6 research outputs found
Evaluation of second and third dielectric virial coefficients for non-polarisable molecular models
<p>The dielectric constant, Īµ, of a dilute vapour can be estimated from the dielectric virial equation of state (VEOS), but the long-ranged nature of the electrostatic interactions complicates the evaluation of coefficients of this series. We propose a formulation of the second and third dielectric coefficients of a general non-polarisable molecular model that permits their reliable calculation using Mayer sampling Monte Carlo. We demonstrate for three models: dipolar hard spheres, dipolar LennardāJones, and TIP4P water. The coefficients are used to compute Īµ for each model as a function of density, which are compared to molecular-simulation data. The form of the VEOS relating Īµ to density depends on the dielectric constant Īµā² of the embedding medium. Three choices are examined: vacuum (Īµā² = 1), self-consistent (Īµā² = Īµ) and tin foil (Īµā² = ā). The vacuum-boundary form is found to be unreliable, losing accuracy at low density and yielding divergent results for Īµ at moderate densities. In contrast, the series formulated using the tin-foil boundary produces accurate and stable values of Īµ for almost all conditions and models examined here, even when truncated at second order (which itself is shown to be a large improvement over the first-order ClausiusāMossottiāDebye formula).</p> <p></p
Quantum virial coefficients of molecular nitrogen
<p>We report virial coefficients up to third order in density for molecular nitrogen, investigating 103 temperatures in the range (15 K, 3000 K). All calculations are based on an <i>ab initio</i>-based potential taken from the literature. Path-integral Monte Carlo (PIMC) is applied to account for nuclear quantum effects, and these results are compared to a more approximate but faster semiclassical treatment. Additionally, we examine a PIMC approach that employs semiclassical beads for the path-integral images, but find that it offers marginal advantage. A recently developed orientation sampling algorithm is used in conjunction with Mayer sampling to compute precise virial coefficients. We find that, within the precision of our calculations of the second-order coefficient (<i>B</i><sub>2</sub>), semiclassical methods are adequate for temperatures greater than 250 K, and are needed to correct classical behaviour for temperatures as high as 800 K. For the third-order coefficient (<i>B</i><sub>3</sub>), the semiclassical methods are adequate above 150 K, and are required up to the highest temperature examined (3000 K) in order to correct the classical treatment within the precision of the calculations. However, three-body contributions to the potential are much more significant than nuclear quantum effects for the evaluation of <i>B</i><sub>3</sub>.</p
Thermodynamic Properties of Supercritical CO<sub>2</sub>/CH<sub>4</sub> Mixtures from the Virial Equation of State
Mixture virial coefficients
to seventh order are presented for
the system CO<sub>2</sub>/CH<sub>4</sub> at four supercritical temperatures:
323.15, 373.15, 473.15, and 573.15 K. Values are evaluated via the
Mayer sampling Monte Carlo method using a three-site TraPPE model
for CO<sub>2</sub> and a one-site model for CH<sub>4</sub>. The coefficients
are used to compute seven thermodynamic properties (viz., compressibility
factor, isothermal compressibility, volume expansivity, isochoric
and isobaric heat capacities, JouleāThomson coefficient, and
speed of sound) as a function of mole fraction and density for these
temperatures. Comparison is made with corresponding data in the literature
as obtained by molecular dynamics simulation, covering densities up
to about twice the critical density. Key conclusions are as follows,
noting that some exceptions are observed in each case: (a) The virial
equation of state (VEOS) to fourth or fifth order describes all properties
to within the simulation uncertainty for densities up to at least
the critical density, and the addition of terms up to seventh order
extends this range considerably. (b) The accuracy of the VEOS is severely
diminished for conditions approaching the critical point (the present
work extends down to a reduced temperature of 1.06 for CO<sub>2</sub>), and the study of the pure component behavior suggests the critical
singularity blocks convergence for conditions at considerably higher
temperatures, albeit at correspondingly higher pressures. (c) Comparison
of the VEOS at different orders provides a reliable guide to its accuracy
at a given order, so the VEOS can provide a self-assessment of its
accuracy when independent data for comparison are unavailable. (d)
The VEOS provides a good description of the JouleāThomson coefficient,
including the inversion point in particular. The third-order series
is needed to obtain behavior that is qualitatively correct, and the
addition of higher-order terms steadily improves the accuracy quantitatively.
(e) Under conditions where the seventh-order series is converged,
properties can be computed to a given precision with VEOS using much
less computational effort in comparison to molecular simulation
Effects of Finite Size and Proton Disorder on Lattice-Dynamics Estimates of the Free Energy of Clathrate Hydrates
We
consider lattice dynamics methods for calculation of the free
energy of clathrate hydrate phases, specifically the cubic structure
I (sI), cubic structure II (sII), and hexagonal structure H (sH) phases,
in the absence of guest molecules; water molecules are modeled with
the TIP4P potential. We examine in particular the effects of finite
size and proton disorder on the calculated free energies and consider
these in the context of the free-energy differences between the phases.
We find that at 300 K, the finite-size, proton-disorder, and quantum
effects between phases are, respectively, on the order of 0.4, 0.03,
and 0.1 kJ/mol. Details of the calculations are provided, with emphasis
on efficiencies developed to handle various aspects related to rigid-molecule
lattice dynamics with electrostatic interactions in large crystalline
systems
Virial Coefficients and Equations of State for Hard Polyhedron Fluids
Hard polyhedra are
a natural extension of the hard sphere model
for simple fluids, but there is no general scheme for predicting the
effect of shape on thermodynamic properties, even in moderate-density
fluids. Only the second virial coefficient is known analytically for
general convex shapes, so higher-order equations of state have been
elusive. Here we investigate high-precision state functions in the
fluid phase of 14 representative polyhedra with different assembly
behaviors. We discuss historic efforts in analytically approximating
virial coefficients up to <i>B</i><sub>4</sub> and numerically
evaluating them to <i>B</i><sub>8</sub>. Using virial coefficients
as inputs, we show the convergence properties for four equations of
state for hard convex bodies. In particular, the exponential approximant
of Barlow et al. (<i>J. Chem. Phys</i>. <b>2012</b>, <i>137</i>, 204102) is found to be useful up to the first
ordering transition for most polyhedra. The convergence behavior we
explore can guide choices in expending additional resources for improved
estimates. Fluids of arbitrary hard convex bodies are too complicated
to be described in a general way at high densities, so the high-precision
state data we provide can serve as a reference for future work in
calculating state data or as a basis for thermodynamic integration
Free energy and concentration of crystalline vacancies by molecular simulation
<p>We present an approach for evaluating the concentration of vacancy defects in crystalline materials by molecular simulation. The proposed method circumvents the problem of equilibration of the number of ālattice sitesā <i>M</i>, which characterises the trade-off between more, smaller lattice cells (with some vacant), versus fewer, larger cells. Working in a grand-canonical framework, we instead fix <i>M</i> and solve for the chemical potential <i>Ī¼</i> that ensures thermodynamic consistency of the ensemble-averaged pressure and the grand potential. Having determined <i>Ī¼</i> this way for the given <i>M</i>, the equilibrium vacancy concentration and free energy are easily determined. Methods are demonstrated for the classical LennardāJones fcc crystal, examining all states where the crystal is stable. We find for this system that the effect of equilibrating <i>M</i> is negligible at all conditions. Also, although the vacancy fraction varies by many orders of magnitude with temperature and density, we find that the value at melting is nearly independent of density, equal to about . Results further show that a lattice-energy approximation (ignoring entropic effects) underestimates the correct concentration by four orders of magnitude at almost all conditions; ignoring only anharmonic contributions underestimates the vacancy concentration at melting by nearly one order of magnitude.</p