Transport of Caffeine Through Milliporem Filter Manit Rujlmethabhas' and John Crossley Lakehead University, Thunder Bay, Ontario P7B 5E1, Canada The transport of a chemical substance through a membrane under the influence of a concentration gradient is of fundamental interest and has numerous a .~.~ l i c a t i o n sSuch . a transport prucess is commonly known as diffusion or permeation. Both natural (1-3)and synthetic memhranes ( 4 4 1have been used in previous diffusion studies, and the diffusion of simple ions across synthetic memhranes has been discussed (7). The present paper provides recently in THIS JOURNAL details of a simple experimental approach to this important topic. The experiment described here has two major advantages: (1)the apparatus is inexpensive and simple to construct and (2) the whole experiment may be performed within a single 3-hr laboratory period. There are diverse opinions concerning the definitions of diffusion and permeation (2,8);we have adopted those used by many investigators (9,IO). Fick's first law forms the hasis of diffusion studies and i t can he expressed as:
where n is the amount of diffusant, dnldt is the rate of transfer of diffusant through a membrane whose area is A in he direction perpendicula; to the membrane cross section, D is thadiffusion coefficient, C is the concentration ofdiffusant, x is the position coordinate in the direction normal to the membrane, and dcldx is the concentration gradient at the membrane. The negative sign in (1) indicates that the flow of the diffusant is in the opposite direction to the direction of
' Author to whom correspondence should be addressed.
Canadian Tire Corpwation. Ltd., Twonto, Ontario. Canada M4P 2V8. The authors have no affiliation with this corporation.
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Journal of Chemical Education
positive concentration gradient. For a finite change, eqn. (1) can be written as:
when A(' is the mncentration difference across the membrane whose thickness is I. If the membrane thickness is constant, it may be incorporated in the diffusion cuet'ficient to give a permrat~ilityconstant, 1'. Thus, eqn. ( 2 ) becomes:
Here, n is the amount of substance leaving the diffusion cell, C , is the concentration of the suhstance inside the diffusion cell and Ct is the concentration of the suhstance outside the diffusion cell. If it is now realized that the amount of suhstance n outside the diffusion cell divided by the volume of water V, is actually the concentration Ct (amount of substance per unit volume), then nlV = C,. Thus, n = CtV. Using this relation for n in equ. (3), we have:
Next, we assume that the volume V outside the diffusion cell is constant, eqn. (4) can he integrated using the conditions that Ct = 0 a t t = 0 and Ct = Ct a t any time, t. We get:
In-=-
Co Co- Ct
Co Co - Ct
log-=-
PAt
v PAt
2.303V
Figure 2. Experimental setup: P. water bath; 0. 1-1 baker; R, diffusion cell: S. mechanical stirrer; T, magnetic bar: U. magnetic stirrer. Figure I. Various pans of diffusion cell: A, polymeric pipe with screw thread: B. O-ring (4.2 cm 0.d.); C, f i i t washer: D, membrane; E, secMxl washw F. 8aew cap With circular opening whose diameter is 3.8 cm. If t h e concentration is followed spectrophotometrically, eqn. ( 6 )m a y be expressed i n the form:
fAo log-=fAo - At
PAt 2.303V
where A 0 is the absorbance of t h e solution which has been diluted f t i m e s from t h e concentration C o , At is t h e absorbance of t h e solution at time t. Equation (7) will be used in the present study.
Diffusion Cell Preparation A pirceof polymericpipe 178cm in lenprh and 4.Rcm o.d., fitted with a rubber washrr and n screw cap, may be rhraply purchased from the plumoing division g l f a storeAat the cost oi8I.50. The cap has a circular opening which may be used to seat a piece of membrane (Fig. 1).A second washer, made from a smwth piece of rubber sheet having about the same diameter as the one purchased, and a ruhher O-ring (4.2 cm ad.) which fits the edge of the cylinder are also required. A Milliporem filter (pore size 22 p ) is cut such that the diameter of the disc is slightly less than the a d . of the washers. T o check for a good seal, a piece of thin polymeric film (fwd wrapping, e.g., Saran Wrap*) which is impermeable to water, is cut so that its diameter is about the same as the prepared Milliporee filter and inserted between the two washers in place of the membrane as shown in Figure 1.The O-ring is positioned on top of the washer and the cap on the pipe is screwed tight. Dilute KMnOl solution is poured into the diffusion cell and left in a beaker partially flled with distilled water. If, after a period of 2-3 hr, the KMnOa leaks into the beaker, the seal is not good and improvement is necessary until there is no further leak. We tested our seal over aperiod of several days withno visible sign of leakage. Exactly 100 ml of distilled water is poured into the clean diffusion cell and the level of the water is located and clearly marked on the outer wall of the diffusion cell, since the wall of the diffusion cell is opaque. The diffusion eell is reassembled using the prepared Millipore@filter and is ready to be used in experiments.
Experimental Procedure (1) I'our 850 rnl of distilled water into a 1.1 beaker. Hare the diffusibn cell into the beaker. Make sure that the membrane entering the water is at an angle, otherwise air bubbles may become trapped undrr the rnemhrane. 12) Transfer 100 ml cjfdirtilled water intorhe diffusion eell slowly. At the samc rime.nllow the cell tosink madually into the water in the beaker so that the water levels inside an> outside the cell are approximately the same. This procedure ensures that the net volume of water passing through the membrane is kept to the minimum. (3) Place the beaker into a thermostatted bath a t 25'C. Clamp the diffusion cell and adjust it such that the water level outside the cell is right on the calibrated mark on the outer wall of the cell. The mark is used only as an indicator for the water Level inside the cell; without it, it is difficult to equalize accurately the water levels between the opaque wall of the cell. (4) Stir the water in the diffusion cell with a small mechanical stirrer and stir the water in the heaker
Figre 3. Plot of t d X lag f&/fA. - A, vmur tlmin).meresultswerecbtained with a stock solution of caffeine (Baker) 1.9993 g dissolved to make 100 ml of solution.Abswtmces w e abtained h m lk spectra racaded on a Fye L h l i l SP800A.
with a magnetic stirrer arranged as shown in Figure 2. The setup is now left to reach thermal equilibrium. (5) Prepare 100 ml of stock solution of caffeine in a volumetric flask by dissolving 2 g of caffeine in distilled water. A small amount of heat may be necessary to speed up the solution process. (6) When the water in the beaker and in the diffusion cell reachea thermal equilihrium with the bath, pipet 5 ml of water out of the diffusion eell. Check to be sure that both stirrers are working. Then pipet 5 ml of the stock solution prepared in Step5 into thediffusion cell. Start a stopwatch when half of the solution has been transferred into the cell. (7) Remove an aliquot from the beaker with a 2-ml pipet every 1,5, and 10 min and then a t 10-min intervals thereafter until a total of 90 min has elapsed. Each sample is transferred to a small test tube. When a sample is removed from the beeker, it creates a very small drop in the level of the solution in the beaker; this may be compensated by dropping in small glass heads. However, since the erws-sectional area of the beaker is large, there is only asmall change in the level of the solution. (8)Remove the diffusion cell and measure the volume of the solution in the beaker. (9)Prepare a solution having the same concentration as the solution in the diffusion cell a t the heginning of the experimental run by diluting 5 mlof thestoeksolu250 times. (11) tion into 100 ml. (10) Dilute the solution i n s t e n 9 hv ~, Record the spectra oiall the rampies in Steps :and 10 with a UVvis~blespectn>photornetrrrmployng only the UV range and meaaure the absorbance a t X = 274 nm.
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Results
A p l o t of log ( f A o l f A o - At) against t ( m i d for o n e experim e n t a l r u n is shown in Figure 3. A straight line is obtained Volume 59
Number 10
October 1982
877
whose slope is PAl2.303V (min-I). For this run, P was calculated from the slope using an effective membrane area A = 9.35 cm2 and the volume V = 838 ml (averaged from the initial volume of 850 ml and the final volume of 826 ml). The value of P was 2.5 X 10-6m s-1. Two further runs were made and the average P from the three runs was (2.6 i0.1) X 10-6m
10-10m2s-1 may be arranged with other values of D in order of decreasing magnitude as follows:
D (water) > D (MF)> D (DPS) D (water) > D (MF) is expected, since caffeine molecules have
- .
to penetrate through the membrane. The relation D (MF) > D (DPS) suggests that the pore size of MF is larger than that of DPS, assuming that pore size is the only determining factor to account for the difference in the values of D. The pore size of MF (mixed cellulose esters) is known, but the pore size of DPS has not been reported. One of the sources of error in this experiment arises from the use of eqn. (7) which is derived from eqn. (4) on the assumption that V is constant in the integration of (4). I t is evident in this experiment that V is not strictly constant. However, the change in V is rather small compared to the large volume of the solution in the beaker. Another source of error lies in the effective membrane thickness. The overall error in P is estimated to be about f 5 % and the error in D is approximately f7%. This experiment was performed by a student and the value of I ) for caffeine through Millipore" filter ar 2S0(1was found to be 3.4 X 10-'"m+i which is in reasonable agreement with our value. In conclusion, we have described the construction and operation of a simple diffusion cell, which may he employed to obtain reasonahle values of transport coefficients during a normal 3-hr laboratory session.
E-1
The magnitude of the diffusion coefficient, D, was estimated from the relation (10) D = P1 where 1is the membrane thickness which was measured from a dry membrane with a micrometer. The value of 1 (0.014 cm) should be considered as an a~oroximation.since it is the thickness of the wet memhrade that should he used in the calculation. Thus the value of D is (3.6 f 0.2) X 10-10m2s-L. Discussion I t is instructive to note that this is the kinetic approach to the diffusion problem. Equation (5) may he reduced to a more familiar form by realizing that the concentration difference, (CO- Ct) indirectly represents the concentration of the substance, C', remaining in the diffusion cell a t any given time t. And the constant term (PAIV) has the dimension of a reciprocal time which is the same dimension as the first-order rate constant k'. Writing eqn. (5)in terms of C' and k' we get
co = k't or C' = Coe-'t In C' which is the integrated form of the first-order rate eauation. Thus, a process in which a chemiral substance leaving the diffusion cell through the membrane due to the presence of a concrntrarion gradient (a diffusion process) which oheys first-order rate eqn. (S),may alsc~111. viewed as an apparent .. process. Figure 3 shows that a linear plot is obtained; however, the straight line does not pass through the origin. This is not unusual, since it takes a short initial period of time before the solute flnw rearhesa steady stare, and this is exploited when I) is determined using the rime-lag method (4.11). 'l'here is no liwrature \.slue for rhe diffusion coefficient - ~ ~ -of .- caffeine through a Millipore@filter. It is interesting, however, to compare the present results with those obtained from the study of caffeine through other materials. The permeability constant of caffeine through dimethylpolysiloxane (DPS, thickness 5mm) was found to he (12)6.0 X 10-9m s-I a t 30°C. This value of P would zive a calculated D of 3.0 X 10-"m2s-'. The diffusion coefficieLt of caffeine in water (13) was reported to he (6.79 f 0.01) X 10-10m2s-1 a t 25% The magnitude of D for caffeine in agar gels was about the same as D of caffeine in water, and the agar gels were found to retard the diffusion process hy only a smalfamount (13). Thus, our value of D for caffeine through Millipore" filter (MF) of (3.6 f 0.2) X ~
878
Journal of Chemical Education
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Acknowledgment We thank Dr. T. Griffith for providing us with Millipore" filters. Dm. N. A. Weir, L. D. Hawton and Mr. D. A. Jones are thanked for their interests in our work. Literature Cited (1) Davson, H.,and Danielli, J. F., "ThePermeability of Netvral Membranes; Hafner Publ.Co., Darien,CT. 1970,pp.38.80. (2) Stein, W . D.,'TheMovement ofMaleculeaAeraasCellMembrsne,"AeademicPrsss.
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hk".""., . ,*C" " 3a " .,p-. (3) Nikaido. H.,Anpew.Chem. Inter. Edit., 18,337 (1919). 14) Crank,J.,andPark, G.S. (Editors),"Diffusion in Polymem,"AcedemiePI~~,Lo~odon and New York. 1968. 15) Collins, M. C., and Ramme, W. F.,J. Phys. Chem, 88,2294 (1919). 16) Kurninr, C. A. (Edi1or);'TransportPhenornena in Polymeric Filma;lJ. Polym. S c i , ClO),lnterseience. New York, 1965. (7) Gsrbarini, G. R., Eaton, R. F., Kwei,T.K.. and Tobo1sLy.A.V., J. CHEM. EDUC..~~,
226119711.
(N ~ e w n s ;A. c., J TGI. Irefit., 41.T269 (1950). (9) Stein, W. D.,"TheMovementofMoleculesAcraesCellMembrane,"AcademiePress, hhruY*.&
1s ".,"."".
19CI
n
(LO) Stein, W. D.,"TheMavernentofMoleeul~gAcraa.CellMcmbrana;AcedemiePrear, Now Yotk. 1967, p. 37. (11) Crank,J.,"TheMathemsti~1ofDddion:'2nd Ed.,OIfodUni. P m . London, 1915, 0.51.
M., sad Patel, N.K., J . Pharm. Sci..59,77 11970). 113) McCabe,M.,Biochem. J.. 127.249(1972). (12) N& . ,;
