Molecular dynamics osmotic

R. L. Rowley, M. Henrichsen. Calculation of chemical potential for structured molecules using osmotic molecular dynamics simulations. Fluid Phase Equil 137 15, 1997. 

First of all, the comparison of the PB-theory and experiment shown in Fig. 8 proceeds virtually without adjustable parameters. The osmotic coefficient (j) is solely determined by the charge parameter polyelectrolyte concentration. The latter parameter determines the cell radius R0 (see the discussion in Sect. 2.1) Figure 8 summarizes the results. It shows the osmotic coefficient of an aqueous PPP-1 solution as a function of counterion concentration as predicted by Poisson-Boltzmann theory, the DHHC correlation-corrected treatment from Sect. 2.2, Molecular Dynamics simulations [29, 59] and experiment [58]. 

Liao, Q., Dobrynin, A.V., and Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions Osmotic coefficient and counterion condensation. Macromolecules, 2003, 36, No. 9, p. 3399-3410. 

Since the experimentally determined osmotic coefficient appears to be smaller even than the molecular dynamics results, this indicates effects to be relevant that go beyond the model used for simulation. Most obvious candidates for this are the neglect of additional chemical interactions between the ions and the polyelectrolyte as well as solvation effects, i.e., interactions between the ions or the polyelectrolyte with the water molecules from the solution. It is for instance demonstrated in Ref. 46 that the osmotic coefficient also depends on whether one uses chlorine or iodine counterions. While one could certainly account for the different radii of these ions when computing the distance of closest approach entering the PB equation, the implications of the different hydration energies is much less obvious to incorporate and in principle requires very expensive all-atom simulations. 

Abstract Aqueous solutions of star-like polyelectrolytes (PEs) exhibit distinctive features that originate from the topological complexity of branched macromolecules. In a salt-free solution of branched PEs, mobile counterions preferentially localize in the intramolecular volume of branched macroions. Counterion localization manifests itself in a dramatic reduction of the osmotic coefficient in solutions of branched polyions as compared with those of linear PEs. The intramolecular osmotic pressure, created by entrapped counterions, imposes stretched conformations of branches and this leads to dramatic intramolecular conformational transitions upon variations in environmental conditions. In this chapter, we overview the theory of conformations and stimuli-induced conformational transitions in star-like PEs in aqueous solutions and compare these to the data from experiments and Monte Carlo and molecular dynamics simulations. 

Keywords Coarse-grained model Protein-protein interactions Discontinuous molecular dynamics Square-well potential Osmotic second virial coefficient... 

Without the need of any fitting parameter, molecular dynamics (MD) simulations play a unique role in studying FO phenomena because MD simulations can allow for computing water transportation, analyzing molecular interactions and structures, as well as quantitatively probing various properties at atomic and molecular scales. The current literature on the use of MD simulations to study osmotic pressure-driven water flow is quite limited, and more studies are needed. 

Computation of shear viscosity of hard spheres has been attempted using NEMD [11], Modified non-equilibrium molecular dynamics methods have also been developed for study of fluid flows with energy conservation [12], NEMD simulations have also been recently performed to compare and contrast the Poiseuille and Electro-osmotic flow situations. Viscosity profiles obtained from the two types of flows are found to be in good mutual agreement at all locations. The simulation results show that both type of flows conform to continuum transport theories except in the first monolayer of the fluid at the pore wall. The simulations further confirm the existence of enhanced transport rates in the first layer of the fluid in both the cases [13, 14]. 

Pendergast and Hoek (2011) report that molecular dynamics simulations showed that zeolite membranes - previously applied solely for gas separations - may be applicable for aqueous osmotic separations. Since... 

Ions in Clays, Fig. 2 Electro-osmotic flow profile between two Na-montmorillonite surfaces separated by a 4.5-mn pore containing water. Reference molecular dynamics (MD) simulations allow to test the validity of continuous models based on the Navier-Stokes (NS) and Poisson-Boltzmann (PB) equations. Such equations must be solved for given boundary conditions (stick or slip) at the solid/liquid interface... 

Liao Q, Dobrynin AV, Rubinstein M (2003) Molecular dynamics simulations of poiyeiectrolyte solutions osmotic coefficient and counterion condensation. Macromolecules 36 3399-3410. doi 10.1021/ ma0259968... 

Molecular dynamics simulations of solvated ions give predictions of specific thermodynamic solvation properties like free energies and entropies of solvation as well as dynamic properties like ion conductivities. More complex behavior is observed for properties like the osmotic pressure or the activity coefficient of a salt solution. In addition to the ion-water interactions, ion-ion interactions are important. Much of these specific effects can be understood by looking at the ion-ion potentials of mean force, which are linked to thermodynamic properties along the lines of the liquid state theories of Kirkwood and Buff or McMillan and Mayer. Figure 1 shows the short-ranged part of ion-ion potentials of mean force that were obtained by molecular dynamics simulations [4]. 

To investigate the effect of the Debye-Huckel approximation on the solution properties, Stevens and Kremer [152] performed molecular dynamics simulations of salt-free solutions of bead-spring polyelectrolyte chains in which the presence of counterions was treated via a screened Coulomb potential, and compared the results with their simulations with explicit counterions [146,148]. To elucidate the effect of the Debye-Hiickel approximation, the dependence of the mean square end-to-end distance, R ), osmotic pressure, and chain structure factor on polymer concentration was examined. Stevens and Kremer found that (i ) tends to be larger at low densities for DH simulations and is smaller at higher densities. However, the difference in (i ) between DH simulations and simulations with explicit counterions is within 10%. This trend seems to be a generic feature for all N in their simulations. The functional form and density dependence of the chain structure factor are very close in both simulations. The most severe Debye-Huckel approximation affects the dependence of the osmotic pressure on polymer concentration. It appears that in the DH simulations not only is the magnitude of the osmotic pressure incorrect, but also the concentration dependence is wrong. 

Once the force field is chosen, a proper simulation method needs to be selected. Molecular dynamics simulations are applied to determine the solvation behaviour of ionic liquids by means of solving the Newtonian equations of motion for all molecules in the presence of a gradient in potential energy. Ionic liquid phase equilibria are determined by using Monte Carlo simulations in the isothermal isobaric Gibbs ensemble, grand canonical ensemble or osmotic ensemble with clever sampling schemes. 

Applications for molecular dynamics in microfluidic systems include, for example, protein folding in solution, transport of amino acids in ion channels, and locally driven electro-osmotic flows with rigid particles. However, these applications do not involve the bulk motion of a fluid and are extremely small, specialized systems. In general, the systems that microfluidic researchers consider are multi-scale in that they require knowledge of the bulk fluid motion, far-fleld boundary conditions, interactions with other molecules, walls and fluid structures, and other experimental conditions. Consequently, the molecular dynamics approach is rarely feasible or even necessary for multi-scale systems. Instead, researchers and analysts rely on coarse-graining techniques to reduce the degrees of fi eedom, where tractable solutions are more accessible. 

Electro-osmotic drag phenomena are closely related to the distribution and mobility of protons in pores. The molecular contribution can be obtained by direct molecular dynamics simulations of protons and water in single ionomer pores, as reviewed in the sections Proton Transport in Water and Stimulating Proton Transport in a Pore. The hydrodynamic contribution to nd can be studied, at least qualitatively, using continuum dielectric approaches. The solution of the Poisson-Boltzmann equation... 

Fig. 5. a Double logarithmic plot of the osmotic pressure n vs the monomer density derived by molecular dynamics simulations. The dotted curves represent the theoretical exponents 9/8 and 9/4, respectively, and the full curves are the best lit to the data (from [83]). b Experimental values for the osmotic pressure rt as a function of the polyion concentration cf for various molar masses. (Taken from [66])... 

Aksimentiev, A. and Schulten, K., 2005. Imaging a-hemolysin with molecular dynamics Ionic conductance, osmotic permeability, and the electrostatic potential map, Biophys. /., 88, 3745-3761. 

The potential can be obtained from the (r) profile through a simple integration (Eq. [230]). The difference in (r)/r between the DH and PB values is also shown in Figure 23 (top frame, dotted line) with most of the difference occurring within one Debye length of the surface = 13.6 A). Of particular relevance to biophysical systems is the competition between mono- and divalent counterions at the cylindrical surface,the discussion of which we defer until later, and that between monovalent counterions with different radii. Also, Deserno and Holm have compared molecular dynamics simulations with the prediction of PB cell model theory for the calculation of osmotic coefficients and the quantification of counterion condensation. ... 

The reptation model for polymer diffusion would predict that the thickness of the gel phase reflects the dynamics of disentanglement. The important factors here are chain length, solvent quality and temperature since they affect the dimensions of the polymer coils in the gel phase. The precursor phase, on the other hand, depends upon solvency and temperature only through the osmotic force it can generate in the system and the viscoelastic response of the system in the region of the front. These factors should be independent of the PMMA molecular weight. 

The experimental techniques for the study of conformational branched properties in solution are the same as used for linear chains. These are, in particular, static and dynamic light scattering, small angle X-ray (SAXS) and small angle neutron (SANS) scattering methods, and common capillary viscometry. These methods are supported by osmotic pressure measurements and, nowadays extensively applied, size exclusion chromatography (SEC) in on-line combination with several detectors. These measurements result in a list of molecular parameters which are given in Table 1. 

Analysis of polyelectrolytes in the semi-dilute regime is even more complicated as a result of inter-molecular interactions. It has been established, via dynamic light-scattering and time-dependent electric birefringence measurements, that the behavior of polyelectrolytes is qualitatively different in dilute and semi-dilute regimes. The qualitative behavior of osmotic pressure has been described by a power-law relationship, but no theory approaching quantitative description is available. 

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