Ion Pair Formation in Solutions of Fremy’s Salt
Engineering Laboratory of the U S . Army Natick Development Center and the US. Department of Energy for support of this work, The authors also thank Professor L. Kevan and Dr. S. Schlick of Wayne State University for extending the use of the facilities in their lab and also for useful discussions. References and Notes (1) I. Miyagawa and K. Itoh, J. Chem. Pbys., 36, 2157 (1962). (2) W. L. Gamble, I. Miyagawa, and R. L. Hartman, Phys. Rev. Lett., 20, 415 (1968). (3) (a) R. B. DavMson and I. Miyagawa, J. Chem. Phys., 52, 1727 (1970); (b) ibid., 57, 1815 (1972); (c) Bull. Am. Phys. SOC.,14, 336 (1969). (4) J. H. Freed, J . Chem. Phys., 43, 1710 (1965). (5) C. Helier, J. Chem. Pbys., 38, 175 (1962). (6) (a) S.Ciough and F. Poldy, Pbys. Lett. A , 24, 545 (1967); ibid., 25, 186 (1967); (b)S. Clough and F. Poldy, J. Chem. Pbys., 51, 2076 (1969); (c) S.Clough, J. R. Hill, and M. Punkkinen, J. Pbys. C, 7, 3779 (19741. and references therein. (7) W. P. Unruh,’T. Gedayioo, and J. D. Zimbrick, J. Phys. Chem., 82, 2016 (1978).
The Journal of Physical Chemistry, Vol. 83, No. 10, 1979
1327
(8) (a) J. W. Wells and H. C. Box, J. Chem. Pbys., 48, 2935 (1967); (b) ibid., 48, 2542 (1968). (9) (a) M. D. Sevilla, J. Phys. Chem., 74, 669 (1970); (b) ibid., 74, 2096 (1970). (10) M. D. Sevilla and V. L. Brooks, J. Phys. Chem., 77, 2954 (1973). (1 1) M. D. Seviiia, J. B. D’Arcy, and D. Suryanarayana, J. Phys. Cbem., 82, 2589 (1978). (12) I. Miyagawa and W. Gordy, J. Am. Cbem. Soc., 83, 1036 (1961). (13) J. E. Bennett and L. H. Gale, Trans. Faraday SOC.,64, 1174 (1968). (14) M. Slmlc and E. Hayon, J . Phys. Chem., 77, 996 (1973). (15) P. D. Sullivan and J. R. Bolton, “The Alternating Line Width Effect” in “Advances in Magnetic Resonance,” Vol. 4, J. S. Waugh, Ed., Academic Press, New York, pp 39-85. See for references therein and a computer program to simulate the ESR spectra. (16) K. S. Chen, P. J. Krusic, P. Meakin, and J. K. Kochi, J. Pbys. Chem., 78, 2014 (1974). (17) C. Gaze, B. C. Gilbert, and M. C. R. Symons, J. Chem. Soc., Perkin Trans. 2, 235 (1978). (18) L. C. Krishmer and E. Saegebarth, J. Chem. Phys., 54, 4553 (1971). (19) M. Kltano, T. Fukuyama, and K. Kuchitsu, Bull. Chem. SOC.Jpn., 46, 384 (1973). (20) R. A. Nemenoff, J. Snir, and H. A. Scheraga, J . Phys. Chem., 82, 2521 (1978), and related references therein.
Electron Spin Resonance Studies of Ion Pair Formation in Solutions of Fremy’s Salt M. Thomas Jones,* Rarla Ahmed, Rodney Kastrup,+ and Vincent Rapinit Departmen! of Chemistry, University of Missouri- St. Louis, St. Louis, Missouri 63 721 (Received September 18, 7978; Revised Manuscript Received January 22, 1979)
It is shown that Fremy’s salt ((KS03)2NO)is ion paired under a variety of experimental conditions. When dissolved in dioxane-water solutions in the presence of CsC104,two superimposed spectra are observed. One spectrum is that normally observed. The other has an additional splitting by a single cesium ion. An estimate of the dissociation constant has been made. Solutions of (KSO&NO when in the presence of such salts as RbCl and CsCl show g value shifts which are interpreted in terms of the formation of ion pairs with the added alkali metal ions. Analysis of the shifts yields estimates of the dissociation constants of 1.7(h0.4) and 1.4(h0.4) for the RbCl and CsCl salts, respectively, for a single dissociation/association process. Finally, the ESR line shapes for dilute solutions of (KS0J2N0 as a function of added alkali metal ions have been studied. It is shown that in previous work some of the reported distortion was the result of magnetic field modulation at too large a frequency. However, when lower frequencies are used there still remains a small distortion which can be interpreted in terms of a small unresolved metal hfs in the range of 5-20 mG depending upon the salt.
Introduction We report here ESR studies of ion-pair formation in solutions of Fremy’s salt ((KSO&NO or dipotassium peroxylaminedisulfonate K2PADS). These studies were carried out along three lines. First, under certain limited experimental conditions, water-dioxane solutions of K2PADS in the presence of CsClO, display two sets of superimposed ESR spectra. One set is identical with that normally observed for water solutions of K2PADS. In the second set, each of the nitrogen hyperfine lines is split into eight equally intense and rather closely spaced lines, which indicates the presence of a cesium ion pair. Second, an investigation of the effect of the presence of various counterions in solutions of PADS2- indicates that the observed g values are dependent upon the particular cation which is present and upon its concentration. Recently, Stevenson and co-workers’,2 have used this type of phenomenon to experimentally evaluate equilibrium constants which describe ion-pair dissociation. We apply their procedure here. Third, it has been reported that the ESR line shapes of aqueous solutions of K2PADS are distorted Undergraduate research assistants.
0022-3654/79/2083-1327$0 1.OO/O
under certain experimental condition^.^-^ The recent development of line shape analysis techniques for the measurement of unresolved hyperfine splitting ( h f ~ ) , ~ - ’ ~ especially, metal hfs arising from ion-pair formation, suggests that the source of the line shape distortion might be the result of ion-pair formation. We report the details of such an investigation here. Experimental Section ESR Spectrometer. The ESR measurements were performed on a Varian E-12 spectrometer equipped with a dual cavity. The dual cavity spectra were recorded on a dual channel L & N Speedomax XL recorder. The magnetic field drift was minimized by careful control of the magnet and room temperatures and by allowing the magnet to warm overnight. The temperature of the magnet cooling water was controlled within h0.5 “C at a temperature approximately 3 “C above room temperature, with a Neslab refrigerated recirculating heat exchanger (HX-3000). The exterior of the dual cavity was thermally insulated with urethane foam rubber to reduce klystron frequency drift relative to the magnetic field. For variable temperature studies, the sample temperature was maintained to fl “C with a Varian V-4540 0 1979 American Chemical Society
1328
The Journal of Physical Chemistty, Vol. 83, No. 10, 1979
temperature control. The actual sample temperature was measured with a copper-constantan thermocouple which was inserted into the variable temperature dewar along side the sample. g Value Measurements. The g value and magnetic field scan reference standard was a dilute sample of lithium tetracyanoethylene in tetrahydrofuran. The g value of this reference sample relative to these reported for the ant h r a c e n e a n d pyrene anion radicals is 2.002766(f0.000002).13 This g value is corrected for the error reported by Allendoerfer15J6but is not corrected for second-order shifts. The hyperfine splitting is equal to 1.574 G.17 The reference sample was field modulated at 100 kHz and the unknown at 10 kHz. The unknown samples were contained in 2-mm 0.d. pyrex tubes. For the g value measurements a combination of magnetic field scan rate and recorder chart speed was selected so that (a) slower magnetic field scan rates did not result in changes in the observed magnetic field differences between the reference and unknown samples and (b) the precision of the measurements of the magnetic field difference between the reference and unknown sample was equivalent to f l part in lo6 (i.e., to f3.4 mG) in the g value. In general, two forward and two reverse field scans were averaged to give a single g value. Measurements were taken only after the sample had reached thermal equilibrium. The following relationship between the g value of the reference and the unknown sample was used: (1) gunk = g r e f - (gref)2mfl/(hv) gunk and grefare the g values of the unknown and reference samples, respectively, AH is the magnetic field difference between the reference and unknown samples; fl, the Bohr magneton; h, Planck’s constant; and v, the spectrometer frequency. The spectrometer frequency was obtained by directly counting the microwave radiation with a Hewlett-Packard 5245L frequency counter and a matched 5260A frequency divider. Line Shape and Line Width Measurements. All the spectra for the line shape and line width studies were recorded at 10-kHz field modulation. Since all the spectral line widths were equal to or greater than approximately 115 mG there were no problems with either line shape distortion or line width increase due to field modulation (see ref 12). The field modulation amplitude was nominally maintained at 5 mG which again caused no line shape or line width distortions. Finally, a power level of 1mW incident on the cavity was maintained; this was sufficient to broaden slightly (i.e., -4 mG) the observed line widths, but there was no observable effect on the line shape. Several comparitive field scans were made using the flux stabilizerla and the normal Varian E-12 magnetic field scan mechanism. No significant differences in the spectral line shapes were obtained. Therefore, the easier to use of the two methods was preferred (i.e., the normal Varian E-12 scan). In general, four scans were run for each sample and the results averaged. Approximately 600 line shapes were analyzed. The line shapes were analyzed with the techniques in ref 8 and 9. All samples whose line shapes were analyzed were degassed on the vacuum line. The spectra were recorded for samples in flat aqueous cells. Materials and Sample Preparation. The K2PADS was both purchased from K & K Laboratories and prepared in our laboratory according to previously described method^.^^,^^ Samples of (Ph,As)2PADS were prepared by the procedure described by Eastman et al.5 Two new salts, (Ph3AsCH3)2PADS and (Ph3PCH3)2PADS,were also
Jones et al.
prepared by this procedure. All three of the polycrystalline samples with large cations were purple in color. Their solid state ESR spectra were broad single lines. Atomic absorption measurements on the above three salts indicated that less than 2% of the cations were potassium. Two different attempts to prepare Na2PADS were tried. First, 0.40 g of K2PADS was dissolved in 28 mL of 0.1 N aqueous NaOH. Then, 1.5 g of dibenzo-18-crown-6-ether (Aldrich) was dissolved in 20 mL of CH2C12. The aqueous K2PADS-NaOH solution was extracted, successively,with 20-mL portions of the CH2Clzsolution.21r22The violet color of the PADS2- did not cross into the CH2C12phase. An atomic absorption analysis of the water phase showed that 68% of the potassium originally present was removed. There were no differences between the ESR spectra or g values of solutions so prepared and solutions of K2PADS. The second attempt to prepare NazPADS followed outlines by Cram and Reevedg except that sodium permanganate was used in the oxidation step and potassium chloride was replaced by sodium chloride in the final precipitation step. However, it appears that Na2PADS is much more soluble than K2PADS as we were never able to obtain the Na2PADS in crystalline form. ESR spectra and g values of dilute solutions of the above were identical with those observed for solutions of K,PADS. The dioxane was spectra grade obtained from Fisher. It was distilled before use. The various alkali metal salts were obtained from either Fisher Scientific or Alfa. To prevent rapid decomposition of Fremy’s salt in aqueous solutions, it is necessary to keep the solutions alkaline (pH 8-10). This was done by the addition of various carbonates or hydroxides at concenor M, respectively. The presence trations of 5 X of the dioxane caused the decomposition rate to increase, especially at temperatures above 25 OC.
Results Dioxane-Water Solutions of K2PADS in the Presence of C S C ~ OAs ~ .the ~ ~relative amounts of dioxane and water are varied (over the range of 95-75% dioxane by volume) in solutions at fixed temperatures and fixed concentrations of K2PADS and CsC102, ESR spectra as shown in Figure 1 are observed. We shall demonstrate that these spectra result from the superposition of spectra which arise from the PADS2- species which is normally observed in water solutions of KaPADS (the narrow line spectrum) and from a cesium ion-paired PADS2- species (the broader, more complex resonance). If one carefully looks at the spectra labeled A in Figures 1 and 2 it can be seen that a total of six peaks can be resolved plus the narrower center line in each of the nitrogen triplets. The relative positions of each of the six peaks observed in the broader resonance envelope are such as to suggest the envelope arises from eight equally spaced and equally intense spectral lines as would be the case if they were to arise from splitting by Cs+ (I = 7/2). We have computer simulated the superimposed spectra observed in Figures 1A and 2A based on the assumption that the experimentally observed spectra arise from the superposition of spectra from the normal PADS2and a cesium ion-paired PADS2- entity. Taking into account the slight upfield shift of 0.1 G (lower g value by 6. X of the cesium split spectrum, extremely good fits of the experimental and simulated spectra have been obtained (see Figure 3). The computer simulation is also consistent with a value of 0.5 G for the cesium hfs. When the dioxane concentration exceeds 95% by volume, no ESR spectra are observed. This appears to be the result of the limited solubility of the various PADS2- salts in dioxane.
The Journal of Physical Chemistty, Vol. 83, No. 70, 1979
Ion Pair Formation in Solutions of Fremy’s Salt
Figure 1. K,PADS (2X lo4 M) in the presence of CsClO, (1.3X M) and KOH (1 X lo3 M), The temperature is 10 OC: (A) dbxane:water = 94:6 by volume; (B) dioxane:water = 8515 by volume; (C) dioxane:water = 81:19 by volume; and (D) dioxane:water = 70:30 by volume.
1320
lo-,
Flgure 2. K,PADS (4 X M) in dioxane:water 9O:lO by volume. M), temperature = 10 OC: (A) CsCIO, = 1.38X KOH (2X M. M; and (C) CsCIO, = 4.04 X M; (B) CsCIO, = 2.76 X (Note the solution Is saturated in CsCIO, at 4.7 X M).
As the dioxane concentration is reduced from 95 to 70%, a series of spectra arle observed as shown in Figure 1. The last indication of superposition of spectra occurs a t a dioxane concentration of 75%. At the 70% dioxane level and lower the PADS”- spectra are those normally observed in pure water solutioins. Inspection of the spectra in Figure 1shows that as the dioxane concentration is decreased the spectral envelope which arises from the ion pair loses resolution and becomes narrower. This can be explained as being primarily due to the cesium ion exchange process described in eq 2. Cs*+ CsPADS&*PADS- + Cs+ (2)
+
The alternative possibilities shown in eq 3 and 4 (where CsPADS- e Cs+ + PADS2-
(3)
CsPADSCs+llPADS2(4) Cs+llPADS2-is a solvent-separated ion pair) can be ruled out (i.e., they must be considerably slower than that shown in eq 2) because each one would result in uniquely observable changes in the spectral envelope which are not seen. The process shown in eq 3 is much slower than that of eq 2 because if it were to contribute significantly to the exchange broadening and the collapse of the cesium split spectrum then one would observe a corresponding broadening of the “normal” spectrum. Such a broadening is not observed. Therefore, the process shown in eq 3 must occur a t a frequency of less than lo6 Hz. The process shown in eq 4 would lead to a greater broadening of the outermost cesium hyperfine lines relative to the innermost lines. At first glance, the spectra in
Figure 3. K,PADS (2X lo4 M) in the presence of CsCIO, (1.3X lo3 M) and KOH (1 X lo-, M). The temperature is 10 ‘C. This is a comparison of the experimental and simulated central portion of the overall spectrum. See text for additional details.
Figures 1and 2 appear to support the conclusion that this is indeed the case. However, the careful spectral simulations described above, which also take into account the process of eq 2, give agreement between calculated and experimental spectra equivalent to that shown in Figure 3. It is on this basis the process shown in eq 4 has been
1330
The Journal of Physical Chemistry, Vol. 83, No. 10, 1979
Jones et al.
ge2.0055+
\
' CsCl 30
\
201 10
t
I
IQ-~
I
,,,I111
lo.*
I
, 1 1 1 1 1 1 1
lo"
I
I 1 1 1 1 1 1 1
1
,
\
I
,,,,,,I0\
10
(M') Figure 4. Plot of the gvalue of K,PADS against concentration of various added salts. The temperature was 25 'C.
ruled out. The spectral simulations show that each of the cesium hyperfine lines is equally broadened. However, when they are combined to form the eight-line envelope, the spectral overlap causes an apparent narrowing of the innermost spectral lines. The spectral simulations which take into account the exchange process of eq 2 are consistent with a frequency of exchange of 2-3 X lo6 and -los Hz for dioxane concentrations of 95 and 75%, respectively. The simulation calculations were also programed so that it was possible to integrate the areas under the two different sets of spectral curves. This information can be used to estimate the dissociation constant defined by eq 3. The curve fitting which is necessary to obtain this data is' extremely time consuming and tedious. Therefore, only a limited number of fits were made. Experimental values of the dissociation constants so determined are 7 ( i 2 ) X and 13(*8) X a t 0 and 25 "C, respectively. The solvent was a dioxane-water (85:15) mixture. The uncertainties given are the rms deviations from the average of three experiments in each instance. The greater uncertainty at the higher temperature may be due to more rapid decomposition of the PADS2- than at lower temperatures but it still appears rather certain that the dissociation constant as one varies the relative dioxanewater concentrations for a fixed concentration of KzPADS and CsC104 indicates that it varies inversely with the dioxane concentration. This behavior parallels that reported for tetraisoamylammonium nitrate.23 Figure 2 demonstrates the effect of increasing the concentration of CsC104, while keeping everything else constant. As the C-C104concentration is increased, the relative area under ' I ion-paired resonance to that of the normal resonance irueases as does the er,change frequency between the cesium ions in solution and those in the ion pair. Attempts to reproduce the results described above by using other salts of cesium and rubidium were unsuccessful. The salts which were tried are CsC1, Cs2C03, RbC104, PbC1, and Rb2C03. One possible explanation of this is that the solvent (dioxane:water) is not strongly enough ionizing in the case of the Cs2C03and CsCl salts to provide the needed cesium ions. This may also explain all of the rubidium results. Under conditions that the cesium hfs was observed no potassium hfs could be resolved. We did not apply the line shape analysis techniques described elsewhere in this paper. However, if the same amount of spin density were to be transfered to the potassium ion as is transfered to the cesium ion, one would expect to observe a hfs of
5
0
10
I/( M+) Figure 5. Plot of the l/Agagainst 1/(M+) for one of the experiments in Figure 4. The salt is RbCI.
approximately 50 mG. This would show up in the form of an increase in line width or as a distorted line shape. It is too small to resolve directly. g Value Shifts. Figure 4 shows the effect upon the g values of solutions of K2PADS of the variation of different alkali metal ions and their concentrations. The alkali metal ions which were studied were potassium, rubidium, and cesium. Extensive studies with lithium and/or sodium were not attempted because their very small spin-orbit interaction parameters should lead to even smaller shifts than those observed for the potassium salts. Limited experiments with sodium salts confirmed this. Stevenson and co-workers1,2 have shown the type of phenomena displayed in Figure 4 is what one expects to observe if there is a rapid averaging between two different species, each with its own g value. Specifically, consider the equilibrium between an ion pair and its dissociated form: MPADS-
F!
PADS2- + M+
(5)
The difference between the g value of the dissociated species and that observed at any given set of experimental conditions is given by the following expression: Ag = (gPADS2-- gobsd) = Ag'(MPADS-)/[(MPADS-)
+ (PADS2-)] ( 6 )
where gobsd =
gpADsz-(PADS2-) gMpADs-(MPADS-) [(MPADS-) + (PADS2-)]
(7)
and
&' = &?PADS"
- gMPADS-
(8)
Substitution of the thermodynamic dissociation constant, Kd, defined by eq 5 in eq 6 yields
l/Ag = [(Kd/Ag'kf+)] I/&' (9) A plot of l/Ag vs. l/(M+) yields a straight line with a slope equal to Kd/ Ag ' and an intercept equal to I/Ag '. Figure 5 shows one set of experimental data so plotted. Several separate experiments of the type shown in Figure 4 were run and analyzed according to eq 9. The results are shown in Table I. Also shown in Table I are the results in 85% dioxane solutions. The shifts for the potassium solutions were too small to furnish reliable data.
The Journal of Physical Chemistty, Vol. 83,No. 10, 1979
Ion Pair Formation in Solutions of Fremy's Salt
Experiments performed on water solutions of rubidium and cesium salts show that as the solutions are progressively diluted the g values increase. A typical set of data is shown in Table 11. We have also observed a dependence of the g value of K2PADS in water solution upon the total PADS2- concentration. Note this experiment differs from the dilution experiment in that the buffer concentration (K2C03)was kept constant. The data are shown in Table 111. This above observation accounts for some of the variation one sees in the literature for the reported g values of K2PADS in water solutions. Most of the variation in the observed g value (see Table 111) must be due to the ion-pair formation/dissociation process. However, we note that Fraenkel et a1.16 have suggested that spin-spin exchange effects ought to cause shifts in g values also. We know of no experiments, to date, which have tested this particular point. However, we are compelled to point out that such experiments will have to be conducted with neutral radicals or in solvents and with systems which avoid ion pair effects. It is of interest to determine the position of the alkali metal ion (or ions) in the PADS2- ion pair in solution. Unfortunately, the problem is not so easily solved here as it is in the case of planar aromatic anion radical systems (see, for example, ref 24). However, since the crystal structure of solid K2PADS is known,25it was a relatively easy task to calculate the g value of PADS2-in the presence or absence of alkali metal ions. Of most interest was whether such calculations would show shifts to smaller values as is observed experimentally for the ion-paired species. The calculations were carried out using the program described by Dalgard and Linderberg.26127The results are shown in Table IV. The two potassium ions in the K2PADS unit cell are not equivalent positions. One is much closer to the nitroso oxygen than the other. Thus, it was not too surprising to calculate a negative shift of 23 X in the g value for the potassium ion closer to the for the other. The two nitroso oxygen and only 4 X shifts are additive. The calculated shifts for the rubidium and cesium ions although negative are not as negative as those of the potassium ions. We are not overly concerned by this. First, one would not expect the rubidium and cesium ions to occupy exactly the same positions as the potassium ion. Second, the important point is that for all three ions the shift is negative which gives additional support to the use of the ion-pair concept to explain the g value data variation. The observation that salts of rubidium and cesium caused shifts in the g values observed for solutions of K2PADS prompted us to look for pure salts of PADS2-for which ion pair shifts ought to be minimal. We, therefore, report the g value for solutions of Na2PADS, (Ph4As)2PADS, (Ph3AsCH3),PADS, and (Ph3PCHJ2PADS. It should be noted that solid state
TABLE I: Dissociation Constants no. of
teomg.,
salt added
C
RbCla CsCP CSCl0,b CSClO,~
25 25 0 25
SFP
dissociatn const
experiments
3 4 3 3
1.7(*0.4) 1.4(*0.4) 7 ( & 2 )x 13(i8)x
a (K,PADS) = 6.25 x 10-3 M; (K,co,) = 2 x 10-2 M; and solvent is water. (K,PADS) = 3 x (K,CO,) = lo-, M; and solvent is 85% dioxane and 15% water by volume,
TABLE 11: Dilution Experiment in Water with CsCl and K,PA.DSa CsCl concn, M
g value
CsCl concn, M
g value
0 2.005558 1.37 2.005542 8.5 X lo-' 2.005554 2.75 2.005537 1.7 X l o - ' 2.005554 5.5 2.005522 2.005536 11 2.005504 3.4 X lo-' 2.005544 6.8 X l o - ' a At 11M CsCl the initial concentration of K,(SO,),NO and KOH was 5 X 1 1 0 ' and ~ 5 x lo-, M, respectively, They were reduced by a factor of 2 for each successive measurement. The temperature was 25 O C. TABLE 111: K,PAI)S g Value of Various PADS2Concentrations for Fixed Buffer Concentrations in WateP K,PADS K,PADS concn, M g value concn, M g value 2.005559 1.25 x lo-' 7.81 x lo', 2.005551 1.56 X lo-' 2.005560 2.50 X lo-' 2.005531 2,005560 1.0 X lo-' 3.13 X 2.005515 Buffer = 6 X 10'' M K,C03, temperature = 25 "C.
The g value measurements can also be used to distinguish between the ion-pair formation/dissociation process in eq 5 or a metal ion exchange process of the type described by
+ K2PADS + MKPADS + Kt Mt + KF'ADS- ~t MPADS- + K+
Mt
1331
(10)
(11) Consider a dilution experiment, Le., an experiment in which the g values are measured for a series of solutions which are progressively more and more dilute but in which the relative concentrations of the starting materials are kept constant. According to eq 7, the observed g value will vary as the relative concentrations of the ion pair and free ion varies. For the processes described in eq 10 and 11, one would not expect to observe a change in g value upon dilution because the relative concentrations of all the species present would stay fixed. However, in the case of the process described by eq 5, dilution will shift the relative concentrations toward more free ion. The free ion has the larger g value, thus one would expect to see a shift toward larger g values as the samples are progressively diluted. TABLE IV: Calculated P Values for Various PADS2' Salts L
g,
g1
2.006306 2.002659 a 2.002659 2.006269 2.002657 2.006308 2.002658 2.006268 2.002659 2.006272 Rb2(S03)2N0 Cs,(SO,),NO 2.002663 2.006301 2.00589( r 6 ) K,(SO,),NOC 2.00259( 5) a The potassium ion is closest to the nitroso oxygen atom. The potassium atoms. Experimental. See ref 28. (S0,),N02 K(SO,),NOiK(SO,),NOlK,(SO,),NQ
_+
g3
(g)
2.010409 2.006459 2.010381 2.006436 2.010401 2.006455 2.010368 2.006431 2.010393 2.006441 2.010374 2.006446 2.00832(* 2) 2.00560( r 4 ) ion is closest to two of the sulfonate oxygen
1332
The Journal of Physical Chemistry, Vol. 83, No. IO, 1979
TABLE V: g Values for Various Salts of PADSzin Water Solution salt
temr,. C P value 25 2.005560(~0.000004) K,PADSa NazPADSb 25 2.005560(f0.000004) NaKPADSb 25 2.005560( i0.000004) (Ph,As),PADSb 25 2.005558(~0.000004) (Ph3AsCH3),PADSb 25 2.005557(~0.000004) (Ph3PCH,),PADSb 25 2.005568( f 0.000004) K2PADS t RbCla 25 2.005512(+0.000004) K,PADS t CsCla 25 2.005510(~0.000018) a Buf€er = KzC03. No buffer present. No secondorder shift corrections have been made, O
samples of Na2PADS could not be obtained. These g values are shown in Table V. Also shown in Table V are estimates of the g values for the rubidium and cesium salts obtained from the relationship, given in eq 8. They are consistent with the calculations reported above. Line Shape and Line Width Studies. It has been reported by two separate groups of investigators3* that very dilute solutions of KzPADS (Le., concentrations less than 2X M) which have been degassed display distorted line shapes. These distorted line shapes fall off more rapidly in the wings than does a Lorentz line (see ref 3, Figure 4). This behavior resembles that associated with the presence of unresolved hfs and suggests that previously developed line shape analysis techniques might be useful.7-12 We found that part of the line shape distortion was due to the 100-kHz magnetic field modulation used in the previously reported ~ o r k . ~However, J~ when 10-kHz field modulation was used, a smaller but yet detectable distortion remained. The use of lower modulation frequencies (e.g., 1kHz) did not further reduce the distortion, indicating there may be a small amount of unresolved metal hfs. In the case of a M KzPADS solution line shape analysis gave an estimate of N 15 mG. This is in agreement with the work of Goldman et aL6 As the concentration of the K2PADS is increased the line shapes become more Lorentzian in character and the line shape analysis suggests that the unresolved hfs decreases. Why this might appear to occur is discussed in ref 12. In addition, the line shapes of solutions of K2PADSwere studied as the concentrations of LiC1, Na2C03,and RbCl were varied. The results were similar to those observed for the variation of potassium ion. At radical concentrations of M, the line shape analysis indicated an unresolved metal hfs of 5-8 mG for both the lithium and sodium salts and 15-20 mG in the case of the rubidium salt. Just as in the case of the potassium salt, an increase in radical concentration caused a decrease in the value obtained for the unresolved hfs. An increase in metal ion concentration had no observable effect upon the values of the unresolved hfs obtained. A phenomenon was observed which was a bit puzzling until its source was recognized. Table VI gives the line widths for various solutions of KzPADS plus additional salts as a function of radical concentration and added salt concentration. For dilute radical solutions the addition of salt causes the line to narrow. As the radical concentration is increased the narrowing obtained by the addition of various salts decreases until at some point the line width actually increases. The latter effect is known to be the result of increased spinspin exchange processes due to the increased ionic concentration (see ref 28). The line narrowing effect is due to the increased viscosity of the more concentrated solutions. Freed and co-workers6have shown that there is a linear dependence of the line width upon
Jones et al.
TABLE VI: K,PADS Line Width Data as a Function of Radical and Added Salt Concentrationsaib K,PADS t 0.05M K,CO. t LiCl LiCl PADS 2 concn,M 0.1 M 0 . 3 M 0.5 M 0.7 M ~~
1x 3x 1x
lo-,
0.9M 1 149 f 2 1 150 f 1 2 165 f 1 ~~
153 i 1 152 f 2 151 f 2 146 i 155 ?: 1 154 i 1 152 f 1 152 f 160 i 1 165 i 1 1 6 8 * 1 162 f K,PADS t NaCO.
PADS2concn, M 1x 3x 1x
lo-, lo-,
0.1 M
0.3 M
Na,CO, 0.5 M
*
K2CO3 0.1 M 0.3 M 0.5 M 145 i- 4 135 f 2 132 i 2 1 5 0 i 2 1 3 8 f 2 139 * 2 211 f 2 207 i 2 213 f 2 K2PADS t 0.05M K2C0, t RbCl PADS2c0ncn.M 0.1 M 0.3 M 0.5 M
a
lo-,
0.9 M
116 f 1 142 i 3 129 1 129 * 1 125 i 147 * 1 1 4 0 * 1 139 i 1 136 i 1 1 3 2 f 2 164 c 1 161 * 1 163 f 1 157 i 1 154 i 1 K,PADS t K2C03
PADS2concn. M 1 X lo-, 3 x lo-, 1X
1X 3X
0.7 M
150 f 3 146 i 1 143 157 i 2 1 6 0 2 1 157
i i
0.7 M 133 i 1 132 i 1 208 i 1 RbCl
0.9 M 124 i 1 218 f 5 205 i 2
0.7 M
0.9 M
I
1 138 1 154
Peak-to-peak line widths in milligauss.
1 137 f 1 156i 2 Temperature
i
*1
= 25°C.
the value of T/q. Here we are keeping the temperature constant but varying the viscosity. An increase in viscosity should result in a somewhat narrower resonance line width. A check of the “International Critical Tables” indicates the following changes in viscosity at room temperature: LiCl (0.1 to 1.0 M) 13% increase Na2C03(0.1 to 1.0 M) 8% increase K,C03 (0.1 to 0.5 M) 13% increase RbCl (0.25 to 1.0 M) 1%increase Clearly for the most part there is a rough parallel between the bulk viscosity change and the changes in line width. Perhaps the example of RbCl is there to remind us that it is the microscopic viscosity and not the macroscopic solution viscosity which is important.
Discussion and Conclusions The most important question one can answer at this point concerns the possible structure of the ion pair under study here. Both the results of the mixed solvent experiments and the g value shifts support a simple dissociation process, i.e., of the form shown in eq 2. The mixed solvent experiments show metal hfs from a single cesium ion. Spectral simulations based on the presence of two cesium ions did not give agreement with experimentally observed spectra whereas those based on the presence of a single cesium ion are in good agreement. The plot of the g values against various alkali metal ion concentrations and the subsequent analysis of the data are consistent with a single metal ion dissociation. A second dissociation or association process would introduce nonlinearities into the analysis of the data. Nonlinearities are not observed as long as the metal ion concentrations are equal to or greater than the potassium ion. At lower metal ion concentrations the g value shifts are small and the relative error in their
Deconvolution of Fluorescence Decay Curves
measurement is large but no detectable nonlinearities were observed.
Acknowledgment. The support of the National Science Foundation through Grant GP-28436 and an Undergraduate Research Participation Grant EPP 75-04388 is gratefully acknowledged. References and Notes (1) G. R. Stevenson find A. E. Alegrla, J. Phys. Chem., 79, 1042 (1975). (2) G. R. Stevenson, A. E. Alegria, and A. McB. Block, J . Am. Chem. SOC.,97, 4859 (1975). (3) M. T. Jones, J . Chem. Phys., 38, 2892 (1963). (4) R. G. Kooser, W. Y.Volland, and J. H. Freed, J. Chem. Phys., 50, 5243 (1969). (5) M. P. Eastman, G.V. Bruno, and J. H. Freed, J. Chem. Phys., 52, 2511 (1970). (6) S. A. Goldman, G.V. Bruno, and J. H. Freed, J. Chem. Phys., 59, 3071 (1973). (7) C. Jolicoeur and H. L. Freidman, Ber. Bunsenges. Phys. Chem., 75, 248 (1971). (8) M. T. Jones, M. Komarynsky, and R. D. Rataiczak, J. Phys. Chem., 75, 2769 (1971), (9) M. T. Jones and M. Komarynsky, J. Chem. Phys., 56,4404 (1972). (10) A. S. Mason and W. H. Bruning, Chem. Phys. Lett., 15,299 (1972). (11) M. T. Jones, Chem. Phys. Lett., 20, 151 (1973).
The Journal of Physical Chemistry, Vol. 83, No. 10, 1979
1333
(12) M. T. Jones, J. Mag. Reson., 11, 207 (1973). (13) Note the value reported in ref 14 was not corrected for the error reported by Allendoerfer (ref 15). All other g values reported therein were so corrected. (14) M. T. Jones, T. C. Kuechler, and S. Metz, J . Mag. Reson., 10, 149 (1973). (15) R. D. Allendoerfer, J. Chem. Phys., 55, 3615 (1971). (16) 6.G. Segal, M. Kaplan, and G. K. Fraenkel, J . Chem. Phys., 43, 4191 (1965). (17) M. T. Jonesand W. R. Hertler, J. Am. Chem. Soc., 86, 1881 (1964). (18) R. D. Rataiczak and M. T. Jones, J. Chem. Phys., 56, 3898 (1972). (19) D. J. Cram and R. A. Reeves, J. Am. Chem. Soc., 80, 3099 (1958). (20) W. Moser and R. A. Howle, J. Chem. SOC.A , 3039 (1968). (21) C. J. Pederson, J . Am. Chem. SOC.,89, 7017 (1967). (22) C. J. Pederson and H. K. Frensdorff, Agnew. Chem., 11, 16 (1972). (23) R. A. Roblnson and R. H. Stokes in “Electrolyte Solutions”, Academic Press, New York, 1955, p 389. (24) M. T. Jones and T. C. Kuechler, J. Phys. Chem., 81, 360 (1977). (25) R. A. Howie, L. S. D. Glasser, and W. Moser, J . Chem. SOC.A , 3043 (1968). (26) E. Dalgard and J. Llnderberg, Int. J. Quantum. Chem.,59, 269 (1975). (27) E. Dalgard and J. Linderberg, J . Chem. Phys., 65, 292 (1976). (28) M. T. Jones, S. A. Trugman, V. Rapini, and R. Hameed, J . Phys. Chem., 81, 664 (1977). (29) This phenomena was first discovered by R. Ahmed and Professor S. I. Weissman at Washington University, St. Louis. We are Indebted to Professor Weissman for his interest in and help with thls portion of this study.
Deconvolutiori of Fluorescence Decay Curves. A Critical Comparison of Techniquest D. V. O’Connor, W. R. Ware,* The! PhotochemlstfyUnit, Department of Chemistry, Universlty of Western Ontario, London, Ontario, Canada, N6A 587
anid J. C. Andre Laboratoire de Chimie (.%%&ale, E R A . No. 136 du C.N.R.S., 54042-Nancy, Revised Manuscript Received November 20, 1978)
Cedex, France (Received September 7, 1978;
Several methods of deconvoluting fluorescence decay curves are compared. Real data for which the decay times were known provide tests of each method’s ability (1)to deconvolute two-component decays having decay times of 1 and 5 ns, (2) to cope with distortions in the data resulting from instrumental artifacts, (3) to analyze subnanosecond decay times, and (4)to separate two closely spaced decays. A new method based on Fourier transformation of the observed time profiles is included in the study, and some modifications of existing techniques are tested. It is found that all methods are satisfactory for undistorted one-component data but least-squares iterative reconvolution is most suitable for analysis when distortions are present. Only iterative reconvolution techniques and the method of modulating functions resolved satisfactorily two closely spaced decays.
I. Introduction The observed fluorescence decay curve of a molecule excited by a short pulse of light is a convolution of the pulse shape of the excitation (distorted by the detection system) with the 8-pulse response of the luminescent system, i.e. f(t) = l t g ( t ’ ) d(t - t’) dt’ 0
in which f(t) represents the measured decay curve, g(t) represents the measured intensity-time profile of the exciting pulse, and d(t) represents the undistorted decay law of the system. Difficulties in recovering d(t) from the observed f(t) and g(t) may arise from (i) distortions in the data of which the most frequently encountered are the wavelength depenPublication No. 211 from the Photochemistry Unit, Department
of Chemistry, University of Western Ontario, London, Canada.
dence of the excitation profile, the dependence of the response of the detector on the energy of the incident photons and on the area of the photocathode illuminated, interference of radiofrequency noise and scattered exciting light, walk and jitter in the electronics, and the time dependence of the excitation profile and (ii) the mathematical treatment of eq 1. Although some of the factors listed under (i) may be treated in the deconvolution process, it is generally preferable to arrange the experimental conditions in such a way that distortions are almost negligible and that the validity of eq 1 may be safely assumed. A variety of deconvolution techniques have been devised for the analysis of data collected with the single photon counting technique. In a recent publication’ McKinnon et al. compared the most common of these with each other and recommended the use of the iterative convolution method (vide infra) as the most reliable technique. This publication dealt almost entirely with simulated data; the
0022-3654/79/2083-1333$01 .001Q 0 1979 American Chemical Society
