On the extension of polysoaps: The Gaussian approximation

Polysoaps are linear hydrophilic chains that incorporate, at intervals, covalently bound amphiphilic monomers. In water, the amphiphilic monomers self assemble into intrachain micelles thus endowing the chain with a secondary structure. The relaxation of the secondary structure upon deformation qualitatively modifies the elastic behaviour of polysoaps in accordance with the LeChatelier principle. For long polysoaps a regime in which the tension in the chain, f, is independent of the end to end distance R, f similar to R degrees is predicted. The extension of long polysoaps is analysed for the particularly simple case when the backbone obeys Gaussian statistics and excluded volume interactions are neglected.