The Soret effect in dilute polymer solutions: influence of chain length, chain stiffness, and solvent quality

Thermal diffusion in dilute polymer solutions is studied by reverse nonequilibrium molecular dynamics. The polymers are represented by a generic bead-spring model. The influence of the solvent quality on the Soret coefficient is investigated. At constant temperature and monomer fraction, a better solvent quality causes a higher affinity for the polymer to the cold region. This may even go to thermal-diffusion-induced phase separation. The sign of the Soret coefficient changes in a symmetric nonideal binary Lennard-Jones solution when the solvent quality switches from good to poor. The known independence of the thermal diffusion coefficients of the molecular weight is reproduced for three groups of polymers with different chain stiffnesses. The thermal diffusion coefficients reach constant values at chain lengths of around two to three times the persistence length. Moreover, rigid polymers have higher Soret coefficients and thermal diffusion coefficients than more flexible polymers.     

Reverse nonequilibrium molecular dynamics calculation of the Soret coefficient in liquid heptane/benzene mixtures

We studied the thermal diffusion behavior of mixtures of benzene and heptane isomers by reverse nonequilibrium molecular dynamics. For n-heptane/benzene mixtures, we investigated the concentration dependence of the Soret coefficient. The Soret coefficient for equimolar mixtures of the three heptane isomers 3-methylhexane, 2,3-dimethylpentane, and 2,4-dimethylpentane in benzene has been calculated. Compared to the experimental data, the simulation results show the same trend in dependence of the mole fraction and degree of branching. The negative Soret coefficient indicates the enrichment of alkanes in the warm side. In the case of the heptane isomers in benzene, we could study the influence of the difference in shape and size on the thermal diffusion behavior at constant mass. In the simulation as well as in the experiment, we found that the Soret coefficients become higher with increasing degree of branching. Such behavior cannot be explained only by mass and size effects. The effect of the molecular shape needs to be considered additionally.     

Study of the thermal diffusion behavior of alkane/benzene mixtures by thermal diffusion forced rayleigh scattering experiments and lattice model calculations

In this work the thermal diffusion behavior of binary mixtures of linear alkanes (heptane, nonane, undecane, tridecane, pentadecane, heptadecane) in benzene has been investigated by thermal diffusion forced Rayleigh scattering (TDFRS) for a range of concentrations and temperatures. The Soret coefficient ST of the alkane was found to be negative for these n-alkane/benzene mixtures indicating that the alkanes are enriched in the warmer regions of the liquid mixtures. For the compositions investigated in this work, the magnitude of the Soret coefficient decreases with increasing chain length and increasing alkane content of the mixtures. The temperature dependence of the Soret coefficient depends on mixture composition and alkane chain length; the slope of ST versus temperature changes from positive to negative with increasing chain length at intermediate compositions. To study the influence of molecular architecture on the Soret effect, mixtures of branched alkanes (2-methylhexane, 3-methylhexane, 2,3-dimethylpentane, 2,4-dimethylpentane, 2,2,3-trimethylbutane, and 2,2,4-trimethylpentane) in benzene were also investigated. Our results for the Soret coefficients show that the tendency for the alkanes to move to the warmer regions of the fluid decreases with increasing degree of branching. The branching effect is so strong that for 2,2,4-trimethylpentane/benzene mixtures the Soret coefficient changes sign at high alkane content and that equimolar 2,2,3-trimethylbutane/benzene mixtures have positive Soret coefficients in the investigated temperature range. In order to investigate the effect of molecular interactions on thermal diffusion, we adapted a recently developed two-chamber lattice model to n-alkane/benzene mixtures. The model includes the effects of chain-length, compressibility, and orientation dependence of benzene-benzene interactions and yields good qualitative predictions for the Soret effect in n-alkane/benzene mixtures. For the branched isomers, we find some correlations between the moments of inertia of the molecules and the Soret coefficients. PACS numbers: 66.10.Cb, 61.25.Hq.     

Thermal diffusion behavior of nonionic surfactants in water

We studied the thermal diffusion behavior of hexaethylene glycol monododecyl ether (C12E6) in water by means of thermal diffusion forced Rayleigh scattering (TDFRS) and determined Soret coefficients, thermal diffusion coefficients, and diffusion constants at different temperatures and concentrations. At low surfactant concentrations, the measured Soret coefficient is positive, which implies that surfactant micelles move toward the cold region in a temperature gradient. For C12E6/water at a high surfactant concentration of w1 = 90 wt % and a temperature of T = 25 degrees C, however, a negative Soret coefficient S(T) was observed. Because the concentration part of the TDFRS diffraction signal for binary systems is expected to consist of a single mode, we were surprised to find a second, slow mode for C12E6/water system in a certain temperature and concentration range. To clarify the origin of this second mode, we investigated also, tetraethylene glycol monohexyl ether (C6E4), tetraethylene glycol monooctyl ether (C8E4), pentaethylene glycol monododecyl ether (C12E5), and octaethylene glycol monohexadecyl ether (C16E8) and compared the results with the previous results for octaethylene glycol monodecyl ether (C10E8). Except for C6E4 and C10E8, a second slow mode was observed in all systems usually for state points close to the phase boundary. The diffusion coefficient and Soret coefficient derived from the fast mode can be identified as the typical mutual diffusion and Soret coefficients of the micellar solutions and compare well with the independently determined diffusion coefficients in a dynamic light scattering experiment. Experiments with added salt show that the slow mode is suppressed by the addition of w(NaCl) = 0.02 mol/L sodium chloride. This suggests that the slow mode is related to the small amount of absorbing ionic dye, less than 10(-5) by weight, which is added in TDFRS experiments to create a temperature grating. The origin of the slow mode of the TDFRS signal will be tentatively interpreted in terms of a ternary mixture of neutral micelles, dye-charged micelles, and water.     

Sign change of the Soret coefficient of poly(ethylene oxide) in water/ethanol mixtures observed by thermal diffusion forced Rayleigh scattering

Soret coefficients of the ternary system of poly(ethylene oxide) in mixed water/ethanol solvent were measured over a wide solvent composition range by means of thermal diffusion forced Rayleigh scattering. The Soret coefficient S(T) of the polymer was found to change sign as the water content of the solvent increases with the sign change taking place at a water mass fraction of 0.83 at a temperature of 22 degrees C. For high water concentrations, the value of S(T) of poly(ethylene oxide) is positive, i.e., the polymer migrates to the cooler regions of the fluid, as is typical for polymers in good solvents. For low water content, on the other hand, the Soret coefficient of the polymer is negative, i.e., the polymer migrates to the warmer regions of the fluid. Measurements for two different polymer concentrations showed a larger magnitude of the Soret coefficient for the smaller polymer concentration. The temperature dependence of the Soret coefficient was investigated for water-rich polymer solutions and revealed a sign change from negative to positive as the temperature is increased. Thermodiffusion experiments were also performed on the binary mixture water/ethanol. For the binary mixtures, the Soret coefficient of water was observed to change sign at a water mass fraction of 0.71. This is in agreement with experimental results from the literature. Our results show that specific interactions (hydrogen bonds) between solvent molecules and between polymer and solvent molecules play an important role in thermodiffusion for this system.     

Soret coefficients of mixed electrolytes

Practical equations are developed which relate the Soret coefficients of mixed electrolytes to the entropies and enthalpies of transport. The derived equations together with published binary thermal diffusion data can be used to estimate the Soret coefficients of mixed electrolytes. The procedure is illustrated for the systems NaCl+HCl+ water and NaCl+MgCl₂+ water. Aqueous NaCl, like most salts, diffuses to the cold plate in binary Soret experiments. In aqueous HCl solutions, however, NaCl can diffuse to the warm plate, and the magnitude of its Soret coefficient can take values twice as large as those for binary solutions. The thermal diffusion of trace amounts of a salt in a solution containing a large excess of another salt is discussed. Exceptionally large Soret effects are predicted for traces of strong acids in aqueous salt solutions.     

On the mutual diffusion properties of ethanol-water mixtures

The structural organization, the number of hydrogen bonds (H bond), and the self- and mutual diffusion coefficients of ethanol-water mixtures were studied by molecular dynamics simulation. It was found that both the numbers of H bonds per water and per ethanol decrease as the mole fraction of ethanol increases. The composition dependences and the relationships between the self- and the mutual diffusion coefficients were further discussed. The self-diffusion coefficient of water has a large drop as the concentration of ethanol increases from 0 to 0.3 and then it nearly keeps constant, while that of ethanol has a minimum around ethanol mole fraction of 0.5. The mutual diffusion coefficient could be divided into two parts, the kinematic factor and the thermodynamic factor. Both the kinematic and thermodynamic factors for ethanol-water mixtures were calculated. It was found that the change trend of mutual diffusion coefficients with the composition is mainly dependent on the thermodynamic factors.     

Thermal diffusion in Lennard–Jones fluids in the frame of the law of the corresponding states

This work is related to the definition of a reduced thermal diffusion coefficient thanks to numerical microscale molecular dynamics simulations. This cross transport process, also called Soret effect, couples mass flux and thermal gradient and is still largely misunderstood. For this study, we have applied a boundary driven non-equilibrium molecular dynamics algorithm on Lennard–Jones spheres mixtures. Simulations have been performed at a constant reduced supercritical state, using a van der Waals’ one fluid approximation in order to fulfil the law of the corresponding states. In binary mixtures, we have studied the molecular parameters and the molar fraction influences on thermal diffusion separately and then combined. It is shown that, on pressure and on thermal conductivity, the corresponding states law is fulfilled for a wide range of molecular parameters ratios. In this frame, we have then constructed simple correlations which relate thermal diffusion factor to the mixture parameters. Combining the relations obtained, a reduced thermal diffusion factor taking into account all the various contributions has been defined. Finally, it is shown that this relation enables us to estimate thermal diffusion in various binary and ternary mixtures of Lennard–Jones spheres representing alkanes with a maximum deviation of 15%.     

Heats of transfer in the diffusion layer before the surface and the surface temperature for a catalytic hydrogen oxidation (H2 + (1/2)O2 --> H2O) reaction

The surface temperature and surface mole fractions are calculated for a catalytic hydrogen oxidation reaction over a Pt/Al2O3 catalyst pellet. The thermodynamics of irreversible processes was used in order to ensure the correct introduction of coupled heat and mass transfer. Two pathways, one using the 4 x 4 resistivity matrix and the other using a simplified effective conductivity matrix, were proven to yield equivalent results. By using expressions for the thermal diffusion coefficients, heats of transfer, and the Maxwell-Stefan diffusion coefficients given in the literature, available experimental data could be reproduced. The Dufour effect was found to be negligible for the prediction of the surface temperature. Neglecting the Soret effect would increase the predicted value of the surface temperature significantly-more than 30 K out of an average of about 400 K. It is found that the reaction rate can be used to predict the surface temperature.     

Systematic study of the thermal diffusion in associated mixtures

We performed systematic temperature and concentration dependent measurements of the Soret coefficient in different associated binary mixtures of water, deuterated water, dimethyl sulfoxide (DMSO), methanol, ethanol, acetone, methanol, 1-propanol, 2-propanol, and propionaldehyde using the so-called thermal diffusion forced Rayleigh scattering method. For some of the associating binary mixtures such as ethanol/water, acetone/water, and DMSO/water, the concentration xw+/- at which the Soret coefficient changes its sign does not depend on temperature and is equal to the concentration xw x where the Soret coefficient isotherms intersect. For others such as 1-propanol/water, 2-propanol/water, and ethanol/DMSO, the sign change concentration is temperature dependent, which is the typical behavior observed for nonassociating mixtures. For systems with xw+/-=xw x, we found that xw+/- depends linearly on the ratio of the vaporization enthalpies of the pure components. Probably due to the similarity of methanol and DMSO, we do not observe a sign change for this mixture. The obtained results are related to structural changes in the fluid observed by nuclear magnetic resonance, mass spectrometric, and x-ray experiments in the literature. Furthermore, we discuss the influence of hydrophilic and hydrophobic interactions and the solubility on thermal diffusion behavior.     

Investigation of the diffusion coefficient of polymers and micelles in aqueous solutions using the Soret effect in cw-laser thermal lens spectrometry

The concentration gradient (Soret effect) induced in cw-laser thermal lens spectrometry subsequently to the formation of the thermal gradient (thermal lens effect) has been investigated in aqueous solutions of various macromolecular species including micelles, mixed micelles and polymers. It is shown that the build-up of the concentration gradient is much shorter than that in classical Soret experiments, reaching steady-state values in less than 1 min. The time evolution of the Soret signal has been used to derive mass-diffusion times from which mass-diffusion coefficients were calculated. Our data are in agreement with previous results obtained from quasi-elastic light scattering studies for the micellar solutions and calculated from a known molecular weight-dependent power law for polymer solutions.     

Dependence of thermal diffusion factor of binary mixtures to the thermodynamic state by NEMD simulation

In this paper, we investigate the dependence of thermal diffusion factor and thermal conductivity to the temperature, density and mole fraction in Lennard–Jones binary mixtures of isotopes, noble gases and SF₆–noble gases by non-equilibrium molecular dynamics simulations.The results for the isotopic mixtures indicated that the density has a crucial effect on the dependence of thermal diffusion factor on the temperature. For isotope system at low density, thermal diffusion factor increased with temperature then remains constant at higher temperatures and the slope of thermal diffusion factor vs. temperature is positive while at higher density, thermal diffusion factor decreased with temperature and then fluctuate. For noble gas mixtures, thermal diffusion factor reduces with increasing of temperature and remain constant at high temperatures. For SF₆–Ar system, thermal diffusion factor has a negative slope and reduced with increasing of temperature, but remain nearly constant at high temperatures. For Xe–SF₆ thermal diffusion factor changed sign and the slope of thermal diffusion factor vs. temperature was negative. The results also show that thermal conductivity increases with temperature for all systems.The dependence of thermal diffusion factor to mole fraction of heavier component also investigated. The inverse of thermal diffusion factor versus mole fraction of heavier component is linear for isotope mixtures at thermodynamic conditions: (a) Low temperature, large mass ratio and all densities. (b) High temperature, large mass ratio and low densities. For Ne–Kr mixture, the inverse of thermal diffusion factor shows a linear dependence to the mole fraction of heavier component in moderate temperatures and all densities. For SF₆–Ar and Xe–SF₆ mixtures, the inverse of thermal diffusion factor has linear behaviour at moderate temperatures and low density and high temperature and low density, respectively.     

Transport properties of 2F <==> F2 in a temperature gradient as studied by molecular dynamics simulations

We calculate transport properties of a reacting mixture of F and F(2) from results of non-equilibrium molecular dynamics simulations. The reaction investigated is controlled by thermal diffusion and is close to local chemical equilibrium. The simulations show that a formulation of the transport problem in terms of classical non-equilibrium thermodynamics theory is sound. The chemical reaction has a large effect on the magnitude and temperature dependence of the thermal conductivity and the interdiffusion coefficient. The increase in the thermal conductivity in the presence of the chemical reaction, can be understood as a response to an imposed temperature gradient, which reduces the entropy production. The heat of transfer for the Soret stationary state was more than 100 kJ mol(-1), meaning that the Dufour and Soret effects are non-negligible in reacting mixtures. This sheds new light on the transport properties of reacting mixtures.     

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.     

Cause and effect reversed in non-equilibrium molecular dynamics: an easy route to transport coefficients

A novel non-equilibrium method for calculating transport coefficients is presented. It reverses the experimental cause-and-effect picture, e.g. for the calculation of viscosities: the effect, the momentum flux or stress, is imposed, whereas the cause, the velocity gradient or shear rates, is obtained from the simulation. It differs from other Norton-ensemble methods by the way, in which the steady-state fluxes are maintained. This method involves a simple exchange of particle momenta, which is easy to implement and to analyse. Moreover, it can be made to conserve the total energy as well as the total linear momentum, so no thermostatting is needed. The resulting raw data are robust and rapidly converging. The method is tested on the calculation of the shear viscosity, the thermal conductivity and the Soret coefficient (thermal diffusion) for the Lennard–Jones (LJ) fluid near its triple point. Possible applications to other transport coefficients and more complicated systems are discussed.     

Thermodiffusion of interacting colloids. I. A statistical thermodynamics approach

The thermal diffusion coefficient of colloids consists of two additive contributions, one related to specific interactions between the surfaces of colloidal particles with solvent molecules, and a contribution due to interactions between the colloidal particles. In the present paper, the effect of intercolloidal particle interactions on their thermodiffusive behavior is discussed within a statistical thermodynamics framework. Transport coefficients are expressed in terms of the interaction potential between the colloidal spheres. A special feature of macromolecular systems is that this interaction potential is a potential of mean force, which is temperature dependent. It is shown that under certain conditions this implicit temperature dependence gives rise to negative Soret coefficients, that is, to diffusion of macromolecules to hot regions.     

Thermal lens spectrometry in aqueous solutions of Brij 35: investigation of micelle effects on the time-resolved and steady-state signals

This work investigates the effect of micelles on the time-resolved and steady-state thermal lens signals in aqueous solutions. The temperature gradient produced subsequently to non-radiative relaxation of the sample induces migration of micelles towards the colder region of the irradiated area along with an opposite flow of solute molecules. This phenomenon, known as the Soret effect, produces an additional probe beam signal with a rise time that is much longer than the thermal time constant and depends on the surfactant and solute concentrations. Extrapolation of the mass-diffusion constant at zero solute concentration allowed the determination of diffusion coefficients that are close to those derived by other methods for Brij 35 micelles in water. It is also shown that the surfactant has only a small effect on the thermal lens signal and that the enhancement produced by micelles with respect to pure water originates mainly firom the Soret effect. It follows that interpretation of experimental data without discriminating both components of the probe beam signal can lead to erroneous values of dn/dT.     

Soret effect of nonionic surfactants in water studied by different transient grating setups

We studied the thermal diffusion behavior of the nonionic surfactant solutions C 12E 6/water and C 12E 5/water at different concentrations and temperatures using thermal diffusion forced Rayleigh scattering (TDFRS). Two different types of TDFRS setups have been applied. In the classical TDFRS, we use an argon laser to write the optical grating into the sample by using a small amount of ionic dye to convert the optical grating into a temperature grating. In the other setup, called IR-TDFRS, we use an infrared laser as the writing beam, which utilizes the water absorption band to convert the optical grating into a temperature grating. The measurements by IR-TDFRS show a one-mode signal for all concentrations and temperatures, while the signal in the classical TDFRS consists of two modes for higher temperatures and lower surfactant concentrations (Ning, H.; et al. J. Phys. Chem. B 2006, 110, 10746). We find good agreement between the Soret coefficient determined in the IR-TDFRS and the one derived from the first fast mode in the previous studies. The Soret coefficient of the nonionic solutions is positive and enhanced at the critical point. In general, the Soret coefficient of the micelles tends to increase with temperature. We found that the presence of the second mode observed in the classical TDFRS is related to the addition of the ionic dye, but even with the ionic dye it is not possible to observe a second mode in the IR-TDFRS. The origin of the second mode is discussed in terms of charged micelles and an inhomogenous dye distribution in the temperature gradient.     

Thermodiffusion in compact clays

An experimental cell has been devised in order to measure the Soret coefficients in a compact clay, namely argilite, when a concentration difference of a binary mixture is applied simultaneously with a temperature difference. Temperature gradients have been imposed in the same direction as concentration gradients or in the opposite one. The sign of the Soret coefficients is related to the respective direction of these gradients. Generally, mass transfer was found to be enhanced by the Soret effect. Experimental values of the Soret coefficient are given.