J . Phys. Chem. 1987, 91, 2915-2917
2915
A Capillary-Tube Method for the Measurement of Solute Transport across Liquid-Liquid Interfaces Robert S. Hinz and Richard H. Guy* Departments of Pharmacy & Pharmaceutical Chemistry, University of California, San Francisco, San Francisco, California 94143 (Received: October 10, 1986; In Final Form: January 20, 1987)
Solute transfer kinetics across aqueous-solution/organic-liquidinterfaces have been measured by a method based upon the capillary-tubeprocedure for self-diffusion. A short capillary containing radiolabeled solute dissolved in one phase is immersed in a large stirred volume of the second liquid phase, into which the movement of marker is followed. Demonstration and validation of the approach have been performed with a number of systems of various configurations including the transport of salicylic and acetic acids across water/isopropyl myristate and water/dodecane interfaces. The results are in good general agreement with data obtained by the rotating diffusion cell technique. The temperature dependence of the kinetics determined with the capillary tube procedure shows Arrhenius behavior and should permit, therefore, thermodynamic parameters associated with interfacial transport to be evaluated.
Introduction
Interfacial transport at the boundary between two immiscible liquids represents a complex solution chemistry problem of industrial and biological relevance. Accurate measurement of this process, however, has proven difficult and a recent, excellent review summarizes the field in detail.' Further investigation of a relatively new approach,* which is an application of the capillary tube procedure for self-diff~sion,~ is described here. A capillary containing a radiolabeled solute dissolved in one liquid phase is immersed in a large stirred volume of a second liquid phase (immiscible with the first). Solute transport is determined by measuring radioactivity lost from the capillary as a function of time. By solving the diffusion equation with the appropriate boundary condition for the interface at the mouth of the capillary, the rate constant for solute interfacial transfer may be evaluated. The theory, which has been developed,* represents simplification of earlier attempts4d to evaluate interfacial and membrane transport resistances in different configurations contained within the capillary tube. Experimental exploration of the procedure considering different solute-solvent systems at various temperatures is reported and, where possible, the results are compared to previously published data obtained with a rotating diffusion cell.' In the latter technique, which has been used to study many systems,'-I6 a liquid-liquid interface is established on the surface of a rotating filter disk. Careful control of the hydrodynamics permits the interfacial kinetics to be separated from stagnant layer and membrane permeabilities. Coincidence between results from the capillary tube and rotating cell methods, therefore, should provide good validation of the techniques since the different ap( 1 ) Hanna, G. J.; Noble, R. D. Chem. Reu. 1985,85, 583. (2) Guy, R. H.; Hinz, R. S . ; Amantea, M. Faraday Discuss. Chem. SOC. 1984, 77, 127. (3) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1959; 2nd ed, pp 261-264. (4) Guy, R. H.; Fleming, R. Int. J . Pharm. 1980, 4, 241. (5) Guy, R. H.; Hadgraft, J. J . Colloid Interface Sci. 1981, 80, 386. (6) Fleming, R.; Guy, R. H.; Hadgraft, J. J . Colloid Inferface Sci. 1983, 94, 54. (7) Albery, W. J.; Burke, J. F.; Leffler, E. B.; Hadgraft, J. J . Chem. SOC., Faraday Trans. 1 1976, 72, 1618. (8) Albery, W. J.; Hadgraft, J. J . Pharm. Pharmacol. 1979, 31, 65. (9) Sagert, N. J.: Quinn, M. J.; Dixon, R. S . Can. J. Chem. 1981.59, 1096. (10) Guy, R. H.; Aquino, T. R.; Honda, D. H. J . Phys. Chem. 1982,86, 280 -..
(1 1) Guy, R. H.; Honda, D. H.; Aquino, T. R. J . Colloid Interface Sci. 1982, 87, 107. (12) Guy, R. H.; Aquino, T. R.; Honda, D. H. J. Phys. Chem. 1982,86,
2861.
(13) Ahmed, M.; Hadgraft, J.; Kellaway, I. W. Inr. J . Pharm. 1982, 12,
219.
(14) Fleming, R.; Guy, R. H.; Hadgraft, J. J . Pharm. Sci. 1983, 72, 142. (15) Ahmed, M.; Hadgraft, J.: Kellaway, I . W. Int. 1.Pharm. 1983, 13, 227. (16) Guy, R. H.; Honda, D. H. Inr. J . Pharm. 1984, 19, 129.
0022-365418712091-2915$01.50/0 , I
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TABLE I: Initial Experimental Configurations of the Systems Studied
system A
B C D
soluteR salicyclic acidb salicyclic acidb salicyclic acidb acetic acidC
capillary phase IPMd IPMd I O mM HCl(aq) 10 mM HCl(aq)
receptor stirring phase speed(s), rpm water 0, 400, 800 water 800 dodecane 800 IPMd 800
'Solutes were I4C labeled. bSpecificactivity of salicyclic acid was 27 mCi/mmol. CSpecificactivity of acetic acid was 56 mCi/mmol. dIPM = isopropyl myristate. TABLE 11: Effect of Stirring Speed on Transport Kiaetics (System A) stirring speed, rpm N" t,b s 1o2M,(ivf,Il):cm-I 0 6 200 1.248 f 0.1 98d 400 6 200 2.122 f 0.249 800 8 200 2.190 f 0.116'
"Number of capillaries. Experiment duration. 'Mean f standard deviation. dValue is significantly less (p < 0.01) than that at 400 rpm. CValueis not significantly different from that at 400 rpm. TABLE 111: CaDillarv Tube Results for Svstem B' I O ~ M , / ( M - / ~ ) ,I~O ~ D ~ : i o 2 ~ - , d 104k,,' temp, 'C cm-I cm2/s cm-' cm/s 3.07 1.01 20 1.27 f 0.04 0.37 25 1.40 f 0.04 0.43 3.27 1.14 30 1.66 f 0.20 0.49 3.53 1.44
35 40
1.94 f 0.27 2.46 f 0.22
0.56 0.63
3.74 4.01
1.83 2.82
"Experiment duration = 200 s. bMean f standard deviation. CValuesfrom ref 2. dCalculated from eq 6. eCalculated from M,/ ( M - / l ) by using eq 5 . proaches are unlikely to be subject to similar artifacts. Experimental Section
A glass capillary (length 1.1-1.2 cm, i.d. = 0.84 mm) was filled, using a Hamilton syringe, with a solution of radiolabeled solute in liquid phase A (e.g., the organic liquid isopropyl myristate (IPM)). The capillary was inserted into a simple wire support and was lowered to 90% of its length into a receptor phase (kept at fixed temperature) of liquid phase B (e.g., aqueous buffer) contained within a small (4 cm3 total volume) scintillation vial. The receptor phase volume was 2 cm3 (ca. 300 times that in the capillary) and was magnetically stirred. Upon full immersion of the capillary into the receptor phase (at t = 0), solute transport commenced. Experimental duration depended upon the solute/solvents system studied but was generally between 1 and 10 min, at the end of which the capillary 0 1987 American Chemical Society
2916
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 Capillary
Receptor (Aq.)
(Or . )
solute Concentrotion
O(I.0)
Diffuslon C o e t f i c i e n t
TABLE I V Capillary Tube Results for System C" I O ~ M , / ( M , / ~ ) , 1~ 0 ~ 4 , ' i o 2 ~ - , d 104k,,,'
temp, O C 20
I I
00
0
Distance
Hinz and Guy
25 30
-11
x
I Inlarfoclai
40
-% I
Cross- eec t l o n a I Areo
A
cm2/s 0.84 0.96 1.09 1.38
cm-' 4.60 4.94 5.39 5.93
cm/s 1.07 0.98 1.42 2.48
"Experiment duration = 200 s. bMean f standard deviation. 'Values from ref 10. dCalculated from eq 6. eCalculated from Mt/ ( M - / / ) by using eq 5.
I
Tran8port
cm-' 1.51 f 0.10 1.45 f 0.13 1.94 k 0.24 2.84 f 0.61
I
TABLE V: Capillary Tube Results for System Do temp, OC
20
was quickly removed from the receptor phase. The latter was mixed with 10 mL of scintillation fluid (Beckman Ready-Soh CP) and the amount of initially entrapped radioactivity, which had transported out of the capillary, was measured with a Searle Analytic Inc., Mark I11 liquid scintillation system (Model 6880). Initial experimental configurations studied are summarized in Table I.
Theory The physicochemical and geometric parameters of the capillary system are defined in Figure 1. For the purpose of illustration, the capillary is assumed to contain an organic phase; the receptor is aqueous. To describe solute loss from the capillary with time requires solution of Fick's second law of diffusion: &,/at = Do(d2co/dx2)
(1)
for 0 < x
< I , at
t
= 0, co = c,
30
35 40
i o S ~ , , b i o 2 ~ - , e 104k,,,d cm2/s cm-' cm/s 8.18 0.12 1.05 8.74 0.17 1.20 1.36 9.30 0.27 1.54 9.90 0.40 10.5 0.45 1.73
"Experiment duration = 500 s. bValues from ref 7. 'Calculated from eq 6. dCalculated from M t / ( M a / l )by using eq 5.
.
E
V
ZI
-10-
2 -J
- II-
with appropriate boundary conditions: (a)
25
io2~J(+/l), cm0.56 0.76 1.21 1.69 1.91
(2)
The initial solute concentration in the capillary is c, (b) at x = 0, (dc/dx), = 0 (3) There is a finite supply of solute in the capillary and no replenishment at x = 0. (c) at x = I , Do(dc/dx), = -k,,~,=~ (4) Flux of solute at the open end of the capillary depends upon the heterogeneous interfacial transfer rate constant (koa). The result at short times ( t
