Pressure of Linear and Ring Polymers Confined in a Cavity

Abstract

Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.

Continuous Crossover from the Dilute to Semidilute Concentration Regime in Spherically Confined Polymers

“…The Monte Carlo (MC) simulation method used in earlier reports ,,, is employed to compute the properties of single flexible polymers in a good solvent entrapped in an impenetrable spherical cavity of the effective radius R. The polymer is modeled by the bead–spring model of partially fused spherical beads of N = 300 and the radius σ connected by bonds of the effective mean length l (Figure ). The potential energy U of the system is given by contributions from the bond deformation U FENE , nonbonded interactions between beads U nb , and the bead-cavity wall interaction U w .…”

“…The simulation was performed by the MC protocol employed earlier to evaluate the pressure of polymers inside a sphere. The protocol was designed in analogy with the piston technique for a tube channel. , In the constant pressure ensemble ( NpT ) employed, the applied pressure p is fixed in the simulation and the average value of the radius R is computed. The choice of an NpT ensemble differentiates our approach from the previous simulation studies of polymers inside a sphere based on the NVT ensemble. ,, The applied pressure expressed in the dimensionless form pl 3 / kT determines the pressure of the polymer exerted on the inner surface of the cavity.…”

“…The choice of an NpT ensemble differentiates our approach from the previous simulation studies of polymers inside a sphere based on the NVT ensemble. ,, The applied pressure expressed in the dimensionless form pl 3 / kT determines the pressure of the polymer exerted on the inner surface of the cavity. The equilibrium conformations of a confined polymer are sampled by using the Metropolis algorithm at constant temperature kT /ε = 1, where ε is the interaction energy parameter in the nonbonded potential U nb . , The Boltzmann factor in the Metropolis scheme includes an extra volume fluctuation term − p d V / kT = ( p l 3 k T ) normald V / l 3 , where d V = 4π R 2 d R represents a small random change in the spherical volume (Figure ). The chain moves in ring polymers include the small random displacement of beads and consequential evaluation of changes in interactions with all beads and walls.…”

“…The simulation was performed by the MC protocol employed earlier 20 to evaluate the pressure of polymers inside a sphere. The protocol 20 was designed in analogy with the piston technique for a tube channel.…”

“…The equilibrium conformations of a confined polymer are sampled by using the Metropolis algorithm at constant temperature kT/ε = 1, where ε is the interaction energy parameter in the nonbonded potential U nb . 20,27 The Boltzmann factor in the Metropolis scheme includes an extra volume fluctuation term −pdV/kT =…”