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 105 N m-2 and is primarily due to entropic effects. By contrast, K is of order 109 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/rr+ D/r 12, and assuming pairwise addition, the free surface energy ~ of rubber may be calculated and compared with typical experimental values (~ = 35 mJ m-2). From this, a typical value is obtained for C of order 60 x 10-79j m s (corresponding to a Hamaker constant ~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.
Посилання на статтю:
The bulk modulus of rubber / D. Tabor // Polymer. – 1994. – Vol 35. – P. 2759-2763.