Specific ion effects on ion exchange kinetics in charged clay

Colloids and Surfaces A: Physicochem. Eng. Aspects 509 (2016) 427–432

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Specific ion effects on ion exchange kinetics in charged clay Wei Du, Rui Li, Xin-Min Liu ∗ , Rui Tian, Hang Li ∗ Chongqing Key Laboratory of Soil Multi-Scale Interfacial Processes, College of Resources and Environment, Southwest University, Chongqing 400715, PR China

h i g h l i g h t s

g r a p h i c a l

a b s t r a c t

• The adsorption kinetics exhibited strong specific ion effects.

• New kinetic models can describe cationic exchange adsorption based on specific ion effects. • The strength of the specific ion effects could be quantitatively characterized by the defined Hofmeister energy.

a r t i c l e

i n f o

Article history: Received 6 May 2016 Received in revised form 6 September 2016 Accepted 11 September 2016 Available online 12 September 2016 Keywords: Specific ion effects Ionic adsorption kinetics Ionic non-classical polarization Hofmeister energy Dipole moment

a b s t r a c t Ion exchange adsorption is a physical-chemical process ubiquitously occurring in a wide range of systems, and it is possible that specific ion effects exist universally in cation adsorption processes. In this study, the adsorption kinetics of Li+ , Na+ and Cs+ in the exchange systems (Li+ /K+ , Na+ /K+ and Cs+ /K+ ) occurring at a negatively charged montmorillonite surface were explored under different dilute electrolyte concentrations. The results show that (1) the adsorption kinetics exhibited strong specific ion effects; and (2) the strength of the specific ion effects could be quantitatively characterized by the defined Hofmeister energy, wH (0), additionally, the wH (0) values for Cs+ , K+ , Na+ and Li+ were respectively 1.40, 0.942, 0.180 and 0.0630 time larger than the corresponding Coulomb energies. Based on those results, new kinetic theories of cationic adsorption taking specific ion effects into account were established. We theoretically conclude that: large wH (0) value will result in fast adsorption rate, and the adsorption will obey a zeroorder kinetics during the first stage of adsorption, and subsequently changed to a first-order kinetics; however, for a cation with low wH (0) value, only the first-order kinetics could be observed. All those theoretical predictions were verified by experimental results. © 2016 Published by Elsevier B.V.

1. Introduction Ion exchange adsorption is a physical-chemical process that occurs ubiquitously in a wide range of colloidal systems, such as

∗ Corresponding authors. E-mail addresses: [email protected] (X.-M. Liu), [email protected] (H. Li). http://dx.doi.org/10.1016/j.colsurfa.2016.09.042 0927-7757/© 2016 Published by Elsevier B.V.

protein solutions, membranes, clay and engineering nano-colloidal particles [1–3]. To understand and describe the mechanisms of ion exchange adsorption in aqueous solutions, numerous equations, such as the parabolic diffusion equation, fractional power equation, first- and second-order rate equations, and the Elovich equation, etc. have been employed [4–7]. However, ion exchange adsorption in colloidal systems often involves complex multi-processes comprising heterogeneous diffusion and surface reactions. In classical

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theory, complex diffusion processes occur during ion exchange [7], thus, understanding the mechanism of ion exchange adsorption remains a challenge. It is well known that colloidal particles are often strongly charged. To maintain the electrical neutrality, dissolved counterions in a liquid solution will accumulate close to the charged surface and the thermal motion of counterions makes the accumulated counterions exhibiting Boltzmann distribution in the electric double layer (EDL). In addition, the adsorbed counterions combined with the surface charges could set up an electric field (approximately 108 –109 V m−1 ), which is distributed over the EDL and gradually weakens until it disappears in the bulk solution [8]. Thus, the diffusion of counterions in the EDL is the diffusion of ions in an external electric field. Certainly the strongest electric field exists in the inner space of the EDL, but even at a distance of the Debye length away from the particle surface (e.g. 30 nm in a 0.0001 M 1:1 type electrolyte solution) the electric field is not zero and the electric field would still directly influence ion diffusion. Actually, the Boltzmann distribution of adsorbed ions in the diffusion layer (with a width of the Debye length) definitely shows that the electric field will influence ion diffusion. Ion diffusion in an external electric field of the one-dimensional case can be classically described by the well-known Fokker–Planck or Smoluchowski equation [9,10]. However, because of its complexity, an exact solution of which is difficult to obtain. Using a local equilibrium assumption, Li and Wu [9,11,12] found that this classical nonlinear differential equation is equivalent to a linear form and the ionic flux equation has been obtained. On the other hand, Li et al. [12] proved that the electrostatic adsorption process would be essentially a diffusion process for the ions in the electric field. Based on this concept, Li et al. [13,14] and Li et al. [15–17] established new kinetic mechanism models for describing the process of ion exchange adsorption. However, all current kinetic models neglect the specific ionic effects, which are ubiquitous in physical, chemical and biological processes and have been a focus of research recently [18,19]. A host of theories have been proposed to account for specific ion effects [20–27]. For quite some time, ion hydration was widely accepted to be the sole origin of specific ion effects, but this hypothesis is at odds with recent advances in research. Jungwirth and Cremer indicated that the original thesis that the specific ion effects or Hofmeister effects can be fully rationalized in terms of the hydration behaviour of ions in bulk solution has clearly been disproven [18]; Parsons et al. indicated that the hydration thesis skirts over the true source of Hofmeister effects for a long time [27]. The quantum fluctuation (dispersion) forces have been considered to be associated with specific ion effects at high ion concentrations (>0.1 mol L−1 ) because the electrostatic field could be strongly screened by counterions [27]. However, recently, strong specific ion effects were found in very low electrolyte concentrations in clay and soil systems [8,28–31]. In those studies, a strong additional interaction effect, referred to as non-classical induction force [8] arising from the non-classical ionic polarization, was proposed to account for specific ion effects [8,28–32]. It was referred to as “non-classical” because the observed dipole moment or polarizability was several tens to hundreds times larger than the classical value. Even though the experimental results of specific ion effects in clay and soil systems could be well explained by the ionic nonclassical polarization [8,28–32], when we further calculate the corresponding polarizabilities and the dipole moments of ions, we found the obtained dipole moments were “unbelievably” large from the classical point of view [8,28–32]. For example, as the ionic strength was 0.001296 mol L−1 in the Ca2+ -Na+ -illite exchange system [8], the obtained dipole moment difference between Ca2+ and Na+ was 448.6 D, while the classical value was only 0.013 D [8]. When the ionic strength increased to 0.6052 mol L−1 , the

obtained dipole moment difference between Ca2+ and Na+ was also a large value, 36.05 D, whereas the classical value was only 0.126 D [8]. Obviously, such large values for dipole moments are physically puzzling from the classical point of view. Therefore, one could infer that the obtained large dipole moment was merely a representation occurring in the clay and soil systems. Such large dipole moment, however, undoubtedly implies that the additional energies in cation-clay and cation-soil interaction arising from the specific ion effects were very large. Thus, it is possible to conjecture that cation exchange/adsorption kinetics in clay and soil systems would be powerfully influenced by the additional energies, no matter what is their origin. The objectives of this study were to (1) demonstrate the presence of specific ion effects on cation exchange kinetics in clay; (2) estimate the strength of the specific ion effects on the exchange kinetics; and (3) establish a new theory taking specific ion effects into account to describe the cation exchange kinetics. 2. Theory of cation adsorption kinetics, taking specific ion effects into account If specific ion effects present, an additional energy must be taken into account in the ion-surface interaction. The total energies for an ion with charges Z could be expressed as: w(x) = ZF

(x) + wH (x) = [ (x) Z] F

(1)

(x)

where w(x) is the total potential energy arising from molecular interaction and the external fields; ZF (x) is the Coulomb mean potential energy at position x; wH (x) is the additional potential energy arising from specific effects at position x, here we refer to it as the Hofmeister Energy; F is Faraday’s constant; Z is the valence of the cation; (x) is the potential at position x; (x) is defined as:



 (x) = 1 +

wH (x) ZF (x)



(2)

Note that, in this study we do not need to figure out the origins of the specific ion effects, which might be the ionic size, hydration, dispersion force, classical or non-classical polarization etc. Eq. (1) implies that, no matter what interactions produce the additional potential energy wH (x), we could apparently take its contribution to the total potential energy w(x) as a modification of the charge number Z, thus the (x) could be taken as the effective charge coefficient [28,31,33–35] of an ion and Z(x) could be taken as the apparent charge number as specific ion effects present. Based on the theory put forward by Li et al. [16,17], the real ion flux taking Eq. (1) into account is: j(x, t) =

dN(t) 2 D0 = Sdt 4l

  1 l

l

 exp −

Z(x)F (x) RT



 [f0 − A(x, t)] dx

(3)

0

where N(t) is the quantity of adsorbed ions at time t during the adsorption/diffusion process; S is the specific surface area of the sample; D0 is the ionic diffusion coefficient; l is the average thickness of the fixed liquid adjacent to the particle surface; R and T are the gas constant and absolute temperature, respectively; f0 is the ionic concentration in bulk solution; and A(x,t) is the activity or apparent concentration for a non-ideal system in external fields. In this paper, we focus our discussion on the exchange between two equally charged cation species. When specific ion effects absent, two equally charged cations involved in the exchange bear the same electrostatic attractive force in the electric field. However, when the specific ion effects present (it means wH (x) = / 0), and if the wH (x) value of the adsorbing cation is larger than that of the desorbing cation in the exchange, a strong force adsorption process will possibly occur in the exchange adsorption kinetics. Conversely, if the wH (x) value of the adsorbing cation is smaller than that of the

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desorbing cation in the exchange, a weak force adsorption process will possibly occur during the exchange adsorption kinetics.

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3. Material and methods 3.1. Material and sample preparation

2.1. For the adsorption process of an adsorbing cation with relatively strong specific ion effects The cation with strong specific ion effects will bear a large  value, indicating only the inner space of the diffuse layer bearing a large (potential) value, thus possibly ew (x)/RT = eZ␥(x)F (x)/RT « 1, and then we have f0 -A(x,t) = f0 (1 − eZ␥(x)F (x)/RT ) ≈ f0 when x → 0. For this case, from Eq. (3) we have [15–17]:

Permanently charged montmorillonite was used as an experimental material. The montmorillonite was saturated with 0.1 mol L−1 KNO3 solution and passed through a 0.25 mm sieve after the sample was dried at 343 K. According to the combined measurement method [36], the specific surface area of montmorillonite was 725 m2 g−1 , the surface charge number was 1150 mmol(−) kg−1 , and the surface charge density was 0.15C m−2 .

dNi (t) = ki(0) Ni (t)0 dt

3.2. Ion adsorption kinetics

in which: ki(0)

2 Di0 = Sfi0 4l2



(4)



l

exp −

ZFi (x) (x) RT





dx ≈

0

ZFi (0) (0) 2 Di0 Sfi0 exp − 2RT 2l

 (5)

where Di0 is the diffusion coefficient of the ith cation; fi0 is the concentration of the ith cation in bulk solution; (0) is the surface potential,  i (0) is the effective charge coefficient at the surface, and, from Eq. (2),  i (0) can be expressed as:



wH (0) ZF (0)

 (0) = 1 +



(6)

where wH (0) is the Hofmeister energy of cation at particle surface. Eq. (4) shows that, for the adsorption process of an adsorbing cation with relatively strong specific ion effects, the adsorption rate will obey a zero-order rate equation during the first stage of adsorption. Obviously, after the inner space has been occupied by the adsorbed cation, the adsorption process will transform to the outer space adsorption, where both  and decrease. For this case, the approximation f0 − A(x,t) ≈ f0 used to obtain Eq. (4) is no longer correct, thus from Eq. (3) we have [13,15–17]:



N (t) dNi (t) = ki(1) 1 − i Ni(eq) dt in which:



Ni(eq) = Sfi0



l

exp −



ZFi (x) (x) RT

(7)



 dx ≈ 2Slfi0 exp −

ZFi (0) (0) 2RT

 (8)

0

and ki(1)

2 Di0 = Sfi0 4l2



l

 exp −

0

Ion adsorption kinetics were studied using the miscible displacement technique [14]. Approximate 0.5 g of K+ saturated sample was placed on the exchange column. To eliminate the influence of ion diffusion caused by the longitudinal concentration gradient, the thickness of the sample should be as small as possible (0.02–0.03 cm in this study). The spreading area of the sample was approximately 15 cm2 . The exchange solutions (CsNO3 , NaNO3 and LiNO3 ) with given concentrations (1 × 10−4 –1 × 10−2 mol L−1 ) flowed across the layered sample with a constant flow (0.5 ml min−1 ) under room temperature (298 K). All effluents were collected using an automatic collector (DBS100, Shang-Hai QPHX Instrument Co., Ltd., Shanghai, China) for each 20-min time interval. Note that the time interval was 5 min when the ionic concentration increased to 1 × 10−2 mol L−1 according to an increased velocity. The concentrations of Li+ , Na+ and Cs+ in effluents were determined by the flame photometer (AP1401, Shang-Hai AP Analysis instrument Co., Ltd.). The quantity of each cations adsorbed was calculated by the difference between concentrations before and after exchange experiments.

ZFi (x) (x) RT





dx ≈

ZFi (0) (0) 2 Di0 Sfi0 exp − 2RT 2l

 (9)

Eq. (9) shows that, for the adsorption process of an adsorbing cation with relatively strong specific ion effects, the adsorption rate will obey a first-order rate equation during the second stage of adsorption. 2.2. For the adsorption process of an adsorbing cation with relatively weak specific ion effects For the adsorption of a cation with relatively weak specific ion effects, there are two possible cases. On the one hand, if the  value for the adsorbing cation is not too low, during the inner space adsorption with a relatively large value, the adsorption process will probably obey a zero-order rate equation, but the duration of the zero-order process will be much shorter than that for a cation with a relatively strong specific ion effects. On the other hand, if the  value for the adsorbing cation is too low, only a first-order process would be observed during the adsorption process. Therefore, according to the above discussion, the theoretical relationships of v = dNi (t)/dt vs. Ni (t) will exhibit different straight lines, depending on the strength of the specific ion effects of the adsorbing cation.

4. Results and discussion The quantities of cations adsorbed at different times in the three exchange systems are shown in Fig. 1. As can be seen, although Cs+ , Na+ and Li+ are all mono-valence cation species, their adsorption rates differed markedly and increased in the order Li+ < Na+ « Cs+ , indicating the occurrence of specific ion effects during the cationic exchange adsorption. We note that these results might not be explained by ionic size, hydration and dispersion forces, because these effects are important only when cationic concentrations higher than 0.1 mol L−1 [27]. In the present studies, however, the highest electrolyte concentration was 10−2 mol L−1 . Koelsch et al. [37] indicated that unless the chemical nature of cations is considered, we cannot predict the different ions effects based only on the Coulombic interactions arising from their charges. Recently, based on the observations of specific ion effects in dilute solutions, as discussed in the Introduction section, a number of researchers found that non-classical polarization of ion plays an important role in the specific ion effects [8,28,31,32]. Moreover, it was verified that the strength of non-classical polarization of the three cationic species was in the order Li+ < Na+ « Cs+ [28], supporting the observed order of adsorption rates. However, as discussed in the Introduction section, if the additional potential energy attributing to the non-classical ionic polarization, the obtained dipole moments were “unbelievably” large, which are physically puzzling from the classical point of view. To directly employ the experimental data, we used [Ni (tm + 1 ) − Ni (tm )]/(tm + 1 − tm ) to approximate dNi (t)/dt; and correspondingly used Ni (tm + 1/2 ) = Ni (tm ) + 0.5[Ni (tm + 1 ) − Ni (tm )] to approximate Ni (t), where m = 1,2,3. . . [13,17]. Using the experimental data shown in Fig. 1, the relationships for

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Fig. 1. The relationship of accumulate adsorption quantities N(t) of Cs+ , Na+ and Li+ vs. time t for exchange systems Cs+ /K+ , Na+ /K+ and Li+ /K+ under electrolyte concentrations of (a) 1 × 10−4 , (b) 10 × 10−4 and (c) 100 × 10−4 mol L−1 respectively.

Fig. 2. The relationship curves of [Ni (tm + 1 ) − Ni (tm )]/(tm + 1 − tm ) vs. Ni (tm + 1/2 ) under cationic concentrations of 1 × 10−4 mol L−1 ; y0 and y1 represent the zero order rate and first order rate respectively.

Fig. 3. The relationship curves of [Ni (tm + 1 ) − Ni (tm )]/(tm + 1 − tm ) vs. Ni (tm + 1/2 ) under cationic concentrations of 10 × 10−4 mol L−1 ; y0 and y1 represent the zero order rate and first order rate respectively.

Fig. 4. The relationship curves of [Ni (tm + 1 ) − Ni (tm )]/(tm + 1 − tm ) vs. Ni (tm + 1/2 ) under cationic concentrations of 100 × 10−4 mol L−1 respectively; y0 and y1 represent the zero order rate and first order rate respectively.

[Ni (tm + 1 ) − Ni (tm )]/(tm + 1 − tm ) vs. Ni (tm + 1/2 ) in the three cation exchange systems are respectively shown in Figs. 2, 3 and 4. From Figs. 2, 3 and 4, we can see that the kinetics curves of cation exchange adsorption showed markedly specific ion effects, which could be described by the theoretical rate equations of Eqs. (5) and (9), in which the specific ion effects were taken into account.

To understand the experimental results shown in Figs. 2, 3 and 4 clearly, the effective charge coefficients of Li+ , Na+ , K+ and Cs+ arising from the specific ion effects should be discussed in advance. Based on the dynamic laser light scattering measurements of activation energies for montmorillonite colloidal aggregation, Li et al. estimated the effective charge coefficient of

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431

Table 1 The measured rate coefficient ki (1) and equilibrium adsorbed quantity Ni (eq) for different cation species under different electrolyte concentrations. f0 (mol L−1 )

−1

ki (1) (min

)

Ni (eq) (mmol kg−1 )

Cation species Cs+ [wH (0) = 1.40 × F (0)]

Na+ [wH (0) = 0.18 × F (0)]

Li+ [wH (0) = 0.063 × F (0)]

0.01 0.001 0.0001

1324 161.0 13.39

1094 95.85 9.509

1030 73.79 8.479

0.01 0.001 0.0001

1098 647.4 523.0

373.9 165.8 103.9

272.2 123.0 79.32

The bold values represent the difference between effective charge and static charge, i.e. Zeff - Z for a given ion.

Table 2 The estimated non-classical polarizabilities and dipole moments of the cation species. f0 (mol L−1 )

Cation species Cs+ ( = 2.404)

K+ ( = 1.942)

Na+ ( = 1.180)

Li+ ( = 1.063)

polarizability (Å )

0.01 0.001 0.0001

220.9 698.6 2209

170.2 538.2 1702

41.79 132.1 417.9

∼0 ∼0 ∼0

Dipole moment (D)

0.01 0.001 0.0001

129.1 408.4 1291

99.50 314.7 995.0

24.43 77.26 244.3

∼0 ∼0 ∼0

3

Na+ at particle surface ((0)) and found  Na (0) = 1.18 [34]. Liu et al. estimated the relative effective charge coefficients of Li+ and K+ from Na+ /Li+ and Na+ /K+ exchange with an electrolyte concentration range from 0.001 to 0.03 mol L−1 , and found  Li (0)/ Na (0) = 0.901 and  K (0)/ Na (0) = 1.646 [29]. Thus we could get  Li (0) = 0.901 × 1.18 = 1.063 and  K (0) = 1.18 × 1.646 = 1.942. Hu et al. estimated the relative effective charge coefficient of Cs+ from clay aggregate stability when taking Li+ as a reference, and the average value of  Cs (0)/ Li (0) in 0.010.0001 mol L−1 electrolyte concentration range was 2.262 [28]. Thus  Cs (0) = 2.262 × 1.063 = 2.404. From the obtained  values, the Hofmeister energy of the four cation species at particle surface could be estimated based on Eq. (6). For Cs+ , K+ , Na+ and Li+ , the Hofmeister energies (wH (0)) are wH (0)Cs = 1.40 × F (0), wH (0)K = 0.942 × F (0), wH (0)Na = 0.180 × F (0) and wH (0)Li = 0.063 × F (0), respectively. We now provide a detailed discussion on the results shown in Figs. 2, 3 and 4 based on the obtained Hofmeister energies of the four cation species. As can be seen from Figs. 2, 3 and 4, the cationic adsorption rates indeed obey the theoretically predicted zero- and first-order rate equations which take into account the specific ion effects of cation. As predicted theoretically, for an adsorbing cation bearing a relatively strong specific ion effects (characterized by the Hofmeister energy, wH (0)), a zeroorder kinetic process would appear during the first stage of adsorption. For Cs+ adsorption in the Cs+ /K+ exchange, because wH (0)Cs = 1.404 × F (0) > wH (0)K = 0.942 × F (0), a zeroorder kinetic process would occur under all the three electrolyte concentrations. Figs. 2, 3, and 4 indeed show that when the zero-order kinetic process during the first stage of adsorption is complete, cationic adsorption was then transformed to a first-order kinetic process, as predicted from theory. adsorption in Na+ /K+ exchange, because For Na+ wH (0)Na = 0.18 × F (0) < wH (0)K = 0.942 × F (0), under the lowest electrolyte concentration of 0.0001 mol L−1 , only a very short duration of zero-order kinetics appeared. The lowest electrolyte concentration means the strongest electric field or the highest potential ( ) value within the inner space of the diffuse layer. For

example, under the electrolyte concentrations of 0.0001, 0.001 and 0.01 mol L−1 , the surface potentials at x = 0 were (0) = −285.8, −228.0 and −172.5 mV, respectively. As analyzed in the Theory section, even for a cation species with a relatively low  value, if the value of is large, the product of  would possibly ensure eZF␥␺/RT « 1 and f0 − A(x,t) = f0 (1 − eZF␥␺/RT ) ≈ f0 , thus still possibly leading to zero-order adsorption kinetics. However, because of the relatively weak specific ion effects of Na+ , its adsorption during Na+ /K+ exchange mainly followed the first-order kinetics. Li+ adsorption in Li+ /K+ exchange, because For wH (0)Li = 0.063 × F (0) « wH (0)K = 0.942 × F (0), zero-order kinetics were absent under all the three electrolyte concentrations, and only first-order kinetics applied. In addition, the adsorption rates and maximum quantities adsorbed at equilibrium shown in Figs. 2, 3 and 4 exhibited strong specific ion effects. The data in Table 1, which were calculated from Figs. 2, 3 and 4, show the specific ion effects quantitatively. As can be seen from Table 1, the differences in ki(1) and Ni(eq) between each two of the cations match the corresponding differences in their wH (0) values. Moreover, the larger the difference in the wH (0) value between each two cations, the larger the corresponding difference in ki(1) and Ni(eq) would be. This observation also implies that the difference in ki(1) or Ni(eq) between two cation species would arise from differences in their specific ion effects. The above discussion showed that, the adsorption kinetics during cation exchange exhibited strong specific ion effects. Cs+ is a cation with the strongest specific ion effects in our experiments; because wH (0)Cs > wH (0)K under all the electrolyte concentrations (0.0001 to 0.01 mol L−1 ), Cs+ adsorption during Cs+ /K+ exchange exhibits zero-order kinetics during the first stage of adsorption and then changes into first-order kinetics. Na+ is a cation with relatively weak specific ion effects; because wH (0)Na < wH (0)K , Na+ adsorption during Na+ /K+ exchange exhibits zero-order kinetics only when the adsorption of Na+ occurs in a very strong electric field (e.g. 0.0001 mol L−1 electrolyte concentration), whereas its adsorption exhibits first-order kinetic process in most instances. Li+ is a cation with the weakest specific ion effects for the applied cation species in our experiments, and wH (0)Li « wH (0)K , so that only first-order

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kinetics was observed under the whole electrolyte concentration ranges from 0.0001 to 0.01 mol L−1 . In addition, if the specific ion effects were attributed to the cationic non-classical polarization, the dipole moments of the cation could be estimated from the following equation [28]:



 = 1+

p(x → 0) ZF

 (10)

Introducing the corresponding  values into Eq. (10), the dipole moments and the polarizabilities of the cation species could be estimated. The results are shown in Table 2. It can be seen that the values of polarizabilities and dipole moments are so large that is physically puzzling from the classical point of view. Therefore, in addition to the strong cationic non-classical polarization, other unknown interaction between cation and clay surface might be presented. A possible new interaction might be that, when the quantum state of the cationic electrons is essentially changed by the strong polarization occurring in the strong electric field near a clay surface, new quantum interactions between the inner orbits of the cation and the oxygen atom at clay surface may also produce; and if this process occurred, such large polarizability or dipole moment would not be required. Even so, strong polarization of cation would be the prerequisite of the new quantum interactions. In our following papers, we will show the related results based on the analysis of Density Functional Theory (DFT). 5. Conclusions The strong specific ion effects on the adsorption kinetics of cation exchange were quantitatively characterized by the established new theoretical models. The Hofmeister energy wH (0) was adopted to characterize the strength of the specific ion effects. We found the wH (0) values for Cs+ , K+ , Na+ and Li+ were 1.40, 0.942, 0.180 and 0.0630 time larger than the Coulomb energies. The adsorption rate and maximum adsorption quantity at equilibrium increase with the increasing wH (0) value for the given cation species. For cation with large wH (0) value, both the zero- and first-order kinetics will be theoretically predicted and experimentally determined; for cation with low wH (0) value, however, only first-order kinetics were theoretically predicted and experimentally observed. Moreover, the zero-order kinetics applied during the first stage of adsorption, and subsequently changed to firstorder kinetics. The experimental phenomena of specific ion effects on ion exchange kinetics could be rationally explained only when ion-surface interactions take into consideration Hofmeister energy. Acknowledgements This work was supported by the Natural Science Foundation of China (Grant No. 41530855, 41371249, 41201223 and 41501240) and Fundamental Research Funds for the Central Universities (Grant No.XDJK2015C174 and XDJK2015C177). References [1] A.B. Albadarin, C. Mangwandi, H. Ala’a, G.M. Walker, S.J. Allen, M.N. Ahmad, Kinetic and thermodynamics of chromium ions adsorption onto low-cost dolomite adsorbent, Chem. Eng. J. 179 (2012) 193–202. [2] T. Xu, Ion exchange membranes: state of their development and perspective, J. Membr. Sci. 263 (2005) 1–29. [3] W.H. Yu, N. Li, D.S. Tong, C.H. Zhou, C.X.C. Lin, C.Y. Xu, Adsorption of proteins and nucleic acids on clay minerals and their interactions: a review, Appl. Clay Sci. 80 (2013) 443–452. [4] C. Aharoni, S. Levinson, I. Ravina, D.L. Sparks, Kinetics of soil chemical reactions: relationships between empirical equations and diffusion models, Soil Sci. Soc. Am. J. 55 (1991) 1307–1312. [5] S. Azizian, Kinetic models of sorption: a theoretical analysis, J. Colloid Interface Sci. 276 (2004) 47–52.

[6] H. Qiu, L. Lu, B.C. Pan, Q.J. Zhang, W.M. Zhang, Q.X. Zhang, Critical review in adsorption kinetic models, J. Zhejiang Univ. Sci. A 10 (2009) 716–724. [7] D.L. Sparks, Kinetics of ionic reactions in clay minerals and soils, Adv. Agron. 38 (1985) 231–266. [8] X.M. Liu, H. Li, R. Li, D.T. Xie, J.P. Ni, L.S. Wu, Strong non-classical induction forces in ion-surface interactions: general origin of Hofmeister effects, Sci. Rep. 4 (2014), http://dx.doi.org/10.1038/srep05047. [9] H. Li, L.S. Wu, A generalized linear equation for non-linear diffusion in external fields and non-ideal systems, New J. Phys. 9 (2007) 357. [10] H. Li, L.S. Wu, H.L. Zhu, J. Hou, Ion diffusion in the time-dependent potential of the dynamic electric double layer, J. Phys. Chem. C 113 (2009) 13241–13248. [11] H. Li, L.S. Wu, On the relationship between thermal diffusion and molecular interaction energy in binary mixtures, J. Phys. Chem. B 108 (2004) 13821–13826. [12] H. Li, L.S. Wu, A new approach to estimate ion distribution between the exchanger and solution phases, Soil Sci. Soc. Am. J. 71 (2007) 1694–1698. [13] H. Li, R. Li, H.L. Zhu, L.S. Wu, Influence of electrostatic field from soil particle surfaces on ion adsorption–diffusion, Soil Sci. Soc. Am. J. 74 (2010) 1129–1138. [14] H. Li, L.S. Wu, H.L. Zhu, J. Hou, Ion diffusion in the time-dependent potential of the dynamic electric double layer, J. Phys. Chem. C 113 (2009) 13241–13248. [15] R. Li, H. Li, X.M. Liu, R. Tian, H.L. Zhu, H.L. Xiong, Combined measurement of surface properties of particles and equilibrium parameters of cation exchange from a single kinetic experiment, RSC Adv. 4 (2014) 24671–24678. [16] R. Li, H. Li, C.Y. Xu, X.M. Liu, R. Tian, H.L. Zhu, L.S. Wu, Analytical models for describing cation adsorption/desorption kinetics as considering the electrostatic field from surface charges of particles, Colloids Surf. A 392 (2011) 55–66. [17] R. Li, H. Li, H.L. Zhu, L.S. Wu, Kinetics of cation adsorption on charged soil mineral as strong electrostatic force presence or absence, J. Soils Sediments 11 (2011) 53–61. [18] P. Jungwirth, P.S. Cremer, Beyond hofmeister, Nat. Chem. 6 (2014) 261–263. [19] D.J. Tobias, J.C. Hemminger, Chemistry. Getting specific about specific ion effects, Science 319 (2008) 1197–1198. [20] M. Boström, D. Williams, B. Ninham, Specific ion effects: why DLVO theory fails for biology and colloid systems, Phys. Rev. Lett. 87 (2001) 168103. [21] M. Boström, D. Williams, B. Ninham, Ion specificity of micelles explained by ionic dispersion forces, Langmuir 18 (2002) 6010–6014. [22] M. Boström, D. Williams, B. Ninham, Why the properties of proteins in salt solutions follow a Hofmeister series, Curr. Opin. Colloid Interface Sci. 9 (2004) 48–52. [23] M. Boström, D. Williams, B.W. Ninham, Specific ion effects: why the properties of lysozyme in salt solutions follow a Hofmeister series, Biophys. J. 85 (2003) 686–694. [24] A.P. Dos Santos, Y. Levin, Ion specificity and the theory of stability of colloidal suspensions, Phys. Rev. Lett. 106 (2011) 167801. [25] M.C. Gurau, S.-M. Lim, E.T. Castellana, F. Albertorio, S. Kataoka, P.S. Cremer, On the mechanism of the Hofmeister effect, J. Am. Chem. Soc. 126 (2004) 10522–10523. [26] Y. Levin, A.P. Dos Santos, A. Diehl, Ions at the air-water interface: an end to a hundred-year-old mystery? Phys. Rev. Lett. 103 (2009) 257802. [27] D.F. Parsons, M. Boström, P.L. Nostro, B.W. Ninham, Hofmeister effects: interplay of hydration, nonelectrostatic potentials, and ion size, Phys. Chem. Chem. Phys. 13 (2011) 12352–12367. [28] F.N. Hu, H. Li, X.M. Liu, S. Li, W.Q. Ding, C.Y. Xu, Y. Li, L.H. Zhu, Quantitative characterization of non-classic polarization of cations on clay aggregate stability, PLoS One (2015), http://dx.doi.org/10.1371/journal.pone.0122460. [29] X.M. Liu, H. Li, W. Du, R. Tian, R. Li, X.J. Jiang, Hofmeister effects on cation exchange equilibrium: quantification of ion exchange selectivity, J. Phys. Chem. C 117 (2013) 6245–6251. [30] R. Tian, G. Yang, H. Li, X.D. Gao, X.M. Liu, H.L. Zhu, Y. Tang, Activation energies of colloidal particle aggregation: towards a quantitative characterization of specific ion effects, Phys. Chem. Chem. Phys. 16 (2014) 8828–8836. [31] C.Y. Xu, H. Li, F.N. Hu, S. Li, X.M. Liu, Y. Li, Non-classical polarization of cations increases the stability of clay aggregates: specific ion effects on the stability of aggregates, Eur. J. Soil Sci. 66 (2015) 615–623. [32] R. Tian, G. Yang, C. Zhu, X.M. Liu, H. Li, Specific anion effects for aggregation of colloidal minerals: a joint experimental and theoretical study, J. Phys. Chem. C 119 (2015) 4856–4864. [33] X.D. Gao, H. Li, R. Tian, X.M. Liu, H.L. Zhu, Quantitative characterization of specific ion effects using an effective charge number based on the gouy-chapman model, Acta Phys. Chim. Sin. 30 (2014) 2272–2282. [34] Q.Y. Li, Y. Tang, X.H. He, H. Li, Approach to theoretical estimation of the activation energy of particle aggregation taking ionic nonclassic polarization into account, AIP Adv. 5 (2015) 107218. [35] S. Li, H. Li, F.N. Hu, X.R. Huang, D.T. Xie, J.P. Ni, Effects of strong ionic polarization in the soil electric field on soil particle transport during rainfall, Eur. J. Soil Sci. 66 (2015) 921–929. [36] H. Li, J. Hou, X.M. Liu, R. Li, H.L. Zhu, L.S. Wu, Combined determination of specific surface area and surface charge properties of charged particles from a single experiment, Soil Sci. Soc. Am. J. 75 (2011) 2128–2135. [37] P. Koelsch, P. Viswanath, H. Motschmann, V. Shapovalov, G. Brezesinski, H. Möhwald, D. Horinek, R.R. Netz, K. Giewekemeyer, T. Salditt, Specific ion effects in physicochemical and biological systems: simulations, theory and experiments, Colloids Surf. A 303 (2007) 110–136.