Jamming probabilities for a vacancy in the dimer model.

Following the recent proposal made by [J. Bouttier, Phys. Rev. E 76, 041140 (2007)], we study analytically the mobility properties of a single vacancy in the close-packed dimer model on the square lattice. Using the spanning web representation, we find determinantal expressions for various observable quantities. In the limiting case of large lattices, they can be reduced to the calculation of Toeplitz determinants and minors thereof. The probability for the vacancy to be strictly jammed and other diffusion characteristics are computed exactly.

The hydrophobic propensity of water toward amphiprotic solutes: predicton and molecular origin of the aqueous solubility of aliphatic alcohols.

A quantitative expression of the hydrophobic effect for amphiphilic solutes in water is developed in the frame of the nonergodic thermodynamics of mobile order in hydrogen-bonded liquids. In the case of aliphatic alcohols, the new expression leads to reduction of the hydrophobic propensity of water with respect to that exerted towards substances with no hydrogen bonding capacity. The reduction originates from the possible insertion of the alcohol molecules in the weakest hydrogen bond chain of water; hence, strengthening the hydrogen bonding network of water. Combined with the previous solubility model derived from mobile order thermodynamics, the new expression allows correct predictions of the solubility of 86 liquid and solid branched- and straight-chain alcohols in water at 25 degrees C, and provides better understanding of their behavior in aqueous solution. The model is furthermore applied to the estimation of the aqueous solubility of 12 monohydroxysteroids.

The hydrophobic effect. 2. Relative importance of the hydrophobic effect on the solubility of hydrophobes and pharmaceuticals in H-bonded solvents.

The quantitative development of the nonergodic mobile order thermodynamics involving the new interpretation of the hydrophobic effect leads to a general solubility equation. This equation is applied to predict the aqueous and alcohol solubility of chemicals ranging from nonpolar or slightly polar with no H-bonding capacity to polyfunctional polar compounds including pharmaceuticals. The analysis of the relative importance of the contributions involved in the solubility model [i.e., the fluidization of the solute (for solids), the correction for the mixing entropy, the change of the nonspecific cohesion forces, and the formation of solvent-solvent (hydrophobic effect), solute-solute, and solute-solvent H-bonds] unambiguously demonstrates that the hydrophobic effect is essential for predicting the aqueous or alcohol solubility of any substance in general, and of nonpolar compounds in particular. The difference between the origin of the solubility of hydrocarbons in water and of water in hydrocarbons is furthermore presented. In both cases, the quasilinear solubility dependence on the molar volume of the hydrocarbon is of an entropic nature.

The hydrophobic effect. 1. A consequence of the mobile order in H-bonded liquids.

The hydrophobic effect has an entropic nature that cannot be explained by classical multicomponent treatments that do not explicitly take into account both the mobility and the nonergodicity of the H-bonds in amphiphilic liquids. The nonergodic thermodynamics of mobile order in H-bonded liquids based on time fractions rather than on concentrations provides a novel qualitative and quantitative explanation for the molecular origin of the hydrophobic effect. Chiefly, this effect corresponds to the loss of the mobile order entropy of associated molecules by dilution with foreign substances. Not being a unique property of water, the propensity of an amphiphilic solvent to induce a solvophobic effect increases primarily as its structuration factor increases, and secondarity as the solute/solvent molar volume ratio increases. On this basis, it can be expected that in the absence of strong solute-solvent specific interactions, the solubility of nonelectrolytes will generally decrease in the following order: butanol > propanol > ethanol > methanol > propylene glycol > ethylene glycol > formamide > water.

The hydrophobic effect. 3. A key ingredient in predicting n-octanol-water partition coefficients.

The quantitative development of the mobile order theory in H-bonded liquids is extended to predict the n-octanol/water partition coefficient (P). The log P predictive equation strictly issued from a thermodynamic treatment reduces to a simple linear volume-log P relationship whose intercept and slope encode, respectively, the solvation and entropy effects. For noncomplexing substances, the partition coefficient values result from two volume-dependent entropic contributions reflecting (a) the difference in the exchange entropy between the solute and solvent molecules in the n-octanol and water phases, and (b) the propensity difference between the two H-bonded solvents to induce a hydrophobic effect toward the solute. Although both effects increase, although with opposite signs, compared with the growing molar volume of the partitioned compound, the hydrophobic contribution always predominates favoring the transfer of the solute into the organic phase and hence increasing its partition coefficient. When dealing with complexing chemicals, the hydrophobic effect-related term, though remaining the dominant factor in most cases, is more or less counterbalanced by the formation of H-bonds between the interacting sites of the solute and the n-octanol and water solvent molecules. The log P, corrected for the substantial content of water into n-octanol, is estimated for a number of compounds of environmental and pharmaceutical interest. The extent to which the entropic and enthalpic factors affect the overall partition coefficient value is analyzed.

Hydrophobic effect at the origin of the low solubility of inert solid substances in hydrogen-bonded solvents.

The new solubility equation derived from the thermodynamics of mobile order in liquids is used to predict the solubility of four solid aliphatic and aromatic hydrocarbons, namely, tricosane, octacosane, biphenyl and pyrene, in nonassociated and hydrogen-bonded solvents. The analysis of the relative importance of the different terms contributing to the solubility shows that (1) the fluidization of the solute always represents a barrier to the solubility, (2) in non-hydrogen-bonded solvents, the solubility essentially results from the balance of the exchange entropy correction and the change in the nonspecific cohesion forces upon mixing, (3) in alcohols or in water, the solubility is mainly determined by the hydrophobic effect which corresponds to a solute rejecting effect of the solvent. This effect is responsible for the lower solubility values of the inert substances in associated solvents with respect to those in nonassociated solvents.

Determination of partial solubility parameters of lactose by gas-solid chromatography.

On the basis of the Snyder/Karger-Hansen interaction model, where delta EA = Vi(delta di delta dj + delta pi delta pi + delta hi delta nj), the partial solubility parameters of a solid used as the stationary phase may be determined through gas-solid chromatography by null-injection of solutes with known solubility parameters. Using n-decane, acetonitrile, and 1-propanol as molecular probes, the values found for unhydrated lactose were 9.6, 12.8, 11.3, and 19.5 (cal1/2/cm3/2) for delta d, delta p, delta h, and delta t, respectively; relative standard errors were better than 3%. The choice and the minimum number of the best molecular probes were determined by optimization of the experimental matrix according to the D-criterion, which permits considerable reduction of experimental time yet enhances total precision.

Scaling fields in the two-dimensional Abelian sandpile model.

We consider the unoriented two-dimensional Abelian sandpile model from a perspective based on two-dimensional (conformal) field theory. We compute lattice correlation functions for various cluster variables (at and off criticality), from which we infer the field-theoretic description in the scaling limit. We find perfect agreement with the predictions of a c=-2 conformal field theory and its massive perturbation, thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory. The question of the height 2 variable is also addressed, with, however, no definite conclusion yet.

The n-octanol and n-hexane/water partition coefficient of environmentally relevant chemicals predicted from the mobile order and disorder (MOD) thermodynamics.

The quantitative thermodynamic development of the mobile order and disorder theory in H-bonded liquids is extended in order to predict the partition coefficient. With respect to the classical predictive methods, the great advantage of the present approach resides in the possibility of predicting partition coefficient not only in the reference n-octanol/water partitioning system, but also in any mutually saturated two-phase system made up of two largely immiscible solvents. Constructed from the various free energy contributions encoded in the distribution process, the model furthermore provides a useful tool to understand both the origin and the factors, like the solute molar volume, that determine the partitioning of non-electrolytes between two immiscible liquid phases. From the comparison of the relative magnitude of the terms which contribute to the overall log P value, much information can also be gained concerning the variation of the partition coefficients of the same substances in different distribution systems. For example, the model has successfully been applied to the log P prediction of a number of environmentally important chemicals of varying structure, size and chemical nature in the n-octanol/water and n-hexane/water systems. Whatever the complexing or non-complexing substances studied, the hydrophobic effect always represent the driving force that rules distribution processes in the aqueous environments. As the dominant contribution to the partition coefficient in any organic/aqueous binary system, it is evidenced why hydrophobicity is usually considered to be a good measure of lipophilicity.

Numerical study of the correspondence between the dissipative and fixed-energy Abelian sandpile models.

We consider the Abelian sandpile model (ASM) on the square lattice with a single dissipative site (sink). Particles are added one by one per unit time at random sites and the resulting density of particles is calculated as a function of time. We observe different scenarios of evolution depending on the value of initial uniform density (height) h(0). During the first stage of the evolution, the density of particles increases linearly. Reaching a critical density ρ(c)(h(0)), the system changes its behavior and relaxes exponentially to the stationary state of the ASM with density ρ(s). Considering initial heights -1 ≤ h(0) ≤ 4, we observe a dramatic decrease of the difference ρ(c)(h(0)) - ρ(s) when h(0) is zero or negative. In parallel with the ASM, we consider the conservative fixed energy sandpile (FES). The extensive Monte Carlo simulations show that the threshold density ρ(th)(h(0)) of the FES converges rapidly to ρ(s) for h(0) < 1.

Universal model based on the mobile order and disorder theory for predicting lipophilicity and partition coefficients in all mutually immiscible two-phase liquid systems

The quantitative thermodynamic development of the mobile order and disorder theory in H-bonded liquids has been extended in order to predict partition coefficients. The model enables "a priori" estimation of the partition coefficient (log P) of neutral solutes, not only in the conventional 1-octanol/water reference but also in all mutually saturated two-phase systems made up of largely immiscible solvents. The model is obtained from the thermodynamic treatment of the various physicochemical free energy processes encoded in the overall distribution process and accordingly provides a useful tool for better understanding both the origin and the factors, such as the solute molar volume, that determine the partition coefficient of nonelectrolytes in a given system. From the comparison of the relative magnitude of the processes contributing to the log P value, a lot of information can also be gained regarding the variation in log P of the same substance partitioned between different solvent systems. As a demonstration, the model has been successfully applied to predict the log P of a great number of chemicals of varying structure, size, and chemical nature partitioned in a large set of essentially immiscible solvent pairs, differing either by their nonpolar or by their polar phase. In the systems involving water as the polar phase, the hydrophobic effect is always the driving force that governs the distribution process irrespective of the interacting or noninteracting nature of the substances studied. In the other two-phase systems, the partitioning of complexing solutes in particular appears to be ruled rather by their hydrogen-bonding capabilities than by their hydrophobicities.

Solubility predictions for solid nitriles and tertiary amides based on the mobile order theory.

The solubilities of hexadecanenitrile, octadecanenitrile, N,N-diphenyl capramide, and N,N-diphenyl lauramide are predicted in common organic nonelectrolyte solvents using the solubility equation derived from the mobile order theory. In the framework of this theory, the formation of hydrogen bonds is treated on the basis of stability constants. Two values characterizing the nitrile-alcohol and the tertiary amide-alcohol hydrogen bonds, 175 and 600 cm3 mol-1, respectively, are determined. Although the formation of solute-solvent specific molecular interactions brings about a net increase in the solubility, the solubilities of the nitriles and amides in alcohols remain lower than those measured in nonassociated solvents because of the large negative hydrophobic effect of the alcohol molecules.

The mobile order theory versus UNIFAC and regular solution theory-derived models for predicting the solubility of solid substances.

The theory of mobile order of Huyskens is tested against the UNIFAC model, the regular solution model, and the extended Hildebrand or Hansen solubility approaches in predicting the solubility of naphthalene in both polar and nonpolar solvents at 40 degrees C. While all models correctly predict the solubility in nonpolar and moderately polar solvents, a substantial improvement is achieved by Huyskens' model, particularly in alcohols. This improvement originates from the correct description of the entropy effects as well as of the hydrophobic effects in the particular case of the alcohols. The model necessitates the knowledge of only one parameter not known a priori, i.e., the naphthalene modified nonspecific solubility parameter, the value of which is deduced from its solubility in hexane.

Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water.

The thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the pi electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability constant KO which can be derived from solubility data. At 25 degrees C, this constant amounts to 80 cm3/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.

Significance of partial and total cohesion parameters of pharmaceutical solids determined from dissolution calorimetric measurements.

The total and partial adhesion-derived cohesion parameters of three solid pharmaceutical substances (caffeine, theophylline, and phenylbutazone) were determined from dissolution calorimetric measurements, a new technique devised for this purpose. Calorimetry has the advantage of leading directly to enthalpies, from which the solute cohesion parameter(s) is(are) deduced. An equation was developed that relates partial molar enthalpies of mixing (obtained by subtracting enthalpies of fusion from enthalpies of dissolution) to the cohesion parameters of the solute and of the solvents. Solvents were selected on the basis of their known cohesion parameters by applying the experimental research methodology.

The mobile order solubility equation applied to polyfunctional molecules: The non-hydroxysteroids in aqueous and non aqueous solvents.

The solubility equation for real solutions derived from the thermodynamics of mobile order in liquids is used to predict the solubility of non-hydroxysteroids in water and in common polar and nonpolar organic solvents. Strictly obtained on a thermodynamic basis, the model allows not only correct predictions of the solubilities from the knowledge of a limited number of characteristics of solutes and solvents, but also enables a better understanding of the solution process and of the factors that determine solubility. Some practical rules are derived which might help to orient the choice of a solvent for liquid pharmaceutical forms.

A new predictive equation for the solubility of drugs based on the thermodynamics of mobile disorder.

The thermodynamics of mobile disorder rejects the static model of the quasi-lattice for liquids. Because cause of the perpetual change of neighbors, during the observation time of thermodynamics of the order of seconds, each molecule of a given kind in a solution has experienced the same environment and had at its disposal the same mobile volume. This domain is not localizable and not orientable. Each molecular group perpetually "visits" successively all parts of this domain. The highest entropy is obtained when the groups visit all the parts of the domain without preference. H-bonds are preferential contacts with given sites of the neighbors that cause deviations with respect to such "random" visiting, thereby decreasing the entropy. The quantitative development of these ideas leads to equations describing the effect of solvent-solvent, solute-solvent, and solute-solute hydrogen bonds on the chemical potential of the solute. A universal equation predicting the solubility of drugs in a given solvent is derived. The effect of H-bonds is governed not by "solubility parameters" but by stability constants from which the order of magnitude can be estimated. From the sole knowledge of the solubility of methylparaben in pentane, the method predicts correctly the order of magnitude of its solubility in 26 other solvents, including alcohols and water.