Langmuir 1996,11, 57-60
57
Reliability of the Experimental Methods To Determine Equilibrium Constants for SurfactantKyclodextrin Inclusion Complexes H. Mwakibete, R. Cristantino,? D. M. Bloor, E. Wyn-Jones,” and J. F. Holzwarth* Department of Chemistry and Applied Chemistry, University of Salford, Salford M5 4WT,U.K. Received May 24, 1994. In Final Form: September 26, 1994@ Aliterature survey reveals that the values of the equilibriumconstants for inclusion complexesinvolving surfactants and cyclodextrins can vary by several order of magnitude for the same system when different experimental methods are employed. In this paper we consider the problem of the reliability of binding constants. We report here our emf studies of the inclusion of cetyltrimethylammonium bromide and tetradecyltrimethylammonium bromide with a-and ,B-cyclodextrinand compare these data with other independent studies. The potential of the isothermal titration calorimetry as a method to determine these constants is also examined. We conclude that techniques which yield direct measurements of ‘‘free” and “included”surfactant and also isothermal titration calorimetry appear to give results which are consistent.
Introduction It has been demonstrated that the addition of cyclodextrins (CD’s) to an aqueous solution of surfactant dramatically affects the physicochemical properties of the so1ution.l-l5 The reason for these changes is the ability of CD’s to screen the hydrophobic moieties of surfactant molecules from contact with the surrounding aqueous media by the formation of an inclusion complex in which the hydrophobic chain of the surfactant is inserted into the CD cavity. As a result, surfactants are ideal guests which allow a systematic study of complexation with cyclodextrins since both their hydrophobic and hydrophilic moieties can be systematically changed. Indeed, the ability of cyclodextrins to modify the physicochemical properties of such aqueous solutions has been used to study their complexation behavior with surfactants, and a variety of experimental techniques have been used for this purpose. These techniques include conductivity,3 competitive binding using W, visible and fluorescent probes,4J2J4 NMR,5 surface tension: sound velocity,’J3 and electrochemica12J3 methods. A literature survey t Dipartimento di Chimica Fisica, University di Palermo, Italy.
*
Fritz-Haber-Institut der Max Planck Gesellschaft, Faradayweg 4-6,14195 Berlin, Germany. Abstract published in Advance ACS Abstracts, December 1, 1994. (1)Saint Aman, E.;Serve, D. J.Colloid Interface Sci. 1990,183,365 (and references therein). (2)WanYunus, W.M.Z.; Taylor, J.; Bloor, D. M.; Hall, D. G.; WynJones, E. J. Phys. Chem. 1992,96,8979. (3)Palepu, R.; Reinsborough, V. C. Can. J. Chem. 1988,66,325. (4)Sasaki, K. J.;Christian, S. D.; Tucker, E. E. J. Colloid Interface Sci. 1990,134, 412. (5)Fung, B. M.; Guo, W.; Christian, S. D. Langmuir 1992,8,446. (6)Dharmawardana, U.R.;Christian, S. D.; Tucker, E. E.; Taylor, R. W.; Scamehom, J. F. Langmuir 1993,9,2258. (7) Junquera, E.; Tardajos, G.; Aicart, E. J. Colloid Interface Sci. 1993,158, 388. ( 8 )Satake, I.; Ikenoue, T.; Takeshita, T.; Hayakawa, K.; Maeda, T. Bull. Chem. Soc. Jpn. 1986,58,2746. (9) Funasaki, N.; Yodo, H.; Hada, S.; Neya, S. Bull. Chem. SOC.Jpn. 1992,65,1323 (and references therein). (10)Okubo, T.; Kitano, H.; Ise, N. J. Phys. Chem. 1976,80,2661. (11)Satake, I.; Yoshida, S.; Hayakawa, K.; Maeda, T.; Kusumoto,Y. Bull. Chem. Soc. Jpn. 1986,59, 3991. (12)Park, J. W.; Song, H. J. J. Phys. Chem. 1989,93,6454. (13)Jezequel, D.;Mayaffre, A.; Letellier, P. Can. J.Chem. 1991,69, 1865. (14)Park, J. W.; Park, K. H. J. Inclusion Phenom. Mol. Recognit. Chem. in press. (15)Liveri,V. T.; Cavallaro,G.;Giammona,G.; Pitarresi, G.;Puglisi, G.; and Ventuna, C. Thermochim. Acta 1992,199,125. @
reveals that after an initial period that has produced ambiguous and inconclusive information, it is now generally regarded that the existence of 1:1and 2:1cyclodextrid surfactant complexes can O C C W . ~ - ~ Despite ~ this progress there remains a serious question mark concerning the reliability of many of the binding constants that have been quoted. A typical example concerns the inclusion of sodium dodecyl sulfate intoj3-CDwhich are known to form both 1:l and 2:l j3-CDlSDS complexes according to the scheme:
Scheme 1
p-CD
Kl + SDS =p-CD-SDS
p-CD + p-CD-SDS
KZ a (p-CD),-SDS
The first step in the above scheme is the dominating equilibrium. The following values ofK1 (in units of mol-’ dm3)have been quoted: 210,1° 356,11 1300-7230,3 320018000,9 3630,11 8360; 18 500: 21 000,2and 25 600.12 At first sight this clearly represents a very unsatisfactory state of affairs which as far as we are aware still exists in the current literature. In practice two different approaches are normally used to determine ligand/ macromolecule binding constants: (a) The first relys on direct measurements of the free and bound ligand in a solution containing a known amount of the macromolecule. In surfactant‘cyclodextrin work the techniques that have been used under this category include emf methods using surfactant selective electrodes and competitive binding studies using W, visible, and fluorescence probe^.^ (b)A second approach takes advantage of the existence of any physically observable properties that are proportional in some way to the extent of binding. The measurements under this category involve conductivity, sound velocity, surface tension, and counterion binding. A close inspection of the data published for the SDS/ j3-CD system shows that three independent studies involving the techniques spelled out under criterion (a) above, namely competitive binding using both fluorescent12 and W and visible absorbance4 probes and emf methods involving the use of a SDS membrane selective electrode,2 interestingly give values of Kl in Scheme 1 that are
0743-7463/95/2411-0057$09.00/00 1995 American Chemical Society
58 Langmuir, Vol. 11, No. 1, 1995 reasonably close, viz. 18 500, 25 600, and 21 600 mol-l dm3, respectively. In the competitive binding study, involving a solvatochromic probe showing changes in its W-visible spectrum, only aKl was estimated, whereas in the fluorescence probe and emf studies values of Kz of 220 and 210 mol-’ dm3, respectively, were quoted. On the other hand, all the other techniques that have been used to study the SDS//I-CD system come under category (b) above, giving values of K1 values ranging from 210 to 8360 mol-l dm3, which are clearly unacceptable. In all these studies the experiments are reliable and indeed have contributed to a better understanding of the solution properties of the system in the sense that the existence of both 1:l and 2:l /I-CD/SDScomplexes were discovered. Unfortunately the theoretical basis used in interpreting these bulk measurements in terms of equilibrium concentrations of the species in Scheme 1 apparently fails for surfactant.‘ cyclodextrin inclusion complexes. The experimental evidence that is currently available suggests that cyclodextrins recognize surfactant in a specific manner. In order to measure such specificity, reliable binding constants for the inclusion compounds are required. In view of the current interest shown in these systems, we wish to address the above problem concerning the consistency of experimentally determined complexation constants. Reliable values of K will serve to quantify the affinity of surfactants to cyclodextrins which in turn can lead to an understanding of the relationship between the surfactant chemical structure and its ability to form inclusion complexes. In theory, the key ingredients that are required to determine the equilibrium constants for Scheme 1 are the equilibrium concentrations of the various species involved. On this basis, consistency of the K values can only be achieved conclusively if the experiments are carried out under the criteria spelled out in (a) above. With this in mind we have investigated the inclusion complexes of the two surfactants cetyltrimethylammonium bromide (CTAB) and tetradecyltrimethylammonium bromide (TTAB)with a-and ,8-CD using surfactant membrane selective electrodes. We will compare our data with an independent emfstudyl3using surfactant electrodes employing a liquid junction and also a report of a competitive binding study using fluorescent probes.14 We have also used isothermal titration calorimetry (ITC) to investigate the 1:l binding constants of dodecyltrimethylammonium bromide (DTAB)and also dodecylpyridinium bromide (DPyBr) with /I-CD. Although this technique comes under the umbrella of category (b) methods as described in the Introduction, recent developments in both instrumentation and application suggest that it has great potential for use to study surfactantJCD complexes. Indeed the technique has been specifically designed to measure binding isotherms and comdexation constants associated with lkand/macromolecule interactions. 16,172021 Experimental Section The surfactantsused in this work DTAB, “TAB (Sigma),and CTAB (BDH)were purified commercial samples and DPyBr was (16) Wiseman, T.; Williston, S.;Brandts, J. F.; Lim, L.-N. Anal. Biochem. 1989.179.131. (17) Reire, E.; Mayorga, 0. L.; Straume, M. Anal. Chem. 1990,62, 950A. (WMwakibete, H.; Bloor, D. M.; Wyn-Jones, E. Submitted for publication in Langmuir. (19) Mwakibete, H.;Bloor,D. M.; Wyn-Jones,E. J .InclusionPhenom. Mol. Recognit. Chem. 1991,10,492. (20) Inone, Y.; Liu, Y.; Tong, K.-H.; Shen, B.4.; Jen, D. S.J . Am. Chem. Sac. 1993,115,10637. (21)Halton, D.; Schon, A.; Shehatta, I.; Wadso, I. J. Chem. SOC., Faraday Trans. 1992,88, 2859.
Mwakibete et al. 360 340 320
300
-
-
7 280E . 260-
5 240: 220 200
-
180-
,
1
m, =
(C,- Cl- m,) (KlK2m!- 1)
here m, represents the “free” (uncomplexed) cyclodextrin concentration and C, the total cyclodextrin concentration. In the analysis of the data for two state complexation according to the above Scheme 1 we have used a mean least squares computer
Equilibrium Constants for Inclusion Complexes
Langmuir, Vol. 11, No. 1, 1995 59 Table 2. Equilibrium Constant IC1 and AH for DTAB and DPyBr Interactions with B-Cyclodextrin K1 (mol-l dm3) AH (kcal mol-') DTAB emf studies2 18 100 ITC studies 23 700 -2.3 DPvBr emf studiedg 24 900 ITC studies 18 700 -2.3
0.1
IO
1
Total TTAB Concentration x IO3 [mol d ~ n - ~ ]
Figure 2. Fits to eqs 1and 2 for the 'M'AB/a-CD system: (A) 0.5 mM a-CD; (W) 0.75 mM a-CD. Table 1. Equilibrium Constants K1, Ea (mol-' d m 3 ) for
"AB and CTAB Interactions with a- and /?-Cyclodextrin a-cyclodextrin j3-cyclodextrin ?TAB this work
Jezequel et aL.13 Park et a1.l4 CTAB this work
Ki KZ Ki KZ Ki KZ
Ki KZ Dharmawardana et ~ 1 IC1 . ~ K2 Jezequel et aZ.l3 Ki KZ Park et aL.14 Ki K2
61 000
7 000
99 200 20 400
39 750 3 060 39 811 56 44 000 118
fitting program using KI, KZas adjustable parameters and the criteria that we have used for "goodness of fit" is the difference between ml calculated via eqs 1and 2 and the measured value using the surfactant electrode. This procedure is repeated for all surfactant concentrations used for a particular experiment and for all the experiments in which the cyclodextrin concentration was varied. Typicalfits are shown in Figure 2 and the results are presented in Table 1. Isothermal Titration Calorimetry (ITC). The calorimeter used in this work was the Microcal ITC instrument. In the ITC experiment one measures directly the energetics (enthalpy changes) associated with processes occurring at constant temperature. Experiments were carried out by titration of a ligand (surfactant) into a sample solution containing a known amount ofb-CD. An injection schedule (number of injections, volume for injection, and time between injections) is set up usinginteractive software, and this schedule was automatically carried out with all data stored to disk. After each addition the heat released or absorbed as a result of the formation of an inclusion compound is monitored by the calorimeter. In principle the total heat content Q of the solution contained in volume Vis given by
Q=VAH(C,-m,) where AH is the enthalpy of inclusion (mol of surfactant)-'. The foundation for the analysis of the data rests on the basis of the above equation which relates heat change to included surfactant concentration. Asoftware package is available in which the data can be processed to fit various binding models. In the present work involving both DTAB and DPyBr complexing with @-CD, only 1:1 complexes ~ c c u r . ~ JUnder * these circumstances the data are analyzed for K1, and AH for the process. The values are listed in Table 2. Typical data are shown in Figures 3 and 4. When these measurements are carried out, it is essential that the surfactant concentration in the injection solution used is less than the cmc. If the surfactant concentration is greater than its cmc, an additional heat contribution due to micellar dissociation occurs.
0.4
0.6 0.8 Molar Ratio
1.2
1.0
Figure 3. ITC titration curve for the system DTAB B-CD.
67 700 9 600 65 500 398 70 790 126 59 800 390
0.2
0.0
s-
0.0
3
1.4
+ 2 mM
-
.$ -0.5.I
58 -1.0-.
-
c
'u -1.5-
5i
E
; -
-2.0-
5
-2.5 4
J
I
0.0
I
I
0.5
1.o
I .5
Molar Ratio
Figure 4. ITC titration curve for the system DF'yBr 8-CD.
2.0
+ 2 mM
Discussion The values of the complexation constants determined in this work are listed in Tables 1 and 2. The emf data show that inclusion of the surfactants TTAB and CTAB into a- and /3-CD involve both a 1:l and 1:2 surfactant/ cyclodextrin complex. The values of K1 and KZfor the different concentrations of CD were analyzed separately. At present we are not aware of any published work involving the inclusion of the surfactants with a-CD. On the other hand there are values of K1 and KZavailable for the complexation of both surfactants with p-CD. These involve an independent emf study using a surfactant selective electrode employing a liquid junction,13 a spectroscopic study14using fluorescent probes in competitive binding, and a surface tension study6-all values of K1 and KZare in Table 1. From these studies the values of K1 for !M'AB/p-CD all fall within the range (42 f 3) x lo3 mol-l dm3 and those for CTABIP-CD are in the range (65 f 6) x lo3mol-' dm3. In addition, for the system DTAB/ p-CD two independent emf studies,2J3 fluorescence competitive binding14and the present ITC, give K1 within (21 f 3) x lo3 mol-' dm3 and for DPyBr, an emP8 and the present ITC study give K1 = (22 f 4) x lo3 mol-' dm3.
60 Langmuir, Vol. 11,No. 1, 1995
The values of K1 for the surfactants used in this work are very high, which means that the equilibrium in Scheme 1is heavily biased toward the 1:1complex. It is therefore encouraging to observe good agreement between independent experiments for such high values of K1. The situation regarding Kz, however, is far more uncertain, and discrepancies of 2 orders of magnitude are observed in Table 1between different experiments. The question therefore arises as to the significance of low KZvalues in comparison to very high K1-indeed the Kz’s are less than the experimental error in Kl. There is no question that the second step in Scheme 1exists in these systems in the sense that the simple equation for the 1:l complex fails to describe the experimental data. The fitting procedure involving eqs 1and 2, which is used to obtain the KI and Kz values, involves a third unknown parameter, namely m,, the free CD concentration and the solution of a cubic equation. Where high values of K1 occur, the m,values are of the order mol dm-3. We have observed that during the fitting procedure for different sets of data the Kl values can always be generated to within f 1 0 % or so, whereas the Kz values are extremely sensitive. Clearly more work is required in order to assess the significance of these equilibria data. At present we are confident that consistent values ofK1 can be obtained for surfactant/CD complexes provided the experiments used are emf, com-
Mwakibete et al. petitive binding, or ITC. The& values are, however, only qualitative estimates, especiallyifKz K1. A recent report of an ITC study16 on the P-CDICTAB system quoted a value of 5 x lo5mol-1 dm3for &-this is almost an order of magnitude higher than the Kl value in Table 1. In this work micellar CTAB was titrated into p-CD solution and an attempt to compensate for the heat of dissolution of the CTAB micelles was made. In polymer/surfactant studies we have found that this is not possible. Finally it is interesting to note recent reports on the comparison of 1:l inclusion constants of small neutral molecules with cyclodextrins have shown excellent agreement betweenK1values found using different methods.20s21 In these circumstances the Rs are much smaller (by a factor of lo2or so) than those for surfactants and therefore easier to estimate more accurately.
Acknowledgment. R.C. wishes to thank University di Palermo and the University of Salford for financial support. H.M. thanks NORAD for a maintenance grant. We also wish to thank the British Council for financial support under the Academic Research Collaboration Programme, and the Deutschen Academischen Austanschohenst-DAAD for a travel grant to J.F.H. LA940422K
