Langmuir 1999, 15, 5977-5983
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Calorimetric Effects of Simple Ion Adsorption at the Silica/Electrolyte Interface: Quantitative Analysis of Surface Energetic Heterogeneity† W. Rudzinski,*,‡ R. Charmas,‡ W. Piasecki,‡ B. Prelot,§ F. Thomas,§ F. Villieras,‡ and J. M. Cases‡ Department of Theoretical Chemistry, Faculty of Chemistry, Maria Curie-Sklodowska University, M. Curie Sklodowska Sq. 3, 20-031 Lublin, Poland, and Laboratoire Environnement et Mineralurgie, ENSG, INPL et UMR 7569 du CNRS, BP 40, 54501 Vandoeuvre les Nancy Cedex, France Received September 28, 1998. In Final Form: January 7, 1999
The equations developed by us for the triple layer surface complexation approach, taking into account energetic heterogeneity of surface oxygens, are applied here to study the heterogeneity influences on the enthalpic effects accompanying ion adsorption at the silica/NaCl aqueous solution interface. That study is accompanied by the parallel experimental/theoretical study of the energetic heterogeneity of surface oxygens for adsorption of argon molecules which are known to interact practically only with surface oxygens. Such studies provide a simpler interpretation for information of the surface energetic heterogeneity. That additional study confirms a proper choice of the model of surface heterogeneity, accepted by us in our description of ion adsorption at the oxide/electrolyte interfaces. Our quantitative analysis also confirms quite different features of the silica/electrolyte interface, compared to those formed by other metal oxides. Namely, in the case of the silica/electrolyte interface, the adsorption of water molecules on the surface oxygens SO- is a process highly competitive with proton adsorption leading to that of formation of the neutral surface complexes SOH0.
Introduction The features of the silica/electrolyte interface are crucial for many processes important for life on the earth as well as for science and technology. At the same time the features of silica are quite different from those of other oxides and still not well understood. So far, studies of the oxide/ electrolyte interfaces have been oriented almost exclusively toward measuring the adsorption isotherms of ions (titration isotherms or individual isotherms) and investigating electrokinetic effects. The determined equilibrium constants provided, thus, the information about the appropriate values of the free energies of ion adsorption. However, it has been realized for a long time that knowledge of the enthalpic effects accompanying the adsorption of ions may bring more light onto fundamental features of these adsorption systems. The first attempts to estimate these enthalpic effects started 25 years ago. The enthalpic effects were elucidated first from the temperature dependence of ion adsorption, but now they are more and more frequently measured directly in appropriate calorimetric experiments. The measured calorimetric effects carry, however, very complicated information about the enthalpic effects accompanying a number of surface complexation reactions occurring simultaneously. All the reported experimental works have been revised in one of our previous publications.1 * Corresponding author. Tel.: +48 81 5375633. Fax: +48 81 5375685. E-mail:
[email protected]. † Presented at the Third International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland, August 9-16, 1998. ‡ Maria Curie-Sklodowska University. § Laboratoire Environment et Mineralurgie. (1) Rudzinski, W.; Charmas, R.; Piasecki, W.; Thomas, F.; Villieras, F.; Prelot, B.; Cases, J. M. Langmuir 1998, 14, 5210.
Attempts to analyze quantitatively these calorimetric effects have been the subject of a series of papers published by us.1-6 That quantitative analysis showed a big risk of simple interpretation, on a qualitative level, of the enthalpic effects accompanying ion adsorption. Our studies confirmed also what has been known in adsorption science for a long time. Namely, that calorimetric effects of adsorption are much more sensitive to the nature of an adsorption system than adsorption isotherms. So, in the case of oxides like alumina and silica, for instance, the energetic heterogeneity of surface oxygens must affect strongly the calorimetric effects accompanying simple ion adsorption.1 A number of oxide/electrolyte systems have been studied by us so far, but the main difficulty here lies in the fact that only few directly measured calorimetric data have been reported so far in literature.7-13 This was also the reason why enthalpic effects of ion adsorption on silica have not been subjected to our analysis yet. In our present work we are going to carry out a quantitative analysis of (2) Rudzinski, W.; Charmas, R.; Partyka, S.; Foissy, A. New J. Chem. 1991, 15, 327. (3) Rudzinski, W.; Charmas, R.; Partyka, S. Langmuir 1991, 7, 354. (4) Rudzinski, W.; Charmas, R.; Cases, J. M.; Francois, M.; Villieras, F.; Michot, L. J. Langmuir 1997, 13, 83. (5) Rudzinski, W.; Charmas, R.; Piasecki, W.; Cases, J. M.; Francois, M.; Villieras, F.; Michot, L. J. Colloids Surf. A. 1998, 137, 57. (6) Rudzinski, W.; Charmas, R.; Piasecki, W.; Kallay, N.; Cases, J. M.; Francois, M.; Villieras, F.; Michot, L. J. Adsorption 1998, 4, 287. (7) Machesky, M. L.; Anderson, M. A. Langmuir 1986, 2, 582. (8) Mehr, S. R.; Eatough, D. J.; Hansen, L. D.; Lewis, E. A.; Davis, J. A. Thermochim. Acta 1989, 154, 129. (9) De Keizer, A.; Fokkink, L. G. J.; Lyklema, J. Colloids Surf. 1990, 49, 149. (10) Machesky, M. L.; Jacobs, P. F. Colloids Surf. 1991, 52, 297. (11) Machesky, M. L.; Jacobs, P. F. Colloids Surf. 1991, 52, 315. (12) Kallay, N.; Zalac, S.; Stefanic, G. Langmuir 1993, 9, 3457. (13) Casay, W. H. J. Colloid Interface Sci. 1994, 163, 407.
10.1021/la981336d CCC: $18.00 © 1999 American Chemical Society Published on Web 03/16/1999
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Rudzinski et al. Table 1. Surface Reactions, Equilibrium Constants, and Heats of Adsorption Commonly Considered When the TLM Description Is Applieda reaction type
equil consts
heats of reacn
SOH0 + H+ T SOH+ 2 SO- + H+ T SOH0 SOH0 + H+ + A- T SOH2+ASO-C+ + H+ T SOH0 + C+ SO- + 2H+ T SOH2+ SO- + 2H+ + A- T SOH2+ASO- + C+ T SO-C+ SOH2+ + A- T SOH2+A-
-pKint a1 -pKint a2 -p*Kint A -p*Kint C int -pKa1 - pKint a2 int -pKint a2 - p*KA int int p*KC - pKa2 int pKint a1 - p*KA
Qa1 Qa2 QaA - Qa2 Qa2 - QaC Qa1 + Qa2 QaA QaC QaA - Qa1 - Qa2
a
int int int pKint a1 ) -logKai (i ) 1, 2) and p*K i ) -log*Ki (i ) C, A).
θ0 ) [SOH0]/Ns θ+ ) [SOH2+]/Ns θA ) [SOH2+A-]/Ns θC ) [SO-C+]/Ns θ- ) [SO-]/Ns ) 1 -
∑iθi (i ) 0, +, A, C)
where
Ns ) [SO-] + [SOH0] + [SOH2+] + [SO-C+] + [SOH2+A-] (1) the surface charge δ0 can be defined as follows1,2,
δ0 ) Bs[θ+ + θA - θ- - θC] Bs ) eNs
Figure 1. Diagramatic presentation of the triple layer model (TLM). ψ0 and δ0 are the surface potential and the charge density in the 0-plane; ψβ and δβ, the potential and the charge coming from the specifically adsorbed ions (cations C+ and anions A-) of the inert electrolyte; ψd and δd, the diffuse layer potential and its charge; and c1 and c2, the electrical capacitances, constant within the regions between the adsorption planes.
that kind for the silica/electrolyte interface, taking into account our own and some recently published literature data. The equations used here by us have been developed in our previous publication,1 but for the reader’s convenience we repeat here not only some basic definitions but also equations used in our computer calculations. The main goal of the present publication is to apply our thoretical approach to study the effects of the surface energetic heterogeneity on ion adsorption on silica which exhibits such an unusual behaviour compared to other oxides. Theory Of all the models of the oxide/electrolyte interface published so far, the most frequently used for quantitative analysis is the so called triple layer modelsTLM.14,15 For readers’ convenience, its schematic picture is shown in Figure 1. The surface reactions which occur, the related equilibrium constants, and nonconfigurational heats of adsorption are presented in Table 1. With introduction of the notation (14) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface Sci. 1978, 63, 480. (15) Davis, J. A.; Leckie, J. O. J. Colloid Interface Sci. 1978, 67, 90.
(2)
where Ns is the surface sites density (sites/m2). The relationships between the capacitances, the potentials, and the charges within the individual electric layers are commonly known and were presented in our previous papers.1-3 In our recent theoretical investigations, we modified that model by taking into account the smaller degree of crystallographic organization of the surface oxygens, compared to the situation in the interior of an oxide crystal. That surface disorder leads to a diversity in the features of the surface oxygens, resulting in what is called “surface energetic heterogeneity”.1,16,17 Namely, the free energy of complex formation changes from one to another surface oxygen. We took into account two physical situations: the case of high correlations between the adsorption energies of different surface complexes when going from one to another oxygen and the case of small correlations between these energies. Our analysis showed, however, that the most realistic model seems to be that one assuming small correlations between the adsorption energies of different complexes.1,18 It was proved by the analysis of the behaviour of potentiometric, electrokinetic, and radiometric data16 and bivalent ion adsorption at low ion concentrations,17 as well as of calorimetric effects accompanying ion adsorption.1 Here, we will apply that model while analysing the experimental data for the silica/ electrolyte interface. With the assumption of small correlations between adsorption energies the nonlinear equation system for the TLM model takes the following Langmuir-like form1 (16) Rudzinski, W.; Charmas, R.; Partyka, S.; Thomas, F.; Bottero, J. Y. Langmuir 1992, 8, 1154. (17) Rudzinski, W.; Charmas, R.; Partyka, S.; Bottero, J. Y. Langmuir 1993, 9, 2641. (18) Rusch, U.; Borkovec, M.; Daicic, J.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1997, 191, 247.
Calorimetric Effects of Simple Ion Adsorption
θi )
(Kifi)kT/ci 1+
∑i (Kifi)
Langmuir, Vol. 15, No. 18, 1999 5979
i ) 0, +, A, C
(3)
kT/ci
where int
K0 )
*KC 1 1 K+ ) int int KC ) int int Ka2 Ka1 Ka2 Ka2
KA )
1 int Kint ‚*K a2 A (4)
fi (i ) 0, +, A, C) are the following functions of proton and salt concentrations:
{
f0 ) exp -
eψ0 - 2.3pH kT
{
fC ) aC exp -
{
fA ) aA exp -
}
f+ ) f02
}
eδ0 eψ0 + kT kTc1
(5a,b)
(5c)
eδ0 eψ0 - 4.6pH kT kTc1
}
where β is given by
β)
( )
eψ0 eψ0 + sinh-1 kT βkT
(6)
( )
(7)
2e2Ns Kint a2 ctkT Kint a1
We have been the first to draw readers’ attention to the fact that such independence of PZC of salt concentration can formally be expressed by the set of the two equations1,2
(5d)
aH is the proton activity in the equilibrium bulk phase, and aA and aC are the bulk activities of anion and cation respectively. In eq 3 ci (i ) 0, +, A, C) are the heterogeneity parameters proportional to the variance πci/x3 of a gaussian-like, fully symmetrical function describing the dispersion of adsorption energies on different surface complexes across the surface.1 To express the ψ0(pH) dependence, which occurs in the equations for the individual adsorption isotherms, we accepted the relation used by Yates et al.,19 Bousse et al.,20 and Van der Vlekkert et al.,21
2.303(PZC - pH) )
Figure 2. Schematic presentation of the common intersection point (CIP) for three titration curves corresponding to different concentrations (activities) of inert electrolyte, ai, i ) 1, 2, and 3.
1/2
and where ct is the linear capacitance of the double electrical layer that can be calculated in the way proposed by Bousse et al.20 The way of solving the set of equations 3-7 for TLM, to arrive at the individual adsorption isotherms θi’s and at the surface charge δ0 as functions of pH, was shown in our previous papers.1,2 The experimental titration curves corresponding to different concentrations of the basic (inert) electrolyte usually have a common intersection point (CIP) at the point of zero charge (PZC), such that PZC ) pHδ0)0,ψ0)0. It means that the PZC value for a given system of oxide/ electrolyte does not practically depend on salt concentration in the bulk solution. It is schematically shown in Figure 2. (19) Yates, D. E.; Levine, S.; Healy, T. W. J. Chem. Soc. Faraday Trans. 1 1974, 70, 1807. (20) Bousse, L.; De Rooij, N. F.; Bergveld, P. IEEE Trans. Electron Devices 1983, 30, 1263. (21) Van den Vlekkert, H.; Bousse, L.; De Rooij, N. F. J. Colloid Interface Sci. 1988, 122, 336.
δ0(pH ) PZC) ) 0
∂δ0(pH ) PZC) ∂(a ) aC ) aA)
)0
(8)
Application of the above formal criterion decreases by 2 int int the number of the equilibrium constants Kint a1 , Ka2 , *KA , int and *KC (best-fit parameters) determined by fitting suitable experimental data. So far, only a few experiments using titration calorimetry for different oxide/electrolyte systems have been reported where, in the course of titration, also the accompanying heat effects were measured upon the addition of an acid or base. The first experiments of that kind were performed by Machesky and Anderson7 in 1986, Mehr et al.8 in 1989, De Keizer et al.9 in 1990, Machesky and Jacobs10,11 in 1991, Kallay et al.12 in 1993, and Casey13 in 1994. In the titration calorimetry experiment, after introduction of an outgassed solid sample into a solution, the pH of that solution is measured. Then, a titration step is carried out (from the base or acid side) and the evolved heat is recorded. Depending on the reported experiments the consumption (adsorption) of protons and ions of the inert electrolyte is monitored, accompanying the change of pH by ∆pH. We have shown in our previous publications1,4,5 that the heat data reported by Machesky et al.,7,10,11 working on the goethite/NaNO3 and alumina/ NaCl interfaces, Mehr et al..8 working on the TiO2/NaCl interface, and Casey,13 working on the silica/different electrolyte interfaces, are described by the equation
Qpr )
∫pH
∑iQi(∂θi/∂pH)T dpH
pH+∆pH
∫pH
pH+∆pH
[2(∂θ+/∂pH)T + 2(∂θA/∂pH)T + (∂θ0/∂pH)T] dpH
(9) where Q0, Q+, QC, and QA are the molar differential heats accompanying formation of the SOH, SOH2+, SO-C+, and SOH2+A- surface complexes, respectively. For the heterogeneous TLM model, assuming small correlations beween adsorption energies of various surface complexes, Qi’s take the form
5980 Langmuir, Vol. 15, No. 18, 1999
Qi ) Qhom - ci ln i
Rudzinski et al.
θi i ) 0, +, C, A θ-
(10)
where Qhom ’s are the expressions for the homogeneous i TLM,1,2
) Qa2 - eψ0 Qhom 0
Qhom ) Qa1 + Qa2 - 2eψ0 +
) QC - eψ0 Qhom C
( ) ( ) ( ) ( )
e ∂ψ0 T ∂(1/T)
eδ0T ∂c1 (c )2 ∂T 1
Qhom ) QA - eψ0 A
1
{θi},pH
{θi},pH
{θi},pH
(11b)
δ0 + c1
+e
+k
{θi},pH
(11a)
{θi},pH
2e ∂ψ0 T ∂(1/T)
{θi},pH
e ∂ψ0 T ∂(1/T)
eδ0T ∂c1 (c )2 ∂T
( ) ( )
e ∂ψ0 T ∂(1/T)
(
)
(11c)
)
(11d)
∂(ln aC) ∂(1/T)
pH
δ0 c1
-e
+k
(
∂(ln aA) ∂(1/T)
pH
The analytical expressions for (dθi/dpH)T’s (i ) 0, +, A, C) are the functions of pH and the concentration of the inert electrolyte ions.1 In our previous paper, eqs 9-11 were applied by us to analyze the experimental data reported by Machesky and Jacobs10,11 for the alumina/ NaCl system. Here, a similar quantitative analysis of the heats accompanying the proton adsorption in the silica/ NaCl system studied by Casey13 is presented.
was created by dispersing 500 mg of Aerosil-380 particles into 1 dm3 of NaCl. Then 50 cm3 aliquotes were used for each pH (adjusting HCl and NaOH). Around 20 cm3 of that suspension was then introduced into the electrophoretic cell. The particles located in the stationary layer were illuminated by a laser beam. Velocity of the particles was directly computed from a video analysis of the images obtained at fixed time intervals under the applied voltage (80 V). The obtained values of mobility were recalculated into ζ-potential using the Smoluchowsky’s equation. The experimentally determined ζ(pH) curves for the two inert electrolyte concentrations, 0.1 and 0.01 mol‚dm-3, have a common intersection point at pH ) IEP ) 3.8 ( 0.1. Thus, we had at our disposal three kinds of the experimental data, δ0(pH), ζ(pH), and Qpr(pH), which were next subjected to our theoretical analysis. However, as we have already emphasized, these three kinds of data carry combined information (effect) coming from a number of surface reactions which occur simultaneously. Thus, any other additional information should be very useful in a further theoretical analysis of these data. In particular, information about the energetic heterogeneity of the surface oxygens of our silica sample might be very useful. Studies of energetic heterogeneity of silica surfaces have been frequently carried out in gas adsorption on the silica surfaces.23 So, we decided to carry out an additional study of energetic surface heterogeneities of the Aerosil-380 surface for argon and nitrogen adsorption from a gas phase. They were studied by using the high resolution quasiequilibrium nitrogen and argon adsorption at 77 K. The experimental set up used for obtaining the low pressure isotherms was described in our previous publication.24 A sample of Aerosil300 (0.1073 g) was outgassed directly in the adsorption device for 6 hours at 473 K. Argon N56 (purity > 99.9996) and nitrogen N60 (purity > 99.9999) were used in our experiment. The frequency of pressure recording was adjusted after each measurement to register 100-200 experimental points per unit of ln(p/ps). It allowed us to collect 2000-3000 experimental data points for the relative pressures lower than 0.15. Due to the large number of the recorded experimental points, the derivative of the gas adsorbed quantity with respect to the logarithm of relative pressure could be calculated with very good accuracy to determine the spectrum of surface energetic heterogeneities.
Experimental Methods Heat changes were determined by Casey,13 by monitoring the temperature and surface charge of the colloidal suspension of commercial pyrogenic silica (Aerosil-380, Degusa Corp.) during titration with a standard acid or base. The detailed description of this experiment and of the properties of the silica was presented in Casey’s paper.13 The inert electrolytes NaCl, KCl, and (CH3)4NCl were used in Casey’s experiment, but only in the case of NaCl was the surface charge curve δ0(pH) also was reported in his paper.13 The titration curves exhibited a hysteresis loop when going from the acid to base side and back. Such hystereses were also reported by other researches,7,8,10,11 but their origin is still not well understood. Most likely they are due to kinetics of ion adsorption/desorption. Of all the three NaCl concentrations used in Casey’s experiment, the data for 0.1 mol/dm3 showed the smallest hysteresis. Thus, we took only these data for consideration in our theoretical analysis. The heat data, Qpr(pH) were collected in the Appendix of Casey’s paper,13 whereas the surface charge data for this system, δ0(pH), have been tabularized in the paper by Sahai and Sverjensky.22 Well known is the difficulty of determining precisely the value of the point of zero charge (PZC) for the silica/electrolyte systems when using the titration method.13 It is believed to lie in the pH range between 2 and 4. Meanwhile, the calculations based on our theoretical model are very sensitive to the exact value of PZC, so our study was based on the assumption that the values of PZC and IEP (isoelectric point) are the same. For that purpose, the evolution of the electrophoretic mobility of Aerosil-380 particles with pH was monitored in our laboratory, using a Zetaphoremeter II Sephy 2100 (France). The suspension (22) Sahai, N.; Sverjensky, D. A. Geochim. Cosmochim. Acta 1997, 61, 2801.
Results and Discussion Using the derivative isotherm summation method (DIS)25 makes it possible to characterize quantitatively the adsorption energy distribution. The obtained curves are shown in Figure 3A,B. Our sample looks more heterogeneous for nitrogen than for argon adsorption, because the nitrogen molecules can also exhibit specific interactions with polar sites of the surface. The calculated specific surface areas are 310 and 400 m2/g for argon and nitrogen, respectively. The isotherm derivatives could be fitted by a combination of two or three “local” derivatives for argon and nitrogen, respectively. Argon is more appropriate for studies of heterogeneity effects in adsorption at the oxide/electrolyte interface, because argon interacts only with the surface oxygen atoms. Therefore only the argon isotherm derivative was subjected to further studies. First the effect of multilayer adsorption on the argon isotherm derivative was eliminated, by multiplying the adsorbed amount Vads by (1 - p/ps).25 The argon isotherm derivative “cleaned” in that way is shown in Figure 4A. Next, that function has been redrawn in Figure 4B by (23) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press, London/New York, 1992. (24) Villieras, F.; Michot, L. J.; Cases, J. M.; Berend, I.; Bardot, F.; Francois, M.; Gerard, G.; Yvon, J. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces; Rudzinski, W., Steele, W. A., Zgrablich, G., Eds.; Studies in Surface Science and Catalysis, Vol. 104; Elsevier Sci. Publ. B.V.: Amsterdam, 1997, p 573. (25) Villieras, F.; Michot, L. J.; Bardot, F.; Cases, J. M.; Francois, M.; Rudzinski, W. Langmuir 1997, 13, 1104.
Calorimetric Effects of Simple Ion Adsorption
Langmuir, Vol. 15, No. 18, 1999 5981
Figure 3. (A) Computer fit of the derivative of the argonadsorbed amount Vads, with respect to ln(p/ps), by two “local” derivatives of the isotherms representing adsorption on two kinds of adsorption sites. For a theoretical description see our previous paper.25 (B) Same fit for nitrogen adsorption likely to be made by using three “local” derivatives.
Figure 4. (A) Argon isotherm derivative calculated by removing the effects of multilayer adsorption. (B) Derivative shown previously in part A now recalculated to represent the condensation approximation χc(c) for the true argon adsorption energy distribution χ().25
introducing the energy scale RT ln(p/ps) to represent the condensation approximation for the argon adsorption energy distribution. That scale does not show the true values of adsorption energy, but it shows correctly the shape of the condensation approximation for the true distribution of the argon adsorption energy. That condensation approximation function χc(c) has the following relation to the true adsorption energy distribution, χ(),23
χc (c) )
∫0∞ χ()
(
)
∂θ(,c) d ∂
(12)
where is the argon adsorption energy and θ(,c) is the function representing the fraction of the surface sites occupied by the adsorbed argon molecules (the argon adsorption isotherm). For the Langmuir model of adsorption, θ(,c) takes the form
( ) ( )
- c kT θ(,c) ) - c 1 + exp kT
(13a)
c ) -kT ln(Kp)
(13b)
exp
where K is the Langmuir constant. The averaging in eq 13 makes the function χc(c) wider than χ() but has a secondary effect on the shape of χc(c). So, Figure 4B suggests that the true adsorption energy
Figure 5. Electrophoretic mobilities of the Aerosil-380 particles measured in our experiment for the two concentrations, 0.1 mol/dm3 NaCl (b), and 0.01 mol/dm3 NaCl (O).
distribution χ() is a one-modal gaussian-like function, like those accepted by us to represent the distributions of the adsorption energies of the complexes formed on the surface oxygens at the silica/electrolyte interface. Figure 5 shows the results of the electrokinetic studies carried out in our laboratory in France. They suggest IEP to lie around 3.8, which value was, later on, identified with the PZC value in our theoretical analysis of all the experimental data. Let us remark at this moment that the PZC value assumed by us was slightly different from the 3.5 value suggested by Sahai and Sverjensky,22 for the Aerosil-380/NaCl system.
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Rudzinski et al.
Table 2. Parameter Values Determined by Us While Fitting Simultaneously the δ0(pH), ζ(pH), and Qpr(pH) Experimental Data for the Aerosil-380/NaCl System best-fit params
calcd values
parameters for Fitting Potentiometric, Electrokinetic, and Calorimetric Data pKint pKint a1 ) 0.1 (-0.7, ref 22) a2 ) 7.46 (7.7, ref 22) int ) 7.3 (7.1, ref 22) p*K p*Kint C A ) 0.19 (-0.5, ref 22) 2 2 c1 ) 0.95 F/m (0.95 F/m , ref 22) kT/c0 ) kT/cC ) 0.8, kT/c+ ) kT/cA ) 0.6 Parameters for Fitting Only Calorimetric Data Qa1 ) 2 kJ/mol QaC ) 0 kJ/mol (assumed) Qa2 ) 28 kJ/mol QaA ) 32 kJ/mol 2 R1 ) dc1/dT ) -0.003 F/(m deg)
Figure 6. Simultaneous fits (solid line) of the surface charge δ0(pH) data, found in Casey’s experiment13 (Figure 6A), and of ζ(pH) data determined in our experiment (Figure 6B), for the Aerosil-380/NaCl interface, with NaCl concentration 0.1 mol/ dm3. The parameters used are collected in Table 2.
Table 2 presents the collection of the parameters which were used to fit simultaneously the δ0(pH), ζ(pH), and Qpr(pH) data obtained in our and Casey’s experiments, by the equations developed for the heterogeneous TLM (Figures 6 and 7). In Table 2, there are also given the values of the parameters found by Sahai and Sverjensky,22 who used the classical homogeneous TLM to fit only the titration data δ0(pH) for three concentrations of the inert electrolyte NaCl. It should be mentioned here that Sahai and Sverjensky did not apply condition (8) for the CIP to exist. In spite of that their values of parameters are not much different from ours. The differences must partially be attributed to the fact that their estimation based on the homogeneous TLM did not take into account the energetic heterogeneity of the silica surface. Another source of these differences must be also attributed to different estimations of surface site density. While Sahai and Sverjensky assumed Ns to be 4.6 sites/nm2, we took Ns ) 2.5 sites/nm2 (the same
Figure 7. Fit (solid line) of the experimental heats of ion adsorption Qpr, measured by Casey13 for the NaCl concentration 0.1 mol/dm3. The black squares (9) and black circles (b) represent the calorimetric titration data going from the acid and base sides, respectively. The parameters used in that computer fit are collected in Table 2.
value as Casey13), deduced by us from the commercial information (total silanol site density equals 4.15 × 10-10 mol/cm2).26 As our studies are focused on the calorimetric effects accompanying ion adsorption, Figure 7 deserves some additional comments. Namely, the lack of experimental data in the region 3 < pH < 5.5 does not allow for a precise estimation of the heat effect accompanying the second proton adsorption on the neutral complex SOH, Qa1. This is because Qa1 affects Qpr only at low pH values, smaller than 5. Nevertheless, one may surely say that this enthalpic effect is either nonexistent or that the second proton adsorption is a slightly endothermic process. This would mean that the driving force for the second proton adsorption is the accompanying change of entropy. For the temperature 25 °C, at which all the experiments were carried out, the entropic contribution T∆S ) ∆H - ∆G is, for the second proton adsorption, equal to -1.4 kJ/mol. In the case of the first proton adsorption that entropic contribution T∆S is equal to +14.6 kJ/mol. Let us remark that the results of our quantitative analysis here are much differerent from what was suggested by Casey13 using the two-layer model of an energetically homogeneous surface to analyze these experimental data. In his theoretical analysis, Casey did not take into account formation of the surface complexes others than SOH. So, he neglected the heat effects due, for instance, to the formation of SO-C+ complexes, QCpr, whose contribution appears to be dominant over the heat contribution Q0pr for pH > 6.5, in which pH region all the heat data but one were recorded. This is shown in Figure 8. There, the contributions Qipr’s are drawn,
Qipr )
∫pH
pH+∆pH
∫pH
Qi(∂θi/∂pH)T dpH
pH+∆pH
[2(∂θ+/∂pH)T + 2(∂θA/∂pH)T + (∂θ0/∂pH)T] dpH i ) 0, +, A, C (14)
to the total heat effect Qpr ) ∑iQipr, due to the formation of various surface complexes. The fact that the features of the silica/electrolyte interfaces are much different from those formed by other (26) Degussa Corp. pamphlet describing the properties of Aerosil380.
Calorimetric Effects of Simple Ion Adsorption
Figure 8. Contribution Qipr’s defined in eq 15 to Qpr, coming from the formation of various complexes, calculated by the parameters collected in Table 2.
Langmuir, Vol. 15, No. 18, 1999 5983
Such calculations, carried out for other oxides in our previous publications,1,9 showed, that θ- was usually twice of magnitude smaller than θ0. Here, in the case of silica, the ratio θ-/θ0 is about ten times larger than usual. Of course, there is nothing like “empty (free)” surface oxygens SO-. They are occupied by water molecules adsorbed via hydrogen bonding. Thus, in the case of silica, the water adsorption via hydrogen bonds is a process remarkably competitive with the first proton adsorption. This may probably explain many unusual adsorptive features of silica, for instance the features of some anionic surfactants adsorption reported by Somasundaran.27 At the same time Figure 9B suggests that formation of SOH2+ and SOH2+A- complexes plays a negligible role in ion adsorption at the silica/electrolyte interfaces. Only electrokinetic behaviour is sensitive to the formation of the SOH2+ and SOH2+A- complexes, because the surface charge of the diffuse layer is governed by the difference (θ+ - θ-). Conclusions The studies of argon adsorption on silica show that the energetic heterogeneity of the silica surface oxygens should be represented well by the gaussian-like functions. As the silica belongs to the most heterogeneous oxides, that conclusion should be valid for all oxides. This provides an impressive confirmation for our choice of a gaussian-like function to represent the surface heterogeneity effects in simple ion adsorption at the oxide/electrolyte interfaces. That model of surface heterogeneity made it possible to fit in a quantitative way the data obtained in the three independent experiments: surface charge measurements (titration), measurements of electrophoretic mobility, and monitoring enthalpic effects accompanying the potentiometric titration. Contrary to typical oxides, silica exhibits an unusual tendency for strong adsorption of water molecules on the negatively charged adsorption sites SO-. That water adsorption appears to be process remarkably competitive to the formation of the neutral surface complexes SOH0. We guess that this feature may be responsible for the strange behaviour of silica in many adsorption processes.
Figure 9. Surface coverages θi’s calculated from eqs 3-7 by using the parameters collected in Table 2.
frequently studied oxides finds another impressive illustration presented in Figure 9A. There we have drawn the individual functions θ-, θ0, and θC, calculated by using the parameters collected in Table 2.
Acknowledgment. This work has been carried out as a part of POLONIUM project. R.Ch. wishes to express his thanks and gratitude to the Foundation for Polish Science for the grant making his 1-year stay in the Laboratoire Environnement et Mineralurgie, ENSG, CNRS-UMR 7569, Vandoeuvre les Nancy, France, possible. LA981336D (27) Zhang, L.; Somasundaran, P.; Maltesh, C. J. Colloid Interface Sci. 1997, 191, 202.
