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.     

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.     

Thermal diffusion measurements and simulations of binary mixtures of spherical molecules

Thermal diffusion forced Rayleigh scattering measurements on binary mixtures of carbon tetrabromide (CBr(4)), tetraethylsilane, and di-tert-butylsilane in carbon tetrachloride (CCl(4)) are reported at different temperatures and concentrations. The Soret coefficient of CBr(4) in CCl(4) is positive and S(T) of both silanes in CCl(4) is negative, which implies that the heavier component always moves to the cold side. This is the expected behavior for unpolar simple molecules. Both silanes have the same mass so the influence of the difference in shape and moment of inertia could be studied. For all three systems, S(T) decreases with decreasing CCl(4) concentration. The results are discussed in the framework of thermodynamic theories and the Hildebrand parameter concept. Additionally, the Soret coefficients for both silaneCCl(4) systems were determined by nonequilibrium molecular-dynamics calculations. The simulations predict the correct direction of the thermophoretic motion and reflect the stronger drive toward the warm side for di-tert-butylsilane compared to the more symmetric tetraethylsilane. The values deviate systematically between 9% and 18% from the experimental values.     

Thermal diffusion with stepwise association equilibria in aqueous solutions of the ionic dyes methylene blue and methyl orange

Soret coefficients are measured conductimetrically for dilute aqueous solutions of the stepwise-associating ionic dyes methylene blue (chloride salt) and methyl orange (sodium salt) at 25°C. In contrast to the behavior of other dilute aqueous electrolytes, the Soret coefficients of the dyes increase with concentration. An approximate treatment of thermal diffusion of stepwise-associating solutes is developed to interpret the results. The analysis is used to estimate the intrinsic enthalpies of transport of the monomeric and the associated forms of the dyes. The enthalpy of association makes a large reactive contribution to the enthalpy of transport of methyl orange.     

Universal isotope effect in thermal diffusion of mixtures containing cyclohexane and cyclohexane-d12

The Soret coefficients S(T) of the liquids acetone, benzene, benzene-d1, 1,3,5-benzene-d3, benzene-d5, benzene-13C6, benzene-d6, n-hexane, toluene, 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and 1,6-dibromohexane have been measured in protonated and perdeuterated cyclohexane by a transient holographic grating technique. It has been found that S(T) can be either positive or negative and even change its sign as a function of concentration. The isotope effect DeltaS(T)=-0.99 x 10(-3) K(-1), which is the change of S(T) after isotopic substitution of cyclohexane, neither depends on concentration nor on the nature of the mixing partner. Only in the case of the polar acetone is DeltaS(T) approximately 30% larger but still concentration independent. Based on the experimental findings, some general conclusions about the dependence of the Soret coefficient on molecular properties are drawn.     

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.     

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.     

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.     

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 diffusion and partial molar enthalpy variations of n-butane in silicalite-1

We report for the first time the heat of transfer and the Soret coefficient for n-butane in silicalite-1. The heat of transfer was typically 10 kJ/mol. The Soret coefficient was typically 0.006 K(-1) at 360 K. Both varied with the temperature and the concentration. The thermal conductivity of the crystal with butane adsorbed was 1.46 +/- 0.07 W/m K. Literature values of the isosteric enthalpy of adsorption, the concentration at saturation, and the diffusion coefficients were reproduced. Nonequilibrium molecular dynamics simulations were used to find these results, and a modified heat-exchange algorithm, Soft-HEX, was developed for the purpose. Enthalpies of butane were also determined. We use these results to give numerical proof for a recently proposed relation, that the heat of transfer plus the partial molar enthalpy of butane is constant at a given temperature. The proof is offered for a regime where the partial molar enthalpy can be approximated by the molar internal energy. This result may add to the understanding of the sign of the Soret coefficient. The technical importance of the heat of transfer is discussed.     

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.     

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.     

The Ludwig–Soret effect and stochastic processes

New general stochastic models of thermodiffusion are proposed, which include velocity-dependent friction coefficient and noise tensor. These coefficients are computed exactly from the Boltzmann equation for the particular case of thermodiffusion in dilute gas mixtures. The Soret coefficients predicted by the new thermodiffusion models are computed via a Chapman–Enskog expansion and compared favorably to predictions of earlier models. In particular, the new models can accommodate for Soret coefficients of both signs, as observed experimentally.     

Photophysical properties of long rodlike meso-meso-linked zinc(II) porphyrins investigated by time-resolved laser spectroscopic methods

The molecular design of directly meso-meso-linked porphyrin arrays as a new model of light-harvesting antenna as well as a molecular photonic wire was envisaged to bring the porphyrin units closer for rapid energy transfer. For this purpose, zinc(II) 5,15-bis(3,5-bis(octyloxy)phenyl)porphyrin (Z1) and its directly meso-meso-linked porphyrin arrays up to Z128 (Zn, n represents the number of porphyrins) were synthesized. The absorption spectra of these porphyrin arrays change in a systematic manner with an increase in the number of porphyrins; the high-energy Soret bands remain at nearly the same wavelength (413-414 nm), while the low-energy exciton split Soret bands are gradually red-shifted, resulting in a progressive increase in the exciton splitting energy. The exciton splitting is nicely correlated with the values of cos[pi/(N + 1)] according to Kasha's exciton coupling theory, providing a value of 4250 cm(-1) for the exciton coupling energy in the S(2) state. The increasing red-shifts for the Q-bands are rather modest. The fluorescence excitation anisotropy spectra of the porphyrin arrays show that the photoexcitation of the high-energy Soret bands exhibits a large angle difference between absorption and emission dipoles in contrast with the photoexcitation of the low-energy exciton split Soret and Q-bands. This result indicates that the high-energy Soret bands are characteristic of the summation of the individual monomeric transitions with its overall dipole moment deviated from the array chain direction, while the low-energy Soret bands result from the exciton splitting between the monomeric transition dipoles in line with the array chain direction. From the fluorescence quantum yields and fluorescence lifetime measurements, the radiative coherent length was estimated to be 6-8 porphyrin units in the porphyrin arrays. Ultrafast fluorescence decay measurements show that the S(2) --> S(1) internal conversion process occurs in less than 1 ps in the porphyrin arrays due to the existence of exciton split band as a ladder-type deactivation channel, while this process is relatively slow in Z1 (approximately 1.6 ps). The rate of this process seems to follow the energy gap law, which is mainly determined by the energy gap between the two Soret bands of the porphyrin arrays.     

Thermal diffusion of dilute aqueous Na2MgEDTA and Na2CaEDTA solutions at 25°C

The Soret effect in dilute aqueous solutions (0.01–0.1m) of Na₂MgEDTA and Na₂CaEDTA is investigated using the flow-cell method. The Soret coefficients obtained from thermal diffusion experiments conducted at 25°C are reported. Heats of transport have been estimated based on the Debye-Hückel theory and the molar entropies of transport, calculated. Results of the present work have been compared with the Soret data for MgCl₂ and CaCl₂. It is suggested that the solvent exchange effect may account for the differences in the Soret effect observed between the pairs (Mg⁺², Ca⁺²) and (MgEDTA^–2, CaEDTA^–2).     

Effective concentration difference model to study the effect of various factors on the effective diffusion coefficient in the dialysis membrane

Cellulose acetate dialysis membrane (CDM) has been used in the diffusive gradients in thin films (DGT) technique, where accurate diffusion coefficients are essential for the assessment of the concentrations of labile metal in solution. Effective concentration difference model (ECDM), based on the assumption that the effective diffusion coefficient of metal ion in the dialysis membrane is determined by the effective concentration difference (ΔC(e)) across the dialysis membrane, is proposed and applied to study the effect of ionic strength, binding agent, ligands and Donnan potential on the effective diffusion coefficient. The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in receptor solutions with binding agent were almost the same as those in receptor solutions without binding agent at higher ionic strengths (0.01-1 M) but much higher than those at lower ionic strengths (0.001-0.0001 M). The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in deionized water receptor solutions with binding agent were not significantly different from those in synthetic receptor solutions (receptor solutions with various ionic strengths) with binding agent. The DGT-labile fractions were measured in synthetic solutions and natural waters, which indicated that the effective diffusion coefficients, through the dialysis membrane immersed in the deionized water solution with binding agent as receptor solution and in the spiked natural water as source solution, were more suitable for DGT application.     

Measurement of odour permeability of polypropylene packaging films at low odourant levels

An apparatus has been designed to measure the permeability coefficients of packaging films to odours at low odour concentration gradients. Use of the apparatus is illustrated by comparison between the permeation behaviour of coextruded and coated polypropylene packaging films, using the test odourants benzyl acetate, 2-methoxyphenol and limonene. For the coextruded films, permeability coefficients decrease logarithmically with concentration at odour levels in the parts per million range. The coated films exhibit more complex behaviour; at low concentrations extremely long induction periods occur prior to odourant detection, whilst at higher odourant levels the barrier coatings become less effective and the permeability coefficients approach those of coextruded film.     

Theoretical study of interdiffusion of aqueous solutions of 1 : 1 electrolytes having the same anion through a cation-exchange membrane

The interdiffusion of aqueous 1: 1 electrolytes having the same anion through a negatively charged (cation-exchange) membrane has been studied without taking into account the diffusive layers. It has been established that the interdiffusion coefficients of the cations depend (in addition to their own diffusion coefficients in the membrane) on the ratio of the diffusion coefficients of both cations to the diffusion coefficient of the anion and the ratio of the density of charges fixed in the membrane to the equal concentration of the electrolytes on both sides of the membrane, as well as the equilibrium distribution coefficients of cationanion ion pairs in the membrane matrix. The conditions have been found under which the membrane plays the role of a “blocking system” (like a diode) that is impenetrable to cations located on both sides of the membranes in spite of the existence of their concentration gradients. The developed approach can be used to describe the interdiffusion of 1: 1 electrolytes through any uniformly charged membrane.     

A comprehensive study of diffusion, thermodiffusion, and Soret coefficients of water-isopropanol mixtures

We report on the measurement of diffusion (D), thermodiffusion (D(T)), and Soret (S(T)) coefficients in water-isopropanol mixtures by three different instrumental techniques: thermogravitational column in combination with sliding symmetric tubes, optical beam deflection, and optical digital interferometry. All the coefficients have been measured over the full concentration range. Results from different instruments are in excellent agreement over a broad overlapping composition (water mass fraction) range 0.2 < c < 0.7, providing new reliable benchmark data. Comparison with microgravity measurements (SODI/IVIDIL (Selected Optical Diagnostic Instrument/Influence of VIbration on DIffusion in Liquids)) onboard the International Space Station and with literature data (where available) generally gives a good agreement. Contrary to theoretical predictions and previous experimental expectations we have not observed a second sign change of S(T) at low water concentrations.     

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.