M. R. Stukan

Chain length dependence of the state diagram of a single stiff-chain macromolecule: Theory and Monte Carlo simulation

We present a Monte Carlo computer simulation and theoretical results for the dependence of the state diagram of a single semiflexible chain on the chain length. The calculated transition lines between different structures in the state diagrams for both studied chain lengths N=40 and N=80 can be described by theoretical predictions which include chain length dependence explicitly. The stability criteria of different structures are discussed. The theoretically predicted exponent in the dependence of the toroid size on the chain length is compatible with computer simulation results.

Structures of stiff macromolecules of finite chain length near the coil-globule transition: A Monte Carlo simulation

Using a coarse-grained model of a semiflexible macromolecule, the equilibrium shapes of the chain have been studied varying both the temperature and the chain stiffness. We have applied Monte Carlo techniques using the bond fluctuation model for a chain length of N = 80 effective monomers, and two different types of interactions: a potential depending on the angle between successive bonds along the chain to control the chain stiffness, and an attractive interaction between non-bonded effective monomers to model variable solvent quality. In a diagram of states where chain stiffness and inverse temperature and used as variables, we find regions where the chain exists as coil, as spherical globule, and as toroidal globule, respectively. Some of these regions are not limited by sharply defined boundaries, but rather wide two-state coexistence regions occur in between them, where also intermediate metastable structures (such as rods and disks) occur. Recording histograms of energy, orientational order parameters, etc., which exhibit a two peak structure in the two-state coexistence regions, we perform a subensemble analysis of the individual structures corresponding to these peaks.

Dense orientationally ordered states of a single semiflexible macromolecule: An expanded ensemble Monte Carlo simulation

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N = 256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid-solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N = 256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry.

Phase diagram of solutions of stiff-chain macromolecules: A Monte Carlo simulation

The phase diagram of solutions of semiflexible macromolecules consisting of N=20 effective monomer units has been studied by means of grand canonical Monte Carlo computer simulation using the bond fluctuation model and the configurational bias scheme. Two different types of interactions were taken into account: an intramolecular potential controlling the chain stiffness and an attractive interaction between effective monomer units to model variable solvent quality. A very broad region of density from dilute solution to melt has been covered in the simulation. The phase diagram shows a strong increase of the density difference between isotropic dilute and nematic dense phases upon increasing attraction between monomer units (i.e., decreasing the temperature). We discuss methods of locating the isotropic–nematic transition point and the effects of the vicinity of the polymer–solvent critical point on the properties of the liquid crystalline transition.

Osmotic pressure acting on a semipermeable shell immersed in a solution of polyions.

We study theoretically the osmotic equilibria for a shell immersed in a suspension of polyions (e.g., colloids, polyelectrolytes, etc.). The shell is treated as impermeable for polyions, but allowing free diffusion of counterions that permeate inside the shell. From the solution of linearized Poisson-Boltzmann equation, we obtain the distribution of a potential and concentration profiles for polyions and counterions. We then obtain an explicit formula for the excess osmotic pressure of a polyion solution exerted on the shell, which includes a quadratic term in order to provide a self-consistency of a linear theory. As a result this pressure is larger than given by a concentration of polyions at the outer shell boundary obtained within linearized theory. It is, however, always smaller than or equal to the bulk osmotic pressure. This difference is attributed to a repulsive electrostatic disjoining pressure due to an overlap of counterion clouds inside the shell. A comparison with molecular dynamics simulations is provided and demonstrates that although the concentration profiles obtained within a linear theory deviate from simulation data at large potential, the theoretical and simulation pressures are in surprisingly good harmony.

Finite size effects in pressure measurements for Monte Carlo simulations of lattice polymer models

We report on a careful analysis of finite size effects on pressure measurements in Monte Carlo computer simulations of isotropic athermal solutions of flexible polymer chains by means of the repulsive wall method. We find finite size corrections to the pressure due to surface effects. These corrections are inversely proportional to the thickness of the simulation box, both if we keep the average density (in the canonical ensemble) or the chemical potential (in the grand canonical ensemble) constant in course of the preparation of the starting conformation. We propose a modification of the repulsive wall method which allows avoidance of these finite size effects and to estimate the pressure for an infinite system when running simulations in a finite box.

Monte Carlo Simulations of Semi-Flexible Polymers

We present Monte Carlo simulations on the phase behavior of semiflexible macromolecules. For a single chain this question is of biophysical interest given the fact that long and stiff DNA chains are typically folded up into very tight compartments. So one can ask the question how the state diagram of a semiflexible chain differs from the coilglobule behavior of a flexible macromolecule. Another effect connected with rigidity of the chains is their tendency to aggregate and form nematically ordered structures. As a consequence one has two competing phase transitions: a gas-liquid and an isotropic-nematic transition potentially giving rise to a complicated phase diagram.

On the kinetics of nematic ordering in solutions of semiflexible macromolecules: a Monte Carlo simulation

Abstract The occurrence of nematic liquid-crystalline ordering in semidilute and concentrated solutions of semiflexible macromolecules has been studied by means of grand canonical Monte Carlo computer simulations using the bond fluctuation model and the configurational bias scheme. Chain length was equal to 20 monomer units, while the persistence length was about 5 monomer units. We used an intramolecular stiffness potential depending on the angle between successive bonds along the chain and on the bond length, and an attractive interaction between monomer units to model variable solvent quality. We have monitored the processes of appearance and destruction of monodomain and multidomain nematic configurations. Our findings are that the first stages of both the ordering and disordering processes occur upon sufficient oversaturation through the spinodal ordering scenario. Possible screening of nucleation processes and the applicability of our model to real kinetics are discussed. Results of our simulations are visualized in six movies.