Collapse of a single polymer chain: Effects of chain stiffness and attraction range

Abstract

Chain-like macromolecules in solution, whether biological or synthetic, transform from an extended conformation to a compact one when temperature or other system parameters change. This collapse transition is relevant in various phenomena, including DNA condensation, protein folding, and the behavior of polymers in solution. We investigate the interplay of chain stiffness and range of attraction between monomers in the collapse of a single polymer chain. We use Monte Carlo simulations based on the pruned-enriched Rosenbluth method. We demonstrate that the competition between the persistence length, l_p, and the range of attraction, r_c, determines whether the chain's collapse behavior resembles that of flexible chains or stiff ones. When l_p is larger than r_c, the chain collapses sharply with decreasing temperature, whereas if l_p is smaller than r_c, it contracts gradually. Notably, in the regime of small l_p and large r_c, this rounding into a gradual compaction persists upon increasing the chain length and may remain in place in the limit of infinite chain length. Furthermore, for small r_c, the transition temperature (theta-temperature) increases with l_p, whereas for large r_c the theta-temperature decreases with l_p. Thus, stiffness promotes collapse for small r_c but suppresses it for large r_c. Our findings are in agreement with recent experiments on the contraction of single-stranded RNA as compared to double-stranded DNA, and provide valuable insights for understanding polymer collapse and the essential polymer parameters affecting it.