Kinetic laws at the collapse transition of a homopolymer

Abstract

We present results from numerical analysis of the equations derived in the Gaussian self-consistent method for kinetics at the collapse transition of a homopolymer in dilute solution. The kinetic laws are obtained with and without hydrodynamics for different quench depths and viscosities of the solvent. Some of our earlier analytical estimates are confirmed, and new ones generated. Thus the first kinetic stage for small quenches is described by a power law decrease in time of the squared radius of gyration with the universal exponent ␣ i ϭ9/11 ͑7/11͒ with ͑without͒ hydrodynamics. We find the scaling laws of the characteristic time of the coarsening stage, m ϳN ␥m , and the final relaxation time, f ϳN ␥ f , as a function of the degree of polymerization N. These exponents are equal to ␥ m ϭ3/2, ␥ f ϭ1 in the regime of strong hydrodynamic interaction, and ␥ m ϭ2, ␥ f ϭ5/3 without hydrodynamics. We regard this paper as the completion of our work on the collapse kinetics of a bead and spring model of a homopolymer, but discuss the possibility of studying more complex systems.

Coil-to-globule transition by dissipative particle dynamics simulation

“…Generally, we find the scaling law of this stage as τ 1 ∼ ξ −0.39±0.05 N 0 . Independence of this time scale on the chain length has also been obtained by other authors, 8,14 while no previous result has been given on the scaling with the quench depths ξ .…”

“…According to their theory, homopolymer first collapses into an unknotted, crumpled globule and then, through a slow process that involves knotting, reaches an equilibrium globule, the characteristic times for these two steps scaling as N 2 , N 3 , respectively. Approximate theories based on Langevin dynamics [12][13][14][15][16][17][18] similarly have not reached consensus with respect to the mechanisms and the scaling behaviors because of the different approximations invoked in the different studies. However, it is generally agreed that hydrodynamic interactions play a significant role in the transition kinetics by accelerating the collapse process.…”

Universality and Specificity of Polymer Gels Viewed by Scattering Methods

“…One is a formation of the skin layer, and the other is a twostep shrinking via crumpled globule formation proposed by Grosberg and Nechaev 60 and by Dawson et al, 61,62 i.e., chain shrinking and subsequent intra-cluster association. Let us first discuss the first possibility in more detail.…”

Slow relaxation and solvent effects in the collapse of a polymer

“…The glassy behavior of a homopolymer quenched below the Θ-point was recently addressed numerically in [14], where it was shown that a close resemblance exists between the correlation or structure functions measured in glasses and in single polymer chains. The usual picture of polymer collapse when quenched below the Θ-point [9,[17][18][19][20][21][22][23][24], shows that non-equilibrium effects are important, especially the influence of the solvent, the relaxation pathways and the glassy properties of the globular state.…”