Towards understanding specific ion effects in aqueous media using thermodiffusion

Abstract Specific ion effects play an important role in scientific and technological processes. According to Hofmeister, the influence on the hydrogen bond network depends on the ion and leads to a specific order of the ions. Also thermodiffusion the mass transport caused by a temperature gradient is very sensitive to changes of the hydrogen bond network leading to a ranking according to hydrophilicity of the salt. Hence, we investigate various salt solutions in order to compare with the Hofmeister concept. We have studied three different sodium salts in water as a function of temperature (25–45\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ $$\end{document}∘C) and concentration (0.5–5 mol kg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1) using Thermal Diffusion Forced Rayleigh Scattering (TDFRS). The three anions studied, carbonate, acetate and thiocyanate, span the entire range of the Hofmeister series from hydrophilic to hydrophobic. We compare the results with the recent measurements of the corresponding potassium salts to see to what extent the cation changes the thermodiffusion of the salt. Graphic abstract Supplementary Information The online version contains supplementary material available at 10.1140/epje/s10189-022-00164-8.


S1.1 Thermal Diffusion Forced Rayleigh Scattering
Thermodiffusion of the electrolyte solutions was measured by infrared thermal diffusion forced Rayleigh scattering (IR-TDFRS) [1,2]. This method uses the interference grating of two infrared laser beams (λ = 980 nm) to generate a temperature grating inside an aqueous sample due to the inherent absorbtion of water in that range [3]. A third laser beam is refracted by this grating and the intensity of the refracted beam is measured. This intensity is proportional to the refractive index contrast of the grating, showing a fast rise over time due to the thermal gradient, then a slower change of intensity due to diffusion of the solute along the temperature gradient (cf. Fig 1).
The heterodyne scattering intensity ζ het (t) of the read-out beam is measured and fitted with With the lifetimes τ th = (D th q 2 ) (−1) and τ = (Dq 2 ) (−1) of the temperature and concentration grating, respectively, where q, D th and D denote the grating wave vector, the thermal diffusivity and the mutual diffusion coefficient, respectively. The Soret coefficient(S T ) can be calculated from the amplitude A, if the so-called contrast factors, the change of refractive index with temperature and concentration, (∂n/∂T ) c,p and (∂n/∂c) T,p , are known:

S1.2 Refractive index contrast measurements
Refractive index contract factors are required to calculate S T . The refractive index as function of concentration was measured with an Abbe refractometer (Anton Paar Abbemat MW) at a wavelength of 632.8 nm. For all salts, refractive index at five concentrations around the desired contraction were measured. The slope of the linear interpolation of the refractive index as a function of concentration gives (∂n/∂c) p,T . The refractive index increments with temperature (∂n/∂T ) p,c was measured interferometrically [4]. Measurements were performed over a temperature range of 25-45 • C, with a heating rate of 1.6 mK/sec. The refractive index varied linearly with concentration and temperature in the investigated range.
S2 Temperature dependence of S T for CH 3 COOK and CH 3 COONa As mentioned in the main manuscript, temperature dependence of S T of CH 3 COOK and CH 3 COONa is similar to that of carbonate salts. This is shown in Fig.S1.  Figure S1: Soret coefficient of CH 3 COOK and CH 3 COONa as a function of temperature. Open and half-filled symbols correspond to concentrations 1 and 4 mol kg −1 , respectively. The lines correspond to fit according to Eq. (1) in the main manuscript.

S3 Concentration dependence of S T
The concentration dependence of different salt systems studied at three different temperatures (25 • C, 35 • C, 45 • C) is shown in Figs.S2, S3 and S4. It can be seen that the concentration dependent slope of all the studied systems doesn't change vastly with temperature.

S4 TDFRS signal
An example of the TDFRS raw-data is shown in Fig.S5. Fig.S5(a) and Fig.S5(b) corresponds to the signal measured for NaSCN, at 1 mol kg −1 and 4 mol kg −1 respectively at 25 • C and the corresponding residual plots. The black dots marks the data points, the red line represents the fit according the Eq.S2 and the red dots mark the residuals, which are within the 2σ range and do not show systematic deviations.  Table S1. It has to be noted here that for all salts except Na 2 CO 3 the fitting corresponds to S6 third order and second order polynomials for concentration and temperature respectively. Due to the low solubility of Na 2 CO 3 , we were only able to measure the three lowest concentration, therefore we had to reduce the number of fit parameters by using first order polynomials of concentration and temperature to describe the data. For NaCl as well, for which the S T values were only reported at three concentrations [5], we used first order polynomials of concentration and temperature to fit the data.

S5.2 Used log P -values
In order to correlate S i T with the hydrophilicity, we also determined the log P . Calculator Plugins were used for calculation of log P within Marvin 16.5.2.0, 2016, ChemAxon (http://www.chemaxon.com). The calculation method is based on the publication by Viswanadhan et al. [6]. Note that different methods exists, which give slightly different values and it is important to stay in one method to compare results. Values obtained are listed in Table S2. It has to be noted that log P has ionic and non-ionic contributions and the values listed here corresponds to the sum of these contributions.

S6 Concentration and temperature dependence of D T
Dependence of D T with concentration at 25 • C is shown in Fig.S6. The behavior of D T is similar to that of S T , which has been discussed in the main manuscript in Sec. 3.  Figure S7: Thermal diffusion coefficient of all investigated salts as a function of temperature at a concentration of 1 mol kg −1 . We used the symbols as follows: CH 3 COOK(orange pentagons), CH 3 COONa(blue pentagons), K 2 CO 3 (violet circles), Na 2 CO 3 (black circles), KSCN(green squares) and NaSCN(pink squares).

S7 Concentration dependence of activity coefficient
As discussed in the main manuscript (cf. Eq.4), D of electrolyte solutions depends on the mean ionic activity coefficient, γ ± . The concentration dependence of D for aqueous solutions of KSCN and NaSCN shows an decrease and increase, respectively. Both systems show an increase of the viscosity with increasing concentration. To understand the difference in the concentration dependence in the diffusion of the two salts, we examined additionally the concentration dependence of the mean ionic activity coefficient γ ± , which has been studied by Robinson et al. [7]. We have used these values to calculate the corresponding term 1 + c(d ln γ ± /dc) in Eq.4 in the main manuscript. This term shows for both salts a minimum at a low concentration around 0.25 mol/Kg and a gradual increase with increasing concentration. Within the measured concentration range (1-4 mol kg −1 ), the increase of 1+c(d ln γ ± /dc) is 4-times steeper for NaSCN compared to KSCN.