9904
J. Phys. Chem. 1993,97, 9904-9915
Internal Energy Distributions from Nitrogen Dioxide Fluorescence. 2. Collisional Energy Transfer from Excited Nitrogen Dioxide Kenneth 0. Patten, Jr., and Harold S. Johnston' Department of Chemistry, University of California at Berkeley, and Chemical Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 Received: November 22, 1991; In Final Form: July 13, 1993.
We follow the collisional deactivation of laser-excited nitrogen dioxide through its dispersed fluorescence. The energy acceptor gases areNO2 at four excitation energies ranging from 18 828 to 24 989 cm-l and five monatomic gases, four diatomicgases, and three polyatomic gases with 18 828-cm-l excitation energy. The nominal products are the shapes of the internal energy distributions, which are obtained and plotted for several representative cases. From these distributions, the first three moments of the internal energy distributions are derived as a function of molecular collisions and tabulated as (i) the average internal energy, (ii) energy spread, and (iii) skewness. These quantities are plotted against c ( M ) t , the product of buffer gas concentration c ( M ) and delay time after laser excitation t(0.5-2 ps), which is a quantity proportional to number of collisions. The negative slope of average energy vs c(M)t is the macroscopic energy-transfer rate constant, kE(M). Average energies ( E ) for all NOz-buffered data taken at four excitation wavelengths are well represented by the single equation, fourth order in energy: d(E)/d(mo2t) = - I c ~ ( E ) ~where , &4 = 8.06 X 10-25 ( ~ m 3 molecule-1 ) ~ ~ ~cm3 ~ s-1. Energy-transfer rates increase in the order monatomics, diatomics, and polyatomics. The energy-transfer rate constants are in reasonable agreement with most values reported in the literature. Second and third moments of the internal energy population of collisionally deactivated nitrogen dioxide are the novel products of this article and show interesting trends with the number of Lennard-Jones collisions.
Introduction This article uses the method and nomenclature of the previous article,' to discussthe collision-induced evolution of highly excited nitrogen dioxide from a narrow laser-prepared initial energy to deactivatedand spread laterdistributions. In theliterature, there are theoretical analysesof collisional deactivation of highly excited polyatomic molecules, which show the decreasing average energy and the increasing energy spread of calculated populations of molecules undergoing collision,2 but experimental examples showing changingspread are scarce. Methods of studying energy transfer from highly excited molecules include theclassical SternVolmer method illustrated by work from Kaufman's group' and Troe's group;'dircct observation of excited molecules by ultraviolet absorption spectroscopy in Troe's laboratory;s12 infrared fluorescence illustrated by Barker's groupt3-15and by McAndrew et al.;16 experiments in which time-resolved diode-laser absorption monitored the vibrationally excited C02, NzO, and CO produced by collisions with excited NO2 (Chou et al.I7); multiphoton ionization studies by Luther and co-workers;l8J9 and Barker's timedependent thermal lensing measurementsfrom highly excited nitrogen di0xide.m Photoexcited cycloheptatrienerapidly isomerizes to highly vibrationallyexcited toluene in its ground electronic state; Luther and Reihslg measured the collision-dependent internal energy of this excited toluene by multiphoton ionization, and they noted their 1988 study to be 'the first experimental determination of (aE2)and therefore the population distribution during the relaxation". The other experimental methods cited above do not give second and higher moments of the population distribution during collisional deactivation. The experimental method reported in this article nominally gives a method of estimating the first, second, and third moments of the internal energy distribution of highly excited nitrogen dioxide as it is deactivated by collisions. In article 1,' we estimated the random errors associated with the first two moments by means of studies with noisy synthetic spectra, and in this article we measure the empirical precision of the first three moments with replicate runs. Abstract published in Advance ACS Abstracts. September 1, 1993.
We present this article in view of the theoretical interest in2 and scarcity oF9 higher moment data. Nitrogen dioxide (N02) is an example of the transition from the quantum state-specific behavior of diatomics and some triatomics to the statistical behavior of large polyatomic molecules.21Jz Strong coupling between its lowest excited electronic state, A2B2,and its ground state, R2At, leads to eigenstateswhich behave predominantly as high vibrational levels of the ground electronic state.23 The density of states is considerably greater than would otherwise be e~pected,~3-25 and the radiative lifetime of these states is considerably longer than would ordinarily occur for an electronicallyexcited state.2t.zz26g27 These properties, while complicating traditional spectro~copy,~~ make NO2 a good candidate for the study of vibrational energy transfer. In the Stern-Volmer mehtod, one measures the fluorescence intensity as a function of time and concentration of buffer gas M, c(M)t. Our method1 spectroscopically finds a shape of the intemalenergy distribution. Werepeatedly set up thesame initial photoexcitation, waited for a known delay time, and measured a dispersed fluorescence spectrum. From thesedata, wededuced a shape of the internal energy population. The moments of the population, Mt = (E),M2 = ( ( E - M # ) andM3 = ((MI- E l 3 ) , are derived from the spectroscopicallydeduced population at each of several values of c(M)t. We measure -A(E)/A(ct) as our energy-transfer constant, where the average is over the shape of the inferred population. This is a new method of studying collisional energy transfer, and it is free from some of the limitationsz7 of the Stern-Volmer method. We measure the relaxation of NOz* by NO2 from excitation energies of approxima tely 19 000,2 1 000,23 000,and 25 OOO cm-l in order to obtain the dependence of the energy transfer rate constant upon the. initial energy of N02*. We determine the deactivation of N02* excited with 532 nm light by each of 12 buffer gases. Collision Rate Constants. In Table I, we list the parameters for the Lennard-Jones (LJ) potential,6J1J0the LJ collision rate constants, and the value of c(M)t required to give one LJ collision
0022-3654/93/2091-9904$04.00 f 0 0 1993 American Chemical Society
Collisional Energy Transfer from N02*
The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 9905
TABLE I: 'Lennard-Jones Parameters and Rate Constants (molecule-l cm3 s-l), Where Reactant A Is NO2 and Buffer Gases Are M (298 K), and Value of q,~tTo Give One Lennard-JonesCollision of M with NO** M OU/A (ru/k)/K ( k ~~O-")AM l (ctl lo9)'e ~ l l NO26
He
Ne Ar Kr Xe Nz
co
NO 0 2
co2
S02C
s Fs a
20.
4.68 2.55 2.82 3.47 3.66 4.05 3.74 3.70 3.49 3.48 3.94 4.1 1 5.20
146.3 10.2" 32 114 178 230 82 105 117 103 20 1 336 212
4.21 4.61 2.82 3.18 3.05 3.27 3.58 3.68 3.48 3.34 3.83 4.06 4.07
2.38 2.17 3.55 3.14 3.28 3.06 2.79 2.72 2.87 2.99 2.61 2.46 2.46
Lcnnard-Jonesare from ref 6 unless otherwisespecified. Reference Reference 11.
e
for each buffer gas M. The LJ collision constant is
We employ the usual combining rules of arithmetic average for sigma and geometric mean for epsilon.28 The reduced collision integral f W ) * is given by ref 6, pp 6712-6713. The number of collisions undergone by a molecule in the gas phase is equal to the collision rate constant times the concentration of gas c(M) times the elapsed time t between laser excitation and observation collision no. = k,ct (2) The product ct is an appropriate variable in collision rate calculations.29J0 Quantitative results of this study and comparisons with previous results are based upon the energy-transfer rate constant. k , = -d(E)/d(ct)
(3) Theunits of k~ are (cm-l)cncrpy molecule-' (cm3) s-1. The number of collisionsis a more readily grasped quantity than k ~and , using the entries in Table I, we occasionally state the the number of Lennard-Jones collisions. Experimental Section The procedures and apparatus employed for this experiment are primarily the same as for the collection of nascent LIFspectra in the previous paper of this series.' Differences in conditions for this study of energy transfer are discussed below. Briefly, fluorescence of NO2 in a glass cell is excited by a pulsed laser, dispersed by a monochromator,measured by a photon multiplier, and stored in (more or less) 200 equally spaced wavelength bins, typically between 400 and 800 nm. 1. Excitation and FluorescenceCollection. A Nd:YAG laser (Quanta-Ray DCR-1) with a KDP doubling crystal is set to give approximately 50 mJ/pulse of 532-nm light with a duration of
