T H E
l
[C(EM
-
o*o'k
E)]
I-
and
u
=
(1 -. I/%)log
[EM
- r n / n ] + l/n
-I
0.004t ' ' ' ' ' I '
log (Q/n)
Measurement of the absorbance a t different total vanadium(1W)-TSPC concentrations allows x and y to be calculated providing EM and E , are known. The molar absorptivity of the monomer, EM, was obtained by heating a 5.0 X lo-' M VIV-TSPC solution with no added salts until there was no further increase in the absorbance a t 692 nm, the absorption maximum of the monomer. This occurred at a temperature of about 75". It has previously been demonstrated that organic solvents favor the monomer in equilibrium involving tetrasulfonated metallophthalocyanine systems.'O The addition of either pyridine or methanol in this system favors the formation of the monomer and a t a concentration of 5% by weight of the former solvent, the equilibrium shifts completely in favor of the monomer a t 28". The optical absorptivity of the monomer (692 nm) obtained by heating (75") was in excellent agreement with the value obtained a t 28" in the presence of pyridine after a correction is made for solvent expansion. This indicates that the change in optical absorptivity with temperature over a range of 28 to 75" is small and within experimental error.4 Low concentrations enhance the formation of monomer as is evidenced by the absorption maximum of the monomer (692 nm) which decreases less than expected when the solutions are diluted while the absorption maximum of the dimer (660 nm) decreases more than expected. The molar absorptivities of the monomer a t 692 and 660 nm are 1.6 X lo6and 4.4 X lo4M-l cm-l, respectively, a t 28". Added salts convert the monomeric species into the dimeric form as proposed by Bernauer and Fallab.2 The conversion appears complete a t 0,009 M NaC104 and 10" for a solution 5.0 X 10-5 M in vanadium(1V)TSPC. Molar absorptivities of the dimer at 660 and 692 nm are 2.4 X lo6 and 4.8 X lo4M-l cm-', respectively, a t 28". Under the above conditions, the absorbance a t 660 nm due to the dimer is at a maximum.
0.03
I I : ,
0.I
1.0
I
t
IO
Iox ~ 10~ (see eq 4), at 28, 38, and 50" Figure 2. Plot of 1 0 us. with p = 0.006 (NaC104) and h 692 nm.
At this point it should be mentioned that when the concentration of NaC104 exceeds 0.009 M , there is a slight absorbance decrease at both 692 and 660 nm. This suggests higher polymers form at greater salt concentrations or that association of the constituents of the salt with the monomer or dimer alters their spectral characteristics. Figure 2 shows plots of loz vs. 1Ov taken over a total vanadium(1V)-TSPC concentration range of 5.0 X M a t 692 nm. The plots are linear 10-7 t o 5.0 X a t different temperatures with a slope of l / n (from eq 4). Substitution of the l / n value back into eq 4 allows the concentration quot,ient, Q, to be calculated. The following results obtained for n at p = 0.006 (NaClO,) and different temperatures are 1.94 (28"), 1.95 (38"), and 1.97 (50"). These results indicate that the primary equilibrium is that between monomer and dimer. Spectrophotometric measurements made on 5.0 X lo-' and 5.0 X lo-&M vanadium(1V)-TSPC solutions, the extremes of the concentration range examined, yield a single isosbestic point (see Figure 1) which is also consistent with a monomer-dimer equilibrium. Table I shows typical values of the monomer-dimer concentration quotients, Q, calculated from the absorbance of different VIv concentrations a t 50" and = 0.006 (NaC104). Spectral measurements on the dilute solutions were made with a spectral cell of 10-cm path length, while (9) H. Kuhn, E. Schnabel, and H. Nother in "Recent Progress in the Chemistry of Natural and Synthetic Coloring Matter and Related Fields," T. S. Gore, Ed., Academic Press, New York, N. Y.,1962, pp 561-572. (10) H.Sigel, P. Waldmeir, and B. Prijs, Imrg. Nuel. Chem. Leit., 1, 161 (1971).
The Journal of Physical Chemistry, Vol. 76, No. 17, 1979
R. D. FARINA, D. J. HALKO, AND J. H. SWINEHART
2346
I
Table I: Spectral Concentration Quotients Absorband
0.041 0.068 0.230 0.395 0.855 1.570
[VOTsPC]T,b M
lo'&,
5.0 x 1.0 x 5.0 x 1.0 x 2.5 X
3.0
5.0
10-7 10-8
I
I
IO
15
20
I
t
2.9 3.0 2.8
10-6 10-6
3.0 3.0
a LMeasured a t 692 nm. b Represents the total concentration, C, of VrV-TSPC. cThe monomer and dimer concentrations were calculated from theequationA = (EX - E D / ~ ) M (ED/~)C.
-u I
aJ
+
measurements on the more concentrated solutions were done with a cell of 1-mm path length. The concentration quotients determined spectrally a t the diff erent temperatures are 1.1 Et 0.1 X lo-' M (28"), 1.9 f 0.2 X lo-' M (38"), 2.9 f 0.1 X lov7M (50°), respectively, a t p = 0.006 (NaC104). Kinetic Results. Kinetic data obtained at total vanadium(1V)-TSPC concentrations 5 X M or less give linear plots for the logarithm of the light transmission os. time indicating a single relaxation process. The results are consistent with a dimer-monomer equilibrium kf
2VOTSPCZkb
with the reciprocal relaxation time being 7-l
I
MG
x
(VOTSPC)22t-
I
= 4kb[VOTSPC"-]
+ ki
where [VOTSPC"] is the equilibrium monomer concentration having charge i. Spectral measurements of the monomer-dimer equilibrium made under the same experimental conditions allows the concentration of the monomer t o be calculated from the total vanadium(1V)TSPC used. Figure 3 is a plot of 7-l vs. monomer concentration a t diff erent temperatures from which the rate constants were obtained. The values of kf and k b a t different temperatures are 0.9 f 0.1 sec-l, 4.5 f 0.3 X lo6 M-l sec-' (28"); 2.0 f 0.2 sec-I, 5.5 f 0.5 X lo6 M-I sec-l (38") ; and 4.5 f 0.2sec-', 8.4 f 0.8 X lo6 M-' sec-l (50"), respectively, at 1 = 0.006 (n'aClO4). The ratio of the rate constants gives the following concentration quotients at various temperaM (28") ; 3.6 f 0.5 X loT7M tures: 2.0 f 0.7 X (38'); 5.4 f 0.7 X M (50°), respectively, at 1= 0.006 (NaC104). From plots of In ( k / T ) vs. 1/T the activation parameters AHt and A S t are 13.6 f 1.5 kcal/moI and - 14 f 5 eu for kf and 4.9 f 1.5 kcal/mol and - 12 f 5 eu for Jcb. The difference in the enthalpies of activation for the rate constants kf and k b yields a AH" of 8.7 f 3.0ltcal/mol. A comparison of the concentration quotients deterThe Journal of Physical Chemistry, Vol. 76, N o . 17, 1978
c
t'
Y
I
5
0
I
I
25
30
35
1
Figure 3. 1 / us. ~ [VOTSPCs-] at 28, 38, and 50" at p = 0.006 (NaC104).
mined from rate data with the values obtained from spectral measurements shows a discrepancy which is outside the limit of experimental error. If the sodium salt of Na4VOTSPC is completely dissociated in aqueous solution, then the monomeric species would assume a charge of -4 and the dimer - 8, respectively. These charges are very high indeed, and it seems rather unlikely that no cation association occurs especially since 0.006 M sodium perchlorate is added. Therefore, it is quite possible that one or more species of the type NaVOTSPC3-, Na2VOTSPC2-, etc., can form having essentially the same intrinsic optical absorptivities. If it is assumed that a relatively simple condition exists where the following equilibria are proposed kf
(VOTSPC)2s-
2VOTSPC4-
(5)
kb
Na+
fast
+ VOTSPC4-
NaVOTSPC3-
(6)
kf '
(NaVOTSPC)$-
2NaVOTSPC3-
(7)
kb'
and the equilibrium of (6) occurs rapidly compared to ( 5 ) and (7) with (6) being coupled to (7), then the inverse of one relaxation time becomes
1_
=
4kb'[NaVOTSPC3-] X
7
+
K([Na+] [VOTSPC4-]) 1 K ( [Na+] [VOTSPC4-])
+
+
+
kr,
MONOMER-I)IMER EQUILIBRIUM IN VIv TETRASULFOPHTHALOCYANINE whkh may be simplified to 1
- ‘v 4kb’[NaVOTSPC3-11 7
K [Na+] K[ha T +]
+
+ kf’
where KEZ
[NaVOTSPC3-] [Na+][VOTSPC4-]
The equilibration of (5) is assumed to be sufficiently slow so that it will not contribute to the relaxation expression shown above. Slower rates would be expected for the higher charged species based on electrostatic a r g ~ r n e n t s . ~The concentration quotient obtained from spectral measurements need not be a ratio of a single monomeric and dimeric species but a ratio of their concentration sums &spectral
=
[monomer, total12 [dimer, total]
+ [NaVOTSPC3-])2 + [ (NaVOTSPC)z6-]
( [VOTSPC4-] [(VOTSPC)2s-]
Substitution of VOTSPC4- in terms of its equilibrium constant, K yields the alternate expression for &spectral [NaVOTSPCa_]ZIKINaC1 K [Na+] + &spectral =:
By using
[(VOTSPC)?-]
Qspeotral,the
‘1’
+ [(NaVOTSPC)26--]
quantity
can be calculated which is not the expression to be plotted to obtain k b ’ and kf‘. Under the proposed conditions the ratio kr’/kb’ will not be in agreement with the Qspeotral value. I n an analogous manner it can be shown that there will also be nonagreement between the ratio kf/kb and the &spectral value. A second plausible explanation for the discrepancy between the ltinctic and spectral concentration quotients may be due to the formation of small amounts of higher polymers which cannot be detected by spectroscopic methods. Support for both these arguments is presented below from the kinetic studies. When the total vanadium(1V)-TSPC concentration M , plots of the logarithm of the light exceeds 5 X transmission us. time are slightly curved. If two relaxations are assumed, this is sufficient to represent the data quantitatively. The two relaxation times can be obtained by first determining the longer relaxation time from the linear portion of the curve at long times. The linear portion of the curve is then extended to shorter times and subtracted from the experimental curve. The shorter relaxation time can then be determined from the resultant straight line. Owing to the small absorbance change, the shorter re-
2347
laxation time could not be obtained. However, there were several interesting characteristics associated with the shorter relaxation process. First, two relaxations are detected at the monomer band (692 nm), while only the one slow relaxation is observed a t the 660-nm band (dimer maximum). Second, the shorter relaxation process is observed only at concentrations in excess of 5 X M where both monomer and dimer are present in appreciable amounts. The change in light transmittance associated with the shorter relaxation time increases slightly as the total concentration of VIV-TSPC is increased. The two relaxations are consistent with the proposed cation association in that the faster relaxation time would be associated with the coupled equilibria between (6) and (7), while the slower relaxation would be attributed to equilibrium 5. When the total concentration of VIV-TSPC is increased, larger amounts of (NaVOTSPC)26- could be generated, and this would explain the increase in light transmittance observed. Equations 5 , 6, and 7 are not the only set of equilibria possible since another set of equilibria could be postulated involving cation associated species such as NanVOTSPC2-, (NazVOTSPC)z4-,etc. The kinetic measurements made a t 660 nm either are of insufficient sensitivity to detect two relaxations or there is no measurable difference in the optical absorptivity of the dimeric species. Two relaxations could also be attributed to higher polymer formation a t concentrations exceeding 5 X M , where the polymer is formed from monomer(s) and/or dimer(s) with no cation associated species present. However, in the higher polymer, the dimer either maintains its spectral integrity or measurements carried out at 660 nm are not of sufficient sensitivity to detect the more rapid relaxation process. Kuhn and coworker^^^^' have shown from spectral studies of metal-free phthalocyanine sulfonate and copper(I1)-TSPC solutions with no added salts, that M total dye concentration is presabout 4% of a ent as a tetramer. Addition of salts increases the tetramer concentration. lo Therefore, it seems quite plausible that a small amount of complexes having a higher degree of association (i.e., greater than the dimer) can form at the more concentrated vanadium(1V)-TSPC solutions. However, the primary equilibrium at vanadium(1V)-TSPC concentrations of 5.0 X lo-’ to 5.0 X M is that between monomer and dimer. A study of the pH dependence was made to determine whether the dimerization process involves hydrolysis. The pH of the VIV-TSPC solutions in the concentration range of 10-7 to 5 X M varies slightly assuming a value of 5.8 =t 0.1. Introduction of either acid or base has the same effect as salt in that (11) U. Ahrens and H. Kuhn, 2. Phys. Chem. (Frankfurt a m Main), 37, 1 (1963).
The Journal of Physical Chemistry, Vol. 7 6 , No. 17, 1978
2348 the equilibrium is shifted in favor of the dimer. This is presumably due to the increase in the ionic strength of the solution. Kinetics studies made a t pH values of 9.1 and 3.0, a range where the monomer-dimer equilibrium is still maintained, give relaxation times which are slower than tbe values obtained at a pH of 5.8. This observation is consistent with the decrease in the monomer concentration as indicated by spectral measurements. A comparison of these relaxation times at the proposed lower monomer concentration with the l monomer concenvalues extrapolated from the ~ - os. tration plot show good agreement and are well within the discrepancy between the spectral and kinetic results. This same effect has also been observed in the CuII-TSPC system12 so hydrolysis can be excluded from the reaction mechanism. Any further discussion regarding the mechanism by which the dimer is formed should preferably require some knowledge of the dimer structure in solution which is unknown. It has been proposed in the CoIITSPC system13 that the dimer is formed by the overlapping of the extended ?r-electron clouds of the highly conjugated TSPC molecules of two parallel monomeric species (staggered, stacking), and this structure would certainly be applicable to the VIV-TSPC dimer. Magnetic studies14 on the oxyvanadium(1V) phthalocyanine complex suggest a five-coordinate structure which is presumably square pyramidal. If this structure represents the monomeric species of VIV-TSPC in solution, then the structure of the dimer could be as described above with the vanadyl oxygen groups probably occupying the two axial trans positions. However, an alternate mechanism involving the formation of a VOV bridged structure cannot be ruled out. Such structures have been proposed in the Mn111-TSPC6and aluminum phthalocyanine systems. Some experiments were conducted with the (DurrumGibson) stopped flow apparatus to examine the effect of different reducing agents on the monomer-dimer equilibrium. Preliminary studies using sodium di-
The Journal of Physical Chemistry, Vol. 76, No. 17,1972
R. D. FARINA, D. J. HALKO,AND J. H. SWINEHART thionite indicate the rate of reduction is independent of dithionite concentration. The results are consistent with the following reaction scheme kr
(VOTSPC)22* kb
2VOTSPC'- (rate determining) (8) VOTSPCI-
+ SZO4'-
kr A
product (rapid)
(9)
Assuming steady-state conditions for the monomeric species the observed rate constant is equal to kr. The value of the observed rate constant is 0.5 sec-' at about 22' and p = 0.006 M which is within experimental error of an extrapolated value of 0.45 sec-l obtained for kf under the same conditions. This suggests that the monomcr is preferentially reduced by dithionite. A few stopped-flow experiments were also carried out using aqueous vanadium(I1) as the reducing agent. The rate of reduction of vanadium(1V)-TSPC was followed spectrophotometrically at 425 nm. When aqueous vanadium(I1) and vanadium(1V)-TSPC are mixed, a large absorbance increase occurs at 425 nm which decreases over several minutes. A similar absorbance change is observed for the V2+--VOaq2+ reaction where an intermediate VOV4+is obscrved.16 This suggests reduction occurs by attack of the aqueous vanadium(I1) at the vanadium(1V) oxygen in VOTSPCI-. More work will be done in this area to clarify this point.
Acknowledgment. The authors wish to acknowledge support of this work by the National Institutes of Health through Grant CM 11767. (12) R. Farina, presented at the 23rd Southeastern Regional Meeting of the American Chemical Society, Nashville, Tenn. (13) Z. A. Schelly, D. J. Harward, P. Hemmes, and E. M . Eyring, J . Phys. Chem., 74, 3040 (1970). (14) A. B. P. Lever, J. Chem. Soc., 1821 (1965). (15) F. B. Baker and T . W. Newton, Inmg. Chem., 3, 569 (1964).
