Thermodynamic Investigation (Volume and Compressibility) of the

J. Phys. Chem. B 2000, 104, 1869-1879

1869

Thermodynamic Investigation (Volume and Compressibility) of the Systems β-Cyclodextrin + n-Alkyltrimethylammonium Bromides + Water G. Gonza´ lez-Gaitano,† A. Crespo,‡ and G. Tardajos*,‡ Departamento de Quı´mica y Edafologıá (seccio´ n de Quı´mica Fı´sica), Facultad de Ciencias, UniVersidad de NaVarra, 31080 Pamplona, Spain and Departamento de Quı´mica-Fı´sica I, Facultad de Quı´micas, UniVersidad Complutense, 28040 Madrid, Spain ReceiVed: July 30, 1999; In Final Form: NoVember 10, 1999

Density and sound velocity data for aqueous solutions at 298 K containing a homologue series of alkyltrymethylammonium bromides (CnTAB, n ) 10, 12, 14, 16) in the absence and presence of β-cyclodextrin were analyzed to calculate the molar apparent and partial volumes and adiabatic compressibilities. For the binary systems, the molar partial compressibilities and volumes of the pure surfactants in water have been obtained as a function of the concentration and compared with the literature data, and the methylene group contributions have been deduced. For the ternary systems, a remarkable increase of both the molar partial volume and compressibility of the surfactant at infinite dilution with respect to the value in water is observed. The large values of the transfer properties of the surfactants at infinite dilution, molar partial compressibilities and volumes, can be discussed in terms of a simple model in which the balance between the released water from the cavity and the methylene groups of the substrate that enter into the macrocycle is considered. The positive molar compressibility of the surfactant when it is forming the complex, compared to the negative value when it is in pure water, proves the hydrophobic component of the interaction. Both partial molar volumes and compressibilities of the surfactants are the same in the absence and in the presence of β-CD at high surfactant molalities, indicating the nonparticipation of the complex into the micelles, and the cmcs are displaced in an extension that shows the participation of a 2:1 stoichiometry with the longest homologues (n ) 14, 16). The application of Young’s rule permits to calculate the reaction parameters from the bibliographic data of the binding constants. The transfer volumes and compressibilities increase with n, indicating that the predominant stoichiometry turns to 2:1 when the hydrocarbon chain is long enough.

1. Introduction The main feature that makes cyclodextrins (CDs) of interest is their ability to form inclusion complexes with a wide variety of guest molecules in solution. This property offers many interesting applications which are described extensively in the literature.1 These macrocycles consists of several R-D-glucopyranose residues (6, 7, or 8 rings, named R-, β-, and γ-CD, respectively) linked by glycosidic bonds R-1,4. Due to the lack of free rotation about the glycosidic bonds these molecules display a cylindrical or hollow truncated cone shape (Figure 1). The cavity has a hydrophobic character compared to water, whereas the rims, constituted by the primary and secondary OH groups, are hydrophilic. The first condition required to have an inclusion complex with CDs is the fit, total or partial, of the guest in the cavity, and a favorable energetic balance, which depends on the size of the CD, its degree of substitution and the nature of the guest.2 The use of surfactants as target molecules offers certain advantages to understand the thermodynamics of complexation, since it is easy to modulate their properties to study the effect that a determined factor may have in the process (e.g., the polar nature of the head, charge, length of the hydrocarbon tail, etc.). These variables affect the binding constants and the stoichiom* To whom correspondence should be addressed. E-mail: tardajos@ eucmax.sim.ucm.es. † Universidad de Navarra. E-mail: [email protected]. ‡ Universidad Complutense.

Figure 1. Structure of the β-cyclodextrin (β-CD).

etry of the complexes and modify the aggregation properties of the surfactants in their aggregation properties. For example, surfactants quite different from the structural point of view form inclusion complexes with CDs strong enough to displace the critical micelle concentration (cmc) in a certain extension. Volumetric and, particularly, compressibility properties of solutes are known to be sensitive to the degree and nature of the solute hydration, and many studies have been carried out on more or less simple compounds containing hydrophobic and hydrophilic groups, such as alcohols,3 monosaccharides,4 amino acids,5 etc. In the case of a complex with CDs, the transference of a guest molecule from water to the nonpolar cavity of a CD must produce remarkable changes in its molar compressibility or volume, as are observed, for instance, in micellization processes, in which a surfactant molecule passes from water to the hydrocarbon-like core of a micelle.6 These changes are

10.1021/jp9926995 CCC: $19.00 © 2000 American Chemical Society Published on Web 02/04/2000

1870 J. Phys. Chem. B, Vol. 104, No. 8, 2000 chiefly due to alteration in the degree of hydration both of the host and guest molecules, since the CD must release its inclusion water molecules to allow the entrance of the guest, and the latter must lose its hydration shell also. Linear surfactants are interesting families of compounds in order to study the role that hydration water has in the thermodynamics of complexation and the effect that the length of the hydrocarbon chain has in the inclusion parameters. To our knowledge, only a few papers take up volumetric studies in systems CD + surfactant + water, using natural7 or modified cyclodextrins.8,9 Compressibility investigations are even scarcer, being limited to the studies of Gonza´lez-Gaitano et al. with sodium cholate10 and decyltrimethylammonium bromide11(DTAB). In this work we have focused our attention on a series of n-alkyltrimethylammonium bromides, dodecyl, tetradecyl, and hexadecyltrimethylammonium bromide (DoTAB, TTAB, and CTAB respectively), continuing the mentioned previous work with the system DTAB + β-CD + water. The speed of sound and density have been measured in a wide range of concentration in the absence and in the presence of β-CD, and from these measurements the molar partial volumes and adiabatic compressibilities have been calculated. These experiments give us information at a molecular level of the nature of the complex, the stoichiometry, and the effect that the CD has on the micellization, by application of a simple model that considers the released water molecules from the cavity and the part of the guest that enters the macrocycle. 2. Experimental Section Materials. Decyltrimethylammonium bromide (DTAB) and dodecyltrimethylammonium bromide (DoTAB) were obtained from Eastman-Kodak, tetradecyltrimethylammonium bromide (TTAB) was from Aldrich, and hexadecyltrimethylammonium bromide (CTAB) from Fluka. β-CD was purchased from Sigma, with a water content of 13.5%, as determined from thermal analysis. Purity of the reactants was in each case better than 99%, and all of the substances were used as received without further purification. The solutions were prepared by weight in redistilled, deionized (Millipore super-Q system), and degassed water. Density and Speed of Sound Measurements. Measurements of speed of sound and density have been performed simultaneously with a computerized technique designed in this laboratory and described extensively elsewhere.11,12 For the density, it uses an Anton Paar DMA 601 HT vibrating tube densitometer equipped with a frequency meter DMA 60. Temperature control of the tube is maintained with recirculation from a water bath using a temperature controller designed by us. The speed of sound is measured with a pulse-echo type technique, using a transducer of 13 MHz excited with pulses of the same frequency. The ultrasonic cell is immersed in the same bath, and the concentration changed by addition of stock solution from a digital buret Metrohm 665. Thus, both the velocity and the density are measured simultaneously by increasing the concentration at equal intervals. Before the experiments, the ultrasonic cell is calibrated with pure water (1496.739 m s-1, ref 13), and the densitometer with pure water (997.045 m3 mol-1, ref 14) and air.15 All of the measurements were carried out at 298.15 K, with a stability better than 1 mK. Under these conditions, the precisions in the speed of sound and density are 2 × 10-3 m s-1 and 1.5 × 10-3 kg m-3, respectively.

Gonza´lez-Gaitano et al. The molar properties that can be calculated from F and u are apparent and partial volumes and adiabatic compressibilities. In ternary systems such as the studied, in which the CD molality is kept constant, the apparent molar volume of the surfactant is related to the density of the solution, F, through

νφ,s )

Ms (1 + mCDMCD)(F - F0) F msFF0

(1)

where Ms, ms, MCD, and mCD are the molar masses and molalities for the surfactant and β-CD, respectively, and F0 is the density of the solution when ms is zero. The molality in this formula is defined as mole of solute per kg of water. If the speed of sound, u, is known, the apparent molar compressibility can be calculated as

κφ,s ) βνφ,s +

(1 + mCDMCD)(β - β0) msF0

(2)

where β ) 1/Fu2 is the adiabatic compressibility of the solution and β0 that of the system when ms is zero. From Vφ,s and κφ,s, the corresponding molar partial properties can be readily obtained taking derivatives with ms

νs ) κs ) -

( ) ∂V ∂ns

) nw,nCD

( ( )) ∂ ∂V ∂ns ∂P S

d (ν m ) dms φ,s s

nw,nCD

)

d (κ m ) dms φ,s s

(3)

(4)

All of the experiments were carried out at 298.15 K, keeping mCD fixed in the ternary systems. The concentration range was swept in two experiments, at high and low molalities, to minimize errors in the concentration (except for CTAB). 3. Results and Discussion System CnTAB + Water. cmc Calculations. The cmc of the surfactants may be calculated through any property which changes around the critical concentration, e.g., from the plots of density or sound velocity versus the surfactant molality. However, considering that the speed of sound changes are greater than those of the density around the cmc, we have used that property instead. The method consisted of obtaining the derivatives of the plots with respect to the surfactant molality, provided that many measurements at close constant intervals of concentration are available. This gives an inflection point in the first derivative, ∂u/∂m, and a minimum in ∂2u/∂m2 plots (Figure 2). Table 1 contains the cmcs thus estimated, in perfect accordance to the literature data within the experimental uncertainty.16 Molar Partial Volumes. In Figures 3, 5, and 6 the apparent and partial volumes versus the surfactant concentration are plotted. For TTAB and CTAB we have only plotted the apparent properties. Below the cmc, the properties change smoothly with the surfactant molality, ms, and the extrapolations at infinite dilution give the volumes and compressibilities of the monomers. At concentrations above the cmc the property increases as a result of micelle formation, until a constant value is reached. The apparent molar volume of the pure surfactants in the monomer region has been fitted to an equation of the form

νφ,s ) ν0s + Aνm1/2 s + Bνms

(6)

where ν0s is the molar partial volume of the surfactant, AV is the

Molar Partial Volume and Compressibility

J. Phys. Chem. B, Vol. 104, No. 8, 2000 1871

Figure 2. Plot of the second derivative of sound velocity versus the surfactant molality for DoTAB and CTAB.

TABLE 1: Thermodynamic Parameters for Alkyltrimethylammonium Bromides in Micelle Form in Water at 298.15 K cmc (mmol kg-1)a 3 -1 6 b Vm s (m mol × 10 )

3 -1 6 c ∆Vm s (m mol × 10 ) m -1 3 -1 d κs (PPa m mol )

∆κms (PPa-1 m3 mol-1)e

DTAB

DoTAB

TTAB

CTAB

65.7 262.1 ( 0.4 261.2 ( 0.6 262.3 ( 0.2 262.2

15.0 295.3 ( 0.2 294.4 ( 0.4 295.5 ( 0.2 296.2 294.8

3.80 327.9 ( 0.3 326.8 ( 0.7 327.9 ( 0.2 329.4 327.8

0.92 360 ( 1 360 ( 10 360.7 ( 0.3

6.3, 6.4 118 ( 1 119 ( 1 117.5 ( 0.5 112 112

11.2, 10.8 136 ( 1 136 ( 2 136.9 ( 0.4 137 133

15, 17 157 ( 4 156 ( 20 154.4 ( 0.5

125, 127

151, 147

173, 173

261.6 5.2, 5.1 96.3 ( 0.09 98 ( 6 96.5 ( 0.4 98.8 119.4 102.9, 106

153

f 18 20 19 36

g 18 20 19 36

cmc - critical micelle concentration. - micellization volume. - change in the micellization volume. d κm s - adiabatic micellization f Calculated from eq 7. g Calculated from eq 9. compressibility. e ∆κm change in the adiabatic micellization compressibility. s a

b

Vm s

360.4

ref

Debye-Hu¨ckel limiting slope (1.865 cm3 kg1/2 mol3/2 at 25 °C for a 1:1 electrolyte), and BV is a deviation parameter of the limiting law. Table 2 summarizes the fitted parameters for the surfactant in monomer form, together with recent literature values. The volume of the surfactant in the micellar state, Vm s , can be calculated from the extrapolations of the molar partial volume, Vs, at high concentrations. Since this property quickly reaches a plateau above the cmc, we have calculated the average value of Vs in this zone. The corresponding change in the micellization m volume, ∆Vm s , has been calculated as the difference between Vs and the apparent property at the cmc (Table 1). There is another calculation method to obtain the monomer volume which assumes a pseudophase model. This strategy has been employed by Zielinski et al.17 and more recently by Mosquera et al.16 The model considers the cmc as the solubility of the surfactant by defining two different phases, a monomeric phase and a micellar one. Below the cmc, the concentration (g cm-3) of the surfactant is cs ) c, and the micelle concentration,

c

∆Vm s

cm ) 0; above the critical concentration that of the monomer is cs ) cmc and cm (micelle concentration) ) c - cmc. If it is presumed that the molar volume of the surfactant remains constant in each of the zones of concentration, the density of the solution can be written as

F ) F0 + (1 - V0s /MsF0)cs + (1 - Vm s /MsF0)cm

(7)

where Ms is the molecular weight of the surfactant, V0s its molar volume when it is in the free state, and Vm s the volume in the micelle form. Thus, it is possible to calculate from the slope of F versus c curves the volume of the surfactant in both forms, provided it remains constant within the fitting intervals. In Tables 1 and 2 are included the volumes thus calculated. The results for the volumes of the surfactant in monomer form agree well with the literature data and they are practically the same, independent of the method used for the calculation. As can be seen in Table 2, the errors in the estimation of the property increase with the chain length as the concentration

1872 J. Phys. Chem. B, Vol. 104, No. 8, 2000

Gonza´lez-Gaitano et al.

Figure 3. Apparent and partial molar volumes for DoTAB (open circles) and mixture with β-CD (solid circles, mCD ) 10.078 mmol kg-1).

becomes increasingly low. However, the calculated errors in the volume are smaller if they are obtained from the apparent molar property instead of from the pseudophase model. The latter model is usually applied to surfactants with low cmcs in which it is expected that the volume of the monomer will not change very much with the concentration. However, the reduced interval of concentration makes the errors in the slope, and hence in V0s , higher. Our values for DTAB and DoTAB agree well with Kudryashov18 and De Lisi data,19 but for TTAB they agree better with those of Zielinsky et al.20 For CTAB, De Lisi and Kudryashov’s results are higher than ours. To calculate the CH2 group contribution to the monomer volume it would be unwise to give the same weight to all of

the values, since those of the longer hydrocarbon chains have higher errors than those of the shorter homologues. So, we have performed the fit using the error in V0s for each surfactant in order to weigh its contribution. The function to be minimized is the sum of the square of the residuals, but as a difference to a simple linear fit, each residual is divided by the corresponding error. In this way, the resulting fit with data calculated from the apparent molar volumes gives V0(CH2) ) (15.89 ( 0.04) × 10-6 m3 mol-1 and the intercept is (97.5 ( 0.4) × 10-6 m3 mol-1. With the pseudophase model, the fit gives V0(CH2) ) (15.9 ( 0.4) × 10-6 m3 mol-1 and (97 ( 3) × 10-6 m3 mol-1, virtually the same, but with higher errors, so being those of the volumes. The reported group contribution for this same series, ranging from n ) 8 to n ) 16 is (15.7 ( 0.2) × 10-6 m3 mol-1 (Kudriashov et al.), and the average value calculated for homologous series of several organic compounds21 is 15.9 × 10-6 m3 mol-1. Buwalda et al.,22 with shorter homologues (n ) 3 to 6), give V0(CH2) ) 16.0 × 10-6 m3 mol-1. If we extrapolate the fit to n ) 1 we obtain (113.4 ( 0.4) × 10-6 m3 mol-1, which is very close to the reported value of 114.2 × 10-6 m3 mol-1 for tetramethylammonium bromide (TMAB), (CH3)4NBr (ref 23). As far as micelle volumes are concerned, the accordance with literature data is good, irrespective of the method employed for the calculation of Vm s , and the CH2 group contribution to the volume of the surfactant in micelle state is (16.32 ( 0.09) × 10-6 m3 mol-1, the same obtained by Kudriashov et al. (16.3 ( 0.1) ×10-6 m3 mol-1 and slightly lower than that of Zielinski et al. (16.8 × 10-6 m3 mol-1). The value is higher than the CH2 contribution for the monomer in the free form, as corresponds to a surfactant in an environment similar to a liquid hydrocarbon. It is also interesting to analyze the behavior of the DebyeHu¨ckel limiting law deviation parameter, BV, which increases in a non linear tendency with n (Figure 8). Although the error in this coefficient increases considerably, the trend is clear, proving that the increase in the hydrophobicity of the surfactant makes it more different than an 1:1 ideal electrolyte, as it is to be expected from a molecule of these features. This coefficient makes V0s quite different from the volume that the surfactant has at the cmc and, thus, the assumption that it is established with the pseudophase model could not be valid. Molar Partial Compressibilities. In Figures 4 to 6 the molar adiabatic compressibilities are plotted. The shape of the curves is the same as the volumes and, for the surfactant in the

TABLE 2: Thermodynamic Parameters for Alkyltrimethylammonium Bromides in Monomer Form in Water at 298.15 K DTAB V0s (m3 mol-1 × 106)a

(m3 mol-2 kg)c

Bv κ0s (PPa-1 m3 mol-1)b

Bκ (PPa-1 m3 mol-2 kg)c

256.57 0.95 ( 0.5 -13.85 ( 0.07 -7.56 ( 0.03 -8.3 ( 0.6 -14.8 -16.4 98 ( 2

CTAB

ref

( 0.08 288.0 ( 0.7 288.8 ( 0.3 283.4 288.2

DoTAB

( 0.8 316 ( 12 320.2 ( 0.5 309.6 319.8

TTAB

341 ( 2 343 ( 19 350.7 ( 2

18 ( 9 -17.9 ( 0.5 -8.28 ( 0.08 -9.9 ( 1 -42.2 -24

1200 ( 400 -20 ( 2 -11.1 ( 0.5 -11.8 ( 0.7 -78.0 -34

5300 ( 3000 -23 ( 3 -17 ( 1 -13.9 ( 2.5

d e 18 20 19 36

-44

730 ( 40

1920 ( 700

7600 ( 4500

351.4

f g 18 20 19 36

- molar volume of the monomer. - adiabatic compressibility of the monomer. Bv and Bκ - deviation parameters of the DebyeHu¨ckel limiting law for the molar volume and compressibility. d Calculated from eq 6. e Calculated from eq 7. f Calculated from eq 8. g Calculated from eq 9. a

V0s

256.46 ( 0.02 256.1 ( 0.2 257.0 ( 0.2 255.0

b

κ0s

c



Figure 4. Apparent and partial molar compressibilities for DoTAB (open circles) and mixture with β-CD (solid circles, mCD ) 10.078 mmol kg-1).

Figure 5. Apparent molar volumes and compressibilities for TTAB (open circles) and mixture with β-CD (solid circles, mCD ) 3.206 mmol kg-1).

monomer region, we can apply an equation similar to eq 6:

is approximately the same as these authors obtain at 7.5 MHz. Thus, we conclude with them that the relaxation contribution is insignificant and it is worthless to consider its effect in u and, hence, in κφ,s. To estimate the change in the compressibility of the monomers from free form to micelle form, ∆κm, we have used the same procedure as with the volumes, taking the mean value of the molar property in the micelles region to obtain κm s and subtracting κφ,s at the beginning of the aggregation (Table 1). Zielinski et al. apply the pseudophase model to the adiabatic compressibility of the solution, simply by taking derivatives in eq 7 with pressure at adiabatic conditions, so thus

κφ,s ) κ0s + Aκm1/2 s + Bκms

(8)

To our knowledge, there are no numerical estimations of the limiting law parameter for the adiabatic compressibility, Aκ. Hence, we have used Aκ ) 2.55 PPa-1 m3 mol-3/2 kg1/2, that is, the same as that of the isothermal compressibility, since the plots of both properties have the same shape. The results are collected in Table 2, together with recent literature values, and plotted in Figure 7. When dealing with u, it is sometimes necessary to consider losses in the energy of the ultrasonic wave due to relaxation processes which could modify the adiabatic compressibility, especially in micellar systems, in which these processes (for instance, the equilibrium of a monomer with the micelle) take place. If such is the case, the relaxation contribution to the compressibility must be taken into account in β. It is possible to quantify this effect by measuring the ultrasound absorption per wavelength as a function of the concentration. We have performed simultaneously the measurement of R and u versus the concentration finding that, for the surfactants in the monomer state, the absorption is negligible for all of the surfactants under study. The micelle zone is more susceptible of undergoing these relaxation processes, but the absorption is small and it only reaches manifest values in DTAB. Kudryashov et al. have measured this contribution too, concluding that at their operating frequency for C8TAB (7.5 MHz) the relaxation term is small but not negligible, but for DTAB the corrections to be done in κφ,s remain within the margin of error of the technique. In the worst of our cases, that is, for the highest DTAB concentration employed, Rλ ) 1.3 × 10-3 Np (working at 13.5 MHz) which

m β ) β0 + (κ0s - β0V0s )Mscs + (κm s - β0Vs )Mscm

(9)

where β is the adiabatic compressibility of the solution, β0 that of the solvent, and V0s and Vm s are the values obtained with eq 7. Therefore, it is possible to obtain from the slope of the plots of β of the solution versus c the compressibility of the surfactant in both phases. In Tables 1 and 2 we have included the corresponding values obtained with this procedure. The compressibility of the surfactant in free form differs in absolute number depending on the calculation used, as evidenced in Table 2. The measurements for these systems in the literature are scarce and fall between two different ranges. There are the values of Kudryashov et al., which are similar to our values obtained with the pseudophase model, and there are those of De Lisi et al. and Zielinsky et al., which are markedly large (especially for the latter). If we analyze the methylene group contribution to the monomer compressibility, κ0(CH2), it results in -1.5 ( 0.1


Gonza´lez-Gaitano et al. TABLE 3: Thermodinamic Parameters for CnTAB + β-CD + Water Systems at 298.15 K cmc* (mmol kg-1) 0 Vs,CD (m3 mol-1 × 106)b ∆V0t (m3 mol-1 × 106)c 0 κs,CD (PPa-1 m3 mol-1)b 0 ∆κt (PPa-1 m3 mol-1)c

DTABa

DoTAB

TTAB

CTAB

78.6 275.7 19.2 52.8 66.7

22.3 310.3 21.8 58.5 76.4

5.79 347 36 67 87

2.63 381 40 78 101

a Data from ref 11. Transfer volumes and compressibilities are the average value calculated with the three concentrations of β-CD given in the reference. The given cmc* was measured at a constant mCD ) 0 0 11.462 mmol kg-1. b Vs,CD and κs,CD molar volume and compressibility of the monomer in the presence of β-CD at ms ) 0. c ∆V0t and ∆κ0t transfer volume and compressibility at ms ) 0.

Figure 6. Apparent molar volumes and compressibilities for CTAB (open circles) and mixture with β-CD (solid circles, mCD ) 2.241 mmol kg-1).

PPa-1 m3 mol-1 from the apparent molar compressibilities and -1.6 ( 0.4 PPa-1 m3 mol-1 with the pseudophase model. Although the CH2 group contributions are similar, the absolute values of the compressibilities obtained by applying a pseudophase model are significantly lower, so we have used in our further studies the values obtained directly from the partial properties, that is, without making any approximation. Kudryashov et al obtain -0.87 ( 0.05 PPa-1 m3 mol-1 with our same homologue series. Measurements on sodium alkylcarboxylates give κ0(CH2) ) -1.5 PPa-1 m3 mol-1 (ref 24), and the average value employing different homologous series of organic compounds yields -1.8 PPa-1 m3 mol-1 (ref 25). The data of Zielinsky et al. do not permit to give such a group contribution, since they do not follow a linear trend, falling dramatically with n. De Lisi et al. give κ0(CH2) ) -5 PPa-1 m3 mol-1, which seems quite different compared to the rest of literature data. The deviation coefficients in eq 8, Bκ, follow the same trend as the corresponding BV (Figure 8), a fact that does not seem to be casual. The interpretation would be the same than for the volume: the deviations of the Debye-Hu¨ckel law are expected to be higher when the surfactant turns more hydrophobic. The similarities among literature data are abundant in the case of micellization compressibilities (Table 1). Once more, our values agree better with those of Kudryashov et al. The compressibility of the monomer forming micelles permits to estimate a methylene group contribution of 10.0 ( 0.2 PPa-1 m3 mol-1, close to 9.7 PPa-1 m3 mol-1 obtained by these authors. The positive value corresponds to a higher compressibility of the surfactant when it is forming the micelle, suggesting a more hydrophobic environment, with more free accessible volume than in water, and similar to a liquid hydrocarbon.

System CnTAB + β-CD + Water. Molar Apparent and Partial Volumes. The ternary systems have been measured in all cases, keeping the β-CD concentration, mCD, constant. The apparent molar volumes are plotted in Figures 3, 5, and 6. For DTAB, the measurements have been presented previously. For DoTAB, TTAB, and CTAB the β-CD concentrations were 10.078, 3.206, and 2.241 mmol kg-1, respectively. In all cases the apparent cmc*, calculated from u data, is reached at concentrations above that for the pure surfactant. For DTAB, the cmc in the ternary system is practically cmc + mCD, but with the longest homologues it is less than cmc + mCD (Table 3). This is evidence that the stoichiometry of the complex is not only 1:1, but there is also a participation of 2:1 (that is to say, two macrocycles per one molecule of surfactant). The shift of the cmc implies that the competitive equilibrium due to the affinity of the monomer for the micelle or for the β-CD is resolved in favor of the latter; that is, only when all of the available cavities are occupied can the monomers aggregate to form the micelles. According to the Anianson and Wall analysis,26 the equilibrium constant for the incorporation of a monomer to a forming micelle with aggregation number n -1 is related to the kinetic constants of the entrance and release of the monomer, kn and kn-1, respectively, by Kn ) kn/kn-1 ) 1/cmc, provided the n steps in the process have the same equilibrium constant. Considering the cmcs in Table 1, the binding constant for the nth step, Kn, would fall between 15 l mol-1 for DTAB and 1.1 × 103 for CTAB. In the first case the micellization constant seems to be low enough to be noncompetitive with the binding equilibrium, but that of CTAB is rather high. However, the plots of Vφ,s versus ms suggest that the binding constant must be larger compared to Kn. Indeed, emf studies from Mwakibete et al. prove that this is the case,27 yielding a value of 67700 L mol-1 for K1 and 9600 L mol-1 for K2 with CTAB. For TTAB the same authors obtain 39750 and 3060 L mol-1 for both binding constants. At higher molalities of CnTAB, the curves in the absence and presence of β-CD coalesce, which indicates that when the complex forms, it does not take part into the micelles. The transfer volume is defined as the change in the volume 0 ) and of the monomer at infinite dilution in the presence (Vs,CD 0 0 0 0 absence of β-CD (Vs ), that is, ∆Vt ) Vs,CD - Vs . This volume increases gradually with the chain length from 19.2 to 40 × 10-6 m3 mol-1 (Table 3). The large changes in ∆V0t and, especially in the compressibility, ∆κ0t , prove that when the surfactant is forming the complex, the molecular surroundings are quite different to the water. In fact, when the complex forms, the water that is lodged inside the cavity will be lost and the same will occur with the hydration water that is covering the surfactant. This effect of dehydration is obvious at the sight of



Figure 7. (a) Plot of the molar partial volume of the surfactant versus the number of carbons in the alkyl chain (solid squares, monomer form; open squares, micelle form). (b) Plot of the molar partial compressibility of the surfactant versus the number of carbons in the alkyl chain (solid squares, micelle form; solid circles, calculated from eq 8; open circles, calculated from eq 9).

Figure 8. Debye-Hu¨ckel limiting law coefficients in ms for the apparent molar volume (solid squares) and compressibility (open squares).

Figure 9, in which the CTAB density versus mCTAB is plotted in both the binary and ternary systems. The cmc* is cmc + f‚mCD, with f being a value between 0 and 1, meaning that the stoichiometry is going to be neither 1:1 nor 2:1, but a combination of both whose relative proportion will depend on the concentration range considered (low ms will favor the 2:1 stoichiometry due to the excess of cyclodextrin, and the 1:1 will be predominant if ms increases). In the same figure can be observed a dramatic change in the density, which decreases when increasing the amount of surfactant added, up to a concentration slightly higher than mCD. This indicates that the solution volume is increasing to the detriment of the overall

mass in the solution, as a consequence of the released water from the cavity. Above the cmc*, the slopes for the binary and ternary systems are the same, indicating that the complexes have no effect on the aggregates. Due to the geometry of the CD, we can assume that the only water that is going to be involved in the binding process is the water of the cavity and the part of the hydration shell that covers the surfactant, which will be lost in the inclusion. The change in the volume of the surfactant, according to this model, is the difference between the water expelled from the cavity, which is incorporated into the bulk, and the hole occupied by the segment of the surfactant that is included. Hence, the reaction


Gonza´lez-Gaitano et al. with ms being the total surfactant molality at each point, msf the molality of the free monomer, and mcx s the molality of the surfactant in complex form. Thus, eq 12 can be brought into eq 14 to give us

K1mCD V0s,CD ) V0s + (V01:1 - V0s ) 1 + K1mCD K1mCD ∆V0t ) ∆V01:1 1 + K1mCD

Figure 9. Plot of density in CTAB + water (open circles) and CTAB + β-CD + water (solid circles) versus ms, showing the cmc’s.

volume would be, for a 1:1 complex, 0 ∆V01:1 ) V0wnw - nCH2VCH 2

(10)

where V0w is the volume of 1 mole of pure water (18.068 × 10-6 m3), nCH2 the number of CH2 groups buried into the CDs, 0 the volume of a methylene group in water (15.8 × and VCH 2 -6 10 m3 mol-1). It must be remarked that in eq 10 it is assumed a complete complex formation. If this were not the case, the observed transfer volume, ∆V0t , would not correspond to that of the totally formed complex, which we are calling ∆V01:1. Indeed, both parameters, ∆V0t and ∆V01:1, are connected by the equilibrium constant and mCD. Let K1 the binding constant of the reaction between a surfactant, S, and the cyclodextrin, CD, S + CD / S:CD. Since we are dealing with dilute solutions, we can reasonably approximate the activities to molalities, so that the equilibrium constant can be written as

K1 )

mcx s cx (mCD - mcx s )(ms - ms )

(11)

in which mCD is the fixed CD molality and mcx s is that of the surfactant forming complex. Equation 11 stands for each point of the plot of the apparent volume versus ms whenever we consider the premicellar domain. Nevertheless, since we are dealing with the infinite dilution zone, where mCD is much higher cx than mcx s , eq 11 is simplified and permits us to express ms as a function of K1 and mCD, so thus

mcx s )

K1msmCD 1 + K1mCD

(12)

According to Young’s rule,28 the apparent volume can be split into the contributions due to the noncomplexed monomer, V0s , and to the monomer forming complex, V01:1. In the case considered (or two site model), the apparent molar volume results in

Vφ,s )

χsV0s

+

χ1:1V01:1

(13)

or, substituting the mole fraction, χi, by the correspondent molalities in the solution we have

Vφ,s )

mfs 0 mcx s 0 V + V ms s ms 1:1

(14)

(15)

which establishes the desired relationship between the measured transfer volume and ∆V01:1, which is independent of the cyclodextrin concentration. Notice that only if K1mCD is much higher than 1 will both volumes, ∆V0t and ∆V01:1, be the same, but ∆ V01:1 will always be higher than or equal to ∆V0t . With binding constants of 103-104 mol-1 and concentrations of CD between 10-2-10-3 mol kg-1, it can be stated practically that ∆V01:1 ) ∆V0t . In the case where we had a two step equilibrium (three site binding process, that is, to consider the 2:1 stoichiometry together with the 1:1), the model can be extended, so thus

Vφ,s ) χsV0s + χ1:1V01:1 + χ2:1V02:1

(16)

It is not difficult to prove that, when ms f 0,

K1mCD ∆V0t ) ∆V01:1 + 1 + K1mCD + K1K2m2CD K1K2m2CD (17) ∆V02:1 1 + K1mCD + K1K2m2CD where K1 and K2 are the association constants for the first and second binding of the surfactant to the cyclodextrin, and ∆V01:1 ) V01:1 - V0s , ∆V02:1 ) V02:1 - V0s . We can use eq 10 to calculate the CH2 groups that have entered in the cavity. The height of the β-CD is about 7.9 Å, which is going to be, at most, the surfactant length included in its all-staggered conformation. This length is equivalent to 6.3 CH2 groups, taking the length of a C-C bond with C in sp3 hybridization.29 In our previous study with DTAB using the transfer volume of this surfactant, which is well known to form a 1:1 complex, and by application of this model, we have calculated that approximately 6.5 water molecules are expelled when the complex forms, exactly the number of molecules found by XRD30 and neutron diffraction31 for the solid β-CD inside the cavity that remains within the CD when it is dissolved. Considering that 6.3 CH2 groups displace 6.5 water molecules, it can be proposed, according to eq 10, that the surfactant forms the complex

nCH2 )

∆V0t V0w6.5/6.3 - VCH2

)

∆V0t 2.84

(18)

In these arguments we are considering that, at infinite dilution, the most favored complex will be that of the highest stoichiometry possible, provided K2 is high enough. From eq 17 it is straightforward to deduce that the ratio between the proportion of 2:1 and 1:1 complexes, when ms tends to zero, results in χ2:1/χ1:1 ) K2mCD. However, in a more general case in which


Figure 10. Transfer volumes and compressibilities at infinite dilution of the surfactants versus the number of carbon atoms in the alkyl chain (triangles: this work; open circles, ref 34; open squares, ref 7).

mCD and K2 are both low, eq 10 must take into account the different contributions of each complex, 1:1 and 2:1, according to eq 17. By substituting in this equation the measured ∆V0t , we obtain for the homologue series an increasing number of CH2 groups of 6.8, 7.7, 12.7, and 14, quite consistent with the length of the surfactants studied. This implies that for DTAB the stoichiometry must be 1:1, and almost the same for DoTAB (a slight participation of the 2:1 should be observed), but TTAB and CTAB must exhibit the 2:1 binding. This latter observation is firmly asserted in the literature.27,32 Of course, the most difficult case will be that of DoTAB, since the small 2:1 participation could not be noticed, and it will depend on the sensitivity of the technique or method of study. Something similar occurs with sodium decanoate (NaD) with β-CD. In these systems, there are authors that state the 2:1 stoichiometry,33 and others that do not. With our compressibility and volume measurements it seems that the former opinion is the correct one, but the total amount of the complex must be very small.34 In Figure 10 the observed change in volume of the monomer versus the number of carbons is plotted. ∆V0t increases progressively with n, that is, the longer the surfactant the higher the amount of water released. This same behavior has been observed with anionic hydrocarbon and fluorocarbon surfactants.7,8 In the same figure we have plotted our results together with literature studies of sodium alkylcarboxylates with β-CD from refs 7 and 34. It is very interesting the parallel trend for both series of data, although the volumes for the alkanoates from Wilson et al. are about 6 × 10-6 m3 mol-1 above (to our knowledge, sodium hexadecanoate has not been measured yet). However, with our reported data for sodium alkanoates, the volumes for the surfactants with 10 and 12 methylene groups are exactly the same, irrespective of the series considered. The increasing volume is a consequence of the participation of the

J. Phys. Chem. B, Vol. 104, No. 8, 2000 1877 2:1 stoichiometry, which becomes more important when the surfactant is longer. Since DTAB fills the CD, with 6.3 methylene groups lodged in the cavity assuming an all-trans conformation, CTAB would be long enough to thread completely a second CD. In fact, in Figure 10 it can be observed that ∆V0t for the latter is practically twice the value of DTAB. It can be deduced too that the charged nature of the head does not affect the volumes very much, at least for the shorter homologues. Equations 15 and 17 assume that Ki is known beforehand to perform such calculation. However, with Young’s rule all of these parameters can be obtained together from the plots of Vφ,s versus ms. The numerical problem can be solved by a nonlinear least-squares fitting (NLSF) with the Levenberg-Marquardt algorithm (LM), in which V01:1 (or ∆V01:1, since V0s is known) and K1 are adjustable parameters and Vφ,s is the measured volume at each ms. The function to be minimized is the sum of the squares of the residuals. In recent studies, Wilson et al.7,8 use this strategy to estimate the binding constant from the apparent volumes dealing with natural and modified CDs and their complexes with sodium alkanoates and sodium perfluoroalkanoates with a fair fit quality. We have tried to apply the model to the series of CnTAB for both properties, but reliable results have been obtained only for DTAB. The difficulty with the rest of the surfactants arises from the fact that the aggregation occurs immediately after all of the free β-CD has disappeared to form the complex, so the data cannot be obtained over a sufficiently wide range of concentration. Since the premicellar concentrations for surfactants longer than DTAB are rather low, the error in the apparent volume or compressibility increases and poorer or meaningless fits are obtained, independent of the model used (two or three site). Although we have not been able to calculate by means of NLSF all of the parameters in eq 17 for the other surfactants, it is possible to calculate ∆V02:1 in each case taking the binding constants from the literature and considering the constant mCD. Indeed, the binding of a second CD to the 1:1 complex assumes that the latter has formed completely. It is not harsh to state that ∆V01:1 is going to be the same for DTAB as for DoTAB, TTAB, and CTAB, since the first CD has released all of the inclusion water. The additional factor that will contribute to ∆ V0t will be the total weight of 2:1, which is given by ∆V02:1. If the surfactant is long enough, we can expect ∆V02:1 to be approximately twice ∆V01:1. According to data of Mwakibete et al. for CTAB, if we consider K1 ) 67700, K2 ) 9600, and mCD ) 2.241 mmol kg-1, we conclude that ∆V02:1 ) 41 ×10-6 m3 mol-1, which is approximately 2∆V01:1, a result that makes sense considering the length of CTAB which permits the stoichiometry 2:1. For TTAB the calculation with eq 17 yields ∆V02:1 ) 37.7 × 10-6 m3 mol-1. All of these considerations are valid whenever ms f 0. When ms increases, the proportion of 1:1 complex becomes higher and that of 2:1 decreases. The overall effect on the cmc is a shift to a cmc* that is smaller than cmc + mCD (which would point to a unique 1:1 stoichiometry) but higher than cmc + mCD/2 (2:1 stoichiometry). Molar Apparent and Partial Compressibilities. The apparent and partial molar compressibilities show a trend similar to the volumes: at low ms concentrations κφ,s becomes much higher than for the pure surfactant in water, and beyond the cmc*, all of the curves merge. The plots of κφ,s versus ms are less noisy than the plots of Vφ,s since the relative changes in the compressibility are more important compared to the volumes. This is an


Gonza´lez-Gaitano et al.

indication of the strong influence of the solvation effects involved in the inclusion process. In Figure 10 the differences in compressibility of the surfactant, ∆κ0t , versus the number of methylene groups, n, are plotted. The points are quite well aligned and show a trend similar to that of ∆V0t . The qualitative interpretation of this property can be imputed to the sum of several contributions. First, there is an effect of the hydration water. Indeed, when the complex forms, the released water molecules that were inside the cavity become bulk water. We can consider the water molecules included as highly structured water which will have a rather low compressibility, similar to that of ice, compared to bulk water (8.081 PPa-1 m3 mol-1). Second, there is a more hydrophobic environment the surfactant feels when forming the complex compared to water. Indeed, one of the main driving forces in this complex formation is the hydrophobic interaction.35 There would be other effects in this case, such as the iondipole interaction of the charged head of the surfactant, and the break of intramolecular hydrogen bonding of the OH groups of the rims. If the surfactant becomes longer, we will have more conversion to bulk water of the molecules that are inside, and an increasing surface or volume of the hydrophobic cavity for the surfactant. This explanation for the compressibility can be done quantitatively, in the same way as in the case of the volume, although a careful analysis of the inclusion process must include one more contribution. Thus, if we consider a complex that forms completely, in which nCH2 groups enter the CD, we have 0 ∆κ0t ) κ0wnw - nCH2κCH + (κsCD - κwCD)cavity 2

(19)

0 with κ0w being the compressibility of the bulk water and κCH 2 the compressibility of a methylene group in water. This equation states that the compressibility of reaction is the difference between the compressibility of the water expelled from the cavity, which is incorporated to the bulk having the same compressibility as that of bulk water (8.081 PPa-1 m3 mol-1), and the compressibility of the included surfactant moiety in 0 water, nCH2κCH . The last contribution in eq 19 accounts for the 2 different compressibility of the cavity when it is filled with the alkyl chain or with water. When we are dealing with volumes, it can be assumed that the differences in volume of the cavity when it is filled with water or with the surfactant are going to be negligible. This is the reason we do not consider this effect in eq 10. However, this is not the case for the compressibility since is expected to be easier to compress the CD when it is filled with an alkyl chain than when it is filled with water. The last term in eq 19 considers this effect. Substituting in eq 18 the water molecules expelled and the CH2 groups that enter, data known from the molar volumes, and the transfer compressibilities in the limit of ms f 0, it is possible to estimate the last contribution, provided the compressibility per methylene group is known. From the three contributions to ∆κ0t , the highest will be that of the bulk water, in the same way as the volumes. For instance, for DTAB, whose stoichiometry is 1:1, there will be 6.8 methylene groups, from the measured ∆V0t , which displace an equivalent of seven water molecules. This contribution to ∆κ0t is about 57 PPa-1 m3 mol-1, which leaves 9 PPa-1 m3 mol-1, for (κsCD - κwCD)cavity. Note that in these calculations we are assuming that the chain is in its all-trans conformation. Moreover, it is presumed that the inclusion of a second CD does not affect the position of the cationic head of the surfactant. For DoTAB, with data from Table 3, (κsCD - κwCD)cavity results

in 1 PPa-1 m3 mol-1. However, for TTAB and CTAB the values obtained of -38 and -37 PPa-1 m3 mol-1are negative and quite different. A positive value for the compressibility of the cavity makes sense when the hydrocarbon chain of the surfactant is lodged within the cavity, since it will be easier to compress when it is filled with the surfactant than with water. The negative value for the last surfactants of the series could be explained by the effect of the polar head. Indeed, when the 2:1 stoichiometry is possible, there remains the possibility that the head can enter partially in the cavity. Another explanation could be the effect of the interactions between the OH groups of two adjacent rims, which would give such negative values. 1H NMR studies on n-alkylcarboxylates with natural and modified CDs have proved that when the surfactant is long enough, the polar head seems to approximate more to the inner part of the CD. This effect probably will not be reflected in the volume, since the water molecules released will be nearly the same. Young’s rule can be extended to the apparent adiabatic compressibilities in the same way as for the volumes following analogous considerations, provided the compressibility of the surfactant in water is known. Thus, for a 1:1 complex

κφ,s ) χsκ0s + χ1:1κ01:1

(20)

with κ0s and κ01:1 being the adiabatic molar compressibilities of the monomer in free or in complex form. By applying the method to this property, the association constants and ∆κ01:1 can be estimated. The compressibilities have the advantage over the volumes that their changes are usually more remarkable. For DTAB, V0s changes from 256.46 × 10-6 m3 mol-1 from water to 275.7 into the β-CD, but the molar partial compressibility at infinite dilution, κ0s , changes from -13.85 to 52.8 PPa-1 m3 mol-1, which represents a relative change almost 70 times higher for the latter. Due to the same arguments given for the volumes, we could not apply this model but for DTAB. The binding constants are 1800 and 2000 L mol-1 with both β-CD concentrations in good accordance with the reported 1H NMR literature data.11 It is possible to establish a relationship for the compressibility as we did with Vφ,s in eqs 16 and 17, just by replacing the volumes with compressibilities. So thus, in a more general case

κφ,s ) χsκ0s + χ1:1κ01:1 + χ2:1κ02:1

(21)

K1mCD + ∆κ0t ) ∆κ01:1 1 + K1mCD + K1K2m2CD K1K2m2CD (22) ∆κ02:1 1 + K1mCD + K1K2m2CD For ∆κ01:1 we can use the average value estimated with the nonlinear fit for DTAB compressibilities, 76 PPa-1 m3 mol-1, and the binding constants from the literature for the other surfactants. We obtain ∆κ02:1 of 88 and 102 PPa-1 m3 mol-1 for TTAB and CTAB, which are practically the same as ∆κ0t , which proves that the predominant stoichiometry at infinite dilution will be 2:1. 4. Conclusion The molar apparent and partial volumes and adiabatic compressibilities have been obtained from density and sound velocity data for aqueous solutions of alkyltrymethylammonium

Molar Partial Volume and Compressibility bromides (CnTAB, n ) 10, 12, 14, 16) in the absence and presence of β-CD at 298 K. For the binary systems (surfactant + water), the molar partial compressibilities and volumes of the pure surfactants in water as a function of concentration have been obtained and compared with the literature data. For the surfactant in monomer form, the methylene group contributions to the partial volume and compressibility are 15.9 × 10-6 m3 mol-1 and -1.5 PPa-1 m3 mol-1, and 16.32 × 10-6 m3 mol-1 and 10 PPa-1 m3 mol-1 for the surfactant in micelle form. For the surfactants in the presence of β-CD, a remarkable increase of the molar partial volume and compressibility of the 0 0 and κs,CD , with respect to its monomer at infinite dilution, Vs,CD value in water, is observed. The transfer properties at infinite dilution, ∆V0t and ∆κ0t , can be discussed in terms of a simple model which considers the balance between the released water from the cavity and the methylene groups of the substrate that enter the macrocycle. Both ∆V0t and ∆κ0t increase with n, indicating that the stoichiometry turns to 2:1 when the hydrocarbon chain is long enough. The calculated methylene groups that enter are 6.8, 7.7, 12.7, and 14 for DTAB, DoTAB, TTAB, and CTAB, respectively, which is consistent with the length of the surfactants. This implies a slight participation of the 2:1 complex for DoTAB and a full 2:1 complex with TTAB and CTAB. The 2:1 stoichiometry contribution to any of the properties becomes more important at conditions of low surfactant molalities. The application of Young’s rule permits to estimate the binding constant for DTAB but not for the other surfactants, due to their low cmcs. With the other surfactants, and taking the binding constants from the literature, the reaction volumes and compressibilities, ∆V01:1 and ∆V02:1 and ∆κ01:1 and ∆κ02:1, have been obtained, yielding values that are in accordance with the length of the hydrocarbon chain. Both partial molar volumes and compressibilities are the same at high surfactant molalities, indicating that there is no participation of the complex into the micelles, and the cmcs are shifted in an extension that shows the participation of 2:1 stoichiometry with the longest homologues TTAB and CTAB. The analysis of the compressibility with arguments analogous to those of the volume reflects the interactions between the OH groups of adjacent CDs, or suggests the possibility of an inclusion within the cavity of the polar head, as a result of the negative value of the compressibility of the cavity. An 1H NMR study has been started by the authors to verify this supposition. Acknowledgment. Authors acknowledge financial assistance provided by the M.E.C. through DGES (grant number PB970324) and by the U.C.M. (grant number PR486/97-7489) and wish to thank J. R. Isasi for the revision of the original manuscript. References and Notes (1) (a) Szejtli, J. Cyclodextrins and Their Inclusion Complexes; Kluwer Academic Publishers: Dordrecht, 1988. (b) Duchene, D. Cyclodextrins and

J. Phys. Chem. B, Vol. 104, No. 8, 2000 1879 Their Industrial Uses; Editions de Sante´: Paris, 1987. (c) Duchene, D. New Trends in Cyclodextrins and DeriVatiVes; Editions de Sante´: Paris, 1991. (2) D’Souza, V. T.; Lipkowitz, K. B. Chem. ReV. 1998, 98, 1741. (3) Wurzburger, S.; Sartorio, R.; Elia, V.; Cascella, C. J. Chem. Soc., Faraday Trans. 1990, 86, 3891. (4) Nomura, H.; Onoda, M.; Miyahara, Y. Polym. J. 1982, 14, 249. (5) Kharakoz, D. P. J. Phys. Chem. 1991, 95, 5634. (6) Zana, R. Surfactant Solutions: New Methods of InVestigation; Marcel Dekker Inc.: New York, 1987. (7) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 1997, 101, 9270. (8) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 1998, 102, 480. (9) De Lisi, R.; Milioto, S.; Pellerito, A.; Inglese, A. Langmuir 1998, 14, 6045. (10) Gonza´lez-Gaitano, G.; Compostizo, A.; Sańchez-Martıń, L.; Tardajos, G. Langmuir 1997, 13, 2235. (11) Gonza´lez-Gaitano, G.; Crespo, A.; Compostizo, A.; Tardajos, G. J. Phys. Chem. B 1997, 101, 4413. (12) Tardajos, G.; Gonza´lez-Gaitano, G.; Montero de Espinosa, F. ReV. Sci. Instrum. 1994, 65 (9), 2933. (13) Kroebel, W.; Mahrt, K. H. Acustica 1976, 35. (14) Brown, I.; Lane, J. E. Pure Appl. Chem. 1976, 45, 1. (15) The air density can be calculated by FA ) (0.001293/(1 + 0.00367t))(P/760), with t being the temperature in °C and P the pressure in mmHg. See Kohlrausch. Praktische Physik; Teubner: Stuttgart, 1968; Vol. 3. (16) Mosquera, V.; Del Rıó, J. M.; Atwood, D.; Garcıá, M.; Jones, M. N.; Prieto, G.; Suarez, M. J.; Sarmiento, F. J. Colloid Interface Sci. 1998, 206, 66. (17) Zielinski, R.; Ikeda, S.; Nomura, H.; Kato, S. J. Chem. Soc., Faraday Trans. 1 1988, 84, 151. (18) Kudryashov, E.; Kapuskina, T.; Morrissey, S.; Buckin, V.; Dawson, K. J. Colloid Interface Sci. 1998, 203, 59. (19) De Lisi, R.; Milioto, S.; Verrall, R. E. J. Sol. Chem. 1990, 19 (7), 665. (20) Zielinski, R.; Ikeda, S.; Nomura, H.; Kato, S. J. Colloid Interface Sci. 1987, 119, 398. (21) Høiland, H. Thermodynamic Data for Biochemistry and Biotechnology; Hinz, H. J., Ed.; Springer-Verlag: Berlin, 1986; Chapter 2. (22) Buwalda, R.; Engberts, J. B. F. N.; Høiland, H.; Blandamer, M. J. J. Phys. Org. Chem. 1998, 11, 59. (23) Millero, F. J. Chem. ReV. 1971, 71, 147. (24) Vikingstad, E. J. Colloid Interface Sci. 1979, 72, 75. (25) Nakajima, T.; Komatsu, T.; Magawa, T. Bull. Chem. Soc. Jpn. 1975, 48, 788. (26) Anianson, E. A. G.; Wall, S. N.; Almgrem, M.; Hoffman, H.; Keilman, I.; Ulbritch, W.; Zana, R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976, 80, 905. (27) Mwakibete, H.; Crisantino, R.; Bloor, D. M. Langmuir 1995, 11, 57. (28) Young, T. F.; Smith, M. B. J. Phys. Chem. 1954, 58, 716. (29) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley: New York, 1973. (30) Lindner, K.; Saenger, W. Carbohydrate Res. 1982, 99, 103. (31) Zabel, V.; Saenger, W.; Mason, S. A. J. Am. Chem. Soc. 1986, 108, 3664. (32) Dharmawardana, U.; Christian, S. D.; Tucker, E. E.; Taylor, R. W.; Scamehorn, J. F. Langmuir 1993, 9, 2258. (33) Gelb, R. I.; Schwartz, L. M. J. Inclusion Phenom. Mol. Recognit. Chem. 1989, 7, 465. (34) Gonza´lez-Gaitano, G.; Sanz, T.; Tardajos, G. Langmuir 1999, 15 (23), 7963. (35) Rekharsky, M. V.; Inoue, Y. Chem. ReV. 1998, 98, 1875. (36) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71 (1), 147.

Thermodynamic Investigation (Volume and Compressibility) of the

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