1 AIDS FOR ANALYTICAL CHEMISTS Continuous Measurement of Mass Transport across Membranes Carter L. Olson, Theodore D. Sokoloski, Shrikant N. Pagay, and David Michaels1 College of Pharmacy, The Ohio State University, Columbus, Ohio 43210
THEREHAVE been numerous studies involving the measurement of mass transport of drug and drug-like molecules across a large variety of membranes or barriers. Some of the barriers that have been used include biological membranes such as the rabbit mesentery ( I ) , pseudobiological membranes such as artificial phospholipids (2), model biological membranes ranging from liquid barriers (3, 4 ) to polymeric films such as silastic membranes ( 5 ) , modified gelatin membranes (6))and nonbiological barriers such as polyethylene (7). In all instances, the actual measurement of mass transport has been conducted along rather classical lines where the barrier separates two compartments of solution; the contents of which are measured as a function of time. The usual mass transport measurement is, as a result, rather slow, taking from several hours to over a day because the ratio of compartment volume to barrier surface area is fairly large requiring a substantial amount of time before a significant fraction of the transported material can cross the barrier, permitting the rate of transport to be measured. It was thought that by utilizing flow stream methodology and a cell with appropriate volume to barrier surface ratio, a continuous steady state measurement could be made which would be directly related to the rate of mass transport across the barrier. A relatively simple and easy-to-construct semi-micro flow cell was developed for making continuous measurement of mass transport across membranes. The effluent solution from the cell is pumped to a spectrophotometric flow cell where a steady state reading is reached within minutes that is directly proportional to the rate of mass transfer of measured species across the membrane. Studies were conducted to determine the response time of the system, the linearity of flux with concentration gradient across the membrane, and the reproducibility with which mass transport could be measured. EXPERIMEKTAL
Instrumentation and Flow Stream. The relative positioning of the flow stream components is illustrated in Figure 1 . Solutions are pumped by means of a Harvard Apparatus Model 6OO-1200 peristaltic pump. Solution from a reservoir contain'NSF URP participant from Baldwin-Wallace College, Berea,
Ohio. (1) L. S. Shenouda and A. M. Mattocks, J. Pharm. Sci., 56, 464 (1967). (2) A. L. Misra, A. Hunger, and H. Keberle, J. Phavm. Pharrnacol., 18, 531 (1966). (3) J. T.Dolusio and J. V. Swintosky, J. Pharm. Sci,, 53,597 (1964). (4) S. A. Khalil and A. N. Martin, ibid., 56, 1225 (1967). (5) E. R. Garrett and P. B. Chemburkar, ibid., 57, 944, 948, 1401 (1968). (6) M. A. Gonzales, J. Nematollahi, W. L. Guess, and J. Autian, ibid., 56, 1288 (1967). (7) M. von Stackelberg, M. Pilgram, and V. Toome, Z . Electrochem., 57, 342 (1943).
LOW C
O
HIGH CONC.,
N
C
.
-
fm 1 (67)
/, 4
PERISTALTIC PUUP
+
'
TO WASTE
1
+ 1
TEFLON TUBE
CELL COMPARTMENTS STIRRERS BARRIER INITIAL H l Q H CONC. SOLVENT SPECTROPHOTOMETRLC FLOW CELL
Figure 1. Schematic showing relative positioning of components used to measure mass transport of substances through barriers utilizing flow stream technology
ing the sample (concn C D )is pumped to chamber I of the flow cell (concn Cl), then through the pump and on to waste. A blank solution is pumped to Chamber I1 where it acquires sample (concn C,) by mass transfer through the membrane. This stream then flows to an Arthur H. Thomas No. 9120-NO5 spectrophotometric flow cell which is placed in a Cary 16 spectrophotometer, then through the pump and on to waste or to a volumetric flask for collection. The solution flow rate is determined by measuring the time required to fill a 10-ml volumetric flask. Flow lines were constructed from 16-gauge Teflon tubing except through the pump head where wall thickness Tygon formulation B-44-3 1/16'' i.d. by tubing was used. In some instances, the effluent from the flow cell (concn C,) was collected and measured either spectrophotometrically or polarographically at a dropping mercury electrode. Solutions were pumped at a flow rate of about 2.4 ml per minute. Mass Transport Flow Cell. The flow cell used throughout the experiments is illustrated in Figure 2 . The cell machined from Plexiglas consists of two chambers separated by the membrane. The chambers are identical being 1 cm in diameter and 0.3 cm deep holding a volume of around 0.24 ml. Each chamber is fitted with stainless steel inlet and outlet tubes for connection to the flow system. A small magnetic stirring bar is placed in each chamber of the cell. The cell is mounted in a Plexiglas holder which is machined to position water/air driven magnetic stirrers on each side of the cell to drive the stirring bars placed in the cell chambers. The whole assembly is immersed in a constant temperature bath at 25 "C. Reagents. Meta-Nitrobenzoic acid and para-nitrophenol were recrystallized from water alcohol mixtures. All other chemicals were reagent grade and used without further purification. Solutions were prepared using double-distilled deionized water. All solutions contained a background supporting electrolyte of 0.1M KCI except TI+ which contained 0.1M K N 0 3 . AI1 solutions were adjusted to pH 3. Two types of membranes were used during the course of the experiments. These were Dialysis Tubing (Precision Nojax, VOL. 41,NO, 6 , MAY 1969
865
r I
1// 1
i
b
TEFLON TUBING
0 , 0-NITROBENZOIC ACID
CELL AND AIR STIRRER HOLDER
0 , 0-NITROPHENOL v
AIR DRIVEN STIRRERS
14-
W
$12W
d 10-
STAlNLESS STEEL FITTINGS
I
X
2 -I LL
CELL COMPARTMENT, 0.24 ml.
8-
6t
'If
TEFLON COATED STIRRERS BARRIER BETWEEN COMPARTMENTS
2
INLET, SOLVENT
2
0
4 6 8 IO 12 14 CONCENTRATION, M x io3
INLET, SOLUTION
16
Figure 3. Flux of o-nitrobenzoic acid and o-nitrophenol in moles/second as a function of concentration of these materials in moles/liter initially entering the diffusion cell
Figure 2. Diagram illustrating flow cell used in determining mass transport through barriers Union Carbide) and Millipore filter (regular type V M , Millipore Corp. RESULTS AND DISCUSSION
Studies were made to evaluate the performance of the cell. In theory, one can easily describe the change in concentration inside the flow cell as a function of time and predict the minimum time required for the flux across the barrier to reach a steady state. The actual steady state times will be longer because of solution holdup in the flow lines and measuring devices. Future modifications of the system will be concerned mainly with minimizing these holdup volumes. The derivation of time to reach steady state is as follows: The flow technique provides a non-equilibrium process with attainment of steady state transport. The change of concentration of transported material in chamber 11 of the cell is given by, dCz
= j/V2dt -
(C?F:V,)dt
effect of the convective diffusion layer. If the rate of stirring is such that essentially homogeneous solutions are maintained on both sides of the membrane at Cl and CZ,respectively, one may write the following mass balance equation : vz c1 = c, - -cz
(3)
VI where V I = volume of chamber I, C , = initial solute concentration before entering chamber I and C1 and Cz = concentration of transported material in chamber I and I1 at time t . The equation for flux may now be written: r
Equation 1 and 4 combine to yield: 1
c
if
v1= V z =
V and k l
=
k? = k then,
(1)
where Cz = concentration of transported material in moles/ ems, j = flux of material at time t in moles/sec, V z = volume of chamber 11, and F = flow rate of solution through chamber I1 in cms/sec. Using Fick's first law,
Integration of Equation 6 between the limits (0, CZ)and (0, t ) gives : DAkC, (7) F, c2 = 2DAk -+F L +
where L = thickness of the membrane in cm, A = cross sectional membrane area in cm2, D = diffusion coefficient of transported material in cmzisec, Cls = surface concentration on chamber I side of membrane, and Czs = surface concentration on chamber I1 side of membrane. The concentration at the surface can be related to the solution concentrations in the cell chambers by CIS = klCl and Czs = kzCz where C1 and C? are the solution concentrations in chambers I and 11, respectively, and kl and kz are constants relating surface concentration to solution concentration. In the case of an inert barrier with no adsorption or partitioning characteristics, k would equal unity ignoring the 866
ANALYTICAL CHEMISTRY
when F
>> 2DAk, Equation 7 simplifies to: L
at longer times, Equation 8 reduces to:
cz
=
DAk --eo LF
(9)
Table I. Permeability Constants, [KDI=k Per Cent Average Deviation of Several Compounds through Dialysis Tubing' at pH 3 in 1M KCl Using Two Different Samples of Same Batch of Membrane and Reproducibility Obtained between the Two Samplesb Membrane sample 2 Membrane sample 1 (KD),, cm3/sec x lo4 (KD),, cm3/sec x lo4 Compound f % av. dev. f % av. dev. (KD)Z/(KD)lb 1.47 f 2.1 1 .oo 1.48 f 0.5 p-Nitrophenol 1.31 f 2.5 0.92 1.43 f 2.7 m-Nitrophenol 1.41 f 2.2 0.89 1.59 f 6.0 o-Nitrophenol 0.95 f 3.5 1.01 o-Nitrobenzoic acid 0.94 f 1.9 1.11 f 1.1 1.03 m-Nitrobenzoic acid 1.09 f 1.0 1.05 f 1.5 1.15 f 10 1.09 Benzoic acid 1.24 f 1.9 1.07 1.16 f 0.1 p-Aminobenzoic acid 0.67 f 1.2 1.04 Potassium ferricyanide 0.64 f 3.2 Dry thickness 0.001 inch. b The reproducibility is indicated by the ratio of the permeability constants obtained with each sample, ideally the ratios would be 1. The average ratio is 1.01 5.0%. Table 11. Mass Transport of Several Compounds through Millipore Filter at pH 3.0 and Determination of Cell Constant K
Compound Potassium ferricyanide Nickel(I1) chloride Potassium iodate Cadmium(I1) chloride Thallium(1) sulfate rn-Nitrobenzoic acid p-Nitrophenol
Diffusion coefficient (literature) cmz/sec x lo5 0.75b 0.66~
Concentration, CO,
moles/ml x lo5
1. o o C 0.73~ 1.820 0.582d 0.674e
1 .oo 1 .oo 1 .oo 1.oo 1 .oo 0.116 0.102
Flux Cis,), moles/sec x lo9 1.318 1.165 1.800 1.306 3.050 1.102 1.174 Av. cell constant 17.43 f 2.07% f av. dev.
Cell constant' K = j,,/C,Dk 17.57 17.57 18.00 17.80 16.75 17.11
17.10
k is assumed to be unity.
Reference (7). Reference (8). d Reference (9). e Reference (IO). b c
since CzF represents a steady state flux or mass transport reached at longer times one may write:
is,= C2F =
DAk -c, L
Under the experimental conditions used, 2DA/L(-10-4) is much smaller than F(-10-2). Using experimental values for V 2 and F and assuming k = 1 , Equation 8 predicts that a steady state flux should be reached within 1 % in less than 30 seconds. A cell constant, K , can be defined as:
In practice attainment of steady state usually required about three minutes. This longer time is due to the time required to flush out the connecting tubing and measuring cell and illustrates the desirability of low holdup volume in the flow components. In choosing the solution flow rate, several factors must be considered. If the flow rate is small, the response time of the measurement is slow and the assumption that C2
