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Redox equilibria in glass
ELSEVIER
Journal
of Non-Crystalline Solids196(1996)45-50
Redox equilibria in glass J.A. Duffy Depurtment
of Chemistry,
University
*
of Aberdeen,
Aberdeen,
Scotland,
VK
Abstract Data for redox equilibriain silicateglassmelts,for the ion couples:Fe2+/Fe3’, Cr3+/Cr6’, Ce3’/Ce4’, Snzf/Sn4’ and As3‘/As5+, can be relatedto the glasscompositionand indicatethat increasingbasicity favours the upperoxidation state.The relationshipsare simplifiedby makingthe correlationwith the optical basicity of the glassrather than with its composition.The optical basicity modelis concernedwith the electrondensityenvironmentprovidedby oxygenatomsfor the hostedmetal ions and, in principle, allows comparisonbetweenany oxidic environment.Comparisonbetweenglass melts and aqueoussolution establishes a relationshipbetweenthe redox behaviour in the melt and standardelectrode potentialsin aqueoussolution.The applicationsof this relationshipare discussed.
1. Introduction
There have been several studies of redox behaviour in glass for elements existing in more than
one oxidation state (see, e.g., Refs. [l-14]). Taking iron as an example, the equilibrium can be written: Fe3++ e-= Fe2+.
(1) This is countered in the molten glass by the equilibrium involving atmospheric oxygen and oxygen atoms (in the oxidation state of -2) of the glass so that overall: 4Fe3+ + 202- = 4Fe2+ + 0
2’
(2)
The position of equilibrium in Eq. (2) is affected by the composition of the glass melt and, at first sight, it may appear that the lower oxidation state is favoured by increasing glass basicity, since this increase corresponds to increasing oxide ion activity.
* Tel: +44-1224212901.Telefax:+44-1224212921.
For the Fe2+/Fe3+ and most other couples, it is generally found that increasing basicity favours the upper oxidation state (although, in some glass systems, the redox behaviour is less straightforward). For sodium silicate melts at 1400°C and air atmosphere, analysis of the resulting glasses shows that, with increasing Na,O, there is an increase in the +3 state; furthermore, at a given SiO, content, the Fe2’ concentration is lower in a K,O-SiO,, glass but higher in a Li,O-SiO, glass [13]. This difference is shown in Fig. l(a) in which the logarithm of the redox ratio, R, (R = [Fe2’]/[Fe3’]> is plotted against mol% of the basic oxide. These results indicate that there must be another factor in operation which accompanies, but counters, the increase in oxide ion activity. This factor arises from the increasing negative charge borne by the glass network and the effect this charge has on the stability of a hosted metal ion when surrounded by the oxygen atoms. Under normal chemical conditions, metal ions try to achieve charges which are less positive than their oxidation numbers in order to comply with elec-
0022-3093/96,&15.00 0 1996ElsevierScienceB.V. All rightsreserved SSDI0022-3093(95)00560-9
46
J.A. Du#y/Journal
10
20
30 Mol % M20
40
0.50
0.55
ofNon-Crystalline
0.60
Optical
0.65
Basicity
Fig. 1. Variation of log{[Fe*+ ]/[Fe3’ 11in alkali silicate melts at 1400°C in air atmosphere with (a) mol% alkali oxide content, (b) optical basicity.
troneutrality. In a glass, this occurs through donation of negative charge by the oxygen atoms surrounding the metal ion. Increasing the basicity of a glass leads to a greater degree of negative charge on the constituent oxygen atoms and, hence, to a greater ‘electron donor power’. This increase will be of greater benefit to the upper oxidation state metal ions, since they need more negative charge for decreasing their positive charge than the lower oxidation state ions. Indeed, it is conceivable that an environment may provide too much negative charge for the lower state.
Solids 196 (1996) 45-50
This aspect of glass behaviour is in the context of Pauling’s electroneutrality principle [ 151 and indicates how the higher oxidation state is favoured by increasing basicity. It is possible to express, numerically, the (average) electron donor power of the oxygen atoms in glass by the optical basicity value, A [8,161. Optical basicity was originally developed to express the acid-base nature of oxidic media generally [17]. Values of A were obtained experimentally from orbital expansion spectroscopy 1181in the ultra-violet region, and analysis of these data made it possible to calculate an ‘ideal’ or ‘theoretical’ value directly from the glass composition using Eq. (3): A=X,A(A)
+X,A(B)
+ .-a.
x,, x,,... are the molar proportions contributed by the constituent oxides, A, B, . .. to the total oxide(-II) content of the glass (that is, the equivalent fractions) and A(A), A(B), .. . are the optical basicity values of these individual oxides. Values of A for some oxides are: K,O, 1.4; Na,O, 1.15; CaO, 1.00; FeO, 1.00; Al,O,, 0.60; SiO,, 0.48; B,O,, 0.42; P,O,, 0.33 [8,16]. Calculation of A for a soda lime silica glass requires A(Na,O), A(CaO> and A(SiO,>; thus, a glass of composition Na,O-CaO-SiO, (1:2:7, molar ratio) has A equal to [l X 1.15/17+2X 1.00/17 t 14X O-48/17], i.e., 0.58.
Table 1 Dependence of redox ratio on optical basicity a Equilibrium 1 2 3 4 5 6
I 8 9 10 11 12
13
Redox relationship 4Fe3f+202-=4Fe2tt0 4Cr6++ 60*-= 4Cr3’ + 36 2 4Ce4+t202-=4Ce3+t0 2 2Sn4+ + 20*-= 2Sn*+ + 0 2‘4s5++ 20*-= 2*s3++ 4Cu2++202-=?Cu++O,*
0’
2Ni4++ 20*-= 2Ni*+ + 0 2Pb4++202-=2Pb*++O*
2
2Tl3++20*-=2Tl++o 4C03++202-=4Co*++*O
4Mn3++ 20*-= 4Mn*++ 0’ 2 2Sb”++20*-=2Sb3”+0 2 4V5++202-=4V4++0 2
a For silicate melts at 1400°C in air atmosphere.
(3)
log{[Fe2+]/[Fe3+]) = 3.2 - 6.5A log{[Cr3+]/[Cr6+]) = 8.2 - 13.7A log([Ce3’ ]/[Ce4’ 1) = 5.4 - 8.3 A log([Sn*+ ]/[Sn4+ ]I= 0.6 - 3.6 A log([As3+]/[As5+]] = 5.2 - 8.9A log([Cu+]/[Cu’+]) = -6.5 + 10.0/i log([Niz+]/[Ni4+]) = 17 -25A log([Pb2’]/[Pb4+]) = 15 -22A 10g([~+]/[T1~+]) = 13 -20A log([Co2+]/[Co3+11 = 9 - 14A log([Mn2+]/[Mn3’]) = 7 - 12 A log{[Sb3+]/[Sb5+]) = 6- 11 A log([V4+]/[V5+]) =4- 8A
JA. Dufi/Joumal
2. Redox equilibria
of Non-Crystalline
Solids 196 (1996)
47
(a)
and optical basicity
When the data in Fig. l(a) are replotted so that the alkali oxide content on the abscissa is replaced by optical basicity, the three trends are united into a single line, as shown in Fig. l(b). Redox data also exist for Cr3+/Cr6+, Ce3+/Ce4+, Sn2+/Sn4+, As3+/Assf and Cu +/Cu* + in alkali and/or alkaline earth silicate melts at 1400°C and air atmosphere. [lo-131 For all of these, except Cu+/Cu*+, increasing the basicity of the glass favours the upper oxidation state, and when log R, is plotted versus A, relationships similar to that for Fe2+/Fe3+ (Fig. l(b)) are obtained (with opposite slope for Cu+/Cu2’ >. The relationships are almost linear and can be expressed, as indicated in Table 1. In principle, they can be used for calculating the position of equilibrium for any alkali (or alkaline earth) silicate glass at 1400°C and air atmosphere simply by substituting the value for A, calculated from the glass composition using Eq. (3). It is emphasised that the relationships between redox ratio and optical basicity (Table 1) are empirical. Furthermore, whereas the redox ratios are for molten glass (at 14OO”C), the optical basicity value is calculated from parameters obtained ultimately from glass and other media at ambient temperature. One reason preventing a more fundamental approach to the equilibria in Table 1 is the impossibility of specifying the environment for metal ions in terms of proper coordination spheres, owing to the lack of a well-defined boundary which normally does not develop in oxyanion network systems. The optical basicity method circumvents this shortcoming and provides, in effect, a measure representing the electron density available at the ‘average’ site for occupation by a hosted metal ion. The study of redox behaviour in glass melts at elevated temperatures has been restricted to relatively few systems owing to the experimental difficulties associated with the measurements. It would be advantageous, therefore, if a reliable link could be established between the known behaviour of ion couples in glass melts and in aqueous solution [l]. Such a link might then enable the use of standard electrode potentials (E”’ data) for predicting the redox equilibria of ion couples in glass melts. The optical basicity model views the solvated
45-50
nE"
log R
Fig. 2. Plot of nE” for metal ion couples versus logarithm of redox ratio,:R, calculated from Table 1 by setting A at (a) 0.70 (alkaline conditions) and (b) 0.40 (acidic conditions).
metal ions in oxide melts no differently from those in water. In both media, the metal ion is in a field of negative charge provided by polarised oxygen(-II) atoms (polarised by Si4+, Naf, etc. in the melt and by HS in water). Bearing in mind the Nemst equation, it might be expected that a relationship exists between E” X n (where n is the number of electrons involved in the redox equilibrium) and the redox ratio obtained from the expressions in Table 1 with A4set at the value appropriate to the aqueous medium. For alkaline conditions, it has been previously shown that A for hydroxide species is 0.70 while, for acidic conditions, in which the ions are solvated by H,O molecules, A = 0.40. Plotting E” X n against the logarithm of the redox ratio, R, obtained by substituting A = 0.70 in the expressions in Table 1 for alkaline solution, and 4 = 0.40 for acidic, (Fig. 2) indicates that a proportionality factor, constant for all the ion couples, operates and takes into account the extreme difference in the conditions so that log R = 0.42nE” - 1.1
(4)
for alkaline solutions, and log R = 2.5nE” - 1.5 for acidic solutions [ 191.
(5)
48
J.A. Duffy/Journal
ofNon-C’rystalline
3. Applications
45-50
following series for the upper state, becoming an increasingly important species in the glass:
If the assumption is made that these expressions, Eqs. (4) and (51, apply to other ion couples, it is possible to obtain values of log R from the E” values in aqueous solutions. These will be for A = 0.70 and 0.40 and, thus, by the reverse procedure, the linear equation relating log R with A for the conditions of the silicate melt at 1400°C (and air atmosphere) are obtained. The ion couples for which E" is known, in both alkaline and acidic solutions, are those numbered 7 to 13 in Table 1. The expressions for these couples, derived from E" values in aqueous solutions, are less precise than the ‘experimental’ (1 to 6 in Table J), but all the expressions indicate that increasing basicity of the glass melt moves the equilibrium in favour of the upper oxidation state except for cu+/cu 2+ . The situation 1‘s aoraphically illustrated in Fig. 3 by plotting the logarithm of [oxidised]/[reduced] (i.e., - log R) versus the optical basicity over the approximate range for alkali/alkaline earth silicate glasses (0.5 and 0.7). For the soda-lime-silica glass referred to earlier (where A = 0.58), for example, Fig. 3 indicates the
Ni4+< Pb4+< T13’< Co3+< Ce4+< Cr6’<
Mn3+
< As5+ < Sb5’ < Fe3’ < V5’ < Sn4’. Towards the left hand side of this series, the species are present in minute quantity. For example, [Ni4’] = [Ni2’] X 10e3, taking A = 0.56. Bearing in mind the approximations (especially for equilibria 7-13 in Table l), the series conveys an overall pattern rather than rigid detail. Nevertheless, the behaviour predicted by the expressions in Table 1 (Fig. 3) for equilibria 7-13 conforms to the limited chemical knowledge available. This conformation is seen for manganese and vanadium, for example, by calculating their redox ratios. Over the optical basicity range, 0.55 to 0.65, [Mn2’]/[Mn3’] is between 2.5 and 0.16, and [V4+]/[V5+ I between 0.55 and 0.06, indicating that both oxidation states are readily obtained in the glass systems, conforming to experimental observations. On the other hand, it is difficult to generate Co3+ and T13’ unless the glass has a high basicity, while the Ni4’ ion is unknown in glass. Turning now to redox reactions generally, that is, where the counter redox couple is other than 02-/O,, the equilibria can be expressed as: mM(Z+“)t+
2
ntMLt +
&pYf’
&/f’(Y+“‘)+*
(6)
Writing the equilibrium in the form, Eq. (6), avoids the problem of defining the actual species in the melt. However, it follows that in the expression below, Eq. (71, the quotient, Q, cannot be regarded as a true constant:
1
0 2X-E2 -1 zm 82 -2 E -3
[ M”t]m[ log
Q= log
M’(Y+‘“)+]n
[M(:t”)t]“‘[M’yt]”
Pm
= nzlog [ M(:t")t]
-4 -5
Solids 196 (1996)
! 0.50 0.k
1 I 0.60 0.65
1 0.70
Optical basicity Fig. 3. Plot of logarithm of [oxidized]/[reduced] for metal ion couples (at 1400°C and air atmosphere) versus optical basicity for silicate glass systems.For clarity, data for copper are omitted.
[Mtyt] - n log [ M,(y+,ll)+] -
(7) It is possible to express log Q in terms of A using the expressions in Table 1. For example, for the equilibrium Cr6’ + 3Fe2” = Cr3’ t 3Fe3’
(8)
JA.
of Non-Crystalline
Dufjt/Journal
Eq. (7) becomes logQ= (8.2- 13.711) -3(3.2-6SA), (9) for which log Q is 5.8 A - 1.4. The 13 equilibria in Table 1 allow the generation of expressions for another 77 two-ion-couple equilibria of the type, Eq. (6). (It should be noted that, without the equilibria 7-13 in Table 1, there are only 15 two-ion-couple equilibria generated [9].) In all of these expressions, the quotient, Q, depends on the optical basicity of the glass. It is important to note that, even though the 0*-/O, couple does not appear in Eq. (6); nevertheless, the conditions are still for air atmosphere (and 1400°C) because the expressions in Table 1 are for these conditions. Some of the trends are shown, in Fig. 4, to illustrate the extent to which Q is affected, and it is apparent that a sharp change in Q occurs when one of the ion couples is cu+/cu 2+. The reason for this sharp change is that, as previously noted, increasing basicity favours Cu+ rather than Cu*+ (i.e., negative A in Table 1, and therefore, the right-hand side of Eq. (7) involves summation rather than difference of A values). Experimental data for several of the expressions (Eq. (7)) derived from Table 1 are available from half wave potentials obtained in molten Na,O-SiO, and Na,O-CaO-SiO, glasses [6]. When these data are compared with values of Q obtained for the A values of these two glass melts, the agreement, with one or two exceptions, is good [20]. The relationship between log R (for the melt) and electrode potential in aqueous solution, Eqs. (4) and (5), can also be applied to the reduction of metal ions log4 2
0
= c 3Fer+C? A?
3F8+C?’
c Sb” = As” + Sb”
Fe% + Mn” = Fe* + MnY
-2
-4
2Cu2’+As3+=2Cu’+Ask i
0.50
0.55
0.60
0.65
0.70
Solids 196 (1996145-50
-2
49
Be I’ I
I
I
0.5
0.6 Optical basicity
0.7
Fig. 5. Plot of electrode potentials (relative to the O’-/O, couple) of selected metal-ion/metal couples versus optical basicity of silicate melts (at 1400°C and air atmosphere).
to the metallic element in the glass melt. The electrode potential in the melt, Emelt, at 1400°C is given by 0.332 Emelt = -log R. (10) n
Values of log R for A = 0.70 and 0.40 are obtained from Eqs. (4) and (5), and these then provide a link between Emeltand the optical basicity of the molten glass. For example, the E” values for the reduction of arsenic (III) to the element are - 0.71 V in alkaline solution (A = 0.70) and 0.234 V in acidic (0.40) [21]. Eqs. (4) and (5) yield values of log R of - 1.995 and 0.255 to give Emeltvalues (Eq. (10)) of -0.22 and 0.03 V, corresponding to the relationship Eme,t= 0.36 - 0.83A. (11) This equation is illustrated, together with several other metal/ion couples, relative to the 0*-/O, couple, in Fig. 5. The significance of these results is discussed elsewhere [22]. Acknowledgements
Optical Basicity
Fig. 4. Variation of log Q, for equilibria in silicate melts (at 1400°C and air atmosphere) versus optical basic@ (taken from Ref. [91).
Parts of this work are the result of a continuing collaboration with Dr F.G.K. Baucke, whose input is gratefully acknowledged.,
50
JA
Dufi/Journal
ofNon-Crystalline
References [ll H.D. Screiber and M.T. Coolbaugh, J. Non-Cryst. Solids 181 (1995) 225. [2] R. Bruckner and H. Hessenkemper, Glastech. Ber. 66 (1993) 245. [3] H. Muller-Simon, Glastech. Ber. 67 (1994) 297. 141 K. Karlsson, Glastech. Ber. 62 (1989). [5] C. Russel and E. Freude, Phys. Chem. Glasses 30 (1989) 62. [61 K. Takahashi and Y. Miura, J. Non-Cryst. Solids 95&96 (1987) 119. 171 R.J. Araujo and N.F. Borrelli, SPIE Submolecular Glass Chem. Phys. 1590 (1991) 138. [81 J.A. Duffy and M.D. Ingram, J. Non-Cryst. Solids 21 (1976) 373. [9] F.G.K. Baucke and J.A. Duffy, Phys. Chem. Glasses 34 (1993) 158. [lo] M. Cable and Z.D. Xiang, Phys. Chem. Glasses 33 (1992) 154. [l I] R. Pyare and P. Nath, J. Am. Ceram. Sot. 65 (1982) 549.
Solids 196 (1996)
45-50
[12] R. Pyare, S.P. Singh, A. Singh and P, Nath, Phys. Chem. Glasses 23 (1982) 158. [13] A. Paul and R.W. Douglas, Phys. Chem. Glasses 6 (1965) 207; 6 (1965) 197; 6 (1965) 212. [14] P. Buhler and R. Weissmann, Glass Phys. Chcm. 20 (1994) 157. 1151 L. Pauling, J. Chem. Sot. (1948) 1461. [16] J.A. Duffy, Chem. Britain 30 (1994) 562. [I71 J.A. Duffy and M.D. Ingram, J. Am. Chem. Sot. 93 (1971) 6448. 1181 C.K. Jorgensen, Oxidation Numbers and Oxidation States (Springer, Berlin, 1969) ch. 5. [191 F.G.K. Baucke and J.A. Duffy, Phys. Chem. Glasses 35 (1994) 17. 1201 J.A. Duffy, unpublished resulrs, [21] Handbook of Chemistry and Physics, 55th Ed. (CRC, Cleveland, OH, 1974-75). [22l J.A. Duffy and F.G.K. Baucke, J. Phys. Chem. 99 (1995) 9189.
Journal
of Non-Crystalline Solids196(1996)45-50
Redox equilibria in glass J.A. Duffy Depurtment
of Chemistry,
University
*
of Aberdeen,
Aberdeen,
Scotland,
VK
Abstract Data for redox equilibriain silicateglassmelts,for the ion couples:Fe2+/Fe3’, Cr3+/Cr6’, Ce3’/Ce4’, Snzf/Sn4’ and As3‘/As5+, can be relatedto the glasscompositionand indicatethat increasingbasicity favours the upperoxidation state.The relationshipsare simplifiedby makingthe correlationwith the optical basicity of the glassrather than with its composition.The optical basicity modelis concernedwith the electrondensityenvironmentprovidedby oxygenatomsfor the hostedmetal ions and, in principle, allows comparisonbetweenany oxidic environment.Comparisonbetweenglass melts and aqueoussolution establishes a relationshipbetweenthe redox behaviour in the melt and standardelectrode potentialsin aqueoussolution.The applicationsof this relationshipare discussed.
1. Introduction
There have been several studies of redox behaviour in glass for elements existing in more than
one oxidation state (see, e.g., Refs. [l-14]). Taking iron as an example, the equilibrium can be written: Fe3++ e-= Fe2+.
(1) This is countered in the molten glass by the equilibrium involving atmospheric oxygen and oxygen atoms (in the oxidation state of -2) of the glass so that overall: 4Fe3+ + 202- = 4Fe2+ + 0
2’
(2)
The position of equilibrium in Eq. (2) is affected by the composition of the glass melt and, at first sight, it may appear that the lower oxidation state is favoured by increasing glass basicity, since this increase corresponds to increasing oxide ion activity.
* Tel: +44-1224212901.Telefax:+44-1224212921.
For the Fe2+/Fe3+ and most other couples, it is generally found that increasing basicity favours the upper oxidation state (although, in some glass systems, the redox behaviour is less straightforward). For sodium silicate melts at 1400°C and air atmosphere, analysis of the resulting glasses shows that, with increasing Na,O, there is an increase in the +3 state; furthermore, at a given SiO, content, the Fe2’ concentration is lower in a K,O-SiO,, glass but higher in a Li,O-SiO, glass [13]. This difference is shown in Fig. l(a) in which the logarithm of the redox ratio, R, (R = [Fe2’]/[Fe3’]> is plotted against mol% of the basic oxide. These results indicate that there must be another factor in operation which accompanies, but counters, the increase in oxide ion activity. This factor arises from the increasing negative charge borne by the glass network and the effect this charge has on the stability of a hosted metal ion when surrounded by the oxygen atoms. Under normal chemical conditions, metal ions try to achieve charges which are less positive than their oxidation numbers in order to comply with elec-
0022-3093/96,&15.00 0 1996ElsevierScienceB.V. All rightsreserved SSDI0022-3093(95)00560-9
46
J.A. Du#y/Journal
10
20
30 Mol % M20
40
0.50
0.55
ofNon-Crystalline
0.60
Optical
0.65
Basicity
Fig. 1. Variation of log{[Fe*+ ]/[Fe3’ 11in alkali silicate melts at 1400°C in air atmosphere with (a) mol% alkali oxide content, (b) optical basicity.
troneutrality. In a glass, this occurs through donation of negative charge by the oxygen atoms surrounding the metal ion. Increasing the basicity of a glass leads to a greater degree of negative charge on the constituent oxygen atoms and, hence, to a greater ‘electron donor power’. This increase will be of greater benefit to the upper oxidation state metal ions, since they need more negative charge for decreasing their positive charge than the lower oxidation state ions. Indeed, it is conceivable that an environment may provide too much negative charge for the lower state.
Solids 196 (1996) 45-50
This aspect of glass behaviour is in the context of Pauling’s electroneutrality principle [ 151 and indicates how the higher oxidation state is favoured by increasing basicity. It is possible to express, numerically, the (average) electron donor power of the oxygen atoms in glass by the optical basicity value, A [8,161. Optical basicity was originally developed to express the acid-base nature of oxidic media generally [17]. Values of A were obtained experimentally from orbital expansion spectroscopy 1181in the ultra-violet region, and analysis of these data made it possible to calculate an ‘ideal’ or ‘theoretical’ value directly from the glass composition using Eq. (3): A=X,A(A)
+X,A(B)
+ .-a.
x,, x,,... are the molar proportions contributed by the constituent oxides, A, B, . .. to the total oxide(-II) content of the glass (that is, the equivalent fractions) and A(A), A(B), .. . are the optical basicity values of these individual oxides. Values of A for some oxides are: K,O, 1.4; Na,O, 1.15; CaO, 1.00; FeO, 1.00; Al,O,, 0.60; SiO,, 0.48; B,O,, 0.42; P,O,, 0.33 [8,16]. Calculation of A for a soda lime silica glass requires A(Na,O), A(CaO> and A(SiO,>; thus, a glass of composition Na,O-CaO-SiO, (1:2:7, molar ratio) has A equal to [l X 1.15/17+2X 1.00/17 t 14X O-48/17], i.e., 0.58.
Table 1 Dependence of redox ratio on optical basicity a Equilibrium 1 2 3 4 5 6
I 8 9 10 11 12
13
Redox relationship 4Fe3f+202-=4Fe2tt0 4Cr6++ 60*-= 4Cr3’ + 36 2 4Ce4+t202-=4Ce3+t0 2 2Sn4+ + 20*-= 2Sn*+ + 0 2‘4s5++ 20*-= 2*s3++ 4Cu2++202-=?Cu++O,*
0’
2Ni4++ 20*-= 2Ni*+ + 0 2Pb4++202-=2Pb*++O*
2
2Tl3++20*-=2Tl++o 4C03++202-=4Co*++*O
4Mn3++ 20*-= 4Mn*++ 0’ 2 2Sb”++20*-=2Sb3”+0 2 4V5++202-=4V4++0 2
a For silicate melts at 1400°C in air atmosphere.
(3)
log{[Fe2+]/[Fe3+]) = 3.2 - 6.5A log{[Cr3+]/[Cr6+]) = 8.2 - 13.7A log([Ce3’ ]/[Ce4’ 1) = 5.4 - 8.3 A log([Sn*+ ]/[Sn4+ ]I= 0.6 - 3.6 A log([As3+]/[As5+]] = 5.2 - 8.9A log([Cu+]/[Cu’+]) = -6.5 + 10.0/i log([Niz+]/[Ni4+]) = 17 -25A log([Pb2’]/[Pb4+]) = 15 -22A 10g([~+]/[T1~+]) = 13 -20A log([Co2+]/[Co3+11 = 9 - 14A log([Mn2+]/[Mn3’]) = 7 - 12 A log{[Sb3+]/[Sb5+]) = 6- 11 A log([V4+]/[V5+]) =4- 8A
JA. Dufi/Joumal
2. Redox equilibria
of Non-Crystalline
Solids 196 (1996)
47
(a)
and optical basicity
When the data in Fig. l(a) are replotted so that the alkali oxide content on the abscissa is replaced by optical basicity, the three trends are united into a single line, as shown in Fig. l(b). Redox data also exist for Cr3+/Cr6+, Ce3+/Ce4+, Sn2+/Sn4+, As3+/Assf and Cu +/Cu* + in alkali and/or alkaline earth silicate melts at 1400°C and air atmosphere. [lo-131 For all of these, except Cu+/Cu*+, increasing the basicity of the glass favours the upper oxidation state, and when log R, is plotted versus A, relationships similar to that for Fe2+/Fe3+ (Fig. l(b)) are obtained (with opposite slope for Cu+/Cu2’ >. The relationships are almost linear and can be expressed, as indicated in Table 1. In principle, they can be used for calculating the position of equilibrium for any alkali (or alkaline earth) silicate glass at 1400°C and air atmosphere simply by substituting the value for A, calculated from the glass composition using Eq. (3). It is emphasised that the relationships between redox ratio and optical basicity (Table 1) are empirical. Furthermore, whereas the redox ratios are for molten glass (at 14OO”C), the optical basicity value is calculated from parameters obtained ultimately from glass and other media at ambient temperature. One reason preventing a more fundamental approach to the equilibria in Table 1 is the impossibility of specifying the environment for metal ions in terms of proper coordination spheres, owing to the lack of a well-defined boundary which normally does not develop in oxyanion network systems. The optical basicity method circumvents this shortcoming and provides, in effect, a measure representing the electron density available at the ‘average’ site for occupation by a hosted metal ion. The study of redox behaviour in glass melts at elevated temperatures has been restricted to relatively few systems owing to the experimental difficulties associated with the measurements. It would be advantageous, therefore, if a reliable link could be established between the known behaviour of ion couples in glass melts and in aqueous solution [l]. Such a link might then enable the use of standard electrode potentials (E”’ data) for predicting the redox equilibria of ion couples in glass melts. The optical basicity model views the solvated
45-50
nE"
log R
Fig. 2. Plot of nE” for metal ion couples versus logarithm of redox ratio,:R, calculated from Table 1 by setting A at (a) 0.70 (alkaline conditions) and (b) 0.40 (acidic conditions).
metal ions in oxide melts no differently from those in water. In both media, the metal ion is in a field of negative charge provided by polarised oxygen(-II) atoms (polarised by Si4+, Naf, etc. in the melt and by HS in water). Bearing in mind the Nemst equation, it might be expected that a relationship exists between E” X n (where n is the number of electrons involved in the redox equilibrium) and the redox ratio obtained from the expressions in Table 1 with A4set at the value appropriate to the aqueous medium. For alkaline conditions, it has been previously shown that A for hydroxide species is 0.70 while, for acidic conditions, in which the ions are solvated by H,O molecules, A = 0.40. Plotting E” X n against the logarithm of the redox ratio, R, obtained by substituting A = 0.70 in the expressions in Table 1 for alkaline solution, and 4 = 0.40 for acidic, (Fig. 2) indicates that a proportionality factor, constant for all the ion couples, operates and takes into account the extreme difference in the conditions so that log R = 0.42nE” - 1.1
(4)
for alkaline solutions, and log R = 2.5nE” - 1.5 for acidic solutions [ 191.
(5)
48
J.A. Duffy/Journal
ofNon-C’rystalline
3. Applications
45-50
following series for the upper state, becoming an increasingly important species in the glass:
If the assumption is made that these expressions, Eqs. (4) and (51, apply to other ion couples, it is possible to obtain values of log R from the E” values in aqueous solutions. These will be for A = 0.70 and 0.40 and, thus, by the reverse procedure, the linear equation relating log R with A for the conditions of the silicate melt at 1400°C (and air atmosphere) are obtained. The ion couples for which E" is known, in both alkaline and acidic solutions, are those numbered 7 to 13 in Table 1. The expressions for these couples, derived from E" values in aqueous solutions, are less precise than the ‘experimental’ (1 to 6 in Table J), but all the expressions indicate that increasing basicity of the glass melt moves the equilibrium in favour of the upper oxidation state except for cu+/cu 2+ . The situation 1‘s aoraphically illustrated in Fig. 3 by plotting the logarithm of [oxidised]/[reduced] (i.e., - log R) versus the optical basicity over the approximate range for alkali/alkaline earth silicate glasses (0.5 and 0.7). For the soda-lime-silica glass referred to earlier (where A = 0.58), for example, Fig. 3 indicates the
Ni4+< Pb4+< T13’< Co3+< Ce4+< Cr6’<
Mn3+
< As5+ < Sb5’ < Fe3’ < V5’ < Sn4’. Towards the left hand side of this series, the species are present in minute quantity. For example, [Ni4’] = [Ni2’] X 10e3, taking A = 0.56. Bearing in mind the approximations (especially for equilibria 7-13 in Table l), the series conveys an overall pattern rather than rigid detail. Nevertheless, the behaviour predicted by the expressions in Table 1 (Fig. 3) for equilibria 7-13 conforms to the limited chemical knowledge available. This conformation is seen for manganese and vanadium, for example, by calculating their redox ratios. Over the optical basicity range, 0.55 to 0.65, [Mn2’]/[Mn3’] is between 2.5 and 0.16, and [V4+]/[V5+ I between 0.55 and 0.06, indicating that both oxidation states are readily obtained in the glass systems, conforming to experimental observations. On the other hand, it is difficult to generate Co3+ and T13’ unless the glass has a high basicity, while the Ni4’ ion is unknown in glass. Turning now to redox reactions generally, that is, where the counter redox couple is other than 02-/O,, the equilibria can be expressed as: mM(Z+“)t+
2
ntMLt +
&pYf’
&/f’(Y+“‘)+*
(6)
Writing the equilibrium in the form, Eq. (6), avoids the problem of defining the actual species in the melt. However, it follows that in the expression below, Eq. (71, the quotient, Q, cannot be regarded as a true constant:
1
0 2X-E2 -1 zm 82 -2 E -3
[ M”t]m[ log
Q= log
M’(Y+‘“)+]n
[M(:t”)t]“‘[M’yt]”
Pm
= nzlog [ M(:t")t]
-4 -5
Solids 196 (1996)
! 0.50 0.k
1 I 0.60 0.65
1 0.70
Optical basicity Fig. 3. Plot of logarithm of [oxidized]/[reduced] for metal ion couples (at 1400°C and air atmosphere) versus optical basicity for silicate glass systems.For clarity, data for copper are omitted.
[Mtyt] - n log [ M,(y+,ll)+] -
(7) It is possible to express log Q in terms of A using the expressions in Table 1. For example, for the equilibrium Cr6’ + 3Fe2” = Cr3’ t 3Fe3’
(8)
JA.
of Non-Crystalline
Dufjt/Journal
Eq. (7) becomes logQ= (8.2- 13.711) -3(3.2-6SA), (9) for which log Q is 5.8 A - 1.4. The 13 equilibria in Table 1 allow the generation of expressions for another 77 two-ion-couple equilibria of the type, Eq. (6). (It should be noted that, without the equilibria 7-13 in Table 1, there are only 15 two-ion-couple equilibria generated [9].) In all of these expressions, the quotient, Q, depends on the optical basicity of the glass. It is important to note that, even though the 0*-/O, couple does not appear in Eq. (6); nevertheless, the conditions are still for air atmosphere (and 1400°C) because the expressions in Table 1 are for these conditions. Some of the trends are shown, in Fig. 4, to illustrate the extent to which Q is affected, and it is apparent that a sharp change in Q occurs when one of the ion couples is cu+/cu 2+. The reason for this sharp change is that, as previously noted, increasing basicity favours Cu+ rather than Cu*+ (i.e., negative A in Table 1, and therefore, the right-hand side of Eq. (7) involves summation rather than difference of A values). Experimental data for several of the expressions (Eq. (7)) derived from Table 1 are available from half wave potentials obtained in molten Na,O-SiO, and Na,O-CaO-SiO, glasses [6]. When these data are compared with values of Q obtained for the A values of these two glass melts, the agreement, with one or two exceptions, is good [20]. The relationship between log R (for the melt) and electrode potential in aqueous solution, Eqs. (4) and (5), can also be applied to the reduction of metal ions log4 2
0
= c 3Fer+C? A?
3F8+C?’
c Sb” = As” + Sb”
Fe% + Mn” = Fe* + MnY
-2
-4
2Cu2’+As3+=2Cu’+Ask i
0.50
0.55
0.60
0.65
0.70
Solids 196 (1996145-50
-2
49
Be I’ I
I
I
0.5
0.6 Optical basicity
0.7
Fig. 5. Plot of electrode potentials (relative to the O’-/O, couple) of selected metal-ion/metal couples versus optical basicity of silicate melts (at 1400°C and air atmosphere).
to the metallic element in the glass melt. The electrode potential in the melt, Emelt, at 1400°C is given by 0.332 Emelt = -log R. (10) n
Values of log R for A = 0.70 and 0.40 are obtained from Eqs. (4) and (5), and these then provide a link between Emeltand the optical basicity of the molten glass. For example, the E” values for the reduction of arsenic (III) to the element are - 0.71 V in alkaline solution (A = 0.70) and 0.234 V in acidic (0.40) [21]. Eqs. (4) and (5) yield values of log R of - 1.995 and 0.255 to give Emeltvalues (Eq. (10)) of -0.22 and 0.03 V, corresponding to the relationship Eme,t= 0.36 - 0.83A. (11) This equation is illustrated, together with several other metal/ion couples, relative to the 0*-/O, couple, in Fig. 5. The significance of these results is discussed elsewhere [22]. Acknowledgements
Optical Basicity
Fig. 4. Variation of log Q, for equilibria in silicate melts (at 1400°C and air atmosphere) versus optical basic@ (taken from Ref. [91).
Parts of this work are the result of a continuing collaboration with Dr F.G.K. Baucke, whose input is gratefully acknowledged.,
50
JA
Dufi/Journal
ofNon-Crystalline
References [ll H.D. Screiber and M.T. Coolbaugh, J. Non-Cryst. Solids 181 (1995) 225. [2] R. Bruckner and H. Hessenkemper, Glastech. Ber. 66 (1993) 245. [3] H. Muller-Simon, Glastech. Ber. 67 (1994) 297. 141 K. Karlsson, Glastech. Ber. 62 (1989). [5] C. Russel and E. Freude, Phys. Chem. Glasses 30 (1989) 62. [61 K. Takahashi and Y. Miura, J. Non-Cryst. Solids 95&96 (1987) 119. 171 R.J. Araujo and N.F. Borrelli, SPIE Submolecular Glass Chem. Phys. 1590 (1991) 138. [81 J.A. Duffy and M.D. Ingram, J. Non-Cryst. Solids 21 (1976) 373. [9] F.G.K. Baucke and J.A. Duffy, Phys. Chem. Glasses 34 (1993) 158. [lo] M. Cable and Z.D. Xiang, Phys. Chem. Glasses 33 (1992) 154. [l I] R. Pyare and P. Nath, J. Am. Ceram. Sot. 65 (1982) 549.
Solids 196 (1996)
45-50
[12] R. Pyare, S.P. Singh, A. Singh and P, Nath, Phys. Chem. Glasses 23 (1982) 158. [13] A. Paul and R.W. Douglas, Phys. Chem. Glasses 6 (1965) 207; 6 (1965) 197; 6 (1965) 212. [14] P. Buhler and R. Weissmann, Glass Phys. Chcm. 20 (1994) 157. 1151 L. Pauling, J. Chem. Sot. (1948) 1461. [16] J.A. Duffy, Chem. Britain 30 (1994) 562. [I71 J.A. Duffy and M.D. Ingram, J. Am. Chem. Sot. 93 (1971) 6448. 1181 C.K. Jorgensen, Oxidation Numbers and Oxidation States (Springer, Berlin, 1969) ch. 5. [191 F.G.K. Baucke and J.A. Duffy, Phys. Chem. Glasses 35 (1994) 17. 1201 J.A. Duffy, unpublished resulrs, [21] Handbook of Chemistry and Physics, 55th Ed. (CRC, Cleveland, OH, 1974-75). [22l J.A. Duffy and F.G.K. Baucke, J. Phys. Chem. 99 (1995) 9189.