Confinement Free Energy Research Articles

Free energy and confinement force of macromolecules in a slit at full equilibrium with a bulk solution

Nondilute athermal and theta solutions of nonadsorbing flexible macromolecules in equilibrium with repulsive slit-like pores were examined by the lattice Monte Carlo simulations. The free energy of confinement Δ A/ kT and the force f/ kT exerted by polymers on the slit were computed as a function of the slit width D in a wide range of bulk concentrations φ. The free energy and force profiles in nondilute solutions were found to deviate considerably from the ideal chain theory; the perturbation of chains by a presence of the slit walls were substantially reduced in nondilute solutions. The free energy and force functions appropriate for nondilute solutions were derived by fitting the simulation data. Further, the relative pressure p I/ p E exerted by the nonadsorbing confined molecules on the slit walls was calculated. The depletion effect relevant to colloid stabilization was found in dilute solutions to be slightly weaker for excluded-volume chains than for ideal chains. The relative pressure equation was modified to cover semidilute solutions, by using the mean-field and scaling expressions of the osmotic pressure. Both the relative pressure p I/ p E and the intra-slit concentration profiles φ I( x) in tandem display a suppression of the depletion effect with increasing φ in simidilute solutions.

Simulation of a semiflexible polymer in a narrow cylindrical pore

The probability that a randomly accelerated particle in two dimensions has not yet left a simply connected domain ${\cal A}$ after a time $t$ decays as $e^{-E_0t}$ for long times. The same quantity $E_0$ also determines the confinement free energy per unit length $\Delta f=k_BT\thinspace E_0$ of a semiflexible polymer in a narrow cylindrical pore with cross section ${\cal A}$. From simulations of a randomly accelerated particle we estimate the universal amplitude of $\Delta f$ for both circular and rectangular cross sections.

Simulations of Partitioning in Size Exclusion Chromatography

The systematic investigations by Monte Carlo (MC) simulations of parameters involved in partitioning in size exclusion chromatography (SEC) are reported. Specifically, three realistic features involved in the separation mechanism are treated: (a) real chain features as contrast to ideal chain behavior, (b) finite concentration of macromolecules in partitioning, and (c) adsorption of polymer on pore walls. In all cases an enhancement of the partitioning relative to the ideal circumstances was found. The partitioning rules in these cases significantly deviate from the Casassa relation for ideal chains. The factors mentioned affect the shape of the universal calibration dependence and reduce its selectivity. The rationalization of the free energy of confinement in SEC based on a loss of orientational entropy of coil ellipsoids in a pore is suggested.

Partition Coefficients and the Free Energy of Confinement from Simulations of Nonideal Polymer Systems

The investigation of the partitioning equilibrium in real polymer systems by Monte Carlo (MC) simulations is reported. In contrast to ideal chain treatments the factors such as flexibility and excluded volume in real chains, the finite concentration of macromolecules φ, and polymer adsorption on pore walls of the attractive strength εw are considered in computations. The free energy change ΔA/kT due to chain confinement in slitlike structures under nonideal conditions is estimated from simulations. The dependencies of the partition coefficient K on λ, the solute to pore size ratio, relevant to the static partitioning and to size exclusion chromatography (SEC), were computed. In all cases the factors considered enhance the partition coefficient K for a given λ and lead to more gradual changes of K with λ; i.e., the resolving power of the nonideal partitioning decreases relative to a case of ideal chain partitioning. The concentration effect on the steric partitioning coefficient K was found to depend markedly on the solvent quality in dilute solutions. In mixed-mode partitioning by a combination of steric exclusion and adsorption, the function K(λ,εw) is computed by a fit of the simulation data. This function properly reproduces for nonideal chains all liquid chromatography regimes, including the critical chromatography. An interpretation of the free energy changes ΔA/kT in nonideal partitioning, based on the loss of conformational and orientational entropies of coils on their confinement, is discussed.

Free energy of a semiflexible polymer in a tube and statistics of a randomly-accelerated particle

The confinement free energy per unit length of a continuous semiflexible polymer or wormlike chain in a tube with a rectangular cross section is derived in the regime of strong confinement. Here P is the persistence length, and and are the sides of the rectangle. The result is also interpreted in terms of the escape probability of a randomly-accelerated particle from a rectangular domain.

Free energy of a semiflexible polymer confined along an axis

A continuum model of a fluctuating semiflexible polymer chain confined along an axis is considered. In the regime of strong confinement, configurations with overhangs are negligible, and the partition function is determined by a partial differential equation. An extremum principle for eigensolutions is formulated. The exact solution of the differential equation for a polymer in a harmonic potential is given. A lower bound for the confinement free energy of a polymer in a tube is obtained.

Confinement free energy of semiflexible polymers

Using a novel scheme to compute the chemical potential of semiflexible polymers, we have measured the confinement free energy of a wormlike chain in a tube. We compare our result for the dependence of the free energy on the chain length, the persistence length and the diameter of the cylinder with the corresponding theoretical predictions based on the scaling theory of Odijk and the fluctuation theory of Helfrich. Our simulation data agree well with the exponents of the theoretically predicted power laws. We find evidence that, for long wavelengths, the mode damping assumption underlying Helfrich’s theory is valid.