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Quadrature phase relationships in phosphorescence microwave double resonance spectroscopy
Volume 12, number 1
CHEM!CAL
PHYiKS LETTERS
I December 1971
QUADRATURE PHASE RELAr(TONSHiPS IN :. PHOSPHORESCENCE MICROWAVE DOUBLE RESONANCE iPECTROSCOPY C.B. HARRIS*
and R.J. HOOVER
Department of Chemirhy, Vniuersity of Cblifonh, and the Inorganic Materials Research Divisiorr, Luwrexe Berkzky Labomtory, Ber&eky, Cidifomia94720, U&f
Received 17 keptember 1971
The functional dependence of the phase shift of a time-dependent phosphorescence intensity changeMative to a repetitive delta-function microwave perturbation is @ven in terms of the aipkt state kinetic par;rrnet= =d the perturbation repetition rate. This extension of quadrature measurements to the phosphorescent microwave doubk
resonance (LWDR) technique is found to be particularly useful since the phase shift is independent of the degree of spin aligilment of the magnetic sublevels, the degree of microwave saturation, and the poluization of the microwve transition moment It is shown thit the symmetries of vibronic bands in the phosphorescence can be distinguished and s-tetracblorobenzene. by measuring the phase shift. Experimental results are reported for ~chlorolmzeae
1. Introduction As a consequence of spin-orbit coupling, phosphorescence from the lowest triplet state of a molecule to the ground state vibrational manifold is selective from the individual magnetic sublevels and can be thought of as a sum of three components, one from each of the zero field magnetic sublevels, TV, ry and rz. The amplitude of each component is determined by the radiative rates and the populations which are in turn determined by intersystem crossing rates, total decay rates, and spin lattice relaxation effects; Advantage has been taken of these facts in the method of phosphorescence-microwave double-rksonance (PMDR) spectroscopy which isohtes two of the magnetic sublevels with a’microwave field and monitors the change in phosphorescence’it induces at low temperatures (1.3-2°K). The sublevels active in emission, and the degree of spin alignment in the Iowest triplet state, can be determined via standard PhlDR techniques [l] . This information is useful in determining triplet state properties, such as the relative rates and routes of intersystem crossing, as w~I as the specific spin Ievei contributions to tibronic bands. In some cases the magnetic sublevels active to a particular vibration Progression can be anal~d in greater det@l by polarized PMDR [2] yielding information lost in standard techniques. Depending upon the specific case under investigation, the polarized components from the individual magnetic sublevels of the triplet may only be resolved to a varying degree. The same basic information can be obtained by time resolved techniques such as that developed by van der Waals et al. [3] ; however as a diagnostic tool for simply determining which sublevels are active in emission to particular vibrational barids it is usually more time consuming tin relatively siraightforward PMDR techniqws. In this communication we would like to outline an additional PMDR method which retains the basic features of standard PMDR techniques but adds t&e advkages of time resolved spectroscopy.
2.4ua&ature
P’MDR
.,
It is well known that time-resoived spectroscopy can b-eexecuted in two ways. First is simply to measure the * Alfred P’.‘Sloan Fellow,
.;
_...’
,’ 7.5
Volume 12. number 1
CHEMICAL PHySICS LETTERS
1 Dry-da
1971
..,
amplitude of a.s&nal whichhas one or more sources as a function of time akdecompose the $$I& into its fie$rency components. The second method is to measure the-phase shift of a signal as a function &frequency. One &ndard
exknple
of thk-latter is called quadrature
detection
and is simply the measurement
of thk in-phase and
otit-ofip~se
components of a signal relative to a periodic perturbatkn. The application of quadrature methods to the dete nnination of kinetic parameters in photochemical processes has been extensivejy developed by Johnston it can be valuab!e in resolving phosphorescence components in .and co-workers 141. As will be demonstrated,
much the same vein since the emission amplitude is intrinsically kinetically determined.. Let us treat the kinetics of a microwave induced change in triplet phosphorescence resulting from the saturation or inversion of the populations of two of the thee triplet spin sublevels. Consider explicitly the case when the microwave puke is short compared to any radiative or radiationleSs process and is applied repeatedly every r seconds in the presence of continuous exciting optical radiation. At the time of the pulse the phosphorescence intensity will acquire a new value because of the microwave induced population change and will relax back to some boundary value, determined by 7, as a function of the time, t, after the pulse. Differential equations of the intensity of phosphorescence induced by a microwave field connecting two spin sublevels rX and T,, , under such condition can be solved and the solutions are given by eqs. (1) through (5). L&r) = k’xNJ0
+ ~$&r)
-
(1)
withO<_r
r) + &!!lkX)N, ,
N,,(f) = c2 =p(-kY
t) + ($,/ky)Ns
,
(2)
.-where the constants for saturation of the sublevel populations are c1 = oAS/(l +a), or alternatively
c2 = -AS/(1 +a) ,
for adiabatic
cl = --t$A”/[a(l
-fl
inversion
exp(-ki
(3)
of the subIevs1 populations
7) -fexp(-kj
7) -(uJ
[S] ,
, cz =fA”/[or(l
-fl
exp(-k,
7) -fexp(-ky
T) - CT] ,(4)
where. Ass = (kIy~~~--~lkxWs
,
Q:=
11-
exp(-k,,
7))/ (1 - exp(-kx
T)} ,
(5)
and f is the fraction of inversiori, Jcs and k; are the radiative rate constants from the sublevels 7X and T,, respectively, k, and kj are the total triplet decay rate constants, k’, and gY are the intersystem crossing rate constants, Ns is the excited singlet state population, and T is the period between microwave pulses. Dividing the period 7 into four equal parts of duration
r/4, -we define. integrated
microwave
Combinations of the quadrants q1 through q4 tan be corrstructed and subtract @$=a1
all emission
W2-q3
except that induced
-q4
and
by the microwave
@LA =-4t
t42
tag
induced
intensities
in these periods as
which subtract random noise that is present field. Two such combinations are
(7)
-4.+3
and represent two~si&als displaced by 90’ from each other: From these two signals a ‘oe defmed as --q
= tan-lcQy/Qgp
=-tar&J) ,
general
phase angle, 4, can
(8)
where the subscript ti denbtes the particular vibrational le’&l in the ground singlet manifold to which phosphorescenti is being monitored and the superscript denotes the &vo t&let sp&,suble.?els,beiig periodically perturbed with the microwave field. ‘Ihe’phosphorescence intenisty changes.and,?te quadrants thioughq q4 are : .1 through .. s@vn schematically in fig, 1. .’ .76-
‘. _.
:
:,. .
:
. ..
Volume 12, number 1
(SHEMICAL PHYSICS LEmERS
I
.
8
2t
T
I December
L971
37
Time
FE. 1. (a) ?,:&dic modulation of phosphorescence intensity (rp) caused by delta-function miaowzve @ses at t =m. II = I, 2, ... . @). Breakdownof the modulation period T into four quadrsnts. The perturbing microwave p~k is applied during 3 short time (heavy
vertical
line) at the beginning of each cycle.
The importance of ‘these phase relationships in PMDR spectroscopy is that they are expected to be the same for measurements made monitoring phosphorescence to vibrational states of the same overall symmetry. They are also independent of microwave power, and hence to the degree of saturation of the magnetic sublevels, and to the polarization of the microwave transition moment. The difference in the magnitude of the phase angle and its functionality in r for phosphorescence to singlet vibronic states of different symmetries is easily obtained. Substitution of eqs. (l)-(5) into (6) and integration yields a closed analytic form for A of eq. (8) as:
-(C,/C it = (C&J
(exp(-kx
d-
) (1 +exp(-k, 2 exp(-3kX
T)-2 exp(-kX r/2)} + (1 +exp(k 7-/4)+2 exp(-kx
7)-2 exp(-k
7/4)} - {exp(-ky?)-2
7/2))
exp(-3k,;/4)-2exp(-kYr/4)-l} (9)
where
The above equations assume the spin sublevels to be isolated and therefore neglect any spin-lattice relaxation effects. The same result [eq. (9)] is obtained for saturating microwave pulses and inversion pulses as is expected in quadrature techniques since the phase angle is independeni of the amplitude of a repetitive signal. This means that the phase angle is also independent of the extent of spin alignment in the magnetic sublevek The important feature of eqs. (9) and (10) is that th e functionality of the phase angle ig restricted to only mtios of radiative rate constants from the magnetic sublevels being connected by the microwave field since the EotaldepIetive rates k, and k can be considered constant at any one temperature. Naturally CX/CY is different for vibrations of different over& symmetries because of selective spin-orbit plus vibronic and/or spin-vibronic coupling. What is not so obvious, however, are the reasons why the phase angle is expected to he independent of a partic&r vibration being monitored so long as the overall symmetry of the vibrations remains constant. Within the framework of the Born-Oppenheimer approximation, the ratio of the radiative rate’constants (icy,/k;) to vibrations of the same total symmetry are equal, since vibronic coupling within the triplet manifold 77
Volume 12, mmtm I
1 December 197!
CHEMIC.ALPHYSICS LETTERS _.’ : I ./,-.
affects all three spLn sublevels equally and &ny differences in the nu&ar.poter& &nctions of the spin g&levels c&ed by spic-oibit interactions aie extremely small. Thus, thy Frtick-Condon fact&s u;V> in the ratio kI/kyy = &lr@;rc cancel and the ratiu is determined by the ratio df the electronk contributions to the tr$sition IQment (k~r) for a given symmetry lY’ and polark%.ion. Thus the ratios arti independent of the particulahvit;cc’,ion being monitored in PMDR provided the overall symmetry of the transition remains unchanged.. Measuiement of the phase an$e
3. Expe~ectaI
should ‘Aen allow one to separate
vibrations
according
to their symmetries.
and results
Trap phosphorescence from single crystals (zone relined - 200 passes at 2 inches/hr) of paradichlorobenzene (whose electronic origin at 1.3% is 3588.3 a) and s-tetrachlorobenzene (doped with 1% paradichlorobenzene to enhance Y-trap emission [6]) were investigated. The microwave perturbation used consisted of a frequencymodulated pulse (see fig. 1) which resulted in an inversion of the magnetic sublevel populations via adiabatic fast passage, larger signal changes could be obtained via inversion than by saturation. The duration of the p&e was only
100 psec in order to ensure that the microwave perturbation could be considered Like a delta function as was assumed in eqs.,(2)-(5). The crystals were, placed in a helical slow-wave stnlcture to which microwaves of the appropriate frequency were applied. The crystal was continuously irradiated through the windings with the 2800 A
region of a Hg short arc isolated by a Schott UV 280 interference ftiter. The helical slow wave structure was supported in a d&war that was pumped to 1.2-l .3%. The phosphorescence to the vibrational band under investigation was isolated at 90’ angle to the incident exciting sour& by a 3/4 meter Jarrell-Ash spectrometer equipped with a cooied EMI 9856-QB photomultiplier. The photomultiplier was terminated in a 50 52 load to ensure a fast rise time to facilitate photon ccmnting. Standard photon counting threshol&discriminated signals were gated such that four quadrants ofeqs. (6) could be obtained on separate channels. Reversible up-down counters then performed the additions and subtractions of eqs. (7) and the diffeiences were displayed on separate channels of a dual recorder after averaging for a suitable prescribed number of periods of length 7. In this manner the absolute errors could be determined from photon counting statistics. For convenience the values of X are prcsenied rather than the phase angla [cf. eq. (8)] because the observed differences are numerically larger. The errors iisted in table 1 are the standard detiations obtained from counting statistics. Errors for the 25 msec period are higher due to greater fluctuations in tQe exciting source intensity at
frequencies -0 Hz and the fact that the absolute intensity change due to the microwave perturbation is small at high modulation frequencies [see eq. (2)-(S)]. The data in tab!= 1 for paradichlorobenzene clearly show the separation of bands of different symmetry via quadrature PMDR even though the kife:imes of the two connected levels are quite different (35 msec and 700 msec). The dda for s-tetrachlorobenzene are not as good F terms of separation or constancy for a given symmetry. This is probably in part due to the fact that the populations of the trap sublevels are dependent to a great extent on exciton deactivation [8]. This results in a nonexponential decay (and buildup) for the traps while eqs. (l)-(S) are derived assuming simple exponential behavior. Table 2 shows an.example of a quantitative comparison of experimental and calculated data [eq. (S)] for the sretrachlorobenzene 2jEI transition monitoring the origin. The value of k;lk;, for the origin was experimentally determined by decay techniques [3] to be ~5, indicating mixed emission. The data were calculated using this value and various combinations of lifetimes, with values of ~20 msec giving the best overall fit. These lifetimes are shorter than those experimentally determined (-25 msec) by decay teclukpses (31. The overall fit is good with .the Iargest err&r at high modulation frequencies.
4. Discus&m Ais a timfini
78
technique
for distinguishing
vibrational
symmetries
and d&mining
rate cons&s,
the method
lume 12, xi&x
I
CHEMICAL
PHYSICS
1 Decanber
LETIERS
1971
.
Table 1
The valxs of A [<. (8)] obtained for various phosphorescence bands and Tvalues pi3radicMorobknzene (D - IEI)
!7]
dmsed 25 86 68 28 11 04
8.80 f 8.462 9.34 f 9.07 f 10.25 *
200 0.14 0.10 0.15 0.12 0.35
4.04 zt0.03 1.98 * 0.03 4.37 Et0.04
-
4.26 * O.G4 4.80 f 0.04
-
(D + WI) [ 61
ptekachlcrobenzene $2 x bzgI “zg
6.92 f 0.37 6.16 0.18
3.40 *f 0.03 3.11 G.02
1.83 2 1.60 it 0.01
0.87 1.11 *t 0.01
7.76 2 0.10
3.66 t 0.10
2.12 * 0.01
1.18 L O.OL
“zg
7.31 f 0.15
3.51 * 0.05
1.88 L 0.01
I.17 f 0.01
Table 2 A-valuefor s;tetrshlorobenzene
21E1transition
[6]
7(mOc)
Calculateda)
Observed
25 50 100 200
6.49 3.32 1.81 1.18
5.71 3.16 1.85 1.20
a)T,= qs.
18msec T = 19.5 msec, and k?j?j,fly = 4.5; (9) arld (k$.
see
rfers some shorxomings. These can be illustrated by considering two limiting cases of eq. (9). if the total life3es of the two magnetic sublevels being connected by a microwave field are equal or very different, i.e., k, >> , eq. (9) is reduced to = -(I
+exp(-kY
T) - 2 exp(-kY ~/2))/ (exp(+
7) - 2 exp(3ky 7/4) + 2 exp(-ky
T/4) - 1J ,
0 1)
d unfortunately
is independent of any radiative rate constant ratios. This means that the phase angle is the ne for all vibrations. In many aromatic molecules, particularly those with higher symmetries, the rate proce~ phosphorescencz approaches the limits leading to eq. (11); consequently, great care must be exercised in measng the phase angle since the differentis are expected to be small. Large differences in the phase angle are excted, however, in intermediate cases. Although the factors described above may limit the utility of quadrature techniques in PMDR, the general m of the 7 dkpendence of @can yield useful information. As the modulation period r is made longer than the ,level lifetimes the value of h [eq. (8)] approaches unity; however, the value of Q for a given T w-3 be Iarger for &ion from a sublevel w& a short lifetime than from one with a long lifetime. This can provide information as which sublevel.is
most active in emission.
This information
used in conjunction
with polarization
data m
be
determining assignments. Such information may be difkult to obtain from simple decay measurements cases where the lifetimes of the levels are nearly equal. In these cases ~uadrature.techniques are particuIarIy at-
:ful in
7.9
Volume 12, numkr ., -.
I
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CHEMICAL PHYSICS L3XTERS
:
1 December
1971
‘. -sactive sin’ce 9 is’indeendent of the magnitude of the population difftirences between sublevels. Thus data ob: tained fro+ alJ three z&o field microwave transitions can,be compared witrlout wor@ng abd&he complications -iiztrW&d
by the lack of unifonkmicrowave
induced
pop&&k
changes. %is.is
only true, &&ever,
when the
spin
subleveL &anbe c&sidered independbnt: This is equivalent to neglectig spin,lattice relaxation effects. If spin-lattice relaxation is included in the derivation of eq. (9), the phase angle 4 is found to be dependent on the degree of spin alignment since the rate of pop&ion equilibration depends on the population difference between subbvels, Thus, one expects to fmd a dependence of $I on the degree of saturation or inversion. The equations des@bi?g Q are complex and will not be presented here. We wish only to point out that the quadrature method may provide a n&w tool for directly studying spin-lattice relaxation effects or other phenomena such as exciton averaging of triplet stat* sublevel populations. A study of @versus saturating power, for example, may show deviations which would indicate whether or not such relamtion processes are important. Quantitative evaluation, however, of these effects is made difficult by the complexity of the differential equations describing coupled spin sublevels.
Acknowledgment This work w&,supported by the Inorganic Materials Research Division of the Lawrence Berkeley Laboratory under the auspices of the US. At&nic Energy Commission.
References [I] D.&T&i, M.A.EbSayed, A.H.Maki and C.B.Hanis, Chem. Phys. Letters 3 (1969) 343. 121 M.AEl-Sayed, !. Chem. Phys. 54 (1971) 680. [3] Jdchmidt, W.S.Veeman and J.H.van der WaaIs, Chem. Phys. Letters 4 (1969) 341. [4] xs.fohnston. GE_McG~w, T.TL&ett LW_RL&tk tid J-van den E&wrde. Froc. Nstl
E.D.Morrisand H.S.Jolmston, Rev. Sci. Instr. 39 (1968) 620; H.SJohnston, G.E.McGraw
[S]
[6] [7] [8]
EarLD.Morris Jr. and J.van den Bogaerdc, J. Am. Cbem. Sot. 91 (1969) 7712; and H.S.Johnston, J. Chem. Kinetics 1 (1969) 89. C.B.Hanis, J. Cliem. Phys. 54 (1971) 972; C.B.Harris and RJ.Hodver, unpublished results. A.H.Francis and C.B.Harris, Chem. Phys. Letters 9 (1971) 188. M.Y.BucMey, C.B.Harris and R.Panos, I. Am. Chem. 5$x., to be pubtied. A.H,Francis and CB.Hati, J. Chem. Phys., td be published.
Acad. Sci. 57 (1967) 1146;
CHEM!CAL
PHYiKS LETTERS
I December 1971
QUADRATURE PHASE RELAr(TONSHiPS IN :. PHOSPHORESCENCE MICROWAVE DOUBLE RESONANCE iPECTROSCOPY C.B. HARRIS*
and R.J. HOOVER
Department of Chemirhy, Vniuersity of Cblifonh, and the Inorganic Materials Research Divisiorr, Luwrexe Berkzky Labomtory, Ber&eky, Cidifomia94720, U&f
Received 17 keptember 1971
The functional dependence of the phase shift of a time-dependent phosphorescence intensity changeMative to a repetitive delta-function microwave perturbation is @ven in terms of the aipkt state kinetic par;rrnet= =d the perturbation repetition rate. This extension of quadrature measurements to the phosphorescent microwave doubk
resonance (LWDR) technique is found to be particularly useful since the phase shift is independent of the degree of spin aligilment of the magnetic sublevels, the degree of microwave saturation, and the poluization of the microwve transition moment It is shown thit the symmetries of vibronic bands in the phosphorescence can be distinguished and s-tetracblorobenzene. by measuring the phase shift. Experimental results are reported for ~chlorolmzeae
1. Introduction As a consequence of spin-orbit coupling, phosphorescence from the lowest triplet state of a molecule to the ground state vibrational manifold is selective from the individual magnetic sublevels and can be thought of as a sum of three components, one from each of the zero field magnetic sublevels, TV, ry and rz. The amplitude of each component is determined by the radiative rates and the populations which are in turn determined by intersystem crossing rates, total decay rates, and spin lattice relaxation effects; Advantage has been taken of these facts in the method of phosphorescence-microwave double-rksonance (PMDR) spectroscopy which isohtes two of the magnetic sublevels with a’microwave field and monitors the change in phosphorescence’it induces at low temperatures (1.3-2°K). The sublevels active in emission, and the degree of spin alignment in the Iowest triplet state, can be determined via standard PhlDR techniques [l] . This information is useful in determining triplet state properties, such as the relative rates and routes of intersystem crossing, as w~I as the specific spin Ievei contributions to tibronic bands. In some cases the magnetic sublevels active to a particular vibration Progression can be anal~d in greater det@l by polarized PMDR [2] yielding information lost in standard techniques. Depending upon the specific case under investigation, the polarized components from the individual magnetic sublevels of the triplet may only be resolved to a varying degree. The same basic information can be obtained by time resolved techniques such as that developed by van der Waals et al. [3] ; however as a diagnostic tool for simply determining which sublevels are active in emission to particular vibrational barids it is usually more time consuming tin relatively siraightforward PMDR techniqws. In this communication we would like to outline an additional PMDR method which retains the basic features of standard PMDR techniques but adds t&e advkages of time resolved spectroscopy.
2.4ua&ature
P’MDR
.,
It is well known that time-resoived spectroscopy can b-eexecuted in two ways. First is simply to measure the * Alfred P’.‘Sloan Fellow,
.;
_...’
,’ 7.5
Volume 12. number 1
CHEMICAL PHySICS LETTERS
1 Dry-da
1971
..,
amplitude of a.s&nal whichhas one or more sources as a function of time akdecompose the $$I& into its fie$rency components. The second method is to measure the-phase shift of a signal as a function &frequency. One &ndard
exknple
of thk-latter is called quadrature
detection
and is simply the measurement
of thk in-phase and
otit-ofip~se
components of a signal relative to a periodic perturbatkn. The application of quadrature methods to the dete nnination of kinetic parameters in photochemical processes has been extensivejy developed by Johnston it can be valuab!e in resolving phosphorescence components in .and co-workers 141. As will be demonstrated,
much the same vein since the emission amplitude is intrinsically kinetically determined.. Let us treat the kinetics of a microwave induced change in triplet phosphorescence resulting from the saturation or inversion of the populations of two of the thee triplet spin sublevels. Consider explicitly the case when the microwave puke is short compared to any radiative or radiationleSs process and is applied repeatedly every r seconds in the presence of continuous exciting optical radiation. At the time of the pulse the phosphorescence intensity will acquire a new value because of the microwave induced population change and will relax back to some boundary value, determined by 7, as a function of the time, t, after the pulse. Differential equations of the intensity of phosphorescence induced by a microwave field connecting two spin sublevels rX and T,, , under such condition can be solved and the solutions are given by eqs. (1) through (5). L&r) = k’xNJ0
+ ~$&r)
-
(1)
withO<_r
r) + &!!lkX)N, ,
N,,(f) = c2 =p(-kY
t) + ($,/ky)Ns
,
(2)
.-where the constants for saturation of the sublevel populations are c1 = oAS/(l +a), or alternatively
c2 = -AS/(1 +a) ,
for adiabatic
cl = --t$A”/[a(l
-fl
inversion
exp(-ki
(3)
of the subIevs1 populations
7) -fexp(-kj
7) -(uJ
[S] ,
, cz =fA”/[or(l
-fl
exp(-k,
7) -fexp(-ky
T) - CT] ,(4)
where. Ass = (kIy~~~--~lkxWs
,
Q:=
11-
exp(-k,,
7))/ (1 - exp(-kx
T)} ,
(5)
and f is the fraction of inversiori, Jcs and k; are the radiative rate constants from the sublevels 7X and T,, respectively, k, and kj are the total triplet decay rate constants, k’, and gY are the intersystem crossing rate constants, Ns is the excited singlet state population, and T is the period between microwave pulses. Dividing the period 7 into four equal parts of duration
r/4, -we define. integrated
microwave
Combinations of the quadrants q1 through q4 tan be corrstructed and subtract @$=a1
all emission
W2-q3
except that induced
-q4
and
by the microwave
@LA =-4t
t42
tag
induced
intensities
in these periods as
which subtract random noise that is present field. Two such combinations are
(7)
-4.+3
and represent two~si&als displaced by 90’ from each other: From these two signals a ‘oe defmed as --q
= tan-lcQy/Qgp
=-tar&J) ,
general
phase angle, 4, can
(8)
where the subscript ti denbtes the particular vibrational le’&l in the ground singlet manifold to which phosphorescenti is being monitored and the superscript denotes the &vo t&let sp&,suble.?els,beiig periodically perturbed with the microwave field. ‘Ihe’phosphorescence intenisty changes.and,?te quadrants thioughq q4 are : .1 through .. s@vn schematically in fig, 1. .’ .76-
‘. _.
:
:,. .
:
. ..
Volume 12, number 1
(SHEMICAL PHYSICS LEmERS
I
.
8
2t
T
I December
L971
37
Time
FE. 1. (a) ?,:&dic modulation of phosphorescence intensity (rp) caused by delta-function miaowzve @ses at t =m. II = I, 2, ... . @). Breakdownof the modulation period T into four quadrsnts. The perturbing microwave p~k is applied during 3 short time (heavy
vertical
line) at the beginning of each cycle.
The importance of ‘these phase relationships in PMDR spectroscopy is that they are expected to be the same for measurements made monitoring phosphorescence to vibrational states of the same overall symmetry. They are also independent of microwave power, and hence to the degree of saturation of the magnetic sublevels, and to the polarization of the microwave transition moment. The difference in the magnitude of the phase angle and its functionality in r for phosphorescence to singlet vibronic states of different symmetries is easily obtained. Substitution of eqs. (l)-(5) into (6) and integration yields a closed analytic form for A of eq. (8) as:
-(C,/C it = (C&J
(exp(-kx
d-
) (1 +exp(-k, 2 exp(-3kX
T)-2 exp(-kX r/2)} + (1 +exp(k 7-/4)+2 exp(-kx
7)-2 exp(-k
7/4)} - {exp(-ky?)-2
7/2))
exp(-3k,;/4)-2exp(-kYr/4)-l} (9)
where
The above equations assume the spin sublevels to be isolated and therefore neglect any spin-lattice relaxation effects. The same result [eq. (9)] is obtained for saturating microwave pulses and inversion pulses as is expected in quadrature techniques since the phase angle is independeni of the amplitude of a repetitive signal. This means that the phase angle is also independent of the extent of spin alignment in the magnetic sublevek The important feature of eqs. (9) and (10) is that th e functionality of the phase angle ig restricted to only mtios of radiative rate constants from the magnetic sublevels being connected by the microwave field since the EotaldepIetive rates k, and k can be considered constant at any one temperature. Naturally CX/CY is different for vibrations of different over& symmetries because of selective spin-orbit plus vibronic and/or spin-vibronic coupling. What is not so obvious, however, are the reasons why the phase angle is expected to he independent of a partic&r vibration being monitored so long as the overall symmetry of the vibrations remains constant. Within the framework of the Born-Oppenheimer approximation, the ratio of the radiative rate’constants (icy,/k;) to vibrations of the same total symmetry are equal, since vibronic coupling within the triplet manifold 77
Volume 12, mmtm I
1 December 197!
CHEMIC.ALPHYSICS LETTERS _.’ : I ./,-.
affects all three spLn sublevels equally and &ny differences in the nu&ar.poter& &nctions of the spin g&levels c&ed by spic-oibit interactions aie extremely small. Thus, thy Frtick-Condon fact&s u;V> in the ratio kI/kyy = &lr@;rc cancel and the ratiu is determined by the ratio df the electronk contributions to the tr$sition IQment (k~r) for a given symmetry lY’ and polark%.ion. Thus the ratios arti independent of the particulahvit;cc’,ion being monitored in PMDR provided the overall symmetry of the transition remains unchanged.. Measuiement of the phase an$e
3. Expe~ectaI
should ‘Aen allow one to separate
vibrations
according
to their symmetries.
and results
Trap phosphorescence from single crystals (zone relined - 200 passes at 2 inches/hr) of paradichlorobenzene (whose electronic origin at 1.3% is 3588.3 a) and s-tetrachlorobenzene (doped with 1% paradichlorobenzene to enhance Y-trap emission [6]) were investigated. The microwave perturbation used consisted of a frequencymodulated pulse (see fig. 1) which resulted in an inversion of the magnetic sublevel populations via adiabatic fast passage, larger signal changes could be obtained via inversion than by saturation. The duration of the p&e was only
100 psec in order to ensure that the microwave perturbation could be considered Like a delta function as was assumed in eqs.,(2)-(5). The crystals were, placed in a helical slow-wave stnlcture to which microwaves of the appropriate frequency were applied. The crystal was continuously irradiated through the windings with the 2800 A
region of a Hg short arc isolated by a Schott UV 280 interference ftiter. The helical slow wave structure was supported in a d&war that was pumped to 1.2-l .3%. The phosphorescence to the vibrational band under investigation was isolated at 90’ angle to the incident exciting sour& by a 3/4 meter Jarrell-Ash spectrometer equipped with a cooied EMI 9856-QB photomultiplier. The photomultiplier was terminated in a 50 52 load to ensure a fast rise time to facilitate photon ccmnting. Standard photon counting threshol&discriminated signals were gated such that four quadrants ofeqs. (6) could be obtained on separate channels. Reversible up-down counters then performed the additions and subtractions of eqs. (7) and the diffeiences were displayed on separate channels of a dual recorder after averaging for a suitable prescribed number of periods of length 7. In this manner the absolute errors could be determined from photon counting statistics. For convenience the values of X are prcsenied rather than the phase angla [cf. eq. (8)] because the observed differences are numerically larger. The errors iisted in table 1 are the standard detiations obtained from counting statistics. Errors for the 25 msec period are higher due to greater fluctuations in tQe exciting source intensity at
frequencies -0 Hz and the fact that the absolute intensity change due to the microwave perturbation is small at high modulation frequencies [see eq. (2)-(S)]. The data in tab!= 1 for paradichlorobenzene clearly show the separation of bands of different symmetry via quadrature PMDR even though the kife:imes of the two connected levels are quite different (35 msec and 700 msec). The dda for s-tetrachlorobenzene are not as good F terms of separation or constancy for a given symmetry. This is probably in part due to the fact that the populations of the trap sublevels are dependent to a great extent on exciton deactivation [8]. This results in a nonexponential decay (and buildup) for the traps while eqs. (l)-(S) are derived assuming simple exponential behavior. Table 2 shows an.example of a quantitative comparison of experimental and calculated data [eq. (S)] for the sretrachlorobenzene 2jEI transition monitoring the origin. The value of k;lk;, for the origin was experimentally determined by decay techniques [3] to be ~5, indicating mixed emission. The data were calculated using this value and various combinations of lifetimes, with values of ~20 msec giving the best overall fit. These lifetimes are shorter than those experimentally determined (-25 msec) by decay teclukpses (31. The overall fit is good with .the Iargest err&r at high modulation frequencies.
4. Discus&m Ais a timfini
78
technique
for distinguishing
vibrational
symmetries
and d&mining
rate cons&s,
the method
lume 12, xi&x
I
CHEMICAL
PHYSICS
1 Decanber
LETIERS
1971
.
Table 1
The valxs of A [<. (8)] obtained for various phosphorescence bands and Tvalues pi3radicMorobknzene (D - IEI)
!7]
dmsed 25 86 68 28 11 04
8.80 f 8.462 9.34 f 9.07 f 10.25 *
200 0.14 0.10 0.15 0.12 0.35
4.04 zt0.03 1.98 * 0.03 4.37 Et0.04
-
4.26 * O.G4 4.80 f 0.04
-
(D + WI) [ 61
ptekachlcrobenzene $2 x bzgI “zg
6.92 f 0.37 6.16 0.18
3.40 *f 0.03 3.11 G.02
1.83 2 1.60 it 0.01
0.87 1.11 *t 0.01
7.76 2 0.10
3.66 t 0.10
2.12 * 0.01
1.18 L O.OL
“zg
7.31 f 0.15
3.51 * 0.05
1.88 L 0.01
I.17 f 0.01
Table 2 A-valuefor s;tetrshlorobenzene
21E1transition
[6]
7(mOc)
Calculateda)
Observed
25 50 100 200
6.49 3.32 1.81 1.18
5.71 3.16 1.85 1.20
a)T,= qs.
18msec T = 19.5 msec, and k?j?j,fly = 4.5; (9) arld (k$.
see
rfers some shorxomings. These can be illustrated by considering two limiting cases of eq. (9). if the total life3es of the two magnetic sublevels being connected by a microwave field are equal or very different, i.e., k, >> , eq. (9) is reduced to = -(I
+exp(-kY
T) - 2 exp(-kY ~/2))/ (exp(+
7) - 2 exp(3ky 7/4) + 2 exp(-ky
T/4) - 1J ,
0 1)
d unfortunately
is independent of any radiative rate constant ratios. This means that the phase angle is the ne for all vibrations. In many aromatic molecules, particularly those with higher symmetries, the rate proce~ phosphorescencz approaches the limits leading to eq. (11); consequently, great care must be exercised in measng the phase angle since the differentis are expected to be small. Large differences in the phase angle are excted, however, in intermediate cases. Although the factors described above may limit the utility of quadrature techniques in PMDR, the general m of the 7 dkpendence of @can yield useful information. As the modulation period r is made longer than the ,level lifetimes the value of h [eq. (8)] approaches unity; however, the value of Q for a given T w-3 be Iarger for &ion from a sublevel w& a short lifetime than from one with a long lifetime. This can provide information as which sublevel.is
most active in emission.
This information
used in conjunction
with polarization
data m
be
determining assignments. Such information may be difkult to obtain from simple decay measurements cases where the lifetimes of the levels are nearly equal. In these cases ~uadrature.techniques are particuIarIy at-
:ful in
7.9
Volume 12, numkr ., -.
I
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CHEMICAL PHYSICS L3XTERS
:
1 December
1971
‘. -sactive sin’ce 9 is’indeendent of the magnitude of the population difftirences between sublevels. Thus data ob: tained fro+ alJ three z&o field microwave transitions can,be compared witrlout wor@ng abd&he complications -iiztrW&d
by the lack of unifonkmicrowave
induced
pop&&k
changes. %is.is
only true, &&ever,
when the
spin
subleveL &anbe c&sidered independbnt: This is equivalent to neglectig spin,lattice relaxation effects. If spin-lattice relaxation is included in the derivation of eq. (9), the phase angle 4 is found to be dependent on the degree of spin alignment since the rate of pop&ion equilibration depends on the population difference between subbvels, Thus, one expects to fmd a dependence of $I on the degree of saturation or inversion. The equations des@bi?g Q are complex and will not be presented here. We wish only to point out that the quadrature method may provide a n&w tool for directly studying spin-lattice relaxation effects or other phenomena such as exciton averaging of triplet stat* sublevel populations. A study of @versus saturating power, for example, may show deviations which would indicate whether or not such relamtion processes are important. Quantitative evaluation, however, of these effects is made difficult by the complexity of the differential equations describing coupled spin sublevels.
Acknowledgment This work w&,supported by the Inorganic Materials Research Division of the Lawrence Berkeley Laboratory under the auspices of the US. At&nic Energy Commission.
References [I] D.&T&i, M.A.EbSayed, A.H.Maki and C.B.Hanis, Chem. Phys. Letters 3 (1969) 343. 121 M.AEl-Sayed, !. Chem. Phys. 54 (1971) 680. [3] Jdchmidt, W.S.Veeman and J.H.van der WaaIs, Chem. Phys. Letters 4 (1969) 341. [4] xs.fohnston. GE_McG~w, T.TL&ett LW_RL&tk tid J-van den E&wrde. Froc. Nstl
E.D.Morrisand H.S.Jolmston, Rev. Sci. Instr. 39 (1968) 620; H.SJohnston, G.E.McGraw
[S]
[6] [7] [8]
EarLD.Morris Jr. and J.van den Bogaerdc, J. Am. Cbem. Sot. 91 (1969) 7712; and H.S.Johnston, J. Chem. Kinetics 1 (1969) 89. C.B.Hanis, J. Cliem. Phys. 54 (1971) 972; C.B.Harris and RJ.Hodver, unpublished results. A.H.Francis and C.B.Harris, Chem. Phys. Letters 9 (1971) 188. M.Y.BucMey, C.B.Harris and R.Panos, I. Am. Chem. 5$x., to be pubtied. A.H,Francis and CB.Hati, J. Chem. Phys., td be published.
Acad. Sci. 57 (1967) 1146;