J. Phys. Chem. lB82, 86,103-107
103
Crystal Growth of Calcium Carbonate. A Controlled Composition Kinetic Study 1. F. Kazmlerczak, M. B. Tomron, and 0. H. Nancollas' Chemistry Department, State Unlvefslty of New York at Buffab, Buffalo, New York 14214 (Received: January 13, 1981; In Flnal Form: August 19, 1981)
A new constant composition method is described for the study of the kinetics of calcium carbonate crystallization in which the activities of ionic species in the supersaturated solutions are maintained constant by the potentiometrically controlled addition of reagents. The rate of crystallization is proportional to the square of the supersaturation, expressed in terms of the activities of free calcium and carbonate ions over a pH range 8.25 to 10.0 and from 15 to 35 OC. This evidence, together with a corresponding activation energy of 39.2 f 3.6 kJ mol-', points to a surface-controlled reaction. The rate constant for crystal growth is strikingly independent of the ionic strength of the supersaturated solutions from 0.007 to 0.20 mol dnr3,when the rate law is written in terms of ionic activities rather than concentrations.
Introduction The precipitation and dissolution of carbonate minerals of divalent metal ions such as calcium carbonate (calcite and aragonite) and calcium magnesium carbonate (dolomite) are of considerable importance in a wide variety of fields such as limnology,' oceanography,2 and sedimentology? The crystal growth of calcium carbonate also has important applications in water purification and energy production t e ~ h n o l ~ g yThe . ~ ~concentration of calcium carbonate in many natural waters is equal to or greater than the saturation level' and as a consequence, calcium carbonate precipitation and crystal growth takes place in water treatment and desalination facilities. Since the solubilities of the calcium carbonate polymorphs decrease with increasing temperature, the petroleum engineer also has to contend with carbonate scaling at the relatively high ambient temperatures. Calcium carbonate has probably received the greatest attention in connection with its precipitation and dissolution in natural water systems. In seawater, the effect of various ionic constituents upon the rate of calcium carbonate crystallization may explain the existence of metastable polymorphs of the salt. In studies aimed at modeling natural water systems, experiments are frequently made to determine spontaneous precipitation thresholds by mixing solutions of salts containing the lattice ions and observing the appearance of the first solid phase. In such systems, it is impossible to eliminate entirely the foreign substances or dust particles that can act as sites for heterogeneous nucleation. Thermodynamic interpretations of the results assume the attainment of equilibrium and involve the thermodynamic solubility products of the precipitating material. The assumption of thermodynamic equilibrium a t each stage of the precipitation reaction is open to question since kinetic considerations may be of paramount importance in determining the nature of the phase which forms initially. In view of the importance of kinetic considerations for the elucidation of the mechanism of calcium carbonate (1)W. S t u " and J. J. Morgan, "Aquatic Chemistry",Wiley-Interscience, New York, 1970. (2)P. E. Cloud in 'Chemical Oceanography",Vol. 2,J. P. Diley and G. Skirrow, Ede., Academic Press, New York, 1965;pp 127-158. (3) R. A. Berner, 'Principles of Chemical Sedimentology-,McGrawHill,New York, 1971. (4)G. M.Fair, J. C. Geyer, and D. A. Okun, 'Elementa of Water Supply and Wastewater Dispoeal",Wiley, New York, 1971,pp 474-483. (5) M. N. Elliot, Desalination, 8, 221 (1970). (6)M.N. Elliot, Desalination, 6, 87 (1969). (7)J. P. Ranck, Desalination, 6, 75 (1969). 0022-3654/82/2086-0103$01.25/0
precipitation and dissolution, a highly reproducible seeded growth technique has been employed to characterize calcite crystal These experiments, unlike the spontaneous precipitation studies discussed above, allow reliable measurement of the crystal growth rate in the presence and absence of additives.loJ1 An additional advantage of utilizing the seeded growth technique is that crystal growth occurs on a well-defined surface of known area and morphology. In the field, precipitation invariably takes place on a surface already present, either of the mineral itself or of a metal offering available sites for adsorption of lattice ions. Seeded crystal growth methods therefore simulate field conditions much more closely than spontaneous precipitation studies. In the latter, the surface characteristics are not well known and change appreciably during the course of an experiment. In the seeded growth techniques which have been previously established, the pH may either be allowed tc decrease in the solution during the reaction8 or it may be maintained by the pH-stat controlled addition of base. In both cases, the concentrations of calcium, bicarbonate, and carbonate ions change rapidly with time, especially during the initial stages of reaction following the addition of seed crystals. In addition, these methods are difficult to use at the very low supersaturations typically found in the environment. In the present work, we have developed a method by which all solution concentrations are maintained constant during the crystal growth reaction, so that the kinetics of crystallization can be studied over a wide range of supersaturation. The method is particularly useful for investigating the mechanism of crystal growth since the extent of reaction at any chosen level of supersaturation can be varied appreciably. Factors such as secondary nucleation and the effect of foreign ions can also be studied under highly reproducible conditions.
Experimental Section For the control of pH, a Metrohm E512 pH meter was used in combination with a Metrohm Impulsomat E473 and Recording Dosimat E415. To maintain the composition of the supersaturated solution at a constant value (8) M. M. Reddy and G . H.Nancollas, J. Colloid Interface Sci., 36, 166 (1971). (9)G . H.Nancollas and M. M. Reddy, J . Colloid Interface Sci., 37, 824 (1971). (10)G. H. Nancollas and N. Purdie, Quart. Reu. (London), 18, 1 (1964). (11)G.H.Nancollas, J. Cryst. Growth, 3 , 335 (1968).
0 1982 American Chemical Society
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The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
during the crystal growth reaction, the Dosimat E415 was modified so as to incorporate mechanically coupled burets to deliver two solutions simultaneously. Calcium analyses were made by atomic absorption (Perkin-Elmer Model 503 Atomic Absorption Spectrophotometer) or by ion exchange of calcium for hydrogen ions (Dowex 5OW-XS) and titration of the eluted acid. Calcite seed crystals were prepared, using the method described previously,8 by adding 0.20 M calcium chloride to 0.20 M sodium carbonate solution at 25 "C. The crystals were aged for at least three weeks before me. Specific surface areas, SSA, of the crystals were determined by nitrogen adsorption using a Quantasorb BET apparatus (Quantachrome Corporation). Seed preparations A, B, and C had SSA values of 0.53 f 0.01, 0.87 f 0.01, and 1.04 f 0.01, m2 g-l, respectively. pH-Stat Experiments. Crystal growth experiments were made in a water-jacketed cell of 530 mL capacity with water, thermostated at the desired temperature (k0.05K), circulating in the jacket. Five hundred milliliters of stable supersaturated solution of calcium carbonate was prepared by the addition of a known volume of calcium chloride solution (ca. 0.05 M) and the subsequent careful dropwise addition of sodium bicarbonate solution (ca. 0.10 M). The mixed solutions were brought to the desired pH (usually 8.50), by the controlled addition of 0.050 mol dm-3 potassium hydroxide solution. Following confirmation of the stability of solutions for at least 1h, a weighed amount of calcite seed crystals was added, which had been dispersed ultrasonically, in 5 mL of saturated calcium carbonate solution. Aliquots of solution were rapidly removed during the reaction and analyzed for total calcium. The pH was maintained constant during these experiments by the pH-stat controlled addition of 0.05 mol dms potassium hydroxide solution. The solids formed were examined by X- powder diffraction (Philips XRG-3000 diffractometer, Cu K a radiation with Ni filter) and were confirmed as ca1cite.l2 No evidence for aragonite formation was obtained. The scanning electron micrographs, SEM (IS1 Super I1 scanning electron microscope), showed characteristic calcite rhombs which became more perfected as growth proceeded. Constant Composition Experiments. In these experiments, following the addition of seed crystals to the calcium carbonate supersaturated solutions, the pH was maintained constant by the simultaneous addition of two titrant solutions, one consisting of calcium chloride and the other, a mixture of sodium carbonate and bicarbonate. Neutral electrolyte (potassium chloride) was added to all the solutions to maintain the ionic strength at the desired value. The carbonate titrant contained sodium carbonate at an arbitrary molarity (usually 0.01 to 0.1 mol dmm3depending upon the anticipated crystallization rate) to replace the precipitated carbonate. The calcium titrant contained calcium chloride at the same molarity as that of the carbonate titrant to replace the precipitated calcium ions. In addition, the two titrants contained carbonate and calcium to correct for dilution of the supersaturated solution by the addition of these solutions. Thus, to the carbonate titrant was added sodium carbonatelbicarbonate at the same pH and twice the concentration of the carbonate in the supersaturated solution. The calcium titrant contained a similarly calculated amount of calcium chloride. Following the introduction of seed crystals, the rate of titrant addition, controlled by the emf of the glass electrode, was such as to replace the calcium and carbonate ions which precipitated and to bring the supersaturation ~
-
_
I
_
_
~
(12) ASTM Special Technical Publication 48-5. American Society for Testing Materials.
Kazmierczak et ai.
of the added volume to the value in the original supersaturated solution. The rate of crystallization was calculated from the volume of titrant solutions added, and constancy (f0.3%) of concentration of calcium ions during the experiments was verified analytically by atomic absorption after filtration (0.22 pm) of aliquots withdrawn from the crystallization cell.
Results and Discussion The concentrationsof ionic species in the supersaturated solutions were calculated from the experimental pH values and mass balance expressions by successive approximations for the ionic strength.13 Activity coefficients, yz,of z-valent ions were calculated using the modified DebyeHuckel equation proposed by Davies.14 Concentrations of the ion pairs CaC03 and CaHC03+,having thermodynamic stability constants of 1420 and 9.95, respectively,15 were less than 3% of the total molar calcium concentration, Tea, in the supersaturated solutions. The calcium carbonate system is complicated by the relatively slow gas/solution equilibrium C02 + H 2 0 + H+ + HC03-. In the present work, this problem was avoided by keeping to a minimum the volume of the gas space above the solution in the crystallization cell. The effective isolation of the system was verified by the constancy of the pH of the supersaturated solutions for periods of hours in the absence of inoculating seed crystals. The rate of crystallization of a number of sparingly soluble 2-2 electrolytes has been shown to be proportional to the square of the relative supersaturation.16 For calcium carbonate, the kinetic equation can be written in terms of the activities of the ionic species
where Tca is the total molar calcium ion concentration at time t, k is the rate constant for growth, s is a function of the seed crystal surface area, and the braces enclose the activity of the ionic species. Kso, the thermodynamic solubility product, was calculated using the expression pKso = 0.01183t + 8.03,16where t is the centigrade temperature. The value of Ks0 at 25 "C, 4.72 X (mol dm-3)2,was confirmed (14%) by allowing growth experiments to proceed to equilibrium. In a previous conventional study of calcite crystallization, the concentrations of lattice ions decreased during the reaction: and the rate was shown to be proportional to (TCa - Tcao),2where Tcao is the value of TC, at equilibrium. In these experiments the activity of the carbonate ion was approximately constant. The results of typical crystallization experiments are summarized in Table I. In experiments 31 and 35-37, potassium hydroxide solution (0.05 M) was added to maintain the pH of the supersaturated solutions at a constant value (8.50 or 10.0). Typical plots of Tca as a function of time following inoculation with seed crystals are shown in Figure 1. It can be seen in Figure 2 that the kinetic equation (1)satisfactorily represents the data. The value of the rate constant, k, normalized for specific surface area of the seed preparations, is strikingly independent of supersaturation, pH, and seed concentration. This confirms the absence of secondary nucleation and that crys(13)G.H.Nancoh, 'Interactions in Electrolyte Solutions", Elsevier Publishing Co., Amsterdam, 1966. (14)C. . Daviea, "Ion Association", Buttenvorths, London, 1962. (15)R. E.hwenthal and G. V. R. Mar&, "Carbonate Chemistry of Aquatic Systems. Theory and Application", Ann Arbor Science Publishers Inc., Ann Arbor, 1976. (16)G. H.Nancollaa, Adu. Colloid Interface Sci., 10,215 (1979).
Crystal Growth of Calcium Carbonate
The Journal of Physical Chemistty, Vol. 88, No. I , 1982 105
TABLE I: Crystallization of Calcite from Supersaturated Solutions at 25 'C, pH 8.50
expt no. 31 3 50 36a 37a
a
Tcax lo4,
T~ x 103,
mol dm'3
mol dm-3
9.891 2.497 2.4 84 2.555
I x io3, mol dm-'
k x seed concn, mg dm-'
dm6 mol-' min-' m-2
B B B
245 60.45 61.0 60.4
24.5 29.5 22.2 21.1
Experiments 5.00 207 207 208 208 208 208 109 7.00 7.00 7.00
B B B B B B B B B B B
100 100 99.5 198 198 198 198 99.4 99.7 99.6 99.6
27.8 21.9 26.4 31.0 30.3 29.6 29.1 30.7 31.2 22.1 21.9
Composition Experiments 1.8 9.00 1.8 9.00 2.3 13.0 2.3 13.0 2.3 29.0 2.3 29.0 2.9 30.0 2.9 30.0 2.9 30.0 2.9 30.0 2.4 11.0 2.4 11.0 3.1 26.0 3.1 26.0
B B B B B B B B B B B B B B
99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 198 39.8 99.6 99.6 99.6 99.6
32.4 26.7 26.7 26.7 22.9 22.9 24.5 24.3 26.3 25.3 28.5 28.9 24.4 23.2
Sb
seed type
pH-Stat Experiments 2.9 5.00 4.2 2.00 4.2 2.00 4.3 2.00
2.000 0.5022 0.5018 0.5019
Constant Composition 3.2 1.5 1.4 4.4 4.4 4.4 4.4 5.5 0.93 0.93 0.93
41 42 43 44 45 46 47 48 49 50 51
10.66 13.64 13.17 19.87 19.92 19.93 19.86 19.85 10.05 10.05 10.05
2.013 2.662 2.663 3.963 3.959 3,957 3.964 3.959 0.985 0.985 0.979
52 53 54 55 56 57 58 59 60 61 62 63 64 65
15.08 15.08 20.09 20.10 25.00 25.00 30.16 30.16 30.16 30.16 10.05 10.05 10.05 10.05
Constant 0.982 0.980 0.958 0.951 0.951 0.951 0.968 0.978 0.97 5 0.976 1.953 1.97 1 3.003 2.953
A
Experiments 35-37 were made at PH 10.00. For all other experiments, pH = 8.50.
9l o000 o0
L
1
3 000
150
S = supersaturation =
-
*ooo
k5
A'
MZxlC9
Flgurr 2. Plots of rate eq 1 for experiments 31 (0) and 35 (0). Flgm 1. pkts of total molar calcium concentration against time: (0) expt 31; (0)expt 35.
tallization occurred on the added seed. Constant Composition Crystal Growth. In the experiments described above, the concentrations of lattice ions decreased appreciably during the crystal growth experiments since only the pH of the supersaturated solutions was held const. Consequently, the extent of growth was small, amounting to only 15% (expt 31) and 8% (expt 35-37) of the initial mass of seed crystals, so that changes in s (eq 1) could be ignored. In experiments made at sustained supersaturations,summarized in Table I, the pH and concentrations of all other species in the supersatu-
rated solutions were maintained constant to within 0.5% by the potentiometrically controlled addition of reagents. Typical plots of the volume of mixed titrant added as a function of time are shown in Figure 3. In experiments at low supersaturation and constant I, involving a relatively small amount of growth (e.g., expt no. 49-65,Table I), the plots are strikingly linear (Figure 3). In experiments 41-48 however, with titrant concentrations of 0.1 mol d d ,it can be seen in Figure 3 that the initial linear rate of crystallization increased after about 16 mL of titrant solutions had been added, due to the concomitant increase in area. During this experiment, the calcite surface available for growth increased more than fivefold from 0.087 to 0.476 m2 dm-3 when about 160 mL of titrants had been added.
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The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
Kazmierczak et al.
TABLE 11: Influence of pH o n the Growth of Calcite Seed C at 25 "C
!rCax io3,
expt no.
T~ x io3,
mol dm-3
mol dm-3
90 91 92 93 94 95 96 97 98
1.994 1.993 1.994 1.995 1.995 1.995 2.990 2.991 3.988
3.939 3.947 2.941 2.932 1.981 1.963 2.010 1.992 1.976
100 101 102 103 104 105 106 107 108
1.996 1.996 2,970 2.993 2.494 2.495 2.994 2.994 2.993
3.827 3.817 3.774 3.857 3.866 3.829 2.866 2.875 2.870
111 112 113 114 115 116 117 119 120
0.998 0.998 0.998 1.995 1.995 1.495 1.494 1.995 1.996
1.901 1.892 1.902 1.924 1.933 1.904 1.923 0.986 0.950
I x 103, mol dm-3
S
k x dm6 mol-' min-' m-z
110 110 109 109 108 108 111 111 114
5.9 5.9 4.2 4.2 2.5 2.5 4.3 4.2 5.8
17.6 16.4 15.8 16.6 16.3 16.6 17.9 17.7 15.8
110 110 112 113 111 111 112 112 112
2.9 2.9 4.6 4.8 3.8 3.8 3.3 3.3 3.3
19.9 18.9 18.8 17.9 18.3 17.4 18.0 18.8 10.4
105 105 105 108 108 106 106 107 107
2.2 2.2 2.2 5.3 5.3 3.7 3.7 2.3 2.1
17.6 17.1 18.7 17.2 17.0 18.5 17.3 18.7 20.0
pH 8.50
pH 8.25
pH 8.78
TABLE 111: Calcite Crystallization (Seed C). Influence of Temperaturea
expt no.
temp, "C
T~,X io3, mol dm-'
mol dmT3
PH
I x 103, mol dm-3
S
k x dm6 mol-' min-' m+
16 77 78 70 71 72 73 74 75
15 15 15 25 25 35 35 35 35
1.988 1.988 1.988 1.994 1.994 1.988 1.988 1.988 1.988
2.028 2.028 2.028 1.906 1.906 1.965 1.965 1.965 1.965
8.520 8.520 8.520 8.500 8.500 8.500 8.500 8.500 8.500
108 108 108 108 108 107 107 107 107
1.2 1.2 1.2 2.2 2.2 4.2 4.2 4.2 4.2
13.6 12.9 13.5 18.9 18.8 34.1 35.5 34.8 32.5
T~ x io3,
Seed C (79.8 mg) was used t o initiate growth. and concentrations were maintained by the addition of 2.00 x dm'3 titrants in all experiments.
As shown in Figure 3, a linear growth curve was obtained after correction for the change in calcite surface area. The rate constants, k, in Table I were calculated using the rate equation (1)expressed in terms of ionic activities. The importance of maintaining the ionic strength during the constant composition experiments was illustrated by curved rate plots, similar to that shown in Figure 3, which were obtained whenever the titrant and supersaturated solution ionic strengths were not equal. The crystallization experiments summarized in Table I the molar ionic ratio calcium/carbonate ranged from 14 to 134,the supersaturation, S, from 0.93 to 5.5, and the ionic strengths and seed concentrations varied by factors of 40X and 5X, respectively. Despite these wide variations, the rate constant, k, for each seed preparation is constant to within f12%. This provides striking justification for the use of activity coefficients calculated from the Davies equationI4 in the rate equation (1). In previous conventional seeded crystallization studies, the rate constant reported by Nancollas and redd^,^ 0.1 dme mol-' min-' mg-', was recalculated, taking into account the activity coefficients of the lattice ions and the specific surface area,
lo-'
mol
20 C C
16 O C
-
12
:o
i
E -
00
20 0
100 1 , m e l""I
60 0
80 0
Flgure 3. Constant composition experiments. Plots of mixed titrant uptake as a function of time: (0)expt 57; (0)expt 47. The dotted line represents expt 47 co*rected for the change in surface area dulng crystallization.
0.3 m2 g-', of the seed crystals. The value, normalized for surface area, was 15 X lo3 dm6 mo-' min-l m-2, in satisfactory agreement with the data of Table I. In the calcite
J. Phys. Che" 1882, 86,107-111
growth studies of Wiechers, Sturrock, and Marais," the rate of reaction was also interpreted in terms of a parabolic rate law with a rate constant, 2.4 dm6 mol-' min-' (mg of seed)-'. Unfortunately, the data cannot be compared with those of the present studies since the specific surface area of the crystals was not reported. The proportionality, demonstrated in Table I, between the rate of growth and amount of inoculating seed crystals confirms the absence of secondary nucleation within this range of supersaturation. Crystal growth was therefore confined to active sites on the added seed crystals. A number of experiments, summarized in Table 11,were made with seed preparation C at pH values in the range 8.25-8.78 and carbonate/bicarbonate ratios varying from 0.20 to 1.08. The constancy of the calculatedrate constant, (17)H.N. S.Wiechers, P. Sturrock,and G. V. R. Marais, Water Res., 9,835 (1975).
107
normalized for seed surface area, 17.8 f 1.2 X lo3 dm6 mol-' min-' m-2, again points to the applicability of eq 1. A series of experiments, summarized in Table 111, were made at 15 and 35 "C with seed preparation C and 0.020 mol dm-3 calcium and carbonate titrant solutions. The marked influence of temperature, illustrated by the values of the rate constants k , corresponds to an activation energy, 39.2 f 3.6 kJ mol-' consistent with the proposed surface controlled mechanism for the crystal growth of ~ a l c i t e . ~ J ~ The constant composition method enables the rates of growth to be studied even at very low supersaturations with a precision hitherto unobtainable by conventional seeding experiments.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to the Gas Research Institute for the support of this research.
Hydrogen Bonding Interaction Effect on Carbazole Triplet State Photophysics M. M. Martin' and E. BrOhOret Labwatoke de Photophyslque Mol6culelre du CNRS, a t l m n t 213, UniversU Paris-Sud, 91405 Orsay, France (Received: April 30, 1981; In Final Form: August 20, 1981)
Hydrogen bonding interaction between the first triplet state (T,) of carbazole and pyridine was studied by means of the conventional flash photolysis technique. The carbazole triplet lifetime was determined in cyclohexane solutions at low pyridine concentration, that is when hydrogen bonding between carbazole and pyridine occurs neither in the ground state (So)nor in the first excited singlet state (Sl).Kinetics of carbazole triplet quenching by pyridine were examined on the basis of the Mataga kinetic scheme for hydrogen bond formation and dissociation reactions in the excited state. Formation of the hydrogen bonded complex carbazole-pyridine in the triplet state was found to be diffusion controlled. Equilibrium between free and bonded carbazole was shown to be established during the triplet lifetime. Bonded carbazole triplet lifetime was found to be 0.077 of that of free carbazole. Besides triplet-triplet absorption, carbazyl radical absorption was observed and was found to increase with increasing pyridine concentration. The carbazyl radical formation in the presence of pyridine was attributed to hydrogen atom transfer from carbazole to pyridine through the hydrogen bond. Photocomplexation of protonated and deuterated carbazole was compared and the hydrogen atom transfer process was shown to be responsible for the nonradiative deactivation of the hydrogen bonded triplet.
Introduction It is known that hydrogen bonding interaction may have considerable effects on deactivation processes of excited ?r-electronicsystems.' In particular, very low fluorescence yield of hydrogen-bonded complexes compared to that of corresponding unbonded molecules has often been observed and is generally explained in terms of chargetransfer interaction through the hydrogen bond. The first direct observation of a transient charge-transfer state of an excited singlet hydrogen-bonded complex has been reported recently for the 2-naphthylaminepyridine system by Ikeda, Okada, and Mataga.2 Excited state quenching by hydrogen bond acceptor has also been observed for triplet states. Hydrogen atom transfer from proton donor to acceptor has been shown to be responsible for triplet quenching of compounds such as 2-naphthol or 1-anthrol by N- heterocycle^.^ In this paper, we report on carbazole triplet quenching due to hydrogen bonding with pyridine and substituted pyridine. Conventional microsecond flash photolysis technique was used to measure carbazole triplet lifetimes Laboratoire associ6 B l'Universit6 Paris-Sud. 0022-3654/82/2086-0107$01.25/0
with increasing pyridine concentration. Low quencher M-were chosen in order to concentrations-below avoid hydrogen bonding complexation in the ground state and in the first excited singlet states4 The kinetics of carbazole triplet quenching by pyridine were studied on the basis of the Mataga scheme for hydrogen bond formation and dissociation reactions in the excited state.' Furthermore, nonradiative processes in the triplet hydrogen bonded complex were investigated. In a previous paper, Martin and Ware4presented a detailed study of the fluorescence quenching kinetics of these systems and examined the nonradiative deactivation of the hydrogen bonded complex in the excited singlet state. The lifetime of the carbazolepyridine complex S1state was estimated to be 28 ps, whereas that of free carbazole is 15 ns. (1) N. Mataga and T. Kubota, 'Molecular Interactions and Electronic Spectra";Marcel Dekker, New York, 1970. (2)N. Ikeda, T.Okada, and N. Mataga, Chem. Phys. Lett., 69,251 (1980). (3)K. Kikuchi, H.Watarai, and M. Koizumi, Bull. Chem. SOC.Jpn., 46,749(1973);S.A. Yamamoto, K. Kikuchi, and H. Kokubun, J. Photochem.. 6.469 (1976): (1976): . .. Bull. Chem. Jnn.. _ .49.2950 . . .. J. Photochem.. 7, 177 (i977). (4) M. M. Martin and W. R. Ware, J.Phys. Chem., 82, 2770 (1978).
0 1982 American Chemical Society
