The interactions between ion and charged particle determine the surface properties of the particles, ion adsorption, interactions between particles, colloidal suspension stability and settlement etc. Ion adsorption obeys Boltzmann distribution law at the particle/water interface, suggesting the interaction between ion and the surface is restricted by concentration gradient and electric potential gradient1. The Boltzmann equation is a basic equation in electrical double layer theory, and it is therefore a very important approach to study the ion-surface interactions.
The classical double layer theory only considered the Coulomb interaction between ion and surface. Thus the interaction between particles and ions with equal valence causes the same interfacial reaction phenomena. This obviously does not match a large number of experimental phenomena2-6. Some studies indicated that ion volume7, hydration8-10 and dispersion11 etc. also strongly affect the ion-surface interactions. These factors may be the origin of ion specificity or Hofmeister effects, which were discovered through protein aggregation experiments during the 1880s and 1890 s 12. Hofmeister effects affect the ion-particle interactions, and then influence many of the micro processes and macro phenomena, such as the adsorption/desorption of ions on charged surface, surface properties of charged particles, particle-particle interactions, the stability of soil aggregates, the structure of the electrical double layer, and so on. But the physical mechanism of the Hofmeister effects is not clear, for more than one hundred years, many researchers demonstrated that this difference is caused only by the radius of the ion or the hydration radius of the ion13. Ion dispersion force or quantum fluctuation is one of origins of Hofmeister effects at high electrolyte concentration or for low charge density of colloidal particles. The changes of Hofmeister effects with different electrolyte concentrations5, 14, 15, however, cannot be explained by the ion dispersion. On the deep discussion of the driving force of ion-surface interactions, we further find that a strong electric field near the surface exists due to surface charges of nano/colloidal particles16-26. Induced ionic dipole moments in such a strong electric field are different from the softness of ionic electron cloud, and this makes the Hofmeister effects on ion exchange adsorption5.
The activation energy has been considered as a crucial parameter to characterize the ion-surface interactions27. Generally, the activation energy of ion exchange reaction was estimated using the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which has not taken Hofmeister effects into account, although Hofmeister effects may play a considerable role28. In this study, a model of ion-surface interactions considering the Hofmeister effects was established in 2 : 1 electrolyte (MgCl2, CaCl2, CuCl2) solutions. Based on the model, the activation energy of ion exchange adsorption at the solid/liquid interface would be estimated. Ion exchange adsorption is a useful approach to study interfacial reactions, and the study of Hofmeister effects on ion exchange adsorption is also helpful to reveal the mechanism of ion-surface interactions.
The adsorption capacity of ions in the diffuse layer can be expressed as:
where S is the specific surface area of the particles; κ is Debye parameter, 1/κ is the thickness of the electrical double layer; l is the distance between surface and the diffusion position of exchangeable counterion. l = 1/κ indicates that the ion does not diffuse into the electrical double layer, and the adsorption capacity is 0. On the contrary, l = 0 indicates that the ion diffuses to the surface of the particles. At this point, the adsorption capacity reached the maximum, i.e. saturated adsorption capacity. The fi(x) is the concentration distribution in the diffuse layer, which obeys the Boltzmann distribution considering the ion-ion interactions in bulk solution29:
where ai0 is the activity of ion i species in bulk solution; wi(x) is the adsorption energy of ion i species at the x position in the diffuse layer, R is gas constant, T is absolute temperature.
Taking the additional energies arising from the Hofmeister effects into account, the ion-surface interaction energy can be expressed as30:
where Zi is the valence of i ion species; F is Faraday constant; φ(x) is the potential at the x position in the diffuse layer; wiadd(x) is the additional energy arising from the Hofmeister effects.
Since the Poisson-Boltzmann equation with Hofmeister effects is considered to have no analytical solution, and we consider the correction of the ion specificity on the analytical solution of the classical nonlinear Poisson-Boltzmann equation. In 2 : 1 electrolyte system (2 : 1 electrolyte refers to the two valence cations and monovalent anions form a chemical electrolyte, e.g. CaCl2), the solution of the Poisson-Boltzmann equation taking ion specificity into consideration is31:
where m is a function of mean interaction energy between ion and surface in 2 : 1 electrolyte. When x = l, the actual adsorption energy wi(l) could be calculated as
Combining Eqs.(1)-(4), we have:
In which, wi0 =
ZiFφ0 + wiadd(0) is the mean adsorption energy between ion and surface.
In Eq.(5), the adsorption would reach the maximum when l = 0, and the adsorption capacity could be expressed as:
The NiT is the total adsorption amount, wi0could be calculated using Eq.(7).
Once the parameter m is obtained, the distance l could be calculated correspondingly using Eq.(5). Thus the activation energy of ion exchange adsorption is:
Equations (5)-(8) show that the activation energy is a function of Ni and NiT which depends on the values of m and l. The Ni/NiT represents the adsorption saturation.
Purified montmorillonite was purchased from Wuhuatianbao Mineral Resources Co., Lid, in Inner Mongolia in China. The average particle size and specific surface area are determined to be 1480 nm and 731 m2·g-1, respectively.
Pretreatment of samples: the Na-saturated montmorillonite was prepared by equilibrating with 0.5 mol·L-1 NaCl (AR) solution for five times (mass ratio of montmorillonite and water is 1 : 10), the adsorbed cations were saturated by Na+. After repeatedly washing the Na+-equilibrated samples with pure water for two times, and then the Na-saturated montmorillonite was dried at a temperature of 298 K, and sieved through a 0.25 mm sieve.
Exchange adsorption: approximate 1 g Na-saturated montmorillonite was weighed and transferred into the triangular bottles, 30 mL 0.05, 0.1, 0.2 and 0.3 mol·L-1 MgCl2 (AR) solutions were added into each group, respectively (the low concentration was selected to test the ion adsorption saturation). The suspensions in the triangular bottles were allowed to equilibrate for 12 h at 298 K, and then centrifugal separation, the supernatant was then collected in a 200 mL volumetric flask. To make the cation exchange completely, the experiment was repeated four times, and each supernatant was preserved in the same corresponding volumetric flask, and then diluted with deionized water to 200 mL.
The same method was applied to the Ca/Na and Cu/Na exchange adsorption experiment. The concentration of Na+ was determined by flame photometer. The experimental method was proposed by Low32.
In the experiment, the supernatant was collected to make the exchange adsorption more fully through adding adsorption ion repeatedly (Mg2+, Ca2+ and Cu2+). Since the adsorbed ions were added repeatedly, the adsorption capacity could not be calculated by the difference between the added and remaining amount. Considering montmorillonite is constantly charged mineral, the chemical adsorption could be neglected. According to the charge balance principle, the adsorption capacity of Na-montmorillonite was calculated by the desorption of Na+.
The data in Table 1 showed that the adsorption capacity of the three ions increased with increasing ion concentrations. Obviously, there was a significant difference among the adsorption capacities for the three species of bivalent ions, suggesting Hofmeister effects exert influence on ion exchange adsorption equilibrium. Due to the constant charge of the montmorillonite surface, the chemical adsorption could be ignored, and the ion adsorption specificity is equal to the ion exchange specificity. In addition, the adsorption in montmorillonite is not controlled by the Stern layer. The experimental results could not be explained by the classical theory which only takes Coulomb interaction into account.
Based on the experimental process, the true equilibrium adsorption of montmorillonite should be a constant in different electrolyte solutions, and this value is the total surface charge number. By comparing the equilibrium adsorption capacity of montmorillonite under four different concentrations (Table 1), the adsorption capacity of the three ion species can be found: Mg2+ < Ca2+ < Cu2+, indicating strong Hofmeister effects on ion adsorption at montmorillonite surface exist on the one hand. On the other hand, the experimental adsorption capacity suggests that the achieved ion exchange equilibrium is not in a real state of equilibrium, but a metastable equilibrium. At this time, the exchange reaction rate is so slow that it cannot be determined during the experiment. This may be result from the fact that the adsorption energy and the exchange energy are different and the former is higher than the latter. Here we suppose the adsorption capacity of Cu2+ at 0.3 mol·L-1 reach approximately the real equilibrium, thus the surface charge of montmorillonite in this study is 1.2 mmol·g-1, this value is approximately equal to the experimental result in the previous study30. The maximum adsorption capacity of the bivalent ions is 0.6 mmol·g-1.
As long as the surface charge number of particle was obtained, the relationship between the maximum adsorption energy (negative value) and the ion concentration could be described by Eq.(7) (Fig. 1). Only when the adsorption energy reaches the maximum value, the counterion adsorption could be saturation.
Fig. 1 shows that the adsorption energy between ion and surface decreases with increasing ion concentration.The larger the surface charge density is (e.g. 0.3168 C·m-2), the higher the adsorption energy will be (the dot line in Fig. 1). Obtaining the total saturated adsorption energy, the relationship between the adsorption saturation of ions and the diffusion distance in the double layer can be quantitatively calculated by Eq.(5), as shown in Fig. 2. When κl is 0, the adsorbed ions reach the surface and the ion adsorption reaches saturation (100%); when κl is 1, the ions are not adsorbed and the ion adsorption is zero. Simultaneously, ion concentration also affects the adsorption saturation. The higher the ion concentration is, the larger the ion adsorption will be. According to the Eq.(5) or Fig. 2, the position could be estimated when the ions are adsorbed in the diffuse layer.
The activation energy, the difference between the actual adsorption energy and the saturated adsorption energy, is the determining factor of the ion adsorption saturation. Generally, higher activation energy indicates lower adsorption saturation. When the activation energy is zero, the ion can get closer to the particle surface (κl = 0). After determining the position of the ion in the diffuse layer, the actual adsorption energy of the ion and the surface can be calculated.
The metastable equilibrium of ion adsorption depends on the diffusion distance of ions in the diffuse layer. The actual adsorption energy is not the saturation adsorption energy, but the adsorption energy at the diffusion position l. If the diffusion distance of counterions from bulk phase (Gouy plane) equal 1/κ, the actual adsorption energy is equal to saturation adsorption, and the activation energy is approximately zero. Fig. 3 shows that the activation energy decreases with increasing ion concentration. The activation energies for different cations exhibit Hofmeister effects. According to Eq.(8), the higher activation energy represents the lower adsorption energy.
The adsorption energy of ions decreases with the increase of the ionic concentration in the diffuse layer, the series for ions is Cu2+ > Ca2+ > Mg2+. Although activation energies for the above bivalent cations were different (Fig. 3), the adsorption saturation could be expressed as the same function of activation energy (Fig. 4). In other words, the model of the interactions between ion and surface considering the Hofmeister effects is universal.
The existing theories reveal that the ionic dispersion force and the volume effect are the main factors of the Hofmeister effects11, 33. However, these factors only work at high concentrations, but the Hofmeister effects vanish slowly at low concentrations. In this study, the strong Hofmeister effects are observed from low concentration (0.05 mol·L-1) to high concentration (0.3 mol·L-1). The surface electric field of montmorillonite is 2.2 × 108 V·m-1 in this experiment, and the distribution of the electric field in the diffuse layer increases with ion concentration decreasing. Such a strong electric field can inevitably change the structure of electron clouds of the adsorbed ions. This effect is called the coupling effect between electric field and quantum fluctuation5. Recently, Parsons et al.34 hold that surface charge transfer was a new origin of Hofmeister effects at low salt concentration. Therefore, we predict that the combined effects among ion dispersion forces, ionic volume, charge transfer and the coupling effect between electric field and quantum fluctuation exist in the interaction between ion and particle, but the main factor changes with different conditions. The coupling effect between the electric field and the quantum fluctuation for higher surface charge density and charge transfer for very low surface charge density are the main factor under low concentration, while the dispersion force and volume effect are enhanced at very high concentration.
Ion-surface interactions strongly affect the ion adsorption. A new model of ion adsorption with Hofmeister effects was established, and the activation energy of ion exchange adsorption was estimated in this study. Ionic adsorption saturation at the montmorillonite surface obeys the sequence Cu2+ > Ca2+ > Mg2+. Hofmeister effects result in the difference of activation energy of ion exchange adsorption, and then determine the ion adsorption saturation. The calculated activation energies for the tested bivalent cations based on the new model was a same function of adsorption saturation. For the constant charge surfaces, the model of the interaction between ions and the surface considering the Hofmeister effects is universal, which must be included in the ion interface reactions.