Thermophobicity of liquids: heats of transport in mixtures as pure component properties

Quantitative predictive theories through integrating quantum, statistical, equilibrium, and nonequilibrium thermodynamics

Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and quantitatively solved in terms of density functional theory (DFT) in 1960s. These three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author's group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined law for nonequilibrium systems presented by Hillert, the author developed the theory of cross phenomena beyond the phenomenological Onsager Theorem. The zentropy theory and theory of cross phenomena jointly provide quantitative predictive theories for systems from electronic to any observable scales as reviewed in the present work.

Connection between partial pressure, volatility, and the Soret effect elucidated using simulations of nonideal supercritical fluid mixtures

Building on recent simulation work, it is demonstrated using molecular dynamics simulations of two-component fluid mixtures that the chemical contribution to the Soret effect in two-component nonideal fluid mixtures arises due to differences in how the partial pressures of the components respond to temperature and density gradients. Further insight is obtained by reviewing the connection between activity and deviations from Raoult's law in the measurement of the vapor pressure of a liquid mixture. A new parameter γsS, defined in a manner similar to the activity coefficient, is used to characterize differences deviations from "ideal" behavior. It is then shown that the difference γ2S-γ1S is predictive of the sign of the Soret coefficient and is correlated to its magnitude. We hence connect the Soret effect to the relative volatility of the components of a fluid mixture, with the more volatile component enriched in the low-density, high-temperature region, and the less volatile component enriched in the high-density, low-temperature region. Because γsS is closely connected to the activity coefficient, this suggests the possibility that measurement of partial vapor pressures might be used to indirectly determine the Soret coefficient. It is proposed that the insight obtained here is quite general and should be applicable to a wide range of materials systems. An attempt is made to understand how these results might apply to other materials systems including interstitials in solids and multicomponent solids with interdiffusion occurring via a vacancy mechanism.

Ultra-high temperature Soret effect in a silicate melt: SiO2 migration to cold side

The Soret effect, temperature gradient driven diffusion, in silicate melts has been investigated intensively in the earth sciences from the 1980s. The SiO2 component is generally concentrated in the hotter region of silicate melts under a temperature gradient. Here, we report that at ultra-high temperatures above ∼3000 K, SiO2 becomes concentrated in the colder region of the silicate melts under a temperature gradient. The interior of an aluminosilicate glass [63.3SiO2-16.3Al2O3-20.4CaO (mol. %)] was irradiated with a 250 kHz femtosecond laser pulse for local heating. SiO2 migrated to the colder region during irradiation with an 800 pulse (3.2 ms irradiation). The temperature analysis indicated that migration to the colder region occurred above 3060 K. In the non-equilibrium molecular dynamics (NEMD) simulation, SiO2 migrated to the colder region under a temperature gradient, which had an average temperature of 4000 K; this result supports the experimental result. On the other hand, SiO2 exhibited a tendency to migrate to the hotter region at 2400 K in both the NEMD and experimental study. The molar volume calculated by molecular dynamics simulation without a temperature gradient indicates two bends at 1650 and 3250 K under 500 MPa. Therefore, the discontinuous (first order) transition with coexistence of two phases of different composition could be related to the migration of SiO2 to colder region. However, the detailed mechanism has not been elucidated.

Physical mechanisms of the Soret effect in binary Lennard-Jones liquids elucidated with thermal-response calculations

The Soret effect is the tendency of fluid mixtures to exhibit concentration gradients in the presence of a temperature gradient. Using molecular-dynamics simulation of two-component Lennard-Jones liquids, it is demonstrated that spatially sinusoidal heat pulses generate both temperature and pressure gradients. Over short timescales, the dominant effect is the generation of compressional waves, which dissipate over time as the system approaches mechanical equilibrium. The approach to mechanical equilibrium is also characterized by a decrease in particle density in the high-temperature region and an increase in particle density in the low-temperature region. It is demonstrated that concentration gradients develop rapidly during the propagation of compressional waves through the liquid. Over longer timescales, heat conduction occurs to return the system to thermal equilibrium, with the particle current acting to restore a more uniform particle density. It is shown that the Soret effect arises due to the fact that the two components of the fluid exhibit different responses to pressure gradients. First, the so-called isotope effect occurs because light atoms tend to respond more rapidly to evolving conditions. In this case, there appears to be a connection to previous observations of "fast sound" in binary fluids. Second, it is shown that the partial pressures of the two components in equilibrium, and more directly, the relative magnitudes of their derivatives with respect to temperature and density, determine which species accumulate in the high- and low-temperature regions. In the conditions simulated here, the dependence of the partial pressure on density gradients is larger than the dependence on temperature gradients. This is directly connected to the accumulation of the species with the largest partial pressure in the high-temperature region and the accumulation of the species with the smallest partial pressure in the low-temperature region. The results suggest that further development of theoretical descriptions of the Soret effect might begin with hydrodynamical equations in two-component liquids. Finally, it is suggested that the recently proposed concept of "thermophobicity" may be related to the sensitivity of partial pressures in a multicomponent fluid to changes in temperature and density.

Transport properties of n-ethylene glycol aqueous solutions with focus on triethylene glycol–water

Soret effect and diffusion in triethylene glycol (TEG)–water mixtures were investigated as a function of concentration at 25 °C by means of optical digital interferometry, with the use of a classical Soret cell. Diffusion D, thermal diffusion D T, and Soret S T coefficients are described for the full concentration range and an analysis is made individually for TEG–water mixture and within a series of n-ethylene glycol ( n-EG) aqueous systems. All coefficients decrease with increasing the concentration of TEG and n-EG. S T shows a change of sign with concentration, and this change is directly related to the ability of the n-EG molecule to establish hydrogen bonding with water. Diffusion and thermal diffusion coefficients present a plateau behavior with increasing concentration, showing the occurrence of changes in the preferential interactions in aqueous solution with concentration and meaning that, at high TEG composition, ether oxygens can be involved in the molecular interactions.

A novel gravity-assisted automatic docking device for studying diffusion in liquid metal melts assisted by a strong static magnetic field

A novel gravity-assisted automatic docking (GAAD) method is presented for the study of interdiffusion processes in liquid Al-Cu melts. A novel GAAD device was designed to be suitable in a strong static magnetic field (SSMF) with a bore size of 50 mm. Energy dispersive x-ray spectroscopy was used to quantitatively analyze the concentration profiles of diffusion capillaries. The interdiffusion coefficient (D_AlCu) was measured by applying Fick's second law. The combination of SSMF and GAAD made the original diffusion interface be easily determined and not be oxidized. The melt convection was completely reduced to reach the pure diffusion state. The performance of this GAAD measurement method assisted by a SSMF was successfully verified by a diffusion experiment in an Al-Cu melt.

Simultaneous determination of multiple transport properties over a wide range of temperatures and pressures from the analysis of non-equilibrium fluctuations by the shadowgraph method

The present work demonstrates that by the analysis of the dynamics of non-equilibrium fluctuations using the shadowgraph method, the thermal diffusivity, the Fick diffusion coefficient, the kinematic viscosity, and the Soret coefficient of a binary mixture can be determined from a single thermodiffusion experiment. The study was performed for a mixture consisting of equal masses of 1,2,3,4-tetrahydronaphthalene and n-dodecane in a newly developed shadowgraph apparatus at temperatures up to 373 K and pressures up to 40 MPa. The obtained results are mainly discussed in the light of their uncertainties at varying thermodynamic states for evaluating the benefits, drawbacks, and potentials of the apparatus. The Fick diffusion coefficient and the thermal diffusivity obtained with average expanded uncertainties of 2.8% and 6.6% agree with literature data and measurements for the same mixture taken by heterodyne dynamic light scattering. Current limitations of the method are reflected by the distinctly larger uncertainties of the kinematic viscosity and the Soret coefficient. Corresponding reasons and potential measures to overcome the limitations are discussed.

The Soret effect of halobenzenes in n-alkanes: The pseudo-isotope effect and thermophobicities

We have measured the Soret coefficients of three halobenzenes-fluoro-, chloro-, and bromobenzene-in n-alkanes ranging from hexane to hexadecane over the entire composition range at a temperature of 25 °C. With these new results, two semi-empirical models for the Soret effect, which are based on the pseudo-isotope effect and on the single-component thermophobicities, could significantly be expanded and put on a broader common experimental basis. In particular, for the longer alkanes, above decane, a simplified version of the pseudo-isotope effect yields a good description. In the dilute limit, the agreement of the chemical contributions to the Soret coefficient is perfect, but there are some unexplained systematic deviations at finite concentrations. We have used these Soret coefficients, together with the measurements of 1-bromonaphthalene in the n-alkanes, to expand the database for the thermophobicities of equimolar binary mixtures. Due to a vanishing mixing term in symmetric mixtures, the heats of transport computed from the Soret coefficients can be considered as differences in additive single component properties, the thermophobicities. This allows an ordering of the substances according to these numbers. In a binary mixture, the component with the higher thermophobicity migrates toward the cold side. With the new measurements, the database now contains 24 compounds with 107 out of 276 possible binary mixtures measured.

In situ Measurement of Thermodiffusion in Liquid Alloys

Temperature gradients can change the concentration distribution in multicomponent materials. This cross-coupling effect of heat and mass transfer is difficult to measure in liquid alloys. We present a new method using x-ray radiography in combination with a high temperature furnace to measure thermodiffusion in melts time and space resolved. This greatly improves the process control and allows us to determine diffusion and thermodiffusion simultaneously. In a first experiment we demonstrate that in liquid Al_{78.5}Ni_{21.5} the component nickel diffuses to the cold end of the sample with a Soret coefficient on the order of 10^{-3}  K^{-1}.

Thermophoresis of biological and biocompatible compounds in aqueous solution

With rising popularity of microscale thermophoresis for the characterisation of protein-ligand binding reactions and possible applications in microfluidic devices, there is a growing interest in considering thermodiffusion in the context of life sciences. But although the understanding of thermodiffusion in non-polar mixtures has grown rapidly in recent years, predictions for associated mixtures like aqueous solutions remain challenging. This review aims to give an overview of the literature on thermodiffusion in aqueous systems, show the difficulties in theoretical description that arise from the non-ideal behaviour of water-mixtures, and highlight the relevance of thermodiffusion in a biological context. We find that the thermodiffusion in aqueous systems is dominated by contributions from heat of transfer, hydrogen bond interactions and charge effects. However, the separation of these effects is often difficult, especially in case of biological systems where a systematic exclusion of contributions may not be feasible.

European Space Agency experiments on thermodiffusion of fluid mixtures in space

This paper describes the European Space Agency (ESA) experiments devoted to study thermodiffusion of fluid mixtures in microgravity environment, where sedimentation and convection do not affect the mass flow induced by the Soret effect. First, the experiments performed on binary mixtures in the IVIDIL and GRADFLEX experiments are described. Then, further experiments on ternary mixtures and complex fluids performed in DCMIX and planned to be performed in the context of the NEUF-DIX project are presented. Finally, multi-component mixtures studied in the SCCO project are detailed.

Thermophoresis of a Colloidal Rod: Contributions of Charge and Grafted Polymers

In this study, we investigated the thermodiffusion behavior of a colloidal model system as a function of the Debye length, λ_DH, which is controlled by the ionic strength. Our system consists of an fd-virus grafted with poly(ethylene glycol) (PEG) with a molecular mass of 5000 g mol^-1. The results are compared with recent measurements on a bare fd-virus and with results of PEG. The diffusion coefficients of both viruses are comparable and increase with the increasing Debye length. The thermal diffusion coefficient, D_T, of the bare virus increases strongly with the Debye length, whereas D_T of the grafted fd-virus shows only a very weak increase. The Debye length dependence of both systems can be described with an expression derived for charged rods using the surface charge density and an offset of D_T as adjustable parameters. It turns out that the ratio of the determined surface charges is inverse to the ratio of the surfaces of the two systems, which means that the total charge remains almost constant. The determined offset of the grafted fd-virus describing the chemical contributions is the sum of D_T of PEG and the offset of the bare fd-virus. At high λ_DH, corresponding to the low ionic strength, the S_T values of both colloidal model systems approach each other. This implies a contribution from the polymer layer, which is strong at short λ_DH and fades out for the longer Debye lengths, when the electric double layer reaches further than the polymer chains and therefore dominates interactions with the surrounding water.

Composition effect on thermophobicity of ternary mixtures: An enhanced molecular dynamics method

Thermodiffusion or the Ludwig-Soret effect is known as the cross effect between the temperature gradient and induced separation of mixture species in multicomponent mixtures. The performance of the boundary driven non-equilibrium molecular dynamics enhanced heat exchange (eHEX) algorithm was validated by evaluating the sign and magnitude of the thermodiffusion process in methane/n-butane/n-dodecane (nC₁-nC₄-nC₁₂) ternary mixtures. The eHEX algorithm consists of an extended version of the HEX algorithm with an improved energy conservation property. In addition to this, the transferable potentials for phase equilibria-united atom augmented force field was employed in all molecular dynamics (MD) simulations to accurately represent molecular interactions in the fluid. Our newly employed MD algorithm was capable to appropriately reflect the thermophobicity concept and the coupled effect of relative density and mole fraction of the mixture species on the thermodiffusion process. The separation ratio of the ternary mixture for five different compositions (at 333.15 K and 35 MPa) showed good agreement with experimental data and better accuracy in predicting the sign change of the intermediate component (nC₄) as its concentration in the mixture increases, when compared to other MD models.

Role of Hydrogen Bonding of Cyclodextrin-Drug Complexes Probed by Thermodiffusion

Temperature gradient-induced migration of biomolecules, known as thermophoresis or thermodiffusion, changes upon ligand binding. In recent years, this effect has been used to determine protein-ligand binding constants. The mechanism through which thermodiffusive properties change when complexes are formed, however, is not understood. An important contribution to thermodiffusive properties originates from the thermal response of hydrogen bonds. Because there is a considerable difference between the degree of solvation of the protein-ligand complex and its isolated components, ligand-binding is accompanied by a significant change in hydration. The aim of the present work is therefore to investigate the role played by hydrogen bonding on the change in thermodiffusive behavior upon ligand-binding. As a model system, we use cyclodextrins (CDs) and acetylsalicylic acid (ASA), where quite a significant change in hydration is expected and where no conformational changes occur when a CD/ASA complex is formed in aqueous solution. Thermophoresis was investigated in the temperature range of 10-50 °C by infrared thermal diffusion forced Rayleigh scattering. Nuclear magnetic resonance measurements were performed at 25 °C to obtain information about the structure of the complexes. All CD/ASA complexes show a stronger affinity toward regions of lower temperature compared to the free CDs. We found that the temperature sensitivity of thermophoresis correlates with the 1-octanol/water partition coefficient. This observation not only establishes the relation between thermodiffusion and degree of hydrogen bonding but also opens the possibility to relate thermodiffusive properties of complexes to their partition coefficient, which cannot be determined otherwise. This concept is especially interesting for protein-ligand complexes where the protein undergoes a conformational change, different from the CD/ASA complexes, giving rise to additional changes in their hydrophilicity.

Influence of temperature and charge effects on thermophoresis of polystyrene beads⋆

We study the thermodiffusion behavior of spherical polystyrene beads with a diameter of 25 nm by infrared thermal diffusion Forced Rayleigh Scattering (IR-TDFRS). Similar beads were used to investigate the radial dependence of the Soret coefficient by different authors. While Duhr and Braun (Proc. Natl. Acad. Sci. U.S.A. 104, 9346 (2007)) observed a quadratic radial dependence Braibanti et al. (Phys. Rev. Lett. 100, 108303 (2008)) found a linear radial dependence of the Soret coefficient. We demonstrated that special care needs to be taken to obtain reliable thermophoretic data, because the measurements are very sensitive to surface properties. The colloidal particles were characterized by transmission electron microscopy and dynamic light scattering (DLS) experiments were performed. We carried out systematic thermophoretic measurements as a function of temperature, buffer and surfactant concentration. The temperature dependence was analyzed using an empirical formula. To describe the Debye length dependence we used a theoretical model by Dhont. The resulting surface charge density is in agreement with previous literature results. Finally, we analyze the dependence of the Soret coefficient on the concentration of the anionic surfactant sodium dodecyl sulfate (SDS), applying an empirical thermodynamic approach accounting for chemical contributions.

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection

In a recent letter (C. Giraudet et al., EPL 111, 60013 (2015)) we reported preliminary data showing evidence of a slowing-down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing-down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing-down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results.

Thermodiffusion, molecular diffusion and Soret coefficients of aromatic+n-alkane binary mixtures

In the present work, we have measured the thermodiffusion coefficient of 51 binary liquid mixtures at 25 ^oC. These mixtures correspond to the series of the aromatics toluene and 1-methylnaphthalene with n-alkanes nCi (i = 6, 8, 10, 12, and 14) at different mass fractions in the whole range. For that, we have used the thermogravitational technique. It is shown that the thermodiffusion coefficient is a linear function of the mass fraction in all the mixtures. Extrapolating the lines, we obtain the thermodiffusion coefficient in dilute solutions of n-alkanes for both toluene and 1-methylnaphthalene. These limiting values show a linear dependence with the inverse of the product of the molecular weights. In addition, we have measured the molecular diffusion coefficient of all the mixtures at 0.5 of mass fraction and at 25 ^oC, by the sliding symmetric tubes technique. It is observed that the product of this coefficient with the viscosity at the same concentrations takes a constant value for each of the series considered. Finally, we have also determined the Soret coefficient of the equimass mixtures by the combination of the measurements of thermodiffusion and molecular diffusion coefficients.

Quantitative thermophoretic study of disease-related protein aggregates

Amyloid fibrils are a hallmark of a range of neurodegenerative disorders, including Alzheimer's and Parkinson's diseases. A detailed understanding of the physico-chemical properties of the different aggregated forms of proteins, and of their interactions with other compounds of diagnostic or therapeutic interest, is crucial for devising effective strategies against such diseases. Protein aggregates are situated at the boundary between soluble and insoluble structures, and are challenging to study because classical biophysical techniques, such as scattering, spectroscopic and calorimetric methods, are not well adapted for their study. Here we present a detailed characterization of the thermophoretic behavior of different forms of the protein α-synuclein, whose aggregation is associated with Parkinson's disease. Thermophoresis is the directed net diffusional flux of molecules and colloidal particles in a temperature gradient. Because of their low volume requirements and rapidity, analytical methods based on this effect have considerable potential for high throughput screening for drug discovery. In this paper we rationalize and describe in quantitative terms the thermophoretic behavior of monomeric, oligomeric and fibrillar forms of α-synuclein. Furthermore, we demonstrate that microscale thermophoresis (MST) is a valuable method for screening for ligands and binding partners of even such highly challenging samples as supramolecular protein aggregates.

Statistical thermodynamics of material transport in nonisothermal suspensions

An approach to the transport of material in a temperature gradient is outlined using nonequilibrium thermodynamics theory. The model is applicable to the thermophoresis of colloids and nanoparticles in systems with limited miscibility. Component chemical potentials in binary systems are calculated using statistical mechanics. The local pressure distribution is obtained using the condition of local thermodynamic equilibrium around the suspended particle. The Laplace contribution of the local pressure distribution within the layer of liquid surrounding the particle leads to a size dependence that is consistent with empirical data. The contribution of Keezom interaction to the thermodiffusion coefficient is calculated using empirical values of the thermodiffusion coefficient for silica particles in water and acetonitrile. The resulting interaction energies are consistent with those found in the literature.

Thermodiffusion, molecular diffusion and Soret coefficient of binary and ternary mixtures of n-hexane, n-dodecane and toluene

In this study, the thermodiffusion, molecular diffusion, and Soret coefficients of 12 binary mixtures composed of toluene, n-hexane and n-dodecane in the whole range of concentrations at atmospheric pressure and temperatures of 298.15 K and 308.15 K have been determined. The experimental measurements have been carried out using the Thermogravitational Column, the Sliding Symmetric Tubes and the Thermal Diffusion Forced Rayleigh Scattering techniques. The results obtained using the different techniques show a maximum deviation of 9% for the thermodiffusion coefficient, 8% for the molecular diffusion coefficient and 2% for the Soret coefficient. For the first time we report a decrease of the thermodiffusion coefficient with increasing ratio of the thermal expansion coefficient and viscosity for a binary mixture of an organic ring compound with a short n-alkane. This observation is discussed in terms of interactions between the different components. Additionally, the thermogravitational technique has been used to measure the thermodiffusion coefficients of four ternary mixtures consisting of toluene, n-hexane and n-dodecane at 298.15 K. In order to complete the study, the values obtained for the molecular diffusion coefficient in binary mixtures, and the thermodiffusion coefficient of binary and ternary mixtures have been compared with recently derived correlations.

Mass effect on the Soret coefficient in n-alkane mixtures

We have determined the Soret coefficient of different equimolar and non equimolar n-alkane mixtures from measurements of the molecular diffusion and thermal diffusion coefficients. It is shown that equimolar mixtures behave as isotopic-like mixtures in which only the mass effect contributes to the Soret effect. In non equimolar mixtures, a small linear dependence with the molar fraction is observed. Finally, we have obtained a new correlation, which allows the determination of the Soret coefficient of n-alkane mixtures using the data of viscosity, the thermal expansion coefficient of the pure components, and the density of the equimolar mixture.

How does thermodiffusion of aqueous solutions depend on concentration and hydrophobicity?

The thermal diffusion of aqueous solutions of mono-, di-ethylene glycols, poly(ethylene glycol), methanol, and glycerol is investigated systematically as a function of concentration using the Thermal Diffusion Forced Rayleigh Scattering (TDFRS). For all investigated binary mixtures, the Soret coefficient, S(T), decays with increasing concentration of the non-aqueous component showing two regions. For aqueous solution of ethylene glycol, at a very low solute content the decay is steep, while it becomes less steep for higher solute concentration. All mixtures show a sign change of S(T) with concentration. The sign change concentration is discussed with respect to chemical structures of solute molecules and the partition coefficient, log p. It turns out that the number of hydroxyl groups plays an important role. For the investigated aqueous mixtures, we find empirical linear relations between the sign change concentration and the ratio of the number of hydroxyl groups to the number of carbon atoms as well as the partition coefficient, log p.

Do thermal diffusion and Dufour coefficients satisfy Onsager's reciprocity relation?

It is commonly admitted that in liquids the thermal diffusion and Dufour coefficients D(T) and D(F) satisfy Onsager's reciprocity. From their relation to the cross-coefficients of the phenomenological equations, we are led to the conclusion that this is not the case in general. As illustrative and physically relevant examples, we discuss micellar solutions and colloidal suspensions, where D(T) arises from chemical reactions or viscous effects but is not related to the Dufour coefficient D(F). The situation is less clear for binary molecular mixtures; available experimental and simulation data do not settle the question whether D(T) and DF are reciprocal coefficients.

Influence of confinement on thermodiffusion

This work focuses on a possible influence of a nanoporous medium on the thermodiffusion of a fluid "isotopic" mixture. To do so, we performed molecular dynamics simulations of confined Lennard-Jones binary equimolar mixtures using grand-canonical like and non-equilibrium approaches in sub- and super-critical conditions. The study was conducted in atomistic slit pore of three adsorbent natures for various widths (from 5 to 35 times the size of a molecule). The simulation results indicate that for all thermodynamic conditions and whatever the pore characteristics, the confinement has a negligible effect on the thermal diffusion factor/Soret coefficient. However, when considered separately, the mass diffusion and thermodiffusion coefficients have been found to be largely influenced by the pore characteristics. These two coefficients decrease noticeably when adsorption is stronger and pore width smaller, a behavior that is consistent with a simple hydrodynamic explanation.

Theory of Soret coefficients in binary organic solvents

Thermodiffusion in binary molecular liquids is examined using the nonequilibrium thermodynamic model, where the thermodynamic parameters are calculated using equations based on statistical mechanics. In this approach, thermodiffusion is quantified through the variation in binary chemical potential and its temperature and concentration dependence. The model is applied to solutions of organic solvents, in order to compare our theoretical results to experimental results from the literature. A measurable contribution of the orientation-dependent Keezom interaction is shown, where the possible orientations are averaged using the Boltzmann weighting factor. Calculations of enthalpies of evaporation from the model yield good agreement with experimental values from the literature. However, calculations of the associated energetic parameters were several times larger than those reported in the literature from numeric simulations of material transport.

Thermodiffusion in binary liquids: the role of irreversibility

We study thermal diffusion in binary mixtures in the framework of non-equilibrium thermodynamics. Our formal result displays the role of partial enthalpies hi and Onsager's generalized mobilities Ai. The ratio A1/A2 provides a measure for the irreversible character of thermal diffusion. Comparison with experimental data on benzene, cyclohexane, toluene and n-alkanes shows that irreversibility is essential for thermal diffusion, and in particular for the isotope effect.