Competitive Adsorption of Toluene and n-Alkanes at Binary Solution

J. Phys. Chem. C 2009, 113, 20355–20359

20355

Competitive Adsorption of Toluene and n-Alkanes at Binary Solution/Silica Interfaces Zheng Yang,† Qifeng Li,† Rui Hua,† Murray R. Gray,‡ and Keng C. Chou*,† Department of Chemistry, UniVersity of British Columbia, VancouVer, BC V6T 1Z1, Canada, and Chemical and Materials Engineering, UniVersity of Alberta, Edmonton, AB T6G 2G6, Canada ReceiVed: May 8, 2009; ReVised Manuscript ReceiVed: August 26, 2009

The competitive adsorption of toluene and n-alkanes at binary solution/silica interfaces was studied at room temperature using IR-visible sum frequency generation vibrational spectroscopy. The surface coverage of toluene for toluene-pentane, toluene-heptane, and toluene-tetradecane mixtures was measured over the complete mole fraction range from 0 to 1. The competitive adsorption process was reversible, and the toluene coverage only depended on the bulk mole fraction, not on the history of the system. The estimated molar adsorption free energy of toluene is 3.4 ( 0.3, 1.8 ( 0.3, and 0.84 ( 0.3 kJ/mol higher than pentane, heptane, and tetradecane, respectively. Overall, toluene competes favorably on silica, and the molar adsorption free energy of alkanes increases as the chain length increases. It is consistent with the observed SFG spectra, indicating that the alkanes lie flat on the silica surface. I. Introduction The competitive adsorption of hydrocarbons at liquid/mineral interfaces plays a critical role in many industrial and environmental processes, such as oilsands processing,1-4 petroleum recovery,5 contamination removal,6-9 and many extraction techniques.10,11 Toluene and alkanes are particularly important because they are the most commonly used solvents for both industrial and scientific applications. At a binary solution/mineral interface, it is expected that the surface chemical composition is different from the bulk composition because of the interaction of the molecules with the surface.12 In many cases, the competitive adsorption of solvents at liquid/solid interfaces is a critical factor determining the effectiveness of a technological process. In the 1950s and 1960s, the adsorption isotherms for binary mixtures at liquid/solid interfaces were studied by various immersion methods, and a number of theories were developed.13,14 Despite this effort, the problem was not completely resolved,15 because the macroscopic measurements were indirect, and the theories require molecular-level information about the adsorbates as input parameters.13 Even with modern technologies, it remains challenging to directly measure the surface coverage of a particular component at a liquid/solid interface. Recent developments in IR-visible sum frequency generation (SFG) vibrational spectroscopy have shown that SFG is an effective technique to obtain molecular-level information at buried liquid interfaces, and many studies have been done at water interfaces.16 As compared to water interfaces, little is known about solvent/solid interfaces.17 SFG vibrational spectroscopy has been used for a broad range of studies by a rapidly growing number of research groups.18-22 As a second-order nonlinear optical process, SFG is forbidden in centrosymmetric media, such as liquids, but the symmetry is broken at an interface. For this reason, SFG is highly surfacespecific and capable of measuring surface vibrational spectra under ambient conditions. For liquid surfaces, it has been shown that SFG from a water surface is dominated by the top * Corresponding author. E-mail: [email protected]. † University of British Columbia. ‡ University of Alberta.

monolayer.23 With the monolayer sensitivity and short probing depth, SFG provides a new opportunity to directly measure the adsorption isotherms at solvent/mineral interfaces. In this article, SFG vibrational spectroscopy was used to study the competitive adsorption of toluene and n-alkanes on silica, which is one of the most abundant minerals and has also been used in liquid chromatography.24-27 The adsorption process at a liquid/solid interface is significantly different from that at a gas/solid interface because there is no empty site at a liquid/solid interface. A change in the bulk composition results in the replacement of one component by the other component. The Langmuir isotherm has often been used to describe the adsorption process for dilute solutions at liquid/solid interfaces,17,28-33 but it is a good approximation only for strongly adsorbed molecules. In the current study, the adsorption free energies for the solvents are of the same order of magnitude. Therefore, the Langmuir isotherm is not suitable for the current study. In this article, we obtained the surface coverage of toluene using SFG and used the Everett isotherm to fit the measured adsorption isotherm over the complete toluene fraction range. II. Experimental Section The visible and IR laser beams for SFG vibrational spectroscopy were obtained from a Nd:YAG (yttrium aluminum garnet) laser with an output wavelength of 1064 nm (30 ps, 40 mJ/pulse, and 10 Hz). The laser was used to generate a second harmonic beam at 532 nm in a KTiOPO4 (KTP) crystal. The tunable IR beam was produced by difference frequency mixing of the 1064 nm beam with the output of a KTP optical parametric generator/amplifier pumped by the 532 nm beam. The 532 nm and IR beams were overlapped, both spatially and temporally, on the sample, as shown in Figure 1. The energy of the laser beams was ∼200 µJ/pulse for both the visible and the IR beams. The SFG intensity was detected by a photomultiplier tube and normalized against that from a z-cut quartz. Each spectrum shown in the current study was an average of four scans in a 5 cm-1 step, and each scan was obtained by averaging the SFG intensity of 40 laser shots at each step.

10.1021/jp9043122 CCC: $40.75  2009 American Chemical Society Published on Web 10/29/2009

20356

J. Phys. Chem. C, Vol. 113, No. 47, 2009

Yang et al.

Figure 1. Schematic layout of the spectroscopic setup. The frequency of the visible beam was fixed at 532 nm, and the frequency of the IR beam was tunable. The 532 nm and IR beams were overlapped both spatially and temporally on the top surface of the solution. The thickness of the solvent layer is 3 mm.

Fused silica plates, with a thickness of 3 mm, were cleaned with a commercial cleaning agent (Extran AP12) for 3 min. Next, they were immersed in a 50/50 (v/v) HNO3/H2SO4 solution for ∼12 h, followed by rinsing in pure water (resistivity >18.2 MΩ · cm), and finally dried at 100 °C for 2 h to remove residual surface water. After these treatments, the silica plates were kept in toluene to prevent further water adsorption on the surface. Toluene, pentane, heptane, and tetradecane (Fisher; HPLC grade) were used as received to prepare binary mixtures with different volume fractions. The SFG spectrum of the pure toluene/silica interface was monitored at the beginning and the end of the experiment for each toluene-alkane mixture to ensure that the sample had stayed consistent during the experimental period. After the pure toluene/silica SFG spectrum was measured, the SFG spectra of a series of toluene-heptane mixtures with B ) 0.8, 0.6, 0.4, 0.2, and 0 were toluene volume fraction φtoluene measured in the sequence from the highest toluene fraction to the lowest. For each binary mixture with a particular toluene fraction, the cell and silica plates were rinsed thoroughly with the mixture before the spectroscopic measurement. The rinsing process ensured that the bulk mixture in the cell had the intended toluene fraction. For each toluene fraction, four scans were collected in a period of 30 min during which no change of the SFG spectrum was observed. The cell and silica plates were then cleaned with acids as described above for experiments with a different alkane. All spectra were taken at room temperature. III. Results and Analysis The SFG vibrational spectra of toluene/silica interfaces in ssp (SFG, visible, and IR polarizations are s-, s-, and p-polarized, respectively) and ppp are shown in Figure 2A. The peaks are assigned as follows: 2860 and 2875 cm-1 to the combination/ overtone modes, 2920 cm-1 to the symmetric stretch of the CH3, 3022 cm-1 to the ν20a CH stretching mode of the phenyl group, and 3075 cm-1 to the ν2 CH stretching mode of the phenyl group.34 Previously, Hommel et al. have observed a peak at 2945 cm-1 at the air/toluene surface using SFG and assigned the peak to the CH3 asymmetric mode. However, the ssp and ppp intensity ratio of the 2945 cm-1 peak in Figure 2A is not consistent with the CH3 asymmetric mode. Assuming the orientational distribution of the CH3 groups is a delta function, the ratio of the second-order nonlinear susceptibility in ssp and (2) (2) )/(χppp ) can be calculated as a function ppp configurations (χssp 35 of the CH3 tilting angle, and the results are shown in Figure 2B. (The detailed calculation is available in the Supporting Information.) For the CH3 asymmetric mode, the calculated ratio (2) (2) (χssp )/(χppp ) is always less than 1, even with a finite distribution (2) )/ width, but the spectrum in Figure 2A indicates a ratio of (χssp

Figure 2. (A) SFG vibrational spectra of toluene in ssp and ppp polarization configurations. The ssp and ppp spectra are offset from (2) each other by 0.5 arbitrary units for clarity. (B) Calculated (χssp )/(χ(2) ppp) for CH3 symmetric (solid line) and asymmetric (dashed line) modes as a function of the CH3 tilting angle with respect to the surface normal. The orientational distribution of the CH3 groups was assumed to be a (2) delta function. The “b” indicates the measured (χssp )/(χ(2) ppp) value of 4.4, which corresponds to a tilting angle of 25°. (2) ) ≈ 3. Therefore, the 2945 cm-1 peak is unlikely an (χppp asymmetric mode and could be a Fermi resonance associated with the symmetric mode. For the CH3 symmetric mode, the (2) measured ratio (χ(2) ssp)/(χppp) is ∼4.4, which corresponds to a tilting angle of 25° with respect to the surface normal, as indicated by the “b” and the dotted lines in Figure 2B. This tilting angle is in reasonable agreement with the molecular dynamic simulation for adsorption of toluene on silica, showing the plane of the phenyl ring mostly adopts an upright geometry with a tilting angle of about 30° with respect to the surface normal because of the interaction of its π electrons with the silica surface.36 Figure 3a-f shows the ssp SFG spectra of toluene-pentane mixtures with the bulk toluene volume fraction φBtoluene ) 1, 0.8, 0.6, 0.4, 0.2, and 0, respectively. Previously, Selfer et al. studied the adsorption of alkanes on silica and showed that hexadecane lies flat on the silica surface.37 When the axis of the CH3 group is along the surface, the asymmetric peak will dominate, and the symmetric peak will be missing. If the axis of the CH3 group is along the surface normal, the situation will be reversed. The spectrum of pure pentane on silica in Figure 2f shows two peaks at 2857 and 2951 cm-1, which are consistent with the CH2 symmetric and CH3 asymmetric modes, respectively.38-41 Figure 3a-f shows that the peak intensities of the toluene ν20a and ν2 modes decrease as φBtoluene decreases. The spectra shown in Figure 3 were collected in the sequence from the highest toluene volume fraction (φBtoluene ) 1) to the lowest (φBtoluene ) 0). Within the measurement error, similar spectra were obtained for experiments carried out in a reversed order. Therefore, the competitive adsorption process is reversible, and the surface composition depends only on the bulk mole fraction of toluene, not on the history of the system.

Competitive Adsorption of Toluene and n-Alkanes

J. Phys. Chem. C, Vol. 113, No. 47, 2009 20357

I( ωSFG) ∝ |[L(ωSFG) · e(ωSFG)] · χ(2):[L(ωvis) · e(ωvis)][L(ωIR) · e(ωIR)]| 2 · I(ωvis) · I(ωIR) (1) where L(ωi) is the tensorial Fresnel coefficient, e(ωi) is the unit polarization vector, χ(2) is the surface nonlinear susceptibility tensor, and I(ωvis) and I(ωIR) are the intensities of the incident visible and IR beams, respectively. The surface nonlinear susceptibility χ(2) ijk can be expressed as

(2) (2) χijk ) χNR +

A

∑ ωIR - ωq,ijkq + iΓq

(2)

q

Figure 3. SFG vibrational spectra of toluene-pentane mixtures on B silica with toluene volume fraction φtoluene ) (a) 1, (b) 0.8, (c) 0.6, (d) 0.4, (e) 0.2, and (f) 0.

where χ(2) NR describes the nonresonant contribution, and Aq,ijk, ωq, and Γq are the amplitude, frequency, and damping constant of the qth vibrational mode, respectively. The amplitude Aq,ijk in the lab coordinate is related to the molecular hyperpolarizability Rq,lmn in the molecular coordinates:

Aq,ijk ) nS

∑ Rq,lmn〈(iˆ · ˆl)(jˆ · mˆ)(kˆ · nˆ)〉

(3)

l,m,n

Figure 4. SFG vibrational spectra of toluene-heptane mixtures on B silica with toluene volume fraction φtoluene ) (a) 1, (b) 0.8, (c) 0.6, (d) 0.4, (e) 0.2, and (f) 0.

Experiments were repeated for toluene-heptane and toluenetetradecane binary mixtures on silica, as shown in Figures 4 and 5, respectively. While the spectrum of pure heptane on silica (Figure 4f) is similar to that of pure pentane on silica in Figure 3f, a significant CH3 symmetric peak at 2875 cm-1 and a CH2 asymmetric peak at 2920 cm-1 were observed at tetradecane/ silica interfaces.39 Therefore, there is an increasing conformational disorder for longer alkane chains. Because both toluene and alkanes have CH peaks, the CH peaks are not good indicators for the adsorbed chemical species on silica. On the other hand, the ν20a and ν2 peaks from the phenyl group are the unique signature of toluene and allow us to quantitatively study toluene absorption on the silica surface. Because the intensity of the ν20a peak is higher than that of the ν2 peak, the following analysis will focus on the ν20a peak to obtain the absorption isotherm of toluene on silica. To obtain quantitative information, further theoretical analysis of the SFG spectra is required. The detailed theoretical background of SFG can be found in ref 16. Briefly, the SFG intensity is given by

where nS is the surface number density, and the angular brackets refer to an average over the molecular orientation. If the orientation of the molecule on a surface is not strongly dependent on the coverage, the amplitude Aq,ijk is proportional to the surface density nS. In the current study, the orientation of toluene was verified using the ratio of the ν20a peak in ssp and ppp configurations.17 The amplitude ratio (Appp)/(Assp) was found to be ∼0.42 and independent of the toluene coverage. Therefore, it is feasible to correlate the amplitude of the ν20a peak to the surface number density of toluene on silica. The SFG spectra in Figures 3-5 were fitted using eqs 1 and 2 to obtain the amplitude Aq,ijk. Calculating the Fresnel coefficients described in eq 1 requires the refractive index of the mixture nmix. In general, nmix changes with the mixture composition. The refractive index of a mixture follows a “mixture rule”42

Figure 5. SFG vibrational spectra of toluene-tetradecane mixtures B ) (a) 1, (b) 0.8, (c) 0.6, on silica with toluene volume fraction φtoluene (d) 0.4, (e) 0.2, and (f) 0.

20358

J. Phys. Chem. C, Vol. 113, No. 47, 2009

Yang et al.

nmix ) φ1n1 + φ2n2

(4)

where φi and ni are the volume fraction and the refractive index of component i, respectively. Although small deviations from eq 4 have been reported,43 the small deviations are insignificant for the current study. The refractive indices for toluene, pentane, heptane, and tetradecane are 1.4963, 1.357, 1.38, and 1.428, respectively.44 The amplitude Aq,ijk was then calibrated using eqs 1 and 4 so that Aq,ijk is proportional to the surface number density nS. The toluene surface coverage θc ≡ (nS)/(nSmax), where nSmax is the maximum density adsorbed on the surface when only toluene is presented in the solution, was then derived using the amplitude of the ν20a peak. Figure 6 shows the toluene surface coverage as a function of the bulk mole fraction. As shown in Figure 6, toluene competes favorably against pentane, but the advantage decreases as the chain length of the alkane increases. This is consistent with the conclusion that alkanes lie flat on the silica surface. In this geometry, the molar adsorption energy of the alkanes increases as the chain length increases. To gain better insight into the competitive adsorption process, a theoretical model is needed. The well-known Langmuir equation is not a good description for the adsorption at liquid/solid interface because there is no empty site at a liquid/ solid interface. A number of theories have been developed for the adsorption isotherm at binary liquid/solid interfaces over the complete mole fraction range.13,15,45-48 It has been shown that, for adsorption on a homogeneous surface from an ideal miscible binary liquid with components 1 and 2, the surface mole fraction of component 1 can be written as15

xS1 )

K1xB1

(5)

1 + (K1 - 1)xB1

Figure 6. Adsorption isotherms of toluene on silica for binary mixtures of pentane-toluene (9), heptane-toluene (b), and tetradecane-toluene (2). The solid curves are fitting curves using eq 8.

of toluene and alkanes are comparable, this approximation is not valid for the current study. The Everett isotherm will be used in the following analysis. The amplitude of SFG peaks, as described in eq 3, measures the surface number density nS, instead of the surface mole fraction x1S shown in eq 5. Therefore, it is desirable to express eq 5 in terms of surface coverage θc. Equation 5 can be rewritten as15

θc ≡

nS1 S nmax,1

)

βK1xB1 1 + (βK1 - 1)xB1

with

β≡

with

{

(µ°S1 - µ°B1 ) - (µ°S2 - µ°B2 ) K1 ) exp RT ∆a µ°1 - ∆a µ°2 ) exp RT

{

}

} (6)

where x1B and x2B are the bulk mole fractions for components 1 and 2, respectively, x1S and x2S are the surface mole fractions for components 1 and 2, respectively, R is the gas constant, T is the temperature, µ°Bi and µ°Si are the chemical potential (or partial molar Gibbs free energy) of component i in its standard state for the bulk and surface, respectively, and ∆a µ°i ≡ µ°Si - µ°Bi is the chemical potential change associated with the adsorption of component i. The above expression was derived by Everett,46 and it is often called the Everett isotherm. If component 1 is a molecule strongly adsorbed on the surface, or -(∆a µ°1 - ∆a µ°2) . RT, one gets K1 . 1. In this case, eq 5 can be approximated by

xS1

)

K1xB1 1 + K1xB1

(7)

This expression is analogous to the Langmuir equation. However, the Langmuir equation is a good approximation only for a strongly adsorbed component. As the adsorption free energies

(8)

S nmax,2 S nmax,1

(9)

Equations 8 and 9 indicate that the adsorption isotherm is governed by the values of β and K1. The value of β describes the relative footprint on the surface for components 1 and 2, and the value of K1 is determined by the adsorption free energy difference between the two components. The Everett isotherm as described in eq 8 allows a more quantitative analysis for the measured isotherms in Figure 6. The values of β and K1 are coupled in eq 8. Without additional information, the measured adsorption isotherms in Figure 6 are not sensitive to the individual value of β and K1. Using βK1 as a single parameter to fit the measured adsorption isotherms in Figure 6, we obtained the best fit with βK1 ) 1.69, 0.659, and 0.296 for pentane, heptane, and tetradecane mixtures, respectively. To estimate K1, further assumptions must be made for S S )/(nmax,1 ), is mainly β. The value of β, defined as β ≡ (nmax,2 determined by the sizes of the molecules because a larger molecule has a larger footprint on the surface and a smaller S . The space that a molecule occupies can be value of nmax estimated using the molar volume. The molar volumes Vm of toluene, pentane, heptane, and tetradecane are 106.29, 115.26, 146.51, and 260.3 mL/mol. To a first approximation, the value of β should scale as ((Vm,2)/(Vm,1))2/3, which corresponds to a random adsorption geometry on silica. With this assumption, the values of β are 0.95, 0.81, and 0.55 for the toluene-pentane, toluene-heptane, and toluene-tetradecane mixtures, respectively. However, molecules adsorbed on a surface have a

Competitive Adsorption of Toluene and n-Alkanes preferred orientation, and the β values need to be calibrated with an orientation factor. As described above, the tilting angle of toluene with respect to the surface normal was estimated at θ ≈ 25°, and the alkanes mostly lie flat on the silica surface with θ ≈ 90°. With a preferred orientation, the average footprint of molecules on the surface scales as (〈sin θ〉oriented)/(〈sin θ〉random), where the angle brackets denote the orientational average 〈sin θ〉 ) (∫f(θ) sin θ dΩ)/(∫f(θ) dΩ) with f(θ) denoting the orientational distribution function. Assuming the orientational distribution function is a delta function with θ ) 25° for toluene and θ ) 90° for alkane, the values of β become 0.40, 0.34, and 0.23 for toluene-pentane, toluene-heptane, and toluenetetradecane mixtures, respectively. The best fit for K1 then was obtained with ∆a µ°toluene - ∆a µ°pentane ) -3.4 ( 0.3 kJ/mol, ∆a µ°toluene - ∆a µ°heptane ) -1.8 ( 0.3 kJ/mol, and ∆a µ°toluene - ∆a µ°tetradecane ) -0.84 ( 0.3 kJ/mol. The best-fit curves are shown in Figure 6. Overall, toluene competes favorably against the alkanes on silica, and the adsorption free energy of the alkanes increases as the chain length increases. IV. Conclusions IR-visible sum frequency vibrational spectroscopy was applied to study the competitive adsorption of toluene and n-alkanes at binary solution/silica interfaces. The surface coverage of toluene on silica for toluene-pentane, tolueneheptane, and toluene-tetradecane mixtures was obtained using the measured SFG peak intensity of toluene. The competitive adsorption processes are reversible, and the surface coverage of toluene only depends on the toluene molar fraction in the binary mixture, not on the history of the mixture in contact with the silica. The measured adsorption isotherms fitted well with the Everett isotherm over the complete mole fraction range. The estimated molar adsorption free energy of toluene is 3.4 ( 0.3, 1.8 ( 0.3, and 0.84 ( 0.3 kJ/mol higher than pentane, heptanes, and tetradecane, respectively. Overall, toluene competes favorably on silica against the alkanes, and the molar adsorption free energy difference between toluene and alkane decreases as the chain length of the alkane increases. Acknowledgment. This work was financially supported by the Imperial Oil-Alberta Ingenuity Centre for Oil Sands Innovation (COSI) and the Natural Sciences and Engineering Research Council of Canada (NSERC). Supporting Information Available: Theory for calculating the orientation of CH3 group. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Long, Y. C.; Dabros, T.; Hamza, H. Fuel 2004, 83, 823. (2) Stasiuk, E. N.; Schramm, L. L. Fuel Process. Technol. 2001, 73, 95. (3) Arabshahi, S. H.; Ackerson, M. D.; Rye, W. C.; Babcock, R. E. Chem. Eng. Commun. 1990, 89, 195.

J. Phys. Chem. C, Vol. 113, No. 47, 2009 20359 (4) Acevedo, S.; Ranaudo, M. A.; Garcia, C.; Castillo, J.; Fernandez, A. Energy Fuels 2003, 17, 257. (5) Kenchington, J. M.; Phillips, C. R. Energy Sources 1981, 5, 317. (6) Grandel, S.; Dahmke, A. Biodegradation 2004, 15, 371. (7) Scullion, J. Naturwissenschaften 2006, 93, 51. (8) Khaitan, S.; Kalainesan, S.; Erickson, L. E.; Kulakow, P.; Martin, S.; Karthikeyan, R.; Hutchinson, S. L. L.; Davis, L. C.; Illangasekare, T. H.; Ng’oma, C. EnViron. Prog. 2006, 25, 20. (9) Luo, Y.; Zou, L.; Hu, E. EnViron. Technol. 2006, 27, 359. (10) Hubert, A.; Wenzel, K. D.; Manz, M.; Weissflog, L.; Engewald, W.; Schuurmann, G. Anal. Chem. 2000, 72, 1294. (11) Saim, N.; Dean, J. R.; Abdullah, M. P.; Zakaria, Z. J. Chromatogr., A 1997, 791, 361. (12) Fowkes, F. M. Ind. Eng. Chem. 1964, 56, 40. (13) Everett, D. H. Pure Appl. Chem. 1986, 58, 967. (14) Blackburn, A.; Kipling, J. J. J. Chem. Soc. 1954, 3819. (15) Oscik, J. Adsorption; Chichester: New York, 1982. (16) Miranda, P. B.; Shen, Y. R. J. Phys. Chem. B 1999, 103, 3292. (17) Zhang, L. N.; Liu, W. T.; Shen, Y. R.; Cahill, D. G. J. Phys. Chem. C 2007, 111, 2069. (18) Lambert, A. G.; Davies, P. B.; Neivandt, D. J. Appl. Spectrosc. ReV. 2005, 40, 103. (19) Gracias, D. H.; Chen, Z.; Shen, Y. R.; Somorjai, G. A. Acc. Chem. Res. 1999, 32, 930. (20) Shultz, M. J.; Schnitzer, C.; Simonelli, D.; Baldelli, S. Int. ReV. Phys. Chem. 2000, 19, 123. (21) Chen, Z.; Shen, Y. R.; Somorjai, G. A. Annu. ReV. Phys. Chem. 2002, 53, 437. (22) Shen, Y. R.; Ostroverkhov, V. Chem. ReV. 2006, 106, 1140. (23) Morita, A.; Hynes, J. T. Chem. Phys. 2000, 258, 371. (24) Taylor, D. R.; Maher, K. J. Chromatogr. Sci. 1992, 30, 67. (25) Crego, A. L.; Gonzalez, A.; Marina, M. L. Crit. ReV. Anal. Chem. 1996, 26, 261. (26) Vissers, J. P. C.; Claessens, H. A.; Cramers, C. A. J. Chromatogr., A 1997, 779, 1. (27) Vervoort, R. J. M.; Debets, A. J. J.; Claessens, H. A.; Cramers, C. A.; de Jong, G. J. J. Chromatogr., A 2000, 897, 1. (28) Blum, L.; Huckaby, D. A. J. Chem. Phys. 1991, 94, 6887. (29) Zhu, B. Y.; Gu, T. R. AdV. Colloid Interface Sci. 1991, 37, 1. (30) Chang, C. H.; Franses, E. I. Colloids Surf., A 1995, 100, 1. (31) Zhang, Z. H.; Tsuyumoto, I.; Takahashi, S.; Kitamori, T.; Sawada, T. J. Phys. Chem. A 1997, 101, 4163. (32) Cosman, N. P.; Roscoe, S. G. Langmuir 2004, 20, 1711. (33) Mohan, D.; Pittman, C. U.; Steele, P. H. J. Colloid Interface Sci. 2006, 297, 489. (34) Hommel, E. L.; Allen, H. C. Analyst 2003, 128, 750. (35) Zhuang, X.; Miranda, P. B.; Kim, D.; Shen, Y. R. Phys. ReV. B 1999, 59, 12632. (36) Choi, P. Private communication, 2009. (37) Sefler, G. A.; Du, Q.; Miranda, P. B.; Shen, Y. R. Chem. Phys. Lett. 1995, 235, 347. (38) Snyder, R. G.; Strauss, H. L.; Elliger, C. A. J. Phys. Chem. 1982, 86, 5145. (39) Macphail, R. A.; Strauss, H. L.; Snyder, R. G.; Elliger, C. A. J. Phys. Chem. 1984, 88, 334. (40) Snyder, R. G. J. Chem. Phys. 1967, 47, 1316. (41) Snyder, R. G. J. Chem. Phys. 1965, 42, 1744. (42) Heller, W. J. Phys. Chem. 1965, 69, 1123. (43) Brocos, P.; Pineiro, A.; Bravo, R.; Amigo, A. Phys. Chem. Chem. Phys. 2003, 5, 550. (44) Dean, J. A.; Lange, N. A. Lange’s Handbook of Chemistry, 15th ed.; McGraw-Hill: New York, 1999. (45) Fu, Y.; Hansen, R. S.; Bartell, F. E. J. Phys. Colloid Chem. 1948, 52, 374. (46) Everett, D. H.; Munn, R. J. Trans. Faraday Soc. 1964, 60, 1951. (47) Ash, S. G.; Everett, D. H.; Findeneg, Gh. Trans. Faraday Soc. 1970, 66, 708. (48) Ash, S. G.; Bown, R.; Everett, D. H. J. Chem. Thermodyn. 1973, 5, 239.

JP9043122