J. Phys. Chem. B 2000, 104, 11923-11935
11923
A Combined Temperature-Calorimetric Study of Ion Adsorption at the Hematite-Electrolyte Interface: II. Models of a Heterogeneous Oxide Surface W. Rudzin´ ski,* G. Panas, and R. Charmas Department of Theoretical Chemistry, Maria Curie-Sklodowska UniVersity, M. Curie-Sklodowska Sq.3, Lublin, 20-031 Poland
N. Kallay and T. Preocˇ anin Laboratory of Physical Chemistry, Faculty of Science, UniVersity of Zagreb, P.O. Box 163, 10001 Zagreb, Croatia
W. Piasecki Laboratory for Theoretical Problems of Adsorption, Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Ul. Niezapominajek, Krako´ w, 30-239 Poland ReceiVed: April 4, 2000; In Final Form: August 29, 2000
The two hematite/KNO3 adsorption systems investigated in Part I are now subjected to a more refined quantitative analysis based on the models of an energetically heterogeneous oxide surface. The estimated parameters lead to a much more consistent, simultaneous fit of both titration isotherms and the related directly measured enthalpic effects. That quantitative analysis reveals that the differences in the preparation of these two hematite samples result in substantial differences in the heats accompanying ion adsorption. Generally, the more porous surface is, the lower are the heats of proton and cation adsorption, due probably to a deeper dehydratation of adsorbed ions. Our quantitative analysis also reveals substantial electrostatic contributions to the observed enthalpic effects, as well as contributions caused by surface energetic heterogeneity.
Introduction It has been known for a long time that existing oxides have a strong tendency to form geometrically distorted structures. These were first shown as defects in the bulk structure, which were extensively investigated.1 It has been shown more recently that the degree of surface organization of oxides is even lower than in their bulk phase. A variety of techniques has been applied to study the distorted nature of oxide surfaces. As a result of these extensive studies, dozens of papers have been published, including reviews and books.2 However, a major breakthrough in views on the structure of the actual oxide surfaces is due to the recent development of STM and AFM spectroscopies. There already exists vast literature reporting how the surface heterogeneity of real oxides affects adsorption of gases on the oxide surfaces. These are both experimental and theoretical works.3-5 Here, adsorption isotherms were the most extensively studied physical quantity. The inapplicability of the Langmuir isotherm equation was detected very early; instead, some other isotherm equations were successfully applied, such as Freundlich, Toth, Bradley, or Dubinin-Radushkevich equations.3-5 Used initially as empirical equations, they were developed theoretically by averaging the Langmuir isotherm with some functions describing the dispersion of adsorption energies on various adsorption centers. The Freundlich equation was found to correspond to the exponentially decreasing distribution of adsorption energies * To whom correspondence should be addressed.
which, later on, was found to be the high-energy limit of a Gaussian-like adsorption energy distribution.3-5 However, although experimental adsorption isotherms were most frequently investigated, the experimentally measured heats of adsorption provided a more impressive picture of the surface energetic heterogeneity. Since the pioneering works by Drain and Morrison6,7 reporting on heats of nitrogen, oxygen and argon adsorption on rutile, a large body of experimental data has already been collected. Very essential information about the surface energetic heterogeneity of oxides has been elucidated from the calorimetric measurements of the enthalpic effects accompanying adsorption of other gases such as H2O,8-24 NH3,25-33 CO2,28,29,34 or CO.34-42 All these papers report on differential heats of adsorption decreasing with increasing surface coverage, due to the energetic surface heterogeneity. Although other techniques, like IR spectroscopy for instance, also provide valuable information, calorimetric studies have provided most of the information about gas-oxide interactions and their dispersion. It is natural to assume that we shall face a similar situation in the case of ion adsorption at the oxide/ electrolyte interface. However, although the important role of the energetic heterogeneity in gas adsorption on the actual oxide surfaces is now generally recognized, much less is known about this role in ion adsorption at the oxide/electrolyte interface. The reason was that the popular surface complexation approach has appeared “too much successful” in describing the behavior of the experimental titration isothermssthe most frequently studied adsorption characteristics. The titration isotherms can be successfully fitted by a variety of theoretical approaches and
10.1021/jp001312r CCC: $19.00 © 2000 American Chemical Society Published on Web 11/23/2000
11924 J. Phys. Chem. B, Vol. 104, No. 50, 2000 corresponding parameters. So, there was no need to introduce the concept of surface heterogeneity if the simpler models, assuming an energetically homogeneous oxide surface, led to an excellent fit of the experimental titration isotherms. Van Riemsdijk and Kopal44-47 first studied the effects of oxide surface heterogeneity on simple ion adsorption. However, in their first works they investigated mainly titration isotherms, so they did not arrive at conclusive statements about the role of the surface energetic heterogeneity. Of course, the variation in the surface of oxides must affect the charging behavior of the surface oxygens, having a different local environment. In effect, the binding-to-surface energies of the complexes formed with surface oxygens will vary. The important role of the surface energetic heterogeneity has, meanwhile, been discovered in the bivalent ion adsorption at the oxide/electrolyte interface. In the late 1970s, Benjamin and Leckie48 reported that the adsorption of bivalent metal ions onto ferrihydride cannot be described by theories of ion adsorption onto a homogeneous solid surface. An agreement between theory and experiment could be obtained only by assuming a large dispersion of site affinities. Two years later, Kinniburgh et al.49 demonstrated applicability of Toth’s50 isotherm equation. In most cases, however, the Freundlich isotherm equation has been successfully used to correlate the experimental adsorption isotherms, measured usually at low concentrations of bivalent cations.51-59 As the Freundlich isotherm is a low-concentration limit of the Langmuir-Freundlich isotherm, one can assume that the dispersion of adsorption energies of bivalent cations has the Gaussian-like form.1 Using such a function has led Rudzin´ski et al.60 to a successful fit of the isotherms of Cd2+ adsorption on an iron oxyhydroxide at various pH, reported earlier by Benjamin and Leckie.48 They also explained why the tangent of the double log-log plots becomes equal to unity at very low concentrations. This was reported, for instance, by Matijevic and co-workers.61,62 There is no doubt that the effects of oxide surface heterogeneity are demonstrated more strongly in the case of bivalent ions. This can be explained by the theory of multisite-occupancy adsorption on the heterogeneous solid surface, developed by Rudzin´ski et al.;2 namely, the bivalent ions usually interact with two surface oxygens, occupying, thus, two adsorption sites. In such a case, the width (variance) of the adsorption energy distribution (for pairs of sites) is either two times larger than for one-site(oxygen)-occupancy adsorption (for patchwise topography), or is larger by the factor x2 (for random topography). However, even in the case of one-site-occupancy adsorption of monovalent cations, the effects of surface energetic heterogeneity come into light, when the individual adsorption isotherms cations are studied.63 Bruemmer and co-workers64 have reported that oxide surface heterogeneity affects strongly the kinetics of ion adsorption. Very recently, Rudzin´ski et al.65-67 have shown how the surface energetic heterogeneity affects the enthalpic effects accompanying the adsorption of ions. At present, the important role of oxide surface heterogeneity is not questioned. There are only differences in the strategies of approaching that problem. Generally, there are two schools. One of them has its roots in the works in which Freundlich, or Toth adsorption isotherms were used to correlate experimental adsorption isotherms. Using these isotherms means assuming, explicitly or implicitly, the existence of a continuous dispersion of adsorption energies, typical for a small degree of surface organization. Such a view
Rudzin´ski et al. has been accepted in the theoretical works by Rudzin´ski and co-workers, not only in the case of ion adsorption65-68 but also in their theoretical description of enthalpic effects of adsorption at the oxide/nonelectrolyte interfaces.67 The other school follows the assumption that the degree of surface organization is so high that one could discuss it still in crystallographic terms. The different status (energetic heterogeneity) of surface oxygens is due to a different mode of their coordination to metal ions, at one or more crystallographic planes exposed to solution. The roots of that school go back to the work by Dzombak and Morel,69,70 who in 1985 lunched the two-site model, assuming also the 2-pK charging mechanism. More recently, Van Riemsdijk and co-workers71-73 proposed their multisite model (MUSIC), along with their idea of the 1-pK charging mechanism. Their approach is based on assuming that the adsorption energy distribution is a linear combination of a number of Dirac delta functions, each representing surface oxygens having well-defined status (coordination), arising from the ideal crystallographic structure. It is still assumed that the creation of oxide surface introduces only a lack of symmetry in oxygen-metal interactions but does not affect the crystallographic structure. The charge of surface oxygens is calculated by using Pauling’s principle for the unperturbed oxide structure. As far as the adsorption of monovalent ions is concerned, the MUSIC approach has mainly been applied to correlate the experimental titration isotherms. Machesky et al.74 used MUSIC in their qualitative discussion of the enthalpies of ion adsorption at the alumina/NaCl interface. More impressive is the fit by Machesky et al.75 of their titration isotherms measured at different temperatures for the rutile/NaCl interface. So far, no quantitative analysis, using the MUSIC approach, has been presented of some directly (calorimetrically) measured enthalpic effects of ion adsorption. There is no doubt that a certain degree of surface organization must exist in the case of the actual oxide/electrolyte interface. The question is only whether this degree of correlation is closer to chaos or to the ideal unperturbed crystallographic structure. Below, we present some arguments, for which we have followed in our works the first school of thinking, that is, assuming a small degree of surface organization and a “diffuse” continuous adsorption energy distribution. First, we would like to draw attention to the very interesting calorimetric study reported by Rouqueroll and co-workers.76 They investigated the enthalpy of adsorption of nitrogen and argon on a crystalline rutile and, next, partially coated by amorphous silica. The enthalpies of nitrogen adsorption were different, due to the particular electric field pattern near the rutile surface “felt” by the nitrogen molecule. Argon atoms, on the contrary, are insensitive to the difference in electric fields, so the close similarity of their enthalpy of adsorption on pure and coated rutile must testify to similarities in their surface structure. As the silica-coated rutile is, presumably, an amorphous surface, the similarity of the enthalpies of adsorption of argon indicates the amorphous structure of pure rutile, too. The adsorption potential of argon is mainly determined by the large oxygen ions, since their polarizability is much larger than that of cations. The physical adsorption of argon on oxides is mainly determined by the amorphous structure of the oxygen atoms near the surface. Further support for the amorphous-like structure of the real oxide surfaces provides the now so vigorously developing computer simulations of solid surfaces formation. Here, we would like to draw attention to the classical but still impressive computer simulation study published by Bakaev and Steele.77 They did their simulation twice. First, they assumed that
Ion Adsorption at a Heterogeneous Oxide Surface adsorption of argon is occurring on the ideal unperturbed surface of TiO2, deduced from its crystallographic structure. The simulated adsorption isotherms did not even reproduce qualitatively the experimental isotherms of argon adsorption on TiO2. Next, they assumed that surface oxygens can be visualized as dense randomly packed hard balls, as in the Bernal model. While accepting such a model of a distorted oxide surface, their computer simulations of argon adsorption led them to an impressive agreement with experiment. As usual, the truth lies somewhere in between. Much depends on the preparation of an oxide sample. So, for the same oxide, one may arrive at samples exhibiting quite different adsorption properties. This is also the case for Fokkink’s hematite sample78 and the hematite sample used in our experiments. Even a simplified analysis of their adsorption properties, based on a homogeneous surface model and presented in the first part of this publication,79 suggested that strong differences exist between their adsorption properties. Here, in the second part of this publication, a more refined analysis of their adsorption properties will be made based on models of a heterogeneous oxide surface. While anticipating the results of our analysis, we may say that, using the Gaussianlike continuous function,3-5 leads to a much better agreement between theory and experiment. This better fit also yields a somewhat different value of adsorption parameters and of functions characterizing ion adsorption at the hematite/KNO3 interface. Theory As in Part I of this publication79 (where we interpreted the data from the paper80 assuming a homogeneous surface), we repeat briefly the principles and only the final expressions developed in our previous publications.65,66 Analysis of Experimental Data Based on the Models of an Energetically Heterogeneous Oxide Surface. The surface heterogeneity will cause the variation of Ki across the surface, from one surface oxygen to another. Also, variations in the local Coulombic force fields ψ0 and ψβ will occur, as suggested by Barrow63 and Bruemmer,64 but we will neglect them because Coulombic interactions are long-ranged. This will cause “smoothing” of these variations over the local structure of the outermost surface oxygens. Thus, as in the model of a homogeneous oxide surface, we will consider ψ0 and ψβ to be functions of the average composition of the adsorbed phase θit. So far, two extreme models have been considered. The first one assumes that for all the adsorption sites, the ratio of Ki and Kj is constant. The other extreme model assumes that the equilibrium constants Ki and Kj*i are not correlated at all. We begin with considering the first model assuming the high correlations exist between the equilibrium constants Ki and Kj*i. Then, θjt takes the following explicit form:
θjt ) -
K ˜ i fi
∑j K˜ j fj
Xi (ic) )
K 0i fi
[∑ ] [∑ ]
∑j K 0j fj 1 +
kT/c K 0j fj
j
K 0j fj
kT/c
j
j ) 0, +, A, C (1)
where the heterogeneity parameter kT/c < 1. Using the Rudzin´ski-Charmas criterion65 to establish the int int relations between the intrinsic constants K int a1 , K a2 , *K C , and int *K A leads in this model to the following equations:
J. Phys. Chem. B, Vol. 104, No. 50, 2000 11925
K int a2 )
(
)
H2 H H2 + int int int int K a1 K a2 K a1 K a2
kT/c-1
and *K int A )
H2 (2a,b) *K int C
reducing the number of the “free” (best-fit) equilibrium constants from four to two. The molar differential heats of adsorption Qi are given by
Q (h) i ) Qi - k
∂ ln φi , i ) 0, +, C, A 1 ∂ T
(3)
where
φi )
(
)
θit 1 - θ-t 1 - θ-t θ-t
kT/c
θ-t ) 1 -
, i ) 0, +, C, A
(3a)
∑i θit
(3b)
θ-t is the fraction of the free surface oxygens, and Qi’s are the expressions for the heats of adsorption on a homogeneous oxide surface, given in the first part of this publication.79 From eq 2a we obtain
∂PZC ) ∂(1/T) Qa1 + Qa2 Qa1 kT Qa2 kT 2 H2 - 1+ rˇ ln int int 2k c 2k 2k c K a1 K a2 rˇ (4) 1 kT 1- 1[1 + rˇ] 2 c
2.3
( )[
]
(
(
)
)
where
H K int a1 + H
(4a)
∂PZC QaA - QaC ) 2k ∂(1/T)
(5)
rˇ ) Next, from eq 2b we have
2.3
From eqs 4 and 5, we can eliminate one of the four parameters, Qa1, Qa2, QaC, and QaA, as we did previously in the case of the homogeneous surface model.79 Now, let us consider the situation where the equilibrium constants KO, K+, KC, and KA are not correlated at all. Then, θjt’s take the form,
[Kj fj]kT/cj
θjt )
1+
∑j
j ) 0, +, A, C
(6)
[Kj fj]kT/cj
where kT/cj are the heterogeneity parameters. While applying the Rudzinski-Charmas criterion for CIP to exist, we arrive at the following interrelations:
( ) ( )( ) ( ) ( ) H2 int K int a1 K a2
kT/c+
+
kT/cC *K int Ca -1 int kT/cA K a2
H2a kT cA K int *K int a2 A
kT/cA
int kT *K C a + cc K int a2
kT/cC
- 1 ) 0 (7a)
kT/cC
)0
(7b)
11926 J. Phys. Chem. B, Vol. 104, No. 50, 2000
Rudzin´ski et al.
reducing the number of the “free” (best-fit) equilibrium constants from four to two. The molar heats of adsorption Qi take now the following form:
Q(h) i ) Qi - ci ln
θit , i ) 0, +, C, A θ-t
(8)
From eqs 7a,b, we arrive at the following interrelation of the nonconfigurational heats of adsorption:65 Qa1 + Qa2 k
-
[ (
(
)( )
kT/cC kT/cC *K int Ca -1 int kT/c+ kT/cA K a2
( ) ( )( ) ( )(
T ln
*K int Ca
1-
) ]
)(
kT/cC *K int Ca T ln 1 -1 int kT/c+ kT/cA K a2
-
K int a2
QaC 1 ∂a a ∂(1/T) k
kT/cC *K int Ca -1 kT/cA K int a2
kT/cC
kT/cC
-
kT/cC
×
QaA -
-
kT/cC Q kT/cA aC + k
)
kT/cC kT/cC 1 ∂a T ln - 1) 0 (9) kT/cA kT/cA kT/cA a ∂(1/T)
And, again, from eq 9, we can eliminate one of the four parameters: Qa1, Qa2, Qac, and QaA. Now, ∂PZC/∂(1/T) is given by
4.6
) [ ( )] ( ) ( )( ) ( )( ) [ ( )] ( ) ( )( )
∂PZC ) ∂(1/T)
(
Qa1 + Qa2 H2 - T ln int int k K a1 K a2 + kT/c+ 2 kT/cA kT/cA Ha + 1kT/cC K int *K int
H2 kT int c+ K K int a1 a2 2
H K int a2
K int a1
kT/cA H kT 1cA kT/cC K int *K int a2 A
a2
A
Qa2 1 ∂a H 2a + - T ln int k a ∂(1/T) K a2 *K int A kT/c+ 2 kT/c A kT/cA Ha + 1kT/cC K int *K int 2
H2 int K int a1 K a2
kT/c+
kT/cA
a2
A
(10)
Equation 9 and the related eqs 4 and 5 for the previous model that assumes high adsorption energy correlation, are very important for fundamental reasons; namely, even if QaC ) 0, QaA is no longer equal to (Qa1 + Qa2), as suggested by eq 21 in Part I79 for the model of a homogeneous solid surface. Thus, assuming that QaC * 0 no longer means also that the attachment of the anion to the already existing complex SOH+ 2 is necessarily accompanied by enthalpic effects. This conclusion is very important for the forthcoming analysis of the experimental data based on the models of adsorption on an energetically heterogeneous oxide surface. Numerical Results and Discussion Our quantitative analysis of the calorimetric titration data for the alumina/NaCl system reported by Machesky and Jacobs,74 favored the model that assumed a lack of correlations between adsorption energies of various surface complexes. However, it seems reasonable to check whether our present quantitative analysis of adsorption in the hematite/KNO3 systems also would favor that adsorption model. Therefore, we decided to prove again the applicability of both these adsorption models.
We start by applying the TLM model, assuming that no correlations exist, to analyze again Fokkink’s78 data on the temperature dependence of titration isotherms and the related De Kaizer81 data on the Qpr(δ0) function, directly measured in calorimetric experiments. We carried out numerous computer calculations to see how the choice of the heterogeneity parameters c0, c+, cC, and cA affects the simultaneous fit of both the three titration isotherms measured at 5 °C, 20 °C, and 60 °C and the experimental function Qpr(δ0), measured at 20 °C. While stressing the results of our numerical studies, we may say that for every reasonable choice of the heterogeneity parameters: c0, c+, cC, and cA, we could frequently find other parameters leading to an excellent fit of the titration isotherms. We also remember from the previous part of this publication79 that an excellent fit of the temperature dependence of these titration isotherms could also be achieved by applying the model of an energetically homogeneous oxide surface. However, there we could also see that a simultaneous analysis of both the titration isotherms, and of the directly measured calorimetric data Q ∆pr(δ0), suggested the inapplicability of the homogeneous surface model. Now, we are going to check whether the model assuming an energetically heterogeneous hematite surface could lead us to a simultaneous good fit of both the titration isotherms δ0(pH, T) and the calorimetric data Qpr(δ0). For that purpose, we carried out our model calculations for a variety of the sets of the heterogeneity parameters c0, c+, cC, and cA. In that way, we collected a large body of information for discussion. Here, we will show only certain examples (pieces) of that information to illustrate the general conclusions drawn from our numerical studies. The strategy of our best-fit exercises was the same as in part I of this paper.79 They are described in the tables. The criteria for a choice of a certain set of the heterogeneity parameters: c0, c+, cC, and cA were the following: (1) The sets of parameters obtained should lead to a good fit of both the three titration isotherms measured at 5 °C, 20 °C, and 60 °C, and the experimental Qpr data measured at 20 °C. (2) The value of each of the parameters Qa1, Qa2, RL1 , and RR1 used to fit the Qpr data measured at 20 °C should lie between the values listed in footnotes c and d below Tables 1, 2, and 3, i.e., between its average values determined for the temperature intervals 5 °C-20 °C, and 20 °C-60 °C, respectively. While fitting the Qpr data measured at 20 °C, the calculated values of the derivative 4.6R(∂PZC/∂(1/T)) should be around 100 kJ/mol, as suggested by the temperature dependence of Fokkink’s PZC data, shown in Figure 3B in Part I of this publication.79 Of course, we may not ignore the critical attitude of these authors toward the reliability of their PZC data, and their suggestion that the “∆T titration” method suggests somewhat different values of the derivative 4.6R(∂PZC/∂(1/T)) above 70 kJ/mol. Let us, however, remark that the congruence of Fokkink’s δ0(pH) data measured at various temperatures is not perfect so the estimation 4.6R(∂PZC/∂(1/T)) ) 72.5 kJ/mol should also be treated with caution. Therefore, while checking the values of 4.6R(∂PZC/∂(1/T)) corresponding to various sets of best-fit parameters, the derivative values ranging from 70100 kJ/mol will be treated as physically reasonable. In the first series of our numerical studies, we followed the suggestion in Barrow’s papers,59,63 that the experimental isotherms of adsorption of anions seem not to be affected by surface energetic heterogeneity. The log-log plots of the individual isotherms of anion adsorption seem to have tangents
Ion Adsorption at a Heterogeneous Oxide Surface
J. Phys. Chem. B, Vol. 104, No. 50, 2000 11927
TABLE 1: List of the Parameters Used to Fit the Three Fokkink’s Titration Isotherms and a Brief Description of Our Best-Fit Calculations T °Ca
5 20 °Cc 60 °Cd
pK int a1 8.1 7.35 6.54
p*K int C 10.45 9.64 8.27
cL1 0.98 0.85 0.91
cR1 1.15 1.25 1.31
kT/c0 0.80 0.84 0.95
kT/c+ 1.0 1.0 1.0
kT/cC 0.80 0.84 0.95
kT/cA 1.0 1.0 1.0
pK int a2 10.91 10.10 8.73
b
p*K int A b
8.71 7.97 7.13
PZC 9.50 8.72 7.63
For the temperature 5 °C, the best fit calculations yield the values listed. b Parameters calculated. c To fit simultaneously the titration isotherms at 5 °C and 20 °C, the following best fit parameters had to be accepted: Qa1 ) 78 kJ/mol, Qa2 ) 84 kJ/mol, RL1 ) -0.009, RR1 ) 0.007. It was assumed that QaC ) 0. So, QaA ) 161.2. In this row the values of parameters are given for the temperature of 20 °C, calculated using these listed parameter values. d While accepting the parameters from the second row, the following other best-fit parameters had to be accepted to arrive at a good fit of the titration isotherm at 60 °C: Qa1 ) 38 kJ/mol, Qa2 ) 64 kJ/mol, RL1 ) 0.0015, RR1 ) 0.0015. As usual, we assumed that QaC ) 0, so QaA ) 101.5. In this way, parameters from this row were found for the temperature of 60 °C. a
Figure 1. The comparison of the experimental function Qpr(δ0) (ffff), determined from the Kaizer’s cumulative plot, and the theoretical Qpr function calculated by us for the model assuming that no correlations exist between the adsorption energies of surface complexes. The solid line (s) was calculated for the parameters collected in Table 1 for the temperature 20 °C, and taking Qa1 ) 40 kJ/mol, Qa2 ) 78 kJ/mol, RL1 ) -0.0023, and RR1 ) 0.0015. The theoretical value of the corresponding derivative 4.6R(∂PZC/∂(1/T)) ) 112 kJ/mol.
close to unity at very small anion concentrations. On the contrary, the log-log plots of cation adsorption are Freundlich’s log-log plots with tangent smaller than unity. In the first series of our best-fit calculations we assumed that + formation of the complexes SOH+ 2 and SOH2 A is similar to that on a homogeneous solid surface, that is, we put kT/c+ ) kT/cA ) 1 in our computer program and c+ ) cA ) 0 in eqs 8. At the same time, we assumed that adsorption of the first proton and cation is similar to that on a heterogeneous solid surface, so we put kT/c0 < 1 and kT/cc < 1 in our computer program. Figure 1 shows one of the best examples of such calculations. The related parameters are collected in Table 1. A certain improvement can be seen in Figure 1 and in Table 1, when compared to Figure 9 and Table 4 in the first Part of this paper.79 First of all, the values of 4.6R(∂PZC/∂(1/T)) are closer to their values of ≈100 kJ/mol determined from the temperature dependence of PZC, as shown in Figure 3B in the first part of this paper.79 Second, the estimated Qa1 values are lower than Qa2 values, as suggested by some fundamental features of these systems.82 Furthermore, the minimum of the theoretical function Qpr(δ0) coincides with the position of the minimum of the experimental Q ∆pr(δ0) function. One serious problem is that with any choice of heterogeneity parameters, the right hand side branches of the theoretical Qpr functions, corresponding to negative values of δ0, cannot fit experimental data. Thus, in the next series of our numerical studies, we tried to solve that problem by assuming that cation adsorption is also similar to that on a homogeneous solid surface. So, we put kT/cc ) 1 and cc ) 0 in eq 8. This assumption did not help, and the right hand side branch of the theoretical curve Qpr(δ0 < 0), could not match experimental data.
Figure 2. The comparison of the De Kaizer’s [81] experimental function Qpr, (ffff) with the theoretical one calculated for the model assuming that no correlations exist. The solid line, (s) was calculated by taking Qa1 ) 34.5 kJ/mol, Qa2 ) 78.0 kJ/mol, RL1 ) -0.0032, and RR1 ) 0.011. The other parameters were the same as those collected in Table 2, corresponding to the temperature 20 °C. At this temperature the calculated value of the derivative 4.6R(∂PZC/∂(1/T)) ) 91 kJ/mol.
Then, in the next series of our computer investigations, we assumed that the oxide surface heterogeneity affects the formation of all the surface complexes. To stress the results obtained, we will say that the best ones were achieved by assuming a relatively strong surface heterogeneity effect on the first proton and on cation adsorption and weaker but still existing hetero+ geneity effects on the formation of SOH+ 2 and SOH2 A complexes. One of the best examples of such best-fit calculations is shown in Figure 2 and the related parameters are collected in Table 2. The agreement between the experimental and theoretical surface charge curves is excellent, and the Qpr function are shown in Figure 2. The value of the derivative 4.6R(∂PZC/∂(1/T)) ≈ 90 kJ/mol is closer to 100 kJ/mol, estimated in Figure 3B in Part I of this paper79 from the temperature dependence of the actual PZC values, than to 70 kJ/mol, found by the “∆T titration”. This would advocate for direct measurements of the temperature dependence of PZC and would suggest that even small deviations from the congruence of δ0(pH) curves measured at different temperatures may seriously affect the PZC(T) functions determined by the “∆T titration”. The comparison with the previous figures indicates that the assumption about surface heterogeneity also affecting the + formation of SOH+ 2 and SOH2 A complexes is very essential for a good fit of the calorimetric data Qpr(δ0) and for physical reliability of the estimated parameters. However, it should be emphasized that the oxide surface heterogeneity affects the anion adsorption less. This would, eventually, make clear why the studies of the individual isotherms of anion adsorption did not reveal the effects of surface energetic heterogeneity; namely, at small anion concentrations, the tangents of the log-log plots might be around 0.85 or more, suggesting, thus, that they are
11928 J. Phys. Chem. B, Vol. 104, No. 50, 2000
Rudzin´ski et al.
TABLE 2: List of the Parameters Used to Fit the Three Fokkink’s Titration Isotherms and a Brief Description of Our Best-Fit Calculations T °Ca
5 20 °Cc 60 °Cd
pK int a1 8.3 7.54 6.82
p*K int C 11.12 10.34 8.84
cL1 1.03 0.88 0.96
cR1 1.15 1.30 1.74
kT/c0 0.57 0.60 0.68
kT/c+
kT/cC
0.80 0.84 0.96
pK int a2
kT/cA
0.57 0.60 0.68
0.80 0.84 0.96
10.71 9.93 8.43
b
p*Kint A
PZC
b
9.50 8.73 7.62
8.32 7.57 6.88
For the temperature 5 °C, the best fit calculations yield the values listed. b Parameters calculated. c To fit simultaneously the titration isotherms at 5 °C and 20 °C, the following best fit parameters had to be accepted: Qa1 ) 79 kJ/mol, Qa2 ) 81.5 kJ/mol, RL1 ) -0.01, RR1 ) 0.01. It was assumed that QaC ) 0. So, QaA ) 159.3. In this row the values of parameters are given for the temperature of 20 °C, calculated using these listed parameter values. d While accepting the parameters from the second row, the following other best-fit parameters had to be accepted to arrive at a good fit of the titration isotherm at 60 °C: Qa1 ) 33.5 kJ/mol, Qa2 ) 70 kJ/mol, RL1 ) 0.002, RR1 ) 0.011. As usual, we assumed that QaC ) 0, so QaA ) 102.3. In this way, parameters from this row were found for the temperature of 60 °C. a
TABLE 3: List of the Parameters Used to Fit the Three Fokkink’s Titration Isotherms78 and a Brief Description of Our Best-Fit Calculations pK int a1
T 5 °C 20 °Cc 60 °Cd a
7.2 6.35 5.14
p*K int C 10.06 9.20 7.97
cL1 1.0 0.84 0.84
cR1 1.2 1.17 0.97
kT/c
pK int a2
p*K int A
PZC
0.80 0.84 0.96
12.38b
8.94b
11.51 10.28
8.22 7.33
9.5 8.71 7.62
Figure 3. The comparison of the De Kaizer’s experimental function Qpr, (ffff) [81] with the theoretical one, calculated for the model assuming high correlations between the adsorption energies of surface complexes, The solid line (s) is for the parameter values collected in Table 3 and Qa1 ) 52.0 kJ/mol, Qa2 ) 38.0 kJ/mol, RL1 ) -0.0036, and RR1 ) 0.012. The theoretical derivative 4.6R(∂PZC/∂(1/T)) ) 104 kJ/mol.
a For the temperature 5 °C, the best fit calculations yield the values listed. b Parameters calculated. c To fit simultaneously the titration isotherms at 5 °C and 20 °C, the following best fit parameters had to be accepted: Qa1 ) 88 kJ/mol, Qa2 ) 90 kJ/mol, RL1 ) -0.011, RR1 ) -0.0023. It was assumed that QaC ) 0. So, QaA ) 164.2. In this row the values of parameters are given for the temperature of 20 °C, calculated using these listed parameter values. d While accepting the parameters from the second row, the following other best-fit parameters had to be accepted to arrive at a good fit of the titration isotherm at 60 °C: Qa1 ) 56.5 kJ/mol, Qa2 ) 57.5 kJ/mol, RL1 ) 0.00, RR1 ) -0.005. As usual, we assumed that QaC ) 0, so QaA ) 99.5. In this way, parameters from this row were found for the temperature of 60 °C.
equal to unity. The deviations from unity could easily be ascribed to experimental errors. On the basis of the model of a heterogeneous surface, the derivative 4.6R(∂PZC/∂(1/T)) can no longer be interpreted as (Qa1 + Qa2), as in eq 18a in the first part of this paper.79 Now, the derivative ∂PZC/∂(1/T) must be analyzed by using eq 10. To check which difference results in the new interpretation in eq 10, compared to that in eq (18a) in ref 79, we should compare the sum (Qa1 + Qa2) ) 112 kJ/mol, in Figure 2, with the corresponding value of the derivative 4.6R(∂PZC/∂(1/T)) ) 91 kJ/mol. Although the fit seen in Figure 2 and the related Table 2 may look as fairly satisfactory, there is one result that may still raise a question, namely, the estimated derivative 4.6R(∂PZC/ ∂(1/T)) ≈ 90 kJ/mol (Figure 3B in the first part of this paper79 suggests a values around 100 kJ/mol). We decided also to check whether the model assuming high correlations between the adsorption energies of surface complexes might not solve this problem. Figure 3 and Table 3 show an example of the corresponding best-fit calculations. Figure 3 and Table 3 show that assuming high correlations between the adsorption energies of surface complexes does not solve the problem. Although the agreement between theory and experiment looks pretty good, and the value of the derivative, 104 kJ/mol is very close to that estimated in Figure 3B79 from the temperature dependence of PZC, some serious objections are to be raised; namely the observed trend that Qa1 > Qa2 seems to be a little bit strange, in view of what we know about these adsorption systems.81 In the last attempt to arrive at still better theoretical values of 4.6R(∂PZC/∂(1/T)), we tried to put QaC * 0. Surprisingly, for the first time, the assumption QaC * 0 created difficulties in fitting the experimental titration isotherms.
Thus, in summarizing the results of our computer exercises, aimed at explaining the thermodynamic features of the hematite/ KNO3 adsorption system studied by Fokkink et al.78 and De Kaizer et al.,81 we stress the following. (1) The model of an energetically homogeneous oxide surface is inapplicable. One cannot find a reasonable set of parameters leading to a simultaneous good fit of both titration isotherms and directly measured calorimetric effects accompanying ion adsorption. (2) The model of a heterogeneous solid surface assuming that high correlations exist between the adsorption energies of the surface complexes appears also to be inapplicable. (3) A fairly good agreement between theory and experiment can only be achieved by accepting the model of a heterogeneous oxide surface and the assumption that no correlations exist between the adsorption energies of the surface complexes. (4) For the last adsorption model, best results are achieved by assuming that oxide surface heterogeneity affects the formation of all kinds of surface complexes. (5) Then, the best agreement between theory and experiment is obtained by assuming that the oxide surface heterogeneity affects more strongly the formation of SOH0 and SO-C+ complexes, and less strongly the formation of the complexes + SOH+ 2 or SOH2 A . For Fokkink’s hematite sample,78 no enthalpic effects are found to accompany cation adsorption. Now, let us turn to the hematite/KNO3 system studied in our experiments. In view of the success of the model assuming small correlations, we tried to apply it first. The related best-fit calculations led us to a much different but consistent picture of the thermodynamic features of our hematite/KNO3 adsorption system.
Ion Adsorption at a Heterogeneous Oxide Surface
J. Phys. Chem. B, Vol. 104, No. 50, 2000 11929
Figure 5. The temperature dependence of PZC, calculated for Qa1 and Qa2 values, corresponding to QaC. Then the corresponding parameters are Qa1 ) 13.0 kJ/mol and Qa2 ) 38.5 kJ/mol. Other parameters are the same as those used to prepare Figure 4.
Figure 4. The dependence of the best-fit parameters Qa1 and Qa2 on the assumed value of QaC, when the heterogeneity parameters are following: c0, and cC ) 0.6 kT, and c+ ) cA ) 0.85 kT. Also, the controlling derivative 4.6R(∂PZC/∂(1/T)) is shown. The discrete data (b, ), 4) denote the values of Qa1 (444), Qa2 ()))), and 4.6R(∂PZc/ ∂(1/T)) (bbb) found in various computer runs, made for a fixed value of QaC. The solid lines are approximations by spline functions.
Checking the value of the derivative 4.6R(∂PZC/∂(1/T)) appears to be a strong control of the reliability of the estimated parameters; namely, our calculations have shown that an equally good fit of both the titration isotherm and the Qpr calorimetric data, measured at 25 °C, can be achieved for a large variety of parameter sets. However, our calculations also show, that there is a relatively narrow class of parameter sets for which the derivative 4.6R(∂PZC/∂(1/T)) takes values lying in the interval 40-42 kJ/mol. After having carried out numerous calculations, we found such a class of parameter sets. This happens when c0/kT ) cC/kT ≈ 0.6, and c+/kT ) cA/kT ≈ 0.85. Then, we made the following discovery. One has to assign QaC a negative value to arrive at a good, but also physically meaningful, fit of the experimental data. This is illustrated in Figure 4. For every set of the three parameters, Qa1, Qa2, and QaC in Figure 4, an excellent fit is achieved of both titration isotherms δ0(pH) and the calorimetric data Qpr(pH). However, only for a certain class of these parameter sets does the controlling function 4.6R(∂PZC/∂(1/T)) fall into the interval 4041 kJ/mol suggested by the temperature dependence of the experimental PZC data, shown in Figure 3B in Part I.79 It was also interesting to see that for the parameter values Qa1, Qa2, and QaC corresponding to the lowest values of the theoretical derivative 4.6R(∂PZC/∂(1/T)) in Figure 4, the temperature dependence of PZC has a minimum, similar to the experimental temperature dependence of PZC shown in Figure 3B in Part I.79 This is shown in Figure 5. The theoretical minimum is more shallow and is located at a somewhat higher temperature. Nevertheless, this qualitative similarity deserves some consideration. The somewhat different locations of the theoretical and experimental minima of 4.6R(∂PZC/∂(1/T)) may partially be due to experimental errors in determining our PZC(T) function. Still another reason seems to be of a more fundamental nature; namely, our analysis of Fokkink’s data suggested that both Qa1, and Qa2 are temperature-dependent. Meanwhile, our theoretical dependence of PZC was calculated by taking Qa1, Qa2, and QaC values that are correct only for the temperature 25 °C. So, the temperature dependence of the experimental PZC values may be a combined effect of surface energetic heterogeneity and of
Figure 6. The solid line (s) is the fit of our experimental data, obtained for the model of heterogeneous surface (small correlations), using the parameters collected in Table 4.
changes in Qa1, Qa2, and QaC due to changing temperature. Also, the heterogeneity parameters, c0, c+, cC, and cA may depend on temperature to some extent. Obviously, more accurate and complete experimental studies are needed to analyze quantitatively the dependence of PZC on temperature. Figure 6 shows the corresponding to theoretical Qpr(pH) function, calculated by using the values of Qa1 and Qa2, corresponding to QaC ) -57 kJ/mol. The corresponding parameters are collected in Table 4. Let us remark that the Qa1 and Qa2 values determined previously for Fokkink’s hematite sample are roughly two times larger than the Qa1, and Qa2 values found for our hematite sample. Thus, the proportions between Qa1 and Qa2 remain unchanged. Something new is the relatively high negative value Qac ) -59.0 kJ/mol found for our hematite sample. Before trying to find its theoretical interpretation, we decided to check whether the model assuming high correlations might not offer a simpler interpretation. Thus, Figure 7 shows the result of our best-fit exercises made by assuming that high correlations exist and Qac ) 0. Table 5 collects the related parameters. The solid line in Figure 7 has the same drawback as the broken line corresponding to the homogeneous surface model, namely, the theoretical maximum does not coincide with the maximum in the experimental Qpr(pH) data. Next, any other choice of the best-fit parameters can shift that theoretical maximum toward higher pH values. Although the theoretical Qa1 and Qa2 values look more realistic than those found for the homogeneous surface model, the theoretical derivative 4.6R(∂PZC/ ∂(1/T)) ) 30 kJ/mol is much lower than its values determined from the temperature dependence of experimental PZC values. Putting in some values of QaC < 0 does not help. One arrives, then, at a very similar graphical fit but much less reasonable
11930 J. Phys. Chem. B, Vol. 104, No. 50, 2000
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TABLE 4: Parameters Used to Fit the Experimental Qs and Qpr Data in Figure 6: The Ns Value Was Taken as Equal to 8 sites/nm2 and PZC ) 6.23 Best-Fit Parameters pK int a1
p*K int C
Qa1
4.6
6.3
13
Qa2
RL1
RR1
cL1
cR1
kT/c0
kT/c+
kT/cC
kT/cA
38.5
-0.013
-0.015
1.02
1.16
0.60
0.85
0.60
0.85
Calculated Parameters pK int a2
p*K int A
QaA
7.88
6.40
11.5
Figure 7. The solid line (s) was calculated by using the parameter collected in Table 5, i.e., by assuming that high correlations exist between adsorption energies of the surface complexes formed on a heterogeneous solid surface. Also, for comparison, the broken line (---) shows the fit obtained for the homogeneous surface model. The theoretical derivative 4.6R(∂PZC/∂(1/T)) ) 30 kJ/mol.
TABLE 5: Parameters Used to Fit the Experimental Qs and Qpr Data in Figure 7: The Ns Value Was Taken as Equal to 8 sites/nm2 and QaC ) 0.0 Best-Fit Paramters pK int a1
p*K int C
Qa1
Qa2
RL1
RR1
cL1
cR1
kT/c
4.0
5.3
15
62
-0.009
-0.006
1.0
0.97
0.80
Calculated Parameters pK int a2
p*K int A
QaA
9.02
7.16
57.6
values of Qa1 and Qa2. For instance, while assuming that QaC ) -50 kJ/mol, one estimates Qa1 ) 55 kJ/mol and Qa2 ) 11 kJ/ mol. Also the theoretical Qpr curve is not able to reproduce the S shape of the experimental data at high pH. Thus once again, we arrive at the conclusion that the heterogeneous surface model assuming high correlations is inapplicable. But then we face the necessity of finding a physical explanation for QaC ) -59 kJ/mol, found by applying the model assuming small correlations. Negative values of QaC might be explained by assuming dehydration of the cations, leaving bulk solutions, and adsorbtion on the surface within the β plane. Provided that the water molecules coordinated by cations in the bulk solution have icelike structures, losing just one coordinated water molecule should be compared to the heat of ice melting, ≈6 kJ/mol. Thus, the value of Qac ) -57kJ/mol would mean losing (statistically) ten water molecules in the course of cation adsorption. While accepting that explanation, we are obliged to explain why the potassium (K+) cations adsorbing on the surface of Fokkinks hematite sample are not dehydrated, while those adsorbing on the surface of our hematite sample lose ten water molecules. It seems that this explanation may be found in two papers by Lyklema and co-workers83,84 on the interfacial chemistry of the hematite/electrolyte interface.
Figure 8. The comparison of the surface charge (2b[) data δ0(pH) found in our experiments at 25 °C and Fokkink’s δ0(pH) data at 20 °C, (fff). The solid line (s) denotes Fokkink’s theoretical curve δ0(pH) calculated for 20 °C by using the parameters in Table 2.
The clue is the difference in the surface charge values δ0(pH) found in our experiment. Figure 8 shows their comparison. Looking into Figure 8, we can see that much larger surface charges are formed on our hematite sample, compared to Fokkink’s sample.78 This takes place at δ0 < 0, where cation adsorption dominates strongly over anion adsorption. While discussing the features of the hematite/electrolyte interfaces, Breeuwsma and Lyklema83 wrote, “the actual values of δ0 tend to be higher the more porous the surface is”. Thus, it can be assumed that our hematite sample has a more porous surface than Fokkink’s sample. Furthermore, Breuwsma and Lyklema emphasize that the shape of the δ0(pH) curves in these systems (on the positive side of PZC) suggests “that anions such as chloride and nitrate do not penetrate”. Cations, on the contrary, could penetrate under the condition of when they lose the surrounding, coordinated water molecules. Thus, the cation adsorption on the somewhat porous surface of our hematite sample must be accompanied by its partial dehydration, at least. As a matter of fact, Fokkink at al.78 prepared their sample in a similar way to Breeuwsma and Lyklema.83 All these authors reported that their studies of nitrogen adsorption revealed only a small surface porosity. Provided that after dehydration, the cation may penetrate closer to the solid surface, the porous structure should create better energetic conditions for cation adsorption than the flat surface of Fokkink’s sample. As a consequence, the KC parameter should be higher for our porous surface. And this is what we observe. For the best-fit parameters found for Fokkink’s sample and collected in Table 2, log KC ) -0.22 whereas for our more porous sample, log KC ) 1.53 for the temperature 25 °C. Thus, we can say that potassium cations K+ are adsorbed on our hematite sample almost a hundred times more strongly than on the surface of Fokkink’s sample. Such strong cation adsorption is frequently called “specific adsorption”. Breeuwsma and Lyklema emphasize that “specific adsorption of cations leads to shift of the PZC to lower pH
Ion Adsorption at a Heterogeneous Oxide Surface values”. This is what we observe when comparing our PZC ) 6.2 at 25 °C with Fokkink’s PZC ) 8.8 at the same temperature. The difference in the surface porosity of these two hematite samples has strong effects on the equilibrium constants, (free energies) of formation of surface complexes, and the accompanying enthalpic effects. This should not surprise us. After reviewing the results of many studies of the interfacial properties of the hematite/electrolyte interfaces, Breeuwsma and Lyklema82 wrote, “The porosity of the surface even appears to be a more important parameter than its chemical composition”. As in the case of cation (K+) adsorption, the surface porosity effects might offer also an explanation for the differences in Qa1 and Qa2 values, found for Fokkink’s hematite sample and the sample used in our experiments; namely, it has been believed for a long time that water molecules adsorbed on the oxide surfaces have ice-like structures induced by hydrogen bonding to both Me-OH groups and the “free” surface oxygens O-. The fact that one adsorbed water molecule is coordinated by two hydrogen bonds to two MeOH groups has been known for a long time. This was deduced long ago by Morimoto and coworkers85 studying the isotherms of the “first” and the “secondary” water adsorption on the outgassed hematite samples. More recently, Ishikawa et al.86 used in situ FTIR to also show the possibility of hydrogen bonding to the empty O- ions. At the same time, Clarke and Hall,87 using inelastic incoherent neutron scattering from the adsorbed water molecules, provided evidence for an ice-like structure of water adsorbed on magnetite. They also obtained similar results for hematite. Although, in the latter case the resolution was poor, the graph of intensity versus coverage of water adsorbed was linear, just as in the case of magnetite. A different state of adsorbed molecules has also been discovered by calorimetric measurements of the heat capacity, of the adsorbed (vicinal) water, studied extensively by DrostHansen, Etzler, and co-workers.88-91 They subjected their measurements to a theoretical analysis based on the “two state” model of water molecules.92 Their studies suggest that vicinal water differs from the bulk in the fact that hydrogen bonding between water molecules is enhanced by propinquity to the solid surface. Thus, much of the enthalpic effects accompanying the proton adsorption must come from the different water environment of protons in the bulk and on the oxide surface. Etzler and Conners91 have found that the heat capacity of adsorbed water molecules depends on the diameter of pores. It can be expected that adsorption of protons in the pores of different dimensions will be accompanied by dehydratation, depending on the pore diameter. Obviously, that dehydration will be different for the protons adsorbing on the slightly porous surface of Fokkink’s sample and the more porous surface of our sample. The lower values of Qa1 and Qa2 found for our sample would suggest that protons adsorbing on the more porous surface of our sample are less coordinated to the vicinal water molecules,that is, they undergo a deeper “dehydration” in the course of adsorption. The same is true in the case of cation adsorption. The presence of the structured (vicinal) water molecules is not explicitly taken into account in the surface complexation models of ion adsorption at the oxide/electrolyte interfaces. Meanwhile, it was found that the vicinal structuring of water may extend to a few nanometers from the surface.92 This would mean that the structured water may extend up to the slipping plane, as discussed in the works by Kallay and Matijevic.93-95 Thus, the presence of structural water, not explicitly considered, may be a source of some phenomena which can hardly
J. Phys. Chem. B, Vol. 104, No. 50, 2000 11931
Figure 9. The contributions of Q (i) pr to Qpr measured for (A) Fokkink’s hematite sample and (B) the hematite sample used in our experiments. The meaning of the data is the following: The contribution of Q (C) pr due to the cation adsorption is shown as the solid line (s). The broken line (---) shows the contribution of Q (A) pr due to the anion adsorption; next, (bbb) is the contribution of Q (0) pr due to the first proton adsorption, and (+++) denotes Q (+) pr coming from formation of the SOH+ 2 complexes. For (A) Fokkink’s hematite sample, the calculations were done by using the same parameter values, leading to the best fit shown in Figure 2. In the case of the (B), our hematite sample, these were the parameters leading to the best fit shown in Figure 6.
be understood. Perhaps, it may be a source of changing Qa1 and Qa2 with temperature. Temperature changing 5 °C to 60 °C does not seem to induce dramatic changes in the structure of the oxide sample. Meanwhile, even for large pores of silica of about 140 Å, such temperature changes induce remarkable changes in the heat capacity of the adsorbed water molecules.92 Therefore, when carrying out our further model investigations, we will limit them to one temperature. The forthcoming model investigations will show how the formation of various surface complexes contributes to the combined, experimentally monitored values of Qpr. Next, we will study the electrostatic contributions to the observed enthalpic effects. Their role is still not understood well. Finally, we will show how surface energetic heterogeneity and other physical factors affect these enthalpic effects. Thus, Figure 9 shows separately the contributions to Qpr, Q (i) pr (i ) 0, +, A, C) due to formation of various surface complexes:
( ) ( ) ( ) ( )
∂θi Q (h) i ∂pH T (i) Q pr ) ∂θ+ ∂θA ∂θ0 2 +2 + ∂pH T ∂pH T ∂pH
(11)
T
Looking at Figure 9, we can see similarities in the behavior of the Q (i) pr functions calculated for these two hematite samples. In particular, this can be clearly seen around δ0 ) 0. Also, one can easily see that these are the contributions due to cation and anion adsorption, affecting predominantly the behavior of Qpr data. This is particularly true in the case of the more porous surface of our hematite sample. In the case of Fokkink’s sample, formation of the complexes SOH0 also contribute substantially to Qpr data. One striking feature seen in Figure 9A is the high contribution from the cation adsorption, through the nonconfigurational heat of cation adsorption Qac ) 0 in the case of Fokkink’s sample.
11932 J. Phys. Chem. B, Vol. 104, No. 50, 2000
Rudzin´ski et al.
Figure 10. The behavior of QC,el, (- - -) and of DC (---), affecting the electrostatic contribution to Qpr due to the cation adsorption, Q (C) pr,el (s) in the case of (A) Fokkink’s hematite sample and (B) our sample. All the parameters are the same as those used to prepare Figure 9.
Our calculations show that this high contribution is due to the clectrostatic contribution to QaC and QC,el:
QC,el ) -eψ0 -
()
e ∂ψ0 T 1 ∂ T
+e
( )
δ0 eδ0T ∂c1 + c1 (c )2 ∂T
{θi},pH
1
Figure 11. (A) The total electrostatic contribution of Qpr (///) to the experimentally monitored function Qpr (fff) in the case of Fokkink’s hematite sample. (B) Separately, the electrostatic contributions Q (i) pr,el 0 are shown from the complexes SO-C+ (s), SOH+ 2 A (- - -), SOH (bbb), and SOH+ (+++). 2
{θi},pH
(12)
Our calculations have also shown that the contribution k(∂ ln ac/∂(1/T)) coming from the temperature dependence of bulk activities is negligible compared to all other terms in the functions Qi’s, defined in eqs 24 in Part I.79 Thus, in Figure 10, we show the QC,el function eq 12, the relative derivative DC
( ) ( ) ( ) ( )
∂θC ∂pH T DC ) ∂θ+ ∂θA ∂θ0 2 +2 + ∂pH T ∂pH T ∂pH
(13)
T
and the electrostatic contribution due to cation adsorption Q (C) pr,el ) DCQC,el. Figures 11 and 12 bring full information about the electrostatic contributions to Qpr due to formation of various surface complexes, Q (i) pr,el
( ) ( ) ( ) ( )
∂θi Q ∂pH T i,el (i) Q pr,el ) ∂θ+ ∂θA ∂θ0 2 +2 + ∂pH T ∂pH T ∂pH
Figure 12. The electrostatic contributions to the experimentally monitored Qpr function in the case of our hematite sample. The meaning of symbols and lines is the same as in Figure 13.
(14)
T
and the total electrostatic contribution
Qpr,el )
∑i Q (i)pr,el
(15)
Figures 11 and 12 show that the trends in the dependence of experimental functions Qpr on δ0 is similar to that in the theoretically calculated electrostatic contributions. This would advocate for an important role of these electrostatic contributions. They do not disappear at δ0 ) 0, as it is sometimes assumed, because of the term, e/T(∂ψ0/∂(1/T)) in the molar nonconfigurational heats, Qi’s defined in eqs 24 in Part I of this paper.79
Figure 13. (A) The total heterogeneity contribution of Qpr,h (///) to the total experimentally monitored Qpr, (fff) in the case of Fokkink’s hematite sample. (B) Separately, the heterogeneity contributions of 0 Q ipr,h are shown, from the complexes SO-C+ (s), SOH+ 2 (---), SOH (bbb), and SOH+ (+++). 2
Looking at Figures 13 and 14, we can see a striking similarity in Qpr,h values, which are the contributions to Qpr due to the
Ion Adsorption at a Heterogeneous Oxide Surface
Figure 14. The heterogeneity contributions to the experimentally monitored Qpr, in the case of our hematite sample. The meaning of symbols and lines is the same as in Figure 13.
energetic heterogeneity of the hematite surface. This should not surprise us, because both Fokkink’s and our hematite sample are characterized by similar heterogeneity parameters. Figures 9-14 show that the experimentally monitored Qpr data are a complicated sum of various contributions, each of them changing with the charge of the oxide surface. Thus, every simple interpretation of the experimental Qpr data may be strongly misleading and should be treated with caution. However, the general conclusion is very optimistic. A proper theoretical analysis of both temperature dependence and calorimetric effects of ion adsorption may provide a consistent picture of the thermodynamic features of the oxide/ electrolyte system. Such an analysis provides us with parameters and functions, bringing us to understanding better the features of these systems. Conclusions To draw some more general conclusions about the thermodynamic features of the hematite/electrolyte interfaces, a comparative study should be carried out in which various hematite samples could be investigated. Numerous experiments of that kind have already been reported and were next subjected to an exhaustive theoretical analysis in the papers by Lyklema and co-workers,78,81-84 Matijevic and co-workers,95-99 and by other authors. However, almost all the reported experimental data were measured at one temperature. The data provided scientists mostly with information about free enthalpies of adsorption. This is a quantity combining the enthalpy and entropy of adsorption. Substantial progress in understanding the features of these systems has already been made by studying the free enthalpies of adsorption. However, further essential progress could only be made by determining separately the enthalpies and entropies of ion adsorption. As the entropic contribution can only be calculated, some methods were necessary to determine the enthalpic effects. These enthalpic effects can be deduced either from the temperature dependence of adsorption isotherms or directly measured in appropriate calorimetric experiments. Although the temperature dependence of PZC has long been monitored, studies of the temperature dependence of the whole titration isotherms are scarce. Also, only a few experiments have been reported so far in the literature, in which direct calorimetric measurements were conducted.
J. Phys. Chem. B, Vol. 104, No. 50, 2000 11933 Nevertheless, it seems that the body of the data collected during the last two decades makes it possible to attempt an advanced theoretical analysis. So, Blesa et al. began the theoretical analysis of the temperature dependence of titration isotherms, whereas Machesky et al., Lyklema and co-workers, and Kallay and co-workers began the analysis of the directly measured calorimetric effects. More recently, these enthalpic effects have been analyzed in more detail by Rudzin´ski and co-workers. Our theoretical group in Lublin has also made substantial progress in refining theoretical models used for that purpose. In particular, we have brought into light strong effects of the surface energetic heterogeneity on the temperature dependence and on the calorimetric effects accompanying ion adsorption. This paper is the first attempt to study quantitatively both the temperature dependence of ion adsorption and the related enthalpic effects measured directly in calorimetric experiments. Our present study shows that studying the temperature dependence of titration isotherms might provide a picture of the thermodynamic features of these adsorption systems, but better results are obtained when they are combined with direct calorimetric measurements. However, our present study also shows that direct calorimetric studies should be accompanied by measurements of adsorption isotherms and their temperature dependence. Only their simultaneous quantitative analysis may provide an entirely correct picture of the thermodynamic features of the adsorption system under investigation. Such a quantitative theoretical analysis has been developed in a series of our recent publications.65-67,82 Our first quantitative study of both the temperature dependence and the calorimetric effects accompanying ion adsorption is focused here on the hematite/electrolyte interfaces. Two facts stimulated our interest to study these adsorption systems: first, their enormous importance for life and technology, and second, the already existing body of experimental data that could be suitable for an advanced quantitative analysis. Thus, we had at our disposal the data reported earlier by Lyklema, Fokkink, and De Kaizer, and the body of experimental data obtained by us. A quantitative analysis of these two sets of experimental data provides a consistent picture of the thermodynamic features of these adsorption systems and very interesting material for discussion. That comparative study reveals some similarities in the features of these two hematite/KNO3 systems as well as substantial differences due to their different preparation. Our hematite sample seems to have a more porous surface, manifested by higher values of the surface charge δ0 developed in the region of negative surface charges. A more porous surface enhances strongly the cation adsorption, accompanied by its dehydration in the course of adsorption. Small, or nonexistent, dehydratation effects are observed in the cation adsorption on the less porous surface of Fokkink’s sample. A similar trend is observed in the first and the second proton adsorption. While the proportions between Qa1 and Qa2 remain basically unchanged, these heats are thoroughly two times higher in the case of Fokkink’s sample. This could be ascribed to a smaller degree of dehydration in the course of adsorption on a less porous hematite surface. The source of that effect is, probably related to differences in the features of the structured water molecules adsorbed in large and small pores. The changes in the structured water molecules caused by changing temperature may be a source of the temperature dependence of the nonconfigurational heats of proton adsorption Qa1 and Qa2 observed in our adsorption systems. Our theoretical analysis shows how misleading simple interpretations of the observed calorimetric effects of adsorption
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