Abstract
We develop an analytical model to predict the collapse conformation for a single semiflexible polymer chain in solution, given its length, diameter, stiffness, and self-attractiveness. We construct conformational phase diagrams containing three collapsed states, namely torus, bundle, and globule over a range of dimensionless ratios of the three energy parameters, namely solvent-water surface energy (), energy of bundle end folds (), and bending energy per unit length in a torus (). Our phase diagram captures the general phase behavior of a single long chain (>10 Kuhn lengths) at moderately high (order unity) dimensionless temperature, which is the ratio of thermal energy to the attractive interaction between neighboring monomers. We find that the phase behavior approaches an asymptotic limit when the dimensionless chain length to diameter ratio (L*) exceeds 300. We successfully validate our analytical results with Brownian Dynamics (BD) simulations, using a mapping of the simulation parameters to those used in the phase diagram. We evaluate the effect of three different bending potentials in the range of moderately high dimensionless temperature, a regime not been previously explored by simulations, and find qualitative agreement between the model and simulation results. We, thus, demonstrate that a rather simplified analytical model can be used to qualitatively predict the final collapsed state of a given polymer chain.
Highlights
Polymer chains collapse into compact globules when the solvent condition changes from good to poor
The collapsed state of a single polymer chain is controlled by three dimensionless quantities, namely γb {γe σ3, γe {γs, and L* “ L{σ
On the “phase diagram” shown in Figure 3, the y-axis is the ratio of the end fold energy to the surface energy, while the x axis is the ratio of the bending energy to the product of end fold energy and bead diameter cubed
Summary
Polymer chains collapse into compact globules when the solvent condition changes from good to poor. Their model was derived for collapsed structures of bead spring “pearl necklace” chains at low dimensionless temperature, where the packing order (number of bead-bead contacts) of the filaments in both torus and bundle was considered For both conformations, they found periodicities in the minimum energy state as a function of chain length due to the periodic completion of windings around the torus, or of parallel filaments in the bundle, respectively. They compared the energy of a torus with perfect hexagonal filament packing to a bundle with ideal tight back folding at the ends, and concluded the torus is always energetically more favorable than the bundle This is a somewhat striking finding, since bundle structures are generally considered to be stable equilibrium collapsed structures for semiflexible polymer chains and have been observed in both simulations and theoretical studies [10,15,18].
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