Polymer, Vol.35, No.13, 2759-2763, 1994
The Bulk Modulus of Rubber
It is well known that there is an enormous disparity between the tensile elastic modulus E of a rubber and its bulk modulus K. For a typical rubber, E is of order 10(5) N m-2 and is primarily due to entropic effects. By contrast, K is of order 10(9) N m-2. This paper suggests that K arises from van der Waals interactions between groups in one chain and groups in neighbouring chains. Using a Lennard-Jones type of potential, U = - C/r6 + D/r12, and assuming pairwise addition, the free surface energy gamma of rubber may be calculated and compared with typical experimental values (gamma = 35 mJ m-2). From this, a typical value is obtained for C of order 60 x 10(-79) J m6 (corresponding to a Hamaker constant congruent-to 9.3 x 10(-20) J). This value may be used to calculate the bulk modulus, assuming a regular arrangement of interacting groups. The result agrees with the experimental value of K to better than an order of magnitude.
Keywords:SURFACE