Kinetic laws at the collapse transition of a homopolymer

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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 α i =9/11 (7/11) with (without) hydrodynamics. We find the scaling laws of the characteristic time of the coarsening stage, τ m ∼N γm , and the final relaxation time, τ f ∼N γf , as a function of the degree of polymerizationN. These exponents are equal to γ m =3/2, γ f =1 in the regime of strong hydrodynamicinteraction, and γ m =2, γ f =5/3 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.