SCALING THEORY FOR THE SIZE OF CRUMBLED MEMBRANES IN PRESENCE OF LINEAR-POLYMERS AND OTHER OBJECTS

Condensed systems of polymers and membranes are studied. First it is shown that melts of membranes behave quite differently to melts of linear polymers. Whereas polymer chains in melts exhibit random walk behaviour, surfaces are always saturated. Most striking are results where surfaces are dissolved in linear polymers, where the size of the membrane is not changed, i.e. nu = 4/5 as in the crumbled phase. The general value of nu for D-dimensional manifolds is given by nu = 2 D/(2 + d) where in the crumbled phase nu = 2 + D/2 + d. Both values are identical for D = 2. It is further shown that even for mixtures of membranes and stiff objects (Tobacco mosaic virusses) the crumbling exponent is also nu = 4/5. This is a speciality for D = 2 membranes. For general values of D new exponents are predicted.