Excess Charge Density and its Relationship with Surface Tension

Feb 3, 2011 - pubs.acs.org/JPCB. Excess Charge Density and its Relationship with Surface Tension. Increment at the Air-Electrolyte Solution Interface...
0 downloads 0 Views 3MB Size
Download PDF
ARTICLE pubs.acs.org/JPCB

Excess Charge Density and its Relationship with Surface Tension Increment at the Air-Electrolyte Solution Interface Jinsuk Song*,† and Mahn Won Kim Department of Physics, KAIST, Daejeon 305-701, Republic of Korea

bS Supporting Information ABSTRACT: The adsorption isotherms of probe cationic molecules were measured at various electrolyte solution interfaces by resonant second harmonic generation. The excess charge density was obtained by analyzing the isotherms; it increases with square root of the bulk electrolyte concentration. Its value is ion-specific and the amount of probe molecular adsorption follows the Hofmeister series. By calculating the pressure anisotropy at the interface, it is found that the ratio of surface tension increment to the bulk electrolyte concentration decreases with the square of the excess charge density. This is in good agreement with the experimental observations.

’ INTRODUCTION Most inorganic electrolyte solutions exhibit higher surface tensions than that of pure water.1-4 The interfacial tension increases linearly with bulk electrolyte concentration and follows the Hofmeister series.5 The slope of the surface tension increment (STI) with electrolyte concentration slightly increases with temperature.6 Onsager et al.7 attempted to explain the surface tension increase associated with the added electrolyte. They concluded that ions are repelled from the interface via interaction with their images and this ion depletion increases the surface tension. It is in good agreement with experiment at low concentration up to 0.18 M. Levin et al.8 included ion depletion layers of finite thickness explicitly and calculated the surface tension increase. According to the Gibbs adsorption equation, the surface tension increase is correlated with the depletion of adsorbates from the Gibbs dividing surface (GDS) of the solvent.9 Suppose that there is a liquid as in Figure 1a. The depth is in arbitrary units for convenience and its density is normalized with the bulk density. In reality, thickness of the interface is finite. In Figure 1a, it is about 20 for the interface as the curve shown. To simplify all the complicated details of the interfacial structure, GDS can be defined so that the surface excess becomes zero. Surface excess at the arbitrary interface positioned x normal to the interface, Γx, is defined as Z ¥ Z ¥ Z x Γx ¼ FðxÞdx Fð¥Þdx Fð-¥Þdx ð1Þ -¥

x

-¥

r 2011 American Chemical Society

where F(x) is the density profile in the normal direction to the interface. F(¥) and F(-¥) are the bulk densities of the two phases, which are constant. The position of GDS, wGDS, is defined as Z ¥ Z ¥ Z wGDS FðxÞdx ¼ Fð¥Þdx þ Fð - ¥Þdx ð2Þ -¥

wGDS

-¥

It is positioned at 0 shown as the vertical line in Figure 1a so the area of the two shaded region becomes the same. By defining GDS in this way, the interface with finite thickness and continuously varying density can be reduced to that with zero thickness and stepwise varying density. When there are more than one component in the liquid, such as solvent and solute in Figure 1b, one choice of dividing surface cannot make the surface excess of both components zero, in general. There is a GDS for each species. For example, Figure 1b shows the density profile made of solvent and solute. The solid curve is the solvent density profile and the dotted curve is the solute density profile. Considering the density of each species separately, GDS of the solvent and solute can be defined as shown as solid and dotted vertical lines, respectively, in Figure 1b. GDS of solute is where the surface excess of solute becomes zero. Putting these GDS’ together (shown as the solid and dotted boxes in Figure 1b), liquid interface whose solvent and solute Received: November 15, 2010 Revised: January 13, 2011 Published: February 3, 2011 1856

dx.doi.org/10.1021/jp110921m | J. Phys. Chem. B 2011, 115, 1856–1862

The Journal of Physical Chemistry B

Figure 1. (a) Model for an arbitrary liquid interface made of one component. Smoothly varying curve is the actual density profile normalized with its bulk density. Depth is in arbitrary units for convenience. The solid vertical line is the GDS. (b) Model for an arbitrary liquid interface made of two components. Smoothly varying curves are the actual density profile normalized with their bulk density. Solid curve is for the solvent, and the dotted one is for the solute, respectively. Vertical lines are corresponding GDS. (c) Idealized picture of the interface using GDS in panel b.

densities vary as the curves in Figure 1b can be simplified as shown in Figure 1c. Gibbs adsorption equation, Δγ = -ΓxΔμ, relates the surface tension increase Δγ with the chemical potential change Δμ of the solute and the surface excess Γx of the solute at the GDS of the solvent. The surface excess of the solute at the solvent GDS is the total number of solutes minus the number of solutes when they are assumed to have the same concentration (same as the bulk concentration in the thermodynamic limit) up to the solvent GDS. Therefore, because the interface shown in Figure 1b can be reduced to that in Figure 1c with solvent GDS as a solid line and the solute GDS as a dotted line, surface excess of the solute at the solvent GDS becomes negative whose magnitude is the same as the shaded area and gives rise to surface tension increase. In Gibbs’ idealized picture, negative surface excess corresponds to the depletion of solute as in Figure 1c and surface tension increase, and vice versa. In addition, adsorption tends to decrease surface tension, that is, the surface energy.

ARTICLE

However, it has been reported for large ions, the ion concentration at the interface can be larger than that of the bulk10-12 while the surface tension increases. There have been numerous theoretical studies to understand this contradiction. Bostrom et al.13,14 took ionic solvation and dispersion energies into account by numerically solving the Poisson-Boltzmann (PB) equation and found out that the density of larger size ions at the interface has the peak in which its concentration is higher than the bulk, and the dip in which its concentration is lower than the bulk. Larger size ions have higher peak density than the smaller size ions while the surface tension increases in both cases. Details of ion density and the increased surface tension vary substantially with the dispersion constant. Levin et al.15,16 considered the ion polarizability and solvation energy and obtained the similar result. In both cases, Gibbs adsorption equation is used to obtain surface tension change. Unlike numerical studies13-16 in which the dielectric discontinuous boundary was assumed to be GDS of solvent, it can be considered explicitly in simulation. Horinek et al.17 calculated the surface excess while considering GDS of water explicitly and obtained the surface tension increases, which agrees well with the experimental data. Jungwirth et al.10 calcuated forces between water molecules and ions directly instead of using the Gibbs adsorption equation to obtain the surface tension increase. Most of theoretical studies about surface tension change in electrolyte solution were done on the basis of the Gibbs adsorption equation. This approach has the advantage of reducing the complicated interfacial structure into a simple, clear, and idealized one as shown in Figure 1c. When it is applied, it is essential to know the surface excess of the solute at the GDS of the solvent. However, although there are a few attempts,11,12 measuring ion and water densities at the interface is extremely hard. Therefore, it is complementary to calculate the surface tension change from the forces between molecules at the interface and to compare it with the Gibbs adsorption scheme to get a better understanding on the interfacial structure. In a previous study,18 we reported the effective excess charge density at the air-NaCl and the air-NaI solution interfaces arising from the differential adsorption between cations and anions.12 In this paper, excess charge densities of various electrolyte solutions and their relationship with the STI are presented. The excess charge density was obtained by analyzing the adsorption isotherm of probe cationic molecules at the electrolyte solution interface at various electrolyte concentrations. To understand the relationship between the forces arising from the excess charge density and STI, pressure due to the ions at the interface was calculated explicitly. The calculated STI is compared with the experimental results reported in the literature.19 Its relationship to the Gibbs adsorption equation will be discussed.

’ EXPERIMENTAL METHOD When electrolytes are dissolved in water, they are dissociated into cations and anions. The density of some anions, which generally have larger sizes than the cations, is greater than that of the cations near the interface.10,12 Because the density profile at the interface is different for cations and anions, electrolytes induce effective excess charge density near interface. When other probecharged molecules are put into the electrolyte solution, the excess charge density changes the adsorption of the probe molecules because of the electrostatic interaction between excess charge 1857

dx.doi.org/10.1021/jp110921m |J. Phys. Chem. B 2011, 115, 1856–1862

The Journal of Physical Chemistry B

ARTICLE

Figure 2. The measured adsorption isotherms at the air-DI water interface (a) and at various electrolyte solution interfaces (b-h). The electrolyte species and concentrations are indicated in the legends. Generally, as the bulk electrolyte concentration increases, MG adsorption also increases. At the MG concentration range used in electrolyte solution (b-h), that is, up to a few hundred micromolar, the MG adsorption at the air-DI water interface is nearly the same as the thermal background. The range of x- and y-axis scale for each electrolyte was set different to show each isotherm clearly.

and probe charge. From the change in the probe molecular adsorption as a function of electrolyte concentration, the excess charge density can be obtained. Positively charged Malachite Green (Aldrich, 213020) was used as a probe molecule. The second harmonic (SH) intensity was measured to obtain the Malachite Green (MG) adsorption isotherm in various electrolyte solutions. The SH field amplitude is proportional to the number of adsorbed MG molecules.

Details of the experimental method and analysis method used to obtain the excess charge density can be found elsewhere.18 Sodium fluoride (Samchun chemicals, >97.0%, S5309), chloride (Junsei, >99.5%, 19015-1250), bromide (Junsei, >99.0%, 362851201), nitrate (Junsei, >99.0%, 37515-1250), iodide (Junsei, >99.0%, 80240-1201), ammonium chloride (Junsei, >97.0%, 18075-1250), and potassium chloride (Yakuri pure chemicals, >99.5%, 28514) were used as electrolytes. The bulk electrolyte 1858

dx.doi.org/10.1021/jp110921m |J. Phys. Chem. B 2011, 115, 1856–1862

The Journal of Physical Chemistry B

ARTICLE

Figure 3. The slopes (a) and the excess charge density (b) obtained by fitting the measured isotherm with eq 4. The electrolytes used are specified in the legends. The slopes and the excess charge densities are functions of electrolyte species and concentration. The excess charge density is the increased charge density from that at the air-DI water interface, calculated from (y-intercept)solution - (y-intercept)DI water = -Δ(4πlBσ/κ).

concentration range varied from 0 to 1 M. All experiments were done at room temperature and ambient pressure. Deionized (DI) water from Millipore (>18.2 MΩ) was used.

’ RESULTS AND DISCUSSION Figure 2a-h shows the measured adsorption isotherms at various electrolyte solution interfaces. The SH field amplitude is proportional to the number of adsorbed MG molecules at the interface. It is scaled so that the output SH amplitude of 20 μM MG solution in 1 M NaCl is 1. Figure 2a is the MG adsorption isotherm at the air-DI water interface and Figure 2b-h are those at the electrolyte solution interfaces. The electrolytes used and their concentration are indicated in the legends. All the concentrations including electrolytes and MG are bulk concentration. The bulk MG concentration range in DI water (Figure 2a) is different from the rest. For concentration lower than 200 μM, MG hardly adsorbs at the air-DI water interface. The maximum solubility of MG in DI water is 2.6 mM. MG adsorbs more at the interface as the bulk electrolyte concentration increases. Its adsorption depends not only on the electrolyte concentration but also on the electrolyte species. For example, MG adsorbs 3 times more at the air-1 M NaI solution interface than at the air-1 M NaCl solution interface at the same bulk concentration, 20 μM. The MG adsorption generally follows the Hofmeister series. At the same electrolyte and MG concentrations, when the cation is fixed as Naþ, it increases with the anion in the order, Cl- < Br- ≈ NO3- < I- and when the anion is fixed as Cl-, it increases with the cation in the order, NH4þ < Naþ ≈ Kþ. The Gibbs adsorption free energy and method to analyze the excess charge density were introduced in the previous work.18 In brief, they are as follows: when MG adsorbs at the interface, it loses its bulk entropy while gaining the electrostatic energy due to the excess anionic charge density induced by the electrolyte, eq 3    N0 k μ 4πlB σ ¼ þ1lnðcM υ0 Þ ð3Þ 4πlB kB T k A N0 is the equilibrium number of adsorbed molecules at the interface, A is the area of the interface, κ is the inverse Debye screening length, lB is the Bjerrum length, cM the bulk MG concentration, υ0 the specific volume, and μ is the intrinsic energy difference per molecule between MG at the surface and in the bulk. kB is the Boltzmann constant, T is the temperature, and

σ is the excess number of charges per unit area induced by the electrolytes. The effects of electrolytes were assumed to be only from electrostatics. Equation 3 can be written as   4πlB N0 μ 4πlB σ þ þ1ð4Þ - ln υ0 ln cM ¼ kB T k k A ln c versus the adsorption density at the interface has a slope which is proportional to the Debye screening length and an intercept that is a function of the excess charge density σ. Figure 3a,b shows the fitted results of adsorption isotherms in Figure 2 with eq 4. Figure 3a shows the slopes, and Figure 3b is the excess charge density. The excess charge density is the increment over that of the air-DI water interface. The electrolytes used are specified in the legends. The obtained excess charge density increases with the bulk electrolyte concentration as shown in Figure 3b. It is the difference between the equilibrium adsorption number of cations and anions of electrolytes at the interface, and increases with the inverse Debye screening length, κ, such as σ¼ -

k ðμ - μ - Þ 8πlB kB T þ

ð5Þ

as demonstrated in the previous report.18 μþ is the intrinsic energy difference per cation between at the interface and in the bulk, and μ- is that for anion. As seen in Figure 4a-f, the obtained excess charge density increases linearly with square root of the bulk electrolyte concentration as expected. μþ μ- for each electrolyte was obtained by linearly fitting the excess charge density with the inverse Debye screening length κ as the lines shown in Figure 4a-f. They are listed in the Table 1. Excess charge density shown in Figure 4 is an effective charge density that affects MG molecular adsorption. However, its microscopic meaning is not very clear. Density difference between anion and cation depends on the distance from the interface.10,12 It becomes smaller and eventually becomes zero sufficiently deep inside the bulk. The obtained excess charge density may be the surface excess difference between cation and . It is about the same anion at the solvent GDS, which is about 5 Å with the size of MG. Nevertheless, the excess charge density should be clarified with the further experiment and PB calculation. 1859

dx.doi.org/10.1021/jp110921m |J. Phys. Chem. B 2011, 115, 1856–1862

The Journal of Physical Chemistry B

ARTICLE

Figure 4. The excess charge density as a function of an inverse Debye screening length κ. κ is proportional to the square root of the bulk electrolyte concentration. The excess charge density is proportional to κ, as expected in eq 5. The electrolytes used are indicated in the legends. The lines are the linear fit.

Figure 5. The excess charge density at 1 M electrolyte solution interface versus the surface tension increase at 1 M electrolyte solution (a) and STI versus the obtained μþ - μ- squared (b). STI data from Pegram et al.19 were used. STI decreases linearly with μþ - μ- squared, which agrees with eq 8. Linear fit is shown as solid line in the figure.

Excess charge density contributes to the change of surface tension at the air-electrolyte solution interface. Their relationship is shown in Figure 5a. The x-axis is the surface tension increase at 1 M electrolyte solution and the y-axis is the excess charge density at 1 M

electrolyte solution interface. They show the negative correlation. We used the surface tension data that Pegram et al.19 summarized. To relate the obtained excess charge density with the surface tension change quantitatively, we used the microscopic equation 1860

dx.doi.org/10.1021/jp110921m |J. Phys. Chem. B 2011, 115, 1856–1862

The Journal of Physical Chemistry B

ARTICLE

Table 1. μþ - μ- for Each Electrolyte Obtained from the Fitting the Excess Charge Density with the Inverse Debye Screening Length and ΔH0hyd,- - ΔH0hyd,þ electrolyte

ΔH0hyd,- - ΔH0hyd,þa [kBT/mol]

NaCl

7.22 ( 1.17

11.3

NaBr

8.23 ( 1.21

25.0

NaNO3

10.36 ( 1.18

38.3

NaI

12.20 ( 1.73

42.0

9.35 ( 1.44 8.31 ( 1.07

-23.8 -29.9

KCl NH4Cl a

μþ - μ- [kBT]

From ref 24.

defining the surface tension as the pressure anisotropy at the interface,20 as in eq 6 ð6Þ -A dγ ¼ - V S dðPN - PT Þ A is the interfacial area, and γ is the surface tension, VS is the interfacial volume, and PN and PT are the pressure tensor, normal and tangential to the interface, respectively. It is known to be equivalent to γ = (∂F∂A)V,T, that is, to the Gibbs adsorption equation, when the liquid is incompressible and the interface is planar.21 When ions in solution are treated as ideal gases with shortranged electrostatic forces, from eq 6, surface tension increase from the added electrolytes can be expressed as follows VS ΔðPN - PT Þ ¼ 2w1 ckB T Δγ ¼ A !# Z w20 Z ¥ " 1 2 d e2 - kr e dz 2π - σþ F dF 2 dr 4πεw r 0 aþ !# Z w20 Z ¥ " 1 2 d e2 - kr e - σdz 2π F dF þ σþσ 2 dr 4πεw r 0 a!# Z ¥ " Z w20 d e2 - kr e dz 2π F dF ð7Þ dr 4πεw r 0 aþ where σþ and σ- are the cation and anion density per unit area, respectively. w1 and w02 are the interfacial depth of density gradient and differential adsorption. They were assumed to be different for generality. aþ is the shortest distance between cations, a- is that for anions, and aþ- is the shortest distance between cations and anions. z is the coordinate that is normal to the interface, and F is the cylindrical coordinate. r is (F2 þ z2)1/2. First term corresponds to the kinetic pressure due to the dissolved ions and the rest are the electrostatic forces between positive and negative charges at the interface. Yukawa potential was used as the interaction between ions, although ions at the interface are not in the isotropic environment in z-direction. The factor 2 in front of the first term comes from that both cation and anion contributes to the pressure and 1/2 in front of the second and third term are used to avoid double counting. The variation of σ with the depth z was ignored. Assuming aþ ≈ a- ≈ aþ-  a for simplicity, eq 7 can be written as   Z ¥ w20 e2 2 - ka 1 -t e dt Δγ ¼ 2w1 ckB T σ e þ 4εw ka t   w2  2w1 kB T ðμ þ - μ - Þ2 c ð8Þ 8kB T

where σ = σþ - σ-. This is the case in which ions are homogeneously spread over the interfacial depth. When ions have a density peak at the depth where their free energy minimized and the distance between peaks is similar to the distance between ions at the same depth,22 eq 8 also holds. To get the last term, eq 5 is used. The term in the bracket in the middle depends only on κa. Because κ depends on square root of the local charge concentration and a depends on the inverse of it, their product is relatively constant over the whole bulk electrolyte concentration. This is valid at the interface. The product of w02 and those in the bracket was rewritten as w2. The kinetic pressure is linear in bulk electrolyte concentration. Because the excess charge density increases with the square root of the bulk electrolyte concentration, the electrostatic pressure, which increases square of the charge density, is also linear in bulk electrolyte concentration. STI defined as Δγ/c, is constant so the surface tension increases linearly with the bulk electrolyte concentration. Increasing part comes from the kinetic pressure of bulk electrolytes. In addition, it increases with the temperature.6 The forces, arising from the ions at the interface, tend to decrease the surface energy. For surfactants, the bulk kinetic term is extremely small compared with the electrolytes, because of its low solubility. Therefore, they decrease surface tension when they are adsorbed at the interface. From eq 8, STI decreases with the square of the excess charge density, that is, square of μþ - μ-. Figure 5b shows STI versus the obtained μþ - μ- squared. Although the details of the interfacial structure needs to be considered to get the better estimation of STI, it is in good agreement with eq 8 to the first approximation. The resulted w1 of the linear fit is 3.9 Å, similar to the reported8 and w2, which is a product of w02 and exponential decay factor, is 0.18. When w02 is similar to w1, for bulk electrolyte concentration from 100 mM to 1 M, the ratio of Debye screening length and the distance between homogeneously distributed charges is about 3. In this case, w2 is approximately 0.2. However, it is not clear that the mean-field approximation of this kind holds at short distances. To understand the surface tension change in terms of the Gibbs adsorption equation, sum of the surface excesses, Γx of cation and anion at the GDS of water, should be considered. It can be written as c  ΔwþGDS þ c  Δw-GDS as described in Figure 1. c is the bulk electrolyte concentration. ΔwþGDS and Δw-GDS are the distances between GDS of water and cation and anion, respectively. Unlike the realistic interfacial width of ion concentration change w1 and w2 in eq 8, ΔwGDS represents an idealistic width. It can be either positive or negative depending on the relative position of GDS of water and the ions as explained in Figure 1. When ions in water are treated as ideal gases, surface tension decrease due to the dissolved ions is kBT times the surface excess from that of pure water according to the Gibbs adsorption equation Δγ = -kBT Γx. In the case of negative adsorption in which ΔwþGDS þ Δw-GDS is negative, surface tension increases. ΔwþGDS þ Δw-GDS can be negative, although either one of them is positive. In some electrolyte solutions, such as NaI, the surface excess of large size anion can be positive.10,12 Although this is the case, the average surface excess of the cations and anions can be negative so that the surface tension increases.23 In addition, the GDS of ion can be still negative even though the ion density shows the peak density which is higher than that of the bulk. It depends on the details of the ion density profile. From that the surface tension increases linearly with the bulk electrolyte concentration, it seems that the ΔwþGDS þ Δw-GDS 1861

dx.doi.org/10.1021/jp110921m |J. Phys. Chem. B 2011, 115, 1856–1862

The Journal of Physical Chemistry B does not vary with the bulk electrolyte concentration. By combining eq 8 and Gibbs adsorption equation, the negative adsorption, defined as negative of ΔwþGDS þ Δw-GDS, increases with [2w1 w2/8{(μþ - μ-)/kBT}2] through μþ - μ-. Therefore, the smaller the excess charge density is, the larger the surface tension increases. It is worthwhile to note the relationship between the obtained μþ - μ- and the hydration enthalpy differences24 (ΔH0hyd,- ΔH0hyd,þ), between anion and cation. They are listed in Table 1. When the cation is fixed, such as Naþ, they are well correlated. The former is a fraction of the latter. The ratio of μþ - μ- to the hydration enthalpy difference ranges from 1/4 to 2/3. Because hydration enthalpy is the energy difference of an ion in the gas and in water, it is reasonable for μ, the energy needed to be at the interface, to be a fraction of it. Both of them tend to increase with the size of the ion. However, it depends on the specific ion species and how much it retains its hydrated structure at the air-water interface. It reflects different hydration environments at the interface and in bulk for ions.25 The deviation of KCl and NH4Cl is partly because of this and partly because of the discrepancies between the reported hydration enthalpies24,26 for Kþ and NH4þ compared with Naþ.

’ CONCLUSION The excess charge density at the various electrolyte solution interfaces was obtained by analyzing the adsorption isotherm of probe cationic molecules. It increases with square root of the bulk electrolyte concentration and depends on the electrolyte species. The adsorption amount follows Hofmeister series. By considering the surface tension as the pressure anisotropy at the interface, surface tension at the air-electrolyte solution interface was found to change with the square of the excess charge density. It agrees well with the experiment. The obtained values of an energy change for an ion at the interface and in the bulk, μ, shows strong correlation with the hydration enthalpy and size of an ion. ’ ASSOCIATED CONTENT

bS

ARTICLE

(3) Randles, J. E. B. Phys. Chem. Liq. 1977, 7, 107–179. (4) Weissenborn, P. K.; Pugh, R. J. J. Colloid Interface Sci. 1996, 184, 550–563. (5) Hofmeister, F. Arch. Exp. Pathol. Pharmakol. 1888, 24, 247–260. (6) Matubayasi, N.; Tsunetomo, K.; Sato, I.; Akizuki, R.; Morishita, T.; Matuzawa, A.; Natsukari, Y. J. Colloid Interface Sci. 2001, 243, 444–456. (7) Onsager, L.; Samaras, N. T. J. Chem. Phys. 1934, 2, 528–536. (8) Levin, Y.; Flores-Mena, J. E. Europhys. Lett. 2001, 56, 187–192. (9) Chattoraj, D. K.; Birdi, K. S. Adsorption and Gibbs Surface Excess; Plenum: New York, 1984; Chapter 3. (10) Jungwirth, P.; Tobias, D. J. J. Phys. Chem. B 2001, 105, 10468– 10472. (11) Padmanabhan, V.; Daillant, J; Belloni, L; Mora, S; Alba, M; Konovalov, O. Phys. Rev. Lett. 2007, 99, No. 086105. (12) Ghosal, S.; Hemminger, J. C.; Bluhm, H.; Mun, B. S.; Hebenstreit, E. L. D.; Ketteler, G.; Ogletree, D. F.; Requejo, F. G.; Salmeron, M. Science 2005, 307, 563–566. (13) Bostrom, M.; Williams, D. R. M.; Ninham, B. W. Langmuir 2001, 17, 4475–4478. (14) Bostrom, M.; Kunz, W.; Ninham, B. W. Langmuir 2005, 21, 2619–2623. (15) Levin, Y. Phys. Rev. Lett. 2009, 102, No. 147803. (16) Levin, Y.; dos Santos, A. P.; Diehl, A. Phys. Rev. Lett. 2009, 103, No. 257802. (17) Horinek, D.; Herz, A.; Vrbka, L.; Sedlmeier, F.; Mamatkulov, S. I.; Netz, R. R. Chem. Phys. Lett. 2009, 479, 173–183. (18) Song, J.; Kim, M. W. J. Phys. Chem. B 2010, 114, 3236–3241. (19) Pegram, L. M.; Record, M. T., Jr. J. Phys. Chem. B 2007, 111, 5411–5417. (20) Kirkwood, J. G.; Buff, F. P. J. Phys. Chem. 1949, 17, 338–343. (21) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Dover Pub., Inc.: New York, 2002; Chapter 4. (22) Dang, L. X.; Chang, T.-M. J. Phys. Chem. B 2002, 106, 235–238. (23) Pegram, L. M.; Record, M. T., Jr. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 14278–14281. (24) Smith, D. W. J. Chem. Educ. 1977, 54, 540–542. (25) Goswami, T.; Kumar, S. K. K.; Dutta, A.; Goswami, D. J. Phys. Chem. B 2009, 113, 16332–16336. (26) Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. H.; Earhart, A. D.; Coe, J. V.; Tuttle, T. R., Jr. J. Phys. Chem. A 1998, 102, 7787–7794.

Supporting Information. Adsorption Gibbs free energy and the derivation of adsorption equation included. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Telephone: 82-42-350-2575. Fax: 82-42-350-8150. Present Addresses †

Department of Bioengineering, UCLA, Los Angeles, CA 90095.

’ ACKNOWLEDGMENT This research was supported by WCU program through NRF funded by MEST (R33-2008-000-10163-0), by a grant of the Korea Healthcare technology R&D Project, MHWFA No. A040041 and by NRD (20090078717) and Basic Science Research Program (2009-0087691) through NRF funded by MEST. The authors thank P. Pincus for insightful comments and discussions. ’ REFERENCES (1) Heydweiller, A. Ann. Physik 1910, 338, 145–185. (2) Jarvis, N. L.; Scheiman, M. A. J. Phys. Chem. 1968, 72, 74–78. 1862

dx.doi.org/10.1021/jp110921m |J. Phys. Chem. B 2011, 115, 1856–1862