Free energy, energy, and entropy of swelling in Cs-, Na-, and Sr-montmorillonite clays

A Monte Carlo method for grand canonical and grand isoshear ensemble simulations has been used to characterize the free energy, energy, and entropy of clay mineral swelling. The Monte Carlo approach was found to be more efficient at simulating water content fluctuations in the highly constrained clay environment than a previously developed molecular dynamics method. Swelling thermodynamics calculated for Cs-, Na-, and Sr-montmorillonite clays indicate a strong dependence of swelling on the interlayer ion identity, in agreement with various experimental measurements. The Sr clay swells most readily, and both the Na and Sr clays prefer expanded states (two-layer hydrate or greater) when in contact with bulk water. In contrast, swelling is inhibited in the Cs clay. Differences in swelling behavior are traced directly to the tendency of the different ions to hydrate. The swelling free energies are decomposed into their energetic and entropic components, revealing an overall energetic driving force for the swelling phenomena. Entropic effects provide a smaller, mediating role in the swelling processes. The results provide a unique molecular perspective on experimentally well-characterized swelling phenomena.     

Pressure and temperature dependence of hydrophobic hydration: volumetric, compressibility, and thermodynamic signatures

The combined effect of pressure and temperature on hydrophobic hydration of a nonpolar methanelike solute is investigated by extensive simulations in the TIP4P model of water. Using test-particle insertion techniques, free energies of hydration under a range of pressures from 1 to 3000 atm are computed at eight temperatures ranging from 278.15 to 368.15 K. Corresponding enthalpy, entropy, and heat capacity accompanying the hydration process are estimated from the temperature dependence of the free energies. Partial molar and excess volumes calculated using pressure derivatives of the simulated free energies are consistent with those determined by direct volume simulations; but direct volume determination offers more reliable estimates for compressibility. At 298.15 K, partial molar and excess isothermal compressibilities of methane are negative at 1 atm. Partial molar and excess adiabatic (isentropic) compressibilities are estimated to be also negative under the same conditions. But partial molar and excess isothermal compressibilities are positive at high pressures, with a crossover from negative to positive compressibility at approximately 100-1000 atm. This trend is consistent with experiments on aliphatic amino acids and pressure-unfolded states of proteins. For the range of pressures simulated, hydration heat capacity exhibits little pressure dependence, also in apparent agreement with experiment. When pressure is raised at constant room temperature, hydration free energy increases while its entropic component remains essentially constant. Thus, the increasing unfavorability of hydration under raised pressure is seen as largely an enthalpic effect. Ramifications of the findings of the authors for biopolymer conformational transitions are discussed.     

Novel poly(N‐isopropylacrylamide)/clay/poly(acrylamide) IPN hydrogels with the response rate and drug release controlled by clay content

Novel interpenetrating network (IPN) hydrogels (PNIPAAm/clay/PAAm hydrogels) based on poly(N‐isopropylacrylamide) (PNIPAAm) crosslinked by inorganic clay and poly(acrylamide) (PAAm) crosslinked by organic crosslinker were prepared in situ by ultraviolet (UV) irradiation polymerization. The effects of clay content on temperature dependence of equilibrium swelling ratio, deswelling behavior, thermal behavior, and the interior morphology of resultant IPN hydrogels were investigated with the help of Fourier transform infrared spectroscopy, differential scanning calorimeter (DSC), scanning electron microscope (SEM). Study on temperature dependence of equilibrium swelling ratio showed that all IPN hydrogels exhibited temperature‐sensitivity. DSC further revealed that the temperature‐sensitivity was weakened with increasing amount of clay. Study on deswelling behavior revealed that IPN hydrogels had much faster response rate when comparing with PNIPAAm/clay hydrogels, and the response rate of IPN hydrogels could be controlled by clay content. SEM revealed that there existed difference in the interior morphology of IPN hydrogels between 20 [below lower critical solution temperature (LCST)] and 50 °C (above LCST), and this difference would become obvious with a decrease in clay content. For the standpoint of applications, oscillating swelling/deswelling behavior was investigated to determine whether properties of IPN hydrogels would be stable for potential applications. Bovine serum albumin (BSA) was used as model drug for in vitro experiment, the release data suggested that the controlled drug release could be achieved by modulating clay content. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 96–106, 2009     

Thermal conductivity of molten alkali halides from equilibrium molecular dynamics simulations

The thermal conductivity of molten sodium chloride and potassium chloride has been computed through equilibrium molecular dynamics Green-Kubo simulations in the microcanonical ensemble (N,V,E). In order to access the temperature dependence of the thermal conductivity coefficient of these materials, the simulations were performed at five different state points. The form of the microscopic energy flux for ionic systems whose Coulombic interactions are calculated through the Ewald method is discussed in detail and an efficient formula is used by analogy with the methods used to evaluate the stress tensor in Coulombic systems. The results show that the Born-Mayer-Huggins-Tosi-Fumi potential predicts a weak negative temperature dependence for the thermal conductivity of NaCl and KCl. The simulation results are in agreement with part of the experimental data available in the literature with simulation values generally overpredicting the thermal conductivity by 10%-20%.     

Theoretical and computational investigations on thermodynamic properties, effective site diameters, and molecular free volume of carbon disulfide fluid

A newly proposed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was extended to polyatomics and applied to compute the density and temperature dependence of the effective site diameters of carbon disulfide fluids. The generic van der Waals (GvdW) theory was also extended to polyatomics in order to calculate the GvdW parameters and the molecular free volume using the effective site diameters as the repulsion-attraction separation distance. A three-site Lennard-Jones potential available in the literature was slightly modified and used in Monte Carlo simulations to obtain the functions appearing in the effective site diameter and GvdW expressions. The interaction potential was examined to reproduce the fluid phase thermodynamic properties using Gibbs ensemble Monte Carlo simulations and also the equation of state in the liquid phase using NVT Monte Carlo (NVT-MC) simulations. Comparison between the simulation results and experimental data shows excellent agreement for the densities of the coexisting phases, the vapor pressure, properties of the predicted critical point, and the equation of state. NVT-MC simulations were performed over a wide range of densities and temperatures in sub- and supercritical regions to compute the effective site diameters, the GvdW parameters, and the molecular free volume. The molecular structure in terms of the site-site pair correlation functions, the density dependence of the effective site diameters, and the density and temperature dependence of the GvdW parameters and molecular free volume were studied and discussed. The GvdW parameters were fitted to empirical expressions as a function of density and temperature. The computed molecular free volume will be used in future investigations to study the transport properties of carbon disulfide.     

Introducing interacting diffuse layers in TLM calculations: a reappraisal of the influence of the pore size on the swelling pressure and the osmotic efficiency of compacted bentonites

The truncation of the Gouy-Chapman diffuse part in compacted clay-rocks and bentonite is introduced into the electrical triple-layer model (TLM) recently developed by P. Leroy and A. Revil [J. Colloid Interface Sci. 270 (2004) 371]. The new model is used to explain the dependence of the osmotic efficiency and the swelling pressure as functions of the mean pore size of the medium, determined from the porosity and the specific surface. The truncation of the diffuse layer introduces a new variable in the system of equations to be solved, the electrical potential at the midplane between adjacent charged surfaces. This new variable is evaluated through a Taylor expansion of the electrical potential. The present model is able to capture the variation of the osmotic efficiency and the swelling pressure with the mean pore size. The partition of counterions between the Stern layer and the diffuse layer as a function of the pore size calculated by the TLM also shows a good consistency with the model. This implies that more than 90% of the counterions are located in the Stern layer.     

Temperature dependence of NMR order parameters and protein dynamics

The helical subdomain, HP36, of the F-actin-binding headpiece domain of chicken villin, is the smallest naturally occurring polypeptide that folds to a thermostable compact structure. Unconstrained molecular dynamics simulations and constrained molecular dynamics simulations using umbrella sampling are used to study the temperature dependence of internal motions of the backbone amide moieties of HP36. The potential of mean force (PMF) for the N-H bond vector, determined from the constrained simulations, is found to be temperature dependent. A simple analytical expression is derived that describes the temperature dependence of the PMF. The parameters of this model are obtained from the PMF, from the unconstrained molecular dynamics simulations, or from experimental values of the generalized order parameter. The results provide a linkage between experimental and theoretical measures of the temperature dependence of protein motions.     

Relationship of swelling and swelling pressure on silica-water interactions in montmorillonite

In this work, we have used the previously designed controlled uniaxial swelling (CUS) cell to obtain predetermined extents of swelling in montmorillonite. Using the CUS cell, a simultaneous measurement of swelling pressure is done with controlled swelling. Undisturbed clay samples at well-defined swelling (0%-75%) were removed from the CUS cell and analyzed using scanning electron microscopy (SEM) and Fourier transform infrared (FTIR) spectroscopy. In addition, orientation-dependent microattenuated total reflectance (micro-ATR) spectroscopic investigations are also conducted on the controlled swelled samples. Significant changes in the silicate (Si-O) stretching region (1150-950 cm(-1)) have been observed with changes in swelling and orientation. The band at 1005 cm(-1) (attributed in the literature to arising from Si-O vibrations when montmorillonite platelets are normal to incident radiation) is most pronounced for the 0%-swelled sample and diminishes with swelling. The band associated with perpendicular vibration (at 1078 cm(-1)) increases with swelling. Thus, the intensity of this band increases with misorientation of clay particles. Our results indicate that the reduced particle size, as ascertained from SEM cryoimaging, with increased swelling is related to increased misorientation of the clay platelets. At 0% swelling, the clay platelets are most oriented and have largest particle size. The rearrangement of clay platelets as seen in the orientation-dependent spectra is a direct result of the breakdown of the clay particles with increased hydration resulting from increased swelling.     

Diffusion Dynamics of Cux Cluster on Cu(111) Surface

The diffusion dynamics of small two-dimensional atomic clusters Cux (1·x·8) on Cu(111) surface were studied using the molecular dynamics simulations and a modified analytic embedded-atom method in the temperature range from 200 K to 800 K. The cluster size and temperature dependence of the diffusion coefficients and migration energies are presented. Our simulations show that the diffusion migration energy of the Cu7 cluster is the highest and the prefactor for the Cu7 cluster is almost three orders of magnitude larger than that for single atom diffusion. This conclusion is consistent with the experimental results for similar metals. In addition, the dependence of cluster diffusion on film growth is also discussed.     

Two-dimensional Monte Carlo studies of lipid molecules in a bilayer membrane

We present a new model to study in-plane liquid properties of lipid membranes. The different conformations of lipids are represented by a seven-state system of hard triatomic particles, or triples, of varying lengths which correspond to the different cross-sectional areas of the lipids in the plane of the membrane. Two-dimensional Monte Carlo simulations are performed in both the constant NVT and NPT ensembles. The distribution of states has a strong density dependence and a small temperature dependence over the biologically relevant range. There is no long range orientational order in the systems before freezing. The short range orientational order increases with density. Widom's particle insertion method is used to obtain the excess chemical potential of the system for the seven states. These values, along with the pressure, are in excellent agreement with estimates from scaled particle theory.     

An experimental and modeling study of the oxidation of n-heptane,ethylbenzene, and n-butylbenzene in a jet-stirred reactor at pressures up to 10 bar

In the context of better understanding pollutant formation from internal combustion engines, new experimental speciation data were obtained in a high-pressure jet-stirred reactor for the oxidation of three molecules, which are considered in surrogates of diesel fuel, n-heptane, ethylbenzene, and n-butylbenzene. These experiments were performed at pressures up to 10 bar, at temperatures ranging from 500 to 1 100 K, and for a residence time of 2 s. Based on results previously obtained close to the atmospheric pressure for the same molecules, the pressure effect on fuel conversion and product selectivity was discussed. In addition, for the three fuels, the experimental temperature dependence of species mole fractions was compared with simulations using recent literature models with generally a good agreement. For n-heptane, the obtained experimental data, at 10 bar for stoichiometric mixtures, included the temperature dependence of the mole fractions of the reactants and those of 21 products. Interestingly, the formation of species previously identified as C₇ diones was found significantly enhanced at 10 bar compared with lower pressures. The oxidation of ethyl- and n-butylbenzenes was investigated at 10 bar for equivalence ratios of 0.5, 1, and 2. The obtained experimental data included the temperature dependence of the mole fractions of the reactants and those of 13 products for the C₈ fuels and of 19 products for the C₁₀ one. For ethylbenzene under stoichiometric conditions, the pressure dependence (from 1 to 10 bar) of species mole fraction was also recorded and compared with simulations with more deviations obtained than for temperature dependence. For both aromatic reactants, a flow rate analysis was used to discuss the main pressure influence on product selectivities.     

A combined pressure-controlled scanning calorimetry and Monte Carlo determination of the Joule-Thomson inversion curve. Application to methane

A combination of a pressure-controlled scanning calorimetry (PCSC) and Monte Carlo simulations (MCS) is presented for an unequivocal determination of the Joule-Thomson inversion curve (JTIC) with high accuracy over wide ranges of pressure and temperature. The MCS performed with the fluctuation method are fast and easy to operate, but the results can vary significantly depend on the set of primary molecular data needed for the calculations. The PCSC is an experimental and more laborious technique, but supplies data of high quality. Thus, it can be used to check the MCS data and to verify the molecular parameters used for the calculations. Such a combined procedure was used in the present study for determination of the JTIC for methane, for which a correlation equation was established valid from 302.9 to 586.5 K. A combination of a direct experimental technique with molecular simulations permits also to better understand the complex behavior of the Joule-Thomson inversion phenomenon over wide ranges of pressure and temperature.     

Hysteresis in clay swelling induced by hydrogen bonding: accurate prediction of swelling states

We perform grand-canonical molecular simulations to study the molecular mechanism of clay swelling hysteresis as a function of the relative humidity. In particular, we focus on the transition from the one- to the two-layer hydrate and the influence of three types of counterions (Li+, Na+, and K+). Our results cover the experimental relative humidity region where swelling and shrinking usually occur. We show that the thermodynamic origin of swelling hysteresis is a free-energy barrier separating the layered hydrates. This free-energy barrier is dominated by breaking and formation of hydrogen bonds between and within water layers. This network of water molecules is similar for all counterions, but the positions of these counterions depend upon their size. The relatively large K+ counterions show more affinity for clay surface adsorption, which increases the free-energy barrier and inhibits swelling. On the other hand, the relatively small Li+ counterions are quite well-accommodated in the water network, and thereby, they can form a new swelling state with a basal spacing of approximately 13.5 A. This new swelling state is an alternative explanation for the widely accepted simultaneous occurrence of two or more swelling phases.     

Fictive temperature, cooling rate, and viscosity of glasses

The physical correlation between the fictive temperature dependence of the cooling rate of the melts and the temperature dependence of the equilibrium viscosity has been found by doing differential scanning calorimetric and viscometric measurements on a silicate melt, and by performing finite element simulations of the fiber drawing from that melt. This correlation is governed by a correlation factor Kc (in Pa K) which is constant and universal for silicate glasses. The factor Kc is obtained in the cooling rate range from 10(-2) to 10(6) K/s and is in good agreement with that theoretically predicted. The physical feature of the correlation is discussed in the paper. When the fictive temperature equals the actual temperature, a linear relation exists between the cooling rate and the Maxwell relaxation rate, the slope of which depends on the fragility of the glass melts. The Avramov equation is extended to describe the cooling rate dependence of the fictive temperature. The cooling rate equation contains only one adjusting parameter, i.e., the fragility parameter alpha.     

Atmospheric degradation of 2-butanol, 2-methyl-2-butanol, and 2,3-dimethyl-2-butanol: OH kinetics and UV absorption cross sections

The absolute rate coefficients for the reactions of hydroxyl radical (OH) with 2-butanol (k(1)), 2-methyl-2-butanol (k(2)), and 2,3-dimethyl-2-butanol (k(3)) were measured as a function of temperature (263-354 K) and pressure (41-193 Torr of He, Ar, and N(2)) by the pulsed laser photolysis/laser-induced fluorescence technique. This work represents the first absolute determination of k(1)(-)k(3) and their temperature dependence. No pressure dependence of the rate coefficients was observed in the range studied. Thus, k(i)(298 K) values (x10(-12) cm(3) molecule(-1) s(-1) with an uncertainty of +/-2sigma) were averaged over the pressure range studied yielding 8.77 +/- 1.46, 3.64 +/- 0.60, and 9.01 +/- 1.00 for 2-butanol (k(1)), 2-methyl-2-butanol (k(2)), and 2,3-dimethyl-2-butanol (k(3)), respectively. k(1) and k(3) exhibit a slightly negative temperature dependence over the temperature range studied. In contrast, the rate coefficient for the reaction of OH with 2-methyl-2-butanol (k(2)) did not show any temperature dependence. Some deviation of the conventional Arrhenius behavior was clearly observed for k(3). In this case, the best fit to our data was found to be described by the three-parameter expression k(T) = A + B exp(-C/T). The UV absorption cross sections of 2-butanol, 2-methyl-2-butanol, and 2,3-dimethyl-2-butanol have also been measured at room temperature between 208 and 230 nm. The values reported constitute the first determination of the UV cross sections of those alcohols. Our results are compared with previous studies, when possible, and are discussed in terms of the H-abstraction by OH radicals. The atmospheric implications of these reactions and the photochemistry of these alcohols are also discussed.     

气体在无定型聚异戊二烯中扩散的分子动力学模拟

采用分子动力学模拟方法研究了多个温度下氧气、氮气及甲烷在无定型顺式1,4-聚异戊二烯中的扩散系数。在模拟过程中,使用COMPASS力场作为分子力场。应用COMPASS力场的势能函数,聚合物的密度及玻璃化转变温度的计算结果与实验值有较好吻合。在278-378 K的温度范围内,通过3或1.5 ns时长的正则系综动力学模拟,计算了不同温度下氧气、氮气及甲烷的扩散系数。结果表明,根据爱因斯坦关系式计算得到的扩散系数与实验结果比较接近。对气体扩散系数与温度的关系进一步研究,发现在278-378 K温度范围内,甲烷的扩散系数随温度变化的半对数曲线图是非线性的,而氧气和氮气的扩散系数随温度变化的半对数曲线图是线性的。本文研究结果有助于理解温度对气体扩散的影响机制,并为高温下气体在天然橡胶中扩散系数的测定及天然橡胶热氧老化建模分析提供依据。     

Theory of swelling of a crosslinked substance in equilibrium with a pure solvent in various phases. Part II: The variation of the pressure

A theory of swelling is presented which describes the equilibrium swelling of a body in a solvent in its various states. The pressure dependence of the pressure-concentration swelling curves is treated for the swelling agent occurring in the liquid, crystalline or vapor phase. The slopes of the pressureconcentration swelling curves are dependent on the differential volume of dilution of the solvent and, additionally, on the volume changes of vaporization, crystallization, and sublimation of the solvent corresponding to the state of the swelling agent. At the melting and boiling pressure of the swelling agent the swelling curves change their slopes with a discontinuity, which is most distinct at the evaporation transition. By measurements of the slopes of the swelling curves at the transition pressure the derivative ₁/w₁ at constant temperature and pressure, which is the change of the chemical potential of the solvent with its weight fraction, is obtained. Thus, a further equation is given to test statistical theories at the transition pressures. Simultaneous variations of the swelling with changes of temperature are also treated.     

Hydration of a synthetic clay with tetrahedral charges: a multidisciplinary experimental and numerical study

The interaction of water with a synthetic saponite clay sample, with a layer charge of 1 per unit cell (0.165 C m(-2)), was investigated by following along water adsorption and desorption in the relative pressure range from 10(-6) to 0.99 (i) the adsorbed amount by gravimetric and near-infrared techniques, (ii) the basal distance and arrangement of water molecules in the interlayer by X-ray and neutron diffraction under controlled water pressure, and (iii) the molecular structure and interaction of adsorbed water molecules by near-infrared (NIR) and Raman spectroscopy under controlled water pressure. The results thus obtained were confronted with Grand Canonical Monte Carlo (GC/MC) simulations. Using such an approach, various well-distinct hydration ranges can be distinguished. In the two first ranges, at low water relative pressure, adsorption occurs on external surfaces only, with no swelling associated. The next range corresponds to the adsorption of water molecules around the interlayer cation without removing it from its position on top of the ditrigonal cavity of the tetrahedral layer and is associated with limited swelling. In the following range, the cation is displaced toward the mid-interlayer region. The interlamellar spacing thus reached, around 12.3 A, corresponds to what is classically referred to as a "one-layer hydrate," whereas no water layer is present in the interlayer region. The next hydration range corresponds to the filling of the interlayer at nearly constant spacing. This leads to the formation of a well-organized network of interlayer water molecules with significant interactions with the clay layer. The structure thus formed leads to a complete extinction of the d001 line in D2O neutron diffraction patterns that are correctly simulated by directly using the molecular configurations derived by GC/MC. The next range (0.50 < P/P0 < 0.80) corresponds to the final swelling of the structure to reach d spacing values of 15.2 A (usually referred to the "two-layer hydrate"). It is associated with the development of a network of liquidlike water molecules more structured than in bulk water. The final hydration range at high relative pressure mainly corresponds to the filling of pores between clay particles.     

Precision of free energies calculated by molecular dynamics simulations of peptides in solution

Errors in free energies for molecular replacement and for conformation change of a small model peptide have been determined empirically by repeated simulations from different starting points. All calculations have been done using thermodynamic integration, in which the system's potential energy is coupled to a parameter λ, that is increased or decreased by a small amount at each step of the simulation. The effects of several factors that may alter the precision are evaluated. These factors include: the length of the simulation, the dependence of the potential energy on λ, the use of conformational restraints, and their magnitude and form. The methods used for restraint and conformational forcing are described in detail. The free energy change, calculated as the mean from several successive simulations with alternately increasing and decreasing λ, is found to be independent of the length of the simulations. As expected, longer simulations produce more precise results. The variation of the calculated free energies is found to consist of two parts, a random error and a systematic hysteresis, i.e., a dependence on the direction in which λ changes. The hysteresis varies as the inverse of the length of the simulation and the random error as the inverse square root The advantage of the use of a different (nonlinear) dependence of the attractive and repulsive parts of the nonbonded potential energy on the coupling parameter when “creating” particles in solution is found to be very large. This nonlinear coupling was found to be superior to the use of linear coupling and a nonlinear change of the coupling parameter with the simulation time. The hysteresis in conformational free energy calculations is found to increase markedly if too weak a forcing restraint is chosen. It is shown how to deconvolute the contribution of a torsional restraint from the dependence of the free energy on a torsion angle.