The linearityof the escapecurves of the monomer-monomer systems has the practical result that these systems will often be overlooked experimentally. However, if other data indicate that there is a system of this type, the linearity of the escape curves can be quite useful. The equilibrium system of monomer-monomer interconversion of Figure 1B can easily be shown to have a first order escape curve for the solute described by Equation 3. -dC dt
-=[
a+KeqP
l+Ke,]
(3)
The diffusion rates of solutes A and B are a and 0,respectively, C is the total inside solute concentration and KBpis the equilibrium constant of the A to B conversion. Since the escape curves are straight lines even when a and /3 are in the same range as kl and kz, all these systems can be treated by the approximation that A and B are in rapid equilibrium. That is, any time a monomer-monomer system gives a straight escape curve, the system may be treated as an equilibrium system.
Thus if a and /3 can be determined, the equilibrium constant can be calculated. Likewise, if the equilibrium constant can be determined, then a and /3 can be calculated in terms of each other. If neither a, 0,nor the equilibrium constant can be determined, then the method is more limited. Although we may be able to get a series of linear escape curves under a series of conditions, it becomes quite difficult, if not impossible, to determine whether we have only one species for each concentration or two states with fixed diffusion rates but a different equilibrium constant for each condition, or whether we have multistates each with its own diffusion constant and equilibrium constant. ACKNOWLEDGMENT
The skillful technical assistance of Mrs. Helen Kac is gratefully acknowledged. RECEIVED for review May 4, 1970. Accepted July 2, 1970. Investigation supported in part by a grant from the National Institutes of Health No. AM 02493.
I
NOTES
Thin Film Dialysis Studies with Highly Acetylated Cellophane Membranes Kent K. Stewart’ and Lyman C. Craig The Rockefeller University, New Y o r k , N . Y . 10021
INPREVIOUS REPORTS from this laboratory (1-5) we have shown that standard Cellophane dialysis casing can be modified easily so that it has the range of pore sizes optimum for studying the dialysis of organic compounds of any specific molecular size from a molecular weight of 100 to that of 135,000. Pore sizes can be altered in a useful way by mechanical stretching while the membrane is wet (I). They can be made much larger by treatment with zinc chloride or made much smaller by a simple acetylation procedure. In connection with certain projected investigations dealing with the binding of inorganic solutes to proteins and nucleotides, it seemed of interest to explore further the behavior of very highly acetylated cellophane casing. It has been demonstrated that Visking cellophane tubing carries very little if any 1 Present address, The Human Nutrition Research Division, Agricultural Research Service, United States Department of Agriculture, Beltsville, Md. 20705
(1) L. C. Craig and William Konigsberg, J. Phys. Chem., 65, 166 (1961). (2) L. C. Craig and A. 0. Pulley, Biochemistry, 1,89 (1962). ( 3 ) L. C. Craig and A. Ansevin, ibid., 2, 1268 (1963). (4) G. Guidotti and L. C. Craig, Proc. Natl. Acad. Sci. U.S., 50, 46 (1963). ( 5 ) L. C. Craig, William Konigsberg, A. Stracher, and T. P. King, in “Symposium on Protein Structure,” A Neuberger, Ed., IUPAC Symposium, July 1957, John Wiley and Sons, Inc., New York, N. Y., 1958, p 104.
fixed charge (3) and that diffusional size can be the major parameter determining whether or not dialysis will occur, It therefore seemed of interest to explore if this would necessarily be true for highly acetylated membranes showing high selectivity for inorganic solutes. Although the charge on the molecule with the larger organic solutes with ionizable groups seemed to have little or no direct effect on dialyzability, a different behavior might be expected in the case of the inorganic solutes with high charge density. Selective, low porosity membranes have been prepared and the diffusion of a number of solutes through these membranes has been measured. In this paper we present the results of our studies on the effect of molecular size and change of temperature on the diffusion rates of some low molecular weight solutes through these membranes. EXPERIMENTAL. Materials. All solvents were distilled before use, and all
chemicals were reagent grade. The isotopically labeled compounds were purchased from New England Nuclear. The dialysis membranes were purchased from the Food Products Division of the Union Carbide Corporation. Membranes. The dialysis casing (Visking seamless cellulose No. 23) was stretched almost to breaking with the stretching trough described earlier (1) and then acetylated. We have used 25% acetic anhydride and 75% dry pyridine a t temperatures of 80 to 90 O C for periods of 1 to 4 hours for the acetylation. The membranes appeared to melt against the
ANALYTICAL CHEMISTRY,
VOL. 42, NO. 11, SEPTEMBER 1970
1257
inside l u b e glass collar clamp
Figure 1. Schematic drawing for glass holder for acetylation of the membrane
fixed o/pulley
The dialysis cell employed is shown schematically in Figure 2 and is a slightly modified version of previous cells used in this laboratory (6). The membrane surface area approximates 45 cmz, the inside solution volume about 0.7 cc, and the outside volume about 7 cc. The addition of the Luer-tip and the sampling syringe facilitates the removal of the diffusate and its replacement with fresh solvent. The apparatus can be fitted easily with a water jacket for temperature control. The analytical dialyses were performed in the following standardized manner. The solute was dissolved in the solvent and placed inside the membrane and the inner tube then inserted. The outside solution was added by drawing the solution up the sample tube into the syringe, turning the valve, and then transferring the solution to the dialysis cell with the aid of the syringe. The reverse procedure was used to remove the outside solution. At fixed sampling intervals, the diffusate was removed, set aside, and replaced with fresh solvent. At the end of the dialysis both the inside and the outside solutions were set aside for analysis, and the cell and the membrane were thoroughly washed. Tritiated water, 14C-methanol, 14C-urea, 14C-glycine, and IC-glucose were each dissolved in 0.10M potassium chloride, p H 5 . 5 , and dialyzed against the same solvent. The conditions were the same for the 14C-acetic acid except that the p H was 2.4 and for the 14C-potassium acetate except that here the p H was 7. Preliminary dialyses of sodium and/or potassium chloride were done by dialyzing 1 M solutions against water. The detailed comparison of the dialysis rates of sodium chloride and potassium chloride was made by dialyzing a solution of 0.05M sodium chloride, 0.05M potassium chloride, 0.10M ammonium chloride, and 0.01 5M lithium chloride (internal standard) against a solution of 0.2M ammonium chloride and 0.015M lithium chloride. Most solutes were isotopically labeled so that their concentrations could be assayed by liquid scintillation counting using Bray’s solution (7) in a Tricarb Scintillation counter. Sodium chloride and potassium chloride, when they were not mixed, were estimated by conductance or in later experiments, when they were mixed, estimated a t the same time by flame photometry with a n Instrumentation Laboratory Model 143 Flame Photometer. The hydrochloric acid concentration was measured by pH measurements on a Radiometer PHM-4 and/or determined by titration with 0.01N potassium hydroxide. The results of each experiment were plotted with the standard first order plot of ln(a/a - x) us. time, where a equals the initial concentration of the solute and x equals the concentration of the solute passed through the membrane a t time t. A typical plot is shown in Figure 3. Half escape times were calculated from the slopes of these plots. Total recoveries were always calculated as a check on the analytical procedure. All the results reported here come from duplicate experiments in which the first order plot was linear and the solute recovery was 85 or better.
- \bx] 15 r p m
inside tube glass collar
sample tube
Figure 2. Schematic drawing of cell for measuring escape rates
inner tube at the high acetylation temperatures and were very easily stretched. The simple apparatus shown in Figure 1 was used in the acetylation to prevent unwanted stretching and to produce uniform membranes. The acetylation reaction was stopped by placing the membrane assembly in cold water. The hydrophobic, firm membrane which had now shrunk t o fit snugly to the inside tube, was washed in 0.1M acetic acid until all the pyridine had been removed (2 to 4 days). The inside tube was removed a t the beginning of the washing. After washing, the membrane was first checked for absence of pin holes and then assembled as part of the dialysis cell shown in Figure 2. Membranes modified under these conditions have shown reasonably reproducible porosities as determined by the dialysis rate of 1M sodium chloride and t o have closely reproducible inside diameters. Although extensive studies have not as yet been made, it is probable that this process will yield membranes sufficiently uniform to fit into standardized dialysis cells. 1258
RESULTS
Preliminary investigations of the porosity of these very heavily acetylated membranes showed that they had a low porosity and were quite selective. Dialysis at room temperature with membrane A , for example, gave a half escape time of 12 minutes for tritiated water, 35 minutes for IC-methanol, 100 minutes for hydrochloric acid, 12 X lo2 minutes for sodium chloride, and 4 X l o a minutes for 65ZnC12. For comparison, identical membranes which were strongly acetylated, but less so than membrane A , gave half escape times (6) L. C. Craig, in “Advances in Analytical Chemistry and Instrumentation,” Vol. 4, C. N. Reilley, Ed., Interscience, New York, N. Y., 1965, p 35. (7) G. A. Bray, Anal. Biochem., 1, 279 (1960).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
for sodium chloride of 3 to 8 minutes. The decreased porosity of membrane A stimulated further detailed studies, the results of which are shown in Table I. The data given in Table I are the results obtained from two different membranes prepared in a similar manner. The low porosity of both membranes to these low molecular weight solutes is both reproducible and selective. The selectivity is nicely shown by the difference in the half escape times of water, methanol, acetic acid, and potassium acetate, and by the differences in the half escape times of hydrochloric acid, sodium chloride, and potassium chloride From the data on the membrane diffusion of the solutes, we can order the solutes in order of increasing membrane diffusional size: HzO < CHIOH < urea < HC1 < KC1 < NaCl < CHICO2-Na+ < glycine < glucose < EDTA. It is of considerable interest to compare the effect of a change of temperature on membrane diffusion and free diffusion. The temperature effect on free diffusion is given by a combination of Fick's law and Stokes' law in Equation 1:
0.8 r
a -
I
When this ratio is calculated for free diffusion at 20 and 40 "C with the measured viscosities of 0.1M potassium chloride at these temperatures, a value of 1.64 is obtained. The mean of the ratios in Table I is 1.65 + 0.10. All the experimentally determined ratios are equal to the calculated ratio within the observed experimental error. Preliminary studies with membrane A indicated that the half escape time of tritiated water was not influenced by pH or ionic strength. When membrane B was used, tritiated water had a half escape time of 10 f 1 minutes at 20 "C whether the dialysis was done in water, in 0.1M potassium chloride, pH 5.56, or in 0.1M potassium chloride, p H 2.0. Similarly the half escape time of IC-methanol at 40 "C was 11 1 minutes in 0.1Mpotassium chloride, pH 5.56 or p H 2.09, or in water alone. DISCUSSION
The very low porosity dialysis membranes reported here extend the range of the size of solutes which may be studied by
In a-x
P O aa24 I
P u
0
IO
20
30
40
Minutes Figure 3. Typical first order escape plots: Dialysis of I4Curea in 0.10M potassium chloride, pH 5.5 dialyzed against 0.10M potassium chloride; CI and CII duplicate runs at 40 "C, CIII and CIV duplicate runs at 20 "C
analytical dialysis down to the molecular size of water and methanol. This range of molecular dimensions is one where other techniques may also be used to correlate and test the phenomena observed in analytical thin film dialysis. We thus should be able to probe further possible mechanisms of diffusion through membranes and the effects of molecular interactions in solution. The lack of effect of the pH or ionic strength on the dialysis rates of methanol or water strongly indicates that the membrane porosity is not basically changed by alteration of these solvent parameters. Thus these membranes should be useful
Table 1. Comparison of Dialysis Rates of Different Solutes at 20 and 40 "C
Mean half escaDe time Solute
Membrane A
3
~
~
0
"CHrOH ~
~
~
1
4
CHa"COO-K+ B
aHtO
"CHsOH CHa14COOH Urea-14C HCl KCl NaCl C H ~~~ C O O - K +
~
0
(Min. X 10-a) 20" 40" 0.15 0.087 0.32 0.18 0 0.52 ~ 0.29 5.3 ... 0.11 0.07 ... 0.11 0.23 0.14 0.40 0.26
...
0.440
... ...
0.22b 2.2 3.2 10.0
16.0
Half escaoe - - time -----relative towater x 10-2 r
20 0.01 0.021 0.035 0.35 0.01
40 '
Ratio of half escape time at 20" and 40"
0.01 0.020 0.033
1.75 f 0.22 1 . 8 3 f 0.19 1 . 8 0 f 0.10
0.01
1 . 5 1 i 0.16
0.022 0.038
0.020 0.037
...
...
... ...
1.6
...
...
0.015 1 . 6 7 . i0.06 1.56 i 0.04
0.064
0.032 0.33 0.47 1.5
... ...
1.63 j=0.12
Glycine-14C 23.0 13.5 2.2 2.0 1.71 zk 0.24 D-Glucose-14C 29.0 20.0 2.8 2.9 1.46 i 0.16 EDTA-"C 28.0 19.0 2.6 1.8 1.62 & 0.52 The half escape times were determined from the slope of the first order escape plots. See the experimental section for the details. The half escape times for the sodium chloride and potassium chloride were determined in the same experiments. a Determined with 1-hour time intervals as were the half escape times for the sodium and potassium chloride. Determined with 15-minute time intervals for sampling.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
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in any investigation of the effect of ionic strength and hydrogen ion concentration on the diffusion behavior of other solutes. These preliminary studies have demonstrated that the effect of a change in temperature on the dialysis rate of the solute is the same even when the range of molecular size is such that it covers solutes with greater than a hundredfold difference in their dialysis rates. The temperature effect moreover is close to that which is predicted on the basis of free diffusion in the solvent. These two observations make quite unlikely any model of diffusion which is based solely on solubility in the membrane matrix. The fact that water diffuses more rapidly than methanol or acetic acid through these relatively hydrophobic membranes adds strength to this belief as does the observation that the escape plots are strictly linear. One might be tempted to suggest that the rate of membrane diffusion is strictly size controlled with these low porosity membranes and that the order of the rates would be the same as that of free diffusion as appears to be the case with more porous membranes (3). This, however, is not strictly the case. The uncharged species such as water, methanol, and acetic acid by themselves have the same order of diffusion rates in both free and membrane diffusion. Likewise the charged species such as hydrochloric acid, potassium chloride, sodium chloride, and glycine by themselves have the same order of diffusion rates in both free and membrane diffusion. But in free diffusion the order is hydrochloric acid, deuterated water, potassium chloride, methanol about equal to sodium chloride, and urea (8). The order in the present membrane diffusion work is water, methanol, urea about equal to hydrochloric acid, potassium chloride, sodium chloride. It is thus quite apparent that the presence of a charge on a molecule makes a large difference in its apparent membrane diffusional size with these membranes of low porosity. This is in contrast to the published experience with the more porous membranes. This charge effect is also quite noticeable in the ten to hundredfold difference found between the diffusion rates of acetic acid and potassium acetate. Thus, with these particular membranes, any model which states that membrane diffusion has the same mechanism as free diffusion only more selective, is not correct. Although no new mechanism of (8) L. G. Longsworth in “American Institute of Physics Handbook,” 2nd ed., D. E. Gray, Ed., McGraw Hill, New York, N. Y., 1963, pp 2-205.
1260
membrane permeation is suggested from the data, it would appear that as the porosity of a cellophane membrane is decreased by acetylation, the effect of the charge on the solute is increased. Highly acetylated cellulose membranes are known to reject salt in so-called reverse osmosis (9) for recovery of seawater by a mechanism that is not entirely understood. Another anomalous characteristic observed with these membranes is the lack of selectivity for distinguishing glycine, glucose, and EDTA as shown by the data in Table I. The conclusion to be drawn from these data is that such extremely slow permeation (of the order of 40-50 hours for a half escape time) is not a reliable reflection of diffusional size. The recent reports of the use of kinetic dialysis as a concentration probe is a welcome addition to our limited arsenal of probes of solute activity (10, ZZ). Briefly this technique uses the measured rate of dialysis of the solute as a probe of the concentration of the free solute. This technique has been used both for very rapid measurements of enzyme substrate association complexes (10) and for measurement of proteinsolute association constants such as the binding of phosphate to ribonuclease (ZZ). We would like to suggest that the membranes and dialysis cell described here could be used ideally for this type of kinetic dialysis study. The high selectivity and low porosity of the membranes make them ideally suited for kinetic dialysis probes of free solute concentration. The analytical thin film dialysis cell has the advantage of a small volume and easy temperature control. ACKNOWLEDGMENT
The skillful technical assistance of Mrs. Helen Kac is gratefully acknowledged. RECEIVED for review May 4, 1970. Accepted July 2, 1970. Investigation supported in part by a grant from the National Institutes of Health No. AM 02493.
(9) C. E. Reid and E. J. Breton, J . Appl. Polym. Sci., 1, 133 (1959); 2, 264 (1959). (10) S. P. Colowick and F. C. Womack, J. Biol. Chem., 244, 774 (1969). (11) J. Ridlington and L. B. Butler, ibid., p 777.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
