Automated High-Performance Purification of Surfactant Solutions

The advantages and reliability of the new technique are demonstrated by the purification characteristics of different solutions of as-received surfact...
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Automated High-Performance Purification of Surfactant Solutions: Study of Convective-Enhanced Adsorption K. Lunkenheimer,* G. Wienskol, and A. J. Prosser Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, D-14424 Potsdam-Golm, Germany Received December 23, 2003. In Final Form: April 16, 2004 Due to the amphiphilic nature of surfactants, they generally contain traces of their more surface-active parent components irrespective of the as received surfactant’s label declaration. These trace impurities are preferentially enriched in the surfactant’s adsorbed layer. To attain the state of “surface chemical purity” that implies the absence of impurities in the adsorbed layer, we had developed an automatic high-performance purification apparatus years ago. Here we put forward an improved version of this successful technique that considerably reduces the time required to purify surfactant solutions by accelerating the adsorption through convection. The advantages and reliability of the new technique are demonstrated by the purification characteristics of different solutions of as-received surfactants of varying degree of purity. As the overall time gained with convective purification is of 1 order of magnitude, the improved technique is particularly favorable for surfactant solutions that are prone to hydrolysis or degradation.

Introduction Substances produced by a chemical synthesis usually contain traces of the synthesis’ parent compounds. Their extent depends on the grade of purity that is marked on the substance’s label, such assin the sequence of purported increasing puritys“for synthesis”, “pure”, “purissimum”, “pro analysis”, “ultrapure”, etc. This also holds for surfaceactive substances: surfactants, amphiphiles, tensides. However, there is a very important peculiarity regarding the purity of surface-active substances that has to be taken into account when dealing with the adsorption of surfactants at interfaces: the surface activity of the hydrophobic parent compound is usually much stronger than that of the surfactant itself. Thus, the grade of purity marked on the label refers to the relative content or percentage of this compound only for the “as received” bulk material. However, if such “as received” product is dissolved in a solvent, usually water, the more hydrophobic trace component will be preferentially enriched in the adsorbed layer. In 1970 Mysels and Florence had concluded in their review on the purification of aqueous surfaces that “it is difficult to know when a surface characteristic of the pure surfactant has been produced because there is no standard surface or point of reference”.1 Many scientists have addressed this problem,2-32 often using the surfactant * To whom correspondence should be [email protected].

sent.

E-mail:

(1) Mysels, K. J.; Florence, A. T. In Clean Surfaces. Their Preparation and Characterization for Interfacial Studies; Goldfinger, G., Ed.; Marcel Dekker: New York, 1970; pp 227-268. (2) Miles, G. D.; Shedlovsky, L. J. Phys. Chem. 1944, 48, 60. (3) Miles, G. D. J. Phys. Chem. 1945, 49, 71. (4) Brady, A. P. J. Phys. Chem. 1949, 53, 56. (5) Harrold, S. P. J. Colloid Sci. 1960, 15, 260. (6) Elworthy, P. H.; Mysels, K. J. J. Colloid Interface Sci. 1966, 21, 321. (7) Mysels, K. J.; Florence, A. T. J. Colloid Interface Sci. 1973, 43, 577. (8) Gilanyi, T.; Stergiopulos, C.; Wolfram, E. Colloid Polym. Sci. 1976, 254, 1018. (9) Lunkenheimer, K.; Miller, R. Tenside Deterg. 1979, 16, 312. (10) Ashani, Y.; Catravas, G. N. Anal. Biochem. 1980, 109, 55. (11) Rosen, M. J. J. Colloid Interface Sci. 1981, 79, 587. (12) Carroll, B. J. J. Colloid Interface Sci. 1981, 86, 686.

sodium dodecyl sulfate (SDS), still considered to be the “standard”.2,3,5,6,30,33-36 However, over time it appears that the issue of surfactant purity is again forgotten. Therefore it seems appropriate to quote a conclusion of Gebhardt and Fu¨rstenau from 1984 in discussing the oft-cited conclusion that the absence of a minimum in the surface tension-concentration curve is a sufficient criterion for surfactant purity: “... the absence of a minimum does not always ensure high purity, especially in the case of nonionic surfactants. The importance of obtaining well(13) Lunkenheimer, K.; Fruhner, H.; Miller, R. Colloid Polym. Sci. 1982, 260, 599. (14) Miller, R. und Lunkenheimer, K. Colloid Polym. Sci. 1982, 260, 1148. (15) Gebhardt, J. E.; Fuerstenau, D. W. J. Colloid Interface Sci. 1984, 101, 278. (16) Tabata, Y.; Ueno, M.; Meguro, K. J. Am. Oil Chem. Soc. 1984, 61, 1123. (17) Pallas, N. R.; Pethica, B. A. Langmuir 1985, 1, 509. (18) Scamehorn, J. F. J. Colloid Interface Sci. 1982, 85, 463. (19) Lunkenheimer, K. und Miller, R. J. Colloid Interface Sci. 1987, 120, 176. (20) Lunkenheimer, K.; Pergande, H.-J.; Kru¨ger, H. Rev. Sci. Instrum. 1987, 58, 2313. (21) Graciaa, A.; Lachaise, J.; Marion, G.; Bourrel, M.; Rico, I.; Lattes, A. Tenside, Surfactants, Deterg. 1989, 26, 384. (22) Schubert, K.-V.; Strey, R.; Kahlweit, M. J. Colloid Interface Sci. 1991, 141, 21. (23) Smaby, J. M.; Brockman, H. L. Chem. Phys. Lipids 1991, 58, 249. (24) Lunkenheimer, K.; Theil, F.; Lerche, K. H. Langmuir 1992, 8, 403. (25) Eaglesham, D. J.; Unterwald, D. C.; Jacobson, D. C. Phys. Rev. Lett. 1993, 70, 966. (26) Sager, W.; Srey, R.; Ku¨hnle, W.; Kahlweit, M. Prog. Colloid Polym. Sci. 1994, 97, 141. (27) Ishida, K.; Mori, Y. H. Int. Commun. Heat Mass 1996, 23, 907. (28) Marinova, K. G.; Alargova, R. G.; Denkov, N. D.; Velev, O. D.; Petsev, D. N.; Ivanov, I. B.; Borwankar, R. P. Langmuir 1996, 12, 2045. (29) Colic, M.; Fu¨rstenau, D. W. Powder Technol. 1997, 2, 129. (30) Crison, J. R.; Weiner, N. D.; Amidon, G. L. J. Pharm. Sci. 1997, 86, 384. (31) Stubenrauch, C.; Schlarmann, J.; Sottmann, T.; Strey, R. J. Colloid Interface Sci. 2001, 244, 447. (32) Lunkenheimer, K. Purity of Surfactants and Interfacial Research. In Encyclopedia of Surface and Colloid Science; Marcel Dekker: New York, 2002; pp 3739-3772. (33) Vijayendran, B. R. J. Colloid Interface Sci. 1977, 60, 418. (34) Smith, A. J. Colloid Interface Sci. 1978, 66, 575. (35) Mysels, K. J. Langmuir 1986, 2, 423. (36) Lunkenheimer, K.; Czichocki, G. J. Colloid Interface Sci. 1993, 160, 509.

10.1021/la036442g CCC: $27.50 © 2004 American Chemical Society Published on Web 06/02/2004

Purification of Surfactant Solutions

characterized surfactants for adsorption studies cannot be overemphasized.”15 The crucial point in the purity of surfactants is that one cannot know the number of impurity components, their concentration, or their surface activity a priori. Moreover, there have been no generally agreed upon criteria to judge the degree of purity or an advantageous procedure to effectively remove any impurities. Hence the classification of a surfactant’s purity given on the label, although correctly denoting the content of impurity in the bulk phase, does not refer to the grade of purity in the adsorbed surfactant layer. Therefore another special grade of purity is required to characterize the state of purity of the adsorbed layer. When the content of the impurity component is negligible in the adsorbed layer, the grade of purity is denoted as “surface chemically pure”.9,14,20 To achieve the quality of surface chemical purity, special techniques are required.1,6,20,24 A thermodynamic criterion was derived from which it is possible to judge the surfactant solution’s grade of purity.19 Purification procedures designed to remove contaminants are usually based on differences in the physical bulk properties of the main component and of the contaminant, like solubility (crystallization, chromatography) or boiling and melting points (distillation, melting). Since it is not possible to achieve the state of surface chemical purity by these techniques, we had developed an “apparatus for programmed high-performance purification of surfactant solutions” (HPPS), also previously called “Flunder”.20 The principle of this device consists of directly removing the adsorbed contaminant from the surface by repeated aspiration. With this apparatus, many novel features of surfactant adsorption have been discovered by us, as summarized in ref 32. Although this device operates reliably and has been used by us permanently, there is one drawback in the procedure, namely, that it often takes too much time to reach the required grade of surface chemical purity, especially in cases when the original quality of the “as received” surfactant was rather pure. Here we put forward a further developed apparatus, HPPS-2, that reduces the time necessary to reach the solution’s grade of surface chemical purity by 1 order of magnitude. Experimental Results 2.1. Purification with Convection. The principle of the automated purification apparatus described in refs 20 and 32 is schematically illustrated in Figure 1. The surfactant solution is kept in a flat glass container of relatively large diameter to allow a large surface area. The container is maintained in this position until the solution has almost reached adsorption equilibrium. For solutions prepared from “as received” surfactant, this usually takes several hours, more or less independent of the concentration of the surfactant solution. The long time dynamics is due to the contaminants’ high surface activity and low (bulk) concentration. Then, the whole glassware is tilted such that the solution gently flows into the narrow neck of this container. The adsorbed layer at the air/water interface is drastically compressed. In this position, the surface is sensitively aspirated for half a second by a thin capillary. The small loss of bulk solution is measured electronically by approaching the already siphoned solution surface anew with the capillary. By comparison of the two levels before and after aspiration, the volume of solution siphoned during one cycle can be calculated.

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Figure 1. Schematic of the container of the improved highperformance purification apparatus HPPS-2 (Flunder 2) in its alternate positions: left, initial state allowing for large surface area of the surfactant solution to be purified; right, tilted container in the state of highly compressed adsorbed layer ready to be siphoned. Capillary and sensor wire are mounted parallel in the stopcock. The stir bar for producing convection by alternative rotations remains fixed in the center of the flat glass container at all times.

Additionally, the new level for the subsequent aspiration is recorded. The second platinum sensor located parallel to the platinum capillary serves as a counter electrode for the electric signal. Afterward, the container is returned to the initial position. This cyclic process is repeated until the grade of surface chemical purity (scp) is reached. Usually 50-300 such cycles are required. This means that several days are necessary to bring the solution into the grade of surface chemical purity. Hence we wanted to reduce the purification time. As we intended to maintain the successful principle of purification, we would have to accelerate the process when the impurity adsorbs at the surface. This was achieved with convection. We put a stirrer in the middle of the flat glass container. The solution to be purified was stirred for some time, continuously alternating the direction of rotation. A time interval of about 10 min is usually sufficient to approximately establish adsorption equilibrium at the surface (for one adsorption cycle). The time required was experimentally determined by comparing the dynamic surface tension behavior of unstirred surfactant solutions with ones stirred for some time. Now one cycle of purification with convective accelerated adsorption consists of establishing adsorption equilibrium by stirring the solution in the initial position. The stirring is then stopped, and the glass container is gently tilted into the position for aspiration. After having sucked off the compressed surface in the narrow neck, the loss of solution is electronically measured. Then the container is tilted back into the initial position. To check how much the establishment of the adsorption equilibrium can be accelerated by convection, we measured the dynamic surface tension of surfactant solutions at rest and after having stirred them for some time. To simulate this process we used a flat glass container (Figure 2) of the same dimensions as the flat container of the HPPS-2 apparatus. Stirring does not disturb the surface layer; i.e., the adsorbed surfactant is not mixed back into solution. The top part with the neck was kept open to transfer the solution, to aspirate the surface, and to measure surface tension. This container was fitted under a Lauda tensiometer. The ring for surface tension measurement was put into the solution via the neck. The motor of an electromagnetic stirrer system was mounted below the center of the flat container. A stirrer was put into the solution to allow for stirring. The magnetic stirrer was

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Figure 2. Flat glass container of the Flunder apparatus for simulating the effectiveness of convection on the establishment of adsorption equilibrium of as received surfactant solutions. A small electromagnetic motor is fixed below the solution. Surface tension is measured by a ring tensiometer (cf. text). Figure 4. Comparison between purification in a calm and in a stirred solution: surfactant solution, 1 × 10-3 M sodium dodecyl sulfate; producer, Ferak; 9, calm solution; ‚‚‚, stirred solution. Conditions were as follows: speed, 150 revolutions/ min; time on, 19 s; time off, 1 s; duration of stirring, 5 min, 15 min, 20 min, and 25 min intervals. t* ) 5 min of stirring. t is time when surface tension of the unstirred solution had reached the corresponding surface tension value of the stirred solution at time t* (after 5 min of stirring).

Figure 3. Comparison between purification in a calm and in a stirred solution: surfactant solution, 4 × 10-3 M sodium dodecyl sulfate; producer, Ferak; 9, calm solution; open symbols, surface tension of stirred solution measured directly after repeated intervals of stirring, duration of stirring interval was 10 min (corresponding to 200 iterations). Conditions were as follows: speed, 150 revolutions/min; time on, 3 s; time off, 0 s. t* ) 10 min of stirring, t is time when surface tension of the unstirred solution had reached the corresponding surface tension value of the stirred solution at time t* (after 10 min of stirring).

covered with a hydrophobic layer (PTFE). The thickness of the rod was 4 mm to ensure that the rod was almost completely covered by the solution. The dynamic surface tension was measured after the surface had been carefully aspirated. The stirring was performed at different intervals. After the sample was stirred for a certain period, the ring was immersed and the surface tension was measured. Then the ring was detached from the surface and the next period of stirring started. In Figure 3 the dynamic tension results of an experiment with an “as received” solution of 4 × 10-3 M sodium dodecyl sulfate (Ferak) are shown. The stirring was started directly after aspiration of the surface. In this figure the dynamic surface tension of the static solution reveals a long time dependence typical of contaminated (as received) surfactant solutions. The final, almost constant surface tension value at rest, σ j e ≈ 40.6 mN/m, was approached after about 150 min. After 10 min of alternately stirring, a surface tension value of 41.6 mN/m was reached. Without stirring, this surface tension value was reached only after about 80 min. Thus, stirring resulted in an acceleration of adsorption by a factor q ) t/t* of about 8. Stirring was then continued

in 10 min intervals. The curve of such discontinuous stirring is also shown in Figure 3. Stirring for about 40 min is enough to reach the equilibrium surface tension value of this solution. Figure 4 shows the results of a like experiment for a solution of 1 × 10-3 M sodium dodecyl sulfate (Ferak). The dynamic surface tension has not yet reached equilibrium after 160 min when the surface tension was 51.6 mN/m. The stirring was performed in intervals of 5 min only. Within the first 5 min, the surface tension decreased to 52.5 mN/m. This surface tension value was reached for the nonstirred solution after 70 min. Thus, the factor q of acceleration of adsorption is about 14. After 15 min of stirring, a surface tension value of 51.5 mN/m was reached. This value was reached for the unstirred solution at about 180 min (not shown) resulting in a factor q of about 12. This experiment also convincingly demonstrates that the equilibrium surface tension value of the nonstirred solution will be reached only after adsorption times considerably greater than 160 min. However, the equilibrium surface tension value of 51.0 mN/m was quickly reached after an overall period of 20 min of stirring. Comparing the results of Figures 3 and 4, where we have used the same substance but different concentrations, one can conclude that the convection is even more effective for the lower concentration. This effect is obvious because we required a 10 min stirring period for the higher concentrated SDS solution but only half that for the lower concentrated solution. Finally, Figure 5 shows the results of a like experiment using an aqueous as received solution of 1 × 10-3 M sodium dodecanesulfonate (Aldrich). The very long time dependence of the surface tension of the nonstirred solution indicates that this solution is more contaminated than that of the sodium dodecyl sulfate solution of equal concentration. The first surface tension value measured after 5 min of stirring amounted to 61.8 mN/m. Comparing this value with the same value of the dynamic surface tension dependence, σ(t), of the calm solution shows that about 160 min was required to arrive at it. Thus, the acceleration factor q becomes rather large, i.e., about 32. Moreover, as was observed already in the experiment of Figure 4, only by applying an overall time of stirring of 15-20 min makes the solution reach the

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Figure 5. Comparison between purification in a calm and in a stirred solution: surfactant solution, 1 × 10-3 M sodium dodecanesulfonate; producer, Aldrich; 9, calm solution; ‚‚‚, stirred. Conditions were as follows: speed, 150 revolutions/min; time on, 19 s; time off, 1 s; duration of stirring, 5 min, 15 min, 20 min, and 25 min intervals.

equilibrium surface tension value, which was not yet reached after 180 min for the calm solution. Comparing the results of Figures 4 and 5, we have the same concentration of the solutions but two different anionic surfactants. The acceleration by convection is more effective for the sodium dodecanesulfonate solution (Figure 5). However, these results show that the sodium dodecanesulfonate contains more hydrophobic impurities that are preferentially enriched in the adsorbed layer under convection. Concerning the highly surface-active, slightly soluble parent trace impurities such as 1-dodecanol, it is imaginable that condensation of it could occur in the compressed adsorbed layer that in turn might result in the formation of solid condensates or droplets. However, the presence of aggregates or drops in the bulk or base of the sample vessel has never been observed. This is due to the particular conditions of surface purification. First, as a result of various postsynthesis purification procedures, the impurities are present only at concentrations below their solubility limits. For hydrocarbon-based surfactants, the bulk density of the impurities is expected to be less than that for water, so that any large solid condensates or liquid drops should float to the surface. Second, the effective compression factor would be very high, amounting to a value of about 35, if the ratio of the solution’s surface areas in the initial state (large container) to that in the compressed state (in the neck of the tilted glass container) was considered. However, the effective compression factor is much lower because the compression of the adsorbed layer in the Flunder apparatus is performed by flow of the solution into the rather narrow neck of the glass container. There is some part of the neck left uncovered when the solution reached the final position. As this free glass surface is of high surface energy, the compressed surface film will spread across the wetted wall above it, especially if high surface pressures are applied.37 This results in a considerably lower compression ratio. A detailed calculation shows that an average effective compression ratio of about 6 results then. These conditions are usually not sufficient to allow for condensation of impurities present in trace amounts. Finally, if there was indeed a relatively high concentration of dodecanol, its condensation in the surface induced by drastic compression would presumably be counteracted by the following processes: first, a rapid

desorption of SDS molecules resulting in a very high local concentration near the interface and subsequent formation of micelles; second, the ability of the micelles to solubilize any interfacial material of the solid aggregates/drops; third, the aspiration of the surface and part of this underlying sublayer. Experience has shown that only in certain rare, extreme cases of the purification of nonmicelle forming, almost insoluble surfactants at concentrations close to their solubility limits need one be concerned with the presence of interfacial aggregates.38 In this case, the adsorbed layer can be purified by the aspiration of the noncompressed adsorbed layer a few times. Generally, one need not be afraid of a formation of insoluble aggregates in the compressed adsorbed layer in the Flunder apparatus. 2.2. Optimal Stirring Conditions. We have searched for the optimal stirring conditions. Stirring with constant rotation in a single direction is not very effective because steady-state conditions within a laminar flow field were rapidly achieved. However, turbulence is desired to accelerate diffusion. Consequently, we altered the stirrer’s direction of revolution as often as possible to escape the flow’s steadystate. This indeed resulted in a much more effective acceleration of adsorption. However, the more drastically we made the stirrer alter its direction of rotation, the more prone the stirrer was to break out of the center of the solution and to fly aside. In addition, every outbreak produced some foam at the solution’s surface that prevented the apparatus from reliably aspirating the surface. Moreover, abruptly starting stirring also favored foam production because the movement was very unstable after every turn on and turn off. Eventually we succeeded in maintaining an even motion of the stirrer by ramping the speed up and down, preventing any breakout. With that, not only stable conditions of stirring could be guaranteed but also any foam production was avoided. The optimal conditions for stirring we have found are as follows: rotation speed, 150 rotations/min; time on, 3 s; time off (toggle), 0 s; diameter of flat container, 17 cm; length of stirrer, 4-5 cm. Summarizing the experiments described in Figures 3-5, we can conclude that convective diffusion brought about by alternately stirring the solutions results in a remarkable reduction of the adsorption time. The relative

(37) Lunkenheimer, K.; Wantke, K.-D. Colloid Polym. Sci. 1981, 259, 354.

(38) Prosser, A. J.; Retter, U.; Lunkenheimer, K. Langmuir 2004, 20, 272.

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acceleration due to convective adsorption is of about 1 order of magnitude. However, it is difficult to give exact data because the effect depends on the concentration of and kind of surfactant. The long adsorption time is caused by the trace impurity components due to their relatively low bulk concentrations, but since their nature and their precise concentration are generally not known, we need to directly compare the purification procedures in the highperformance purification apparatus under conditions when the solution remains calm and when it is stirred. Before doing so, we have performed some theoretical estimations about the acceleration of surfactant adsorption by convection, taking into account the conditions used in our experiments. 2.3. Theoretical Estimation about Convective Diffusion. 2.3.1. Diffusion in Calm Solution. For quiescent solutions of soluble surfactants, adsorption is conceptualized as a two-step process. First, bulk molecules diffuse to and adsorb within the interfacial sublayer. Second, molecules within the sublayer transfer to or exchange with those already adsorbed at the interface. When the first process controls the overall rate of adsorption, the process is termed “diffusion limited”. When the second process controls the rate of adsorption, the process is termed “kinetic limited”.39,40 When there exists no activation energy barrier to the adsorption/desorption process, diffusion is the only process needed to establish adsorption equilibrium and the surfactant partitions between the sublayer and the interface according to an equilibrium adsorption isotherm. The problem of diffusion-limited adsorption was first formulated and solved by Ward and Tordai,41 and has since been the foundation of various initial and boundary value problems.42-45 The instantaneous surface density Γ(t) is simply determined from a surfactant mass balance at the interface

∫

∂c(x)0,t) dt Γ(t) ) t)0 D ∂x t

(1)

where D is the diffusion coefficient and the interface is located at the plane x ) 0. The surface tension σ(t) is assumed to instantaneously reflect the surface density Γ(t) via an appropriate surface equation of state. Implicit in this type of analysis are two characteristic scaling parameters, the adsorption layer thickness h and the adsorption time τD46

Γe co

(2)

2 h2 (Γe/co) ) D D

(3)

h)

τD )

where Γe is the equilibrium surface density and co is the bulk concentration. For aqueous surfactants, D is approximately constant, so the parameter that controls τD is h, the value of which can be estimated from an equilibrium adsorption isotherm. (39) Chang, C.-H.; Franses, E. I. Colloids Surf. 1995, A100, 1. (40) Eastoe, J.; Dalton, J. S. Adv. Colloid Interface Sci. 2000, 85, 103. (41) Ward, A. F.; Tordai, L. J. Phys. Chem. 1946, 14, 453. (42) Miller, R. Colloid Polym. Sci. 1981, 259, 375. (43) Mysels, K. J. J. Phys. Chem. 1982, 86, 4648. (44) Lin, S.-Y.; McKeigue, K.; Maldarelli, C. Langmuir 1991, 7, 1055. (45) Liao, Y.-C.; Franses, E. I.; Basaran, O. A. J. Colloid Interface Sci. 2003, 258, 310. (46) Ferri, J. K.; Stebe, K. J. Adv. Colloid Interface Sci. 2000, 85, 61.

2.3.2. Convective Diffusion. Convection, either natural or forced, enhances the adsorption of surfactants. To solve the convective diffusion equation, the velocity profile of the solution must also be known.47 The coupled mass and momentum equations for convective enhanced diffusion via stirring cannot be easily solved. The primary reason for the complexity is that the flow field must be considered as fully three-dimensional. In this case, even a numerical solution would be quite difficult to obtain. The simplest treatments of convective systems are based on a diffusion layer approach in which it is assumed that convection maintains the concentrations of all species uniform and equal to the bulk values up to a certain distance δ from the surface. Within the adsorption layer, 0 < x < δ, no solution movement occurs and mass transfer takes place via diffusion.48,49 Thus the convection problem is converted into a diffusion problem. By use of the simplest adsorption isotherm, the Henry isotherm, Γ(t) ) Kc(t), eq 1 can be approximated as

Kc(x)0,t) ) Γ(t) ≈

t D ∫t)0

co - c(x)0,t) dt δ

(4)

Equation 4 can readily be solved to yield expressions for c(t) and Γ(t). The characteristic time scale of this process, denoted τD+C, is simply

τD+C )

(Γe/co)δ D

(5)

The value of δ can be estimated from the expression for the Levich boundary layer thickness for convective diffusion to the surface of a rotating disk50

δ ) 1.61D1/3ω-1/2ν1/6

(6)

where ω is the disk rotation rate and ν is the kinematic viscosity of the solution. 2.3.3. Estimation of Acceleration Factor q. An acceleration factor q due to convection is defined as

q≡

τD τD+C

)

()(

)

Γe Γeω1/2 ≈ co δ 1.61coD1/3ν1/6

(7)

In general, the values of Γe and δ vary little so that q is primarily determined by co. Using typical parameter values (D ) 5 × 10-6 cm2/s; ω ) 2.4 rev/s; ν ) 10-2 cm2/s; Γe ) 4 × 10-10 mol/cm2), one would expect the adsorption enhancement due to added convection to range from a factor of 5 to 100. In agreement with the experimental findings, the key issue in accelerating the adsorption kinetics is the avoidance of steady-state flow conditions rather than the type of flow. The more rapid attainment of a steady-state surface tension by application of alternating stirring is a direct result of the compression of the diffusion boundary layer. 2.4. Experimental Comparison of Purification at Rest and with Convection. In Figure 6 the characteristic purification curve of the Flunder apparatus is given for a calm and for a stirred solution of an aqueous as received solution of 1 × 10-5 M dimethyl-n-tetradecyl(47) Zapryanov, Z.; Chervenivanova, E. Int. J. Multiphase Flow 1982, 8, 393. (48) Delahay, P.; Trachtenberg, I. J. Am. Chem. Soc. 1957, 79, 2355. (49) Bhugun, I.; Anson, R. C. J. Electroanal. Chem. 1997, 439, 1. (50) Levich, V. G. Physicochemical Hydrodynamics; Prentice Hall: Englewood Cliffs, NJ, 1962.

Purification of Surfactant Solutions

Figure 6. Comparison of purification in the HPSP-2 apparatus under conditions of calm and of stirred solution: aqueous solution of 1 × 10-5 M dimethyl-n-tetradecylphosphine oxide; 9, calm solution; O, convection (stirred solution). Conditions were as follows: rotation speed, 150 revolutions/min; time on, 3 s; time off, 0 s; duration of stirring interval, 10 min.

phosphine oxide. The data show the typical behavior of contaminated surfactant solutions within the first 90 purification cycles. These data reveal a steep slope at the beginning and then level off at higher cycles. However, for higher purification cycles, j g 120, there is a straight line (linear dependence of σ on j). The reason for this behavior is the following. At first the trace impurity component having a stronger surface activity but a considerably lower concentration than the main component is removed. As long as the amount of main component that has been removed from the surface by aspiration together with the impurity remains negligible, the purification characteristic approaches a constant value when the state of surface chemical purity is reached, i.e., dσe/dj ) 0.9 However, when the concentration of the main component is rather low, the loss of the main component during continuous aspiration of the adsorbed layer cannot be neglected. By simple calculations, it is possible to show that the linear part of the curve is due to a loss of the main component from the already surface chemically pure solution. The linear part tells us also about the extent of removal of adsorbed material during one purification step because we know the adsorption parameters of this surfactant exactly.51 However, with respect to the problem under study, it is important to see that there is practically no difference between purification at rest and with convection, within the limit of error. The only difference between the two procedures is that by using convective purification we have accelerated the adsorption kinetics by a factor of about 120 min/10 min ) 12, because the adsorption time for one purification cycle at rest was 2 h, whereas that for the stirred solution was only 10 min. Thus, our conclusion about the order of magnitude of the acceleration factor of the convectivedriven purification seems to hold and is in agreement with the theoretical estimation given above. Figure 7 illustrates the comparison of the purification characteristics of 5 × 10-3 M sodium dodecyl sulfate solutions. There are two independent characteristics for convective (by stirring) and one for unstirred purification. The results of the convective purification slightly scatter at lower cycle (51) Lunkenheimer, K.; Haage, K.; Hirte, R. Langmuir 1999, 15, 1052.

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Figure 7. Comparison of purification characteristics of 5 × 10-3 M sodium dodecyl sulfate solutions (Ferak, as received). × and 4, with stirring: rotation speed, 150 revolutions/min; time on, 3 s; time off, 0 s; duration of stirring interval, 5min. O, purification without stirring: adsorption time per purification cycle, 1 h.

numbers when the influence of the contaminant is strong. However, with increasing grade of the solutions’ purity, identical surface tension values of 46.5 mN/m were obtained for the two purification experiments. For the unstirred purification, the resulting surface tension value of the scp solution was slightly lower by 0.3 mN/m. However, careful examination of this experiment shows that its purification characteristic has not yet fully reached the state of surface chemical purity because the dependence σe(j) did not yet exactly reach the required plateau value where dσe/dj ) 0. The extrapolation of this curve will approach the surface tension value of the scp solution at j numbers of about 500. The results of the experiments of Figure 7 show that the convective purification procedures are somewhat more efficient than the unstirred procedure. The rather slow progress in the purification of the unstirred solution at j g 200 cycles reveals another important prerequisite of surfactant research, i.e., the surfactant’s stability in solution. We know that sodium dodecyl sulfate slowly hydrolyses in aqueous solution.36 Realizing that for unstirred purification the interval 175 e j e 390 covers (390 - 175) × 2 h ) 430 h, or 18 days, we have to take into consideration that during this time period some hydrolysis has occurred. This, in turn, hinders the purification progress. Thus, the very slowly approached state of surface chemical purity becomes understandable. Moreover, this example convincingly demonstrates the necessity for a faster purification procedure. The last experiment shown in Figures 8 and 9 illustrates that the improved version of the HPPS-2 apparatus is able to purify very highly contaminated surfactant solutions. We on purpose have chosen a surfactant of poor grade of purity. From the purification characteristic σe(j), the apparent equilibrium surface tension value of the as received solution is 32.9 mN/m, but the true equilibrium value of the scp solution is as high as 57.2 mN/m. Thus, the surface pressure difference of (57.2 - 32.9) mN/m ) 24.3 mN/m was only caused by the impurity in the adsorbed layer. This experiment also reveals what was already indicated in the experiments of Figure 7, that convective purification is preferable to the original operating procedure under conditions of a calm solution. Convective diffusion is not only much faster but also more efficient than diffusion alone. Whereas about 350 ×

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Figure 8. Comparison of purification characteristics of 1 × 10-1 M tetrabutylammonium bromide solution (Merck, pro synthesis). 0, convective purification: rotation speed, 150 revolutions/min; time on, 3 s; time off, 0 s; duration of stirring interval, 10 min. O, purification without stirring: adsorption time per purification cycle, 2 h.

10 min ) 3500 min, or 21/2 days, was required to achieve the solution’s scp grade, about 4 weeks was required to do so for the conventional procedure without convection. Finally, the capability of the modernized version of the HPPS-2 apparatus is illustrated by the comparison of the adsorption kinetics of this solution in the state as received and/or scp. Whereas the as received 1 × 10-1 M tetrabutylammonium bromide solution needs about 5 h to arrive at its equilibrium state (Figure 9), the equilibrium surface tension of the corresponding scp solution occurs so fast that it was impossible to measure (the first measuring surface tension value can only be registered after about 20 s). Thus, the difference in the adsorption kinetics of the solution in the two grades of purity is at least 3 orders of magnitude. This means that studies of as received surfactant systems yield wrong dynamics, wrong steady states, wrong conclusions, and useless information. 3. Conclusions The already successful automated high-performance purification apparatus HPPS has been significantly

Lunkenheimer et al.

Figure 9. Dynamic surface tension of an aqueous 1 × 10-1 M tetrabutylammonium bromide solution: 9, original solution of the as received product (Merck, pro synthesis); b, surface chemically pure solution.

improved by reducing the time necessary to achieve the solution’s grade of surface chemical purity by a factor of about 10 using convective diffusion. Moreover, the purification procedure itself becomes more efficient. The gain in time is very important because there are surfactants that may hydrolyze or degrade in aqueous solution. Hence, the improvement is especially important in basic research of surfactant adsorption. Since as-received surfactants are usually rather contaminated by very surface active parent compounds which (may) completely falsify the main component’s true adsorption properties, the surfactant grade of surface chemical purity is necessary for obtaining consistent and reliable data. The improved apparatus will soon become commercially available. Acknowledgment. We are grateful to the Gesellschaft fu¨r Innovative Technologien (GiT), Osterholz-Scharmbeck, Germany, for incorporating the latest technical advance in the HPPS-2-apparatus. One of us (A.J.P.) is grateful for a grant of the Deutsche Forschungsgemeinschaft (DFG), Grant No. LU 455. LA036442G