J. Phys. Chem. 1991, 95, 413-417 low-temperature end of phase I1 becomes less favorable at high temperatures, and vice versa. Thus, we may conclude that species A is favored a t lower temperatures while the site of species C at higher temperatures. It is interesting to note that in the corresponding intermediate range in UTIC, phases I1 and 111, two trioxane species are observeds at constant relative intensities over the whole temperature range. Indeed in this system the unit cell dimensions appear to be constant or to change only very little within the intermediate-temperature region.Is As for phase 111 the residence sites of the guest molecules in phase I I of TClC are not known. In the present case the situation is even more complicated because it is not known whether the different cyclohexane species coexist in the same unit cells or whether they are distributed in different domains of the sample. It is also not clear how two highly disordered species, one with uniaxial (C) and the other with biaxial (B) quadrupole tensors, can coexist in the same lattice. The same problem is also encountered in UTIC, where two disordered species of trioxane with different symmetries coexist within the hexagonal channels in the intermediate-temperature range (phases I1 and Here too N M R studies of single crystals, more detailed X-ray measurements, and perhaps also computation of potential energy surfaces16 within the channels can shed more light on the problem. (16) Parsonage, N. G.; Pemberton,R.C . Trans. Faraday SOC.1967,63, 311.
413
The high-temperature region of the inclusion compounds corresponds to phase I in both TCIC and UTIC. This phase is characterized by hexagonal channels in which the guest molecules occupy the two 32 sites in the unit (hexagonal) ceL4 The guest molecules exhibit a very small orientational order parameter which decreases slightly upon heating. In TCIC the transformation between phases I1 and I is continuous and coincides with the completion of the conversion of species B to C, which then remains as the only species in phase I. At around -30 "C characteristic line-shape changes take place, which can quantitatively be accounted for in terms of the cyclohexane ring inversion process. At about the same temperature range the signal of the I4N NQR disappears, apparently due to reorientation of the host thiourea molecules.2*6 It is clear however that these effects are not due to any phase transition process, as was originally thought to be the case.*^^.^ This region is in fact the least problematic in the TCIC system as it appears that the structure and dynamics of both the host and guest molecules are pretty well understood and there are no anomalies in most of the other physical measurements. (Exceptions are the anomalous C, peak' at -100 "C and the discontinuity6 in the thiourea proton T I at -106 "C.)
Acknowfedgment. This work was partially supported by the US.-Israel Binational Science Foundation, Jerusalem. We thank Dr. Felix Frolow for helpful discussions concerning the crystal structure of TCIC. Registry No. TCIC-d,,, 58368-61-9.
Relation between the Thermodynamics and Kinetics of a Complex Reaction System at Constant Temperature and Pressure Robert A. Alberty Department of Chemistry, Massachusetts institute of Technology, Cambridge, Massachusetts 02139 (Received: June 28, 1990)
For complex systems, it is convenient to express both the thermodynamic condition for chemical equilibrium and the rate equation in matrix notation. Chemical equilibrium calculations at constant temperature and pressure are generally made on the assumption that the only constraints on the minimization of the Gibbs energy are the element balances. This can be accomplished in terms of chemical reactions (the so-called stoichiometric formulation of the problem) by the use of any independent set of R reactions that can provide for all possible compositions permitted by the conservation of elements. The rate equation for a complex system is written in terms of a mechanism that may involve a larger or smaller number of reactions. An equilibrium composition can be calculated from the rate equation by integration to infinite time, but this composition may or may not agree with that calculated from thermodynamics on the assumption that the only constraints are the element balances. I f the mechanism includes R independent reactions, the equilibrium compositions calculated in these two ways should agree if the forward and reverse rate constants for each step are in agreement with the equilibrium constants for those steps. I f the mechanism involves fewer than R independent reactions, a different equilibrium composition will be calculated from the rate equation because constraints are implicitly involved in the mechanism. These constraints can be taken into account in the thermodynamic calculation to obtain the same equilibrium composition. This is illustrated for a system involving polycyclic aromatic hydrocarbons.
Introduction This article is concerned with the thermodynamics and kinetics of chemical changes in a closed system involving many species and many reactions in a single phase. Such systems can be studied at constant temperature and pressure or constant temperature and volume, but we will consider here only systems containing ideal gases at constant temperature and pressure. By use of matrix notation, the basic equations for thermodynamic equilibrium' and the rates of of the amounts of various species in a system ~
~~~
( I ) Smith, W. R.; Missen, R. W . Chemical Reaction Equilibrium Analysis: Theory and Algorithms; Wiley: New York, 1982. (2)Othmer, H.G.Chem. Eng. Sci. 1976,31,993.
0022-3654/9 1/2095-0413$02.50/0
can be written in compact form. The rate equation contains the thermodynamic condition for chemical equilibrium in the sense that the equilibrium composition can be calculated by numerical integration to infinite time. However, there is a class of mechanisms that yield a different equilibrium composition than that obtained from thermodynamics on the assumption that the only constraints on the minimization of the Gibbs energy are the el(3) CBme, G. M. Compur. Chem. Eng. 1979,3,603. (4)Gardiner, W. C. Jr. Combusrion Chemistry; Springer: New York,
1984. ( 5 ) Smooke, M. D. J. Compul. Phys. Commun. 1982,48,12. ( 6 ) Villermaux, J. Report of IUPAC Commission 1.4.
(7) Alberty, R. A. J . Chem. Phys. 1987,87, 3660.
0 1991 American Chemical Society
414
The Journal of Physical Chemistry, Vol. 95, No. 1. 1991
ement balances. If a mechanism has fewer independent reactions than the number of reactions required to provide for all possible changes permitted by the conservation of elements, a different equilibrium composition will be calculated by using the rate equation. However, a thermodynamic calculation can also yield this equilibrium composition if the conservation equations implicit in the mechanism are included in the thermodynamic calculation.
Thermodynamics of Chemical Equilibrium in a Closed System at Constant Temperature and Pressure The fundamental equation for a system involving N species and R independent reactions can be written in matrix notation’ as (dG)T,P = PV d5
(1)
where G is the Gibbs energy of the system, is the 1 X N matrix of chemical potentials of the species, v is the N X R matrix of stoichiometric numbers, and 4 is the R X 1 matrix of extents of reaction. The stoichiometric numbers are positive for products and negative for reactants. Since (dC),, = 0 at chemical equilibrium, the equilibrium condition is PU = 0
(2)
where 0 is a 1 X R matrix of zeros. The stoichiometric number matrix v in eqs 1 and 2 can be calculated’ from the system matrix A by use of
Au = 0
(3)
where A is a M X N matrix of the numbers of atoms of the M elements in the N species. The zero matrix 0 is M X R. The stoichiometric number matrix v is the null space of the system matrix A. The v matrix for a complex system is not unique, but it provides the stoichiometric numbers for a set of R independent reactions that can represent all possible changes in the composition of the system that are permitted by the conservation of elements. The number of independent reactions is equal to the rank of the v matrix. R = rank v
(4)
If we start with the system matrix A for the elements and calculate v using eq 3, the sum of the ranks of the A and v matrices is equal to the number of species: N = rank A
+ rank v
(5)
This equation can also be used when A includes other linear constraints introduced by the mechanism. When a system contains isomers, the number of independent reactions included in eq 1 can be greatly reduced by using isomer groups and the chemical potentials of isomer The terms for isomers with a given formula can be aggregated because they all have the same chemical potential at equilibrium. Thus groups of isomers can be treated as species in the fundamental equation of thermodynamics when the standard Gibbs energies of formation of isomer groups are used in calculations. The system matrix A can be calculated from the stoichiometric number matrix v since vTAT = 0
(6)
Thus AT is the null space of vT. Equilibrium condition 2 is the basis of the stoichiometric formulation of the general equilibrium problem.’ However, most computer programs for solving the general equilibrium problem use the nonstoichiometric formulation that involves Lagrange (8) Smith, B. D. AIChE J. 1959, 5, 26. (9) Danzig, G. B.; DeHaven, J. C. J . Chem. Phys. 1962, 36, 2620. (IO) Duff, R. E.; Bauer, S. H. J . Chem. Phys. 1962, 36, 1754. ( I I ) Smith, W. R.; Missen, R. W. Can. J . Chem. Eng. 1974, 52, 280. ( 12) Alberty, R. A. Ind. Eng. Chem. Fundam. 1983, 22, 3 18. (13) Alberty, R. A.; Oppenheim, 1. J. Chem. Phys. 1988, 89, 3689.
Alberty m~ltipliers.’~’~ The other necessary input for a calculation of the equilibrium composition is, of course, the initial composition. The initial composition is assumed here to be arbitrary: that is, it does not involve any special conditions. The A matrix includes a row for each conservation equation that must be satisfied. If charged species are involved, this matrix must include a row to ensure electrical neutrality, but we will consider only neutral species here. If two elements in the A matrix always occur in species in a certain ratio, one row in the A matrix will not be independent and should be discarded. In other words, the two elements are treated together as a pseudoelement, and the rank of the A matrix is reduced. Mechanisms may implicitly involve conservation equations. Additional conservation equations increase the rank of the A matrix and decrease the rank of the v matrix, as can be seen in eq 5, and consequently decrease the number of independent reactions. Here we will use R for the number of independent reactions calculated without consideration of the mechanism, in order to be able to emphasize that the number of reactions R’in a mechanism can be smaller than R, equal to R. or greater than R. Usually, R’> R.
Kinetic Equations for a Closed System at Constant Temperature and Pressure The composition of a complex system can be calculated as a function of time by use of a mechanism that includes all of the elementary reactions that can occur in the system and their rate constants. Since temperature and pressure are held constant, we can imagine that the system is in a cylinder in a thermostat with a sliding piston to maintain constant pressure. In considering the kinetics of chemical change in a closed system containing N species on the basis of a mechanism involving R’ reactions, it is convenient to use matrix notation.*-’ ViIIermaux6 has treated flow systems as well as closed systems and has pointed out advantages in writing rate equations as transposes of the equations given here. If the initial composition and all of the rate constants are known, the composition at any later time can be calculated by numerical integration of the basic kinetic equation dn/dt = (vb - vf)(d5/dt) = vdS/dt
(7)
where n is the N X 1 matrix of amounts of species, v b is the N X R’ stoichiometric number matrix for the backward reactions in the mechanism, v f is the N X R’stoichiometric number matrix for the forward reactions in the mechanism, v is the N X R’matrix of stoichiometric numbers of the R‘reactions in the mechanism, and [ is the R X 1 matrix of extents of reaction. The stoichiometric numbers are taken as positive in v f and vb. The reason for writing v as a difference between two matrices is that a mechanism can include reactions of the type 2A
+ B = AB + A
(8)
+
In thermodynamics this reaction would simply be written A B = AB. The stoichiometric numbers in vf and v b are used in the rate equations for the matrix d[/dt. As a simplification, it is assumed here that if isomer groups are involved, they remain in equilibrium; in other words, it is assumed that isomerization rates are faster than other reactions so that isomer groups can be aggregated in the kinetics as well as in the thermodynamics. The v matrix for a mechanism is in general different from that arising in the thermodynamic treatment of the system, but we will not use a different symbol here in order to simplify the terminology. This v matrix can be used in a thermodynamic calculation since it is equivalent, as illustrated by the examples shown later. The basic kinetic equation is more general than the fundamental equation of thermodynamics in that it gives the time course of the reaction and must yield the equilibrium composition at infinite time. At infinite time where 0 is an N
X
v(d[/dt), = 0 (9) 1 matrix of zeros. The only way for this
( I 4) Krambeck, F. J. Presented at the 71st Annual Meeting of the AIChE, Miami Beach, FL, Nov 16, 1978.
Thermodynamics and Kinetics of a Complex Reaction System
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 415
condition to be met is for (d(/dt)- = 0, where 0 is a R ’ x 1 matrix of zeros. Various computer p r o g r a m ~ ~ J +have ~ ’ been written to implement the calculation of compositions during chemical change in a complex system using eq 7, but here we are only concerned with the composition at infinite time. The R’reactions in the mechanism need not be independent. However, it is important to know how many of the reactions in the mechanism are independent from the standpoint of the eventual equilibrium. This can be determined by use of a Gaussian reduction (now reduction) of the Y matrix. The number of independent reactions in the mechanism can be equal to R or less than R. First, we will consider a general mechanism with R reactions that happen to be independent, but then we will consider mechanisms with more than R reactions and mechanisms with fewer than R reactions. The mechanism for a system with N species and R independent reactions can be represented by
where Po is the standard state pressure. These two dimensionless equilibrium constants are related by
V‘ilAl
vfi2A2 +
... -t vf&N
= ubi1Al
+ vbi2A2 4- ... 4- vbiNAN
(10) where the stoichiometric numbers are all positive and i = 1, 2, ..., R. The rate of conversion matrix d[/dt is an R X 1 matrix of rates of change of extents of reaction (d&/dt). The components in this column matrix have the form N j=I
c [A,]’b~~}
J=
I
(1 1)
where kfi and kbi are forward and backward rate constants of reaction i. It is assumed here that these rate constants are independent of the composition of the system. Multiplying and dividing the right-hand side by the first term in brackets yields the following expression for the rate of conversion of the ith reaction in the mechanism:
since ubij - ufij = vi’. Because of the principle of detailed balance, dti/dt = 0 at equiibrium for each reaction in the mechanism. At equilibrium, eq 12 shows that the ratio of forward and backward rate constants for a reaction in the mechanism is given by
The right-hand side is simply the expression for the equilibrium constant in terms of concentrations. If K, represents the dimensionless equilibrium constant in terms of concentrations KCi= j= fi([Ajl/co),,‘u I
(14)
where co is the standard state concentration, then where N
vi =
(1 8 )
In order to emphasize the thermodynamic aspect of eq 11, kci/kbiis replaced with kfj/kbi = Kpi(P”/RT)”i and [A,] is replaced by [Aj] = njP/RTn, where N
n, =
Enj j=1
In addition, Kpi is replaced by N
Kpi = exp(-Cpojvu/RT) j= I
Thus eq 12 becomes N
fI [Aj]”‘u[1 - exp( Cvijpj/RT)]
dEi/dt = Vkfi
N
d&/dt = q k f i c[Aj]”tj - kbi
K,, = Kpi(Po/coRT)”~
xuij
j= I
Since we are dealing with gas reactions, chemical potentials are generally expressed in terms of pressure, and so it is convenient to use KPi that is defined by
(15) Kee, R. J.; Miller, J. A.; Jefferson, T. H. CHEMKIN: a General Purpose, Problem Independent, Transportable FORTRAN Chemical Kinetics Code Package. Report SAND 80-8003; Sandia National Laboratories: Albuquerque, NM, 1980. (16) Stabler, R. N.; Chesick, J. Inr. J . Chem. Kiner. 1978, 10, 461-469. (17) McKinney, R. J.; Weigert, F. J. Quantum Chemistry Program Exchange, Program No. QCMP022, or Project SERAPHIM, Program No. IB- 1407.
j= 1
j- I
At equilibrium, the rate of conversion is zero for each reaction, and so the condition is that each of the terms in the vector of Cui.uj values is equal to zero. This is equivalent to eq 2, since the reactions in the mechanism are assumed to be independent, even though they may be different from those used in the calculation of the equilibrium composition using thermodynamics. Thus, when the mechanism has R independent reactions, the thermodynamic and kinetic conditions for equilibrium are the same. If there are independent paths for the overall reaction, these considerations apply to each path separately.
Mechanisms with More Than R Reactions Although a mechanism may involve more than R reactions, the maximum number of independent reactions is R because this is the number of reactions required to represent all possible changes in composition permitted by the conservation of elements. A set of independent reactions can be derived from a mechanism by use of a Gaussian reduction, as shown by Smith and Missen.l The nonindependent reactions in a mechanism can be obtained by adding and subtracting the independent reactions. The reactions in a set of independent reactions are not unique. The number of independent reactions, which is unique, is equal to the rank of the Y matrix. For small matrices, the matrix operations described here can be done by hand, but a computer is needed for large matrices. Computer programs for manipulating large matrices have been available for some time on large computersi8and have only recently become available on personal computers. Helzer19 has published computer programs in APL for a number of matrix operations. Matrix operations are provided by Mathematica20 and P C - M A T L A B . ~ ~ The calculations presented here have been obtained with Mathematica, which provides results in terms of integers when the input matrices are in terms of integers. The system matrix A that corresponds with a particular v matrix can be calculated because AT is the null space of UT, as shown in eq 6. The system matrix A is not unique. However, the equivalence of two forms of a matrix can be demonstrated by carrying out a Gaussian reduction on both to see that the same result is obtained. Since the A matrix is equivalent to the Y matrix from ( I 8) NAG Fortran Mini Manual, Numerical Algorithms Group, Downers Grove, IL, 1983. (19) Helzer, G. Appried Linear Algebra with APL; Little Brown: Boston, 1983. (20) Mathematica, Wolfram Research, Inc., P.O. Box 6059, Champaign, IL 61821. (21) The Mathworks, Inc., 21 Eliot St., S.Natick, MA 01760.
Alberty
416 The Journal of Physical Chemistry, Vol. 95, No. I , 1991
which it is derived, the equilibrium composition calculated from thermodynamics is the same as that calculated from kinetics using the v matrix for the mechanism, provided the mechanism involves R independent reactions. The nature of the constraint in an equilibrium calculation that arises in a mechanism can be clarified by considering a specific example. The example discussed here arises in a system consisting of acetylene (C2H2),molecular hydrogen (H2), benzene (C6H6), naphthalene (CioHe),and the anthracene-phenanthrene isomer group (C14Hlo).In this section, we assume that the only constraints on the minimization of the Gibbs energy at constant temperature and pressure are the element balances. The formula matrix for this system is A , . The first row of this matrix gives the numbers for carbon atoms of the five species involved, and the second row gives the numbers of hydrogen atoms. The null space of A , , which can be calculated by hand or by use of a computer, is the stoichiometric number matrix v I . More properly, the stoichiometric number matrix shown should be written as a 5 X 3 matrix, but this distinction is not made here in order to simplify the following flow chart.
-
101
lo*
tuka
Ai
2 2
-7
0 2
6
10 8
6
2
0 0
14 10
1
- 5 1 0 1 0 - 3 0 1 0 0 Vl
1
0
rc&m
A2
0 1
3 0
c-
5 -1
41n)
7 -2
(24
ndus
I01
1 0 0 42'3) (ldl) 0 1 0 4-m (W 0 0 1 - 2 1
rc&m
Ai 4Y3J -1
0
2
1
cm)
-t
chiometric restrictions that arise in mechanisms by adding a row (or rows) to the A matrix. Smith and Missen2' have discussed the constraint in the reaction of hydrogen peroxide with potassium permanganate. Two additional examples of stoichiometric restrictions arising in mechanisms are provided by mechanisms that have been considered for the formation of benzenoid polycyclic aromatic hydrocarbons in a flame.28 The important conclusion here is that when there is a constraint in the mechanism, a different equilibrium composition is calculated than it its absence, and thermodynamics will yield this same composition if the conservation equation for the constraint is included in the equilibrium calculation. The following are the first two lines of a mechanism that has been used for the formation of polycyclic aromatic hydrocarbons in a benzene flame:2E
The corresponding stoichiometric number matrix is V6, which has the null space As. This does not look like a familiar system matrix, but A4 does.
1 0
t u k a
2 0 6 10 14 2 2 6 8 10 0 0 1 1 1
w
-3 0 1 0 0 - 5 1 0 1 0 - 7 2 0 0 1
ledw
1 0 0 2 0 1 0 -1 0 0 1 1
1" -
The Y , matrix represents the following three independent reactions: 7C2H2 = C14HIO 2H2 5C2H2 = CloH8 + H2
+
3C2H2 = C6H6 (25) This set of reactions can represent all possible composition changes in the system that are permitted by the element balances, but it is not unique. Another possible set of independent reactions is given by v3. This may seem trivial because the reactions in v3 are simply arranged in another order, but there is an important point here. The null space of v3 is A3, which is not easily recognized as a system formula matrix. However, A, and A3 can be shown to be equivalent by making a row reduction (Gaussian reduction) on each to obtain AZ. This matter is discussed by Smith and Missen." The equivalence of v I and v3 can also be shown by performing row reductions on each. The matrix product Au is a 2 X 3 matrix of zeros, as required by eq 3. The set of reactions in eq 25 is suitable for the calculation of the equilibrium composition of the closed system. Usually the equilibrium composition of a closed system is calculated by minimizing the Gibbs energy, subject to the constraints represented by A,.
-4
2
-2
1
-1
-1
v4
0 1 1 0
luka
1 -(le)
0 0
&
c-
As 4
-2 1
1 0 - 2 0 2 - 1 0 4 2 0 1 2 0 0 0
t
IPaa I01
lo*
(24)
"2
mr
Io1
+
A4
Nl'
0 1/2 -(1/2)_Isducs -2 1 -1 1 - 2 1 -2 1 0 V5
v6
1 -1
0 1
(27)
The third row in A4 represents the aromatic constraint in mechanism 26. Since the amount of aromatic substance is conserved, this amount must be treated as a constraint, just like amounts of the elements. A4 and A6 both reduce to A,, which shows that they are equivalent. The null space of A4 is v4, which represents a set of reactions that can provide for all possible changes in composition permitted by mechanism 26. Row reduction shows that y4 and Y6 are equivalent. In order to calculate the equilibrium composition subject to the constraint in mechanism 26, the three constraints in A4 are used in the minimization of the Gibbs energy. When this is done, the same equilibrium composition is calculated as would be obtained by integration of the rate equations for the mechanism.
Discussion The chemical reactions in a mechanism do not have to be independent, but it is important to know how many of them are independent. If the number of independent reactions in the mechanism is equal to the number R of independent reactions required to represent all possible chemical changes that are Mechanisms with Fewer Than R Reactions permitted by the conservation of the elements, the mechanism should yield the same equilibrium composition as thermodynamics. If the mechanism involves fewer than R reactions, it will, of course, have fewer than R independent reactions, which is the If the number of independent reactions in the mechanism is less important thing. Such a mechanism implicitly involves conserthan R, the mechanism will yield a different equilibrium comvation equations in addition to element balances. In this case, position. This altered equilibrium composition can be calculated by using thermodynamics if the conservation equations that are the equilibrium composition calculated from the kinetics (eq 7) will be different from that calculated from thermodynamics (eq implicit in the mechanism are included in the minimization of G 2). This subject has a long history since in 1921 JouguetZ2pointed along with conservation of the elements. The way this is done out the advantages of calculating the equilibrium composition using has been discussed by Smith and Missen.' The fact that a the reaction paths actually available for chemical change. S ~ h o t t ~ ~ mechanism may not provide enough reactions to allow all possible showed how the necessary constraints for the restricted equilibrium composition changes permitted by the conservation of elements can be used in a general equilibrium program. Bjornbom2e26has may be considered to be the result of the specificity of the catalyst discussed examples of restricted equilibria, and Krambeck14 and or the result of the temperature being so low that certain additional Smith and Missen' have shown how to handle additional stoireactions are too slow to be observed in kinetic experiments. At a higher temperature, additional reactions might contribute to the kinetics, and the mechanism would then yield the same (22) Jouguet, E. J . Ec. Polyrech. (Paris) 1921, [2] 21, 61. (23) (24) (25) (26)
Schott, G.L. J . Chem. Phys. 1964, 40, 2065. Bjornbom, P. H. Ind. Eng. Chem. Fundam. 1975, 14, 102. Bjornbom, P. H. AIChE J . 1977, 23, 285. Bjornbom, P. H. Ind. Eng. Chem. Fundam. 1981, 20, 161.
(27) Missen, R. W.; Smith, W. R.J . Chem. Ed., in press. (28) Alberty, R. A. J. Phys. Chem. 1989, 93, 3299.
J. Phys. Chem. 1991, 95, 417-423 equilibrium composition as thermodynamic calculations assuming only conservation of elements. However, for short times relative to the time required to reach this final equilibrium, we have the interesting situation that equilibrium measurements can tell us something about the mechanism.
417
Acknowledgment. This research was supported by a grant from Basic Energy Sciences of the Department of Energy (Grant No. DE-FG02-85ER13454). I am indebted to Prof. Garry Helzer, Department of Mathematics, University of Maryland, for advice on the calculation of null spaces using computers.
Functional Metallomacrocycles and Their Polymers. 25. Kinetics and Mechanism of the Biomimetic Oxidation of Thiol by Oxygen Catalyzed by Homogeneous (Polycarboxyphtha1ocyaninato)metaIs H. Shirai,* H. Tsuiki, E. Masuda, T. Koyama, K. Hanabusa, Department of Functional Polymer Science, Faculty of Textile Science and Technology, Shinshu University, Ueda-shi, 386 Japan
and N. Kobayashi Pharmaceutical Institute, Tohoku University, Aobayama, Sendai, 980 Japan (Received: July 19, 1989: In Final Form: June 12, 1990)
The oxidation of 2-mercaptoethanol (RSH) catalyzed by (polycarboxyphtha1ocyaninato)metal acid (M-papc, M = Fe( III), Co(ll). Ni(ll), Cu(Il), pa = -(COOH)2, -(COOH),,-(COOH),) in the presence of molecular oxygen has been studied in aqueous homogeneous solution at pH 7.0 and at 25 OC. The catalytic effects of M-papc have been determined the oxygen consumption in the reaction mixture with a Warburg respirometer. The central metal ions and the number of carboxylate ions on M-papc affected the catalytic activities for the aerobic oxidation of RSH. (Octacarboxyphthalocyaninato)iron(IIl) and -cobalt(lI) are remarkably effective catalysts. (Dicarboxyphtha1ocyaninato)metals and Ni(l1)- as well as Cu(l1)phthalocyanine derivatives are less effective catalysts. The kinetics of the aerobic oxidation catalyzed by (octacarboxyphthalocyaninato)iron(IIl) and -cobalt(II) have been characterized in terms of a bisubstrate Michaelis-Menten rate law ( k , = 600-800 min-I, at pH 7.0,25 "C). The rate law and spectral experiments indicate that the catalyzed reactions proceed via the formation of a ternary activated complex where RS- and O2reversibly coordinate with the central metal on the phthalocyanine rings. The activation parameters were also determined for this reaction at pH 7.0 and at 25 "C. The catalytic activities followed the order of Co(l1)-oapc > Fe(II1)-oapc > Co(I1)-tapc = Fe(II1)-tapc. Differences in catalytic ability have been explained in terms of the aggregation and spin state of metallophthalocyanine derivatives in aqueous solution at pH 7.0. The (tetracarboxyphthalocyaninato)cobalt(II) covalently bound to poly(2-vinylpyridine-c~styrene), despite of being a heterogeneous system, is a remarkably effective catalyst ( k , = 2210 min-') because of polymer effects.
Introduction Transition-metal complexes or a metal ion anchored to polymer matricies represent useful model systems of natural metalloenzymes.IJ Metallophthalocyanines have attracted considerable interest because of their structural similarity to the active center of naturally occurring haemproteins.3 We have studied the synthcsis of functional metallophthalocyanines and their polymers and their catalase-like as well as peroxidase activities as enzyme The oxidation of thiol to disulfides is an important ( I ) Shirai, H.; Hojo, N. Polymeric Catalysts. Functional Monomers and Polymers; Takemoto, K., Inaki, Y., Ottenbrite, R. M., Eds.; Marcel Dekker: New York, 1987, p 49. (2) Kaneko, M.; Tsuchida, E. Makromol. Reu. 1981, 16, 397. (3) Berezin, B. D. Coordination Compounds of Porphyrins and Phthalocyanines; Wiley: New York, 198 I . (4) Shirai, H.; Maruyama, A.; Takano, J.; Kobayashi, K.; Hojo, N. Makromol. Chem. 1980, 181, 565. (5) Shirai, H.; Maruyama, A.; Kobayashi, K.; Hojo, N.; Urushido, K. Makromol. Chem. 1980, 181, 575.
biological process, and the role of metal ions in the reactions of the sulfhydryl-containing substrate is of significance in view of the nature of electron-transport enzymes. Numerous attempts have been made in recent years to determined the catalyzed aerobic oxidation of thiol to disulfide by cobalt sulfophthalocyanine and its polymeric systems.8-1s However, no evidence for an en(6) Shirai, H.; Maruyama, A.; Konishi, M.; Hojo, N. Makromol. Chem. 1980, 181, 1003. (7) Shirai, H.; Higaki, S.;Hanabusa, K.;Kondo, Y.;Hojo, N. J . Polym. Sci. 1984, 22, 1309. (8) Wagnerova, D. M.;Schwertnerova, E.;Veprek-Siska, J. Collect. Czech. Chem. Commun. 1974, 39, 3036. (9) Cook, A. H. J . Chem. SOC.1938, 1761. (IO) Maas, T. A. M. M.; Kuijer, M.; Zwart, J. J . Chem. Soc., Chem. Commun. 1976, 86. ( 1 1 ) Alt, H. H.; Sandstede, G. J . Coral. 1973, 28, 8. (12) Brouwer, W. M.; Piet, P.; German, A. L. J . Mol. Catal. 1985, 31,
._. .
169
(13) Van Herk, A. M.; Tullemans, A. H. L.; Van Welzen, J.; German, A. L. J . Mol. Catal. 1988, 44, 269.
0022-3654/91/2095-0417!$02.50/00 1991 American Chemical Society
