J . Phys. Chem. 1984, 88, 3451-3454 imental data showed no detectable deviations from single-exponential behavior. Therefore, we conclude that, in the cases where the T-T* is excited but the n-?r* fluorescence dominates, the formal T-T* states relax very rapidly, probably in a time less than our experimental pulse width. This is confirmed by the good agreement between data obtained by upper state fluorescence excitation and through time-resolved fluorescence measurements. W e have found that the temperature dependence of the fluorescence decay times is consistent with a level-inversion model as depicted in Figure 3. There is an activation energy of -3.5 kcal mol-’ in ethanol, by which thermal activation of the molecule allows coupling of the T-T* singlet state through n-?r* states to
3451
facilitate intersystem crossing. We found a different situation in hexane solution. In this case, the temperature-independent part of the rate constant apparently dominates completely, which implies little advantage to coupling in other states in a case where an n--P* state is the lowest excited singlet state.
Acknowledgment. We are grateful to the National Science Foundation for the support of this project through Grant No. CHE-78-253 12 and through the Materials Research Program (Grant No. DMR-7923647). We are also grateful to Bruce Boczar for assistance with some of the measurements. Registry No. Acridine, 260-94-6.
Flashlamp-Pumped HCN Gas Laser Dean W. Robinson Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21 21 8 (Received: February 7, 1984)
Laser oscillation has been observed in HCN gas excited with a bank of flashlamps. The output characteristics have been considered and found to be consistent with initial absorption in the HC stretch, u j . This excitation is then redistributed during collisional relaxation and passes through (u, + u2) on the way to equilibrium. The latter is the upper state of the laser transition. In the right pressure range gain is sufficient to overcome the low, long wavelength cavity losses. Interesting modulation of the output occurs when the gas is diluted with CO. This is explained as relaxation oscillations in which the CO participates in storing the vibrational energy of the CN stretching vibration by virtue of an almost resonant frequency. The result is consistent with an incremental gain constant 0.029 m-’,and a very long apparent inversion lifetime of 35 ms.
Laser oscillation or superfluorescent emission has been observed following flashlamp pumping of several small gas-phase molecules, namely, HCN,’ H20,2NH3, H2S, and H2C0.3 This has so far been observed only in the far-infrared at wavelengths common to some of the lines of the gas discharge lasers using these same molecules. The possibility of flashlamp pumping is quite surprising due to the extreme inefficiency of exciting narrow transitions with a broad continuum. The fact that the threshold inversion required for oscillation increases roughly as the inverse cube of the wavelength4 favors the far-infrared for this method of pumping. In H 2 0and H C N the stimulated emission is made possible by quantum mechanical mixing of energetically close levels of the correct symmetry, thereby conferring pure rotational transition moments upon vibrationally forbidden transition^.^.^ The detailed mechanism of establishment of the requisite inversions in the discharge will probably never be well understood because of the complexity of the plasma. There should be a much better chance of understanding the pumping mechanism with flashlamp excitation. The explanation is, however, less evident than that of single level population selection in the case of laser-pumped far IR lasers, “optically pumped” lasers, but a reasonable picture can be presented for the H C N case.
Experimental Section The apparatus and some of the observations have been described before.’ The cavity consists of a 4-m cylinder with 17 cm diameter, (1) D. W. Robinson, Opt. Commun., 27, 281 (1978). (2) D. W. Robinson and N. M. Lawandy, Appl. Phys. B, 26,61 (1981); N. M. Lawandy and D. W. Robinson, Appl. Phys. Lett., 38, 750 (1981). (3) D. W. Robinson, unpublished results. (4) A. E. Siegman, “An Introduction to Lasers and Masers”, McGrawHill, New York, 1971, p 395. (5) W. S.Benedict, M. A. Pollack, and W. J. Tomlinson, 111, IEEE J . Quantum Electron., QE-5,108 (1969). (6) D. R. Lide, Jr., and A. G. Maki, Appl. Phys. Lett., 11, 62 (1967).
0022-3654/84/2088-345 1$01.50/0
semiconfocal mirrors surrounded by six Suprasil flashtubes and an aluminized reflector. These lamps are energized by a 2-pF, 50-kV capacitor controlled by a manually triggered spark gap. A 1-cm TPX outcoupling window and a TPX lens guide the 30-cm-’ output to an epitaxial GaAs detector at 4 K. The cogent results are as follows: 1. Laser action is observed in 5-100 mtorr of H C N after excitation with Xe- or air-filled Suprasil flashlamps. 2. The characteristic lines at 337 and 31 1 pm are both observed. 3. The flash pulse, attaining its maximum at 5 p s , produces the submillimeter laser pulse which peaks in the neighborhood of 20 ps. This peak is hard to fix due to the distortion of the scope trace by short relaxation oscillations. It does peak at a later time as the pressure of H C N is reduced. 4. The delay-to-onset of laser action is less ambiguous than the time-to-peak and is seen to increase sharply with decreasing pressure below 20 mtorr. Above this it is more or less independent of pressure and amounts to about 7 ps. This is depicted in Figure 1. The data are consistent with a 1/ p dependence but the scatter is too great to establish this with certainty. 5. At pressures below about 20 mtorr the molecular laser intensity decreases with increasing flashlamp energy and the delay-to-onset of oscillation increases with flashlamp energy. 6. Dilution with foreign gases has little effect upon the intensity other than a normal pressure effect. The exception to this is CO which has an intensifying effect upon the decay side of the pulse at high pressures (90-100 mtorr) and produces remarkably long relaxation oscillations. These have a period of 400 ps and a decay time of 850 ps. There is no apparent difference between the effect of C l 6 0 and Cl80.
Discussion The absorption of flashlamp radiation by the HCN could occur in the two extreme ends of the Suprasil transmission, the electronic A X bands near 1800 A or the vibrational ug (CH stretch) and
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0 1984 American Chemical Society
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3452 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
I
”f, 4000
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(060)
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a22 c 20 0 0
/
5
Y
>
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z
0
W L
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
2000--
F
1000
O
(PRESSURE in rntorr1-l
Figure 1. Plot of the delay-to-threshold following flash initiation, against l/p. A linear relationship is indicated by the least-squares fit to a straight line.
t
VI
y3
v2
1
\ b
J=ll
132.3 cm-I
32.2cm-’ , 311 pn
J = IO
29.7 cm-’ , 3 3 7 p m
J=9
I J=8
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I26.8cm-’
+ (04b)
WAVENUMBER,
CM-’
Figure 2. Infrared absorption of Suprasil (S) and 5 cm atm of HCN gas.
perhaps v1 + u2 (combination C N stretch and bend) near 3000 cm-’. Selective pumping by Xe emission lines would not be consistent with the observation that air-filled lamps produce the same results; thus, absorption is from the “continuum”. There are several reasons why the infrared end of the continuum must provide the excitation. First, the cleaning of the flashlamps of accumulated deposits has little effect upon the lasing. It would be expected that the short wavelength transmission would deteriorate very rapidly with dirty lamps. Second, addition of near-UV absorbing gases like NO and Br2 likewise have no deleterious effect upon the submillimeter laser output. The result with the scavenger NO further proves that H C N dissociation is not involved in the laser excitation. Third, the fact that similar results are observed with other dissimilar hydrides, which have different or even inaccessible electronic spectra (e.g., H 2 0 ) , is strong, circumstantial evidence for a hydrogen stretch absorption as the primary energizing act. Although electronic absorption cannot be ruled out unequivocally, and might be included in the system of directly pumped states (level 3, below), the discussion will assume the simpler picture of initial absorption in the H C stretch, u3. In Figure 2 are shown the spectra of H C N and the Suprasil flashlamp envelope. In Figure 3a the low vibrational level structure of H C N is given, and Figure 3b shows the lasing transitions. Unlike the picture for the waterZcase, the H C stretch does not coincide with the edge of the Suprasil band, and so the upper levels of the laser (1 10) J = 1 0 , l l cannot be pumped selectively over the lower levels (040) J = 9,lO through any lack of “whiteness” of the radiation. Although there may be some direct pumping of (110) J = 10,ll with respect to (040) J = 9,10, (to be discussed below) most of the output occurs after the flash has turned off, so the bulk of the inversion must be pumped indirectly by collisional redistribution from u j to ul u2. In this connection it is to be noted that although v, u2 (1 10) is uncommonly intense for a combination band, and 4u2 (040) is not, the levels (04OO) J = 9,lO which are mixed with (1 1‘0) J = 9,lO will be made
+
+
Figure 3. (a) Low vibrational states of HCN. (b) Lasing transitions shown by solid arrows (satellite transitions, seen in discharges and indicated with dashed lines, were not found in the flash-pumped version). “LEVEL” 3
LEVEL 0
10011t
10001
Figure 4. Depiction (not to scale) of the ”four-level” scheme for modeling this laser. “Level” 3 includes all states, presumed to be largely (OOl), which collisionally pump level 2, the upper laser level.
accessible from (000) according to the extent of this interaction so that these too might be directly populated early in the event. If one starts with a four-level system consisting of (OOl), (1 1lo), (04OO),and the ground state (000) the experimental observations can be semiquantitatively reproduced. One can estimate, from the absorption coefficient of the band u 2 and a guess at the fraction of lamp energy falling in that band, that a maximum of about 0.03% of the molecules could be excited. The excitation of the sample is thus far below the saturation often encountered with IR laser-pumped systems, as opposed to continuum-pumped. The assumptions can be made that at t = 0 only (001) is populated (although an explanation of the low-pressure effect of flash energy on laser delay and intensity will demand examination of this assumption), that stimulated emission has only a secondary effect upon the laser pulse shape, and that on the tens of microseconds time scale rotational equilibrium is maintained. Figure 4 shows the assumed scheme, with the transfer rates W,, Wr2,and Wrl. W, is the collisional pumping rate of (1 10) from (001). It can be seen from Figure 3a that if intermediate vibrational levels of (7) G. E. Hyde and D. F. Hornig, J . Chem. Phys., 20,647 (1952); G. C. Lie, S.D. Peyerimhoff, and R. J. Buenker, ibid.,75, 2892 (1981).
Flashlamp-Pumped H C N Gas Laser H C N are important in the relaxation mechanism of (OOl), as has been rather firmly established,* then (1 10) and (040) are the first step down the energy ladder. The state (1 1'0) must somehow be favored over (04OO) or there wwld be no inversion and no laser. Considering the huge numbers involved in the ensemble of molecules, it would not require a large dynamic bias to give (1 10) a significant, absolute population inversion with respect to (040). An advantage conferred by the smaller change in vibrational quanta should be sufficient. Furthermore, on the relaxation side, bending vibrations traditionally relax faster than stretching modes. Although (1 10) can cross to (040) through the two, closely mixed states, it can only relax down the bending stack after passing through this bottleneck. N o such restriction applies to all of the rotational states of (040) which can more rapidly empty the lower states of the laser. Wr2and W,, are the collisional relaxation rates of (1 10) and (040). Due to the near zero energy difference between these states, collisional transfers out of each will be rapid, and predominantly into each other. That is, the inversion will probably be curtailed in time by the equilibration of these states rather than their relaxation to lower levels. The conversion (1 10) (040) and (040) (1 10) should occur on the order of every collision. It seems, therefore, not unreasonable to take the following rate equations, in which the population changes due to stimulated emission have not been included: N l = -WrIN1 + aWr2N2 (1)
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3453
1
0
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1
1
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Figure 5. Calculated population inversion N 2 - N , vs. time.
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fits to the data than the set initially deduced by the arguments above. Plots of 40 and 20 mtorr are shown in Figure 5 along with the parameters used. The flashlamp function was triangular with a 5-ps rise and a 7-ps decay. This simplified model does not account for two observations, the high-pressure quenching and the low-pressure inverse dependence of intensity on flashlamp energy. With this model raising the pressure increases the height and the ascending and descending slopes, and decreases the rise time to maximum. The model, N2 = PWrlNl - Wr2N2 WpN30e-w~t (2) however, does not take into account the fact that above about 40 mtorr the line width changes from Doppler to collision dominated. Here N I and N2 are the populations of (04OO) and (1 1IO), reAt higher pressures the gain, which varies inversely with the line spectively, and N30e-WR'is that of (001). The quantity a is the width and hence the pressure, will in real life decrease relative fraction of molecules removed by collisions from (1 1'0) that land to the inversion. Although the early inversion may increase with in (04OO) and, likewise, P is the fraction of (04°0)-destroying increasing pressure, so does the threshold for oscillation and the collisions that transfer to (1 1'0). Although this many-level system laser action eventually is quenched. is vastly more complicated than these equations warrant, the On the low-pressure side, since saturation has been ruled out, dominant pathways for energy transfer, if correctly identified, the explanation has to involve increasing the population of N I ; should govern the main properties of this laser. It is gratifying strengthening the flash could not possibly decrease the population that, with very little leeway in the choice of parameters, the of N2. Because of the selection rules only the rotational levels calculations support this model. At 40 mtorr, the density N = 1.3 X l O I 5 molecules ~ m - ~ . of (04"O) in interaction with (1 1'0) can be excited from the ground state, whereas (1 1'0) provides an abnormally strong combination Relaxation of (001) has been measured to proceed with a rate band. It is suggested that at the low pressures, 5-10 mtorr where coefficient WR/N = 2.4 X cm3 molecule-1 s-l;* this will yield this effect is observed, the collisional migration out of these roan upper limit to the pumping rate Wp. The preferred channel tational levels is slow compared to the inversion pumping. At out of (001) would be expected to involve the next lower states, higher pressures the spreading out over adjacent rotational states (1 10) and (040) [PE i= -500 cm-'1. It was assumed that a large of (04OO) is rapid enough to diminish the peaked population of percentage of the (001) molecules chose this route, and, for the the interacting levels and open them up to receive the lasing purpose of estimating the output pulse behavior, a dynamical bias transition. of two was arbitrarily taken to favor (1 10) over (040). Of the seven vibrational states clumped within kT, (1 l'O), (04OO), (0420), Relaxation Oscillations and (0440), only one component of (1 1'0) is associated with the The term, relaxation oscillations, is employed because the laser transition. Thus, Wp i= (2/7)WR = 890 s-' at 40 mtorr. unusual phenomenon of regular, 400-ps intensity oscillations in In this scheme, all of the population of (040) comes from (1 10). the output in the presence of excess CO is consistent with such This should have close to 100% efficiency and dominate the early an explanation. Although previously known examples of such relaxation of (1 10). These states should come rapidly into mutual oscillations have been orders of magnitude shorter, the lengthening equilibrium and this will be the quenching mechanism of the laser. is quite reasonable in the present system. Casperson and Yarivg Much later they will approach Boltzmannization with the rotagive, for the period To and the damping time Td,the following tional and translational bath. The gas kinetic rate constant would relations: be about cm3 molecular-' s-'. In these nearly single collision transfers, as contrasted with the multiple collision relaxation from To = 2 r ( and Td = 27 (OOl), the levels' quantum mechanical interactions rather than (3) a 1 a the statistics should dominate the transfer probabilities. That is (1 1'0) (04OO), the transfer between the mixed states, should where 7 is the inversion lifetime due to all causes except stimulated outpace (1 1'0) (04%), (04%). The best fits to the experimental emission, r, is the photon cavity lifetime, and a = gct, in which output pulse shapes demanded a ratio of p / a = 0.8, which g is the incremental unsaturated intensity gain constant and c is physically can be taken to reflect the faster downward relaxation the velocity of light. First of all, it is to be noted that the viof the bending stack. brational frequency of CI6O is 2143 cm-', that of CI8O is 2092 The rate equations were solved and AN = N2- N1was plotted. cm-', and that of the C N stretch of H C N is 2097 cm-'. The The shapes of the curves were quite sensitive to pressure (on which self-relaxation of CO v = 1 is extremely slow requiring some 1Olo all of the pseudo-first-order rate coefficients linearly depend), W,, collisions.I0 One can estimate from the energy level separation" (= Wr2),and a / & N o tampering with the parameters gave better
+
')'"
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~~
(8) J. A. McGarvey, Jr., N. E. Friedman, and T.A. Cool, J . Chem. Phys., 66, 3189 (1977); A. B. Peterson and I. W. M. Smith, ibid., 71, 3346 (1979).
~
(9) L. W. Casperson and A. Yariv, IEEE J. Quantum Electron., QE-8, 69 (1972). (10) M. A. Kovacs and M. E. Mack, Appl. Phys. Lett., 20, 487 (1972).
J. Phys. Chem. 1984,88, 3454-3465
3454
that H C N would relax C O with a probability of about 5 X lo-“, which in a mixture, H C N / C O = 1/7, at 90 mtorr, would give a relaxation time of 35 ms. This is a very long time to “store” the 2100 cm-’ per molecule, which is available to be fed back into the H C N (100) state. For the 6% of the molecules which are in (010) [at 300 K] this feeds the upper state of the (1 1’0) (04OO) laser oscillation. This calculated 35-ms inversion lifetime is consistent with the observations of the oscillations. When the relations (3) are used with the observed To = 400 ps, Td = 850 ps with r = 35 ms, the s and the photon cavity lifetime t, comes out to be 9.5 X incremental gain constant g = 0.029 m-I. Thus, although the origin of these oscillations with C O dilution has not been proved to be due to the energy storage suggested, this does seem to fit the observations quite well. It is also clear why there was no isotopic effect when C l 8 0 was substituted for C l 6 0 . Although the energy match was better, and the transfer rate undoubtedly improved, the effect would have been to alter the inversion lifetime, r, upon which the observed times Td and To only very weakly depend. Eliminating a between eq 3 we have
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-4*’rt, - - -27To’
Td
1
and since 2 r / T d is large compared to one, r can be cancelled to within 2% error and T02/Td = 2r2t,. Given the electric dipole moment of 3.0 D for HCN, one can estimate the spontaneous emission lifetime for a transition of this frequency12 to be 9 s. Taking this with the above-calculated cavity lifetime of t, = 9.5 (11) J. T.Yardley, “Introduction to Molecular Energy Transfer”, Academic Press, New York, 1980, p 89. (12) W. H. Flygare, “Molecular Structure and Dynamics”, Prentice-Hall, Englewood Cliffs, New Jersey, 1978, p 113.
X s and a line width of 2 MHz, one calculate^'^ AN = lo6 cm-3 for the threshold inversion. The photon lifetime calculated from the relaxation oscillations is an apparent one, sustained by the energy storage of CO. It is not a property of the cavity. If one were to take the position that the threshold inversion and the incremental gain obtained from the relaxation oscillations could reasonably be considered steady-state properties of the HCN lasing system in the absence as well as the presence of the CO, then a natural photon cavity lifetime could be estimated from t, = l / c g to be 10”s.
Conclusion The output characteristics of a flashlamp-pumped H C N gas laser have been interpreted on the basis of initial excitation of u3, the C H stretch, by the infrared tail of the flashlamps, followed by collisional transfer to (u, + v2), the upper laser level. This picture led to a calculation of the time evolution of the inversion which largely mimics the time behavior of the submillimeter output pulse. Interpretation of some long-time output modulation of the pulse tail by added C O yielded cavity parameters which agreed well with the inversion evolution based solely upon known and closely estimated energy transfer rates. Although proof of this picture cannot be offered, internal consistency of loosely related phenomena provides good reason for confidence in the results. Acknowledgment. The author thanks the Department of Energy, Office of Basic Energy Sciences, for support of this research, Harris J. Silverstone for a valuable discussion, and especially Nabil M. Lawandy for his long time interest in and expert input into this work. Registry No. HCN, 74-90-8; CO, 630-08-0. (13) A. Yariv, “Quantum Electronics”, Wiley, New York, 1975, p 179.
Analysis of Protein-Lipid Interactions Based on Model Simulations of Electron Spin Resonance Spectra Eva Meirovitch,+*Akbar Nayeem,? and Jack H. Freed*+ Baker Laboratory of Chemistry, Cornell University, Ithaca, New York 14853, and Isotope Department, The Weizmann Institute of Science, 76100 Rehovot, Israel (Received: February 9, 1984) ESR spectra from protein-containing lipid dispersions have been interpreted in the past primarily in terms of two nitroxide species related respectively to ”fluid” and “immobile” phospholipid environments. In this report we consider interpretations based primarily on a single type of lipid, for the two cases of spin-probe-dopedmembranes and of chemically labeled membrane proteins. The doped membranes are viewed as bilayer fragments with considerable local order but with macroscopic disorder of such fragments in the dispersion. In this “one-site” model all lipids are similar. They are fluid and oriented in their local environment. This model does not require a second species immobilized by contact with the proteins. The labeled proteins are considered as very slowly reorienting macromolecular complexes such that the dynamic effects on the ESR spectrum arise mainly from faster internal processes. The importance of, and the potential inherent in, detailed spectral simulation based on well-conceived models are emphasized by illustrating the great range of spectral line shapes that these models can yield with suitable parameters. Simulations are compared with some recent experimental examples previously interpreted in terms of a two-site model. Reasonably good results are obtained for spin-probe-doped membranes when allowance is made for local ordering as well as for some distortion of the alkyl chain ends. Such effects are modeled by introducing an ordering potential X and a diffusion tilt angle 9 which describes the tilt of the nitroxide moiety relative to the rest of the alkyl chain. The effects of adding protein or of lowering the temperature are modeled by increasing the local ordering while decreasing somewhat the motional rates with some increase in alkyl chain distortions. In the case of spin-labeled membrane proteins, the model of very anisotropic rotation, in which the side chain containing the nitroxide is rotating more rapidly than the protein about an effective axis tilted relative to the N-O axis, is found to account for the extra splittings with just a single-site model. I. Introduction The model of a boundary layer of lipids coating a protein molecule is based, to a large extent, on the interpretation of the +
Cornell University.
* Weizmann Institute of Science. 0022-3654/84/2088-3454$01.50/0
ESR spectra from spin probes (mainly nitroxide free radicals) doped into biological or reconstituted membranes or from Systems wherein membrane Proteins have been labeled chemically with a paramagnetic moiety. In many case$, one observes what appears to be two (or more) superimposed ESR spectra corresponding to a population of “fluid” lipids and to one (or more) species of 0 1984 American Chemical Society
