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Isothermal Titration Calorimetry Studies of Neutral Salt Effects on the Thermodynamics of Micelle Formation Gordon C. Kresheck† Department of Chemistry, UniVersity of Colorado at Colorado Springs, Colorado Springs, Colorado 80933-7150 ReceiVed: December 15, 2008; ReVised Manuscript ReceiVed: March 2, 2009
Isothermal titration calorimetry, ITC, was used to determine the enthalpy and heat capacity changes that accompany micelle formation of decyldimethylphosphine oxide, APO10, from 15-79 °C in the presence of representative neutral salts from the Hofmeister series. The solutions investigated were water, 0.2, 0.5, and 1.0 NaCl, 0.5 M NaF, KCl, KI, guanidinium chloride (GuHCl) and mannitol, and 0.333 M Na2SO4. The heat capacity change at 25 °C (but not the cmc) and the parameter that describes the temperature dependence of the heat capacity change, B (cal/(mol K2)), appear to be correlated. Calculated values of the ion effects on micelle formation from a recent salt ion partitioning model (SPM) of Pegram and Record [J. Phys. Chem. B 2007, 111, 5411-5417] were quantitatively related to the experimental value of the solute free energy increment (SFEI). Use of this model requires a calculation of the solvent accessible area (ASA), which yields values for the extent of hydration of the micelle interior. An alternate method to determine the ASA based on the heat capacity change for micelle formation at 25 °C of APO8-12 yielded values for the number of buried carbon atoms (5-12) versus previous estimates (4-8) from analysis of the B parameter. Introduction Understanding the influence of neutral salts on the physical properties of aqueous solutions has been a challenge for more than 60 years.1 Early interest focused on the salting-in or saltingout of nonelectrolytes by neutral salts.2 Attention later turned to amphipathic molecules, mainly surfactants, since the critical micelle concentration (cmc) could be accurately and easily measured. It was discovered that the cmc was systematically decreased or increased by the addition of neutral salts in a manner that followed a lyotropic series.3 A similar trend was shown to describe the thermal stability of biopolymers.4 A model was recently proposed, the salt ion partitioning model (SPM), that quantified the possible partitioning of individual ions between the bulk solution and the air-water interphase5 or protein surfaces.6,7 The resulting theory was used to predict the Hofmeister effect of neutral salts on the cmc of a nonionic micelle.7 This theory required a knowledge of the water accessible surface area (ASA) of the surfactant molecule that could either be calculated or derived from the heat capacity change that accompanies hydrophobic interactions. One interesting observation from this study was that the extent of hydration of the micelle interior derived from use of the SPM theory was consistent with previous NMR results.8 Titration calorimetry was shown to be a reliable, simple, and rapid technique to obtain the enthalpy, entropy, and heat capacity changes that accompany micelle formation.9,10 Recent studies demonstrated that the heat capacity change for micelle formation for a group of nonionic surfactants in water varied as much as 1.0 cal/(mol K2) over a broad temperature range.11 The depth of penetration of solvent into the micelle interior was estimated from an empirical analysis of the parameter that describes the temperature dependent heat capacity changes. However, similar calorimetric studies in the presence of neutral salts have not been reported. † E-mail:
[email protected].
The purpose of this study was to obtain calorimetric data that describe micelle formation of a nonionic surfactant, n-decyldimethylphosphine oxide (APO10), in the presence of a series of neutral salts over a broad temperature range. This information will provide fundamental information regarding the energetics of micelle formation for surfactants and possibly other hydrophobic interactions as well. Finally, the results obtained with APO10 may be compared with the results of a recent theory of salt effects on the solubility of nonelectrolytes and micelle formation.7 Experimental Section The sample of APO10 used in this study was the same sample used previously that was obtained from BioAffinity Systems (Rockford, IL).12 Reagent grade salts were used without further purification. Deionized distilled water (17 MΩ/cm) was used for the preparation of all solutions of a given molarity, M (mol/ L). Isothermal titration calorimetry (ITC) experiments were performed with a MicroCal Omega isothermal titration calorimeter (MicroCal, Inc., Northampton, MA) with a 0.115 M solution of APO10 in a 300 µL syringe. Injection volumes ranged from 3 to 10 µL. Samples were degassed prior to placing into the calorimeter cell. The baseline for integration of each peak was adjusted manually. Electrical heating was used for calibration purposes. The MicroCal Origin software supplied by MicroCal, Inc. was used for data collection, analysis, and plotting. The cmc was defined as the midpoint of an empirical sigmoidal curve used to fit the data with the Origin software as previously described.10 A second method fit the derivative of the titration curve to a single Gaussian curve.13 The average value obtained by the two methods is reported and the difference represents the estimated error. The molar enthalpy of micelle formation was obtained as the difference between the limiting values of the heat of mixing at
10.1021/jp811048d CCC: $40.75 2009 American Chemical Society Published on Web 04/20/2009
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TABLE 1: Summary of the Thermodynamic Parameters Obtained for APO10 over the Temperature Range Described in the Text at 298.2 Ka,b solvent water 0.2 M NaCl 0.5 M NaCl 1.0 M NaCl 0.5 M NaF 0.33 M Na2SO4 0.5 M KCl 0.5 M KI 0.5 M GuHCl 0.5 M mannitol
cmc (mM)
∆Hr (cal/mol)
-∆Cpr (cal/(mol K))
B (cal/(mol K2))
4.09 ( 0.01 (4.185 ( 0.01) 3.54 ( 0.01 2.92 ( 0.01 2.09 ( 0.01 2.29 ( 0.01 2.06 ( 0.01 2.86 ( 0.02 2.75 ( 0.01 4.49 ( 0.02 3.42 ( 0.02
2307 ( 11 (2321 ( 5) 2287 ( 8 2102 ( 10 1897 ( 9 2010 ( 12 2012 ( 11 2212 ( 11 1142 ( 6 2021 ( 10 1765 ( 14
123.5 ( 0.9 (123 ( 2) 123.6 ( 0.8 119.5 ( 1.1 116.7 ( 0.8 124.2 ( 1.2 123.3 ( 1.4 124.6 ( 0.9 106.3 ( 0.6 106.2 ( 0.8 119.3 ( 1.4
0.88 ( 0.04 (0.75 ( 0.1) 0.83 ( 0.04 0.77 ( 0.06 0.70 ( 0.03 0.78 ( 0.05 0.58 ( 0.08 0.89 ( 0.04 0.69 ( 0.02 0.62 ( 0.04 0.85 ( 0.06
ks 0.28 0.28 0.28 0.50 0.86 0.30 0.34 -0.09 0.15
a The errors given for the cmc and ∆Hr represent the mean standard deviation and standard errors are given for B and ∆Cpr. b The values in parentheses were determined approximately 10 years ago at Northern Illinois University with a MicroCal Titration Calorimeter and were previously reported.12
the start and end of the titration as previously described.11 The standard error for each parameter was obtained by curve fitting using the Origin software. Theory Experimental values of the standard enthalpy change at a given temperature, ∆H(T), over a broad temperature range, T, were used along with eq 1 to obtain the reference values, ∆Hr and ∆Cpr, at the reference temperature, Tr ) 298.2. using Origin software10
∆H(T) ) ∆Hr + (∆Cpr - BTr)(T - Tr) + B ⁄ 2(T2 - Tr2)
(1)
The standard heat capacity change at a given temperature, ∆Cp(T), is given by the equation
∆Cp(T) ) ∆Cpr + B(T - Tr)
(2)
where the coefficient B, which has units of cal/(mol K2), reflects the variation of ∆Cp(T) with temperature. The values of ∆Hr, ∆Cpr, and B may be used to express the temperature dependence of the cmc10-12 if the cmc at the reference temperature, cmcr, is known with the equation14
R ln(cmc) ) R ln(cmcr) + [(∆Hr - Tr∆Cpr + B ⁄ 2Tr2)(1 ⁄ T 1 ⁄ Tr)] - (∆Cpr - BTr) ln(T ⁄ Tr) - B ⁄ 2(T - Tr)
(3)
The effect of neutral salts on the cmc may be described by the equation3
log cmc ) constant - ksCs
solute first hydration layer for various salts and was calculated from values for average single ion coefficients for hydrorcarbons.6 ASA is the water-accessible surface area and was calculated for decane and several APO surfactants using Surface Racer 5.0 with a probe radius of 1.4 Å and van der Waal radii set 1.16 Programs such as MOPAC17 that calculate the surface area of molecules are not appropriate for this purpose unless they include one solvent radius in addition to the solute radii before smoothing the resulting surface. The determination (Kp - 1)b1 values must use an ASA that is calculated by the same method as Surface Racer.
(4)
where Cs and ks represent the molarity of added salt and a salt/ surfactant specific parameter, respectively. This equation is similar in form to the Setschenow equation15 that describes the effect of neutral salts on the solubility of nonpolar solutes, and both processes follow the Hofmeister series. A solute partitioning model (SPM) has recently been developed that relates ks to a solubility free energy increment (SFEI) by the equations7
SFEI ≡ 2.303RTks ≡ -RT d ln cmc ⁄ dCs ≡ SPM
(5)
SFEI = -RTυb1ASA(Kp - 1)(1 + () ⁄ 55.5
(6)
where υ is the number of ions per formula unit (3 for Na2SO4 and 2 for the remaining salts), b1 corresponds to the number of water molecules per unit area in the first hydration layer surrounding the surfactant (0.18 H2O Å-2),7 and the term (1 + () represents the nonideality correction.6 The coefficient Kp describes the partitioning of ions between bulk solution and
Results and Discussion The general features of ITC curves obtained for the dilution of surfactant solutions which are more concentrated than the cmc are well-known.9-12 The curves are exothermic at low temperatures and progressively become endothermic at high temperatures, reflecting the negative heat capacity change that accompanies micelle formation. The results obtained in this study over a temperature range from 15 to 79 °C at small temperature intervals follow this general pattern and a summary of the thermodynamic data obtained for the dilution of 0.115 M APO10 in water, 0.2, 0.5, and 1.0 M NaCl, 0.33 M Na2SO4 and 0.5 M NaF, KCl, KI, guanidinium chloride (GuHCl) and mannitol are given in Table 1. The cmc and ks were determined as described in the Experimental Section and ∆Hr, ∆Cpr, and B were determined by fitting the titration data to eq 1. The data from Table 1 were used with eq 3 to describe the temperature dependence of the cmc of APO10 and the results are shown in Figure 1 for each solvent. As expected,10-12 the calculated curves represent the data very well and exhibit minima near 320 K, which is the temperature where minima appear with DSC scans of micellar solutions of APO1018 and other surfactants as well.19 The B values from Table 1 do not exhibit an obvious relationship to the cmc. However, a definite trend exists excluding the Na2SO4 data when the value of B is plotted (Figure 2) versus ∆Cpr for the solvents listed in Table 1. Previous data for APO8 and APO9 in the absence of added salts are included.11 Selective differences in the solvation of the monomer in the presence of neutral salts with different Kp values as well as variations in the of extent of hydration of the micelle core could be responsible for this relationship. Experiments with 0.333 M NaSO4 solutions were limited to below 65 °C due to phase separation above this temperature.
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Kresheck TABLE 2: Accessible Surface Areas (ASA) Determined for APO10 As Described in the Texta component
ASA (Å)
APO10 decane decyl group CH2 groupb CH3 group
515 410 (350) (29) (89)
a
Values in parentheses were determined from the calculated values assuming additivity. b From calculated values for APO8 (457), APO9 (486), APO10 (515), APO11 (544) and APO12 (573).
Figure 1. Experimental (symbols) and calculated values for APO10 according to eq 4 (lines) for values of R ln cmc versus temperature (T) for the following solvents: 0.5 M GuHCl (open squares), water (filled squares), 0.2 M NaCl (open circles), 0.5 M mannitol (filled down triangles), 0.5 M KI (open triangles), 0.5 N KCl (filled diamonds), 0.5 M NaF (closed diamonds), 1.0 M NaCl (open down triangles) 0.5 M NaCl (filled circles), and 0.333 M Na2SO4 (filled up triangles).
Figure 3. Plot of calculated values of SPM, eq 6, versus SFEI, eq 5, for APO10 and OPE30. All values of ks, b1(Kp - 1) and (1 + ()) used for the calculations are listed in the Supporting Information, Table S1. A reference line with a slope of 1.0 that passes through the origin is also shown.
Figure 2. Plot of B values versus -∆Cpr for the data given Table 1 in the presence (filled squares) and absence (open squares) of salts including data for APO8 and APO9 from ref 11. The down triangle represents the data for Na2SO4. The solid line corresponds to an empirical second degree fit of the data for all of the solvents except for Na2SO4.
The lower temperature limit was responsible for a lower value of B since deviations from a linear fit of the enthalpy data to eq 1 occur at the higher temperatures. It is interesting that the sulfate anion has such a profound lowering effect on the cloud point: 124 °C in water and 65 °C in 0.333 M NaSO4 for dilute APO10 solutions. The sulfate anion is known to favor processes that reduce the exposure of protein surfaces to water such as folding, aggregation and precipitation,6 and the phase separation of APO10 at lower temperatures is consistent with this behavior. The solvents selected for this investigation reflect a range of ks values from the Hofmeister series, and attempts were made to describe the data using eqs 5 and 6. The ks data were taken from Table 1 for APO10. Calculations using eq 6 made using literature values of b1(Kp - 1)7 and (1 + ()6 and are given in Table S1 in the Supporting Information. The ASA values obtained for the nonpolar portions of APO10 are summarized in Table 2. Preliminary plots of SPM versus the SFEI using an ASA obtained for APO10 were linear and had nonzero intercepts and slopes. Therefore, the ASA was used as an adjustable parameter with eq 6 to determine the ASA values that were
required to give a slope equal to 1.0 since the values for the intercepts and standard deviations did not converge. The results from this analysis for APO10 and OPE307 for comparison are given in Figure 3. The data for APO10 are well represented by the reference line with the solid line in the figure a slope of 1.0 that passes through the origin. An ASA value of 350 Å2 was used for these calculations. An ASA value of 350 corresponds to the burial of the entire decyl group. A similar procedure was used to obtain the data for OPE30 represented in Figure 3 with a value of 730 for the ASA, which corresponds to the burial of five ethoxy and one p-t-octylphenoxyl groups. The similarity of the two data sets, considering the 10-fold difference in magnitude of the cmc of the two surfactants, constitutes support for the SPM-theory used to treat the data. The difference between the values of the intercepts, -15 and 314 cal/mol for APO10 and OPE30, respectively, may be attributed to a headgroup effect15 that is not taken into account by this analysis (see below). It is also possible that structural changes related to the change in molecular weight of the micelles may be of greater importance for OPE30 micelles. Finally, it should be noted that the interpretation of OPE30 data in this study is not the same as the literature7 which attributed differences between SPM and SFEI values for a given salt to a difference in the extent of burial of the polyethoxy segment. A simple relationship exists between heat capacity changes and accessible surface area determined by Surface Racer for the burial of nonpolar groups during folding or interactions between macromolecules.20 This relationship was used to determine the number of buried methylene groups, nburied, along with the methyl group for APO8-APO12 and the resulting
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TABLE 3: Determination of the Extent of Hydration of the Micelle Interior Using the Experimental ∆Cp and ASA Calculated with SR surfactant APO8 APO9 APO10 APO11 APO12
-∆Cp (cal/(mol K))a
ASA (Å2)b
nburiedc
77 94 123 141 155
220 269 351 403 433
5 (4) 6 (5) 9 (6) 11 (7) 12 (8)
a Data from ref 11. b Defined as ASA ) ∆Cp (cal/(mol K))/ -0.3521 (cal/(mol K Å)2). c Defined as nburied ) (ASA-89)/29. The values in parentheses are from ref 11.
values, are give in Table 3. The uncertainty in the value in the 0.35 factor used for the SR calculations is estimated as (1 methylene group.21 The ASA value for APO10 was 351 Å versus 350 Å required for analysis of the data in Figure 3 using the single ion partitioning theory.7 Values are also given in Table 3 from previous estimates of the number of buried methylene groups from an analysis of the temperature dependence of the heat capacity change/methylene group for micelle formation.11 The results from using SR may overestimate the number of buried methylene groups since31P NMR studies22 indicated that the phosphorus atom exists in a low dielectric environment when the surfactant concentrations are above the cmc compared to when concentrations are below the cmc. Therefore, the dimethyl groups attached to the phosphorus atom may be partially removed from water when micelles form and this change may contribute to the observed ∆Cp for all of the alkyldimethylphosphine oxides. An extensive analysis of the literature recently revealed that temperature-dependent heat capacity changes in protein-DNA interactions are not the result of coupled folding,23 but model compound data for animo acids24 and micelle formation11 suggest that solvent effects could be an important contributing factor. A process that resembles the reverse of micelle formation, i.e., micelle dissociation, that involves the hydration of nonpolar groups would contribute a negative temperature-dependent heat capacity change. Acknowledgment. It is a pleasure to acknowledge the assistance of Oleg Tsodikov for downloading Surface Racer 5.0,
Sonja Braun-Sand for making the PDF files of the alkyldimethylphosphine compounds and decane, and M. Thomas Record, Jr. and Laurel M. Pegram for valuable advice. Supporting Information Available: Table S1 contains the values of ks, b1(Kp - 1), and (1 + () used in the calculation of SMP and SFEI. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Frank, H. S.; Evans, W. F. J. Chem. Phys. 1945, 13, 507–532. (2) Long, F. A.; Evans, W. F. Chem. ReV. 1952, 51, 119–164. (3) Ray, A.; Ne´methy, G. J. Am. Chem. Soc. 1971, 93, 6787–6793. (4) Von Hippel, P. H.; Wong, K. Y. J. Biol. Chem. 1965, 240, 3909– 3923. (5) Pegram, L. M.; Record, M. T. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 333–364. (6) Pegram, L. M.; Record, M. T. J. Phys. Chem. B 2007, 111, 5411– 5417. (7) Pegram, L. M.; Record, M. T. J. Phys. Chem. B 2008, 112, 9428– 9436. (8) Podo, F.; Ray, A.; Ne´methy, G. J. Am. Chem. Soc. 1973, 95, 6164– 6171. (9) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481–493. (10) Kresheck, G. C. J. Phys. Chem. B 1998, 102, 6596–6600. (11) Kresheck, G. C. J. Colloid Interface Sci. 2006, 298, 432–440. (12) Kresheck, G. C. J. Am. Chem. Soc. 1998, 120, 10964–10969. (13) Paula, S.; Su¨s, W.; Tuchenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742–11751. (14) Desnoyers, J. E.; Caron, G. C.; DeLisi, R.; Roberts, D.; Roux, A.; Peron, G. J. Phys. Chem. 1983, 87, 1397–1406. (15) Kresheck, G. C. In Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum, New York, 1975; Vol. IV, pp 95-167. (16) Tsodikov, O. V.; Record, M. T.; Sergeev, Y. V. J. Comput. Chem. 2002, 23, 600–608. (17) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209–220. (18) Kresheck, G. C. Langmuir 2000, 16, 3067–3069. (19) Majhi, P. R.; Blume, A. Langmuir 2001, 17, 3844–3851. (20) Livingston, J. R.; Spolar, R. S.; Record, M. T. Biochemistry 2000, 30, 4237–4244. (21) Record, M. T. Private communication. (22) Kresheck, G. C.; Jones, C. J. Colloid Interface Sci. 1980, 77, 278– 279. (23) Liu, C.-C.; Richard, A. J.; Datta, K; LiCata, V. J. Biophys. J. 2008, 94, 3256–3265. (24) Makhatadze, G. I.; Privalov, P. L. J. Mol. Biol. 1990, 213, 375–384.
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