Experimental Observation of the Ion–Ion Correlation Effects on Charge

Article pubs.acs.org/Langmuir

Experimental Observation of the Ion−Ion Correlation Effects on Charge Inversion and Strong Adhesion between Mica Surfaces in Aqueous Electrolyte Solutions Qiyan Tan, Gutian Zhao, Yinghua Qiu, Yajing Kan, Zhonghua Ni, and Yunfei Chen* School of Mechanical Engineering and Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, Southeast University, Nanjing 211189, People’s Republic of China ABSTRACT: Direct force measurements between two mica surfaces in aqueous electrolyte solutions over broad ranges of LaCl3 concentrations and pH values were carried out with a surface forces apparatus. Charge inversion on mica surfaces is detected once the LaCl3 concentration reaches a critical value. With the continual increase of LaCl3 concentrations, the mica surface will be overscreened by the counterions. It is demonstrated that the two mica surfaces may experience the jump-in contact even at high LaCl3 concentrations, which is seldom seen in monovalent salt solutions. The strong adhesion cannot be attributed to the van der Waals force alone, but should include the ion−ion correlation forces. Through adjusting the pH values in LaCl3 solutions, the ion−ion correlation force can be evaluated quantitatively. These results provide important insight into the fundamental understanding in the role of ion−ion correlations in ion screening mechanism and interactions between charged objects.

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INTRODUCTION When a solid surface is in contact with an electrolyte solution, an electrical double layer (EDL) is formed as a result of the interaction between the electrolyte solution and the surface. Repulsion arises between the two surfaces when two such surfaces approach close in electrolyte solution due to the overlap of EDLs. The interaction is strongly affected by the screening counterions and the net charges of surfaces. Understanding the screening mechanism of counterions and interactions between charged surfaces in electrolyte solution is of fundamental importance in a broad range of phenomena such as in colloid science,1 nanofluidics,2−5 and biophysics.6,7 Colloid stability, for example, is determined by the surface interactions among charged colloidal particles. The transportation of solvents and solutes in nanofluidic systems is influenced by their interactions with channel walls. For nanopore DNA sequencing and single-molecule sensors, the interactions among biomolecules (DNA, proteins), ions, and walls of solid-state nanopores are of paramount importance in understanding and exploiting the translocation mechanism of biomolecules through nanopores. The basic paradigm for ion screening a charged surface in electrolyte solution divides the screening ions into two layers: the Stern layer and the diffuse layer. Ions bind to the surface in the Stern layer and decay exponentially in density with distance far from the surface in the diffuse layer. The distribution of ions and potential in the diffuse layer can be predicted by the Poisson−Boltzmann (PB) equation, which considers ions as pointlike charges but neglects the ion size, specificity, and ion− ion correlations. This theory successfully predicted ion profiles close to charged surfaces and the surface interactions resulted © 2014 American Chemical Society

from EDLs, particularly applying to weakly charged surfaces in monovalent electrolyte solutions. The repulsive interaction between two EDLs combined with the van der Waals interaction form the celebrated Derjaguin−Landau−Verwey− Overbeek (DLVO) theory,8 which lays the foundation for explaining colloidal stability. However, if multivalent ions are present in an electrolyte solution, a counterintuitive phenomenon called charge inversion or overcharge emerges, which is attributed to that a charged surface binds strongly so many counterions in aqueous solution that the net surface charge inverts sign. Different mechanisms about charge inversion have been put forward over the years. The specific adsorption of ions is recommended in the colloid and interface science community. This mechanism necessarily depends on the chemical structures of the substances involved.9 However, this mechanism is challenged by computer simulation and experimental results that overcharge can arise even in the absence of any chemical attraction between ions and surfaces.10,11 Moreover, ion−ion correlations, which are neglected in the mean field approximations, have been suggested to underlie the charge inversion and like-charge attraction. The correlations will become significant when the electrostatic interaction energy between neighboring ions is larger than the thermal energy. The driving force for the extra adsorption of ions can mainly attribute to electrostatic many-body correlations.12−14 A remarkable achievement of ion correlation theory in recent years has Received: June 21, 2014 Revised: August 20, 2014 Published: August 21, 2014 10845

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attributed to conventional van der Waals force alone. The ion−ion correlation may be behind. 32 Thus, ion−ion correlation between the surfaces may play an important role in the additional attraction mechanism in multivalent aqueous solutions. Adhesion measurement between surfaces can provide an insightful investigation for ion−ion correlation and charge inversion in multivalent solutions. Recent studies shed light on charge inversion and ion−ion correlation in the presence of multivalent ions, but this complicated question remains a challenging topic and still lacks a deep physical understanding. In the present work, SFA was used to investigate the interaction and adhesion forces between mica surfaces in LaCl3 solutions over a board range of LaCl3 concentrations and pH values. We presented the experimental results on charge inversion and strong adhesion mediated by multivalent ions. The analytical results from the ion−ion correlation model were provided. Those theoretical predictions are consistent well with the experimental data. Furthermore, the ion−ion correlation forces can be quantitatively evaluated through adjusting the pH values of the salt solutions. In this way, the effects of ion−ion correlation on charge inversion and like-charge attraction between two charged objects with the same sign can be explained.

been made by considering strong electrostatic coupling between ions in multivalent salt solutions. Rouzina and Bloomfield triggered the work and found that significant correlation occurred when the counterion distributions have a pseudo-two-dimensional character.15 The strong correlations can cause surface charge inversion and attraction between EDLs. This theory was extended by these authors,10,16−19 and a new proposal was provided that multivalent ions at highly charged surface form a two-dimensional strongly correlated liquid (SCL), in which the short order of ions is similar to that of a Wigner crystal (WC). The cohesive energy of a SCL can lead to strong additional attraction of ions to the surface. A new boundary condition for PB theory is provided, based on which the ion distribution can be described by the classical PB equation even in the presence of multivalent ions. Later, Netz formalized an ion−ion electrostatic coupling theory, and gave one coupling parameter to describe the coupling strength between ions.20 The ion distribution follows the PB prediction when the coupling strength is small; otherwise, the ion distribution should be described by the SCL theory. Charge inversion has also been directly observed by experiments. It has been shown that a charged silica surface inverts charge sign in trivalent and quadrivalent electrolyte solutions.11,21 These observations confirm the theoretical proposals that the dominant driving mechanism behind charge inversion is spatial correlations among counterions. Force measurements between mica surfaces immersed in LaCl3 solutions were reported by Pashley,22 using the surface forces apparatus (SFA) technique. They demonstrated that the mica surface reversed its sign and became positively charged due to over adsorption of La3+ ions in a 10−5 M LaCl3 solution. They described this phenomenon using a simple ion-exchange adsorption model, but neglected the correlations between La3+ ions. With the help of X-ray reflectivity, Schlossman et al. observed the effect of ion−ion correlation strength from weak to strong on the ion distribution. Their experimental results confirmed that the ion distribution in the EDL for large coupling strengths does not obey the PB theory, but follows the prediction of ion correlation models.23 For high concentrations of divalent ions, charge inversion is also observed by streaming currents, and it is suppressed or even canceled by the addition of monovalent ions.24 The measured ζ potentials of charged surfaces in Co(NH3)6Cl3 solutions were well consistent with the SCL theoretic predictions.25 Besides, other correlation effects, such as transverse correlations,26 that is, correlations between interfacial charges and counterions, may also play a great role in the generation of charge inversion. In biological systems, overcharge of peptide and reentrant condensation of proteins are also directly observed by different experimental methods,27−29 and the interaction among multivalent counterions and the biomolecules is the underlying origin. In addition, the ion−ion correlation may be the cause of the strong adhesion between charged surfaces in multivalent electrolyte solutions, which was attributed to ion affinity and its bridging mechanism previously.22 With divalent counterions (e.g., Ca2+), the electric double layer interactions between two mica surfaces can become attractive below about 2 nm.30 The adhesion force of silica surfaces in trivalent cation solutions is greater than that in mono- and divalent cation solutions at the same ionic strength.31 Two surfaces each bearing randomly distributed positive and negative charge patches, which are overall close to neutral respectively, may also experience longranged strong attraction. These observations cannot be

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EXPERIMENTAL SECTION

Atomically smooth mica sheets with thickness of 3−5 μm were manually cleaved from the muscovite ruby mica of grade 1 in a laminar cabinet, and melt cut using a Pt wire into pieces of about 1 cm2 in a standard way.33 The cut mica pieces were deposited on a thicker, freshly cleaved mica block for further handling. The mica pieces were then coated with a silver film of 50 nm thickness in a physical vapor deposition system. The silvered mica pieces were finally lifted off and glued, silver down, onto two cylindrical silica disks using epoxy resin glue (Shell, EPON 1004F). The two silica disks were then mounted in a surface forces apparatus box facing each other in a crossed-cylinder configuration, equivalent to the geometry of a sphere over a flat. Ultrapure water was obtained from a water purification system (Ulupure Corporation, China). The specific resistivity of the water was higher than 18.25 MΩ·cm, and the pH was in the range 5.2−5.8 due to the dissolution of CO2. Solutions were prepared with the purified water and high purity chemical reagent LaCl3 (99.999%, from SigmaAldrich). The pH values of solutions can be adjusted by titration with NaOH and HCl solution (from Sigma-Aldrich). All LaCl3 solutions were filtered and degassed with a 0.2 μm membrane (from Corning). All chemicals were used as received. The interactions between two mica surfaces were measured by the SFA 2000 system from SURFORCE, LLC at Santa Barbara,8 as shown in Figure 1. With the SFA technique, the two freshly cleaved mica surfaces glued on each disk immersed in a liquid are brought toward each other in a highly controlled way. The approach process of the two mica surfaces is controlled by use of a three-stage mechanism of increasing sensitivity with a normal resolution at 0.1 nm. In the approach process, the surfaces are visualized optically with multiple beam interferometry (MBI) using “fringes of equal chromatic order” (FECO). From the positions of the colored FECO fringes seen in the spectrogram, the distance between the two atomically smooth mica surfaces can be measured at the angstrom resolution level. The sharpness of FECO can also reveal the interaction geometry. The interaction forces between two mica surfaces are measured from the deflection of a double cantilever spring, the stiffness of which can be calibrated by a vertical traveling microscope. The zero separation between two mica surfaces was first measured by bringing them into adhesive contact in dry nitrogen atmosphere. Then, the SFA box was filled with ultrapure water until the two mica surfaces were immersed. The interaction force between the two mica surfaces immersed in ultrapure water as a function of the distance can be measured through bringing the two mica surfaces to approach each 10846

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Figure 1. Schematic picture of the SFA 2000 setup. other at various rates. Only experiments free of contaminants and with the presence of sharp FECO were continued. Following the above measurement, the water in the chamber was replaced by LaCl3 solutions. The interaction forces were measured after 20 min equilibration in solutions. Two to four approach−separation cycles were repeated in measuring the force laws between the two mica surfaces with different LaCl3 concentrations at approaching speeds ranging from 2 to 5 nm·s−1. The force measurements in LaCl3 solutions started from low to high LaCl3 concentrations. All of the force measurements including that in dry nitrogen, ultrapure water, and various LaCl3 solutions are expected to be carried out on the same pair of mica sheets. A series of measurements were carried out with different pairs of mica sheets to check the repeatability and precision of the force measurements. To prevent contamination and preserve cleanliness, the lifetime of each pair of mica sheets is set at 72 h. All experiments were performed at a controlled temperature of 22.0 ± 0.1 °C.

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Figure 2. Measured forces as a function of the distance between two mica surfaces immersed in different LaCl3 concentration solutions.

RESULTS AND DISCUSSION Ion−Ion Correlation Effects on Charge Inversion. Figure 2 shows the measured interaction forces versus distance D between two mica surfaces for LaCl3 solutions at concentrations of 10−7−10−2 M. The interaction forces were normalized by mean radius of the curved mica surface R. The value F/R is equal to 2πE, based on the Derjaguin approximation, where E is the corresponding surface energy per unit area for two flat parallel surfaces. A general trend can be found from the force profiles. With the LaCl3 solution increasing from very low to high molar concentrations, the total repulsion interaction is observed to decrease, reach to zero, and then grow again. The repulsion observed at low LaCl3 concentrations can be interpreted as the overlap of EDLs based on the DLVO theory. It is postulated from the force profile that the surface charges on the mica surface are completely neutralized by the counterions so that no measurable repulsion can be detected at a critical concentration. The reappearance of repulsion at high LaCl3 concentrations suggests that the mica surface has reversed its sign and become positively charged. Based on the force profiles, a critical LaCl3 concentration ρc between 10−5 and 10−6 M is estimated that corresponds to the zero surface potential, which leads to the disappearance of the interaction force between the two mica surfaces. The charge inversion can be viewed as the continuous adsorption of additional La3+ ions after mica surfaces are neutralized at a critical LaCl3 concentration ρc. Thus, the observed repulsion above the critical concentration ρc can be ascribed to an electrostatic interaction between EDLs of

positively charged surfaces. This indicates that the negative charged mica surfaces become positive once the LaCl 3 concentrations are higher than the critical concentration ρc. The charge inversion cannot be explained from the classical PB equations that are based on the mean field approximation. In the mean field approximation, the counterions at most neutralize the surface charges but never over screen the charged surface. The charge inversion is attributed to the strong binding of counterions on the charged surface due to the formation of SCL. If we take the SCL as a new boundary for the electrical double layer structure, the ions away from the SCL are assumed to obey the Boltzmann equation. In this way, the effective surface potential φ0 can be fitted from the measured long-range interaction force laws. Assuming the SCL constituting the new boundary for the diffusion layer, the potential φ distribution in LaCl3 solutions far away from the SCL can be expressed as8 kBTκ 2 eφ / kBT d2φ = − e−3eφ / kBT ) (e 4e dx 2

(1)

Here εε0 is the solvent dielectric constant, e is the electron charge, ρbulk is the bulk concentration (in molecules per m3), kB is the Boltzmann constant, and T is the temperature. The inverse Debye screening length κ−1 is defined by κ2 = (12ρbulke2)/(εε0kBT). 10847

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Given the potential, the uniform pressure Π across the gap can be expressed as34 Π = kBTρbulk (e−3eφm / kBT + 3eeφm / kBT − 4)

(2)

where φm is the potential at the midplane between two mica surfaces. The effective surface potential can be obtained by fitting the measured long-range interaction forces as shown in Figure 3.

Figure 4. Fitted and correlation theory predicted surface potentials of mica surfaces immersed in LaCl3 solution. Error bars are obtained from several different measurements.

where Γ is a measure of the coupling energy relative to kBT that each counterion gains upon the formation of a SCL, which can be defined as Figure 3. Interaction forces between two mica surfaces immersed in LaCl3 solutions in log scale. Dashed lines give the calculated forces according the DLVO theory assuming a constant surface potential.

Γ=

ρ0 = (3)

(5)

⎛ μ ⎞ n exp⎜ − c ⎟ w ⎝ kBT ⎠

(6)

where ρ0 is the concentration at D = l/4, where ions start to follow the PB equation. n = (σmica + σ*)/Ze is the twodimensional concentration of La3+ ions at the SCL, w is the length of the water molecule order size (here w = 0.3 nm was used),19 and as described above the chemical potential μc can be obtained by eq 4. Alternatively, the ion distribution ρ0 on the interface between the SCL and the diffuse layer at D = l/4, can also be calculated from the PB equations, which is read as

where σmica is the charge density of bare mica surface, Z is the valence of multivalent ion, rion is the ion radius (0.104 nm for La3+ ion), e is the charge of an electron, kBT is the thermal energy, and μc is the ion correlation chemical potential that can be approximated by the value of a WC μc = − kBT(1.65Γ − 2.61Γ1/4 + 0.26ln Γ + 1.95)

4kBTεε0

where ε and ε0 are the permittivity of solution and free space, respectively. The dependence of ρc on surface charge, dielectric constant was demonstrated by Besteman et al.11 Trivalent or quadrivalent solutions can be described by eq 3 properly. For mica surfaces in LaCl3 solution, Z = 3, σmica = 0.5 e/nm2, and ε = 78.4; the value of Γ is 5.4. From this model, the predicted critical concentration ρc is at 8.78 × 10−6 M, which falls into the range of experimental measurement. The mica surface potential changes to positive sign as the LaCl3 concentration above ρc, that is, charge inversion of mica surface occurs. In addition, we also tried to predict the surface potential from the SCL theory.10 Based on SCL theory, the La3+ ions in the layer of SCL distribute in a WC structure, which can be deduced from the chemical potential. The thickness of the SCL is estimated to be l/4. It is believed that the ion correlation effect becomes very weak at the position with D = l/4 away from the solid surface [10, 16, 19]. Where l = Z2λb, λb is the Bjerrum length. Z is the valence of the counterions. Away from the layer of SCL, the ion distribution follows the PB equation. The ion distribution on the interface between the SCL and the diffuse layer at D = l/4 can be deduced from the chemical potential in the SCL, which is read as19

The DLVO force can be calculated from the summation of the double-layer force from eq 2 and the van der Waals forces with a Hamaker constant of 2.2 × 10−20 J between mica surfaces in LaCl3 concentrations. A reasonable fit between the calculated and measured forces can be found at a concentration of 10−7 M. At high LaCl3 concentrations, the fitted Debye lengths agree within 15% with those expected from the known solution concentrations. As seen from Figure 3, the interaction forces in the diffuse layer decay approximately exponentially with the distance. The fitted surface potentials are presented in Figure 4. It demonstrates that the charge of mica surfaces changes its sign from 10−6 to 10−5 M, which indicates charge inversion occurred. In the above fitting procedure, the microstructure of the SCL is not discussed. In fact, the charge inversion can also be explained from the SCL theory, in which a strongly correlated liquid with a WC structure10,11,24 is assumed to form near the mica surface due to ion−ion correlations. From this model, the effective surface potential can also be predicted. From the SCL theory, the charge inversion occurs at a critical concentrations ρc, which can be expressed as ⎛ μ ⎞ σmica ρc = exp⎜ c ⎟ 2rionZe ⎝ kBT ⎠

|σmicaZ3e 3/π |

(4) 10848

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3+ ρ03 + = ρbulk exp( −3eφ0 /kBT )

(7)

− ρ0− = ρbulk exp(eφ0 /kBT )

(8)

interaction below about 3 nm. The strong repulsion between mica surfaces was dominated by hydrated La3+ ions at short distance. The final contact positions shift to at about 1.2−1.4 nm separation, which is close to the thickness of two layer hydrated La3+ ions. This indicates that a monolayer of hydrated La3+ ions is present on each mica surface. This monolayer cannot be squeezed out easily even the normal load is up to 40 mN·m−1. Increasing the LaCl3 concentration, the short-range repulsion became stronger and the long-range interactions disappeared. Meanwhile, hydration force was greatly enhanced due to the increase of the LaCl3 concentrations. At short separations, it is the hydration and the steric forces dominate the interactions between two mica surfaces. With the increase of the external load, hydrated ions will be squeezed out and the ion layering structures can be clearly observed at concentration of 0.496 and 1.894 M, which occurred at the separation about 5.7 and 6.8 nm, respectively. The contact positions, with normal load of 40 mN·m−1, shift out at about 1.8−2.0 nm and 2.4−2.6 nm separations, respectively. We can estimate that there are three to four layers of hydrated La3+ ions confined between the two mica surfaces. The repulsion forces are apparently caused by adsorption of La3+ ions and hydrated La3+ ions at the mica surface. The hydrated La3+ ions combined with its volume effects strongly enhanced the short repulsion at high concentrations. The hydrated La3+ ions correlations and ordering are the origin of ion layering at high concentrations.37 Direct Measurement of Ion−Ion Correlation Forces. The interesting finding is that the two mica surfaces jump into contact at short distance even when the LaCl3 concentration is as high as 10−2 M as shown in Figure 2, which is different from the observations for two mica surfaces in monovalent salt solutions. For examples, when two mica surfaces are immersed in NaCl solutions, the hydration force suppresses the van der Waals force at the separation below 4 nm for NaCl concentration exceeding 10−3 M, which results in the disappearance of the jump in contact of the two mica surfaces.38−42 It is speculated that additional attraction mechanism may underlie the sudden jump-into contact of mica surfaces in LaCl3 solutions at short distance. The La3+ ions bridge binding mechanism was assumed by Pashley.22 The La3+ ions remain adsorbed on mica surface and lose their water molecules as the facing mica surface approached, which results in the La3+ ions to bridge the two mica surfaces together. However, the bridge binding cation mechanism is in very shortrange that usually is below about 0.5 nm. In contrast, the mica sheets jump into contact at a separation even up to 6 nm in LaCl3 solutions, which is also longer than the 4 nm jump in contact position in ultrapure water. Considering that many La3+ ions will be accumulated on the mica surfaces at high concentrations, these ions strongly couple and form the strong correlated liquid. The cohesive energy of this liquid leads to adsorbing excessive La3+ ions and results in the charge inversion of mica surface. In this case, the interactions between such two mica surfaces cannot be described by the repulsive osmotic pressure of counterions at small separations. The correlation between La3+ ions will play a great role in the interactions. Based on the SCL theory, La3+ ions are highly separated from each other when they are attracted near mica surfaces. Once the separation between the two mica surfaces is small enough, the layered La3+ ions tend to form an interlocking pattern in equilibrium.15 The mica−mica system in our experiments may be thought of as a collection of laterally frozen correlation cells, each consisting of a single La3+

where φ0 is the surface potential on the interface between the − SCL and the diffuse layer, ρ3+ bulk and ρbulk represent the 3+ − concentrations of La ions and Cl ions in bulk solution, − respectively, and ρ3+ 0 and ρ0 stand for the concentrations of 3+ − La ions and Cl ions on the interface between the SCL and the diffuse layer, respectively. Considering that both eqs 6 and 7 stand for the La3+ ion concentration at D = l/4, the relation between the mica surface charge σmica and the surface potential φ0 at D = l/4 is set up. Then, substituting eqs 6−8 into the Grahame equation for 3:1 electrolyte solution, the surface potential φ0 at D = l/4 and the bulk solution concentration ρbulk can be described by the following expression σ * = [2ε0εkBTρbulk (e−3eφ0 / kBT + 3eeφ0 / kBT − 4)]1/2

(9)

where ρbulk is the solution concentration. From this we can obtain the solid line in Figure 4 predicting the mica surface potential as a function of the LaCl3 concentrations. It is found that the predicted surface potential from eq 9 agreed well with the fitted surface potential from the measurement. Thus, the SCL theory successfully captures the features of mica surface interactions immerging in LaCl3 solutions, including the critical concentration of charge inversion and the trend of surface potential changing with LaCl3 concentrations. The correlations of multivalent counterions in solutions play a great role in the charge inversion, although specific absorption of ions remains as options for the origin of the charge inversion. The interaction forces versus the separation between two mica surfaces are also presented in Figure 5 for LaCl 3

Figure 5. Interaction forces between mica surfaces immerged in 0.123 M, 0.496 and 1.894 M LaCl3 solutions. The two dashed lines on the right are a guide for molecular layering.

concentrations at 0.123, 0.496, and 1.894 M. At very longrange separation away from 34 nm, repulsion force is detected in 0.123 M LaCl3 solution as shown in Figure 5. This force bears no resemblance of DLVO force and has much longer interaction range than that of hydration forces. The similar long-range force was reported previously,22,35,36 which was attributed to extensively cation hydrolysis. Once larger polynuclear complexes are formed, these polynuclear hydrolysis layers may overadsorb on the mica surface and give rise to longrange repulsion forces. Hydration force wins out this long-range 10849

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ion sandwiched between two mica walls with lateral size of about half ion spacing. The effective interaction between mica surfaces is dominated by the contribution from individual La3+ ion fluctuating in each correlation cell, and the lateral interactions can be neglected. The mica surfaces will attract each other due to a dominant single-particle attraction mediated by ions that are isolated in correlation cells of large lateral extension,15,43 as shown in Figure 6. The Bjerrum length for trivalent is about 6.5 nm, which is the ion spacing S between trivalent ions.

Figure 7. Pull-off forces of mica surfaces in different concentrations of LaCl3 solutions. Figure 6. Sketch of the strong adhesion of mica surfaces mediated by La3+ ions at short distances.

concentrations.8 With the increase of LaCl3 concentrations, the measured pull-off force is increased gradually and reached over −80 mN/m for the LaCl3 concentrations ranging from 10−3 to 10−2 M (Figure 7), which is significantly stronger than the expected van der Waals force contribution. Here, we ignored the effect of salt concentrations on the dielectric constant between two mica surfaces. In this way, the van der Waals force between two mica surfaces in different LaCl3 concentration solutions is considered as a constant. Therefore, our result indicates that ion correlation attraction at short distance dominates the surface adhesion at high concentration. The trend of the measured adhesion represents the significant influence of electrolyte concentration on the ion correlation effect. From the force−distance profiles, repulsive hydration forces between mica surfaces are not observed below the LaCl3 concentration of 10−2 M. The weak hydration forces are negligible compared to the strong attraction at short distances. However, with the increase of salt concentrations, more and more hydrated cations are trapped in the thin slit between two mica surfaces, which leads to the increase of the final contact positions D between the two mica surfaces and even alters the correlation structure. Hence, the hydration force at this high concentration will cancel part of the adhesion force. The strong attraction disappears when the concentration is above 0.123 M. The hydration force and steric effects of highly hydrated ions, at high concentrations, strongly inhibit the van der Waals attraction force and short-range correlation attraction. It is found from the final contact position that two to four layers of highly hydrated ions are trapped in slit between two mica surfaces. The marked reduction of adhesion at high concentration solutions strongly suggests the interface structure of mica surfaces is changed by hydrated ions. Effect of pH on the Ion−Ion Correlation Forces. Lanthanum and hydronium ions competitively adsorb on mica

When the two complementary mica surface patterns come close, each ion, being located in the center of a strong correlation hole, feels the unscreened attractive electric field E0 of the opposite surface. This results in strong attraction between mica surfaces and pulls them together suddenly. The maximum attraction pressure at contact can be approximated15 by the formula P = −2E0σ = −σ 2/ε0ε ≈ −7.38 × 107 N·m−2

(10)

The attraction pressure is as strong as van der Waals attraction between mica surfaces in water, with a cutoff distance 0.25 nm and Hamaker constant 2.0 × 10−20, corresponding to adhesion energy at about 6.6 mJ·m−2. The combinational attraction forces due to the ion correlation and that resulting from the van der Waals forces lead to jump-into contact and strong adhesion of mica surface at high multivalent concentrations. Table 1 shows the measured values of mica adhesion in different LaCl3 concentrations. Based on JKR theory, the interfacial energy of mica surface (γ) representing the adhesion energy between two mica surface is given by γ = Fpull‑off/3πR, where Fpull‑off is the pull-off force (adhesive force) measured at the jump-out distance. Figure 7 illustrates the pull-off forces of mica surfaces in different LaCl3 concentration solutions. The adhesion force seems to be dependent on the density of La3+ ions adsorbed on the mica sheet, which is related to the coupling strength between La3+ ions. In 10−7 M LaCl3 solutions, the measured pull-off forces (∼ −23.7 mN/m) is equivalent to theoretical van der Waals forces at a cutoff distance of 0.4 nm (∼ −23 mN/m) with a Hamaker constant 2.2 × 10−20 J, which suggests that the van der Waals forces dominates in mica adhesion at low

Table 1. Measured Data of Mica Surfaces in Different LaCl3 Concentrations concn of LaCl3 (M)

10−7

10−6

10−5

10−4

10−3

10−2

0.123

0.496

1.89

jump-in distance (nm) fitted surface potential (mV) interfacial energy (mJ·m−2)

2.9 −61 2.94

5.7 −32 4.39

5.8 3 6.77

6.5 25 7.5

4.5 56 9.04

4.1 75 9.03

no

no

no

0

0.15

0.11

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lattice sites, when mica surface is immerged in LaCl3 solutions. The distribution of La3+ ions adsorbed on mica surface will be changed due to the interference of the competition hydronium ions. The pH values of the electrolyte solution, hence, become significant in the interactions between two mica surfaces and charge inversion. Furthermore, the complex formation of cations, depending on the pH, was considered as the origin of excessive adsorption of cations and overcharging.9,12,44 Thus, it is mandatory to study the influence of pH value on the ion− ion correlations for two mica surfaces immersed in LaCl3 solution. The pH effects on the surface and adhesion forces between mica sheets in the electrolyte concentration range 10−7−10−3 M are presented in Figures 8−11.

Figure 9. Interaction forces between mica surfaces immerged in LaCl3 solutions at pH 2−3 during detachment process.

Figure 8. Interaction forces between mica surfaces immerged in LaCl3 solutions at pH 2−3 during approach process. Figure 10. Summary of pull-off forces between mica surfaces immerged in LaCl3 solutions at different pH values.

At pH 2−3, the trends for the interactions between two mica surfaces are similar to that at pH 5.2−5.8, as shown in Figure 8. A critical concentration ρca falls into the range of 10−6 to 10−5 M, at which the interaction is too small to measure, implying that the negative charged mica surface is almost neutralized. For the salt solution with LaCl3 concentration lower than the critical concentration ρca, the magnitude of mica surface interaction forces decreased with growing concentrations. When the LaCl3 concentration is higher than critical concentration ρca, the interaction forces rise with increasing LaCl3 concentrations. Once the mica surfaces become positive charged, chloride ions act as counterions. It can be found that the magnitude of interactions in 10−4 and 10−3 M LaCl3 solutions is greater than that in the same LaCl3 concentration but with higher pH value (5.2−5.8). This is attributed to the enhanced ionic strength at low pH value. At low pH solutions, Cl− ions act as the counterions when the mica surface is over screened by the La3+ ions when the LaCl3 concentrations are in range between 10−2 and 10−3 M at pH 2−3. Also, the interaction range becomes shorter than that at higher pH 5.2− 5.8, which is due to the decreased Debye length at low pH. However, the pull-off forces, at pH 2−3, are very different from that at pH 5.2−5.8, as show in Figures 9 and 10. The pulloff force is measured by probing the distance at which the two mica surfaces jump out instantly as shown in Figure 9. It ascends to maximum at 10−6 M, and then falls to zero at 10−3 M. Even at the very low LaCl3 concentration 10−6 M at pH 2− 3, the pull-off force is smaller than that at pH 5.2−5.8. At pH 2−3, the mica surface is weakly charged. So less La3+ ions bind

to mica surface. This leads to the attraction due to the ion correlation becomes weak. The mainly contribution to attraction force comes from the van der Waals force. Compared the measured pull-off force at pH 2−3 with that at pH 5.2−5.8, it is suggested that La3+ ions cannot form strong correlation liquid. So, the strong adhesion disappeared at pH 2−3. The measured adhesion force decreases with increasing LaCl3 concentrations above10−5 M and finally vanishes at 10−3 M, which is different from the strong adhesion at LaCl3 solution with pH at 5.2−5.8. Furthermore, the trend of the total repulsions of mica surfaces at pH 9−10, is similar to that at pH 2−3, but the magnitude is stronger than that corresponding at the same LaCl3 concentration as shown in Figures 11 and 12. The jump into contact disappeared at pH 9−10, except at LaCl3 concentration lower than 10−5 M, where charge inversion occurs around this concentration. The strong total repulsions can be attributed to the enhanced electric double layer forces, as mica surface become more negatively charged at pH 9−10 value.45 In addition the steric force at pH 9−10 also strengthens the total repulsion. This is attributed to hydration layers and adsorbed ions at the mica surface. The similar phenomenon46 was found between mica surfaces in sodium chloride aqueous solution at pH 10. The force hysteresis was observed at pH 9− 10 for LaCl3 solutions. This is speculated that the hydrated La3+ ions were adsorbed forcedly in the extreme confinement gap 10851

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We fitted the effective surface potentials of mica surfaces presented in Figure 13 for solutions at different pH values.

Figure 11. Interaction forces as a function of the distance between two mica surfaces immerged in LaCl3 solutions at pH 9−10 when the two mica surfaces are brought together. Figure 13. Effective surface potentials of mica surfaces at different pH solutions. The solid green line is predicted from the SCL model.

Charge inversion was found at LaCl3 concentration of around 10−5 M in different pH solutions. The effective surface potential at pH 9−10 is larger than that at pH 2−3 as shown in Figure 13, which can be found from the force−distance curves in Figures 8 and 11, too. At pH 9−10, the mica surface becomes more charged, so the critical LaCl3 concentration for charge inversion shifts right slightly. The effective surface potential does not change strictly linearly with the logarithm solution concentrations as that predicted from the SCL model, which is attributed to the individual properties of mica surface and charge regulation47 at short distance. These results indicated that the pH value plays a paramount role in the interactions of mica surfaces.

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Figure 12. Interaction forces as a function of the distance between two mica surfaces immerged in LaCl3 solutions at pH 9−10 when the two mica surfaces are taken apart.

CONCLUSIONS In this work, we presented surface interaction measurements demonstrating charge inversion and strong adhesion of mica surfaces in the presence of multivalent cations using surface forces apparatus technique. The surface potential of the mica surface changes its sign when the LaCl3 concentration reached at about 10−5 M. With the continual increase of LaCl3 concentration, more La3+ ions are accumulated near the mica surfaces and enhance the effective surface potential. The main driving force of attracting the excessive La3+ ions is attributed to the correlation among the La3+ cations. The strong coupling of cations helps the formation of the SCL, which can provide extra energy for excessive adsorption of La3+ ions and result in the charge inversion on mica surfaces. At short distance, charged mica surfaces were pulled into contact strongly mediated by the correlation hole of strongly coupling La3+ ions, even at high concentration up to 10−2 M. The pull-off forces of mica surfaces increased with the LaCl3 concentrations below concentration of 10−3 M, which indicates that the increase of La3+ ions coverage can enhances the adhesion. The analytical model based on the ion correlations gave good qualitative and even reasonable quantitative agreement predictions with the experimental data, supporting the view of the general feature governing the charge inversion and strong adhesion in multivalent solutions.

between the two mica surfaces. With the continual approaching of the two mica surfaces, the hydrated La3+ ions and hydrolysis layers were squeezed out under the action of the normal load. The outer Helmholtz plane from which the diffuse double-layer repulsion originates could be irreversibly shifted inward as two surfaces approach each other, which causes the force hysteresis. Similar hysteresis effects have been reported between mica surfaces in potassium nitrate and calcium nitrate solutions.42 From Figure 12, it is found that the pull-off forces are weaker than that corresponding to the same LaCl3 concentrations at pH 2−3 or that at pH 5.2−5.8. The steric effect of hydrated La3+ ions and hydration force win out the combination of van der Waals force and correlation attraction even at short distance. The peak of adhesion force appeared at LaCl3 concentration 10−5 M. With the continual increase of LaCl3 concentrations, the adhesion force diminishes to zero. This is attributed to that the La3+ ions are highly hydrated, which may weaken the formation of two layer interlocking pattern ions at pH 9−10. 10852

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(7) Keyser, U. F.; Koeleman, B. N.; Van Dorp, S.; Krapf, D.; Smeets, R. M. M.; Lemay, S. G.; Dekker, N. H.; Dekker, C. Direct Force Measurements on DNA in a Solid-State Nanopore. Nat. Phys. 2006, 2, 473−477. (8) Israelachvili, J. N. Intermolecular and Surface Forces, 3rd ed.; Elsevier Science: New York, 2011. (9) Jiménez, M. L.; Delgado, Á . V.; Lyklema, J. Hydrolysis Versus Ion Correlation Models in Electrokinetic Charge Inversion: Establishing Application Ranges. Langmuir 2012, 28, 6786−6793. (10) Perel, V. I.; Shklovskii, B. I. Screening of a Macroion by Multivalent Ions: A New Boundary Condition for the Poisson− Boltzmann Equation and Charge Inversion. Phys. A 1999, 274, 446− 453. (11) Besteman, K.; Zevenbergen, M. A. G.; Lemay, S. G. Charge Inversion by Multivalent Ions: Dependence on Dielectric Constant and Surface-Charge Density. Phys. Rev. E 2005, 72, 061501. (12) Travesset, A.; Vangaveti, S. Electrostatic Correlations at the Stern Layer: Physics or Chemistry? J. Chem. Phys. 2009, 131, 185102− 185111. (13) Lyklema, J. Overcharging, Charge Reversal: Chemistry or Physics? Colloids Surf., A 2006, 291, 3−12. (14) Wernersson, E.; Kjellander, R.; Lyklema, J. Charge Inversion and Ion−Ion Correlation Effects at the Mercury/Aqueous MgSO4 Interface: Toward the Solution of a Long-Standing Issue. J. Phys. Chem. C 2010, 114, 1849−1866. (15) Rouzina, I.; Bloomfield, V. A. Macroion Attraction Due to Electrostatic Correlation between Screening Counterions.1. Mobile Surface-Adsorbed Ions and Diffuse Ion Cloud. J. Phys. Chem. 1996, 100, 9977−9989. (16) Grosberg, A. Y.; Nguyen, T. T.; Shklovskii, B. I. Colloquium: The Physics of Charge Inversion in Chemical and Biological Systems. Rev. Mod. Phys. 2002, 74, 329−345. (17) Nguyen, T. T.; Grosberg, A. Y.; Shklovskii, B. I. Macroions in Salty Water with Multivalent Ions: Giant Inversion of Charge. Phys. Rev. Lett. 2000, 85, 1568−1571. (18) Nguyen, T. T.; Grosberg, A. Y.; Shklovskii, B. I. Screening of a Charged Particle by Multivalent Counterions in Salty Water: Strong Charge Inversion. J. Chem. Phys. 2000, 113, 1110−1125. (19) Shklovskii, B. I. Screening of a Macroion by Multivalent Ions: Correlation-Induced Inversion of Charge. Phys. Rev. E 1999, 60, 5802−5811. (20) Netz, R. R. Electrostatistics of Counter-Ions at and between Planar Charged Walls: From Poisson-Boltzmann to the StrongCoupling Theory. Eur. Phys. J. E 2001, 5, 557−574. (21) Besteman, K.; Zevenbergen, M. A. G.; Heering, H. A.; Lemay, S. G. Direct Observation of Charge Inversion by Multivalent Ions as a Universal Electrostatic Phenomenon. Phys. Rev. Lett. 2004, 93, 170802. (22) Pashley, R. M. Forces between Mica Surfaces in La3+ and Cr3+ Electrolyte Solutions. J. Colloid Interface Sci. 1984, 102, 23−35. (23) Laanait, N.; Mihaylov, M.; Hou, B.; Yu, H.; Vanýsek, P.; Meron, M.; Lin, B.; Benjamin, I.; Schlossman, M. L. Tuning Ion Correlations at an Electrified Soft Interface. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 20326−20331. (24) van der Heyden, F. H. J.; Stein, D.; Besteman, K.; Lemay, S. G.; Dekker, C. Charge Inversion at High Ionic Strength Studied by Streaming Currents. Phys. Rev. Lett. 2006, 96, 224502. (25) Li, R.; Todd, B. A. Multivalent Ion Screening of Charged Glass Surface Studied by Streaming Potential Measurements. J. Chem. Phys. 2013, 139, 194704. (26) Pittler, J.; Bu, W.; Vaknin, D.; Travesset, A.; McGillivray, D. J.; Loesche, M. Charge Inversion at Minute Electrolyte Concentrations. Phys. Rev. Lett. 2006, 97, 046102. (27) Kubickova, A.; Krizek, T.; Coufal, P.; Vazdar, M.; Wernersson, E.; Heyda, J.; Jungwirth, P. Overcharging in Biological Systems: Reversal of Electrophoretic Mobility of Aqueous Polyaspartate by Multivalent Cations. Phys. Rev. Lett. 2012, 108, 186101. (28) Martin-Molina, A.; Rodriguez-Beas, C.; Faraudo, J. Charge Reversal in Anionic Liposomes: Experimental Demonstration and Molecular Origin. Phys. Rev. Lett. 2010, 104, 168103.

Our work also demonstrated clear evidence of surface interactions dependent on pH values at LaCl3 concentrations. The charge inversion was observed at different pH conditions, but the magnitude of the interaction forces between the two mica surfaces varied greatly with the pH values. At pH 2−3, the magnitude of surface forces is equivalent to that at nearly neutral pH (5.2−5.8) before the mica reverses it surface charge sign. However, the surface forces are stronger than that at nearly neutral pH (5.2−5.8) after the charge inversion of mica. The adhesion between two mica surfaces is weakened at pH 2− 3 than that at pH 5.2−5.8. This is attributed to the interplay of hydrogen ions and hydrated La3+ ions. With the competition of hydrogen ions adsorbed on the mica surfaces, the number of La3+ ions accumulating near the mica surface is reduced compared with that in the neutral solutions for pH 5.2−5.8, which leads to the decreases of the ion correlation attraction. At pH 9−10, the steric−hydration repulsion enhanced the repulsion, and the jump into contact disappeared for the LaCl3 concentration higher than 10−5 M. This demonstrates that the ion−ion correlation is disturbed with the introduction of largely hydrated La3+ ions at pH 9−10. In this case, the adhesion forces between two mica surfaces are weaker than that corresponding to the same LaCl3 concentration at pH 2−3 and pH 5.2−5.8 solutions. Our results provide important insights into the strong correlations among multivalent ions, which may induce counterintuitive phenomena such as charge inversion, like charge attraction and strong adhesion.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

Q.T. and Y.C. conceived and designed this work. Q.T. and Y.C. prepared the manuscript. Q.T. performed the experiments. Q.T. and G.Z. analyzed the experimental data. G.Z. prepared Figures 1 and 6. Q.T., Y.C., Y.Q., Y.K., and Z.N. interpreted the results. All authors discussed the results and commented on the manuscript at all stages. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are thankful for the financial support from the National Basic Research Program of China (2011CB707601, 2011CB707605) and Natural Science Foundation of China (Grant No. 50925519).

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