4380
J. Phys. Chem. B 2001, 105, 4380-4385
Comparison of the DSC Curves Obtained for Aqueous Solutions of Nonionic and Ionic Surfactants Gordon C. Kresheck Department of Chemistry, UniVersity of Colorado at Colorado Springs, Colorado Springs, Colorado 80933-7150 ReceiVed: October 31, 2000; In Final Form: January 3, 2001
An interpretation of the differential scanning calorimetry (DSC) curves that were obtained for aqueous solutions of three nonionic surfactants, n-C8DPO, -C9DPO, and -C10DPO, was recently reported (Kresheck, G. C. Langmuir 2000, 16, 3067) and reanalyzed. These investigations have now been extended to include three cationic, DTAB, TTAB, and DPB, and one anionic, SDecS, surfactants. The curves obtained for the ionic surfactants exhibited the same pattern as for the nonionic surfactants. Below the critical micelle concentration, cmc, the heat capacity of the solutions gradually decreased and did not exhibit any systematic variation within the limits of experimental error (( 0.2 mcal/deg). Solutions which were 2-3 times more concentrated than the cmc exhibited curvature that resembled the temperature dependence of the cmc. However, studies with solutions of intermediate concentrations produced curves with either distinct maxima, minima, or both. These slope changes all occurred at temperatures where the cmc became equal to that of the concentration of surfactant in the cell. All of the heating curves were reversible and independent of scan rate. A small change in the shape of the DSC curves at surfactant concentrations well above the cmc may result from micellar growth. A simple two-state model that was used to describe the data for nonionic surfactants could also be used to describe similar data for ionic surfactants.
Introduction It has recently been shown1 that the contribution of the solute to the total enthalpy of a surfactant solution, which is more concentrated than the critical micelle concentration (cmc), can be modeled in such a manner so as to reflect the relative contributions of the monomeric and micellar states to the heat capacity of the solution. The latter can be studied by modern, highly sensitive, differential scanning calorimetry (DSC). Our previous data up to 79 °C with three nonionic surfactants were described by this method. However, a simple modification of this model provided a means to extend our analysis for data up to 107 °C for the same surfactants. We also show that it is possible to describe DSC data for one anionic and three cationic surfactants by this method as well. Unfortunately, not all of the parameters are independent, including the change in heat capacity that accompanies micelle formation. Once the heat capacity is known or assumed, however, it is possible to estimate it’s temperature dependence from the DSC data. Values for this quantity which accompany micelle formation have only been reported in a few cases.1-5 Such information is of interest when modeling thermodynamic properties of various processes in solution, especially those involving hydrophobic interactions. It is the goal of this research to provide further estimates of how the heat capacity change that accompanies micelle formation varies with temperature for ionic as well as nonionic surfactants. Finally, it is possible to describe the temperature dependence of the cmc, if it is known at one reference temperature, using data derived from the DSC curves as previously reported.1 Experimental Section All of the surfactants used in this investigation were obtained from commercial sources and were used without purification.
The three alkyldimethylphosphine oxides, n-C8DPO, -C9DPO, and -C10DPO (APO8, APO9, and APO10) were obtained from BioAffinity Systems (Rockford, IL). The dodecyl- and tetradecyltrimethylammonium bromides (DTAB and TTAB) were obtained from Sigma Chemical Co. Sodium decyl sulfate (SDecS) was acquired from Mann Research Labs. and dodecylpyridinium bromide (DPB) was purchased from K & K Laboratories, Inc. Solutions were freshly prepared by mass using deionized distilled water. The DSC studies were carried out with a MC-2 differential scanning calorimeter (MicroCal, Amherst, MA) which was interfaced to a Gateway P55C-166 computer. Data were normally collected at between 20 and 107 °C at a scanning nominal rate of 90 °C/h, since no dependence on scanning rate was observed for scans at either10 or 90 °C/h. Repetitive scans of samples that were cooled within the cells and rerun were reproducible within an estimated precision of (5 µcal/min. The reference cell was filled with distilled water for all of these studies. A water-water calibration scan was subtracted from each recorded differential scan produced by each surfactant solution. An electrical pulse of 5 mcal/min was administered for 6 min periodically to verify the calibration of the instrument. Corrections were made for the influence of the change in molarity that occurs as the temperature is raised due to expansion of water as previously described1. The cell volume was 1.235 mL, and reported by MicroCal to not change over the temperature range of the apparatus. A steady pressure of about 2 atm was maintained on top of the cell unit by the means of an attached nitrogen tank. Data analysis and curve fitting were performed using the Origin software provided by MicroCal.
10.1021/jp004022j CCC: $20.00 © 2001 American Chemical Society Published on Web 04/20/2001
Nonionic and Ionic Surfactants
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4381
Theoretical Section We have previously shown that the temperature dependence of the heat capacity of aqueous nonionic surfactant solutions reflects the shift between the monomer and micellar states.1 An empirical second degree equation with coefficients a, b, and c was used to represent the temperature dependence of the monomer concentration M1 between 20 and 79 °C. This concentration was assumed to be equal to the cmc whenever the total surfactant concentration of the solution exceeded the cmc, so that
M1 ) a + bT + cT2
(1)
The resulting equation, eq 2, relates the differential heat capacity of the solution, (cal/C),7 cell volume, V, molarity of the solution, M, partial molar heat capacity of the surfactant in the micellar state, Cp2, and heat capacity change for micelle formation, -∆Cp, as
cp/V - MCp2 ) [(b2/2c + a) ∆Cp] + [3b∆Cp] T + [3c∆Cp]T2 (2) If a reference temperature, Tr, is chosen such that ∆H ) zero when T ) Tr, then ∆Cp ) ∆Cpr, and a more general equation is obtained1
cp/V - MCp2 ) (b + 2cT)[(∆Cpr - B′Tr)(T - Tr) + 2
2
This equation includes a coefficient, B′, which accounts for the temperature dependence of the heat capacity and is defined by the relationship, ∆Cp ) ∆Cpr - B′(T - Tr). The values for B′ and ∆Cpr may then used to describe the temperature dependence of the cmc.1,2,4,5 The value of Tr is found to be equal to -b/2c after fitting to eq 2. One problem with the use of eq 2 for curve fitting that we have not solved is that the form of this equation requires that a value of ∆Cp must be known, or assumed, to find the empirical parameters. However, the ratio -b/2c, and hence Tr, does not depend on the value used for ∆Cp. Some of the data that were obtained for ionic surfactants could be described by eq 2 or 3. However, this was not true for all of the data and a third degree representation of eq 1 was required. This was also necessary in order to extend our data analysis for the nonionic surfactants above 79° C. Therefore, eq 1 was expanded to include an additional term so that
M1 ) A + BT + CT2 + DT3
surfactant SDecS DPB DTAB TTAB APO8 APO9 APO10
(4)
With this modification, Tr is equal to (-2C - (4C2 - 12BD)1/2)/ 6D. To reduce the number of parameters used for curve fitting, B was replaced by -2CTr - 3DTr2, and eq 2 is simplified to
cp/V - MCp2 ) [(-2CTr - 3DTr2) + 2CT+ 3DT2] × [∆Cp(T - Tr)]+ [∆Cp(A + (-2CTr - 3DTr )T + 2
CT2 + DT3)] (5) Accordingly, eq 3 becomes
cp/V - MCp2 ) [(-2CTr - 3DTr2) + 2CT + 3DT2] × [∆Cpr + B′(T - Tr)](T - Tr)+ [(∆Cpr + B′(T - Tr)] × [A + (-2CTr - 3DTr2)T + CT2 + DT3)] (6) The value of Tr that is obtained from fitting the data to eq 5
concentration (mM)
Tr (K)
∆Cp (cal/mol K)a
B′ (cal/mol K2)
150 100 100 60 100 60 100 50 25 100 60 40 30 50 20
303 303 288 288 294 294 288 288 288 332 335 326 326 313 315
-100(9) -100 -76(10) -76 -101(11) -101 -120(12) -120 -120 -66(5) -66 -80(5) -80 -108(5) -108
0.28 ( 0.03 0.25 ( 0.02 0.11 ( 0.01 0.14 ( 0.01 0.082 ( 0.01 0.089 ( 0.01 -0.04 ( 0.02 -0.14 ( 0.02 0.14 ( 0.02 0.034 ( 0.03 0.044 ( 0.04 0.013 ( 0.02 0.024 ( 0.06 -0.013 ( 0.01 -0.002 ( 0.02
a All of the values of ∆Cp were obtained by calorimetry from the references given in parentheses.
TABLE 2: Comparison of the Values Obtained for the Heat of Micelle Formation at 25 °C for Several Surfactants Obtained by Calorimetry or from the Temperature Dependence of the cmc ∆Hm (cal/mol) surfactant
reference
calorimetry
ref
310 ( 30
12
DPB
-1130 ( 70
12
DTAB
-280 ( 700
12
TTAB
-1250 ( 200
6
APO8
2400 ( 330
5
APO9
2100 ( 200
5
APO10
2043 ( 70
5
420 ( 20 500 ( 1 -830 ( 70 -750 ( 1 -333 ( 22 -558 ( 12 -400 ( 1 -1200 ( 7 -1166 ( 6 2526 ( 4 2400 ( 100 2086 ( 4 2460 ( 1 2321 ( 5 1700 ( 110
9 this study 10 this study 11 12 this study this study 12 5 this study 5 this study 5 this study
SDecS
B′/2 (T - Tr )] +(a + bT + cT ) (∆Cpr + B′(T - Tr)) (3) 2
TABLE 1: Summary of the Thermodynamic Data that Describes the DSC Curves for Several Surfactants
equation 7
along with the same value used for ∆Cp are inserted into eq 6 for the determination of the best values for B′. This procedure is similar to the one used previously with eqs 2 and 3. We also used an integrated form of the van’t Hoff equation1 to determine the enthalpy change that accompanies micelle formation at 25° C, ∆H,25 from the known temperature dependence of the cmc. The equation used for this purpose with B′ assumed to be equal to zero in order to minimize the number of fitting parameters was2
ln(cmc) ) ln(cmcr) + [(∆H25 - 298∆Cp)/1.987] × (T - 298)/(298T) + ∆Cp/1.987 ln(T/298) (7) The value of ∆H25 was also determined from the DSC data using the values of B′, Tr, and ∆Cpr contained in Table 2 using eq 81,2,4,5
∆H25 ) (∆Cpr -B′Tr)(T - Tr) + 0.5B′(T2 - Tr2)
(8)
for comparison with values that came from either heat of dilution data or the van’t Hoff analysis. Results The differential heat capacity curves for aqueous solutions of three nonionic surfactants that were obtained by DSC
4382 J. Phys. Chem. B, Vol. 105, No. 19, 2001
Kresheck
Figure 1. The solid lines represent the directly measured property (cal/ C) obtained from DSC experiments (baseline corrected) with several concentrations of APO8 and are associated with the left axis. The right axis corresponds to the scale used to represent the cmc values (filled symbols). The surfactant concentration used for each trial is given next to the corresponding curve.
Figure 3. The solid lines represent the directly measured property (cal/ C) obtained from DSC experiments (baseline corrected) with several concentrations of SDecS and are associated with the left axis. The right axis corresponds to the scale used to represent the cmc values (filled symbols). The surfactant concentration used for each trial is given next to the corresponding curve.
Figure 2. The solid lines represent the directly measured property (cal/ C) obtained from DSC experiments (baseline corrected) with several concentrations of APO9 and are associated with the left axis. The right axis corresponds to the scale used to represent the cmc values (filled symbols). The surfactant concentration used for each trial is given next to the corresponding curve.
Figure 4. The solid lines represent the directly measured property (cal/ C) obtained from DSC experiments (baseline corrected) with several concentrations of DPB and are associated with the left axis. The right axis corresponds to the scale used to represent the cmc values (filled symbols). The surfactant concentration used for each trial is given next to the corresponding curve.
resemble the curves that describe the temperature dependence of the cmc when the surfactant concentration was 2-3 times greater than the cmc.1 Initial attempts to extend these studies to aqueous solutions of ionic surfactants with DPB concentrations about 2 times greater than the cmc exhibited an unexpected maximum near 80 °C. It seemed possible that micelle aggregation and/or a decreasing cmc was responsible for this behavior. The added complication due to possible electrostatic contributions caused us to initially conduct additional trials for solutions of the three alkylphosphine oxide samples previously investigated, at surfactant concentrations which were closer to that of the cmc for comparison with the data previously reported for the same compounds and the ionic surfactants. The results obtained suggested an explanation for the behavior of ionic surfactants in general, and a more complete understanding of DSC data for the nonionic surfactants as well. The results obtained from studies of each surfactant will be presented separately. The curves given in Figures 1-6 were adjusted vertically in order to make it possible to compare the shape of the DSC curves at different concentrations without overlapping. APO8. A summary of the results previously considered1 for APO8 solutions below (20 mM) and above (50, 60, and 100 mM) the cmc are given in Figure 1. Also shown are new data with surfactant concentrations close to that of the cmc (40 and 50 mM). It is clear that the curve for the 40 mM solution is not
Figure 5. The solid lines represent the directly measured property (cal/ C) obtained from DSC experiments (baseline corrected) with several concentrations of DTAB and are associated with the left axis. The right axis corresponds to the scale used to represent the cmc values (filled symbols). The surfactant concentration used for each trial is given next to the corresponding curve.
characteristic of either type of curve previously reported. A distinct leveling of the curves for the 40 and 50 mM solutions around 100 °C is evident. A possible explanation for the shape of these curves is suggested by comparing the curve for 40 mM APO8 with the curve that represents the cmc at various temperatures, which are plotted according to the right-hand axis.
Nonionic and Ionic Surfactants
Figure 6. The solid lines represent the directly measured property (cal/ C) obtained from DSC experiments (baseline corrected) with several concentrations of TTAB and are associated with the left axis. The right axis corresponds to the scale used to represent the cmc values (filled symbols). The surfactant concentration used for each trial is given next to the corresponding curve.
Below 30 °C, a surfactant concentration of 40 mM is less than the cmc and the curve resembles that of the sample (20 mM) which is below the cmc at all temperatures between 20 and 107 °C. After the solution was heated to 40 °C, the cmc is now less than 40 mM, and a characteristic curve is obtained for solutions which are above the cmc. Continued heating to about 80 °C produces a solution which is once again below the cmc, and the trace resembles that of a solution with a concentration less than the cmc (20 mM). It seems likely that the depth of a minimum (when observed) corresponds to the change in the amount of surfactant in either the monomer or micellar states. Finally, it is possible to visually estimate the cmc at each temperature from the point on the DSC curve where a slope change occurs. For example, the cmc would be 40 mM at about 30 and 80 °C and 45-50 mM near 100 °C. APO9. We previously reported a DSC curve for 40 mM APO9 and treated the data from that trial and data for a 30 mM sample up to the temperature limit for which cmc values were known, 79 °C.1 The complete data up to 107 °C for these two concentrations as well lower ones are given in Figure 2. As with the APO8 solutions, maxima are observed at higher temperatures which decrease as the surfactant concentration in the cell is decreased. Comparison of the surfactant concentration in the cell with the cmc values, which are again plotted on the right axis, provides additional insights as to the origin of the factors which are responsible for the shapes of the curves. Clearly, the 10 mM sample is less than the cmc throughout the scan. However, by comparison with the data for the other two scans with that of the APO8 solutions suggests that the cmc is 15 mM at about 80 °C and 20 mM at about 100 °C. APO10. The shape of the DSC curve for a 50 mM sample was previously reported,1 and the data were quite similar to those also observed with 10 and 20 mM solutions. The temperature dependence of the cmc for this sample exhibited a minimum value of 3.7 mM at 45 °C.4 The DSC curves for the 10, 20, and 50 mM samples also closely resembled the curve that describes the temperature dependence of the cmc over the same temperature range. However, a sample with a concentration of 3.2 mM was nearly flat between 20 and 107 °C. The curve noted for a sample with a concentration of 5 mM started to level off around 90 °C. This suggests that the cmc of APO10 is 5 mM close to that temperature. The negative sign for the coefficient c previously reported1 for the 20 mM solution of this surfactant was in error, and it should have had a positive sign.
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4383 SDecS. The results obtained from DSC studies with several concentrations of aqueous solutions of the anionic surfactant SDecS are give in Figure 3 along with literature values for the cmc between 15 and 90 °C. Since the shapes of the DSC curves observed for the 100 and 150 mM samples resemble the temperature dependence of the cmc above 20 °C, their behavior may be ascribed to a decrease in heat capacity of the surfactant solution with increasing temperature due to an increase in monomer concentration caused by micelle dissociation. Maxima located at approximately 60, 90, and 100 °C may be identified with cmc values of 40, 60, and 80 mM. A nearly linear curve was noted for the 30 mM sample, which was less concentrated than necessary to form micelles at any temperature during the scan. DPB. The DSC curves obtained for one of the three cationic surfactants investigated exhibited a maximum near 90 °C for the 30 mM solution. It was this behavior that prompted a reinvestigation of the alkyphosphine oxides. The results for this sample along with data for more and less concentrated solutions are given in Figure 4. Data are presented for duplicate runs between which the cell was emptied and refilled for the 50 mM sample. The shape of the curves obtained for the 50 and 60 mM samples parallel that of the temperature dependence of the cmc. However, when the surfactant concentration approaches that of the cmc, as with the 25 and 30 mM solutions, either a clear maximum or leveling were observed. A cmc of 30 mM at about 80 °C is suggested for this sample. As with the other surfactants with concentrations approaching the cmc, the depth of the minimum for the less concentrated solution is less than that of the more concentrated solutions. As before, this difference likely reflects the magnitude of the change in monomer/micelle concentrations as the temperature changes. DTAB. A collection the DSC curves which were obtained for six different concentrations of DTAB ranging from 15 to 100 mM is given in Figure 5. The sample with a surfactant concentration of 15 mM has about the same concentration as the cmc, and a nearly linear decrease in heat capacity is noted between 20 and 107 °C. As with the other surfactants, the curves for the more concentrated solutions, 60 and 100 mM, resemble the variation of the cmc with temperature changes. The maxima observed for the 20, 30, and 45 mM samples correspond to the cmc being near 55, 80, and 100 °C, respectively, for this surfactant. TTAB. An investigation of the thermal properties of TTAB is of interest since the cmc has been measured from room temperature up to 166 °C.6 The shape of the curve that represents the data is continuous throughout. However, the DSC curves exhibit maxima, like those for the other surfactants, as the surfactant concentrations approach the cmc. This behavior is shown for the 5 and 12.5 mM samples in Figure 6. Again, the heat capacity for the sample with a concentration well below the cmc, 3.5 mM, decreases in a nearly linear manner with increasing temperature. The shape of the curve for the 50 mM sample closely resembles the temperature dependence of the cmc. A cmc of 5 and 12.5 mM at about 70 and 100 °C is suggested from the shape of these curves. Of special interest is the lack of a sharp endotherm around 15 °C for the 20 mM sample, although one was previously reported to occur at this temperature.7,8 This temperature region was thoroughly investigated at scan rates of 10 and 90 °K, without being able to reproduce the previous work. Overall. A summary of the literature and experimental values determined in this study for the cmc at various temperatures for the four ionic surfactants included in this study and APO8
4384 J. Phys. Chem. B, Vol. 105, No. 19, 2001
Kresheck Finally, data contained in Table 1 were used together with eq 8 to obtain the heat of micelle formation at 25 °C, and these results are given in Table 2 together with calorimetric values (heat of dilution studies) taken from the literature and ones derived from the temperature dependence of the cmc (eq 7). The errors given for the values obtained from this study represent the average results from two or three trials using the data given in Table 1. The standard deviations assigned to ∆Hm result from fitting cmc data with eq 7 using the Origin software. These errors are quite large as opposed to those derived from calorimetry. However, the agreement between all values is generally good when considering the error limits listed.
Figure 7. Plot of the cmc values obtained from the literature citations given in Table 2 (filled symbols) or slope changes which occurred at various temperatures during the DSC scans (open symbols) for TTAB (squares), DTAB (circles), DPB (up triangles), SDecS (down triangles), and APO8 (diamonds) between 15 and 114 °C.
Figure 8. Plot of the experimental DSC data obtained with 150 mM SDecS, 100 mM DTAB, 50 mM TTAB, 100 mM APO8, 40 mM APO9, and 50 mM APO10 (solid lines) and the curves that represent the fit of the data to either eq 3 or 6 (broken lines).
is given in Figure 7. In every case, the cmc values which were estimated from the DSC data are consistent with the literature values. The DSC data for each surfactant for the two or three most concentrated samples were fit according to eq 3 for the ionic surfactants (except for SDecS and the most concentrated TTAB solution) or eq 6 for the other surfactants. Typical results that were obtained with one of the more concentrated samples for each surfactant are given in Figure 8. The agreement between the experimental and calculated curves is excellent in each case as was also true when fitting the data for the other more concentrated samples (data not shown). A summary of the parameters that accompany micelle formation which were used to fit these data to either eq 3 or 6 for each surfactant investigated is given in Table 1. The standard errors assigned to the values of B′ contained in Table 1 were generated using the Origin software provided by MicroCal. Many of the values for B′ were greater positive for the more concentrated solutions, perhaps reflecting the more nonideality of the more concentrated solutions. The values for ∆Cp listed in Table 1 were taken from the literature. The values of Tr given for SDecS and DPB correspond to the temperature where the cmc exhibits a clear minimum. This is approximately true for the Tr values listed for the alkylphoshine oxides, the exception being that they came from fitting the DSC data to eq 5 and setting the first derivative equal to zero and solving for the temperature. Finally, a similar procedure was used to find Tr for DTAB and TTAB except a simple cubic polynomial was used to represent the heat capacity data.
Discussion The main conclusion to come from this study is that the shape of the DSC heating curves which one obtains for dilute surfactant solutions of ionic as well as nonionic surfactants to a first approximation reflects the equilibrium that exists between the monomer and micellar states. The particular shape one observes depends on the total surfactant concentration with respect to the cmc at a given temperature. For solutions less concentrated than the cmc, the gradual decrease in heat capacity reflects the lower partial molar heat capacity of the monomer as the temperature is increased. For solutions 2-3 times more concentrated than the cmc, the shapes of the DSC curves resemble the temperature dependence of the cmc. This behavior reflects the change in heat capacity of the solution as monomer is converted to micelles at low temperatures (not always observed) and the reverse at higher temperatures. For intermediate concentrations, either positive or negative slope changes may occur when the temperature at a particular point in the scan correspond to the situation when the concentration of surfactant in the cell is equal to the cmc. In one case (40 mM APO8), the cmc was below the surfactant concentration in the cell at low temperatures, above the cmc at intermediate temperatures, and again below the cmc toward the end of the scan. The behavior of the alkylphosphine oxides is unusual when compared with existing cmc data for other nonionic surfactants, which seem to level off at higher temperatures. We were unable to reproduce the asymmetric peak previously reported7,8 to be centered around 14 °C, using several scan rates with solutions of TTAB at, below, or above 20 mM. The reason for this disagreement is not known, but it is may result from some form of experimental error since a stable baseline was not evident before the “peak” was observed in the earlier work. Values for the reference temperature, Tr, correspond to the minimum in the heat capacity curves (where ∆H ) zero and eliminates the need to include ∆H25 in the fitting functions) for solutions which are 2-3 times more concentrated than the cmc. This temperature is calculated from the coefficients that are described by fitting the data to either eq 2 or 5. In the event that a clear minimum is not observed for the heat capacity curve, a minimum in the cmc vs temperature curve may be identified as Tr. Finally, an extrapolated minimum in the heat capacity curve may be found by setting the first derivative of an empirical equation that describes the DSC curve equal to zero and solving for the temperature. Because of the form of eq 2, 3, 5, and 6, it is not possible to find values for both ∆Cp and the coefficients in these equations. We elected to fix ∆Cp for our analysis. It may be possible in the future to fix all of the coefficients except a or A and obtain ∆Cp directly from the DSC data, but a precise knowledge of the temperature dependence of the cmc would be required. Finally, the coefficients in eq 1 and 4 are the same as the
Nonionic and Ionic Surfactants coefficients in the equations derived from them. However, once known, they only reflect the relative temperature dependence of the cmc. When used together with eq 1 and 4, e.g., they are offset vertically from the actual values. This difference results from the fact that a differential specific heat is determined by DSC7 and it is a relative rather than an absolute quantity. The use of eq 7 or another similar one1 requires that the cmc be known at some reference temperature in order to account for the offset, which is otherwise unknown. Simple polynomial regression analysis of the resulting cmc data will provide coefficients for use with either eq 1 or 4. The apparent molar heat capacity for various concentrations of n-dodecylpyridinium chloride, DPC, have been measured14 at temperatures ranging from 283 to 393 °K at a pressure of 0.35 Mpa, and it is possible to compare our data for DPB with the results from this study. Despite the difference in counterion, the shape of our DSC curves are similar to those reported for DPC. For example, our normalized data for 0.1 M DPB (obtained by adjusting the heat capacity at 25 °C to 639 J/mol K) were found to only average 2.5% lower at any given temperature than similar data for 0.10004 m DPC between 298 and 373 °K. Slightly different values of Tr and ∆Cp than the ones reported in Table 1 were used for fitting the heat capacity data to eq 3 and 6 for the ionic surfactants, and we found that the absolute value of B′ was sensitive to each quantity. However, in each case, the sign and magnitude of the resulting values did not generally change. Therefore, it is our opinion that the absolute values for B′ reported in Table 1 must be corroborated by some other method, like performing heat of dilution experiments. This has been done for all three alkylphosphine oxides and the values obtained for B′ by the two methods are consistent using ∆Cp data from titration calorimetry to fit the DSC curves. Our use of an integrated form of the van’t Hoff equation, eq 7, to describe the temperature dependence of the cmc for ionic
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4385 surfactants requires some discussion. The standard free energy change that accompanies the exchange of a surfactant monomer between existing micelles has been identified with the cmc.15,16 The interpretation of the results from this calculation for ionic surfactants requires consideration of the electrical contribution to micelle formation. However, it is possible that a mathematical relationship in the form of the van’t Hoff (or equivalent form such as the Classius Clapyron equation) may still be used to describe the temperature dependence of the cmc for ionic surfactants. This approach is seen to yield values for the heat of micelle formation at 25 °C that are similar to those derived from calorimetry. References and Notes (1) Kresheck, G. C. Langmuir 2000, 16, 3067. (2) Desnoyers, J. E.; Caron, G. C.; DeLisi, R.; Roberts, D.; Roux, A.; Perron, G. J. Phys. Chem. 1983, 87, 1397. (3) Andersson, B.; Olofsson, G. J. Chem. Soc., Faraday Trans. 1 1988 84, 4087. (4) Kresheck, G. C. J. Phys. Chem. B 1998, 102, 6596. (5) Kresheck, G. C. J. Am. Chem. Soc. 1998, 120, 10964. (6) Evans, D. F.: Wightman, P. J. J. Colloid Interface Sci. 1982, 86, 515. (7) Blandamer, M. J.; Briggs, B.; Burgess, J.; Cullis, P. M.; Eaton, G. J. Chem. Soc., Faraday Trans. 1991, 87, 1169. (8) Blandamer, M. J.; Briggs, B.; Burgess, J.; Butt, M. D.; Brown, H. R.; Cullis, P. M.; Engberts, J. B. F. N. J. Colloid Interface Sci. 1992, 150, 285. (9) Woolley, E. M.; Burchfield, T. E. J. Phys. Chem. 1985, 89, 714. (10) Kresheck, G. C.; Hargraves, W. H. J. Colloid Interface Sci. 1974, 48, 481. (11) Espada, L.; Jones, M. N.; Pilcher, G. J. Chem. Thermodyn. 1970, 2, 1. (12) Bashford, M. T.; Woolley, E. M. J. Phys. Chem. 1985, 89, 3173. (13) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; U. S. Superintendent of Documents: Washington, DC, 1971. (14) Ballerat-Busserolles, K.; Bizzo, C.; Pezzini, L.; Sullivan, K.; Woolley, E. J. Chem. Thermodyn. 1998, 30, 971. (15) Emerson, M. F.: Holtzer, A. J. Phys. Chem. 1965, 69, 3718. (16) Holtzer, A.; Emerson, M. F. J. Phys. Chem. 1974, 78, 1442.
