Two simple approaches to sol-gel transition

We represent a theory of polymer gelation as an analogue of liquid-glass tr ansition in which elastic fields of stress and strain shear components appe ar spontaneously as a consequence of the cross-linking of macromolecules. T his circumstance is explained on the basis of obvious combinatoric argument s as well as a synergetic Lorenz system, where the strain acts as an order parameter, a conjugate field is reduced to the elastic stress, and the numb er of cross-links is a control parameter. Both the combinatoric and synerge tic approaches show that an anomalous slow dependence of the shear modulus on the number of cross-links is obtained. (C) 2001 Elsevier Science B.V. Al l rights reserved.