Wim J. Briels

Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.

A structure-based coarse-grained model for polymer melts

In this study we explore a systematic procedure to coarsen a microscopic model towards a mesoscopic model. The procedure is applied to a system of chains of ten beads, representing a low molecular weight polymer melt. Our method consists of defining coarse-grained sites in the microscopic system, and calculating their spatial distribution on the pair level. The effective interaction between the coarse-grained sites is then obtained by bringing the pair interaction in consistence with the pair density. We investigate both a dynamic and a stochastic method for this step. The so obtained mesoscopic interaction is used in a molecular dynamics simulation to investigate the pressure of the coarse-grained system. We found that the pair interaction that reproduces the pair density predicts a pressure that is significantly lower than the microscopic value, even if we take the state-dependency of the coarse-grained interactions into account. We therefore conclude that coarse-grained models lack thermodynamic consistency.

Coarse-grained dynamics of one chain in a polymer melt

In this study we present the coarse-graining of one polymer chain in a melt to a single dimer. By using the projector operator formalism we derive the equation of motions for the dimer. The different forces that occur in this equation of motion are calculated from molecular dynamics simulations of the microscopic model, using constraint forces to fix the dimer configuration. The mean constraint force serves as the conserved part of the interaction, whereas the time correlation of the constraint force fluctuation leads to the nonconserved interactions: the dissipative and fluctuating forces. Using the configurational dependent coarse-grained interactions we have performed stochastic dynamics simulations of the dimer. Dimer properties of the microscopic and the coarse-grained model are shown to be in reasonable agreement. We also discuss the application of the framework to coarse-graining polymer melts into more detail, i.e., beyond the dimer.

Free energy calculations of small molecules in dense amorphous polymers. Effect of the initial guess configuration in molecular dynamics studies

The excess free energy of small molecules in the amorphous polymers poly(ethylene) and poly(dimethylsiloxane) was calculated, using the test-particle-insertion method. The method was applied to polymer configurations obtained from molecular dynamics simulations with differently prepared initial guess configurations. It was found that the calculated solubility coefficients strongly depend on the quality of the initial guess configuration. Slow compression of dilute systems, during which process only the repulsive parts of the nonbonded Lennard-Jones potentials are taken into account, yields polymer melts which are better relaxed, and which offer lower solubilities for guest molecules compared with polymer melts generated at the experimental density or prepared by compressing boxes with soft-core nonbonded potentials. For the last two methods initial stresses relax by straining the internal modes (bond angles, torsion angles) of the chains

Analysis of Morphology of Crystals Based on Identification of Interfacial Structure

A new theoretical approach for the prediction of the growth habit of crystals is presented. This approach is based on a newly derived relation between the growth rate of crystal surfaces and habit-controlling factors, and includes a key step: a so-called interface structure ~IS! analysis. This analysis is to formulate the influence of the fluid phase on the crystal morphology. The essential of the IS analysis is to identify the adsorbed growth units which is in dynamic equilibrium with solid units at the crystal surface, and to calculate their concentration. It follows that a key external habit-controlling factor, the so-called surface scaling factor, can be calculated from the analysis. Based on detailed molecular dynamic ~MD! simulation data, our formalism is applied to predict the morphology of urea crystals grown from aqueous solutions. Urea crystals grown from the solutions turn out to possess a needlelike shape, in excellent agreement with experiments. This is one of the first examples of the successful theoretical prediction of morphology of crystals, and will provide a new way of thinking and understanding of the influence of the mother phase on crystal habits.

Free energy from molecular dynamics with multiple constraints

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to constrain the reaction coordinate to a constant value, but the metric tensor effect of the constraint on the sampled phase space distribution complicates this relation. The appropriately corrected expression for the potential of mean constraint force method (PMCF) for systems in which only the reaction coordinate is constrained was published recently. Here we will consider the general case of a system with multiple constraints. This situation arises when both the reaction coordinate and the hard coordinates are constrained, and also in systems with several reaction coordinates. The obvious advantage of this method over the established thermodynamic integration and free energy perturbation methods is that it avoids the cumbersome introduction of a full set of generalized coordinates complementing the constrained coordinates. Simulations of n -butane and n -pentane in vacuum illustrate the method.

The sorption induced glass transition in amorphous glassy polymers

Sorption of CO2 in both the glassy and the rubbery state of an amorphous polyethylenelike polymer was investigated using molecular dynamics simulations. The temperature was chosen such that the system was in its glassy state at low solute concentrations and its rubbery state at large solute concentrations. Both the pressure and the volume isotherms changed character at the transition concentration. The physical origin of these changes was clarified by investigation of the excess thermodynamic properties of the solute both below and above the transition concentration. Dynamical changes occuring at the glass transition were studied through the self-intermediate scattering function of the polymer atoms. This function was found to excellently reveal the difference between the dynamics of the glassy and rubbery state and therefore served as an independent tool monitoring the glass transition

Molecular dynamics of polymer growth

The irreversible polymerization of a monomer liquid has been studied by molecular-dynamics simulation in two and three dimensions. The growth process is studied under good solvent conditions in the dilute regime and up to semidilute and concentrated regimes. In the dilute regime we observe a reaction limitation due to trapping of the growing centers, which is more pronounced in the lower dimension. At higher concentrations the presence of other chains decreases the monomer mobility and reaction rate. Conformational properties are studied by scaling analysis of end-to-end and gyration radii. A crossover from swollen conformations towards screened conformations is observed as growth proceeds.

Zero-shear stress relaxation and long time dynamics of a linear polyethylene melt: A test of Rouse theory

Results of united atom molecular dynamics simulations of a n-C120H242 melt at 450 K are presented. It is shown that the results of mean square displacement, dynamic structure factor, end-to-end vector autocorrelation, and shear relaxation modulus can consistently be described by the Rouse model with a single set of fit parameters, provided the length scales involved are larger than the statistical segment length b = 1.2 nm. On smaller length scales the stiffness of the chain becomes prominent, and the results deviate increasingly from the Rouse predictions. The shear relaxation modulus G(t) is determined from the stress autocorrelation function from both atomic and molecular points of view. The integrals G(t)dt are found to be identical after 1 ps and a Rouse description is shown to coincide for time scales larger than 0.4 ns. Compared to experimental values, the measured diffusion coefficient is overestimated by 63% and the viscosity is underestimated by 38%, consistent with molecular dynamics simulations of small molecules.

Brownian dynamics simulations of the self- and collective rotational diffusion coefficients of rigid long thin rods

Recently a microscopic theory for the dynamics of suspensions of long thin rigid rods was presented, confirming and expanding the well-known theory by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] and Kuzuu [J. Phys. Soc. Jpn. 52, 3486 (1983)]. Here this theory is put to the test by comparing it against computer simulations. A Brownian dynamics simulation program was developed to follow the dynamics of the rods, with a length over a diameter ratio of 60, on the Smoluchowski time scale. The model accounts for excluded volume interactions between rods, but neglects hydrodynamic interactions. The self-rotational diffusion coefficients D(r)(phi) of the rods were calculated by standard methods and by a new, more efficient method based on calculating average restoring torques. Collective decay of orientational order was calculated by means of equilibrium and nonequilibrium simulations. Our results show that, for the currently accessible volume fractions, the decay times in both cases are virtually identical. Moreover, the observed decay of diffusion coefficients with volume fraction is much quicker than predicted by the theory, which is attributed to an oversimplification of dynamic correlations in the theory.