Showcasing research from the group of Prof. Hang Li and Prof. Gang Yang at Chongqing Key Laboratory of Soil Multi-Scale Interfacial Process, Southwest University, China.
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Title: Activation energies of colloidal particle aggregation: towards a quantitative characterization of specific ion effects The aggregation processes of colloidal particles in various alkali ion solutions are monitored in situ, and on the basis of kinetic analysis, the expressions of activation energies in each solution are obtained. In addition to Hofmeister series, activation energies can quantitatively characterize the implicated specific ion effects, and such ion specificities are ascribed mainly to polarization effect. See Gang Yang, Hang Li et al., Phys. Chem. Chem. Phys., 2014, 16, 8828.
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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 8828
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Activation energies of colloidal particle aggregation: towards a quantitative characterization of specific ion effects† Rui Tian, Gang Yang,* Hang Li,* Xiaodan Gao, Xinmin Liu, Hualing Zhu and Ying Tang A quantitative description of specific ion effects is an essential and focused topic in colloidal and biological science. In this work, the dynamic light scattering technique was employed to study the aggregation kinetics of colloidal particles in the various alkali ion solutions with a wide range of concentrations. It indicated that the activation energies could be used to quantitatively characterize specific ion effects, which was supported by the results of effective hydrodynamic diameters, aggregation rates and critical coagulation concentrations. At a given concentration of 25 mmol L1, the activation energies for Li+ are 1.2, 5.7, 28, and 126 times as much for Na+, K+, Rb+, and Cs+, respectively. Most importantly, the activation energy differences between two alkali cation species increase sharply with decrease of electrolyte concentrations, implying the more pronounced specific ion effects at lower concentrations. The dominant role of electrolyte cations during the aggregation of negatively charged
Received 14th November 2013, Accepted 18th February 2014 DOI: 10.1039/c3cp54813a
colloidal particles was confirmed by alternative anions. Among the various theories, only the polarization effect can give a rational interpretation of the above specific ion effects, and this is substantially supported by the presence of strong electric fields from montmorillonite surfaces and its association mainly with electrolyte cations and montmorillonite particles. The classical induction theory, although with inclusion of electric field, requires significant corrections because it predicts an opposite trend to
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the experimentally observed specific ion effects.
1. Introduction Hofmeister or specific ion effects1 control the stability and dynamics of a variety of colloidal and biological systems. A quantitative description of Hofmeister effects is essential to understand the related processes, such as the interfacial tension of electrolyte solutions,2 chemical reaction rate,3,4 protein conformation and stability,5–7 colloidal interaction,6 and even mudslides.8 It is known that the interactions of colloidal suspensions are dependent not only on the surface properties, but also on the composition and concentration of the ambient electrolyte solutions. Electrolytes that regulate the colloidal behavior were often found to exist in dilute concentrations,9 and the Hofmeister series have been respectively determined for the electrolyte cations10–12 and anions.12–16 Recently, there has been enough attention given to specific ion effects.4,7,9,17–20 Many researchers6,10,20–22 claimed specific Chongqing Key Laboratory of Soil Multi-scale Interfacial Process, College of Resources and Environment, Southwest University, 400715, Chongqing, P.R. China. E-mail: [email protected], [email protected]; Fax: +86-023-68250444; Tel: +86-023-68251504 † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c3cp54813a
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ion effects at relatively high electrolyte concentrations, typically biological concentrations, whereas others observed their occurrence at as low as 0.5 mmol L1 during the adsorption of organic acid at mineral oxide–electrolyte interfaces and the ion exchange at charged surfaces.23–26 An issue that arouses general interest is the origin of such specific ion effects. It was found that the dispersion forces acting on the dissolved ions are at the same level as the electrostatic forces;27 in addition, at relatively high electrolyte concentrations (40.1 mol L1), the electrostatic forces should be dominated by the ionic dispersion28,29 that shows a dependence on the ion polarizability and size.11,30 The ionic quantum fluctuation potential that has been neglected before was also proposed to play an important role;29,31 nonetheless, this does not seem convincing as it does not deal with the hydration of ions or surfaces,28 and the surface hydration can be a major factor that decides the colloidal particle interactions.32–34 The electrolyte ions modify the dynamics of colloidal particles through strong interactions with the surrounding water molecules and surfaces, and hence the hydration effect was suggested to be necessary for studying specific ion effects. In the past few years, several approaches have been developed with the aim to clarify how ions interact with water and other ions,14,35 but no satisfactory
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results have been reached yet. This is partially due to the difficulty in accounting for the hydration effect.36 Based on the solvation energy calculations, the significant dispersion contribution to specific ion effects has been emphasized, while the specific water structure and chemical interactions was thought to be negligible.37 For ions with close sizes the solvation energy difference can arise and was ascribed to the larger dispersion interaction for more polarizable ions.38 As a matter of fact, interactions of ions and water were also affected by those of ions and ions as well as ions and surfaces, which further add to the difficulty in their clarification.39,40 Peula-Garcı´a et al.13 found that the inclusion of the hydration effects for ions and surfaces is necessary for investigation of charge inversion, and a subsequent study of chaotropic/kosmotropic ions suggested that the solvation thermodynamics and resulting hydrophobic effect should be responsible for both charge inversion and specific ion effects.41 The activation energy has been considered as a crucial parameter to characterize the interactions of ions and colloidal particles.42 Although extensively investigated, the determination of the activation energy in polydisperse colloidal suspensions remains elusive. Generally, the activation energy of colloidal particles was calculated using the classical Derjaguin–Landau– Verwey–Overbeek (DLVO) theory.43 However the subsequent studies indicated that this theory has not taken into account specific ion effects that may play a considerable role.44–46 A number of corrections have been made, e.g., Lifschitz ion theory of attractive energy,27,47 ion fluctuation energy,48,49 and charge regulation in the electric double layer.50,51 Unfortunately, even with the addition of five adjustable parameters, the DLVO theory often shows serious disagreement with the experimental results,52,53 probably due to the improper accounting of specific ion effects that are ubiquitous in colloidal and biological systems. It thus becomes intractable to obtain the activation energies that are closely related to specific ion effects. With use of multi-angle static and dynamic light scattering experiments, Holthoff et al.54 demonstrated a linear relationship between the aggregate size and initial coagulation rate, offering a possible route to determine the coagulation rate constant. However, the latter study of our group55 showed that this approach did not give accurate results for polydisperse suspensions; instead, a phenomenological linear relationship between the total aggregation rate and electrolyte concentration can be established for polydisperse suspensions. In this work, the time-resolved dynamic light scattering technique was employed to study the aggregation kinetics of montmorillonite colloidal particles within the various alkali ion (M+) solutions (M = Li, Na, K, Rb and Cs) for a wide range of concentrations. The aggregation rates and critical coagulation concentrations were measured and analyzed, and then the activation energies in each of these alkali ion solutions were derived as functions of the alkali ion concentrations. The results thus obtained provide a quantitative characterization of specific ion effects. The various theories were then used to interpret the experimentally observed specific ion effects, and only the polarization effect was found to give a rational explanation, while the classical induction theory,
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although with inclusion of electric fields, failed to account for the polarization effect and the resulting specific ion effects.
2. Materials and methods 2.1.
Material preparation
The clay K+-montmorillonite used in this study is a nanoscale material composed of two tetrahedral Si–O layers sandwiching an octahedral Al–O layer.56 The thickness of montmorillonite particles is approximately 1.0 nm, and the lateral dimension can vary from 30.0 nm to several mm. Isomorphic substitution within the layers generates permanent negative charges. Although the siloxanes (Si–O–Si) are hydrophobic,57 the negative surface charges result in an overall hydrophility for montmorillonite particles that show little affinity for hydrophobic molecules.57,58 The surface area and charge density of montmorillonite particles were respectively determined to be 725.0 m2 g1 and 0.1586 C m2,59,60 see more details in the ESI† (S1 and S2). The K+-montmorillonite suspensions were prepared according to the following procedure. 50.0 g montmorillonite particles and 10 mL 0.1 mol L1 KOH solutions were successively added into a 500 mL beaker, and then diluted with ultrapure water until 500 mL. After 15 min of intensive sonication, the suspension was further diluted to 5 L using ultrapure water. The montmorillonite particles with the effective hydrodynamic diameter o300 nm were extracted and collected using the static sedimentation method,61 which were estimated by the oven drying method to be about 1.88 g L1. As measured by the flame photometer, the concentration of K+ in the bulk suspension is below 0.01 mmol L1 and hence can be neglected. Then these K+-montmorillonite suspensions were diluted 10 times and the pH value was measured to be approximately 8.0. 2.2.
The dynamic light scattering (DLS) measurement
A BI-200SM multi-angle laser light scattering instrument (Brookhaven Instruments Corporation, New York, USA) with a BI-9000AT autocorrelator (Brookhaven Instruments Corporation) was used for measurement of the montmorillonite particle size and effective hydrodynamic diameter that will change during the aggregation process.55,62 The power of the laser device equals 15 mW and is vertically polarized with a wavelength of 532 nm. Note that the montmorillonite particle size was taken directly from DLS measurements, regardless of whether spherical, cuboid, or other irregular shapes. The DLS experiments were performed to measure the aggregation kinetics of montmorillonite particles in the blank solution (i.e., without electrolytes) and then in the various alkali ion solutions of changing concentrations. Experimentally, the suspensions containing montmorillonite particles were subjected to a 2 min sonication and then added into the LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions of different concentrations. The electrolyte concentrations that have been uniformly mixed with montmorillonite particles are equal to 10, 30, 50, 70, 100, 150, 200, 300, and 500 mmol L1 for LiNO3 and NaNO3; 10, 20, 30, 40, 50, 70, 100, 150, and 200 mmol L1 for KNO3; 5, 7, 10, 15,
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20, 30, 40, 50, and 70 mmol L1 for RbNO3 and 3, 5, 7, 10, 15, 20, 30, 40, and 50 mmol L1 for CsNO3, respectively. The density of montmorillonite particles in these alkali ion solutions was determined to be 0.094 g L1. The effective hydrodynamic diameters and the size distributions of montmorillonite particles were recorded every 30 s at a scattering angle of 901. The DLS experiments were carried out at normal temperature (298 0.5 K).
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2.3.
Interaction energies for particle aggregation
Based on the results of Jia et al.,55 the aggregation kinetics of montmorillonite particles in electrolyte solutions can be described by the aggregation rate [TAA rate, ˜vT( f0)]. The TAA rate was expressed as, ð ð ð 1 t0 1 t0 1 t n~ðt; f0 Þdt ¼ vðt; f0 Þdt dt (1) v~T ð f0 Þ ¼ t0 0 t0 0 t 0 where ˜vT ( f0) (nm min1) is the TAA rate from t = 0 to a given time t = t0 (t0 4 0), and the upper limit of t0 can be the ending time of the aggregation process; f0 (mmol L1) is the electrolyte concentration. For the polydisperse colloidal particles, v(t, f0) (nm min1) is the growth rate of the effective diameter for the aggregates in the DLS measurements, whereas ˜v(t, f0) represents the growth rate from t = 0 to an arbitrary time t (t 4 0). Jia et al.55 showed that (a) at relatively low electrolyte concentrations, ˜vT ( f0) vs. f0 was fitted to be a linear function, and (b) at higher electrolyte concentrations, the ˜vT ( f0) value can be considered to be a constant. Accordingly, there is an intersection point of these two linear lines described by (a) and (b), and the concentration at this intersection was defined as the critical coagulation concentration (CCC). The activation energy defines the minimum energy required for the aggregation of colloidal particles. At a given electrolyte concentration, the various alkali cations correspond to different activation energies and the concentration-dependent behaviors of the aggregation processes can be evaluated by means of activation energies. A more detailed description of the activation energy has been given in the ESI† (S3). The activation energy [DE( f0)] and aggregation rate [TAA rate, ˜vT ( f0)] are correlated with the expressions as,55,63 v~T ð f0 Þ ¼ K f0 e v~T ð f0 Þ ¼ K e
DEð f0 Þ RT
DEð f0 Þ RT
concentrations, and the activation energy for the aggregation process can thus be derived with use of eqn (2).
3. Results and discussion 3.1.
Kinetics of particle aggregation
Fig. 1 shows the size distribution of the primary montmorillonite colloidal particles. A large portion of the effective hydrodynamic diameter of montmorillonite particles falls at around 235 nm, albeit the actual distribution is wider, ranging from 100 to 500 nm. The montmorillonite particles with the average effective hydrodynamic diameter o300 nm are extracted and the montmorillonite suspensions are then prepared following the procedure described in Section 2.2. The growth curves of montmorillonite suspensions in LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions are shown in Fig. 2. The growth rates in the effective hydrodynamic diameters of montmorillonite aggregates clearly demonstrate the presence of specific ion effects for these alkali cation species. For example, at an alkali ion concentration of 30 mmol L1 and an aggregation time of 60 min, the average effective hydrodynamic diameters of the montmorillonite aggregates are equal to 332.9, 518.7 (1.6), 2110.0 (6.3), 2588.0 (7.8), and 2819.0 (8.5) nm in LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, respectively. The values in parentheses refer to the ratios of the other alkali cation species vs. Li+. In another example, at an alkali ion concentration of 50 mmol L1 and an aggregation time of 30 min, the average effective hydrodynamic diameters of montmorillonite aggregates change to 633.5, 1461.0 (2.3), 2186.0 (3.5), 2582.0 (4.1), and 2640.0 (4.2) nm in the LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, respectively. It is clear that the aggregation rates of montmorillonite particles are dependent on not only the electrolyte concentration but also the experimental time. When the alkali ion concentration and experimental time are identical for these alkali ion solutions, the average effective hydrodynamic diameters should increase in the order Li+ { Na+ { K+ o Rb+ o Cs+. This is consistent with the trend of the ionic sizes for these alkali cation species. In addition, it has been observed that the aggregation rates are obviously more easily affected for the lighter alkali cation
ð f0 CCCÞ (2) ð f0 CCCÞ
where K = ˜vT (CCC)/CCC ( f0 r CCC) K = ˜vT (CCC)
( f0 Z CCC)
(3)
In eqn (2), R is the gas constant and T is the absolute temperature. Whether below or above CCC, K can be regarded as constant, see the ESI† (S3). The experimental results showed that the TAA rate for the aggregation of montmorillonite particles determined by the DLS measurements represents a function of electrolyte
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Fig. 1
The size distribution of the primary montmorillonite particles.
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Fig. 2 The average effective hydrodynamic diameters of the montmorillonite particle aggregates change with the experimental time in (A) LiNO3, (B) NaNO3, (C) KNO3, (D) RbNO3 and (E) CsNO3 solutions (mmol L1).
species (Li+ B K+) rather than for the heavier alkali cation species (K+ B Cs+). In addition to the aggregation rate, CCC is another important parameter for characterization of the aggregation process. Considering that v(t, f0) = dD(t)/dt, we can arrive to, v~ðt; f0 Þ ¼
ð ð 1 t dDðtÞ 1 DðtÞ DðtÞ Dð0Þ dt ¼ dDðtÞ ¼ t 0 dt t D0 t
(4)
where D(t) (nm) is the average effective hydrodynamic diameter of montmorillonite aggregates at the aggregation time t (t 4 0), and D(0) (nm) corresponds to the average effective hydrodynamic
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diameter of montmorillonite particles at the beginning of the aggregation process (t = 0). Using the experimental data given in Fig. 2, the TAA rates ˜vT ( f0) of montmorillonite particles within the various alkali ion solutions are calculated through a combination of eqn (1) and (4), and their relationships with the alkali ion concentration f0 are displayed in Fig. 3. For each of LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, the TAA rate ˜vT ( f0) increases significantly at relatively low alkali ion concentrations whereas much milder at higher concentrations, and as a result, the TAA rate ˜vT ( f0) of each alkali ion solution can be described by two linear functions for the low and high concentrations,
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Fig. 3 The TAA rates ˜vT(f0) for the aggregation of the montmorillonite particles as a function of the electrolyte concentration f0 in (A) LiNO3, (B) NaNO3, (C) KNO3, (D) RbNO3 and (E) CsNO3 solutions.
respectively. The alkali ion concentration corresponding to the intersection point of these two straight lines is defined as CCC. The CCC values are found to be equal to 277.2, 132.8, 80.3, 31.7, and 27.2 mmol L1 for Li+, Na+, K+, Rb+ and Cs+, respectively, which also exhibits strong specific ion effects. It has also been observed that the aggregation rates of lighter alkali cations are significantly lower, whereas their corresponding CCC values are much larger. As compared to the obvious changes from Li+ to Rb+, the CCC values of Rb+ and Cs+ are rather close to each other, further evidencing that specific ion effects undergo a serious recession with increase of the ionic size.
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As indicated from the TAA rates and CCC values, specific ion effects are apparent for the various alkali cations (Li+, Na+, K+, Rb+ and Cs+). For electrolyte solutions comprising these various alkali cation species, their differences in the activation energies with montmorillonite particles should be the underlying reason responsible for the production of specific ion effects observed above (Scheme S1, ESI†). Thus, in order to give a more in-depth insight regarding specific ion effects in the montmorillonite particle aggregation process, it is necessary to investigate the activation energies in LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, which will be presented in the following Section 3.2.
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3.2.
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Activation energy for particle aggregation
The activation energies for the aggregation of montmorillonite particles within the various alkali ion solutions are calculated using eqn (2). The expressions of the activation energies DE( f0) are given in Table 1 and further plotted in Fig. 4. It clearly shows that at any given alkali ion concentration below CCC, the activation energies DE( f0) of two alkali cation species are significantly different. For example, when the alkali ion concentration equals 25 mmol L1, the activation energies for the aggregation of montmorillonite particles are calculated to be 0.91RT, 0.75RT, 0.16RT, 0.033RT, and 0.0072RT for Li+, Na+, K+, Rb+, and Cs+, respectively. It can be seen that, at this concentration, the activation energy for Li+ is 1.2, 5.7, 28, and 126 times as much as those for Na+, K+, Rb+, and Cs+, respectively. That is, the activation energies for the aggregation of montmorillonite particles increase in the order Li+ c Na+ c K+ 4 Rb+ 4 Cs+ and show good agreement with the above results of specific ion effects on the TAA rates and CCC values. Obviously, the changing trends of the TAA rates and CCC values in the various alkali ion solutions can be satisfactorily interpreted using the activation energies. Li+ results in the lowest aggregation rate and highest CCC value for the aggregation of montmorillonite particles, and this can be attributed to the fact that Li+ produces the highest activation energy for the aggregation process. It can be seen that as the activation energies decrease
Table 1 Expressions of the activation energy DE(f0) for the aggregation of montmorillonite particles in the various alkali ion solutionsa
Alkali cation (CCC) +
Li (277.2) Na+ (132.8) K+ (80.3) Rb+ (31.7) Cs+ (27.2) a
DE( f0) = (for f0 r CCC) RT ln(16.35/f0 RT ln(16.21/f0 RT ln(5.448/f0 RT ln(4.004/f0 RT ln(3.060/f0
(for f0 Z CCC) + + + + +
1.058) 1.125) 1.066) 1.127) 1.115)
RT ln(2.96 RT ln(2.71 RT ln(8.57 RT ln(4.58 RT ln(6.67
104/f0 104/f0 104/f0 104/f0 103/f0
+ + + + +
0.918) 0.964) 0.931) 0.986) 0.819)
Units of DE( f0) and CCC are RT and mmol L1, respectively.
Fig. 4 The activation energies DE(f0) for the aggregation of the montmorillonite particles in the various electrolyte solutions: LiNO3 ( ), NaNO3 ( ), KNO3 ( ), RbNO3 ( ), and CsNO3 ( ).
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from Li+ to Na+, to K+, to Rb+, and finally to Cs+, the corresponding aggregation rates show an increasing trend whereas the CCC values show a decreasing trend. Thus, the determination of activation energies provides us with an effective approach for the quantitative evaluation of specific ion effects. In a similar manner to that in KNO3 solution, the activation energies for the aggregation of montmorillonite particles are determined in KCl solution that also changes with a wide range of concentrations. The results are then collected and compared with those of KNO3 solution, see Fig. S1 (ESI†). It has been found that at any given alkali ion concentration, the activation energies in these two solutions are rather close to each other. Accordingly, the choice of electrolyte anions exhibits only a minor influence on the aggregation kinetics of montmorillonite particles, and it gives substantial support to the assumption that the aggregation of negatively charged montmorillonite particles should be dominated by the electrolyte cations rather than anions. 3.3.
Interpretation of specific ion effects
A number of epidemic theories, such as classical electric double layer, DLVO and hydration effects, have been employed and all of them failed to interpret the experimentally observed specific ion effects, see the details in the ESI† (S4). Then we turn to the polarization effect. The montmorillonite particles possess a charge density of 0.1586 C m2 and generate an electric field of approximately 2.2 108 V m1 at their surfaces.59 This further causes a significant polarization effect to the alkali cations by alteration of their electron clouds. Both non-electrostatic and electrostatic interactions have been included in the polarization effect. Generally, the heavier the alkali cations, the easier alteration of their electron clouds, and this further results in a larger polarization effect; e.g., under a specific electric field, Cs+ is obviously more polarized than Li+. It implies that Cs+ rather than Li+ has a higher probability to appear in close proximity to the charged surface, and as a result, the electric field is more screened in the case of Cs+ solutions, which leads to a lower activation energy for the aggregation of montmorillonite particles. Thus, it clearly shows that the polarization effect should account for the experimentally observed specific ion effects, consistent with the results of the corrected classical electric double layer and DLVO theories by considering the ion difference.64 In addition, it is expected that for a given electric field strength, the alkali cations are relatively few at lower concentrations and hence can be affected to a larger degree, especially for those whose electron clouds are more apt to reconstruct. This results in a more polarization difference for two selected alkali cations (e.g., Cs+ vs. Li+) and coincides exactly with the experimental results. Fig. 5 shows that for two different alkali cations, their activation energy differences for the aggregation of montmorillonite particles increase sharply with the decrease of alkali ion concentrations. That is, the decrease of alkali ion concentrations leads to an obvious increase of specific ion effects for the alkali cation species. These cannot be explained by the ionic hydration or ionic dispersion forces that are assumed to play a significant role and have larger activation
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that closely relates to alkali cations and montmorillonite particles. Accordingly, the polarization effect rather than the others should be responsible for the experimentally observed specific ion effects and thus provides a rational explanation for Hofmeister series for the aggregation of montmorillonite particles in the various alkali ion solutions and more pronounced specific ion effects at lower concentrations. The classical induction energy that considers the electric field is then used, with the aim to give a theoretical account of the polarization effect. It is noteworthy to mention that the classical induction energy is mainly for the qualitative rather than quantitative analysis. The classical induction energy of ion i (–wi*) can be expressed as, ð 1=k i ¼ k w E ðxÞpi ðxÞdx
(5)
0
where 1/k is the Debye length, pi(x) is the dipole moment of cation i and E(x) is the electric field strength. More details of the classical induction theory are given in the ESI† (S5). The classical induction energy differences for two alkali cations are calculated as a function of alkali ion concentrations and those with involvement of Li+ are illustrated in Fig. 6 and Fig. S2 (ESI†). It can be observed that the classical induction energy differences are obviously much less than those of the experimentally determined activation energies, probably because the electric field arising from montmorillonite surface charges is obviously stronger than that from a single charge used in the classical induction energy. Notwithstanding, this does not hamper a qualitative characterization of specific ion effects. Fig. 6 and Fig. S2 (ESI†) indicate that the classical induction energy differences decrease with decrease of alkali ion concentrations,
Fig. 5 The correlations of the activation energy differences [D E(i) D E(j)] between cations i and j with the electrolyte concentration f0.
energy differences at higher electrolyte concentrations.21,22,64,65 The more pronounced specific ion effects at lower electrolyte concentrations have also been observed in other systems, such as the K+/Na+, Mg2+/Na+, K+/Li+, and Na+/Li+ exchange,66 the enzyme activities in LiCl, NaCl and CsCl solutions67 as well as the interfacial water structure on quartz surfaces in alkali, alkaline earth and transition metal chloride solutions.17 As indicated in the ESI† (S3), the activation energy is mainly associated with alkali cations and montmorillonite particles. This gives further support to the significant role played by the polarization effect
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Fig. 6 The correlations of the classical induction energy differences [w(i) w(j)] between cations i and j with the electrolyte concentration f0.
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which is essentially opposite to the change trends observed experimentally (Fig. 5). That is, the classical induction energy that includes the electric field even fails to give a qualitative evaluation of the experimentally observed specific ion effects. Accordingly, substantial improvement should be made in order to correctly describe the polarization effect and predict the resulting specific ion effects.
4. Conclusions Specific ion effects occur everywhere while the quantitative characterization represents a grand challenge, especially in the presence of strong electric fields that exist in a variety of systems such as colloidal particles, proteins and membranes. In this work, the activation energies for the aggregation of colloidal particles have been determined in the various alkali ion solutions with a wide range of concentrations, and thus it provides an effective approach to quantitatively characterize specific ion effects. The expressions of activation energies vs. electrolyte concentrations have been presented for the aggregation of colloidal particles in the various alkali ion solutions. At a given concentration, the activation energies below CCC are significantly different for the various alkali cations and increase in the order of Li+ c Na+ c K+ 4 Rb+ 4 Cs+, consistent with the results of effective hydrodynamic diameters, TAA rates and CCC values. The CCC values for Li+, Na+, K+, Rb+ and Cs+ are equal to 277.0, 133.0, 80.3, 31.7, and 27.2 mmol L1, respectively. All these parameters evidence the presence of strong specific ion effects, and the determination of activation energies provides an effective approach for the quantitative evaluation of specific ion effects. Most importantly, the activation energy differences between two alkali cation species increase sharply with the decrease of electrolyte concentrations and this implies more pronounced specific ion effects at lower concentrations. The minor influence of electrolyte anions confirms the predominant role of cations for the aggregation of negatively charged colloidal particles. The various theories are then used to interpret the experimentally observed specific ion effects, and only the polarization effect can give a rational explanation. However, the classical induction theory that includes the electric field is unable to account for the polarization effect of the surface charges and as a result, predicts an opposite trend to the observed specific ion effects.
Acknowledgements This work was supported by the Major Science and Technology Program for Water Pollution Control and Treatment (2012ZX07104-003), National Basic Research Program of China (2010CB134511), Natural Science Foundation Project of CQ CSTC (2011BA70011), Fundamental Research Funds for the Central Colleges (SWU113049 and XDJK2014C106), and Scientific and Technological Innovation Foundation of Southwest University for Graduates (Grant No. ky2011009).
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Title: Activation energies of colloidal particle aggregation: towards a quantitative characterization of specific ion effects The aggregation processes of colloidal particles in various alkali ion solutions are monitored in situ, and on the basis of kinetic analysis, the expressions of activation energies in each solution are obtained. In addition to Hofmeister series, activation energies can quantitatively characterize the implicated specific ion effects, and such ion specificities are ascribed mainly to polarization effect. See Gang Yang, Hang Li et al., Phys. Chem. Chem. Phys., 2014, 16, 8828.
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Activation energies of colloidal particle aggregation: towards a quantitative characterization of specific ion effects† Rui Tian, Gang Yang,* Hang Li,* Xiaodan Gao, Xinmin Liu, Hualing Zhu and Ying Tang A quantitative description of specific ion effects is an essential and focused topic in colloidal and biological science. In this work, the dynamic light scattering technique was employed to study the aggregation kinetics of colloidal particles in the various alkali ion solutions with a wide range of concentrations. It indicated that the activation energies could be used to quantitatively characterize specific ion effects, which was supported by the results of effective hydrodynamic diameters, aggregation rates and critical coagulation concentrations. At a given concentration of 25 mmol L1, the activation energies for Li+ are 1.2, 5.7, 28, and 126 times as much for Na+, K+, Rb+, and Cs+, respectively. Most importantly, the activation energy differences between two alkali cation species increase sharply with decrease of electrolyte concentrations, implying the more pronounced specific ion effects at lower concentrations. The dominant role of electrolyte cations during the aggregation of negatively charged
Received 14th November 2013, Accepted 18th February 2014 DOI: 10.1039/c3cp54813a
colloidal particles was confirmed by alternative anions. Among the various theories, only the polarization effect can give a rational interpretation of the above specific ion effects, and this is substantially supported by the presence of strong electric fields from montmorillonite surfaces and its association mainly with electrolyte cations and montmorillonite particles. The classical induction theory, although with inclusion of electric field, requires significant corrections because it predicts an opposite trend to
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the experimentally observed specific ion effects.
1. Introduction Hofmeister or specific ion effects1 control the stability and dynamics of a variety of colloidal and biological systems. A quantitative description of Hofmeister effects is essential to understand the related processes, such as the interfacial tension of electrolyte solutions,2 chemical reaction rate,3,4 protein conformation and stability,5–7 colloidal interaction,6 and even mudslides.8 It is known that the interactions of colloidal suspensions are dependent not only on the surface properties, but also on the composition and concentration of the ambient electrolyte solutions. Electrolytes that regulate the colloidal behavior were often found to exist in dilute concentrations,9 and the Hofmeister series have been respectively determined for the electrolyte cations10–12 and anions.12–16 Recently, there has been enough attention given to specific ion effects.4,7,9,17–20 Many researchers6,10,20–22 claimed specific Chongqing Key Laboratory of Soil Multi-scale Interfacial Process, College of Resources and Environment, Southwest University, 400715, Chongqing, P.R. China. E-mail: [email protected], [email protected]; Fax: +86-023-68250444; Tel: +86-023-68251504 † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c3cp54813a
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ion effects at relatively high electrolyte concentrations, typically biological concentrations, whereas others observed their occurrence at as low as 0.5 mmol L1 during the adsorption of organic acid at mineral oxide–electrolyte interfaces and the ion exchange at charged surfaces.23–26 An issue that arouses general interest is the origin of such specific ion effects. It was found that the dispersion forces acting on the dissolved ions are at the same level as the electrostatic forces;27 in addition, at relatively high electrolyte concentrations (40.1 mol L1), the electrostatic forces should be dominated by the ionic dispersion28,29 that shows a dependence on the ion polarizability and size.11,30 The ionic quantum fluctuation potential that has been neglected before was also proposed to play an important role;29,31 nonetheless, this does not seem convincing as it does not deal with the hydration of ions or surfaces,28 and the surface hydration can be a major factor that decides the colloidal particle interactions.32–34 The electrolyte ions modify the dynamics of colloidal particles through strong interactions with the surrounding water molecules and surfaces, and hence the hydration effect was suggested to be necessary for studying specific ion effects. In the past few years, several approaches have been developed with the aim to clarify how ions interact with water and other ions,14,35 but no satisfactory
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results have been reached yet. This is partially due to the difficulty in accounting for the hydration effect.36 Based on the solvation energy calculations, the significant dispersion contribution to specific ion effects has been emphasized, while the specific water structure and chemical interactions was thought to be negligible.37 For ions with close sizes the solvation energy difference can arise and was ascribed to the larger dispersion interaction for more polarizable ions.38 As a matter of fact, interactions of ions and water were also affected by those of ions and ions as well as ions and surfaces, which further add to the difficulty in their clarification.39,40 Peula-Garcı´a et al.13 found that the inclusion of the hydration effects for ions and surfaces is necessary for investigation of charge inversion, and a subsequent study of chaotropic/kosmotropic ions suggested that the solvation thermodynamics and resulting hydrophobic effect should be responsible for both charge inversion and specific ion effects.41 The activation energy has been considered as a crucial parameter to characterize the interactions of ions and colloidal particles.42 Although extensively investigated, the determination of the activation energy in polydisperse colloidal suspensions remains elusive. Generally, the activation energy of colloidal particles was calculated using the classical Derjaguin–Landau– Verwey–Overbeek (DLVO) theory.43 However the subsequent studies indicated that this theory has not taken into account specific ion effects that may play a considerable role.44–46 A number of corrections have been made, e.g., Lifschitz ion theory of attractive energy,27,47 ion fluctuation energy,48,49 and charge regulation in the electric double layer.50,51 Unfortunately, even with the addition of five adjustable parameters, the DLVO theory often shows serious disagreement with the experimental results,52,53 probably due to the improper accounting of specific ion effects that are ubiquitous in colloidal and biological systems. It thus becomes intractable to obtain the activation energies that are closely related to specific ion effects. With use of multi-angle static and dynamic light scattering experiments, Holthoff et al.54 demonstrated a linear relationship between the aggregate size and initial coagulation rate, offering a possible route to determine the coagulation rate constant. However, the latter study of our group55 showed that this approach did not give accurate results for polydisperse suspensions; instead, a phenomenological linear relationship between the total aggregation rate and electrolyte concentration can be established for polydisperse suspensions. In this work, the time-resolved dynamic light scattering technique was employed to study the aggregation kinetics of montmorillonite colloidal particles within the various alkali ion (M+) solutions (M = Li, Na, K, Rb and Cs) for a wide range of concentrations. The aggregation rates and critical coagulation concentrations were measured and analyzed, and then the activation energies in each of these alkali ion solutions were derived as functions of the alkali ion concentrations. The results thus obtained provide a quantitative characterization of specific ion effects. The various theories were then used to interpret the experimentally observed specific ion effects, and only the polarization effect was found to give a rational explanation, while the classical induction theory,
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although with inclusion of electric fields, failed to account for the polarization effect and the resulting specific ion effects.
2. Materials and methods 2.1.
Material preparation
The clay K+-montmorillonite used in this study is a nanoscale material composed of two tetrahedral Si–O layers sandwiching an octahedral Al–O layer.56 The thickness of montmorillonite particles is approximately 1.0 nm, and the lateral dimension can vary from 30.0 nm to several mm. Isomorphic substitution within the layers generates permanent negative charges. Although the siloxanes (Si–O–Si) are hydrophobic,57 the negative surface charges result in an overall hydrophility for montmorillonite particles that show little affinity for hydrophobic molecules.57,58 The surface area and charge density of montmorillonite particles were respectively determined to be 725.0 m2 g1 and 0.1586 C m2,59,60 see more details in the ESI† (S1 and S2). The K+-montmorillonite suspensions were prepared according to the following procedure. 50.0 g montmorillonite particles and 10 mL 0.1 mol L1 KOH solutions were successively added into a 500 mL beaker, and then diluted with ultrapure water until 500 mL. After 15 min of intensive sonication, the suspension was further diluted to 5 L using ultrapure water. The montmorillonite particles with the effective hydrodynamic diameter o300 nm were extracted and collected using the static sedimentation method,61 which were estimated by the oven drying method to be about 1.88 g L1. As measured by the flame photometer, the concentration of K+ in the bulk suspension is below 0.01 mmol L1 and hence can be neglected. Then these K+-montmorillonite suspensions were diluted 10 times and the pH value was measured to be approximately 8.0. 2.2.
The dynamic light scattering (DLS) measurement
A BI-200SM multi-angle laser light scattering instrument (Brookhaven Instruments Corporation, New York, USA) with a BI-9000AT autocorrelator (Brookhaven Instruments Corporation) was used for measurement of the montmorillonite particle size and effective hydrodynamic diameter that will change during the aggregation process.55,62 The power of the laser device equals 15 mW and is vertically polarized with a wavelength of 532 nm. Note that the montmorillonite particle size was taken directly from DLS measurements, regardless of whether spherical, cuboid, or other irregular shapes. The DLS experiments were performed to measure the aggregation kinetics of montmorillonite particles in the blank solution (i.e., without electrolytes) and then in the various alkali ion solutions of changing concentrations. Experimentally, the suspensions containing montmorillonite particles were subjected to a 2 min sonication and then added into the LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions of different concentrations. The electrolyte concentrations that have been uniformly mixed with montmorillonite particles are equal to 10, 30, 50, 70, 100, 150, 200, 300, and 500 mmol L1 for LiNO3 and NaNO3; 10, 20, 30, 40, 50, 70, 100, 150, and 200 mmol L1 for KNO3; 5, 7, 10, 15,
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20, 30, 40, 50, and 70 mmol L1 for RbNO3 and 3, 5, 7, 10, 15, 20, 30, 40, and 50 mmol L1 for CsNO3, respectively. The density of montmorillonite particles in these alkali ion solutions was determined to be 0.094 g L1. The effective hydrodynamic diameters and the size distributions of montmorillonite particles were recorded every 30 s at a scattering angle of 901. The DLS experiments were carried out at normal temperature (298 0.5 K).
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2.3.
Interaction energies for particle aggregation
Based on the results of Jia et al.,55 the aggregation kinetics of montmorillonite particles in electrolyte solutions can be described by the aggregation rate [TAA rate, ˜vT( f0)]. The TAA rate was expressed as, ð ð ð 1 t0 1 t0 1 t n~ðt; f0 Þdt ¼ vðt; f0 Þdt dt (1) v~T ð f0 Þ ¼ t0 0 t0 0 t 0 where ˜vT ( f0) (nm min1) is the TAA rate from t = 0 to a given time t = t0 (t0 4 0), and the upper limit of t0 can be the ending time of the aggregation process; f0 (mmol L1) is the electrolyte concentration. For the polydisperse colloidal particles, v(t, f0) (nm min1) is the growth rate of the effective diameter for the aggregates in the DLS measurements, whereas ˜v(t, f0) represents the growth rate from t = 0 to an arbitrary time t (t 4 0). Jia et al.55 showed that (a) at relatively low electrolyte concentrations, ˜vT ( f0) vs. f0 was fitted to be a linear function, and (b) at higher electrolyte concentrations, the ˜vT ( f0) value can be considered to be a constant. Accordingly, there is an intersection point of these two linear lines described by (a) and (b), and the concentration at this intersection was defined as the critical coagulation concentration (CCC). The activation energy defines the minimum energy required for the aggregation of colloidal particles. At a given electrolyte concentration, the various alkali cations correspond to different activation energies and the concentration-dependent behaviors of the aggregation processes can be evaluated by means of activation energies. A more detailed description of the activation energy has been given in the ESI† (S3). The activation energy [DE( f0)] and aggregation rate [TAA rate, ˜vT ( f0)] are correlated with the expressions as,55,63 v~T ð f0 Þ ¼ K f0 e v~T ð f0 Þ ¼ K e
DEð f0 Þ RT
DEð f0 Þ RT
concentrations, and the activation energy for the aggregation process can thus be derived with use of eqn (2).
3. Results and discussion 3.1.
Kinetics of particle aggregation
Fig. 1 shows the size distribution of the primary montmorillonite colloidal particles. A large portion of the effective hydrodynamic diameter of montmorillonite particles falls at around 235 nm, albeit the actual distribution is wider, ranging from 100 to 500 nm. The montmorillonite particles with the average effective hydrodynamic diameter o300 nm are extracted and the montmorillonite suspensions are then prepared following the procedure described in Section 2.2. The growth curves of montmorillonite suspensions in LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions are shown in Fig. 2. The growth rates in the effective hydrodynamic diameters of montmorillonite aggregates clearly demonstrate the presence of specific ion effects for these alkali cation species. For example, at an alkali ion concentration of 30 mmol L1 and an aggregation time of 60 min, the average effective hydrodynamic diameters of the montmorillonite aggregates are equal to 332.9, 518.7 (1.6), 2110.0 (6.3), 2588.0 (7.8), and 2819.0 (8.5) nm in LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, respectively. The values in parentheses refer to the ratios of the other alkali cation species vs. Li+. In another example, at an alkali ion concentration of 50 mmol L1 and an aggregation time of 30 min, the average effective hydrodynamic diameters of montmorillonite aggregates change to 633.5, 1461.0 (2.3), 2186.0 (3.5), 2582.0 (4.1), and 2640.0 (4.2) nm in the LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, respectively. It is clear that the aggregation rates of montmorillonite particles are dependent on not only the electrolyte concentration but also the experimental time. When the alkali ion concentration and experimental time are identical for these alkali ion solutions, the average effective hydrodynamic diameters should increase in the order Li+ { Na+ { K+ o Rb+ o Cs+. This is consistent with the trend of the ionic sizes for these alkali cation species. In addition, it has been observed that the aggregation rates are obviously more easily affected for the lighter alkali cation
ð f0 CCCÞ (2) ð f0 CCCÞ
where K = ˜vT (CCC)/CCC ( f0 r CCC) K = ˜vT (CCC)
( f0 Z CCC)
(3)
In eqn (2), R is the gas constant and T is the absolute temperature. Whether below or above CCC, K can be regarded as constant, see the ESI† (S3). The experimental results showed that the TAA rate for the aggregation of montmorillonite particles determined by the DLS measurements represents a function of electrolyte
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Fig. 1
The size distribution of the primary montmorillonite particles.
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Fig. 2 The average effective hydrodynamic diameters of the montmorillonite particle aggregates change with the experimental time in (A) LiNO3, (B) NaNO3, (C) KNO3, (D) RbNO3 and (E) CsNO3 solutions (mmol L1).
species (Li+ B K+) rather than for the heavier alkali cation species (K+ B Cs+). In addition to the aggregation rate, CCC is another important parameter for characterization of the aggregation process. Considering that v(t, f0) = dD(t)/dt, we can arrive to, v~ðt; f0 Þ ¼
ð ð 1 t dDðtÞ 1 DðtÞ DðtÞ Dð0Þ dt ¼ dDðtÞ ¼ t 0 dt t D0 t
(4)
where D(t) (nm) is the average effective hydrodynamic diameter of montmorillonite aggregates at the aggregation time t (t 4 0), and D(0) (nm) corresponds to the average effective hydrodynamic
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diameter of montmorillonite particles at the beginning of the aggregation process (t = 0). Using the experimental data given in Fig. 2, the TAA rates ˜vT ( f0) of montmorillonite particles within the various alkali ion solutions are calculated through a combination of eqn (1) and (4), and their relationships with the alkali ion concentration f0 are displayed in Fig. 3. For each of LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, the TAA rate ˜vT ( f0) increases significantly at relatively low alkali ion concentrations whereas much milder at higher concentrations, and as a result, the TAA rate ˜vT ( f0) of each alkali ion solution can be described by two linear functions for the low and high concentrations,
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Fig. 3 The TAA rates ˜vT(f0) for the aggregation of the montmorillonite particles as a function of the electrolyte concentration f0 in (A) LiNO3, (B) NaNO3, (C) KNO3, (D) RbNO3 and (E) CsNO3 solutions.
respectively. The alkali ion concentration corresponding to the intersection point of these two straight lines is defined as CCC. The CCC values are found to be equal to 277.2, 132.8, 80.3, 31.7, and 27.2 mmol L1 for Li+, Na+, K+, Rb+ and Cs+, respectively, which also exhibits strong specific ion effects. It has also been observed that the aggregation rates of lighter alkali cations are significantly lower, whereas their corresponding CCC values are much larger. As compared to the obvious changes from Li+ to Rb+, the CCC values of Rb+ and Cs+ are rather close to each other, further evidencing that specific ion effects undergo a serious recession with increase of the ionic size.
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As indicated from the TAA rates and CCC values, specific ion effects are apparent for the various alkali cations (Li+, Na+, K+, Rb+ and Cs+). For electrolyte solutions comprising these various alkali cation species, their differences in the activation energies with montmorillonite particles should be the underlying reason responsible for the production of specific ion effects observed above (Scheme S1, ESI†). Thus, in order to give a more in-depth insight regarding specific ion effects in the montmorillonite particle aggregation process, it is necessary to investigate the activation energies in LiNO3, NaNO3, KNO3, RbNO3, and CsNO3 solutions, which will be presented in the following Section 3.2.
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3.2.
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Activation energy for particle aggregation
The activation energies for the aggregation of montmorillonite particles within the various alkali ion solutions are calculated using eqn (2). The expressions of the activation energies DE( f0) are given in Table 1 and further plotted in Fig. 4. It clearly shows that at any given alkali ion concentration below CCC, the activation energies DE( f0) of two alkali cation species are significantly different. For example, when the alkali ion concentration equals 25 mmol L1, the activation energies for the aggregation of montmorillonite particles are calculated to be 0.91RT, 0.75RT, 0.16RT, 0.033RT, and 0.0072RT for Li+, Na+, K+, Rb+, and Cs+, respectively. It can be seen that, at this concentration, the activation energy for Li+ is 1.2, 5.7, 28, and 126 times as much as those for Na+, K+, Rb+, and Cs+, respectively. That is, the activation energies for the aggregation of montmorillonite particles increase in the order Li+ c Na+ c K+ 4 Rb+ 4 Cs+ and show good agreement with the above results of specific ion effects on the TAA rates and CCC values. Obviously, the changing trends of the TAA rates and CCC values in the various alkali ion solutions can be satisfactorily interpreted using the activation energies. Li+ results in the lowest aggregation rate and highest CCC value for the aggregation of montmorillonite particles, and this can be attributed to the fact that Li+ produces the highest activation energy for the aggregation process. It can be seen that as the activation energies decrease
Table 1 Expressions of the activation energy DE(f0) for the aggregation of montmorillonite particles in the various alkali ion solutionsa
Alkali cation (CCC) +
Li (277.2) Na+ (132.8) K+ (80.3) Rb+ (31.7) Cs+ (27.2) a
DE( f0) = (for f0 r CCC) RT ln(16.35/f0 RT ln(16.21/f0 RT ln(5.448/f0 RT ln(4.004/f0 RT ln(3.060/f0
(for f0 Z CCC) + + + + +
1.058) 1.125) 1.066) 1.127) 1.115)
RT ln(2.96 RT ln(2.71 RT ln(8.57 RT ln(4.58 RT ln(6.67
104/f0 104/f0 104/f0 104/f0 103/f0
+ + + + +
0.918) 0.964) 0.931) 0.986) 0.819)
Units of DE( f0) and CCC are RT and mmol L1, respectively.
Fig. 4 The activation energies DE(f0) for the aggregation of the montmorillonite particles in the various electrolyte solutions: LiNO3 ( ), NaNO3 ( ), KNO3 ( ), RbNO3 ( ), and CsNO3 ( ).
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from Li+ to Na+, to K+, to Rb+, and finally to Cs+, the corresponding aggregation rates show an increasing trend whereas the CCC values show a decreasing trend. Thus, the determination of activation energies provides us with an effective approach for the quantitative evaluation of specific ion effects. In a similar manner to that in KNO3 solution, the activation energies for the aggregation of montmorillonite particles are determined in KCl solution that also changes with a wide range of concentrations. The results are then collected and compared with those of KNO3 solution, see Fig. S1 (ESI†). It has been found that at any given alkali ion concentration, the activation energies in these two solutions are rather close to each other. Accordingly, the choice of electrolyte anions exhibits only a minor influence on the aggregation kinetics of montmorillonite particles, and it gives substantial support to the assumption that the aggregation of negatively charged montmorillonite particles should be dominated by the electrolyte cations rather than anions. 3.3.
Interpretation of specific ion effects
A number of epidemic theories, such as classical electric double layer, DLVO and hydration effects, have been employed and all of them failed to interpret the experimentally observed specific ion effects, see the details in the ESI† (S4). Then we turn to the polarization effect. The montmorillonite particles possess a charge density of 0.1586 C m2 and generate an electric field of approximately 2.2 108 V m1 at their surfaces.59 This further causes a significant polarization effect to the alkali cations by alteration of their electron clouds. Both non-electrostatic and electrostatic interactions have been included in the polarization effect. Generally, the heavier the alkali cations, the easier alteration of their electron clouds, and this further results in a larger polarization effect; e.g., under a specific electric field, Cs+ is obviously more polarized than Li+. It implies that Cs+ rather than Li+ has a higher probability to appear in close proximity to the charged surface, and as a result, the electric field is more screened in the case of Cs+ solutions, which leads to a lower activation energy for the aggregation of montmorillonite particles. Thus, it clearly shows that the polarization effect should account for the experimentally observed specific ion effects, consistent with the results of the corrected classical electric double layer and DLVO theories by considering the ion difference.64 In addition, it is expected that for a given electric field strength, the alkali cations are relatively few at lower concentrations and hence can be affected to a larger degree, especially for those whose electron clouds are more apt to reconstruct. This results in a more polarization difference for two selected alkali cations (e.g., Cs+ vs. Li+) and coincides exactly with the experimental results. Fig. 5 shows that for two different alkali cations, their activation energy differences for the aggregation of montmorillonite particles increase sharply with the decrease of alkali ion concentrations. That is, the decrease of alkali ion concentrations leads to an obvious increase of specific ion effects for the alkali cation species. These cannot be explained by the ionic hydration or ionic dispersion forces that are assumed to play a significant role and have larger activation
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that closely relates to alkali cations and montmorillonite particles. Accordingly, the polarization effect rather than the others should be responsible for the experimentally observed specific ion effects and thus provides a rational explanation for Hofmeister series for the aggregation of montmorillonite particles in the various alkali ion solutions and more pronounced specific ion effects at lower concentrations. The classical induction energy that considers the electric field is then used, with the aim to give a theoretical account of the polarization effect. It is noteworthy to mention that the classical induction energy is mainly for the qualitative rather than quantitative analysis. The classical induction energy of ion i (–wi*) can be expressed as, ð 1=k i ¼ k w E ðxÞpi ðxÞdx
(5)
0
where 1/k is the Debye length, pi(x) is the dipole moment of cation i and E(x) is the electric field strength. More details of the classical induction theory are given in the ESI† (S5). The classical induction energy differences for two alkali cations are calculated as a function of alkali ion concentrations and those with involvement of Li+ are illustrated in Fig. 6 and Fig. S2 (ESI†). It can be observed that the classical induction energy differences are obviously much less than those of the experimentally determined activation energies, probably because the electric field arising from montmorillonite surface charges is obviously stronger than that from a single charge used in the classical induction energy. Notwithstanding, this does not hamper a qualitative characterization of specific ion effects. Fig. 6 and Fig. S2 (ESI†) indicate that the classical induction energy differences decrease with decrease of alkali ion concentrations,
Fig. 5 The correlations of the activation energy differences [D E(i) D E(j)] between cations i and j with the electrolyte concentration f0.
energy differences at higher electrolyte concentrations.21,22,64,65 The more pronounced specific ion effects at lower electrolyte concentrations have also been observed in other systems, such as the K+/Na+, Mg2+/Na+, K+/Li+, and Na+/Li+ exchange,66 the enzyme activities in LiCl, NaCl and CsCl solutions67 as well as the interfacial water structure on quartz surfaces in alkali, alkaline earth and transition metal chloride solutions.17 As indicated in the ESI† (S3), the activation energy is mainly associated with alkali cations and montmorillonite particles. This gives further support to the significant role played by the polarization effect
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Fig. 6 The correlations of the classical induction energy differences [w(i) w(j)] between cations i and j with the electrolyte concentration f0.
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which is essentially opposite to the change trends observed experimentally (Fig. 5). That is, the classical induction energy that includes the electric field even fails to give a qualitative evaluation of the experimentally observed specific ion effects. Accordingly, substantial improvement should be made in order to correctly describe the polarization effect and predict the resulting specific ion effects.
4. Conclusions Specific ion effects occur everywhere while the quantitative characterization represents a grand challenge, especially in the presence of strong electric fields that exist in a variety of systems such as colloidal particles, proteins and membranes. In this work, the activation energies for the aggregation of colloidal particles have been determined in the various alkali ion solutions with a wide range of concentrations, and thus it provides an effective approach to quantitatively characterize specific ion effects. The expressions of activation energies vs. electrolyte concentrations have been presented for the aggregation of colloidal particles in the various alkali ion solutions. At a given concentration, the activation energies below CCC are significantly different for the various alkali cations and increase in the order of Li+ c Na+ c K+ 4 Rb+ 4 Cs+, consistent with the results of effective hydrodynamic diameters, TAA rates and CCC values. The CCC values for Li+, Na+, K+, Rb+ and Cs+ are equal to 277.0, 133.0, 80.3, 31.7, and 27.2 mmol L1, respectively. All these parameters evidence the presence of strong specific ion effects, and the determination of activation energies provides an effective approach for the quantitative evaluation of specific ion effects. Most importantly, the activation energy differences between two alkali cation species increase sharply with the decrease of electrolyte concentrations and this implies more pronounced specific ion effects at lower concentrations. The minor influence of electrolyte anions confirms the predominant role of cations for the aggregation of negatively charged colloidal particles. The various theories are then used to interpret the experimentally observed specific ion effects, and only the polarization effect can give a rational explanation. However, the classical induction theory that includes the electric field is unable to account for the polarization effect of the surface charges and as a result, predicts an opposite trend to the observed specific ion effects.
Acknowledgements This work was supported by the Major Science and Technology Program for Water Pollution Control and Treatment (2012ZX07104-003), National Basic Research Program of China (2010CB134511), Natural Science Foundation Project of CQ CSTC (2011BA70011), Fundamental Research Funds for the Central Colleges (SWU113049 and XDJK2014C106), and Scientific and Technological Innovation Foundation of Southwest University for Graduates (Grant No. ky2011009).
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