Langmuir 2002, 18, 8079-8084
8079
1pK and 2pK Protonation Models in the Theoretical Description of Simple Ion Adsorption at the Oxide/ Electrolyte Interface: Studying of the Role of the Energetic Heterogeneity of Oxide Surfaces Wojciech Piasecki* Laboratory for Theoretical Problems of Adsorption, Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Ul. Niezapominajek 8, Krakow 30-239, Poland Received May 21, 2002. In Final Form: July 19, 2002 Two theoretical approachessthe 2pK triple layer model and the 1pK basic Stern modelsdescribing the charging process at oxide/electrolyte interfaces were applied to analyze the surface charge isotherms and the heats of proton adsorption. The presented analysis was carried out by accepting both the frequently employed model of an energetically homogeneous oxide surface and a more realistic model taking into account the energetic heterogeneity of the actual oxide surfaces. The developed theoretical expressions were applied to analyze experimental data sets reported for three adsorption systems: Al2O3/NaCl, TiO2/ NaCl, and SiO2/NaCl. It was found that both the 2pK and the 1pK surface charging models could well describe potentiometric titration curves, and can represent the most characteristic features of the measured enthalpy of proton adsorption. In the case of the 1pK model, introducing the concept of surface energetic heterogeneity does not affect much the fit of the experimentally measured heats of proton adsorption. Best fits were obtained by applying the 2pK model taking into account the surface energetic heterogeneity. These best fits, however, were obtained at the expense of introducing more best-fit parameters. So, the general conclusion is that, for some adsorption systems, the use of the simpler 1pK model leads to a sufficiently accurate description of experimental data, whereas, for some other systems, the use of the 2pK model seems to be necessary.
Introduction The process of charging a (hydr)oxide surface in an electrolyte solution is most frequently described by means of a 1pK or 2pK model. In the 1pK approach one assumes that on an oxide surface there exists an equilibrium between the oppositely charged species SOH1/2- and SOH21/2+ described by one equilibrium constant and governed by solution pH.1 In contrast to the 1pK approach, in the 2pK model there are neutral amphoteric groups SOH on the oxide surface, which can be protonated or deprotonated, transforming into SOH+ 2 and SO groups, respectively.2,3 The above process can be described by means of two equilibrium constants. So far the above models have been considered as competitive ones corresponding to different actual physical situations. A few years ago Borkovec4 showed that these approaches represent two approximate solutions of a many-body problem, which are obtained by treating rigorously the adsorption of ions at the oxide/electrolyte interface by using methods of statistical thermodynamics. The physical pictures behind these two approaches should be treated merely as tools to arrive at approximate, but simple solutions. However, we should mention also the recent report by Dural et al.5 showing that in some systems these models represent quite stable surface complexes. * Correspondence should be forwarded to the following address: Department of Theoretical Chemistry, Faculty of Chemistry, Maria Curie Skłodowska University, Pl. Marii Curie Skłodowskiej 3, 20031 Lublin, Poland. Phone: (48) (81) 5375519. Fax: (48) (81) 5375685. E-mail:
[email protected]. (1) Bolt, G. H.; Van Riemsdijk, W. H. Physicochemical Models. In Soil Chemistry, 2nd ed.; Bolt, G. H., Ed.; Elsevier: Amsterdam, 1982. (2) Yates, D. E.; Levine, S.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1 1974, 70, 1807. (3) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface Sci. 1978, 63, 480. (4) Borkovec, M. Langmuir 1997, 13, 2608.
Both the 1pK and 2pK approaches can result in a variety of theoretical descriptions obtained by assuming various mechanistic models of the structure of the solid/electrolyte interface. The effectiveness of these theoretical descriptions has been studied in the previous publication.6 No decisive proof has been deduced in favor of either the 1pK or the 2pK charging mechanism in investigated TiO2/NaCl solution systems, but certain important conclusions have been drawn concerning the applicability of the various theoretical descriptions. It was shown that, in order to arrive at a reasonable theoretical description, the assumed model of surface charging should be combined with a certain model of the oxide/electrolyte interface structure.6 It has been known for a long time in adsorption science that calorimetric effects of adsorption are much more sensitive to the nature of an adsorption system than adsorption isotherms. The first studies of enthalpic effects of ion adsorption, based on the temperature dependence of the point of zero charge (PZC) and adsorption isotherms, started in the end of the sixties7 and gained significant popularity. However, the next developed titration calorimetry8-13 is a better experiment for theoretical interpretation. (5) Dural, Y.; Mielczarski, J. A.; Pokrovsky, O. S.; Mielczarski, E.; Ehrhardt, J. J. J. Phys. Chem. B 2002, 106, 2937. (6) Piasecki, W.; Rudzinski, W.; Charmas, R. J. Phys. Chem. B 2001, 105, 9755. (7) Berube, Y. G.; De Bruyn, P. L. J. Colloid Interface Sci. 1968, 27, 305. (8) De Keizer, A.; Fokkink, L. G. J.; Lyklema. J. Colloids Surf. 1990, 49, 149. (9) Machesky, M. L.; Jacobs, P. F. Colloids Surf. 1991, 53, 297. (10) Machesky, M. L.; Jacobs, P. F. Colloids Surf. 1991, 53, 315. (11) Mehr, S. R.; Eatough, D. J.; Hansen, L. D.; Lewis, E. A.; Davis, J. A. Thermochim. Acta 1989, 154, 129. (12) Casey, W. H. J. Colloid Interface Sci. 1994, 163, 407. (13) Kallay, N.; Zalac, S.; Stefanic, G. Langmuir 1993, 9, 3457.
10.1021/la0259712 CCC: $22.00 © 2002 American Chemical Society Published on Web 09/06/2002
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Piasecki
Recently the author has published a paper14 where for the first time a quantitative interpretation of titration calorimetry results was presented. The analysis was based on applying the 1pK basic Stern model (BSM) and the commonly assumed model of an energetically homogeneous oxide surface. That was the newest interpretation among some others based on the 2pK triple layer model (TLM) and presented in the series of theoretical papers concerning that problem.15-20 These theoretical studies of the enthalpic effects accompanying ion adsorption at the oxide/electrolyte interface have shown that such investigations may contribute substantially to our understanding of the mechanism of ion adsorption in these systems. The comparison of the 1pK and the 2pK approaches can be carried out at various levels of approximation accepted to develop the related theoretical expressions. The classical theoretical descriptions can be further generalized by taking into consideration the surface energetic heterogeneity of real oxide surfaces. At the expense of growing complications in the related theoretical descriptions, a visible improvement of the agreement between theory and experiment should be seen for the studied systems. The surface energetic heterogeneity is due to the different status of various surface oxygens, determined by their molecular environment. In the theoretical papers the dispersion of the energetic properties of surface oxygens has usually been represented by some continuous (smoothed) functions. Thus, to compare the effectiveness of these two charging models to represent the behavior of the enthalpic effects, the continuous adsorption energy dispersion will be assumed here in both cases. The aim of the present paper is to arrive at a more reliable comparison of the two 1pK and 2pK models of surface charging through accepting a more realistic model of an energetically heterogeneous oxide surface to analyze the experimentally measured enthalpies of ion adsorption. Thus, the present paper is a continuation of the author’s previous paper14 where the idealized model of a homogeneous surface was accepted.
in the following way:
SO- + H+ T SOH0,
K0, Qa2
SO- + 2H+ T SOH2+,
K+, Qa1 + Qa2 (2b)
SO- + C+ T SO-C+,
KC, QaC
(2c)
SO- + 2H+ + A- T SOH2+ A-,
KA, QaA
(2d)
The equilibrium constants of these reactions are related to intrinsic ones: K0 ) 1/Ka2int, K+ ) 1/(Ka1intKa2int), KC ) *K int/K int, and K ) 1/(K int*K int) (see ref 14). The C a2 A a2 A diagram of the 2pK TLM was presented in Figure 2 in previous paper.14 In the eighties Van Riemsdijk and Koopal21-24 started the first theoretical studies of the influence of the energetic heterogeneity of a surface on adsorption at the metal oxide/ electrolyte interface. These investigations were next extended by Rudzin´ski and co-workers,15,17,19,20 who focused on enthalpic effects. The best results were obtained with the assumption that adsorption energies of different surface complexes on various adsorption sites are not correlated.19,20 Rudzin´ski and co-workers assumed that for a given surface complex the distribution of adsorption sites among various adsorption energies i could be approximated by the following quasi-Gaussian function,17,25
SOH1/2- + H+ T SOH21/2+,
K+1, QaH1 (1a)
SOH1/2- + C+ T SOH1/2- C+,
KC1, QaC1
(1b)
SOH1/2- + H+ + A- T SOH21/2+ A-, KA1, QaA1
(1c)
The equilibrium constants of the above reactions are connected with intrinsic ones: K+1 ) 1/1KHint, KC1 ) 1KCint, and KA1 ) 1KAint/1KHint (see ref 14). The reactions considered in the 2pK TLM are written (14) Piasecki, W. Langmuir, 2002, 18, 4809. (15) Rudzinski, W.; Charmas, R.; Partyka, S. Langmuir 1991, 7, 354. (16) Rudzinski, W.; Charmas, R.; Partyka, S.; Foissy, A. New J. Chem. 1991, 15, 327. (17) Rudzinski, W.; Charmas, R.; Partyka, S.; Thomas, F.; Bottero, J. Y. Langmuir 1992, 8, 1154. (18) Charmas, R. Langmuir 1998, 14, 6179. (19) Rudzinski, W.; Charmas, R.; Piasecki, W.; Thomas, F.; Villieras, F.; Prelot, B.; Cases, J. M. Langmuir 1998, 14, 5210. (20) Rudzinski, W.; Piasecki, W.; Charmas, R.; Panas, G. Adv. Colloid Interface Sci. 2002, 95, 95.
{ } { }]
i - °i 1 exp ci ci χi(i) ) i - °i 1 + exp ci
[
2
(3)
This function reaches its maximum at ) 0, and the width of the peak (variation σ2) is determined by the heterogeneity parameter ci (σ2 ) πci/x3). While assuming the above distribution of energies and the 2pK triple layer model, one arrives at the following function, θit, for the mean surface coverage by the i-th adsorption complex,19
Theory The double-layer structure of the 1pK BSM was presented in Figure 1 in the previous paper.14 The surface reactions assumed in this model, their equilibrium constants, and the heats are as follows:
(2a)
θit )
[Kifi]kT/ci 1+
∑i
, i ) 0, +, A, C
(4)
[Kifi]kT/ci
where kT/ci are the dimensionless heterogeneity parameters and fi are functions of proton and electrolyte ions activity.19 Furthermore, the molar differential heats of surface complex formation Qi(h) are now expressed as follows:
Qi(h) ) Qi - ci ln
θit , i ) 0, +, C, A θ-t
(5)
where Qi are the configurational heats of reactions 2a-d in the case of a homogeneous surface, expressed by eqs 18a-d from the preceding paper,14 and θ-t represents the fraction of free adsorption sites SO-. (21) Van Riemsdijk, W. H.; Bolt, G. H.; Koopal, L. K. J. Colloid Interface Sci. 1986, 109, 219. (22) Van Riemsdijk, W. H.; De Wit, J. C. M.; Koopal, L. K.; Bolt, G. H. J. Colloid Interface Sci. 1987, 116, 511. (23) Koopal, L. K.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1989, 128, 188. (24) Gibb, A. W. M.; Koopal, L. K. J. Colloid Interface Sci. 1990, 134, 122. (25) Rudzinski, W.; Michalek, J.; Brun, B.; Partyka, S. J. Chromatography 1987, 406, 295.
Ion Adsorption at the Oxide/Electrolyte Interface
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Table 1. Set of the Parameters for the Three Investigated Systems in the Case of the 2pK TLM kT/c0
kT/c+
kT/cC
pKa1int
kT/cA
4.0 0.8
0.8
0.8
0.8
5.0
4.0 0.9
0.9
0.9
0.9
4.8
1.0 0.8
0.8
0.8
-0.4
0.8
QaC (kJ/mol)
c1L (F/m2)
c1R (F/m2)
R1L (F/m2‚K)
R1R (F/m2‚K
13.0
System: Al2O3/NaCl Solution Homogeneous Surface 9.1 7.9 27.0 55.0
0.0
0.8
0.9
-0.003
-0.004
12.0
Heterogeneous Surface 7.5 20.0 68.0
0.0
0.8
0.8
-0.0025
-0.0025
8.8
System: TiO2/NaCl Solution Homogeneous Surface 7.0 5.8 26.0 43.0
0.0
0.8
1.05
0.0
-0.003
8.0
7.1
Heterogeneous Surface 5.7 18.0 61.0
0.0
0.7
1.0
0.001
-0.005
6.6
System: SiO2/NaCl Solution Homogeneous Surface 6.9 0.7 10.0 14.0
0.0
0.95
0.95
0.0
-0.001
8.0
Heterogeneous Surface 0.4 10.0 28.0
0.0
1.0
1.0
0.0
-0.003
pKa2int
p*KCint
9.5
7.2
p*KAint
Qa1 (kJ/mol)
Qa2 (kJ/mol)
Table 2. Set of the Parameters for the Three Investigated Systems in the Case of the 1pK BSM kT/cx
p1KHint
p1KCint -0.5
8.5 0.8
-0.4 -0.4
6.4
3.8 0.8
-0.5
-0.5
8.5
6.4 0.8
p1KAint
3.8
System: Al2O3/NaCl Solution Homogeneous Surface 46.0 0.0 0.70 Heterogeneous Surface 0.0
θit )
1+
∑i [Ki fi]
-0.002 -0.002
0.0
-0.4
0.65
0.001
0.0
0.45
0.60
0.001
0.0005
System: SiO2/NaCl Solution Homogeneous Surface 17.0 0.0 0.25
0.25
0.0
0.0
0.25
0.0
0.0
31.0
18.0
Heterogeneous Surface 0.0
Heterogeneous Surface 0.0
, i ) +, A, C
(6)
kT/ci
While drawing the formal consequences of the existing CIP, we arrive at the following two relations between the three equilibrium constants 1KHint, 1KCint, and 1KAint:
[(
1
(7)
where Qi1 are defined by eqs 11a-c from the preceding paper14 and θ-t is the fraction of the free adsorption sites SOH1/2-.
)
kT/cC 1 int kT/cc ( KC a) +1 kT/cA
KHint ) H 1 -
[
1 1
KAint )
KHint kT/cC 1 int kT/cc ( K a) aH kT/cA C
]
-c+/kT
(8a)
]
cA/kT
(8b)
where H and a denote protons’ and electrolyte ions’ activities, respectively. Calculating from the above equations the derivatives with respect to 1/T, we obtain the following interrelation of the three heats of adsorption QaH1, QaC1, and QaA1:
[(
)
]
kT/cC - 1 (1Kcinta)kT/cc + 1 + kT/cA c+ kT/cC kT/cC - 1 (1Kcinta)kT/cc - 1 (1Kcinta)kT/cc + kT kT/cA kT/cA
QaA1 ) QaH1 - c+ ln
( ][
)
[(
(
)
)]
kT kT d ln a ln(1Kcinta) + -QaC1 - k cC cC d(1/T) kT/cC kT/cC d ln a d ln a k -QaC1 - k + cA ln kT/cA kT/cA d(1/T) d(1/T) (9)
1
θit , i ) +, C, A θ-t
0.25
-1
where Ki1 are the equilibrium constants of reactions 1ac. The molar differential heats of surface complex formation Qi1(h) are now expressed as follows:
Qi1(h) ) Qi1 - ci ln
0.0
0.70
kT/ci
1
0.70
0.70
0.7
[Ki fi]
R1R (F/m2‚K)
System: TiO2/NaCl Solution Homogeneous Surface 33.0 0.0 0.50
The existence of a common intersection point (CIP) of the potentiometric titration curves was taken advantage of to eliminate some of the parameters.14 Namely, it makes it possible to eliminate from further calculations two of the four parameters: Ka1int, Ka2int, *KCint, and *KAint.17,19 Moreover, like in the case of the homogeneous 2pK TLM, an equation is developed which relates the heats of adsorption Qa1, Qa2, QaC, and QaA. Obviously, that equation is much more complicated, but it allows eliminating one of these parameters.19 Now, let us consider how taking into account the energetic heterogeneity of the surface changes the corresponding equations in the case of the 1pK basic Stern model. As in the case of the 2pK TLM, we assume small correlations exist between adsorption energies of different surface complexes.19,20 After appropriate calculations were carried out, it turned out that the mean surface coverage by the i-th adsorption complex, θit, is expressed by the following equation: 1
R1L (F/m2‚K)
c1R (F/m2)
45.0
0.6
0.7
c1L (F/m2)
QaC1 (kJ/mol)
-0.5
-0.4
0.6
QaH1 (kJ/mol)
kT
( )
(
)
While assuming the values of the parameters QaH1 and QaC1 from the above equation, we can calculate the value of the parameter QaA1. To calculate the molar heat of proton adsorption Qpr by using the 1pK BSM and the 2pK TLM, we used eqs 15 and
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Figure 1. Comparison of the potentiometric titration data (b) for the Al2O3/NaCl solution system with the theoretical δ0(pH) curves calculated by means of the 2pK model (A) and the 1pK model (B) using the model of a homogeneous surface (s) and a heterogeneous surface (- - -). The parameters used in calculations were collected in Tables 1 and 2.
23 from ref 14. In the case of the 1pK BSM, first we have to express the surface potential ψ0 as an explicit function of the surface charge δ0, pH, and the activity of inert electrolyte ions. In the case of the 2pK TLM, we have an independent equation for ψ0.19,20 The derivative ∂ψ0/∂(1/ T) is essential for calculating the heats Qi and Qi1 in eqs 5 and 7, and it can be calculated only if one knows the analytical form of the function ψ0(δ0,pH,a). For the 1pK BSM, the surface potential is expressed by formula 6 from the earlier paper14 (incidentally, that equation was mistyped). In the case of a heterogeneous surface, such a simple compact equation can be obtained only if we assume that all the heterogeneity parameters are equal, that is, kT/c+ ) kT/cC ) kT/cA ) kT/cX, where kT/cX is the common value for these three parameters. Then, we arrive at the following expression:
ψ0 ) -
{
cX ln [1/2B[(aHKA1X)kT/cX - 1] - δ0[1 + e
/[ ( (
(aHKA1X)kT/cX]]
( ) ) ( ) )]}
aKC1 X aKC1 1 1 kT/cX B (HK+ ) 2 X δ0 (HK+1)kT/cX +
kT/cX
-
kT/cX
(10)
Our previous analysis of some real adsorption systems based on applying the 2pK model yielded values of kT/ci which differed less than 20% (for various surface complexes).19,20 Thus, taking some average value (kT/ci) for all of them should not affect considerably the analysis of these systems based now on the 1pK model. Furthermore, taking such an average value will expose clearly the
Figure 2. Comparison of the experimental molar heat of proton adsorption Qpr (b) for the Al2O3/NaCl solution system with the theoretical Qpr(pH) functions calculated by means of the 2pK model (A) and the 1pK model (B) using the model of a homogeneous surface (s) and a heterogeneous surface (- - -). The parameters used in calculations were collected in Tables 1 and 2.
differences between the 2pK and 1pK approaches arising from the surface energetic heterogeneity of the real oxide surfaces. Results and Discussion The vast majority of the papers on theoretical modeling of ion adsorption at metal oxide/electrolyte interfaces dealt with only the isotherms of adsorption. In particular, the isotherms of proton adsorption (i.e., the surface charge curves vs pH) were most thoroughly analyzed. Generally, the theoretical analysis was limited to this one kind of experimental data. In our opinion, for testing various adsorption models, one should consider results coming from at least two different experiments. Conclusions drawn in such a way should be much more reliable. Therefore, in addition to adsorption isotherms, the heat effects accompanying proton adsorption onto metal oxides will be analyzed. Three adsorption systems, formed by Al2O3, TiO2, and SiO2 being in contact with NaCl solution, were subjected to our analysis. The related experimental data were published by Machesky et al.,9,10 Mehr et al.,11 and Casey.12 The properties of these adsorption systems and the quality of those experimental data were discussed in detail in earlier papers.14,20 These three adsorption systems have already been investigated in the author’s previous paper14 by adopting the commonly assumed model of an energetic homogeneous surface of oxides. While investigating these data in terms of the 1pK or the 2pK model, the following procedure was applied. In
Ion Adsorption at the Oxide/Electrolyte Interface
Figure 3. Comparison of the potentiometric titration data (b) for the TiO2/NaCl solution system with the theoretical δ0(pH) curves calculated by means of the 2pK model (A) and the 1pK model (B) using the model of a homogeneous surface (s) and a heterogeneous surface (- - -). The parameters used in calculations were collected in Tables 1 and 2.
the first step the surface charge isotherm δ0(pH) was calculated in a rough way. The relations resulting from the existence of a CIP were taken into account to decrease the number of the best-fit parameters both for the homogeneous model and for the heterogeneous one. In the next step the calorimetric data were fitted. The parameter values obtained in the first step were precisely adjusted, and the values of additional parameters were found at this stage (see ref 14). The parameter values found in that way are listed in Tables 1 and 2. There are two values of electric capacitance (c1L, c1R) and the parameter describing its temperature dependence (R1L, R1R) because it is assumed that these quantities can be different on both sides of PZC. The aim of this study is to analyze how taking into account the surface energetic heterogeneity of oxides affects the estimated parameters, the values of surface charge, and the enthalpies of proton adsorption studied by means of the 2pK and 1pK approaches. We intended to see by best fitting the experimental data whether taking into account the surface heterogeneity does improve (or not) the agreement between theory and experiment. One should realize that taking into account the energetic heterogeneity of a surface causes introduction of additional parameters into calculations. As we have already mentioned above, our previous studies of the enthalpic effects of ion adsorption based on the 2pK model were carried out by assuming that all four heterogeneity parameters kT/c0, kT/c+, kT/cC, and kT/cA may have different values. However, the earlier results suggest that they differ little from each other.20 Therefore, in our present comparison of the 2pK and the 1pK models,
Langmuir, Vol. 18, No. 21, 2002 8083
Figure 4. Comparison of experimental molar heat of proton adsorption Qpr (b) for the TiO2/NaCl solution system with the theoretical Qpr(pH) functions calculated by means of the 2pK model (A) and the 1pK model (B) using the model of a homogeneous surface (s) and a heterogeneous surface (- - -). The parameters used in calculations were collected in Tables 1 and 2.
we assume one average value for all the heterogeneity parameters. Consequently, for the 2pK model we will repeat the earlier calculations by adopting one value for all the heterogeneity parameters appearing in that model. As can be seen in Figure 1, both models fit equally well the potentiometric titration data for the system Al2O3/ NaCl solution. However, in the case of the heat of proton adsorption presented in Figure 2, these models provide different theoretical Qpr(pH) curves. The 2pK approach is generally more flexible than the 1pK one. It is easy to shape the Qpr(pH) curve in the 2pK model, and it is difficult to obtain the desired shape in the latter case. Moreover, the 2pK-HET approach gives better results than the 2pK-HOM approach, but the 1pK-HOM and the 1pKHET methods work equally well. However, in the 2pKHET approach, we have a few parameters more than the amount in the 1pK approach. In this situation the question arises whether to apply a more advanced approach for some system or a simpler one. The answer depends on the goal to be achieved in the theoretical modeling. If we aim at fitting best the experimental values, then applying the more advanced model will be justified, but the consequence is introducing a larger number of best-fit parameters in calculations. Also, in the case of the TiO2/NaCl solution system, the best results are obtained by applying the 2pK-HET model. This is especially visible in Figure 4, where the heat of proton adsorption is presented. As follows from Figure 3, all the models satisfactorily fit the potentiometric data. However, in the pH range 9-10, the 1pK approach fails.
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Figure 5. Comparison of the potentiometric titration data (b) for the SiO2/NaCl solution system with the theoretical δ0(pH) curves calculated by means of the 2pK model (A) and the 1pK model (B) using the model of a homogeneous surface (s) and a heterogeneous surface (- - -). The parameters used in calculations were collected in Tables 1 and 2.
As we can see in Figure 5, in the case of the SiO2/NaCl system, it is impossible to fit the surface charge isotherm by using the 1pK approach because the charging curve of silica is quite different from that of most other metal (hydr)oxides. This is due to the specific charging mechanism in the case of silica. The reactive neutral surface group SiOH releases a proton to evolve into the negative group SiO-. So, the 1pK model is not a proper approach to describe charging of silica. The 2pK approach (homogeneous and heterogeneous) does it quite well. Then, the heat of proton adsorption Qpr(pH), shown in Figure 6, suggests that all models describe it satisfactorily. It should be noticed, however, that we have at our disposal only calorimetric data for the narrow pH range from 6 to 9. In the course of the calculations discussed above, the assumptions QaC1 ) 0 and QaC ) 0 were taken into consideration. That means that both the nonconfigurational heat of cation attachment to the free surface site SOH1/2(or SO-) and the nonconfigurational heat of anion attachment to the SOH21/2+ (or SOH2+) group were assumed
Piasecki
Figure 6. Comparison of the experimental molar heat of proton adsorption Qpr (b) for the SiO2/NaCl solution system with the theoretical Qpr(pH) functions calculated by means of the 2pK model (A) and the 1pK model (B) using the model of a homogeneous surface (s) and a heterogeneous surface (- - -). The parameters used in calculations were collected in Tables 1 and 2.
to be equal to zero.14 This conclusion might be supported by the assumption that the interactions of electrolyte ions with an oxide surface are purely electrostatic. From the above discussion, the following conclusions can be drawn. Both the 2pK and 1pK surface charging models are able to represent the most characteristic features of the potentiometric titration curves and the heats of proton adsorption. However, the best results are obtained by applying the 2pK-HET model. This is most clearly visible in the case of enthalpic effects. Further, no significant differences can be seen between theoretical fits obtained by using either the 1pK-HOM or the 1pKHET model. Acknowledgment. The author wishes to express his gratitude to prof. W. Rudzin´ski for many helpful discussions. LA0259712
