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The Journal of Physical Chemisfry, Vol. 83, No. 20, 1979
J. R. Morton, K. F. Preston, and
(17) B. D. Flockhart, J . Colloid Sci., 16,484 (1961). 118) P. Murkerlee and K. J. Mvsels. “Critical Micelle Concentrations of .
S.J.
Strach
(22) G. M. Musbally, G. Perron, and J. E. Desnoyers, J. ColioM Interface Sci.. 40. 494 (19741. (23) T. S: Brun, H. Hdland, and E. Vikingstad, J. Colloid Interface Sci., 63, 89 (1978). (24) K. S. Pltzer and J. J. Kim. J. Am. Chem. Soc.. 96.5701 119741. . , (25j R. A. Robinson, J . fhys. Chem., 65, 662 (1961). (26) K. J. Mysels and L. H. Prlncen, J. Phys. Chem., 63,1696 (1959). (27) R. B. Beard, T. F. McMaster, and S. Takashlma, J. ColloM Interface Sci., 48,92 (1974).
I
Aqueous -Surfactant Syitems”, National Bureau of Standards, Washington, D.C., 1971. (19) J. M. Corkill, J. F. Goodman, and T. Walker, Trans. Faraday Soc.,
63,768 (1967). (20) K. Shlnoda and T. Soda, J . fhys. Chem., 67, 2072 (1963). (21) F. Franks, M. J. Quickenden, J. R. Ravenhill, and H. T. Smith, J. fhys, Chem., 72, 2668 (1968).
Temperature-Dependent Hyperfine Interactions of Pyramidal Radicals Trapped in KPF,+ J. R. Morton,” K. F. Preston, and S. J. Strach’ Division of Chemistty, National Research Council of Canada, Ottawa, Ontario, Canada K I A OR9 (Received May 30, 1979) Publication costs assisted by the National Research Council of Canada
A study has been made of the temperature dependence of the central atom hyperfine interaction of various radicals trapped in KPF6. It is concluded that certain tetratomic, pyramidal species are inverting at 300 K and above, and that the barrier height is approximately 2 kcal/mol. Introduction I t has been known for many years that paramagnetic defects can be formed and trapped in NH4PF6and KPF6 a.t room temperature by ionizing radiation.’ These species include2 PF, (first thought1 to be PF4),and various other species (FP02-, derived from low concentrations of hydrolysis products. An interesting property of NH4PF6 and KPF6 is that, at room temperature, they are “rotator solids”, and electron paramagnetic resonance spectra of radicals trapped therein are isotropic. Individual spectral lines are sharp (AH 2 G), and exact measurement and analysis are possible. Of course, the hexafluorophosphates are not unique in this regard: SF6 is the rotator solid pur excellence over the temperature range 93-140 KS4The unique property of KPF6, however, is that it is a rotator solid at room temperature, and that isotropic EPR spectra can be detected in it over the temperature range 250-475 K. The ammonium salt has a similar, although lower, range over which isotropic EPR spectra are exhibited: 190-390 K. These matrices therefore offer the possibility of measuring the temperature dependence of the EPR spectral parameters (a) very accurately and (b) over a wide, and relatively high-temperature range. Because of recent interest in the temperature dependence of hyperfine interactions, we report herewith data for the following species which we have observed in y-irradiated KPF6: PFC, AsFc, FPO,, HP02-, P032-,and AsOs2-. The latter two species have previously been studied in a calcite m a t r i ~ the ,~ (anisotropic) hyperfine interactions being studied over the temperature range 4-300 K.
TABLE I : EPR Parameters of Radicals at 295 K
Trapped in KPF,
hfi, MHz ~
-
Experimental Section Potassium hexafluorophosphatewas obtained from PCR Inc., Gainesville, Fla. After irradiation at 300 K in a 6oCo y cell, the EPR spectra not only of PFs-but also (weakly) of AsF6-, FP02-,and PO:- were obtained. This indicates (a) that the KPF6 contained traces of KAsF6,and (b) that some hydrolysis had taken place. The spectra of HP02and As02- were obtained by recrystallizing the KPF6 from an aqueous solution containing 2% KHzPOz (Pfaltz and NRCC No. 17727. t NRCC Research Associate 1977-1979. 0022-3654/79/2083-2628$01 .OO/O
central atom
ligand
PF,-
2.00174(2)‘
3800.8(2)
554.1(5)b
hF,-
2.00060(5)
5063.(5)
FPO,-
2.00129(2) 2.00319(1) 2.00163( 2) 2.00328(2)
1890.2(2) 1178.1(2) 1684.3(2) 1558.5(1)
505.4(5)b 15.(1) 491.6(2) 262.1(2)
HP0,PO,’-
N
~
g factor
radical
941)
As0,’Numbers in parentheses are the estimated errors in the last digit. Four equivalent 19Fnuclei have this
’
hyperfine interaction.
Bauer). This process apparently brought about hydrolysis of the AsF6- impurity. The EPR spectra of the irradiated samples were detected and measured with a Varian E-12 spectrometer equipped with a variable temperature accessory. The microwave frequency was measured with a Systron-Donner Model 6054 frequency counter, and the magnetic field was measured with a Cyclotron Corp. Model 5300 NMR gaussmeter. The spectra were analyzed by standard methods, the spectral parameters being obtained by iterative computer diagonalization of the spin matrix. In many cases the precision was sufficient to determine the relative signs3 of the central atom and ligand hyperfine interactions. The samples were contained in 4-mm 0.d. thin-walled Suprasil tubes. These tubes were equipped with a reentrant capillary tube which enabled a fine copperconstantan thermocouple to be inserted and imbedded in the center of the sample. Overall temperature measurement and control were thought to be accurate to better than 1 K. Results and Discussion In Table I we collect the spectral parameters of the various radicals we have detected in y-irradiated KPF6 at 295 K. Most of these species have been reported elsewhere, although not necessarily in a KPF6 matrix. The identity of PF5-(originally misidentified as PF4)is now well es0 1979 American Chemical Society
Hyperfine Interactions of Radicals Trapped in KPF6
tablished,2as is that of its analogue AsF;.~ Note that the hyperfine interaction (hfi) of the fifth l9F nucleus, barely resolved in PF,, has increased to 15 MHz in AsF,. The radical HPO, has previously been studied in single-crystal or powdered matrices; this is, however, the first report of their isotropic spectra. The same is true of AsO:-, a species widely studied in irradiated arsenate crystals. In Figure 1 is shown the variation of the central-atom hyperfine interactions of these radicals over the temperature range 295-450 K. The temperature variation of each hfi is expressed as a percentage of its value at 295 K, listed in Table I. It will be seen that, although the effect of temperature change is small (approximately l % )the , sharp lines and large absolute values of the hyperfine interactions render the measurement of such small changes perfectly feasible. With regard to interpreting these changes, we shall attempt to answer the following questions: (1)Why does the central-atom hfi change with temperature? (2) Why does it decrease for some species (PO?-, AsO?-, and FP02-)and increase for the others (PF6-and AsF5-)? In the solid phase, three mechanisms, or combinations of them, can cause hyperfine interactions to vary with temperature. The first is the thermal expansion of the lattice (sometimes called the “implicit” effect). Since EPR measurements are usually made at constant pressure rather than constant volume, a contribution from lattice expansion to the observed temperature dependence should normally be ~onsidered.~ Fortunately, such contributions are often extremely small and, in the absence of the high-pressure data needed to estimate the importance of this effect, we are obliged to ignore it. The second mechanism also involves the surrounding lattice. If there is an interaction between the phonon continuum of the lattice and the vibrational energy levels of the radical, the spin-density distribution will be modulated so that the individual hyperfine interactions vary with temperature according to an equation of the form
where OD is the Debye temperature of the lattice.* In the case of the halogen hexafluorides: we were able to discount this mechanism after determining the changes in apparent BD between one radical and another in the same matrix. A third mechanism is that of modulation by a molecular vibration. Even at very low temperatures, when most of the radicals are in the ground vibrational level, the hyperfine interaction may differ from that of the (hypothetical) nonvibrating species because of changes in the spin-density distribution during the period of the vibration. Each vibrational level will, in fact, have a different hyperfine interaction whose value will depend on time avof the normal coordinate for the particular erages, ( level:1° Since vibrational energy exchange will normally be very fast compared to differences in hyperfine interaction between the levels, the observed hyperfine interaction will be an average over the populated levels. As the temperature is raised, changes in the Boltzmann distribution of vibrational energy will thus result in a change in the measured hyperfine interaction. The magnitude of the change will depend upon the vibrational frequency and the sensitivity of the hyperfine interaction a to changes in the normal coordinate as determined by the values of the coefficients in (2). The largest temperature variations of
The Journal of Physlcal Chemistry, Vol. 83, No. 20, 1979 2629
-0
FPO;
K
Figure 1. Percentage change in the central-atom hyperfine interactions of various radicals trapped in KPF, as a function of temperature.
hyperfine interactions arise in cases of “soft”, Le., low force constant, vibrations which are usually bending motions, e.g., the out-of-plane vibrations of carbon-centered radicalsll or the tl, deformation of the halogen hexafluoride~.~ For a potential energy well symmetric in 4, averages of odd powers of 4 are zeroloand the time-averaged hyperfine interaction for each level is a function of even powers of 4 only. In the particularly simple case of a simple harmonic oscillator for which terms in (4 4, and higher may be neglected, the temperature dependence is governed by a relationship of the form a(T) =
+ b coth (0/2T)
(3)
In this equation, a. is the (hypothetical) hyperfine interaction of the nonvibrating radical, (ao+ b) the observed hfi as T 0 K, and 0 is the vibrational temperature hcu/k = 1.44~ K if u is in cm-l. The parameter b, which governs the temperature dependence, is proportional to a2 in expression 2 and thus may be large for modes belonging to group representations other than that of the ground electronic wave function. For a vibration of the same symmetry as the electronic wave function, one would, on this simplistic basis, anticipate a much smaller (or even zero) value of a2and a correspondingly weaker temperature dependence. Anharmonic effects, which may be considerable for bending motions, would indubitably modify this conclusion. Temperature variation of the form (3) is exhibited by the centrd-atom hyperfine interactions of PF6- and AsF6(Figure l),although the total change over a 100 K range is only -0.3%. A fit of the data for AsF,- to the above equation is shown in Figure 2, and yields for the vibrational frequency 1200 f 200 cm-’. By contrast, a fit of the same data to expression 1 was poor and, furthermore, yielded an unacceptably high Debye temperature of 3200 f 1700 K. The magnitude of the vibrational frequency indicated by the hypercotangent fit strongly suggests that the temperature dependence of the central-atom hyperfine interactions in AsF6- (and PF5-) is due to the al (in C4J stretch. Another interesting point emerges from Figure 2: the 7SAshyperfine interaction is virtually constant below 200 K. In such a situation, it is usually assumed that the 4s
-
2830
J. R. Morton, K. F. Preston, and S. J. Strach
The Journal of Physical Chemistty, Vol. 83, No. 20, 1979
50 4689.7t 371.6 coth (861/T)
\
508050801
/ I
75As hfi
(MHz 1 5070-
5060 200
I 300
K
I 400
500
Flgure 2. 75As hyperfine interaction (circles) of AsF,- in KPF, as a function of temperature. The curve is a least-squares hypercotangent fit to the data points.
spin density in the radical can be estimated by dividing (at 250 K, say 5062 MHz) by some factor determined from atomic wave f ~ n c t i 0 n s . lHowever, ~ as will be seen from Figure 2, a fit of u75to a hypercotangent function above 300 K indicates the vibrationless radical to have a 75Ashyperfine interaction of -4700 MHz. It is clear then that (a) a temperature invariant hyperfine interaction cannot be assumed to be that of the vibration-free (equilibrium) state of the radical, and (b) errors of 5-10% in spin-density calculations can be expected from such an assumption, irrespective of errors in the calculation of ( 8 ~ / 3 ) y ~ y ~ $ from ~ ( O )available wave functions. We turn now to a consideration of the other radicals whose hyperfine interactions are depicted in Figure 1: AsO:-, FP02-,PO:-, and HP02-. Note (1)the slopes of their curves are nonzero at room temperature, (2) their hyperfine interactions decrease with increasing temperature, and (3) the slope of their curves decreases with increasing temperature. In each of these respects the radicals AsOt-, FP02-,PO?-, and HPO, differ from PF5and AsF6-. From (1)above it may be concluded that the vibration frequency generating the temperature dependence is very much lower for these four radicals than for PF,- or AsF5-. The active vibration is probably the motion of the central atom against the plane of the other three. This vibration would not only be “soft” (i.e,, low frequency) but would also cause the central-atom hyperfine interaction to decrease as the planar configuration is approached. Unfortunately, one cannot estimate the frequency of this vibration from such a small portion of the a ( T ) curve, although some credence is lent to this interpretation by a comparison of the curves for PO?- and AsOZ-, or HP02and FP02-. Clearly, the heavier radical has a lower vibration frequency and hence a more pronounced temperature variation. One has also to consider the possibility of inversion in these tetraatomic species. Because of the large centralatom contribution to their semioccupied orbitals, these radicals have always been considered to be “pyramidal”, that is, the central atom does not lie in the plane of the other three. As far as we are aware, the possibility of these (and similar) species undergoing inversion has not pre-
viously been suggested. Nevertheless, for all such pyramidal species, the potential well for the “umbrella” vibration (movement of the cental atom in a line perpendicular to the plane of the other three) must possess a double minimum; the rate of inversion is merely a question of the temperature and the number of levels below the barrier. If the vibration is “soft”, as appears to be the case here, the number of levels below the barrier will be small, and inversion will take place at accessible temperatures. Is there a diagnostic test for inversion? We know that in the absence of inversion the central-atom interaction increases or decreases monotonically according to the above hypercotangent equation (eq 2). It has been shown13 that in a radical which is inverting (for example, tertbutyl’l) the central-atom hyperfine interaction at first decreases (with increasing temperature), reaches a minimum, and eventually increases again at sufficiently high temperature. In fact, the central 13Chyperfine interaction in tert-butyl has been shownll to reach a minimum around 210 K. Furthermore, Krusic and Meakin have shown that13the barrier height to inversion is approximately 2.33. Tmincal/mol, where TminK is the temperature at which the central-atom hyperfine interaction reaches its minimum. For tert-butyl the barrier height is therefore approximately 0.5 kcal/mol. The decreasing slope of the a ( T ) vs. T curves for these four radicals can be interpreted in this light. Admittedly, Tminis not attained, due to the disappearance of the radicals at approximately 450 K. However, by assuming a parabolic shape to these curves, we can give a crude estimate of Tminfor each radical: HP02-, 600 K; FP02-, 540 K; P032-,710 K; AsO?-, 610 K. From Krusic’s relationship, a barrier height of approximately 1.5 kcal/mol is indicated. Comparing P032-with A s O ~ ~we - , find a slightly lower barrier height for the latter. This is consistent with the fact that the semioccupied orbital in AsOz- has less As(4s) character than PO?- has P(3s) character,12indicating that As02- is less bent than PO:-. Conclusions We conclude from the central-atom hfi of certain pyramidal radicals trapped in KPF6 that these species are probably inverting at temperatures above 300 K. The barrier height appears to be approximately 2 kcal/mol. References and Notes (1) (2) (3) (4) (5) (6) (7) (8)
(9) (10) (1 1) (12) (13)
J. R. Morton, Can. J. Phys., 41, 706 (1963). S. P. Mishra and M. C. R. Symons, Chem. Commun., 279 (1974). R. W. Fessenden, J. Magn. Reson., 1, 277 (1969). R. W. Fessenden and R. H. Schubr, J. Chem. phys., 45, 1845 (1966). R. A. Serway, S. S. L. Chan, and S. A. Marshall, Phys. Status SdMl (4, 57, 269 (1973). A. R. Boate, A. J. Colussi, J. R. Morton, and K. F. Preston, Chem. Phys. Lett., 37, 135 (1976). H. Klein, U. Scherz, M. Schulz, H. Setyono, and K. Wisznewski, Z. Phyz. B, 28, 149 (1977). K. Zdansky, Phys. Status Solidi, 28, 181 (1968). A. R. Boate, J. R. Morton, K. F. Preston, and S. J. Strach, J . Chem. Phys., 71, 388 (1979). R. W. Fessenden, J. Chem. Phys., 71, 74 (1967). D. Grlller, K. U. Ingold, P. J. Krusic, and H. Fischer, J . Am. Chem. Soc., 100, 6750 (1978). J. R. Morton and K. F. Preston, J . Magn. Reson., 30, 577 (1978). P. J. Krusic and P. Meakin, J . Am. Chem. Soc., 98, 228 (1976).
