An exact real space renormalisation group is applied to study the adsorption of a single self-avoiding walk on fractal spaces. Exact results of critical exponent ν and crossover exponent φ show that de Gennes' conjecture φ =1-ν is invalid. The phase diagram has qualitatively the same shape as it has on Euclidean space, except for a unique and important difference that the adsorption transition would take place for a single polymer chain at a hard wail exerting a infinitesimal short-range attractive force on the fractal space instead of a finite one as on Euclidean space.
下载:
