and the concentration of the filler particles and are almost independent of the size and the surface characteristics of the filler. The author's theory of these properties is patterned after the theory of viscosity of suspensions, and implies nonspecific wetting between rubber and filler particles, making possible considerable mobility of the filler particles in the rubber. Such mobility is in agreement with studies of the electrical conductivity of carbon black loaded stocks and of the adsorption of gases by carbon blacks. Fillers with spherical particle shape like calcium carbonate and P-33 (which do not form chainlike structures) obey the theoretical equations for spherical particles. Fillers like high modulus and channel carbon blacks whose primary spherical particles agglomerate into chainlike secondary particles obey theoretical equations for the secondary particles characterized by a shape factor. The assumed chain formation and the values for the shape factors are in approximate agreement with conclusions from electron micrographs. Experimental arguments are given for the validity of the theoretical equations up to 25 per cent volume concentration, which is the usual technical loading. The agreement between theory and experiment is within the rather large error caused by nonuniformity between and within the test samples, and in some work by the use of commercial testers, and the difficulty of comparable vulcanizations. Refinements of the theory are introduced, including possible solvation, difference between the modulus of rubber in absence (“gum” stock) and in presence of the filler particles, and various degrees of wetting from nonwetting to strong wetting (implying specific chemical bonds between rubber and filler). The above mentioned sources of error in the experimental work prevent safe conclusions about the necessity of introducing such refinements. The experiments include new measurements of stress-strain properties of loaded vulcanized stocks and of the Mooney viscosities of unvulcanized rubber-filler mixes, and a discussion of the pertinent literature. For the dielectric constant of stocks loaded with fillers of spherical primary particle shape, a simple formula is derived.