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Precipitation zones with membrane properties in gels
Precipitation Zones with Membrane Properties in Gels ROLF-DIETER REINHARDT, RAINER ORTMANN, AND DIETRICH WOERMANN Institut J~r Physikalische Chemie, Universitdt Krln, Luxemburger Strasse 116, D-5000 Krln 41, Federal Republic of Germany Received March 19, 1984; accepted August 24, 1984 Polyacrylamide gels containing Na2SO, are brought into contact with aqueous solutions of BaC12 (or SrC12). The electrolyte concentrations in the gel phase and in the solution are varied systematically. There exists a characteristic concentration c* below which advancing precipitation zones of BaSO4 (or SrSO4) in the gel are observed. Above this concentration the precipitation zones do not grow after advancing for about 3 to 5 ram. Such a precipitation zone has the properties of a membrane, exhibiting osmotic properties and varying diffusional resistance to different ionic species present in the system. The characteristic concentration c* is related to a characteristic saturation ratio leading to the formation of a thin layer (thickness ~< 10 ~tm) of small densely packed crystallites. The crystallites carry absorption charges whose counterion clouds overlap. This gives the precipitation zone the properties of a membrane. The difference between the values of the characteristic concentration c~* leading to the formation of BaSO4 and SrSO4 precipitation membranes is related to the difference between the concentrations of BaSO4 and SrSO4 at which instantaneous formation of precipitate begins in free solution. © 1985 AcademicPress,Inc. 1. INTRODUCTION
It is known that crystalline precipitation zones formed by interdiffusion of two aqueous electrolyte solutions containing ions forming a sparsely soluble precipitate can act as selective barriers (precipitation membrane). They exhibit varying diffusional resistance to different ionic species of the bulk phases. Usually, precipitation membranes are formed within gel plugs separating two solutions containing the precipitate-forming ionic species. The membrane properties are studied by measurements of membrane potentials and current-voltage characteristics. A typical example is the BaSO4 membrane first described and extensively studied by HirschAyalon (1-4). On the other hand, there has been recurrent interest in studies of periodic precipitation patterns within gels in the presence and absence of concentration gradients (5-11). This prompted us to study whether it is possible to generate precipitation mem-
branes in gels in an experimental arrangement similar to that in which periodic precipitation patterns are observed: test tubes filled with a NaESO4 containing a hydrogel (polyacrylamide) are brought into contact with aqueous BaC12 (or SrC12) solutions. Advancing precipRation zones are observed. The thickness of these zones is studied as a function of time. 2. MATERIALS AND METHODS
2.1. Preparation of Polyacrylamide Gel Three aqueous solutions of substances necessary for gel formation are prepared. Solution 1 contains 0.23 cm 3 N,N,N'N'-tetramethylethylenediamine (TEMED) dissolved in 100 cm 3 aqueous Na2SO4 solution. Solution 2 contains 30 g acrylamide and 0.8 g N,N'-methylenebisacrylamide dissolved in 100 cm 3 aqueous Na2SO4 solution; solution 3 contains 8.7 × 10-4 mole (NH4)2S208 (initiator) dissolved in 100 cm 3 aqueous
136 0021-9797/85 $3.00 Copyright© 1985by AcademicPress,Inc. All rightsof reproductionin any form reserved.
Journalof Colloidand InterfaceScience,Vol. 104,No. 1, March 1985
PRECIPITATION
Na2SO4 solution. The concentration of Na2SO4 in the solutions is the salt concentration within the gel after polymerization. The standard solution for the preparation of the gel is a mixture of solution l, solution 2, and water in the ratio 1:2:1. Gel formation is started by mixing equal volumes of the standard solution and solution 3. Air is removed from the mixture by pressure reduction. A syringe is used to fill the test tubes (length: 100 ram, internal diameter: 10 mm) with the reaction mixture. The completely filled test tubes are tightly covered with Parafilm and turned upside down during the polymerization process. Care is taken that no air bubbles are trapped at the phase boundary gel/Parafilm. By this procedure gels with a fairly welldefined surfaces are obtained. The gel has a water content of about 90%.
137
MEMBRANES I
6
I
i
BaCl 2: 0.1 c*
/
No.SO,.:o.osc'(oet) 7 ' 5
/f
4
L
cm
J
3
g
o'
/
z
/d
/ I
0
50
tT
10o
150
mid/2
FIG. 1. Space coordinate ~ o f the front o f the precipitation zone relative to the phase b o u n d a r y g e l / a q u e o u s solution as a function o f time. c' = 0.1c + BaCI2; e" = 0.05e + Na2SO4 (c + = 1 m o l e din-3). Index ' = gel; index " = a q u e o u s solution.
2.2. Precipitation Zones in Gels Test tubes filled with polyacrylamide gel containing NazSO4 at a known concentration (5 × 10-3c+ ~ cs ~ 0.3c+; c + = 1 mole d m -3) are brought into contact with well-stirred aqueous solutions of BaClz (or SrC12) of known composition (BaCI2:5 × 10-3c+ ~< cs ~< 0.3c+; SrClz: 0.5c+ ~< cs ~< 1.1c+) at constant temperature. The test tubes are maintained in a vertical position with the open end facing upward. Three types of experiments it. are carried out: c'~ = c~; c~ < c~, c~~ > c,?! (index ' = gel phase; index " = aqueous phase). At the phase boundary gel/aqueous solution precipitation of BaSO4 (or SrSO4) sets in (BaCI: + Na2SO4 ~ BaSO4(s) + NaC1). The distance between the phase boundary gel/aqueous solution and the front of the advancing precipitation zone within the gel (thickness of precipitation zone) is measured with a cathetometer. A typical result of such measurements is shown in Fig. 1. There is a linear relation between the thickness ~ of the precipitation zone and the square root of the diffusion time t 1/2. It holds for ~/L <~ 0.75 (L = length of the gel plug). The straight line does not pass through the origin. This is due to the uncertainty with which the location of r
the phase boundary gel/solution can be determined. Periodic precipitation patterns are observed with the following concentrations: cs(Na2SO4) = 2 × 10-3c+; cs(BaC12) = 0.1c+ (index ' = gel phase; index " = aqueous phase) (12). 3. R E S U L T S
3.1. Precipitation Zone Assuming (a) that the formation of the precipitate can be represented by the simplified schema A + B ---, AB(s), (b) that the influence of osmotic phenomena (osmotic volume flo "~can be neglected, (c) that species A and B ha,~e the same diffusion coefficients within the gel and that the formation of precipitate AB does not impede the diffusion processes, the concentration profiles of A and B within the gel can be calculated (13-16):
CA=C°(1--erf(z)/K)
for
x~<~
[1]
cB = c°((1 -- erfc(z))/(1 -- K)) for with
x >i ~
[2]
z = x/(2(Dt) u2) and
K = erf((/(2(Dt)U2)) Journal o f Colloid and Interface ~Seience, Vol. 104, No. 1, March 1985
138
REINHARDT, ORTMANN, AND WOERMANN
D = diffusion coefficient, x = space coordinate, ( = length of precipitation zone, err(z) = error function; c° = concentration of species A in the aqueous phase at the phase boundary gel/solution and assumed to be constant during the experiment, c° = concentration of species B within the gel at the phase boundary gel/solution at the beginning of the experiment. It is assumed that far from the front of the advancing precipitation zone the concentration of B still has the value c° (gel phase of infinite length). In this model precipitation occurs only at that point in space at which CA = Ca = 0 (i.e., erf(z) = K). Concentration profiles o f A and B within the gel calculated from Eqs. [1] and [2] for two diffusion times are shown in Fig. 2. At time t the precipitation zone extends from x = 0 to x = 4. The coordinate ~ of the front of the precipitation zone changes in a characteristic way as a function of time (~ = 2a(Dt)m). At the front of the precipitation zone Eq. [3] holds. D(OCA/OX)~ =
--D(OcB/OX)~
[3]
1.0
f
0.5
o
II,II,. I
0.1
0.15
0.2
0.25
0.3
cs/c + FIG. 3. Fraction f of the number of test tubes filled with Na2SO4 gel and brought into contact with a BaCI2 solution in which the precipitation zone has stopped growing as a function of concentration c~. c'(BaC12) = c"(Na2SO4) = cs. Index ' = gel phase; index " = aqueous phase.
This equation together with the known values of c°, c°, and the slope m (=~/t 1/2) of the experimental ~ versus t l/z curve is used to calculate the value of the diffusion coefficient by an iterative procedure. Evaluation of the data shown in Fig. 1 gives a value of D = (7.39 _+- 1.75) × 10-6 cm 2 see -l.
3.2. Precipitation Membrane
If experiments are carded out with equal Calculating the differential coefficients (OCA/ electrolyte concentrations in the gel phase Ox)~ and (OCB/OX)~ from Eqs. [1] and [2] and and in the aqueous phase as a function o f substituting them into Eq. [3] yields concentration cs (cs(BaC12) = cs(Na2SO4) cOA/(C° + C°) = erf(~/(2Dt)l/2)). [41 = Cs; 5 X 10 -3 C+ ~< Cs ~< 0.3c +) it is observed that in a narrow concentration range near cs -~ 0.2c + the growth of the precipitation zone stops after it has reached a thickness of about 0.1 I I I I 3 to 5 mm. The experiments are carded out in groups of ten test tubes filled with gel under identical conditions. The fraction of c--~- 0.05 test tubes in which the precipitation zone CA CB does not grow after the test tubes have been brought into contact with a BaC12 solution is V V I shown in Fig. 3. There is a rather well0 2 ,(, 6 S 10 defined characteristic concentration c* sepaX crn rating the concentration range in which the FIG. 2. Concentration profiles of CA and cB within a precipitation zone grows continuously from gel for two different diffusion times calculated from Eqs. that in which the precipitation zone stops [1] and [2]. Diffusion coefficient D = 10-s cm 2 sec-~; cA growing. A precipitation zone has never been = 0.1c+; cB = 0.05c +. x = space coordinate; ~ , ~2 = space coordinates of the front of the precipitation zone observed to stop growing after its thickness relative to the phase boundary gel/aqueous solution at exceeds a value of about 5 m m ("all or two different diffusion times, t2 > ft. nothing" process). -
Journal of Colloid and Interface Science, VoL 104,No. 1, March 1985
PRECIPITATION MEMBRANES Experiments have also been carried out with Na2SO4-containing gels brought into contact with SrC12 solutions. The results of these experiments are similar to those obtained for the system Na2SO4 (gel)/BaC12 (aq). Only the characteristic concentration c* is higher by a factor of about 5 (BaSO4: Cs* -----0.2C+; SrSO4: Cs* --- 1.0c+). A precipitation zone which has stopped growing acts like a membrane. It exhibits varying diffusional resistance to different ionic species present in the system. This can be seen from measurements of current-voltage curves. To carry out these measurements the bottom part of a test tube containing a precipitation zone which has stopped growing is cut away. The upper part of the test tube with the gel plug is placed between aqueous solutions of BaC12 (or SrC12) and Na2SO4. These solutions have the same concentration as those with which the precipitation zone had been in contact previously. Two current electrodes and two Luggin capillaries (connected to reference electrodes) are introduced. The Luggin capillaries are used to measure the electrical potential difference across the precipitation membrane. One of the capillaries is placed within the gel phase about 5 m m away from the precipitation layer. A typical result for a'BaSO4 membrane is shown in Fig. 4. The curve reflects rectifying properties typical for BaSO4 precipitation membranes (1-4). Furthermore the experiments show that a BaSO4 precipitation membrane exhibits osmotic properties. It is observed that the precipitate-free part of the gel begins to shrink after the BaSO4 (or SrSO4) membranes has been formed. This phenomenon can be understood by taking into account the fact that the osmotic coefficient ~/, of a BaC12 solution is larger than that of an Na2SO4 solution of equal concentration (e.g., cs = 0.2c+: BaC12: qP = 0.84; NazSO4: ~' = 0.75) (17). The volume flow Jv across the precipitation membrane which is expected to be proportional to the osmotic difference 2x~-. A~- is given by A r = R T ( ~ " ~ c 7 - , b ' ~ c ~ ) index' = gel phase; index " = aqueous phase). For the values of
139
mA o
-1 0
500
1 O0 mV
FIG. 4. Current-voltage curve of gel plug containing a BaSO4 membrane. The curve is measured under dynamic conditions. A symmetric scanner is used to vary the electricalcurrent flowingacross the membrane. Current amplitude = +1.25 mA; sweep rate = 500 see for a full triangular period, c~(BaCI2,aq) = c~(Na2SOa,aq) = 0.1c+ (c+ = 1 mole din-3). A4~ = ~b(BaCl2, aq) ~b(NazSO4,aq). A4>o= membrane potential. -
the concentrations and osmotic coefficients given above the volume flow Jv is directed from the gel phase to the aqueous phase. Consequently the gel shrinks. The direction of Jv can be reversed by choosing c's > c~ (c's, c~ > c*). Under these conditions thin tubes (diameter about 0.2 ram) formed by BaSO4 crystallites start to grow out of the precipitation layer into the BaCI2 solution. The volume flow which is directed into the gel phase drives Na2SO4 solution out of the gel phase into the BaCI2 solution. After the "hairs" have reached a length of about 3-5 cm they stop growing. The Na2SO4 solution driven into the BaC12 solution has become dilute by osmotic water flow and does not contain enough material for continued formation of the tube wall. Some of the tubes seem to open up at the upper end and a jet of dilute NazSO4 solution streams into the BaClz solution through the BaSO4 tubes. This jet becomes visible by BaSO4 crystallites formed at the mouth of the jet and suspended in the BaC12 solution. 4. DISCUSSION The properties of the BaSO4 and SrSO4 membranes can be explained by a model Journal of Colloid and Interface Science, Vol. 104, No. 1, March 1985
140
REINHARDT,
ORTMANN,
proposed by Hirsch-Ayalon (1-4). Experimental evidence is accumulating in support of the proposed layered structure in crystalline precipitation membranes (18). Only a precipitation zone which has stopped growing has the properties of a membrane. The concentration range in which the moving precipitation zone stops growing is rather well defined and several orders of magnitude higher than the concentration of saturation (C~at) of the precipitate (BaSO4: - 0.2c+; c~t = 1 X 10-5c+; SrSO4: C~s --- 1.0c+; c~t = 6.2 × 10 -4 C+ (19). The velocity with which the front of a precipitation zone advances decreases slightly (by a factor of about 3 at the most) with increasing electrolyte concentration. However, there is no gradual transition from an advancing precipitation zone to a precipitation zone which has stopped growing. These observations are interpreted in the following way: A precipitation membrane within the gel can only be formed if two requirements are met: (a) There must be available enough BaSO4 (or SrSO4) in the unit volume of the gel to form a layer of densely packed crystallites. (b) The saturation ratio S (=cs/csat) must be large so that a large number of small crystallites per unit volume of the gel are formed after homogeneous nucleation has taken place. Both requirements are met at concentrations above c*. The thickness of a BaSO4 precipitation membrane has an estimated value of I 0 um as an upper limit. It is found experimentally that the mass of BaSO4 forming a membrane is of the order of 1 mg cm -2 corresponding to 4 X 10 -6 mole. At c* (-0.2c +) there are available only 10-7 mole of BaSO4 in a gel layer of 10-urn thickness. But the missing amount of substance can be supplied from the surrounding gel phase by diffusion within minutes at the beginning of the experiment because only then the concentration profiles are steep. (The diffusion flow density is proportional to 1/~.) At the saturation ratio S is large enough so that small crystallites can form, generating a densely packed layer of precipitate (BaSO4: Journal of Colloid and Interface Science, Vol. 104, No. 1, March 1985
AND WOERMANN
c* "" 0.2c +, S = 2 × 104; SrSO4: 6s* "~ 1.0c+, S = 1.6 × 103). The average distance between the crystallites will be smaller than or comparable to the radius of the ion cloud surrounding the crystallites carrying adsorption charges (4). Thus, the layer of precipitate gains the properties of a cation-anion exchange sandwich membrane (4). The divalent co-ions (ionic species having the same sign as that of the adsorption charges) are more effectively expelled from the region with cation and anion exchange properties than monovalent co-ions. This may be one of the reasons that not all sparsely soluble precipitates form precipitation membranes (e.g., silver and lead halides). Hengst and Honig (20) published an electron microscopic photo of a BaSO4 crystallite with dimensions of the order of 30 nm which they had obtained from a BaSO4 precipitation membrane formed in cellophane. They used a solution containing cadmium oxide, ethylenediamine, and water to dissolve the cellophane. However, this procedure raises the question whether the crystallites shown in the electron microscopic photo are really the crystallites which had formed the precipitation membrane. BaSO4 membranes lose their transport properties within minutes by recrystallization and ripening processes if the aqueous solutions containing Ba 2÷ ions and SOl- respectively are removed and replaced by aqueous solutions not containing these ions (18). Another size estimate of BaSO4 crystallites in a precipitation membrane based on X-ray line broadening is given in Ref. (2). A smaller value, 50 nm, is reported. However, it is not stated by which method the crystallites were separated from the membrane matrix (cellophane or hydrogel). Therefore, both findings can represent only an upper limit of the size of the crystallites in a functioning BaSO4 membrane. For a discussion of the threshold concentration ratio ~(SrSO4)/~(BaSO4) ~ 5 we turn to an analysis of supersaturation of these salts in free solution. It is a well-known fact that in free solution high values of the saturation ratio S can be obtained with BaSO4.
141
PRECIPITATION MEMBRANES
The values of S for SrSO4 are smaller (21). by which the characteristic concentrations We want to compare the values of S at which cs of BaSO4 and SrSO4 differ (6~s(SrSO4) instantaneous formation of precipitate begins -~ 5 cs*(BaSO4)). in both systems under comparable conditions. For this purpose equal volumes of equally 5. SUMMARY concentrated solutions of Na2SO4 and BaC12 (or SrC12) solutions are rapidly mixed in a Diffusion of BaCI2 (or SrC12) into a hydrospectral photometric cell (optical path length: gel containing Na2SO4 leads to the formation 1 cm) placed in a spectral photometer at o f a BaSO4 (or SrSO4) precipitation zone. 25°C (mixing time: 0.8 sec). The extinction Under certain conditions this zone acts as a of the solution is measured as a function of membrane, exhibiting osmotic properties and time. The time at which the extinction starts varying diffusional resistance to different ionic to increase due to scattering of the primary species present in the system. Two experilight intensity at the growing crystallites is mental conditions have to be met: (a) There determined. These experiments are carried must be available enough BaSO4 (or SrSO4) out as a function of concentration. For each in the unit volume of the gel to form a layer experiment a new cell is used to avoid con- of densely packed crystallites. (b) The satutamination with crystal seeds. The results of ration ratio of BaSO4 (or SrSO4) in the gel the experiments are shown in Fig. 5. The must be large enough so that a large number concentration of BaSO4 at which the delay of small crystallites per unit volume of the time for the formation of precipitate ap- gel are formed after homogeneous nucleation proaches 1 sec has about the same value as has taken place. This requirement is met at that reported by Nielsen for the onset of concentrations equal to or larger than the homogeneous nucleation (cs ~- 10-2c+; S characteristic concentration c*. The mem= l03) (22). From the data shown in Fig. 5 brane properties are caused by adsorption it can be concluded that the value of super- charges on the surface of the crystallites. The saturation for SrSO4 for the onset of homo- average distance between the crystallites must geneous nucleation is larger by a factor of be smaller than or comparable with the exabout 4. This is about the same factor tension of the counterion cloud of the abI
I
\o
20
%
\ \
\ 1.5 \
_ Baso4
Iog(~ s)
~\ Sr SO4
Ne
1.0
\
x
\ N
\
,.
x \
\\o
"~
\
0.5
o,~, %,., Ba SO4 and _ seeds
~% N
0.0 I
-3.5
-3'.0
\
\\
\ \
g
9
i
-I.0
-0.5
Iog{~-}
FIG. 5. Double logarithmic plot of delay time ~- of onset of turbidity after rapid mixing (mixing time 0.8 sec) of equal concentrated aqueous solutions of Na2SO4 and BaCI2 (or SrCI2) as a function of concentration. The presence of BaSO4 seeds in the solution shortens the delay time considerably. Journal of Colloid and Interface Science, Vol. 104, NO. 1, March 1985
142
REINHARDT, ORTMANN, AND WOERMANN
s o r p t i o n charges. T h e c o u n t e r i o n c l o u d s o f different crystallites m u s t o v e r l a p to p r o d u c e the membrane properties of the precipitation zone. ACKNOWLEDGMENTS Our study of precipitation membranes was started after Dr. P. Hirsch-Ayalon drew our attention to these systems. We thank him for his continued interest in our work. R. Forke had carried out the experiments with SrSO4 gels. U. Ditcher determined the saturation ratio of BaSO4 and SrSO4 in free solution. We thank them for their help. The financial support of the Minister f'dr Wissenschaft und Forschung des Landes NordrheinWestfalen is gratefully acknowledged. REFERENCES 1. Hirsch-Ayalon, P., Chem. Weekblad 52, 557 (1956); Rec. Tray. Chim. 75, 1065 (1956); J. Polym. Sci. 23, 697 (1957); Rec. Tray. Chim. 79, 382 (1960); Rec. Tray. Chim. 80, 365 (1961); Rec. Trav. Chim. 80, 367 (1961); Electrochim. Acta 10, 773 (1965); J. Membr. BioL 12, 349 (1973); J. Membr. Biol. 51, 1 (1979). 2. Honig, E. P., Hengst, J. H. Th., and Hirsch-Ayalon, P., Ber. Bunsenges. Phys. Chem. 72, 1231 (1968). 3. Katzir-Katchalsky, A., Hirsch-Ayalon, P., and Michaeli, I., Isr. J. Chem. 11, 357 (1973). 4. B~ihr, G., and Hirsch-Ayalon, P., J. Membr. Biol. 51, 405 (1974).
Journal of Colloid and Interface Science, Vol. 104, No. 1, March 1985
5. Flicker, M., and Ross, J., J. Chem. Phys. 60, 3458 (1974). 6. Feeney, R., Schmidt, S. L., Strickholm, P., Chadam, J., and Ortoleva, P., J. Chem. Phys. 78, 1293 (1978). 7. Feinn, D., Ortoleva, P., Scalf, W., Schmidt, S., and Wolff, M., J. Chem. Phys. 69, 27 (1978). 8. MOiler, S. C., Kai, S., and Ross, J., J. Phys. Chem. 86, 4078 (1982). 9. Miiller, S. C., Kai, S., and Ross, J., J. Phys. Chem. 86, 4294 (1982). 10. Feeney, R., Schmidt, S. L., Strickholm, P,, Chadam, J., and Ortoleva, P., J. Chem. Phys. 86, 4294 (1982). 11. Kai, S., Miiller, S. C., and Ross, J., J. Phys. Chem. 87, 806 (1983). 12. Fischer, W. M., Z. Anorg. Chem. 145, 311 (1925). 13. Adair, G. S., Biochem. J. 14, 762 (1920). 14. Hill, A. V., Proc. R. Soc. London Ser. B 104, 39 (1929). 15. Wagner, C., J. ColloidSci. 5, 85 (1950). 16. Hermans, J. J., J. Colloid Sci. 2, 387 (1947). 17. Robinson, R. A., and Stokes, R. H., "Electrolyte Solutions," 2nd ed., Butterworth, London, 1959. 18. Ortmann, R., and Woermann, D., React. Polym. 2, 133 (1984). 19. "Handbook of Chemistry and Physics," B-254, CRC Press, Cleveland, Ohio, 1976. 20. Hengst, J. H. Th., and Honig, E. P., Electrochim. Acta 17, 75 (1972). 21. Nielsen, A. E., "Kinetics of Precipitation," Pergamon, Elmsford, N. Y., 1964. 22. Nielsen, A. E., Acta Chem. Scand. 15, 441 (1961).
It is known that crystalline precipitation zones formed by interdiffusion of two aqueous electrolyte solutions containing ions forming a sparsely soluble precipitate can act as selective barriers (precipitation membrane). They exhibit varying diffusional resistance to different ionic species of the bulk phases. Usually, precipitation membranes are formed within gel plugs separating two solutions containing the precipitate-forming ionic species. The membrane properties are studied by measurements of membrane potentials and current-voltage characteristics. A typical example is the BaSO4 membrane first described and extensively studied by HirschAyalon (1-4). On the other hand, there has been recurrent interest in studies of periodic precipitation patterns within gels in the presence and absence of concentration gradients (5-11). This prompted us to study whether it is possible to generate precipitation mem-
branes in gels in an experimental arrangement similar to that in which periodic precipitation patterns are observed: test tubes filled with a NaESO4 containing a hydrogel (polyacrylamide) are brought into contact with aqueous BaC12 (or SrC12) solutions. Advancing precipRation zones are observed. The thickness of these zones is studied as a function of time. 2. MATERIALS AND METHODS
2.1. Preparation of Polyacrylamide Gel Three aqueous solutions of substances necessary for gel formation are prepared. Solution 1 contains 0.23 cm 3 N,N,N'N'-tetramethylethylenediamine (TEMED) dissolved in 100 cm 3 aqueous Na2SO4 solution. Solution 2 contains 30 g acrylamide and 0.8 g N,N'-methylenebisacrylamide dissolved in 100 cm 3 aqueous Na2SO4 solution; solution 3 contains 8.7 × 10-4 mole (NH4)2S208 (initiator) dissolved in 100 cm 3 aqueous
136 0021-9797/85 $3.00 Copyright© 1985by AcademicPress,Inc. All rightsof reproductionin any form reserved.
Journalof Colloidand InterfaceScience,Vol. 104,No. 1, March 1985
PRECIPITATION
Na2SO4 solution. The concentration of Na2SO4 in the solutions is the salt concentration within the gel after polymerization. The standard solution for the preparation of the gel is a mixture of solution l, solution 2, and water in the ratio 1:2:1. Gel formation is started by mixing equal volumes of the standard solution and solution 3. Air is removed from the mixture by pressure reduction. A syringe is used to fill the test tubes (length: 100 ram, internal diameter: 10 mm) with the reaction mixture. The completely filled test tubes are tightly covered with Parafilm and turned upside down during the polymerization process. Care is taken that no air bubbles are trapped at the phase boundary gel/Parafilm. By this procedure gels with a fairly welldefined surfaces are obtained. The gel has a water content of about 90%.
137
MEMBRANES I
6
I
i
BaCl 2: 0.1 c*
/
No.SO,.:o.osc'(oet) 7 ' 5
/f
4
L
cm
J
3
g
o'
/
z
/d
/ I
0
50
tT
10o
150
mid/2
FIG. 1. Space coordinate ~ o f the front o f the precipitation zone relative to the phase b o u n d a r y g e l / a q u e o u s solution as a function o f time. c' = 0.1c + BaCI2; e" = 0.05e + Na2SO4 (c + = 1 m o l e din-3). Index ' = gel; index " = a q u e o u s solution.
2.2. Precipitation Zones in Gels Test tubes filled with polyacrylamide gel containing NazSO4 at a known concentration (5 × 10-3c+ ~ cs ~ 0.3c+; c + = 1 mole d m -3) are brought into contact with well-stirred aqueous solutions of BaClz (or SrC12) of known composition (BaCI2:5 × 10-3c+ ~< cs ~< 0.3c+; SrClz: 0.5c+ ~< cs ~< 1.1c+) at constant temperature. The test tubes are maintained in a vertical position with the open end facing upward. Three types of experiments it. are carried out: c'~ = c~; c~ < c~, c~~ > c,?! (index ' = gel phase; index " = aqueous phase). At the phase boundary gel/aqueous solution precipitation of BaSO4 (or SrSO4) sets in (BaCI: + Na2SO4 ~ BaSO4(s) + NaC1). The distance between the phase boundary gel/aqueous solution and the front of the advancing precipitation zone within the gel (thickness of precipitation zone) is measured with a cathetometer. A typical result of such measurements is shown in Fig. 1. There is a linear relation between the thickness ~ of the precipitation zone and the square root of the diffusion time t 1/2. It holds for ~/L <~ 0.75 (L = length of the gel plug). The straight line does not pass through the origin. This is due to the uncertainty with which the location of r
the phase boundary gel/solution can be determined. Periodic precipitation patterns are observed with the following concentrations: cs(Na2SO4) = 2 × 10-3c+; cs(BaC12) = 0.1c+ (index ' = gel phase; index " = aqueous phase) (12). 3. R E S U L T S
3.1. Precipitation Zone Assuming (a) that the formation of the precipitate can be represented by the simplified schema A + B ---, AB(s), (b) that the influence of osmotic phenomena (osmotic volume flo "~can be neglected, (c) that species A and B ha,~e the same diffusion coefficients within the gel and that the formation of precipitate AB does not impede the diffusion processes, the concentration profiles of A and B within the gel can be calculated (13-16):
CA=C°(1--erf(z)/K)
for
x~<~
[1]
cB = c°((1 -- erfc(z))/(1 -- K)) for with
x >i ~
[2]
z = x/(2(Dt) u2) and
K = erf((/(2(Dt)U2)) Journal o f Colloid and Interface ~Seience, Vol. 104, No. 1, March 1985
138
REINHARDT, ORTMANN, AND WOERMANN
D = diffusion coefficient, x = space coordinate, ( = length of precipitation zone, err(z) = error function; c° = concentration of species A in the aqueous phase at the phase boundary gel/solution and assumed to be constant during the experiment, c° = concentration of species B within the gel at the phase boundary gel/solution at the beginning of the experiment. It is assumed that far from the front of the advancing precipitation zone the concentration of B still has the value c° (gel phase of infinite length). In this model precipitation occurs only at that point in space at which CA = Ca = 0 (i.e., erf(z) = K). Concentration profiles o f A and B within the gel calculated from Eqs. [1] and [2] for two diffusion times are shown in Fig. 2. At time t the precipitation zone extends from x = 0 to x = 4. The coordinate ~ of the front of the precipitation zone changes in a characteristic way as a function of time (~ = 2a(Dt)m). At the front of the precipitation zone Eq. [3] holds. D(OCA/OX)~ =
--D(OcB/OX)~
[3]
1.0
f
0.5
o
II,II,. I
0.1
0.15
0.2
0.25
0.3
cs/c + FIG. 3. Fraction f of the number of test tubes filled with Na2SO4 gel and brought into contact with a BaCI2 solution in which the precipitation zone has stopped growing as a function of concentration c~. c'(BaC12) = c"(Na2SO4) = cs. Index ' = gel phase; index " = aqueous phase.
This equation together with the known values of c°, c°, and the slope m (=~/t 1/2) of the experimental ~ versus t l/z curve is used to calculate the value of the diffusion coefficient by an iterative procedure. Evaluation of the data shown in Fig. 1 gives a value of D = (7.39 _+- 1.75) × 10-6 cm 2 see -l.
3.2. Precipitation Membrane
If experiments are carded out with equal Calculating the differential coefficients (OCA/ electrolyte concentrations in the gel phase Ox)~ and (OCB/OX)~ from Eqs. [1] and [2] and and in the aqueous phase as a function o f substituting them into Eq. [3] yields concentration cs (cs(BaC12) = cs(Na2SO4) cOA/(C° + C°) = erf(~/(2Dt)l/2)). [41 = Cs; 5 X 10 -3 C+ ~< Cs ~< 0.3c +) it is observed that in a narrow concentration range near cs -~ 0.2c + the growth of the precipitation zone stops after it has reached a thickness of about 0.1 I I I I 3 to 5 mm. The experiments are carded out in groups of ten test tubes filled with gel under identical conditions. The fraction of c--~- 0.05 test tubes in which the precipitation zone CA CB does not grow after the test tubes have been brought into contact with a BaC12 solution is V V I shown in Fig. 3. There is a rather well0 2 ,(, 6 S 10 defined characteristic concentration c* sepaX crn rating the concentration range in which the FIG. 2. Concentration profiles of CA and cB within a precipitation zone grows continuously from gel for two different diffusion times calculated from Eqs. that in which the precipitation zone stops [1] and [2]. Diffusion coefficient D = 10-s cm 2 sec-~; cA growing. A precipitation zone has never been = 0.1c+; cB = 0.05c +. x = space coordinate; ~ , ~2 = space coordinates of the front of the precipitation zone observed to stop growing after its thickness relative to the phase boundary gel/aqueous solution at exceeds a value of about 5 m m ("all or two different diffusion times, t2 > ft. nothing" process). -
Journal of Colloid and Interface Science, VoL 104,No. 1, March 1985
PRECIPITATION MEMBRANES Experiments have also been carried out with Na2SO4-containing gels brought into contact with SrC12 solutions. The results of these experiments are similar to those obtained for the system Na2SO4 (gel)/BaC12 (aq). Only the characteristic concentration c* is higher by a factor of about 5 (BaSO4: Cs* -----0.2C+; SrSO4: Cs* --- 1.0c+). A precipitation zone which has stopped growing acts like a membrane. It exhibits varying diffusional resistance to different ionic species present in the system. This can be seen from measurements of current-voltage curves. To carry out these measurements the bottom part of a test tube containing a precipitation zone which has stopped growing is cut away. The upper part of the test tube with the gel plug is placed between aqueous solutions of BaC12 (or SrC12) and Na2SO4. These solutions have the same concentration as those with which the precipitation zone had been in contact previously. Two current electrodes and two Luggin capillaries (connected to reference electrodes) are introduced. The Luggin capillaries are used to measure the electrical potential difference across the precipitation membrane. One of the capillaries is placed within the gel phase about 5 m m away from the precipitation layer. A typical result for a'BaSO4 membrane is shown in Fig. 4. The curve reflects rectifying properties typical for BaSO4 precipitation membranes (1-4). Furthermore the experiments show that a BaSO4 precipitation membrane exhibits osmotic properties. It is observed that the precipitate-free part of the gel begins to shrink after the BaSO4 (or SrSO4) membranes has been formed. This phenomenon can be understood by taking into account the fact that the osmotic coefficient ~/, of a BaC12 solution is larger than that of an Na2SO4 solution of equal concentration (e.g., cs = 0.2c+: BaC12: qP = 0.84; NazSO4: ~' = 0.75) (17). The volume flow Jv across the precipitation membrane which is expected to be proportional to the osmotic difference 2x~-. A~- is given by A r = R T ( ~ " ~ c 7 - , b ' ~ c ~ ) index' = gel phase; index " = aqueous phase). For the values of
139
mA o
-1 0
500
1 O0 mV
FIG. 4. Current-voltage curve of gel plug containing a BaSO4 membrane. The curve is measured under dynamic conditions. A symmetric scanner is used to vary the electricalcurrent flowingacross the membrane. Current amplitude = +1.25 mA; sweep rate = 500 see for a full triangular period, c~(BaCI2,aq) = c~(Na2SOa,aq) = 0.1c+ (c+ = 1 mole din-3). A4~ = ~b(BaCl2, aq) ~b(NazSO4,aq). A4>o= membrane potential. -
the concentrations and osmotic coefficients given above the volume flow Jv is directed from the gel phase to the aqueous phase. Consequently the gel shrinks. The direction of Jv can be reversed by choosing c's > c~ (c's, c~ > c*). Under these conditions thin tubes (diameter about 0.2 ram) formed by BaSO4 crystallites start to grow out of the precipitation layer into the BaCI2 solution. The volume flow which is directed into the gel phase drives Na2SO4 solution out of the gel phase into the BaCI2 solution. After the "hairs" have reached a length of about 3-5 cm they stop growing. The Na2SO4 solution driven into the BaC12 solution has become dilute by osmotic water flow and does not contain enough material for continued formation of the tube wall. Some of the tubes seem to open up at the upper end and a jet of dilute NazSO4 solution streams into the BaClz solution through the BaSO4 tubes. This jet becomes visible by BaSO4 crystallites formed at the mouth of the jet and suspended in the BaC12 solution. 4. DISCUSSION The properties of the BaSO4 and SrSO4 membranes can be explained by a model Journal of Colloid and Interface Science, Vol. 104, No. 1, March 1985
140
REINHARDT,
ORTMANN,
proposed by Hirsch-Ayalon (1-4). Experimental evidence is accumulating in support of the proposed layered structure in crystalline precipitation membranes (18). Only a precipitation zone which has stopped growing has the properties of a membrane. The concentration range in which the moving precipitation zone stops growing is rather well defined and several orders of magnitude higher than the concentration of saturation (C~at) of the precipitate (BaSO4: - 0.2c+; c~t = 1 X 10-5c+; SrSO4: C~s --- 1.0c+; c~t = 6.2 × 10 -4 C+ (19). The velocity with which the front of a precipitation zone advances decreases slightly (by a factor of about 3 at the most) with increasing electrolyte concentration. However, there is no gradual transition from an advancing precipitation zone to a precipitation zone which has stopped growing. These observations are interpreted in the following way: A precipitation membrane within the gel can only be formed if two requirements are met: (a) There must be available enough BaSO4 (or SrSO4) in the unit volume of the gel to form a layer of densely packed crystallites. (b) The saturation ratio S (=cs/csat) must be large so that a large number of small crystallites per unit volume of the gel are formed after homogeneous nucleation has taken place. Both requirements are met at concentrations above c*. The thickness of a BaSO4 precipitation membrane has an estimated value of I 0 um as an upper limit. It is found experimentally that the mass of BaSO4 forming a membrane is of the order of 1 mg cm -2 corresponding to 4 X 10 -6 mole. At c* (-0.2c +) there are available only 10-7 mole of BaSO4 in a gel layer of 10-urn thickness. But the missing amount of substance can be supplied from the surrounding gel phase by diffusion within minutes at the beginning of the experiment because only then the concentration profiles are steep. (The diffusion flow density is proportional to 1/~.) At the saturation ratio S is large enough so that small crystallites can form, generating a densely packed layer of precipitate (BaSO4: Journal of Colloid and Interface Science, Vol. 104, No. 1, March 1985
AND WOERMANN
c* "" 0.2c +, S = 2 × 104; SrSO4: 6s* "~ 1.0c+, S = 1.6 × 103). The average distance between the crystallites will be smaller than or comparable to the radius of the ion cloud surrounding the crystallites carrying adsorption charges (4). Thus, the layer of precipitate gains the properties of a cation-anion exchange sandwich membrane (4). The divalent co-ions (ionic species having the same sign as that of the adsorption charges) are more effectively expelled from the region with cation and anion exchange properties than monovalent co-ions. This may be one of the reasons that not all sparsely soluble precipitates form precipitation membranes (e.g., silver and lead halides). Hengst and Honig (20) published an electron microscopic photo of a BaSO4 crystallite with dimensions of the order of 30 nm which they had obtained from a BaSO4 precipitation membrane formed in cellophane. They used a solution containing cadmium oxide, ethylenediamine, and water to dissolve the cellophane. However, this procedure raises the question whether the crystallites shown in the electron microscopic photo are really the crystallites which had formed the precipitation membrane. BaSO4 membranes lose their transport properties within minutes by recrystallization and ripening processes if the aqueous solutions containing Ba 2÷ ions and SOl- respectively are removed and replaced by aqueous solutions not containing these ions (18). Another size estimate of BaSO4 crystallites in a precipitation membrane based on X-ray line broadening is given in Ref. (2). A smaller value, 50 nm, is reported. However, it is not stated by which method the crystallites were separated from the membrane matrix (cellophane or hydrogel). Therefore, both findings can represent only an upper limit of the size of the crystallites in a functioning BaSO4 membrane. For a discussion of the threshold concentration ratio ~(SrSO4)/~(BaSO4) ~ 5 we turn to an analysis of supersaturation of these salts in free solution. It is a well-known fact that in free solution high values of the saturation ratio S can be obtained with BaSO4.
141
PRECIPITATION MEMBRANES
The values of S for SrSO4 are smaller (21). by which the characteristic concentrations We want to compare the values of S at which cs of BaSO4 and SrSO4 differ (6~s(SrSO4) instantaneous formation of precipitate begins -~ 5 cs*(BaSO4)). in both systems under comparable conditions. For this purpose equal volumes of equally 5. SUMMARY concentrated solutions of Na2SO4 and BaC12 (or SrC12) solutions are rapidly mixed in a Diffusion of BaCI2 (or SrC12) into a hydrospectral photometric cell (optical path length: gel containing Na2SO4 leads to the formation 1 cm) placed in a spectral photometer at o f a BaSO4 (or SrSO4) precipitation zone. 25°C (mixing time: 0.8 sec). The extinction Under certain conditions this zone acts as a of the solution is measured as a function of membrane, exhibiting osmotic properties and time. The time at which the extinction starts varying diffusional resistance to different ionic to increase due to scattering of the primary species present in the system. Two experilight intensity at the growing crystallites is mental conditions have to be met: (a) There determined. These experiments are carried must be available enough BaSO4 (or SrSO4) out as a function of concentration. For each in the unit volume of the gel to form a layer experiment a new cell is used to avoid con- of densely packed crystallites. (b) The satutamination with crystal seeds. The results of ration ratio of BaSO4 (or SrSO4) in the gel the experiments are shown in Fig. 5. The must be large enough so that a large number concentration of BaSO4 at which the delay of small crystallites per unit volume of the time for the formation of precipitate ap- gel are formed after homogeneous nucleation proaches 1 sec has about the same value as has taken place. This requirement is met at that reported by Nielsen for the onset of concentrations equal to or larger than the homogeneous nucleation (cs ~- 10-2c+; S characteristic concentration c*. The mem= l03) (22). From the data shown in Fig. 5 brane properties are caused by adsorption it can be concluded that the value of super- charges on the surface of the crystallites. The saturation for SrSO4 for the onset of homo- average distance between the crystallites must geneous nucleation is larger by a factor of be smaller than or comparable with the exabout 4. This is about the same factor tension of the counterion cloud of the abI
I
\o
20
%
\ \
\ 1.5 \
_ Baso4
Iog(~ s)
~\ Sr SO4
Ne
1.0
\
x
\ N
\
,.
x \
\\o
"~
\
0.5
o,~, %,., Ba SO4 and _ seeds
~% N
0.0 I
-3.5
-3'.0
\
\\
\ \
g
9
i
-I.0
-0.5
Iog{~-}
FIG. 5. Double logarithmic plot of delay time ~- of onset of turbidity after rapid mixing (mixing time 0.8 sec) of equal concentrated aqueous solutions of Na2SO4 and BaCI2 (or SrCI2) as a function of concentration. The presence of BaSO4 seeds in the solution shortens the delay time considerably. Journal of Colloid and Interface Science, Vol. 104, NO. 1, March 1985
142
REINHARDT, ORTMANN, AND WOERMANN
s o r p t i o n charges. T h e c o u n t e r i o n c l o u d s o f different crystallites m u s t o v e r l a p to p r o d u c e the membrane properties of the precipitation zone. ACKNOWLEDGMENTS Our study of precipitation membranes was started after Dr. P. Hirsch-Ayalon drew our attention to these systems. We thank him for his continued interest in our work. R. Forke had carried out the experiments with SrSO4 gels. U. Ditcher determined the saturation ratio of BaSO4 and SrSO4 in free solution. We thank them for their help. The financial support of the Minister f'dr Wissenschaft und Forschung des Landes NordrheinWestfalen is gratefully acknowledged. REFERENCES 1. Hirsch-Ayalon, P., Chem. Weekblad 52, 557 (1956); Rec. Tray. Chim. 75, 1065 (1956); J. Polym. Sci. 23, 697 (1957); Rec. Tray. Chim. 79, 382 (1960); Rec. Tray. Chim. 80, 365 (1961); Rec. Trav. Chim. 80, 367 (1961); Electrochim. Acta 10, 773 (1965); J. Membr. BioL 12, 349 (1973); J. Membr. Biol. 51, 1 (1979). 2. Honig, E. P., Hengst, J. H. Th., and Hirsch-Ayalon, P., Ber. Bunsenges. Phys. Chem. 72, 1231 (1968). 3. Katzir-Katchalsky, A., Hirsch-Ayalon, P., and Michaeli, I., Isr. J. Chem. 11, 357 (1973). 4. B~ihr, G., and Hirsch-Ayalon, P., J. Membr. Biol. 51, 405 (1974).
Journal of Colloid and Interface Science, Vol. 104, No. 1, March 1985
5. Flicker, M., and Ross, J., J. Chem. Phys. 60, 3458 (1974). 6. Feeney, R., Schmidt, S. L., Strickholm, P., Chadam, J., and Ortoleva, P., J. Chem. Phys. 78, 1293 (1978). 7. Feinn, D., Ortoleva, P., Scalf, W., Schmidt, S., and Wolff, M., J. Chem. Phys. 69, 27 (1978). 8. MOiler, S. C., Kai, S., and Ross, J., J. Phys. Chem. 86, 4078 (1982). 9. Miiller, S. C., Kai, S., and Ross, J., J. Phys. Chem. 86, 4294 (1982). 10. Feeney, R., Schmidt, S. L., Strickholm, P,, Chadam, J., and Ortoleva, P., J. Chem. Phys. 86, 4294 (1982). 11. Kai, S., Miiller, S. C., and Ross, J., J. Phys. Chem. 87, 806 (1983). 12. Fischer, W. M., Z. Anorg. Chem. 145, 311 (1925). 13. Adair, G. S., Biochem. J. 14, 762 (1920). 14. Hill, A. V., Proc. R. Soc. London Ser. B 104, 39 (1929). 15. Wagner, C., J. ColloidSci. 5, 85 (1950). 16. Hermans, J. J., J. Colloid Sci. 2, 387 (1947). 17. Robinson, R. A., and Stokes, R. H., "Electrolyte Solutions," 2nd ed., Butterworth, London, 1959. 18. Ortmann, R., and Woermann, D., React. Polym. 2, 133 (1984). 19. "Handbook of Chemistry and Physics," B-254, CRC Press, Cleveland, Ohio, 1976. 20. Hengst, J. H. Th., and Honig, E. P., Electrochim. Acta 17, 75 (1972). 21. Nielsen, A. E., "Kinetics of Precipitation," Pergamon, Elmsford, N. Y., 1964. 22. Nielsen, A. E., Acta Chem. Scand. 15, 441 (1961).