3776
J . Phys. Chem. 1990,94, 3776-3780
Transport of Fatty Acids Facilitated by n -Hexadecyltrimethylammonium Bromide Micelles through a Liquid Membrane Manabu Seno, Yuya Shiraishi, Shigeru Takeuchi, and Joe Otsuki* Institute of Industrial Science, University of Tokyo, 7 - 2 2 - 1 , Roppongi, Minato-ku, Tokyo 106, Japan (Received: October 6, 1989)
Transport of various fatty acids (FA) by micelles of n-hexadecyltrimethylammonium bromide (HTAB) in a liquid membrane system was examined experimentally, and the mechanism of the transport is proposed. The system consists of three phases: a heptane solution of FA as a source phase, an aqueous HTAB solution as a membrane phase, and heptane as a receiving phase. The effect of HTAB concentration on the transport rate of each FA was investigated. The shorter the hydrocarbon chain of FA is, the larger the transport rate is. HTAB transports FA at larger concentrations than its critical micelle concentration, which is clear evidence that micelles of HTAB dissolve and carry FA through the aqueous membrane. The transport rates increase with increasing HTAB concentration but then pass through maxima and decline again with more concentrated HTAB solutions. On the other hand, FA concentration in the aqueous phase at the steady state increases nearly proportional to the HTAB concentration. These behaviors were analyzed kinetically. It is shown that the rate constant of uptake increases to reach a maximum value and that of release decreases with an increase in the HTAB concentration. These changes in rate constants are naturally derived by assuming a mechanism in which FA dissolves at first in water and then is uptaken by HTAB micelles at the source/membrane interface; FA goes out of the micelles to water and then to the receiving oil phase at the membrane/receiving-phase interface. This model is also consistent with the other transport characteristics, such as that the transport rate of shorter FA reaches the maxirnum value at higher HTAB concentration and the maximum rate is larger.
Introduction Applications of liquid membrane system for separation of materials were initiated by N. N. Li in 1968.' Since E. L. Cussler introduced a concept of the carrier transport into the liquid membrane system,* which frequently takes place in biological membrane systems, many carriers have been reported in literatures aimed at good selectivity and/or active t r a n ~ p o r t . ~Most of these works focused on molecular design of the carrier compounds which form 1:l or 1.2 complexes with their substrates. Amphiphilic molecules form a molecular assembly called a micelle, where nonpolar ends of the molecule huddle together in the center and the polar ends project outward into the polar solvent, water. Although it is well-known that micelles solubilize hydrophobic substances in an aqueous solution, to the best of our knowledge there are no reports of utilizing micelles as carriers except our report of the transport of azobenzene by micelles of HTAB in a liquid membrane system4 Micelles are usually utilized not as carriers but as emulsifiers in liquid membrane proces~es.~Reversely, in a report by E. L. Cussler et al., transport stagnation by assembled molecules of hexadecyltributylammonium bromide was suggested for chloride transport since the flux passes through a maximum as the carrier concentration becomes higher and higher,6 opposed to the usual carrier transport behavior. A micelle dissolved in water has a hydrophobic interior. At that point, it is similar to serum albumin, which is a spherical (1) Li, N. N . U S . Patent 3,410,794, Nov 12, 1968. (2) Cussler, E. L. AIChE J . 1971, 17, 1300. (3) For reviews see: (a) McBride Jr., D. W.; Izatt, R. M.; Lamb, J. D.;
Christensen, J. J. In Inclusion Compounds: Physical Properties and Applicationr; Atwwd, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic: New York, NY, 1984; Vol. 3, pp 571-628. (b) Schwind, R. A,; Gilligan, T. J.; Cussler, E. L. In Synthetic Multidentate Macrocyclic Compounds; Izatt, R. M., Christensen, J. J., Eds.; Academic: New York, NY, 1978: pp 289-308. (c) Frankenfeld, J. W.; Asher, W. J.; Li, N. N. In Recenf Deoelopments in SeparationScience; Li, N. N., Ed.; CRC: West Palm Beach, FL, 1978; Vol. 4, pp 39-50. (d) Kimura. S. S.; Matson, S . L.; Ward, W. J. Ibid. 1979; Vol. 5 , pp 11-25. (e) Way, J. D.; Noble, R. D.; Flynn. T. M.; Sloan, E. D. J . Membr. Sei. 1982, 12, 239-259. (4) Seno, M.: Kise. H.; Kobayashi, 1. Seisankenkyu 1983, 35, 281-284. (5) Gu, Z. M.; Wasan, D. T.; Li, N . N. In Surfactants In Chemical/ Process Engineering; Wasan, D. T., Ginn, M. E., Shah, D. O., Eds.; Marcel Dekker: New York, NY, 1988; pp 127-168. (6) Molnar, W. J.; Wang, C. P.; Evans, D. F.; Cussler, E. L. J . Membr. Sci. 1978, 4, 129.
0022-3654/90/2094-3776$02.50/0
hydrophilic molecule having hydrophobic sites on the ~ u r f a c e . ~ The hydrophobic sites of serum albumin bind, solubilize, and transport many metabolites such as lipids, chromophores, and drugs which are insoluble in blood by themselves. We reported the behavior of bovine serum albumin (BSA) facilitated fatty acid transport in a liquid membrane system.* More hydrophilic or shorter fatty acids are transported faster through the aqueous membrane by BSA. We explained the transport behavior by assuming that BSA binds FA which was dissolved in water at the vicinity of the surface of the membrane. In this paper, we report further studies of micelle-facilitated transport of FA, propose the mechanism of the transport, and compare the transport behavior with that by BSA. Experimental Section Materials. Extrapure grade HTAB was purchased from Tokyo Kasei Kogyo Co. and recrystallized from ethanol-ether if necessary. Special grade n-heptane was purchased from Wako Pure Chemical Co. Special grade capric, lauric, myristic, palmitic, and stearic acids were purchased from Tokyo Kasei Kogyo Co. and Wako Pure Chemical Co. All reagents were used without further purification except HTAB. Doubly distilled water was used. Determination of Critical Micelle Concentration. The critical micelle concentration, cmc, of HTAB under the experimental conditions (37 "C) was determined to be 0.3 mmol/L by plotting solubilized 7,7,8,8-tetracyanoquinodimethaneconcentration against HTAB con~entration.~ Procedures of Transport Experiments. Transport experiments were performed with a U-shaped glass tube with an air channel for homogenizing the pressure in the tube. (Figure 1). The HTAB solution was stirred at 400 rpm by means of a magnetic stirrer. The source phase was connected to a bottle and circulated at 3 mL/min by a pump. The tube and the bottle were placed in a water bath controlled at 37 "C. The changes in the concentration of FA in each phase were followed by sampling 5 p L of solution (7) Spector, A. A.; John, K.; Fletcher, J . E. J. Lipid Res. 1975, 16, 165-179. (8) Otsuki, J.; Iwamoto, K.; Seno, M. J . Phys. Chem. 1988,92,7251-7255. (9) (a) Deguchi, K.; Meguro, K. J . Colloid Interface Sci. 1972, 38, 596-600. (b) Muto, S.; Deguchi, K.; Kobayashi, K.; Kaneko, E.; Meguro, K. Ibid. 1970, 33, 475-477. (c) Muto, S.: Meguro, K . Bull. Chem. Sor. Jpn. 1973, 46, 2812-2873.
0 1990 American Chemical Society
-
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3111
Transport by Micelles through a Liquid Membrane
'
/
Lauric
K
f
Figure 1. Schematic representation of a experimental apparatus: a, 5
mL of aqueous membrane phase containing HTAB; b, 350 or 450 mL of source phase containing 3 mmol/L FA; c, 1 mL of receiving phase; d, water bath controlled at 37 OC; e, pump that circulates the sourcephase solution at the rate 3 mL/min; f, magnetic stirrer. 1.0
2
I
1
I Capric acid
HTAB concentration (mmol/L) Figure 3. Transport rate dependences of various FA on HTAB concen-
tration in the membrane phase.
-
3
0.6
P !
Mvristic O 10.' 0
5 Time (hr)
10
Figure 2. Time course of FA concentrations in the receiving phase in the transport experiments. HTAB concentration in the membrane is 10
mmol/L. from each phase and analyzing with an HPLC conductometer. The column was octadecylsilane and the eluent was acetonitrile/water = 70/30 (v/v). The procedures of the transport experiments were the same as those in our previous report* except for the following: (1) Pure water was used as a medium of aqueous membrane phase instead of phosphate buffer since HTAB is insoluble in the buffer. (2) The volume of the source phase was 350 or 450 mL. (3) HTAB was used as a carrier instead of BSA. Determination of Partition Ratios of Lauric Acid between n-Heptane and Aqueous HTAB Solutions. The partition ratios were determined by liquid-liquid extraction where lauric acid in heptane was extracted with aqueous solution of given concentrations of HTAB by stirring with a magnetic stirrer in a water bath controlled at 37 OC. The initial concentration of lauric acid was chosen so that it would be around 3 mmol/L in heptane at the equilibrium. After the equilibrium was attained, the heptane solutions were analyzed as described for the transport experiments. The partition ratio Khmwas calculated when the lauric acid concentration was around 3 mmol/L and plotted against the lauric acid concentration. The partition ratio at the lauric acid concentration of exactly 3 mmol/L was determined by use of this graph.
Results and Discussion Transport of Various FA. Figure 2 shows examples of changes in FA concentrations in the receiving phase in the transport experiments. The concentration of HTAB in the membrane is 10 mmol/L, which is well above the cmc of HTAB (0.3 mmol/L). The FA concentration in the source phase scarcely changes during the transport since its volume is large. The shorter the hydrocarbon chain of FA is, the greater the rate of transport is. Capric acid with the shortest length of carbon chain is transported at the rate of 7.1 X IO-" mol/(cm*.s). On the other hand, stearic acid with the longest carbon chain length is no longer transported. The
I00
101 0.0
HTAB conc. (mmol/L)
Figure 4. Dependences of rate and concentration in aqueous phase on HTAB concentration in the membrane at the initial stages of the steady state in the case of lauric acid transport.
rates of transport by the HTAB micelles are comparable with those by 0.5 mM of BSA (ca. lo-" mol/(cm*.s)).* The selectivity is the same as that of BSA, which transports more hydrophilic FA faster though it binds more hydrophobic FA strongly in water. The transport rate dependences on HTAB concentration of all studied FA are shown in Figure 3. Several characteristics can be seen from the graph. In this concentration range the shorter FA is transported faster. The rates for all FA rise with an increasing HTAB concentration in a dilute solution but then pass through a maximum and decline again with a more concentrated solution. The sequence of the maximum value is concordant with that of hydrophilicity. The more hydrophilic the FA is, the larger the concentration of HTAB at the maximum rate is. These characteristics of the transport are explained in a later section. The rate of capric acid transport increases steeply when HTAB concentration exceeds 100 mmol/L. Some sorts of shape transition as from spherical to rodlike micelles might occur at this high HTAB concentration. There are no data available now, however, about the shape of HTAB micelles in such an high concentration range, although rodlike micelles have not been observed without added salts in less concentrated HTAB solution.I0 Another question is that the steep increase of the rate is specific for capric acid. We cannot elaborate this behavior with the present data. The decline of the rate at higher HTAB concentrations is attributed to the increase of the viscosity of the solution. In order to analyze the transport behavior precisely, the dependence of transport rate of lauric acid on the HTAB concentration was investigated in detail in the range from 0.1 to 10 mmol/L HTAB. The results are shown in Figure 4 along with the concentration of lauric acid in the membrane phase at the steady state in the initial stages of the transport. The transport (10) Imae, T.; Kamiya, R.; Ikeda, S.J . Colloid Interface Sci. 1985, 108, 21 5-225.
3778 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
Seno et al.
I
10'~
Source phase
10
.'
100
Membrane (a)
Receiving phase
10'
HTAB conc. (mmol/L)
Figure 5. Relationship between rate constants of uptake k l and release k2 and HTAB concentration in the membrane phase. Plots represent experimental results (eq 4), and interpolated plots represent results of calculations with the model shown in Figure 6b (eqs 22 and 23).
rate increases when the HTAB concentration exceeds 0.3 mmol/L, which is the cmc of HTAB under the experimental conditions. This fact clearly shows that lauric acid is solubilized and transported by the micelles of HTAB. Thus the micelle of HTAB works as a carrier in the aqueous liquid membrane. The concentration of lauric acid in the membrane phase begins to increase when HTAB concentration exceeds its cmc owing to the solubilization by the micelle. While the amount of solubilized lauric acid continues to increase with increasing HTAB concentration, the transport rate reaches a maximum value at high HTAB concentration. These results suggest that the uptake rate increases to reach saturation and the release rate decreases with an increasing concentration of HTAB. The quantitative analysis of the rates is attempted in the following section. Rates of Uptake and Release. The transport begins with the first step in which FA in the source phase S is solubilized by HTAB micelles to form complexes in the membrane phase M . FA is released to the receiving phase R in the second step. The reverse processes take place simultaneously. The simplest mechanism of this type of process would be k
k
k-1
k-2
S+M&R
The rate of change of M reaches the steady state:
d [ M ] / d t = kI[S] - (k2 + k - l ) [ M ] + k-,[R] = 0
(1)
The steady-state concentration [MI is, therefore
From eq 2, the rate of the micelle facilitated transport (per unit area) would become
It is natural to put k , = k-2 and k-, = k2,for the system is symmetrical, and the term k2k-,[R] will become negligible in the early stages of transport when [ R ] is very low. With this approximation, the flux of FA is simplified as J =
( k 1 / 2 ) [ S l= k2[MI
(4)
Since [SI is always 3 mmol/L in the present experiments and J and [ M I can be measured directly, the values of kl and k2 can be obtained and the results are shown in Figure 5 . When the concentration of HTAB is less than 10 mmol/L, the release rate constant k2 from the membrane to the receiving phase is larger than the uptake rate constant k , from the source to the membrane phase. Therefore, the rate-determining step of the transport under the conditions is the uptake process into the membrane phase. As the HTAB concentration increases, k , increases to reach a
Source phase
Membrane
Receiving phase
(b)
Figure 6. Schematic representationsof the liquid membrane system. The double lines indicate the water/heptane interfaces. The vertical axis shows the concentration of FA at each position. (a) A model in which FA is uptaken directly by micelles at the source-phase/membrane interface and released directly from micelles to the organic phase at the membrane/receiving-phase interface. (b) A model in which FA migrates into water and then is uptaken by HTAB micelles in the diffusion layer at the source-phase/membrane interface and is released from micelles into water to transfer into the organic phase at the membrane/receiving-phase interface.
maximum value while k2 continues to decrease. These characteristics are explained on the basis of a transport model proposed in the next section. Mechanism ofthe Transport. The simplest model of a diffusion-limited membrane transport process shown in Figure 6a is considered first. In this model, FA is uptaken directly by micelles at the source-phase/membrane interface and released directly from the micelles at the membrane/receiving-phase interface. The horizontal axis represents the source, the membrane, and the receiving phases from left to right. The membrane phase consists of diffusion layers at the interfaces and the membrane bulk. The positions are indicated by subscripts attached to variables. The vertical axis represents the concentration of FA. It is assumed that the rate of FA partition at the water/oil interfaces is fast compared to the rate of the diffusion. The partitions at the interfaces take place according to the partition rate Khm = F4/FI = F5/Fa, if the partition ratio is constant regardless of concentration of FA. At the steady state under these conditions, the flux is given by
where D, is the diffusion coefficient of micelle and I is the total length of the diffusion layers at both sides. Therefore, k , and k2 become
(7) where we used eq 4 and 5 and the relations [SI = F , and [MI
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3779
Transport by Micelles through a Liquid Membrane
2
k2 = 2 J / ( F 4 + FJ = 12
1,
(16)
- + 2-K,,
Dm Df where we used eq 4 and 14. The FA concentration in the bulk membrane is given, by using eqs 11-13, as
Fm = (F4 + FS)/2 = KhwKwmFI/2 1
,
1
,
1
I
40
0
I
,
I
80
.
120
Conc. of HTAB (mmol/L) Figure 7. Plots of aqueous HTAB concentration versus partition ratio Kh, of lauric acid between heptane and HTAB micelle solution.
+
= (F4 Fs)/2. Since F, >> F8 at the initial stages of the transport, k , and k2 are simplified to
kl = 2(Dm/[)Khm
(8)
k2 = 2D,/1
(9)
Meanwhile, FA concentration in the bulk membrane at the steady state in the initial stages is given by
F, = (F4
+ F s ) / ~= KhmF1/2
(10)
Since the value of Kh, is proportional to the HTAB concentration as shown in Figure 7, eq 8 indicates that k , increases and shows no saturation with an increase in the HTAB concentration. This prediction is not in agreement with the experimental results where k , saturates at high HTAB concentrations. Equation 9 is also contradictory to the experimental results in which k2 does not remain constant but decreases with an increase in the HTAB concentration. The discussion just described indicates that the simple model where FA is taken up and released by micelles directly at the interfaces does not explain the transport behavior of the present liquid membrane system. The fact that a more hydrophilic FA is transported faster suggests that FA at first migrates in water and then is taken up by micelles. This mechanism is illustrated in Figure 6b. The principle of the model is the same as that applied to the facilitated transports with macrocyclic carriers,, and bovine serum albumin8 The partition ratios of FA between heptane and water Khw and water and micelle Kw, are defined as
(17)
Equations 15-17 have already been simplified by the relation FI >> F8. In these equations, Khw is a constant and then K,, is proportional to HTAB concentration over its cmc. When the HTAB concentration is low, eq 15 and 16 reduce to
k~ = 2(Dm/l2)KhwKwm
(18)
k2 = 2D,/1,
(19)
which show that k, is proportional to K,, or the HTAB concentration and k 2 is a constant; the transport rate is determined by diffusion of micelles. When the HTAB concentration is high, eq 15 and 16 reduce to = (Df/ll)Khw
(20)
= (Df/lI)(l/Kwm)
(21)
kl k2
which show that k , is a constant and k2 decreases with an increase in K,, or the HTAB concentration; the transport rate is determined by diffusion of FA. These equations well illustrate the observations on the dependence of rates on the concentration of HTAB, in which k , increases at low HTAB concentration and reaches a maximum value at high HTAB concentration and k2 is a constant at low HTAB concentration and decreases with an increase in the HTAB concentration. One of the ways to confirm the validity of the model is to calculate numerically k , and k2 from F, by using eq 15 and 16 and compare the results with those obtained with eq 4. Substitutions of eq 17 into eq 15 and 16 give the relationship between k , and k2, and F,.
. l
Khw = F2/F1 = F 1 / F 8
(11)
= F4/F3 =
(12)
Kwm
FS/F6
Since the fluxes are equal at all phases at the steady state, the flux J is represented as J =
( D f / l l ) ( F 2- F3) = (Dm/12)(F4 - FS) = (Df/11)(F6- F 7 ) (13)
where D f is the diffusion coefficient of FA in water and 1, and 12/2 is the lengths of the diffusion layers in water phase and micelle phase, respectively. In other words, I , 12/2 is the length of the aqueous diffusion layer and 1, is the mean distance through which FA diffuses in the diffusion layer before reaching equilibrium with HTAB micelles. Then, the flux J is represented with F1 and F8 by using eqs 11-13, as
+
J =
KhwKwm 12
11
Dm
Df
- + 2-Kw,
(FI - Fa)
(14)
Then the rate constants k , and k2 are represented in this model as ( I 1) Lamb, J. D.; Christensen, J. J.; Oscarson, J . L.; Nielsen, B. L.; Asey, B. W.; Izatt, R . M . J . Am. Chem. SOC.1980, 102, 6820-6824.
To give the best fits to the experimental results, 12/Dmand I,/ (DfKhw)are adjusted to be 3 X lo3 and 6 X lo4 s/cm, respectively. These results of the calculations are shown in Figure 5 . The dependences of calculated k , and k2 on HTAB concentration are in excellent agreement with the values calculated by using eq 4 . The diffusion coefficient of the micelle is ca. lod cm2/s in this HTAB concentration range.I2 Then 1, becomes a value of around cm, which is a value comparable with the total length of the diffusion layer (1 5 pm) obtained previously under the same experimental conditions.8 The diffusion coefficient D f of the lauric acid in water can be estimated by using Wilke’s equation to be cm as in the case of 5.0 X IOd cm2/s.8,13 If I , is around the transport by BSA,’ Khw becomes the value of around lo-’, which is a value comparable with the reported partition ratio of lauric acid between n-heptane and 0.016 M phosphate buffer (pH 7.4) at 37 O C . I 4 Thus these values used in the calculations are (12) Dorshow, R.; Briggs, J.; Bunton, C. A.; Nicoli, D. F. J . Phys. Chem. 1982,86, 2388-2395. (13) Wilke, C. R.; Chang, P. AIChE. J . 1955, I , 264. (14) Simpson, R. B.; Ashbrwk, J. D.; Santos, E. C.; Spector. A. A. J . Lipid Res. 1974, IS, 415-422.
3780
J . Phys. Chem. 1990,94, 3780-3784
shown to be reasonable. Although exact estimations of these values are not possible from the present experiments, the above agreement of the calculations using these reasonable values in spite of many simplifications of equations suggests that the proposed mechanism is correct. Since the transport rate is proportional to kl from eq 4 for constant [SI, the rate can be calculated just by multiplying k , with [S]/2, and the results are quite similar to k , in Figure 5.
This model correctly predicts some other characteristics of the transport qualitatively. In all the concentration ranges the shorter FA are transported faster. Since a shorter FA has a larger value of Khm= Kh,K,, and smaller value of K,,, the rate of shorter FA is always larger from eq 14. The rates for all FA rise with increasing HTAB concentration in dilute solution but then pass through maxima and decline again with more concentrated solutions. The saturation behavior has already been explained above. The decline of the transport rate is probably owing to the viscosity increase of the membrane at high HTAB concentrations. Actually, a solution of HTAB concentration higher than 200 mmol/L is quite viscous. An increase in the viscosity leads to decrease in the diffusion coefficients of FA and micelles, and thus the transport rates. The more hydrophilic FA is, the larger is the concentration of HTAB at which the rate reaches its maximum. The value of K,, of shorter FA is smaller when the HTAB concentration is the same. Therefore, in the case of shorter FA larger HTAB concentration is required to fulfill the relation 12/Dm
