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Equilibrium morphologies and force extension behavior for polymers with hydrophobic patches: Role of quenched disorder

Motivated by single molecule experiments on biopolymers we explore equilibrium morphologies and force-extension behavior of copolymers with hydrophobic segments using Langevin dynamics simulations. We find that the interplay between different length scales, namely, the persistence length $\ell_{p}$, and the disorder correlation length $p$, in addition to the fraction of hydrophobic patches $f$ play a major role in altering the equilibrium morphologies and mechanical response. In particular, we show a plethora of equilibrium morphologies for this system, \textit{e.g.} core-shell, looped (with hybridised hydrophilic-hydrophobic sections), and extended coils as a function of these parameters. A competition of bending energy and hybridisation energies between two types of beads determines the equilibrium morphology. Further, mechanical properties of such polymer architectures are crucially dependent on their native conformations, and in turn on the disorder realisation along the chain backbone. Thus, for flexible chains, a globule to extended coil transition is effected via a tensile force for all disorder realisations. However, the exact nature of the force-extension curves are different for the different disorder realisations. In contrast, we find that force-extension behavior of semi-flexible chains with different equilibrium configurations \textit{e.g.} core-shell, looped, \textit{etc.} reveal a cascade of force-induced conformational transitions.