Vibrational Relaxation of Nitric Oxide BY A. B. CALLEAR Dept . of Physical Chemistry, The University, Cambridge Received 29th January, 1962 A method of over-populating the first vibrational level of the ground electronic states of NO was described, by flashing mixtures of NO with He, Kr and N2. Production of vibrationally ex- cited molecules is due either to fluorescence or collisional quenching of NO . A*C+, according to the conditions. The rates of vibrational relaxation were determined by plate photometry. In experi- ments using high nitric-oxide pressures, the observed temperature rise makes possible the estimation of the quantum yield for conversion of electronic energy to vibrational energy. The rate of decay of NO X2II(u = 1) was increased by inclusion of small partial pressures of H20 and CO in the mixtures.Detection of vibrationally excited CO was presented as evidence for the occurrence of the exchange reaction : NO(# = l)+CO(tr = O)+NO(V = O)+CO(u = 1). The logarithms of the probabilities of vibrational exchange for three different reactions were found to be a linear function of energy difference between the vibrational quanta of the colliding molecules. Vibrational relaxation of nitric oxide has been studied by Robben1 in shock- heated gas using ultra-violet absorption spectroscopy to measure the population of molecules in the first vibrationally excited level. He observed an abnormally fast self relaxation, PO-1 being 103-104 according to the temperature. This fast re- laxation was interpreted by means of sticky collisions between NO molecules.Relaxation processes in nitric oxide have also heen studied recently by Bauer, Kneser and Sittig 2 by sound absorption. They also showed that the process, NO(u = l)+NO(V = 0)+2NO(u = 0), is very fast, the observed probability of vibrational relaxation being 3-7 x 10-4 at 20°C. The present spectroscopic study arose out of examination of the principle that it should be possible to produce an appreciable concentration of vibrationally excited diatomic molecules with a flash of ultra-violet light without causing decomposition. Absorption of light in the ultra-violet and visible regions produces electronically excited species which re-ernit the fluorescence spectrum, populating the excited vibrational levels of the ground electronic states according to the probabilities of the various transitions.Nitric oxide was selected for study (a) because of the occurrence of the y bands in the quartz ultra-violet region and (b) because radiation down to 2000 A causes very little decomposition. The first experiments were unsuccessful because of the high intensity of the fluor- escence ; instead of observing the y(0,l) band in absorption it appeared in emission. After improvement of the optics and recognition of the importance of the pressure broadening effect, the phenomenon was demonstrated satisfactorily and was applied to the study of the vibrational relaxation of nitric oxide and the effect of added gases.3 Information was also obtained about conversion of electronic energy to vibrational energy. This study was later extended to the vacuum ultra-violet region to obtain evidence for the occurrence of vibrational exchange processes.4 Spin orbit relaxation occurred once in 16 collisions.28A . B. CALLEAR 29 The same principle was extended to the CS molecule which can be conveniently produced by photo-chemical dissociation of carbon bisulphide.5 Secondary absorp- tion of light by CS overpopulates the vibrational levels of the ground electronic states though in this case the CS are also produced with some vibrational energy. The simultaneous decay of molecules with up to at least seven vibrational quanta can be observed and the system promises to be of value in studying highly vibrationally excited molecules, first because of the stability of CS which persists for several minutes after flashing, and secondly because of the occurrence of the main band system in a convenient wavelength region.One of the main objects of presenting this paper is to bring together some aspects of the vibrational relaxation of nitric oxide which have been or are still being studied in these laboratories. In the discussion the evidence for occurrence of exchange of vibrational quanta between molecules is examined and an attempt is made to correlate the efficiency of vibrational transfer with the difference in energy of the vibrational quanta of the two colliding molecules. EXPERIMENTAL Most of the experimental details have been described.3~4 For the quartz u.-v. region experiments, the reaction vessel and flash lamp were both 50cm long and enclosed in a cylindrical reflector coated with magnesium oxide.The absorption spectra were obtained using a Hilger-Littrow Spectrograph and a single pass through the reaction vessel. It was important to line up the capillary of the spectroscopic flash very carefully so as to obtain the maximum possible useful light output, because the intensity of the fluorescence was very strong with NO pressures of 5 m or less. Quantitative measurements could only be made under conditions where the blackening of the plates due to fluorescence was very small compared to the plate density obtained from the spectroscopic flash. The intense fluorescence would present considerable difficulties if a photoelectric method was used. Spectra were taken on Ilford HP3 plates using standardized development.Absorption spectra of carbon monoxide were obtained using a 1 m vacuum spectro- graph. The reaction vessel for these experiments was 7.5 cm long, placed along the axis of a flash lamp constructed in the form of a helix, the whole being enclosed in a cylindrical reflector coated with magnesium oxide. Spectra were taken on Kodak V. 6002 experi- mental film. To avoid the appearance of CO bands in the spectroscopic flash, it was re- filled after each exposure. Plates were photometered on a Joyce-Loebl double-beam re- cording microphotometer, model E. 12, &. 111. The preparation of the materials has been described.3 RESULTS AND DISCUSSION PRODUCTION OF NO. x2n(u = 1) If nitric oxide is subjected to a high intensity flash of ultra-violet light, the con- centration of molecules with one vibrational quantum in the ground electronic states (NO.X2II(u = 1)) is greatly overpopulated due to absorption of light by the y bands ; the production and decay of the vibrationally excited molecules can be conveniently studied by kinetic spectroscopy because of the occurrence of the y bands in the quartz ultra-violet region. If an ammonia filter is used to cut out absorption below about 2200 A, the effect is still observed strongly and under these conditions it is due entirely to absorption by the y(0,O) band. The maximum concentration produced by flashing 2 mm of NO with 600 mm of N2, flash energy 1600 J, is about 0.1 mm of excited molecules which is about the same concentration of NO . X2II(u = 1) which is present in a full atmosphere of pure nitric oxide at 20°C.Under these conditions, the absolute concentration of NO . X2rI(u = 1) can be estimated by comparing plate densities of the (0,l) band in pure nitric oxide with those in flashed mixtures of nitric oxide and inert gas. This procedure is not exact because the pressure broadening30 VIBRATIONAL RELAXATION OF NITRIC OXIDE of the y bands under these two different types of conditions is not identical. How- ever, except for the determination of the quantumyield, the precision of the absolute values is not an important factor since the decay of NO. XW(u = 1) is first order, the relaxation time being independent of the absolute concentration. The maximum concentrations of NO. X2II(u = 1) produced and the intensity of the y fluorescence are very dependent on the pressure of inert gas.Fig. 1 shows the increase with nitrogen pressure of the y fluorescence and the (0,O) absorption. Under these conditions where absorption is very strong at the line centres, pressure broadening causes a very marked increase in total light absorption by the broadening of thewings of the lines. A similar effect can be observed if the mercuryresonance line at 2537 A is excited with a continuous light source.6 Fig. 2, 3 and 4 are sets of absorption spectra taken during and after the exciting flash. The NO. X2rI(u = 1) reaches a slightly higher concentration in N2 than in krypton and the decay is slightly faster in N2 than in krypton, though this difference was not sufficiently marked to be recorded satisfactorily by plate photometry.The decay is in fact determined almost entirely by the partial pressure of nitric oxide itself. With helium as inert gas, the maximum concentration of vibrationally excited mole- cules is lower than that produced in N2 or krypton because helium causes less pres- sure broadening of the y bands than the other two gases, resulting in a lower light absorption. By photometering plates of the types given on fig. 2, 3 and 4, the con- centration of NO. X2rI(u = 1) can be expressed as a function of time and some re- sults are plotted on fig. 5. The time zero corresponds to the minimum delay of the photocell circuit and firing unit. The exciting flash decayed to one half of its peak intensity in 25 psec and is effectively terminated by 50 pee, so that by plotting the logarithm of the concentration remaining after the flash with time, the relaxation rates can be determined.MECHANISM OF EXCITATION The first step in the vibrational excitation is formation of NO . A%+(u = n). These species either radiate, or are quenched to overpopulate the excited vibrational levels of the ground electronic states. The latter process predominates, except at very low nitric-oxide pressures, since the self- quenching of the fluorescence is very marked, the half pressure being < 1 mm. Vibrationally excited molecules are only observed in the first vibrational level possibly because fast vibrational exchange processes between nitric-oxide molecules rapidly produce a Bolzman vibrational distribution, the temperature being well above that of the other degrees of freedom.NO. A2Z'(v = n)+NO. X211(v = m)+hv, NO. A2E+(v = n)+NO. X211(v = ())-+NO. X2rI(u = p)+NO . X211(u = q), VIBRATION-TRANSLATION RELAXATION OF NO. X2n(U = 1) From the slopes of the log plots of the data of fig. 5, the first order rate constants The rate constant k can be split into two terms, given in table 1 were determined. The temperature is estimated at 23f.3"C. k = k,(NO) + k,(N,), and the best fit with the data of table 1 leads to for NO = 3.6k0.4 xblank abs. no N2 fluor. abs. 120 mm N2 fluor. abs. 240 mm N2 fluor. abs. 360 mm N2 fluor. abs. 480 mm N2 fluor. abs. 600 mm NZ fluor. abs. 700 mm N2 fluor. NO (y system) FIG. 1 .-The effect of pressure broadening on light absorption and fluorescence. Nitric oxide pressure 2 mm.[To face page 302270 A 2370 8, blank before 3 psec 7 11 16.5 23-5 30 35 45 59 70 80 96 120 150 190 250 325 03 NO (1, 1) NO (0,O) NO ( 0 9 1 ) FIG. 2.-Formation and decay of vibrationally excited nitric oxide 2.2 mm NO with 430 mm N2, 1600 J flash energy.II II 2270 8, I II II 2370 A blank before 3 psec 7 psec 1 1 16.5 23.5 30 35 45 59 70 80 96 120 150 190 250 325 II II FIG. 3.-Fdrrnation and decay of vibrationally excited nitric oxide. 2.2 mrn NO with 430 rnm Kr, 1600 J flash energy.2270 A I 2370 A i before 3 dsec 7 11 16-5 23.5 30 35 45 59 70 80 96 120 150 190 250 cr, II II II II T n T NO ( 1 9 1 ) NO ( 0 , O ) NO (0, 1 ) FIG. 4.-Formation and decay of vibrationally excited nitric oxide. 2.25 mm NO with 540 mm He, 1600 J flash energy.1600 A + A I before 50 psec 07 1 070 1,o FIG. 7.-Formation of vibrationally excited CO. 5 nim NO, 100 mm CO with 650 mi N?.A. B. CALLEAR 31 and PI-0 for N2 = 4 x 10-7, the latter being accurate to about an order of magnitude. The value for the probability of self-relaxation by NO is in good argeement with that obtained by Bauer et aZ.2 by ultrasonic absorption and with the extrapolated shock- wave results of Robben. TABLE 1 mixtures (mm) 2 NO+ 600 N 2 2 NOf220 N2 5 NO+600 N 2 5 N0+560 N 2 1 N O + 6 W N 2 104 k (sec-1) 0.90 0.55 0.667 1 -72 1 -93 According to Robben,l the abnormally fast rate of relaxation by NO is due to sticky collisions and using an interaction potential of the N 2 0 2 molecule and the equations of Schwartz, Slawsky and Herzfeld,7 he obtained good agreement between theory and experiment.The ground state of nitric oxide is split into two spin orbit E- E 0.1 II a 0 x 2 0.05 2 f? W M n rcl 0 0 .- c) u 8 0 0 50 100 150 200 time (psec) FIG. 5.Variation of vibrationally excited nitric oxide molecules with time. 0 2 mm NO+6OO mm N2,16OO J 0 2 mm NO+220 lll~ N2,16OO J (> 1 ~III NOf600 mm N2, 1600 J 8 5 mm N0+600 N2,16OO J - - - 50 fll~ NO+457 mm N2, 900 J components, 2II3/2 and 2II112, the separation being 121 cm-1. Bauer et aZ.2 showed that spin orbit relaxation occurs about once in 16 collisions at 20°C and it seems likely that if the kinetic energy of the collision is high enough to cause vibration- translation relaxation, then the weak spin orbit interaction will be swamped and simultaneous spin orbit relaxation will occur.On this basis the most rapid process causing vibrational relaxation should be NO. X21T1,z(~ = 1)+NO . X2ITll2(u = 0)+2NO . X211312(~ = 0).32 VIBRATIONAL RELAXATION OF NITRIC OXIDE In this case the energy to be converted from vibration to translation is 1662 cm-1 instead of 1904 cm-1 for the fundamental frequency. This difference, however, is still not large enough to account for the fast relaxation observed using the theoretical equations.7 It would appear, therefore, that the sticky collision theory is the only possible interpretation of the abnormally fast relaxation, unless there are some special theoretical reasons why the occurrence of simultaneous spin orbit relaxation requires a modified treatment. QUANTUM YIELD FOR CONVERSION OF ELECTRONIC ENERGY TO VIBRATIONAL ENERGY Included on fig.5 is a curve showing the formation and decay of NO . X2rI(u = 1) with 50 mm of NO and 457 mm of N2. Under these conditions, the concentration of vibrationally excited molecules does not return to its initial very small value but remains at 0.025 mm for several msec and thereafter decays very slowly ; this is due to the increase in temperature caused by flashing. Under these conditions the fluor- escence is almost entirely quenched and the conversion of the electric energy to trans- lational energy heats the gas. Comparing with the absorption in pure NO at 20°C and applying the distribution law, the temperature is found to be 68°C; this is not precisely correct since, as previously mentioned, the conditions of pressure broadening are different in pure NO.The heat capacity of the gas is 0.02 cal/deg. (150 ml at 500mm pressure) and since one Einstein of radiation at 2270A is equivalent to 125 kcal, it follows that 7.6 x 10-6 Einstein have been absorbed which corresponds to the excitation of 0.95mm of NO. The maximum observed concentration of NO . X2II(u = 1) was 0.07 mm. From this the total number of vibrationally excited molecules can be estimated 3 by substituting an analytic function I = st exp (-p) for the variation of intensity of the flash with time and solving the linear differential equation, the first-order rate constant for the decay being determined with 50 mm of nitric oxide from the data of table 1. Thus it can be shown that under these condi- tions the total number of vibrationally excited molecules produced is about 0.7 mm.Thus, the quantum yield for the process NO. A2Z+(v = O)-++NO. X211(u = 1) is approximately unity. CHEMICAL REACTIONS I N FLASHED NITRIC OXIDE A very small fraction of the nitric oxide is photolyzed under the conditions de- scribed above, about 0.01 mm of NO being decomposed with a 1600 J flash. The decomposition can be almost entirely eliminated by use of an ammonia filter. It can be demonstrated experimentally by reflashing the same nitric oxide + inert-gas mixture several times that the decomposition has no detectable effect on the concentra- tion of NO. X2II(u = 1). Direct photolysis may occur due to absorption by the 6 bands or decomposition may arise by formation of NO.a4II and its reaction with other NO molecules. CATALYSIS OF VIBRATIONAL RELAXATION BY ADDED MATERIALS Addition of very small partial pressures of NH3 or H20 or a substantial pressure of CO, increased the rate of decay of vibrationally excited nitric oxide molecules. For H20 and CO, PI-0 was recorded as 7 x 10-3 and 2-5 x 10-5 respectively, by study- ing the decay after the fiash by plate photometry. The very fast rate of relaxation by water cannot be fully accounted for by means of a vibrational exchange mechanismA . B . CALLEAR 33 and is presumably due to a strong interaction between water and nitric oxide mole- cules. Fig. 6 shows the change in the rate of decay of NO. X2II(u = 1) in the presence of CO. Although the CO vibrational quantum is larger than that of NO, the prob- ability that the difference can be made up from kinetic energy is quite high even at 0 50 I00 150 time (psec) 200 FIG. 6.-Effect of carbon monoxide on the decay of vibrationally excited nitric oxide. (A) 2 mm NO with 600 mm N2.(B) 2 mm NO, 40 mm COY with 560 mm N2. Flash energy 1600 J. 20"C, so that the possibility of a vibrational exchange mechanism was investigated by carrying out some experiments in the vacuum ultra-violet region. Fig. 7 shows that on flashing a mixture of CO, N2 and NO, there was an increase in absorption of the CO (0,l) band ; the pressure of CO(u = 1) present initially was 8 x 10-4 mm and was increased by flashing to about 2-4 x 10-3 mni. Fig. 8 shows the variation of plate density with time of the CO (0,l) band. No change in absorption was observed in this wavelength region by flashing NO with N2, or CO with N2.In these vacuum ultra-violet experiments, the experimental arrangement was such that the temperature rise could not be measured satisfactorily because no " permanent " change in absorp- tion could be observed in the CO (0,l) band or any of the NO (u',l) bands due to a temperature rise. Consequently the quantum yield for formation of CO(u = 1) was not measured. The decay of the vibrationally excited CO is at least 50 times faster than it would be if the excitation was simply due to a temperature rise. VIBRATIONAL EXCHANGE PROCESSES The increased rate of decay of vibrationally excited nitric oxide molecules in the presence of CO is due to the exchange reaction. NO(U = l)+CQ(u = O)+NO(v = O)+CQ(v = 1).When vibrational equilibrium is reached in an equimolar mixture, there are 3.6 vibrationally excited NO molecules for each vibrationally excited CO molecule. Thus, if the CO is in large excess, the vibrational energy is drained away to the CO and at equilibrium, the concentration of NO . X2II(v = 1) is too small to be detected. The exchange reaction with N2 is very much slower because the energy discrepancy B34 VIBRATIONAL RELAXATION OF NITRIC OXIDE is larger. PI-0 = 0.4~ 10-6 recorded for relaxation of NO by N2 must be the probability of the exchange reaction, NO(v = 1)+N2(~ = O)+NO(V = O)+N,(u = l), since this value is very much larger than the theoretical probability of vibration- translation relaxation. It is difficult to obtain direct proof that this process occurs because absorption spectra of N2 can only be obtained at very short wavelengths.0.525 h + .* 0.55 5 0 0. c, e 0.575 0.5 1.0 1.5 2.0 2.5 time (msec) FIG. 8.-Photometer recording of the production and decay of vibrationally excited carbon monoxide. NO pressure = 5.0 mm CO pressure = 100 mm N2 pressure = 650 mm At vibrational equilibrium in an equimolar mixture of NO and N2, there are 9 vibrationally excited NO molecules for each N2 molecule. Since the maximum concentration of NO. X2II(v = 1) produced using either krypton or N2 as inert gases were about the same (fig. 2 and 3) and since the fluorescence is about the same intensity in either case, it follows that the NO. X2II(u = 1) is not in vibrational equilibrium with the N2 at short delay times, though equilibrium may be approached at long delay times. As pointed out above, the decay of NO.X2rl[(v = 1) in He, N2 and krypton is largely determined by self-relaxation by NO and in the presence of N2 the vibrational exchange process has only a minor effect. The reaction, CO(u = 1) + N2(u = O)+CO(U = 0) + N2(u = l), should be the fastest of the three exchange processes since it has the smallest energy discrepancy. It follows that the inclusion of CO in NO + N2 mixtures should cause vibrational equilibration of all three species. It can be shown 4 that the rate of decay of the vibrationally excited CO shown on fig. 8 is consistent with full vibrational equilibrium, the rate-determining step being Gaydon and Hurle 8 measured the vibrational relaxation times of N2 containing about 0.6 mm of CO, using chromium-atom reversal to measure the vibrational temperature of shock-heated gas.The relaxation times were shorter than in pure N2, which is consistent with the above discussion, since the translation-vibration relaxation time of CO is shorter than N2 and exchange of quanta occurs rapidly between CO and N2. NO(U = l)+NO(v = 0)+2NO(v = 0).A . B . CALLEAR 35 VARIATION OF THE RATE OF VIBRATIONAL EXCHANGE WITH ENERGY DISCREPANCY In order to determine the rate of vibrational exchange at exact resonance, Callear and Smith9 have studied the effect of nitrogen on the y fluorescence of NO. The fluorescence was excited with light from a xenon arc which produced molecules in the zeroth, first and second vibrational levels of the NO.A2Z+ state. The variation of the intensity in emission of the three progressions with inert gas pressure leads to values for the rates of vibrational relaxation in the electronically excited state. Thus, it can be shown that the number of collisions for vibrational exchange with N2 is approximately 500. It is seen from table 2 that the energy discrepancy is only 12 cm-1 in this case. TABLE 2 O'e (cm-1) 1904 2170 2359 2371 Fig. 9(a) shows the variation of the probability of vibrational exchange with the energy discrepancy. The number of collisions 2 refers to the exothermic exchange reaction in each case. A plot of log2 against energy discrepancy is linear, though 3 5 6 0 100 200 300 400 500 600 Av (cm-1) FIG. 9.Variation of the probability of vibrational exchange with energy discrepancy. this may be fortuitous since there may be a considerable experimental error in the point at 455cm-1. Curve (21) is obtained from the theory of Schwartz et aZ.7 using eqn. 65-9 and 65-14 given by Herzfeld and Litovitz.10 YO was taken as 3.6 A, 2" = 9 and the atomic weights of all the atoms were taken as 15. An ex- ponential function was fitted to the Lennard-Jones interaction potential at ro and at36 VIBRATIONAL RELAXATION OF NITRIC OXIDE the critical value of Y. The straight line c is an interpolation between curve (b) and the theoretical value at exact resonance. The agreement between experiment and theory is satisfactory. 1 Robben, J. Chem. Physics, 1959,31,420. 2 Bauer, Kneser and Sittig, J. Chem. Physics, 1959, 30, 11 19. 3 Basco, Callear and Norrish, Proc. Roy. Soc. A , 1961,260,459. 4 Basco, Callear and Norrish, Proc. Roy. SOC. A, 1962, 269, 180. 5 Callear and Norrish, Nature, 1960, 188, 5 3 . 6 Callear and Norrish, Proc. Roy. Soc. A, 1962, 266, 299. 7 Schwartz, Slawsky and Herzfeld, J. Chem. Physics, 1952, 20, 1591. 8 Gaydon and Hurle, Proc. Roy. Soc. A , 1961,262, 38. 9 Callear and Smith, to be published. 10 Herzfeld and Litovitz, Absorption and Dispersion of UZtrasonic Waves (Academic Press, New York and London, 1959).