Entropy, diffusivity, and structural order in liquids with waterlike anomalies

The excess entropy, defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is studied as a function of density and temperature for liquid silica and a two-scale ramp potential, both of which are known to possess waterlike liquid state anomalies. The excess entropy for both systems is evaluated using a fairly accurate pair correlation approximation. The connection between the excess entropy and the density and diffusional anomalies is demonstrated. Using the pair correlation approximation to the excess entropy, it can be shown that if the energetically favorable local geometries in the low and high density limits have different symmetries, then a structurally anomalous regime can be defined in terms of orientational and translational order parameters, as in the case of silica and the two-scale ramp system but not for the one-scale ramp liquid. Within the category of liquids with waterlike anomalies, we show that the relationship between the macroscopic entropy and internal energy is sufficient to distinguish between those with local anisotropy and consequent open packings at low densities and those with isotropic interactions but multiple length scales. Since it is straightforward to evaluate the pair correlation entropy and internal energy from simulations or experimental data, such plots should provide a convenient means to diagnose the existence as well as type of anomalous behavior in a range of liquids, including ionic and intermetallic melts and complex fluids with ultrasoft repulsions.     

Experimental and Theoretical Study of Two Pyridinium-Based Ionic Liquids

Thermophysical properties of two pyridinium-based ionic liquids, 1-ethyl-2-methylpyridinium bis(trifluoromethylsulfonyl)imide and 1-propyl-2-methylpyridinium bis(trifluoromethylsulfonyl)imide, have been measured from 278.15 to 323.15?K, with a temperature step of 2.5?K. The properties measured were: densities, speeds of sound, refractive indices, surface tensions, isobaric molar heat capacities, electrical conductivities and viscosities. Thermal properties were also recorded in the temperature range from 100 to 320?K. From the experimental results coefficients of thermal expansion, isentropic compressibilities, molar refraction and surface enthalpies and entropies have been determined. Moreover, a theoretical study has been performed using ab initio calculations, level of theory HF/6-31G(d). From this study, we have obtained qualitative information about the magnitude and the directionality of the cation?Canion interactions which allows a better understanding of the physico-chemical properties of these ionic liquids.     

Absolute and relative entropies from computer simulation with applications to ligand binding

A comparison between two related methods, Schlitter's formula and quasiharmonic analysis, for calculating absolute entropies from the covariance matrix of atomic fluctuations using molecular dynamics (MD) simulations is presented. Calculations for a set of organic compounds in the gas phase are compared to the corresponding statistical thermodynamics results for translational and rotational entropies and to experimental data for vibrational entropies. Encouraging agreement is obtained for translational entropies, but for the rotational contribution, both methods fail to reproduce the theoretically calculated values. Absolute and relative vibrational entropies are found to be better reproduced using quasiharmonic analysis compared to Schlitter's formula. For rotational entropies, we propose a method based on the variances in Euler angles, which gives good agreement with theory. Alternative methods for estimating translational entropies based on principal root mean-square (rms) fluctuations of the center of mass are also presented, and these reproduce theoretically calculated values well. These methodologies are applied to the binding of benzene to T4-lysozyme, where close agreement with the literature is obtained for translational and rotational entropies.     

Entropy of single-file water in (6,6) carbon nanotubes

We used molecular dynamics simulations to investigate the thermodynamics of filling of a (6,6) open carbon nanotube (diameter D = 0.806 nm) solvated in TIP3P water over a temperature range from 280 K to 320 K at atmospheric pressure. In simulations of tubes with slightly weakened carbon-water attractive interactions, we observed multiple filling and emptying events. From the water occupancy statistics, we directly obtained the free energy of filling, and from its temperature dependence the entropy of filling. We found a negative entropy of about -1.3 k(B) per molecule for filling the nanotube with a hydrogen-bonded single-file chain of water molecules. The entropy of filling is nearly independent of the strength of the attractive carbon-water interactions over the range studied. In contrast, the energy of transfer depends strongly on the carbon-water attraction strength. These results are in good agreement with entropies of about -0.5 k(B) per water molecule obtained from grand-canonical Monte Carlo calculations of water in quasi-infinite tubes in vacuum under periodic boundary conditions. Overall, for realistic carbon-water interactions we expect that at ambient conditions filling of a (6,6) carbon nanotube open to a water reservoir is driven by a favorable decrease in energy, and opposed by a small loss of water entropy.     

Entropy of adsorption of carbon monoxide on energetically heterogeneous surfaces

Standard entropies of adsorption (Δs ⁰) of CO on different materials (Cu catalysts, Au catalysts, ZnO and to TiO₂) are obtained from static adsorption microcalorimetry, adsorption isobars and temperature-programmed desorption, based on the thermodynamics of adsorption on energetically heterogeneous surfaces. Vibrational entropies of the surfaces s _vib^α are normally between the rotational and the standard translational entropy of CO in gas phase, and decrease with increasing adsorption energy, which agrees with the explanation of statistical thermodynamics. Δs ⁰ reflects both the mobility of adsorbates and the specific adsorbate-adsorbent interaction. Limits for reasonable values of the entropy of adsorption are proposed.     

Ionic melts with waterlike anomalies: thermodynamic properties of liquid BeF2

Thermodynamic properties of liquid beryllium difluoride (BeF(2)) are studied using canonical ensemble molecular dynamics simulations of the transferable rigid ion model potential. The negative slope of the locus of points of maximum density in the temperature-pressure plane is mapped out. The excess entropy, computed within the pair correlation approximation, is found to show an anomalous increase with isothermal compression at low temperatures which will lead to diffusional as well as structural anomalies resembling those in water. The anomalous behavior of the entropy is largely connected with the behavior of the Be-F pair correlation function. The internal energy shows a T(35) temperature dependence. The pair correlation entropy shows a T(-25) temperature dependence only at high densities and temperatures. The correlation plots between internal energy and the pair correlation entropy for isothermal compression show the characteristic features expected of network-forming liquids with waterlike anomalies. The tagged particle potential energy distributions are shown to have a multimodal form at low temperatures and densities similar to those seen in other liquids with three-dimensional tetrahedral networks, such as water and silica.     

Water-DMF-L-α-alanine and water-carbamide-L-α-alanine systems. Thermodynamic properties, solvation, and interspecies interactions at 273–333 K

Thermal effects of dissolution of L-α-alanine in water-N,N-dimethylformamide mixtures (0–0.1 molar parts of DMF) at 283–318 K were measured calorimetrically. Standard enthalpies and heat capacities of dissolution of the amino acid and also thermal variations in entropies and free energies were calculated. The comparison with previously obtained data on the thermodynamics of dissolution of L-α-alamine in the carbamide water solution was performed. Temperature variations in the reduced Gibbs energy in the course of dissolution of L-α-alanine in water-DMF and water-carbamide mixtures have negative values originating from the prevalence of the entropy component. At the increase in temperature both mixtures become less structured. The interaction of L-α-alanine with hydrophilic and hydrophobic amides differs fundamentally: In the first case it is enthalpy-attractive and does not depend on temperature, while in the second case it is repulsive and decreases with the increase in temperature.     

Thermal Analysis of Binary Mixtures of Imidazolium,Pyridinium, Pyrrolidinium,and Piperidinium Ionic Liquids

Ionic liquids (ILs) are being widely studied due to their unique properties, which make them potential candidates for conventional solvents. To study whether binary mixtures of pure ionic liquids provide a viable alternative to pure ionic liquids for different applications, in this work, the thermal analysis and molar heat capacities of five equimolar binary mixtures of ionic liquids based on imidazolium, pyridinium, pyrrolidinium, and piperidinium cations with dicyanamide, trifluoromethanesulfonate, and bis(trifluoromethylsulfonyl)imide anions have been performed. Furthermore, two pure ionic liquids based on piperidinium cation have been thermally characterized and the heat capacity of one of them has been measured. The determination and evaluation of both the transition temperatures and the molar heat capacities was carried out using differential scanning calorimetry (DSC). It was observed that the thermal behavior of the mixtures was completely different than the thermal behavior of the pure ionic liquids present, while the molar heat capacities of the binary mixtures were very similar to the value of the average of molar heat capacities of the two pure ionic liquids.     

Confinement, entropy, and single-particle dynamics of equilibrium hard-sphere mixtures

We use discontinuous molecular dynamics and grand-canonical transition-matrix Monte Carlo simulations to explore how confinement between parallel hard walls modifies the relationships between packing fraction, self-diffusivity, partial molar excess entropy, and total excess entropy for binary hard-sphere mixtures. To accomplish this, we introduce an efficient algorithm to calculate partial molar excess entropies from the transition-matrix Monte Carlo simulation data. We find that the species-dependent self-diffusivities of confined fluids are very similar to those of the bulk mixture if compared at the same, appropriately defined, packing fraction up to intermediate values, but then deviate negatively from the bulk behavior at higher packing fractions. On the other hand, the relationships between self-diffusivity and partial molar excess entropy (or total excess entropy) observed in the bulk fluid are preserved under confinement even at relatively high packing fractions and for different mixture compositions. This suggests that the excess entropy, calculable from classical density functional theories of inhomogeneous fluids, can be used to predict some of the nontrivial dynamical behaviors of fluid mixtures in confined environments.     

Temperature‐Dependent Prediction of the Liquid Entropy of Ionic Liquids

Modeling of the temperature‐dependent liquid entropy of ionic liquids (ILs) with great accuracy using COSMO‐RS is demonstrated. The minimum structures of eight IL ion pairs are investigated and the entropy, calculated from ion pairs, is found to differ on average only 2 % from the available experimental values (119 data points). For calculations with single ions, the average error amounts to 2.6 % and stronger‐coordinating ions tend to give higher deviations. Additionally, the first parameterization of the standard liquid entropy for ILs is presented in the context of traditional volume‐based thermodynamics (S_l⁰=1.585 kJ mol^?1 K^?1 nm^?3?r_m³+14.09 J mol^?1 K^?1), which sheds light on the statistical treatment of ionic interactions. The findings provide the first direct access to accurate predictions of liquid entropies of ILs, which are tedious and time‐consuming to measure.     

Calculations of solute and solvent entropies from molecular dynamics simulations

The translational, rotational and conformational (vibrational) entropy contributions to ligand-receptor binding free energies are analyzed within the standard formulation of statistical thermodynamics. It is shown that the partitioning of the binding entropy into different components is to some extent arbitrary, but an appropriate method to calculate both translational and rotational entropy contributions to noncovalent association is by estimating the configurational volumes of the ligand in the bound and free states. Different approaches to calculating solute entropies using free energy perturbation calculations, configurational volumes based on root-mean-square fluctuations and covariance matrix based quasiharmonic analysis are illustrated for some simple molecular systems. Numerical examples for the different contributions demonstrate that theoretically derived results are well reproduced by the approximations. Calculation of solvent entropies, either using total potential energy averages or van't Hoff plots, are carried out for the case of ion solvation in water. Although convergence problems will persist for large and complex simulation systems, good agreement with experiment is obtained here for relative and absolute ion hydration entropies. We also outline how solvent and solute entropic contributions are taken into account in empirical binding free energy calculations using the linear interaction energy method. In particular it is shown that empirical scaling of the nonpolar intermolecular ligand interaction energy effectively takes into account size dependent contributions to the binding free energy.     

Confusing cause and effect: energy-entropy compensation in the preferential solvation of a nonpolar solute in dimethyl sulfoxide/water mixtures

We performed molecular simulations to analyze the thermodynamics of methane solvation in dimethyl sulfoxide (DMSO)/water mixtures (298 K, 1 atm). Two contributions to the interaction thermodynamics are studied separately: (i) the introduction of solute-solvent interactions (primary contribution) and (ii) the solute-induced disruption of cohesive solvent-solvent interactions (secondary contribution). The energy and entropy changes of the secondary contribution always exactly cancel in the free energy (energy-entropy compensation), hence only the primary contribution is important for understanding changes of the free energy. We analyze the physical significance of the solute-solvent energy and solute-solvent entropy associated with the primary contribution and discuss how to obtain these quantities from experiments combining solvation thermodynamic and solvent equation of state data. We show that the secondary contribution dominates changes in the methane solvation entropy and enthalpy: below 30 mol % DMSO in the mixture, methane, because of more favorable dispersion interactions with DMSO molecules, preferentially attracts DMSO molecules, which, in response, release water molecules into the bulk, causing an increase in the entropy. This large energy-entropy compensating process easily causes a confusion in the cause for and the effect of preferred methane-DMSO interactions. Methane-DMSO dispersion interactions are the cause, and the entropy change is the effect. Procedures that infer thermodynamic driving forces from analyses of the solvation entropies and enthalpies should therefore be used with caution.     

Prediction of vapour pressure using descriptors derived from molecular dynamics

Vapour pressures of organic materials can be predicted to high levels of accuracy using cohesive energies and solubility parameters derived from molecular dynamics simulations that use good forcefields. It is found that over 90% of the correlation with vapour pressure is accounted for by a single cross term involving the product of either the molecular weight or molar volume of a molecule and its cohesive energy density.     

Estimation of the lattice entropy of rare-earth compounds

Resolution of excess entropy of many types of transitions and estimation of standard entropy at 298.15K of compounds, for which experimental entropies have not yet been measured, depend on a reliable estimation of the lattice entropy. By taking into account the effects of cation mass and molar volume of the rare-earth compounds, the following formula is proposed for the estimation of the lattice entropy of isostructural iso-anionic rare-earth compounds. We have investigated 32 compounds, and found good agreements between estimated and experimental entropies.     

Thermodynamic properties of N-octyl- and N-dodecylnicotinamide chlorides in water

Densities, heat capacities and enthalpies of dilution at 25°C and osmotic coefficients at 37°C were measured for N-octyl- and N-dodecylnicotinamide chlorides in water over an extended concentration region. Partial molar volumes, heat capacities, relative enthalpies and nonideal free energies and entropies at 25°C were derived as a function of the surfactant concentration. For both surfactants, plots of volumes, enthalpies and free energies vs. concentration are regular whereas those of heat capacities and entropies present anomalies at about 0.8 and 0.1m for the octyl and dodecyl compounds, respectively. Changes in the slope of a plot of osmotic coefficients times molality vs. molality were also observed at these same concentrations. These peculiarities are ascribed to micelle structural transitions. The nonideal free energies do not seem to depend on the alkyl chain length when they are plotted vs. m/C _cmc . Also, a plot of the nonideal free energy vs. logm/C _cmc is roughly independent of the nature of the surfactant because of the constant activity of surfactants in micellar solutions. Nonideal free energies, enthalpies and entropies have been calculated at 15 and 35°C. At each concentration the nonideal free energy is temperature independent as a result of a compensatory effect between enthalpy and entropy. The thermodynamic functions of micellization were graphically evaluated on the basis of the pseudo-phase transition model. These data suggest that the nicotinamide group possesses less hydrophilic character than the ammonium group.     

Phase transition thermodynamics of phenyl and biphenyl naphthalenes

This work is focussed on the thermodynamics of phase transition for some naphthalene derivatives: 1-phenylnaphthalene, 2-phenylnaphthalene, 2-(biphen-3-yl)naphthalene, and 2-(biphen-4-yl)naphthalene.The Knudsen mass-loss effusion technique was used to measure the vapour pressures of the following compounds: 2-phenylnaphthalene (cr), between T= (333.11 and 353.19) K; 2-(biphen-4-yl)naphthalene (cr), between T = (405.17 and 437.19) K; 2-(biphen-3-yl)naphthalene (l), betweenT = (381.08 and 413.17) K. From the temperature dependence of the vapour pressure, the standard, (p = 10⁵ Pa), molar enthalpies, entropies, and Gibbs free energies of sublimation for 2-phenylnaphthalene and 2-(biphen-4-yl)naphthalene were derived as well as the standard molar enthalpy, entropy, and Gibbs free energy of vaporization for 2-(biphen-3-yl)naphthalene at 298.15 K. The temperatures and the standard molar enthalpies of fusion were measured by differential scanning calorimetry and the standard molar entropies of fusion were derived. For 1-phenylnaphthalene the standard molar enthalpy of vaporization at 298.15 K was measured directly using the Calvet microcalorimetry drop method.The 1-phenylnaphthalene is liquid at room temperature, showing a remarkably low melting point when compared to the 2-phenylnaphthalene isomer and naphthalene. A regular decrease of volatility with the increase of a phenyl group in para position at the 2-naphthalene derivatives was observed. In 2-(biphen-3-yl)naphthalene, the meta substitution of the phenyl group results in a significantly higher volatility than in the respective para isomer.     

Quantum chemical studies of the hydration of Sr2+ in vacuum and aqueous solution

The geometric structures of gas-phase Sr(2+) hydrates are calculated quantum chemically by using hybrid (B3LYP) and meta-GGA (TPSS) density functional theory, and a range of thermodynamic data (including sequential bond enthalpies, entropies and free energies for the reactions Sr(2+)(H(2)O)(n-1)+H(2)O→Sr(2+)(H(2)O)(n)) are shown to be in excellent agreement with experiment. When the number of coordinating water molecules exceeds six, such that water begins to occupy the second solvation shell, it is found that detailed analysis based on both geometrical and conformational entropy is required in order to confidently identify the experimentally observed structures. The significant increase in coordination number observed experimentally between the gas- and aqueous-phase species is successfully reproduced, as is the first solvation shell geometry. Inaccurate second shell geometries imply that larger model systems may be required to achieve agreement with experiment. Candidate species for on-going computational studies of the interaction of hydrated Sr(2+) with brucite surfaces have been identified.     

New parametrization method for dissipative particle dynamics

We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle dynamics (DPD) by exploiting a correspondence between DPD and Scatchard-Hildebrand regular solution theory. The new parametrization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities. We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing, obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids, providing an alternative method of calculating the self-interaction parameters as well as a route to the cross interaction parameter. We validate the new parametrization by modeling the binary system SnI(4)SiCl(4), which displays liquid-liquid coexistence below an upper critical solution temperature around 140 degrees C. A series of DPD simulations were conducted at a set of temperatures ranging from 0 degrees C to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume. Our simulations recover the expected phase behavior ranging from solid-liquid coexistence to liquid-liquid coexistence and eventually leading to a homogeneous single phase system. The results yield a binodal curve in close agreement with the one predicted using regular solution theory, but, significantly, in closer agreement with actual solubility measurements.     

Thermal behaviour of the system lead(II) dodecanoate/lead acetate

Data are presented for the heats and entropies of phase changes for the system lead(II) dodecanoate/lead acetate. A phase diagram has also been constructed for the system.Optical observation under a polarising microscope suggests that the phase sequence in this system is the same as in pure lead dodecanoate i.e. crystal → G (smectic) → V₂ (cubic isomorphous) → liquid.The entropy of the V₂ → liquid transition in the mixtures is the same as for pure lead dodecanoate which suggests that addition of lead acetate to lead dodecanoate does not affect the state of aggregation of the soap in the liquid phase.     

Calorimetric study of the relationship between molecular structure and liquid crystallinity of rod-like mesogens II. Heat capacities and phase transitions of 4-(trans-4-propylcyclohexyl)benzonitrile

The molar heat capacity of the rod-like compound 4-(trans-4-propylcyclohexyl)benzonitrile (3-CBCN), purity of 99.8mol%, has been measured with an adiabatic calorimeter at temperatures between 15 and 385K. 3-CBCN is a nematogenic mesogen, whose melting and clearing points are 316.33 and 319.09 K, respectively. The enthalpy and entropy gained at fusion are 20.4 kJmol -1 and 64.4 J K -1 mol -1, respectively; those for the nematic-to-isotropic transition are 1.1 kJmol -1 and 3.5 J K -1 mol -1 respectively. 3-CBCN exhibits a supercooled nematic phase, whose molar heat capacities have been measured from 25 K below the melting point. The molar and transition entropies of 3-CBCN are discussed in relation to those of 4-propylbiphenyl-4-carbonitrile (3-BBCN) and trans,trans-4'-propylbicyclohexyl- 4-carbonitrile (3-CCCN). There seems to exist a correlation between these values and mesophase stability. Finally, Eidenschink's theoretical model for the nematic-to-isotropic transition has been applied to 3-CBCN; the transition enthalpy estimated according to this model agrees well with the observed value.