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Predicting points of zero charge of oxides and hydroxides
Predicting Points of Zero Charge of Oxides and Hydroxides ROE HOAN YOON, 1"* TALAT SALMAN,t AND GABRIELLE DONNAY$ *Ore Processing Laboratory, Canada Center for Mineral and Energy Technology, Ottawa, Ontario, Canada; tDepartment of Mining and Metallurgical Engineering and *Departrnent of Geological Sciences, McGill University, Montreal, Quebec H3A 2A7, Canada Received July 10, 1978; accepted October 9, 1978 Pauling's electrostatic valence principle has been applied to describe the surface-charging mechanism of oxides in an aqueous environment. This approach has led to the development of an equation with which one can predict the points of zero charge (PZC) of oxides and hydroxides from crystallographic data. The equation proposed in the present work is an improved version of Parks' PZC equation. The improvements are the following: (i) The equation does not incorporate correction terms to take the cation coordination numbers into account; (ii) the PZC of a complex oxide can be predicted directly from crystallographic data instead of from "assumed" PZCs of its component oxides; and (iii) one can use the mean metal-oxygen bond distance of a crystal instead of the ionic radii tabulated by Parks, which are not consistent with the up-to-date values. INTRODUCTION
It has been well established that an oxide or a hydroxide suspended in an aqueous environment can acquire its surface charge by adsorbing H ÷ or OH- ions. The pH at which the solid has no net surface charge is defined as the point of zero charge (PZC). There are two methods of predicting PZCs of simple oxides and hydroxides, One is to use the minimum solubility theory (1, 2), according to which a PZC should be identical to the isoelectric point of the aqueous solution [IEP (aq)] suspending the solid. The IEP (aq), which is often found at the pH of minimum solubility of the solid, can be determined by constructing the solubility diagram. The other method of predicting a PZC is to use Parks' equation (2, 3), which is essentially a function of (Z/R), where Z is the formal charge of the cation and R t Present address: Associate Professor, Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061. To whom correspondence should be addressed.
is the sum of the cationic radius (r+) and the oxygen diameter (2.8 A). The use of Parks' equation may be advantageous over the use of minimum solubility theory in that the crystallographic data, such as Z and r+, are readily available for most oxides/hydroxides while the thermodynamic data required to construct the solubility diagrams are limited to only a number of solids. There are difficulties, however, in using Parks' PZC equation. First, the ionic radii that he tabulated and that were used in formulating and testing the equation differ significantly from those that are more widely accepted. For example, the ionic radii of ViAp+ and ivsi4+ [the prescript in small Roman numerals denotes the coordination number (CN)] used by Parks are 0.85 and 0.80 A, respectively, while Shannon (4) reported them to be 0.535 and 0.26 A, respectively. Second, Parks' equation introduces different correction terms, depending on the CN and the hydration states of the solids. An improved version of Parks' PZC equation is now proposed. The new equation is
483
Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
0021-9797/79/090483 - 11$02.00/0 Copyright© 1979by AcademicPress,Inc. All rightsof reproductionin any formreserved.
484
YOON ET AL.
developed by utilizing Pauling's electrostatic valence principle (5), which has been found to be useful in describing the charge balance of the ions in the surface layer of a crystal. THEORY A. A MODEL FOR SURFACE-CHARGING MECHANISMS
The bond valence (v) was defined by Pauling as the formal charge of a cation divided by the CN. He enunciated the electrostatic valence principle by which the sum of bond valences reaching an anion is equal to the charge of the anion. This principle in extended form has been put to many uses recently (6-8) in structure determinations of crystals by X ray. Pauling's principle is often called the principle of local neutralization of charge since it is an expression of the tendency of ions in the interior of a crystal to surround themselves with neighbors of opposite signs, so that the charges are neutralized locally. However, the charges of ions exposed on the surface of a crystal are not balanced and may contribute to the surface charge of the solid suspended in an aqueous medium. The charging mechanism of oxides and hydroxides is generally ascribed to the hydrolysis of surface metal ions or to the protonation of surface 02-/ OH- ions (1-3). Pauling's principle may be useful in describing these surface reactions. Choi and Oh (9) utilized it first in explaining the PZC differences among aluminum silicate polymorphs. Let us consider the oxygen atoms on the surface of an oxide crystal randomly fractured in a vacuum. If such a crystal is immersed in water, the oxygen ions which present broken (or unsatisfied) bonds to the aqueous phase will be unstable and, hence, may accept protons to become OH- and/or H20 species. A broken bond, although it is not physically tangible, may be considered to represent a surface force which tries to complete a bonding of one type or another Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
depending on the environment. Then, it might be said that the oxygen ions that have the maximum possible number of broken bonds are most unstable or most susceptible to protonation. Thus, when the number of H ÷ ions in solution is limited, the protonation will occur preferentially on those oxygens that have the maximum number of broken bonds (or the minimum number of satisfied bonds). These are the ones that have the so-called "dangling bonds"; i.e., the CN of such oxygen is unity. The protonation of a danglingly bonded oxygen may be represented by the reaction M - O tz-~)- + 2H + ~ M~+-OHz,
[1]
in which M is the metal ion on the surface layer and v the bond valence reaching the oxygen ion. Assuming that none of the oxygen ions in the coordination polyhedron around M are protonated, the total strength of the bond valence which the danglingly bonded oxygen receives is v. Therefore, the oxygen on the left-hand side of Eq. [1] has an unbalanced charge of -(2 - v), which may be considered the effective charge of the negative site M - O <2-~')-. The danglingly bonded oxygen can take up a maximum of two protons to become a coordinated water molecule, which should give an unbalanced charge of +v to M. The positive site may then be represented by M~+-OH2. One may question the existence of the bare oxygen ion in the negative site M - O ~2-~-. However, this may be considered thermodynamically equivalent to M - ( O H h (2-~)- or to M - O H ~l-v)- . . . OH-. Equation [1] represents an equilibrium at or near the PZC, at which the protonation is most likely to be limited to the danglingly bonded oxygen. However, if the pH is considerably lower than the PZC, the protonation may occur on other oxygens around M which have more than one unbroken bond per oxygen. In this case, the effective charge of the positive site could become larger than + v depending on the total number of oxygens protonated around M. If all the oxy-
PREDICTING POINTS OF ZERO CHARGE gens in the coordination polyhedron around M are protonated, the metal ion will leave the surface and enter the solution as a hydrated metal ion and/or as a hydrated hydroxo complex. In this respect, the surfacecharging mechanism represented by Eq. [1] may be viewed as an incipient dissolution process of the solid. This view is perhaps supported by the fact that the minimum solubility theory (1, 2) can predict the PZCs of many simple solids. Equation [1] may be compared with the widely accepted charging mechanism, M - O - + 2H + ~- M-OH2 +,
[2]
which was used by Parks in deriving his PZC equation. Equation [2] suggests that the effective charges of the positive and negative sites are + 1 and - 1 , respectively, regardless of Z, CN, and pH, which distinguishes it from Eq. [1]. Another difference between the two equations is that the center of a positive charge is M in Eq. [1] while Eq. [2] implies that it is one of the protons of the coordinated water molecule. The implication of Eq. [1], that the metal ions in the surface layer are the locus of positive surface charge, can be supported by the observation that the charge of a hydrated metal ion in solution resides on the ion itself, but not on any of the protons of the coordinated water molecules. B . D E V E L O P M E N T OF P Z C
EQUATION
(a) Simple Oxides
The total free energy change of Eq. [1] or [2] can be considered to be made up of electrical and chemical contributions: AG ° = AG°el + AG°ch.
[3]
In deriving his PZC equation, Parks (2) assumed that Eq. [2] involves primarily the electrical energy gained by the approach of 2H + to M - O - . AG°e~ was then taken to he the sum of energy gained by the approach of the protons toward the oxygen of charge - 2 and the energy spent in moving the pro-
485
tons against the surface metal ion of charge +Z. Since the equilibrium O - 2 H distance was taken to be a constant (1.4/~) for all oxides, AG°elas calculated by Parks was effectively a function of (Z/R), R being the linear M - O - 2 H distance. A AG°el calculation as such assumes that the ions in the M - O - 2 H array are isolated from the rest of the surface. However, it is more realistic to include at least those oxygen ions that are within the first coordination sphere of M. There are CN - 1 other oxygens to be considered in addition to the danglingly bonded one. The attractive energies between these oxygens and the protons under consideration can have a significant effect in determining AG°~I. The calculation of AG°~, which takes into account all the ions within the coordination polyhedron around M, is not difficult for a given crystal if the interionic distances and bond angles are accurately known. However, it is virtually impossible to obtain a generalized formula for AG°~ that is applicable for solids of different crystal structure with a minimum number of parameters. The problem may be resolved by utilizing the surface-charging mechanism represented by Eq. [1]. In calculating AG°el, one may be able to consider that the M~+-O-2H array is isolated from the rest of the surface if M is given an effective charge of v. This may be a simplification that can account for the potential fields exerted by the CN - 1 other oxygens around M being canceled out by the positive charge of Z - v. AG°~ gained by the approach of 2H + to the Mv+-O2- site may be calculated by assuming as a first approximation that each ion is a point-charge separated from other ions by the equilibrium distances as shown in Fig. I. The two hydrogen ions are treated as a doubly positive entity. The free energy change involved is then (2) AG °
=
2ZHZo Ne2 2ZHvNe 2 + ~- AG°ch ¢lr ~2L
= - 2 . 3 R T log K,
[4]
Journal of Colloid and Interface Science, Vol. 70, No. 3, July.1979
486
YOON ET AL.
and B can be determined properly by using Eqs. [9] and [ 10], respectively. For practical purposes, /~ may be represented by the mean M - O bond length at the interior of a crystal and r may be taken to be 1.01/~, which is the O - H distance in ice (10, p. 269) and is close to the O - H distances in water, hydroxides, and hydrated solids ( l l , 12). L"
L
(b) Complex Oxides
FIG. 1. A model o f positive site, Mv+-OH~, on oxide surface.
in which ZH = 1 and Zo = 2 are the formal charges of the subscript ions, N is Avogadro's number, e is the electronic charge, and ~j and ~2 are the effective dielectric constants. The equilibrium constant K of Eq. [1] is K =
[Mv+-OHz] , [M-O(~-v)-][H+]Z
[5]
assuming unit activity coefficients, which at the PZC becomes K =
(2-
l
1
2
[6]
since (2 - v) [ M - O <2-v)-] = v[Mv+-OH2] if v < 2. Taking the logarithms of Eq. [6], l o g K = log ( ~ ---~) + 2PZC.
[7]
By substituting Eq. [7] into Eq. [4] one can obtain for PZC the expression 1
PZC = A - B
2e 2
AG°ch
2.3kT¢lr
4.6kT
,
[11]
where K -
R T ~K , F 47r
[12]
in which PZC~ is the PZC of the component oxide i,f~ the atomic fraction on the surface, o.l the intrinsic structural charge, e the appropriate dielectric constant, and K the reciprocal thickness of the electrical double layer around the solid; R, T, and F have the usual meanings. Examples of nonzero values of o-i are the basal planes of micas and clay minerals (13). Equation [11] suggests that, if o'i = 0, the PZC of a complex oxide is simply the weighted average of PZCis. Parks (3) used " a s s u m e d " PZCi values in predicting PZCs of complex oxides with Eq. [11]. Instead, one may substitute Eq. [8] into Eq. [11] to obtain a theoretical PZC equation, n v ~fi(--t i=1 \ L / i
[9] --
e 2
B - - 2.3kT~2
PZC = o--2 + ~ f~PZC~, K i=l
PZC = o.i --+A-B K
where A-
For the PZC of a complex oxide containing n distinct component oxides, Parks (3) showed that
[10]
Equation [8] allows one to calculate the PZC of an oxide from v and L ( = L + r), if A Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
Ef~log
2 ~=~
~
v
/~
,
[13]
so that a PZC of a complex oxide can be predicted directly from crystallographic data if o-i, A, and B are known. One can best interpretf~ of Eq. [13] to be the fraction
487
PREDICTING POINTS OF ZERO CHARGE
of oxygens that are danglingly bonded to the surface metal ion i. DISCUSSION
In predicting the PZC of a simple oxide or a hydroxide with Eq. [8], the knowledge of A and B is a prerequisite. It is unfortunate, however, that the values of ~1 E2, and AG%h, which are required to determine A and B (see Eqs. [9] and [10]), are difficult to evaluate at present. Thus, an assumption has been made that A and B are constants within limits for most oxides and hydroxides, which would allow them to be determined from reliable experimental PZC values. Note, however, that AG°ehs for most transition metal oxides and hydroxides are larger than those of non-transition metal compounds due to the crystal field stabilization energy (CFSE) (2, 3). Hence, it is neces-
sary to make appropriate corrections for CFSE, when the constants A and B are determined by using the experimental PZCs of solids of zero CFSE. A . SIMPLE OXIDES/HYDROXIDES OF ZERO C F S E
From the experimental PZCs of a-A1203 [pH 9.1 (14)] and MgO [pH 12.4 (15)], the constants A and B of Eq. [8] have been determined so that it may be written as:
(L/) The PZC values of a-A1203 and MgO are
TABLE I Calculated and Experimental PZCs of Oxides/Hydroxides of Zero CFSE a CN
PZC
Sample
Z
M
(O.OH)
(A)
v
Calculated
A B C D E F
MgO Mg(OH)2 La2Oa ZrO2 BeO ZnO
2 2 3 4 2 2
6 6 6 8 4 4
6 3 4 4 4 4
2,106 2.06 2.44 2,26 1,65 1,978
1/3 I/3 1/2 1/2 1/2 1/2
0.1070 0.1086 0.1449 0.1529 0.1880 0.1673
G
Zn(OHh
2
4
2
1.95
1/2
0.1689
9.22
H
a-A1203
3
6
4
1.91
1/2
0.1712
9.10
9.1
1 J K
AI(OH)3* o~AlO(OH) y-AIO(OH)
3 3 3
6 6 6
2 ---
1.89 1.935 1.913
1/2 1/2 1/2
0.1724 0.1698 0.1711
9.03 9.17 9.10
5.0-3.2 7.7 7.5
12.40 12.31 10.49 12.07 8.20 9.30
Experimental 12.4 +_ 0.3 -12 10.4 10-11 10.2 9.3 7.8
L
a-Fe2Oa
3
6
4
2.03
1/2
0,1645
9.45
9.04
M N
y-FeO(OH) a-FeO(OH)
3 3
6 6
-~
2.00 2.04
1/2 1/2
0.1661 0.1639
9.37 9.48
7.4 6.7
O P Q R S T U V
ThO2 PuO~ Y2Oa HgO SnO2 TiO~ WOa SiO~
4 4 3 2 4 4 6 4
8 8 6 6 6 6 6 4
4 4 4 6 3 3 2 2
2.425 2.336 2.28 2.57 2,053 1.969 1.927 1.61
1/2 1/2 1/2 1/3 2/3 2/3 1 1
0.1456 0.1492 0.1520 0.09311 0.2177 0.2245 0.3405 0.3817
10.46 10.27 10.12 13.14 6.71 6.35 0,34 -1.85
9.0-9.3 9.0 9.0 7.3 6.6 6.7 -0.5 1,8
" Italics are for H-bonded solids. Z, cationic charge; CN, coordination number; M, metal ion; v, bond balance;/,, mean M-(O,OH) distance, L = L + r, r = 1.01 A; *, natural gibbsite. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
488
YOON ET AL. 14
P
i
I
~. ~, '%
12
.._10
I
"ml'd~ t.~
1
I
C D E F G H I J K L M N 0 P Q R S T U V
~ :A F
,'~,~ p~l~:U% 'L '~ ~I~K '~, ~r"G ~
-4~ 6 N
"~[]T % '~. ~W, X
0
ACN=4
i-ICN=6
[
I
MglOH]z L0203 Zr 02 BeO ZnO Zn(OH)2 =-AIz03 AI(OH)3 a-AIO(OH) r-AlO(OH) a- Fez03 T-Fe O(OH) =-FeO(OH) Th02 PuOz Y20~ HgO Sn02 TiOz W03 Si02
OCN=8 I
0 H-Bonded
Solids
vA
X PZC+ ½ Io(:J( - ~ ) = 18.43-53.12(~-) . I
I
0.05
0.10
I
l
0.15 0.20
N
I
l
0.25
0.30
[]
t,I
0.35
I
0.40
F~G. 2. [PZC + ½ log ((2 - v)/v)] as a functionof(v/L) for solids of zero CFSE. considered to be the most reliable among the PZCs of simple oxides and hydroxides reported in the literature. These two oxides require no corrections for CFSE and the metal-oxygen bondings are predominantly ionic in nature. By using Eq. [14], the PZCs of various oxides and hydroxides requiring no corrections for CFSE have been calculated from their values of v and L. The calculated PZCs are given in Table I and are compared with the experimental values. Figure 2 shows 1
plotted against (v/L), which should be linear according to Eq. [14]. The experimental PZC values that are given in Table I and are used in the plot are taken from the compilation by Parks (3), except for those of ZnO (16) and Zn(OI-I)2 (17). Among the PZCs listed in the Parks paper, those of samples of unknown structures have not been used in the present work. Also excluded from the present work are the PZCs of ternJournal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
pered oxides since they shift to lower pHs depending on the temperature to which they have been subjected. The values of/~ in Table I are taken primarily from the original papers on structure determination as traced from the data compiled by Donnay et al. (18) and Wyckoff (19). If accurate bond lengths are not available in the literature, they have been calculated from the atomic coordinates and the space groups given by Wyckoff (19). A linear relationship between
[PZCex
1
and
demonstrated in Fig. 2, shows that Eq. [14] can predict the PZCs of many oxides and hydroxides to a reasonable accuracy. Notable exceptions, however, are the hydrogenbonded hydroxides and oxyhydroxides: The PZCs are lower than the predicted values and are mostly located at or near neutral pH. A possible explanation for these PZC shifts would be to postulate that the structure-
PREDICTING POINTS OF ZERO CHARGE forming O H - ions have specific affinity toward the broken H-bonds on the surface layer. Such an adsorption may be classified as "nondissociative adsorption," a term first introduced by Parks (2). The PZC of HgO shows the largest deviation, which may be attributed to the chain structure of the greatly distorted octahedra (19). Equation [ 14] appears to be most successful with those oxides/hydroxides of CN = 6, which is not surprising considering that its constants (A and B) have been determined from the experimental PZCs of two 6coordinated oxides, i.e., MgO and AlzO3. Equation [14] can also accurately predict the PZC of ZnO, in which Zn 2+ ions are tetrahedrally coordinated. BeO is isostructural to ZnO, but the experimental PZC is considerably higher than the predicted value. This may be attributed to the exceptionally small ionic radius of i~Be2+ (0.27 ,~) and, hence, a small effective dielectric constant of water in the immediate vicinity (20). It should be remembered that the constants A and B, which are dependent on E 1 and Ez (see Eqs. [9] and [10]), have been assumed to be constant for most oxides and hydroxides in obtaining Eq. [14]. It now appears that this assumption is valid only in a limited range of el and e2. Likewise, the discrepancy between the experimental and predicted PZCs of SiO2 may be ascribed in part to the small ionic radius of ivSi4÷ (0.26 A), although another likely reason for the large discrepancy could be the pronounced covalency of the S i - O bonding which would contribute significantly to AG°ch. As for the oxides of CN = 8, the predicted PZC of ZrO2 is in good agreement with the experimental value. However, others such as ThOz and PuO~ show lower experimental than predicted PZC values, which could be due to the large ionic radii of viiiTh4+ (1.05/~) and viiiPu4+ (0.96/~) and consequently large values of E. Conversely, the success of Eq. [14] with ZrO2 is probably due to the relatively smaller ionic radius of vulz#+ (0.84 A) as an 8-coordinated ion.
489
B. OXIDES/HYDROXIDE OF NONZERO CFSE Crystals of some transition metal compounds need special consideration for CFSE, which contributes to AG°chof Eq. [1]. This is because d-electrons are involved in forming hybrid orbitals. The transition metal compounds or ions exhibit hydration energies greater than those calculated from the electrostatic model. However, the additional energy does not appear if a transition metal ion has a symmetrical charge distribution with 0, 5, or 10 d-electrons. Therefore, no corrections for CFSE are necessary for the solids containing these transition metal ions. Equation [14] may be written to take into account the CFSE as follows:
c
PZC = 18.43 - 53.12
+ ~ x C 53.12
j
2 in which C represents the CFSE andc/53.12 is a constant. The latter may be determined using the experimental PZC (pH = 11.4) of Co(OH)2 and C = 33 kcal/mole for the Co2+.6H20 ion (3), so that Eq. [151 becomes PZC = 18.43 - 5 3 . 1 2 [ ( L ) + 5 . 6 1 × 10-4C]
--
m
2 = 18.43- 53.12(vt \L/~tt
Equation [16] has been written in such a manner that the quantity 5.61 x 10.4 C is regarded as an effective change in (v/L) necessary to account for the CFSE contriJournal of Colloid and Interface Science, V o l . 70, N o . 3, J u l y 1979
490
YOON ET AL.
bution to AG°ch. The PZC of Co(OH)2 has been chosen because the experimental values determined by four independent investigators (21-24) are consistent with each other. Note that Eq. [14] is a special case of Eq. [16] when C = 0. By using Eq. [16], the PZCs of solids of CFSE = 0 have been calculated and are given in Table II along with the experimental values. Figure 3 shows the 1
vs
plot. eft
The values of CFSE used for the calculation of (v/L)eff have been estimated by Parks (3) from the heats of hydration of ions with octahedral symmetry of the ligands. Figure 3 shows that Eq. [16], which incorporates a correction factor (5.61 x 10-4) determined from the experimental PZC of Co(OH)2, can predict the PZCs of other transition metal compounds such as Fe(OH)2, Ni(OH)2, and Cr203. However, the PZC of CuO deviates considerably from the predicted value. This is most likely due to the fact that the value of CFSE used in the calculation is for an octahedrally coordinated ion, while Cu(II) in CuO has a square-planar coordination. The apparent fit between the experimental and predicted PZCs of Cu(OH)2 could be a fortuitous coincidence considering, first,
that all other H-bonded solids show their PZCs at or near neutral pH (see Fig. 2) and, second, that the CFSE used in the calculation is for Cu ~+- 6H20 while the CN of Cu(II) in Cu(OH)2 is effectively 4 despite the octahedral configuration of O H - ions around the Cu(II). Cu(OH)2 is considered as an effectively 4-coordinated compound in the present work since two of the six O H - ions around a Cu(II) ion are at a distance of 2.63 A from the metal ion (25), which exceeds the maximum bond limit for Cu-(O,OH) bonds (2.5 /~) calculated by Donnay and Allman (6). It is well recognized that AI(OH)3, Zn(OH)2, and Cu(OH)2 are H-bonded hydroxides (2527). However, other hydroxides such as Mg(OH)2, Co(OH)z, Ni(OH)2, and Fe(OH)2 are not considered to be H-bonded solids. These hydroxides have a C6 (CdI2) type of structure, in which the octahedral layers are held together probably by van der Waals forces rather than by H-bonding. Bernal and Megaw (28) ruled out the possibility of Hbonding in both Mg(OH)~ and Ca(OH)~ (also of a C6 type structure), and this has been confirmed by neutron diffraction (11) and NMR studies (12). Also, Evans (10) suggested that H-bonding in hydroxides is possible only when v, which is a measure of the polarizing power of a cation, is ½ or greater. Since all the Cs-type hydroxides have v = V3, they are not likely to be Hbonded. On the other hand, vs of H-bonded
TABLE II Calculated and Experimental PZCs of Transition Metal Compounds of Nonzero CFSE a CN
CFSE
Sample
Z
M
(O,OH)
[,
v
A Fe(OH)~ B Co(OH)2 C Ni(OH)2 D CuO E Cu(OH)~ F CrzO3
2 2 2 2 2 3
6 6 6 4 4 6
3 3 3 4 2 4
2.11 2.10 2.04 1.95 1.935 1.995
1/3 1/3 1/3 1/2 1/2 1/2
a Italics indicate an H-bonded solid. Journal of Colloid and Interface Science, Vol. 70, No. 3. July 1979
mole)
0.1068 0.1072 0.1093 0.1689 0.1698 0.1664
18 33 42 39 39 70
PZC n
0.1169 0.1257 0.1329 0.1908 0.1917 0.2057
Calculated
Experimental
11.87 11.40 I 1.02 8.06 8.01 7.26
12 _+ 0.5 11.4 11.1 9.4 -+ 0.4 7.7 7.0
491
PREDICTING POINTS OF ZERO CHARGE I
I
I
I
l
I
I
A
Fe(OH)z
\ h--ll I~:.~l I
12
B Co(OH)2
\"
.
+
o
N
Ni [OH)~
E
Cu(OH)~ Cra03
o F
I0
o
C
\
®---@~ [].........•
8
6
fit.
Corecte~d
4
ACN=4 &CN=4,CFSE [] CN=6 • CN=6,CFSE Corrected N 0 H-Bonded • H-Bonded,CFSE Corrected ~ .
0
I
l
0.05
0.10
I
I
I
0 . 1 5 0.20
I
0.25
I
O.~PO (~35
0.40
FIG. 3. [PZC + ½ log ((2 - v)/v)] as a function of ( v / L ) e f f for solids of nonzero CFSE.
hydroxides such as AI(OH)3, Zn(OH)2, and Cu(OH)2 are ½. C . GIBBS FREE ENERGY OF ADSORPTION AT P Z C
onstrates that both PZC and AG ° can be predicted successfully from (v/L)en.
H+
Equation [16] may be used in calculating the standard Gibbs free energy of proton adsorption at the PZC (Eq. [1]). From Eqs. [4] and [7], AG ° = -2.3RT
D. COMPLEX OXIDES
(v/L)~ of Eq. [13] may be replaced by (v/ that the equation can be used in predicting the PZCs of complex oxides containing transition metal ions of CFSE =~ 0 as their structure-forming ions. By substituting A = 18.43 and B = 53.12 into Eq. [13] the PZC equation for complex oxides may be written as
L)eff i, SO
__
per mole of H ÷, which at 25°C becomes AG ° = : 1 . 3 7
18.43
-
53.12 ~- eff
by substituting Eq. [16] into Eq. [17]. Equation [18] is represented in Fig. 4, in which AG ° values calculated by substituting the experimental PZCs into Eq. [17] are also plotted. AG ° values for H-bonded solids, HgO, and CuO are not shown. Figure 4 dem-
n
/V\i
PZC = tri + 18.43 - 53.12 ~ fi | - - | K i=I \L /eft 1 ~f~log 2 i=1
2-
v
i"
[19]
Note that Eq. [19] can be used as a general equation, whether the oxide is complex or simple, since it reduces to Eq. [16] when c r l = 0 a n d n = 1. It may be of interest to calculate the PZCs of three aluminum silicate polymorphs, i.e., Journal of Colloid andlnterface Science, Vo|. 70, No. 3, July 1979
492
YOON ET AL. I
~]
I
I
I
I
R
16
~i[~ I
I
A B C D
MgO Mq(OH)z L0203 Zr02
E
BeO
~'~
F
ZnO
I0
H a-F G Ae 1~ 203 I Th02
~ jK~H~ X
.~ 12
12
•
"6
o~ 8 <3
b
d K L M N 0 P Q R S
M ~. ~ .
I
PuO2 Y203 Sn02 Ti02 WO3 Si02 Fe(OH)2 Co(OH)2 Ni(OH)2 Cr20~
e ~'_.L.o 6
+ (3 N I1.
4
4
0
A C N = 4 E]CN=60CN=8 • CN=6, CFSE Corrected
~
o~
I
I
I
I
I
1
0.05
0.10
0.15
Q20
0.25
0.30
%1
0.35
2 •
0.40
0
FIo. 4. Free energyofproton adsorption(~ G°) on oxidesand hydroxidesat PZC as a functionof( v/L)e.. kyanite, andalusite, and sillimanite, by using Eq. [19] and to compare them with the experimental values reported in the literature. The PZCs of these minerals differ from one another despite their identical chemical compositions (AI~SiOs). Qualitative explanations have been given by Choi and Oh (9) and Smolik and Fuerstenau (29) on the basis of the AI/Si ratio in the surface region. In calculating the PZCs of the aluminum silicates,f~'s of S i - O and A1-O bonds may be determined from the bond ratio within the unit cell (Table I). This would be a good approximation only if the mineral particles used for the PZC determination were randomly fractured. The fine particles used for electrophoretic measurements might have a random surface arrangement since the samples are generally crushed and abraded using a mortar and pestle (29). The value of (v/L)e, for S i - O bonds has been multiplied by a factor of 0.82 in order to take into account the fact that the PZC of SiO2 predicted by using Eq. [14] deviates subJournal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
stantially from the experimental value. The correction factor of 0.82 has been determined such that in calculating the PZC of SiO2 by using Eq. [14] the substitution of 0.82 (v/L) for (v/L) gives a calculated PZC to fit the experimental value of pH 1.8. o'i's for the aluminum silicates have been assumed to be zero. Table III gives the PZCs of the three aluminum silicates calculated by using Eq. [19], which may be compared with the experimental values reported by Smolik and Fuerstenau (29) and Choi and Oh (9). The two sets of experimental PZCs were determined by electrophoretic measurements. No supporting electrolytes were used during the measurements, and the samples received no pretreatment after grinding to micron sizes. Also given in Table III for comparison are the PZC values calculated by using Parks' equation. The PZC values predicted by using either Eq. [19] or Parks' equation are in reasonable agreement with the calculated PZCs considering the discrepancy between the
493
PREDICTING POINTS OF ZERO CHARGE TABLE III Calculated and Experimental PZCs of Aluminum Silicates PZC Calculated
Experimental Mean bond length (A)
No. of bonds per unit ceil
Using Parks'
Using
Smolik
~vSi-O 'vAI-O vAl-O v~AI-O hvSi-O ~VAI-O vAI-O V'AI-O
Eq.a
Eq. [19]
et al. (29)
Choi and Oh (9)
1.625 1.62 1.61
7.4 -6.4
7.3 6.5 5.6
7.9 7.2 6.8
6.9 5.2 6.0
Minerals
(AI2SiO~) Kyanite Andalusite Sillimanite
--1.77
-1.84 --
1.91 1.93 1.91
16 16 16
--16
-20 --
48 24 24
a PZCs of the lvSi-O, ivA1-O, and v'A1-O components are assumed to be pH 1.8, 6.8, and 9.2, respectively (3).
two sets of experimental values. F r o m the sample calculations given in Table III, it is difficult to state which of the two PZC equations is more accurate. H o w e v e r , Eq. [19] has a distinct advantage over Parks' equation in that it can predict the PZC of a complex oxide without having to assume the PZCs of its component oxides. Also, in assuming the PZCs of some c o m p o n e n t oxides such as VA1-O or lvA1-O difficulties may be encountered since there are no simple oxides occurring in nature where the AP + ions have a CN of 4 or 5 exclusively. ACKNOWLEDGMENTS Our thanks go to Messrs. L. L. Sirois, M. D. Pritzker, M. C. Campbell, and Dr. A. H. Webster for critically reading the manuscript and for offering helpful comments.
11. 12. 13. 14. 15. 16. 17. 18.
19. 20. 21.
REFERENCES 22. 1. Parks, G. A., and deBruyn, P. L . , J . Phys. Chem. 66, 967 (1962). 2. Parks, G. A., Chem. Rev. 65, 177 (1965). 3. Parks, G. A., Advan, Chem. Set. 67, 121 (1967). 4. Shannon, R. D., Acta Crystallogr. Sect. A 32, 751
23. 24.
(1976). 5. Pauling, L . , J . Amer. Chem. Soc. 51, 1010 (1929). 6. Donnay, G., and Allman, R., Amer. Mineral. 55, 1002 (1970). 7. Donnay, G., and Donnay, J. D. H., Acta Crystallogr. Sect. B 29, 1417 (1973). 8. Martin, R. F., and Donnay, G., Amer. Mineral. 57, 554 (1972). 9. Choi, H. S., and Oh, J. H., J. Mining Met. Inst. Japan 81,614 (1965). 10. Evans, R. C., in " A n Introduction to Crystal
25. 26. 27. 28. 29.
Chemistry," 2nd ed., pp. 269, 276. Cambridge Univ. Press, London/New York, 1965. Elleman, D. D., and WiUiams, D., J. Chem. Phys. 25, 742 (1956). Busing, W. R., and Levy, H. A., J. Chem. Phys. 26, 563 (1957). Van Orphen, H., " A n Introduction to Clay Colloid Chemistry." Interscience, New York, 1963. Yopps, J. A., and Fuerstenau, D. W., J. Colloid Sci. 19, 61 (1964). Robinson, M., Pask, H. A., and Fuerstenau, D. W., J. Amer. Ceram. Soc. 47, 516 (1964). Blok, L., and deBruyn, P. L., J. Colloid Interface Sci. 32, 527 (1970). Cliche, D., Project report submitted to Professor T. Salman, McGill University, 1976. Donnay, J. D..H., and Ondik, Helen M., "Crystal Data Determinative Tables," 3rd ed. National Bureau of Standards, 1972. Wyckoff, R. W. G., "Crystal Structures," 2nd ed. Interscience, New York, 1963. Noyes, R. M.,J. Amer. Chem. Soc. 84, 513 (1962). Mattson, S., and Pugh, A. J., Soil Sci. 38, 229 (1934). Healy, J. W., James, R. O., and Cooper, R., Advan. Chem. Set. 73, 62 (1968). Tewari, P. H., and Campbell, A. B., J. Colloid Interface Sci. 55, 531 (1976). Yoon, R. H., "The Role of Crystal Structure in the Surface Chemistry of Flotation," Ph.D. thesis, McGill University, Montreal, 1977. Jaggi, H., and Oswald, H. R., Acta Crystallogr. 14, 1041 (1961). Giese, R. F., Jr., Acta Crystallogr. Sect. B 32, 1719 (1976). Christensen, A. N., Acta Chem. Scand. 23, 2016 (1969). Bernal, J. D., and Megaw, H. D., Proc. Roy. Soc., Ser. A 151, 384 (1935). Smolik, T. J., Harman, and Fuerstenau, D. W., AIME Trans. 235, 367 (1966).
Journal of Colloidand Interface Science. Vol. 70, No. 3, July 1979
It has been well established that an oxide or a hydroxide suspended in an aqueous environment can acquire its surface charge by adsorbing H ÷ or OH- ions. The pH at which the solid has no net surface charge is defined as the point of zero charge (PZC). There are two methods of predicting PZCs of simple oxides and hydroxides, One is to use the minimum solubility theory (1, 2), according to which a PZC should be identical to the isoelectric point of the aqueous solution [IEP (aq)] suspending the solid. The IEP (aq), which is often found at the pH of minimum solubility of the solid, can be determined by constructing the solubility diagram. The other method of predicting a PZC is to use Parks' equation (2, 3), which is essentially a function of (Z/R), where Z is the formal charge of the cation and R t Present address: Associate Professor, Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061. To whom correspondence should be addressed.
is the sum of the cationic radius (r+) and the oxygen diameter (2.8 A). The use of Parks' equation may be advantageous over the use of minimum solubility theory in that the crystallographic data, such as Z and r+, are readily available for most oxides/hydroxides while the thermodynamic data required to construct the solubility diagrams are limited to only a number of solids. There are difficulties, however, in using Parks' PZC equation. First, the ionic radii that he tabulated and that were used in formulating and testing the equation differ significantly from those that are more widely accepted. For example, the ionic radii of ViAp+ and ivsi4+ [the prescript in small Roman numerals denotes the coordination number (CN)] used by Parks are 0.85 and 0.80 A, respectively, while Shannon (4) reported them to be 0.535 and 0.26 A, respectively. Second, Parks' equation introduces different correction terms, depending on the CN and the hydration states of the solids. An improved version of Parks' PZC equation is now proposed. The new equation is
483
Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
0021-9797/79/090483 - 11$02.00/0 Copyright© 1979by AcademicPress,Inc. All rightsof reproductionin any formreserved.
484
YOON ET AL.
developed by utilizing Pauling's electrostatic valence principle (5), which has been found to be useful in describing the charge balance of the ions in the surface layer of a crystal. THEORY A. A MODEL FOR SURFACE-CHARGING MECHANISMS
The bond valence (v) was defined by Pauling as the formal charge of a cation divided by the CN. He enunciated the electrostatic valence principle by which the sum of bond valences reaching an anion is equal to the charge of the anion. This principle in extended form has been put to many uses recently (6-8) in structure determinations of crystals by X ray. Pauling's principle is often called the principle of local neutralization of charge since it is an expression of the tendency of ions in the interior of a crystal to surround themselves with neighbors of opposite signs, so that the charges are neutralized locally. However, the charges of ions exposed on the surface of a crystal are not balanced and may contribute to the surface charge of the solid suspended in an aqueous medium. The charging mechanism of oxides and hydroxides is generally ascribed to the hydrolysis of surface metal ions or to the protonation of surface 02-/ OH- ions (1-3). Pauling's principle may be useful in describing these surface reactions. Choi and Oh (9) utilized it first in explaining the PZC differences among aluminum silicate polymorphs. Let us consider the oxygen atoms on the surface of an oxide crystal randomly fractured in a vacuum. If such a crystal is immersed in water, the oxygen ions which present broken (or unsatisfied) bonds to the aqueous phase will be unstable and, hence, may accept protons to become OH- and/or H20 species. A broken bond, although it is not physically tangible, may be considered to represent a surface force which tries to complete a bonding of one type or another Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
depending on the environment. Then, it might be said that the oxygen ions that have the maximum possible number of broken bonds are most unstable or most susceptible to protonation. Thus, when the number of H ÷ ions in solution is limited, the protonation will occur preferentially on those oxygens that have the maximum number of broken bonds (or the minimum number of satisfied bonds). These are the ones that have the so-called "dangling bonds"; i.e., the CN of such oxygen is unity. The protonation of a danglingly bonded oxygen may be represented by the reaction M - O tz-~)- + 2H + ~ M~+-OHz,
[1]
in which M is the metal ion on the surface layer and v the bond valence reaching the oxygen ion. Assuming that none of the oxygen ions in the coordination polyhedron around M are protonated, the total strength of the bond valence which the danglingly bonded oxygen receives is v. Therefore, the oxygen on the left-hand side of Eq. [1] has an unbalanced charge of -(2 - v), which may be considered the effective charge of the negative site M - O <2-~')-. The danglingly bonded oxygen can take up a maximum of two protons to become a coordinated water molecule, which should give an unbalanced charge of +v to M. The positive site may then be represented by M~+-OH2. One may question the existence of the bare oxygen ion in the negative site M - O ~2-~-. However, this may be considered thermodynamically equivalent to M - ( O H h (2-~)- or to M - O H ~l-v)- . . . OH-. Equation [1] represents an equilibrium at or near the PZC, at which the protonation is most likely to be limited to the danglingly bonded oxygen. However, if the pH is considerably lower than the PZC, the protonation may occur on other oxygens around M which have more than one unbroken bond per oxygen. In this case, the effective charge of the positive site could become larger than + v depending on the total number of oxygens protonated around M. If all the oxy-
PREDICTING POINTS OF ZERO CHARGE gens in the coordination polyhedron around M are protonated, the metal ion will leave the surface and enter the solution as a hydrated metal ion and/or as a hydrated hydroxo complex. In this respect, the surfacecharging mechanism represented by Eq. [1] may be viewed as an incipient dissolution process of the solid. This view is perhaps supported by the fact that the minimum solubility theory (1, 2) can predict the PZCs of many simple solids. Equation [1] may be compared with the widely accepted charging mechanism, M - O - + 2H + ~- M-OH2 +,
[2]
which was used by Parks in deriving his PZC equation. Equation [2] suggests that the effective charges of the positive and negative sites are + 1 and - 1 , respectively, regardless of Z, CN, and pH, which distinguishes it from Eq. [1]. Another difference between the two equations is that the center of a positive charge is M in Eq. [1] while Eq. [2] implies that it is one of the protons of the coordinated water molecule. The implication of Eq. [1], that the metal ions in the surface layer are the locus of positive surface charge, can be supported by the observation that the charge of a hydrated metal ion in solution resides on the ion itself, but not on any of the protons of the coordinated water molecules. B . D E V E L O P M E N T OF P Z C
EQUATION
(a) Simple Oxides
The total free energy change of Eq. [1] or [2] can be considered to be made up of electrical and chemical contributions: AG ° = AG°el + AG°ch.
[3]
In deriving his PZC equation, Parks (2) assumed that Eq. [2] involves primarily the electrical energy gained by the approach of 2H + to M - O - . AG°e~ was then taken to he the sum of energy gained by the approach of the protons toward the oxygen of charge - 2 and the energy spent in moving the pro-
485
tons against the surface metal ion of charge +Z. Since the equilibrium O - 2 H distance was taken to be a constant (1.4/~) for all oxides, AG°elas calculated by Parks was effectively a function of (Z/R), R being the linear M - O - 2 H distance. A AG°el calculation as such assumes that the ions in the M - O - 2 H array are isolated from the rest of the surface. However, it is more realistic to include at least those oxygen ions that are within the first coordination sphere of M. There are CN - 1 other oxygens to be considered in addition to the danglingly bonded one. The attractive energies between these oxygens and the protons under consideration can have a significant effect in determining AG°~I. The calculation of AG°~, which takes into account all the ions within the coordination polyhedron around M, is not difficult for a given crystal if the interionic distances and bond angles are accurately known. However, it is virtually impossible to obtain a generalized formula for AG°~ that is applicable for solids of different crystal structure with a minimum number of parameters. The problem may be resolved by utilizing the surface-charging mechanism represented by Eq. [1]. In calculating AG°el, one may be able to consider that the M~+-O-2H array is isolated from the rest of the surface if M is given an effective charge of v. This may be a simplification that can account for the potential fields exerted by the CN - 1 other oxygens around M being canceled out by the positive charge of Z - v. AG°~ gained by the approach of 2H + to the Mv+-O2- site may be calculated by assuming as a first approximation that each ion is a point-charge separated from other ions by the equilibrium distances as shown in Fig. I. The two hydrogen ions are treated as a doubly positive entity. The free energy change involved is then (2) AG °
=
2ZHZo Ne2 2ZHvNe 2 + ~- AG°ch ¢lr ~2L
= - 2 . 3 R T log K,
[4]
Journal of Colloid and Interface Science, Vol. 70, No. 3, July.1979
486
YOON ET AL.
and B can be determined properly by using Eqs. [9] and [ 10], respectively. For practical purposes, /~ may be represented by the mean M - O bond length at the interior of a crystal and r may be taken to be 1.01/~, which is the O - H distance in ice (10, p. 269) and is close to the O - H distances in water, hydroxides, and hydrated solids ( l l , 12). L"
L
(b) Complex Oxides
FIG. 1. A model o f positive site, Mv+-OH~, on oxide surface.
in which ZH = 1 and Zo = 2 are the formal charges of the subscript ions, N is Avogadro's number, e is the electronic charge, and ~j and ~2 are the effective dielectric constants. The equilibrium constant K of Eq. [1] is K =
[Mv+-OHz] , [M-O(~-v)-][H+]Z
[5]
assuming unit activity coefficients, which at the PZC becomes K =
(2-
l
1
2
[6]
since (2 - v) [ M - O <2-v)-] = v[Mv+-OH2] if v < 2. Taking the logarithms of Eq. [6], l o g K = log ( ~ ---~) + 2PZC.
[7]
By substituting Eq. [7] into Eq. [4] one can obtain for PZC the expression 1
PZC = A - B
2e 2
AG°ch
2.3kT¢lr
4.6kT
,
[11]
where K -
R T ~K , F 47r
[12]
in which PZC~ is the PZC of the component oxide i,f~ the atomic fraction on the surface, o.l the intrinsic structural charge, e the appropriate dielectric constant, and K the reciprocal thickness of the electrical double layer around the solid; R, T, and F have the usual meanings. Examples of nonzero values of o-i are the basal planes of micas and clay minerals (13). Equation [11] suggests that, if o'i = 0, the PZC of a complex oxide is simply the weighted average of PZCis. Parks (3) used " a s s u m e d " PZCi values in predicting PZCs of complex oxides with Eq. [11]. Instead, one may substitute Eq. [8] into Eq. [11] to obtain a theoretical PZC equation, n v ~fi(--t i=1 \ L / i
[9] --
e 2
B - - 2.3kT~2
PZC = o--2 + ~ f~PZC~, K i=l
PZC = o.i --+A-B K
where A-
For the PZC of a complex oxide containing n distinct component oxides, Parks (3) showed that
[10]
Equation [8] allows one to calculate the PZC of an oxide from v and L ( = L + r), if A Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
Ef~log
2 ~=~
~
v
/~
,
[13]
so that a PZC of a complex oxide can be predicted directly from crystallographic data if o-i, A, and B are known. One can best interpretf~ of Eq. [13] to be the fraction
487
PREDICTING POINTS OF ZERO CHARGE
of oxygens that are danglingly bonded to the surface metal ion i. DISCUSSION
In predicting the PZC of a simple oxide or a hydroxide with Eq. [8], the knowledge of A and B is a prerequisite. It is unfortunate, however, that the values of ~1 E2, and AG%h, which are required to determine A and B (see Eqs. [9] and [10]), are difficult to evaluate at present. Thus, an assumption has been made that A and B are constants within limits for most oxides and hydroxides, which would allow them to be determined from reliable experimental PZC values. Note, however, that AG°ehs for most transition metal oxides and hydroxides are larger than those of non-transition metal compounds due to the crystal field stabilization energy (CFSE) (2, 3). Hence, it is neces-
sary to make appropriate corrections for CFSE, when the constants A and B are determined by using the experimental PZCs of solids of zero CFSE. A . SIMPLE OXIDES/HYDROXIDES OF ZERO C F S E
From the experimental PZCs of a-A1203 [pH 9.1 (14)] and MgO [pH 12.4 (15)], the constants A and B of Eq. [8] have been determined so that it may be written as:
(L/) The PZC values of a-A1203 and MgO are
TABLE I Calculated and Experimental PZCs of Oxides/Hydroxides of Zero CFSE a CN
PZC
Sample
Z
M
(O.OH)
(A)
v
Calculated
A B C D E F
MgO Mg(OH)2 La2Oa ZrO2 BeO ZnO
2 2 3 4 2 2
6 6 6 8 4 4
6 3 4 4 4 4
2,106 2.06 2.44 2,26 1,65 1,978
1/3 I/3 1/2 1/2 1/2 1/2
0.1070 0.1086 0.1449 0.1529 0.1880 0.1673
G
Zn(OHh
2
4
2
1.95
1/2
0.1689
9.22
H
a-A1203
3
6
4
1.91
1/2
0.1712
9.10
9.1
1 J K
AI(OH)3* o~AlO(OH) y-AIO(OH)
3 3 3
6 6 6
2 ---
1.89 1.935 1.913
1/2 1/2 1/2
0.1724 0.1698 0.1711
9.03 9.17 9.10
5.0-3.2 7.7 7.5
12.40 12.31 10.49 12.07 8.20 9.30
Experimental 12.4 +_ 0.3 -12 10.4 10-11 10.2 9.3 7.8
L
a-Fe2Oa
3
6
4
2.03
1/2
0,1645
9.45
9.04
M N
y-FeO(OH) a-FeO(OH)
3 3
6 6
-~
2.00 2.04
1/2 1/2
0.1661 0.1639
9.37 9.48
7.4 6.7
O P Q R S T U V
ThO2 PuO~ Y2Oa HgO SnO2 TiO~ WOa SiO~
4 4 3 2 4 4 6 4
8 8 6 6 6 6 6 4
4 4 4 6 3 3 2 2
2.425 2.336 2.28 2.57 2,053 1.969 1.927 1.61
1/2 1/2 1/2 1/3 2/3 2/3 1 1
0.1456 0.1492 0.1520 0.09311 0.2177 0.2245 0.3405 0.3817
10.46 10.27 10.12 13.14 6.71 6.35 0,34 -1.85
9.0-9.3 9.0 9.0 7.3 6.6 6.7 -0.5 1,8
" Italics are for H-bonded solids. Z, cationic charge; CN, coordination number; M, metal ion; v, bond balance;/,, mean M-(O,OH) distance, L = L + r, r = 1.01 A; *, natural gibbsite. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
488
YOON ET AL. 14
P
i
I
~. ~, '%
12
.._10
I
"ml'd~ t.~
1
I
C D E F G H I J K L M N 0 P Q R S T U V
~ :A F
,'~,~ p~l~:U% 'L '~ ~I~K '~, ~r"G ~
-4~ 6 N
"~[]T % '~. ~W, X
0
ACN=4
i-ICN=6
[
I
MglOH]z L0203 Zr 02 BeO ZnO Zn(OH)2 =-AIz03 AI(OH)3 a-AIO(OH) r-AlO(OH) a- Fez03 T-Fe O(OH) =-FeO(OH) Th02 PuOz Y20~ HgO Sn02 TiOz W03 Si02
OCN=8 I
0 H-Bonded
Solids
vA
X PZC+ ½ Io(:J( - ~ ) = 18.43-53.12(~-) . I
I
0.05
0.10
I
l
0.15 0.20
N
I
l
0.25
0.30
[]
t,I
0.35
I
0.40
F~G. 2. [PZC + ½ log ((2 - v)/v)] as a functionof(v/L) for solids of zero CFSE. considered to be the most reliable among the PZCs of simple oxides and hydroxides reported in the literature. These two oxides require no corrections for CFSE and the metal-oxygen bondings are predominantly ionic in nature. By using Eq. [14], the PZCs of various oxides and hydroxides requiring no corrections for CFSE have been calculated from their values of v and L. The calculated PZCs are given in Table I and are compared with the experimental values. Figure 2 shows 1
plotted against (v/L), which should be linear according to Eq. [14]. The experimental PZC values that are given in Table I and are used in the plot are taken from the compilation by Parks (3), except for those of ZnO (16) and Zn(OI-I)2 (17). Among the PZCs listed in the Parks paper, those of samples of unknown structures have not been used in the present work. Also excluded from the present work are the PZCs of ternJournal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
pered oxides since they shift to lower pHs depending on the temperature to which they have been subjected. The values of/~ in Table I are taken primarily from the original papers on structure determination as traced from the data compiled by Donnay et al. (18) and Wyckoff (19). If accurate bond lengths are not available in the literature, they have been calculated from the atomic coordinates and the space groups given by Wyckoff (19). A linear relationship between
[PZCex
1
and
demonstrated in Fig. 2, shows that Eq. [14] can predict the PZCs of many oxides and hydroxides to a reasonable accuracy. Notable exceptions, however, are the hydrogenbonded hydroxides and oxyhydroxides: The PZCs are lower than the predicted values and are mostly located at or near neutral pH. A possible explanation for these PZC shifts would be to postulate that the structure-
PREDICTING POINTS OF ZERO CHARGE forming O H - ions have specific affinity toward the broken H-bonds on the surface layer. Such an adsorption may be classified as "nondissociative adsorption," a term first introduced by Parks (2). The PZC of HgO shows the largest deviation, which may be attributed to the chain structure of the greatly distorted octahedra (19). Equation [ 14] appears to be most successful with those oxides/hydroxides of CN = 6, which is not surprising considering that its constants (A and B) have been determined from the experimental PZCs of two 6coordinated oxides, i.e., MgO and AlzO3. Equation [14] can also accurately predict the PZC of ZnO, in which Zn 2+ ions are tetrahedrally coordinated. BeO is isostructural to ZnO, but the experimental PZC is considerably higher than the predicted value. This may be attributed to the exceptionally small ionic radius of i~Be2+ (0.27 ,~) and, hence, a small effective dielectric constant of water in the immediate vicinity (20). It should be remembered that the constants A and B, which are dependent on E 1 and Ez (see Eqs. [9] and [10]), have been assumed to be constant for most oxides and hydroxides in obtaining Eq. [14]. It now appears that this assumption is valid only in a limited range of el and e2. Likewise, the discrepancy between the experimental and predicted PZCs of SiO2 may be ascribed in part to the small ionic radius of ivSi4÷ (0.26 A), although another likely reason for the large discrepancy could be the pronounced covalency of the S i - O bonding which would contribute significantly to AG°ch. As for the oxides of CN = 8, the predicted PZC of ZrO2 is in good agreement with the experimental value. However, others such as ThOz and PuO~ show lower experimental than predicted PZC values, which could be due to the large ionic radii of viiiTh4+ (1.05/~) and viiiPu4+ (0.96/~) and consequently large values of E. Conversely, the success of Eq. [14] with ZrO2 is probably due to the relatively smaller ionic radius of vulz#+ (0.84 A) as an 8-coordinated ion.
489
B. OXIDES/HYDROXIDE OF NONZERO CFSE Crystals of some transition metal compounds need special consideration for CFSE, which contributes to AG°chof Eq. [1]. This is because d-electrons are involved in forming hybrid orbitals. The transition metal compounds or ions exhibit hydration energies greater than those calculated from the electrostatic model. However, the additional energy does not appear if a transition metal ion has a symmetrical charge distribution with 0, 5, or 10 d-electrons. Therefore, no corrections for CFSE are necessary for the solids containing these transition metal ions. Equation [14] may be written to take into account the CFSE as follows:
c
PZC = 18.43 - 53.12
+ ~ x C 53.12
j
2 in which C represents the CFSE andc/53.12 is a constant. The latter may be determined using the experimental PZC (pH = 11.4) of Co(OH)2 and C = 33 kcal/mole for the Co2+.6H20 ion (3), so that Eq. [151 becomes PZC = 18.43 - 5 3 . 1 2 [ ( L ) + 5 . 6 1 × 10-4C]
--
m
2 = 18.43- 53.12(vt \L/~tt
Equation [16] has been written in such a manner that the quantity 5.61 x 10.4 C is regarded as an effective change in (v/L) necessary to account for the CFSE contriJournal of Colloid and Interface Science, V o l . 70, N o . 3, J u l y 1979
490
YOON ET AL.
bution to AG°ch. The PZC of Co(OH)2 has been chosen because the experimental values determined by four independent investigators (21-24) are consistent with each other. Note that Eq. [14] is a special case of Eq. [16] when C = 0. By using Eq. [16], the PZCs of solids of CFSE = 0 have been calculated and are given in Table II along with the experimental values. Figure 3 shows the 1
vs
plot. eft
The values of CFSE used for the calculation of (v/L)eff have been estimated by Parks (3) from the heats of hydration of ions with octahedral symmetry of the ligands. Figure 3 shows that Eq. [16], which incorporates a correction factor (5.61 x 10-4) determined from the experimental PZC of Co(OH)2, can predict the PZCs of other transition metal compounds such as Fe(OH)2, Ni(OH)2, and Cr203. However, the PZC of CuO deviates considerably from the predicted value. This is most likely due to the fact that the value of CFSE used in the calculation is for an octahedrally coordinated ion, while Cu(II) in CuO has a square-planar coordination. The apparent fit between the experimental and predicted PZCs of Cu(OH)2 could be a fortuitous coincidence considering, first,
that all other H-bonded solids show their PZCs at or near neutral pH (see Fig. 2) and, second, that the CFSE used in the calculation is for Cu ~+- 6H20 while the CN of Cu(II) in Cu(OH)2 is effectively 4 despite the octahedral configuration of O H - ions around the Cu(II). Cu(OH)2 is considered as an effectively 4-coordinated compound in the present work since two of the six O H - ions around a Cu(II) ion are at a distance of 2.63 A from the metal ion (25), which exceeds the maximum bond limit for Cu-(O,OH) bonds (2.5 /~) calculated by Donnay and Allman (6). It is well recognized that AI(OH)3, Zn(OH)2, and Cu(OH)2 are H-bonded hydroxides (2527). However, other hydroxides such as Mg(OH)2, Co(OH)z, Ni(OH)2, and Fe(OH)2 are not considered to be H-bonded solids. These hydroxides have a C6 (CdI2) type of structure, in which the octahedral layers are held together probably by van der Waals forces rather than by H-bonding. Bernal and Megaw (28) ruled out the possibility of Hbonding in both Mg(OH)~ and Ca(OH)~ (also of a C6 type structure), and this has been confirmed by neutron diffraction (11) and NMR studies (12). Also, Evans (10) suggested that H-bonding in hydroxides is possible only when v, which is a measure of the polarizing power of a cation, is ½ or greater. Since all the Cs-type hydroxides have v = V3, they are not likely to be Hbonded. On the other hand, vs of H-bonded
TABLE II Calculated and Experimental PZCs of Transition Metal Compounds of Nonzero CFSE a CN
CFSE
Sample
Z
M
(O,OH)
[,
v
A Fe(OH)~ B Co(OH)2 C Ni(OH)2 D CuO E Cu(OH)~ F CrzO3
2 2 2 2 2 3
6 6 6 4 4 6
3 3 3 4 2 4
2.11 2.10 2.04 1.95 1.935 1.995
1/3 1/3 1/3 1/2 1/2 1/2
a Italics indicate an H-bonded solid. Journal of Colloid and Interface Science, Vol. 70, No. 3. July 1979
mole)
0.1068 0.1072 0.1093 0.1689 0.1698 0.1664
18 33 42 39 39 70
PZC n
0.1169 0.1257 0.1329 0.1908 0.1917 0.2057
Calculated
Experimental
11.87 11.40 I 1.02 8.06 8.01 7.26
12 _+ 0.5 11.4 11.1 9.4 -+ 0.4 7.7 7.0
491
PREDICTING POINTS OF ZERO CHARGE I
I
I
I
l
I
I
A
Fe(OH)z
\ h--ll I~:.~l I
12
B Co(OH)2
\"
.
+
o
N
Ni [OH)~
E
Cu(OH)~ Cra03
o F
I0
o
C
\
®---@~ [].........•
8
6
fit.
Corecte~d
4
ACN=4 &CN=4,CFSE [] CN=6 • CN=6,CFSE Corrected N 0 H-Bonded • H-Bonded,CFSE Corrected ~ .
0
I
l
0.05
0.10
I
I
I
0 . 1 5 0.20
I
0.25
I
O.~PO (~35
0.40
FIG. 3. [PZC + ½ log ((2 - v)/v)] as a function of ( v / L ) e f f for solids of nonzero CFSE.
hydroxides such as AI(OH)3, Zn(OH)2, and Cu(OH)2 are ½. C . GIBBS FREE ENERGY OF ADSORPTION AT P Z C
onstrates that both PZC and AG ° can be predicted successfully from (v/L)en.
H+
Equation [16] may be used in calculating the standard Gibbs free energy of proton adsorption at the PZC (Eq. [1]). From Eqs. [4] and [7], AG ° = -2.3RT
D. COMPLEX OXIDES
(v/L)~ of Eq. [13] may be replaced by (v/ that the equation can be used in predicting the PZCs of complex oxides containing transition metal ions of CFSE =~ 0 as their structure-forming ions. By substituting A = 18.43 and B = 53.12 into Eq. [13] the PZC equation for complex oxides may be written as
L)eff i, SO
__
per mole of H ÷, which at 25°C becomes AG ° = : 1 . 3 7
18.43
-
53.12 ~- eff
by substituting Eq. [16] into Eq. [17]. Equation [18] is represented in Fig. 4, in which AG ° values calculated by substituting the experimental PZCs into Eq. [17] are also plotted. AG ° values for H-bonded solids, HgO, and CuO are not shown. Figure 4 dem-
n
/V\i
PZC = tri + 18.43 - 53.12 ~ fi | - - | K i=I \L /eft 1 ~f~log 2 i=1
2-
v
i"
[19]
Note that Eq. [19] can be used as a general equation, whether the oxide is complex or simple, since it reduces to Eq. [16] when c r l = 0 a n d n = 1. It may be of interest to calculate the PZCs of three aluminum silicate polymorphs, i.e., Journal of Colloid andlnterface Science, Vo|. 70, No. 3, July 1979
492
YOON ET AL. I
~]
I
I
I
I
R
16
~i[~ I
I
A B C D
MgO Mq(OH)z L0203 Zr02
E
BeO
~'~
F
ZnO
I0
H a-F G Ae 1~ 203 I Th02
~ jK~H~ X
.~ 12
12
•
"6
o~ 8 <3
b
d K L M N 0 P Q R S
M ~. ~ .
I
PuO2 Y203 Sn02 Ti02 WO3 Si02 Fe(OH)2 Co(OH)2 Ni(OH)2 Cr20~
e ~'_.L.o 6
+ (3 N I1.
4
4
0
A C N = 4 E]CN=60CN=8 • CN=6, CFSE Corrected
~
o~
I
I
I
I
I
1
0.05
0.10
0.15
Q20
0.25
0.30
%1
0.35
2 •
0.40
0
FIo. 4. Free energyofproton adsorption(~ G°) on oxidesand hydroxidesat PZC as a functionof( v/L)e.. kyanite, andalusite, and sillimanite, by using Eq. [19] and to compare them with the experimental values reported in the literature. The PZCs of these minerals differ from one another despite their identical chemical compositions (AI~SiOs). Qualitative explanations have been given by Choi and Oh (9) and Smolik and Fuerstenau (29) on the basis of the AI/Si ratio in the surface region. In calculating the PZCs of the aluminum silicates,f~'s of S i - O and A1-O bonds may be determined from the bond ratio within the unit cell (Table I). This would be a good approximation only if the mineral particles used for the PZC determination were randomly fractured. The fine particles used for electrophoretic measurements might have a random surface arrangement since the samples are generally crushed and abraded using a mortar and pestle (29). The value of (v/L)e, for S i - O bonds has been multiplied by a factor of 0.82 in order to take into account the fact that the PZC of SiO2 predicted by using Eq. [14] deviates subJournal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
stantially from the experimental value. The correction factor of 0.82 has been determined such that in calculating the PZC of SiO2 by using Eq. [14] the substitution of 0.82 (v/L) for (v/L) gives a calculated PZC to fit the experimental value of pH 1.8. o'i's for the aluminum silicates have been assumed to be zero. Table III gives the PZCs of the three aluminum silicates calculated by using Eq. [19], which may be compared with the experimental values reported by Smolik and Fuerstenau (29) and Choi and Oh (9). The two sets of experimental PZCs were determined by electrophoretic measurements. No supporting electrolytes were used during the measurements, and the samples received no pretreatment after grinding to micron sizes. Also given in Table III for comparison are the PZC values calculated by using Parks' equation. The PZC values predicted by using either Eq. [19] or Parks' equation are in reasonable agreement with the calculated PZCs considering the discrepancy between the
493
PREDICTING POINTS OF ZERO CHARGE TABLE III Calculated and Experimental PZCs of Aluminum Silicates PZC Calculated
Experimental Mean bond length (A)
No. of bonds per unit ceil
Using Parks'
Using
Smolik
~vSi-O 'vAI-O vAl-O v~AI-O hvSi-O ~VAI-O vAI-O V'AI-O
Eq.a
Eq. [19]
et al. (29)
Choi and Oh (9)
1.625 1.62 1.61
7.4 -6.4
7.3 6.5 5.6
7.9 7.2 6.8
6.9 5.2 6.0
Minerals
(AI2SiO~) Kyanite Andalusite Sillimanite
--1.77
-1.84 --
1.91 1.93 1.91
16 16 16
--16
-20 --
48 24 24
a PZCs of the lvSi-O, ivA1-O, and v'A1-O components are assumed to be pH 1.8, 6.8, and 9.2, respectively (3).
two sets of experimental values. F r o m the sample calculations given in Table III, it is difficult to state which of the two PZC equations is more accurate. H o w e v e r , Eq. [19] has a distinct advantage over Parks' equation in that it can predict the PZC of a complex oxide without having to assume the PZCs of its component oxides. Also, in assuming the PZCs of some c o m p o n e n t oxides such as VA1-O or lvA1-O difficulties may be encountered since there are no simple oxides occurring in nature where the AP + ions have a CN of 4 or 5 exclusively. ACKNOWLEDGMENTS Our thanks go to Messrs. L. L. Sirois, M. D. Pritzker, M. C. Campbell, and Dr. A. H. Webster for critically reading the manuscript and for offering helpful comments.
11. 12. 13. 14. 15. 16. 17. 18.
19. 20. 21.
REFERENCES 22. 1. Parks, G. A., and deBruyn, P. L . , J . Phys. Chem. 66, 967 (1962). 2. Parks, G. A., Chem. Rev. 65, 177 (1965). 3. Parks, G. A., Advan, Chem. Set. 67, 121 (1967). 4. Shannon, R. D., Acta Crystallogr. Sect. A 32, 751
23. 24.
(1976). 5. Pauling, L . , J . Amer. Chem. Soc. 51, 1010 (1929). 6. Donnay, G., and Allman, R., Amer. Mineral. 55, 1002 (1970). 7. Donnay, G., and Donnay, J. D. H., Acta Crystallogr. Sect. B 29, 1417 (1973). 8. Martin, R. F., and Donnay, G., Amer. Mineral. 57, 554 (1972). 9. Choi, H. S., and Oh, J. H., J. Mining Met. Inst. Japan 81,614 (1965). 10. Evans, R. C., in " A n Introduction to Crystal
25. 26. 27. 28. 29.
Chemistry," 2nd ed., pp. 269, 276. Cambridge Univ. Press, London/New York, 1965. Elleman, D. D., and WiUiams, D., J. Chem. Phys. 25, 742 (1956). Busing, W. R., and Levy, H. A., J. Chem. Phys. 26, 563 (1957). Van Orphen, H., " A n Introduction to Clay Colloid Chemistry." Interscience, New York, 1963. Yopps, J. A., and Fuerstenau, D. W., J. Colloid Sci. 19, 61 (1964). Robinson, M., Pask, H. A., and Fuerstenau, D. W., J. Amer. Ceram. Soc. 47, 516 (1964). Blok, L., and deBruyn, P. L., J. Colloid Interface Sci. 32, 527 (1970). Cliche, D., Project report submitted to Professor T. Salman, McGill University, 1976. Donnay, J. D..H., and Ondik, Helen M., "Crystal Data Determinative Tables," 3rd ed. National Bureau of Standards, 1972. Wyckoff, R. W. G., "Crystal Structures," 2nd ed. Interscience, New York, 1963. Noyes, R. M.,J. Amer. Chem. Soc. 84, 513 (1962). Mattson, S., and Pugh, A. J., Soil Sci. 38, 229 (1934). Healy, J. W., James, R. O., and Cooper, R., Advan. Chem. Set. 73, 62 (1968). Tewari, P. H., and Campbell, A. B., J. Colloid Interface Sci. 55, 531 (1976). Yoon, R. H., "The Role of Crystal Structure in the Surface Chemistry of Flotation," Ph.D. thesis, McGill University, Montreal, 1977. Jaggi, H., and Oswald, H. R., Acta Crystallogr. 14, 1041 (1961). Giese, R. F., Jr., Acta Crystallogr. Sect. B 32, 1719 (1976). Christensen, A. N., Acta Chem. Scand. 23, 2016 (1969). Bernal, J. D., and Megaw, H. D., Proc. Roy. Soc., Ser. A 151, 384 (1935). Smolik, T. J., Harman, and Fuerstenau, D. W., AIME Trans. 235, 367 (1966).
Journal of Colloidand Interface Science. Vol. 70, No. 3, July 1979