Origin of Hofmeister Effects for Complex Systems

Hofmeister effects have been recognized as important as Mendel’s work was to genetics while remain largely controversial, especially for the mechanistic aspects. Here we demonstrated that complex colloids in electrolyte solutions show resembling aggregation kinetics as model colloid, and then quantitatively evaluated the resulting Hofmeister effects. Mechanism for the aggregation of complex colloids has been proposed that is closely associated with the charges of their constituents; despite that, electrostatic interactions play a minor role while polarization effect is evidenced to be the driving force for the aggregation processes. Polarization effect is further ascribed to arouse the resulting Hofmeister effects, which is supported by the fine correlation of activation energies vs. polarizability data of different alkali ions and the calculations of dipole moments for minerals with different charges and adsorbed alkali ions. Because of neglecting polarization effect, the prevailing DLVO theory is not sufficient to describe Hofmeister effects that are ubiquitous in nature. We speculate that polarization effect should also be responsible for Hofmeister effects of other charged systems such as proteins and membranes.


Introduction
Proteins, membranes, clays and colloids carry a plethora of surface charges that result in strong electric fields and particular adsorption behaviors [1][2][3]. Interactions between colloidal particles can lead to aggregation, and electrolytes dissolved in aqueous solutions have an eminent influence on such aggregation processes, which are known to be Hofmeister effects (specific ion effects) [4][5][6][7]. Hofmeister effects were first observed in the 1880s [8] and currently are experiencing a renaissance. People have gradually recognized that Hofmeister effects can be as important in the scheme of things as Mendel's work was to genetics [9]. Although it is evident that Hofmeister effects are associated with surface charges, mechanistic understanding remains a subject of burgeoning debates [1,6,[10][11][12][13].
A number of previous studies focused on the aggregation of mono-dispersive synthetic colloids (small and spherical particles) [14][15][16][17]. Recently, we have used the dynamic light scattering technique to quantitatively characterize the Hofmeister effects for the aggregation of (polydispersive) montmorillonite particles in electrolyte solutions [18]. Unfortunately, the

Dynamic light scattering (DLS) experiments
Presently, two NSCs were considered, as yellow earth soil colloid (NSC1) and purple soil colloid (NSC2). NSCs were prepared as described in the supplementary information or elsewhere [18]. Then the BI-200SM multi-angle DLS instrument (Brookhaven Instruments Corporation, New York, USA) with the BI-9000AT auto-correlator was used to in situ monitor the hydrodynamic diameter growths of NSCs. The laser device was polarized vertically with a wavelength of 532 nm. NSCs were sonicated for 2 min, and the various alkali ion solutions were respectively added. The alkali ion concentrations are 20 * 150 mmol/L for LiNO 3 , 10 * 150 mmol/ L for NaNO 3 , 5 * 150 mmol/L for KNO 3 , 5 * 150 mmol/L for RbNO 3 and 5 * 150 mmol/L for CsNO 3 , respectively. After thorough mixing, the hydrodynamic diameters of NSCs were recorded every 30 sec at a scattering angle of 90°(298 ± 1 K).

Computational methodologies
One of the most striking properties of NSCs is the carrying of abundant negative charges that is responsible for the exchange and adsorption of metal ions. For different aluminosilicate minerals, the tetrahedral SiO 4 surfaces where metal ions are adsorbed [44] are rather close to each other, and hence cluster models with different negative charges were constructed from kaolinite, one of the most common minerals to us. The chemical formula of neutral kaolinite equals Al 2 Si 2 O 5 (OH) 4 . In this work, the kaolinite cluster models contain 12 Si and 12 Al atoms, and the boundary O atoms were saturated by H atoms, see Fig 1a. The excessive charges of kaolinite are mainly due to the deprotonation/protonation of the hydroxyl groups, which are dependent on the pH values of aqueous solutions [45][46][47]. In accord with the previous studies of aluminosilicates [48][49][50][51], the kaolinite cluster models were divided into two regions and simulated at different theoretical levels. The hexagonal ring of silica surface may interact directly with cations [44] and relating O and Si atoms were selected as the high-level region. As indicated in Fig 1a, the high-level region (represented as ball and stick) also includes the O atoms bonded to the hexagonal Si atoms as well as adsorbents, while the rest atoms of kaolinite cluster models were treated as the low-level region (in stick).

Aggregation kinetics and Hofmeister effects
NSCs are obviously more complex than montmorillonite previously studied [18]. X-ray diffraction patterns shown in S2 Fig indicate that NSC1 is composed of 2% quartz, 22% mica, 5% kaolinite, 48% illite, 23% vermiculite while NSC2 consists of 4% quartz, 13% mica, 15% illite, 24% montmorillonite, 34% vermiculite and 10% albite. All the constituents of NSC1 and NSC2 are negatively charged, which is also applicable for most NSCs. As a result, these two NSCs are preferential to interact with electrolyte cations rather than anions. Accordingly, their aggregation kinetics should be dominated by electrolyte cations, as has been confirmed before in the case of montmorillonite [18].
The hydrodynamic diameters of NSC1 in the various alkali ion solutions that increase with the experimental time are shown in S1 Fig, and on such basis, the total average aggregation (TAA) rates for NSCs can be calculated by [18], whereṽ T ðc 0 Þ (nm/min) represents the TAA rate from t = 0 to an arbitrary time t (t > 0) and for a given time t 0 , it is equivalent toṽ T ðc 0 Þ. Note that t 0 is selected with a given time interval during DLS measurements and its upper limit can be the ending time of the aggregation process. c 0 (mmol/L) is the electrolyte concentration, D(t) (nm) is the hydrodynamic diameter of NSC aggregates at time t (t > 0), and D 0 (nm) is the hydrodynamic diameter at the beginning (i.e. t = 0). Plots of the TAA rates vs. electrolyte concentrations are given in Fig 2, where strong Hofmeister effects have been detected for these five alkali ions. For instance, at 10 mmol/L, the TAA rates are equal to 0, 0.9, 4.8, 10.7 and 15.6 nm/min in Li + , Na + , K + , Rb + and Cs + solutions, respectively. Note that the aggregation process has not started in 10 mmol/L Li + solutions. For each alkali ion solution, the TAA rates increase pronouncedly with electrolyte concentrations at first and then reach the plateau. Although much more complicated, NSC1 shows resembling aggregation kinetics as montmorillonite [18]. The TAA rates at low and high concentration regions are represented by two respective linear functions. Intersection for each plot is defined as CCC (critical coagulation concentration). The CCC values are equal to 84.6, 70.7, 36.4, 33.1 and 25.9 mmol/L for Li + , Na + , K + , Rb + and Cs + , respectively. Thus, the Hofmeister effects during the aggregation of NSC1 should abide by the sequence of Cs + > Rb + > K + >> Na + >> Li + , in the same trend as that of montmorillonite [18].
The Hofmeister effects are further investigated by activation energies ΔE(c 0 ), which have been correlated with the TAA rates through a combined use of reaction rate and Arrhenius expressions [18,58],ṽ with where R is the gas constant, and T is the absolute temperature. K can be regarded as a constant, whether the electrolyte concentration is below or above CCC. The activation energies for the aggregation of NSC1 in the various alkali ion solutions are written as, In Li + solution: In Na + solution: In K + solution: In Rb + solution: In Cs + solution: Eqs 4-8 describe the activation energies of five alkali ions below CCC. As indicated by the TAA rate plots (Fig 2) and Eq 2, the activation energies above CCC approach zero; that is, ΔE (c 0 ) % 0 for c 0 ! CCC. For a given electrolyte concentration below CCC, the activation energies are significantly different for the various alkali ions and decrease as Li + >> Na + >> K + > Rb + > Cs + (Fig 3), which is consistent with the results of montmorillonite [18]. The resembling kinetic behaviors between real and model colloids are further corroborated by the studies of NSC2 aggregation in NaNO 3 and KNO 3 solutions (S12 Fig). On basis of the hydrodynamic diameters, TAA rates and CCC values, Hofmeister effects resulting from NSC2 aggregation should be K + > Na + . As indicated in Fig 4, at a given electrolyte concentration below CCC, the activation energies for Na + are far larger than those for K + and show good agreement with the results of NSC1 and montmorillonite.
Thus, for the aggregation of real and complex soil colloids (e.g., NSCs) in electrolyte solutions, Hofmeister series has been explicitly demonstrated to follow as Cs + > Rb + > K + >> Na + >> Li + . This is consistent with the sequences of ion exchange on montmorillonite [43] and montmorillonite aggregation [18]. Both ion exchange and aggregation processes are closely associated with the strength of ion adsorption. Generally, the negative charges of NSC surfaces are more screened by stronger ion adsorption, which further results in the lower activation energy for aggregation. In addition, Hofmeister effects can be evaluated quantitatively by activation energies, and their differences can be discerned for the various alkali ions; e.g., at 15 mmol/L, the activation energies for the aggregation of NSC1 are equal to 1.34RT, 1.04RT, 0.28RT, 0.21RT and 0.15RT for Li + , Na + , K + , Rb + and Cs + , respectively.

Mechanism for NSC aggregation
The mechanism for the aggregation of NSCs in alkali ion solutions is then demonstrated by first-principles density functional calculations. The cluster models of neutral mineral and its interaction with K + are displayed in    (Table 1). Hence, the aggregation kinetics of NSCs should be closely associated with the negative charges carried by minerals, and the aggregation mechanism should be as follows: mineral constituents with more negative charges are preferential to adsorb metal ions, and metal ions anchored this way then interact with colloid constituents with less negative charges. The aggregation processes will be cycled this way until finished. A bi-component NSC system (e.g., montmorillonite and kaolinite) is illustrated in Fig 5b, where montmorillonite  instead of kaolinite has the priority to interact with alkali ions because of the substantially more abundance of negative charges [26]. This mechanism is significantly different from that of the mono-component colloid (e.g., montmorillonite). For the mono-component colloid, the negative charges are approximately equivalent and the interaction strengths of two colloidal particles with cations can be competitive. Accordingly, the aggregation mechanism proceeds as Fig 5a, where two colloidal particles approach cations almost at the same time. Apparently, NSCs are even much more complicated than the bi-component system of Fig 5b. As the aggregation mechanism is closely associated with the negative charges carried by minerals, electrostatic interactions are assumed to have played a significant role. The electrostatic interaction energies (E ele ) of K + with the adjacent SiO 4 tetrahedra of minerals (relating O and Si atoms are marked in ball and stick, see Fig 1 and S13 Fig) are expressed as, where Q i and Q K refer to the Hirshlfeld charges of mineral O/Si atoms and K + , r is the distance of K + with mineral O/Si atoms, and ε and P represent the dielectric and Coulomb constants, respectively. generally decrease with the increase of negative charges carried by minerals. Accordingly, electrostatic interactions are unlikely to be the driving force for the aggregation of NSCs. Polarization effect has been assumed to arouse Hofmeister effects for the aggregation of model colloid (montmorillonite), while no direct or convincing evidence has been given yet [18]. NSCs are composed of structurally distinct minerals and their aggregation processes are definitely more elusive. Owing to that all the constituents of NSC1 and NSC2 are negatively charged, their aggregation processes should be dominated by electrolyte cations as discussed earlier. Fig 7 presents that there is fine correlation between the activation energies and the polarizablities of alkali ions [56,59]. Alkali ions with larger atomic nuclei are more significantly polarized by negatively charged minerals, consistent with the acquainted fact that alkali ions with larger atomic nuclei have less control for outer electrons. Stronger polarization effects to alkali ions substantially increase the interaction strengths with minerals and further facilitate their aggregation processes, which further result in the lower activation energies and stronger Hofmeister effects. This indicates that polarization effect should be the driving force for the aggregation of NSCs.
As indicated in Table 1, the mineral cluster models with different negative charges have distinct dipole moments (μ). In addition, the μ values show a substantial and monotonous increase with the negative charges, which is in exactly the same trend with that of the interaction energies (E int ) between metal ions and minerals (Fig 8). The further corroborates that polarization effect is the driving force for the aggregation of NSCs. Mineral constituents with more negative charges have larger polarization effects for adsorbents and correspond to stronger interaction strengths, which further result in their priority during the aggregation processes. As a result, polarization effect should be responsible for the strong Hofmeister effects arising during the aggregation processes, as further verified by the dipole moment calculations for adsorbed K + ions (μ K ). The μ K values show a monotonous increase with the negative charges carried by mineral constituents ( Table 1). The DLVO theory has recently experienced not a few failures owing to the neglect of non-DLVO forces [22][23][24]60]. For charged particles, polarization effect is evidenced to be indispensable for explaining the experimental observations and can be the major reason for arousing the Hofmeister effects.

Conclusions
In this work, we have presented the aggregation kinetics for complex colloids such as NSCs and quantitatively evaluated the Hofmeister effects implicated therein. Then the mechanism and driving force for the aggregation processes as well as origin of Hofmeister effects are demonstrated. The results obtained thus far can be extended to other charged systems that are ubiquitous in nature such as proteins, clays, colloids and membranes.
NSCs are obviously more complicated than montmorillonite but show resembling aggregation kinetics. In the case of NSCs, colloidal constituents with more negative charges are preferential to adsorb cations, and the significantly polarized cations then interact with those with less negative charges. The aggregation processes will be cycled this way until finished. It is quite different from the case of mono-component colloids, where particles should approach cations almost simultaneously. Although the aggregation processes are closely associated with the negative charges of colloids, electrostatic interactions, to our surprise, show a gradual decrease with the augment of negative charges and therefore play a minor role during the aggregation processes. Polarization effect has been clearly demonstrated to be the driving force for the aggregation of NSCs. On such basis, polarization effect is ascribed to be responsible for such strong Hofmeister effects during the aggregation of charged particles. This is further corroborated by the fine correlation between activation energies and polarizability data of the various alkali ions as well as the dipole moment calculations for minerals with different negative charges and for the alkali ions adsorbed on these charged minerals. Meanwhile, it indicates that why the prevailing DLVO theory is not applicable for colloidal systems because polarization effect is indispensable to describe relating Hofmeister effects. Thus, the present work represents a significant step towards the comprehension of Hofmeister effects that have been recognized as important as Mendel's work was to genetics.  Table. The fitted equations of the TAA ratesṽ T ðc 0 Þ vs. the electrolyte concentrations c0 for the aggregation of NSC2 in LiNO 3 and CsNO 3 solutions respectively obtained from three independent DLS experiments. (DOCX) S2 Table. Distances between K + and six adjacent O atoms from the hexagonal ring of kaolinite minerals with different charges. (DOCX) S1 File. Experimental details. S1.1. Preparation and characterization of NSCs; S1.2. X-ray diffraction experiments; S1.3. Reproducibility of experimental data; S1.4. The TAA rates and uncertainty bars.