# MODULUS OF TIGHTLY CROSSLINKED POLYMERS RELATED TO CONCENTRATION AND LENGTH OF CHAINS.

## Abstract

The equilibrium shear modulus G of network polymers increases rapidly with the chain concentration nu when nu greater than equivalent to 10** minus **3 mol/cm**3. This behavior is accounted for by the equation G equals PHI //n nu RT GAMMA (1/ lambda //m), where PHI //n(equals r//i**2/r//0**2) may depend on n, the mean number of backbone bonds per chain, and GAMMA (1/ lambda //m) is a function of 1/ lambda //m, the mean fractional extension of chains in the isotropic (undeformed) network. In turn, 1/ lambda //m equals (PHI //nC//n/q**2n)** one-half , where C//n is a characteristic ratio (equals r//0**2/nl**2) which, for short chains, depends on n, and q is a constant determined by bond angles and lengths. An expression for GAMMA , suggested by a well known equation for a regular cubic network of freely jointed volumeless chains, is derived and then shown to be approximated closely by GAMMA //a//p//p equals 5 lambda **2//m/(5 lambda **2//m minus 6) for 1/ lambda //m less than 0. 88. The moduli of some 26 ethyl acrylate-dimethacrylate networks, for which 5 less than n less than 23 and 2 multiplied by 10**7 less than G less than 5 multiplied by 10**9 dyn/cm**2, were represented by the equation through use of effective parameters, phi //e//f and C//e//f, which are independent of n.