Long-Range Electrostatic Colloidal Interactions and Specific Ion Effects in Deep Eutectic Solvents

While the traditional consensus dictates that high ion concentrations lead to negligible long-range electrostatic interactions, we demonstrate that electrostatic correlations prevail in deep eutectic solvents where intrinsic ion concentrations often surpass 2.5 M. Here we present an investigation of intermicellar interactions in 1:2 choline chloride:glycerol and 1:2 choline bromide:glycerol using small-angle neutron scattering. Our results show that long-range electrostatic repulsions between charged colloidal particles occur in these solvents. Interestingly, micelle morphology and electrostatic interactions are modulated by specific counterion condensation at the micelle interface despite the exceedingly high concentration of the native halide from the solvent. This modulation follows the trends described by the Hofmeister series for specific ion effects. The results are rationalized in terms of predominant ion–ion correlations, which explain the reduction in the effective ionic strength of the continuum and the observed specific ion effects.

Data were modelled using the uniform ellipsoid P(q) and RMSA S(q) implemented using the DA. Data and models were scaled for clarity. Where not seen, the error bars are within the markers.
Table S1 Parameters obtained from the analysis of the SANS data presented in Figure S1: equatorial radius -req, aspect ratio -AR, micelle volume fraction -ϕ, q-position of the first peak in the S(q) data -qSmax, S(q) intensity at zero angle -S(0), and Coulomb coupling factor -Gk.
[C12TAC] / mM req / Å AR ϕp / ×10 -2 qSmax / Å -1 S(0) / cm -  . Data were modelled using the uniform ellipsoid P(q) and RMSA S(q) implemented using the DA. Data and models were scaled for clarity. Where not seen, the error bars are within the markers. Table S2 Structural parameters obtained from the analysis of the SANS data presented in Figure S2.  Excluded volume effects from a hard solvent shell An alternative theoretical model that could result in long-range interactions in DES is the presence of a strongly correlated solvent shell around the micelle. In order to validate this model, the experimental S(q) of C12TAC in d-ChCl:d-Glyc and in D2O were fitted to an effective HS model, as presented in the main text. The results from this analysis are presented in Figure S3 and Table S4.

Monomer concentration of counterion exchanged surfactants in DES
As the fitted micelle volume fractions in DES are lower than the total surfactant volume fraction, it is expected that a certain amount of solubilized surfactant monomer remains in solution. Using the total surfactant volume fraction (ϕs), as calculated from the surfactant concentration in the sample, and the fitted micelle volume fraction (ϕp), the volume fraction and concentration of surfactant in the monomeric form (ϕm and [C12TA + ]m, respectively) were calculated for each surfactant concentration. The density of the counterionexchanged surfactants was approximated as 1 g/cm 3 for the calculations. The results from the calculations are presented in Table S5.

Modelling approach for determining Coulomb coupling constants
In order to directly compare the coupling constant for a given surfactant concentration, the experimental results for the coupling constant were modelled using an empirical approach for each of the studied surfactants. The Coulomb coupling constant versus the micelle volume fraction were fitted to the following equation: log (Γ ! ) = + log, " .
( 1) Subsequently, the Coulomb coupling constant of each system was evaluated for an arbitrary micelle volume fraction (ϕp). The results from the modelling are included in Figure S3. The models and calculations are presented in Table S4.   Figure S3 using Equation S1. Variation of the Coulomb coupling constant with the solvent ionic strength As seen in the main text, the strength of long-range interactions in DES is significantly reduced compared to those in water. This difference was attributed to the higher ionic strength of the solvent. Using Equation 5, theoretical calculations of the coupling constant were performed for a model particle with reff=18.35 Å, AR=1.3, zp=40 and ϕp=0.085 in D2O (ε=77.9, 30 ˚C). The coupling constant was determined for different solvent ionic strengths: 10, 25, 50, 100, 250 and 500 mM. Using the values of the Coulomb coupling constant, the theoretical scattering for the particles was determined using a uniform ellipsoid form factor and the RMSA model. The results from the calculations are presented in Table S7 and Figure S5. The theoretical scattering for the same particles interacting through excluded volume effects (HS) is presented for comparison. 3.57E-04 500 3.40E-07 HS 0 Figure S5. Calculated scattering intensities for the model particle interacting electrostatically through different the Coulomb coupling constants (see Table S5).

Sensitivity analysis of the correlation between the solvent ionic strength and particle charge
As introduced in the main text, the coupling between the solvent ionic strength and particle surface charge in the calculation of the Coulomb coupling constant limits the accuracy of the determination of these individual variables. To study this correlation, a sensitivity analysis was performed. Using the experimental data from 1070 mM C12TAC in 1:2 d-ChCl:d-Glyc, the pairs of particle charge and solvent ionic strength were determined for the Coulomb coupling constant that fits the data. Initially, the aggregation number (Nagg) of the micelles was calculated using the equation: Vp is the volume of the micelle and Vm is the volume of the surfactant monomer. The Vm was calculated using Tanford equations and is 350.2 Å 3 (Tanford, J. Phys. Chem. 1972). The particle charge values were obtained considering a realistic upper and lower boundary for the counterion dissociation, i.e. amin=20% and amax=80%, where zp=aNagg. The model was parametrized using and ε=22.8, and reff=17.1 Å and Nagg=52±3 from the structural analysis of the micelles. Using these values in the analysis, the experimental data were fitted to obtain the Coulomb coupling constant, particle surface potential, and the effective ionic strength of the solvent. The results from the sensitivity analysis are presented in Table S8. The analysis shows that the correlation between the surface potential and ionic strength results in pairs of values that give fits of relatively equal quality (χ 2 between 20 and 30). These pairs of values result in the same Coulomb coupling constant, as the contact potential for the interparticle repulsion is determined from the experimental scattering. The difference in the quality of the fits is marginal due to the correlation between the two parameters. However, it is seen that the effective ionic strength of the solvent is around 400-500 mM.