Configurational temperature profile in confined fluids. I. Atomic fluid

Two configurational expressions for the temperature are applied to the calculation of temperature profiles within a confined atomic fluid in a narrow slit pore. The configurational temperatures profiles so obtained are compared to the kinetic temperature, calculated from the equipartition principle, in equilibrium (EMD), and nonequilibrium molecular dynamics (NEMD) simulations of planar Poiseuille flow. We show that one of the configurational expressions exhibits a system-size dependence which prevents its application to the determination of high-resolution temperature profiles. The other expression yields good agreement with the kinetic temperature profile in both equilibrium and nonequilibrium systems

Comparison of thermostatting mechanisms in NVT and NPT simulations of decane under shear

Nonequilibrium molecular dynamics (NEMD) simulations play a major role in characterizing the rheological properties of fluids undergoing shear flow. However, all previous studies of flows in molecular fluids either use an “atomic” thermostat which makes incorrect assumptions concerning the streaming velocity of atoms within their constituent molecules, or they employ a center of mass kinetic (COM) thermostat which only controls the temperature of relatively few degrees of freedom (3) in complex high molecular weight compounds. In the present paper we show how recently developed configurational expressions for the thermodynamic temperature can be used to develop thermostatting mechanisms which avoid both of these problems. We propose a thermostat based on a configurational expression for the temperature and apply it to NEMD simulations of decane undergoing Couette flow at constant volume and at constant pressure. The results so obtained are compared with those obtained using a COM kinetic thermostat. At equilibrium the properties of systems thermostatted in the two different ways are of course equivalent. However, we show that the two responses differ far from equilibrium. In particular, we show that the increase in the potential energy of the internal modes with increasing shear is only observed with a Gaussian isokinetic COM thermostat in both NVT and NPT simulations. There is no such increase with the configurational thermostat, which, unlike the Gaussian isokinetic COM thermostat, correctly accounts for the internal degrees of freedom of the molecular fluid

Correspondence between configurational temperature and molecular kinetic temperature thermostats

Molecular fluids undergoing shear flow are often modeled using a homogeneous nonequilibrium molecular dynamics algorithm. To reach a steady state, this method must be used in conjunction with a thermostating mechanism which duplicates the heat dissipation in the experimental setup (e.g., by conduction to the shearing boundaries). The most commonly used type of thermostat involves fixing the center of mass kinetic (c.m.) temperature. Though perfectly valid, this approach does not seem to be the most realistic for a molecular fluid since heat is removed only through the 3 degrees of freedom of the center of mass for each molecule. The second type of thermostat involves fixing the “atomic” kinetic temperature and therefore takes into account all degrees of freedom. However, since the streaming velocity of atoms within their constituent molecules is unknown, the implementation of such a thermostat is problematic and relies on incorrect assumptions on the streaming velocity of atoms. The recently developed configurational temperature thermostat requires no assumption on the streaming velocity of atoms and takes into account all degrees of freedom. Using a configurational temperature thermostat to thermostat homogeneous shear flow thus seems to be a more realistic approach than the c.m. kinetic thermostat. In this work, we apply this configurational temperature thermostat to the study of linear alkanes (C₁₀ and C₂₀) undergoing shear flow. The results so obtained are compared with those obtained using a c.m. kinetic thermostat. Our aims are (1) to test the influence of the total number of degrees of freedom of the system, (2) to make a connection between the results obtained with the two types of thermostats. By carefully examining the energies of the internal modes, we have been able to characterize the loss of accuracy of a c.m. kinetic thermostat at high shear rates and for high molecular weight compounds. Finally, we establish a correspondence between the two types of thermostats by showing that, for the internal modes, a simulation at a fixed c.m. kinetic temperature is equivalent to a simulation at a fixed but higher configurational temperature

Configurational temperature profile in confined fluids. II. Molecular fluids

In an earlier paper, we applied configurational expressions of the temperature to the calculation of temperature profiles within a confined atomic fluid. This paper focuses on the application of these expressions to confined molecular fluids using ethane and hexane as examples. We first give configurational expressions for the temperature for these constrained systems. The configurational temperature profiles so obtained are compared to the kinetic temperature calculated using the equipartition principle, in equilibrium systems. These expressions are then used in nonequilibrium molecular dynamics (NEMD) simulations of fluids undergoing planar Poiseuille flow. We show that these configurational expressions provide a direct and accurate determination of the temperature profile for these systems

Non-Newtonian behavior in simple fluids

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheology of a microscopic sample of simple fluid. The calculations were performed using a configurational thermostat which unlike previous nonequilibrium molecular dynamics or nonequilibrium Brownian dynamics methods does not exert any additional constraint on the flow profile. Our findings are in agreement with experimental results on concentrated "hard sphere"-like colloidal suspensions. We observe: (i) a shear thickening regime under steady shear; (ii) a strain thickening regime under oscillatory shear at low frequencies; and (iii) shear-induced ordering under oscillatory shear at higher frequencies. These results significantly differ from previous simulation results which showed systematically a strong ordering for all frequencies. They also indicate that shear thickening can occur even in the absence of a solvent.J.D. acknowledges support from the Research School of Chemistry ~ANU! through a visiting fellowship

On the effects of assuming flow profiles in nonequilibrium simulations

Atomic simulation methods modelling fluid flows often incorporate in the equations of motion the steady state flow profile predicted by Navier–Stokes equations. We show in this work that this may lead to significant errors such as spurious shear induced ordering, unphysical steady state flow profiles or artificial dampening of thermal motion even at shear rates regarded as low in simulation applications. Our results also suggest that nonequilibrium molecular dynamics coupled with the recently developed configurational thermostat, which makes no assumption at all on the flow profile, provides a much more realistic way to study these phenomena

Microcanonical temperature for a classical field: application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a UV cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behaviour of the specific heat.Comment: v1: 9 pages, 5 figures, revtex 4. v2: additional text in response to referee's comments, now 11 pages, to appear in Phys. Rev.

Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations

Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F−, Cl−, Br−, and I−) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Åqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4PEW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells