16444
J. Phys. Chem. B 2005, 109, 16444-16454
Structure of Nonpolarizable Water/Nitrobenzene Interface: Potential Distribution, Ion Adsorption, and Interfacial Tension Vladislav S. Markin,*,† Alexander G. Volkov,‡ and Maya I. Volkova-Gugeshashvili‡ Department of Anesthesiology, UT Southwestern Medical Center, Dallas, Texas 75390-9068, and Department of Chemistry, Oakwood College, HuntsVille, Alabama 35896 ReceiVed: June 1, 2005; In Final Form: July 11, 2005
Adsorption of hydrophobic and hydrophilic ions at the nonpolarizable interface between two immiscible electrolyte solutions was investigated. The results were analyzed in three different models: (i) Gouy-Chapman model, (ii) ions as hard spheres, and (iii) ion pair formation at the interface. In the Gouy-Chapman model, an analytical expression for the interfacial tension was obtained. It predicts that interfacial tension should be proportional to the square root of the electrolyte concentration, which does not agree with experimental data. Modeling ions as hard spheres only slightly improves the agreement. The third model of interfacial ion pairing as the main origin of adsorption was analyzed using the amphiphilic isotherm (Markin-Volkov isotherm). A good agreement between ion-pairing theory and experimental values was achieved. The MV isotherm takes into account the limited number of adsorption sites, final size of molecules, complex formation at the interface, and interaction between adsorbed particles. The analysis revealed repulsion between adsorbed tetraalkylammonium ions at the nitrobenzene/water interface and demonstrated linear dependence between adsorption site area and the size of a molecule.
Introduction The physical and chemical properties of the oil/water interface have been actively investigated during the last two centuries.1 Nonpolar solvents, such as liquid hydrocarbons, were used for modeling biomembrane surfaces, interfacial electron and ion transfer in the presence of biologically active compounds,2 electrodeposition of metal monolayers and ultrathin films in nanochemistry,3 catalysis, artificial photosynthesis, organic synthesis, emulsions, and biomedical applications.2 Another type of the oil/water interface is the interface between two immiscible electrolyte solutions (ITIES) in polar solvents, such as water/nitrobenzene, water/1,2-dichloroethane, and water/ methylbutyl ketone. There are two different electrochemical classes of ITIES:4-8 polarizable and nonpolarizable interfaces. At the polarizable interfaces, Faraday processes are neglectable, and charge transfer between two phases practically does not occur in a potential window, which depends on Gibbs free energy of ion transfer. At the nonpolarizable oil/water interface, the electrolyte is distributed between two phases, and interfacial potential of symmetrical 1:1 or 2:2 electrolytes does not depend on its concentration.9,10 The nonpolarizable oil/water interfaces are very important in the electrochemistry of ion-selective electrodes, extraction, separations, liquid ion-exchange membranes, and electroanalytical applications.2,11 The specific adsorption of ions at the oil/water interface is believed to be the result of formation of interfacial ion pairs. At electrified nitrobenzene/water and 1,2-dichloroethane/water interfaces, as has been shown by Cheng et al.,12 the dependence * Author to whom correspondence should be addressed. E-mail:
[email protected]. Telephone: 214-648-5632. Fax 214648-6532. † Department of Anesthesiology, UT Southwestern Medical Center. ‡ Department of Chemistry, Oakwood College.
of interfacial capacitance at polarizable ITIES on interfacial potential difference shows the effect of ion pair formation between ions in the aqueous and the organic phases. For polarizable 2-heptanone/water, 2-octanone/water, and 1,3-dibromopropane/water interfaces, Pereira et al.13 showed that the interfacial ion pairing model is capable of explaining measured capacitances. The Bjerrum theory has been transposed to analyze the formation of interfacial ion pairs. Experimental study of the adsorption of tetraalkylammonium salts at the water/nitrobenzene interface was performed by Gugeshashvili,14 Boguslavskii et al.,15 Gavach et al.,16 and Gugeshashvili et al.17 The classical treatment of the electric double layer had been extended to the interface between two immiscible electrolyte solutions. Gavach et al.16 suggested a complete ionic dissociation of electrolyte in nitrobenzene and applied the Gouy-Chapman model for estimation of Gibbs adsorption. It was shown that the Gouy-Chapman model18,19 predicts experimental values of Gibbs surface excesses at very low concentration of tetraalkylammonium bromides. The difference between experimental values and theoretical predictions dramatically increases with increasing concentration. Gavach et al.16 suggested the possibility of ion pair formation at ITIES. In this paper, we measured the adsorption of tetraalkylammonium salts at the water/nitrobenzene interface and performed detailed theoretical analysis of interfacial tension, ion adsorption, and potential distribution at the nonpolarizable water/nitrobenzene interface. The experimental results were analyzed in three models: (i) Gouy-Chapman model, (ii) ions as hard spheres, and (iii) ion pair formation at the interface. The first two models failed to account for the observation while the third model was very successful. It is based on the amphiphilic isotherm (MV isotherm).1 The MV isotherm takes into account the limited number of adsorption sites, final size of the molecules, complex
10.1021/jp0529220 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/06/2005
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J. Phys. Chem. B, Vol. 109, No. 34, 2005 16445
formation at the interface, and interaction between adsorbed molecules.1,2,11,20,21 Material and Methods A system consisting of equal volumes of nitrobenzene and water was equilibrated for 48 h. All the solutions were prepared with twice-distilled water. Tetraalkylammonium salts (Sigma) were added to water saturated with nitrobenzene and equilibrated for 48 h with an equal volume of nitrobenzene saturated with water. The interfacial tension at the water/nitrobenzene interface was determined using the drop-weight method at 22 °C. This method determines the weight and volume of the drop falling from the end of a capillary tube under the force of gravity. The surface tension γ is obtained from the equation:
γ)
V(d1 - d2)fg r
where f is a correction factor from the Harkins-Brown table.2 It is a function of r/V1/3 and takes into account the deviation of the drop shape from an ideal sphere. V is the volume of the drop, d1 and d2 are the densities of the immiscible liquids, g is the acceleration due to gravity, and r is the radius of the tip, which is taken as the radius of the outside wall when the drop covered the bottom of the tip or radius of the inside wall when the liquid exuded without wetting the bottom of the orifice. The surface tension apparatus consists of a glass capillary tube, 1 cm3 syringe, micrometer, and a container. The internal capillary diameter was about 0.060 cm and the outer one was 0.522 cm. The drop lifetime used to establish adsorption equilibrium was at least 10 min. If the drops form quickly, they will detach prematurely. This early detachment causes errors in the measurement of interfacial tension. Thus, slow drop formation is imperative prior to detachment.2 The remarkable accuracy of this method arises from the fact that the surface excess Γ is proportional to the surface activity dγ/dc, and the relatively small changes of γ due to changes of the concentration of the surface active compound are more important than the absolute values of the decreasing interfacial tension with increasing concentration. Two important details of the drop-weight method should be noted. First, it is essential to purify all of the solvents and solutes, including water, to remove all possible impurities which can reduce interfacial tension. Second, the apparatus must also be assembled so that the influence of vibration is minimized. Otherwise, the drops will detach too soon and erroneous values of interfacial tension will be obtained. For calibration of the syringe connected to the micrometer, drops of distilled water are permitted to fall into a container, which is weighed before and after a certain number of drops has fallen. The volume of liquid per unit scale of a micrometer can then be estimated. Results When a salt is introduced into the water/nitrobenzene system (Figure 1), it partitions between two phases, creates a potential profile, and changes the interfacial tension at the border between them. The interfacial tension measured in this system is presented in Figure 2 A-D as a function of the electrolyte concentration in the linear plots. Later, we shall also use the semilogarithmic plots. This presentation helps to distinguish between different models of the interface. The interfacial tension decreases with increasing concentration of salts, which suggests
Figure 1. Potential profile at the nonpolarizable interface between two immiscible electrolyte solutions and the model of hard spheres. Designations: a is the ion radius, φd is the distribution potential, and φs is the potential at the interface.
that the electrolytes accumulate at the interface. Qualitatively, this can be explained either by a nonspecific adsorption in the diffuse parts of two back-to-back electric double layers in the Gouy-Chapman model or by specific adsorption of ions at the interface.2 We shall consider both models and some modification of them. The linear representation of data helps to understand the behavior of the system at small concentration of electrolytes. The semilogarithmic plots demonstrate that, at high concentration, this dependence can approach the straight line, indicating that there is a saturation of solute adsorption at the interface with a limited number of adsorption sites. Fitting the appropriate adsorption isotherm to the experimental points permits determining the density of sites and the equilibrium constant of adsorption. The difference of electrical potential between two phases caused by partitioning of an electrolyte is called a distribution potential:2,9
φd ) ∆wnbφ )
∆wnbφ0cat + ∆wnbφ0an γwcat γnb an + w nb 2 γ γ an
(1)
cat
where ∆wnb φ0cat and ∆wnb φ0an are the standard distribution potentials of individual ions. We consider the bulk of the water as a reference point, so φd is the potential in the bulk of nitrobenzene (Figure 1). In practice, the activity coefficients for 1:1 electrolyte nb can be assumed to be equal (γwcat ≈ γwan, γnb cat ≈ γan ), and then the second term in this equation disappears. Salt concentrations cw and cnb in two phases are related by the equation
P)
[
]
F(∆wnbφ0an - ∆wnbφ0cat) cnb ) exp 2RT cw
(2)
0 The standard potentials of distribution ∆nb w φi of ions i can be found in ref 2. They are presented in Table 1. On the basis of these numbers, one can calculate distribution potential and the ratio of salt concentration in nitrobenzene and water (Table 2). These numbers represent thermodynamic data for the bulk of solutions (with exception of φsurface). However, to calculate the profile of potential, electrolyte concentration, and surface excesses, one needs a model of the interface. We shall start with the classical approach of Gouy-Chapman.2,18,19 Gouy-Chapman Model. This model at the nonpolarizable oil/water interface considers ions freely moving between two dielectric continuums, water and nitrobenzene (Figure 1). Electrical potential in the system is determined by the PoissonBoltzmann equation. In water (x < 0) it is:
d2φw 2
dx
)-
[ (
)
( )]
Fφw Fφw Fcw exp - exp 0w RT RT
(3)
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Markin et al.
Figure 2. Dependence of interfacial tension between water and nitrobenzene on electrolyte concentration. Experimental points were measured as described in Materials and Methods and presented in the linear scales. The solid curves were drawn according to Gouy-Chapman model (eqs 24, 25) and the hard sphere model is presented by the dashed lines (eq 30) with the following parameters: (A) TBACl, b1 ) 52.496, g1 ) -23.65, g2 ) 5.40; (B) TBABr, b1 ) 52.016, g1 ) -23.05, g2 ) 5.747; (C) TBAI, b1 ) 48.044, g1 ) -32.395, g2 ) 41.88; (D) TEACl, b1 ) 52.496, g1 ) -4.326, g2 ) 0.899.
The distribution potential of salt, as well as the distribution potential of individual ions can be presented in a similar way:
TABLE 1: Standard Potentials of Distribution ∆wnb φ0i of Ions i and Their Radii ions, i
TBA+
TEA+
Cl-
Br-
I-
∆wnb φ0i , mV ri, nm
-255 0.437
-67 0.348
-316 0.164
-295 0.180
-195 0.205
TABLE 2: Distribution Potential and the Ratio of Salt Concentration in Nitrobenzene and Water nb
w
salt
φd, mV
c /c
TBACl TBABr TBAI TEACl
285.5 275 225 191.5
0.2995 0.4536 3.2732 0.007292
dx2
)-
φsurface, mV
κw )
117.58 117.56 117.25 31.80
cw
)
(
)]
where and are concentrations of the salt in the bulk of water and nitrobenzene, correspondingly. Boundary conditions2 at the interface (x ) 0) are:
|
|
dφnb ) nb dx x)0
d 2ψ ) eψ - e-ψ dξ2
Fφ RT
(10)
The first and the second integrals of this differential equation can be readily found as
dψ ) exp(ψ/2) - exp(-ψ/2) dξ
(5)
x)0
(11)
and
Following the Gouy-Chapman approach, we introduce the dimensionless potential:
ψ)
(9)
With these variables, the Poisson-Boltzmann eq 2 takes a very simple form:
cnb
dφw dx
(8)
we introduce the dimensionless coordinate ξ in water:
F(φnb - φd) F(φnb - φd) Fcnb exp - exp 0nb RT RT (4)
φw(0) ) φnb(0) ≡ φS and w
x
2F2cw 0wRT
ξ ) κ wx
[ (
(7)
Using the Debye constant in water:
and in nitrobenzene (x > 0) it is:
d2φnb
Fφd RT
ψd )
(6)
ψ(ξ) ) 2 ln
exp(ψS/2) + 1 + [exp(ψS/2) - 1] exp(ψ) exp(ψS/2) + 1 - [exp(ψS/2) - 1] exp(ψ)
where ψS is the potential at the interface.
(12)
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J. Phys. Chem. B, Vol. 109, No. 34, 2005 16447
The surface excesses of cations and anions in water can be found in the following way:
cw κw
Γw ) Γwcat + Γwan )
∫-∞0 (e-ψ(ξ) + e+ψ(ξ) - 2) dξ ) cw [exp(ψS/4) - exp(-ψS/4)]2 (13) κw
In the nitrobenzene phase, similar parameters are
κnb )
x
2e20cnb ) 0nbkT
x
2e20cw Pw ) κw × 0wkT nb
x
Pw , σ ) κnbx nb (14)
The first and the second integrals of eq 3 are:
(
)
(
)
ψ - ψd ψ - ψd dψ - exp ) exp dσ 2 2
(15)
and ψ(ξ) )
( (
) )
[ ( [ (
) ] ( ) ] (
) )
ψS - ψ d ψ S - ψd ψd - ψ + 1 + exp - 1 exp 2 2 2 2 ln ψ S - ψd ψS - ψd ψd - ψ exp + 1 - exp - 1 exp 2 2 2 exp
(16) The surface excesses in nitrobenzene are: nb Γnb ) Γnb cat + Γan )
cnb κnb
∫-∞0 (exp[- (ψ(ξ) - ψd)] +
exp[ψ(ξ) - ψd] - 2) dσ )
[ ( (
)
ψS - ψd cnb exp κnb 4 ψS - ψd 2 (17) exp 4
)]
To complete this calculation of surface excesses, we need surface potential ψs. It can be found from the second boundary condition (5). By substituting into it the first integrals (11) and (15), one obtains the equation for ψs:
[ ( )
wκw exp
( )] ) [ (
ψS ψS - exp ) 2 2 ψS - ψd ψS - ψd - exp nbκnb exp 2 2
(
)]
(18)
for 0.1 M TBACl. All other salts give qualitatively similar pictures. Notice the break in the curve in Figure 3B, which is the result of the boundary condition (5). We also calculated concentration of ions presented in Figure 4. The concentration experiences a drastic jump at the interface. Now, we have formulas for the surface potential and surface excesses, and we need to calculate the surface tension. In the isothermal case, the surface tension is related to the surface excesses by the Gibbs adsorption equation: 2
dγ ) -
wκw + nbκnb exp(ψd/2) wκw + nbκnb exp(-ψd/2) ln
1 + xPnb/w exp(-ψd/2)
(20)
w
∫0c (Γwcat + Γwan + Γnbcat + Γnban) dccw
(21)
The total surface excess under the integral is:
)
1 + xPnb/w exp(ψd/2)
Γi(w) dµi ∑ i)1
In the simple case of a 1:1 electrolyte, the increment of the surface tension can be presented as:
∆γ ) γ - γ0 ) - kT
from where it follows:
ψS ) ln
Figure 3. Potential distribution in the water/nitrobenzene system with 0.1 M TBACl. (A) The main change of potential occurs within 6 nm on the both sides of the interface. (B) The central portion of the plot (A) is enlarged to demonstrate the brake of the curve which is the result of the boundary condition (eq 5).
(19)
It is interesting to note that, according to this formula, the surface potential at the nonpolarizable oil/water interface does not depend on the concentration of electrolyte, as it is also the case for the distribution potential. Using eqs 12 and 16, together with 19, one can plot potential profile in the whole system (Figure 3). This example is given
nb Γtot ) Γwcat + Γwan + Γnb cat + Γan )
{[ ( )
( )]
ψS ψS exp - exp 4 4
2
x20wkT × e0
[ ( ) ( )] }x
+ xPnb/w exp exp -
ψd - ψS 4
ψ d - ψS 4 2
cw (22)
Notice that the total surface excess is proportional to the square root of the electrolyte concentration in water, and hence,
16448 J. Phys. Chem. B, Vol. 109, No. 34, 2005
Markin et al.
Figure 4. Distribution of ions in the water/nitrobenzene system with 0.1 M TBACl. (A) Cations. (B) Anions. The curves are presented in separate plots because of large difference in concentration.
it can be presented as
Γtot )
1 b xcw 2kT 1
(23)
where coefficient b1 is defined by eq 16 and does not depend on concentration. Integration in eq 14 is easily performed, giving surface tension:
γ ) γ0 - b1xcw
(24)
with coefficient b1 which does not depend on concentration:
{[ ( ) ( )] )] } [ ( ) (
2kTx20wkT ψS 2 ψS b1 ) exp - exp + e0 4 4 ψd - ψS ψd - ψS - exp xPnb/w exp 4 4
able values. This is a typical situation with Gouy-Chapman model with point ions.11,20 Modeling Ions as Hard Spheres. The drawbacks of the Gouy-Chapman model can be partially mended by visualizing ions as hard spheres with appropriate radii ai. This approach was successfully used for calculation of the surface potential and surface tension at the water/air interface.22 The main idea was to use a continuous solvation energy function describing penetration of ions from one media to another one instead of discontinuous, step function for point ions. If the energy of ion i in water is taken as a reference point, then its energy in the bulk of nitrobenzene is: w 0 Unb i ) zie0∆nbφi
2
(25)
Therefore, the surface tension is also proportional to the square root of the electrolyte concentration in water. This dependence is presented in Figure 2 by continues lines. If surface tension is expressed in mN/m and concentration in M, then for TBACl b1 ) 52.496, for TBABr b1 ) 52.016, for TBAI b1 ) 48.044, and for TEACl b1 ) 52.496. One can see that only TBACl can be satisfactorily described by the Gouy-Chapman model and only at low concentration. In other cases, the model exaggerated variation of the surface tension with electrolyte concentration. This is related to the fact that the Gouy-Chapman model predicts very high concentration of ions at interfaces with high potentials. Simple calculations (Figure 4) demonstrate a very large increase of cation concentration at the organic side of the interface (up to 25 M) and similar increase of anion concentration at the water side of the interface (more than 10 M). These numbers exceed all reason-
(26)
Recall that this is the resolvation energy arising from the interaction of the ion with the media.2,23,24 As in ref 22, we assume that when the ion penetrates from one phase to another (Figure 5), its energy is proportional to the surface area exposed to each phase. Then this continuous function is:
{
if x e -ai 0, if -ai < x < ai 0.5(1 + x/a ), ui ) Unb i i if xg ai 1,
}
(27)
This function is presented in Figure 5 for two ions, TBA+ and Cl-. It gives the opportunity to present the total energy of ions in both phases in the universal way: wi(x) ) zie0φ(x) + ui(x). Then the Poisson-Boltzmann eqs 3-4 will change in aqueous phase (x < 0) to:
d2φw
[ (
)
(
)]
e0cw e0φw ucat e0φw uan ) exp exp 0w kT kT kT kT dx2 (28)
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J. Phys. Chem. B, Vol. 109, No. 34, 2005 16449
Figure 5. Resolvation energy of ions.
and in nitrobenzene (x > 0) to:
d2φnb dx2
)-
[ (
)
(
)]
e0cw e0φnb ucat e0φnb uan exp - exp 0nb kT kT kT kT (29)
Notice that the only difference between these two equations is the dielectric permeability w and nb; concentration cw is the same in both equations. Unfortunately, this set of equations does not allow analytical solutions, so we solved them numerically. Results for the case of 1 M TBACl are presented in Figure 6. The profile of potential distribution (panel A) does not noticeably differ from predictions of the Gouy-Chapman model with point ions (Figure 3A), but the surface potential became concentration dependent as shown in Figure 7. Even bigger differences occur in the distribution of ion concentration (Figure 6B, C). First, these curves are continuous, without jumps as in Figure 4, but with some local peaks. Second, the concentration values are considerably smaller than in Figure 4, although in Figure 6, the bulk electrolyte concentration was 10 times higher. Having obtained the ion concentration distribution, we were able to calculate surface excesses of the ions and to perform numerical integration in eq 21. We obtained the following approximate function for the surface tension:
γ ) γ0 + g1xc + g2c
(30)
These theoretical functions (hard spheres isotherm) are presented in Figure 2 with dashed lines. One can see that, in comparison with the Gouy-Chapman model, the hard spheres isotherm shifted in the direction of experimental points and, in some cases, even overshoots them. Ion Pairs at the Interface. All electrolytes used in this work consist of hydrophobic cations that strongly prefer organic phase and hydrophilic anions that equally strongly prefer aqueous phase. As was shown above, because of such a preference, there is a strongly elevated concentration of anions at the aqueous side of the interface and the high concentration of cations at the organic side of the interface. This gives the possibility of formation of ion pairs right at the interface, and the ion pairs can be trapped in this region. In this sense, the ion pairs behave as an amphiphilic surfactant. The general form of the adsorption isotherm for amphiphilic compounds (MV isotherm) was developed by Markin and Volkov.1,2,11,20,21 It considers surfactant molecule A that can adsorb at the interface with possible aggregation and become the molecule B. It can replace a few molecules from both sides of the interface that can be visualized
Figure 6. Model of hard spheres. Distribution of potential and concentration in the water/nitrobenzene system with 1 M TBACl. (A) Potential. (B) Concentration of cations. (C) Concentration of anions.
as a quasimolecule of solvent Q, so that molecule B replaces p quasimolecules Q. The total amount n of adsorbed molecules Q is limited by the number nmax, so that the fraction Θ of the surface covered with amphiphilic molecules is Θ ) n/nmax. If the molar ratio of the molecules A is X, then the coverage Θ is determined by the equation:
Θ[p - (p - 1)Θ]p-1 exp(- 2aΘ) p (1 - Θ) p
p
) KadsXr
(31)
where a is the so-called attraction constant,24 and Kads ) exp(-∆sbG0/RT) is the constant of equilibrium. As was shown by Volkov et al.,2 the general MV isotherm (31) includes as particular cases many popular isotherms: Henry, Freundlich,
16450 J. Phys. Chem. B, Vol. 109, No. 34, 2005
Markin et al. Parameter h1 is related to the density of adsorption sites nmax ) 2h1/RT or to the area per site Asite ) RT/2h1. Numerically, if concentration is expressed in M (mole/L), surface tension γ in dyn/cm or mN/m, and area in nm2, then at 20 °C
nmax )
Figure 7. Surface potential φsurface, calculated in the model of hard spheres in the system water/nitrobenzene with TBACl as a function of the electrolyte concentration (solid line). Dashed line is the limiting value of 117.58 mV equal to the surface potential in the GouyChapman model with point ions.
Langmuir, and Frumkin.25 These particular isotherms can be deduced from (31) with appropriate selection of parameters a, p, and r. In our case, X is the concentration of ion pairs which is proportional to the product of concentration of anions and cations, X ) Kipccatcan ) Kipc2salt. If the data for adsorption of the salts considered in this paper in the form of surface tension dependence on concentration are presented in the semilogarithmic plots (Figure 8), then at high concentration, the experimental points fall on a straight line with a certain slope. This indicates that there are a limiting number of sites for adsorption. The simplest description of such adsorption is given by the Langmuir isotherm that can be derived from (31) if a ) 0, r ) 1, and p ) 1:
Θ ) Kc2salt 1-Θ
n)
Kcsalt2nmax 1 + Kc2salt
By substituting this into Gibbs eq 34, one obtains
[
dγ ) RTnmax aΘ -
]
1 dΘ 2(1 - Θ)
(40)
1 γ ) γ0 + RTnmax[aΘ2 + ln(1 - Θ)] 2
(41)
(34)
(35)
γ ) γ0 + h1[aΘ2 + ln(1 - Θ)] Θ 1 1 exp(-2aΘ) z ) - log10h2 + log10 2 2 1-Θ
(36)
For practical purposes, it is convenient to present this equation with common logarithm of concentration to the base 10 with z ) Log10c:
γ ) γ0 - h1 ln[1 + h2 exp(4.6z)]
(39)
Coverage Θ is determined by transcendental eq 39, so the surface tension (41) cannot be presented in closed analytical form. These two equations should be solved numerically. We shall present them as we did before with parameters a, h1, and h2:
We dropped here the subscript “salt” at the concentration. After integration, one obtains
1 γ ) γ0 - RTnmax ln(1 + Kc2) 2
(38)
Θ exp(-2aΘ) ) Kc2salt 1-Θ
(33)
can be presented as
Kc2 dc dγ ) - RTnmax (1 + Kc2) c
2.057 h1
and after integration
The variable n plays the role of surface excess Γ of ion pairs, hence the Gibbs equation for surface tension,
dγ ) - Γdµ
Asite )
and
We fitted the experimental data to eq 37 and found parameters of this isotherm, which are presented in Table 3. The curves according to eq 37 are presented by the dashed lines at the left panels of Figure 8. One can see that pretty decent agreement was achieved, although at panels 8A and C, the middle points somewhat fell down from the theoretical curve. We shall return to this observation later. It is interesting to compare the size of the molecules with the adsorption site area at the interface. The size of the ion pair (molecule) can be estimated (rather arbitrarily) by the sum of cross section area of composing ions, Amolec ) π(r2cat + r2an). These geometrical parameters are also presented in Table 3. One can see that the molecule is considerably (from 2 to 3 times) smaller than the adsorption site. Now, we return to the middle points in Figure 8A and C that departed from the theoretical curves, while at the extreme (small and large) concentration, the curves nicely fit the observations. Such departure usually indicates that there is an interaction between adsorbed particles. To account for this, we return to the general amphiphilic isotherm (31), which includes interaction parameter a. Once again assuming r ) 1 and p ) 1, we obtain the particular case of Frumkin isotherm:
(32)
where K ) KadsKip. It follows from here that
h1 2.057
(37)
{
[
]
}
(42)
This set of two equations was solved numerically, and the curve γ(z) was fit to experimental data in the right panels of Figure 8A and B. The best fit produced parameters a, h1, and h2 that are presented in Table 4. At the right side panels 8B and D for TBACl and TBABr, there is a definite improvement of agreement between theory and experiment relative to simple Langmuir isotherm presented at the left side panels. It was achieved due to interaction between adsorbed particles. The interaction parameter a was found correspondingly equal to -12 and -8. Negative sign means that there is repulsion between molecules in the monolayer. Table 4 also listed the area of adsorption sites at the interface
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J. Phys. Chem. B, Vol. 109, No. 34, 2005 16451
Figure 8. Interfacial tension as a function of the electrolyte concentration presented in the semilogarithmic coordinates. The curves in the left panels (dashed lines) represent the Langmuir isotherm (eq 37) with parameters given in Table 3. The curves at the right panels (solid lines) represent the amphiphilic isotherm (eq 42) with parameters given in Table 4. The curves are presented in different panes because otherwise some curves would be undistinguishable. (A) and (B) TBACl; (C) and (D) TBABr; (E) and (F) TBAI; (G) and (H) TEACl.
Asite. Now, it is barely different from the size of molecules: 0.679 vs 0.674 nm2 for TBACl and 0.709 vs 0.702 nm2 for TBABr. Now let us return to panels 8E and G, describing TBAI and TBABr in the simple Langmuir model. Here, the good agree-
ment is already achieved, so from this point of view, there is no incentive to switch to a more complicated model with interaction between molecules. However, Table 3 shows that adsorption sites are found very different from the size of the molecule. This could be a good argument to apply the MV
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Markin et al.
TABLE 3: Geometrical Parameters of Ion Pars and Properties of Adsorption Sites
salt
rcat, nm
TBACl TBABr TBAI TEACl
0.437 0.437 0.437 0.348
Amolec ) π(r2cat + r2an), ran, nm nm2
Asite, nm2
h1, mN/m
h2, M-2
0.154 0.180 0.205 0.154
1.21 1.714 2.236 1.582
1.7 1.2 0.92 1.3
3 × 105 1 × 105 8 × 104 30
0.674 0.702 0.732 0.455
TABLE 4: Fitting Parameters in Eq 42
salt
a
h 1, mN/m
TBACl TBABr TBAI TEACl
-12 -8 -4.5 -4
3.03 2.90 2.80 4.45
h2, M-2
Amolec ) π(r2cat + r2an), nm2
Asite, nm2
7 × 107 5 × 105 5.2 × 104 13
0.674 0.702 0.732 0.455
0.679 0.709 0.735 0.462
isotherm to these salts also with the goal to bring the adsorption site area close to the size of the molecules. This was done in Figure 8F and H, and parameters are presented in Table 4. Here again, we found repulsion between the particles with interaction parameter a equal to -4.5 and -4 and the size of adsorption sites is very close to the size of the molecules. The relationship between Asite on Amolec is presented in Figure 9. As one can see, the area of adsorption sites is proportional to the area of corresponding molecules. All the points sit slightly above but very close to the straight line with slope 1. Discussion In literature, the adsorption of tetraalkylammonium salts was often studied by measuring capacitance of the interface and appropriate interpretation of the data. Pereira et al.13,26,27 studied interfacial capacitance in a number of organic solvents and parametrized the results in the model of ion pair formation. The model was capable of explaining the measured capacitances quite well for 2-heptanone, 2-octanone, and 1,3-dibromopropane as the organic solvent, while for the most common solvent used in liquid-liquid electrochemistry, 1,2-dichloroethane, the model needed to be modified. The authors used the assumption of a mixed boundary layer with an average dielectric constant. The structure of this mixed boundary layer and its dielectric constant depended on the nature of ions. The authors achieved a very good description of experimental data, though one should keep in mind that the thickness of the mixed layer and its dielectric constant actually were the fitting parameters. The most direct method of studying ion pairs formation and their adsorption at the ITIES involves measuring of the surface tension. Samec et al.28 specifically indicated that the previous works did not include the interfacial tension measurements that would directly confirm the existence of the adsorbed ion pairs. For this reason, they measured both interfacial tension and impedance of the nitrobenzene/water interface in the presence of tetraalkylammonium ions at very low concentration, when Gibbs adsorption of tetraalkylammonium ions is neglectable.28 They placed tetrabutylammonium ions in both phases, rendering the interface a nonpolarizable one. Samec et al.28 concluded that specific ionic adsorption in their system was negligible. The concentration of tetraalkylammonium salts employed in the experiments by Samec et al. 28 and Trojanek et al.29 was 0.5 mM, whereas the concentration range employed by other authors14-17,26,27,30 is much higher. Martins et al.30 also measured interfacial tension to study the electrochemical properties of the interface between LiCl in water
Figure 9. Dependence of limiting area Alimit per molecule in the adsorbed monolayer on the molecular size Amolec ) π(r2cat + r2an). The line has the slope 1 representing the one-to-one relationship.
and tetraalkylammonium tetraphenylborate in 1,2-dichloroethane. Their goal was to verify the formation and adsorption of ion pairs at this interface. Their conclusion was positive; there is a pronounced adsorption of ion pairs at this interface. They commented that, although their results seemed to be in contrast with those obtained by Samec et al.,28 their experimental conditions were quite different. Samec et al.28 placed the tetraalkylammonium ions in both adjoining phases, while in Martins et al.,30 the tetraalkylammonium ions were placed only in the organic phase. In the present paper, we studied the interfacial tension in the water/nitrobenzene system with the same ions present in both phases. In that sense, our system was similar to the experimental system studied by Samec et al.28 Our experimental data strongly indicate the existence of ion adsorption at the interface. We tried to parametrize the data in different models, starting with the simplest possible Gouy-Chapman model with two “backto-back” electrical double layers formed on the two sides of the interface and with point ions. In the beginning, we considered only nonspecific adsorption and calculated its amount. Luckily, we were able to obtain analytical expressions for the adsorbed amount, although it was not in agreement with the experiment. Therefore, we switched to a more elaborate model with ions of finite radii. The theoretical curves given by this model shifted somewhat in the direction of experimental data, but the results were still not completely satisfactory. In the third model, we explicitly included specific adsorption of solutes at the interface with limited number of adsorption sites. Although this concept was originally developed for solid surface, it also works at liquid interfaces. To describe this adsorption we used the MV isotherm derived in ref 11. This MV isotherm provided excellent agreement with experimental data and permitted determination of parameters of the system. We found equilibrium constants of pairs formation and their adsorption as well as the density of adsorption sites (Table 4). It was interesting to discover that the density of adsorption sites was inversely proportional to the size of ion pairs. This indicates that there might be a simple geometrical limit for the amount of adsorbed pairs. Of course these estimates were rather approximate without detailed justification of simple assumption employed. Nevertheless, the strong correlation presented in Figure 9 indicates that simple geometry indeed plays an important role. Of course this last model is a rather empirical
Interfacial Tension and Adsorpion at ITIES one, but it provides important information about the water/ nitrobenzene interface and specific adsorption of tetraalkylammonium ions. Martins et al.30 found that the interfacial tension decreased with decreasing of the size of the cation of the organic supporting electrolyte in the order TBA+ < THA+ < THpA+ < TOA+. This was interpreted as evidence that there is an increase of adsorption when the alkyl chain length of the organic cation is reduced. In our experiments, when TBA+ (r ) 0.437 nm) was compared with TEA+ (r ) 0.348 nm), the results were opposite; the larger ion showed bigger adsorption. If the total size of the ion pair is considered, then the interfacial tension decreased with decreasing of the size of the ion pair TBAI < TBABr
