Diffusion Coefficients of Three Organic Solutes in Aqueous Sodium Dodecyl Sulfate Solutions

Journal of Colloid and Interface Science 229, 53–61 (2000) doi:10.1006/jcis.2000.7020, available online at http://www.idealibrary.com on

Diffusion Coefficients of Three Organic Solutes in Aqueous Sodium Dodecyl Sulfate Solutions Xiao-ning Yang and Michael A. Matthews1 Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29208 Received September 22, 1999; accepted June 5, 2000

mild conditions. Surfactant-based methods for the treatment of aqueous streams and solid matrices to remove organic contaminants or for the recovery of valuable substances are promising new areas of great environmental and technological importance. In aqueous solution at or above the critical micelle concentration (cmc), surfactant molecules form micellar structures with the nonpolar tails preferentially assembled in the center and the polar heads projected outward into the bulk polar solvent. The major feature of the micelle is its ability to solubilize hydrophobic substances that are nonsoluble or only slightly soluble in water. At present, most research work concerns the equilibrium state properties of micelle systems, though the mass transfer phenomena that govern solute dissolution are very important (10, 11). Mass transfer rates depend in part upon diffusion of single molecules and micelles. Diffusion in surfactant solutions reveals useful information on solute–solvent and solute–micelle interactions. The presence of surfactant micelles can significantly affect the diffusion behavior of a variety of solutes in solution. Micellar structures are usually much larger than the solute; thus, the mobility of the solute is reduced compared to the mobility when micelles are absent. Diffusion behavior in aqueous micellar solutions has been studied by NMR spectroscopy (12–17), light scattering (18, 19), and concentration gradient methods such as the Taylor–Aris technique (20–23), as well as by other experimental methods (24, 25). NMR provides self-diffusion coefficients for the random thermal motion of labeled species in the systems of a uniform chemical composition (12), while light scattering has been used to measure the diffusion coefficients of micelles. Concentration gradient methods can obtain the tracer diffusion coefficients in micellar solution. The diffusion coefficient (D) of a solute in the micellar solution is usually expressed by (12, 23)

Tracer diffusion coefficients of phenol, toluene, and benzoic acid in aqueous solutions of sodium dodecyl sulfate (SDS) were measured by the Taylor dispersion technique. In addition, the viscosities and densities of the SDS solutions were measured. For phenol and toluene, the effect of micelle formation on the diffusion coefficient is pronounced. When the SDS concentration is below the critical micelle concentration (cmc), the diffusion coefficients are almost independent of the SDS concentration. However, above the cmc there is a rapid decrease in the diffusion coefficients, and the apparent diffusion coefficients of the two solutes are the weighted average of free solute diffusion and the micelle diffusion. A model is presented to describe the diffusion behavior of the two solutes in aqueous micellar solutions of SDS. The interaction between the two solutes and the micelles has been investigated and the fraction of each solute that is solubilized by the micelles is estimated from the measured apparent diffusion coefficient. For benzoic acid, the diffusion coefficient is dependent on the joint contribution of the benzoic acid molecules that are solubilized by the micelles as well as the corresponding benzoate ions. The effect of micelle formation on the diffusion coefficient of benzoic acid is not as pronounced as for phenol and toluene. °C 2000 Academic Press Key Words: sodium dodecyl sulfate (SDS); micelle; diffusion coefficient; critical micelle concentration.

INTRODUCTION

The role of surfactant-based separation techniques is growing due to the unique properties of amphiphilic molecules and their organized assemblies, which have found a great number of useful applications (1, 2). Applications include surfactant-mediated extraction for the preconcentration and removal of organic pollutants (3), surfactant-containing liquid membrane technology (4, 5), and micellar-enhanced ultrafiltration (6, 7). Another important application of surfactants is in analytical technologies (8, 9), especially to provide a very specific environment that can alter analyte properties and reactivity. Particularly important is the use of aqueous micellar solutions that can replace more expensive and dangerous organic solvents, allowing efficient separations to be performed in aqueous media and under

D = (1 − s)Dw + s Dm ,

[1]

where Dw is the diffusion coefficient of free solute in the aqueous phase and Dm is the diffusion coefficient of the solute in the micelle pseudophase. The parameter s, the fraction of solute solubilized in the micelle phase, reflects the interaction between the solute molecule and the micelle. A study of diffusion provides

1 To whom correspondence should be addressed. Fax: (803) 777-8265. E-mail: [email protected].

53

0021-9797/00 $35.00

C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.

54

YANG AND MATTHEWS

a key to a direct determination of the fraction s because all the diffusion coefficients in Eq. [1] are experimentally accessible. The increasing use of surfactants in practical processes makes it necessary to understand the micellar diffusion phenomena more thoroughly. In this paper, the diffusion coefficients of phenol, toluene, and benzoic acid in aqueous solutions of sodium dodecyl sulfate (SDS) have been determined by the Taylor–Aris dispersion technique. Diffusion measurements were made below and above the critical micelle concentration in SDS aqueous solutions. The influence of micelle formation on the diffusion behavior of the different organic solutes has been investigated. In addition, the diffusion coefficients of phenol and benzoic acid in pure water have also been determined for comparison. MATERIALS AND METHODS

In the Taylor dispersion experiment, a slow, laminar flow of a pure liquid or a solution is pumped through a long diffusion column. A small amount of solute or sample solution with slightly different composition is injected into the tube as a δ-function pulse. Due to combined molecular diffusion and convective flow, the concentration profile downstream of the injection point becomes Gaussian (in an ideal experiment), and the diffusion coefficient can be calculated from the response curve. The theory and principles of Taylor dispersion have been thoroughly reported by Taylor (26) and Aris (27). The criteria for the design of a practical apparatus have been reviewed by Alizadeh et al. (28) and Baldauf et al. (29). The dispersion of a narrow pulse of solute flowing in laminar flow in a circular tube is described by the effective dispersion coefficient KD (28) KD = D +

R2u2 , 48D

[2]

where D is the diffusion coefficient, R is the internal radius of the diffusion tubing, and u is the linear velocity averaged over the cross section. The diffusion coefficient can be obtained from the measurement of the normalized first and second temporal moments t and σ 2 . They are given by (29–31) L t = (1 + 2ξ ), u µ ¶2 L (8ξ 2 + 2ξ ), σ2 = u

KD . uL

RESULTS AND DISCUSSION

[3]

Diffusion Coefficients of Phenol and Benzoic Acid in Pure Water

[4]

Table 1 gives the average diffusion coefficients of phenol and benzoic acid in pure water determined from at least four replicate injections. Experimental temperatures were between 298.15 and 318.15 K. Table 1 also shows several reference values for phenol diffusion coefficients from the literature. The diffusion coefficient at 298.15 K for phenol in this work is 9.25 × 10−10 m2 /s, which is close to 9.40 × 10−10 m2 /s obtained by Castillo et al. (33) using the Taylor dispersion method, but higher than the value 6.15 × 10−10 m2 /s from Sharma and Kalia using an estimation technique (34). In general, our measured values are lower than those of Castillo et al. (33), but the differences are less than 12%.

where L is the length of the diffusion tubing. The parameter ξ is given by ξ=

The present Taylor dispersion apparatus comprises a Perkin– Elmer Model 250 pump, a Rheodyne 7125 liquid injection valve, and a UV absorption detector. The dispersion tubing is PEEK (polyether ether ketone) with 3.81 × 10−4 m radius. The PEEK is more inert than conventional stainless steel and it will reduce adsorption effects of solute onto the wall of tubing (32). All experimental conditions were chosen in order to satisfy the requirement of the Taylor dispersion technique (28, 29). A low Reynolds number indicates laminar flow conditions in our experiment. The radial concentration gradient created by convection is eliminated by radial diffusion at the same rate because L 2 /R 2 À Pe, the Peclet number. Because the solute investigated here is very dilute, the coupled effect of the two-component solvent on the diffusion coefficients was ignored. In a typical diffusion experiment, the aqueous surfactant solutions are prepared gravimetrically and are degassed by sparging with helium. Experiments were performed to show that the detector response was linear with surfactant concentration. It was confirmed that, when the concentration of solute in the injected solution (c + 1c) and the carrier solution (c) differed by less 0.01 M, no influence of surfactant concentration was observed. The solute mole fractions in the sample are typically between 10−4 and 10−5 . To observe the changing environment when solutes are solubilized into surfactant media, we collected UV absorbance spectra of various water/SDS/solute mixtures. All absorption spectra were obtained by using a Shimadzu UV-210PC UV–vis scanning spectrophotometer with a thermostated cell. Kinematic viscosities of SDS solutions were measured at 298.15 K with a Canon– Fenske viscometer. The kinematic viscosity was converted into dynamic viscosity through a measurement of the densities of the SDS aqueous solutions with a vibrating tube density meter (Anton Paar, DMA48) at three temperatures. The sodium dodecyl sulfate (SDS) is from Fluka with the purity >99%, the phenol is from Fisher (99.5%), and the toluene and benzoic acid are from Aldrich (99%). All the chemicals under investigation were used without further purification.

[5]

In an actual apparatus, there are minor corrections to be made to the experimentally observed moments according to Alizadeh et al. The apparatus design method has been described in detail elsewhere (28, 29).

55

DIFFUSION COEFFICIENTS IN SDS SOLUTION

TABLE 1 Diffusion Coefficients of Phenol and Benzoic Acid in Water Phenol

tribution of the diffusion of the benzoic acid molecule and the corresponding benzoate ion, and it can be described by the following equation (40, 41):

Benzoic acid

T (K)

D × 1010 (m2 /s)

Dη/kT × 108 (m−1 )

D × 1010 (m2 /s)

DBH × 1010 (m2 /s)

298.15 303.15 308.15 313.15 318.15

9.25 ± 0.07 (9.40)a 10.2 ± 0.2 (11.2) 11.2 ± 0.2 (12.2) 12.1 ± 0.1 (13.3) 13.2 ± 0.3 (14.9)

2.00 1.94 1.89 1.83 1.78

9.08 ± 0.05 9.88 ± 0.67 11.1 ± 0.2 11.6 ± 0.1 12.4 ± 0.2

6.56 7.54 9.10 9.70 10.7

a

Literature values (33) are in parentheses.

For diffusion in liquids, two approaches are commonly used to model the diffusion coefficient: hydrodynamic theory and the rough hard sphere theory (35, 36). In the hydrodynamic theory, solutes are assumed to move through a continuum and the diffusion coefficient is proportional to the temperature and inversely proportional to the fraction factor. The friction factor can be calculated from classical hydrodynamics, which results in the famous Stokes–Einstein relation: kT , D= f πηr

[6]

where r is the effective solute radius, η is the viscosity of the solvent, and the coefficient f is between 4 (slip limit) and 6 (no-slip limit). According to the Stokes–Einstein relation, Dη/kT should be constant for a given solute (35, 37). For phenol as shown in Table 1, the value of Dη/kT shows a small decrease with increasing temperature. This means that the diffusion coefficients of phenol in water do not completely follow the Stokes– Einstein equation. This deviation may be attributed to a solvation effect that enhances the effective size of the diffusing molecules (38). Research has suggested that the Stokes–Einstein equation fails in the situation where the solute and solvent are of similar size (22). The rough hard sphere theory originates from the kinetic theory of gases and is modified for high density (35). From this theory, the diffusion coefficient can be expressed as the linear relation shown in the following equation (39): √ D/ T = β(V − VD ),

D=

¶ 0 µ 2(1 − α)DBH + α D± ∂ ln γ± 1 + αCBH,t , 2−α ∂C

[8]

0 are the limiting diffusion coefficients of where DBH and D± the molecular and the fully ionized forms of the benzoic acid in water, respectively. α is the degree of dissociation that can be calculated by the dissociation constant (40), and γ± is the average activity coefficient in molarity. CBH,t is the total concentration of benzoic acid in the solution. In our study, CBH,t = 2.0 × 10−4 M, and the D± can be calculated from limiting ionic conductances with the Nernst equation (40, 42). Therefore, the value of DBH will be obtained by Eq. [8] if the apparent diffusion coefficient (D) of benzoic acid is known. The calculated values of the diffusion coefficients for the benzoic acid molecule (DBH ) at different temperatures are given in Table 1.

Density and Viscosity of SDS Aqueous Solution The densities of the SDS solutions are fitted to the following equation: ρ=

4 X

Ai Csi ,

[9]

i=0

where ρ is in g/cm3 . Cs is the molar concentration of SDS in the aqueous solutions. The fitting constants are given in Table 2. From these densities, the molar volume (Vm ) of the solution can be obtained. Thus, the partial molar volume of SDS in the aqueous solution can be calculated by the following equation: µ Vs = Vm + (1 − x)

∂ Vm ∂x

¶ ,

[10]

T,P

[7]

where V is the molar volume of fluid. The coefficient β is dependent upon the interaction between solute and solvent, and VD is a function of solvent properties and represents the molar volume at which the diffusion coefficient approaches zero (30, 39). For phenol, the diffusion coefficients at infinite dilution in water can be described well by the rough hard sphere theory as shown in Fig. 1. Benzoic acid, a weak electrolyte, can partly dissociate into benzoate ion and hydrogen ion. Therefore, the measured diffusion coefficient (D) of benzoic acid in water is the joint con-

FIG. 1. Diffusion coefficients for phenol in water plotted according to rough hard sphere theory.

56

YANG AND MATTHEWS

TABLE 2 Fitting Constants for Eq. [9] T (K)

A0

A1

A2

A3

A4

298.15 303.15 313.15

0.9971 0.9957 0.9923

0.0459 0.0447 0.0469

−0.1106 −0.1049 −0.1617

0.6986 0.5515 0.7862

−1.0343 −0.9316 −1.1499

where Vs is the partial molar volume of SDS and x is the molar fraction of SDS. The Vs values obtained in this work are given in Table 3, along with literature values for comparison (43). The viscosities (η) of the aqueous solution of SDS at 298.15 K were determined, and the relative viscosity (ηr ), where ηr = η/η0 and η0 is the viscosity of pure water, is plotted against the molar concentration of SDS in Fig. 2. Figure 2 also compares the present measurements with other reported data (44). The viscosity is a relatively weak function of surfactant concentration; however, very good agreement is obtained. The partial molar volume and viscosity data will be used in the discussion of solute diffusion in the next section. Diffusion Behavior of Phenol and Toluene in SDS Solution Figure 3 shows the diffusion coefficients of phenol in aqueous solutions with different SDS concentrations at three temperatures, and Fig. 4 shows similar experimental results for toluene. In Fig. 4 the diffusion coefficient of toluene in pure water is from the literature (45). For the concentration interval displayed in Figs. 3 and 4, the diffusion coefficients of the solutes are characterized by the presence of two distinct regions, i.e., below the cmc and above the cmc. In the absence of any third electrolyte component, the critical micelle concentrations of aqueous SDS solutions are 0.0082 M at 298.15 K, 0.0083 M at 303.15 K, and 0.0085 M at 313.15 K (46). In this work, the solute concentrations are quite low and the effect of solute on the cmc is neglected. For phenol and toluene, the diffusion coefficients remain approximately unchanged when the SDS concentration is below the cmc. Above the cmc, as expected, there is an apparent decrease in the diffusion coefficients of the two solutes with increasing SDS concentration. From hydrodynamic theory, the solute diffusion coefficient and the viscosity of the solvent bear an inverse relationship to one another at a fixed temperature. As the SDS concentration increases, the diffusion medium becomes more

FIG. 2. Relative viscosity of SDS aqueous solution at 298.15 K.

viscous than pure water. This would tend to reduce the actual diffusion coefficient of solute in SDS solutions. However, according to the present results, the diffusion coefficients of the solutes decrease much more rapidly than would be expected strictly due to the solvent viscosity. This confirms that the formation of a micelle in the aqueous solution strongly affects the diffusion of the solutes, phenol and toluene. The change in the diffusion behavior of the solute is dependent on a number of factors, including concentration of the surfactant and whether or not the solute binds or associates with the micelle (20). As neutral molecules, phenol and toluene can be partitioned between the micellar and aqueous phases (47). Below the cmc, a solute diffuses with the free diffusion coefficient (Dw ) in the bulk aqueous phase. However, above the cmc, the solute molecules in the bulk phase still diffuse with the diffusion coefficient of Dw , while solutes in the micellar pseudophase diffuse with the diffusion coefficient of the micelle (Dm ), which is much lower than Dw . Thus, the diffusion coefficient is the weighted average of the solute diffusion in the two phases (20–23, 48). With an increase of the micelle concentration in the aqueous solutions, the fraction of the solute present in the micellar phase

TABLE 3 Partial Molar Volume of SDS in Water Vs (cm3 /mol)

a

T (K)

This work

Literaturea

298.15 303.15 313.15

250.5 252.2 254.3

250.2 — —

Reference 43.

FIG. 3. Diffusion coefficients of phenol in aqueous SDS micellar solutions.

DIFFUSION COEFFICIENTS IN SDS SOLUTION

57

Thus, the observed diffusion coefficients D in SDS aqueous solution can be expressed as follows: D=

FIG. 4. Diffusion coefficients of toluene in aqueous solutions.

will increase, which leads to an apparent reduction in the observed diffusion coefficient of the solutes. Continuing with the inspection of the data near the critical micelle concentration, the diffusion coefficient for phenol shows a slight reduction over the concentration range between 0.008 and 0.009 M, but that for toluene decreases by 27% over the same concentration range. This indicates that the effect of micelle formation on toluene diffusion is more pronounced. Since the micelle is in a dynamic state, it is assumed that the micelle formation and destruction are much faster than the diffusion process. Mass transfer of solutes measured in an aqueous micelle solution obeys the following diffusion equations (49): ∂Ci,w , ∂t ∂Ci,m + Rm = , ∂t

Dw ∇ 2 Ci,w − Rw =

[11]

Dm ∇ 2 Ci,m

[12]

where Ci,w and Ci,m are the concentration of solute i in the bulk aqueous phase and the micellar pseudophase, respectively. Rw is the interfacial mass transfer rate per unit volume of solute from the bulk phase to the micellar phase, and Rm is that from the micellar phase to the bulk phase. The total concentration Ci,t of solute is governed by Ci,t = (1 − ψ)Ci,w + ψCi,m and the interfacial solute transfer rate is Rw (1 − ψ) = Rm ψ. ψ is the volume fraction of the micelle and, considering the cmc to be unaffected by low concentrations of solute, ψ = (Cs − cmc)Vs . Assuming that an equilibrium distribution of solute is established between the micellar phase and the bulk phase, Ci,m = K c Ci,w .

[13]

Multiplying Eq. [11] by (1 − ψ) and Eq. [12] by ψ and adding give the total flux J of the solute as follows: −J = (1 − ψ)Dw ∇C I,w + ψ Dm ∇C I,m .

[14]

Dw [1 − (Cs − cmc)Vs ] + Dm (Cs − cmc)Vs K c . 1 − (Cs − cmc)Vs + (Cs − cmc)Vs K c

[15]

Equation [15] is similar to an equation due to Armstrong et al. (21), which was derived from Eq. [1]. According to Eq. [15], the equilibrium partition constant K c can be obtained if the two diffusion coefficients and the cmc are known. K c is an equilibrium property and ideally would be measured from a true equilibrium experiment, rather than a dynamic experiment. However, as will be shown subsequently, the values of K c that are obtained by fitting data with Eq. [15] are in reasonable agreement with other measurements. In Eq. [15], the diffusion coefficient of free solute, Dw , should be corrected with Dw = Dw0 (1 − 1.5ψ) due to a so-called obstruction effect from micelles in the solution (48), where Dw0 denotes the diffusion coefficient of free solute in the absence of micelle. The diffusion coefficient of the solute at 0.008 M is used as Dw0 . The value of the micelle diffusion coefficient Dm is somewhat uncertain. The micelle diffusion coefficient of SDS, 0.94 × 10−10 m2 /s, is reported by Johnson et al. (50) at 298.15 K by applying a quasi-elastic light scattering technique. More commonly, one can measure Dm by solubilizing a small amount of a highly hydrophobic molecule and monitoring its tracer diffusion coefficient, which equals the diffusion coefficient of the micelle. An early study by Stigter et al. (24) showed that the diffusion coefficient of an SDS micelle at 298.15 K is 1.09 × 10−10 m2 /s (which was obtained from the observed diffusion coefficient of a dye). Burkey et al. (22) determined the diffusion coefficients of a set of organic substrates in SDS solutions at 298.15 K and obtained the micelle diffusion coefficient (1.06–1.09) × 10−10 m2 /s. A diffusion coefficient of 0.57 × 10−10 m2 /s was obtained by Armstrong et al. (21) for the SDS micelle in aqueous solution at 293.15 K. Leaist measured the diffusion coefficients of n-decanol in SDS solution at 298.15 K and assumed that this value is identical to the Dm (23). Actually, Dm is essentially only a small value and any uncertainty in its actual value does not cause very much error in the partition equilibrium constant calculation (12). Therefore, we used the averaged value 1.0 × 10−10 m2 /s as the input value of Dm for SDS solution in the following calculation. The experimental data for phenol and toluene are fitted by Eq. [15], and the results are shown in Figs. 5 and 6. The parameter K c is given in Table 4. In Figs. 5 and 6, all the curves refer to the correlation of Eq. [15]. The fitted results for the diffusion coefficients are in good agreement with the experimental data. This shows that the weighted-average model is reasonable in describing the diffusion behavior of the two solutes in the SDS solution. In the model, we assumed that the micelle diffusion coefficient is constant, independent of the SDS concentration. The assumption does not seem to compromise the data correlation described above, as it is reasonable at an SDS concentration below 0.1 M

58

YANG AND MATTHEWS

TABLE 4 Solute Partition Equilibrium in SDS Solution Solute

T (K)

Kc a

Kc b

Kc c

−1µ◦t a

−1µ◦t b

−1µ◦c t

Phenol

298.15 303.15 313.15

44.5 41.3 37.8

65.7

22.4

3.81

4.03

3.40

Toluene

298.15

5.14

4.95

4.80

428

307

238

Note. Units in 1µ◦t are kcal/mol. This work. b Reference 47. c Reference 52.

a

solute between the micellar and aqueous phase, 1µ◦t , is calculated by (52) FIG. 5. Comparison of experiment and model for diffusion coefficients of phenol in aqueous SDS micellar solution.

(51). The fitted equilibrium constant K c in Table 4 characterizes the interaction between the solute and micelle. Larger values of K c indicate stronger solute–micelle interaction. The interaction between toluene and the SDS micelle is stronger than for phenol. In addition to the tracer diffusion coefficient method described above, the equilibrium partition constant of some neutral solutes in SDS aqueous solution can be determined by different experimental techniques (12, 47, 52). However, data by different methods show considerable scatter (12). In Table 4, K c (consistent with the definition implied by Eq. [13]) from two other methods is shown for comparison with this work. A reasonable agreement is observed. When the logarithm of the equilibrium partition constant (K c ) for phenol is plotted against 1/T , a linear relationship is obtained, and from the slope one obtains 1H = 2.0 kcal/mol for the transfer of phenol molecules from the aqueous phase to the micellar phase. Additionally, the molar transfer free energy of

FIG. 6. Comparison of experiment and model for diffusion coefficients for toluene in aqueous micellar solution at 298.15 K.

µ ¶ Vs , 1µ◦t = −RT ln K c Vw

[16]

where Vw is the partial molar volume of water (46). The values of 1µ◦t also are given in Table 4 together with two reference values for comparison. The molar transfer free energy of toluene is larger than that for phenol. It is of interest to know the sensitivity of the diffusion coefficients to the magnitude of K c . Figure 7 shows the experimental data and the original fit of K c , as well as the fit that would result of the fitted values of K c were either doubled or reduced by a factor of two. Clearly, the predicted diffusion coefficients are sensitive to the value of K c used. The fraction s of the total solute that is solubilized or associated with the micelle is calculated from the equilibrium partition constant: s=

Kcψ . 1 + Kcψ − ψ

FIG. 7. Effect of K c on diffusivity of solutes in SDS solutions.

[17]

DIFFUSION COEFFICIENTS IN SDS SOLUTION

FIG. 8. Fraction coefficients of solutes solubilized in aqueous SDS micelles at 298.15 K.

Figure 8 represents the plot of s against the surfactant concentration Cs . As can be seen in Fig. 8, not only is the fraction of toluene solubilized larger than that of phenol, but also the toluene concentration increases more rapidly with SDS concentration. For example, at an SDS concentration 0.02 M, only 10% phenol is solubilized in the micelle phase in comparison with almost 60% toluene in the micelle phase. This result is consistent with the fact that toluene is weakly polar and much more hydrophobic than phenol.

59

FIG. 10. UV–vis absorption spectra of toluene (0.0001 M) in different solvents at 298.15 K.

transfer will occur. That is, HB + DS− ↔ B− + HDS,

For benzoic acid, the diffusion behavior is noticeably different from that of phenol and toluene. From Fig. 9, the diffusion coefficient of benzoic acid decreases slightly with increasing SDS concentration. However, above an SDS concentration of about 0.02 M, the diffusion coefficient becomes essentially constant. The above model, Eq. [15], fails to represent the diffusion behavior of benzoic acid in aqueous solutions of SDS. Aqueous benzoic acid is a weak acid electrolyte; thus, when benzoic acid is dissolved in an aqueous SDS solution, a proton

where HB represents the benzoic acid molecule and B− the benzoate ion. DS− and HDS are the dodecyl sulfate ion and dodecylsulfuric acid molecule, respectively. In the SDS solution, there are benzoate ions as well as benzoic acid molecules that are in part solubilized in, or associated with, the micelles (52). However, the benzoate ion, repelled by the like-charged SDS micelles, is not readily solubilized by the hydrocarbon cores of the micelles. At the beginning of micelle formation, the diffusion behavior of benzoic acid is determined by the weightedaverage contribution of the benzoate ions, the free benzoic acid molecules, and the benzoic acid molecules associated with the micelle. Thus, the effect of the micelle on the apparent diffusion coefficients is apparent to some extent at the low SDS concentration. However, as the concentration of SDS is further increased, the overwhelming majority of benzoic acid will be transformed into the benzoate ions by the proton transfer reaction. In this

FIG. 9. Diffusion coefficients of benzoic acid in aqueous SDS micellar solutions.

FIG. 11. UV–vis absorption spectra of phenol (0.0005 M) in different solvents at 298.15 K.

Diffusion Behavior of Benzoic Acid

60

YANG AND MATTHEWS

between the two solutions within experimental error. This suggests that the environment around the benzoic acid molecules and benzoate ions in the SDS solution is almost the same as in water, and the fraction of the total benzoic acid in the micelle is very small. SUMMARY

FIG. 12. UV–vis absorption spectra of benzoic acid (0.0005 M) in different solvents at 298.15 K.

case, it is likely that the measured data represent the diffusion behavior of the benzoate ions, which are less affected by the presence of micelles. Because the electrostatic effects among the different ions are existent in the multicomponent electrolyte system, the diffusion mechanism is much more complex. A more complete theory is required. Solvent Effect on the UV Spectra of Phenol, Toluene, and Benzoic Acid The nature of the interaction between the three solutes and the SDS micelles has been analyzed in terms of the diffusion coefficients of the solutes. The interaction between the solutes and the micelles in the surfactant solutions can also be observed independently via the change in the UV–vis spectra of the solutes in aqueous SDS. Variations in the absorption maxima as well as in the vibrational fine structure of UV spectra have been observed upon solubilization in different solvents (53). These variations indicate a change in the environment around the solute. With this simple technique, a qualitative comparison has been made of the UV spectra of toluene, phenol, and benzoic acid obtained in pure water and SDS aqueous solutions. These results are shown in Figs. 10–12. Figure 10 shows the absorption spectra of toluene. Its spectrum in water exhibits a low intensity and a broadening of the bands as compared with the spectrum obtained in SDS solution at two different concentrations. In addition, the spectrum shows a slight overall shift toward the higher wavelengths. The changes in the toluene spectrum are primarily caused by the change in the refractive index around the solute (54). It may be concluded that toluene in SDS aqueous solution is located preferentially in the nonpolar environment within the micelles. For phenol (Fig. 11) there is a very slight change of the absorption spectra as SDS is added to water. In SDS solution, the spectrum shows a clear fine structure but the spectrum becomes flat in water. This may mean that the environment of phenol in SDS solution is somewhat less polar than in water. For benzoic acid (Fig. 12) no evident differences in the spectra are observed

The diffusion coefficients of phenol, toluene, and benzoic acid in sodium dodecyl sulfate (SDS) aqueous solutions and in pure water were determined. For phenol and toluene, when the SDS concentration is below the critical micelle concentration (cmc), the diffusion coefficients are almost independent of the SDS concentration. However, above the cmc there is a rapid decrease in the diffusion coefficients. The apparent diffusion coefficients of the two solutes are the weighted average of free solute diffusion and the micelle diffusion. A model is presented to describe the diffusion behavior of the two solutes in the aqueous micelle solutions of SDS. The interaction between toluene and the SDS micelles is stronger than that for phenol. For benzoic acid, the diffusion behavior is dependent on the joint contribution of the benzoic acid molecules that are in part solubilized by the micelles as well as the corresponding benzoate ions. The effect of the SDS micelle on the diffusion behavior is not as pronounced as for toluene and phenol. ACKNOWLEDGMENTS Funding for this research was provided by Grant DE-FG02-97EW09999 from the U.S. Department of Energy, Office of Environmental Management, to the Center for Water Research and Policy at the University of South Carolina. Additional funding was provided by DOE through subcontract number F754000088N to the University of South Carolina.

REFERENCES 1. Scamehorn, J. F., and Harwell, J. H. (Eds.), “Surfactant-Based Separation Process.” Dekker, New York, 1989. 2. Pramauro, E., and Bianco Prevet, A., Pure Appl. Chem. 67, 551 (1995). 3. Pramauro, E., and Pelezetti, E., in “Surfactants in Analytical Chemistry: Application of Organized Amphiphilic Media” (S. G. Weber, Ed.), Vol. 31. Elsevier, New York, 1996. 4. Li, N. N., AIChE J. 17, 459 (1971). 5. Draxler, J., Furst , W., and Marr, R., J. Membr. Sci. 38, 281 (1998). 6. Dunn, R. O., Jr., Scamehorn, J. F., and Christian, S. D., Sep. Sci. Technol. 20, 257 (1985). 7. Gibbs, L. L., Scamehorn, J. F., and Christian, S. D., J. Membr. Sci. 30, 67 (1987). 8. Armstrong, D. W., and Nome, F., Anal. Chem. 53, 1662 (1981). 9. Borgerding, M. F., Williams, R. L., Jr., Hinze, W. L., and Quina, F. H., J. Liq. Chromatogr. 12, 1367 (1989). 10. McBain, M. E. L., and Hutchinson, E., “Solubilization and Related Phenomena.” Academic Press, New York, 1995. 11. Otsuki, J., and Seno, M., J. Phys. Chem. 95, 5234 (1991). 12. Christian, S. D., and Scamehorn, J. F. (Eds.), “Solubilization in Surfactant Aggregates.” Dekker, New York, 1995. 13. Panitz, J.-C., Gradzielski, M., Hoffmann, H., and Wokaun, A., J. Phys. Chem. 98, 6812 (1994). 14. Zhang, K., Jonstromer, M., and Lindman, B., J. Phys. Chem. 98, 2459 (1994).

DIFFUSION COEFFICIENTS IN SDS SOLUTION 15. Phillies, G. D. T., Stott, J., and Ren, S. Z., J. Phys. Chem. 97, 11563 (1993). 16. Griffith, P. C., Stilbs, P., Howe, A. M., and Cosgrove, T., Langmuir 12, 2884 (1996). 17. Walderhaug, H., Kjoniksen, A.-L., and Nystrom, B., J. Phys. Chem. B 101(44), 8892 (1997). 18. Degiorgio, V., Corti, M., and Giglio, M., “Light Scattering in Liquids and Macromolecular Solutions.” Plenum, New York, 1980. 19. Kole, T. M., Richards, C. J., and Fisch, M. R., J. Phys. Chem. 98, 4949 (1994). 20. Armstrong, D. M., Menges, R. A., and Han, S. M., J. Colloid Interface Sci. 126(1), 239 (1998). 21. Armstrong, D. M., Ward, T. J., and Berthod, A., Anal. Chem. 58, 579 (1986). 22. Burkey, T. J., Griller, D., Lindsay, D. A., and Scaiano, J. C., J. Am. Chem. Soc. 106, 1983 (1984). 23. Leaist, D. G., J. Solution Chem. 20(2), 175 (1991). 24. Stigter, D., Williams, R. J., and Mysels, K. J., J. Phys. Chem., 59, 330 (1955). 25. Crison, J. R., Shan, V. P., Skelly, J. P., and Amidon, G. L., J. Pharm. Sci. 85(9), 1005 (1996). 26. Taylor, G. I., Proc. R. Soc. London, Ser. A 219, 186 (1953); Taylor, G. I., Proc. R. Soc. London, Ser. A 225, 473 (1954). 27. Aris, R., Proc. R. Soc. London, Ser. A 235, 67 (1956). 28. Alizadeh, A., Nieto de Castro, C. A., and Wakeman, W. A., Int. J. Thermophys. 1, 243 (1980). 29. Baldauf, W., and Knapp, H., Chem. Eng. Sci. 38(7), 1031 (1983). 30. Matthews, M. A., and Akgerman, A., AIChE J. 33, 887 (1987). 31. Matthews, M. A., and Akgerman, A., Int. J. Thermophys. 8(3), 363 (1987). 32. Winters, S. A., Denault, C. A., Nguyen, L. T., and Matthews, M. A., Fluid Phase Equilib. 117, 373 (1996). 33. Castillo, R., Garza, C., and Orozeo, J., J. Phys. Chem. 96, 1475 (1992).

61

34. Sharma, L. R., and Kalia, R. K., J. Chem. Eng. Data 22, 39 (1977). 35. Tyrell, H. J. V., and Harris, K. R., “Diffusion in Liquids.” Butterworths, London, 1984. 36. Dymond, J. H., Millat, J., and Nieto de Castro, C. A., “Transport Properties of Fluids.” Cambridge Univ. Press, New York, 1994. 37. Tominaga, T., Yamamoto, S., and Takanaka, J., J. Chem. Soc., Faraday, Trans. 1 80, 941 (1984). 38. Longsworth, L. G. J., J. Am. Chem. Soc. 75, 5705 (1953). 39. Chen, S. H., Davis, H. T., and Evans, D. F., J. Phys. Chem. 77(5), 2540 (1982). 40. Noulty, R. A., and Leaist, D. G., J. Chem. Eng. Data 32, 418 (1987). 41. Leaist, D. G., and Lyons, P. A., J. Solution Chem. 13(2), 77 (1984). 42. Robinson, R. G., and Stokes, R. H., “Electrolyte Solutions.” Butterworths, London, 1960. 43. Brun, T. S., Hoiland, H., and Vikingstad, E., J. Colloid Interface Sci. 63, 89 (1978). 44. Kodama, M., and Miura, M., Bull. Chem. Soc. Japan 45, 2265 (1972). 45. Gabler, T., Paschke, A., and Schuurmann, G., J. Chem. Eng. Data 41, 33 (1996). 46. Mulcerjee, P., and Mycsels, K., Natl. Stand. Ref. Data Ser. 36, (1971). 47. Treiner, C., and Mannebach, M.-H., J. Colloid Interface Sci. 118(1), 243 (1987). 48. Stilbs, P., J. Colloid Interface Sci. 87(2), 385 (1982). 49. Cussler, E. L., “Diffusion: Mass Transfer in Fluid Systems.” Cambridge Univ. Press, New York, 1984. 50. Johnson, K. A., Westermann-Clark, G. B., and Shan, D. O., J. Colloid Interface Sci. 130(2), 480 (1989). 51. Leaist, D. G., J. Colloid Interface Sci. 111(1), 230 (1986). 52. Hirose, C., and Sepulveda, L., J. Phys. Chem. 85, 3689 (1981). 53. Cardinal, J. K., and Mukerjee, P., J. Phys. Chem. 82, 164 (1978). 54. Eastman, J. W., and Rehfeld, S. J., J. Phys. Chem. 74, 1438 (1970).