A temperature gradient acts like an external field on colloidal suspensions and drives the solute particles to the cold or to the warm, depending on interfacial and solvent properties. We discuss different transport mechanisms for charged colloids, and how a thermal gradient gives rise to companion fields. Particular emphasis is put on the thermal response of the electrolyte solution: positive and negative ions diffuse along the temperature gradient and thus induce a thermoelectric field which in turn acts on the colloidal charges. Regarding polymers in organic solvents, the physical mechanism changes with decreasing molecular weight: high polymers are described in the framework of macroscopic hydrodynamics; for short chains and molecular mixtures of similar size, the Brownian motion of solute and solvent becomes important.

https://iopscience.iop.org/article/10.1088/0034-4885/73/12/126601/pdf

Thermal non-equilibrium transport in colloids

The Seebeck coefficients of the nonaqueous electrolytes tetrabutylammonium nitrate, tetraoctylphosphonium bromide, and tetradodecylammonium nitrate in 1-octanol, 1-dodecanol, and ethylene-glycol are measured in a temperature range from T = 30 °C to T = 45 °C. The Seebeck coefficient is generally of the order of a few hundreds of microvolts per Kelvin for aqueous solution of inorganic ions. Here we report huge values of 7 mV/K at 0.1 M concentration for tetrabutylammonium nitrate in 1-dodecanol. These striking results open the question of unexpectedly large kosmotrope or “structure making” effects of tetraalkylammonium ions on the structure of alcohols.

Huge Seebeck coefficients in nonaqueous electrolytes

The Seeebeck coefficients of the non-aqueous electrolytes tetrabutylammonium nitrate, tetraoctylphosphonium bromide and tetradodecylammonium nitrate in 1-octanol, 1-dodecanol and ethylene-glycol are measured in a temperature range from T=30 to T=45 C. The Seebeck coefficient is generally of the order of a few hundreds of microvolts per Kelvin for aqueous solution of inorganic ions. Here we report huge values of 7 mV/K at 0.1M concentration for tetrabutylammonium nitrate in 1-dodecanol. These striking results open the question of unexpectedly large kosmotrope or "structure making" effects of tetraalkylammonium ions on the structure of alcohols.

Huge Seebeck coefficients in non-aqueous electrolytes

Intrinsic ionic heats of transport q
 *
 (ion) and ionic heats of transport Q
 *
 (ion) have been evaluated for 53 aqueous ions at infinite dilution at 25°C using the reduction rule proposed by the authors and the limiting laws of Agar, and of Helfand and Kirkwood without electrophoretic terms. q
 *
 (ion) have been found to correlate linearly with the standard ionic entropies of hydration for the 38 ions investigated. The correlation yields three distinctive proportionality constants indicating that the ions may be divided into three distinctive groups. Although the sign of Q
 *
 (ion) is not definite, all values of q
 *
 (ion) are positive. For 17 ions Q
 *
 (ion) are in good agreement with TS
 *
 (ion). Here, S
 *
 (ion) is the ‘absolute’ standard ionic entropy of transport which can be obtained from potentiometric measurements on cells. The values of S
 *
 (ion) were determined by Agar, and recently by Lin and coworkers.

Proportionality of Intrinsic Heat of Transport to Standard Entropy of Hydration for Aqueous Ions

We study the thermophoretic coefficient DT of a charged colloid. The non-uniform electrolyte is characterized in terms of densities and diffusion currents of mobile ions. The hydrodynamic treatment in the vicinity of a solute particle relies on the Huckel approximation, which is valid for particles smaller than the Debye length, a ≪ $ \lambda$
 . To leading order in the parameter a/
 $ \lambda$
 , we find that the coefficient DT consists of two contributions, a dielectrophoretic term proportional to the permittivity derivative d
 $ \varepsilon$
 /dT , and a Seebeck term, i.e., the macroscopic electric field induced by the thermal gradient in the electrolyte solution. Depending on the particle valency, these terms may take opposite signs, and their temperature dependence may result in a change of sign of thermophoresis, as observed in several recent experiments.

/pdf/thermoelectric-effect-on-charged-colloids-in-the-huckel-30se8ud8rn.pdf

Thermoelectric effect on charged colloids in the Hückel limit

Heats of transport for dilute aqueous HCl solutions at 25°C have been determined from the measurements of thermoelectric powers of the thermocell

$$(T){\text{ }}Ag{\text{ - }}AgCl/HCl(ag.)/Ag - AgCl{\text{ (T + }}\Delta {\text{T)}}$$

The variation of the heat of transport with concentration has been examined up to 0.04M and the molar heat of transport at infinite dilution obtained by extrapolation. Present experimental results may be summarized by the equation

$${\text{Q}}^ * = {\text{ }}3397 - 3734I^{1/2} {\text{ + }}33610{\text{I}}^{{\text{3/2}}}$$

whereQ* is the heat of transport in cal-mole−1 andI is the ionic strength.

Molar heats of transport of dilute aqueous HCl solutions: A potentiometric study

An exact thermodynamic treatment of the Wagner effect, thermal diffusion in solutions containing two or more species in equilibrium, is given. We consider primarily a solution in which the solute can exist as a monomer A or an n-mer A n . Both A and A n are treated as independent solute species. We do not assume that the solution is ideal or dilute.

Thermal diffusion in solutions containing two or more solute species in equilibrium: the Wagner effect

The Soret effect (thermal diffusion) of dilute aqueous solutions of NH4Cl, Me4NCl, Et4NCl, n-Pr4NCl, and n-Bu4NCl has been investigated potentiometrically using the silver, silver chloride thermocell. The molar entropies (heats) of transport have been derived from the initial and final thermoelectric powers. The concentration dependence of the entropy of transport has been examined and the effect of the ionic size on the heat of transport is discussed. The molar entropy of tetrabutylammonium chloride exhibits a sharp minimum in the neighborhood of 0.002M, the reason of which is as yet unclear.

Thermal diffusion of dilute aqueous NH4Cl, Me4NCl, Et4NCl,n-Pr4NCl, andn-Bu4NCl solutions at 25°C

Heats of transport of 0.01 m HCl, Me4NCl, and Et4NCl in H2O and 0.01 m KCl, NaCl, and CsCl in D2O were determined from the measurement of initial (homogeneous) and final (Soret steady state) thermoelectric powers of the thermocell (T)Ag−AgCl/Solution/AgCl−Ag(T+ΔT) at a mean temperature of 25°C. The results are discussed in terms of ion-solvent interaction and properties of H2O and D2O.

Heats of transport of some chlorides in H2O and D2O

The molar entropy (or heat) of transport of aqueous rare earth chlorides at 0.001, 0.01 and 0.1N have been measured by the potentiometric method using the silver, silver chloride thermocell at a mean temperature of 25°C. Our results indicate that the entropy of transport of rare earth chlorides exhibits a two-series, step function type of dependence on ionic radii. Although this is not the usual S-shaped dependence on ionic radii observed in many thermodynamic and transport properties, the Soret data do seem to show that hydration of the heavier rare earth ions may be rather different from the lighter rare earth ions. The concentration dependence of the entropy of transport have also been investigated for LaCl3, SmCl3, and YbCl3. In all cases the experimental limiting slopes agree well with that predicted by theory based on the electrostatic model.

Jeong-long Lin

Papers

Molar heats of transport of dilute aqueous HCl solutions: A potentiometric study

Thermal diffusion in solutions containing two or more solute species in equilibrium: the Wagner effect

Thermal diffusion of dilute aqueous NH4Cl, Me4NCl, Et4NCl,n-Pr4NCl, andn-Bu4NCl solutions at 25°C

Heats of transport of some chlorides in H2O and D2O

Thermal diffusion of lanthanide chlorides