N. K. Balabaev

A Comparison Between Collisional Dynamics and Brownian Dynamics

Abstract This paper presents an analytical investigation for the velocity relaxation of a test particle coupled to a heat bath by two different mechanisms: the Brownian dynamics (BD) and the collisional dynamics (CD). Relation between the parameters of the methods is established. The velocity relaxation spectrum induced by the coupling in the CD method is shown to be different from the one in the BD method. The difference between the spectra disappears in the limit γ → O, where γ is a mass ratio of the bath atoms and the test particle.

On The Berendsen Thermostat

Abstract The behaviour of the total momentum of a system immersed in the Berendsen thermostat is analyzed. It has been found that under certain conditions the kinetic energy of the system can be transformed from internal degrees of freedom to the external ones, and conversely. A concrete example of such a transformation is presented. The results of molecular dynamics simulations of the Fe4S4(SH)4 complex coupled to different external heat baths are discussed.

Molecular Dynamics Simulation of Thermomechanical Properties of Montmorillonite Crystal. 1. Isolated Clay Nanoplate

The structure and mechanical properties of clay nanoparticles is a subject of growing interest because of their numerous applications in engineering. We present the results of molecular dynamics simulation for a single nanoplate of pyrophyllite - a 2:1 clay mineral consisting of two tetrahedral sheets of SiO4 and an intervening octahedral AlO6 sheet. Simulations were performed in the temperature interval from 5 to 750 K using the ionic-type potentials of Cygan et al. On this basis the temperature dependences of structural parameters, characterizing both tetrahedral and octahedral sheets as well as single lamella, have been studied. Two slightly different structures were observed in this wide temperature interval. The mechanical properties of the nanoplate were calculated from stress-strain diagrams, which have been obtained at relatively slow rates of deformation (for molecular simulations). Using different types of loading, we calculated the full elasticity tensor and estimated the influence of temperature on its components. We estimated also the bending and torsion stiffnesses of the nanoplate as specific characteristics of this type of particle. Because the nanoplate is atomically thin, a reasonable determination of the thickness is a nontrivial problem, both in the modeling of mechanical properties and in physical interpretation of the obtained data. We propose a procedure for its calculation.

Computer simulation study of intermolecular voids in unsaturated phosphatidylcholine lipid bilayers

Computer simulation of the liquid crystalline phase of five different hydrated unsaturated phosphadidylcholine (PC) lipid bilayers, i.e., membranes built up by 18:0/18:1omega9cis PC, 18:0/18:2omega6cis PC, 18:0/18:3omega3cis PC, 18:0/20:4omega6cis PC, and 18:0/22:6omega3cis PC molecules have been performed on the isothermal-isobaric ensemble at 1 atm and 303 K. (The notation n:domegapcis specifies the lipid tails: n refers to the total number of carbon atoms in the chain, d is the number of the methylene-interrupted double bonds, p denotes the number of carbons between the chain terminal CH(3) group and the nearest double bond, and cis refers to the conformation around the double bonds.) The characteristics of the free volume in these systems have been analyzed by means of a generalized version of the Voronoi-Delaunay method [M. G. Alinchenko et al., J. Phys. Chem. B 108, 19056 (2004)]. As a reference system, the hydrated bilayer of the saturated 14:014:0 PC molecules (dimyristoylphosphatidylcholine) has also been analyzed. It has been found that the profiles of the fraction of the free volume across the membrane exhibit a rather complex pattern. This fine structure of the free volume fraction profiles can be interpreted by dividing the membrane into three separate major zones (i.e., zones of the aqueous, polar, and apolar parts of the membrane) and defining five subzones within these zones according to the average position of various atomic groups in the membrane. The fraction of the free volume in the middle of the membrane is found to increase with increasing unsaturation of the sn-2 chain of the lipid molecule. This is due to the fact that with increasing number of methylene-interrupted double bonds the lipid tails become more flexible, and hence they do not extend to the middle of the membrane. It is found that there are no broad enough preformed channels in the bilayers through which small penetrants, such as water molecules, can readily go through; however, the existing channels can largely facilitate the permeation of these molecules.

Molecular dynamics simulation of thermomechanical properties of montmorillonite crystal. 3. montmorillonite crystals with PEO oligomer intercalates.

We present the results of molecular dynamics (MD) simulation of the structure and thermomechanical behavior of Wyoming-type Na+-montmorillonite (MMT) with poly(ethylene oxide) (PEO) oligomer intercalates. Periodic boundary conditions in all three directions and simulation cells containing two MMT lamellae [Si248Al8][Al112Mg16]O640[OH]128 oriented parallel to the XY-plane were used. The interlamellar space, or gallery, between neighboring MMT lamellae was populated by 24 Na+ counterions and PEO macromolecules of different lengths, ranging from 2 up to 240 repeat units. We considered three different loadings of PEO within the gallery: 80, 160, and 240 repeat units, corresponding to 13, 23, and 31 wt % PEO based on total mass of the nanocomposite, respectively. In the cases of 13 and 23 wt %, the polymer chains formed one or two well-defined amorphous layers with interlayer distances of 1.35 and 1.8 nm, respectively. We have observed also formation of a wider monolayer gallery with interlayer distances of 1.6 nm. Three-layer PEO films formed in the case of 31 wt % loading. The thermal properties were analyzed over the range 300-400 K, and the isothermal linear compressibility, transversal moduli, and shear moduli were calculated at 300 K. These properties are compared with the results of our simulation of thermal and mechanical properties of MMT crystal with galleries filled by one or two water layers as well as with those of an isolated clay nanoplate.

Plastic deformation of glassy polymethylene : computer-aided molecular-dynamic simulation

Molecular-dynamic simulation of low-temperature plastic deformation (Tdef = 50 K, Tdef/Tg ≤ 0.3) is studied for glassy polymethylene under the regime of active uniaxial compression and tension for a cell composed of 64 chains containing 100 -CH2 groups in each (as united atoms) and with periodic boundary conditions. Thirty-two such cells are created, and, in each cell, polymethylene chains in the statistical coil conformation are independently constructed. The cells are subjected to isothermal uniaxial compression at Tdef = 50 K by ɛ = 30% and by ɛ = 70% under uniaxial tension. In the course of loading, a σ-ɛ diagram is recorded, while the mechanical work spent on deformation, the changes in the overall potential energy of the system, and the contributions from various potential interactions (noncovalent van der Waals bonds, chemical links, valence and torsional angles) are estimated. The results are averaged over all 32 cells. The relaxation of stored potential energy and residual strain after complete unloading of the deformed sample is studied. The relaxation of stored energy and residual strain is shown to be incomplete. Most of this energy and strain is stored in the sample at the deformation temperature for long period. The conformational composition of chains and the average density of polymer glass during loading are analyzed. Simulation results show that inelastic deformations commence not with the conformational unfolding of coils but with the nucleation of strain-bearing defects of a nonconformational nature. The main contribution to the energy of these defects is provided by van der Waals interactions. Strain-bearing defects are nucleated in a polymer glass during tension and compression primarily as short-scale positive volume fluctuations in the sample. During tension, the average density of the glass decreases; during compression, this parameter slightly increases to ɛ ≈ 8% and then decreases. An initial increase in the density indicates that, during compression and at ɛ < 8%, coils undergo compactization via an increase in chain packing. During compression, the concentration of trans conformers remains unchanged below ɛ ≈ 8% and then decreases. During compression, it means that in a glass, coils do not increase their sizes at strains below ɛ ≈ 8%. During tensile drawing, coils remain unfolded below ɛ ≈ 35%; at higher strains, coils become enriched with trans conformers or unfold. At this stage, the concentration of trans conformers linearly increases. The development of a strain-induced excess volume (strain-bearing defects) entails an increase in the potential energy of the sample. Under the given conditions of deformation, nucleation of strain-bearing defects and an increase in their concentration are found to be the only processes occurring at the initial stage of loading of glassy polymethylene. The results of computer-aided simulation are compared with the experimental data reported in the literature.

Mechanical unfolding of proteins L and G with constant force: Similarities and differences

Mechanical unfolding of proteins L and G, which have similar structures, is considered in this work, and the question arises what changes happen in the unfolding pathways under the action of mechanical force. Molecular dynamics simulations with explicit water (134 trajectories) demonstrate that the mechanical unfolding with constant force occurs through at least two pathways in both proteins. These pathways practically coincide for both proteins and under different constant extensional forces (600, 700, 800, 900, and 1050 pN) and at different temperatures (320, 350, and 400 K at F=1050 pN). Go-like modeling of forced unfolding of proteins L and G does not agree with experimental results that protein G is more mechanically resistant than protein L. At the same time, molecular dynamics simulations of forced unfolding of proteins L and G with explicit water demonstrate that protein G is more mechanically resistant than protein L. Our investigation demonstrates that mechanical stable elements are the same for both proteins, namely, the N-terminal beta-hairpin. This result agrees with experimental data on denaturant unfolding for protein L but not for protein G.

Molecular dynamics study of a lipid bilayer and a polymer liquid

We present molecular dynamics simulation of a lipid bilayer of 2 × 10 freely jointed chain molecules of 16 beads each. All beads interact with each other (via a Lennard-Jones potential) and with an aqueous medium. Terminal beads are bound near the bilayer surfaces by a harmonic potential. An algorithm for integrating the equations of motion of a molecular system in the presence of geometrical constraints, such as fixed bond lengths, is described. All results are compared with those obtained for an isotropic polymer liquid with the same Lennard-Jones interaction and density as for the bilayer. Equilibrium properties of the chains such as end-to-end distance, radius of gyration, molecular order parameters and pair correlation functions are computed. Dynamic properties considered include the time autocorrelation functions of various variables, the translational motion of chain beads and the space-time van Hove correlation functions. It is found that compared with the polymer liquid, the molecular motions in ...

Conformational mobility of carbosilane dendrimer: Molecular dynamics simulation

Molecular dynamic simulations were carried out for carbosilane dendrimers of the 5th generation immersed in CCl4 solvent at different temperatures. The calculations were accomplished by using the AMBER force field in the united atom approximation. Lennard-Jones particles were considered as the solvent molecules with potential parameters corresponding to CCl4. There was one molecule of a dendrimer in each calculation cell, and the cells size was large enough to exclude any interaction between dendrimers. The internal structure of the dendrimer (density distributions for both dendrimer and solvent atoms) as well as dynamics of trans–gauche transitions of single bonds and fluctuations of branching points were analysed. It was shown that the one barrier mechanism of conformational transitions observed earlier in linear polymers occurs to be valid also for the conformational rearrangements in dendrimers with the hindered rotation around chain bonds. The contribution of rotational restrictions is essential only for branching points, which are close to the core.

Investigating hydrogen bonds in liquid ethylene glycol structure by means of molecular dynamics

Models of liquid ethylene glycol are built by means of molecular dynamics at temperatures ranging between 268 and 443 K, with 1000 molecules in rectangular parallelepiped basic cells. The dependences of structures of O-H…O hydrogen bonds on modeling time and temperature are analyzed. It is found that the hydrogen bonds emerge at different sites of a model, thus forming a hydrogen bonds network that is continuously rebuilt under the action of thermal fluctuations. The number of hydrogen bonds in the models is observed to decrease when the temperature is raised. The energy of hydrogen bond formation is found to be −20.0 ± 2.6 kJ mol−1, the average bond lifetime is 370 ps at 268 K and 147 ps at 323 K, and the activation energy of hydrogen bond rupture at these temperatures is ∼12.1 kJ mol−1. It is concluded that the data on the breaking of H-bonds at temperatures of 323 to 443 K can be explained by the molecules moving away from each other as a result of diffusive motion, accompanied by rearrangement of the hydrogen bonds network. The concentration of dimers in the models is shown to be rather low, while the average energy of forming a dimer from two ethylene glycol molecules is −35.4 kJ mol−1.