RESUMEN
We have studied diffusion and thermodiffusion in the ternary system polystyrene + toluene + cyclohexane over the entire composition range of the binary solvent toluene + cyclohexane and for polymer concentrations up to 0.1 mass fractions by multi-color optical beam deflection. The polystyrene molar masses were 4.88 and 17.90 kg/mol. The inversion problem of the contrast factor matrix could be avoided by reasonable a priori assumptions about the diffusion eigenvectors. The fast mode of the bimodal dynamics is attributed to the interdiffusion of the two solvents at constant polymer concentration, whereas the slow mode is due to the diffusion of the polymer with respect to the binary solvent. The amplitude of the fast mode vanishes in the pure toluene and the pure cyclohexane limits of the mixed solvent. The amplitude of the slow mode increases with polymer concentration. The composition and temperature dependence of the slow diffusion eigenvalue, the hydrodynamic correlation length, and the Soret coefficient of the polymer reflect the transition from a good to a theta solvent with increasing cyclohexane content and with decreasing temperature. Due to cross diffusion, cyclohexane reverses its migration direction between the fast and the slow mode, leading to a positive thermodiffusion but a negative Soret coefficient. The polymer thermodiffusion coefficients during the slow mode vary by approximately a factor of two, depending on the solvent composition. Rescaling with the solvent viscosity collapses all data onto a single master curve with an extrapolated value of ηDT ≈ 6 × 10-15 Pa m2 K-1 in the dilute limit. This value is well known from various other binary polymer/solvent mixtures.
RESUMEN
Two-color optical measurements of thermodiffusion in ternary mixtures frequently suffer from ill-conditioned contrast factor matrices, whose inversion leads to very large experimental errors. In this contribution, we show how the error amplification can be avoided in situations where a priori knowledge about the directions of the eigenvectors of the diffusion matrix is available. We present optical beam deflection experiments on solutions of the polymer polystyrene of Mw = 4880 g/mol in a mixed solvent of toluene and cyclohexane. In this system, the two diffusion eigenvalues differ by almost one order of magnitude. The large eigenvalue can be attributed to the interdiffusion of the two solvents and the small one to the polymer diffusion relative to the mixed solvent. The pre-selection of the eigenvectors renders the method stable against fluctuations of the experimental parameters. Both the diffusion and the Soret coefficients attributed to the two modes agree very well with the respective values of corresponding binary mixtures.
RESUMEN
Measurements of the Soret and thermodiffusion coefficients of a symmetric ternary mixture with equal mass fractions of water, ethanol, and triethylene glycol have been performed by two-color optical beam deflection (2-OBD) and the thermogravitational column technique (TGC) in the laboratory and under microgravity conditions in the Selectable Optical Diagnostics Instrument (SODI) aboard the International Space Station. The results from all three experimental techniques agree within the experimental error bars, which result mainly from the inversion of the contrast factor matrices. TGC shows by far the lowest, 2-OBD the highest error amplification. The microgravity measurements are in between. The agreement with the microgravity results shows that thermosolutal convection could be well controlled in the 2-OBD experiments by a proper orientation of the temperature gradient. Despite the different condition numbers, the results are invariant under the choice of the independent compositions. Based on the orientation of the confidence ellipsoid in the ternary composition diagram, not all coefficients are equally affected by experimental errors. Although there are appreciable uncertainties for water and ethanol, the Soret and the thermodiffusion coefficients of triethylene glycol could be obtained with a good accuracy due to the favorable orientation of the confidence ellipsoid. We have found that water behaves thermophobic, corresponding to a positive Soret coefficient, whereas both ethanol and triethylene glycol are thermophilic with negative Soret coefficients. This resembles the behaviour of the binary system ethanol/water above the ethanol concentration of the sign change.
