Soret Coefficient Research Articles

Temperature profile characterization with fluorescence lifetime imaging microscopy in a thermophoretic chip

This study introduces a thermophoretic lab-on-a-chip device to measure the Soret coefficient. We use resistive heating of a microwire on the chip to induce a temperature gradient, which is measured by fluorescence lifetime imaging microscopy (FLIM). To verify the functionality of the device, we used dyed polystyrene particles with a diameter of 25 nm. A confocal microscope is utilized to monitor the concentration profile of colloidal particles in the temperature field. Based on the measured temperature and concentration differences, we calculate the corresponding Soret coefficient. The same particles have been recently investigated with thermal diffusion forced Rayleigh scattering (TDFRS) and we find that the obtained Soret coefficients agree with literature results. This chip offers a simple way to study the thermophoretic behavior of biological systems in multicomponent buffer solutions quantitatively, which are difficult to study with optical methods solely relying on the refractive index contrast.Graphic abstract

Microscale Thermophoresis in Liquids Induced by Plasmonic Heating and Characterized by Phase and Fluorescence Microscopies

Thermophoresis denotes the motion of particles along temperature gradients. Insignificant in most daily-life observations, this peculiar effect can become dominant in applications involving nano- and microscale heating in fluids. Recent studies in nanoplasmonics observed significant thermophoresis of molecules and particles, in particular in plasmonic trapping, SERS, and biosensing. Evidencing the presence of thermophoresis is not obvious and quantifying its magnitude is even less accessible considering existing techniques. In this article, we introduce a method capable of quantifying the thermophoresis of particles in the context of nanoplasmonic applications. A gold nanoparticle array under illumination is used to create microscale temperature gradients, and a dual fluorescence-phase microscopy technique is used to map both temperature and concentration in parallel. This association enables the determination of Soret coefficients for a wide range of temperatures from a single image acquisition. This metrology technique paves the way for broader fundamental research in microscale thermophoresis in liquids and better-controlled applications in nanophotonics involving thermoplasmonic effects.

Soret vector for description of multicomponent mixtures

The Soret effect describes the transport of constituent species in multicomponent mixtures that occurs due to a temperature gradient. This cross-coupling effect of heat and mass transfer has been successfully examined in binary liquid mixtures, while experiments with ternary mixtures are rare as they impose significant difficulties. We introduce a new and innovative concept, the Soret vector, for the characterization of Soret driven separation in ternary mixtures. The presentation of the component separation in the vector form offers several advantages: (i) to predict the Soret sign of a ternary mixture from knowledge of the Soret coefficients in binary subsystems; (ii) to control consistency of measured coefficients, this is especially important when results are obtained using different instruments and methods; (iii) to determine in which regions and which components cause the greatest separation; (iv) to identify the regions where the Soret separation is inaccessible for optical techniques or gravitationally unstable. We demonstrate these features by exploring ternary mixtures of different origins: (a) nearly ideal mixture composed by THN–IBB–nC12 when Soret coefficients in binary subsystems (S_{T}^{bin}) are positive, (b) non-ideal mixture containing water and ethanol TEG–Wat–EtOH when S_{T}^{bin} are positive and negative and (c) Tol–MeOH–Ch mixture containing demixing zone with positive and negative S_{T}^{bin}. Our approach provides a promising systematic framework for the future research of an important and challenging problem of thermodiffusion in multicomponent liquids.

Investigation of molecular interactions in binary mixtures using thermophoresis

In the present work, experimental values of densities and viscosities for the binary systems of cyclohexane and n-alkanol (1-pentanol, 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol, and 1-decanol) at 293.15 K to 323.15 K were measured. Molecular interactions in the above binary mixtures were investigated considering the mutual diffusion coefficient, thermal diffusion coefficient, Soret effect, and the separation ratio. The magnitude of the Soret coefficients strongly depends on the molecular interactions in the binary mixture. The most plausible forces among unlike molecules in the binary mixtures are Debye forces correspond to dipole-induced dipole interactions.Obtained results demonstrate that in the mixtures, increasing the alkyl chain length reinforces molecular interactions among unlike molecules.

Comment on "Thermodiffusion: The physico-chemical mechanics view" [J. Chem. Phys. 154, 024112 (2021)

In a series of publications, Kocherginsky and Gruebele presented a systematic framework for chemical transport and thermodiffusion to predict the Soret coefficients from thermodynamics. A macroscopic derivation of the Onsager reciprocal relations without recourse to microscopic fluctuations or equations of motion was also discussed. Their important contributions and some confusions are discussed.

An Enhanced Non-Equilibrium Molecular Dynamics Algorithm to Simulate the Soret Coefficient in Heptane/Benzene Mixtures

In this work, the accuracy of the Soret effect was investigated at the situation of T = 303.15 K and P = 1.0 atm. The eHEX (enhanced heat exchange) algorithm and the TraPPE-UA force field were applied to simulate this thermal diffusion behavior. The equimolar mixtures of heptane isomers (n-heptane, 2-methylhexane, 3-methylhexane and 2, 3-dimethylpentane) and benzene were chosen to be the research fluids. The Soret coefficients were calculated to compare with the experimental data and other NEMD simulated results. The results showed great agreement with experimental data and a better accuracy compared to other NEMD simulated results. Moreover, the results shows that more branches may decrease the heat affinity of the component and increase the relaxation time of the thermal diffusion behavior.

Investigation of thermal behavior and the Soret effect in binary fluids by thermal lens technique: Effect of alkyl chain

In the present study, pump-probe thermal lens spectroscopy was used to probe the thermal behavior and molecular interactions in the binary liquid mixtures of acetone, and 1-alkanol. Values of thermal conductivity, thermal diffusivity and thermo-optical parameters were measured for the above liquids. Experimental measurement for the pure state and binary fluids are in good agreement with the literature data. Changes in the measured parameters indicate that these result from a combined effect of physical and molecular properties of binary liquids. Furthermore, the Soret coefficient ST of alcohols in the binary mixtures was calculated by two methods. Findings demonstrate that increasing the chain length of alcohol reduces its tendency to interact with acetone.

Study of molecular interactions in binary mixtures by molecular diffusion, thermal diffusion, Soret effect, and separation ratio

In this study, the liquid structures of six binary systems containing methylpropanone (MP) and n-alkanol (1-pentanol, 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol, and 1-decanol) at 293.15 K to 323.15 K were investigated regarding the molecular diffusion coefficient D, thermal diffusion coefficient DT, Soret coefficient ST, and the separation ratio ψ. The molecular interactions in binary mixtures were explained by the calculated parameters. Formation of dipole–dipole interactions and the hydrogen bond among unlike molecules in the binary mixtures have been identified.The Soret coefficient ST of methylpropanone is positive and indicates that this molecule is enriched in the colder regions of the liquids. These parameters were discussed concerning the nature of various molecular interactions in binary mixtures. Obtained values demonstrate that increasing the chain length of alcohol enhances its tendency to move to the warmer regions. This behavior means that molecular interactions are decreased with the alcohol chain length.

Non-Equilibrium Molecular Dynamics Study of the Influence of Branching on the Soret Coefficient of Binary Mixtures of Heptane Isomers

Abstract Equimolar mixtures composed of isomers were firstly used to investigate the molecular branching effect on thermal diffusion behavior, which was not disturbed by factors of molecular mass and composition in this work. Eight heptane isomers, including n-heptane, 2-methylhexane, 3-methylhexane, 2,2-dimethylpentane, 2,3-dimethylpentane, 2,4-dimethylpentane, 3,3-dimethylpentane and 3-ethylpentane, were chosen as the researched mixtures. A non-equilibrium molecular dynamics (NEMD) simulation with enhanced heat exchange (eHEX) algorithm was applied to calculate the Soret coefficient at T = 303.15 T=303.15 K and P = 1.0 atm P=1.0\hspace{0.1667em}\text{atm} . An empirical correlation based on an acentric factor was proposed and its calculation coincides with the simulated results, which showed the validity of the NEMD simulation. It is demonstrated that the isomer with higher acentric factor has a stronger thermophilic property and tends to migrate to the hot region in the heptane isomer mixture, and the extent of thermal diffusion is proportional to the difference between the acentric factors of the isomers.

Molecular Dynamics Approach to Calculate the Thermodiffusion (Soret and Seebeck) Coefficients of Salts in Aqueous Solutions.

An approach to investigate the physical parameters related to ion thermodiffusion in aqueous solutions is proposed herein by calculating the equilibrium hydration free energy and the self-diffusion coefficient as a function of temperature, ranging from 293 to 353 K, using molecular dynamics simulations of infinitely diluted ions in aqueous solutions. Several ion force field parameters are used in the simulations, and new parameters are proposed for some ions to better describe their hydration free energy. Such a theoretical framework enables the calculation of some single-ion properties, such as heat of transport, Soret coefficient, and mass current density, as well as properties of salts, such as effective mass and thermal diffusion, Soret and Seebeck, coefficients. These calculated properties are compared with experimental data available from optical measurements and showed good agreement revealing an excellent theoretical predictability of salt thermodiffusion properties. Differences in single-ion Soret and self-diffusion coefficients of anions and cations give rise to a thermoelectric field, which affects the system response that is quantified by the Seebeck coefficient. The fast and slow Seebeck coefficients are calculated and discussed, resulting in values with mV/K order of magnitude, as observed in experiments involving several salts, such as K+Cl-, Na+Cl-, H+Cl-, Na+OH-, TMA+OH-, and TBA+OH-. The present approach can be adopted for any ion or charged particle dispersed in water with the aim of predicting the thermoelectric field induced through the fluid. It has potential applications in designing electrolytes for ionic thermoelectric devices in order to harvest energy and thermoelectricity in biological nanofluids.

On the time-dependent electrolyte Seebeck effect.

Single-ion Soret coefficients αi characterize the tendency of ions in an electrolyte solution to move in a thermal gradient. When these coefficients differ between cations and anions, an electric field can be generated. For this so-called electrolyte Seebeck effect to occur, different thermodiffusive fluxes need to be blocked by boundaries-electrodes, for example. Local charge neutrality is then broken in the Debye-length vicinity of the electrodes. Confusingly, many authors point to these regions as the source of the thermoelectric field yet ignore them in derivations of the time-dependent Seebeck coefficient S(t), giving a false impression that the electrolyte Seebeck effect is purely a bulk phenomenon. Without enforcing local electroneutrality, we derive S(t) generated by a binary electrolyte with arbitrary ionic valencies subject to a time-dependent thermal gradient. Next, we experimentally measure S(t) for five acids, bases, and salts near titanium electrodes. For the steady state, we find S ≈ 2 mV K-1 for many electrolytes, roughly one order of magnitude larger than the predictions based on literature αi. We fit our expression for S(t) to the experimental data, treating the αi as fit parameters, and also find larger-than-literature values, accordingly.

The relationship between self-diffusion activation energy and Soret coefficient in binary liquid mixtures

The Soret effect is an observed phenomenon in which an applied temperature gradient will induce a concentration gradient in multicomponent mixtures. The Soret coefficient is the ratio of thermally driven diffusion to mutual diffusion driven by concentration gradients. It is measured at steady state when the two driving forces are balanced, i.e. the net flux is zero. This study is designed to explore the potential relationship between the activation energy of self-diffusion of the individual components of a binary mixture and the mixture’s resulting Soret coefficient. This study found a trend of increasingly negative Soret coefficients as the difference in the mole-fraction-weighted self-diffusion activation energies of the components increased.

A new boundary driven NEMD scheme for heat and particle diffusion in binary mixtures

A new method for Boundary Driven Non-Equilibrium Molecular Dynamics (BD-NEMD) simulation is presented. It allows the simultaneous imposition of both a constant temperature and concentration gradient. By varying the strength of the imposed gradients and obtaining stationary values of the mass and energy flux, this new technique can be used to extract the Onsager transport coefficients directly. We demonstrate the setup and measure explicitly the Soret and Dufour effects for a binary mixture of Argon and Krypton. We compare the Soret coefficient computed using this new scheme against the experimentally inspired protocol where the system has no mass current. However, this method is limited to only an estimate of the Soret coefficient rendered inefficient due to the poor signal-to-noise ratio and cannot give the transport coefficients explicitly. The new technique allows for accurate measurements of non-zero flux values and, if run in the linear response domain, the full set of transport coefficients can be extracted directly. We also speculate about how this scheme could be applied to more complex systems with applications for polymer separations and biological activities.

Determination of thermodynamic and microscopic origins of the Soret effect in sodium silicate melts: Prediction of sign change of the Soret coefficient.

The Soret effect in silicate melts has attracted attention in earth and material sciences, particularly in glass science and engineering, because a compositional change caused by the Soret effect modifies the material properties of silicate melts. We investigated the Soret effect in an Na2O-SiO2 system, which is the most common representative of silicate melts. Our theoretical approach based on the modified Kempers model and non-equilibrium molecular dynamics simulation was validated for 30Na2O-70SiO2(mol. %). The sign and order of the absolute values of the calculated Soret coefficients were consistent with the experimental values. The positive Soret coefficient of SiO2 in the SiO2-poor composition range was accurately predicted. Previous experimental studies have focused on SiO2-rich compositions, and only the negative sign, indicating SiO2 migration to the hot side, has been observed. In the SiO2-poor composition range, the Q0 structure was dominant and had four Si-O-Na bonds around an SiO4 unit. The Si-O-Na bond had high enthalpic stability and contributed to the large negative enthalpy of SiO2 mixing. According to our model, components with a large negative partial molar enthalpy of mixing will concentrate in the cold region. The microscopic and thermodynamic origins of the sign change in the Soret effect were determined.

An Interdigital Planar Energy Harvesting/Storage Device Based On an Ionic Solid–Gel Polymer

The generation of efficient self-powered energy harvesting/storage technologies is a milestone demand to the field of the Internet of Things. In this work, an interdigital planar all-in-one thermally chargeable supercapacitor (IPTS) was successfully produced by merging energy harvesting and storage technologies. The smart device was produced through a photolithography process, combining carbon nanotubes as an electrode material with polyvinyl alcohol (PVA) doped with H3PO4 as a solid–gel polyelectrolyte. The ionic conductivity of PVA doped with H3PO4 was tuned by changing the amount of H3PO4 within the PVA matrix, unveiling an optimum ratio of PVA/H3PO4 of 1:1 (m/m). The power generation performance of the IPTS was evaluated. The device reached a Soret coefficient of 2.35 mV K–1, which is one order of magnitude higher than those of thermoelectric materials (few hundreds of μV K–1). Moreover, it reached a voltage generation output of up to 45 mV for ΔT = 20 K. Concerning energy storage features, the device worked as an electric double-layer capacitor, affording an energy density of 1.05 mW h cm–3 at a power density of 1.21 W cm–3. The tailored interdigital configuration, high flexibility, and energy efficiency of the IPTS, combined with a cost-effective production process that offers the possibility of scale-up, open unique horizons in the field of flexible electronics.

Thermodiffusion: The physico-chemical mechanics view.

Thermodiffusion in liquids (the Soret effect) has several unusual properties. In particular, transport can occur with or against a temperature gradient depending on the case. Numerous empirical correlations have been proposed with mixed success or range of applicability. Here, we show that physicochemical mechanics, derived from the Smoluchowski equation as a description of diffusive transport phenomena, is in accord with the experimental and simulated thermodiffusion data from colloidal beads and biomacromolecules to ionic solutions and ultracold fluid mixtures. It yields a simple formula for the Soret coefficient ST based on the reference molar entropy including non-ideality. Hydrodynamic and local non-equilibrium effects are discussed but not included as these are apparently not a major contribution for the wide range of solutes under the near-equilibrium experimental conditions considered here.

A ternary mixture at the border of Soret separation stability.

Ternary mixtures with the Soret effect are prone to triple-diffusive convection in a thermal field. The Soret coefficients of the toluene-methanol-cyclohexane mixture, measured in microgravity at a given composition [0.62-0.31-0.07] in mass fractions, showed that the net separation ratio, Ψ, the parameter responsible for the hydrodynamic stability in a gravity field is close to zero. Furthermore, the large cross-diffusion of toluene leads to a curious situation: the Soret coefficient ST1 is positive while the thermodiffusion coefficient DT1 is negative. The behavior of this ternary mixture on the border of stability, when Ψ is slightly negative or positive, is examined experimentally and numerically. The mixture is placed in an elongated cell between the differently heated walls. Depending on Ψ and the initial temperature of the liquid (mean temperature, linear profile or cold one), the evolution of concentration patterns are classified by four regimes. We observe the emergence of motionless, metastable, and convective patterns. In the case of Ψ > 0, it was found that cross-diffusion fluxes cause a temporarily unstable density pattern. The initially cold mixture at either Ψ sign shows dissimilar Soret separation in the upper and lower parts of the cell. It leads to the formation of a long-lived inverse density gradient at the upper part of the cell, which finally results in a motionless (Ψ > 0) or convective (Ψ < 0) pattern.

Thermal and solutal non-equilibrium fluctuations in a polymer solution.

We have performed shadowgraphy experiments on a dilute polymer solution subjected to a temperature gradient in order to investigate simultaneous thermal and solutal non-equilibrium fluctuations (NEFs). The gravitational quenching of the NEFs at small q-vectors defines the thermal and solutal roll-off wavevectors, which can be extracted from both the static structure function and the time correlation functions. Both methods yield good agreement, and the ∼10% larger static solutal roll-off wavevector coincides with a similar observation reported in the literature. The thermal diffusivity of the solution and the diffusion, thermodiffusion, and Soret coefficients of the polymer can be obtained from the q-dependence of the relaxation times and from the thermal and solutal roll-off wavevectors without explicit knowledge of the optical contrast factors. This provides an alternative route for the measurement of diffusive transport coefficients, albeit with an unfavorable error propagation.

Thermodiffusion of alkali ions in alkali niobophosphate glasses

AbstractA method is proposed for determination of the thermal diffusion coefficients of mobile ions through the study of ionic thermoelectric power. Ionic Seebeck coefficients and the heats of ion transport have been measured in [Li(Na,K)]2O‐Nb2O5‐P2O5 glasses. The mixed alkali effect influence on the thermoelectric power has been reported for the first time in glasses. Soret coefficients have been calculated for all monoalkali glass samples synthesized in this work. Type of the alkali ion and Nb2O5 content dependence of the heat of transfer and thermal diffusion coefficient have been analyzed and discussed.

Thermodiffusion in Electrolyte Between Electric Membranes Under External Electric Field

Thermodiffusion of a binary electrolyte situated in the microgap between two ion-selective surfaces under external electric field is theoretically studied. It is assumed that temperature gradient occurs only by Joule heating of the electrolyte; and the concentration gradient may trigger an inner gravitational instability. There are three types of instability in such setup: electrokinetic, thermoelectrokinetic and internal gravitational instability. The direct numerical simulation of the problem shows that for the typical salts solutions such as NaCl or KCl the termodiffusion effect is negligible, while for some salts with bigger values of the reduced Soret coefficients of ions (for example, for tetra-n-butylammonium fluoride) the thermodiffusion may significantly affect the voltage-current characteristic. It is also obtained, that the negative thermodiffusion leads to the destabilization of the one-dimensional steady state regime and shifts the critical values of governing parameters for each aforementioned type of instability. The thermodiffusion mostly influences the classical electrokinetic instability and less — the internal gravitational instability. Under effect of both types of thermodiffusion (normal and negative), the thermoelectrokinetic instability manifests at smaller values of Rayleigh numbers.