摘要:

Dissociation of Diatomic Molecules * BY THOR A. BAK t AND JOEL L. LEBOWITZ 1 Received 26th Janucry, 1962 A diatomic molecule is considered as two hard spheres connected by a spring. It is imbedded in a gas of hard-sphere atoms, which is assumed to be in thermal equilibrium at all times. Only a one-dimensional model is considered, and the possibility of multiple collisions during an encounter is neglected. The molecule is assumed to dissociate immediately whenever its vibrational energy exceeds E. The density in the phase space of the diatomic molecule is described by the Liouville equation for the isolated molecule with an added collision integral for collisions with the gas atoms. Since the gas is assumed in equilibrium this integral equation is linear. The rate constant for dis- sociations is found directly from the integral equation and (for small mass of the gas atoms) after its reduction to a Fokker-Planck equation. We consider the dissociation of a symmetrical diatomic molecule in a chemically inert gas of monatomic particles.The gas is assumed to be in thermal equilibrium at all times. As an illustration one may think of a dilute solution of iodine molecules in an inert gas. The molecule is assumed to be two hard spheres connected by a spring and the gas atoms are assumed to be mass-points. The problem will be dis- cussed classically and quantum-mechanically, using Bohr-Sommerfeld quantization. In order to simplify the calculations we shall treat only the one-dimensional case, so that the molecule would more correctly be described as two pistons connected by a spring.The criterion for reaction is taken to be that the vibrational energy of the molecule reaches a certain value E, which is assumed to be identical with the spectro- scopic dissociation energy. The reason for choosing this model is that the weak interaction theories, which have been the main centre of interest recently 1-4 generally give rate-constants which are much lower than the experimental values. The hard-core potential we have chosen here is certainly not realistic, but it will probably reveal the more im- portant features of a strong interaction theory. Although the present theory by the choice of interaction potential is a strong interaction theory, we can, by letting the concentration c of gas atoms go to infinity and the mass of the gas atoms go to zero (so that cJin is finite), obtain a Fokker- Planck equation for the inotion of the diatomic molecule in phase-space.In this way the present theory makes contact with weak interaction theories. CLASSICAL THEORY Let M be the mass of the atoms in the molecule, rn the mass of the gas atoms and p(p,q,t) the density in oscillator phase-space. Let us furthermore in the beginning assume that the centre of gravity of the diatomic molecule is fixed in space so that we consider the motion of one piston of mass M, cross-sectional area 2A and co- ordinates in phase-space p,q. The motion takes place in a harmonic potential (for * Sponsored in part by the Aeronautical Research Labs. OAR, through the European Office, t Institute for Physical Chemistry, University of Copenhagen, Denmark.$ Graduate School of Science, Yeshiva University, New York. Aerospace Research, U.S. Air Force. 189190 DISSOCIATION OF DIATOMIC MOLECULES energies smaller than E ) and under the influence of bombardment by particles of mass m coming from a gas at equilibrium. For the density in phase space we then have ap/at + (p,H) = Sk'(p,q,p' ,qf)P(P',4', OdP'W - P(PY Y,t)Sk'(P',q',P,q)dP'dq ' (1) as derived by Bergrnann and Lebowitz.5 Here (p,H) is the Poisson-bracket and the kernel K(p,q,p',qf) is (2) where y = m/M and fl = l/kT. Since the colliding particles are hard spheres, the co-ordinates of the particles do not change during an encounter and the kernel therefore contains 6(q - 4'). In the derivation of this equation, multiple collisions in the sense of Widom 6 have been neglected.Since most cases amenable to an experimental investigation correspond to y< 1, for which multiple collisions are of minor importance, this is presumably a reasonable approximation. If, in the above equation, we change to energy-angle variables and assume the density in oscillator phase-space to be angle-independent, we get where E is the vibrational energy of the oscillator and Z(E) = [~K(E',E)~S']-~ is the relaxation time for change of energy of the oscillator. The kernel K(&) is related to q . M P ' , q ' ) by 9 (4) SK(p,q,p',q')GCH(p,q) - &18[H(P' 4') - e'ldPdqdP'dq' K(E,E') = dV(ef)/dd where V(E) is the volume of phase space for which the energy of the oscillator is less than e.The rate constant for escape is now determined by summing p(d)K(&,e') over all initial energies e' < E and all final energies E > E. This leak of particles out from the potential well will of course change p so that it is not the equilibrium distribution, but if the well is sufficiently deep we can, to a first approximation for p , use the equilibrium distribution Z(E)-1 exp (-BE'), where Z(E) is the partition function for the bound states. This is essentially a perturbational approach, and the resulting rate constant will therefore approximate the true value of the rate constant better than the equilibrium distribution approximates the correct distribution. This argument leads to the following expression for the rate constant, and we shall see later in connection with the quantum case that the value of the rate constant obtained from this expression is identical with the one obtained by a more orthodox perturbation method.The expression for k can be thought of as merely stating the rather obvious fact that the particles which escape from the potential minimum will not all jump from the bottom of the well. Rather there is a distribution of particles on the possible energy levels in the well, and from all these levels there is a possibility of leaving the191 well in one jump. Seen from this point of view the expression seems almost trivial, but one must remember that, without an explicit calculation of K(E,E’), it is still without any practical use. T. A . BAK AND J . L . LEBOWITZ It is convenient to rewrite the expression for k in the following manner, since it is clear that the last two terms are negligible compared to the first.Also in the first integral, we can extend the range of integration to 00, since the interval E<s’ < 00 contributes negligibly. We therefore have and, using detailed balance in the form, we obtain The intuitive meaning of this is particularly striking, since it states that as the activation energy E is increased the rate of dissociation diminishes, because the flow of particles from the surface in phase-space where dissociation takes place back to the potential minimum is increased. From this expression for the derivative of k we get which is our final expression for the rate constant. K(E,E‘) for equal masses. To simplify the presentation, we shall only discuss in details the calculation of For this case, we have where M is the common mass of the atoms. To get the conditional probability that the oscillator goes from energy E’ to E in the time dt we use eqn.(4). The integration is most conveniently carried out after a change to energy-angle variables, since the integrations over the energies are immediate because of two of the &functions. We are left with a( sin 8 - /: sin 8’) (8) where o = JK/M is the frequency of the oscillator and K the spring constant.192 DISSOCIATION OF DIATOMIC MOLECULES The integration over 8 is immediate when the &function is used giving, for E >E', E( 1 - sin' O')]-idD'. (9) Assunling BE' $- 1, this ktegral can be evaluated using Laplace's method,7 i.e., expanding PE' sin2 8' in the exponential function in powers around its maximuill value and retaining only teras up to the second power.In the rest of this integrand 8 is replaced by the value for which the exponential function is largest, and that part thus reduces to a constant. Finally, the limits of integration are extended from --oo to a, since the integrand vanishes rapidly outside its maximum value. It is seen that in this case there are two values of 0, for which the exponential function has a maximum, namely 8 = n/2 and 8 = 3n/2, and that they contribute equally to the integral. In this way we obtain - 2J2Ac M(&,E') = -exp [ - ~ J ' ( E - E ' ) ] ; E 2 e', JMn JE' and using detailed balance we then have In both cases we have assumed that be' is large compared to one, but since we want to use these transition probabilities to calculate the rate of transitions leading to chemical reactions, which in most cases will stem from transitions from fairly high energy levels, this is not a severe limitation.Using these expressions for K(E,E') we obtain where, to the approximation we use here, the last term in the bracket can be neglected. Since for a harnonic oscillator Z(E)=Z(a) = 2n/uB 2nd V(E) = 2 n ~ / o , we finally obtain When these calculations are repeated for y # 1, one obtains precisely the same result for the rate-constant although the intermediate results for K(E,E') difl'er some- what from the results given above. The cnly interesting feature is th2-t one finds for E>E' that K(E,E') is only significantly different from zero in the range, This shows clearly that as y-0, the energy range from wlzicli transit ions to E is possiblc becomes exceedingly narrow.We shall return to this point in connection with the Fokker-Planck equation.T . A . BAK AND J . L . LEBOWITZ 193 So far, we have assumed that the centre of gravity of the molecule is fixed so that the molecule acts as a piston which has twice the area of a single piston, and which is anchored to a fixed point. To investigate the behaviour of a diatomic molecule constrained to move on a straight line through the atomic centres we introduce two collision kernels, one fo; each end of the molecule. We then express that during an impulsive collision between one end of the molecule and a gas atom the other end does not change momentum nor co-ordinate.Furthermore we assume that the translational motion of the centre of gravity is in thermal equilibrium at all times. Let P1,Ql and &,Q2 be the co-ordinates of the two atoms in the molecule, P,Q the co-ordinates of the centre of gravity and p,q the relative co-ordinates. We then have PI = W - P Y p , = 4P+P, and where K(P;, Q&,Qi) is the kernel for atom no. 1 and K(P2,Q&,Q;) is the kernel for atom no. 2, both given by eqn. (2). The integrals involved are all elementary and we obtain Using this kernel we can determine K(E,E‘) for this case and from that the rate constant, using the methods outlined above. We obtain whereas the fixed centre rate constant was independent of rn (or y), we here have a slight y-dependence.It is interesting to note that as y-0 the two rate constants become identical, which is what one would expect, since in that case the translation of the centre of gravity becomes unimportant. QUANTUM-MECHANICAL THEORY An exact quantum mechanical theory of chemical dissociation seems, at present, to be impossible. As an alternative to the full quantum-mechanical treatment we shall now consider the quantum correction to the classical case which arises from dividing phase space into cells. We consider only the case y = 1 and fixed centre of gravity of the oscillator for which the kernel is given by eqn. (7). From this we want to calculate Knnt, the probability of transition from quantum state n’ to quantum state n. It is convenient to introduce a quantity K(n,p’,q’) which gives the probability of transition from the classical state p’,q’ (with energy less than (n++)fico) to the quantum state n.Since the energy of the quantum state n is (n++)Eco, we define the quantum state n as the part of phase space for which the energy of the oscillator lies between n5co and (n+ 1)ha. Furthermore, the value of q is unchanged during a G194 DISSOCIATION OF DIATOMIC MOLECULES change in state since the collision is impulsive. For each value of q' and p' the oscil- lator can therefore jump down to a p-range, - J2M(n + 1)Bco - M2c02qt2 < p < - J2MnBco- M2m2qr2, J2MnBm- M2c02qr2 < p < J 2 ~ ( n i 1)Bco - M2c02qr2. or up to ap-range, The probability of transition to the quantum state n is therefore, provided the energy of the initial state is less than (n+3)iro, 2~~,p - d 2 M n B o - M2ozqz K(n,p',q') = (P' - PI exp (- PP2/2M>dP + (P - P') exp ( -i3P2/2M)dP M J m J- d 2 M ( n + 1)6o-Mzo2q'z d 2 M ( n + 1)IIw-Mzozqz s ~ Z M n f i o - M 2 o Z q i - - - 4cA exp ( -i,2q2) PM exp (-Bnhm)[l-exp (-Plko)].J 2 X j To get Knnp we now average this over the values of p and q' which correspond to JK(n,p',q')G[(n' + 3)iico - (pt2/2M) - +M~~q'~]dp'dq' As before, the integral is most conveniently carried out in energy-angle variables the energy surface E' = (n'+*)fim.. that is, Knn, = [dv(&')/d&'l~~=("* ++)ho and we obtain -...-[l-exp(-/3iim)] exp(-BnAco)exp Knn, = ~ 4Ac J2.nMB where I0 is the hyperbolic Bessel function of zeroth order. That is, I&) = Jo(iz), where Jo(z) is the ordinary Bessel function of zeroth order, and for large z we have, asymptotically, I~(z) = eZ/ JG.From the value of Knn* for n >n' we can get the transition probability for all values of n and n' by using detailed balance and we therefore have [v = min (n,n')]. As a check on the correctness of this we note that assuming PBco < 1 and V B 1 and using the asymptotic expression for 10 we obtain the classical transition probability derived above. Let xn be the population of the nth level of the oscillator and N the largest stable level. A particle which reaches the (N+l)th vibrational level is thus immediately " absorbed ", that is, the molecule dissociates, and as above we neglect the possibility of particles returning from the states n > N+ 1.The populations of the levels satisfy the equationsT. A . BAK AND J . L. LEBOWITZ 195 Following the method used by Montroll and Schuler,l we can now approximate the rate constant for dissociation by the numerical value of the numerically smallest eigenvalue of the matrix Ann,. For N-+co, the numerically smallest eigenvalue is zero, and for finite N we can obtain the eigenvalue by conventional perturbation technique starting from the equilibrium solution, which corresponds to a zero eigenvalue. In this way we obtain which is the quantum-mechanical expression for the rate constant. If pho Q 1 we can expand the first bracket to get 1 - exp (-PAo>] - D m and the expression then to its classical value. The sole effect of the discrete levels of the oscillator is thus to cut down the rate with a factor [I -exp (-piim)]/pEm and the physical reason for this is that the oscillator now cannot split up an energy change Em on two or more jumps.Since the above perturbational calculation in the classical limit leads to the same result as the closely related eqn. (5), it is at least very probable that the latter pro- cedure will have the same property as the ordinary perturbational procedure, namely, that the eigenvalue approximation is better than the eigenfunction approximation. THE FOKKER-PLANCK EQUATION As has been shown by Keilson and Storer,s an integral equation of the type used We J k ( P , 4 , P ’ d l P ( P ’ , q‘, 0 -K(P’,4,’P,4,)P(P,4,tdP’dq ’ = c, I d ” -,[~‘“’(P)P(P,4Yt)l, above may be transformed into a differential equation of infinitely high order.have n = l !dp (19) where d‘”’(P) = SKCp :4’,P,4)(P- P’YdP’d4’. With the kernel used here, we have, retaining only terms up to & so that the integral operator to this approximation becomes and the Liouville equation reduces to the Fokker-Planck equation, where V is the molecular potential and the friction coefficient q is 4Ac d8 ylpnM: The coefficients J&) (n>2) contain only y in higher powers than 3 and as long as y < 1, they can therefore presumably be neglected. It is seen, however, that the expansion is not simply an expansion in powers of 7%. In order for the friction196 DISSOCIATION OF DIATOMIC MOLECULES coefficient to be finite, one must assume that as y-0, c-+oo, so that cJy stays finite.Only then does the integral operator change into a second-order differential operator. It has been shown by Keilson and Storer, for a somewhat simplified kernel, that in spite of the different response of the two types of equations to an initial S-distribu- tion for small times, the two solutions will be almost identical for large times. Since the escape of a particle from a potential minimum is a slow process in the molecular time-scale, one might therefore expect that one will get the same rate constant from the Fokker-Planck equation as the one found above. This, however, is by no means the case. Writing the Fokker-Planck equation in energy-angle variables and assum- ing that the density in phase-space is independent of the angle, we get for which the solution which vanishes at E = E is9 m P = exp ( - B E ) C cn ~ X P ( - ? ~ a n t ) ~ F ~ ( - a n , l , ~ & ) .n=O Here a, are the roots of the equation 1F1(-an,1,flE) =0, 1F1 is the confluent hypergeometric function and the coefficients C, are determined by the initial conditions. The rate constant is therefore approximately quo which by various methods discussed previously can be determined to be, in the limit pE$1, ko = r]a, = ~AC/~---PE exp (-BE). It is seen that the energy dependence of the pre-exponential factor is quite different from that found before and since the previous expression was independent of y, this is a peculiar result. We believe these differences to be due to the very special limiting process used in obtaining the Fokker-Planck equation. Clearly, not both expressions can be correct, say for I2 in He, but it is quite difficult to argue in favour of one of the results, rather than the other. It is perhaps significant that when terms proportional to y are included in eqn. (20) and treated as a perturbation one gets which for instance for I 2 in He at 300°K gives an increase in the rate constant by about a factor of 12.This is quite a large perturbation and naturally leads to a certain scepticism about the validity of this whole approach. CONCLUSION The main purpose of this paper has been to show how a particular kind of strong interaction can be taken into account in dissociation reactions. The theory can, in principle, be extended to any kind of strong interactions by using a linearized Boltz- mann equation rather than eqn.(1). The method which we have used to eliminate the translational motion of the molecule can also be used to eliminate the rotational motion when a three-dimensional problem is treated. In both cases, however, one encounters considerable mathematical difficulties. Although the present work therefore has a preliminary character it is interesting to compare the conclusions with the experimental results. For 12 in He, we have the following experimental values 10 : at 298"K, k = 4.42 x 1015 exp (-E/RT) sec-1,T. A . BAK A N D J . L . LEBOWITZ 197 and at 1400"K, k = 1.76 x 1014 exp (-E/RT) sec-1. The concentration c is measured in molecules/ml and E equals 35,500 cal/mole. Using eqn. (15) and setting A = na2, we calculate from the rate constant a = 10.8 A at 298°K and a = 6.8 A at 1400°K. These a-values are somewhat larger than the sum of the hard-core radii of I and He and the rate constant calculated from eqn. (1 5) will therefore be too low. The change in the calculated a with temperature furthermore shows that the temperature de- pendence of eqn. (15) is incorrect. If instead, we use eqn. (22), we get too low 0- values, namely, 1.3 A and 1.2 A but here the temperature dependence comes out right. In view of the fact that the model is one-dimensional, the agreement must be considered largely fortuitous. 1 Montroll and Shuler, Advances in Chemical Physics (Interscience, New York, 1958), vol. 1, 2 Prigogine and Bak, J. Chem. Physics, 1959, 31, 1368. 3 Chandrasekhar, Rev. Mod. Physics, 1943,15, 1. 4 Brinkmann, Physica, 1956, 22, 29, 149. 5 Bergman and Lebowitz, Physic. Rev., 1955, 99, 578. 1957, 1, 1. Lebowitz, Physic. Rev., 1959, 114, 1192. 6 Widom, J. Chem. Physics, 1958, 28, 918. 7 De Bruijn, Asymptotic Methods in AnaZysis (North Holland Publishing Co., Amsterdam, 8 Keilson and Storer, Quart. J. AppZ. Math., 1952, 10, 243. 9Bak and Andersen, Math. Phys. Medd. KgZ. Danske Vid. Selsk., 1961, 33, no. 7. 10 for a survey of experimental data, see, for instance, Trotman-Dickenson, Gas Kinetics (Butter- p. 361. Lebowitz and Bergman, Ann. Physics, 1958), p. 60. worths, London, 1955).

ISSN:0366-9033    

DOI:10.1039/DF9623300189

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Mechanism of Third-Order Recombination Reactions BY G. PORTER Dept. of Chemistry, The University, Sheffield 10 Received 19th January, 1962 Two theories of third-order recombination and second-order dissociation give a satisfactory explanation of observed negative temperature coefficients and the wide differences in efficiency of chaperon molecules. Recent measurements of iodine atom recombination temperature coefficients in the presence of twelve chaperons are used to test the theories and it is shown that whilst the radical-molecule complex theory predicts both the absolute rates and their dependence on chaperon the energy transfer theory is less successful. The recombination of two atoms or molecules R, in the presence of a chaperon My occurs in two steps since, if we define precisely the separation at which two species are in collision, formation of a bimolecular collision complex must precede formation of the termolecular one.The recombination reaction may therefore proceed in two ways depending on whether R$ or RM* is the first bimolecular complex to be formed. If the complex RM* can be stabilized to a species RM by collision with a second M, a third mechanism of recombination is possible. therefore as follows : 1 2 3 4 5 6 7 8 9 10 11 12 R+R+R: R+M+RM* R: + M+R2 + M RM* +M+RM+ M RM* + R+R2 + M RM+ R+R2 + M The complete reaction scheme is If dissimilar species R and R' are involved 36 equations are necessary but we can If the system is at equilibrium confine discussion to the above case without loss of generality. dCRJ/dt = 0 = CwG + k9K3 + kl 1K3K,1CR12CM1 - Ck6 + kl, 4- kI21CR21CMI- If, as is usually the case, the system is not at equilibrium, the stationary-state treatment is applicable to the recombination reaction provided [RT], [RM*] and [RM] are much smaller than [R], and that the reaction has proceeded to steady state 198G .PORTER 199 conditions. Then the termolecular recombination rate constant k,, when the second term in the above equation is much smaller than the first, is given by k 3 k 7 k l l (k4+ks8[MI)(kt3 +kiiO)+k7kiio[MI where 8 = [R]/[M]. corresponding to a short lifetime of Rg and a weak complex RM. Then If the reaction is third order, ks[M] <kz and k7kllO[M] <(k4+k98[M])(k8 + k d ) klk5 k3k9 k3k7kl 1 k , = - + k2 k4 + k9e"i + (k4 + k 9 o ~ ~ 1 ) ( k 8 + kl If [R] is small so that kgO[M]<k4 and kllO<kg, k1k5 k3k9 k3k7k11 k, = - +-+- k2 k4 jk4ks = k5K1+ k9K3 + kllK&, (1) which is equal to kr at equilibrium. Since [RM*]/([RM*] + [RM]) = exp-AE/RT, where AE is the heat of formation of RM from R and M at constant volume, K7 = exp(AE/RT) - 1.Since kg = kll when AE is small and K7 % 1 when AE is large we obtain k, = k5K1+ kllK3 exp (AEIRT). (2) In atom-recombination reactions the principal experimental facts to be accounted (1) rate constants involving atomic chaperons 1 are about 3 x 1091.2 mole-2 sec-1; (2) the efficiency of different chaperons 2 varies over a factor of at least 103 ; (3) temperature coefficients are negative and become increasingly so as the effici- ency of the chaperon increases.3 Theories of third-order recombination, and the microscopically reversible theories of second-order dissociation, differ widely in the values which they derive for the individual constants in eqn.2, though all are capable of giving reasonable agreement with the observed rate constant for three-atom processes. Most theories assume AE = 0 in eqn. (2) and calculate the efficiency of three-body collisions either of the " billiard ball " type (see ref. (4) for discussion of early theories) or with the intro- duction of energy transfer restrictions, so that k5 and kll are less than the correspond- ing collision numbers 2 5 and &. Thus, Husain and Pritchard5 postulate that deactivation of Rg may only occur when the kinetic energy of R; and M is less than a critical amount E*, in which case k5 = Z5[1 - exp (- E*/RT)].This equation gives a good account of the observed temperature dependence of rate but predicts absolute values which are too low and nearly independent of the chaperon used. The theories of Keck,6,7 Bunker 8 and of Jepson and Hirshfelder 9 predict neither the obssrved temperature dependence nor the dependence on chaperon molecule, though Keck's variational theory predicts the absolute rates in the five inert gases very well. for are as follows :200 THIRD-ORDER RECOMBINATION REACTIONS There are two theories of atom recombination at present in use which give a fairly satisfactory account of all the observations, including temperature coefficients and chaperon effects. We shall first describe the two theories briefly and then attempt to evaluate them in terms of the recent data of Porter and Smith 3 on iodine- atom recombination temperature coefficients.ENERGY TRANSFER THEORY l o AE is assumed to be zero and no distinction is made between the terms kSK1 and kllK3. The value of k5 is calculated via the reverse rate constant kg and the overall equilibrium constant K of 1, = 21, K . The collision (energy transfer) theory expression used to evaluate kg is 11 k6 = kd = Z(gJ$ exp (-2) where 2n+2 is the number of square terms in the collision complex which can con- tribute energy for dissociation, & is the dissociation energy of constant for I2+ M collisions. The recombination constant 12 and 2 is the rate where B is independent of temperature. Since 2 varies as T*, k, = -( C -) E , n! RT where C is independent of temperature at low temperatures and proportional to the first power of temperature at high temperatures.The constant B is independent of chaperon and 2 varies by little more than a factor of two over all the chaperons which we have investigated so that, since we are concerned with variations in the rate constant over a factor of 103 we may treat C as a constant. For iodine-atom re- combination we calculate that k, = 7 x lo7 - - 1.2 mole-2 sec-' at 300°K. (27 :! If the experimental results are plotted in Arrhenius form the apparent negative activation energy Ea = nRT at low temperatures and (n - l)RT at high temperatures. R A D I C AL- MOLE C ULE COMPLEX THEORY 12*3*13 The fundamental assumption here is that AE>RT so that k, = kllK, exp (AEIRT).Since the product R2 of reaction (1 1 ) has energy Eo - AE it cannot dissociate and no energy transfer restrictions are imposed so that kll = 2 1 1 . Statistical evaluation of the constant K3 shows that the product kllK3 is insensitive to the nature of M and is independent of temperature at low temperatures and proportional to T at high temperatures. Again, within a factor of two we can regard the pre-exponentialG . PORTER 201 factor as constant and use the average of the calculated values of Porter and Smith 3 to give k, = 5 x lo8 exp (E,/RT) L2 mole-2 sec- ', where Eu = AE at low temperatures and Eu = AE-RT at high temperatures. COMPARISON OF THE TWO THEORIES The only data which are sufficiently accurate and extensive for this comparison are flash-photolysis studies of halogen-atom recombination, and even these do not allow a distinction to be made between the two theories on the basis of the temperature dependence alone since both expressions give equally good accounts of the experi- mental results, The temperature dependence of reaction rates obtained from shock- tube experiments alone are rather uncertain though a combination of these data with flash-pliotolysis results is more reliable and it has been shown,lO for bromine atom recombination in argon, that the energy transfer theory can account for the dissocia- tion rate over a temperature range corresponding to a variation of rate by a factor of 1027.The complex theory accounts for the data nearly as well though Givens and Willard 14 have shown that the energy transfer theory gives a somewhat better fit if the temperature dependence measured in shock-tube experiments is correct.We have recently measured the temperature coefficients of recombination of iodine atoms in the presence of eight chaperons of widely different efficiencies and four chaperons have been studied by Bunker and Davidson 13 and by Engleman and Davidson.15 All the available data are summarized in table 1, the rate constants being defined by eqn. (2) and therefore equal to one half of those tabulated by Porter and Smith. These results enable us to compare the theories in the following way. TABLE 1 k27 (1.2 mole-2 sec-1) ~ , @ ~ l ) A E (kcal) n ref. x 10-9 M He Ar 12 1.5 1.4 3.0 3.0 2.9 5.7 6.8 13-4 36 80 105 1 60 194 262 405 1600 0.4 0.66 1.3 1.4 1-13 1 *22 1.5 1-75 1.65 1.7 1-97 2.55 2.7 2.4 4.1 4.4 1.0 1.26 1.9 2.0 1-73 1.82 2.1 2.35 2.25 2.3 2.57 3.15 3.3 3-0 4.7 5-0 1-7 2.1 3.2 3.3 2.9 3.0 3.5 3-9 3.7 3.8 4.3 5-2 5.5 5-0 7.8 8-3 3 15 3 16 13 15 3 3 13 3 15 15 3 3 3 13 The value of Eu from the Arrhenius plot gives n and AE from which, by use of the expressions derived above, the rate constants can be calculated absolutely.Since, in each case, we have two observable quantities and only one adjustable parameter a test of the theories can be made. The results are shown in fig. 1 where the rate constants have been plotted on a logarithmic scale against n and AEfor twelve chaper- ons. The points are experimental values and the two lines are calculated from the202 THIRD-ORDER RECOMBINATION REACTIONS two theories.The high-temperature approximation, which should be the more correct in the temperature region investigated, was used in both cases. The agreement between experimental values and the complex theory calculation is within the estimated uncertainties of calculation and experiment, and, since the calculations are absolute, except for the use of the experimental Ea, the good fit, both of gradient and absolute values is significant. On the other hand, the energy transfer theory predicts higher values and a more rapid increase in rate with n than is observed. This reflects what has already been noticed-that in order to account for the large negative temperature coefficients this theory predicts very small collision efficiencies. / / AE(kca1 mole-1) n FIG.1.-Relationship between recombination rate constant kr and the parameters AE and n. The points are experimental ; the full curve is calculated from the complex theory and the broken curve is calculated from the energy transfer theory. This is not surprising since it is difficult to see how theory can be correct in assuming that energy flow from all available degrees of freedom can occur during the time of one collision, i.e., about 10-13 sec. A further objection is that the number of square terms required, 2(n+ I), seems to be impossibly large in many cases and to show a poor correlation with molecular complexity. It seems most improbable that I2 and Br2 would contribute more degrees of freedom as chaperons than hydrocarbons and alkyl iodides. The main objection which can be raised to the complex theory concerns the nature of the RM complex.Clearly, the interaction is unspecific since even iodine itself, the most efficient chaperon, fits the correlation with boiling point, ionization potential and similar properties found by Russell and Simons.2 Attempts to interpret re- combination rates in terms of Van der Waals forces 13 were not, however, successfulG . PORTER 203 since these forces are too small, and show too little variation between chaperon molecules, to account for either temperature coefficients or relative rates. This difficulty is removed in the charge-transfer complex theory of Porter and Smith3 and excellent support for this theory has now been provided by the direct observation of the absorption spectra of the charge-transfer complexes themselves in flash-photo- lysis e~periments.17~18 The question now arises as to what extent the charge-transfer complex theory of recombination will be applicable to systems other than iodine.Similar flash-photo- lysis experiments on bromine-atom recombination,l4 although more limited, have established that the rate coefficients have negative temperature coefficients similar to iodine as well as a similar dependence on chaperon. Recent work on the reactions H + OH + M and OH +OH + M also show a marked variation with chaperon molecule and a good correlation with halogen-atom results.17 Since the electron affinity of OH is at least comparable with that of halogen atoms, charge-transfer complexes are probably involved here as well.It would not be surprising if interactions of a few kcal/mole were found quite commonly between free radicals and molecules for the following reason. The highest filled orbital of the chaperon M will combine with the odd electron orbital of R to form two new molecular orbitals, one bonding and one antibonding, the separation depending on the difference in energy of the original orbitals. Two electrons will occupy the lowest bonding orbital in the complex and one the antibonding orbital so that, by the usual molecular orbital argument, bonding will result. Whether this type of bonding is generally to be termed a charge-transfer complex is largely a matter of definition. Perhaps the less definitive term radical- molecule complex would be more useful until more has been learned about the exist- ence of such species.19 It is unlikely that the radical-molecule complex mechanism will be important in the recombination (or the inverse molecular dissociation) involving larger radicals.The relative importance of the three mechanisms of recombination represented by eqn. (1)-(12) can be estimated in the following way. The rate constants kl, k3, k5 and kll are, by collision theory, of the order of magnitude 1011 1. mole-1 sec-1 at 300°K. For this temperature, eqn. (2) therefore becomes k, = 1022zi, + 1022zrfM exp (AEJRT) 1.2 mole-2 sec-l, where z& and z* cases may be distinguished. are the lifetimes of the collision complexes R; and RM*. Three (a) Three atoms. The lifetimes z will be about 10-13 sec and kr = l o g + 109 exp(AE/RT) so that if AE = 0 the two processes contribute equally and if AE>O the complex mechanism predominates.(b) R are atoms and M is polyatomic. Then z R z ~ 10-13 sec, but & may be greater owing to the increased number of degrees of freedom if there is any attraction between the atoms and molecules. Again, unless AE = 0, the complex mechanism predominates. (c) R are radicals. In this case, z;, will be increased by the increased number of degrees of freedom. If the values of AE are, like those found with iodine, about 1-3 kcal for typical chaperon molecules we may expect that the complex mechanism will still predominate for recombination of diatomic radicals but probably not for triatomic radicals. What little evidence is available supports this ; for example, the rate constants for combination of small radicals such as OH are similar to those for atoms 20 whilst the third-order rate constant for methyl radical recombination 21204 THIRD-ORDER RECOMBINATION REACTIONS is about 105 times greater implying a lifetime of C2H* of 10-8 sec and the utilization of approximately 14 degrees of freedom.It would be helpful to have data on the effects of different chaperons on a wider variety of radical recombination reactions ; those with few atoms, proceeding by the complex mechanism, should show a considerable variation with chaperon, similar to that of the halogen atoms, whilst those like methyl, which become termolecu- lar only at low pressures, should show a dependence on the chaperon determined only by the energy transfer rate constant kg. 1 Christie, Harrison, Norrish and Porter, Proc. Roy. SOC. A, 1955, 216, 446. 2 Russell and Simons, Proc. Roy. SOC. A, 1953, 217, 271. 3 Porter and Smith, Nature, 1959, 184, suppl. 7, 446 ; Proc. Roy. SOC. A, 1961, 261, 28. 4 Christie, Norrish and Porter, Proc. Roy. SOC. A , 1953, 216, 152. 5 Husain and Pritchard, J. Chem. Physics, 1959, 30, 1101. 6 Keck, J. Chem. Physics, 1958, 29,410. 7 Keck, J. Chem. Physics, 1960,32,1035. 8 Bunker, J. Chem. Physics, 1960, 32, 1001. 9 Jepson and Hirshfelder, J. Chem. Physics, 1959, 30, 1032. 10 Palmer and Hornig, J. Chem. Physics, 1957, 26, 98. 11 Fowler and Guggenheim, Statistical Thermodynamics (Oxford, 1952), p. 497. 12 Rice, J. Chem. Physics, 1941, 9, 258. 13 Bunker and Davidson, J. Amer. Chem. Soc., 1958, 80, 5085, 5090. 14 Givens and Willard, J. Amer. Chem. SOC., 1959, 81, 4773. 15 Engleman and Davidson, J. Amer. Chem. SOC., 1960, 82,4770. 16 Strong, Chien, Graf and Willard, J. Chem. Physics, 1957, 26, 1387. 17 Rand and Strong, J. Amer. Chem. Sac., 1960, 82, 5. 18 Gover and Porter, Proc. Roy. Soc. A, 1961,262,476. 19 Hausser and Murrell, J. Chem. Physics, 1957, 27, 500. 20 Black and Porter, Proc. Roy. SOC. A, in course of publication. 21 Dodd and Steacie, Proc. Roy. SOC. A, 1954, 223, 283.

ISSN:0366-9033    

DOI:10.1039/DF9623300198

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

The Kinetics of Hydrogen Atom Recombination BY G. DIXON-LEWIS, M. M. SUTTON AND ALAN WILLIAMS The Houldsworth School of Applied Science, The University, Leeds, 2 Received 23rd February, 1962 The rate of recombination of hydrogen atoms at 1072°K has been measured by studying the decay of H-atom concentration in the burnt gases of suitable hydrogen+ oxygen+nitrogen flames. The methods of study have included measuring the decay of chemiluminescence when traces of sodium salts are added to the flame gases, and studies of H-atom concentration by means of tracer techniques using their reactions with D20 and D2. No significant change in the rates of decay was observed within the range in which it was possible to alter the proportions of N2, H2 and H20 in the burnt gases. This suggests that all these gases give similar third-order recombination constants. Atom and radical recombination plays an important role as a terminating step in many chemical reactions.This is particularly so in the combustion of hydrogen or hydrocarbons when conditions are such that reaction-vessel wall-effects are small. In flames, where wall effects are absent, such recombinations provide the major terminating steps, and a knowledge of their rates is vital if such systems are to be fully understood kinetically. Furthermore, such information would greatly assist our knowledge of the mechanism of recombination. When two hydrogen atoms collide, the presence of a third body is necessary to remove some, or all, of the excess energy if association is to occur. The overall reaction may be represented by H+H+M+H2+ M, where M represents the third body, which may be any other molecule present in the system.Only a few kinetic studies of this reaction have been made. In earlier studies,l-s hydrogen atoms were produced by electrical discharges at low pressures and the rates of recombination studied in a flowing system. Interpretation of these results was complicated by the excessive amount of diffusion of hydrogen atoms and their recombination on the vessel walls. More recently studies have been made by Sugden and collaborators (e.g., ref. (6)-(8)) using hydrogen + oxygen flames as the source of hydrogen atoms. These are well suited for studies of rates of re- combination since variations in temperature and composition can readily be made whilst interference from reaction vessel walls is absent.Sugden’s studies have been made in the burnt gas of flames having temperatures above about 1400°K. Follow- ing the stabilization in this laboratory of slow burning rich hydrogen+oxygen + nitrogen flames having a flame temperature of only 1000-llOO°K,~ rates of recom- bination at these lower temperatures have now been studied. Since both hydrogen atoms and hydroxyl radicals are produced in the flames, the decay of hydrogen atoms occurs by the two reactions, H + H + M+H2 + M, H + OH + M+H20 + M, (i> (ii) where in the hydrogen-rich flames, M may be either H2, N2 or H20. 205206 HYDROGEN ATOM RECOMBINATION EXPERIMENTAL In these experiments the recombination reactions are followed by three methods.First, the chemiluminescence when small amounts of sodium salts are added to the flame gases has been shown by Sugden and collaborators to be due to excited sodium atoms formed by reactions (i) and (ii) when M is a sodium atom. Hence the decay of chemiluminescence in the burnt gas may be used as a measure of relative H-atom concentrations. In these low-temperature flames, thermal emission from sodium is negligible. Secondly, the re- action of H atoms with heavy water to form HD by reaction (iii), H+D20 = OD+HD (iii) has been used to measure their relative concentrations in a few flames. Thirdly, an addi- tional calibration of the H-atom concentration in one flame has been carried out by adding small amounts (about 0-2-0.3 %) of deuterium to the flame gases, and measuring the rate of formation of HD by the exchange reaction.The flames were burned as large flat horizontal discs on a modified flat-flame burner of the Egerton-Powling type.10 The burner was 6 cm in diam., and it was surrounded by a twelve-sided chimney consisting of optically flat quartz windows. It was mounted on a vertical slide which could be traversed at a known rate by a synchronous motor. The gases were taken from cylinders (British Oxygen Gases), dried, metered and well mixed before entering the burner. Cylinder deuterium (99-5 %) was supplied by General Dynamics Corporation. Heavy water (99.83 %) or sodium chloride solution (0.005 M) could be added at a known constant rate to the unburnt gas stream by an atomizer. Water vapour could be added by means of a motor driven syringe into a heated vaporizer.Condensation in the apparatus was avoided by heating. For the photometric measurements, the light from the plane of the flame centre was focused on the sensitive element of a photomultiplier tube. The light actually reaching the photomultiplier was restricted by means of an aperture slit system to that from a narrow horizontal slice of the flame 0.1 mm high at the flame centre and 0.3 mm high at the edges. In early experiments, a monochromator was used to isolate the sodium D lines, but the emission from the flames was so predominantly due to these lines that the monochromator was later found to be unnecessary. The light beam was chopped at 460clsec, and the signal was amplified by means of a homodyne system and presented on a chart recorder.For the deuterium and heavy-water experiments, samples of the gases at various posi- tions in and after the flame were removed by means of a quartz microprobe made from 1 mm ext. diam. tubing drawn down to produce a 25 p orifice. The position of the probe in this non-luminous flame was obtained by measuring the distance of its tip from the schlieren maximum. The samples withdrawn were analyzed mass spectrometrically in order to determine the [HD]/[H2] ratios. ANALYSIS OF EXPERIMENTAL RESULTS DETERMINATION OF APPARENT SECOND-ORDER RECOMBINATION RATE CONSTANTS In a flowing reaction system containing H-atoms, the H-atom concentration is related to distance by means of eqn. (1) : [d[H]/dt]chem is the chemical rate of formation of hydrogen atoms, y represents the distance co-ordinate from some arbitrary plane, S is the linear flow velocity and DH is the diffusion coefficient of H atoms in the mixture.If it is assumed that i n the burnt gas of the ff ame, H and OH are effectively equilibrated and that the chemi- luminescence is due to formation of excited Na* by reactions (iv) and (v), H+H+Na = H2+Na*, H+OH+Na = HzO+Na*,G . DIXON-LEWIS, M. M. SUTTON A N D A. WILLIAMS 207 then the result is obtained that Ipaa = Aku[H]2, where ku is an apparent second-order velocity constant for a given gas composition, and A is a proportionality constant for the mixture. In the chemiluminescence experiments, eqn. (1) may therefore be replaced after some rearrangement by eqn. (2) : The quantity ka/A may therefore be found for each flame by means of a straight line plot.In the flames where D2 or D20 were added to the flame gases, the chemical rates of formation of HD were found by application of a diffusion equation similar to eqn. (1). A kinetic analysisll-13 of the reactions leading to the formation and removal of HD then leads to eqn. (3) and (4) : for D2, (3) for D20, [d[HD]/dtIchem = k3[H][H2lo{ [mo- ""'> - [d[H20]/dtIchem, (4) W210 2[H12 2[H21 where k6 is the velocity constant of H+D2 exchange reaction. In order to convert the experimental values of [HD]/[H2] into H-atom concentrations it is, of course, necessary to know both the hydrogen and water concentration profiles. These also are measured by analysis of samples withdrawn from the flames. A feature of the use of both D2 and D20 as indicators is that the forward exchange reaction (vi), has an activation energy of only about 7 kcal mole-1, whereas the D20 reaction (iii) has an activation energy of about 25 kcal mole-1.Consequently, reaction (vi) reaches equilibrium in the flame much sooner than reaction (iii), and in fact reaction (vi) is not suitable for studying the burnt gases. On the other hand, the velocity constant k3 has not, so far as we are aware, previously been measured experimentally, though Fenimore and Jones 12 quote a value based on an extra- polation to higher temperatures of the rate constant measured by Avromenko and Lorentso 14 for the reaction (vii), H+D2 = HD+D, (Vi) OH+H2 = H20+H. (Vii) Accordingly, in this work, values of k3[H] were first determined from the D20 experiments.The use of these values in conjunction with eqn. (1) leads to values of the ratio ka/k3. Next, for one particular flame, D2 was added and the maximum H-atom concentration from the D2 experiments was assumed to coincide with the maximum chemiluminescent intensity. Thirdly, the position on the chemilumin- escence profile for this flame was found where, with suitable scaling, the curve of [k3[H]]2 against distance could be superimposed upon it. Hence the values of [HI and k3 corresponding to the D20 experiments were found and kg, the apparent second-order H-atom recombination rate constants. were obtained. The method depends on the equilibration of H and OH by reaction (vii) throughout the chemiluminescent region. This will not be strictly true and will tend to lead to low apparent values of the H-atom concentration in the D20 experiments, thus giving an upper limit to the value of k3 and the values for the recombination rate constants ka.208 HYDROGEN ATOM RECOMBINATION CALCULATION OF THIRD-ORDER VELOCITY CONSTANTS The rate of decay of H and OH in the burnt gases from a hydrogen-oxygen flame is given by -d([H] + [OH])/dt = kF[H]2[N2] +kF"[H12[Hz] +kF0[H]2[H2O] + kP[H] [OH][ N2] +kF[H] [OH] [&I + kFOIH][OH] [HzO], (5) here k?, etc., are the appropriate third-order rate constants.If H and OH may be regarded as equilibrated in the hot gases, eqn. (5) may be -d([H] + [OH])/dt = [H]2(ky[N2] +kF[H2] +ky0[H20] +k7 [H201 [Hzl written : [kP[N2] +kp[H2] +kp0[H2O]) = ka[H]', (6) where K7 is the known equilibrium constant of reaction (vii), and ka is the measured apparent second-order velocity constant.If a series of rich hydrogen+oxygen+nitrogen flames is studied such that the water vapour concentration in the burnt gas is constant, then "21 + [H2] = B, a constant, and ka may be expressed as a function of the concentrations by eqn. (7). ka = [H~](kp - ky}+ C/[H2] + D, where C = K7[H20](k~B+kpo~20]) and D = kFB+kp0[H20] +K7[H20](kP-k?). (7) Alteration of the water concentration may be effected without altering the flame temperature by incorporating steam in the gases entering the flame and adjusting the proportions of the other gases accordingly. By studying the variation of C and D with the water-vapour concentration in the burnt gas, values of all the third- order velocity constants may, therefore, be found.RESULTS CHEMILUMINESCENCE Fig. 1 shows the variation in intensity of chemiluminescence with distance in the burnt gas for a few typical flames studied. The measured intensities were corrected to intensities for a standard flame diameter by using constant total gas flows for all the flames and adjusting numerically for the known changes in diameter caused by changes in linear burning velocity. Perhaps the most striking feature of the curves is their near identity within the range of compositions studied. It must be concluded that such variations in overall recombination rate constant as do occur are largely balanced by the changes in flow velocity and diffusion coefficient associated with the changes in composition. The flame temperature used in this lower temperature study was 1072°K. Using this flame temperature, stable flames could be obtained with burnt gas compositions in the approximate range: H2, 2.5-17.5 %; N2, 70-87-5 %; H20, 10-20 %.The burning velocities, determined by photographing stroboscopically illuminated fine MgO particles entrained in the flame gases, varied between 7-5 and 10.5 cm sec-1 (linear velocities at 18"C/760 mm). These correspond to flow velocities Sb in the burnt gas of between about 28 and 35 cm sec-1. The diffusion coefficient of H-atoms, present as a trace component in a mixture of hydrogen, nitrogen and steam, was calculated to be consistent with some of the recent high-temperature diffusion data of Walker and Westenberg 15 and with the data of Wise 16 for H-atoms in hydrogen.G .DIXON-LEWIS, M. M. SUTTON AND A . WILLIAMS 209 -RECOMBINATION REGION - distance mm. IG. 1.-Intensity of chemiluminescence in the burnt gas of some slow burning hydrogen+oxygen+ nitrogen flames Open circles represent scaled D2O results ; line is intensity curve for same flame.210 HYDROGEN ATOM RECOMBINATION For the experimental burnt gas mixtures, the calculated diffusion coefficient for H- atoms varied between 11.1 and 11.9 cm2 sec-1 at 1072°K. Fig. 2 shows a typical graph of SbJGa-DHd/dy(JIG) against JIN,dy (cf. eqn. (2)). Due to small uncertainties about the position of the base line in the intensity curves, these plots were not always perfectly linear, but deviated from the linear law at the larger distances from the flame.In such cases a small baseline adjustment was made to give the best straight line in that distance range. The slope of the resulting line gives the appropriate value of ku/A. In these slow burning flames the diffusion term -DHd(JK/dy is of the same order of magnitude as the.con- vection term SbdGa even far out from the flame where the concentration gradients are comparatively small. Nearer the flame itself the diffusion flow of H-atoms may be two or more times greater than the convection flow. Table 1 summarizes those results which are regarded as reliable. Other com- positions gave lower values of ka/A, and this may well have been due to slight non- flatness of the flame. Such low values were observed particularly for the flames containing added water, and the quality of some of these was visibly not quite as high as for the flames without water addition.TABLE 1 .-RELATIVE APPARENT SECOND ORDER RECOMBINATION VELOCITY CONSTANTS IN THE BURNT GAS AT 1072°K flame moIe fractions +* 1 0.0274 2 0-0523 3 0.101 1 4 0-1432 5 0.1748 6 0.1060 xNZ 0.8776 0.8527 0.8039 0.761 8 0.7302 0.698 expt. calc. - xHzO kalA kalA' kaM' 0.095 0.1421 0.1348 0.1329 0.095 0.1341 0.1292 0.1277 0.095 0.1310 0- 1277 0.1278 0-095 0.1267 0.1255 0.1299 0-095 0.1 347 0.1347 0.1319 0.196 0.1325 0- 1272 The fifth column in table 1 gives values of ku/A derived directly from the experi- mental data. The sixth column shows the relative values ku/A' when corrected by means of a Stern-Volmer factor for differences in the quenching properties of the burnt gas mixtures. It is not easy to estimate values for this factor, and the correction applied here is slightly arbitrary in that it is assumed that the proportion of excited Na* which radiates is small compared with the proportion which is quenched by collision.It follows that the intensity of radiation bears a simple inverse ratio to the number of collisions suffered by Na* in any constant time interval. The mag- nitude of the correction is not large. In order to obtain information on the third-order velocity constants the values of ku/A' in table 1 were fitted to eqn. (7) by the method of least squares. The fit obtained using (kp-kT)rel = 0.777, Drel = 0.1 16 and Crel = 3.97 x 10-4. is shown by the values given in the last column of table 1.D2O AND Dz RESULTS The experiments in which D20 was added to the flame gases lead, by means of eqn. (4) to values of k3(H) at 1072"K, and then by further analysis to values of ku/k3. If k3 is known, this provides an independent method of measuring ku. Satisfactory measurements by this method have so far only been carried out on a single flameG. DIXON-LEWIS, M. M. SUTTON A N D A. WILLIAMS 21 1 (flame 3) and have allowed k3 to be estimated by comparison with the Dz. results described below. Since the chemiluminescent intensity is directly proportional to (k3[H])2 it should be possible to fit values of the latter quantity on to the IN^ curves. This is done in fig. 1. When D2 gas was the trace additive to flame 3, the method of analysis of the results outlined earlier leads to a maximum value of k6[H] of 1.0 x 104 sec-1 at 900°K.Using the recent value of k6 = 6.1 x 1011 cm3 mole-1 sec-1 at 1000°K obtained by Boato et aZ.,17 together with an activation energy of 6-65 kcal mole-1, a maximum H-atom concentration in the flame of 2 . 5 ~ 10-smolecm-3 at 900°K is obtained. In order to calibrate the chemiluminescence curves and in order to evaluate k3, this value was assumed to correspond with the maximum of the intensity curve. This leads in turn to values at 1072°K of k3 = 5-0 x 109 cm3 mole-1 sec-1, together with ku = 4.7 x 1010 cm3 mole-1 sec-1 for flame 3, A' = 3.7 x 1011, and ( k p - k p ) = 2-5 x 1015 cm6 mole-2 sec-1 and = 7 x 10-33 cm6 molecule-2 sec-1; D = 4.3 x 1010 cm3 mole-1 sec-1, C = 1.7 x 103 sec-1 for the flames without added water.DISCUSSION FURTHER ANALYSIS AND COMPARISON WITH OTHER DATA Although with the results at present available it is impossible to derive values for all six of the velocity constants involved in the two recombination reactions (i) and (ii), it is nevertheless possible to assess the order of magnitude of the various terms in the expressions for C and D of eqn. (7). First, the single result with water added initially suggests that the third-body effect of H20 is similar in magnitude to that for N2 (in the composition region of this result reaction (iii) accounts for only 3-4 % of ku). If it is assumed that the two effects are equal in both reactions (i) and (ii), i.e., that k p = kFO and k p = kpo, then the value for C leads to the result that k p = kpO = 9 x 1016cm6mole-2sec-1.Secondly, for the group of flames without initial added water C/p < D, where p is the molar density at 1072°K ; and if it is again assumed that the relative third-body effects in reactions (i) and (ii) are similar then it can be shown that the third term in the expression for D is negligible compared with the other two. The values k p = kpo = 3.8 x 1015 cm6 mole-2 sec-1 = 1 x 10-32 cm6 mole-2 sec-1 then result, together with k? = 6.3 x lO15cm6 mole-2 sec-1 = 1.7 x 10-32 cmsmole-2 sec-1. The earlier work on the recombination of H-atoms was carried out at room temperature using a discharge tube as the source and molecular hydrogen as the third body. Values obtained 1-5 for the third order velocity constant in the region of 300°K varied between 8 x 1015 and 2 x 1016 cm3 mole-1 sec-1.More recently, Sugden and co-workers have made a number of studies of the recombination of atoms and radicals in flame gases at temperatures of 1400°K upwards to the region of 2100°K. At 1650"K, the results of Bulewicz and Sugden 7 would give an apparent second-order velocity constant of about 4 x 1010 cm3 mole-1 sec-1 for the H-atom recombination, and if all the species present were assumed to have equal efficiencies as third bodies, this would correspond with a third-order constant of 5.4 x 101s cm6 mole-2 sec-1. Despite the higher temperature, this result is somewhat higher than that obtained in the present work.212 HYDROGEN A T 0 M RECOMBINATION MECHANISM OF RECOMBINATION Two mechanisms of atom recombination have been postulated.The first, which has recently been discussed by Pritchard 18 and others, assumes that the two atoms come together to form a molecule in the highest vibrational level. On collision with a third body, a molecule in a lower vibrational level is formed which does not dissociate. This may be represented by the pair of equations, (viii) and (ix) ; (viii) From this theory it is predicted that the efficiencies of the third bodies are given simply by the number of collisions of the H - - - H complex with M. For hydrogen atom recombination the rate constants should then be in the approximate ratio, The alternative approach is to use the type of scheme first suggested by Rabino- witch,lg and recently thoroughly investigated by Porter and Smith 20 for iodine- atom recombination.Here the third body acts as a chaperon, forming (in H-atom recombination) a complex HM which then either decomposes or reacts with a second H-atom : H+H+H - - - H, H---H+M+H;!+M. (ix) kH2 1 1 : kN2 : kyzO = 1 : 1 : 0.7. H+M+HM, 6 ) HM + H+H2+ M. (xi) By means of this mechanism it is possible to account for differences in the negative temperature coefficient of the reaction for different chaperons, and for widely different efficiencies of these chaperons, as occurs in the iodine-atom re- combination. In the H-atom recombination the probable error in the results is such that hydrogen may be between one and two times as efficient a third body as nitrogen. Within the limitations of the experiments the recombination constants for H2, N2 and H2O otherwise appear not to be vastly different from each other and they could be con- sistent with either theory. 1 Amdur and Robinson, J. Amer. Chem. SOC., 1933,55, 1395. 2 Amdur, J. Amer. Chem. SOC., 1938,60,2347. 3 Smallwood, J. Amer. Chem. SOC., 1934, 56, 1542. 4 Farkas and Sachsse, 2. ghysik. Chem. B, 1934,27, 11 1. 5 Steiner, Trans. Furuduy SOC., 1935, 31, 623. 6 Bulewicz, James and Sugden, Proc. Roy. SOC. A, 1956,235, 89. 7 Bulewicz and Sugden, Trans. Furuduy SOC., 1958,54, 1855. 8 Padley and Sugden, Proc. Roy. SOC. A , 1958,248,248. 9 Dixon-Lewis and Williams, Combustion and Flame, 1960, 4, 383. 10 Dixon-Lewis and Isles, Trans. Faruday SOC., 1957, 53, 193. 11 Fenimore and Jones, J. Physic, Chem., 1959, 63, 1154. 12 Fenimore and Jones, J. Physic. Chem., 1958, 62, 693. 1 3 Dixon-Lewis and Williams, 5th Int. Symp. Free Radicals, 1961. 14 Avromenko and Lorentso, Zhur. Fiz. Chim., 1950,24, 207. 15 Walker and Westenberg, J. Chem. Physics, 1960, 32, 436. 16 Wise, J. Chem. Physics, 1961, 34, 2139. 17 Boato, Careri, Cimino, Molinari and Volpi, J. Chem. Physics, 1956, 24, 783. 18 Pritchard, J. Chem. Physics, 1961, 65, 504. 19 Rabinowitch, Trans. Furuduy SOC., 1937 33, 283. 20 Porter and Smith, Proc. Roy. SOC. A, 1961,261, 28.

ISSN:0366-9033    

DOI:10.1039/DF9623300205

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Electronic Excitation of Metallic Hydroxides MOH in Hydrogen Flame Gases R. W. REID AND T. M. SUGDEN Dept. of Physical Chemistry, University of Cambridge Received 6th February, 1962 A brief review of the properties of the burnt gases of fuel-rich hydrogen+ oxygen+ nitrogen flames is given, with special reference to the excess amounts of atomic hydrogen and hydroxyl radicals. It is shown how these may influence the distribution of a metallic additive between free atoms M and the compounds MOH, MH and MO. The possible mechanisms for production of electronically excited atoms M* and molecules NOH* are discussed, and a general theoretical expression worked out for the latter case. Experiments in which the metal is copper, manganese, or one of the alkaline earths calcium, strontium or barium are described, in which it is shown that in the first two cases the most likely method of production of MOH* is by M+ OH+N2 -+MOH* +N2, while for alkaline earths, MO+H+H20 +MOH*+H2O is more probable.The principal third bodies available are H20, N2 and H2. The removal of MOH* would appear to be most effectively accomplished in all cases by MOH* + N2 +M+ OH+Nz, together with a contribution from MOH*+H-+M+H20, or MO+Hz. These processes are discussed. 1. THE STATE OF HYDROGEN FLAME GASES When a fuel-rich mixture of hydrogen, oxygen and nitrogen is burnt at a Mkker or sinter-type of burner at atmospheric pressure, there is an almost flat, very thin (ca. 0.1 mm) reaction zone in which the bulk of the branched chain oxidation takes place : (1.1) I H+ 02+0H+O 0 + H2-+OH+ H OH+H2+H20+H.There is a vast proliferation of free radicals, and in the absence of retaining walls these begin to recombine by processes H + H +X+H2 +X, (1.2) H + OH + X+H20 +X, (1.3) which release a great deal of heat. Xis any suitable third body. Within a fraction of a mm from the reaction zone the temperature has risen to within 100°C of its final value for thermal equilibrium of the burnt gas, and the bimolecular reactions (l.l), with their reverse reactions, have become rapid enough to be balanced at all points in the flame gases. In particular, the reaction H + H2O + H2 + OH ; equil. const. KO (1.4) 213214 ELECTRONIC EXCITATION OF MOH is balanced, and the concentrations [HI and [OH] are related to each other by PHI CWJ =KO- CHI CH23 * Water and molecular hydrogen are major constituents of the fuel-rich burnt gases.The termolecular reactions (1 -2, (1 -3) proceed towards final equilibrium against this background of balanced bimolecular reactions. They are relatively slow, and their degree of advancement can be followed over several cm downstream in the gases. In these gases, 1 cm is roughly equivalent to 10-3 sec. Variation of the original composition gives final temperatures ranging from 1500 to 2500"K, as well as the possibility of isothermal changes of burnt gas com- position, with corresponding variation [OH]/[H]. The amounts of atomic hydrogen and hydroxyl emerging from the reaction zone constitute 1-5 % of the total gases, and while with the hottest flames these are close to the final equilibrium values, with consequent little further recombination, for the colder flames the equilibrium amounts are exceeded by several orders of magnitude.This gives rise to a number of interest- ing disequilibrium effects, some of which are discussed below. The information set out in this section has largely been obtained by Sugden and collaborators,l-5 on the basis of measurements of [HI by methods of flame photometry. 2. THE DISTRIBUTION OF SOME METALLIC ADDITIVES AND THEIR COMPOUNDS I N FLAMES If a metal M is added in small amount (1 part in 106 or less) to the flame gases, it may interact with the gases to form various compounds, in particular the hydrox- ide MOH, the oxide MO, and the hydride MH. The proportion of electronically excited forms is a few orders of magnitude below that of the ground state forms, and will be ignored in this section.The hydroxides are formed predominantly by a rapid reversible bimolecular reaction 1 which is balanced in the burnt gases. The magnitude of this hydroxide effect may be assessed roughly as follows. The hydroxides of lithium and caesium, with dis- sociation energies, to give an atom and a hydroxyl radical, of 102 and 92 kcal mole-1 respectively have [Li]/[LiOH]- 1 : 10 and [Cs]/[CsOH]- 1 : 1 in the burnt gases. Thus, 10 kcal mole-1 in the heat of reaction gives an approximate factor of 10 in the distribution. For copper, manganese, calcium, strontium and barium, the elements to be discussed in this paper, although the dissociation energies of the hyd- roxides are not known accurately, comparison with data for the halides given by Cottrell6 and Gaydon 7 indicates that they will not greatly exceed 60 kcal mole-1.The ratio [M]/[MOH] will therefore be in the region of 1 : 0.01. A similar figure holds for hydrides. M+H20+ MOH +H (2.1) For the oxides, the reactions M + H20+ MO + H2 M+ OH+ MO + H will be fast enough to set up the [M]/[MO] balance, which will be the same for both reactions because of the operation of the condition (1.5). Observations on the alka- line earths 8 . 9 show that the oxides are so stable that [M]/[MO]- 1 : 100. On the other hand, for copper,lO [M]/[MO] is probably not far from 1 : 0.1, while for mangan- ese,ll it is about 1 : 1. (2.2) (2.3)R . W. REID A N D T. M. SUGDEN 21 5 If a hydroxide (or any other compound) is sufficiently weakly bonded, then an alternative to reactions of type (2.1) must be considered; The concentration factor [X]/[H] is > 1, and may be large enough to offset the acti- vation of the back reaction of (2.4,) if the bond M-OH is very weak.Reaction (2.4) will give an entirely different distribution [M]/[MOH] from (2.1) since the excess radicals are on opposite sides of the chemical equation in the two cases. It has been believed 11-13 that reaction (2.4) did actually predominate over reaction (2.1) for CuOH and MnOH, inter alia, on the basis of experiments on the emission intensities from MOH* (* denotes electronic excitation). This was sur- prising, since it required that the switch from predominance of (2.1) to that of (2.2) took place at dissociation energies not far from 70 kcal/mole-l, which is improbably high.It will be shown in this paper that this conclusion was mistaken, and that the formation of MOH* occurs mainly by reactions of the type rather than by reactions involving unexcited MOH, so that observations of emission from MOH* have little or nothing to do with the amount of MOH. M+OH+X+MOH+X. (2.4) M + OH+X+MOH* +X (2.5) 3. THE FORMATION AND DESTRUCTION OF ELECTRONICALLY EXCITED ATOMS I N FLAMES It is useful to review briefly the excitation of atoms in flame gases before con- sidering that of simple molecules. Padley and Sugden 149 15 have shown that the two principal types of electronic excitation of metal atoms M in hydrogen flames are: (i) collisional activation M+X+M* +X (3.1) (ii) chemiluminescent excitation M + H+H+M* +H2 M + H + OH+M* + H20 Reaction (3.1) and its inverse would rapidly set up thermal excitation in the flame gases, giving [M*]/[M] = exp (- E/RT), where E is the excitation energy for M+M*, were it not for the intervention of reactions of type (ii).These reactions ((3.2) and (3.3)) produce anomalously high excitation because [HI and [OH] are in general well above their equilibrium values. The relative importance of these two types of reaction have been shown by Padley and Sugden for various temperatures and excitation energies. A useful quantitative measure can be obtained on a rough basis as follows ; an upper limit of about 10-31 cm6 sec-1 can be put on the rate constants of the overall processes (3.2) and (3.3).14 They give a contribution to the excitation of the sodium D-lines ( E = 48.5 kcal mole-1) about equal to that of ordinary collisional activation when T = 2000°K and [HI (and [OH]) are not far from 1017 cm-3 (concentrations are in terms of mole- cules throughout).[XI, the total molecular concentration, is - 3 x 1018 cm-3 in flame gases, and hence for equal rates of activation one obtains Putting the rate constant for reaction (3.1) in the form k3.1 = A exp (-E/RT), then with E = 48.5 kcal mole-1, A becomes approximately 10-10 cm3 sec-1, which is a very reasonable pre-exponential factor for a collisional activation process of small molecules. (3.3) k3.1 = x 1034)/(3 x lo1*) cm3 sec-l = 3 x cm3 sec-l.21 6 ELECTRONIC EXCITATION OF MOH A third type of process can be visualised: (iia) exchange with excited molecular species I MOH* +H+M* +H20 MH*+OH+M*+H20 MH* +H+M* +H2 MO* + H+M* + OH MO* +H2+M* +H20.(3.5) It will be shown below that the first three of these reactions are contingent on the primary production of MOH* or MH* by such reactions as M + OH +X+MOH* +X M + H +X+MH* + X The net effect is to give an overall reaction not distinguishable from type (ii), to whose measured rate constants they will contribute. The reactions (3.5) rely on the previous excitation of MO to MO*. This may be itself thermal (type (i)) or chemiluminescent (type (ii)). It may readily be seen, therefore, that because of the multiplicity of possible reactions, observations will not necessarily lead to unambiguous conclusions about mechanism, although re- actions which differ basically in their dependence on the concentrations of atomic hydrogen and hydroxyl should be resolvable.(3.6) 4. THE FORMATION AND DESTRUCTION OF ELECTRONICALLY EXCITED HYDROXIDES MOH Clearly the ground state species MOH is open to electronic excitation by both types of process available to atoms, called types (i) and (ii) in the preceding section. In addition, the following new types may be envisaged. (iii) direct formation M + OH+X-,MOH* +X MO + H + X-,MOH* +X (iv) exchange with other excited species A rough prediction of relative contributions may be obtained for the first 2 elements to be studied here-copper and manganese, for which $ 2 shows one may fairly reasonably put [M]:[MOH] : [MO] = 1 : 0.01 : 1. Bimolecular rate constants may be taken as 10-10 cm3 sec-1 x exp (- E/RT), and termolecular ones as 10-31 cm6 sec-1.Concentrations of radicals may be taken as lO17cm-3 and of general third bodies as 1018 cm-3. A figure of 10-6 provides an upper limit for the exponential excitation factor, and observation shows that [M*] N 10-6[M]. Then, for the various types, relative rates may be estimated: M*+H20+MOH*+H (9 MOH+X; 10-2~ 10-lox 1 0 - 6 ~ 1018 = 100, (ii) MOH+H+H; 1 0 - 2 ~ 10-31 x 1034 = 101, (iii) M+OH+X; 1 x 10-31 x 1017 x 1018 = 104, (W M*+H20 ;10-6~ 10-lox 1018 = 102. Despite the obvious uncertainty in choice of parameters, there is no doubt that type (iii) processes deserve serious attention. Their effects have been estimatedR. W. REID AND T. M. SUGDEN 21 7 on the whole ungenerously in making the above estimates.For the alkaline earths they will be expected to be important a fortiori because of the excess of MO and the possibility of MO +H+X+MOH* +X. The following reaction scheme will therefore be set up to obtain an expression for MOH* M+OH+X+MOH*+X kl (4.1) MOH+X+MOH"+X k2 MO +H+X+MOH* +X kj, M*+H20+MOH*+H k4 (4.4) X may at this stage be a molecule of H20, Ha, or N2, or a radical H or OH. The general form, e.g., klx will be used for the three molecules, however, while the specific forms k l ~ , k l o ~ will be used for the two radicals in writing rate expressions. The corresponding reverse reactions, by which MOH* is removed, will be written k-lx, etc. Excited metals M* may reasonably be ascribed under the conditions used to chemiluminescent excitation only : M+H+H+M*+H2 k5 k6.M + H+ OH+M* + H20 The following equilibria for ground state species will also be required. H+H,O+OH+H, KO The contribution of emission to removal of MOH* will be negligible beside all the other effects which can occur. A steady-state treatment for MOH* now leads to an expression (4.10) The values of the various parameters in this basic equation may now be written as collisional activation by molecules collisional activation by radicals direct formation with molecules as third bodies direct formation with radicals as third bodies formation by exchange of excited at om with water molecules decomposition by molecules deactivation by molecules decomposition by radicals deactivation by radicals decomposition by exchange re- action with radicals21 8 ELECTRONIC EXCITATION OF MOH It will be sufficient to write bl as c k - ~ [ X ] .The object of the work is now to deter- mine the dependence of the emitted intensity of radiation from MOH" on the con- centration of atomic hydrogen at various points in a wide variety of flames, and hence to attempt as completean interpretation of equation (4.10) as possible. Type($ reactions have been ignored in the mechanism since these appear in a3, which will be dominated by type (iii) reactions. Similar relative roles as in atoms are expected of types (i) and (ii). It will be seen that the assumptions made here are later justified by the form of the results. 5. EXPERIMENTAL The basic experimental arrangement has been described many times (see, e.g., ref.(l), (15)). Metered mixtures of cylinder hydrogen, oxygen and nitrogen are burnt at a MCker type of burner constructed of a bundle of fine stainless steel tubes as shown in fig. 1. The main flame supply is fed with fine sprays of aqueous solutions of salt solutions of metals under study from an atomizer operated by part of the nitrogen supply. The inner flame was in this case surrounded by two annular shield flames, of similar composition, but without additives, to reduce the effects of indrawn air over the first two or three cm in the burnt gas. The burner was water-cooled. A FIG. 1.-Cross-section of streamline flow Meker burner. A, main gas supply; B, shield flame gas supply; C, outer shield gas supply; D, water-cooling. The inner flame is about 1 cm in in diameter.The temperatures of the flames used were measured by the standard sodium D-line reversal method. All the flames were hydrogen-rich, so that the bulk of the burnt gases was made up of water vapour, molecular hydrogen, and molecular nitrogen, The amounts of these for the various flames used are depicted in fig. 2. This is plotted so that the flames are grouped into sets, each set being characterized by a constant m2]/[02] ratio in the unburnt gases, and being made up of four flames with [H2]/[02] ranging from 3-0 to 4-5 in the unburnt gases, in steps of 0.5. It will be seen that the plots of fig. 2 have character- istic appearances for the different constituents, and it is often possible to correlate other observations made on the flames with them by means of these patterns.Thus, H20 is a smooth function of temperature, while both H2 and N2 show (opposite) isothermal vari- ations. Temperatures ranged from 1700 to 2300°K. Light from particular regions of the visible or ultra-violet were selected either by a Hilger constant deviation glass spectrometer, or by a Hilger medium quartz spectrometer. The light entering the spectrometer was previously chopped by a 256clsec sector disc, which also provided synchronization for a phase-sensitive detector and amplifier to which the signal from a 1P 28 photomultiplier, which had received the light selected from the spectrometer, was passed. Relative intensities were obtained directly as pointer readings. The visible bands of CUOH,~~ CaOH, SrOH and BaOH 16 were investigated, as were the uItra-violet bands of MnOH.11 The CuH method was used for atomic hydrogen, calib- rated by the Li/Na method (see next section).R .W. REID AND T. M. SUGDEN -0.2 - 0 6 219 C - * = - \- 4 5u -7 3 - I I I 6. RESULTS THE CONCENTRATIONS OF ATOMIC HYDROGEN AND HYDROXYL An absolute measure of [HI was obtained in some flames by use of the Na/Li flame- photometric method.1 The LiOH molecule is so much more stable than that of NaOH that, while sodium gives negligible compound formation in flame gases, lithium is largely converted into hydroxide by the balanced reaction Li + H20 +LiOH + H. Thus the emission from the lithium resonance line is lower than would be expected from comparison with the sodium-D lines, and hence [LiOH]/[Li] can be measured.[H20] is a b I / T ("~-1 x 104) FIG. 2.-Composition of burnt flame gases for the major constituents H20 (a), H2 (b), N2 (c) as functions of temperature. The flames are grouped into sets which become clearly visible in (6) and (c) ; in each set, [N2]/[02] (unburnt) takes the value given by the number on the curve ; within each set [H2]/[02] (unburnt) takes the successive values 4.5, 4.0, 3.5 and 3.0 towards increasing temperatures. known, and thus [H] can be obtained given a knowledge of the equilibrium constant of the above reaction. This has been measured by Phillips4 using high temperature flames in which [HI has come to its equilibrium value for the measured temperature. The method cannot be used for flames in which either element shows chemiluminescence, since it relies on thermal excitation.However, Bulewicz and Sugdenlo have shown empirically that addition of copper to a flame produces, inter alia, strong emission of the (0,O) band of CuH at 4280A with intensity proportional to [H/. A test of this in the present work is shown in fig. 3a for various points in a hot flame, the results being very satisfactory. Fig. 3b shows the recombination of atomic hydrogen as a bimolecular220 ELECTRONIC EXCITATION OF MOH process (in radicals) as estimated by I c u ~ for four flames. Further comparison with the Li/Na method shows the factor k’ relating I C ~ H to [HI in is sensibly independent of temperature. Thus, I C ~ H can be used as a reliable measure of relative [HI, and can be calibrated against the absolute method.ICuH = k’[H1 (6.1) r a I b 5 10 distance (mm) k u H FIG. 3 . 4 4 Intensity of CuH (0,O) band against [HI from the Li]Na method for a typical hot flame with T = 2180°K and [H2]:[021:[N21 (unburnt)= 4: 1 : 3. FIG. 3 4 b ) IC~H against distance from reaction zone for four flames with [N2]/[02] = 4 : 1, and [Hz]/[O2] as indicated on the separate plots. FIG. 3 . 4 ~ ) IC~OH against [HI (Li/Na method) for the flame of fig. 3a. FIG. 3.-(d) Points 0, intensity of sodium continuum against I c u ~ ; points 0, intensity of Icuo~ against I c ~ H . [H2] : [02] : ”21 = 4.5 : 1 : 3. James and Sugden 2 have shown that the weak continuum emitted in the visible when sodium is added to a flame has an intensity proportional to [OH], and suggest that it may arise through a radiative recombination Na+ OH+NaOH+hv.Fig. 3d shows a plot of this against I c u ~ for a typical flame, and is a straight line as required by operation of the condition (1.5). The green band of CuOH, however, also shown in fig. 3d gives a marked curve. Another example of this is depicted in fig. 3c. THE DEPENDENCE OF IMOH ON [HI Fig. 4a shows curved plots of Icuo~ against I C ~ H (Le. relative [HI) for four flames. Plot- ting the data as Icu~/Icuo~ against I c u ~ gives quite good straight lines, as shown in fig. 4b.R. W . REID AND T. M. SUGDEN 221 Hence, one may write -- ICuH l+plCuH -- ICuOH 4 or, using the relation (6.1), and defining a constant k" by ICuOH = k"[CuOH*], we have ~ W H I [CuOH*] = k"(l + k'p[H])' FIG. 4.4~2) I C ~ O H against Z C ~ H for four flames with "Zl/[O21 = 4 : 1 and [H21/1021 as indicated on the plots.FIG. 4 . 4 b ) ~ H / ~ C ~ O H against I C ~ H for the same flames as 4(a). a 6 0 X 2 +u $0 2 0 20 40 6 0 k u H I I 2 0 40 6 0 ICUH The parameters p and q will be constant for any one flame. The same type of result was obtained for the emission from MnOH*, CaOH*, SrOH* and BaOH*. Results for barium are shown in fig. 5. The curvature of the plot of IMOH against I C ~ H is very marked for the alkaline earths. 7. DISCUSSION THE EMISSION FROM COPPER A N D MANGANESE HYDROXIDES The theoretical dependence of [MOH*]/[M] on [HI is given by the expression obtained in $4, where the a and b depend directly on certain rate constants for production and removal of MOH* respectively. For all five elements used here [MI is independent222 ELECTRONIC EXCITATION OF MOH of distance from the burner, and for copper and manganese makes up the great bulk of the additive.Comparison with eqn. (6.4) established experimentally, shows that the only significant terms in (7.1) are those in a3, bl and b2. This means that collisional activ- ation is ruled out for formation of MOH*, and that free radicals do not act as effective third bodies in its production from M and OH, or from MO and H. ICUOH ICUH FIG. 5 . 4 2 ) IB~OH against 1 c u ~ for four flames with [Nz]/[02] = 4 : 1 and [H2]/[02] as indicated on the plots. FIG. 5 . 4 b ) I C ~ H ~ I B ~ ~ H against I C ~ H for the same flames as 5(4. Equating coefficients of (6.4) and (7.1), a3 k'q b, k'p b,CMI=kK, i;;:=k"' Linear plots such as those of fig. 4b will have slopes of slope = PI4 = b,la,CMI, (7.3) and intercepts on the ordinate axis of with The factors k', k" do not depend on temperature or composition, and hence a study of the slopes and intercepts for a wide variety of flames whould throw some light on the properties of a3, bl and b2.intercept = l / q = k'b,/k"a,[M], (7-41 (interceptlslope) = k'b,/k"b,. (7.5)R. W. REID AND T. M. SUGDEN 223 Fig. 6a shows the intercepts (7.4) for CuOH* from 16 flames, grouped into sets as de- scribed in the experimental section. Inserting the detailed values of the coefficients derived in B 4, The numerator represents destruction of CuOH* by collision with molecules X (as opposed to radicals) while the denominator of the bracket represents the formation of CuOH* at ternarycollisions of Cu, OH and X (first term), and CuO, H and X (second term). Correc- tion by the factor [H2]/[H20] (see fig.2) gives fig. 6c, which is a reasonable straight line, allowing for experimental error. b 1 4.5 5.0 5.5 I / T (oK-~ x 104) FIG. 6 . 4 4 LogI(intercept of eqn. (6.2)) against 1/T for various sets of flames. FIG. 6 . 4 3 ) log ([H2]/&[H20] intercept) against 1/T. FIG. 6 . 4 ~ ) log ([H20] intercept/[H2]) against 1/T. If ~ k l x [ X ] & > ~ k 3 x [ X ] & ~ - ~ , then the temperature dependence of fig. 6c will be that of ~ k - x ~ ] / ~ k l ~ K ] K o . Since fig. 6c is a smooth function of temperature [XI must cancel, and since KO is associated with AH = 15 kcal, and the observed slope corresponds with 9 1 5 kcal, the net heat effect associated with k-x/klx is 6 1 5 kcal.If CuOH* is removed by dissociation rather than deactivation this means that the heat of dissociation into Cu and OH is 6 3 5 kcal. On the other hand, if deactivation predominates, with a very small temperature dependence, the rate constant klx is associated with a "negative energy of activation " of about 6 kcal, a reasonable value for a termolecular reaction. If ~ k 3 X ~ ] & O > ~ k l X [ X ] & ) , then CuOH* is made mainly from CuO+ H. The value of DcUo of 113 kcal mole-1, quoted by Cottrell6 and Gaydon 7 associates KcUo with AH = 4 kcal, and leads to a net heat effect for k-x/k3x of 11 &5 kcal. This implies either a large224 ELECTRONIC EXCITATION OF MOH positive temperature coefficient for the ternary rate constant k 3 ~ or a negative temperature coefficient for destruction of CuOH*, both of which are very improbable.In fact, there is unlikely to be more than 10 % of CuO as against 90 % of Cu,lO which requires a dis- sociation energy in the 90-100kcalmole-1 range. Such a value does not lead to the anomalies that derive from the 113 kcal mole-1 value. It does, however, introduce an in- soluble ambiguity as to whether CuOH* is formed from &+OH, or from CuO+H. The observed smaller proportion of oxide tends to favour the former. Eqn. (7.5) gives n B - I/) N c( 5 intercept Ck-xX k-H + k-OHKO[H20]/[H2 J i I I b 0 (7.7) and is plotted for flames with copper in fig. 7a. The general pattern of fig. 7a resembles that of N2 in fig.2 in the relative spacing of sets. This is evidence that N2 is the most effec- tive third body in destruction of CuOH*, and correction for it is shown in fig. 7b. H20 or H2 as third bodies would have given different patterns. The patterns for [H2] and [H20] shown in fig. 2 also indicate that the k-OH term in the denominator of eqn. (7.7) is negligible. (i) the principal molecule concerned in removing CuOH* is N2, either by dissociation into Cu+OH, or CuO+H, or by collisional deactivation. This is perhaps sur- prising since a higher efficiency might have been expected from the triatomic species H20 ; (ii) the principal radical concerned in removing CuOH* is H, presumably by dissoci- ation into Cu+OH, or CuO+H. The latter processes will have negligible energy of activation, so that the whole of the temperature coefficient in fig.7b devolves on processes of type (i). It amounts to a heat effect of 13 f5 kcal for the activation energy of k-x, which would strongly suggest dis- sociation rather than deactivation. It has, therefore, been demonstrated that :R. W. REID AND T. M. SUGDEN 225 The results for manganese closely parallel those for copper. Again, it is not possible to distinguish between Mn+OH and MnO+H as starting points for making MnOH*, and as its dissociation products. THE EMISSION FROM ALKALINE EARTH HYDROXIDES For the alkaline earths, [MO]> [MI, and it is better to write the theoretical expression as Again, the experiments show that only a3, bl and b2 are significant, as shown by fig. 5. The expressions for the slopes and intercepts of lines like those of fig.5b become : (7.10) [MOI is constant since the great bulk of the metal is present in this form. A plot of log (intercept) against 1fTis shown for calcium in fig. 8. Strontium and barium gave similar I/T(OK-~X 104) FIG. 8.-Log (intercept) from eqn. (6.2) but with CaOH emission instead of CuOH, against 1/T. results. There is a generally high positive slope with a separation of sets most closely re- sembling that for m2] in fig. 2. The slopes (eqn. (7.10)) present a smooth plot against l/T, as shown in fig. 9. Since it is known that [MOI exceeds [MI by two orders of mag- nitude, then one might expect reasonably that the k3x term in the denominators of eqn. (7.9) and (7.10) would be large compared with the klx term, since the former represents formation of CaOH* from CaO+H, and the latter (klx) its formation from Ca+OH.Since fig. 9 shows no marked composition effect, the term in k - 0 ~ must be negligible, and eqn. (7.10) reduces to slope = k-,/[MO]k3x[X). H (7.11)226 ELECTRONIC EXCITATION OF MOH Since fig. 9 has no composition effect, X may be taken to be H20, by comparison with fig. 2. Thus ( k - ~ / k 3 ~ ~ 0 ) has a temperature coefficient associated with a heat change of 25 A5 kcal, and since this can hardly be associated with reactions such as CaOH* + H+CaO+ H2 by way of positive energy of activation, then the reaction CaO+H+H2O+CaOH*+H20 acquires the very large " negative energy of activation " of 25 f5 kcal. This seems improbably large. I / T ( " ~ - 1 x 104) FIG.9.-Log (slope) for CaOH emission against 1/T. If one assumes that despite the large proportion of oxide the klx terms predominate slope = ~ - ~ ~ ~ o l r ~ ~ l ~ l ~ , o ~ ~ 2 0 l K O . (7.12) Reid 9 finds Dcao to be 127 kcal mole-1, which results in a contribution of 24 kcal from Kcao/Ko to the observed heat change of 25 f5 kcal. The temperature dependence of k - ~ / k l ~ ~ ~ then becomes very small, which is more reasonable. in eqn. (7.9) and (7.10), then (7.10) becomes Returning to the intercept eqn. (7.9), then, if the k 3 ~ term >klx term, we have k' k-x[X] k"[MO] k3JX]' intercept = while if the converse is true, (7.13) (7.14) X in the denominator of both expressions being required to be H20, from the observations on the slopes, while fig. 8 now shows that X in the numerator must be N2.For eqn. (7.13), the high positive slope of fig. 8, taken with -25 kcal for the energy of activation of k 3 ~ ~ 0 requires that k - ~ ~ (the rate constant for destruction of CaOH* by N2) have an activaton energy of 22 kcal, i.e., that dissociation must predominate over deactivation, and that the dissociation energy of CaOH (into Ca+ OH, or CaO+ H) be 22 kcal mole-1. If eqn. (7.14) applies, the same conclusion is reached concerning k - ~ ~ . The choice lies between (i) k3 termskl term, CaO+H+H20+CaOH*+H20; E, = -25 kcal, CaOH*+N2+Ca+OH+N2; E, = 22 kcal, and (ii) kl termSk3 term, Ca+ OH+H20+CaOH*+ H20 ; E, = 0 kcal, CaOH*+N2+CaO+H+N2; E, = 22 kcal,R. W. REID AND T. M. SUGDEN 227 since it is difficult to see how the efficiencies of H20 and N2 can change places for the two directions of a reversible reaction. The second of these possibilities is clearly untenable, since it requires that the dissociation energy of CaOH* into Ca+OH be about 47 kcal mole-1, which would require the cor- responding dissociation energy of CaOH to be about 100 kcal mole-1, which it is most clearly not.It is also very unlikely since, if it were true, the rate constant kl would have to be large enough to offset a concentration factor of about 103 to dominate the k3 reaction. CONCLUSION For all five metals studied the conclusion has been reached that the N2 molecule is a good deal more efficient than H20 or H2 in destroying the electronically excited hydroxide MOH*. It would appear to do this by dissociation into M+OH rather than into MO+H, or by simple deactivation. The reverse process appears to be true for the formation of CuOH* and MnOH*, both copper and manganese being elements which exist largely as free atoms in the flames. On the other hand, the molecules CaOH*, SrOH* and BaOH* all appear to be formed from MO+H, with H20 as the most efficient third body. These metals exist principally as the oxide MO in the flames. All the excited hydroxides are readily attacked by atomic hydrogen at simple bimolecular impacts. One of us (R. W. R.) is grateful to the Department of Scientific and Industrial Research for a Research Studentship. We wish to thank the Royal Society for a Grant-in-Aid for apparatus. 1 Bulewicz, James and Sugden, Proc. Roy. SOC. A , 1956, 235, 89. 2 James and Sugden, Proc. Roy. SOC. A, 1958,248,238. 3 Bulewicz, Phillips and Sugden, Truns. Furuduy Soc., 1961, 57, 921. 4 Phillips, L. F., Ph.D. Diss. (Cambridge, 1960). 5 Bulewicz and Sugden, Trans. Furuday SOC., 1958,54, 1855. 6 Cottrell, The Strength of ChemicaZ Bonds (Butterworths Sci. Publ., London, 1958), 2nd ed. 7 Gaydon, Dissociation Energies (Chapman and Hall, London, 1959), 2nd ed. 8 James, C . G., Ph.D. Diss. (Cambridge, 1954). 9 Reid, R. W., Ph.D. Diss. (Cambridge, 1961). 10 Bulewicz and Sugden, Truns. Faraday Soc., 1956, 52, 1475. 11 Padley and Sugden, Trans. Furaday Soc., 1959, 55, 2054. 12 Sugden, Truns. Furuday SOC., 1956,52, 1465. 13 Bulewicz and Sugden, Truns. Furuduy SOC., 1956, 52, 1481. 14 Padley and Sugden, Proc. Roy. Sac. A, 1958,248,248. 15 Padley and Sugden, 7th In?. Symp. Combustion (Oxford, 1958) (Butterworths Sci. Publ. 16 James and Sugden, Nature, 1955, 175, 333. London, 1959), p. 247.

ISSN:0366-9033    

DOI:10.1039/DF9623300213

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Excitation of the and Ogawa Bands of Nitric Oxide in the Association of Atomic Nitrogen and Oxygen BY ROBERT A. YOUNG AND ROBERT L. SHARPLESS Stanford Research Institute Menlo Park California Received 10th March 1962 In the recombination of atomic nitrogen and oxygen the excitation of the NO p y 6 and Ogawa bands have been studied as a function of (a) pressure (b) the addition of He A C02 and N20, and (c) atomic oxygen concentration. Atomic nitrogen was generated by flowing molecular nitrogen through a microwave discharge. Subsequent addition of NO reacted rapidly with atomic nitrogen to produce atomic oxygen. The following facts were established : (1) (a) The intensity of the P(u’ = 0) bands relative to the S(0,O) band depends linearly on the molecular nitrogen pressure and approaches zero as the pressure decreases.(b) The relative in-tensities of the y(u’ = 0) bands are a similar function of pressure but with a non-zero intercept. (c) The relative intensities of the Ogawa bands are independent of pressure. (d) The S(0,O) band intensity is independent of pressure in the 0-2 to 10 mm Hg region. (2) The relative intensities of the p y 6 bands are independent of the atomic oxygen con-centration. (3) (a) The slopes of the relative intensities against pressure curves of the p(v’ = 0) and y(u’ = 0) bands are generally functions of the rare gas (He A) fractional concentration. (b) The intercepts of the intensities against pressure curves of the y(v‘ = 0) band are independent of the rare-gas concentration. (c) The /? bands from levels with v’ >O depend upon pressure differently than for v‘ = 0 i.e.the relative intensity of the #?(3,3) band is proportional to p2/3 ; the constant of propor-tionality and the exponent of p are functions of the rare gas concentration. (d) The S(0,O) band intensity is independent of the fractional concentration of rare gases. (4) (a) The #? bands and y bands are quenched by N20 following the Stern-Volmer formula ( l o / l = 1 + Cp(N20)). (b) The quenching constant C associated with the #? bands when quenched with N20 is dependent on the total pressure while that associated with the y bands is not dependent on pressure. (c) The S(u’ = 0) bands are not quenched by N20. (5) (a) The y bands are quenched by C 0 2 following the Stern-Volmer formula. (b) The quench-ing constant C associated with the y bands when quenched with C02 is independent of the total pressure.(d) The S(u’ = 0) bands are not quenched by C02. The C2111v*=o state is excited through the a4Il state by a “ pre-association ” mechanism. The A2Z+vt=o is excited from the C211v/=o state by cascade radiation and collision processes which result in the vibrational excita-tion of N2 the b4rI state is excited by spontaneous transitions from the a4II state and the B2IIvt=o is excited by collision-induced transitions from the a4II state. The higher vibration levels of both the A2Z+ and B2Il are populated by collision-induced transitions from the 2Z+ b4Z- and a411 states in which the collision partner either abstracts energy (-1 eV) from or changes the internuclear separation (-10 %) of NO.(c) Relatively little quenching of the p bands is observed with C02. The following conclusions are obtained from a discussion of these facts. The spectra emitted following the association of atomic nitrogen with either another nitrogen atom or an oxygen atom is unusual. The levels of N2 or NO from which this radiation arises do not dissociate into exclusively ground-state atoms and so could not be formed by such atoms in a simple association reaction ; some process must transfer the molecules from the state in which it is originally formed into the levels from which radiation occurs. Thus the electronic structure of NO implies that an excited-state intermediary is necessary in the excitation of the observed radiation. By adding a compound which 22 R.A . YOUNG AND R . L. SHARPLESS 229 does not react with the atomic species but may de-activate excited intermediary metastable molecules of NO their role in the excitation process may be investigated. The mechanism by which a molecule in an intermediary state makes the transi-tion to the radiative state is of interest. Although no perturbation of the meta-stable molecular state may be required for non-radiative transitions to be important even when the Kronig selection rules which apply to such processes are not satis-fied (for instance electron spin may not be conserved) the intermediate molecular state is being perturbed by collisions with its neighbours (most of which are chem-ically unreactive). Such collisions may either (i) induce a transition from the intermediate state to a radiative state if the potentials of the radiative state and the intermediate state cross and if the vibrational levels of the intermediate mole-cule near the crossing region are populated (ii) cause a transition to a lower (or higher) vibrational level (iii) cause collisional dissociation (if the state is weakly bound) or (iv) deactivate the “ intermediate ” molecule to some lower electronic state.The importance of such processes has been investigated by studying the pressure variation of the various emission systems with both nitrogen and rare gases (which do not appreciably quench the states concerned) as the predominant collision partner. The potential energy curves of NO are shown in fig. 1 which was compiled by Dr. F. R. Gilmore.1 Only three bound electronic states of NO are formed by ground state atoms the X2l-I molecular ground state the a4H metastable state and the 2C* state which may be weakly bound.These are the initial states of the molecule formed in the association of atomic nitrogen and oxygen. However radiation is only observed from the A2Z+ ( y bands) B2l7I(P bands) C2H (6 bands) and b4X-(Ogawa bands). These states must then be populated from the X2l7 a4n or 2X+ states. The exact shape of the potential curves is not uniquely determined by spectroscopic observations even when these are available and extensive. For such states as the 2X+ and a4H there are very little spectroscopic data of any kind. Thus it is not really known if the 2Z+ state crosses the C2IT state near the dissociation limit of the X2l-I state as shown or crosses the B2l-I state beyond its minimum at this energy as Vanderslice et aZ.2 calculate.The chemiluminescent excitation of the p and y bands of NO was first observed by Lewis 3 in 1904 as a contamination in the spectra of active nitrogen. Rayleigh 4 5 and Lewis 6 later investigated these bands showing that oxygen was necessary for their excitation. Later Sponer and Hopfield 5 using Leifson’s absorption spectra identified the bands observed in emissions as those characteristic of nitric oxide. Knauss 8 in 1928 observed the chemiluminescent excitation of the 6 bands. Brook and Kaplan 9 extended the spectra through the visible and near infra-red finding the Ogawa bands in the latter region. In a thorough investigation of the chemilumines-cently excited spectra of NO Tanaka 10 established that the maximum excitation was within 0.01 eV of the dissociation energy of NO.In 1957 Kaufman and Kelso 11 showed that NO added to a stream of partially dissociated nitrogen was decomposed and not excited the atomic oxygen liberated in the decomposition subsequently associated with atomic nitrogen to form excited NO. Schade 12 in 1961 verified that the intensity of the v’ = 0 p y and 6 bands were proportional to the product of the atomic oxygen and nitrogen concentrations. There has been no investigation of the pressure dependence of the NO bands produced in mixtures of atomic nitrogen and oxygen although Gaydon 13 noticed that low pressures strongly favoured the 6 bands. Incomplete observations of the changes in relative intensity of the NO band systems caused by the addition of com-pounds (CO C02= 10 %) were made by Rayleigh,s and Barth et aZ.12 made similar observations using rare gases ( = 99 %).Rough rotational intensity measurement 230 BANDS OF NITRIC OXIDE of the beta bands from v' = 0 made by Barton et aZ.13 are consistent with rotational equilibrium. Tanaka 10 and Barth et aZ.14 point out vibrational-intensity anomalies associated with the non-thermal excitation mechanism. OBSERVED PERMITTED TRANSITIONS: NO A-X O'BANDS) NO D - A NO B-X ( B BANDS) NO E - A (FEAST BANDS) NO C-X (6BANDSl NO B'-B NOD-X ( C BANDS) NO b - 0 (OGAWA BANDS) 1 2 3 4 internuclear distance R (A) FIG. 1.-The potential diagram of NO NO- and NO+ as compiled by Dr.F. R. Gilmore. EXPERIMENTAL The nitric oxide bands were generated in the flow system sketched in fig. 2. Pre-purified (Matheson Co.) nitrogen was partially dissociated by a microwave discharge and then, passed through a Pyrex-glass-wool plug to remove unwanted excited species 16 such as thos R. A. YOUNG AND R. L. SHARPLESS 23 1 contributing to the pink nitrogen afterglow.16 These species destroy nitric oxide (unpublished results) and could lead to false atom concentrations when measured by the nitric-oxide titration technique.12 On occasions when the glass-wool plug was not used the pink glow has been seen in the observation tube a metre distance from the discharge and could have affected the NO spectrum. The entrance slit of a + m Jarrell-Ash Seya-Namioka scanning monochro-mater was positioned directly in front of the 1 m observation tube.Fairly wide slits (1 50 p) were used which degraded the spectral resolution to -5 A in order to obtain adequate signal-to-noise ratios at the lowest pressures used. An EM1 6256B photomultiplier having a 10-mm diam. S-11 cathode on a quartz window was centred behind the exit slit. Approximately 1000 V were applied to the photomultiplier from a highly regulated ( ~ 0 . 0 1 %) supply and PHOTOMULTIPLIERS AN0 FILTERS COVERING 5000&-70008 AND 3000fi-4000fi . MONITORING SPECTROGRAPH OBSERVATION TUBE CALIBRATED DETECTOR AND FILTER I meter - 75 mm I 0 20 mm I D TO PUMP TO PRESSURE GAUGE GRADED lOmm I D -OUARTZ WEFUCHING INLET NO TlTRATlOh INLET UNWANTED EXCITED SPECIES PREPURIFIED Np MICROWAVE DISCHARGE FIG.2.-Schematic diagram of the flow system for the observation of nitric oxide radiation. the photocurrent detected by a Hewlitt-Packard d.c. micro-voltameter after the dark current had been bucked out with a stable constant current source. A Varian recorder was connected to the output of this chopper stabilized amplifier. The spectrum was scanned at 100A/min with an amplifier having a time constant of 1 sec or less. The dis-sociative discharge is optically shielded from the titration and quenching region to prevent any photochemical interaction. A bend in the entrance tube to the observation region and a blackened aluminium foil covering of the observation tube prevents light (excited in the titration mixing region) and other extraneous radiation from being detected.The linear flow speed is approximately constant at a few m/sec over the pressure region from 0.1 to 15 mm Hg which was measured at the downstream end of the observation tube with a McLeod gauge, Nitric oxide obtained from Matheson Company was stated to be at least 99 % NO. This was passed through Askerite into a 5-1. storage flask connected to a large oil mano-meter (using Fluorolube FS-5) from which it flowed through a sapphire float flow gauge, through a needle valve and into the atomic nitrogen stream. The reservoir pressure was maintained manually at a constant ( m 10 %) pressure. No change in the results of titration, or the NO spectrum could be found when the NO was further purified by fractional dis-tillation after freezing at liquid nitrogen temperatures.Further refinements in the NO titration system were not warranted since only relative concentrations were determined and the NO flow rate needed to be constant for only 30-min periods. The N20 CO2 used as quenching agents were also obtained from the Matheson Com-pany. These compounds were further purified by vacuum distillation. Their partial pressures were determined directly by noting the pressure increase upon their addition to the flow stream. Commercially prepared mixtures of He+N2 and A+N2 were passed through the discharge to observe the effect of large fractional alterations in thegas composition 232 BANDS OF NITRIC OXIDE Two photomultipliers (RCA 6655A) with suitable filters were used to monitor the 5000-6500A region and the 3000-4000A region.The N2 first positive system19 and the NO2 " continuum " 20 were detected by the former while predominantly the NO p bands were detected by the latter. The minimum in the 5000-6500A region intensity coincides with the NO titration null-point.18 If the NO flow-rate had not been adjusted to the null-point the 3000-4000A photomultiplier determined whether more or less NO must be added to reach equivalence. It also verified that during a spectral run there was no change with time of the NO emission which might be incorrectly interpreted as a spectral shift in intensity. A run consisted of setting the total pressure and adjusting the NO flow to obtain a maximum NO /? emission. At this point variations in the flow rate of NO or N had the least intensity effect.Usually the nitrogen atom flow rate (in arbitrary but specified units) was also determined by a NO titration. RESULTS Fig. 3 shows the variations of the NO 6 bands as a function of the pressure of N2 when the initial flow rate of N and the actual flow rate of NO has been held con-stant over short pressure segments and the segments normalized to each other. The CI s II pressure mm Hg FIG. 3.-The pressure dependence of the NO v' = 0,6 bands. Nitric oxide was added to maximize the NO band intensities. The top curve was taken at a higher NO flow rate and thus higher atom concentration than the lower curve. This latter curve is composed of two segments normalized at one point to be contiguous. An A diluent was necessary to cover the large pressure range.The downward slope of the lower curve is due to the decreasing volume pumping speed of the mechanical pump. upper curve was taken at a larger atom concentration than the lower (the curves are indexed with the relative NO flow rates used). If the volume pumping speed of the mechanical pump (Duo-Seal-1402) remains constant over the pressure range used and if the loss of atoms during their passage down the observation tube is either negligible or independent of pressure and if quenching of the C2II state by N2 is negligible, fig. 2 will truly reflect the pressure dependence of the population of the v' = 0 level of the C2IT state. The small variation in the volume pumping speed does account for the downward slope of the lower curve toward higher pressures.A R . A. YOUNG AND R . L . SHARPLESS 233 higher atom concentrations (upper curve) three-body associative losses become significant at high pressures and produce an additional downward curvature to the data. The major loss of atoms when the lower curve of fig. 3 was obtained is atomic association on the observation-tube walls. Previous measurements of the catalytic efficiency of Pyrex surfaces for atomic oxygen and nitrogen 21 give 10-4-10-4. This implies that at the pressures used diffusion is rapid enough to maintain an essentially uniform atom distribution over the cross-section of the observation tube. The atom loss rate (which is [N]CA/4 where [N] is the atom concentration U the mean thermal velocity and A the surface area of the observation tube) is then independent of the pressure.The complex question of the quenching of the C217 state will be discussed later. Thus with the provision that N2 does not significantly quench the C 2 l l state of NO fig. 3 indicates that the rate of excitation of the C2IT state is in-dependent of the nitrogen pressure. 2 I 0 ti - TOTAL PRESSURE,; 1 *.* 4 m m H g L b - t / c -I 0 I 2 3 4 5 6 7 8 9 1 0 1 1 1213 no ff ow arbitrary units and y bands as the atomic oxygen was varied (by changing the FIG. 4.-Relative intensities of NO NO flow rate). No systematic variation is observed. Fig. 4 shows that there was no change in the spectral distribution of radiation excited by the association of nitrogen and oxygen when either the ratio [O]/[N] or the sum [O] + [N] were widely varied (this was true at any pressure within the range studied).This implies that there is no interaction except a linear one involving NO in any state (since [NO] =:p[O] because of the steady state established by the reactions N + 0 + M+NO + M and NO + N-,N2+ 0).12J* Also there is no interaction between the excitation of the NO bands and the N2 bands. These are not trivial results. Metastable NO and N2 are essential in a chemiluminescent excitation of these molecues and could conceivably interact i.e. N2(5Z) or N2(A3EL) could excite NO in the processes NO + N2(5Z) -+ NO* + N; or NO + N2(A3E:;f) +NO* + Ng , where NO* and Nf are energy-rich molecules. The nitrogen and nitric oxide after-glows are independent of one another (though they coexist) except for their use of the common reactant atomic nitrogen.The relative (always to the 6(u’ = 0)) band intensities of different band systems will be denoted by for example 1$(0,7) or I,y(O,O) while the relative (always to th 234 BANDS OF NITRIC OXIDE 0,O level of the C2IT state) population of a state will be denoted by for example, [NO(B2n)lr. Clearly [NO(B2nu‘ = 0)],0cIrfl(0,7) or any other j? band originating from the 0 vibrational level; a similar statement holds for other transitions. Pro-vided radiation represents the major loss of a given state and that this is rapid enough, compared to the rate of production to produce a quasi-steady state the band in-tensities will be proportional to its production rate for example I,P(0,7) ccPr(B2au = 0), where Pr(B2nu’ = 0) is the relative production rate of the B2llu’=O state.Fig. 5 6 7 8 and 9 illustrate the pressure dependence of the chemiluminescently excited NO p and y and Ogawa bands for mixtures of nitrogen with helium or argon. pressure mm Hg FIG. % T h e variation of u’ = 0 fl band relative intensities as a function of the total pressure and with mixtures of A in Nz. A linear variation is generally observed passing through the origin. All intensities are relative to the S(0,O) band which makes them independent of the actual atom concentration and any variation in their spatial distribution. These figures then show that Ir(B21h’ = 0) = Ap Zr(A2X+u’ = 0) = B+Gp Ir(b4C-) = D, where p is the total pressure. The dependence of the Ogawa bands which are not specified as to vibrational level is derived using the pressure dependence of the p(d = 0) bands from fig.5 or 6. Fig. 10 11,12,13 and 14 indicate that there is some dependence of A and G on the composition of the environmental gas. The de-pendence of A and G on the percentage of rare gas is not accurately determined because of the considerable experimental scatter but it can be said to be of a different general form for the different rare gases used. The constant B is not noticeably depenbent upon the composition of the gas (fig. 15 16 and 17). The pressur R . A . YOUNG AND R . L. SHARPLESS 235 dependence of j3 bands originating from v’ = 3 is different from that of the 0 vibrational level of the same system (fig. 18 and 19). In pure nitrogen I’(B2IIv’ = 3) = Ep2/3. Not only is E a function of gas composition but the exponent as well.Replacing molecular nitrogen by argon has a small effect but He has a very large effect for an almost pure He atmosphere I’(B2Hu’ = 3) approaches a linear function of pressure. The data on p bands from other v’ levels is considerably less accurate than that for the /3 band with v’ = 0 or 3. However the v’ = 1,2 3,4 and 6 levels behave as a group and differently from v’ = 0 ; they all have a pressure and compositional dependence similar to that for v’ = 3. No radiation was 24 22 20 18 16 14 12 8 4 2 0 0 2 4 6 8 10 12 14 16 pressure mm Hg FIG. 6.-The variation of the relative intensities of the 0‘ = 0 /3 bands as a function of the total pressure and with mixtures of He in N2.A linear variation is generally observed passing through the origin. isolated from B2nv’ = 5 or A2I=+v’ = 2 levels. The y(3,O) band variation with pressure implies Zr(A2X+v’ = 3) = Fp similar to that observed for the B2IIv’ = 0 and different from that of A2C+v‘ = 0. The results of adding N20 to the [N] = [O] in N2 afterglowing system are dis-played in fig. 20-27. There is a sharp distinction between the behaviour of the 6 bands, which are quenched very little and whose intensity is related directly to the partial pressure of nitrous oxide and the j3 and y bands which are strongly quenched and whose intensity is inversely proportional to the partial pressure of nitrous oxide. If a state may only radiate or be quenched then Io/I = 1 + kzprr where ZO is the un-quenched intensity and I is the quenched intensity k is the quenching rate constant 236 22 20 18 16 .2 14 5 c1 g 12 .d n 6 4 2 0 BANDS OF NITRIC OXIDE I I I I I I I I I -I 0 2 4 6 8 10 12 pressure mm Hg FIG.8.-The variation of the relative intensities of the v' = 0 y bands as a function of the total pressure and with mixtures of He in N2. A linear varia-tion is generally observed having a finite intercept. 20 26 24 22 20 18 16 E/ $ 14 3 -5 + .4 E E 4 i C 14 16 18 FIG. 7.-The variation of the relative intensities of the v' = 0 y bands as a function of the total pres-sure and with mixtures of A in Nz. A linear varia-tion is generally observed with a finite intercept. pressure mm H R . A . YOUNG A N D R .L. SHARPLESS 237 z is the radiative lifetime and pq is the partial pressure of the quenching agent. Since the pressure variation of the /? and y bands (all relative to the G(0,O)band) implies that they are proportional to the intensity of the 6 bands they should be corrected for the decrease of these bands (by multiplying each by 10(6)/1(6)). When this is done all the bands follow a generalized standard quenching relation (10/l = 1 + Cprr), while if they were not corrected there would be a prominent upward curvature. If molecular nitrogen is a competitive quenching agent which is not substantiated by the pressure dependence of the p y 6 or Ogawa bands or if it participates in con-junction with nitrous oxide in the quenching process the slopes of the l o l l curves will 0 2 4 6 8 10 12 pressure mm Hg FIG.9.-The ratio of the u’ = 0 ,!? band intensities to the Ogawa band intensities. Thz linear pressure dependence and zero intercept with the ,8 band pressure variation shown in fig. 5 and 6 implies that the ratio I(Ogawa)/Z(S) is constant. 6 0 0.2 0.4 06 0.8 1.0 fraction of A in N2 FIG. 10.-The dependence on the fraction of A in N2 of the slopes of the curves displayed in fig. 5. be pressure dependent. This is seen to be the case for the bands. To facilitate later discussion the inverse of the slopes are plotted against p in fig. 28. There is a sharp distinction between the pressure dependence of C for the p bands (C decreases as p increases) and the y bands (C remains constant or increases as p increases).Fig. 29 to 33 show the behaviour of the 6(u’ = 0) y(u’ = 0,d = 3) and p(u’ = 0, u’ = 3) bands when C02 is added and the dependence of this behaviour on the nitrogen pressure. The 6 and y bands vary as they did when N20 was added. How-ever the /3 bands show anomalous (but small) change with CO2 addition. Fig. 34 shows that C for the y bands is again essentially independent of the N2 pressure (the low C value at 1 mm Hg is discounted because of experimental difficulties that originate at low pressures) 238 BANDS OF NITRIC OXIDE FIG. 11. 0 0.2 0.4 0-6 0-8 1.0 1.2 fraction of He in N2 -The dependence on the fraction of He in N2 of the slopes of the curves displayed in fig. 6. FIG. 12.-The dependence on the fraction of A in N2 of the slopes of the curves displayed in fig.7 R . A. YOUNG AND R . L . SHARPLESS * 239 0 0.2 0.4 0.6 0.8 1-0 fraction of He in N2 FIG. 13.-The dependence on the fraction of He in N2 of the slopes of the curves displayed in fig. 8 5 4 3 - 4 v) 2 I 0 I I I I I I I I I 0 0.1 0.2 0-3 04 0.5 0 6 0-7 0-8 0-9 1.0 fraction of rare gas in N2 FIG. 14.-The dependence of the y(3,O) band slopes from curves similar to fig. 7 and 8 on the frac-tional concentration of A and He in 240 BANDS OF NITRIC OXIDE I DISCUSSION The excitation of the 6 bands requires an energy approximately 0.01 eV below the dissociation energy of NO(X2n) at 6.50 eV. A molecule which has lost sufficient I 0 0.2 0*4 06 0.8 I.0 1.2 fraction of A in N2 FIG. 15.-The variation of the intercepts of curves displayed in fig.7 on the fractional concentration of A. I I I I I I FIG. 16.-The variation of the intercepts of curves displayed in fig. 8 on the fractional concentration of He. energy to be stable against collisional dissociation cannot be collisionally transferred to the C2T,.=o state. Only the a4n or possibIy the 2Z+ potential (except for those due to excited atoms) cross the C2H level. Several types of processes may con A B C D FIG. 1 .-Nuclear magnetic resonance spectra of AI(BH&. A H1 resonance at 30.0013 Mc/s. B same as A with B11 irradiated at 9.6257 Mc/s. C same as A with A127 irradiated at 7.8177 Mc/s. D B11 resonance at 12.3 Mc/s. [To face page 240 A B C D FIG. 2.-Nuclear magnetic resonance spectra of highly deuterium-substituted compound largely AI(BH2D2)3 and Al(BHD3)j.A H1 resonance at 30.0013 Mcls. B same as A with B11 irradiated at 9.6257 Mc/s. C same as A with A127 irradiated at 7-8177 Mc/s. D B11 resonance at 12.3 Mc/s A B C D FIG. 3.-Nuclear magnetic resonance spectra of " A12B4H18 " + Al(BH& mixture from equilibrium established at 80" C . A HI resonance sample at 30" C. B HI resonance sample at - 60" C. C HI resonance sample at - 80" C. D same as C with A127 irradiated at 7.8177 Mcis A B C D FIG. 4.-Nuclear magnetic resonance spectra of " A12BJH18 " + AI(BH& mixture corresponding to fig. 3. A H1 resonance B11 irradiated sample at 20 C. B same as A sample at - - 60" C. C B11 resonance. D I311 resonance of deuterium-substituted sample, approximating A I ~ B ~ H ~ J D ~ etc R .A. YOUNG AND R . L. SHARPLESS 241 I 1 ceivably occur as the N(4S) and O(3P) atoms approach each other on one of these two curves (a) they may spontaneously cross to the C2H state when their separation is appropriate (b) a collision may sometimes (i) induce the transition to this state (ii) I I I 0.5 0 4 0.3 Y 8 .- 0.2 c1 0- I A Ar 0 He 0 - A 01 0.2 0.3 0 4 0 5 0 6 0.7 0 8 0 9 1.0 fraction of rare gas in N2 FIG. 17.-The variation of the intercepts of the d = 3 y bands with the fraction of rare gas. -91% Ar 0 50% Ar V 25% Ar A 16% Ar o 0% Ar 0 2 4 6 8 10 12 14 16 pressure mm Hg FIG. 18.-The variation of the relative intensity of the j? (3,3) band with total pressure and with mixtures of A in N2 242 BANDS OF NITRIC OXIDE stabilize the atoms into either the a4n or 2E potential or (iii) allow them to rebound and dissociate and (c) a collision may also (i) dissociate (ii) transfer to the C2n state, or ( 5 ) deactivate the molecule formed in (bii) above.20 18 - 16 0- s M o 14 c 2 0 0 91% He 50% He V 25% He L3. 16% He 0 2 4 6 8 10 12 14 16 18 pressure mm Hg FIG. 19.-The variation of the relative intensities of the 8(3,3) band with total pressure and with mixtures of He in N2. pressure of NzO mm Hg FIG. 20.-The dependence of the u’ = 0,6 bands on the partial pressure of N20 for different nitrogen pressures 10 9 8 7 6 5 10 -I 4 3 2 I R. A . YOUNG AND R. L . SHARPLESS 243 0 I 2 3 4 pressure of N20 mm Hg FIG.21.-The ratio of the intensity of u' = 0 /3 bands without ( l o ) and with (I) added N20 as a function of its partial pressure for several nitrogen pressures. Straight lines whose slope depends upon the pressure of N2 are obtained. 5 4 3 10 I -2 1 0 - - --l S = SLOPE x 0 4 (mmHg 0 I 2 3 4 pressure of N20 n m H g FIG. 22.-The ratio of the intensity of v' = 1 /3 bands without ( l o ) and with ( I ) added N20 as a function of its partial pressure for several nitrogen pressures. Straight lines whose slope depends upon the pressure of N2 are obtained 244 BANDS OF NITRIC OXIDE 5 4 3 I0 I -2 I "-A ,- 0 I 2 3 4 pressure of N20 mm Hg FIG. 23.-The ratio of the intensity of the u' = 2 /3 bands without ( l o ) and with ( I ) added N2O as a function of its partial pressures for several nitrogen pressures.Straight lines whose slope depends upon the N2 pressure are obtained. I 1 0 I 2 3 4 pressure of N20 mm Hg FIG. 24.-The ratio of the intensity of the v' = 3 /3 bands without (lo) and with ( I ) added N20 as a function of its partial pressure for several nitrogen pressures. Straight lines whose slope depends upon the N2 pressure are obtained R . A . YOUNG AND R . L . SHARPLESS 245 Process (b) alone could lead to a pressure independence of I(6) only if stabilization (to any state) by a third body is rapid compared to dissociation of unstabilized NO which is impossible except at inconceivably high pressures. The addition of processes (c) to those of (b) makes it even less likely that I(6) would be pressure in-dependent.It appears that only process (a) is feasible. This process need not be very probable to produce the observed intensity and may not imply an appreciable broadening or energy shift in the structure of the 6 bands from o’ = 0. It is also consistent with the photodissociation of NO near 1900 A.22 5 4 3 I0 I 2 -I 0 1 1 0 I 2 3 4 pressure of N20 mm H g FIG. 25.-The ratio of the intensities of v’ = 4 and 5 B bands without ( l o ) and with ( I ) added N20 as a function of its partial pressure for several nitrogen pressures. Straight (at least in long seg-ments) lines whose slope depends upon the pressure of N2 are obtained. Flory and Johnston 22 conclude that photochemical decomposition of nitric oxide by photons near 1900 A occurs by “ predissociation ” from the C2II,.= level, although their evidence for its non-occurrence form the v‘ = 0 level is not strong.Their measured absorption coefficient (based on the assumption that decomposi-tion of NO is much more probable than re-emission) of 152 atm-1 cm-1 corresponds quite well with Bethke’s 12 measurements for the 6(1,0) band if the absorption is averaged over a 30 A interval (Av = 103 cm-I) as his low-pressure spectra indicate is approximately correct which gives 137 atm-1 cm-1. Bethke’s measurements for the 6(0,0) band (which covers ~ 2 0 4 gives an average absorption coefficient of ~ 1 2 0 atm-1 cm-1. Considering the accuracy of the data this discrepancy in the absorption coefficients measured by absorption and photochemical techniques is not sufficient to decide which vibrational level of the C2II state is responsible for the decomposition observed by Flory and Johnston.However it does indicate that dissociation of the C217vt=o,1 state is much more probable than radiation as will be suggested in accounting for the non-quenching of this state by N20. Because of the selection rules 24 + -+ + AK = 0 for non-radiative interaction and the selection rules AK = O_+ 1 + -+ - for radiation between two states both belonging to Hund’s case b only P and R branches should occur in emission betwee 246 BANDS OF NITRIC OXIDE pressure of N20 mm Hg FIG. 26.-The ratio of the intensities of v' = 0 y bands without (lo) and with (I) added N20 as a function of its partial pressure for several nitrogen pressures.Straight lines whose slope does not depend upon the pressure of nitrogen are obtained. I I * --0 - 1 0 I 2 3 4 pressure of N20 mm Hg FIG. 27.The ratio of the intensities of v' = 3 y bands without ( l o ) and with (I) added N20 as a function of its partial pressure for several nitrogen pressures. Straight lines whose slope depends upon the nitrogen pressure are obtained R . A . YOUNG AND R. L. SHARPLESS 247 FIG. 28.-The inverse of the slopes of curves displayed in fig. 21-27 are plotted against the nitrogen pressure. Straight lines are obtained. pressure of C02 mm Hg FIG. 29.-The ratio of the intensities of u' = 0 y bands without ( l o ) and with ( I ) added COz as a function of its partial pressure. Straight lines whose slope is independent of the nitrogen pressure are obtained 248 BANDS OF NITRIC OXIDE the C2II (which is a perfect example of Hund’s case b) 25 and the A2Z+ if the C211 state has been populated through the 2Z+ potential.Infra-red spectrograms on 1-2 film show a sharp line-like feature at the position (12,234A) computed for the Q branches of the C2lT-AZ:f transition. This rules out the 2X+ state as a “pre-cursor ” in the population of the C2lT state by preassociation. With wider spectro-graph slits the P and R branches appear with approximately the intensity to be ex-pected for rotational equilibrium. This would be expected for (spin disallowed) transition from the a4II state but not from the b4Z- state (which would excite only 12.0 I I I I I t I 0 1.0 2.0 3.0 4.0 pressure of C02 mm Hg FIQ.30.-The ratio of the intensities of v’ = 3 y bands without ( l o ) and with ( I ) added CO2 as a function of its partial pressure. Straight lines whose slope is independent of the nitrogen pressure are obtained. the Q branch). Evidently NO(a4IT) is the main “ precursor ” in the excitation of the C2ll state although because of the difficulty in making intensity measurements on film in the infra-red the b4Z- state may contribute somewhat to the subsequent emission of the S bands. It is concluded that N + 0 + NO(a4IT)-+ NO( C2II) +hv + NO(X2II) +hv+ NO(A2X+) are the primary process forming the C2ll state. The pre-association mechanism is consistent with the non-quenching of the S bands. For a quenching agent to appreciably reduce the radiation intensity it must participate in a process which is fast enough to upset a previously established equilibrium.The unidirectional transfer rates to and from the C21Tu,=o state ma R. A . YOUNG AND R. L. SHARPLESS 249 be large i.e. of the order of lO13/cm3 sec if each atom-atom collision that statistically occurs on the a4II potential has a kinetic cross-section and one in 104 crosses to the C2II state assuming approximately 1014 atoms/cm3. Rough estimates of the photon flux (made by comparing the 6 band intensity with the NO+O continuum) indicate a value of N" lOll/cm3 sec which implies an equilibrium concentration of = 103 for [NO( C~Z)]. Neither radiation or efficient collisional quenching would appreciably upset this equilibrium between NO(C2II) and atomic nitrogen and oxygen.No quenching is to be expected under these conditions even if N20 or C02 were to remove NO(C2l-I) molecules as rapidly as it removed NO(A2C+) molecules. 2.2 2.0 1.8 1.6 1-4 I0 1.2 -Z la 0.8 0.6 0-4 0.2 BrnmHp 3 mm Hp - \ 0 1.0 2.0 3.0 4.0 pressure of C02 mm Hg FIG. 31.-The ratio of the intensities of the 0' = 0 /3 bands without ( l o ) and with ( I ) added CO;! as a function of its partial pressure. Relatively small changes in I are observed. The observed reduction in intensity when N20 is added is consistent with the pre-association mechanism only if the atomic concentrations are altered through its addition contrary to the considerations that lead to its choice as a quenching agent.18a The quenching data were taken at an atom concentration comparable to that of the top curve of fig.3 when recombination as the atoms traversed the observation region was an important loss. Under these conditions changing the composition of the gas may alter the three-body association of N and 0 (which is the predominant means of homogeneous atom loss regardless of whether N2 0 2 , or NO is the product molecule) as is indicated by the effects of mixing A with nitrogen. At lower atom concentration argon has no effect on the 6 band intensities in conform-ance with the proposed pre-association excitation mechanism. Since N20 is effective in quenching the B and y bands it may well be a very effective third body in the association of N and 0 and lead to a reduced atom concentration without chemically reacting with either 0 or N.The increased pressure caused by adding the quenchin 250 BANDS OF NITRIC OXIDE agent may also alter the equilibrium flux of atoms leaving the discharge and produce the observed effects. Titration at both the entrance and exit of the observation tube confirm that at low atom concentration the atom loss is predominantly on the walls and at higher concentration recombination loss becomes important. After adjusting the discharge to compensate for its decreased efficiency when the quench-ing agent was added it was verified that reactions of atoms with N20 were slow (z 10-16 cm2lsec) as expected 18a but sufficient to account for the decreased in-tensity observed in the 6(u' = 0) bands. I I 1 1 I I I I.0 2.0 3.0 4.0 pressure of Con mm H g FIG.32.-The ratio of the intensities of the v' = 3 ,8 bands without (10) and with ( I ) added COz as a function of its partial pressure. Relatively small charges in I are observed. The b4Z- state from which the Ogawa bands arise is also populated by a pressure-independent mechanism since the ratio of the Ogawa band intensities to the 6 band intensity is independent of the N2 pressure. The b4C- state cannot preassociate through the 2C+ state because such a transition would violate Kronig's selection rules, but it could pre-associate through the a4II state. The transition NO(a4n)-+NO(b4C-) should occur with high probability since the a4lI and b4X- curves are almost tangent in the crossing region26 near the dissociation limit of X2n. The population of the lower vibration levels of the b4C- state could also occur from a stabilized mole-cule and remarks to follow during the discussion of the collision induced excitation of the A2Cf state will apply.Vibrational relaxation in the A2E+ state from high levels excited by some un-specified process into the v' = 0 level is very unlikely because of the very large vibrational spacing and generally low efficiency of N2 in this process.27 Then the vibrational distribution in the A2Z+ (and B2n) state reflects the relative excitation rates into these levels (especially since collisional electronic quenching may be = 10 R . A. YOUNG AND R. L. SHARPLESS 25 1 more probable than collisional vibrational relaxation in the lower levels of the A%+ (and B2n) states. The quenching equation Io/I = 1 +Cpq where C is independent of pressure, results only when a bimolecular quenching process competes only with a unimolecular process in removing species responsible for the intensity I.If the quenching process competes only with another bimolecular energy removal process involving the ambient species whose concentration is measured (approximately) by the total pressure then the same quenching equation is obtained with C inversly proportional to pressure. If quenching competes with both of the the above processes C = a/ (b+cp) where a is the quenching rate of the quenching compound b is the uni-molecular loss rate and c is the bimolemlar quenching rate of the ambient species. These statements are true regardless of what mechanism produces the species re-sponsible for I as long as the quenching compound does not affect this production mechanism.The finite intercept in the curves showing the pressure variation of the y bands with v’ = 0 and the established pressure independence of the 6 bands implies that the y bands are partially excited by a pressure independent process and the linear slope implies an excitation process proportional to the pressure. Both the a4n and b4E- cross the lower vibrational levels of the A2Z+ state from which the y bands originate. Only the former may interact even in a perturbing collision (which could remove the AS = 0 restriction) because of the different symmetry properties of the b4E- and A2Z+ states.24 The A2X+ state is populated from the C2II state by radiation (at 12,234 A).This would imply that a fraction of the y band intensity be pressure independent. At low pressures (when almost all the y band intensity is due to the pressure-independent process) the 6 and y bands are of comparable intensity requiring that radiation between the C2rI and A2X+ state be of similar intensity to the radiation between the C2II and X2II ground state. If the transition dipole matrix elements were identical the (frequency) 3 factor in the transition probabilities for these transitions would imply that the infra-red emission was 1/25 of the 6 band emission. To compensate for this the dipole matrix element for the C2II - A2Z+ transition must be 25 times the matrix element for the C2II - X2IT transition. This is not impossible considering the almost perfect overlap of wave functions in the C2Il and A2X+ states.Observations at pressures below 0.01 mm Hg show that the ratio of the pressure independent component of the y bands to the 6 bands remains unchanged from its value at much higher pressures. It is unlikely that a balance between pressure-dependent pro-duction and loss mechanisms could be maintained over this pressure interval to produce the observed relative constancy of the populations of the C2II and A2X+ states. The same quenching relation (Io/I = 1 + Cp(N20)) describes the v’ = 0 y bands at 1 and 12mm Hg while the intensity ratio of the pressure-independent to the pressure-dependent components of the total intensity changes from 0.4 to 4. This behaviour of the v’ = 0 y bands implies that either (a) the radiative state itself is quenched or (6) both the pressure-dependent and pressure-independent components are proportional to the concentration of a quenchable species.Even if the latter alternative had not been previously ruled out (as it is since the A2X+ state is populated by cascade radiation from the C2n state) it can be shown that the pressure indepen-dence of C is inconsistent with (b). Assuming process (a) is responsible for the quenching fig. 26 gives T k = 3.8 (mm Hg)-1 (or a pressure for half quenching of 0.25 mm Hg) for the y(0,O) band. Ap-proximately 17 % of the radiation leaving the A2Z$ level is in the A2C =o - X2J3,. 252 BANDS OF NITRIC OXIDE transition28 Using Bethke’s 23 fvalue of 3-99 x 10-4 (which may be a low estimate 29) for this transition the radiative lifetime of the A2Zl$,o state is computed to be 2.5 x 10-7 sec.Then k = 2-5 x 10-10 cm3/sec after converting units in the measured zk. This corresponds to a quenching radius of 4.5 A. The lifetime used here is 25 times that used by Basco et aZ.30 and the quenching radius of 4-5A would correspond to 21 A on their scale N20 and H20 would then quench the A2C+ state with approxi-mately equal probability.30 The excitation of the pressure-dependent component of the gamma bands may occur in a collision-induced transition. If this happens from near the dissociation limit ( ~ 0 . 1 eV) either the a4n or CNI could be involved (as well as the 2Z+ which, however evidently has risen well above the dissociation limit before nearing the 1-8 ;A 1 I I I b I I I 1.6 I I “ I 100 M 30 41) COz pressure mm Hg FIG.33.-The dependence of the 6 bands on the C02 partial pressure. internuclear region of the A2C+ state-the b4C- cannot combine with the A2X+ even if the selection rule A S = 0 is relaxed). Energy-abstracting collisions which convert vibrational energy into kinetic energy are very rare for molecular nitrogen (-one collision in 107 is effective at room temperature) although such processes for other molecules (N20 for instance) may be quite large. The ineffectiveness of N2 in such energy abstracting collisions requires either that the collision-induced transitions to low vibrational level of the A2C+ state occurs from a level at ap-proximately the same energy or that collision-induced transitions occur from higher levels of a state (C2II) with simultaneous vibrational excitation of N2.The a4111 state is unique in that aside from the ground state which does not “ cross ” any of the states seen in emission it has vibrational quanta small enough (in the region within 1 eV of the dissociation limit of NO) that collisional vibrational re-laxation (in which the vibrational energy is removed as kinetic energy) may be faster than collisional electronic quenching and faster than radiative losses. Only in this state may the energy of association be degraded by such an “ adiabatic R. A . YOUNG A N D R . L. SHARPLESS 253 process in the small amounts (<1 eV) necessary to leave the molecule in the ob-served energy states. If no energy is removed from the molecule in the transfer between molecular potential energy states all the lower vibrational levels of the AW- and B2II states must be populated through the a4ll state.For transitions to the A2C+ potential this requires a small relaxation of the Franck-Condon principle, but for the B2II potentinci this principle is strongly violated. The pressure independence of the quenching of the A2Z+ state strongly favours the pressure-dependent excitation mechanism that simultaneously leads to vibra-tional excitation of the collision partner (remembering that the pressure-independent cascade mechanism previously discussed is simultaneously operative). If collision-induced transitions to the A2C+ state occur which abstract only little energy (as kinetic energy) they must occur from " relaxed " vibrational levels of the a4II state.0.8 I t x O P (CO,) FOR HALF QUENCHING 04-005 mm Hg x A -0 0 2 4 6 8 10 12 14 16 N2 pressure mm Hg FIG. 34.-The inverse of the slopes of the C02 quenching curves plotted against nitrogen pressure. The population of these levels is established by collisional production and loss processes which probably result in a pressure-independent population distribution and could produce a linear pressure dependence for the transfer rate to the A2C+ state. Because of the long lifetime in the a4ll state it should be much more sus-ceptible to quenching than the A2C state itself and this would lead to a quenching of the pressure-dependent component which was larger than that for the pressure-independent component. This is not observed.Also the quenching of a given vibrational level of this state would be in competition with the other collision pro-cesses that help establish its equilibrium concentration. Thus the N20 (and C02) quenching coefficient C should be pressure-dependent. This is not observed either. Thus the process, would be supported by the quenching behaviour of the y bands over the process NO(a41T,f=1,,,,)+N2-)NO(A2~+)+N2(X1C:ot=O). If the collision partner is atomic (A He) vibrational excitation would be im-possible and the excitation rate of the lower vibrational levels of the A2C+ state NO(C21T,f,, b4C-,t=high a4n,:=hig.,) + N2+NO(A2C+) + N2(X1Cv#=4) 254 BANDS OF NITRIC OXIDE should be reduced compared to the rate when N2 is the collision partner. This is the general behaviour observed.(The maximum in the He data at %20 % He in N2 may be an experimental artifact.) Apparently 70-80 % of the pressure-dependent gamma-band intensity is excited by a collision-induced transition which results in vibrational excitation and 20-30 % by some other process. The v’ = 3 level of the A2E+ state lies only 0.2 eV below the dissociation limit of NO. Aside from the fact that the Franck-Condon principle would be some-what violated for transitions to this level from the C2n state the v3 dependence of the radiation transition probability would reduce cascade transitions to a neglig-ible value. Radiation from this level should then have no pressure-independent component. Because of the lower intensity of radiation from the v’ = 3 level of the A2E+ state ( z 10-1 that from the v’ = 0 level) the data are somewhat uncertain.However the intercept appears to be considerably less than would be anticipated from scaling the v’ = 0 results by the relative intensities of the v’ = 3 to the v’ = 0 bands. Below 1 mm Hg the strongest v’ = 3 bands were never observed (that is they were less than ~5 % of the v‘ = 0 bands). The A2Z+ potential curve intersects the B2n potential just above ( ~ 0 . 1 6 eV) the v’ = 3 of the former and at v’ = 7 for the latter which is probably also crossed by the 2Z+ curve as well. Most probably the v’ = 3 A2E+ state is populated by a collision-induced transition from the v’ = 7 B2II state which itself is in equilibrium with the 2E+ state. Such a process may explain the absence of radiation from the v’ = 7 level of the B2II state.Although the processes which remove energy from the newly-formed molecule as kinetic and vibrational energy have been separated from each other this is artificial. By comparing the energy that must be removed from the newly formed NO to reach any given vibration level of the A2E+ (or B2n) with that which the N2 molecule can accept as vibration it will be seen that a difference exists ( ~ 0 . 1 eV) which must either be supplied or absorbed as kinetic or rotational energy. Because of this the collisional process which removes ~1 eV to reach the v’ = 0 of the A2E+ state may be no more probable than the conversion of ~ 0 . 1 eV of vibrational energy to kinetic energy. This may explain the similar behaviour of the v’ = 3 and v’ = 0 levels of the A2E state.Excitation of the v’ = 0 level of the B2II state is probably through a collision-induced transition from the b4Z,v‘= state whose population is pressure independent. This would be consistent with the linear pressure dependence and the strong quench-ing by NzO. It is of course necessary that this collision-induced transition represent a small loss of b4E;= molecules compared to other processes if the ratio of the Ogawa band intensity to the 6 band intensities is to remain independent of pressure. A spontaneous transition between these states is not expected. The b4ZG=0,1,2,3 states may be populated either by spontaneous transitions (in both directions) from the a4n state-with increasing internuclear distance changes as u’ decreases (0.03 % for the or by a collision-induced transition to and from the a4n state (however some energy may be removed so different vibration levels of the a471 would be involved in the forward and reverse directions).The higher v’ levels (1 2 3 4 5 6) of the Ban state behave in a more complex manner than any other levels their pressure dependence is not simple; they depend on the precise nature of the gas mixture and their quenching with C02 is anomalous. These observations indicate that an energy-abstraction process is important in their excitation. This is verified by the potential diagram which shows that these levels may only be reached from other states either by relatively large energy changes (of about 1.0 eV) or relatively large internuclear distance changes (9 %).Suc R. A . YOUNG AND R. L. SHARPLESS 255 internuclear changes are characteristic of the activated state in chemical reactions.31 The pressure dependence of the quenching rate C is consistent with a competition between N20 and other collision processes. The quenching of the A2XC,fi=o state by C02 is also compatible with the previous discussion of their excitation. The C02 pressure for half-quenching of the A2E$=o level is 0.4-0.5 mm Hg which is considerably lower than the value (3 mni Hg) obtained by Basco et aZ.30 and also less than the report by Kleinberg and Terenin 30 (1 mm Hg). The discrepancy with Basco et aZ.30 although large may not be of great significance since they arrived indirectly at their results (electronic quenching was not their primary objective).The discrepancy with Kleinberg and Terenin is much less. The conclusion that the observed quenching effects are due to interaction of the quenching agent with the radiative state and not with a precursor is strengthened by the low quenching rate in comparison to other measurements. Although reactions of excited nitric oxide (NO*) do not necessarily occur at the same rate as for ground state NO this will be assumed. Then if “1% 1014/cm3 (which is true for the experiments discussed here) the chemical lifetime Ze of NO is z 10-3-10-4 sec. In this time-interval NO will have made = 103-105 collisions (depending of course, on the assumed kinetic cross-sections) with a quenching gas present at a partial pressure of % 1 mm Hg. In the absence of an added quenching gas some process must limit the lifetime of the (metastable) states involved in the excitation of the NO bands.If this were not true the intensities of the p bands (which may be populated through bound metastable states) relative to the 6 bands (which are not populated through any bound state) would be a function of the nitrogen atom concentration and thus a function of the NO flow rate. Fig. 4 shows that this is not the case. The observed quenching constant C would also show a large scatter if the chemical reactions were a limiting factor. Thus the (metastable) states involved in the chemi-luminescent excitation of the NO bands do not have an actual lifetime greater than 10-3 sec in an environment of N2 at = 1 mm Hg. Despite the great amount of data collected on the excitation of NO in the associa-tion of atomic oxygen and nitrogen few details of individual excitation processes have been established with certainty-in fact all the specific processes may not have been identified.However reasonable processes have been suggested that adequately fit some of the facts so far assembled. There are several additional measurements that should be made. Unusual intensities and small displacements of the rotational structures of the p bands (particularly from 21’ = 0) are expected if the excitation mechanisms that have been suggested are correct (and perhaps even if they are not). The 6 bands may show a strong temperature dependence (particularly if a rotational potential hill must be surmounted in the pre-association into this band).If energy-removing collisions are involved (as appears inevitable) in‘ the excitation of the lower levels of the j’3 and y bands they also should show a temperature effect. By increasing the nitrogen-atom concentration until the p and y bands decrease relative to the 6 bands a measure of the lifetimes of the excited states involved in the excita-tion of the NO radiation may be obtained (and also its dependence on other para-meters). An absolute measurement of the S band intensities concurrent with absolute atom concentration determinations would give the rate of pre-association. Some of the experiments now underway at this laboratory are directed along these lines. Chemical reactions of NO place an upper bound on its lifetime. The present investigations of chemiluminescent reactions resulted from a con-The utility of quenching measure-The support versation with Dr.Joseph Kaplan some time ago. ments was suggested by a careful reading of Dr . Kyle Bayes’ thesis 256 BANDS OF NITRIC OXIDE and facilities of Stanford Research Institute have made this research possible without other assistance. A great deal of the data reduction was done by Miss Kathleen Moran and Mrs. Jill Thomas. Dr. K. C. Clark originally interested both the authors in this general field. 1 The authors wish to thank Dr. F. R. Gilmore of the Rand Corporation Santa Monica Cali-fornia for allowing the use of this very complete potential diagram of NO (and others of 0 2 and N2). Such a diagram is essential for the analysis presented in this paper. It is to be hoped that a loose leaf file of such potential diagrams will become generally available and that con-tinual additions will be made to it by the scientific community.2 Vanderslice Mason and Maisch J. Chem. Physics 1959 31 738. 3 Lewis Astrophys. J. 1904 20 49 58. 4 Strutt (Lord Rayleigh) and Fowler Proc. Roy. SOC. A 1911 85 377. 5 Strutt Proc. Roy. SOC. A 1917 93 254. 6 Lewis Phil. Mag. 1913 25 826. 7 Jenkins Barton and Mulliken Physic. Rev. 1927 30 150 give the history of the NO /3 and y 8 Knauss Physic. Rev. 1928 32 417. 9 Brook and Kaplan Physic. Rev. 1954 96 1540. 10 Tanaka J. Chem. Physics 1954 22 2045 ; J. Sci. Res. Inst. (Japan) 1949 44 28. Tanaka 11 Kaufman and Kelso J. Chem. Physics 1956 27 1209. 12 Schade Technical Report no. 1 (July 1961 Contract AF 19(604)-6657 between UCLA LOS Angeles Calif. and AFCRC Bedford Mass.). Kaplan Schade Barth and Hildebrandt Can. J. Chem. 1960 30 1688; 1959 30 347. 13 Gaydon Proc. Physic. SOC. 1944 56 160. 14 Barth Schade and Kaplan J. Chem. Physics 1959 30 347. 15 Barton Jenkins and Mulliken Physic. Rev. 1927 30 175. 16 Schiff private communication. 17 Beale and Broida J. Chem. Physics 1959 31 1030. 18 (a) Kistiakowsky and Volpi J. Chem. Physics 1957 27 1141 ; 1958 28 665. (b) Clyne and Thrush Proc. Roy. SOC. A 1961 261 259. (c) Kaufman Proc. Roy. SOC. A 1958 247 123. (d) Harteck Reeve and Mannella J. Chem. Physics 1958,29 1333. 19(a) Berkowitz Chupka and Kistiakowsky J. Chem. Physics 1956 25 457. (b) Bayes and Kistiakowsky J. Chem. Physics 1960 32 992. 23 Broida Schiff and Sugden. Trans. Faraday Soc. 1961 57 259. 21 Linnett and Marsden Proc. Roy. Sue. A 1956 234 489 504. Groves and Linnett Trans. Young J. Chem. Physics 1960, band identification. and Ogawa J. Sci. Res. Inst. (Japan) 1949 44 1. Faraday SOC. 1958 54a 1323; 1959 55 1338 1346 1355. 34 1292. 22 Flory and Johnston J. Amer. Chem. SOC. 1935 57 2641. 23 Bethke J. Chem. Physics 1959 31 662. 24 Herzberg Molecular Spectra and Molecular Structure (D. Van Nostrand Co. Inc. New York, 25 Lagerquist and Miescher Helv. physic. Act. 1958 31 221. 26 Nikitin Opt. Spectr. 1961 11 246 (English translation). 27 Herzfeld and Litovitz Absorption and Dispersion of Ultrasonic Waves (Academic Press 1959). 28 Jarmain Fraser and Nicholls Astrophys. J. 1953 118,228. 29 Soshnikov Soviet Physics 1961 4 425 (English translation). 30 Basco Callear and Norrish Proc. Roy. SOC. A 1960 260 459. 31 Glasstone Laidler and Eyring Theory oj’Rate Processes (McGraw-Hill Book Co. Inc. New 32 Bayes Thesis (Chemistry Dept. Harvard University 1959). 1950) pp. 416-19. York 1941) p. 150

ISSN:0366-9033    

DOI:10.1039/DF9623300228

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

The Reaction O++NpNO++N BY V. L. TALROSE, M. I. MARKIN AND I. K. LARIN Institute of Chemical Physics, Academy of Sciences, Moscow Received 16th February, 1962 The reaction O++N2 +NO++ N was investigated mass-spectrometrically. The upper limit of the rate constant of this reaction was estimateed by comparison with the reaction CH++ CH4 +CH; fCH3 and was found to be 6.7 x 10-12 cm3isec. Potter 1 found in 1955 that the rise in pressure of a nitrogen+oxygen mixture in a radio-frequency mass-spectrometer results in increased height of the mass 30 ion peak, which he ascribed to NO+. He associated the formation of this ion with the reaction According to Potter, the rate constant should be (1 k0.25) x 10-8 cm3/sec. Reaction (I) is of great interest as it is one of the probable ionosphere processes.In particular, the O+ atomic ions are converted into molecular NO+ ions by this reaction, and this opens up a path for fast recombination of charged particles. In considering the ensemble of possible ionosphere processes, Krassovsky 2 showed that the coefficients observed in effective recombination could be explained when the rate constant of (1) was taken as 10-10 cm3/sec. Bagaryatzky 3 suggested that process (1) plays the major part in establishing the ion balance of the upper atmosphere. He proceeded from the rate constant of pro- cess (I), as obtained ref. (1). Bates 4 estimated the rate constant of (1) from experimental data on the change in the ionic content of the upper atmosphere during the night. His results show that the rate constant of (1) does not exceed 10-13 cm3/sec.The parameters of the elementary process (1) are of interest not only in connection with its possible part in the mechanism of ionosphere processes, but also for general problems that can be solved by the theory of ion-molecular reactions; these were discussed recently by one of the authors.5 Indeed it is known from studies of ion- molecular reactions carried out during recent years that the ionic reactions of hydro- gen or proton transfer have a large cross-section and proceed, as a rule, practically without activation energy. Matters are more complicated when there is another competing reaction of the same kind, or a charge exchange process. However, for reactions involving more complicated rearrangements than H+ and H transfer, this absence of activation energy is by no means essential.Pshezhetzky and Dmitriev found that reaction proceeds with an activation energy of 7 kcal/mole. On the other hand, it was found that the excited N2+ and 0 2 ions 7 reactions 0' +N2-+NO+ +N. (1) NZ + 02-+NO' +NO (2) Nz +N2-+N: +N, (3) 0; +ope,+ +o, (4) proceeded practically without activation energy. I 257258 THE REACTION 0++N2+NO++N Several years ago, one of the authors and Frankevich carried out experiments on the formation of NO+ ions in the ion source of a mass-spectrometer, using an oxygen +nitrogen mixture. These studies were concerned with problems connected with process (2). No evidence in favour of NO+ formation by ion-molecular reactions was found, and this was consistent with an appreciable activation energy for process (2).This was briefly reported in ref. (8) and later in ref. (5). Reaction (2) is a rather complicated rearrangement involving the transformation of double and triple bonds. In addition, there is a possible (N2 . 02)+ decomposition to charge exchange products. The possible competition of this charge exchange process has not yet been studied. Reaction (I) is considerably more simple in this respect, since at low pressures and at temperatures common to an ion source of a mass-spectrometer or to the ionosphere, only this process need be taken into account in the collision of Of with N2, the charge exchange being endothermic 9 (- 1-94 eV), while association O++Nz+N20+ may be neglected due to the low probability of three-body collisions.Taking into account the importance of process (1) in connection with the above, and the discrepancies of the data on its rate constant, the authors started a more detailed investigation of the appearance and origin of mass 30 ion peaks in the mass- spectra of nitrogen + oxygen mixtures. An ordinary 60" Nier mass-spectrometer, provided with an electron multiplier, was used for this purpose. The resolution of this device was about 100. The first series of experiments dealt with a mixture of 0 2 (90 %) and N2 (10 %). The pressure of this mixture in the ionization chamber attained 1 to 2 x 10-4 mm Hg. The components of the mixture were purified by passing them through a trap cooled with liquid nitrogen. It was found that the mass-spectrum of this mixture contained a mass 30 ion peak of a height considerably in excess of that of the expected 15N2 ion peak.If the former were due to NO+ ions formed by reaction (I), the dependence of its relative height on pressure would be linear. The height of the mass 30 ion peak (130/116) is given in fig. 1 as a function of mass 16 ion peak heights that are proportional to pressure. It may be seen that instead of the expected increase, there is a sharp decrease of 1301116 with pressure ; at higher pressures it becomes practically constant or, perhaps, slightly increases. A suggestion was made that the ions formed were NO+ ions, resulting not by reactoin (l), but from ionization of NO molecules formed in nitrogen oxidation on the hot cathode, or in the " close-to-cathode " region.Two sets of experiments were carried out to verify this suggestion. One set was concerned with the appearance curve for mass 30, 16, 28 and 32 ions in the mass-spectrum of a nitrogen+oxygen mixture. Corresponding curves are shown in fig. 2. The conclusion was so clear that there was no necessity to apply the quasi-mono-chromat- ization of electrons and to make the energy scale absolute. The appearance potential for mass 30 ions is seen to be some 3, 6, and 11 eV lower than those for O,+, NZ, and 0+, respectively ( 0 2 + e+O+ + 0 + 2e - 19-2 eV 9). Thus, within the error of measure- ment, the appearance potential of the mass 30 ion corresponds to the ionization potential of the NO molecule (9.25 eV 9). The second set of experiments involved measurments of the relative heights of mass 30 peaks under conditions when an additional hot tungsten spiral was intro- duced close to the ionization chamber of the ion source.The spiral was situated such that the neutral products formed on it could enter the ionization chamber, whereas the electrons it emitted could not. A schematic view of an ion source with the addi- tional spiral is shown in fig. 3. The dependence of the 130/116 ratio on the power fed to the spiral is shown in fig. 4. It may be seen that, beginning with a certainV . L. TALROSE, M. I . MARKIN AND I . K . LARIN 259 O+ innp ciirrent lnrh iinitpl FIG. l.-The 13()/116 ratio as a function of the current of 0+(116) ions for a mixture of 02+N2. electron energy, V (uncorrected) FIG. 2.-Appearance curves for 0+, N2f, 0; ions and the mass 30 ion peaks.260 THE REACTION O++N2-)NO++N temperature corresponding to that of the tungsten heat, there is a rapid increase in the height of the mass 30 ion peak.In an attempt to suppress the NO formation the authors used a C02+N2 mixture instead of the nitrogen+oxygen one, as the rela- tive height of the peak due to primary Of ion in the C02 spectrum is somewhat high (-9 % of that for C0,C). On the other hand, it was hoped that thermal oxidation of N2 would be less strong with CO2 than with 0 2 . The dependence of the 130/116 Gas i n l e t f c m Mass analyser FIG. 3.4chematic view of the ion source. 1, cathode ; 2, electron-accelerating eIectrode (+30 V relative to the cathode) ; 3, electron-focusing electrode ($7 V relative to the cathode) ; 4, collim- ating electrode (its potential is equal to that of the ionization chamber) ; 5, ionization chamber ; 6, first repelling electrode (- 1 to + 1 V relative to the ionization chamber) ; 7, second repelling electrode (-10 V relative to the ionization chamber); 8, focusing electrode (-35 V relative to the ionization chamber ; 9, accelerating electrode ; 10, deflecting plates ; 11, additional tungsten ratio on 116 for this set of experiments is shown in fig.5. It appears that in this case the relative height of the mass 30 ion peak is also greater than the total height of the primary isotopic peaks of C180 and 15N2 ions. There is again a decrease in the relative height of the mass 30 ion peak with rise in pressure, after which the height becomes practically constant.If the NO+ ions were formed as a result of process (l), the following expression would be valid, spiral ; 12, screen.V. L. TALROSE, M. I . MARKIN A N D I . K . LARIN 261 where kl is the rate constant of process (l), khl is the rate constant for removal of NOS ions from the reaction zone, and “21 is the concentration of N2 molecules in the ionization zone. The kl/khl parameter corresponds to the slope of the tangent to the curves in fig. 1 and 5. As a result of these experiments it may be stated that this parameter differs from zero by an amount not greater than the error in measure- ments of the slopes ; this error was estimated by the authors as - 3 x 102 mm-1. (Esti- mation was made from the dependence shown in fig. 5. There was no point in using the dependence of fig.1 in view of the especially intensive formation of NO molecules in % I White heat point 3 15 2 0 25 power, W FIG. 4.-The 130/116 ratio as a function of power fed to the additional spiral. the “ close-to-cathode ” region, as mentioned above.) To estimate the upper limit of kl it is necessary to know the khl value, accurate determination of which is very difficult. Consequently, for estimating the kl upper limit, the authors used com- parison with process CH2,+CH4+CHl +CH,, since the rate constant of this process is one which has been studied most exten- sively.10-12 This process was carried out with the same mass-spectrometer using the same working parameters of the ion source. The corresponding curve for 117/Z16 as a function of 116 is shown in fig.6. As demonstrated many times before, the linear dependence of Z17/Z16 on pressure, corresponding to (where ks is the rate constant of process (5), and khs the rate constant of removal of CHf ions from the chamber) is realized here.262 % r O+ ions current (arb. units) FIG. 5.-Thc I20/116 ratio as a function of 116 for a mixture of C02+N2. k H 4 " I@rnrnHcq 4 CHQ ions current (arb. units) FIG. 6.-The 117/116 ratio as a function of the current of CHi(I16) ions from methane. 0.5V. L. TALROSE, M. I . MARKIN AND I . K. LARIN 263 It seems feasible to accept, with an accuracy of a factor of 2-3, that khl = kh2. Then, from eqn. (I) and (11), allowing for the above, we obtain accuracy of the slope tangent measurements slope tangent from the plot of fig.6 A tan a30 tan a17 3 x 102 = k5- - 5 x 104 - - = k , kl Gk5 6 x 10-3k5 (tan aI7 = 5 x lo4 mrn-', A tan a30 = 3 x mm-'). Field, Franklin and Lampe measured the k5 value using the constant-repelling method, i.e., in the presence of a constant electric field. They found that, under conditions similar to those of the experiments carried out by ourselves (primary ion path of - 1 mm, E- 10 V/cm), k5 = 8.9 x 10-10 cm3/sec. Under the conditions similar to those of thermal distribution of ion rates, one of the authors and Franke- vich found k5 = 1.16 x 10-9 cm3/sec. In fact, in passing from constant-repelling to conditions of thermal equilibrium the effective k5 changes by a factor not greater than 2-3. Substituting, for example, the second of the values obtained we obtain kl G6.75 x 10-12 cm3/sec.Thus, the kl value is considerably lower than that obtained by Potter.l Ap- parently, he erronously considered that the appearance of mass 30 ions is due to process (I). The relatively small cross-section for process (I) may, in principle, be due both to the low pre-exponential factor and to the activation energy for this pro- cess. If the latter proceeds with an activation energy and if a considerable amount of energy of relative motion of particles is used up in the activation, the inequality obtained for the kl value will only become greater under the most interesting con- ditions of thermal equilibrium at several hundred degrees centigrade. 1 Potter, J. Chem. Physics, 1955, 23, 2462. 2 Krassovsky, Izv. Akad. Nauk S.S.S.R., ser. geophys. Russ., 1957, no. 4. 3 Bagaryatzkii, Izv. Akad. Nauk S.S.S.R., ser. geophys. RUSS., 1959, no. 9. 4Bates, J. Atm. Terr. Phys., 1960, 18, 65. 5 Talrose, 18th Int. Congr. Pure Appl. Chem. (Canada, Montreal, August, 1961). 6 Pshezhetzky and Dmitriev, Dokl. Akad. Nauk S.S.S.R., 1955, 103, 647. 7 Cermak and Herman, J. chim. Physique, 1960,57,717. 8 Talrose and Frankevich, Zhur. Phys. Khim., 1959,23, 955. 9Field and Franklin, Electron Impact Phenomena and the Properties of Gaseous Ions (New York, 1957). 10 Talrose and Lyubimova, Dokl. Akad. Nauk S.S.S.R., 1952, 86, 909. 11 Field, Franklin and Lampe, J. Amer. Chem. SOC., 1957,79, 2419. 12 Talrose and Frankevich, Zhur. Phys. Khim., 1960,34,2709.

ISSN:0366-9033    

DOI:10.1039/DF9623300257

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Ion-Neutral Collisions in Afterglows * BY W. L. FITE, J. A. RUTHERFORD, W. R. SNOW AND V. A. J. VAN LINT General Atomics Division of General Dynamics Corporation, San Diego 12, California, U.S.A. Received 22nd January, 1962 In order to study collisions between ions and neutral particles at thermal energies, a series of experiments have been carried out which utilize high-speed mass-spectrometric monitoring of the afterglows in gases produced by (i) radio-frequency discharges and (ii) 20-MeV electron pulses. Ion-clustering, charge-transfer, and ion-exchange processes have been observed in atmospheric gas mixtures. From the ion histories in the afterglows, approximate values of the pertinent reaction rates are deduced. The technique of using the afterglow of a gas discharge for the study of rates of thermal energy collisions involving free electrons is now well established.Usually, following the methods initiated in the late 1940’s, the afterglow in a microwave cavity has been studied, as the electron density can be determined from the shift of the resonant frequency of the cavity, and tracing this shift as a function of time indicates the decay of electron density with time. From observation of the electron clean-up, a number of coefficients for electron-ion recombination and electron attachment have been determined, as well as ambipolar diffusion constants. Very early in this type of study, it became apparent that ion-neutral collisions were also under study. In an afterglow in helium, for example, it was found that the recombination coefficient values were much higher than could be expected were the electron clean-up occurring through the radiative recombination process, e + He+ +He+hv. In view of the fact that dissociative recombination of molecular ions, e + X’,-+X’ + X’, where the primes designate the possibility of having excited pro- ducts, had been proposed by Bates 1 as a rapid process, and the fact that He; was known to exist, from the much earlier mass-spectrographic work of Tuxen,2 it seemed likely that the observed recombination involved the molecular helium ion rather than the atomic ion.That this was the correct interpretation was shown experimentally by Phelps and Brown,3 who coupled microwave measurements of electron clean-up with mass-spectrometric monitoring of the ions in the afterglow. In addition, from the observed time histories of the ions, Phelps and Brown determined a rate coefficient for the ion-neutral collision process believed responsible for producing the molecular helium ion, He+ + 2He-+He; + He. Despite the fact that in the helium afterglow it had been established that as a result of ion-neutral reactions the principal ion was not the most obvious ion, it was not generally realized that the same situation obtained in other gases.As a case in point, a number of studies of electron clean-up in nitrogen afterglows4-7 were in- terpreted in terms of electron recombination with N%, although some difficulties with the interpretation were evident. Only recently, following the discovery of the ease with which NZ could be formed, * , 9 was it established that N$ is indeed the principal * This research was sponsored by the Defence Atomic Support Agency of the United States Department of Defence under contract no.DA-49-146-XZ-049. 264W. L. FITE, J . A. RUTHERFORD, w. R. SNOW AND V. A. J . V A N LINT 265 ion in nitrogen afterglows, and more recently Kasner, Rogers, and Biondi l o again coupled microwave with mass-spectrometric techniques to study recombination processes under circumstances where positive identification of the responsible ion could be made. Of particular interest is the fact that they have obtained recombina- tion coefficient values which are reliably attributable to Nf and 0; recombination. The fact that mass-spectrometric monitoring could provide direct information on thermal ion-neutral collisions was not overlooked in the interim, however.Dickinson and Sayers 11 studied the charge-transfer process 0++ 0 2 - 0 + 0-5 by mass spectrometric studies of the afterglow in He+02 gas mixtures. To a large extent, their experiment established this technique as one in which simple two-body phenomena could be studied, thus complementing the higher-energy techniques using ion beams and the technique of studying secondary ions in low-pressure mass- spectrometer sources, such as those used by Stevenson and Schissler 12 and Field, Franklin and Lampe.13 Some additional experiments are presented here, using mass spectrometry of afterglows, directed principally toward the ion chemistry of the upper atmosphere. EXPERIMENTAL METHOD The experimental method used in all studies of this type is straightforward.A gas is excited to an ionized state by some means and then the exciting means is suddenly re- moved. Charged particles in the gas diffuse to the walls of the afterglow chamber, and a small hole in the wall permits some of the ions to escape into the accelerating system of a fast-response mass spectrometer. The mass spectrometer is tuned to a particular mass peak and the current is recorded as a function of time on an oscilloscope. In the present experiments, two magnetic-sector mass spectrometers were used. The first, a 90" instrument, is shown diagrammatically in fig. 1. In this instrument a region of differential pumping was interposed between the afterglow chamber and the high-vacuum region of the mass spectrometer proper, and acceleration of the ions was made in the differ- entially pumped chamber. In order to give a fast response time (-2psec), a silver- magnesium electron multiplier and a cathode follower pre-amplifier were used to detect the analyzed ions.The afterglow chamber in this instrument was a fused quartz tube with an inside diameter of approximately 2 cm. It was constructed so as to permit excitation either by capacitat- ively coupled 30-Mc/sec radio-frequency power (by means of the two straps on the tube on either side of the ion exit aperture) or by a pulse of 20-MeV electrons from General Atomic's electron linear accelerator (Linac). The pulses from both excitation sources normally lasted for about 5 psec. The second instrument, the one from which most of the data presented here were taken, was an improved instrument of high resolution ( m / A m ~ 100).It was constructed of stah- less steel with copper gaskets throughout to permit baking-out and had a stainless steel afterglow chamber. The radio-frequency power was applied between the plane wall con- taining the ion exit aperture and a parallel plane " pusher " electrode, so that the E-field of the radio-frequency power was parallel to the direction of the ion extractor. The distance between the electrode and the wall was about 1-5 cm and the plate had a diameter of ap- proximately 4 cm, so that the geometry was, to a crude approximation, one-dimensional. The name " pusher " for this electrode was derived from the fact that it could be slightly biased, following the cessation of an excitation pulse, to provide a drift field across the afterglow chamber.Electron impact excitation studies using the Linac were carried out by passing the high-energy electron beam through two thin stainless steel foil windows. Both instruments were of reversible polarity so that both positive and negative ions could be detected and studied. The energy of the ions during analysis was usually about 400 eV ; after analysis they were accelerated into the first dynode of the multiplier by an additional 2OOO-V potential drop. I*266 ION-NEUTRAL COLLISIONS I N AFTERGLOWS \ f J AM PLlFlER There were two reasons for fitting both instruments with provisions to use either radio- frequency excitation or electron-impact excitation : the first was to permit the comparison of the afterglows excited by the two methods, in order to attempt to determine whether the distributions of ion states differed, as indicated by differing afterglow ion histories ; the second arose from the discovery that with radio-frequency excitation there was a con- siderable accumulation of impurities, particularly of nitrogen oxides in N2+ 0 2 mixtures.e\ f J +-ELECTRON > MULTIPLIER LINEAR r 0 C.R.O. ---- GAS INLET- 4 FIG. 1 .-Schematic diagram of apparatus for mass-spectrometric studies of afterglows. Although the pulse duration was purposely kept short to minimize impurity formation during the pulses, it was found that in order to obtain reliable and reproducible striking of the discharge, it was necessary (especially in electronegative gases) to use a fairly high pulse-repetition rate (-lo00 c/sec) so that each afterglow would provide the pre-ionization required for the next discharge pulse.Since the pump-out time of the source was about 100 sec, -105 times the interval between pulses, the use of short-duration pulses was some- what defeated by using radio-frequency excitation. However, with the Linac no pre- ionization was required, and the interval between pulses could be made arbitrarily long so that the neutral impurities produced following each pulse could be pumped out between pulses. In this manner, pulse-generated impurities could be kept to an insignificant minimum with the Linac. The Linac was also useful in estimating the initial ion-density associated with a given mass-spectrometer signal because the electron-impact ionization cross-sections of the gases were known and the gas pressures were measured.Generally, the initial ion densities using the Linac were 1011 cm-3 or less, and an order of magnitude lower using the radio- frequency excitation. TREATMENT OF DATA The direct data in this experiment were the oscilloscope traces of the instantaneous current of each ion in the afterglow as a function of time. Since most of the ion-neutral reactions that are of primary interest to us are rather fast, the early times in the afterglow have been of particular importance. Unfortunately, these are also the times at which the effects of electron-ion recombination and diffusion of the plasma from its initial, and rather poorly known, spatial distribution would most adversely influence the ratesw. L.FITE, J . A . RUTHERFORD, w. R . SNOW AND v. A. J . VAN LINT 267 obtained from study of single-ion time histories. It has, therefore, been our practice to compare time histories of two ions to effect some cancellation of the adverse effects. The rate of change of number density of a primary ion at some position in the afterglow can be written as dN1lat = -alneNl -Pn,N, -(Cyini)N, +Dl V 2 N , , (1) where a1 is the electron-ion recombination coefficient, n, is the electron density, and p is the rate coefficient for production of a secondary ion when the primary ion interacts with a neutral molecule whose density is given by 122. The third term represents all other loss processes through ion-neutral collisions, and the last term represents ambipolar diffusion, the diffusion constant being given by D1.If we assume that the secondary ions are gener- ated only at the expense of the primary ions, the rate of change of number density of the secondary ion at the same position is given by aN2iGt = -a2neN2 +Pn,N, -(z6ini)N2+D,V2N2, (2) where the third term now represents ion-neutral processes leading to the loss of the secondary ions, and the first and fourth terms are analogous to those in eqn. (1). Defining R = Nz/Nl, it follows that 0.4 0.2 where y = z y i n i and 6 = C6,ni. It is evident from this expression that in the limit of small R, the first term is mathematically negligible and 6R16t-Pn2. Conceivably, this might occur only when R is so small as to be physically impracticable, but it may be noted that each - - 0 I ’ --‘-L___I O L 0 10 20 30 40 50 6 0 time, psec FIG.2.Plot of R(Og/N$) in the radio-frequency afterglow in 100 : 1 N2+02. part of the first term represents differences of similar quantities for the two ions. Thus, one might expect to find some pairs of ions for which the first term would remain negligible even up to fairly large values of R. Generally, this expectation would be most likely for ions of comparable mass, diffusion coefficients, and recombination coefficients, and par- ticularly where the only major ions in the afterglow were the two under study (thus minim- izing y and 6 separately). If we limit ourselves to consideration of such pairs of ions, it is not unreasonable to assume that the measured ion currents are proportional to the number densities near the wall of the plasma, so that R may be taken as the ratio of currents as well as the ratio of number densities.268 ION-NEUTRAL COLLISIONS IN AFTERGLOWS To date, rate coefficients have been taken from the slopes of R(t) in the limit of small R, and no serious attempt has been made to account for the differences in mass, diffusion co- efficients, etc.The only criterion for “ correctness ” has been the existence of linearity of R with time in the limit of small R. A Fairly typical plot of R(t) in practice is shown in fig. 2. In this particular case, R is the ratio of currents of 0; to N;in the afterglow of a radio-frequency discharge in a 100 :1 mixture of N2+02 at 0.2 mm dg.The linearity of R(t) is seen to be well defined, with the most remarkable feature of this and many similar plots being that the linearity is maintained to values of R as high as 0.3. At the present time, we must regard the large extent of the linear region as being fortuitous and a consequence of cancellation of terms in eqn. (3). RESULTS HELIUM Fig. 3 illustrates the ion currents in the afterglow of a radio-frequency dishcarge in spectroscopically pure helium. It is shown primarily to illustrate the importance that impurities can assume in afterglows through ion-neutral reactions. It is seen 200 I00 80 60 40 30 n > 2o E W + .g 10 0 6 4 3 2 I 0 500 1000 1500 2000 2500 3000 3500 time, psec FIG. 3 . 1 o n histories in the afterglow of a radio-frequency discharge in spectroscopically pure helium at 2 0 mm Hg.that Ne+ becomes the major ion present after only 2 msec, despite the fact that the supplier’s analysis of the gas places an upper limit on the neutral neon impurity at 50 p.p.m. The belief that the Ne+ is formed through charge transfer is predicated on the fact that the rate of decay of the helium ions is somewhat more rapid than wasw. L. FITE, J . A. RUTHERFORD, w. R . SNOW AND v. A. J . VAN LINT 269 observed by Phelps and Brown,3 who removed neon impurities in their helium by liquid-helium-trapping of the gas. The ion at mass 12 is not completely identified, but the fact that it is observed only within a limited pressure range suggests that it may be He$ rather than, say, a carbon impurity. OXYGEN Because Dickinson and Sayers 11 had studied the charge-transfer process O+ + 0 2 + O+Oz in He+O mixtures in proportions of the order of 100: 1 alrd obtained a rate coefficient of 2.5 x 10-11 cm3/sec, a check of this charge-transfer rate was made.In the first experiment, pure 0 2 was used in order to circumvent any ionization by helium metastables or charge transfer involving helium. The rapid decay of the O+ in pure 0 2 at the pressures required to obtain usable signals permitted placing only a lower limit on the reaction rate of 1 x 10-11 crn3/sec. When a 10 : 1 mixture of He + 0 2 was used, an apparent rate of 1.5 x 10-10 cm3/sec was obtained. Since the O+ decay time in this mixture was still quite short, production of 0; by metastable helium ionization may have occurred, so that this figure must be tentatively regarded as an upper limit.We therefore think that to within the accuracy presently obtainable, we are not in serious disagreement with Dickinson and Sayers. NITROGEN A typical set of ion curves in the radio-frequency afterglow in nitrogen (With a small water impurity) is shown in fig. 4, which illustrates clearly the formation of "$ and NZ, apparently through clustering. In studying the formation of NZ, using 3000 n 2000 2 d 3 5 W Y g g 1000 .4 0 0 IOC 200 300 400 time, psec FIG. 4.4verlay of positive ion oscilloscope traces in the afterglow of a radio-frequency discharge in nitrogen at 0.5 mm Hg pressure. both the Linac and the radio-frequency data in the pressure range 0.1 to 1.0 mm Hg, it has been found that the parameter p is apparently pressure-independent, implying an effective two-body process (or a three-body process in which the NZ complex is sufficiently long-lived to always be stabilized in this pressure range), which is in accord270 ION-NEUTRAL COLLISIONS I N AFTERGLOWS with the findings of Saporoschenko.9 Interestingly enough, however, the tentative values obtained with two different methods of excitation appear to be slightly different, the radio-frequency excitation value being only about 60 % of the value from the Linac excitation data.The apparent reaction rate, not corrected for the different ambipolar diffusion coefficients and detection efficimcies of the NZ and Nf ions, is about 5 x 10-13 cm3/sec from the Linac data. As noted already one of the problems of working with the N2 + 0 2 mixtures was that nitrogen oxide impurities would accumulate if the rate of exciting pulses was too high.Fig. 5 illustrates a typical set of oscilloscope traces using the radio-frequency excitation at a 1000-c/sec repetition rate and a gas pressure of 0-8 mm Hg. In this fig- ure, it is seen that both NO+ and NO,+ become the dominant ions after about 100 p sec. At much longer times, it is observed that NO+ is the persistent ion, as might be expected if it were possible for charge transfer to occur and terminate the entire process on theW. L. FITE, J. A. RUTHERFORD, w. R . SNOW AND v. A. J . VAN LINT 271 ion of lowest ionization potential. It is an interesting observation that at lower pressures NO+ remains prominent, but NO: disappears only to be replaced by N2Of- It is also evident from data of the type shown in fig.5 that NO+ is formed at the ex- pense of O i , either through the exchange reaction 0; + N2+NO+ + NO or the charge- transfer process 0; + NO+02 + NO+. That the process is charge transfer with accumulated NO rather than exchange with N2 was demonstrated using Linac data taken at sufficiently low pulse rates (minutes between pulses) so that minimum accumulation of NO could occur. Fig. 6 shows a typical set of traces for a pressure of 1 -1 mrn Hg. In this figure, it is seen that the NO+ and 0; decay at sensibly the same rate, arguing that the exchange process 0-5 +N2-+NOf+ NO is negligibly slow and little neutral NO was present. 100 t- I 0 - L 0 50 100 159 203 time, psec FIG.6.--Oscilloscope traces in the afterglow in a 100 : 1 N2+02 mixture excited by high-energy electron impact at a pulse rate of 1 each 2 min. The appearance of NO+ in fig. 6 is interesting for another reason, namely, that its build-up seems to occur only for a very short time. Comparing the decay of N+ in fig. 4 and 6 suggests the explanation. In the absence of 0 2 , the N+ persists for much longer times than in its presence, and in fig. 6 it is shown that the termination of growth of NO+ appears to coincide with the disappearance of N+. Thus, it would seem that the process N++ 02+NO++ 0 is very rapid, and a tentative value for its rate has been placed at 5 x 10-10 cm3/sec. MIXTURES OF NITROGEN AND HYDROGEN Throughout the course of working with nitrogen, great care had to be exercised to limit the existence in the afterglow of N2H+, which was apparently formed by the reaction N;+H20--+N2H++OH.Since this ion at mass 29 could be reduced to negligible proportions through adequate baking of the source chamber, exchange with water seems to be the proper identification of the process. However, in order to eliminate a possible alternative interpretation, namely, through the process NZ + H2-+N2H+ + H, some experiments were carried out in 100 : 1 mixtures of N2 + D2272 ION-NEUTRAL COLLISIONS I N AFTERGLOWS to study mass 30 in the afterglow. It was determined that, using the analysis method outlined above, the apparent two-body rate coefficient ranged from 1-2 to 2.3 x 10-10 cm3/sec. Although the data met the internal consistency criterion, that R be linear with time in the limit of small R, the actual rate coefficient was an order of magnitude less than expected from the data of Stevenson and Schissler,12 as extrapolated down to thermal energies on the basis of the theory of Gioumousis and Stevenson.15 Whether this indicates that the method of analysis which was used to obtain the data in these afterglow experiments was faulty, or whether the ion-exchange process was more complicated than allowed for by Gioumousis and Stevenson remains to be seen.NEGATIVE IONS To the present time, no attempts have been made to obtain rate coefficients for processes involving negative ions, and it appears that a number of difficulties will attend such attempts. First, negative ions are formed by direct attachment of electrons, in addition to charge-transfer and exchange processes ; secondly, the manner in which the ion sheaths are formed at the walls generally permits extraction of negative ions only in the later portions of the afterglow (positive ions on the other hand are best observed early in the afterglows) ; thirdly, impurities seem to be much more troublesome in negative-ion spectra than in positive-ion spectra.Apparently, very small amounts of chlorine, which has been unexcludable from the first apparatus with the fused quartz discharge chamber, result in immense C1- peaks, and other electronegative impurities behave similarly. SUMMARY Although, at the present time, the use of mass spectrometry in the study of after- glows in mixtures of gases can hardly be regarded as giving reliable quantitative reaction-rate values, it seems established that the technique provides positive identifica- tion of the many ions present in afterglows, dramatically displays the various heavy- particle collision processes, and provides estimates for the reaction rates. It seems likely that with increased experience in its use, this technique can be made to provide a great deal of new and reliable experimental information on ion reactions at thermal energies. 1 Bates, Physic. Rev., 1950, 77, 718 and 1950, 78, 492. 2 Tiixen, Z. Physik, 1936, 103,463. 3 Phelps and Brown, Physic. Rev., 1952,86, 102. 4 Biondi and Brown, Physic. Rev., 1949, 75, 1700. Bryan, Holt and Oldenberg, Physic. Rev., 1957, 106, 83. Faire and Champion, Physic. Rev., 1959, 113, 1. Bialecke and Dougal, J. Geophysic. Res., 1958, 63, 539. 5 Kovar, Beaty, and Varney, Physic. Rev., 1957,107, 1490. 6 Saporoschenko, Physic. Rev., 1958, 111, 1550. 7 Kasner, Rogers and Biondi, Physic. Rev. Letters, 1961, 7, 321. 8 Dickinson and Sayers, Proc. Physic. SOC., 1960, 76, 137. 9 Stevenson and Schissler, J. Chem. Physics, 1958, 29, 282. 10 Field, Franklin and Lampe, J. Amer. Chem. SOC., 1957, 79, 2419. 11 Friedman, Proc. I.R.E., 1959, 47, 272. 12 Giournousis and Stevenson, J. Chem. Physics, 1958,29,294.

ISSN:0366-9033    

DOI:10.1039/DF9623300264

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. H. I. SchiH (McGiZZ University) said Prof. Norrish has referred to the (1) reaction 0 + N02+NO + 0 2 in which he and his co-workers have detected oxygen excited to the eighth vibrational level. Such excited molecules have more than the 24 kcal/mole required to decom-pose 0 3 . An attempt was made in our laboratory to study the reaction using the mass-spectrometer technique described in our paper. No such decom-position was detected. This is in agreement with the conclusions of McGrath and Norrish that reaction (2) has a very small rate constant. They find however that the reaction O:(v>,17)+ 03-d02+ O('0) (3) does have a large rate constant. I would like to ask Prof. Norrish why he thinks k3 should be so much greater than k2. Also the reaction q 3 P ) + 03-+ 0; + o2 (4) is sufficiently exothermic to produce 0; in vibrational levels above v = 17 and so might initiate chains.However we found that in the reaction between O(3P) and 0 3 one O3 molecule was consumed per 0-atom. This is again in agreement with the conclusion of McGrath and Norrish. Does Prof. Norrish have any comments on the reason why the higher vibrational levels are not populated in this reaction? (Paper by Basco and Norrish.) Prof. R. G. W. Norrish (Cambridge University) said I wish to refer to the ap-parent anomaly exposed by the paper of Dr. Callear and that which Dr. Basco has just read. It relates to the difference of rates of decay of vibrationally excited NO in the two processes. I have pointed out that in my opinion in the population of the vibrational levels of the X2II state of NO by fluorescence or collisional de-activation from the A2Z+ level it is unrealistic to conclude that only the first level is initially populated.All vibrational levels from t = 0 to v = n must be populated initially but resonant relaxation of the kind NOu=,+NOu=,,-2~ = 2NOu,,,-, (1) must occur so rapidly that the whole process completed by the final stage must be over before spectroscopic observation by means of kinetic spectroscopy can be achieved. This leaves only NO,1 which must be finally deactivated by collisional degradation. Now in the reaction NOCl+ hv = NO* + C1 (2) the NO is produced with up to 11 quanta of vibration in the X2ll state and although its disappearance is rapid it is readily observable spectroscopically.The photo -lysis in this work is almost exclusively produced by light lying between 2600 and 2000& and since D(NOC1) is 38 kcal there is ample energy to populate the level NOu=2+NOu= = NOu=, 27 274 GENERAL DISCUSSION u = 11 which requires 55 kcal. I think the apparent anomaly can be resolved if we assume that all the excited NO is produced in the higher levels say from u = 12 to v = 10. Truly resonant relaxation of the type described above will then stop at v = 11 and lower levels will have to be produced by the much slower process of collisional deactivation with NOCl or other species. Such collisional deactiva-tion will still depend on resonance but of a much lower probability than that repre-sented by eqn. (1) because the vibrational frequencies are not nearly so closely adjusted.There is thus time for all the lower levels to be populated and seen spectroscopically. Molecules such as N2 with no resonance correspondence are quite inefficient and have no observable effect. Added NO,=o is of low efficiency because of the lower probability of the reaction NO,=m+NO"= = NO,=,,-1)+NO,= (3) owing to the lower degree of resonance between widely separated values of v. This is an extreme statement of the case. During the progress of the flash, lower levels of v will become populated and the " gap " will be replaced by an irregular population of levels probably involving a minimum which will have the effect of putting " the brake on " the collapse of the system to v = 1. Since the NO* with the exception of X2IIN0,=1 does not outlive the period of the flash any photograph shows an instantaneous cross-section in time of the distribution of excited molecules " on the way down " there being a continuous feed in from upper levels during the period of the photoflash.Alternatively it may be suggested that any other mechanism which could give rise to an irregularly populated spectrum of v levels-such as the primary reaction itself-would have the effect of slowing down the process of vibrational relaxation in comparison to a mechanism which gives rise to a " smooth " spectrum of u levels, as may be postulated for NO* produced in the experiments cited by Dr. Callear. Finally it may be said that the addition of NO to the NOCl system strongly reverses the photolysis resulting in an overall NOCl continuum which makes any accurate photometric estimation impossible.Such qualitative effects as are observed are not in my opinion of sufficient magnitude to affect the above argument one way or the other. Dr. F. D. Findlay and Prof. J. C. Polanyi (University of Toronto) (communicated): We find that when HCl,=o is introduced into a vessel where H is reacting with CIz to form vibrationally-excited HCl there is a general diminution in emission intensity from all vibrationally-excited levels. (The experiment is performed under condi-tions of temperature and pressure ca. 1-5 mm 7OO0C where a chain reaction is taking place and where it has been demonstrated that H or C1 will promote the reaction hence replacement of H by C1 through H + HCl+H2 + Cl will not diminish the intensity).Successively higher vibrational states in general exhibit increasing amounts of deactivation. However the diminution in intensity is found to be anomalously large for u = 2 (60 % decrease as compared with 31 % for u = 3, 43 % for v = 4 53 % for v = 5 71 % for u = 6 90 % for v = 7) and exceptionally small (4 % decrease) for u = 1. It is difficult to explain this otherwise than by postulating a rapid energy transfer, HC1,=2 + HCl,=o+2HC1,=1 This would be a resonant transfer of the type that Prof. Norrish and others have discussed (energy discrepancy 105 cm-1 0.30 kcal/mole). Dr. J. W. Linnett (University of Oxford) (communicated) Basco and Norrish find that NO molecules produced from chlorine atoms and ClNO are not vibration-ally excited while those produced by photodissociation of ClNO may possess up t GENERAL DISCUSSION 275 eleven vibrational quanta.The first is to be expected because the equilibrium NO bond length in nitric oxide (1.15 A) is in effect the same as that in nitrosyl chloride (1-14A). The second could be readily understood if the NO bond length in the excited state from which dissociation occurs were different from that in nitric oxide in its ground state. It is perhaps worth drawing attention to the conclusion of Johnston and Berth that for the excited state of FNO examined by them the NO bond length is greater than that in the ground state. They suggested that the bond order decreased from 2 to 1+ on excitation; I have proposed that the reduction is from 2$ to 2.If a similar change in NO bond length occurs when ClNO absorbs the radiation producing dissociation then some vibrational excitation in the NO produced is probably to be expected. Prof. R. G. W. Norrish (Cambridge Unioersity) said I think the results obtained with NOCl and NOBr may be ultimately explained if the NO* in these cases is pro-duced initially only in high vibrational states (see discussion following paper by Basco and Norrish). Mr. M. A. A. Clyne and Dr. B. A. Thrush (University of Cambridge) said We have investigated the mechanism of one of the reactions of the type A+BCD = AB* + CD (which results in the formation of vibrationally excited molecules) by studying the isotopic distribution in the products of the stoichiometric reaction of 1 8 0 oxygen atoms with N1602 in a fast flow system.The results can be summarized by the equation 1 8 0 + N1602=$(180160 + N160) + &(I602 + NlsO). This provides clear evidence that the reaction proceeds via an intermediate in which all the 0 atoms are equivalent i.e. having D3h or C3v symmetry. The vibra-tional excitation of the 0 2 molecule formed but not of the NO molecule formed is then explained by the large change in 0-0 distance and small change in N-0 distance in going from the reaction intermediate to the products. No evidence could be found that this reaction yielded electronically excited 0 2 molecules in the 1cg' state. Prof. R. G. W. Norrish (Cambridge University) said I should like to refer to the reaction of chlorine atoms with Ozone1 which provide a remarkable example of specificity of three-body collision.The photosensitized decomposition of ozone by chlorine is a chain reaction involving the propagating steps Cl+03 = C10+02 ClO+O3 = C10+202. This has more recently been confirmed by kinetic spectroscopy and in addition the C10 has been shown to be vibrationally excited.2 The chains are terminated by the reactions C1O+C10 = c12+02 The latter reaction takes place predominantly when the concentrations of chlorine and oxygen are relatively high and gives rise to the short-lived red vapour C1206. The point I wish to make is that M as third body is represented only by C12 or 0 2 nitrogen and carbon dioxide being quite ineffective. This apparent specificity was explained by supposing short-lived complexes (sticky collision) to be formed between chlorine atoms and the third body represented by C13 and Cl.00.C13 Cl+03+M = C103+M'. 1 Norrish and Neville J. Chem. Soc. 1934 1864. 2 McGrath and Norrish Proc. Roy. Soc. A 1960,254 147 276 GENERAL DISCUSSION has been postulated by Rollefson both on theoretical grounds and in connection with the photosynthesis of phosgene where it is found to act similarly in a specific manner. Dr. N. Basco (University of Shefield) (contributed) From the quantum yield for the decomposition of ozone by visible light and from the fact that oxygen mole-cules possessing up to 75 kcal/mole of vibrational energy are observed in the flash photolysis of ozone it appears that the efficiency of vibrationally excited oxygen molecules in decomposing ozone is somewhat limited unless they possess much more energy than is necessary on purely energetic grounds.Since however the average energy of the nitrogen molecules is -21 kcal mole and 75 % of them can decompose ozone the maximum vibrational energy required for decomposition by NZ cannot be much more than 30 kcal/mole i.e. 5 quanta and it may well be that 4 quanta are sufficient. This difference between 0; and N; might be explained by the relative inefficiency of relaxation of NZ by ozone compared with that of 0; by ozone so that in the former case nearly all molecules with sufficient energy eventu-ally decompose ozone. The difference in relaxation is probable by virtue of the closeness of the vibration frequencies in ozone to those of oxygen whereas those of nitrogen are considerably greater.Likewise NO* with up to 55 kcal of vibrational energy can be observed in the presence of nitrosyl chloride and the quantum yield for decomposition of NOCl is two down to at least 2537A. Here again due to the closeness of the vibration frequencies of NO and NOCl relaxation may be more efficient than chemical reaction. The value for the proportion of the nitrogen molecules produced in an excited state may be compared with one of about 30 % estimated by Prof. Norrish and myself for hydroxyl radicals produced in a series of reactions O’D+HR and con-trasted with the very low (or zero) value obtaining in the reaction H+NOa. Clearly no generalization is yet possible on experimental grounds. (The paper by Morgan, Phillips and Schiff.) Prof.A. R. Ubbelohde (Imperial Coll. London) said In connection with the paper by Basco and Norrish our information about the transmission of repulsive forces along a chain of bonded atoms is still scanty. General considerations of the dependence of repulsions on the interpenetration of Thomas-Fermi clouds of non-bonded electrons suggest that in a sequence even strongly repulsive encounters between A and B will normally transmit only weak repulsion between C and D. This in turn determines the maximum potential energy of vibration available in the molecule CD if it splits off after the collision. Only feeble vibrational excitation could be expected. Mr. P. E. Charters Dr. B. N. mare and Prof. J. C. Polanyi (University of Toronto) (communicated) Cashion and Polanyi 1 in a study of the reaction observed infra-red emission from HCl which was ten times as great as that from NO.This could have been due to the fact that vibrational excitation arose prin-H+NOCl-+HCl+NO (1) cipally by a process A + BCD-+AB+ + CD 1 Cashion and Polanyi J. Chern. Physics 1961 35 600 GENERAL DISCUSSION 211 as Prof. Ubbelohde is supposing in his remarks or it could have been due to rapid collisional deactivation of NO. We have now repeated these experiments at two orders of magnitude lower total pressure and find that the NO emission intensity is below the limit of detectability by a thermocouple detector and consequently must be less than 4 % of the total HCl photon intensity. This confirms process (2) and is in agreement with the findings of Basco and Norrish.Prof. D. R. Herschbach (University of California) said Vibrationally excited product molecules have now been detected in about 30 exothermic atomic exchange reactions. However as yet there are only a few studies which indicate what frac-tion of the products are excited. From a theoretical viewpoint this information is essential. Without it we cannot tell whether the excited products represent the main course of the reaction or merely an interesting but practically negligible side effect. The reactions for which there is such information have all been mentioned at this Discussion. For the alkali reactions M2+X+MX+ M (14 and M+ RI-+MI+ R (1b) there is evidence that most of the products are highly excited whereas for some H atom reactions, H+ BC+HB +C (24 and H+BCD-+HB+CD (2b) with BC = C12 BCD = 0 3 ClNO N02 it is now established that the products are formed predominantly in low vibrational states.Perhaps the most fundamental motivation for the study of product excitation is that it may contribute to the experimental characterization of the potential sur-faces for reactions. The pronounced difference between the reactions (1) and (2) is thus encouraging and presumably it can be interpreted along lines indicated in early qualitative discussions of potential surfaces.1 2 The angular distribution of products provides another and in principle a quite direct approach to the study of these surfaces. However the theory of scattering from a multidimensional potential surface has until now remained swaddled in formal theorems.Recently an extensive programme of calculations on reactive scattering has been undertaken by Bunker and Blais,3 who use Monte Carlo methods to integrate the classical equations of motion. They have begun with a study of reaction (lb), based on a surface constructed so that most of the fall in potential energy is associ-ated with attraction between the reactants and not repulsion between the products. This feature was suggested as a necessary condition for vibrational excitation by Evans and Polanyi in their analysis 2 of reaction (la) and has been discussed more recently by Smith.4 In the calculations of Bunker and Blais the three interacting particles (CH3 is treated as a single atom) are not restricted to be collinear.For the sake of economy in computing time however it proved necessary to restrict the trajectories to a plane. Each collision is initiated with a randomly chosen impact parameter and angular orientation of the CH3I molecule. The thermal distributions of relative velocity and rotation and vibration of CH31 are also included. 1 Eyring Gershinowitz and Sun J. Chem. Physics 1935 3 786. Glasstone Laidler and 2 Evans and Polanyi Trans. Faraday Soc. 1939 35 178. 3 private communication from Dr. Bunker (Los Alamos Scientific Laboratory New Mexico, 4Smith J. Chem. Physics 1959 31 1352. Eyring Theory of Rate Processes (McGraw-Hill New York 1941). March 1962) who has kindly permitted me to describe this work here 278 GENERAL DISCUSSION The results obtained indicate that the assumed potential can account for all of the qualitative features inferred from the molecular beam experiments.The predicted distribution of product excitation is broad but shows a pronounced peak which puts most of the energy of reaction into vibrational excitation of the MI molecule. The angular distribution in the plane da/dX falls off more or less linearly from a maximum near x = 0" to a value about one-tenth the maximum at x = 180". Thus the intensity per unit solid angle (derived by averaging do/dx over azimuthal angles) is predicted to be strongly peaked along the direction of the initial relative velocity vector and quite asymmetric about = go" as observed. (It is noted, however that restricting the trajectories to a plane automatically imposes the glory effect regardless of how the angular momentum is partitioned between orbital and rotational motion.) In virtually all the successful collisions the trajectories " turn the corner '' smoothly and the complex proceeds to decompose within a vibrational period.This is not found to be the case when the calculation is limited to head-on collisions (i.e. b = 0 only); a large fraction of the collisions then lead to com-plicated " snarled " trajectories and da/dx has a maximum in the vicinity of = 90". Bunker and Blais are now extending these calculations to different potential surfaces and to other reactions. Dr. H. 0. Pritchard (University of Manchester) said I find the results presented by Charters and Polanyi puzzling. The fact that HC1+ is more likely to be formed in a lower vibrational state than in a higher one means that when we consider the reverse reaction HCl + Cl+H + C12 the more vibrationally excited is the HC1 the slower it will react.Since the reaction co-ordinate can only be described by an extension of the H . . . C1 distance it seems odd that the concentration of energy in the H-Cl vibration actually slows the reaction down. I would like to ask Dr. Herschbach whether it is feasible to settle this problem using a molecular-beam experiment ? We could consider a reaction like HBr + K, and we would need to have a velocity selector in each beam. Then for a fixed value of the relative translational energy one could study the rate of reaction as a function of the internal energy (rotational +vibrational) of HBr by varying the source temperature between say 200 and 1200"K and one could then repeat the process for various values of the relative translational energy.I realize this experiment is difficult but it seems to me that it should be possible from a detailed analysis of the results to decide what relative contribution is made to the activation energy by translational and internal energy and maybe even to find the relative contributions of the vibrational and rotational energy individually. Prof. D. R. Herschbach (University of California) (contributed) Unfortunately the direct experiment suggested by Dr. Pritchard would be extremely difficult. If velocity selectors (with resolution 1 of 10 %) were placed in both beams the yield of product would be reduced by a factor of about 10-5 or 10-6; at the peak of the angular distribution only 103 to lo4 product molecules sec-1 cm-2 would arrive at the detector (a monolayer in 104 years).Signals this weak have been detected in beam experiments,2 but elaborate instrumentation is required. There is the further handicap that even at 1200°K practically all of the HBr would still be in the ground vibrational state. It is possible to select a particular vibrational and rotational state of a beam by means of an electric resonance Stark-effect spectrometer.3 In favourable cases several of the lowest states can be resolved and the fraction of the original intensity 1 Hostettler and Bernstein Rev. Sci. Ins&. 1960 31 872. 2 Ramsey MoZecuZur Beams (Clarendon Press Oxford 1956) p.387. 3 Moran and Trischka J. Chem. Physics 1961 34 923 GENERAL DISCUSSION 279 transmitted in a selected beam is as much as 10-4. Again the apparatus required is complicated however. In a shock tube experiment Schott and Kinseyl have obtained results which indicate that the rate of the reaction H+02-+0+OH is enhanced when the 0 2 is vibrationally excited. Prof. J. C. Polanyi (University of Toronto) said I agree with Dr. Pritchard that it would be odd if concentration of energy in the H-Cl vibration were found to slow down the reaction HCl+Cl+H+C12. However though odd it could still be the case. Consider for a moment the exothermic reaction H+C12-+HCl+C1 that Mr. Charters and I have been studying. It is of course possible to draw a potential energy surface for this reaction across which a point mass (or more properly the average of a statistical assembly of sliding point masses) will prefer to travel by a path which passes smoothly out of the exit valley; that is to say a path involving little vibrational excitation of the products.If we try to send sliding masses in the reverse direction across this same surface we shall not necessarily increase their chances of crossing the barrier if we force them to oscillate to and fro as they move up the entry (previously the exit) valley. I remarked that we would not necessarily increase the chances of crossing the barrier in the reverse direction if we forced the point mass to oscillate. However, I left open the possibility that we might increase the chances of crossing the barrier in the reverse direction by introducing vibrational excitation into the bond under attack.This would not be contrary to the principle of microscopic reversibility, so long as the sliding masses after crossing the barrier in the endothermic direction, emerged in a non-thermal distribution. This point should perhaps be underlined. What precisely is involved in applying “ detailed balancing ” to the system H+ C12-+HCl+Cl? The observation is that when room temperature H is mixed with room temperature C12 (93 % in II = 0), the rate of reaction is greater into lower vibrational levels of the product HC1. It follows that the rate of the reverse reaction HCl+ Cl-H + C12(v = 0) decreases as HC1 is raised to higher vibrational states. It does not follow that the rate of reaction HClfCl to form C12 in any vibrational state decreases as HC1 is vibrationally excited.Dr. Pritchard’s expectation (which I shared2) that the rate of exothermic reaction would be greater into higher vibrationally excited states of the product molecule is probably exemplified in the series of reactions X + Na2jNaX + Na and Na+XM-+NaX+ M (X is Cl Br or I ; M is Cd or Hg).39 4 There are however two rather obvious differences between this family of re-actions and the H+Cl2 reaction. The first of these is that in the H+Cl2 reaction, the attacking atom is very light and the vibrational energy spacing in the product is very wide. As a consequence it is possible that the sliding point mass representa-tion (which is classical) may fail for the H + C12 case but succeed for the more common X+Na2 type of case.If this is so then even without marked dissimilarities be-tween the potential energy surfaces dissimilar behaviour would be expected. The second difference is that the rotational energy spacing is close for the product NaX wide for HCl. Since the total available angular momentum is not too different in the two cases it will be argued that it is less probable that energy will appear as rotation in NaX than in HCl. 1 Schott and Kinsey J. Chem. Physics 1958 29 1177. 2 Polanyi J. Chem. Physics 1959 31 1338. 3 Polanyi Atomic Reactions (Williams and Norgate London 1932). 4 Evans and Polanyi Trans. Faraday Soc. 1939 35 178 280 GENERAL DISCUSSION Fig. 1 and 2 exemplify this. They summarize the results of a calculation in which it is assumed in order to get some actual figures that 80 % of the heat of reaction goes into internal energy (rotation + vibration symbolized W‘) the remaining 20 % being dissipated as recoil energy.(Dr. Herschbach this Discussion reports 10 % as the recoil energy in a number of exchange reactions K+IR). The percentage of the internal energy W’ that will go into vibration is the balance of the percentage that is likely to go into rotation. This latter percentage we shall obtain from the requirement, J‘ < [J + L], where J’ is the rotational angular momentum of the product molecule J and L are the rotational and the orbital angular momenta of the reagents (this symbolism conforms with that of Dr. Herschbach’s paper). Higher values of J than the upper ~ %W b s Vibration FIG.l.-H+C12 (0 is C12). FIG. 2.-Cl+Na2 (+ is Na2). limit set by eqn. (1)* appear less probable much higher values much less probable, since they require for conservation of angular momentum a precise cancellation of J’ with L’ that is cancellation of the rotational angular momentum of the pro-duct molecule with the orbital angular momentum of the products as a whole. This chosen upper bound for J (eqn. (1)) is seen to be somewhat arbitrary. It is interesting nonetheless to compare the consequences of this choice in the two families of reactions under consideration. J is a constant for a given reagent molecule at a given temperature. L varies with the line of approach of the attacking atom. The rings in fig. 1 and 2 indicate various possible approaches characterized in each case by the impact parameter (b,A) which gives the distance of closest approach at the moment of grazing collision.L = pvb where p is the reduced mass and v is the relative velocity. For atomic hydrogen v was taken as 4.5 x 105 cm/sec (kinetic energy 2.5 kcal/mole ; equivalent to the activation energy for the reaction H+C12). For atomic chorine II was taken as 5 x 104 cm/sec (kinetic energy 1 kcallmole; normal thermal energy of 0.5 kcal would probably suffice to bring about the reaction Cl+ Na2 but by somewhat exaggerating the velocity of C1 we are erring on the side that will tend to minimize the striking difference between fig. 1 and 2). From the figures it is seen that as the distance of closest approach is increased to about 2A, the maximum available angular momentum increases by a factor of 1.7 for H+Clz, * In my remarks at the Discussion I neglected these ; I am most grateful to Dr.Herschbach for pointing this out to me GENERAL DISCUSSION 28 1 2.2 for Cl+Na2. This is equivalent to roughly a threefold ((1.7)2) increase in the energy that can go into rotation of the product from H + C12 and a five-fold increase for Cl+NaZ. For HCl product where an appreciable amount of energy can always go into rotation a three-fold increase in that amount of energy is very significant in decreasing the percentage that is bound to go into vibration. For NaX where only a trifling amount of energy can go into rotation a five-fold increase in that energy has no significance. Fig 3 is a schematic potential energy diagram in the reaction co-ordinates of two processes A+BC-+AB+C one of which is depicted as leading to a high vibra-tional level in a “normal” potential energy curve and one as leading to a low vibrational level of a potential energy curve which includes a high energy of rotation.FIG. 3.-Schematic potential energy diagram in the reaction co-ordinates of exothermic processes A+-BC+AB+C; one with low rotational energy of product AB (solid line) and one with high rotational energy of AB (broken line). Both reactions have activation energy E and heat of reaction Q. To sum up except when the product molecule has a very low moment of inertia, a large percentage of the internal energy will be present as vibration in the pro-duct. In the rare event that the product does have a low moment of inertia the distribution among vibrational states of product is likely to be sensitive to the dis-tribution of impact parameters in a statistical sample of “ successful ” collisions (collisions leading to reaction).Prof. D. R. Herschbach (University of California) (contributed) From the con-servation laws alone it is not possible to establish a maximum fraction of W’ that can appear as rotational excitation. The products are allowed to have any values of L’ and J’ consistent with energy conservation as long as the vector sum L’+ J’, equals the total angular momentum supplied by the reactants L+ J. In a reaction A+BC+AB+C the rotational energy of AB is proportional to J’2 = I L+ J 12+L’2-2 I L+ J I L’ cos $, where $ is the angle between L‘ and L+ J.When $ > 4 2 for example the L 282 GENERAL DISCUSSION and J vectors can both have much larger magnitude than L+J. Thus the con-servation laws allow all of the energy released in the reaction to go into rotation of AB; what fraction actually does cannot be predicted without assuming some-thing about the forces involved in reactive collisions. These forces are expected to become effective only in sufficiently close collisions. This permits a rough estimate of the maximum initial impact parameter b and the total angular momentum that can contribute significantly to reaction [as indicated already under eqn. (17) of our paper]. The range of the final impact parameter b’ is likewise expected to be limited by the short range of the forces.Here we define b’ as the distance of closest approach of a pair of product molecules when their asymptotic straight-line trajectories are extrapolated backwards. The maximum values of b and bf in a reactive collision probably cannot be much greater than bond lengths in the reactant and product molecules. The restriction which this assumption imposes on the orbital angular momentum of the products L’ = p’db’ has been discussed elsewhere.1 2 It also implies an upper limit on the rotational momentum J’ given by This limit is determined with L’ oriented oppositely to L+J. Another rough bound probably more representative of the average rotational excitation may be obtained by assuming L is distributed isotropically with respect to L+ J ; an average over all orientations then yields If L‘ is assumed to be negligibly small (1) and (2) are equivalent and we obtain the bound considered by Polanyi, Eqn.(3) may also be derived from the less stringent assumption that L’ < 2 I L + J I cos $ for the dominant contributions to reaction ; this requires $ < n/2 and L’ < 2 I L+ J I however. These various bounds are compared in table 1. For the J’ z I L + Jmax I +L&ax. (1) (J”) t I L + J&ax I +G2ax- (2) J’z I L+ J Imax- (3) reaction Na2+ C1 H+ C12 K+ CH31 Rb+CH31 CS + CH31 TABLE 1 bound to rotational assumed I excitation (kcal/mole) bmax (A) (1) (2) (3) 2.5 43 30 2 any 36 36 36 4-0 10 5 3 4.0 5 3 2 4.0 3 2 2 examples treated by Polanyi we used the same parameters and assumed that the probability of reaction is negligible unless b72.5 A.For the M+ RI reactions we used values of the final relative velocity v’ derived from the observed angular dis-tributions and took b74-0A. The results given in the table refer to the rotational excitation of MI and do not include any excitation of CH3. Since the small moment of inertia of the CH3 radical enables it to carry away large amounts of rotational energy with relatively low angular momentum (e.g. 10 kcal/mole for J3 = 20 h/2n in contrast to KI which has only 1.7 kcal/mole for J4 = 100 h/Zx), the observation that in reactions involving larger R groups the internal excitation does not decrease (but rather increases somewhat) suggests that CH3 must have little rotational momentum probably no more than 10 h/27r GENERAL DISCUSSION 283 Table 1 and other calculations 1 9 2 lead to the rule stated by Polanyi with two amendments which recognize the role of L’.First even for a product with a large moment of inertia we can set a low limit on the rotational excitation only when we have evidence that GaX is not too large. The reason the M + RI reactions conform to the rule is that the v’ estimated from experiment is rather small and thus &ax is less than I L+ J Imax. For the Naz + C1 example this is no longer the case because the value of v’ used is much larger. Also the moment of inertia of NaCl is con-siderably smaller than that of the MI molecules. Second for H atom reactions as well as others we must expect the actual distribution of rotational excitation (in contrast to the upper bound) to be sensitive to the distribution of both b and b’.In the H+C12 example we note that up to 36 kcal/mole (100 % of W’) may go into rotational excitation regardless of the value of b’. However in H atom reactions there is usually a large increase in reduced mass on formation of the pro-ducts (p<p’). Angular momentum therefore can be readily taken up in orbital motion even for rather small values of v’ and b’. Thus the upper bound to the rotational excitation will always be high when a product has a very small moment of inertia but the actual excitation produced in the main course of the reaction may be far below the bound (as in the CH3 example) and will be strongly affected by the forces that govern the break-up of the collision complex.There is a case exemplified by the reactions M + HX- MX + H, in which a high level of rotational excitation in a product is required by the postulated bounds on the impact parameters. On the reactant side L%J whereas on the product side we expect L’QJ and consequently L x J’. That is here we expect pvb+p‘u’b’ since the reduced mass of the products (approximately just the mass of H) is far smaller than that of the reactants (26 times smaller for K+HBr 66 for Cs+HI). Because the reaction is only slightly exothermic u’ cannot become large enough to offset more than a fraction of the mass ratio. The velocity depend-ence of the scattering of K+HBr beams does indeed indicate that KBr is formed with high rotational momentum.2 An interesting consequence of L N J’ is that the angular momentum of MX is predicted to be strongly polarized with J’ nearly perpendicular to the direction of the initial relative velocity vector.In a beam experiment this polarization should have a pronounced effect on the deflection pattern obtained when the MX molecules are made to pass through an inhomo-geneous electric field.1 Such an experiment is being attempted at Berkeley. In principle it should give information about the distribution of L in those collisions which lead to reaction. Dr. A. B. Callear (University of Cambridge) said The relaxation of vibration-ally excited nitrogen by nitrous oxide is probably due to the vibrational exchange process, since nitrous oxide has a vibrational frequency at 2222 cm-1. The energy discrep-ancy is thus about 130 cm-1.According to fig. 9 of my paper such an exchange should require about 1000 collisions. The majority of polyatomic molecules show a single relaxation time 3 corresponding to the vibration-translation relaxation of molecules in their lowest vibrational level which for N20 is 588 cm-1. This would N ~ ( v = l)+N2O(u = 0) = N ~ ( v = O)+N2O(u = l), 1 Herschbach The Vortex 1961 22 348. 2 Beck Greene and Ross J. Chern. Physics (to be published) and private communication. 3 Lambert and Salter Proc. Roy. Soc. A 1959 253 277 284 GENERAL DISCUSSION require 10,000 collisions for relaxation. Thus if N20 does exhibit a single relaxation time (it is doubtful if ultrasonic measurements have been made at temperatures where the highest vibrational frequency makes a significant contribution to the specific heat) the rate of vibrational relaxation in N2+N20 mixtures will be about 106 times faster than in pure N2 when relaxation requires about 1010 collisions at room temperature.Even if the largest energy interval the difference between the two highest frequencies of the N20 molecules (937 cm-I) determines the rate of relaxation the rate of relaxation would still be faster than in pure N2 by several powers of 10. Dr. F. Kaufman (Ballistic Research Lab. Maryland) said I would like to clarify a point in our paper. In all experiments from which kinetic information on the decay of OH was obtained the concentration of NO2 added to the gas stream containing H-atoms was less than that of the H-atoms present. Under these con-ditions OH formed equals NO2 destroyed.When excess NO2 is used however, this equivalence no longer holds because the three reactions H + NO2 -+ OH + N02, 20H+H?O + 0, and OH + 0 - 0 2 + H, produce the over-all stoichiometry 2H + 3N024H20 + 0 2 + 3N0, i.e. 3N02 are destroyed by 2H. This scheme is in accord with Prof. Schiff’s findings and with Dr. Thrush’s recent results but in conflict with Clyne and Thrush’s earlier paper.1 Regarding the effect of M in three-body recombination processes one must not generally expect M effects as large as those in iodine atom recombination. Mr. Kelso and I are now carefully studying the rate of 0 + NO + M+N02 + M for a wide range of M. Though the role of electronically-excited states of NO2 in this reaction has not yet been clarified our early results indicate that a factor of three in the rate constant encompasses the effect of varying M = He Ar 0 2 C02, N20 or SF6.Finally indiscriminate statements should no longer be made about the large fraction of the energy liberated in atom-molecule reactions which goes into vibrational excitation of the newly-formed bond. There is no doubt that many such reactions produce some preferential vibrational excitation in the new bond but it is often implied that most product molecules initially come away with high vibrational energy i.e. that much or most of the total energy of reaction goes into that particular internal degree of freedom. This is not supported by any of the examples studied within the last eight years. On the contrary all quantitative studies have shown that the fraction of product molecules which have very high vibrational excitation is either small or negligible.Prof. G. Porter (University of Shefield) said Mr. G. Black and I 2 have made a preliminary study of the decay of OH radicals produced by the vacuum u.-v. flash photolysis of water vapour and have obtained results which at first sight, appear to conflict with those of Del Greco and Kaufman. We found that the decay 1 Clyne and Thrush Trans. Furaduy Soc. 1961,57,2176. 2 Black and Porter Proc. Roy. SUC. A 1962,266 185 GENERAL DISCUSSIOP\t 28 5 was second order in OH and first order in inert gas pressure and interpreted this in terms of the reactions ki H+OH+ M+H20+M, OH+OH+M+H202+M. k2 The observed termolecular rate constant is then equal to kl+2k2 and since it seems improbable that kl is less than k2 the termolecular recombination process (2) must predominate over the bimolecular reaction k3 OH+OH+H20+0 proposed by Del Greco and Kaufman.These results can however be reconciled in the following way. If the recom-bination rate constant kl has a value in the range 10-30 to 10-31 cm 6 molecule-1 sec-1 and the value of k3 is 2.5 x 10-12 cm3 molecule-1 sec-1 as given in the paper the mechanism should change from 2nd to 3rd order in the pressure range 10-2 to 10-1 atm. Our work was all carried out at higher pressures than 10-1 atm and that of Del Greco and Kaufman at lower pressures than 10-2 atm. The order of magnitude of k2 is reasonable for the recombination of simple radicals of this type.Prof. H. I. SchB (McGiZZ University) said We have recently studied the reaction of H-atoms with NO2 and with 0 3 in a fast-flow system using a mass spectrometer. reactant added mm 10-2 FIG. 1. Fig. 1 shows the amount of 0 3 and NO2 destroyed for the same initial H-atom concentration as a function of the initial reagent concentration. The reaction time was 25 msec. It is apparent that the reactions which consume NO2 are faster than those which consume 03. The plateau values correspond to 1.5&-0.1 NO2 mole-cules reacted per H-atom originally present and 3.1 +O-2 0 3 molecules reacted per H-atom 286 GENERAL DISCUSSION In the reaction with N02 the amount of NO formed was equal to the amount of NO2 consumed. This stoichiometry is consistent with the mechanism H+N02+NO + OH OH+OH-+H20+ 0 0 + OH+Oz + H 0 + N02+NO + 0 2 (3) (4) and the value of kl was found to be 4.8 x 10-11 cm3 molecule-1 sec-1 at room temperature.The same stoichiometry is obtained whether k3> k4 or vice versa. However, Clyne and Thrush 1 have measured the HNO emission accompanying the reaction and concluded that one H-atom is consumed per NO2 molecule. They claim that NO2 can be used as a titrant for H-atoms. However if k3 is as large as Del Greco and Kaufman suggest then the stoichiometry obtained by Clyne and Thrush would not apply. Would Dr. Kaufman care to comment on this point? The corresponding mechanisms for the 0 3 reaction would be H + 03+OH + 0 2 OH+OH+HzO+O 0 + OH+02+ H 0+03+202. (6) Again a maximum of 1-5 0 3 molecules would be destroyed per H-atom initially present as compared with the observed value of 3-1+2.Kaufman has suggested that the reaction may be faster than originally believed. If this reaction were included the 0 3 decomposition could be increased to 2 per H-atom. However addition of H2 actually decreased the amount of 0 3 consumption. OH + H2+H20 + H (7) There may however be a chain reaction resulting from the reaction OH 4- 0 3 - + H02 4- 0 2 (8) followed by HOz + O3-+OH 4- 202 (9 ) and H02+H-+OH+OH. (10) Alternately the OH formed in reaction (3) could be vibrationally excited and de-compose 0 3 by the reaction Inclusion of this reaction could lead to a total of 3-5 moles of 0 3 decomposed per mole of H-atoms. To test these alternatives N20 was added to the system.This should de-activate OH* but have no effect on the chain. The amount of 0 3 decomposed de-creased when N20 was added indicating that reaction (1 1) does play an important role in this system. (Paper by Del Greco and Kaufman.) Mr. M. A A. Clyne and Dr. B. A. Thrush (University of Cambridge) said We are in full agreement with Del Greco and Kaufman regarding the mechanism of the H+NOz reaction and the absence of vibrationally excited OH in this reaction. In experiments on the infra-red emission from this reaction carried out at Ottawa OH' +03+OH+02+O. (1 1) 1 Clyne and Thrush Trans. Faraday Soc. 1961 57,2176 GENERAL DISCUSSION 287 last summer in collaboration with Dr. D. A. Ramsay one of us (B. A. T.) was unable to detect emission by OH but observed strong emission by H20 formed in the subsequent reactions.Our results,l however can only be explained by the gener-ation of hydrogen atoms in the reaction of OH with H2, This is consistent with the results of Del Greco and Kaufman who show that k5 = 7 5 2 x 10-15 cm3 molecule-1 sec-1 at 310"K and suggest an activation energy E5 < 6-5 kcal/mole. The earlier value 2 reported for E5 of 10 kcal/mole is similar to that (9.2+0-6 kcal/mole) for the reaction 3 0 + H2+ OH + €3, and the experimental technique used in the early work suggests that the measured activation energy was actually that of reaction (6) since reaction (2) rapidly converts OH to 0. OH+H2+H20+H. (5) (4) Providing sufficient time is allowed for the rapid subsequent reactions, OH+OH+HzO+O (2) and 0 + OH+H + 0 2 (4) to proceed to completion H atoms in the absence of excess molecular hydrogen can be titrated with NO2 using the disappearance of HNO emission to indicate the end point.The overall stoichiometry is [NO21 = +[HI which agrees with a calori-metric ratio of 0-53 to within the known errors of such measurements.1 We have measured the concentrations of oxygen atoms produced in the H+NOz reaction. These concentrations are governed by reactions (2) and (4) and are given by the relationship 1/[0] = 3k4t when k2t[OH]>l. Under these conditions plots of 1/[0] against time were excellent straight lines yielding kq = 5+2 x 10-11 cm3 molecule-1 sec-1 at 293°K. This is about four times greater than the value reported by Del Greco and Kaufman but the difference may arise from the different methods used to study this reaction i.e.the difference between homogeneously generated 0 atoms and oxygen atoms from a separate flow system. Dr. B. G. Gowenlock (University of Birmingham) contributed The value of D(H-NO) = 48.6 kcal mole-1 reported by Clyne and Thrush enables us to estimate the value of D(CH3-NO). This value has importance in relation to the mechanisms proposed for the inhibition of chain reactions by nitric oxide. Inspection of the table shows that that D(H-X) > D(CH3-X) by about 15-25 kcal mole-1. X CH3 NH2 F C1 Br I OH OCH3 COCH3 C6H5 D(H-X) 102 104 137 102 87 71 118 100 91 102 D(CH3-X) 84 80 110 80 67 54 88 77 73 89 Thus we estimate D(CH3-NO) as 30 + 5 kcal mole-1.This value suggests that the equilibrium may participate in nitric-oxide-inhibited reactions. A previous estimate 4 of D(CH3-NO) = 57 +4 kcal mole-1 was based on the approximate equivalence of B(X-NO) and D(X-NO2). Thus an anomalous position is presented for bond dissociation energy patterns either D(CH3-NO) CH3 + NOSCH3NO 1 Clyne and Thrush Trans. Faraday SOC. 1961,57 2176. 2 Avramenko and Kolesnikova Zhur. Fiz. Khim. 1950 24 207. 3 Clyne and Thrush Nature 1961,189 135. 4 Gowenlock Trotman and Batt Chem. SOC. Spec. Publ. 1957 10,75 288 GENERAL DISCUSSION is much less than D(CH3-N02) or D(CH3-NO)*D(CH3-N02) and thus D(CH3-NO) > D(H-NO). It is a consequence of Clyne and Thrush's value for D(H-NO) that one of these anomalies exists. Mr. M. A. A.Clyne and Dr. B. A. Thrush (University of Cambridge) (contributed) : The values of D(R-NO) may be close to those for D(R-02) since the value of D(H-NO) = 48-6 kcal/mole given in our paper is very close to the accepted value of D(H-02) = 47 k 3 kcal/mole. An additional similarity between HNO and HO2 is that our value for the rate constant for the reaction H+02+Ar = H02+Ar, 1.2f0-3 x 1016 cm6 mole-2 sec-1 at 293"K is remarkably close to the value of 0-8k 0.1 x 1016 for H + NO + Ar at 293°K given in our paper. Our value of D(H-NO) also yields some information about D(N-H) which is thought to be close to 85 kcal.1 Taking D(N-H) = 85-x kcal/mole we obtain D(HN=O) = 114 + x kcal/mole for the related isoelectronic species D(O=O) = 1 18 kcal/mole and D(HN=NH) = 1 10 + 2x f 5 kcal/mole.2 This suggests that D(N-H) lies between 80 and 85 kcal/mole.Dr. B. A. Thrush (University of Cambridge) said Investigations of chemilumin-escent combination reactions such as those reported by Dr. Sugden and by our-selves stress the importance of considering all the stable electronic states of a molecule XY which can be formed in a three-body combination process X+Y + M since com-bination via electronically excited states is comparable in rate to combination directly into the ground state. In cases such as HNO where there is rapid crossing between the radiating state and the excited state formed in the initial combination the vibra-tional intensity distribution in the electronic emission spectrum provides a measure of the steady-state energy distribution of the excited molecules formed in a com-bination reaction.This distribution falls off at an energy which is several times kT below the dissociation limit. These highest levels are presumably depopulated by collisional redissociation a process which would be favoured by the associated increase in entropy and which would account for the observed negative temperature coefficient of these combination reactions. Dr. E. E. Nikitin (Acad. of Sci. Moscow) said The ratio EIkTis a poor criterion for the validity of the perturbation approach to the non-equilibrium rate constant. Generally speaking deviations from the equilibrium distribution at the bottom of the potential well decrease with increasing E/kT ratio but in many cases the rate constant is dependent on the population of the upper energy levels.A good ap-proximation to k can be expected for cases where transitions from the bottom of the well proceed as rapidly as from the top. This is the case for approximately equal masses (m-M). Thus for m-M the energy dependence of k is expected to be the same as that obtained for the simple dissociation model in which perturbation of the equilibrium distribution is neglected and dissociation occurs in every collision for which the total energy (internal energy plus the kinetic energy along the line of collision) exceeds E. For this model the expression for k k- cAv(E/?)* exp (- EP) - Ac(E/M)* exp (-PE) is identical with (12) except for the numerical factor. On the other hand when m+M and the amount of energy transferred is small, it is better to use the ladder model for dissociation in which k-cAu(AE)P exp (-PE), 1 Gaydon Dissociation Energies (Chapman and Hall London 1953).2 Foner and Hudson J. Chem. Physics 1958,28,719 GENERAL DISCUSSION 289 and AE is an energy step near the dissociation limit. Introducing AE-yE for a collision of atom M with energy N E with atom rn with energy - kT and u - (kT/rn)f, one obtains k - Ac(y/flM)*bE exp -flE). This is consistent with (21) but not with (12). Thus the Fokker-Planck equation seems to give the right answer for 7-0 and the perturbation approach fails completely. Dr. E. E. Nikitin (Acad. of Sci. Moscow) said In connection with Bak's paper, it is interesting to consider the applicability of hard-sphere model to the calcxlation of the vibrational relaxation times and the dissociation rate constant of diatomic molecules in a heat bath.The most important parameter in any collision theory is < = wz where w = a(&) is the vibrational frequency near the energy level E of diatomic molecule and z is the collision time. For a Morse potential we can put (E is dissociation energy M reduced mass of the molecule l / a range of action of exchange forces m reduced mass of colliding pair). We obtain therefore, For the hard-sphere model to be applicable the condition c+ 1 must be fulfilled. It is evident from the above that for vibrational relaxation when the energy region concerned is small (&E) condition 5 4 1 is unlikely to be fulfilled. For most cases B- 1 and the adiabatic theory of Landau and Teller is a good approximation.The hard sphere model can be applied to the non-equilibrium dissociations if condi-tion <B- 1 is fulfilled in the energy range kT near the dissociation limit E. Intro-ducing E-C-kT we obtain for this case <-(m/M)*. So under condition m<M, the hard-sphere model is a reasonable one and eqn. (21) of Bak's payer gives the non-equilibrium rate constant. Prof. Thor A. Bak (University of Copenhagen) said I agree with Dr. Nikitin that for small masses eqn. (21) is better than eqn. (12). I believe however that the simple Fokker-Planck approach is only valid for an extremely small mass ratio. As far as I know the range of validity of the expansion of the integral operator is not known and it is therefore a little dubious to use it for finite mass ratios but a correction of this kind to the simple Fokker-Planck results appears to be necessary.I should like to add that we have shown recently 1 that the rate constants derived from the Fokker-Planck equation using the Morse potential and the cut-off harmonic potential only differ by a factor of about 2. In the Fokker-Planck limit anharmoni-cities therefore seem to be of minor importance. Prof. G. Porter (Shefield University) w d Ole o f the consequences of the kinetic scheme given in my paper is that departures from third-order kinetics are predicted at low temperatures or when the heat of formation of the complex is very high. R+M+RM will be shifted so far to the right that most radicals exist as complexes. My col-leagues Dr. Townsend and Prof.Szabo have realized this situation in the system of iodine atoms with nitric oxide as a chaperon. At low pres5urcs of NO the re-Under these conditions the equilibrium 1 Bak and Andersen Mat. Fys. Medd. Dan. Vis. SrAk 1961 33 no. 7. 290 GENERAL DISCUSSION action is third order with the very high rate constant of 3-0 x 1013 1.2 mole-2 sec-1 at 60°C but at high NO concentrations the rate falls off until eventually the recom-bination rate decreases nearly linearly with NO pressure. This system is an interesting extreme case of the complex mechanism of atom recombination and indeed we have been able to observe the absorption spectrum of the NO1 intermediate and to follow the kinetics of the reaction via the 12 and the NO1 concentrations separately.Dr. E. A. Ogryzlo (University of Br. Columbia) said Prof. Porter presents three mechanisms by which " third-order recombination reactions " can occur in the presence of a chaperon M. However eqn. (2) which is derived from this scheme allows only two of these mechanisms to contribute to the process for any given combination of R and M. One of the assumptioiis in the paper which leads to this conclusion is that [RM*]/([RM*] + [RM]) = exp (- AE/RT). (3) Even if one assumes a negligible entropy difference between RM + RM* (is. identical statistical weight factors for the two states) the relation must be P M * I exp( - AE/RT) [RM] + [RM*] = 1 + exp( - AE/RT)' (4) and therefore [RM]/[RM*] = exp (AEIRT) (5) from which K7 = exp (AEIRT). (6) The substitution of eqn.(6) into eqn. (1) yields k = k,K + k,K + kllK exp (AEIRT) = k,' + k,"+ krlll, where ki k:' and kfll are the third-order rate constants for mechanisms 1 2 and 3 respectively. It should be noted that when AE = 0 and there exist no bound states of RM*, [RM] = 0 and hence the third mechanism ceases to exist. It is also important to remember that eqn. (7) is based on an insignificant entropy difference between RM and RM*. This is not likely to be the case for very weakly bound complexes, where the entropy change may well dominate the relative concentrations of these two species. Thus for example when AE is small and M is polyatomic a small equilibrium concentration of RM could result in mechanism (2) dominating the recombination process. Prof. G. Porter (Shefield University) said The modifications suggested by Dr.Ogryzlo are incorrect as can be seen by examination of the limiting condition AE-0 [RM]-+O. His eqn. (4) and ( 5 ) become inequalities as this limit is ap-proached and the last two terms of his eqn. (7) become identical so that the contribu-tion of mechanism 2 is counted twice. The second term of eqn. (2) in my paper incorporates both mechanisms 2 and 3 and is applicable to all values of A,?? down to zero. The validity of the equation [RM*]/([RM*] + [RM]) = exp (- AE/RT) is readily appreciated if the meaning of the two concentration terms is considered carefully. [RM*] is the concentration of complexes of R and M with energy 3 AE and [RM] is the concentration of complexes with energy -c AE. Both sides of the equation are therefore equal to the fraction of complzxes having energy > AE in two square terms.The equation does of course ass;ime negligible entropy differ-ence between RM and RM" GENERAL DISCUSSION 291 Prof. T. L. Cottrell (University of Edinburgh) said If Prof. Porter’s radical-molecule complex theory is correct then there should surely be a detectable equilib-rium concentration of I3 molecules in iodine vapour. The vapour density data of Perlman and Rollefson 1 which lead to an accurate value of the heat of dissociation of iodine do not suggest that any I3 is present. I should like to ask Prof. Porter whether he has calculated the I 3 concentration he would expect under their experi-mental conditions and therefore whether there is a real discrepancy here? Prof.G. Porter (Shefield University) said The equilibrium constant of forma-tion of I3 from I and I2 is estimated from the recombination results to be about 4 x 10-3 exp (5000/RT) 1. mole-1. Under the experimental conditions of Perlman and Rollefson (723-1274°K and 0-1-1 atm) this leads to a concentration of I3 some-what less than the 0.3 mole % given by these authors as the lower limit of 13 which could have been detected. Dr. J. Keck (AVCO Res. Lab. Mass.) said I should like to point out that the variational theory 2 developed by the author also fits the observed recombination rates presented by Porter. In the temperature range from 300 to 500°K where the experiments were performed the variational expression for the recombination rate constant given by eqn.(45) of ref. (1) is k = kB(0) = 2.0 x 10802 (exp (~/RT)-0.6)1.~ molew2 sec-l (1) where CT is the range in 8 and E is the depth in kcal of the Lennard-Jones potential used to represent the interaction between an iodine atom and the chaperon. Note that the numerical factors in eqn. (1) are uniquely determined by the interaction potentials between the particles. The factor exp (EIRT) which gives the main tern-perature dependence of both the variational theory and the radical-molecule complex theory has its origin in the assumption common to both theories that IM is in equilibrium with I+M. A rough criterion for the validity of the assumption is that [R]/[M] < exp ( -E/RT). The apparent negative activation energy implied by eqn. (1) is E = ~/[1-0.6 exp (-E/RT’].If we use the experimental values of to determine E as Porter has done and choose a mean value of 0 = 3.7 A determined from parameters given in Hirschfelder Curtiss and Bird,3 we obtain the results plotted in fig. 1. It is clear that the variational theory fits the observations just as well as the radical-molecule complex theory. However the former theory gives binding energies somewhat smaller than the latter. In the cases involving inert-gas chaperons this leads to binding energies which are closer to those expected for the Van der Waals force and therefore seem more acceptable. In fact considering the possibility 4- 5 of an additional small negative temperature coefficient in the pre-exponential factor of eqn. (1) due to lack of equilibrium in the vibrational degrees of freedom it is possible that there is no additional force in these cases at all.In cases which do not involve inert-gas chaperons there remains a clear indication of additional forces. This possibility was recognized by the author in his earlier work,2 and it is for this reason that absolute calculations of rate constants were limited to inert-gas chaperons. 1 J. Chem. Physics 1941 9 362. 2 Keck J. Chem. Physics 1960,32 1035. 3 Hirschfelder Curtiss and Bird Molecular Theory of Gases and Liquids (John Wiley and Sons, 4 Widom J. Chem. Physics 1960 34 2050. 5 Pritchard J. Physic. Chem. 1961 65 504. Inc. New York 1954) 292 GENERAL DISCUSSION The reason for the difference in the binding energy predicted by the two theories is that the pre-exponential factor in the radical-molecule complex theory is pro-portional to the temperature while that in Athe variational theory is nearly tem-perature independent.This in turn is associated partly with the fact that the vari-ational theory leads to cross-sections which decrease with increasing temperature and partly with the fact that in the variational theory we have averaged over the forces which act on the particles while in the radical-molecule complex theory, the average is over the relative velocity of approach of the particles. VAR I AT ION AL 0 1 I I I I 2 3 4 5 E (kcal mole-1) FIG. 1 .-Comparison of experimentally observed recombination rate constants k for iodine in the presence of various chaperon molecules with curve predicted by the variational theory.The parameter E is the depth of the Lennard-Jones potential used to fit the observed temperature coefficient. Although the agreement between theory and experiment exhibited in fig. 1 is very satisfactory in an overall sense the assumption of a collision diameter in-dependent of the chaperon molecule is certainly unrealistic. We have therefore, analyzed the data to obtain the collision diameters as well as the binding energies with the objective of making more apparent possible correlations between these parameters and the character of the chaperon. The results are shown in fig. 2. The circles indicate the experimental values and the bars are theoretical values com-puted from data given in Hirschfelder Curtiss and Bird on the assumption that iodine is equivaknt to xenon.In obtaining the experimental values we have multiplied eqn. (1) by a correction factor [PI 2/(p3 + p12)]0-9 suggested by the Monte Carlo trajectory calculations reported in the paper submitted to the Discussions by the author. While strictly speaking this correction was calculated only for the inert-gas chaperons it probably has some validity even for complex chaperons and in any case it is not very large. The most obvious trend in results is the tendency for simple molecules to have collision diameters somewhat smaller than the theoretical values. This does not seem unreasonable since the existence of an additional attraction between the iodin GENERAL DISCUSSION 293 and chaperon would certainly tend to move the minimum in the potential curve to smaller values of internuclear separation.For complex chaperons the comparison can only be made for benzene in which case the experimental collision diameter is larger than the theoretical. Whether this is significant is not clear but one possible explanation would be that the possibility of transferring energy to vibrational degrees of freedom in complex molecules makes them more efficient chaperons. This effect is not included in the present calculations. 0 EXP. I HCB I I I I l l 1 1 1 I I I 1 0 0 lo o o 0 0 0 0 0 I I I I 0 0 0 0 0 I l l 0 I I I l l I I I 1 -2 05 I 2 5 E (kcal) FIG. 2.-Lennard-Jones parameters for the interaction of iodine with various chaperon molecules M. The circles are the experimental values deduced from observations presented by Porter; the bars are the theoretical values obtained from data in Hirschfelder Curtiss and Bird on the as-sumption that iodine is equivalent to xenon.Although it is probably somewhat premature to take these observations too seriously the author feels that use of refined theories in conjunction with reaction rate data is a potentially powerful method of obtaining information about the intermolecular forces which operate in chemical reactions. I am sure this feeling is shared by Prof. Porter and one purpose of these comments was to emphasize this point. In concluding I would like to point out some of the advantages of the variational theory over competing theories. First it relates the reaction rate directly to the interaction potential without the usual uncertainty involving the choice of an effective cross-section which arises in most three-dimensional collision theories.Secondly it includes all the classical reaction paths leading to recombination. Thirdly it can be systematically improved using objective mathematical procedures. Finally it can be applied in principle to any chemical reaction and is thus a promising basis for a unified theory of chemical reaction rates. Dr. F. T. Smith (Stanford Res. Inst. Calif.) said In using information on classical trajectories from large-scale computers we must not forget that our prob-lems are really quantal. The classical approximation is good for large quantum numbers (shall we say for vibrations FZ >lo?) but this means large quantum numbers in all degrees of freedom.As an example take the exchange reaction A+BC-+AB+C assuming an activ-ation barrier. First the average This coiidition is not often fulfilled. There are two restrictions to a classical treatment 294 GENERAL DISCUSSION de Broglie wavelength of thermal motion say 1 = h(pkT)-? must be small compared to characteristic lengths (radii of curvature for instance) of the features of the potential surface A Q ao (1). This condition is most obviously violated in reactions involving the lightest atoms especially H and when it is violated quantal interference effects are to be expected. The second condition for a classical treatment can be formulated easily if you consider the region of the saddle-point where the col is long and smooth enough to have ao9A.In this region the co-ordinates are approximately separable and those normal to the reaction co-ordinate include rotations and vibrations of the activated complex. For a completely classical approximation to be valid all these motions must be in states of high quantum number. Thus for even the highest vibration frequency in the transition state we have the condition hvzax <AT (2). Such a condition is seldom satisfied in chemical kinetics. This condition is not new-it was recognized by Eyring and others long ago in their use of the quantal partition function for vibrations and the zero-point vibrational energy in the transition state. As long as the condition (2) is not satisfied deductions from classical trajectory calculations arr. always questionable.In 3-body reactions treatments such as Keck's are somewhat better justified as one is more likely to be in the region of high quantum numbers. Nonetheless, quantum effects may become important-for example in the passage near the top of a rotational barrier where the de Broglie wavelength becomes large. Prof. K. J. Laidler (University of Ottawa) said The two basic mechanisms for atom and free-radical combination may be formulated in a manner slightly different from that of Prof. Porter as follows. The energy-transfer mechanism using Prof. Porter's notation is 1 2R329, R +M+R2+M. 2 5 The species RZ is one in which (following the ideas of and Ramsperger for the reverse unimolecular reactions) Hinshelwood Kassel Rice there is free flow of energy between s of the normal modes.The equilibrium constant for reaction (1) can then be written as fa bs-l j- (s-l)!' K = -where the f are the conventional partition functions (products of translational, rotational and vibrational factors) and b is equal to Eo/RT where Eo is the energy in excess of the zero-point energy No exponential term appears in this equation since there is no transfer of energy. As suggested by Prof. Porter k5 may be set equal to the collision number 2, so that the third-order rate constant for the combination process becomes For the combination of atoms s = 1 and k is found to be of the order of 109 to 1010 1.2 mole-1 sec-1 in agreement with the experimental values for the combination of iodine atoms in the presence of He Ar and H2. The higher rates obtained with 12, C6H6 etc.as third bodies cannot however be explained in terms of this mechanism. 1 Gill and Laidler Proc. Roy. SOC. A 1959 250 121 GENERAL DISCUSSION 295 For radical combinations s is greater than unity (-9 for CH3+CH31) and the As Prof. Porter pointed out such reactions calculated k values are much higher. probably always occur by this energy-transfer mechanism. Porter’s radical-molecule complex mechanism may be written as follows : 3 4 7 R+M+RM*, RM* +M+RM + M + AE, 8 1 1 RM + R+-t+R2 + M, and the combination rate constant is k = klK3K7. (3) If reaction (3) produces an energized species in which there is flow between s’ normal modes Since in reaction (7) there is the disappearance of the species having flow within s’ modes (s‘- l)! AE K = ~ bS’-l exp -RT‘ The combination rate constant is then f R M AE f R f M RT k = 2 - exp -( 5 ) (lo9 to lo1’) exp (AEIRT).(7) For atoms the rate constant corresponding to this mechanism therefore exceeds that for the energy-transfer mechanism by the factor exp (AEIRT). For all except the inert gases this factor may be sufficiently large to ensure that the reaction occurs largely by the complex mechanism. For the inert gases on the other hand since there is a repulsive interaction between the atom and the inert gas molecule it would appear more correct to re-gard AE as negative. The complex mechanism is thus unimportant and the energy-transfer mechanism predominates. This point of view differs slightly from that taken by Prof.Porter. It is important to realize that for atom combinations it does not seem possible to explain high rates in terms of a large number of degrees of freedom. The s appearing in eqn. (2) is unity for atoms and the term bs-l/(s- l)! is unity. The s’ appearing in eqn. (4) relates to the complex RM and therefore can be large if M is a complex molecule but s’ has disappeared in the final rate expression (6). Prof. A. R. Ubbelohde (Imperial College London) said What does Prof. Laidler mean by the “ free flow ” of vibrational energy in different degrees of freedom of a polyatomic molecule? In experiments that point to the intervention of complex collisions in a process such as A*+B-+A*+B V 1 v 2 where v1 and v2 refer to different vibrating modes and not merely harmonics th 296 GENERAL DISCUSSION internal transfer only occurs through collision with B.But the availability of internal energy for disruption of a particular bond in pseudo-unimolecular de-composition needs fresh discussion. Does this internal energy fluctuate from one part to another of the molecule that is about to decompose spontaneously? Dr. J. W. Linnett (University of Oxford) said I would like to say a few words regarding the so-called passage of energy between normal modes and consider what this means. First it must be stressed that a molecule in a given energy level remains in that level until it loses or gains energy on a collision or by the emission or ab-sorption of radiation. However the potential-energy functions of real molecules do not consist solely of quadratic terms and the vibrations are not simple harmonic.Nevertheless it is possible in principle to deduce the simple harmonic wave functions appropriate to the quadratic part of the potential energy function. It is then usual to treat the cubic quartic etc. terms as perturbations and to represent the true wave function of any given level as a linear combination of the wave functions of the simple harmonic system. One might say therefore that for each level there is a certain probability associated with each normal mode whose wave function is present in the linear combination. According to these considerations, it appears that difficulties of comprehension sometimes arise because the states of the real molecule which is an anharmonic oscillator are described in terms of the wave function of the non-existent harmonic oscillato- i.e.in terms of its normal modes. Dr. F. T. Smith (Stanford Res. Inst. Calif.) said It should be emphasized that Keck’s and Porter’s theories are fundamentally different even though it may be possible to obtain a similar pattern of prediction from them. Keck’s theory involves not more than three independent particles in the reaction 2R + M+R2 + M, but Porter’s requires at least 4 particles in all three (or more) to maintain equilibrium in the reaction R+ 2M + RM + M (2) R+ RM+R2 + M. (3) (1) and one more for the final step In principle as the pressure of M is reduced the equilibrium in (2) will fail and its kinetics will ultimately become important. Porter’s overall reaction will then go over to fourth-order kinetics 2R + 2M+R2 + 2M.At some point the third-order process (1) should take over and I would expect a smooth transition from Porter’s mechanism to one like Keck’s. It might be possible to detect this experimentally. There is little doubt that Porter’s mechanism is correct for large and complicated M’s but it is not so clear with regard to atoms and some very small molecules. Porter formally divides process (1) into two parts the formation of a transient pair RR* or RM* and its subsequent collision with the third partner. The dis-tinction is more than merely formal when RR* or RM* has a lifetime much longer than the time they would have spent near each other if there had been no interaction between them (incidentally this point of view leads to a useful general definition of a collision lifetime that is independent of any specific assumptions about the range of the collision.1) The simplest examples are the long-lived orbiting collisions that can occur with attractive intermolecular potentials ; their importance has been stressed by Oldenberg and Bunker.It is often useful and meaningful to distinguish 1 Smith Physic. Res. 1960 118 349 GENERAL DISCUSSION 297 these cases from the pure 3-body collision where all three partners come into inter-action almost simultaneously. In this connection it would be helpful if Keck’s trajectories could be analyzed to see how many of the reaction paths involve long-lived orbiting pairs. This would contribute to our conceptual understanding of the mechanism.Dr. J. W. Linnett (University of Oxford) said Dixon-Lewis Williams and Sutton in the final paragraph of their paper remark that for the recombination of hydrogen atoms hydrogen nitrogen and water are approximately equally effective as third bodies. On the other hand for iodine atoms Porter records a wide range of third-body coefficients. One wonders therefore whether the behaviour of iodine atoms may be different from that of atoms of low atomic number. If this were the case the reason might be that iodine atoms are able to form a transitory com-plex IM of the type suggested by Porter because the outer electron shell can expand beyond the octet so’that a co-ordinate link from M can be formed. On the other hand this might not be possible for atoms of the first short period or for hydrogen.Selley Gould and I have studied the effect of carbon tetrafluoride and sulphur hexafluoride as third bodies for Hf02 D+02 and 0 + 0 2 association reactions and while these relatively large molecules are quite effective as third bodies they are only of the order of ten times as effective as molecular oxygen in the above processes. Perhaps also the study of the recombination of the other halogen atoms might be instructive in deciding whether complexes like IM are important. Dr. G. Martens (University of Brussels) said With reference to the communica-tion of Prof. Porter and the comment of Dr. Linnett I believe a good test of the radical-molecule complex theory could be the study of the bromine and chlorine atom recombinations.Data are now available for bromine due to Britton and Davidson Palmer and Hornig Givens and Willard etc. Much less is known about chlorine atoms. We are able to measure the three-body recombination of chlorine atoms with chlorine molecules as a third body in the photochlorination of carbon monoxide. At about 500°K the rate equation can be written in the form, l l v 2 = A(k,-.+ Kk,-,[Cl,]/[CO]), where A is a factor involving the reactant concentrations and the propagation rate constants; kr-a and are respectively the rate of radical-atom and atom-atom recombination ; K is the equilibrium constant of the CO-Cl dissociation determined by Burns and Dainton. The plot of 1/19 against [Cl2]/[CO] is a straight line whose slope divided by the intercept permits one to calculate keu.A value of approxim-ately 2 x 1010 1.2 mole-2 sec-1 was found. This may be compared with recent results of Hiracka and Hardwick at 1600°K (J. Chem. Physics 1962 36 1715). I believe this permits one to discard some unlikely high values given in the literature. Dr. P. F. Knewstubb (University of Cambridge) said With reference to fig. 4 of Dr. Fite’s paper I should like to suggest that the ion current denoted H20f would perhaps be more correctly assigned to NHt. A similar conclusion has been reached in the study of ions in flames where the inert diluent of the flame is nitrogen. Evidence bearing even more directly on the question arises from some recent studies I have made of ions extracted from glow discharges? where nitrogen was one of the systems studied.The ions were analyzed by a mass spectrometer which was of sufficiently high resolution to separate the peak observed at 18 a.m.u. into a doublet. The upper component was assigned to NH; and the lower to H2Of. Their ratio varied considerably with the conditions but the relevant point is that the NHZ was generalIy the larger 298 GENERAL DISCUSSION Dr. G. F. 0. Langstroth and Dr. J. B. Hasted (University College London) said: For the reactions, 0++0,-+0,++0 (1) Of+N2+NO++N (2) we have measured the respective rate constants ko and kNz at 300°K. The method is essentially that developed by Dickinson and Sayers (1960). A time-resolving mass-spectrometer was used to observe the decay of O+ ions in the afterglows of d.c. discharges pulsed with ten 2 psec pulses per second in oxygen and in oxygen+nitrogen mixture assuming that the above reactions together with diffusion are the only important loss processes for O+ ions after waiting times greater than 200 psec.Mixture pressures were from 10-3 to 3 x 10-2 mm Hg and helium was added to a pressure of approximately 1 mm Hg to inhibit the loss of ions by diffusion. The mass spectrometer is of the miniature radio-frequency type with a resolution m / A r n ~ 3 0 . Ions enter the mass spectrometer through a 0.3 mm diam. circular aperture in a platinum disc of 6 mm diam. In the circumstances appropriate to the experiment we believe that the output current for a given ion species is proportional to the density of that species in the afterglow. In eqn. (1) the Of ion density obeys the relation an,* - - D,V2no+ - ko2pO2no+ dr where no+ denotes the number density of O+ ions D the ambipolar diffusion co-efficient for o+ ions in helium ko the rate constant for the reaction and p ~ the partial pressure of 0 2 expressed in molecules per cm3.The time-dependent part of the solution is given by no+ = + exp (- t]re), 7,' (D,/A2)+ kozpoz, and QI~O+ is a constant. The quantity A is the characteristic diffusion length found by imposing the boundary condition no+ = 0 at the container walls and is a constant for a given geometry. Semi-logarithmic plots of Of ion currents against time in the afterglow show linear regions over nearly a decade in current and 300 p e c in time. Similar plots given by Dickinson and Sayers 1 show linearity over a factor of about three only in current and even over this range some of their plots show considerable curvature.From the slope of a straight line fitted to a plot of 24 experimental values of rgl against PO by the method of least squares we obtain koz = (1.810.2) x crn3/sec. A straight line fitted to a plot of r;l against the partial pressure of an 02+N2 mixture may be shown to have a slope given by (ko,+ a k ~ ~ ) / ( a + 1) where a repre-sents the ratio of nitrogen partial pressure to oxygen partial pressure and is accurately known. This relation allows us to plot (ko,+ a k ~ ) against a. The four points so far obtained representing 600 decays lie very close to a straight line indicating a high degree of internal consistency for the measurements.From its slope we obtain the value, k, = (4-7 0.5) x 10- l2 cm3]sec. 1 Dickinson and Sayers Proc. Physic. SOC. 1960,76 137 GENERAL DISCUSSION 299 Dr. A. J. B. Robertson (King’s College London) (communicated) The occurrence of heterogeneous reactions on the tungsten filament which is present in the usual type of mass-spectrometer ion-source may be troublesome when ion-molecule reactions are investigated as Talrose Markin and Larin have found. Perhaps the difficulty could be eliminated by using an ion source in which the electron beam is produced from a cold cathode by field emission of electrons. Experiments have been carried out here by M. Warrington on the use of thin wires as electron sources of this kind. Much of the early work on field emission was carried out with thin wires stretched along the axis of a coaxial cylinder and electron currents were ob-served as a function of the applied voltage. Several workers observed anomalously large emissions when new wires were used which had not been subjected in vacuum to a drastic heat treatment. We have tried to follow up these observations and have found that several kinds of wires are effective electron sources for example, 10 ,u diam. platinum wires prepared from Wollaston wire 4-10 ,u diam. electro-polished or normal tungsten wires and drawn tungsten wires which have not been cleaned at all and are still coated with graphite and oxides. These last wires are in fact the best emitters in respect of stability of emission and size of emission for a given field and a wire of 25 ,u diam. can be used. A current of mA can be obtained very easily from such wires by placing them mid-way between two parallel plates and applying a voltage of 5-10 kV. An electron beam can be readily extracted using a slit cut in one of the plates. We have not yet investigated the teduction of the energy of the electron beam with retarding potentials. We do not know whether the uniformity in space of an electron beam produced in this way would be good enough for use in mass spectrometers. Emission prob-ably occurs at numerous sharp points on the wire and if there are enough of these the separate emissions might merge to give an electron beam uniform enough for practical use. An ion source using this field emission principle could be operated down to very low temperatures

ISSN:0366-9033    

DOI:10.1039/DF9623300273

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

AUTHOR INDEX * Bak, T. A., 189, 289. Barth, C. A., 162. Basco, N., 99, 276. Bates, D. R., 7. Bauer, H.-J., 86. Brocklehurst, B., 88. Callear, A. B., 28, 87, 88, 93, 94, 283. Carrington, T., 44, 92. Charters, P. E., 107, 276. Clyne, M. A. A., 139,275, 286, 288. Cottrell, T. L., 85, 90, 291. Davison, W. D., 71, 95. Del Greco, F. P., 128. Dickens, P. G., 52, 92. Dixon-Lewis, G., 205. Edwards, A. J., 61. Findlay, F. D., 274. Fite, W. L., 264. Gowenlock, B. G., 287. Hasted, J. B., 90, 298. Herschbach, D. R., 149, 277, 278, 281. Herzfeld, K. F., 22, 86. Hildebrandt, A. F., 162. Karl, G., 93. Kaufman, F., 128, 284. Keck, J., 89, 173, 291. Khare, B. N., 276. Knewstubb, P. F., 297. Laidler, K. J., 85, 91, 294. Lambert, J. D., 61, 93, 95. Langstroth, G. F. O., 298. Larin, I. K., 257.Lebowitz, J. L., 189. Linnett, J. W., 52, 274, 296, 297. Lint, V. A. J. van, 264. Markin, M. I., 257. Martens, G., 297. Matheson, A. J., 94. Morgan, J. E., 118. Nikitin, E. E., 14, 90, 95, 288, 289. Norrish, R. G. W., 87, 99, 273, 275. Ogryzlo, E. A., 290. Patapoff, M., 162. Pemberton, D., 61. Phillips, L. F., 118. PoIanyi, J. C., 93, 107, 274, 276, 279. Porter, G., 198, 284, 289, 290, 291. Pritchard, H. O., 278. Reid, R. W., 213. Robertson, A. J. B., 299. Rutherford, J. A., 264. Schiff, N. I., 118, 273, 285. Sharpless, R. L., 228. Sovers, O., 52. Smith, F. T., 183, 293, 296. Smith, I. W. M., 88. Snow, W. R., 264. Stretton, J. L., 61. Sngden, T. M., 213. Sutton, M. M., 205. Szasz, G., 86. Talrose, V. L., 257. Thrush, B. A., 133, 275, 286, 288. Toennies, J. P., 96. Ubbelohde, A. R., 85, 95, 276, 295. Widom, B., 37, 91. Williams, A., 205. Young, R. A., 228. * The references in heavy type indicate papers submitted for discussion.

ISSN:0366-9033    

DOI:10.1039/DF9623300300

出版商:RSC    

年代:1962

数据来源: RSC