Rapid shear viscosity calculation by momentum impulse relaxation molecular dynamics

Recently, Arya et al. [J. Chem. Phys. 113, 2079 (2000)] introduced a new molecular dynamics method to rapidly compute the viscosity of fluids. The technique, termed momentum impulse relaxation (MIR), involves the imposition of a Gaussian velocity profile on an equilibrated system, after which the decay in the profile is monitored as a function of time. The shear viscosity is computed by matching the rate of decay of the velocity profile to the corresponding solution of the Navier-Stokes equation. The method was originally applied to simple systems (argon and n-butane) and found to give a comparable accuracy to conventional equilibrium and nonequilibrium methods with more than an order of magnitude reduction in computing time. In this work, we extend and generalize the method to examine larger molecules with higher viscosities than have been examined previously. A detailed analysis of the method is given, including the effect the velocity boundary conditions have on the viscosity, the sensitivity of the results to the velocity profile fitting procedure, the effect of preequilibration of the Gaussian profile, and the effect the system size and box shape have on the accuracy and speed of the method. It is shown that the MIR method can be extended to treat multiatom systems without loss of accuracy or computational efficiency.     

Three model-free methods for calculation of activation energy in TG

Two well-known isoconversion methods, the first one developed by Ozawa-Flynn-Wall and the second one developed by Friedman, are confronted with calculations made using modulated thermogravimetry (MTG). The latter variant is free from a number of assumptions and restrictions made in the isoconversion computations. In particular, it allows the use of a single decomposition curve and it remains in force even in the case of multistage decomposition with conjugated processes.To obtain the model-fitting methods from the model-free methods one should replace some functions averaged over isoconversion levels by the functions calculated on the basis of kinetic models. In the Ozawa-Flynn-Wall method it is the averaged reduced time (integral of Arrhenius exponential over time). In the method of Friedman it is the averaged differential conversion function.In MTG, the perturbations caused by the sinusoidal temperature modulation are connected with derivatives of mass loss by simple scaling, where activation energy plays a role of a scaling parameter. The ratio of the experimentally measured perturbations to the experimental derivative is used for the model-free computation of activation energy. If a theoretical derivative replaces the experimental one, this procedure leads to the model-fitting method. Even a rough approximation of the experimental derivative should not lead to an excessive error in activation energy. If in a vicinity of peaks maxima in derivatives of mass loss the decomposition is controlled by single rate-limiting processes, modulated thermogravimetry should give realistic activation energies for these processes. Inasmuch as the results of MTG are weakly sensitive to selection of kinetic models, this method should have a high predictive force.     

On the calculation of the activation energy for solid state reactions

A novel and convenient method for the determination of the activation energy from isothermal kinetic runs has been proposed recently. A significant limitation of this method is discussed and is illustrated with an experimental example. A modification of the proposed method is suggested to circumvent this limitation.     

On the response of an ionic liquid to external perturbations and the calculation of shear viscosity

In this article, attention is directed to three related problems: (1) the response of the ionic liquid (IL) 1-hexyl-3-methylimidazolium chloride ([HMIM+][Cl-]) to different external perturbations, (2) the calculation of its shear viscosity, and (3) the investigation of the range of validity of linear response theory for these types of systems. For this purpose, we derive a set of equations linking bulk hydrodynamic predictions with microscopic simulations which are valid when linear response theory is applicable. As far as we are aware, this article reports results from the largest atomistic simulations ever performed on this liquid. Our study shows that even for systems with a box length as large as 0.03 mu the viscosities computed from perturbation frequencies compatible with this box size have not yet reached the bulk hydrodynamic limit. This is in sharp contrast with the case of other solvents such as water in which the hydrodynamic limit can be achieved by using perturbations on a length scale of typical molecular dynamics simulation box sizes. In order to achieve our goals, we comprehensively investigated how the IL relaxed upon weak external perturbations at different wavenumbers. We also studied the steady-state flow created by external shear acceleration fields. The short time behavior of instantaneous velocity profiles was compared with the results of linear response theory. The short time response appears to match the prediction from linear response theory, while the long time response deviates as the external field becomes stronger. From this study, the range on which a perturbation can be considered "weak" in the linear response sense can be established. The relaxation of initial velocity profiles was also examined and correlated to the decay of the transverse-current autocorrelation function. Even though none of our calculations reached the bulk hydrodynamic limit, we are able to make predictions for the shear viscosity of the bulk system at different temperatures which qualitatively agree with experimental data.     

Theoretical scheme for the shear viscosity of Lennard-Jones fluids

We use the shear viscosity expression from the Enskog theory of dense gases in a perturbative scheme for the Lennard-Jones (LJ) fluid. This perturbative scheme is formulated by combining the analytic rational function approximation method of Bravo Yuste and Santos [Phys. Rev. A 43, 5418 (1991)] for the radial distribution function of hard-sphere fluids and the well known Mansoori-Canfield/Rasaiah-Stell perturbation theory to determine an effective diameter for the LJ fluid. The scheme is reliable on a wide range of temperatures and densities, and is very accurate around the critical point. Using this information, we build an accurate empirical formula for the shear viscosity in the liquid phase, which fits the recent data [K. Meier et al., J. Chem. Phys. 121, 3671 (2004)] in the whole simulation range.     

Integral equation theory for two-dimensional polymer melts

The polymer reference interaction site model theory is investigated for two-dimensional polymer melts composed of freely-jointed hard disk chains and tangent-disk rods. Exact results for the intramolecular pair correlation functions are input into the theory, and predictions of the theory for the intermolecular pair correlation functions are tested via comparison with simulation. The theory is not as accurate for this system as it is for three-dimensional polymer melts, and the quantitative predictions are not good except at the highest area fractions. Possible reasons for the deficiency in the theory are discussed.     

Study on laminar viscosity and zero shear viscosity of latex systems

The flowing nature and rheological properties of polymethyl methacrylate latex systems in a coaxial cylinder viscometer were studied on the basis of laminar shear flow model and rheological experimental data. The physical meaning of laminar viscosity (eta(i,j)) and zero shear viscosity (eta(0)) were described. We assumed that laminar shear flows depended on position and shear time, so microrheological parameters were the function of position and shear time. eta(i,j) was the viscosity of any shear sheet i between two neighboring laminar shear flows at time t; j was denoted as j=t/Deltat; and Deltat was the interacting time of two particles or two laminar shear flows. tau(i,j) and gamma(i,j) were shear stress and shear rate of any shear sheet i at j moment. According to Newton regulation tau(i,j)=eta(i,j)gamma(i,j), apparent viscosity eta(a) should be a statistically mean value of j shear sheets laminar viscosity at j moment, i.e., eta(a)= summation operator(i=j)eta(i,j)gamma(i,j)/ summation operator(i=j)gamma(i,j). eta(0) was defined as shear viscosity between a laminar shear flow and a still fluid surface, i.e., eta(0)=(tau(i,j)/gamma(i,j))(j-i-->0). These new ideas described above may be helpful in the study of the micromechanisms of latex particle systems and worthy of more research.     

Alternative view of self-diffusion and shear viscosity

By performing an elementary transformation, the conventional velocity autocorrelation function expression for the temperature and density dependent self-diffusion constant D(T,rho) has been reformulated to emphasize how initial particle momentum biases final mean displacement. Using collective flow variables, an analogous expression has been derived for 1/eta(T,rho), the inverse of shear viscosity. The Stokes-Einstein relation for liquids declares that D and T/eta should have a fixed ratio as T and rho vary, but experiment reveals substantial violations for deeply supercooled liquids. Upon analyzing the self-diffusion and viscous flow processes in terms of configuration space inherent structures and kinetic transitions between their basins, one possible mechanism for this violation emerges. This stems from the fact that interbasin transitions become increasingly Markovian as T declines, and though self-diffusion is possible in a purely Markovian regime, shear viscosity in the present formulation intrinsically relies on successive correlated transitions.     

Algorithm for rapid calculation of Hessian of conformational energy function of proteins by supercomputer

An improved algorithm is presented for rapid calculation of the hessian matrix for the conformational energy of a protein as a function of only dihedral angles. The speed of the calculation, which is about one order faster than by the previous method, is achieved by two considerations. First, the algorithm is designed to take advantage of the supercomputer pipeline architecture. Second, long-range, nonbonded interactions are cut off and long-range electrostatic interactions are approximated by dipole-dipole interactions in order to reduce the number of pairwise interactions that have to be computed. The results of benchmark tests of the program are given as applied for four globular proteins of different sizes.     

Blip function calculation of the radial distribution functions for a binary liquid mixture

It is shown that the use of the high temperature approximation to blip function theory together with a two-component hard sphere reference fluid leads to reasonably accurate predictions for the radial distribution functions in a moderate temperature, moderate density, binary Lennard-Jones mixture.     

Prediction of viscosity for molecular fluids at experimentally accessible shear rates using the transient time correlation function formalism

Nonequilibrium molecular dynamics (NEMD) simulations were performed and the transient time correlation function (TTCF) method applied to calculate the shear viscosity of n-decane. Using the TTCF method we were able to calculate the viscosity at shear rate orders of magnitude lower than is possible by direct NEMD simulation alone. For the first time for a molecular fluid, we were able to simulate shear rates accessible by experimental measurements, which are typically performed at shear rates well below those accessible by NEMD simulation. The TTCF method allows us to close the gap between the lowest shear rates accessible by MD simulation and the highest shear rates possible in experimental studies. Additionally a multiple time step method for Gaussian thermostatted SLLOD equations of motion was developed following earlier work [G. A. Pan et al., J. Chem. Phys. 122, 4114 (2005)] for atomic fluids.     

Integral equation theory for athermal solutions of linear polymers

An integral equation model is developed for athermal solutions of flexible linear polymers with particular reference to good solvent conditions. Results from scaling theory are used in formulating form factors for describing the single chain structure, and the impact of solvent quality on the chain fractal dimension is accounted for. Calculations are performed within the stringlike implementation of the polymer reference interaction site model with blobs (as opposed to complete chains) treated as the constituent structural units for semidilute solutions. Results are presented for the second virial coefficient between polymer coils and the osmotic compressibility as functions of the chain length and polymer volume fraction, respectively. Findings from this model agree with results from scaling theory and experimental measurements, as well as with an earlier investigation in which self-avoiding chains were described using Gaussian form factors with a chain length and concentration-dependent effective statistical segment length. The volume fractions at the threshold for connectedness percolation are evaluated within a coarse-grained closure relation for the connectedness Ornstein-Zernike equation. Results from these calculations are consistent with the usual interpretation of the semidilute crossover concentration for model solutions of both ideal and swollen polymer coils.     

Nature of the kinematic shear viscosity of water

Nature of the kinematic shear viscosity of water ν is discussed in the work. Dependences of ν on temperature t, reduced volume $ \tilde \upsilon Nature of the kinematic shear viscosity of water ν is discussed in the work. Dependences of ν on temperature t, reduced volume , and the average number of hydrogen bonds per one molecule n _H (t = T/T _c, =υ/υ_c, T _c and υ_c are critical values of temperature and reduced volume) are analyzed in detail on a liquid-vapor coexistence curve. It is shown that at T < T _H (T _H ≈ 310 K is the characteristic temperature of water) the formation of the kinematic shear viscosity is induced by activation. At T > T _H, the shear viscosity of water is the sum of two contributions. One of them is of the same nature as in simple liquids, and another is caused by effects of hydrogen bonds. The temperature dependence of ν in this temperature region has nothing in common with exponential formulas of activation theory. The explicit form of the functional dependence of the kinematic shear viscosity on t, , and n _H is found and substantiated. It is shown that the value and temperature dependence of n _H resulting in the experimental values of the kinematic shear viscosity of water agree well with the values corresponding to density and evaporation heat data. __________ Translated From Zhurnal Strukturnoi Khimii, Vol. 49, No. 6, pp. 1092–1100, November–December, 2008. Original Russian Text Copyright ? 2008 by N. P. Malomuzh and A. V. Oleinik     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

Rotational viscosity of nematic liquid crystals and their shear viscosity under flow alignment

The influence of molecular properties on the rotational viscosity, γ₁, of nematic liquid crystals is studied. The shear viscosity under flow alignment, η_s, is determined for the same liquid crystals. A significant correlation between both quantities is found. An equation is presented which allows the calculation of γ₁ from η_s with an error of about 20 per cent for the liquid crystals studied.     

Computer program for the calculation of radiation damage distribution from the energy spectrum of backscattered ions

The method of Rutherford backscattering for the investigation of radiation damage is briefly described. Advantages and limits in application are mentioned. By the analysis of the energy spectra with the help of a computer this method can become a standard one.     

The roughness factor for polyatomic molecules from the shear viscosity coefficient

The translational-rotational coupling factor, or roughness factor, introduced by Chandler, has been evaluated for twenty five substances in the liquid range (between triple and critical points) from the viscosity coefficient along the saturation line. The influence of experimental data, simulation procedures and different choices for the hard sphere diameter have been included in our study. The results support the validity of this model.