Studies on carbon black. III. Theory of bound rubber

On the hypothesis that “bound rubber” is a gel of carbon black particles, the bonding agent of which consists of the longer polymer molecules, a statistical theory is developed. The probability is first computed that a rubber molecule of i segments will be attached to j carbon black particles. By means of this probability the number and weight of molecules connecting carbon black particles are calculated. The theory predicts loadings below which bound rubber may not be expected (carbon black runs through into extract), and relates amount of bound rubber to total surface area of the black and the molecular weight of the remaining dissolved rubber to that of the rubber originally present. The theory gives a logical explanation of the often observed preferential adsorption by carbon black of polymer molecules of higher molecular weights.