Friction between brush layers of charged and neutral bottle-brush macromolecules. molecular dynamics simulations

Using molecular dynamics simulations, we study the lubricating properties of neutral and charged bottle-brush coatings as a function of the compression and shear stresses and brush grafting density. Our simulations have shown that in charged bottle-brush systems under shear there is a layer with excess counterions located in the middle between brush-bearing surfaces. The main deformation mode of the charged bottle-brush layers is associated with the backbone deformation, resulting in the backbone deformation ratio, α, and shear viscosity, η, being universal functions of the Weissenberg number. In the case of neutral bottle-brush systems, in addition to the backbone deformation there is also side chain deformation. The coupling between backbone and side chain deformation violates universality in the deformation ratio, α, dependence on the Weissenberg number and results in scaling exponents varying with the compression stress and brush grafting density. The existence of different length scales controlling deformation of neutral bottle brushes manifests itself in the shear viscosity, η, dependence on the shear rate, ?γ. Shear viscosity, η, as a function of the shear rate, ?γ, has two plateaus and two shear thinning regimes. The low shear rate plateau and shear thinning regime correspond to the backbone deformation, while the second plateau and shear thinning regime at moderate shear rates are due to side chain deformation. For both systems the value of the friction coefficient increases with increasing shear rate. The values of the friction coefficient for charged bottle-brush systems are about ten times smaller than corresponding values for neutral systems at the same shear rate.     

Molecular dynamics simulations of grafted layers of bottle-brush polyelectrolytes

Using molecular dynamics simulations, we study the effect of the brush grafting density and degree of polymerization of the side chains on conformations of brush layers made of charged bottle-brush macromolecules. The thickness of the brush layer first decreases with increasing brush grafting density; then, it saturates and remains constant in the wide interval of the brush grafting densities. The brush layers consisting of the bottle-brush macromolecules with longer side chains have a larger layer thickness. The elongation of the side chains of the bottle-brush macromolecules decreases with increasing brush grafting density. This contraction of the side chains is due to counterion condensation inside the volume occupied by bottle-brushes. Our simulations showed that counterion condensation is a multiscale process reflecting different symmetries of the bottle-brush layer.     

"Like-charge attraction" between anionic polyelectrolytes: molecular dynamics simulations

"Like-charge attraction" is a phenomenon found in many biological systems containing DNA or proteins, as well as in polyelectrolyte systems of industrial importance. "Like-charge attraction" between polyanions is observed in the presence of mobile multivalent cations. At a certain limiting concentration of cations, the negatively charged macroions cease to repel each other and even an attractive force between the anions is found. With classical molecular dynamics simulations it is possible to elucidate the processes that govern the attractive behavior with atomistic resolution. As an industrially relevant example we study the interaction of negatively charged carboxylate groups of sodium polyacrylate molecules with divalent cationic Ca2+ counterions. Here we show that Ca2+ ions initially associate with single chains of polyacrylates and strongly influence sodium ion distribution; shielded polyanions approach each other and eventually "stick" together (precipitate), contrary to the assumption that precipitation is initially induced by intermolecular Ca2+ bridging.     

Computer simulations of diffusion and dynamics of short-chain polyelectrolytes

Brownian dynamics simulations are conducted to investigate the diffusional and dynamic properties of polyelectrolytes in dilute salt-free solutions. The polyelectrolyte molecule is represented by a bead-spring chain in a primitive model. The long-range hydrodynamic and Coulomb interactions are both taken into consideration through the Ewald summations for the first time. The major finding of our simulations is that the dependence of the long-time chain diffusivity on the Coulomb interaction strength is very different from that of the Kirkwood short-time diffusivity, which simply shows a trend nearly opposite to the chain size. When ignoring the hydrodynamic interaction (HI), the coupling effect between the chain and its counterions gives rise to a noticeable increase in the long-time diffusivity at intermediate electrostatic interaction strengths. However, the incorporation of HI suppresses this effect to a degree that one can no longer discern it. Moreover, the rotational relaxation is found to show a dependence opposite to that of the gyration radius relaxation.     

Interaction between water molecules and zinc sulfide nanoparticles studied by temperature-programmed desorption and molecular dynamics simulations

We have investigated the bonding of water molecules to the surfaces of ZnS nanoparticles (approximately 2-3 nm sphalerite) using temperature-programmed desorption (TPD). The activation energy for water desorption was derived as a function of the surface coverage through kinetic modeling of the experimental TPD curves. The binding energy of water equals the activation energy of desorption if it is assumed that the activation energy for adsorption is nearly zero. Molecular dynamics (MD) simulations of water adsorption on 3 and 5 nm sphalerite nanoparticles provided insights into the adsorption process and water binding at the atomic level. Water binds with the ZnS nanoparticle surface mainly via formation of Zn-O bonds. As compared with bulk ZnS crystals, ZnS nanoparticles can adsorb more water molecules per unit surface area due to the greatly increased curvature, which increases the distance between adjacent adsorbed molecules. Results from both TPD and MD show that the water binding energy increases with decreasing the water surface coverage. We attribute the increase in binding energy with decreasing surface water coverage to the increasing degree of surface under-coordination as removal of water molecules proceeds. MD also suggests that the water binding energy increases with decreasing particle size due to the further distance and hence lower interaction between adsorbed water molecules on highly curved smaller particle surfaces. Results also show that the binding energy, and thus the strength of interaction of water, is highest in isolated nanoparticles, lower in nanoparticle aggregates, and lowest in bulk crystals. Given that water binding is driven by surface energy reduction, we attribute the decreased binding energy for aggregated as compared to isolated particles to the decrease in surface energy that occurs as the result of inter-particle interactions.     

Molecular dynamics simulations of multilayer films of polyelectrolytes and nanoparticles

We performed molecular dynamics simulations of multilayer assemblies of flexible polyelectrolytes and nanoparticles. The film was constructed by sequential adsorption of oppositely charged polymers and nanoparticles in layer-by-layer fashion from dilute solutions. We have studied multilayer films assembled from oppositely charged polyelectrolytes, oppositely charged nanoparticles, and mixed films containing both nanoparticles and polyelectrolytes. For all studied systems, the multilayer assembly proceeds through surface overcharging after completion of each deposition step. There is almost linear growth in the surface coverage and film thickness. The multilayer films assembled from nanoparticles show better layer stratification but at the same time have higher film roughness than those assembled from flexible polyelectrolytes.     

Molecular dynamics simulations of grafted polyelectrolytes on two apposing walls

Molecular dynamics simulations of polyelectrolytes grafted to two apposing surfaces were performed. Bead-spring polymer models are used to treat flexible chains [e.g., sodium poly(styrene sulfonate)] and stiff chains (double-stranded DNA). The counterions are explicitly treated. The effect of the surface density of the grafted polymer, the chain length, and the gap width on the structure and the pressure were studied. Results are compared to experimental measurements and to simulations of polyelectrolyte brushes on a single surface. The density profiles exhibit a maximum not found in single surface data. The maximum is due to the brushes shrinking to avoid interpenetration.     

Interactions between bottle-brush polyelectrolyte layers: effects of ionic strength and oppositely charged surfactant

Interactions between cationic bottle-brush polyelectrolyte layers adsorbed on mica across salt and oppositely charged surfactant solutions were investigated with the interferometric surface force apparatus, and the results were compared with what is known for similarly charged linear polyelectrolytes. Ellipsometric measurements demonstrated that the bottle-brush polyelectrolytes, which contain 45 units long poly(ethylene oxide) side chains, are more readily desorbed than linear equivalents when the ionic strength of the solution is increased. It is argued that this is due to the steric repulsion between the poly(ethylene oxide) side chains that reduces the surface affinity. The preadsorbed bottle-brush polyelectrolyte layers were also exposed to sodium dodecyl sulfate (SDS) solutions. It was found that the presence of SDS affected the force profiles less than observed for similarly charged linear polyelectrolytes. This observation was attributed to excluded volume constraints imposed by the poly(ethylene oxide) side chains that reduces the accessibility of the charged polyelectrolyte segments and counteracts formation of large aggregates within the layer.     

Desorption of bottle-brush polyelectrolytes from silica by addition of linear polyelectrolytes studied by QCM-D and reflectometry

The possibility of exchanging adsorbed layers of PEO(45)MEMA:METAC-X brush polyelectrolytes (with two different charge densities, 10 and 75 mol%, denoted by X), with poly(MAPTAC), a highly charged linear polyelectrolyte, was investigated by quartz crystal microbalance with dissipation and reflectometry. The studies were conducted on a silica substrate at pH 10, conditions under which only electrostatic interactions are effective in the adsorption process. Based on the results, it was concluded that PEO(45)MEMA:METAC-10 forms an inhomogeneous layer at the interface through which poly(MAPTAC) chains can easily diffuse to reach the surface. On the other hand, the PEO(45)MEMA:METAC-75 layer was not affected when exposed to a poly(MAPTAC) solution. We argue that the observed effect for PEO(45)MEMA:METAC-75 is due to the formation of a homogeneous protective brush layer, in combination with the small difference in surface affinity between the bottle-brush polyelectrolyte and poly(MAPTAC), together with the difficulty of displacing highly charged polyelectrolyte chains once they are adsorbed on the oppositely charged surface. We also use the combination of QCM-D and reflectometry data to calculate the water content and layer thickness of the adsorbed layers.     

Coarse-grained protein molecular dynamics simulations

A limiting factor in biological science is the time-scale gap between experimental and computational trajectories. At this point, all-atom explicit solvent molecular dynamics (MD) are clearly too expensive to explore long-range protein motions and extract accurate thermodynamics of proteins in isolated or multimeric forms. To reach the appropriate time scale, we must then resort to coarse graining. Here we couple the coarse-grained OPEP model, which has already been used with activated methods, to MD simulations. Two test cases are studied: the stability of three proteins around their experimental structures and the aggregation mechanisms of the Alzheimer's Abeta16-22 peptides. We find that coarse-grained isolated proteins are stable at room temperature within 50 ns time scale. Based on two 220 ns trajectories starting from disordered chains, we find that four Abeta16-22 peptides can form a three-stranded beta sheet. We also demonstrate that the reptation move of one chain over the others, first observed using the activation-relaxation technique, is a kinetically important mechanism during aggregation. These results show that MD-OPEP is a particularly appropriate tool to study qualitatively the dynamics of long biological processes and the thermodynamics of molecular assemblies.     

Multibaric-multithermal ensemble molecular dynamics simulations

We present new generalized-ensemble molecular dynamics simulation algorithms, which we refer to as the multibaric-multithermal molecular dynamics. We describe three algorithms based on (1) the Nosé thermostat and the Andersen barostat, (2) the Nosé-Poincaré thermostat and the Andersen barostat, and (3) the Gaussian thermostat and the Andersen barostat. The multibaric-multithermal simulations perform random walks widely both in the potential-energy space and in the volume space. Therefore, one can calculate isobaric-isothermal ensemble averages in wide ranges of temperature and pressure from only one simulation run. We test the effectiveness of the multibaric-multithermal algorithm by applying it to a Lennard-Jones 12-6 potential system.     

Surface properties of bottle-brush polyelectrolytes on mica: effects of side chain and charge densities

Surface properties of a series of cationic bottle-brush polyelectrolytes with 45-unit-long poly(ethylene oxide) side chains were investigated by phase modulated ellipsometry and surface force measurements. The evaluation of the adsorbed mass of polymer on mica by means of ellipsometry is complex due to the transparency of mica and its birefringence and low dielectric constant. We therefore employed a new method to overcome these difficulties. The charge and the poly(ethylene oxide) side chain density of the bottle-brush polymers were varied from zero charge density and one side chain per segment to one charge per segment and no side chains, thus spanning the realm from a neutral bottle-brush polymer, via a partly charged brush polyelectrolyte, to a linear fully charged polyelectrolyte. The adsorption properties depend crucially on the polymer architecture. A minimum charge density of the polymer is required to facilitate adsorption to the oppositely charged surface. The maximum adsorbed amount and the maximum side chain density at the surface are obtained for the polymer with 50% charged segments and the remaining 50% of the segments carrying poly(ethylene oxide) side chains. It is found that brushlike layers are formed when 25-50% of the segments carry poly(ethylene oxide) side chains. In this paper, we argue that the repulsion between the side chains results in an adsorbed layer that is non-homogeneous on the molecular level. As a result, not all side chains will contribute equally to the steric repulsion but some will be stretched along the surface rather than perpendicular to it. By comparison with linear polyelectrolytes, it will be shown that the presence of the side chains counteracts adsorption. This is due to the entropic penalty of confining the side chains to the surface region.     

On simulations of complex interfaces: molecular dynamics simulations of stationary phases

Methodological considerations for molecular dynamics simulations of complex interfaces are presented in this article. A slab geometry is examined in the context of stationary phases where selectivity occurs predominantly in pores within silica beads. Specifically, we examine the Whelk-O1 interface with n-hexane/2-propanol, the TMA-(Pro)(2)-N(CH(3))-tether interface with n-hexane/2-propanol, and the C(18)H(37)Si interface with water/methanol. The following methodological issues are considered in detail: The assessment of solvent density within the confined region and excluded volume of the interface; the structural equilibration of surface-bound moieties; solvent equilibration for binary mixtures; surface size effects, and periodic boundary conditions; the treatment of electrostatic interactions; and the impact of pore size.     

Phonostat: thermostatting phonons in molecular dynamics simulations

Thermostat algorithms in a molecular dynamics simulation maintain an average temperature of a system by regulating the atomic velocities rather than the internal degrees of freedom. Herein, we present a "phonostat" algorithm that can regulate the total energy in a given internal degree of freedom. In this algorithm, the modal energies are computed at each time step using a mode-tracking scheme and then the system is driven by an external driving force of desired frequency and amplitude. The rate and amount of energy exchange between the phonostat and the system is controlled by two distinct damping parameters. Two different schemes for controlling the external driving force amplitude are also presented. In order to test our algorithm, the method is applied initially to a simple anharmonic oscillator for which the role of various phonostat parameters can be carefully tested. We then apply the phonostat to a more realistic (10,0) carbon nanotube system and show how such an approach can be used to regulate energy of highly anharmonic modes.     

A comparison between parallelization approaches in molecular dynamics simulations on GPUs

We test the relative performances of two different approaches to the computation of forces for molecular dynamics simulations on graphics processing units. A “vertex‐based” approach, where a computing thread is started per particle, is compared to an “edge‐based” approach, where a thread is started per each potentially non‐zero interaction. We find that the former is more efficient for systems with many simple interactions per particle while the latter is more efficient if the system has more complicated interactions or fewer of them. By comparing computation times on more and less recent graphics processing unit technology, we predict that, if the current trend of increasing the number of processing cores—as opposed to their computing power—remains, the “edge‐based” approach will gradually become the most efficient choice in an increasing number of cases. © 2014 Wiley Periodicals, Inc.     

Interaction between oppositely charged polyelectrolytes in aqueous solution

Oppositely charged polyelectrolytes interact in solution, forming polyelectrolyte complexes, which often appear as gel-like precipitates. This kind of complex formation was studied by means of calorimetric and rheological measurements. The enthalpy effects, though being fairly small, give some information about the binding strength of counterions to the macroion. We studied the system poly(p-styrene sulfonate)/poly(trimethylammonium-2-ethyl methacrylate) (PSS-PTMA), varying systematically the low molar mass counterions of PSS. In every case, the maximum of enthalpy was found around a 1:1 (mol:mol monomer units) composition of the complexes, with the shape of enthalpy versus composition-curve indicating a stoichiometric interaction. The maximum enthalpy decreased with increasing atomic mass of the counterion when the alkaline metal salts of PSS were used and no change was made on the side of the cationic polyelectrolyte. The salts of the alkaline earth metals gave a distinctly higher enthalpy. On the contrary, viscosity measurements showed a very broad minimum as a function of composition, indicating that the formation of non-stoichiometric complexes is also occurring. The conclusion of these observations is that the complex formation is stoichiometric with respect to the monomeric units, but not necessarily stoichiometric with respect to the entire macromolecules.     

Vesicle shapes from molecular dynamics simulations

Lipid bilayer membranes are known to form various structures such as large sheets or vesicles. When the two leaflets of the bilayer have an equal composition, the membrane preferentially forms a flat sheet or a spherical vesicle. However, a difference in the composition of the two leaflets may result in a curved bilayer or in a wide variety of vesicle shapes. Vesicles with different shapes have already been shown in experiments and diverse vesicle shapes have been predicted theoretically from energy minimization of continuous curves. Here we present a molecular dynamics study of the effect of small changes in the phospholipid headgroups on the spontaneous curvature of the bilayer and on the resulting vesicle shape transformations. Small asymmetries in the bilayers already result in high spontaneous curvature and large vesicle deformations. Vesicle shapes that are formed include ellipsoids, discoids, pear-shaped vesicles, cup-shaped vesicles, as well as budded vesicles. Comparison of these vesicles with theoretically derived vesicle shapes shows both resemblances and differences.     

Potential energy constrained molecular dynamics simulations

A method for carrying out molecular dynamics simulations in which the potential energy U of the molecular system is constrained at its initial value is developed and thoroughly tested. The constraint is not introduced within the framework of the Lagrange multipliers technique, rather it is fulfilled in a natural way by carrying out the simulations in terms of suitable sets of delocalized coordinates. Such coordinates are defined by an appropriate tuning of the Baker, Kessi, and Delley internal delocalized nonredundant coordinates technique [J. Chem. Phys. 105, 192 (1996)]. The proposed method requires multiple evaluations of energy and gradients in each step of the molecular dynamics simulation, so that constant U simulations suffer some overhead compared to ordinary simulations. But the particular formulation of the delocalized coordinates and of the equations of motion greatly simplifies all the various steps required by the Baker's technique, thus allowing for the efficient implementation of the method itself. The technique is reliable and allows for very high accuracy in the potential energy conservation during the whole simulation. Moreover, it proved to be free of drift troubles which can occur when standard constraint methods are straightforwardly implemented without the application of appropriate correcting techniques.     

Estimating entropies from molecular dynamics simulations

While the determination of free-energy differences by MD simulation has become a standard procedure for which many techniques have been developed, total entropies and entropy differences are still hardly ever computed. An overview of techniques to determine entropy differences is given, and the accuracy and convergence behavior of five methods based on thermodynamic integration and perturbation techniques was evaluated using liquid water as a test system. Reasonably accurate entropy differences are obtained through thermodynamic integration in which many copies of a solute are desolvated. When only one solute molecule is involved, only two methods seem to yield useful results, the calculation of solute-solvent entropy through thermodynamic integration, and the calculation of solvation entropy through the temperature derivative of the corresponding free-energy difference. One-step perturbation methods seem unsuitable to obtain entropy estimates.