- Email: [email protected]
Critical demicellization concentration as determined by kinetic dialysis
Critical Demicellization Concentration as Determined by Kinetic Dialysis MATTHEW LAKE Wright State University, Dayton, Ohio 45435 Received M a r c h 22, 1982; accepted J u n e 28, 1982 T h e s o d i u m decanoate-perfluorooctanoate m i x e d micelle system was e x a m i n e d for the existence of a critical demicellization concentration. Using kinetic dialysis to follow the m o n o m e r concentration a n d hence the C M C o f decanoate, a plot o f C M C vs mole fraction was constructed. A single point exists at which the micelles o f decanoate disappear at about a 1:1 ratio o f perfluoro to hydrocarbon surfactant. INTRODUCTION
The concept of a critical demicellization concentration (CDC) existing when two surfactants having a limited mutual solubility, e.g., a hydrocarbon and a perfluorocarbon are mixed was given theoretical treatment in a recent article by Mysels (1). The criterion for such a phenomenon is that below the CDC, micelles exist while above only the corresponding monomer is present. The theoretical treatment by Mysels assumes that micelle formation can be described by mathematics that apply to phase separation and a hypothetical phase diagram was constructed relating total concentration to mole fraction. The purpose of the present study is to investigate the use of kinetic dialysis as a means to detect the CDC in a perfluorocarbon-hydrocarbon surfactant mixture. Kinetic dialysis involves the measurement of the amount of surfactant that diffuses through a dialysis membrane at two different time intervals. From this knowledge the original concentration of monomer can be calculated by use of the dialysis equation (2). Since only the monomer diffuses through the membrane and not the micelle, the calculated concentration of monomer originally present is equivalent to the CMC. This method is dependent on the micelle being
thermodynamically stable (3, 4) so that the small amount of monomer that diffuses through the membrane (about 20% of the total monomer content) is not replenished by the dissociation of the micelle during the short time of dialysis. In the present study various mole fractions of two surfactants--one a hydrocarbon and one a perfluorocarbon--are dialyzed to follow the monomer concentration of one surfactant to see if the CDC is observed. METHODS AND MATERIALS
Decanoic acid M.P. 29-30°C was weighed out to give a stock solution containing 0.02 g/ml of sodium decanoate after neutralization of the acid with an equivalent amount of NaOH. The acid was added to a 500-ml beaker with 400 ml of deionized water. The required amount of NaOH for neutralization was added and the solution was heated with stirring. After dissolution, the pH of the solution was adjusted to 9.2 with dilute HC1 or NaOH. The solution was transferred to a 500-ml volumetric flask and diluted to volume. To aliquots of this solution were added the appropriate amounts of sodium perfluorooctanoate and deionized water to bring the volume up to 200 ml. The pH was adjusted to pH 9.2 with dilute NaOH and the solution was transferred to a 250-ml volumetric flask
496 0021-9797/83/020496-04503.00/0 Copyright© 1983by AcademicPress,Inc. All fightsof reproductionin any form reserved.
Journal of Colloid and Interface Science, Vol. 91, No. 2, February 1983
CMC BY KINETIC DIALYSIS TABLE I Concentration of Soaps for Various Mole Fractions at 1/4 CMC Value Mole fraction
Decanoate a
Perfluorooctanoate a
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20
0.25 0.46 0.68 0.91 1.13 1.35 1.59 1.80
a The concentrations are in g/250 ml and the total number of moles at each mole fraction is 5.2 mmoles.
and diluted to volume. The solutions were allowed to equilibrate over night before dialysis. Table I illustrates the amount of soaps added to attain 1/4 the CMC of sodium decanoate. Multiples of these concentrations were made to give 1/2, 3/4, and 1 times the CMC concentration of pure decanoate.
1. Dialysis of Soap Solutions An inexpensive dialysis cell was made by taking two acrylate plastic blocks 15.3 cm square by 1.3 cm thick and machining out a circular cavity in the middle of each block with a diameter 12.6 cm and 0.9 cm deep. A 4-ram hole was drilled into the cavity of each block at the top for filling. A small hole was drilled into the bottom of each cell leading to the outside and a plastic nipple 3 mm o.d. was cemented into the block to allow for drainage. A short piece of rubber tubing and pinch clamp was connected to the outside of the nipple for regulation of drainage. Two round rubber seals were cut from an apron with an inside diameter 12.7 cm and an outside diameter of 15.3 cm. The gaskets were greased on both sides with silicone grease and placed over the cavity of each cell. Spectrapor #2 dialysis tubing, 100 mm in width and 16 cm long was cut, soaked in deionized water, and opened up to cover the cavity. The two blocks were placed so that the membrane was
497
between each block and fastened together by "C" clamps. Thin wood strips were used on each side of the plastic to protect the plastic from the force of the clamps. One side was filled with 100 ml of soap solution using a 50-ml syringe and the other side was filled with 100 ml ofdeionized water pH 9.2. A different 50-ml syringe was used to prevent contamination and a small 2-mm plastic tubing attached to the syringe facilitated the filling. The bottom drain on each cell was kept clamped offat the time offiUing. Also, care must be taken to introduce the soap solution at the bottom of the cell to prevent soap bubble formation. This prevents the proper agitation of the solution during shaking. A piece of tape was used to cover the small filling holes and the unit was clamped to a ring stand and placed on a platform shaker and shaken vigorously for 15 minutes. At the end of the dialysis time the dialyzate was drained into a 150-ml beaker and titrated immediately with 0.05 N HC1 to a pH of 4.25. The dialyzed soap solution was drained from the cell and discarded. A fresh 100 ml of soap solution was added to the same side of the dialysis cell as before and 100 ml of deionized water pH 9.2 was added to the opposite side. The dialysis was continued as before with shaking for 30 minutes. At the end of the dialysis the cell was drained and the dialyzate was titrated as before. The dialysis was performed at room temperature at 20°C.
2. Determination of the CMC of Sodium Decanoate The procedure described above was used on the stock solution of sodium decanoate containing 0.02 g/ml. The amount of soap dialyzing through was calculated by first subtracting the amount of acid required to titrate a blank consisting of 100 ml of deionized water pH 9.2 from the volume of acid used to titrate the two dialyzates. The soap then was calculated as follows: Journal of Colloid and Interface Science, Vol. 91, No. 2, February 1983
498
MATTHEW LAKE
soap in g/100 ml = (ml titrant - Bk) × normality of HC1 × 0.194. The following dialysis equation was used to calculate the CMC: a2
CMC (g/100 ml) - - a - b/2 ' where a = amount of soap dialyzing through in 15' and b = amount of soap in 30'. Table II represents a typical analysis with the value of the CMC determined by dialysis compared to the literature. 3. Determination of the CMC of Sodium Decanoate in the Mixed System The above procedure was repeated using the various mole fraction and concentrations of the perfluoroctanoate;-decanoate system using duplicate determination for each point. The decanoate can be determined in the presence of sodium perfluorooctonate that concomitantly dialyzes through due to the low pKa of perfluorooctanoic acid. The results of these determinations are illustrated in Table III, which includes the total decanoate concentration with the corresponding monomer concentration at equilibrium. Figure 1 is a plot of CMC vs the mole fraction. 4. Determination of the Stability of the Mixed Micelle A 50:50 dilution was made with deionized water pH 9.2 on the 0.8 mole fraction at 3/4 the CMC level and dialyzed immediately. TABLE II CMC Value for Sodium Decanoate as Determined by Dialysis Soap dialyzing through in 15' = Soap dialyzing through in 30' = CMC as determined by dialysis Literature value a
0.1694 g/100 ml 0.3082 g/100 ml 9.6 X 10-2 M at 20°C 9.6 X 10-2 M at 20°C
a Mukerjee, P., and Mysels, K. J., "Critical Micelle Concentrations of Aqueous Surfactant Systems," U. S. Department of Commerce National Bureau of Standards NSRDS-NBS 36. Journal of Colloid and Interface Science, Vol. 91, No. 2, February 1983
TABLE III CMC of Various Mole Fractions of Decanoate Mole fractions
1/4 CMC
1/2 CMC
3/4 CMC
CMC
0.9 ~ 0.9 b 0.8" 0.8 b 0.7 a 0.7 b 0.6 ~ 0.6 b 0.5 a 0.5 b 0.4 a 0.4 b 0.3 a 0.3 b 0.2 a 0.2 b
0.36 0.38 0.32 0.16 0.28 0.20 0.24 0.18 0.20 0.15 0.16 0.14 0.12 0.07 0.08 0.08
0.72 0.67 0.64 0.37 0.56
1.08 0.73 0.96 0.48 0.74 0.34 0.72 0.34 0.60 0.42 0.48 0.24 0.36 0.14 0.24 0.10
1.44 0.81 1.28 0.71 1.12 0.76 0.96 0.94 0.80 0.47 0.64 0.46 0.48 0.26 0.32 0.15
0.48 0.21 0.40 0.24 0.32 0.14 0.24 0.13 0.16 0.06
a Total concentration of sodium decanoate in g/100 ml. b Concentration of m o n o m e r or CMC in g/100 ml.
The monomer concentration was determined as before. RESULTS
The results are shown in Tables II, III, and Fig. 1. DISCUSSION
The CMC value of sodium decanoate as determined by kinetic dialysis agreed very well with the literature value as shown in Table II. The question of whether the miceUe remains intact during the dialysis time period, so that monomer that is depleted is not replaced by dissociation of the micelle, was answered by the last experiment. The value after diluting 50:50 was 1/2 the undiluted value for the 0.8 mole fraction at 3/4 the CMC concentration, i.e., 0.23. If dissocation of the micelle were appreciable the value would have been higher. The results summarized in Fig. 1 do not fit the phase diagram as outlined in Mysels' paper. Rather than a single CMC value at
499
CMC BY KINETIC DIALYSIS 1.0
.9 d ¢
.1
b
.6
.4 .3 .2 .1 I
A
i
~
i
i
MOLEFRACTIONOF B
i
i
B
FIG. 1. Plots of CMS against the mole fractions. Curve a = 1/4 CMC value of decanoate, b = 1/2 CMC, c = 3/4 CMC, and d = full CMC. B is the perfluoro soap.
each mole fraction and concentration the CMC varied according to the concentration. Also, rather than a gradual decline in the CMC as the mole fraction of B is increased, there was a dramatic drop at the first addition of perfluorooctanoate to decanoate. The higher the concentration the higher the CMC, maximizing at 0.6 mole fraction of A. This is the same mole fraction that the ionic fluorocarbon-hydrocarbon system studied by Funasaki and Hada had as its maximum in a similar plot of CMC versus mole fraction (5). The point at the maximum in Fig. 1, curve d corresponds to the disappearance of micelles of sodium decanoate inasmuch as the monomer concentration is identical to the total concentration of decanoate (0.94 vs 0.96). This, then, would correspond to the CDC. As to why the data from Table III plotted in Fig. 1 does not show obedience to the hypothetical phase diagram of Mysels is open to question. It would seem that the CMC concentration dependency would imply a mass action principle operative. The limited
solubility of each monomer for the other could result in a mixed micelle that is thermodynamically less stable and hence dissociates more extensively at a 1:1 mole ratio. Thus, as the total soap concentration is increased the monomer concentration would increase resulting in a higher CMC. As the ratio of perfluoro soap to hydrocarbon increases a point is reached at about a 1:1 ratio at which the mixed micelle is so loosely associated that only monomer exists; hence the CDC. Further increase of perfluoro soap acts to adsorb the hydrocarbon soap resulting in the CMC of the decanoate being lowered. It would have been helpful to follow the concentration of the pedluoro soap during the dialysis but unfortunately no reproducible method for the concurrent determination of this compound could be developed. SUMMARY
The novel method of kinetic dialysis has been used to determine the CMC of sodium decanoate and follow the behavior of this soap in the presence of a perfluoro soap at various concentration and mole fractions. The CDC has been found to occur at a specific concentration and mole fraction. ACKNOWLEDGMENT Thanks are due to Dr. David J. Karl for reading the manuscript and helpful assistance during the study. REFERENCES 1. Mysels, K. J., J. Colloid Interface Sci. 66, 331 (1978). 2. Lake, M., and Rappaport, G., Rubber Chem. TechnoL 53, No. 4, 1006 (1980). 3. Ben-Naim, Arieh, "Hydrophobic Interactions," p. 171. Plenum, New York/London, 1980. 4. Kegeles, G., J. ColloidlnterfaceSci. 73, 274 (1980). 5. Funasald, N., and Hada, S., £ Colloid Interface Sci. 78, 376 (1980).
Journal of Colloid and Interface Science,
V o l . 9 1 , N o . 2, F e b r u a r y
1983
The concept of a critical demicellization concentration (CDC) existing when two surfactants having a limited mutual solubility, e.g., a hydrocarbon and a perfluorocarbon are mixed was given theoretical treatment in a recent article by Mysels (1). The criterion for such a phenomenon is that below the CDC, micelles exist while above only the corresponding monomer is present. The theoretical treatment by Mysels assumes that micelle formation can be described by mathematics that apply to phase separation and a hypothetical phase diagram was constructed relating total concentration to mole fraction. The purpose of the present study is to investigate the use of kinetic dialysis as a means to detect the CDC in a perfluorocarbon-hydrocarbon surfactant mixture. Kinetic dialysis involves the measurement of the amount of surfactant that diffuses through a dialysis membrane at two different time intervals. From this knowledge the original concentration of monomer can be calculated by use of the dialysis equation (2). Since only the monomer diffuses through the membrane and not the micelle, the calculated concentration of monomer originally present is equivalent to the CMC. This method is dependent on the micelle being
thermodynamically stable (3, 4) so that the small amount of monomer that diffuses through the membrane (about 20% of the total monomer content) is not replenished by the dissociation of the micelle during the short time of dialysis. In the present study various mole fractions of two surfactants--one a hydrocarbon and one a perfluorocarbon--are dialyzed to follow the monomer concentration of one surfactant to see if the CDC is observed. METHODS AND MATERIALS
Decanoic acid M.P. 29-30°C was weighed out to give a stock solution containing 0.02 g/ml of sodium decanoate after neutralization of the acid with an equivalent amount of NaOH. The acid was added to a 500-ml beaker with 400 ml of deionized water. The required amount of NaOH for neutralization was added and the solution was heated with stirring. After dissolution, the pH of the solution was adjusted to 9.2 with dilute HC1 or NaOH. The solution was transferred to a 500-ml volumetric flask and diluted to volume. To aliquots of this solution were added the appropriate amounts of sodium perfluorooctanoate and deionized water to bring the volume up to 200 ml. The pH was adjusted to pH 9.2 with dilute NaOH and the solution was transferred to a 250-ml volumetric flask
496 0021-9797/83/020496-04503.00/0 Copyright© 1983by AcademicPress,Inc. All fightsof reproductionin any form reserved.
Journal of Colloid and Interface Science, Vol. 91, No. 2, February 1983
CMC BY KINETIC DIALYSIS TABLE I Concentration of Soaps for Various Mole Fractions at 1/4 CMC Value Mole fraction
Decanoate a
Perfluorooctanoate a
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20
0.25 0.46 0.68 0.91 1.13 1.35 1.59 1.80
a The concentrations are in g/250 ml and the total number of moles at each mole fraction is 5.2 mmoles.
and diluted to volume. The solutions were allowed to equilibrate over night before dialysis. Table I illustrates the amount of soaps added to attain 1/4 the CMC of sodium decanoate. Multiples of these concentrations were made to give 1/2, 3/4, and 1 times the CMC concentration of pure decanoate.
1. Dialysis of Soap Solutions An inexpensive dialysis cell was made by taking two acrylate plastic blocks 15.3 cm square by 1.3 cm thick and machining out a circular cavity in the middle of each block with a diameter 12.6 cm and 0.9 cm deep. A 4-ram hole was drilled into the cavity of each block at the top for filling. A small hole was drilled into the bottom of each cell leading to the outside and a plastic nipple 3 mm o.d. was cemented into the block to allow for drainage. A short piece of rubber tubing and pinch clamp was connected to the outside of the nipple for regulation of drainage. Two round rubber seals were cut from an apron with an inside diameter 12.7 cm and an outside diameter of 15.3 cm. The gaskets were greased on both sides with silicone grease and placed over the cavity of each cell. Spectrapor #2 dialysis tubing, 100 mm in width and 16 cm long was cut, soaked in deionized water, and opened up to cover the cavity. The two blocks were placed so that the membrane was
497
between each block and fastened together by "C" clamps. Thin wood strips were used on each side of the plastic to protect the plastic from the force of the clamps. One side was filled with 100 ml of soap solution using a 50-ml syringe and the other side was filled with 100 ml ofdeionized water pH 9.2. A different 50-ml syringe was used to prevent contamination and a small 2-mm plastic tubing attached to the syringe facilitated the filling. The bottom drain on each cell was kept clamped offat the time offiUing. Also, care must be taken to introduce the soap solution at the bottom of the cell to prevent soap bubble formation. This prevents the proper agitation of the solution during shaking. A piece of tape was used to cover the small filling holes and the unit was clamped to a ring stand and placed on a platform shaker and shaken vigorously for 15 minutes. At the end of the dialysis time the dialyzate was drained into a 150-ml beaker and titrated immediately with 0.05 N HC1 to a pH of 4.25. The dialyzed soap solution was drained from the cell and discarded. A fresh 100 ml of soap solution was added to the same side of the dialysis cell as before and 100 ml of deionized water pH 9.2 was added to the opposite side. The dialysis was continued as before with shaking for 30 minutes. At the end of the dialysis the cell was drained and the dialyzate was titrated as before. The dialysis was performed at room temperature at 20°C.
2. Determination of the CMC of Sodium Decanoate The procedure described above was used on the stock solution of sodium decanoate containing 0.02 g/ml. The amount of soap dialyzing through was calculated by first subtracting the amount of acid required to titrate a blank consisting of 100 ml of deionized water pH 9.2 from the volume of acid used to titrate the two dialyzates. The soap then was calculated as follows: Journal of Colloid and Interface Science, Vol. 91, No. 2, February 1983
498
MATTHEW LAKE
soap in g/100 ml = (ml titrant - Bk) × normality of HC1 × 0.194. The following dialysis equation was used to calculate the CMC: a2
CMC (g/100 ml) - - a - b/2 ' where a = amount of soap dialyzing through in 15' and b = amount of soap in 30'. Table II represents a typical analysis with the value of the CMC determined by dialysis compared to the literature. 3. Determination of the CMC of Sodium Decanoate in the Mixed System The above procedure was repeated using the various mole fraction and concentrations of the perfluoroctanoate;-decanoate system using duplicate determination for each point. The decanoate can be determined in the presence of sodium perfluorooctonate that concomitantly dialyzes through due to the low pKa of perfluorooctanoic acid. The results of these determinations are illustrated in Table III, which includes the total decanoate concentration with the corresponding monomer concentration at equilibrium. Figure 1 is a plot of CMC vs the mole fraction. 4. Determination of the Stability of the Mixed Micelle A 50:50 dilution was made with deionized water pH 9.2 on the 0.8 mole fraction at 3/4 the CMC level and dialyzed immediately. TABLE II CMC Value for Sodium Decanoate as Determined by Dialysis Soap dialyzing through in 15' = Soap dialyzing through in 30' = CMC as determined by dialysis Literature value a
0.1694 g/100 ml 0.3082 g/100 ml 9.6 X 10-2 M at 20°C 9.6 X 10-2 M at 20°C
a Mukerjee, P., and Mysels, K. J., "Critical Micelle Concentrations of Aqueous Surfactant Systems," U. S. Department of Commerce National Bureau of Standards NSRDS-NBS 36. Journal of Colloid and Interface Science, Vol. 91, No. 2, February 1983
TABLE III CMC of Various Mole Fractions of Decanoate Mole fractions
1/4 CMC
1/2 CMC
3/4 CMC
CMC
0.9 ~ 0.9 b 0.8" 0.8 b 0.7 a 0.7 b 0.6 ~ 0.6 b 0.5 a 0.5 b 0.4 a 0.4 b 0.3 a 0.3 b 0.2 a 0.2 b
0.36 0.38 0.32 0.16 0.28 0.20 0.24 0.18 0.20 0.15 0.16 0.14 0.12 0.07 0.08 0.08
0.72 0.67 0.64 0.37 0.56
1.08 0.73 0.96 0.48 0.74 0.34 0.72 0.34 0.60 0.42 0.48 0.24 0.36 0.14 0.24 0.10
1.44 0.81 1.28 0.71 1.12 0.76 0.96 0.94 0.80 0.47 0.64 0.46 0.48 0.26 0.32 0.15
0.48 0.21 0.40 0.24 0.32 0.14 0.24 0.13 0.16 0.06
a Total concentration of sodium decanoate in g/100 ml. b Concentration of m o n o m e r or CMC in g/100 ml.
The monomer concentration was determined as before. RESULTS
The results are shown in Tables II, III, and Fig. 1. DISCUSSION
The CMC value of sodium decanoate as determined by kinetic dialysis agreed very well with the literature value as shown in Table II. The question of whether the miceUe remains intact during the dialysis time period, so that monomer that is depleted is not replaced by dissociation of the micelle, was answered by the last experiment. The value after diluting 50:50 was 1/2 the undiluted value for the 0.8 mole fraction at 3/4 the CMC concentration, i.e., 0.23. If dissocation of the micelle were appreciable the value would have been higher. The results summarized in Fig. 1 do not fit the phase diagram as outlined in Mysels' paper. Rather than a single CMC value at
499
CMC BY KINETIC DIALYSIS 1.0
.9 d ¢
.1
b
.6
.4 .3 .2 .1 I
A
i
~
i
i
MOLEFRACTIONOF B
i
i
B
FIG. 1. Plots of CMS against the mole fractions. Curve a = 1/4 CMC value of decanoate, b = 1/2 CMC, c = 3/4 CMC, and d = full CMC. B is the perfluoro soap.
each mole fraction and concentration the CMC varied according to the concentration. Also, rather than a gradual decline in the CMC as the mole fraction of B is increased, there was a dramatic drop at the first addition of perfluorooctanoate to decanoate. The higher the concentration the higher the CMC, maximizing at 0.6 mole fraction of A. This is the same mole fraction that the ionic fluorocarbon-hydrocarbon system studied by Funasaki and Hada had as its maximum in a similar plot of CMC versus mole fraction (5). The point at the maximum in Fig. 1, curve d corresponds to the disappearance of micelles of sodium decanoate inasmuch as the monomer concentration is identical to the total concentration of decanoate (0.94 vs 0.96). This, then, would correspond to the CDC. As to why the data from Table III plotted in Fig. 1 does not show obedience to the hypothetical phase diagram of Mysels is open to question. It would seem that the CMC concentration dependency would imply a mass action principle operative. The limited
solubility of each monomer for the other could result in a mixed micelle that is thermodynamically less stable and hence dissociates more extensively at a 1:1 mole ratio. Thus, as the total soap concentration is increased the monomer concentration would increase resulting in a higher CMC. As the ratio of perfluoro soap to hydrocarbon increases a point is reached at about a 1:1 ratio at which the mixed micelle is so loosely associated that only monomer exists; hence the CDC. Further increase of perfluoro soap acts to adsorb the hydrocarbon soap resulting in the CMC of the decanoate being lowered. It would have been helpful to follow the concentration of the pedluoro soap during the dialysis but unfortunately no reproducible method for the concurrent determination of this compound could be developed. SUMMARY
The novel method of kinetic dialysis has been used to determine the CMC of sodium decanoate and follow the behavior of this soap in the presence of a perfluoro soap at various concentration and mole fractions. The CDC has been found to occur at a specific concentration and mole fraction. ACKNOWLEDGMENT Thanks are due to Dr. David J. Karl for reading the manuscript and helpful assistance during the study. REFERENCES 1. Mysels, K. J., J. Colloid Interface Sci. 66, 331 (1978). 2. Lake, M., and Rappaport, G., Rubber Chem. TechnoL 53, No. 4, 1006 (1980). 3. Ben-Naim, Arieh, "Hydrophobic Interactions," p. 171. Plenum, New York/London, 1980. 4. Kegeles, G., J. ColloidlnterfaceSci. 73, 274 (1980). 5. Funasald, N., and Hada, S., £ Colloid Interface Sci. 78, 376 (1980).
Journal of Colloid and Interface Science,
V o l . 9 1 , N o . 2, F e b r u a r y
1983