The association of an ionic surfactants with β-cyclodextrin. An isothermal titration calorimeter study

Article abstract of DOI:10.1006/jcht.1999.0539

The association of a series of anionic surfactants (C_nH_2n+1SO₄Na, n = 6, 8, 10, 12, 14) with β-cyclodextrin was studied by means of the isothermal titration calorimeter (i.t.c.) at T = 298.15 K. For these types of inclusion complexes, the results agreed well with a 1:1 association mode. Apparent values for the association constants, and changes in the standard molar Gibbs energies, enthalpies, and entropies were derived for the association process. The results indicated that the association of surfactants with β-cyclodextrin is characterized by both favourable enthalpy and favourable entropy changes. The results also demonstrated that the longer the alkyl chain of the anionic surfactant, the greater the association constant with β-cyclodextrin.

Full text of DOI:10.1006/jcht.1999.0539

J. Chem. Thermodynamics 1999, 31, 1283–1296
Article No. jcht.1999.0539
Available online at http://www.idealibrary.com on
The association of anionic surfactants with
β-cyclodextrin. An isothermal titration
calorimeter study
Wumanjiang Eli,a Wenhai Chen,
Xinjiang Institute of Chemistry, Chinese Academy of Sciences, Urumqi
830011, P. R. C.
and Qunji Xue
Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences,
Lanzhou 730000, P. R. C.
The association of a series of anionic surfactants (C H
SO Na, n = 6, 8, 10, 12, 14)
n
2n+1
4
with β-cyclodextrin was studied by means of the isothermal titration calorimeter (i.t.c.)
at T = 298.15 K. For these types of inclusion complexes, the results agreed well with a
1:1 association model. Apparent values for the association constants, and changes in the
standard molar Gibbs energies, enthalpies, and entropies were derived for the association
process. The results indicated that the association of surfactants with β-cyclodextrin is
characterized by both favourable enthalpy and favourable entropy changes. The results
also demonstrated that the longer the alkyl chain of the anionic surfactant, the greater the
c
association constant with β-cyclodextrin. ꢀ 1999 Academic Press
KEYWORDS: association constant; β-cyclodextrin; anionic surfactants; isothermal titra-
tion calorimeter; thermodynamic parameters
1. Introduction
Cyclodextrins (CDs) are cyclic oligosaccharides built up from 6, or 7, or 8 glucose units,
called α-, β-, and γ -CD, respectively.(1) To a first approximation, they can be regarded as
cylinders with a hydrophilic exterior and a hydrophobic interior. In an aqueous solution of a
hydrophobic guest, the cyclodextrin molecule results in complexation in which no covalent
bonds are formed.(1–4) Surfactants are ideal guests, which allow a systematic study of
complexation with cyclodextrins, since both their hydrophobic and hydrophilic moieties
can be systematically changed.(5–14) Studies on the association of anionic surfactants
a
To whom correspondence should be addressed.
c
0021–9614/99/101283 + 14 $30.00/0
ꢀ 1999 Academic Press

1284
W. Eli, W. Chen, and Q. Xue
with cyclodextrins have been reported.(5–14) Unfortunately, the association constants
of anionic surfactants with β-CD reported in the literature differ widely.(5–14) In this
study, an isothermal titration calorimeter (i.t.c.)(15, 16) was used to measure association
constants and standard molar enthalpies for the reaction of a series of anionic surfactants
(CnH2n+1SO4Na, n = 6, 8, 10, 12, 14) with β-cyclodextrin. The indirect thermodynamic
parameters (enthalpy 1Ho, association constant Ka, and stoichiometry n) were calculated
using the optional ITC Bindworks program.(15, 16) The results obtained in this study were
examined to obtain information about the variation of thermodynamic quantities with
hydrophobic alkyl chain length of surfactants. This information can be useful both for
understanding the chemistry in these reactions and estimating thermodynamic quantities.
2. Experimental
REAGENTS
The β-cyclodextrin (β-CD) was obtained from Aldrich (purity ≥ 0.99 mass fraction) and
dried at 86 ◦C in vacuo for 24 h before use. Sodium alkyl sulfates (CnH2n+1SO4Na,
n = 6, 8, 10, 12, 14) were synthesized in our laboratory, and purified by recrystallization
twice from ethanol.(17) The critical micelle concentrations (c.m.c.s) of the surfactants
were determined by an electrical conduction method, and the values of the c.m.c.s
obtained were 200 mmol · dm−3, 140 mmol · dm−3, 33 mmol · dm−3, 8.7 mmol · dm−3
C14H29SO4Na, respectively. The results are in agreement with the literature.(17)
,
and 2.4 mmol · dm−3 for C6H13SO4Na, C8H17SO4Na, C10H21SO4Na, C12H25SO4Na, and
ISOTHERMAL TITRATION CALORIMETER MEASUREMENTS
The experiments were performed in a Model 4200 isothermal titration calorimeter
(Calorimetry Sciences Corporation, U.S.A.). All solutions were degassed by water
aspiration prior to loading. The sample cell (750 µL) was filled with surfactant solution
at approximately 0.1 mmol · dm−3, and a 250 µL burette syringe was filled with β-CD
solution of approximately 1.2 mmol · dm−3. The titration consisted of 25 injections
of 10 µL each at 300 second intervals. The i.t.c. uses proprietary software to set up
experiments, control the calorimeter, and collect the raw heat rate data. The software ITC
Dataworks is used to integrate the heat pulses and make baseline and/or blank corrections.
The thermodynamic parameters (enthalpy change 1Ho, association constant Ka, and
stoichiometry n) were calculated with the optional Bindworks program.(15, 16)
The binding of Ba2+ to 18-crown-6 is an ideal reaction for verifying the performance
of the calorimeter, and the values for the binding constant and the binding enthalpy has
been very precisely determined by Wadso¨ and co-workers.(19) We performed a single
determination under conditions very similar to those of Wadso¨ et al., and obtained n,
Ka, and 1Ho values of 1, (5754 ± 200) dm3 · mol−1, and −(31.25 ± 0.40) kJ · mol−1
,
respectively. The published values are n = 1, Ka = (5900 ± 200) dm3 · mol−1, and
1Ho = −(31.42 ± 0.20) kJ · mol−1 (19)
.
The enthalpies of dilution of the titrant and surfactants were determined in separate
experiments. Small dilution effects were obtained for surfactants, which were used to

The association of anionic surfactants with β-cyclodextrin
1285
correct results of the associated experiments, whereas no significant effect was found for β-
CD. The dilution of the solution titrated gave no significant contribution in any of the cases.
The calorimeter was frequently calibrated electrically during the course of the study.(15, 16)
The calorimetric measurements were carried out at T = 298.15 K.
3. Results and discussion
Data from a representative titration experiment are given in figure 1. The area under each
peak in figure 1 gives the heat Q for that injection. Data such as these were corrected for
surfactant heats of dilution, processed on the computer, and then deconvoluted using an
algorithm based on the Marquardt method.(20, 21) Results from the deconvolution of one
set of data (corresponding to that in figure 1) are shown in figure 2, where the points are
experimental values and the solid line is the calculated best-fit curve by least-squares de-
convolution. The best values of the fitting parameters are n = 1.03, Ka = 8370 L · mol−1
,
and 1Ho = −(10.9 ± 0.24) kJ · mol−1. The standard deviation of points from the
calculated line is 0.047 per cent of the total heat for association. The titration curve for
the heat of association of C12H25SO4Na with β-CD obtained after subtracting the heat of
dilution of surfactant is shown in figure 3 and represents the best-fit to the 1:1 association
model. The thermodynamic parameters (enthalpy change 1Ho, association constant Ka,
and stoichiometry n) were calculated with the optional Bindworks program.(15, 16) The
entropy change 1So and free energy change 1Go of association were calculated by using
the equation:
1Go = −RT ln Ka = 1Ho − T 1So,
(1)
where R is the universal gas constant.
Table 1 lists the thermodynamic data of anionic surfactants with β-CD and the published
values.(6–11) For these types of inclusion complexes, the results agree well with a 1:1
association model, consistent with the literature.(6–11) (The stoichiometric ratio for the
C12H25SO4Na/β-CD complex can also be obtained from the endpoint of figure 3. The
other stoichiometric ratios for these complexes can be obtained in the same way.) Most
of the published association constants(6, 8–10) are in disagreement with those of this work
(see table 1). However, these values have not been determined at the same surfactant
concentration, and this factor notably influences the association constant value.(11)
The most likely mode of complexation of ligands to cyclodextrins consists of insertion
of the hydrophobic portion of the ligand into the cyclodextrin cavity with the polar
group of the ligand remaining solvent exposed at the wide top end of the cavity.(1–4) In
general, the complexation is non-covalent. A combination of hydrophobic effects and
van der Waals forces and, in some cases, hydrogen bonding between the ligand and
the cyclodextrin are involved.(1–4, 22) The resultant of all these interactions is described
by the thermodynamic quantities in this study. Although, at present, it does not appear
possible to obtain a rigorous, quantitative breakdown of the relative contributions of
these various interactions for any specific (ligand + cyclodextrin) reaction, we believe
that the following qualitative picture is useful for understanding these complexation
reactions.

1286
W. Eli, W. Chen, and Q. Xue
3.0
2.5
2.0
1.5
1.0
0.5
0.0
2000
4000
6000
8000
t /s
FIGURE 1. Plot of heat Q against time for the measurement of the heat produced by chemical
reaction. The raw data were obtained for 25 automatic injections, each of 10 µL, of β-cyclodextrin
solution into the sample cell containing C H SO Na solution.
12 25 4
1500
1000
500
0
0
1
2
3
4
Mole ratio [ –CD]/[C12H25SO4Na]
FIGURE 2. Total integral heat of association −Q of C
H
12 25
SO Na with β-cyclodextrin against
4
mole ratio.
As can be seen from table 1, the inclusion complexes of surfactants with β-CD
are exclusively exothermic and mostly enthalpy driven with varying positive entropic

The association of anionic surfactants with β-cyclodextrin
1287
12
Endpoint
10
8
6
4
2
0
0
1
2
3
4
Mole ratio [ – CD]/[C12H25SO4Na]
FIGURE 3. The heat of association −Q of C SO Na with β-cyclodextrin against mole ratio.
H
12 25
4
TABLE 1. Values of the thermodynamic parameters; stoichiometry n, association constant K , enthalpy change
a
o
o
o
1H , free energy change 1G , and the entropy change 1S for the association of anionic surfactants with β-
a
CD at T = 298.15 K
o
o
o
K
1H
1G
1S
J · K · mol
a
Surfactants
n
3
−1
−1
−1
−1
dm · mol
kJ · mol
kJ · mol
C H SO Na
1 ± 0.01
543 ± 29
−1.17 ± 0.05
−15.6 ± 0.1
48.4 ± 0.5
6
13
4
b
c
[144 ± 37] [350]
C H SO Na
1 ± 0.02
1 ± 0.02
1 ± 0.03
1210 ± 95
−3.63 ± 0.15
−17.6 ± 0.2
46.9 ± 2
8
17
4
b
c
[343 ± 11] [1610]
d
e
[565] [2560]
C
C
H
SO Na
3446 ± 190
−6.82 ± 0.2
−10.9 ± 0.24
−20.2 ± 0.30
−22.3 ± 0.1
44.8 ± 1.7
38.2 ± 1
10 21
4
b
c
c
[2240 ± 150] [5400]
d
e
[2310] [8750]
H
12 25
SO Na
8150 ± 402
4
b
[4320 ± 670] [6600]
d
e
[7230] [25600]
f
g
[3630] [300]
C H
14 29
SO Na
1 ± 0.03
14561 ± 510
−18.1 ± 0.18
(10) c
−23.86 ± 0.1
18.9 ± 0.9
4
a
b
(11) d
Values are the averages of three determinations; n.m.r. spectroscopy;
conductimetry
;
conductance measure-
(7) e
(8) f
ments;
fluorimetric measurements (using fluorescent probes as a competitive inhibitor for association);
conductance
(6) g
Na
(9)
measurements;
conductivity and P measurements.

1288
W. Eli, W. Chen, and Q. Xue
26
24
22
20
18
16
14
4
6
8
10
12
14
16
n
o
FIGURE 4. Relationship between Gibbs free energy (−1G ) and the number (n) of carbon atoms
in the hydrocarbon tail of the surfactants.
contributions. From studies of the thermodynamics of the β-CD–surfactant interaction, we
conclude that there is a significant contribution from the classical hydrophobic effect (i.e. a
positive 1So contribution)(18, 20, 21) but that this contribution is reduced by predominant
binding forces characterized by negative enthalpy and entropy changes. We speculate
that the latter forces may be due to van der Waals interactions and hydrogen bonding
between the surfactant and β-CD. Using the simple qualitative argument that a surfactant
strongly bound within the β-CD cavity has lost some freedom of motion, one expects it to
have a lower entropy than if it were weakly bound within the cavity. The van der Waals
and hydrophobic interactions become stronger with increasing alkyl chain length of the
surfactants.(23, 24) The values of enthalpy change (−1Ho) increase with increasing alkyl
chain length of the surfactants, and this indicates that it is energetically favourable for
the weak polar surfactants to be included in the β-CD cavity (inner diameter of 0.78 µm
wide and a length of 0.78 µm).(1–4, 18) Obviously, the largest changes in enthalpy would be
for the C14H33SO4Na that has the longest alkyl chain length with the highest association
constant. The values of the entropy change (1So) are positive and decrease with increasing
alkyl chain length of the surfactants. This indicates that the degrees of freedom of the
surfactant included in the β-CD cavity become lower with increasing alkyl chain length
of the surfactants. The results also indicate that −1Go increases steadily with increasing
alkyl chain length of the surfactants (see figure 4). The results demonstrate that the longer
chain surfactants lead to a greater association constant with β-CD.
The rationalization of 1Ho and 1So values, while of interest for understanding
the molecular details and driving forces involved in complex formation, is necessarily
somewhat speculative, and it must be realized that other factors such as the displacement
of high-energy water from within the β-CD cavity, or structural changes of the β-CD
molecule may contribute to 1Ho and 1So for the surfactant binding.(18, 24–28) However, a

The association of anionic surfactants with β-cyclodextrin
1289
straightforward interpretation of 1Go for β-CD/surfactant complex formation is possible
in terms of hydrophobic binding forces between the surfactant and the β-CD.
In conclusion, the experiments provide estimates of the heat and entropy of association
in addition to the association constant, leading to a more complete characterization of the
thermodynamics of interaction.
REFERENCES
1. Bender, M. L.; Komiyana, M. Cyclodextrin Chemistry. Springer-Verlag: Berlin. 1987.
2. Fendler, J. H. Membrane Mimetic Chemistry. Wiley-Interscience: New York. 1982, pp. 194–
201.
3. Griffiths, D. W.; Bender, M. L. Adv. Catal. 1973, 23, 209–218.
4. Cramer, E.; Saenger, W.; Spatz, H.-Ch. J. Am. Chem. Soc. 1967, 89, 14–19.
5. Okubo, T.; Kitano, H.; Ise, N. J. Phys. Chem. 1976, 80, 2261–2664.
6. Satake, I.; Yoshida, S.; Hayakawa, K.; Maedaand, T.; Kusumoto, Y. Bull. Chem. Soc. Japan
1986, 59, 3991–3003.
7. Palepu, R.; Reinsborough, V. C. Can. J. Chem. 1988, 66, 325–328.
8. Park, J. W.; Song, H. J. J. Phys. Chem. 1989, 93, 6454–6459.
9. Georgos, J.; Desmettre, S. J. Colloid Interface Sci. 1987, 118, 192–200.
10. Guo, Q.-X.; Li, Z. Z.; Ren, T.; Zhu, X. Q.; Liu, Y.-C. J. Inc. Phenom. 1994, 17, 149–156.
11. Saint Aman, E.; Serve, D. J. Colloid Interface Sci. 1990, 138, 365–375.
12. Junquera, E.; Tardajos, G.; Aicart, E. Langmuir 1993, 9, 1213–1219.
13. Sasaki, K. J.; Christian, S. D.; Turker, E. E. J. Colloid Interface Sci. 1990, 134, 412–416.
14. Lu, R.-H.; Hao, J.-C.; Wang, H.; Tong, L.-H. J. Colloid Interface Sci. 1997, 192, 37–42.
15. Wiseman, T.; Williston, S.; Brandts, J. F.; Lin, L.-N. Anal. Boichem. 1989, 179, 131–137.
16. Freire, E.; Mayorga, O.; Straume, M. Anal. Chem. 1990, 62, 950–959.
17. Jerchel, D.; Becher, H.; Varahamutri, M. K. Z. Naturforsch. Teil 1956, 11, 681–687.
18. Cromwell, W. C.; Bystrom, K.; Eftink, M. R. J. Phys. Chem. 1985, 89, 326–332.
19. Briggner, L. E.; Wadso¨, I. J. Biochem. Biophys. Methods 1991, 22, 101–118.
20. ITC Data Analysis in Origin. MicroCal Software Inc.: MicroCal Origin, Northampton, CA.
1993, pp. 65.
21. Berington, P. R. Data Reduction and Error Analysis for the Physical Science. McGraw-Hill:
New York. 1969, p. 235.
22. Rekharsky, M. V.; Mayhew, M. P.; Goldberg, R. N. J. Phys. Chem. B 1997, 101, 87–100.
23. Tanford, C. The Hydrocarbon Effect: formation micelles and biological membranes. Wiley: New
York. 1980, p. 51.
24. Bastors, M.; Briggner, L. E.; Shehatta, I.; Wadso, I. J. Chem. Thermodynamics 1990, 22, 1181–
1190.
25. Inoue, Y.; Hakushi, T.; Liu, Y.; Tong, L.-H. J. Am. Chem. Soc. 1993, 115, 475–481.
26. Liu, T.; Tong, L.-H.; Inoue, Y.; Hakushi, T. J. Chem. Soc., Perkin Trans. 1990, 2, 1247–1252.
27. Liu, T.; Tong, L.-H.; Inoue, Y.; Hakushi, T. J. Phys. Chem. 1990, 94, 2666–2672.
28. Liu, T.; Tong, L.-H.; Inoue, Y.; Hakushi, T. J. Phys. Chem. 1988, 94, 2371–2374.
(Received 19 January 1999; in final form 19 April 1999)
WE-149

1290
W. Eli, W. Chen, and Q. Xue
Appendix
TABLE A.1. Values of the experimentally determined heats of association −Q for the association of
C H SO Na with β-CD at T = 298.15 K and various mole ratios
6
13
4
Injection
number
Mole
ratio
−Q(µJ) per
injection
Total −Q(µJ)
measured
−Q
kJ · mol
−1
1
2
0.15648
0.31296
0.46944
0.62592
0.7824
13.92851
13.59225
13.05439
12.16845
10.7232
8.61604
6.17007
4.06664
2.63104
1.74983
1.21511
0.88121
0.66229
0.51345
0.40871
0.33312
0.27562
0.23153
0.19766
0.1701
13.92851
27.52076
40.57515
52.7436
0.17687
0.34947
0.51524
0.66976
0.80598
0.91539
0.99374
1.04538
1.07879
1.10101
1.11644
1.12763
1.13604
1.14256
1.14775
1.15198
1.15548
1.15842
1.16093
1.16309
1.16498
1.16663
1.16809
1.1694
3
4
5
63.47092
72.08696
78.25703
82.32367
84.95471
86.70454
87.91965
88.80086
89.46315
89.9766
6
0.93888
1.09535
1.25184
1.40831
1.56479
1.72127
1.87775
2.03422
2.19071
2.34719
2.50368
2.66015
2.81662
2.9731
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
90.38531
90.71843
90.99405
91.22558
91.42324
91.59334
91.74217
91.87211
91.98709
92.09025
92.18239
3.1296
3.28608
3.44255
3.59902
3.75548
3.91198
0.14883
0.12994
0.11498
0.10316
0.09214
1.17057

The association of anionic surfactants with β-cyclodextrin
1291
TABLE A.2. Values of the experimentally determined heats of association −Q for the association
of C H SO Na with β-CD at T = 298.15 K and various mole ratios
8
17
4
Injection
number
Mole
ratio
−Q(µJ) per
injection
Total −Q(µJ)
measured
−Q
kJ · mol
−1
1
2
0.15646
0.31293
0.46939
0.62586
0.78232
0.93879
1.09524
1.25171
1.40817
1.56463
1.7211
43.977
43.9770
0.548
42.91599
41.21801
38.42129
33.86791
27.20395
19.48229
12.83839
8.30748
5.52602
3.83675
2.78147
2.09051
1.62185
1.29122
1.05048
0.86991
0.73188
0.62354
0.53767
0.46866
0.41169
0.36353
0.32501
0.29051
86.89229
1.08277
1.59639
2.07516
2.49719
2.83618
3.07895
3.23893
3.34245
3.41131
3.45912
3.49378
3.51983
3.54004
3.55613
3.56922
3.58006
3.58918
3.59695
3.60365
3.60949
3.61462
3.61915
3.6232
3
128.1103
4
166.53159
200.3995
5
6
227.60345
247.08574
259.92413
268.23161
273.75763
277.59438
280.37585
282.46636
284.08821
285.37943
286.42991
287.29982
288.0317
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1.87756
2.03402
2.19049
2.34696
2.50343
2.65988
2.81634
2.9728
288.65524
289.19291
289.66157
290.07326
290.43679
290.7618
3.12929
3.28575
3.44221
3.59866
3.7551
3.91159
291.05231
3.62682

1292
W. Eli, W. Chen, and Q. Xue
TABLE A.3. Values of the experimentally determined heats of association −Q for the association
of C
H
10 21
SO Na with β-CD at T = 298.15 K and various mole ratios
4
Injection
number
Mole
−Q(µJ) per
injection
Total −Q(µJ)
measured
−Q
kJ · mol
−1
ratio
1
2
0.15725
0.31449
0.47174
0.62899
0.78623
0.94348
1.10072
1.25797
1.41521
1.57246
1.7297
81.916
81.916
1.03039
2.0359
79.93805
76.77633
71.56749
63.08643
50.6733
36.28037
23.9136
15.47387
10.29367
7.14705
5.18022
3.89391
3.02179
2.40488
1.95649
1.62021
1.36343
1.16229
1.0017
161.85405
238.63038
310.19787
373.2843
3
3.00164
3.90186
4.6954
4
5
6
423.9576
5.3328
7
460.24697
484.16057
499.63444
509.92811
517.07516
522.25538
526.14929
529.17108
531.57596
533.53245
535.15266
536.51609
537.67838
538.68008
539.55219
540.31937
540.99671
541.6017
5.78927
6.09007
6.28471
6.41419
6.50409
6.56925
6.61823
6.65624
6.68649
6.7111
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1.88695
2.04419
2.20144
2.35869
2.51595
2.67318
2.83042
2.98767
3.14493
3.30218
3.45942
3.61665
3.77388
3.93115
6.73148
6.74863
6.76325
6.77585
6.78682
6.79647
6.80499
6.8126
0.87211
0.76718
0.67734
0.60499
0.5414
542.1431
6.81941

The association of anionic surfactants with β-cyclodextrin
1293
TABLE A.4. Values of the experimentally determined heats of association −Q for the association
of C
H
12 25
SO Na with β-CD at T = 298.15 K and various mole ratios
4
Injection
number
Mole
−Q(µJ) per
injection
Total −Q(µJ)
measured
−Q
kJ · mol
−1
)
ratio
1
2
0.15789
0.31578
0.47366
0.63155
0.78944
0.94733
1.10521
1.26311
1.42098
1.57887
1.73676
1.89465
2.05253
2.21043
2.36831
2.52621
2.68409
2.84197
2.99986
3.15777
3.31565
3.47353
3.63141
3.78928
3.94719
125.048
122.028
177.202
109.25
96.304
77.354
55.397
36.505
23.622
15.713
10.911
7.907
125.048
247.076
364.278
473.528
569.832
647.186
702.583
739.088
762.71
1.63062
3.22185
4.75016
6.17477
7.43057
8.43926
9.16164
9.63766
9.94569
10.15059
10.29286
10.39597
10.47349
10.53363
10.5815
10.62045
10.65271
10.67985
10.70298
10.72292
10.74029
10.75555
10.76904
10.78108
10.79186
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
778.423
789.334
797.241
803.186
807.798
811.469
814.456
816.93
5.945
4.612
3.671
2.987
2.474
2.081
819.011
820.785
822.314
823.646
824.816
825.851
826.774
827.601
1.774
1.29
1.332
1.17
1.035
0.923
0.827

1294
W. Eli, W. Chen, and Q. Xue
TABLE A.5. Values of the experimentally determined heats of association −Q for the association
of C
H
14 29
SO Na with β-CD at T = 298.15 K and various mole ratios
4
Injection
number
Mole
−Q(µJ) per
injection
Total −Q(µJ)
measured
−Q
kJ · mol
−1
ratio
1
2
0.15773
0.31546
0.4732
207.27245
202.26538
194.26769
181.08644
159.62797
128.21748
91.8234
60.50834
39.15442
26.04512
18.08455
13.10703
9.85356
7.64469
6.08499
4.95102
4.10035
3.44966
2.94061
2.5346
207.27245
409.53783
603.80552
784.89196
944.51993
1072.73741
1164.56081
1225.06915
1264.22357
1290.26869
1308.35324
1321.46027
1331.31383
1338.95852
1345.04351
1349.99453
1354.09488
1357.54454
1360.48515
1363.01975
1365.2271
1367.16706
1368.88204
1370.41219
1371.78251
2.73627
5.40644
3
7.97103
4
0.63093
0.78866
0.94639
1.10411
1.26185
1.41958
1.57731
1.73504
1.89277
2.05049
2.20824
2.36597
2.52371
2.68143
2.83915
2.99688
3.15464
3.31237
3.47009
3.62781
3.78552
3.94328
10.36161
12.46891
14.16155
15.37374
16.17253
16.68942
17.03325
17.27199
17.44502
17.5751
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
17.67602
17.75635
17.82171
17.87584
17.92138
17.9602
17.99366
18.0228
2.20735
1.93996
1.71498
1.53015
1.37032
18.04841
18.07105
18.09125
18.10934

The association of anionic surfactants with β-cyclodextrin
1295

1296
W. Eli, W. Chen, and Q. Xue