J. Phys. Chem. 1996, 100, 11711-11719
11711
Mechanisms of Deposition of Species Containing Catalytically Active Ions on the Oxidic Support/Electrolytic Solution Interfaces: A Unified Approach Based on the Two-pk/One-Site and Triple-Layer Models K. Bourikas, H. K. Matralis, Ch. Kordulis, and A. Lycourghiotis* Department of Chemistry, UniVersity of Patras and the Institute of Chemical Engineering and High Temperature Chemical Processes (ICE/HT), P.O. Box 1414, GR-26500 Patras, Greece ReceiVed: February 22, 1996X
A general methodology for investigating the mechanisms of deposition of ionic species containing catalytically active elements on the oxidic support/electrolytic solution interfaces has been developed. The methodology is based on the “two-pK/one-site” and “triple-layer” models (for the charging mechanism of the surface of the support, and for the electrical double layer developed between the surface of the support, and the impregnating solution, respectively) and exploits the experimental data of the adsorption isotherms at various pH of the impregnation suspension. Starting from a quite general, “postulated”, deposition mechanism, comprising all equilibria that could possibly take place at the “support/impregnation solution” interface, the application of this methodology leads to the “proposed” deposition mechanism, namely, the set of equilibria that actually take place, the kind of deposited species formed, their relative concentrations, and their dependence from the impregnating parameters (pH, concentration of the precursor, ionic strength, and temperature). The derived equations, describing the deposition of a given ionic species on the support surface, show that the concentration of the deposited species depends on various factors among which the most important are the charge of the ionic species, its concentration in the bulk impregnating solution, the surface concentration of the receptor sites on the support surface, the pH, and the Galvani and Volta potentials developed, respectively, on the surface of the solid particles and at the inner Helmholtz plane. As a test for the validity of the proposed deposition model, the theoretical values of some “support/electrolyte interface” parameters (calculated on the basis of the deposition mechanism revealed by applying this methodology) are compared with the corresponding experimental values determined by potentiometric titrations and microelectrophoresis.
Introduction In the present paper we present a general methodology for investigating the mechanisms of deposition of ionic species containing the catalytically active element from the impregnating solution on the surface of an oxidic support. The preparation of supported catalysts usually involves the following steps: (i) impregnation of the support in an electrolytic solution containing the active element to be deposited; (ii) filtration and/or drying; (iii) calcination which in most cases is followed by a suitable activation procedure. Among these steps, impregnation is the most important since it can largely determine critical properties of the final catalyst, such as the dispersity of the supported phase, the kind and relative concentrations of the various supported species formed and, consequently, the catalytic performance of the catalyst. This is especially the case when the catalyst is prepared by the equilibrium deposition filtration (EDF) technique. Following this preparation method, the deposition of the species containing the catalytically active element on the support surface takes place, in a controlled way, exclusively during the impregnation. Depending on the chemical compound used as the precursor and on the pH, the impregnating solution may contain several distinct ions all containing the element to be deposited onto the support. For example, when ammonium tungstate ((NH4)12W12O41‚5H2O) is used for supporting tungsten, the impregnating solution contains in the pH range of 3.5-10 eight W-containing ionic species (namely, the WO42-, HWO4-, W6O20(OH)26-, X
Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)00548-5 CCC: $12.00
HW6O20(OH)25-, H2W12O4210-, H3W12O429-, H4W12O428-, and H5W12O427-) in nonnegligible concentrations.1 On the other hand, the surface (S) of the support particles, when in contact with the electrolytic impregnating solution, is charged forming protonated (SOH2+) and deprotonated (SO-) surface hydroxyl groups in addition to the neutral (SOH) ones. These surface groups (as well as combinations of these; e.g., two adjacent SOH2+, one SOH vicinal to one SO-, etc.) constitute the receptor sites for the ionic species in the impregnating solution. During impregnation and depending on the impregnation parameters (pH, concentration of the precursor, ionic strength, and temperature) certain types of the ionic species will be deposited on the support surface; namely, they will be “connected” to certain types of receptor sites by adsorption, by chemical reaction, or even by a combination of both adsorption and chemical reaction on sites formed by vicinal surface groups. As a result, some kinds of deposited species (namely, combinations of ionic species “connected” to receptor sites) will be formed on the surface of the oxidic carrier. The nature of these deposited species, as well as their relative abundance, will in turn determine the nature, surface concentration, and dispersity of the various supported species on the final catalyst. Knowing the nature of the deposited species, their relative concentrations, and their dependence on the impregnating parameters is equivalent to knowing the deposition mechanism. The elucidation of the deposition mechanism is extremely important when a preparation method is used in which the deposition on the support surface occurs primarily during the impregnation step, as is the case with the EDF technique. © 1996 American Chemical Society
11712 J. Phys. Chem., Vol. 100, No. 28, 1996
Bourikas et al.
Indeed, knowing the deposition mechanism permits the tailoring of the preparation by adjusting the impregnation parameters at their optimal values in order to obtain a catalyst with the desired characteristics. However, due to the complexity of the system (support plus impregnating solution) and to the fact that the deposited species are located at the liquid-solid interface, even the most sophisticated characterization techniques are not able to identify all the deposited species formed or to determine their relative concentrations. We need, thus, an approximate computational methodology that based on certain experimental data will be able to reveal the deposition mechanism. The development of such a methodology, constituting a powerful tool for the controlled preparation of catalysts, is the objective of this work. In the last few years we have used computational methodologies in order to elucidate the mechanism of deposition in some catalytically important systems.2-7 In those studies, however, we used each time a methodology specifically adapted to the system under investigation. In this context, those studies can now be considered as particular cases of the present unified general methodology. Our approach is based on two models. Concerning the charging mechanism of the surface of the support particles it is based on the “two-pK/one-site” homogeneous model. In view of the recent developments concerning the “one-pK/multisite” model,8-11 the homogeneous model used in the present work is of course an approximation. However, we believe that this is a very useful approximation for modeling quite complicated depositions mainly in the cases where more than one ionic species, containing the catalytically active element, are present in the impregnating suspension. Concerning the electrical double layer developed between the surface of the support particles and the impregnating solution, our methodology is based on the “triple-layer” model. The general methodology presented in this article involves the following steps: (i) The postulation of a quite general, tentative, deposition mechanism. This is a set of deposition equilibria that take into account all the general findings concerning deposition reported by us in the last years. (ii) The derivation of thermodynamic equations describing the above equilibria. (iii) The calculation, on the basis of these equations, of various physicochemical parameters of the “support/electrolyte solution” interface. The most important of these parameters is the concentration of each deposited species formed on the support surface during impregnation. (iv) The testing of the validity of the deposition model by comparing the so-calculated “interface parameters” with the corresponding ones drawn from the following experimental techniques, deposition experiments, potentiometric titrations, and microelectrophoresis. Development of the Methodology General Deposition Mechanism. As already mentioned, the first step in our methodology is to write down a quite general deposition mechanism (eqs 1a-1f) describing the deposition of negative and positive ionic species from the impregnating solution onto the surface of an oxidic support.
µiSOH2+ + Aj S (SOH2+)µi‚‚‚Aj
(1a)
ViSOH + Aj S SVi - Aj + ViOH-
(1b)
µiSOH2+ + ViSOH + Aj S SVi - Aj‚‚‚(SOH2+)µi + ViOH- (1c) FiSO- + Bj S (SO-)Fi‚‚‚Bj
(1d)
ViSOH + Bj S (SO)Vi - Bj + ViH+
(1e)
FiSO- + ViSOH + Bj S (SO)Vi-Bj‚‚‚(SO-)Fi + ViH+ (1f) In the above equilibria Aj and Bj represent, respectively, negative (e.g., WO42-) and positive (e.g., Co2+) ionic species containing the catalytically active element. These species are considered to be located in the inner Helmholtz plane (IHP). SOH2+, SOH, and SO- represent, respectively, the protonated, neutral, and deprotonated surface hydroxyls of the support. Finally, µi, Vi, and Fi denote the number of SOH2+, SOH, and SO- groups which are involved in each equilibrium. According to this mechanism a negative, or positive, ionic species is first moved from the bulk impregnating solution to the IHP and then it may be adsorbed on sites created in this plane by the SOH2+ and SO- groups, respectively (eqs 1a, 1d). Moreover, these speciessbeing in the IHPsmay react with the neutral surface hydroxyls, releasing OH- or H+ ions in the IHP (eqs 1b, 1e). Finally, these species may be deposited by simultaneous adsorption and reaction (eqs 1c, 1f). This general mechanism is in full agreement with many experimental results published by our group in the last few years.1,12-18 Derivative of an Equation To Describe the Deposition of an Ionic Species i on the Surface of an Oxidic Support. The second step in our methodology is to derive an equation that may describe the deposition of species i on the surface of an oxidic support. To do that it is necessary to follow the usual thermodynamic procedure and write down relations for the electrochemical potentials involved in the model equilibria.
µSOH2+ ) µ°SOH2+ + RT ln(1 - θSOH2+) + zSOH2+Fφo
(2a)
µSOH ) µ°SOH + RT ln(1 - θSOH) + zSOHFφo
(2b)
µSO- ) µ°SO- + RT ln(1 - θSO-) + zSO-Fφo
(2c)
µAi ) µ°Ai + RT ln θAi + zAiFφIHP
(2d)
µBi ) µ°Bi + RT ln θBi + zBiFφIHP
(2e)
µAj ) µ°Aj + RT ln[Aj]IHP + zAjFφIHP
(2f)
µBj ) µ°Bj + RT ln[Bj]IHP + zBjFφIHP
(2g)
µOH- ) µ°OH- + RT ln[OH-]IHP + zOH-FφIHP
(2h)
µH+ ) µ°H+ + RT ln[H+]IHP + zH+FφIHP
(2i)
In the above relations, by µ j and µ° we denote, respectively, the electrochemical and standard state chemical potentials of the various species involved in the model equilibria 1a-1f. These species are indicated by the corresponding subscripts. Ai and Bi denote, respectively, the A or B deposited species illustrated in the rhs of the model equilibria (e.g., (SOH2+)µi‚‚‚Aj is denoted by Ai). Moreover, by [x]IHP, zx, φo, φIHP, and F we denote, respectively, the concentration of the species x in the IHP, its electrical charge, the Galvani potential at the surface
Deposition on Industrial Supports
J. Phys. Chem., Vol. 100, No. 28, 1996 11713
and in the IHP, and the Faraday constant. It is obvious that zSOH2+ ) 1, zSOH ) 0, zSO- ) -1, zAi ) zAj + Vi and zBi ) zBj - Vi. In the above relations, by θSOH2+, θSOH, and θSO- we symbolize, respectively, the fractions of the groups SOH2+, SOH, and SO- covered by the deposited species. More precisely these fractions are defined by the following relationships: c t θSOH2+ ) CSOH +/CSOH + 2 2
(3)
c t /CSOH θSOH ) CSOH
(4)
c t θSO- ) CSO -/CSO-
(5)
where C denotes concentration. The superscripts t and c indicate total (covered plus uncovered) and covered groups, respectively. The fractions θAi and θBi are defined by the following equations:
CAi
θAi ) λi t t (CSOH2+)µi(CSOH )Vi CBi
θBi ) λi t F t V (CSO-) i(CSOH) i
Therefore, it is convenient to write down the following expressions:
∆G°chem,Ai ) µ°Ai + Viµ°OH- - µiµ°SOH2+ - Viµ°SOH - µ°Aj (16) ∆G°chem,Bi ) µ°Bi + Viµ°H+ - Fiµ°SO- - Viµ°SOH - µ°Bj (17) ∆G°electr,Ai ) -F(µiφo - zAiψIHP)
(18)
∆G°electr,Bi ) -F(Fiφo - zBiψIHP)
(19)
Moreover the standard state free energy related to the chemical interactions may be analyzed into two terms: one for the chemical interactions between the deposited species and the support surface (cs) and one for the chemical interactions between the deposited species themselves (cc):
(6)
(7)
In eqs 6 and 7, λi is a proportionality constant and the other symbols have been already explained. In order to derive the title equation we need the Boltzmann equations relating the concentration of an ionic species in the bulk of the impregnating solution (denoted by b) with its concentration in the inner Helmholtz plane, as well as some simple relations for the concentration of the H+ and OH- ions:
∆G°chem,Ai ) ∆G°cs,Ai + ∆G°cc,Ai
(20)
∆G°chem,Bi ) ∆G°cs,Bi + ∆G°cc,Bi
(21)
It is further assumed that the values of ∆G°cc,Ai and ∆G°cc,Bi depend linearly on the values of the fractions θA and θB, defined respectively by the ratios ΓA/Γm,A and ΓB/Γm,B, where ΓA and ΓB represent, respectively, the surface concentrations of the active elements A and B and Γm,A and Γm,B the corresponding monolayer surface concentrations. Therefore, we may write down the following equations:
∆G°cc,Ai ) -EAiθA ) -EAi(ΓA/Γm,A)
(22)
∆G°cc,Bi ) -EBiθB ) -EBi(ΓB/Γm,B)
(23)
In the above equations EAi and EBi represent the energies of lateral interactions corresponding to a deposited species (Ai or Bi) illustrated in the rhs of the model equilibria 1a-f. By combining eqs 2a,b,d,f,h, 8, 10, 12, 14, 16, 18, 20, and 22 the following equation is derived:
[Aj]IHP ) [Aj]b exp[-zAjFψIHP/RT]
(8)
[Bj]IHP ) [Bj]b exp[-zBjFψIHP/RT]
(9)
[OH-]IHP ) [OH-]b exp[-zOH-FψIHP/RT]
(10)
θ Ai
[H+]IHP ) [H+]b exp[-zH+FψIHP/RT]
(11)
(1 - θSOH2+)µi(1 - θSOH)Vi
[OH-]b-V ) 10V(14-pH)
(12)
exp -
[H+]b-V ) 10VpH
(13)
In the above equations ψIHP represents the Volta potential at the IHP. Following the usual thermodynamic procedure we write down the following two general equations drawn from the model equilibria 1a-1f:
µAi + ViµOH- ) µiµSOH2+ + ViµSOH + µAj
(14)
µBi + ViµH+ ) FiµSO- + ViµSOH + µBj
(15)
It is obvious that when the deposition takes place exclusively by adsorption or surface reaction, Vi and µi take, respectively, zero value and the above two equations are reduced to simpler expressions. The substitution of the values of the electrochemical potentials from eqs 2a-i into eqs 14 and 15 generates expressions where appear the differences in the standard state chemical potentials, as well as the differences in the electrochemical potentials.
[
)
] [ ] [ ] [ ]
∆G°cs,Ai
µiFφo Vi(14-pH) 10 × RT RT zAiFψIHP EAiΓA exp [A ] (24) exp RT Γm,ART j b exp
whereas by combining eqs 2b,c,e,g,i, 9, 11, 13, 15, 17, 19, 21, and 23 we derive the equation below:
θ Bi
) (1 - θSO-)Fi(1 - θSOH)Vi ∆G°cs,Bi zBiFψIHP FiFφo VipH exp 10 exp × exp RT RT RT EBiΓB [B ] (25) exp Γm,BRT j b
[
] [ ]
[ ] [ ]
Equations 24 and 25 describe the deposition of a, respectively, negatively and positively charged ionic species on the surface of an oxidic support. Inspection of the above equations shows that these may be combined into the following unique, more general, expression describing the deposition of an ionic species
11714 J. Phys. Chem., Vol. 100, No. 28, 1996
Bourikas et al.
j, negative or positive, to form a deposited species i on the surface of an oxidic support.
θi (1 - θSOH2+)µi(1 - θSOH)Vi(1 - θSO-)Fi
[
)
] [ ] [ ] [ ]
In this equation R ) 1 and β ) 1 for a negative species, whereas R ) 0 and β ) -1 for a positive one. Finally θi is defined as t µi t Vi t Fi Ciλi/(CSOH +) (CSOH) (CSO-) . 2 The values of Ei appearing in the above equation cannot be determined experimentally. Therefore, an effort was made to replace Ei by a function of the mean energy of the lateral interactions, E h . Intensive trial and error calculations performed concerning the deposition of tungstate species on the γ-alumina surface have shown that an excellent agreement between the experimental and calculated deposition isotherms is finally achieved on the assumption that the energy of the lateral interactions for a deposited species i is proportional to two factors:19 first to a “structural” factor bi and second to a “concentration” factor gi. The structural factor bi takes into account that the lateral interactions exerted between the deposited W(VI) species, through water molecules also located in the IHP, should increase with the number of the W-O bonds and, mainly, with the absolute value of their charge |zi|. To be specific, we assume that bi ) (number of W-O bonds) + 2|zi|. It should be noted that a double WdO bond is considered to correspond to two WsO single bonds. The concentration factor gi is assumed to be equal to 1/|log Ci|. The “initial” value of Ci can be calculated, at a given pH, as we shall see later. Thus we may write
(27)
where δ is the proportionality constant. On the other hand, the mean energy of the lateral interactions is related to the values of Ei through the following expression: n
E h )∑
(28)
where n represents the number of the kinds of the deposited species at a given pH. By combining eqs 27 and 28 we derive the following equation:
Ei )
biginE h n
(30)
n
Substitution of the Ei from eq 29 or eq 30 into eq 26 reduces the later into more convenient expressions, because these involve the experimentally determined mean energy of lateral interactions E h instead of Ei.
θi
(29)
bigi ∑ i)1 The study of deposition with respect to some other catalytically important systems (e.g., deposition of chromates or molybdates on titania3,4) has shown that it is sufficient to assume that the energy of the lateral interactions mentioned before is simply proportional to |zi|. In that case it may easily be demonstrated that
)
(1 - θSOH2+)µi(1 - θSOH)Vi(1 - θSO-)Fi
[
exp -
] [ [ ]
]
(µi - Fi)Fφo
∆G°cs,i
10Vi(R14-βpH) ×
[ ]
exp
RT RT biginE hΓ ziFψIHP exp [speciesj]b (31) exp n RT ΓmRT∑bigi i)1
θi
)
(1 - θSOH2+)µi(1 - θSOH)Vi(1 - θSO-)Fi
[
exp -
] [ [ ]
exp -
RT
ziFψIHP RT
10Vi(R14-βpH) ×
[ ]
exp
RT
]
(µi - Fi)Fφo
∆G°cs,i
exp
|zi|nE hΓ n
[speciesj]b (32)
ΓmRT∑|zi| i)1
Taking into account the eqs 3, 4, and 5, as well as the definition of θi, we may easily transform eqs 31 and 32 into the following eqs 33 and 34, respectively.
[
] [ [ ]
Ci ) λi-1 exp -
∆G°cs,i
exp
exp -
RT ziFψIHP RT
]
(µi - Fi)Fφo
10Vi(R14-βpH) ×
[ ] RT biginE hΓ
exp
n
×
ΓmRT∑bigi
i)1 f µi f Vi f (CSOH2+) (CSOH) (CSO-)Fi[speciesj]b
Ei
i)1 n
|zi|nE h |zi| ∑ i)1
∆G°cs,i (µi - Fi)Fφo Vi(R14-βpH) exp 10 × exp RT RT ziFψIHP EiΓ exp [speciesj]b (26) exp RT ΓmRT
Ei ) δbigi
Ei )
[
] [ [ ]
Ci ) λi-1 exp -
∆G°cs,i
exp
]
(µi - Fi)Fφo
(33)
10Vi(R14-βpH) ×
[ ]
RT RT |zi|nE hΓ ziFψIHP exp × exp n RT ΓmRT∑|zi| i)1
f µi f Vi f Fi (CSOH +) (CSOH) (CSO-) [speciesj]b (34) 2
In the above expressions we symbolize by f the free (uncovered by deposited species) surface groups. Derivation of an Approximate Equation Which Can Be Tested Experimentally. Although, as we shall see later, eqs 33 and 34 describe very well the experimental data for many systems studied so far,2-6,19,20 they cannot be used directly. There are two reasons for this. The first is that the product of the first four terms of the rhs of these equations is unknown
Deposition on Industrial Supports
J. Phys. Chem., Vol. 100, No. 28, 1996 11715
though it is constant at a given pH. We call this constant product Ki.
[
Ki ≡ λi-1 exp -
] [
]
∆G°cs,i (µi - Fi)Fφo Vi(R14-βpH) exp 10 (35) RT RT
The second reason is that the value of E h is also unknown. It is therefore necessary to adopt an approximate procedure in order h and then return to eq 33 or to determine the values of Ki and E 34 in order to calculate the values of Ci. In order to derive an approximate equation that can be tested experimentally, it is necessary to do the following approximations:
Ki involves the term exp(-ziFψIHP/RT)
(i)
h for any value of i Ei ) E
(ii)
θi
∑i
=
(1 - θSOH2+)µi(1 - θSOH)Vi(1 - θSO-)Fi [speciesj]b ) RjCeq
θ 1-θ
(iii)
(iv)
Concerning the last expression, it is assumed that the concentration of an ionic species j (containing the catalytically active element) in the bulk solution, [speciesj]b, is proportional to the total concentration of the active element in the solution at equilibrium (Ceq). Rj is a coefficient almost independent of the Ceq. Taking into account the above approximations we add all the eqs 26 (that is those for all the deposited species i formed) and derive the following equation:
[ ]
E hΓ θ )K h Ceq exp 1-θ ΓmRT
(36)
K h ) ∑KiRj
(37)
where
ij
Taking into account that θ ≡ Γ/Γm, where Γ and Γm represent, respectively, the surface concentration and the monolayer surface concentration of the active element, we may easily transform eq 36 into eq 38:
1 1 + ) Γ Γm
1
[ ]
K h ΓmCeq exp
E hΓ
(38)
ΓmRT
The values of Γ, Γm, and Ceq may be determined experimentally. Thus, the above expression may be tested directly. Intensive experimental work done by us in the last years has shown that eq 38 describes quite well the experimental data1,3,12-18 and this justifies the approximations done to derive this expression. A typical example is illustrated in Figure 1. This approximate expression is extremely useful for determining the values of K h and E h by fitting it to the experimental data though it is not informative concerning the details of the deposition mechanism. Assumptions for Establishing Relationships between the h can be used directly Ki Values. The so-determined value of E when applying the expression 33 or 34. On the other hand, the so-determined value of K h is necessary for calculating the values of Ki required to apply the two expressions mentioned above. However, in order to determine the values of Ki it is necessary to reduce eq 37 into a simpler expression containing only two
Figure 1. Variation of 1/Γ vs 1/Ceq exp(E h Γ/ΓmRT) for the deposition of Mo(VI) species on the γ-alumina surface. The solid line represents the values calculated using eq 38.
Ki values in its rhs. This can be done by establishing some relationships between the various Ki values. The establishment of these relationships is actually based on several reasonable assumptions:2-6,19,20 (i) The Ki values corresponding to the reaction of different ionic species of the same active element with the neutral SOH groups of the same support are identical. (ii) The Ki values corresponding to the adsorption of different ionic species of the same active element on one SOH2+ or SOgroup of the same support are interrelated linearly. Depending on the nature of both the deposited active ion and the support, the coefficient of these linear relations may take different values. For instance, they may be assumed to be equal to 1 or equal to the ratios of the corresponding protonation constants of the ionic species to be deposited. Moreover, they may be assumed to take an intermediate value.19 (iii) The Ki values corresponding to the adsorption of different ionic species of the same active element on two adjacent SOH2+ or SO- groups are also interrelated linearly. The coefficients of these linear relations are equal to the square of the corresponding ones for the adsorption on a single SOH2+ or SO- group. (iv) The value of Ki corresponding to the deposition of one ionic species on two adjacent SOH2+, SOH, or SO- groups of a given support is equal to the square of the corresponding Ki taken for a single SOH2+, SOH, or SO- group. (v) The value of Ki concerning the deposition of an ionic species on a site formed by a neutral surface hydroxyl adjacent to either a protonated or deprotonated one (respectively, HOSOSOH2+ and HOSOSO-) of a support is equal to the product of the corresponding adsorption and reaction constant on the single SOH2+, SOH, or SO- group. Taking into account the above assumptions, eq 37 is reduced into a simpler expression:
K h ) f(KA,KR,Rj)
(39)
where KA and KR represent, respectively, the constant for the adsorption and the reaction of the simplest ionic species in the impregnating solution (e.g., WO42-, MoO42-, Co2+, Ni2+, etc.) on/with a single SOH2+, SOH, or SO- group of the support surface. Due to the second assumption and depending on the nature of the system under study, eq 39 takes various forms2-6,19,20 which are illustrated in Table 1. These expressions are supported on the assumption that all the species illustrated in
11716 J. Phys. Chem., Vol. 100, No. 28, 1996
Bourikas et al.
TABLE 1: General Expressions of the Function K h ) f(KA,KR,rj) Established for Some Catalytically Important Systems
TABLE 2: Parameters Required for the Application of SURFEQL to the Proposed Model parameter
system
expression
Co2+/γ-Al2O3 Ni2+/γ-Al2O3 MoVI/γ-Al2O3 CrVI/γ-Al2O3
K h ) 2KA + 2KR K h ) 2KA + 2KR K h ) 2(R1 + R2)KA + R1KR K h ) (2R1 + 2R2 + R3)KA + (R1 + R2)KR2 + (R2 + R3)KR + (R1 + R2)KAKR K h ) (R1 + 12.59R2 + 6.31 × 104R3 + 6.17 × 103R4 + 6.03 × 102R5 + 58.88R6 + 1.26 × 106R7 + 0.40R8)KA + (1.59 × 102R1 + 3.98 × 109R3 + 3.81 × 107R4 + 3.64 × 105R5 + 3.47 × 103R6 + 1.59 × 1012R7 + 0.16R8)KA2 + (R1 + R2 + R3 + R4 + R5 + R6 + R7 + R8)KR + (R1 + R2 + R3 + R5 + R6 + R7 + R8)KR2 + (R1 + 6.31 × 104R3 + 6.17 × 103R4 + 6.03 × 102R5 + 58.88R6 + 1.26 × 106R7 + 0.40R8)KAKR K h ) 2(R1 + 3.16R2)KA + 2(R1 + 9.9856R2)KA2 + 2R1KR + 2(R1 + R2)KR2 K h ) 2(R1 + 0.1R2 + 0.1R3)KA + 2(R1 + 0.01R2)KA2 + 2(R1 + R2 + 0.1R3)KR + 2(R1 + R2)KR2 + 2(R1 + 0.1R2)KAKR
WVI/γ-Al2O3
MoVI/TiO2 CrVI/TiO2
the rhs of the postulated deposition mechanism (eqs 1a-f) are formed in all pH values. But this is not usually the case. Therefore, each of these expressions becomes simpler at a given pH by neglecting the terms that correspond to the ionic species not formed in that pH. Moreover, on the basis of the assumptions mentioned before, expressions of the form Ki ) f(KA,KR,Rj) are derived for the adsorption and reaction equilibria, respectively. It is therefore, obvious that, once the coefficients Rj are known, one may select a pair of KA and KR and then a set of Ki values which satisfy the proper expression for the function 39 and the experimentally determined value of K h. Calculations in the Impregnating Solution. The main purpose of the calculations in the bulk solution is the determination of the coefficients Rj, which relate the concentration of the ionic species j in the bulk solution, [speciesj]b, with the total concentration of the active element in the solution at equilibrium (Ceq). The values for these coefficients are necessary in order to apply the proper expression for the function 39. In order to do that, it is necessary to get some useful parameters by running SURFEQL, an interactive code for calculating equilibria.21 The following equilibria take place in the impregnating solution: KW
H2O T Hb+ + OHb-
(40)
total surface sites density deprotonation const of the SOH2+ grps deprotonation const of the SOH grps constants of equilibria 42 constant of equilibrium 41 total Aj (Bj) concn total NH4+ (NO3-) concn pH specific surface area solid concn ionic strength inner capacitance outer capacitance
symbol
units sites nm-2
Ns kint 1 kint 2 Kj KNH3 [Aj]t, [Bj]t [NH4+]t, [NO3-]t pH SSA SC I C1 C2
mol dm-3 mol dm-3 m2 g-1 g dm-3 mol dm-3 F m-2 F m-2
calculating procedure is repeated until the following mass balance equations in the bulk solution are satisfied:
[NH3] + [NH4+]b ) [NH4+]t
(43)
∑j dj[speciesj]b ) [active element]t
(44)
where by the subscript t we symbolize total concentration and by dj the number of atoms of the active element in a given ionic species j. Thus, in this step the concentration of each species j and the values of Rj (using the aforementioned [speciesj]b ) RjCeq approximation) are calculated for each pH. Calculations in the Suspension and Elucidation of the Deposition Mechanism. The calculations in the suspension involve various steps. (i) The values of K h and E h at a given pH are calculated using eq 38 and the experimentally determined values for Γ and Ceq. (ii) A pair of values for KA, KR is selected which satisfy the proper general expression for the function K h ) f(KA,KR,Rj) similar to those illustrated in Table 1. (iii) Using the relations established for the functions Ki ) f(KA,KR,Rj), the values of Ki are calculated and then the values h Γ/ΓmRT]10-Vi(R14-βpH), which correfor the amount Ki exp[E sponds to the selected pair of KA, KR, are also calculated. (iv) The values for the aforementioned amount as well as the values of the parameters listed in Table 2 are introduced in the SURFEQL program. Most of these parameters are determined experimentally (pH, SSA, SC, and I); some others are taken from the literature (Ns Kj and KNH4+). C1 and C2 are adjustable parameters. The deprotonation constants kint 1 and kint 2 for the equilibria
KNH3
NH3 + H3+O T NH4+ + H2O
(41)
kint 1
SOH2+ 798 SOH + Hs+, kint 1 )
[Hs+][SOH] [SOH2+]
(45)
Kj
speciesj T speciesj+1
(42)
The second equilibrium takes place because NH4NO3 is used as background electrolyte. To run SURFEQL for the bulk solution we feed the program with the constants KW, KNH3, and Kj taken from the literature, the total concentration of the active element and NH4+ ions, and a guess value for the concentration of the simplest ionic species to be deposited (e.g., MoO42-). The program then calculates the concentrations of the various ionic species j and the concentration of the NH4+ ions using eqs 41 and 42. The
and kint 2
SOH 798 SO- + Hs+, kint 2 )
[Hs+][SO-] [SOH]
(46)
which according to the two-pK/one-site model are responsible for the charging of the support surface are determined using potentiometric titrations in the absence of the ionic species to be deposited in the impregnating suspension.7,22,23 The symbol Hs+ appearing in the above equations denotes hydrogen cations on the surface of the oxidic support.
Deposition on Industrial Supports
J. Phys. Chem., Vol. 100, No. 28, 1996 11717
(v) Starting with these initial values, SURFEQL solves the system of the mass action law and mass balance eqs 33 (or 34) and 40-44, the mass action law eqs 45 and 46, and the following mass and charge balance equations: f + f f TNS ) CSOH + CSOH + + CSO- + [SO ‚‚‚NH4 ] + 2
∑i [Rµi + Vi + (1 - R)Fi]Ci
(47)
TNH4+ ) [NH4+]b + [NH3]b + [SO-‚‚‚NH4+] + [NH4+]IHP (48) TA ) ∑dj[Aj]b + ∑dj[Aj]IHP + ∑diCi
(49)
TB ) ∑dj[Bj]b + ∑dj[Bj]IHP + ∑diCi
(50)
j
j
j
i
j
i
+ f f CSOH + - CSO- - [SO ‚‚‚NH4 ] + ∑(µi - Fi)Ci ) 2 i
C1[ψo - ψIHP]SSA‚SC/F (51) [SO ‚‚‚NH4 ] + ∑ziCi ) -
+
i
[C1(ψIHP - ψo) + C2(ψIHP - ψd)]SSA‚SC/F (52) C2(ψd - ψIHP) ) -(8eeoRTI)1/2 sinh(Fψd/2RT) (53) Equations 47-50 are the mass balance expressions for the surface hydroxyls, the NH4+ ions, and the active element (A or B, giving negative or positive ionic species) in the suspension, respectively. Equations 51 and 52 represent the charge balance in the surface and in the IHP, respectively. Finally, eq 53 expresses the charge in terms of both the capacitance and the Gouy-Chapman theory. In the above equations by TNS, TNH4+, TA, and TB we symbolize, respectively, the total concentrations of the surface hydroxyls, the ammonium ions, and the A and B active elements. ψd, I, e, and eo denote, respectively, the Volta potential at the shear plane of the electrical double layer, the ionic strength of the impregnating solution, and the dielectric constants of the medium and vacuum. Closing with this calculation step it should be stressed that using eq 33 or 34 the program reads the amount exp[E h Γ/ΓmRT] instead of the corresponding one involved in these equations. The procedure described in the previous steps allows the calculation of the parameters illustrated in Table 3. Among these parameters the most important is Ci, namely, the concentration of a species i formed on the surface of an oxidic support, through the equilibrium i, at a given set of impregnating parameters. From Ci one may easily calculate the value of the corresponding surface concentration of the active element due to the formation of the deposited species i, Γi and then the total surface concentration of the active element, Γ. Therefore, the Γ vs Ceq deposition isotherm may be calculated and compared with the corresponding experimental one. The calculating procedure is repeated for various values of KA and KR satisfying eq 39 until an optimum pair of KA and KR is achieved. However, even for this pair the agreement usually achieved between the experimental and model deposition isotherms (Γ vs Ceq) is not sufficiently good. However, now we know which equilibria among those of the postulated mechanism (eqs 1a-f) contribute to a significant extent to the whole deposition at a given pH. Therefore, in the subsequent steps, only these equilibria are considered by eliminating from
TABLE 3: Parameters or Variables Derived from the Application of SURFEQL to the Proposed Model parameter of variable
symbol
units
surface charge density charge density at the IHP charge density at the OHP surface potential potential at the IHP potential at the OHP equilibrium concn of H+ equilibrium concn of species j equilibrium concn of NH4+ (NO3-) equilibrium concn of SOH equilibrium concn of SOH2+ equilibrium concn of SOequilibrium concn of the species illustrated in the rhs of equilibria 1
σo σ1 σd ψo ψIHP ψd [H+]b [speciesj]b [NH4+]b, [NO3-]b f CSOH f CSOH + 2 f CSOCia
C m-2 C m-2 C m-2 V V V mol dm-3 mol dm-3 mol dm-3 mol dm-3 mol dm-3 mol dm-3 mol dm-3
a From these values we may easily calculate the values of the surface concentrations of the active element due to the formation of the deposited species i, Γi (µmol m-2 or atoms nm-2) and then the value of the total surface concentration of the active element, Γ, expressed in the same units.
the appropriate expressions of Table 1 the terms relative to the equilibria with negligible contribution. Thus, a general expression like those illustrated in Table 1 is reduced to a simpler expression. In view of the above in the next step we start with the optimum value of KA and recalculate the value of KR using the modified function K h ) f(KA,KR,Rj). This allows the recalculation of Ki values. On the basis of these values we calculate the amount n
Ki exp[|zi|nE h Γ/ΓmRT∑|zi|] i)1
for the equilibria which practically contribute to the whole deposition at a given pH. This is done in most of cases. However, when eq 33 should be used instead of eq 34, we calculate the amount n
h Γ/ΓmRT∑bigi] Ki exp[biginE i)1
instead of the aforementioned one. The required values of gi ≡ 1/[log Ci] can be now calculated using the initial Γi values. The calculating procedure is repeated by changing the value of KA. After few runs an excellent agreement between the calculated and experimental deposition isotherms Γ vs Ceq is achieved in most cases.2-6,19,20 A typical example is illustrated in Figure 2. In this point it should be stressed that there is only one pair of KA, KR values and a unique set of deposition equilibria, among those initially postulated, for which an excellent agreement can be achieved. The achievement of this excellent agreement strongly suggests that the values of Γi for each of the species formed on the support surface, used for calculating the values of Γ, are correct. Therefore, in this step the deposition isotherms for each of the species mentioned above are, moreover, calculated (see for example Figure 2). Following the procedure stated so far, one may find out the equilibria through which the deposition occurs as well as the concentration of each species formed on the support surface at a given set of values for the impregnating parameters (concentration of active ion in the bulk solution, pH, temperature, ionic strength). Therefore, the deposition mechanism has been elucidated.
11718 J. Phys. Chem., Vol. 100, No. 28, 1996
Figure 2. Variation of the surface concentration of Cr(VI) with equilibrium Cr(VI) concentration: experimental (0) and calculated (×) isotherms for the total Cr deposition. The symbols b, 2, O, and 4 correspond to the calculated isotherms for the Cr(VI) deposition through adsorption of one HCrO4- ion per site created by one AlOH2+ group, through adsorption of one Cr2O72- ion per site created by one AlOH2+ group, through reaction of one HCrO4- ion with one AlOH group, and through reaction of one Cr2O72- ion with one AlOH group, respectively. pH ) 4.0, T ) 25 °C and ionic strength equal to 0.1 mol dm-3 NH4NO3.
Testing of the Selected Deposition Mechanism. The soselected deposition mechanism may be tested using two independent methodologies. The first is based on the fact that the ability of the support to adsorb hydrogen ions is influenced by the presence in the bulk solution of the species which contain the catalytically active ions. In fact, intensive experimentation done by us in the last years1 has shown that the amount of hydrogen consumed, Hc+, on the support surface as a function of the pH is different in the absence and presence of the species j in the impregnating solution. It may be expected that the intensity of this effect should depend on the deposition mechanism. The variation of (Hc+ (in the presence of the species to be deposited) - Hc+ (in the absence of the species to be deposited)) ) ∆Hc+ with the pH may be determined by potentiometric titrations. On the other hand, this variation may be calculated using SURFEQL, on the basis of the selected deposition mechanism, because ∆Hc+ ) ∆([SOH2+] - [SO-])t, where ∆ denotes the difference of the amount in the parentheses in the presence and absence of the species j in the impregnating solution. The subscript t denotes total (free plus covered) concentration of the indicated surface groups. A very good agreement is usually achieved between the experimental and calculated curves, provided that only the equilibria involved in the selected mechanism are taken into account.2-6,19,20 A typical example is illustrated in Figure 3. Following the second methodology to test the selected deposition mechanism we calculate, using SURFEQL and taking into account only the equilibria involved in this mechanism, the variation with the pH of the Volta potential at the shear plane of the electrical double layer, ψd. This is assumed to be equal to the ζ potential. On the other hand, the variation of this parameter with the pH may be determined by electrophoresis in the presence of the species j in the impregnating solution. The achievement of an agreement between the experimental and calculated ζ potential vs pH curves corroborates the selected deposition mechanism. A typical example is illustrated in Figure 4.
Bourikas et al.
Figure 3. Variation with pH, in the differences (in the presence and absence of W(VI) species j in the impregnating suspension) of the hydrogen ions consumed on the surface of γ-alumina, ∆Hc+ (0), as well as of the total protonated minus deprotonated surface hydroxyls, ∆(AlOH2+ - AlO-) (×). T ) 25 °C and ionic strength equal to 0.1 mol dm-3 NH4NO3.
Figure 4. Variation of the ζ-potential of γ-Al2O3, with pH, in the presence of Co2+ (A) or Ni2+ (B) ions. 0 denote experimental and 4 calculated values. Measurements were performed at 25 °C and ionic strength equal to 0.1 mol dm-3 NH4NO3.
Conclusions The methodology described in the present work unifies the methodologies followed so far in order to investigate the mechanism of deposition in some catalytically important systems into a general, powerful, tool for the elucidation of the deposition mechanism. Knowledge of the deposition mechanism permits the precise tailoring of the preparation, by adjusting the impregnation parameters to their optimal values, in order to obtain a supported catalyst with the desired characteristics. This methodology is based on the two-pK/one-site and triple-layer models (for the charging mechanism of the surface of the support and for the electrical double layer developed between the surface of the support particles and the impregnating solution, respectively) and exploits the experimental data of the adsorption isotherms at various pH of the impregnation suspension. Starting from a quite general, “postulated”, deposition mechanism, comprising all equilibria that could possibly take
Deposition on Industrial Supports place at the “support/impregnation solution” interface, the application of this methodology leads to the “proposed” deposition mechanism, namely, the set of equilibria that actually take place, the kind of deposited species formed, their relative concentrations, and their dependence from the impregnating parameters (pH, concentration of the precursor, ionic strength, temperature). Due to the complexity of the system under investigation (support plus impregnating solution; deposited species being located at the solid-liquid interface), the methodology is inevitably based on several simplifying assumptions. However, the excellent agreement achieved between the theoretical values of some support/electrolyte interface parameters (calculated on the basis of the deposition mechanism revealed by applying this methodology) with the corresponding experimental values (determined by potentiometric titrations and microelectrophoresis) demonstrates, both the validity of the proposed deposition mechanism and the merit of the present methodology. References and Notes (1) Karakonstantis, L.; Kordulis, Ch.; Lycourghiotis, A. Langmuir 1992, 8, 1318. (2) Bourikas, K.; Spanos, N.; Lycourghiotis, A., to be published in Langmuir. (3) Spanos, N.; Slavov, S.; Kordulis, Ch.; Lycourghiotis, A. Langmuir 1994, 10, 3134. (4) Spanos, N.; Lycourghiotis, A. J. Chem. Soc., Faraday Trans. 1993, 89, 4101. (5) Spanos, N.; Lycourghiotis, A. J. Catal. 1994, 147, 57. (6) Spanos, N.; Lycourghiotis, A. Langmuir 1994, 10, 2351.
J. Phys. Chem., Vol. 100, No. 28, 1996 11719 (7) Vordonis, L.; Koutsoukos, P.; Lycourghiotis, A. J. Catal. 1986, 98, 296. (8) Contescu, C.; Hu, J.; Schwarz, A. J. J. Chem. Soc., Faraday Trans. 1993, 89, 4091. (9) Contescu, C.; Jagiello, J.; Schwarz, A. J. Langmuir 1993, 9, 1754. (10) Contescu, C.; Contescu, A.; Schwarz, A. J. J. Phys. Chem. 1994, 98, 4327. (11) Contescu, C.; Contescu, A.; Schramm, G.; Sato, R.; Schwarz, A. J. J. Colloid Interface Sci. 1994, 165, 66. (12) Spanos, N.; Vordonis, L.; Kordulis, Ch.; Lycourghiotis, A. J. Catal. 1990, 124, 301. (13) Spanos, N.; Vordonis, L.; Kordulis, Ch.; Koutsoukos, P.; Lycourghiotis, A. J. Catal. 1990, 124, 315. (14) Vordonis, L.; Koutsoukos, P.; Lycourghiotis, A. Colloids Surf. 1990, 50, 353. (15) Spanos, N.; Kordulis, Ch.; Lycourghiotis, A. In Preparation of Catalysts V; Poncelet, G., Jacobs, P., Grange, P., Delmon, B., Eds.; Elsevier: Amsterdam, 1991; p 175. (16) Vordonis, L.; Spanos, N.; Koutsoukos, P.; Lycourghiotis, A. Langmuir 1992, 8, 1736. (17) Spanos, N.; Matralis, H. K.; Kordulis, Ch.; Lycourghiotis, A. J. Catal. 1992, 136, 432. (18) Spanos, N.; Lycourghiotis, A. Langmuir 1993, 9, 2250. (19) Karakonstantis, L.; Bourikas, K.; Lycourghiotis, A. J. Catal., in press. (20) Bourikas, K.; Spanos, N.; Lycourghiotis, A., to be published in J. Colloid Interface Sci. (21) Faughnan, J. SURFEQL. An InteractiVe Code for the Calculation of Chemical Equilibria in Aqueous Systems; W. M. Keck Laboratories 13878, California Institute of Technology, Pasadena, CA, 1981. (22) Vordonis, L.; Koutsoukos, P.; Lycourghiotis, A. J. Catal. 1986, 101, 186. (23) Akratopoulou, K.; Vordonis, L.; Lycourghiotis, A. J. Chem. Soc., Faraday Trans. 1986, 82, 3697.
JP960548L
