Expansion of Single Chains Released from a Spherical Cavity

Abstract

A two-stage model is developed to explain the phenomena of chain expansion, released from a confining cavity. In the first stage, the chain is assumed to expand as a sphere, while in the second stage it expands like a coil. The kinetic equations for the variation of chain size are derived in the two stages by balancing the rate of the free energy change with the rate of the energy dissipation. Langevin dynamics simulations are then performed to examine the theory. We find that the expansion process is dominated by the second stage and the evolution of chain size follows, mainly, the predicted curve for coil expansion, which depends on the chain length and is not sensitive to the confining volume fraction. It permits to define the expansion time for the process. Further study reveals that the chain does undergo a spherical expansion in the first stage with the characteristic time much shorter than the one for the second stage. As a consequence, the first-stage variation of chain size can be regarded as an add-on to the principal curve of expansion designated by the second stage. The scaling behaviors and the associated scaling exponents are analyzed in details. The simulation results well support the theory.

Expansion Kinetics of Flexible Polymers upon Release from a Disk-Shaped Confinement

“…The aforementioned procedures are further utilized to reanalyze the simulation data for polymer expansion in a 3D space, aiming to test the generality of the theory. The collapses of the R̂ and R̃ curves, the scaling behaviors of τ 1 and τ 2 , the exponents α 1 , α 2 , χ 1 , and χ 2 , the universal behaviors of the kinetics, and the crossover between the two expansion stages are newly calculated in Supporting Information, as presented in Figures S14 to S18.…”

“…The characteristic time τ 2 is given by A 2 η 0 σ 2 k B T N 2 + χ 2 , where χ 2 is an exponent that accounts for the additional dependence on the chain length through η normale normalf normalf ∼ η 0 N 1 + χ 2 in the second stage. The constant a c is proposed to be set as 1 based on the simulations presented later and our previous study in 3D space . This choice is applicable for the situation of a long chain released from strong confinement and turns out to be a good approximation for general situations.…”

“…The constant a c is proposed to be set as 1 based on the simulations presented later and our previous study in 3D space. 15 This choice is applicable for the situation of a long chain released from strong confinement and turns out to be a good approximation for general situations. It will be explained later.…”

“…Recently, we have developed a two-stage model to explain the expansion of polymers released from a spherical cavity in a three-dimensional (3D) space. 15 In the model, the chains undergo a rapid spherical expansion in the first stage, followed by a dominant coil-like expansion in the second stage. Importantly, the growth in the latter stage exhibits a hastened exponential recovery, powered by an exponent of 1/5.…”