Coexistence and Growth of Micellar Species in a Sugar-Based

mixedn-dodecyl-β-D-maltoside (DM) and phenol, including the aggregation number, diffusion coefficient, and effective radius, was obtained using an an...
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9188

Langmuir 2007, 23, 9188-9194

Coexistence and Growth of Micellar Species in a Sugar-Based Surfactant/Phenol Mixture Studied by Analytical Ultracentrifugation Shaohua Lu and Ponisseril Somasundaran* Langmuir Center for Colloids and Interfaces, Columbia UniVersity, New York, New York 10027 ReceiVed June 5, 2007. In Final Form: June 19, 2007 Knowledge of the shape and size of surfactant micelles in the presence of small organic molecules is important for understanding the solubilization properties of micellar phases. In this work, structural information on micelles of mixed n-dodecyl-β-D-maltoside (DM) and phenol, including the aggregation number, diffusion coefficient, and effective radius, was obtained using an analytical ultracentrifugation technique. The micelles were found to increase in size and undergo shape transition from quasispherical to cylindrical with an increase in the surfactant and phenol concentrations in the micellar phase. Importantly, the coexistence of different micellar species was observed in certain cases with the larger species double the size of the smaller one. Based on the results obtained, a two-step micellar growth model is proposed to describe the micelles shape transition in the system. In the first step, the micelles expand continuously, whereas in the second step, it undergoes a sudden shift from the existing micellar species to a larger species causing the coexistence of two micellar species. This micellar growth is attributed to molecular packing and intermicellar interaction energy parameters. The mechanism proposed can be applied to other mixed systems and utilized for devising chemicals for the efficient removal of pollutants.

1. Introduction Surfactants have been proposed for various applications for the removal of small organic pollutants from aqueous systems. Dunn et al.1,2 first termed the process as micellar enhanced ultrafiltration (MEUF) and demonstrated the technique by recovering 4-tert-butylphenol from aqueous solutions. In the past, various surfactants have been studied for removal of phenol derivatives from aqueous solutions; they include cationic cetylpiridiniumchloride (CPC),3-5 anionic sodium dodecyl benzenesulfonate,6 sodium dodecylsulfates,3,7 nonionic nonylphenol ethoxylates,6,8 and alkyl polyglucosides.9 With the increased concern about organic pollution, environmentally friendly surfactants have begun to draw attention. Our previous study10 has demonstrated the applicability of a benign surfactant, n-doedyl-β-D-maltoside (DM), for the removal of phenol using an ultrafiltration technique. Besides the removal of pollutants, solubilization of small organic molecules in surfactant micelles also finds applications in the delivery of sparingly soluble drugs.11 Incorporation of small organic molecules into the micellar phase can change the size and shape of the micelles. The micellar shape is affected by the concentration and the geometry of the * To whom correspondence should be addressed. E-mail: ps24@ columbia.edu. (1) Dunn, R. O., Jr.; Scamehorn, J. F. Sep. Sci. Technol. 1985, 20 (4), 257284. (2) Dunn, R. O., Jr.; Scamehorn, J. F.; Christian, S. D. Sep. Sci. Technol. 1987, 22 (2-3), 763-89. (3) Sabate, J.; Pujola, M.; Centelles, E.; Galan, M.; Llorensy, J. Colloids and Surfaces A: Physicochem. Eng. Aspects 1999, 150, 229-245. (4) Sabate, J.; Pujol, M.; Llorensy, J. J. Colloid Interface Sci. 2002, 246, 157-163. (5) Syamal, M.; De, S.; Bhattacharya, R. J. Membrane Sci. 1997, 137, 99107. (6) Kandori, K.; Schechter, R. Sep. Sci. Technol. 1990, 25 (1-2), 83-108. (7) Materna, K.; Goralska, E.; Sobczynska, A.; Szymanowski, J. Green Chem. 2004, 6, 176-182. (8) Kandori, K.; Mcgreevy, R. J.; Schechter, R. S. J. Colloid Interface Sci. 1989, 132 (2), 395-402. (9) Adamczak, H.; Materna, K.; Urbanski, R.; Szymanowski, J. J. Colloid Interface Sci. 1999, 218, 359-368. (10) Lu, S.; Somasundaran, P. Langmuir, accepted. (11) Francis, M. F.; Piredda, M.; Winnik, F. M. J. Controlled Release 2003, 93, 59-68.

additives as well as its orientation in the micellar phase. For instance, solubilized nonpolar molecules may increase the packing parameter, lower the curvature of the micelle, and eventually cause micellar shape transitions.12 Solubilized aliphatics have also been reported to cause long rodlike micelle transform to globular micelles.13 Solubilized polar molecules have a tendency to stay in the palisade layer of micelles due to the polar group, for example, phenol molecules have been revealed to stay in the palisade layer of nonionic surfactant micelles using the 2D NMR technique.10 Although solubilized short-chain alcohols in the palisade layer indicate a greater tendency to form spherical micelles,12 the micellar shape transition from spherical to wormlike has been reported in some surfactant systems in the presence of phenol.10,14 Micellar size and shape have been studied using a range of techniques such as Cryo-TEM,14,15 light scattering,13,16,17 and small angle neutron scattering;18,19 however, these techniques are somehow inadequate to monitor micelles in terms of size and shape, especially in the size range below 5 nm. We therefore turn to analytical ultracentrifugation (AUC), which has proven to be suitable for monitoring the size and shape of various colloidal particles.20,21 Our previous studies have successfully demonstrated the capability of AUC for the identification of the micellar species in solutions of mixed dodecyl maltoside and noneylphenol ethoxylated ester (NP10).22 In this work, we focused on the characterization of the micellar size of nonionic n-dodecyl-β-D-maltoside (DM) in the presence of phenol to understand the effects of solubilized molecules on (12) Rosen, M. J. Surfactants and interfacial phenomena, 3rd ed.; WileyInterscience: New York. (13) Hoffmann, H.; Ulbricht, W. J. Colloid Interface Sci. 1989, 129 (2), 388405. (14) Agarwal, V.; Singh, M.; McPherson, G.; John, V.; Bose, A. Colloids Surf. A 2006, 281, 246-253. (15) Oda, R.; Bourdieu, L. J. Phys. Chem. B 1997, 101, 5913-5916. (16) Anacker, E. W.; Ghose, H. M. J. Phys. Chem. 1963, 67 (8), 1713-16. (17) Sorci, G. A.; Walker, T. D. Langmuir 2005, 21 (3), 803-806. (18) Cummins, P. G.; Penfold, J.; Staples, E. Langmuir 1992, 8 (1), 31-35. (19) Iampietro, D. J.; Kaler, E. W. Langmuir 1999, 15, 8590-8601. (20) Colfen, H.; Volkel, A. Prog. Colloid Polym. Sci. 2004, 127, 31-47. (21) Salvay, A. G.; Ebel, C. Prog. Colloid Polym. Sci. 2006, 131, 74-82. (22) Zhang, R.; Somasundaran, P. Langmuir 2004, 20, 8552-8558.

10.1021/la7016616 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/03/2007

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Figure 1. Molecular structure of n-dodecyl-β-D-maltoside.

the micellar structures using AUC. The samples used were identical to those in the previous ultrafiltration study,10 so that the information on the composition of the micellar phase obtained from the ultrafiltration study can be correlated for AUC data analysis. Micellar size and shape and aggregation number were obtained by analyzing the data from sedimentation velocity tests. 2. Materials and Methods Materials. Surfactant. n-Dodecyl-β-D-maltoside (DM) of 98% purity grade was obtained from Calbio chem and used as received. The critical micellar concentration of DM measured by surface tension experiments is 0.18 mM. Phenol of 99% purity was purchased from Fisher science and used as received. The molecular structure of DM is shown in Figure 1. Water used in all of the experiments was triple distilled. Methods. (1) Density Measurements. The partial specific volume of surfactant micelles, critical for analysis of data of AUC tests, was obtained from the correlation between density and solution concentration. The density of the solutions was measured using an Anton Paar density meter. The accuracies of the density and temperature data are (5 × 10-6g/cm3 and (0.01 °C, respectively. The density of fresh triple distilled water was measured to be 0.99703 ( 0.000005 g/cm3 at 25.00 °C. Acetone was used to rinse the sample chamber between measurements, and the chamber was dried by pumping filtered air into it. (2) AUC Tests. Sedimentation velocity tests were performed using a Beckman Coulter Optima XL-I analytical ultracentrifuge equipped with both absorbance and interference optical detectors. A 12 mm two-channel aluminum cell and quartz windows were used for velocity experiments. Three aluminum cells and a reference cell were counterbalanced in an An-60 Ti rotor. The rotor speed was set at 40 000 rpm, and the temperature was maintained at 25.0 °C. The tests were run after the vacuum reached below 5 µmHg (0.65 Pa). SEDFIT 92 software developed by Schuck was used for the sedimentation velocity data analysis.23

3. Results and Discussion To understand the solubilization of phenol in the DM micellar phase and the effects on phenol on the micellization of the surfactant, it is necessary to get information on the DM micellar shape, size, and aggregation number. Both the concentration of DM and phenol were found to be the determining factor for micellar size and shape. 3.1. Partial Specific Volume. Since the sedimentation velocity of the surfactant is mainly determined by the density of the surfactant micelles, information on the density is required for analysis of the AUC data. The partial specific volume of the surfactant micelle, defined as the volume of unit weight of the micelle, is a quantity essential for acquiring further information such as the sedimentation coefficient and the micelle mass. The partial specific volume Vj can be obtained empirically from the density gradient. The partial specific volume is obtained using the following equation:24

Vj )

1 dF 1F0 dC

(

)

(23) Schuck, P.; http://www.analyticalultracentrifugation.com.

(1)

Figure 2. Density vs concentration curves for dodecyl maltoside, phenol and their 1:1 (mol ratio) mixture at 25 °C. Table 1. Partial Specific Volume of Dodecyl Maltoside, Phenol and Their Mixture phenol DM DM/phenol 1:1

dF/dc

Vj (cm3/g)

0.085 0.184 0.165

0.92 0.82 0.84

where C is the surfactant volumetric concentration in g/mL and F and F0 are the densities of the solution and the solvent, respectively. Densities of solutions of DM, phenol, and their 1:1 molar ratio mixtures were measured using an Anton Paar density meter. The results are plotted in Figure 2 as a function of the concentrations. It was found that the slope decreases in the order of DM, 1:1 mixture, and phenol. dF/dc calculated from the slope obtained is listed in Table 1. The partial specific volume was then obtained using eq 1. The value for DM is in good agreement with the literature values, varying from 0.81 to 0.837 cm3/g. The partial specific volume values are used for the data analysis in analytical ultracentrifuge tests. 3.2. Sedimentation Velocity. In a sedimentation velocity test, the two-channel centerpiece (shown in the top of Figure 3) was used to accommodate the sample and reference solvent (water). The centerpiece is fixed in a cell, which is then put in the rotor seated in the vacuum chamber of the Beckman Coulter Optima XL-I AUC instrument. When the vacuum of the chamber reaches below 5 umHg, the rotor is set to run at 40 000 rpm, at which, the centrifugal acceleration is between 1.07∼1.26 × 106 m/s2 from the top to bottom of the sample channel. Due to the centrifugal force, surfactant micelles move to the bottom of the cell (because the partial volume of this mixed micelle is smaller than that of the solvent) at a terminal velocity of the order of 1 × 10-7 m/s. During the sedimentation process, the concentration profile is scanned by the interference monitor system continu(24) Steele, J. C. H., Jr.; Tanford, C.; Reynolds, J. A. Methods Enzymol. 1978, 48, 11-23.

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D)

RT Nf

(6)

where N is Avogadro’s number and f is the frictional coefficient. The experimental frictional coefficient, f, can be yielded by the combination of eqs 2 and 6. The calculated frication coefficient, f0, is defined as

f0 ) 6πηr0

Figure 3. Sedimentation processes of dodecyl maltoside micelles (50 mM, 25 °C, and 40 000 rpm).

ously. The sedimentation process of n-dodecyl-β-D-maltoside at 50 mM concentration is illustrated in the bottom of Figure 3. The concentration curve consists of several parts, including air/solvent and air/sample meniscus, boundary range, and the plateau range. The sedimentation velocity obtained is further utilized to obtain information on the micellar size and shape. When the partial specific volume is known, information on the size and shape of micelles can be determined by analyzing the sedimentation process. The sedimentation process is often expressed as the Svedberg equation25

s M(1 - νjF) ) D RT

(2)

where s is the sedimentation coefficient, D is the diffusion coefficient of micelles, M is the micellar mass, Vj is the partial specific volume, F is the density of the solvent, R is the gas constant, and T is the temperature in K. The sedimentation coefficient, s, is a key parameter for the interpretation of analytical ultracentrifuge data and is defined as the terminal velocity per unit acceleration force in the sedimentation process shown as the equation below.

s)

dr/dt velocity ) 2 acceleration ωr

(3)

where dr/dt is the velocity of the micelles, ω is the rotating speed and r is the radius. The micellar mass is calculated using the Svedberg equation. The aggregation number, Nagg, for mixed surfactant/phenol micelle is calculated as

Nagg )

M MWs + MWp‚x

(4)

where MWs and MWp are the molecular weight of DM and phenol, respectively, and x is the molar ratio of phenol to DM in the micellar phase, which is obtained previously using ultrafiltration tests. The effective minimum radius of a spherical micelle, r0, is defined as

r0 )

j (3MV 4πN)

1/3

(5)

The diffusion coefficient is defined as (25) Svedberg, T.; Petersen, K. O.; Bauer, J. H. The ultracentrifuge; The Clarendon Press: Oxford, U.K., 1940.

(7)

The experimental and the calculated frictional coefficients, f and f0, can be estimated from the sedimentation coefficient. The ratio f/f0 is a measure of the degree of asymmetry of the micelle. Bound water of hydration also contributes to the experimental frictional coefficient and should be considered in the calculations. In the case of mixed surfactant/phenol micelles, the hydration is taken as 6 water molecules per DM molecule26 and 4 water molecules per phenol.27 The hydration of the mixed DM/phenol micelle is estimated using the molar ratio between phenol and DM. 3.3. Size and Shape of Mixed DM/Phenol Micelles. The sedimentation process of the DM sample at 50 mM concentration is shown in Figure 3. With the concentration boundary moving toward the bottom of the sample channel, the sedimentation velocity is estimated as 3.8 × 10-7 m/s and the sedimentation coefficient is averaged over the sample channel using eq 3 to be 3.3 × 10-13 s or 3.3 Svedberg. Since the centrifugal force increases with the radius, the analysis of sedimentation processes is complicated. Using software Sedfit 92, the size distribution of the DM micelle at 50 mM was obtained and is shown as a function of the sedimentation coefficient in Figure 4. It shows a very narrow Gaussian distribution with an average sedimentation coefficient of 3.21. Further analysis provides a number of other parameters including diffusion coefficient, aggregation number, effective radius, and f/f0 ratio. The average aggregation number obtained for n-dodecyl-β-D-maltoside, 112, is in good agreement with the one obtained using time-resolved fluorescence quenching.26 Solubilization of phenol molecules in the micellar phase is expected to change the size and shape of the DM micelle. Wormlike and spherical micelles were observed with Cryo-TEM micrograph in DM solution with and without the presence of phenol.10 The micellar shape transition can be attributed to the molecular geometries, which determine the curvature of the micelles. To get quantitative information on the DM micellar shape and size in the presence of phenol, mixed DM/phenol samples were studied using AUC at mixing ratios of 3:1, 1:1, and 1:3 with fixed DM concentration 50 mM. The distributions C(s) of micelles over sedimentation coefficients for these three samples are shown in Figure 4. The integrated areas of all of the distributions were standardized to be 1. A similar Gaussian distribution was observed, but the distributions become wider with the mixing ratio, suggesting a broader distribution of the micellar size. Given the molar composition of the micellar phase,10 the aggregation number for mixed DM/phenol micelles can be calculated. The aggregation number increases from 112 to 626 with the mixing ratio and the effective radius increases from 2.7 to 6.0 nm, suggesting the growth of the DM micelle with phenol content. The average f/f0 ratio was found to increase from 1.04 to 2.04 indicating a shape transition from spherical to cylindrical. (26) Warr, G. G.; Drummond, C. J.; Grieser, F. J. Phys. Chem. 1986, 90, 4581-4586. (27) Guedes, R. C.; Cabral, B. J. C.; Simoes, J. A. M.; Diogo, H. P. J. Phys. Chem. A 2000, 104, 6062-6068.

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Figure 4. Size distributions over sedimentation coefficient for mixed n-dodecyl-β-D-maltoside/phenol at 50 mM.

Figure 7. Aggregation numbers for mixed n-dodecyl-β-D-maltoside/ phenol micelles. Table 2. Structural Parameters of DM and DM/phenol Mixtures at Various Concentrations

Figure 5. Size distributions over sedimentation coefficient for mixed n-dodecyl-β-D-maltoside/phenol at 5 mM.

Figure 6. Size distributions over sedimentation coefficient for mixed n-dodecyl-β-D-maltoside/phenol at 25 mM.

Interestingly, the coexistence of two peaks, which is an indication of two different micellar species, was observed in the case of 1:1 DM/phenol ratio mixture. This is the first time, to our knowledge, to provide direct proof for the phenomenon of coexistence of micelles with solubilized organic molecules. The coexistence of two different micelles suggests that the growth of DM micelles is discontinuous with the increase of phenol content in the micellar phase. It is interesting to determine how the aggregation number for mixed DM/phenol changes with surfactant concentration; therefore, similar tests were also conducted at 5 and 25 mM concentrations to test the concentration effects. The Gaussian

Np

S0 (mM)

P0 (mM)

S

Nagg

D (×1011m2/s)

f/f0

r0 (nm)

1 1 1 1 2 1 1 2 1 1 1 2 1

5 5 5 5 5 25 25 25 25 50 50 50 50

0 1.67 5 15 50 0 8.3 25 75 0 16.7 50 150

3.68 3.63 3.65 3.93 6.62 3.41 3.75 4.96 9.12 3.21 4.06 7.80 6.70

133 133 131 126 299 122 154 218 453 112 226 398 626

6.52 6.48 6.46 6.24 3.59 6.69 6.48 5.67 4.08 6.90 6.07 4.48 2.07

1.17 1.17 1.17 1.17 1.40 1.17 1.11 1.12 1.17 1.17 1.04 1.15 2.04

2.6 3.0 3.1 3.3 5.2 2.7 3.1 3.6 5.2 2.7 3.6 4.6 6.0

size distributions were also observed in the cases of lower surfactant concentrations (Figure 5 and 6). In Figure 5, the peaks, indicative of micellar species, shift from left to right with the increase of phenol concentration. At mixing ratios of 3:1 and 1:1, the peaks shift very little. However, the peak shifts from 3.68 to 3.93 at a mixing ratio of 1:3, suggesting the formation of larger surfactant/phenol micelles also with a wider distribution. More interestingly, two peaks were observed at the mixing ratio of 1:10, suggesting the coexistence of two different micelle species. The aggregation number of DM at 5 mM without phenol was determined to be 106, which is smaller than that at 50 mM. Since the average f/f0 ratio was found to remain the same as at 1.17 at 1:0, 3:1, 1:1, and 1:3 ratios, the micellar size can be considered not to change in this range; however, at a mixing ratio of 1:10, the f/f0 ratio increases to 1.4 and the aggregation number increases to 299. In the cases of 25 mM DM concentration, the peaks shift from left to right with an increase in phenol content in the micellar phase, indicating growth of mixed DM/phenol micelles. The coexistence of different micellar species was observed also in the case of the 1:1 mixing ratio. The structural parameters for mixed DM/phenol micelle are summarized in Table 2. The parameters includes peak numbers (Np), initial DM (S0) and phenol concentrations (P0), average sedimentation coefficient (S), aggregation number (Nagg), diffusion coefficient (D), frictional ratio (f/f0), and the effective radius (r0).

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Figure 8. Effects of concentration on the size distribution of mixed n-dodecyl-β-D-maltoside/phenol micelles. Figure 10. Aggregation number vs the phenol concentration in the micellar phase. Filled symbols represent the average aggregation numbers in the cases of coexistence of micellar species. Table 3. Structural Parameters of the Coexisting Micellar Species

Figure 9. Illustration of the growth of mixed DM/phenol micelles.

3.4. Growth of DM/Phenol Micelle with Concentration. As shown in Figure 7, the aggregation number of mixed DM/phenol micelles increases with both the DM/phenol ratio and the DM concentration, indicating the growth of the mixed DM/phenol micelle. In the absence of phenol, the aggregation number changes a little, whereas in the presence of phenol, the aggregation number increases significantly with the phenol concentration. At a fixed DM concentration, the aggregation number increases significantly with the mixing ratio except for the case of 5 mM, at which, the aggregation number increases above the mixing ratio 1:3. In Table 2, it is shown that the diffusion coefficient decreases and the effective radius increases with the phenol concentration at fixed DM concentration. Moreover, the fractional ratio also increases with both DM concentration and DM/phenol ratio, suggesting a shape transition from spherical to cylindrical to even worm-like. The structural information obtained can be used to elucidate the process of micellar growth with the phenol and surfactant concentrations. The structural parameters obtained at a 1:1 mixing ratio suggest that the mixed micelle undergoes size and shape change with an increase in concentration of DM and phenol concentration. The size distribution profiles also indicate possible micelle growth mechanism. At 5 mM DM concentration, there is only one peak with a f/f0 1.17 indicating a single quasispherical micelle species. In contrast, when the concentration increases to 25 mM, a second peak appears in the higher sedimentation coefficient range while the first peak stays at the same position as the single peak at 5 mM. Furthermore, when the concentration increases to 50 mM, interestingly, the first peak is seen to be at

peak no.

S0 (mM)

A0 (mM)

S

Nagg

D

f/f0

r0 (nm)

1 2

5 5

50 50

4.23 6.99

151 319

6.1 5.4

1.17 1.12

4.1 5.3

1 2

25 25

25 25

3.64 5.82

129 261

5.43 4.24

1.15 1.17

3.0 3.8

1 2

50 50

50 50

5.6 8.55

242 449

4.35 3.43

1.46 1.44

3.9 4.8

the position of the second peak at 25 mM and the second peak found in the higher sedimentation coefficient range. The shift of distribution peaks from left to right indicates the increase in the micellar size which is attributed to the molecular packing28 and energy change29 in the system. The packing parameter for DM is found to be 0.3530 with phenol molecules staying in the palisade layer of the micellar phase,10 the overall packing parameter increases with the phenol content in the micellar phase. The increase in packing parameter suggests shape transition from quasispherical to cylindrical. Since the packing parameter theory only considers the intermolecular interaction energy between the molecules in the micellar phase, and the micellar phase is the discontinuous phase in the system, the intermicellar interaction energy29 should also be taken into account. With an increase in the surfactant concentration, the micellar number density increases and thus the intermicellar energy also increases. To lower the overall energy, the system tends to decrease the interphase area and favors swelling of micelle and transition of shape from quasispherical to cylindrical. Based on the quantitative information on the micellar size and shape, a growth model is proposed for the micellization of the mixed DM/phenol system with respect to the packing and intermicellar theory. At low surfactant and phenol concentrations, since the incorporation of phenol molecules in the micellar phase increases the average packing parameter, the micelle swells causing a change in the micelle shape from spherical to cylindrical with the extent of the shape transition depending on the composition of the micellar phase and the micelle number density. (28) Israelachvili, J. N.; Mitchell, D. J. Biochim. Biophys. Acta 1975, 389 (1), 13-19. (29) Bayer, O.; Hoffmann, H.; Ulbricht, H.; Thurn, H. AdV. Colloid Interface Sci. 1986, 26, 177-203. (30) Dupuy, C. Langmuir 1997, 13, 3965-3967.

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Figure 11. Concentration diagram for mixed DM/phenol micellar system.

The proposed growth is illustrated in Figure 9 as step 1. In this step, the micelles grow continuously with phenol content in the micellar phase. When the micellar number density reaches a critical concentration, the micelle undergoes discontinuous growth from species A to B as illustrated in step 2. As some of the molecules form micellar species B, the micellar species A coexist in the system. Such coexistence of the two species is shown as the double peak in the distribution diagram. When the concentration further increases, the micellar species B undergoes further growth to a new micellar species C and the species B and the new species coexist in the system. At higher concentrations, all of species B may be converted to the new species and only one species remains in the system. For example, only a single large micelle species exists in the case of 1:3 DM/phenol ratio and DM 50 mM in Figure 4. 3.5. Coexistence of Micellar Species. The double peaks were observed in the three samples tested: mixing ratio 1:10 at 5 mM, 1:1 at 25 mM, and 1:1 at 50 mM. The double peaks indicate the coexistence of two different species with these conditions. Further analysis revealed structural parameters for the coexisting species in the system. Though the chemical composition of the two coexisting micellar species may vary, the average composition was used for calculating the structural parameters for the two species due to a lack of technique to separate them. The aggregation number, diffusion coefficient, fractional ratio, and effective radius were estimated using the same methodology as for the case of single micellar species, and the results are shown in Table 3. It can be seen that the aggregate number of the larger micellar species is close to double of that of the smaller species, which help to understand the mechanism of the discontinuous micelle growth in step 2 in the model proposed. Similar to droplets in emulsion systems, the frequency of collision between two micellar species statistically depends on the number density. Increase in the surfactant concentration causes an increase in the micellar number density and thus the frequency of collision. Phenol molecules are polar and stay in the palisade layer of the micelle, therefore the presence of phenol decreases the intermicellar repulsion energy. When the collision energy is high enough to overcome the repulsion, two micelles are proposed to merge to form a new species. At certain concentrations in the model, equilibrium between the two species is maintained, and therefore, two different species coexist in the system. The critical concentrations for the discontinuous micellar growth are determined by the content of phenol in the micellar phase.

3.6. Relationship between Aggregation Number and Phenol Concentration in the Micellar Phase. The aggregation number of the mixed DM/phenol system was obtained from the sedimentation velocity tests and was found to increase with both the DM concentration and the phenol concentration. The chemical composition of the micellar phase was obtained using the ultrafiltration technique.10 The relationship between the aggregation number and the phenol concentration in the micellar phase were subjected to polynomial and linear fitting (Figure 10). The error was found to be 0.978 for the polynomial fitting and 0.957 for the linear fitting. This relationship will be helpful for estimating the aggregation number for mixed DM/phenol system at any phenol concentration. When the molar ratio of phenol in the micellar phase is known, the phenol concentration in the micellar phase can be calculated, and then, the aggregation number can be estimated. Also similar relationships may exist for other surfactant/organic mixture systems. 3.7. Micellar Distribution Diagram of Mixed DM/Phenol over Concentration. The proposed model was used to describe the micellar growth with both DM and phenol concentration. The coexistence of two micellar species was attributed to the discontinuous growth of the micelles. To reveal the quantitative relationship between micellar size and shape between surfactant and phenol concentrations, the concentration diagram was divided into three ranges based on the experimental data. In region I, there exists only one type of quasispherical micelle with an aggregation number slightly greater than that of DM alone; in region II, two different types micelles of cylindrical shapes coexist; In region III, there exists only one type of micelle with an elongated worm-like shape and an aggregation number several times of that in region I. In region II, the aggregation number of the second type of micelle is roughly twice that of the first type as per the equilibrium between them as discussed in the proposed model.

Conclusions The structural parameters, including sedimentation coefficient, aggregation number, diffusion coefficient, fractional ratio, and effective radius, for micelles of mixed n-doedyl-β-D-maltoside/ phenol were obtained using sedimentation velocity tests using AUC technique. The aggregation number was found to increase with the concentrations of surfactant and phenol. The micellar shape was shown in this study to undergo transition from quasispherical to cylindrical. In addition, the coexistence of two micellar species was observed in a certain concentration range.

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The size increase and shape transition are attributed to the molecular packing in the micellar phase and the intermicellar interaction energy. A two-step model is proposed for the micellar growth of the mixed DM/phenol system. At low concentrations, the micelles swell continuously due to a decrease in the curvature, whereas at high concentrations, two micelles coexist when the collision overcomes the intermicellar repulsion energy. This growth model may be applied to other mixed surfactant/organic compound systems and help to understand the roles of surfactants in practical applications.

Lu and Somasundaran

Acknowledgment. The authors acknowledge the financial support of Department of Energy (DE-FC26-03NT15413), and the Industrial/University Cooperative Research Center (IUCRC) for advanced studies on novel surfactants at Columbia University. The authors also express gratitude to Dr. Peter Schuck for his software, to Beckman Coulter for the training course, and to the instructors in the AUC workshop at University of Connecticut. LA7016616