Thermodynamic stability of type-I and type-II clathrate hydrates depending on the chemical species of the guest substances

The free energy differences are calculated for various type-I and type-II clathrate hydrates based on molecular-dynamics simulations, thereby evaluating the thermodynamic stability of the hydrates depending on the chemical species of the guest substances. The simulation systems consist of 27 unit cells, that is, 1242 water molecules and 216 guest molecules for type-I hydrates, and 3672 water molecules and 648 guest molecules for type-II hydrates. The water molecules are described by TIP4P potential, while the guest molecules are described by one-site Lennard-Jones potential, U=4epsilon{(sigma/r)12-(sigma/r)6}, where U is the potential energy, r is the particle distance, sigma is the particle diameter, and epsilon is the energy well depth. The optimal values of sigma that yield the minimum free energy (the best thermodynamic stability) were determined to be 0.39 nm for the type-I hydrates and 0.37 nm for the type-II hydrates.     

Phase equilibrium measurements and crystallographic analyses on structure-H type gas hydrate formed from the CH4-CO2-neohexane-water system

Phase equilibrium conditions and the crystallographic properties of structure-H type gas hydrates containing various amounts of methane (CH4), carbon dioxide (CO2), neohexane (2,2-dimethylbutane; NH), and liquid water were investigated. When the CH4 concentration was as high as approximately 70%, the phase equilibrium pressure of the structure-H hydrate, which included NH, was about 1 MPa lower at a given temperature than that of the structure-I hydrate with the same composition (except for a lack of NH). However, as the CO2 concentration increased, the pressure difference between the structures became smaller and, at CO2 concentrations below 50%, the phase equilibrium line for the structure-H hydrate crossed that for the structure I. This cross point occurred at a lower temperature at higher CO2 concentration. Extrapolating this relation between the cross point and the CO2 concentration to 100% CO2 suggests that the cross-point temperature would be far below 273.2 K. It is then difficult to form structure-H hydrates in the CO2-NH-liquid water system. To examine the structure, guest composition, and formation process of structure-H hydrates at various CH4-CO2 compositions, we used the methods of Raman spectroscopy, X-ray diffraction, and gas chromatography. Raman spectroscopic analyses indicated that the CH4 molecules were found to occupy both 5(12) and 4(3)5(6)6(3) cages, but they preferably occupied only the 5(12) cages. On the other hand, the CO2 molecules appeared to be trapped only in the 4(3)5(6)6(3) cages. Thus, the CO2 molecules aided the formation of structure-H hydrates even though they reduced the stability of that structure. This encaged condition of guest molecules was also compared with the theoretical calculations. In the batch-type reactor, this process may cause the fractionation of the remaining vapor composition in the opposite sense as that for CH4-CO2 hydrate (structure-I), and thus may result in an alternating formation of structure-H hydrates and structure-I in the same batch-type reactor.     

The role of pressure in rubber elasticity

We describe a series of molecular dynamics computations that reveal an intimate connection at the atomic scale between difference stress (which resists stretches) and pressure (which resists volume changes) in an idealized elastomer, in contrast to the classical theory of rubber elasticity. Our simulations idealize the elastomer as a "pearl necklace," in which the covalent bonds are stiff linear springs, while nonbonded atoms interact through a Lennard-Jones potential with energy epsilon(LJ) and radius sigma(LJ). We calculate the difference stress t(11)-(t(22)+t(33))/2 and mean stress (t(11)+t(22)+t(33))/3 induced by a constant volume extension in the x(1) direction, as a function of temperature T and reduced density rho(*)=Nsigma(IJ) (3)/nu. Here, N is the number of atoms in the simulation cell and nu is the cell volume. Results show that for rho(*)<1, the difference stress is purely entropic and is in good agreement with the classical affine network model of rubber elasticity, which neglects nonbonded interactions. However, data presented by van Krevelen [Properties of Polymers, 3rd ed. (Elsevier, Amsterdam, 1990), p. 79] indicate that rubber at standard conditions corresponds to rho(*)=1.2. For rho(*)>1, the system is entropic for kT/epsilon(LJ)>2, but at lower temperatures the difference stress contains an additional energy component, which increases as rho(*) increases and temperature decreases. Finally, the model exhibits a glass transition for rho(*)=1.2 and kT/epsilon(LJ) approximately 2. The atomic-scale processes responsible for generating stress are explored in detail. Simulations demonstrate that the repulsive portion of the Lennard-Jones potential provides a contribution sigma(nbr)>0 to the difference stress, the attractive portion provides sigma(nba) approximately 0, while the covalent bonds provide sigma(b)<0. In contrast, their respective contributions to the mean stress satisfy Pi(nbr)<0, Pi(nba)>0, and Pi(b)<0. Analytical calculations, together with simulations, demonstrate that mean and difference stresses are related by sigma(nbr)=-APi(nbr)P(2)(theta(b)), sigma(b)=BPi(b)P(2)(theta(b)), where P(2)(theta(b)) is a measure of the anisotropy of the orientation of the covalent bonds, and A and B are coefficients that depend weakly on rho(*) and temperature. For high values of rho(*), we find that [sigma(nbr)]>[sigma(b)], and in this regime our model predicts behavior that is in good agreement with experimental data of D.L. Quested et al. [J. Appl. Phys. 52, 5977 (1981)] for the influence of pressure on the difference stress induced by stretching solithane.     

Autocorrelation functions of a fluid of molecules interacting through steeply repulsive and attractive forces

A new method is presented for an extension of Enskog's approximation for the evaluation of the autocorrelation functions of a fluid, and this approach is used to evaluate these functions when the interaction between the molecules includes both steeply repulsive and steeply attractive forces. Consequently the correlation functions depend upon the temperature in a nontrivial way. As an example, the method is applied to calculate the velocity and force autocorrelation functions of a fluid when the molecules interact through the specific potential, V(r)=4epsilon[(sigma/r)2n-(sigma/r)n] when the parameter n is large. There is a relationship between this model and the "sticky sphere" one which is exploited in the theoretical computations. The results obtained from the theory are compared with molecular dynamics simulation for n=72 and 144 and for a range of temperatures from T=epsilon/kB down to epsilon/3kB. The two approaches agree very well for a range of state points, especially at short times. At later times the theory predicts a more oscillatory behavior than the simulation especially at very low reduced temperatures.     

Computer simulation study of the global phase behavior of linear rigid Lennard-Jones chain molecules: comparison with flexible models

The global phase behavior (i.e., vapor-liquid and fluid-solid equilibria) of rigid linear Lennard-Jones (LJ) chain molecules is studied. The phase diagrams for three-center and five-center rigid model molecules are obtained by computer simulation. The segment-segment bond lengths are L = sigma, so that models of tangent monomers are considered in this study. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. The phase envelopes and critical conditions are compared with those of flexible LJ molecules of tangent segments. An increase in the critical temperature of linear rigid chains with respect to their flexible counterparts is observed. In the limit of infinitely long chains the critical temperature of linear rigid LJ chains of tangent segments seems to be higher than that of flexible LJ chains. The solid-fluid equilibrium is obtained by Gibbs-Duhem integration, and by performing NPT simulations at zero pressure. A stabilization of the solid phase, an increase in the triple-point temperature, and a widening of the transition region are observed for linear rigid chains when compared to flexible chains with the same number of segments. The triple-point temperature of linear rigid LJ chains increases dramatically with chain length. The results of this work suggest that the fluid-vapor transition could be metastable with respect to the fluid-solid transition for chains with more than six LJ monomer units.     

Hydrate kinetics study in the presence of nonaqueous liquid by nuclear magnetic resonance spectroscopy and imaging

The dynamics of methane hydrate growth and decomposition were studied by nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI). Three well-known large molecule guest substances (LMGS) were used as structure H hydrate formers: 2,2-dimethylbutane (NH), methylcyclohexane (MCH), tert-butyl methyl ether (TBME). In addition, the impact of a non-hydrate former (n-heptane/nC7) was studied. The methane diffusion and hydrate growth were monitored by recording the 2H NMR spectra at 253 K and approximately 4.5 MPa for 20 h. The results revealed that methane diffuses faster in TBME and NH, slower in nC7, and slowest in MCH. The TBME system gives the fastest hydrate formation kinetics followed by NH, MCH, and nC7. The conversion of water into hydrate was also observed. The imaging study showed that TBME has a strong affinity toward ice, which is not the case for the NH and MCH systems. The degree of ice packing was also found to affect the LMGS distribution between ice particles. Highly packed ice increases the mass transfer resistance and hence limits the contact between LMGS and ice. It was also found that "temperature ramping" above the ice point improves the conversion significantly. Finally, hydrates were found to dissociate quickly within the first hour at atmospheric pressure and subsequently at a much slower rate. Methane dissolved in LMGS was also seen. The residual methane in hydrate phase and dissolved in LMGS phase explain the faster kinetics during hydrate re-formation.     

Molecular dynamics study of structure H clathrate hydrates of methane and large guest molecules

Methane storage in structure H (sH) clathrate hydrates is attractive due to the relatively higher stability of sH as compared to structure I methane hydrate. The additional stability is gained without losing a significant amount of gas storage density as happens in the case of structure II (sII) methane clathrate. Our previous work has showed that the selection of a specific large molecule guest substance (LMGS) as the sH hydrate former is critical in obtaining the optimum conditions for crystallization kinetics, hydrate stability, and methane content. In this work, molecular dynamics simulations are employed to provide further insight regarding the dependence of methane occupancy on the type of the LMGS and pressure. Moreover, the preference of methane molecules to occupy the small (5(12)) or medium (4(3)5(6)6(3)) cages and the minimum cage occupancy required to maintain sH clathrate mechanical stability are examined. We found that thermodynamically, methane occupancy depends on pressure but not on the nature of the LMGS. The experimentally observed differences in methane occupancy for different LMGS may be attributed to the differences in crystallization kinetics and/or the nonequilibrium conditions during the formation. It is also predicted that full methane occupancies in both small and medium clathrate cages are preferred at higher pressures but these cages are not fully occupied at lower pressures. It was found that both small and medium cages are equally favored for occupancy by methane guests and at the same methane content, the system suffers a free energy penalty if only one type of cage is occupied. The simulations confirm the instability of the hydrate when the small and medium cages are empty. Hydrate decomposition was observed when less than 40% of the small and medium cages are occupied.     

Nanoscale colloids in a freely adsorbing polymer solution: a Monte Carlo simulation study

A key issue in nanoscale materials and chemical processing is the need for thermodynamic and kinetic models covering colloid-polymer systems over the mesoscopic length scale (approximately 1-100 nm). We have applied Monte Carlo simulations to attractive nanoscale colloid-polymer mixtures toward developing a molecular basis for models of these complex systems. The expanded ensemble Monte Carlo simulation method is applied to calculate colloid chemical potentials (micro(c)) and polymer adsorption (gamma) in the presence of freely adsorbing Lennard-Jones (LJ) homopolymers (surface modifiers). gamma and micro(c) are studied as a function of nanoparticle diameter (sigma(c)), modifier chain length (n) and concentration, and colloid-polymer attractive strength over 0.3 < Rg/sigma(c) < 6 (Rg is the polymer radius of gyration). In the attractive regime, nanocolloid chemical potential decreases and adsorbed amount increases as sigma(c), or n is increased. The scaling of gamma with n from the simulations agrees with the theory of Aubouy and Raphael (Macromolecules 1998, 31, 4357) in the extreme limits of Rg/sigma(c). When Rg/sigma(c) is large, the "colloid" approaches a molecular size and interacts only locally with a few polymer segments and gamma approximately n. When Rg/sigma(c) is small, the system approaches the conventional colloid-polymer size regime where multiple chains interact with a single particle, and gamma approximately sigma(c)2, independent of n. In contrast, adsorption in the mesoscopic range of Rg/sigma(c) investigated here is represented well by a power law gamma approximately n(p), with 0 < p < 1 depending on concentration and LJ attractive strength. Likewise, the chemical potential from our results is fitted well with micro(c) approximately n(q)sigma(c)3, where the cubic term results from the sigma(c) dependence of particle surface area (approximately sigma(c)2) and LJ attractive magnitude (approximately sigma(c)). The q-exponent for micro(c) (micro(c) approximately n(q)) varies with composition and LJ attractive strength but is always very close to the power exponent for gamma (gamma approximately n(p)). This result leads to the conclusion that in attractive systems, polymer adsorption (and thus polymer-colloid attraction) dominates the micro(c) dependence on n, providing a molecular interpretation of the effect of adsorbed organic layers on nanoparticle stability and self-assembly.     

Molecular dynamics simulation of structure H clathrate-hydrates of binary guest molecules

Molecular dynamics (MD) simulations are performed to study the stability of structure H clathrate-hydrates of methane+large-molecule guest substance (LMGS) at temperatures of 270, 273, 278 and 280 K under canonical (NVT-) ensemble condition in a 3×3×3 structure H unit cell replica with 918 TIP4P water molecules. The studied LMGS are 2-methylbutane (2-MB), 2,3-dimethylbutane (2,3-DMB), neohexane (NH), methylcyclohexane (MCH), adamantane and tert-butyl methyl ether (TBME). In the process of MD simulation, achieving equilibrium of the studied system is recognized by stability in calculated pressure for NVT-ensemble. So, for the accuracy of MD simulations, the obtained pressures are compared with the experimental phase diagrams. Therefore, the obtained equilibrium pressures by MD simulations are presented for studying the structure H clathrate-hydrates. The results show that the calculated temperature and pressure conditions by MD simulations are consistent with the experimental phase diagrams. Also, the radial distribution functions (RDFs) of host-host, host-guest and guest-guest molecules are used to analysis the characteristic configurations of the structure H clathrate-hydrate.     

(2n,n) potential and sticky-sphere fluids

The authors investigate the behavior of a model fluid for which the interaction energy between molecules at a separation r is of the form 4epsilon[(sigma/r)2n-(sigma/r)n], where epsilon and sigma are constants and n is a large integer. The particular properties they study are the pressure p, the mean square force F2, the elastic shear modulus at infinite frequency Ginfinity, the bulk modulus at infinite frequency Kinfinity, and the potential energy per molecule u. They show that if n is sufficiently large it is possible to derive the properties of the system in terms of two parameters, the values of the cavity function and of its derivative at the position r=sigma. As an example they examine in detail the cases with n=144 and n=72 for three different temperatures and they test the theory by comparison with a computer simulation of the system. They use the simulated pressure and the average mean square force to determine the two parameters and use these values to evaluate other properties; it is found that the theory produces results which agree with computer simulation to within approximately 3%. It is also shown that the model, when the parameter n is large, is equivalent to Baxter's sticky-sphere model with the strength of the adhesion determined by the value of n and the temperature. They use Baxter's solution of the Percus-Yevick equations for the sticky-sphere model to determine the cavity function and from that the values of the same properties. In this second approach there are no free parameters to determine from simulation; all properties are completely determined by the theory. The results obtained agree with computer simulation only to within approximately 6%. This suggests that for this model one needs a better approximation to the cavity function than that provided by the Percus-Yevick solution. Nevertheless, the model looks promising for the study of (typically small) colloidal liquids where the range of attraction is short but finite when compared to its diameter, in contrast to Baxter's sticky-sphere limit where the attractive interaction range is taken to be infinitely narrow. The continuous function approach developed here enables important physical properties such as the infinite shear modulus to be computed, which are finite in experimental systems but are undefined in the sticky-sphere model.     

Rheological and structural studies of linear polyethylene melts under planar elongational flow using nonequilibrium molecular dynamics simulations

We present various rheological and structural properties of three polyethylene liquids, C50H102, C78H158, and C128H258, using nonequilibrium molecular dynamics simulations of planar elongational flow. All three melts display tension-thinning behavior of both elongational viscosities, eta1 and eta2. This tension thinning appears to follow the power law with respect to the elongation rate, i.e., eta approximately epsilon(b), where the exponent b is shown to be approximately -0.4 for eta1 and eta2. More specifically, b of eta1 is shown to be slightly larger than that of eta2 and to increase in magnitude with the chain length, while b of eta2 appeared to be independent of the chain length. We also investigated separately the contribution of each mode to the two elongational viscosities. For all three liquids, the intermolecular Lennard-Jones (LJ), intramolecular LJ, and bond-stretching modes make positive contributions to both eta1 and eta2, while the bond-torsional and bond-bending modes make negative contributions to both eta1 and eta2. The contribution of each of the five modes decreases in magnitude with increasing elongation rate. The hydrostatic pressure shows a clear minimum at a certain elongation rate for each liquid, and the elongation rate at which the minimum occurs appears to increase with the chain length. The behavior of the hydrostatic pressure with respect to the elongation rate is shown to correlate with the intermolecular LJ energy from a microscopic viewpoint. On the other hand, R(ete)2 and R(g)2 appear to be correlated with the intramolecular LJ energy. The study of the effect of the elongational field on the conformation tensor c shows that the degree of increase of tr(c)-3 with the elongation rate becomes stronger as the chain length increases. Also, the well-known linear reaction between sigma and c does not seem to be satisfactory. It seems that a simple relation between sigma and c would not be valid, in general, for arbitrary flows.     

Box size effects are negligible for solvation free energies of neutral solutes

Hydration free energy calculations in explicit solvent have become an integral part of binding free energy calculations and a valuable test of force fields. Most of these simulations follow the conventional norm of keeping edge length of the periodic solvent box larger than twice the Lennard-Jones (LJ) cutoff distance, with the rationale that this should be sufficient to keep the interactions between copies of the solute to a minimum. However, for charged solutes, hydration free energies can exhibit substantial box size-dependence even at typical box sizes. Here, we examine whether similar size-dependence affects hydration of neutral molecules. Thus, we focused on two strongly polar molecules with large dipole moments, where any size-dependence should be most pronounced, and determined how their hydration free energies vary as a function of simulation box size. In addition to testing a variety of simulation box sizes, we also tested two LJ cut-off distances, 0.65 and 1.0 nm. We show from these simulations that the calculated hydration free energy is independent of the box-size as well as the LJ cut-off distance, suggesting that typical hydration free energy calculations of neutral compounds indeed need not be particularly concerned with finite-size effects as long as standard good practices are followed.     

Enantiomeric purity determination of malic acid in apple juices by multi-beam circular dichroism detection

A multi-beam circular dichroism (CD) detector which is easily constructed by inserting inexpensive optics into a conventional photo-diode array detector has an advantage of simultaneous detection of the absorbance and CD. The enantiomeric purity determination of malic acid in beverages was performed by this detection system. Malic acid when complexed with Cu(II) was found to have an absorbance maximum at around 750 nm. The L-malic acid-Cu(II) complex showed a positive Cotton effect in its absorbance band and its anisotropy factor (delta epsilon/epsilon) was relatively large at about 1/170. This complex was retained on a reversed-phase column with the addition of racemic 2-hydroxy-3-methylbutyric acid to the mobile phase as the ligand. A plot of the relative peak areas between the CD and the absorption (delta abs/abs) versus optical purity showed good linearity with a correlation coefficient of 0.999, and the precision expressed as the relative standard deviation of the errors from the regression line was +/-2.7% (2sigma). The accuracy of the proposed method was assessed by capillary electrophoresis. Eight commercially available juice products were analyzed using this method. Five of them were thought to be adulterated with synthetic malic acid.     

Structure-dependent dc conductivity and relaxation time in the Debye-Stokes-Einstein equation

The basis for a modification of the Debye-Stokes-Einstein (DSE) equation between the dc conductivity, sigma(dc), and dielectric relaxation time, tau, has been examined by using broad-band dielectric spectroscopy of LiClO4 solutions in 5-methyl-2-hexanol and 1-propanol and of pure liquids. According to the DSE equation, the log sigma(dc)-log tau plots should have a slope of -1. We find that sigma(dc) begins to depend upon the structure of an electrolytic solution when a variation of solvent's equilibrium dielectric permittivity, epsilon(s), with temperature causes the ion population to vary. As a consequence of this intrinsic dependence, the log sigma(dc)-log tau plots do not obey the DSE equation. Inclusion of the effect of change in epsilon(s) on the DSE equation may be useful in analyzing the measured quantities in terms of Brownian diffusion of both ions and molecules in ultraviscous liquids. Proton translocation along a hydrogen bond contributes little to sigma(dc), which appears to be predominantly determined by the ion population in the two alcohols and the solutions. The effect is briefly discussed in the potential energy landscape paradigm of structure fluctuations, and it is suggested that the high-frequency shear modulus measurements of ionic solutions would help reveal the temperature-dependent deviation from the DSE equation.     

Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).     

Molecular dynamics simulations for the growth of CH_4-CO_2 mixed hydrate

Molecular dynamics simulations are performed to study the growth mechanism of CH4-CO2 mixed hydrate in xCO2= 75%, xCO2= 50%, and xCO2= 25% systems at T = 250 K, 255 K and 260 K, respectively. Our simulation results show that the growth rate of CH4-CO2 mixed hydrate increases as the CO2 concentration in the initial solution phase increases and the temperature decreases. Via hydrate formation, the composition of CO2 in hydrate phase is higher than that in initial solution phase and the encaging capacity of CO2 in hydrates increases with the decrease in temperature. By analysis of the cage occupancy ratio of CH4 molecules and CO2 molecules in large cages to small cages, we find that CO2 molecules are preferably encaged into the large cages of the hydrate crystal as compared with CH4 molecules. Interestingly, CH4 molecules and CO2 molecules frequently replace with each other in some particular cage sites adjacent to hydrate/solution interface during the crystal growth process. These two species of guest molecules eventually act to stabilize the newly formed hydrates, with CO2 molecules occupying large cages and CH4 molecules occupying small cages in hydrate.     

Molecular dynamics simulations for the growth of CH4-CO2 mixed hydrate

Molecular dynamics simulations are performed to study the growth mechanism of CH4-CO2 mixed hydrate in xco2 = 75%, xco2 = 50%, and zco2 = 25% systems at T = 250 K, 255 K and 260 K, respectively. Our simulation results show that the growth rate of CH4-CO2 mixed hydrate increases as the CO2 concentration in the initial solution phase increases and the temperature decreases. Via hydrate formation, the composition of CO2 in hydrate phase is higher than that in initial solution phase and the encaging capacity of CO2 in hydrates increases with the decrease in temperature. By analysis of the cage occupancy ratio of CH4 molecules and CO2 molecules in large cages to small cages, we find that CO2 molecules are preferably encaged into the large cages of the hydrate crystal as compared with CH4 molecules. Interestingly, CH4 molecules and CO2 molecules frequently replace with each other in some particular cage sites adjacent to hydrate/solution interface during the crystal growth process. These two species of guest molecules eventually act to stabilize the newly formed hydrates, with CO2 molecules occupying large cages and CH4 molecules occupying small cages in hydrate.     

Interatomic potential-based semiclassical theory for Lennard-Jones fluids

An interatomic potential based semiclassical theory is proposed to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid confined in a channel. The inputs to the semiclassical formulation are the LJ parameters of the fluid and the wall, the density of channel wall atoms, and the average concentration of the fluid inside the channel. Using the semiclassical formulation, fluid confinement in channel with widths ranging from 2sigma ff to 100sigma ff, where sigma ff is the fluid-fluid LJ distance parameter, is investigated. The concentration and potential predicted by the semiclassical formulation are found to be in good agreement with those from equilibrium molecular dynamics simulations. While atomistic simulations in large channels are computationally expensive, the proposed semiclassical formulation can rapidly and accurately predict the concentration and potential profiles. The proposed semiclassical theory is thus a robust and fast method to predict the interfacial and "bulk" fluid phenomena in channels with widths ranging from the macroscale down to the scale of a few atomic diameters.