5550
Langmuir 1996, 12, 5550-5556
Adsorption Enthalpies of Cationic and Nonionic Surfactants on Silica Gel. 1. Isosteric Determination of Adsorption Enthalpies C. Wittrock,† H.-H. Kohler,*,† and J. Seidel‡ Institute of Analytical Chemistry, Chemo- and Biosensors, University of Regensburg, D-93040 Regensburg, Germany, and Institute of Physical Chemistry, Freiberg University of Mining and Technology, D-09596 Freiberg/Sa., Germany Received April 15, 1996. In Final Form: August 2, 1996X In general, adsorption enthalpies of surfactants adsorbing on solid particles from aqueous solutions are determined either by calorimetry or by the indirect (isosteric) method, based on the Clausius-Clapeyron equation. This paper is the first part of a two-part contribution dealing with a comparison of both methods. In the present part adsorption isotherms of a nonionic (n-octyltetraoxyethylene, C8E4) and a cationic (cetylpyridinium chloride, CpCl) surfactant on silica gel are presented for different temperatures. The measured values are fitted with the Gu equation. From the generalized Clausius-Clapeyron equation for multicomponent adsorption, simplified equations are derived for the special cases treated in this contribution. The validity ranges of these equations are discussed. The differential molar adsorption enthalpies are determined from the fitted isotherms. We find that the adsorption of the nonionic surfactant is endothermic while that of the ionic surfactant is exothermic. It is shown that the electrostatic contribution of the diffuse double layer to the enthalpy of adsorption of an ionic surfactant is always negative. Advantages and limitations of the indirect method are discussed. The comparison of the indirectly determined enthalpies with directly (i.e., calorimetrically) measured enthalpies will be presented in the second part of this series.
Introduction Investigations of the temperature dependence of adsorption are often used to obtain information about the adsorption mechanism. By variation of adsorbate and adsorbent, different effects like Coulombic forces, hydrophobic and hydrophilic interactions, and the influence of surface properties can be studied. Adsorption enthalpies of surfactants on solid particles in aqueous solutions can be determined by two different methods: indirect determination from adsorption isotherms measured at neighboring temperatures by means of the modified ClausiusClapeyron equation, often called the isosteric method;1-12 Direct determination by microcalorimetric measurements.9-18 The two parts of our contribution are devoted to a direct comparison of these two methods. For this purpose the enthalpy effects related to adsorption of both a common nonionic surfactant (n-octyltetraoxyethylene, C8E4) and * To whom correspondence should be addressed. † University of Regensburg. ‡ Freiberg University of Mining and Technology. X Abstract published in Advance ACS Abstracts, October 15, 1996. (1) Wittrock, C.; Kohler, H.-H. J. Phys. Chem. 1993, 97, 7730. (2) Seidel, J.; Wittrock, C.; Kohler, H.-H. Langmuir 1996, 12, 0000. (3) Rupprecht, H.; Kindl, G. Arch. Pharm. 1974, 308, 46. (4) Partyka, S.; Rudzinski, W.; Brun, B.; Clint, J. H. Langmuir 1989, 5, 297. (5) Rowley, H. H.; Innes, W. B. J. Phys. Chem. 1942, 46, 537. (6) Mehrian, T.; de Keizer, A.; Lyklema, J. Langmuir 1991, 7, 3094. (7) Steinby, K.; Silveston, R.; Kronberg, B. J. Colloid Interface Sci. 1993, 155, 70. (8) Herz, A. H.; Helling, J. O. J. Colloid Interface Sci. 1966, 22, 391. (9) Denoyel, R.; Rouquerol, F.; Rouquerol, J. J. Colloid Interface Sci. 1990, 136, 375. (10) Sircar, S. Langmuir 1991, 7, 3065. (11) Crisp, D. J. J. Colloid Sci. 1956, 11, 356. (12) Mehrian, T.; Keizer, A. Colloids Surf. A 1993, 73, 133. (13) Seidel, J. J. Therm. Anal. 1988, 33, 317. (14) Sivakumar, A.; Somasundaran, P.; Thach, S. J. Colloid Interface Sci. 1993, 159, 481. (15) Douillard, J. M.; Pougnet, S.; Faucompre, B.; Partyka, S. J. Colloid Interface Sci. 1992, 154, 113. (16) Lindheimer, M.; Keh, E.; Zaini, S.; Partyka, S. J. Colloid Interface Sci. 1990, 138, 83. (17) Seidel, J. Thermochim. Acta 1993, 229, 257. (18) Seidel, J. Prog. Colloid Polym. Sci. 1992, 89, 176.
S0743-7463(96)00356-3 CCC: $12.00
common ionic surfactant (cetylpyridinium chloride, CpCl) on a wide pore silica gel are determined both by the indirect and by the direct method. In the past, inconsistencies between the two methods have been reported.5,9,12 In the present part 1, the results of the indirect method are presented. The results of the direct determination, obtained by flow calorimetry, and the comparison of both methods will be subject of part 2.2 The generalized Clausius-Clapeyron equation, which forms the basis of the indirect method, has been derived in some generality in an earlier publication.1 This equation reads
∆Had P ) - RT2
(
n
∑ i)2
| |
∂ ln ci ∂T
∂Γi
P,q
∂Γref T,P
n
-
|
∂Γi
∑ i)2 ∂T P,q
|)
∂ ln ci ∂Γref
(1)
T,P
It is assumed that the solution is ideally diluted and that the pressure p is uniform and constant. Γref is the reference surface excess concentration. P and q denote conditions under which the composition of the bulk and the surface phase is varied. For an n-component system P consists of (n - 2) independent conditions of the form
fP(c2, c3, ..., cn) ) 0
(2)
These conditions leave one degree of freedom for changes of the bulk composition and thus determine the adsorption process as a function of the bulk composition. Consider, for example, a three-component system with Γref ) Γ2. Because of n ) 3 the set P consists of a single condition. If, for example, c2 is varied under the condition c3 ) constant (or fP(c2,c3) ) c3 - constant ) 0) the values of the surface excess concentration, and hence of ∆Had, will be different, in general, from those obtained under the condition c2 ) c3 (or fP(c2,c3) ) c3 - c2 ) 0). Therefore, ∆Had is subscripted by P in eq 1. q is a free condition related to bulk or surface concentrations. The choice of q offers different possibilities to determine ∆Had P from measured isotherms (cf. ref 1). © 1996 American Chemical Society
Adsorption Enthalpies of Surfactants
Langmuir, Vol. 12, No. 23, 1996 5551
Table 1. Properties of Fractosil 10002 property particle size specific surface area pore volume pore radius
value 0.2-0.5 mm 21.1 ( 0.4 m2/g
method declaration of Merck BET multipoint N2 isotherma high pressure Hg porosimetryb
0.82 cm3/g 30-90 nm, max distribution at 60 nm ζ-potential )-(16.2 ( 2.2 pH) mV microelectrophoresisc for 4 < pH < 9 by use of the fines of the Fractosil at a KCl concentration of 1 mmol/L isoelectric point pH ) 2 (PZC)
a ASAP 2000 Micromeritics, USA. b Porosimeter 200 Carlo Erba, Italy. c Zetasizer 4 Malvern Instruments, UK.
Preliminary kinetic studies have been performed to determine the time needed to reach adsorption equilibrium. In order to bring the measured isotherms into a parameterized form, they are fitted to the Gu equation.19,20 These fits are used to calculate the differential molar adsorption enthalpies. An attempt will be made to relate the enthalpy effects to the physicochemical properties of the surfactants. Experimental Section Materials. The flow-calorimetric measurements require silica gel particles above a minimum size of about 50 µm. Smaller particles would be washed out of the measuring cell by the solute flow. In adsorption experiments, the specific surface area of the adsorbent should be very high. On the other hand, to assure access of the surfactant molecules to the interior of the silica gel particles, the pores of the particles should not be too narrow. Under these aspects we have chosen the wide pore Fractosil 1000 (Merck, Darmstadt, Germany) with particles ranging from 0.2 to 0.5 mm in size. In order to remove the fines the Fractosil was suspended in water and decanted after 1 min of sedimentation. The remaining fraction was dried at 105 °C and used for the isosteric and calorimetric experiments. Table 1 shows characteristic properties of the Fractosil. The two surfactants used in our experiments are similar in size. The total length of both is about 2.8 nm. The length of the head group of the nonionic (1.8 nm), however, is 4 times larger than that of the cationic species. The nonionic surfactant C8E4 was obtained from Bachem Biochemica (Heidelberg, Germany) with a purity greater than 98%. Surface tension measurements of the raw product showed a minimum at the critical micelle concentration (cmc) about 2 mN/m deep. The surfactant was purified by extraction with n-hexane/water by means of the 3Phex method.21 After five extraction cycles, the minimum of the surface tension curves had disappeared. As a further purity criterion the cloud point of an aqueous solution of mass fraction 1.0% was determined. The value of 42.3 °C agrees well with the literature value of 42.1 °C.21 The CpCl was obtained from Merck (Darmstadt, Germany) with a purity greater than 97%. For further purification, it was recrystallized several times from an ethanol/acetone mixture and then dried under vacuum. The product obtained had a melting point of 85.2 °C. From thermogravimetric experiments we found a water mass fraction of 5%, corresponding to 1 mol of H2O per mol of CpCl. Surface tension measurements did not show any minimum at the cmc which indicates a high purity of the substance.22 Experimental Equipment and Procedure. For the adsorption experiments 50 mL Erlenmeyer flasks were filled with about 0.3 g of Fractosil and 10-50 g of surfactant solution and stored in a thermostated shaking water bath (B. Braun(19) Gu, T.; Zhu, B.-Y. Colloids Surf. 1990, 44, 81. (20) Zhu, B.-Y.; Gu, T. J. Chem. Soc., Faraday Trans. 1 1989, 85, 3813. (21) Schubert, K.-V.; Strey, R.; Kahlweit, M. J. Colloid Interface Sci. 1991, 141, 21. (22) Semmler, A.; Ferstl, R.; Kohler, H.-H. Langmuir, 1996, 12, 4165.
Melsungen, Melsungen, Germany, or Julabo-SW-21C, Seelbach, Germany). Bulk composition is described by molalities (symbol c) throughout. The amount of solution was decreased with increasing surfactant concentration to obtain an appropriate difference of the surfactant concentration before and after adsorption. Shaking of the samples was preferred to stirring because stirring visibly destroys part of the Fractosil particles. BET surface measurements showed an increase of the specific surface area caused by stirring of up to 10%. After equilibrium had been reached, the bulk solution was separated by filtering through a Teflon fliter of pore size 0.45 µm (Roth GmbH, Karlsruhe, Germany). The solution was analysed at 25 °C by the method described below. Determination of the Amount of Adsorbed Surfactant. In this paper Gibbs’ notation is used.1,23 Bulk quantities are superscripted by b and surface excess quantities by σ. The surface excess of the surfactant, nσ, is the difference of the amount given into solution prior to adsorption, nb0, and the bulk amount measured at equilibrium, nb. Accordingly, the surface excess concentration Γ is given by
Γ)
nb0 - nb A
A ) mFa
(3) (4)
were A is the surface area, mF the mass of the Fractosil, and a its specific surface area. Errors in Γ are mainly due to the analytical determination of nb and to errors in mF. Therefore, the analytical determination should be as accurate as possible. Our isotherms have standard deviations in Γ of less than 10-7 mol/m2. Analytic Methods. The concentration of the nonionic C8E4 was determined by differential refraction measurements (Atago DD5 refractometer, Kuebler GmbH, Karlsruhe, Germany). A linear calibration curve could be established. To reduce experimental errors, the refraction index of each bulk solution was determined as the mean value of at least 10 measurements. Since changes of the refraction index are not specific to C8E4, the measured values were corrected by blank values. The bulk amount of C8E4 was determined with an accuracy better than 8% at low concentrations (c < 5 mmol/kg) and of about 1% at higher concentrations. The pyridinium group (Cp) can be detected by UV spectroscopy (Lambda 18 spectrometer, Perkin-Elmer, U ¨ berlingen, Germany) with high selectivity and over a wide concentration range down to 10-6 M (π f π* transition at a wavelength of 259 nm). The layer thickness of the cuvettes was 0.1-10 cm. For each cuvette linear calibration curves were determined in accordance with Lambert-Beer’s law. The equilibrium concentrations were detected with standard deviations smaller than 6 × 10-6 mol/kg.
Results and Discussion Kinetic Studies. In the case of the C8E4 the equilibrium of adsorption is reached inless than 4 h. The adsorption kinetics of the cationic surfactant (Figure 1) is more complicated. The Γ vs t curve may be divided into three sections. The first is a steep increase of the surface excess concentration within a short period of time (≈3 h). Within this time the surface excess concentration reaches 85% of the equilibrium value. The next section shows an approximately linear increase of Γ with time and lasts for about 1 week. From this time on Γ remains virtually constant (third section). Therefore, the equilibrium value is reached after about 1 week. As can be seen from Figures 2 and 3a, similar values of the surface excess concentrations are assumed by both surfactants. But the corresponding concentrations of the nonionic surfactant are about 10 times higher than those of the ionic one. Therefore, taking into account that the diffusion constants of the two surfactants are of the same (23) Defay, R.; Prigogine, J.; Bellemans, A.; Everett, D. H. Surface Tension and Adsorption; Longmans, Green & Co. Ltd.: London, 1966; p 50.
5552 Langmuir, Vol. 12, No. 23, 1996
Wittrock et al.
Figure 1. Kinetic measurements of CpCl adsorption: Θ ) 20 °C; initial CpCl concentration c ) 1.0 mmol/kg, concentration decreasing during adsorption down to 0.6 mmol/kg. Solid line is drawn to help the eye.
Figure 2. C8E4 isotherms (semilogarithmic plot). The measured values are fitted with the Gu equation. The fitted curves are dashed above the cmc. The cmc values were obtained from surface tension measurements by use of a laser tensiometer.22
order of magnitude, the overall adsorption process of the nonionic surfactant will be about 10 times faster than that of the ionic one.24 The transport of the ionic surfactant may be further slowed down by electrostatic repulsion in narrow parts of the pores. So the observed ratio of total adsorption times of about 1/50 is not unreasonable. Adsorption Isotherms of C8E4. In Figure 2 the adsorption isotherms of C8E4 are shown for 20 and 30 °C. At both temperatures Γ is very small for surfactant concentrations below 6 mmol/kg. At higher concentrations there is a steep cooperative increase turning, rather abruptly, into a slight rise above the cmc. This bend indicates the formation of micelles in the bulk phase. In the steep part both isotherms run in parallel. In this part the adsorption process is favored by higher temperatures. In the literature adsorption isotherms are divided into three classes:20 L-type (Langmuir), S-type, and LS-type. The present C8E4 isotherms could be classified as LStype, with a weak first adsorption step, or as S-type. An attempt was made to fit the measured values with the Gu equation which describes a two-step adsorption mechanism.20 Although good fits are obtained, we do not claim that C8E4 absorption satisfies the specific assumptions (24) Crank, J. The Mathematics of Diffusion, 2nd ed.; Oxford University Press: Oxford, 1975; Chapter 10, p 230.
Figure 3. CpCl isotherms: linear plot (a); semilogarithmic plot (b). The measured values are fitted with the Gu equation. The fitted curves are dashed above the cmc. The cmc values were obtained from surface tension measurements by use of a laser tensiometer.22
underlying the theoretical derivation of the Gu isotherm. The Gu equation reads
Γ ) Γ∞
k1c/c0 (n-1 + k2 (c/c0)n-1) 1 + k1c/c0 (1 + k2 (c/c0)n-1)
(5)
c0 ) 1 mol/kg In the original interpretation n is the mean aggregation number of the adsorbed hemimicelles, Γ∞ the maximum surface excess concentration, and k1 and k2 the reduced equilibrium constants of the first and second adsorption step. For theoretical reasons, c must be interpreted as the surfactant monomer concentration. Therefore we limit the fitting procedure to surfactant concentrations below the cmc. Nevertheless, good agreement is found between fit and experimental points above the cmc, too. The fitted parameters are given in Table 2.
Adsorption Enthalpies of Surfactants
Langmuir, Vol. 12, No. 23, 1996 5553
Table 2. Fitted Gu-Parameters for CpCl and C8E4 C8E4 CpCl
Θ/°C
Γ∞/(mol/m2)
k1
k2
n
20 30 20 40 60
5.85 × 10-6 6.27 × 10-6 4.92 × 10-6 5.00 × 10-6 4.92 × 10-6
2.39 × 103 1.30 × 103 8.38 × 104 2.92 × 104 2.25 × 104
4.06 × 1032 1.80 × 1034 1.61 × 1010 9.18 × 108 4.08 × 107
16.94 17.15 4.306 4.000 3.650
Adsorption Isotherms of CpCl. As shown in Figure 3, the adsorption isotherms are of the LS-type. Again each isotherm may be divided into three sections. At low concentrations adsorption is Langmuir-like and tends to saturate at bulk concentrations around 0.1 mmol/kg. In the second section adsorption is strongly cooperative with an increase not quite as steep as for C8E4. Above the cmc the surface excess concentration is approximately constant (third section). Adsorption of CpCl is less temperaturedependent than that of C8E4. Γ decreases with increasing temperature, except in the middle section (c ≈ 0.2 mmol/ kg) where it is nearly independent of temperature. Again, the measured isotherms were fitted with the Gu equation below the cmc. The fit parameters are given in Table 2. Determination of ∆Had P : Nonionic Surfactant, C8E4. The bulk phase is composed of water (solvent) and C8E4 (index 2, reference substance). With respect to eq 1 we thus have n ) 2 and Γref ) Γ2. The set P is empty. For convenience, the subscript i ) 2 will be omitted. For q we choose
dΓ ) 0 Equation 1 reduces to the Clausius-Clapeyron equation in its simplest (and well-known) form 2 ∆Had P (T, c) ) -RT
|
∂ ln c ∂T Γ
(6a)
For a finite (but small) temperature difference ∆T ) T′′ - T′, with mean temperature T h ) 0.5(T′′ + T′), ∆Had P may be approximated by
∆Had h , cj) ) -RT h2 P (T
|
∆ ln c ∆T Γ
(6b)
The difference ∆ ln c corresponding to a given value of Γ is easily obtained from the fitted curves of Figure 2. The resulting values of the differential molar adsorption enthalpy are plotted in Figure 5a as a function of the bulk concentration c ) cj ) 0.5(c′′ + c′) for Θ h ) 25 °C. The course of the adsorption isotherms is nearly parallel for concentrations between 6 mmol/kg and the cmc. Thus, within this range, the differential molar adsorption enthalpy is approximately constant with a value of about 12-13 kJ/mol. Below a concentration of 5 mmol/kg the errors of the values of the differential molar adsorption enthalpy become very large because of the nearly horizontal course of the fitted isotherms and also because of the relatively high uncertainty of the refraction measurements (interference with blank values). Determination of ∆Had P : Cationic Surfactant, CpCl. Generally, adsorption of the surfactant ion from aqueous solution is accompanied by adsorption of the counterion or of any other ion present in solution, e.g., H+ or OH-. Figure 4 shows the pH of the solution at 20 °C as a function of the surfactant concentration c before the addition of silica gel (curve 1) and after the addition of the gel with adsorption equilibrium being attained (curve 2). As can be seen from curve 1, the Cp+ ion (in its hydrated form) acts as a weak acid with base CpOH and
pKA ≈ 8.2
(7)
Figure 4. pH values of CpCl solutions at 20 °C. The pH of the 2-fold distilled water was 8.0. Curve 1: pH of the pure CpCl solution prior to adsorption; straight line drawn according to relation pH ) 0.5 pKA - 0.5 log(c/(mol/kg)) with pKA ) 8.2. Curve 2: pH of the solution at equilibrium of adsorption; solid line drawn by eye. Θ ) 20 °C.
Hence, the adsorption of the CpCl is an example of adsorption in a real multicomponent system. In our case the system is composed of water, silica gel, and CpCl. We consider these substances as pure. The ci’s appearing in eq 1 are cCp+, cCpOH, cCl-, cH+, and cOH-, with corresponding excess concentrations Γi. Written in detail eq 1 is a long expression with 10 terms on the right hand side. A more concise formulation will be presented below. By virtue of definition, the Γi’s reflect the amounts of substance exchanged between the bulk and the surface phase as seen from the bulk solution. For instance, an H+ ion desorbing from a surface site into an alkaline solution will immediately react with an OH- ion to form H2O. Thus, from the point of view of the solution, desorption of the H+ ion is seen as the adsorption of an OH- ion and therefore is counted as a positive contribution to ΓOH-. Both the surface and the bulk phase are subject to electroneutrality
ΓCp+ + ΓH+ ) ΓCl- + ΓOH-
(8)
cCp+ + cH+ ) cCl- + cOH-
(9)
Equation 9 is one of the conditions forming the set P, which, in total, consists of four conditions. The second and the third conditions are given by the laws of mass action of water and the acid Cp+:
cOH-cH+ ) KH2O
(10)
cCpOHcH+ ) KA cCp+
(11)
The total bulk concentration of Cp, as measured by UV spectroscopy, is given by
c ) cCp+ + cCpOH
(12)
The total amounts of Cp+ and Cl- are equal, that is
mc + (ΓCp+ + ΓCpOH)A ) mcCl- + ΓCl-A
(13)
where m is the mass of the solvent. This is the fourth condition of the set P, now given by eqs 9-11 and 13 (note
5554 Langmuir, Vol. 12, No. 23, 1996
Wittrock et al.
that under equilibrium conditions, the Γi’s are functions of the ci’s). According to eqs 10 and 11 the d ln ci values appearing in eq 1 are coupled by, at constant pressure
d ln cOH- + d ln cH+ )
diss ∆HH 2O
dT
2
RT
d ln cCpOH + d ln cH+ - d ln cCp+ )
(14)
diss ∆HCp +
RT2
dT (15)
Γeff Cp
) ΓCp+ + ΓCpOH
< 1.0 × 10-6 1.3 × 10-6 3.0 × 10-6
3.4 × 10-8 2.1 × 10-7 1.1 × 10-7
4.8 × 10-6 3.0 × 10-5 1.6 × 10-5
a For a given pH value the corresponding concentration c is given in Figure 4. b The surface excess concentration can be read from Figure 3a. c Values calculated from eq 25 and the values from the columns 1 and 2. d For typical values: A ) 7 m2; m ) 50 g.
(17)
By solving eq 20 for Γeff H and using eqs 12 and 9, together with eqs 10, 11, and 23, we obtain
or, see Figure 4, for
Γeff H )
m + cOH- - cH+) (c A CpOH
)
KAc KH2O m cH+ 2 + 2 - 1 A cH+ cH+
(
diss
)
(25)
(19)
On comparing this equation with the experimental results in Figure 4, one finds for concentrations satisfying eq 24b:
A eff Γ m H
(20)
eff Γeff H , ΓCp
(26)
A eff Γ ,c m H
(27)
(21)
|
( | |) | ( |) | )} | |)
∂ ln cCp+ ∂ ln cH+ ∂Γeff H + P,ΓCpeff ∂T ∂T P,ΓCpeff ∂Γeff
+
Cp T,P
(A/m)Γeff H)
∂ ln (c ∂T
P,ΓCpeff
1+
∂Γeff H eff ∂ΓCp T,P
-
Cp
∂ΓCpOH ∂Γeff Cp
T,P
diss + ∆HH 2O
∂ΓOH∂Γeff Cp
(22)
T,P
Unfortunately the concentration cCp+ appearing in the first differential quotient on the right hand side is not directly measured. Yet the differential quotient can be calculated from eqs 7, 11, and 12 if the values of c and pH are measured at each temperature. However, having measured the pH only at 20 °C, we are not able to make these calculations. Therefore, use of eq 22 will be restricted to concentrations where the approximation
cCp+ ≈ c
See Table 3 for additional details. As is shown in Appendix eff (eqs A.5a and b). A, we further have dΓOH-, dΓCpOH , dΓCp In view of these inequalities we neglect all terms in eq 22 proportional to ΓOH-, ΓCpOH, and Γeff H or to one of their derivatives. Hence, eq 22 simplifies to 2 ∆Had P ) -2RT
|
∂ ln c eff ∂T ΓCp,P
(28)
dΓref ) dΓeff Cp
-
∂Γeff ∂ ln cH+ + ∂ ln(c - (A/m)Γeff H H) eff eff T,P ∂T P,ΓCp ∂Γ diss ∆HCp +
< 6.0 × 10-6 3.0 × 10-4 8.0 × 10-4
(24b)
With eqs 9, 14, 15, and 17-21, eq 1, after some intermediate steps, can be rewritten as
(
8.0 7.2 6.5
(18)
dΓeff Cp ) 0
( |
(A/m)Γeff H/ (mol/kg)d
c g 3 × 10-4 mol/kg
As condition q we choose
{
Γeff H/ (mol/(m2)c
eff ΓCl- ) Γeff Cp + ΓH
cCl- ) c -
- RT2
eff ΓCp / (mol/m2)b
(16)
Equations 8 and 13 can be rewritten as
∆Had P )
c/(mol/kg)a
(24a)
eff is identical with the excess quantity Note that ΓCp determined experimentally (see Experimental Section). Therefore, we use it as the reference surface excess concentration:
Γref ) Γeff Cp
pH
pH < 7.2
where the terms on the right hand side result from van’t Hoff’s relation. We now introduce effective excess concentrations of H and Cp
Γeff H ) ΓH+ - ΓOH- - ΓCpOH
Table 3. Selected Values of Bulk and Surface Excess Concentrations
(23)
can be used. According to eq 12 this implies cCpOH , cCp+. As is seen from eqs 7 and 11, the approximation is satisfied with an error of less than 10% for
This formula equals that obtained for the adsorption of a single strong electrolyte.1 We repeat that this simple result can be only applied in the concentration range given by eq 24b. The differential molar adsorption enthalpies calculated from the fitted isotherms by means of eq 28 are shown in Figure 5b for Θ h ) 30 °C and Θ h ) 50 °C. In both cases ∆Had P decreases with increasing c from values near zero to values of about -20 kJ/mol near the cmc. Discussion. Our investigations show that the generalized Clausius-Clapeyron equation, eq 1, is an efficient tool in determining heats of adsorption from adsorption isotherms measured at neighboring temperatures. The efficiency of eq 1 is not so much based on the fact that it can be specialized to simple formulas for solutions containing a single nonionic substance or a single strong electrolyte, eqs 6a and 28, these equations can be obtained from more basic considerations. The important point is that more complex situations can be handled and thatsas has been demonstrated above with respect to eq 28sthe validity range of the “simple” formulas can be determined. Our treatment shows that the validity of eq 28 is restricted
Adsorption Enthalpies of Surfactants
Langmuir, Vol. 12, No. 23, 1996 5555
Figure 5. (a) Differential molar adsorption enthalpy of the nonionic surfactant C8E4. Θ ) 25 °C. Curve calculated from eq 6b and the fitted isotherms of Figure 2. (b) Differential molar adsorption enthalpy of the cationic surfactant CpCl. Θ ) 30 °C; Θ ) 50 °C. Curve calculated from eq 28 and the fitted isotherms of Figure 3b.
to CpCl concentrations above 3 × 10-4 mol/kg and pH values below 7.2 where contributions of ΓH+, ΓOH-, and ΓCpOH, and thus of Γeff H , to the heat of adsorption can be neglected. For small Γeff H the isothermal Gibbs equation
dσ ) - RT
∑
Γi d ln ci
(29)
can also be written as eff dσ ) - RT (Γeff H d ln cH+ + ΓCp d ln cCp+)
(30)
From Schwarz’ identity we get
|
|
∂Γeff ∂Γeff H Cp eff ) ∂ ln cCp+ ΓCp ∂ ln cH+ Γeff H Negligibly small values of Γeff H imply
|
∂Γeff H eff ≈ 0 ∂ ln cCp+ ΓCp From eq 31 we conclude
|
∂Γeff Cp ≈0 ∂ ln cH+ Γeff H
(31)
Thus, with vanishing Γeff H , the adsorption process as a whole becomes independent of pH. As mentioned, determination of ∆Had P could be extended beyond the concentration ranges specified in eqs 24a and b if the equilibrium pH of the suspension and the pKA of Cp+ were measured at each temperature. The results of Figure 5a show that the adsorption of C8E4 is endothermic and therefore entropically driven. The entropic nature of the adsorption process can be easily attributed to the hydrophobic effect. In contrast, adsorption of CpCl is distinctly exothermic near the cmc. Similar curves as for CpCl have been reported for other cationic surfactants.25-28 The exothermic character of CpCl adsorption may be due to the rather long hydrocarbon chain, offering more favorable packing conditions than those for the short C8 tail. In part 2 of this series the temperature effect is related to the hydrophobic effect of the CH2 groups of the alkyl chain. Maybe there is also some exothermic contribution of direct counterion binding.29 One might expect that the electrostatic energy content of the diffuse double layer produced by the adsorption of the ionic surfactant makes a positive, i.e., endothermic, contribution to the adsorption enthalpy. As is shown in Appendix B on the basis of the Guy-Chapman theory, the contrary is true. The contribution of the diffuse double layer is exothermic, though rather small. This strange result is a consequence of the strong temperature dependence of the dielectric constant of water. An obvious difference between the adsorption isotherms presented here and those found in other contributions25-28 is the sharp bend close to the cmc (cf. Figures 2 and 3). As is well-known the increase of the monomer concentration levels off rather abruptly at the cmc. Since the monomer concentration is leading the adsorption process, the amount of adsorbed surfactant should also level off above the cmc and the isotherms should show a distinct bend. The absence of such a bend, frequently observed in literature, can be regarded as a hint of missing thermodynamic equilibrium. Acknowledgment. This work has been financially supported by the Deutsche Forschungsgemeinschaft (DFG). We thank Professor H. Rupprecht, Regensburg, for stimulating discussions. Appendix A CpCl Adsorption: Contribution of the Dissociation Reactions to ∆Had P . The composition of the surface phase is described by the five surface excess concentrations Γi mentioned in the main text. Equivalently, this composition can be described, at constant T and p, by the corresponding chemical potentials µi (which, at equilibrium, have the same value in the bulk and in the surface phase). The Γi’s are subject to the condition of electroneutrality (eq 8). Moreover, the µi’s obey the two laws of mass action given by eqs 10 and 11. Thus, there are only 5 - 3 ) 2 degrees of freedom left for the Γi’s. This means that the values of all dΓi’s are defined as soon as values eff of dΓeff H and dΓCp are specified. To determine the relation between dΓCpOH and dΓOH-, eff on the one hand, and dΓeff H and dΓCp, on the other, we (25) Dobia´sˇ, B. In Surfactant Science Series Coagulation and Floculation (Theory and applications); Marcel Dekker, Inc.: New York, Basel, Hong Kong, 1993, No. 47, p 539. (26) Rupprecht, H.; Gu, T. Colloid Polym. Sci. 1991, 269, 506. (27) Zhu, B.-Y.; Gu, T.; Zhao, X. J. Chem. Soc., Faraday Trans. 1 1989, 85, 3819. (28) Gao, Y.; Du, J.; Gu, T. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2671. (29) Heindl, A.; Kohler, H.-H. Langmuir 1996, 12, 2464.
5556 Langmuir, Vol. 12, No. 23, 1996
Wittrock et al.
consider variation of the bulk composition (according to the set P) and the corresponding process of adsorption in two steps: first step, addition of a differential amount of CpCl to the bulk solution; second step, adsorption taking place in the materially closed system. The following consideration refers to the second step. According to the definition of surface excess we have
In the experimental range of interest we have dΓeff H/ eff , 1 (eq 26) and (cH+ + cOH-)/c , 1 (see first two dΓCp columns of Table 3). Thus we conclude from eqs A.4a and b
A dΓi ) -m dci or A dΓi ) -mci d ln ci (A.1)
dΓOH- cOH- d ln cOH) dΓH+ cH+ d ln cH+
(A.2a)
dΓCpOH cCpOH d ln cCpOH ) dΓCp+ cCp+ d ln cCp+
(A.2b)
dΓCpOH cCpOH d ln cCpOH ) dΓH+ cH+ d ln cH+
(A.2c)
dΓOH- ) -
dΓOH-
{
∆Gel ) RT 2 arsinh y -
cOHdΓH+ cH+
(
)
cH+ + 1 + dΓCpOH ) -dΓeff H cOH-
(A.3a)
where γ is the surface charge density, s the (temperaturedependent) relative dielectric constant of the solvent, and F the density of the solution. If we assume that γ is due to the adsorption of surfactant ions and if we neglect eff (F ) Faraday counterion binding, we have γ ) FΓCp constant). From the Gibbs-Helmholtz relation
∆Hel ) RT
)
cCp+ cCp+ cCp+ + dΓCpOH + +1 ) cH+ cH+ cCpOH cCp+ (A.3b) cH+
Equations A.3a and b are a system of two equations for the unknown dΓOH- and dΓCpOH. Solving for dΓOH- and eff dΓCpOH and dividing by dΓCp we obtain
(
-cOH) cH+ + cOH- + cCpOH
cCp+ c
dΓeff H
dΓeff Cp
+
(B.2)
x8RT0scF
|
∂∆Gel ∂T c,ΓCpeff
(B.3)
(
(B.4)
and eq B.1 one calculates
On substituting dΓH+ and dΓCp+ by eqs 16 and 17 this can be rearranged to
eff dΓeff Cp - dΓH
γ
∆Hel ) ∆Gel - T
dΓCpOH cH+ dΓH+ cCpOH cCpOH dΓCp+ dΓCpOH ) cCp+ dΓCpOH cH+ 1+ dΓH+ cCpOH
(
} (B.1)
2 (x1 + y2 - 1) y
with
Similarly, with eq 11 and eq A.2c, eq A.2b becomes
)
cCpOH (A.4a) c
dΓCpOH dΓeff Cp
(A.5b)
y)
With eq 16 this can be rewritten as
dΓeff Cp
dΓCpOH , dΓeff Cp
Contribution of the Diffuse Double Layer to ∆Had P . We consider a one to one electrolyte of bulk concentration c. The electrostatic contribution of the double layer to the molar Gibbs energy of adsorption is given by29-31
Using eq 10 with dT ) 0 we obtain from eq A.2a
dΓOH-
(A.5a)
Appendix B
and therefore
dΓOH-
dΓOH- , dΓeff Cp
x1 + y2 - 1 y
1+
| )
T ∂s s ∂T c,ΓCpeff
For typical polar solvents the value in parentheses is negative at room temperature.32 For water of 20 °C it amounts to -0.36. With respect to CpCl adsorption we eff ) 2 × 10-6 mol/m2. choose c ) 7 × 10-4 mol/kg and ΓCp With F ) 1 kg/L one obtains y ) 62.6. From eqs 33 and 34 one calculates ∆Gel ) 18.7 kJ/mol and ∆Hel ) -0.86 kJ/mol. Evidently, ∆Hel is small and, consequently, ∆Gel is mainly entropic in nature. The negative value of ∆Hel can be attributed to enhanced binding of neighboring water dipoles (growth of dipole clusters) under the influence of the external field. For y , 1 this effect amounts to ∆Hel ≈ -0.18∆Gel. In this range of small surface potentials the average distance between surface and counterion is given by the Debye length. But with increasing y (increasing field strength at the surface) the average distance between counterions and surface decreases (counterion compression).31 As a result of these two opposing effects ∆Had P reaches a limiting value so that ∆Gel becomes dominated by the purely entropic effect of counterion compression. LA960356H
)
-cCpOH cH+ + cOH- + cCpOH
(
cCp+ c
)
dΓeff cH+ + cOHH cCp+ eff c c dΓ Cp
(A.4b)
(30) Evans, D. F.; Ninham, B. W. J. Phys. Chem. 1983, 87, 5025. (31) Kohler, H.-H. In Coagulation and Flocculation Theory and Applications; Dobia´sˇ, B., Ed.; Marcel Dekker, Inc.: New York, Basel, Hong Kong 1993; Chapter 2, p 37. (32) Moelwyn-Hughes, E. A. Physikalische Chemie; Jaenicke, W., Go¨hr, H. Eds.; Georg Thieme Verlag: Stuttgart 1970; Chapter 17, p 479.
