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.     

Thermally induced sign change of Soret coefficient for dilute and semidilute solutions of poly(N-isopropylacrylamide) in ethanol

We studied the thermal diffusion behavior of poly(N-isopropylacrylamide) (PNiPAM) in ethanol in a temperature range from T = 14.0 degrees C to T = 40.0 degrees C by means of thermal diffusion forced Rayleigh scattering. The obtained Soret coefficient S(T) of PNiPAM was positive for lower temperatures (T < 34 degrees C), while S(T) showed a negative value for higher temperatures (T > 34 degrees C). This means PNiPAM molecules move to the cold side for temperatures T < 34 degrees C, whereas they move to the warm side for T > 34 degrees C. This is the first nonaqueous polymeric system for which a sign change with temperature has been observed. We performed static and dynamic light scattering experiments in the same temperature range. The second virial coefficient determined from dilute solutions by static light scattering (SLS) was positive in the comparable temperature range. The results of SLS for the semidilute solution showed a strong repulsion among PNiPAM chains which was enhanced by increasing temperature. These results imply that the observed thermally induced sign change of S(T) does not depend on the intermolecular interactions among PNiPAM chains.     

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.     

Thermodiffusion of interacting colloids. II. A microscopic approach

A microscopic approach is presented to describe the contribution to the thermal diffusion coefficient of colloids due to intercolloidal particle interactions. An exact expression for the leading-order virial coefficient of the thermal diffusion coefficient of interacting colloidal spheres is derived in terms of the intercolloidal pair-interaction potential and hydrodynamic interaction functions. This general expression is explicitly evaluated for hard-core interactions and for spheres with a short-ranged attractive potential. The derivation is based on a Smoluchowski equation that is generalized to include temperature gradients. For short-ranged attractive potentials, a negative Soret coefficient is predicted under certain conditions, when the depth of the attraction increases with increasing temperature.     

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.     

Interactions between Silica Colloids with Magnetite Cores: Diffusion, Sedimentation and Light Scattering

The magnetic and Van der Waals attraction between uncharged silica spheres with a magnetic core has been studied using sedimentation and static and dynamic light scattering techniques. Specifically the effect of the interactions on the concentration dependence of the sedimentation velocity, diffusion, and the apparent radius of gyration was investigated. It was found experimentally that the concentration dependence is decreased significantly as a result of the Van der Waals and magnetic attractions and even may change sign in comparison to the hard-sphere case. Calculations of the (linear) concentration dependence for weak interactions predict this decrease and also indicate that for the silica-magnetite particles the second virial coefficient passes a maximum with increasing silica layer thickness. Copyright 1999 Academic Press.     

Temperature dependence of thermal diffusion for aqueous solutions of monosaccharides, oligosaccharides, and polysaccharides

We studied the thermal diffusion behavior for binary aqueous solutions of glucose, maltotriose, maltohexaose, pullulan, and dextran by means of thermal diffusion forced Rayleigh scattering (TDFRS). The investigated saccharides with molar masses between 0.180 and 440 kg mol(-1) were studied in the temperature range between 15 and 55 °C. The thermal diffusion coefficient D(T) and the Soret coefficient S(T) of all solutions increase with increasing temperature. For maltohexaose and the polymers the thermal diffusion coefficient changes sign from negative to positive with increasing temperature, whereas glucose and maltotriose show only positive values in the entire investigated temperature range. While we were able to find a master curve to describe the temperature dependence of D(T), we were not able to find a similar expression for S(T). This comprehensive study allows for the first time the determination of the interaction parameters for the polymer and the solvent within the theoretical framework suggested by Würger [Phys. Rev. Lett., 2009, 102, 078302].     

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.     

Heteroaggregation, repeptization and stability in mixtures of oppositely charged colloids

We report a study of mixtures of initially oppositely charged particles with similar size. Dispersions of silica spheres (negatively charged) and alumina-coated silica spheres (positively charged) at low ionic strength, mixed at various volume ratios, exhibited a surprising stability up to compositions of 50% negative colloids as well as spontaneous repeptization of particles from the early-stage formed aggregates. The other mixtures were found to contain large heteroaggregates, which were imaged using cryogenic electron microscopy. Electrophoretic mobility, electrical conductivity, static and dynamic light scattering and sedimentation were studied as a function of volume fraction of the mixed dispersions to investigate particle interactions and elucidate the repeptization phenomenon.     

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.     

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.     

Small-angle neutron scattering study of concentrated colloidal dispersions: the electrostatic/steric composite interactions between colloidal particles

Small-angle neutron scattering was used to investigate the interactions in concentrated colloidal dispersions containing silica or polystyrene latex with adsorbed polyethyleneoxide (PEO). In these dispersions of charged particles, both electrostatic and steric repulsions are present. The PEO layer was made invisible to neutrons through contrast matching. The effect of the interparticle repulsion was clearly shown in the scattering spectra by the appearance of a peak at low Q. The effective potentials can be well described by the Hayter-Penfold/Yukawa (HPY) potential. In the silica dispersions studied, the layer thickness is small, hence the electrostatic potential dominates and the potential has a lower concentration dependence. In the dispersions of polystyrene latex, the adsorbed layer is thicker; consequently, the electrostatic potential dominates at low volume fraction (the potential has a lower concentration dependence), and the steric potential dominates at higher volume fraction (the potential has a higher concentration dependence). This study also suggests that when more than one potential is present the stronger one has a dominant influence in determining the structure factor. This finding makes it possible to describe the multicomponential interactions by a single function.     

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.     

Thermal-diffusive behavior of a dilute solution of charged colloids

Thermal diffusion of a dilute solution of charged silica colloidal particles (Ludox) is studied by a holographic grating technique. The Soret coefficient of the charged colloids is measured as a function of the Debye screening length and the surface charge density of the colloids. The latter is varied by means of variation of the pH. The experimental Soret coefficients are compared with several theoretical predictions. The surface charge density is independently obtained from electrophoresis measurements, the size of the colloidal particles is obtained from electron microscopy, and the Debye length is calculated from ion concentrations. The only adjustable parameter in the comparison with theory is therefore the intercept at zero Debye length, which measures the contribution to the Soret coefficient of the solvation layer and possibly the colloid core material.     

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

Reverse nonequilibrium molecular dynamics is the method applied here for the investigation of thermal diffusion in realistic molecular fluids. The Soret coefficients of benzene/cyclohexane mixtures are calculated using an all-atom model. The autocorrelation functions indicate that the mole fraction gradient converges much slower than the temperature gradient. Compared to experimental data, the results show the same tendency of the Soret coefficient variation versus the mole fraction. Although a systematic error exists for the magnitude of the Soret coefficient, a meanwhile systematic error for both the mutual diffusion and thermal diffusion coefficients provides some explanation of it; and the calculation with different force field parameters indicates a possibility to annihilate the systematic error. The influences of algorithm variables such as cutoff lengths and perturbation intensities are tested. Furthermore the temperature dependence of the Soret effect is observed, yielding the same trend as previous studies.     

Electro-optic characteristics of optically interacting beta-FeOOH particles

In this article the influence of multiple light scattering on the basic electro-optic parameters of optically dense colloidal particles is analyzed. The model system is an aqueous suspension of monodisperse ellipsoidal beta-FeOOH particles that displays large electric light scattering variations, including sign reversal, at very low particle volume fractions (two orders of magnitude below the critical concentration of particle electric interactions). The scaling method permits the relative variations in particle electric polarizability to be followed and its relaxation frequency to be determined. Particle rotational relaxation frequency and the phase shift of the responses at this frequency are obtained by the alternating component of the effects. Characteristic field intensity curves in the low-frequency range are used to follow the relative changes induced by the slow electrokinetic effect. The experimental results show that, despite the drastic variations in the effects with volume fraction, the basic electro-optic parameters are independent of multiple scattering and can be adequately determined for any particle concentration, excluding a narrow range in the vicinity of the electro-optic sign reversal. The investigation demonstrates that the dependence of the frequency behavior of aqueous beta-FeOOH on particle volume fraction reported in the literature is due not to optical interactions but to variation of particle surface electric state in the process of dilution.     

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.     

Viscosity measurements of water at high temperatures and pressures using dynamic light scattering

The application of dynamic light scattering to measure viscosity of water at high temperatures and pressures is demonstrated. Viscosity was obtained from the translational diffusion coefficient of probe particles dispersed in the medium by the Einstein-Stokes relationship. Measurements were carried out with polystyrene latex, colloidal silica, and colloidal gold. Under a constant pressure of 25 MPa, good agreement was found between the measured and calculated viscosities up to 275 degrees C with the polystyrene latex, 200 degrees C with the colloidal silica, and 297 degrees C with the colloidal gold. It was found that failure of the measurements at high temperatures is ascribed to change in either the dispersion stability or chemical stability of the probe particles. The present results indicate that the technique could also be used for other supercritical fluids having high critical temperature and pressure, such as methanol (T(c) = 239.4 degrees C, P(c) = 8.1 MPa) and ethanol (T(c) = 243.1 degrees C, P(c) = 6.4 MPa).     

Rotational and translational self-diffusion in concentrated suspensions of permeable particles

In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45% and for a wide range of permeability values. From the simulation results and earlier results for the first-order virial coefficient, we find that the rotational self-diffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational self-diffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational self-diffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeable-particle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized Stokes-Einstein-Debye relation between rotational self-diffusion coefficient and high-frequency viscosity is not satisfied.     

Diffusion of brownian particles in the isotropic phase of a nematic liquid crystal

We report a light scattering study of the translational diffusion of a suspension of silica spheres in the liquid crystal, 4-n-pentyl-4'-cyanobiphenyl. We observe a small but significant increase of the effective hydrodynamic radius of the colloidal particles as the transition to the nematic phase is approached. This effect can be understood in terms of orientational pre-wetting of the silica spheres.