J. Phys. Chem. 1983, 87,2340-2360
2348
difficult indeed. As is pointed out in the preceding paper, anisotropy in water can be quite considerable, yet might be difficult to detect. Moreover, in most water-solvent systems there is the possibility of a number of different water fractions ("bound" or "free" water, water differently oriented at anions or cations, or exchangeable nuclei of the solute), the relaxation of which is mixed and averaged by chemical exchange. It is clear that, to reach any conclusions on water motion,
Chain-Reaction Mechanism for
NMR results of all nuclei possible have to be combined. Even then, only large motional anisotropies will show up unequivocally in the relative relaxation rates. More information may, of course, be obtained in cases where solvent motion is retarded to such an extent that the extreme narrowing limit is no longer valid and the frequency dependence of the relaxation rates can be studied. Registry No. PMA-Na, 54193-36-1; water, 7732-18-5.
I2 Dissociation in the O,( 'A)-I Atom Laser
R. F. Heldner 111," C. E. Gardner, G. I. Segal, and T. M. El-Sayedt Aerophysics Laboratory, Laboratory Operations, The Aerospace Corporation, El Segundo, California 90245 (Received: October 19, 1982; I n Final Form: January 19, 1983)
A chain-reaction model for 1, dissociation in 0 2 * is proposed. Experiments in a computer-controlled flow tube apparatus indicate that 12(X)dissociation is initiated by collisions with 02(lZ); subsequently, the I atoms formed are pumped to I* by 02(lA). Other initiation mechanisms are also discussed. Chain branching occurs when I* transfers energy to 12(X)to form 1,' and I,* is dissociated into I atoms by collisions with OZ(lA). Chain termination in these experiments is caused by I-atom wall recombination. An analytic model is presented that favors the above explanation over several others that are kinetically similar. Numerical modeling calculations are included to verify this simplified model. Scaling relationships are developed for 12(X)dissociation as a function of [02('A)],[02(3Z)],[Iz],,, [HZO], and [Ar]. The Iz intermediate (Iz$)is not directly observed; however, indirect evidence indicates that it is vibrationally excited Iz(X).
I. Introduction In 1966, Arnold, Finlayson, and Ogryzlo' observed that Iz was rapidly dissociated in the presence of electronically excited oxygen. In addition, strong electronic emission was observed from both molecular Izand the product I atoms. These authors noted that 0#2) (Figure 1)has sufficient energy to dissociate 12(X)by a near-resonant, dissociative E E energy transfer process:
-
o2(1z)+ I,(x)5 21 + oZ(32)
(la)
klb
other products
(Ib)
By means of conventional flow tube techniques, they measured a rapid increase of O&Z) with time when I, was added to the flow. Subsequent workz4 has confirmed their hypothesis that O,('.Z) is initially formed by process 2 and o,('A)+ o,(~A) A
o,(lz) + o2(3z)
then strongly supplemented by process 3. O,(lA)
+ I*
k3
OZ('2)+ I
produced by the near-resonant E O,('A)
+I
k, k-4
-
(2)
The I* is
(3)
E exchange p r o ~ e s s ' ~ ~
02(3.Z) + I*
(4)
where K,, k4/k-4 = 2.9 at T = 295 K. Arnold et al. suggested a second possibility for Iz dissociation: a sequential excitation of Iz(X) by consecutive collisions with two OZ('A) molecules. The Iz intermediate suggested was the then unidentified A'3a2u state of I,, Present address: Department of Chemical Engineering, University of California, Berkeley, CA 94720.
although these authors noted that calculationsfor this state generally placed it well above the 7882-cm-' Tovalue for Oz(a'A): O,('A)
+ IZ(X)
__ kb
k-5
1,'
+ Oz(3Z)
(5)
5
o,(~A) + 12 21 + 0 2 ( 3 2 ) (6) This brief, but incisive, paper still serves as a useful introduction to the subject of I2dissociation in electronically excited oxygen. The recent demonstration of continuous-wave lasing on the I(2P1,z-2P3,2)transition" at 1.315 pm that is pumped by process 4 gave this kinetic problem new urgency. Clearly, the production of the lasing species (I atoms) must be understood if the potential of this laser system is to be realized. In 1970-72, Derwent and T h r ~ s h ~ ,performed ~ ~ ~ - ' ~detailed experiments on the Oz-Iz system to quantify the observations of Arnold et al. Much of their analysis has been proved correct; however, they concluded1° that process l a could quantitatively explain the dissociation of Iz(X)in Oz*. A number of recent observations cast con-
s.
(1) J. Arnold, N. Finlayson, and E. A. Ogryzlo, J. Chem. Phys., 44, 2529 (1966). (2) R. G. Derwent and B. A. Thrush, Trans. Faraday Soc., 67, 2036 (1971). (3) R. G. Derwent and B. A. Thrush, Discuss.Faraday SOC.,53, 162 11972). ~~- . -,(4) R. F. Heidner 111, C. E. Gardner, T. M. El-Sayed, G. I. Segal, and J. V. V. Kasper, J. Chem. Phys., 74, 5618 (1981). (5) W. E. McDermott, N. R. Pchelkin, D. J. Benard, and R. R. Bousek, Appl. Phys. Lett., 32, 469 (1978). (6)D. J. Benard, W. E. McDermott, N. R. Pchelkin, and R. R. Bousek, Appl. Phys. Lett., 34, 40 (1979). (7) R. J. Richardson and C. E. Wiswall, A _ p p l.. Phys. Lett., 35, 138 (1979). (8) R. G. Derwent, D. R. Kearns, and B. A. Thrush, Chem. Phys. Lett., 6, 115 (1970). (9) R. G. Dement and B. A. Thrush, Chem. Phys. Lett., 9,591 (1971). (10) R. G. Dement and B. A. Thrush, J . Chem. Soc., Faraday Trans. 2, 68, 720 (1972).
0022-3654/03/2087-2340$01.50/00 1983 American Chemical Society
Chain-Reaction Mechanism for
The Journal of Physical Chemisfry, Vol. 87, No. 13, 1983 2349
I2 Dissociation
*
I 1B37r +I
z
15
t
t
= X
c
I
t
REMJTE V I DE0 TERMINAL
0,
DIGITAL
1 STEPPING
10.
CMROLLER
Figure 1. Low-lying electronic energy levels for the O2 and I2 molecules and the I atom.
siderable doubt on this conclusion. Houston and coworkersll found by direct laser pumping of 02(lZ) in the presence of I2that the total lZ removal rate coefficient (2 x 10-l’ cm3/(molecule5)) was 10 times smaller than the value of kla needed by Derwent and Thrushlo to model their results. Muller et al.12 estimated kla/kl Q 0.2, although they determined that iZl = 7 X cm3/(molecule s). A lower value for kla was consistent with the failure of laser modeling codes to predict the rate of I2dissociation in the continuous-wave transfer laser devices.13 The principal obstacle to the modeling was the presence of H20, which served as a rapid quencher of 02(lZ). Experiments in our laboratory supported the claim that 02(lZ) could be removed by H 2 0 without totally suppressing I2dissociation,14and led to the conclusion that, although 02( lZ) may be necessary, it is not sufficient to explain the rate of I2dissociation in 02*. The study described in this paper is a major extension of the work reported in ref 14. The dissociation of I2into atoms has been measured as a function of [02(lA)], [02(3Z)],[I2lO,[H20], [Ar], and qualitatively as a function of [I],,. The dissociation curves for I2vs. time exhibit a rather unusual behavior, which is summarized as follows: (1) “Initiator” effects (O(3P)atoms, 02(lZ), ...) are extremely important. (2) The curves often exhibit a substantial induction time. (3) Small amounts of H 2 0 strongly affect the dissociation rate, and large H 2 0 densities have a proportionately smaller effect. (4) The inverse half-life for dissociation, (t1l2)-l, is proportional to [1A]2[32]-1[12]o”o.7[Ar]o over the concentration ranges studied. These data indicate that I* is strongly implicated in the dissociation process. We propose that the dissociation mechanism involves chain branching with I* as the chain carrier. In the following section we review the computer-controlled flow tube apparatus used to obtain these data. An analytical model is developed to simulate the experimental curves, rapidly test the model’s sensitivity to various reactions and rate coefficients, and predict the scaling of the dissociation kinetics into laserlike concentration regimes. A limited number of numerical modeling calculations then are presented for all the measurable system species concentrations. The time behavior of 02(lA) is particularly (11)R.G. Aviles, D. F. Muller, and P. L. Houston, Appl. Phys. Lett., 37,358 (1980). (12)D.F. Muller, R. H. Young, P. L. Houston, and J. R. Wiesenfeld, Appl. Phys. Lett., 38,404 (1981). (13)R. F. Shea, private communication. (14)R.F.Heidner 111,C. E. Gardner, T. M. El-Sayed, and G. I. Segal, Chem. Phys. Lett., 81,142 (1981).
Figure 2. Schematic diagram of the computer-controlled kinetic flow tube apparatus.
crucial. Some sets of modeling parameters. can correctly reproduce the I2dissociation curves; however, they predict an unrealistically large removal of 02(lA) molecules for each I2dissociated. 11. Experimental Apparatus The computer-controlled flow tube apparatus (Figure 2) has been extensively described in earlier publications.4J4 Electronically excited oxygen is created by conventional microwave discharge techniques. The O(3P)atoms created in the discharge are recombined on a heated HgO mirror deposited downstream of the discharge cavity by codischarging Hg + O2prior to a set of experiments. The earlier apparatus was modified to permit a variable fraction of the O2to be passed through the discharge; the remainder is added downstream of the discharge, but well upstream of the I2 addition port. The principal injected gases in this study were I2(+Ar) and H 2 0 (+Ar). We continue to use the method of flow replacement, whereby a pure Ar stream is gradually replaced with an I2 + Ar (or H 2 0 + Ar) mixture to vary minority constituent densities without changing total molar flow or total pressure. Elevated temperature saturators were employed to produce the appropriate mole fractions of I2and H20 in Ar. The saturation efficiency was tested under flowing conditions by visible absorption spectroscopy (I2)and by sampled gas analysis (H20). The flow tube is constructed from 38.5-mm i.d. Pyrex internally coated with halocarbon wax. The usable length of the tube is 60 cm. Two types of I2injectors are used. The first injected I2 axially through a six-prong spoke injector, in which each prong had four holes -0.5 mm in diameter. The second “ring” injector used eight holes -1 mm in diameter, drilled radially in the flow tube walls. This latter technique was generally used. As in our previous studies,4,14the optical emission features 02(1A+3Z) (A = 1.27 pm), I(2P12+2P3/2) (A = 1.315 pm), 02(1Z+3Z) (A = 0.762 pm), and 12(B3110u++X1Z,+) (Amm = 0.580 pm) were monitored by two spectrometer systems mounted on a movable platform. This platform
2350
Heidner et al.
The Journal of Physlcal ch8m/Stv, Vol. 87, No. 13, 1983
230
-
i?
il
0 0
0
-25
00
25
50
75
100
125
2 lcmi
124
130
126 A
122
118
lulr
Flgwe 3. Low-resolution s y m of the I$A-X) transitlon undertying the spectrum of O2('A+ 2 ) and 1(2P,/2-2P3/,).
is moved to discrete positions on the flow tube by a computer-controlled stepping motor. At each flow tube position, the emission intensity monitored by each spectrometer system is sampled by the computer. During this work, it was found necessary to monitor a near-infrared emission system15 (Figure 3) that has been identified as Iz(A-X) emission from u ' = 0 and 1.l6 Under some conditions, a difference spectrum must be computed to accurately determine the O#A) emission intensity at 1.27 pm. Our empirical procedure involves subtracting the emission intensity at 1.24 pm (pure A X) from that at 1.27 pm (Oz(1A-3E) plus IZ(A-+X)).Five species are monitored by optical emission spectroscopy, requiring three scans of the flow tube under fixed experimental conditions. The procedure for converting optical emission signals to absolute densities is described in ref 4. Absolute densities are determined for ['A], ['E], [I*], and computed by mass balance for [Iz]. Relative measurements only are reported for [Iz(A)] and [Iz(B)]. Mixing efficiency is an issue in these experiments for several reasons. We have suggested that I* is implicated in the Iz dissociation process. Thus, the analysis implicitly assumes that Iz (and I*) are homogeneously mixed during the dissociation process. In addition, if mixing is slow, we are forced to work at relatively long dissociation times, where I-atom recombination complicates the analysis. Figure 4 shows that I2 mixing into the Ozflow can be optimized for a specific flow tube geometry by injecting Ar diluent in with the I2 Using the radial ring injector, we studied the mixing by means of Iz(B-.X) laser-induced fluorescence (LIF) pumped at 514.5 nm by a repetitively pulsed Ar+ laser (TRW Model 71B; 40 pJ/pulse) and monitored by the photon counting system. In Figure 4, it can be seen that a relatively small amount of added diluent causes the centerline mixing to approach a step function. All data reported in this flow tube study are sampled every 1.25 cm at flow velocities (6550 cm/s) that are within a factor of 2 of that used in Figure 4. With a modulated continuous-wave Ar+ laser, it is possible to get Iz dissociation curves directly, even in
-
(15) R. F. Heidner 111, "SpectroscopicProperties of the 02*-Iz Flame", TR-0082(2610)-1, The Aerospace Corp., El Segundo, CA, to be submitted
for publication. (16) S. J. Davis and P. D. Whitefield, to be submitted for publication.
Flgwo 4. MUng efficiency of I2 (+Ar)into 02*using the radial injector (Figure2): (0)I, + Ar mixture from the saturator: (A)additional pure Ar injected with I, -I-Ar mix. Optical distortion occurs within AZln,. Plug flow velocity = 250 cm/s.
the presence of background Iz(B-+X) emission.
111. Analytic Modeling of I2 Dissociation Several processes are considered in addition to processes 1-6. It was proposed that I* participates directly in the I2 dissociation process. Although process 3 satisfies that criterion qualitatively, we will consider two additional processes: I*
+ 12(X) 12*+ I*
kl
1,:
k0
+I
(7)
31
(8)
Removal rate coefficient data exist for I* + 12(X). Nothing is presently known about process 8. Quenching of 02(*Z) and I,* must be considered to complete a simple analytic model: 02(12)+ H20
O,(lZ)
+ wall
k9
02(1A,3E)+ HzO
(9)
+ wall
(10)
k10
02(la,32)
-
+ I,* + 0,(32) I ~ ( x+)0,(3z) I,* + Ar 5 12(X)+ Ar 12t + wall 12(X)+ wall I,*
+ H20
kil,
12(X) H20
-
(W (Ilb) (Ilc)
kl2
(12)
Quenching of 12 by I,(X) has been carefully considered and rejected as a major process, because it predicts the wrong dependence of the dissociation rate on [I2lO. A recombination term for I atoms must be included t o represent the experimental observation of residual I2 in the steady-state flow for certain initial values of 02(lA) and I> Under low-pressure flow tube conditions, this process must certainly be wall recombination: I(I*) + wall
k13
l/J2
+ wall
(13)
Because one of the primary goals of the analytic modeling is the sensitivity analysis for various processes, process 13 will be ignored initially to obtain a relatively simple expression. An exact solution is still possible with process 13 included, and this solution will be discussed. The contribution from the O,('Z) model and the sequential
Chaindeaction Mechanism for
The Journal of Physical Chemistry, Vol. 87, No. 13, 1983 2351
I2 Dissociation
TABLE I : Kinetic Model of I, Dissociation by O,* at T = 295 K rate coeff, cm3/(molecules )
Process
< 4 x 10-''a G1.4 X lo-" kl -+
all products
k,
o , ( ~ A ) t o , ( ~ A )-+ o,(lA)
+ I*+
O 2 ( l C )t
k4
o~(~A + )I 2 k-4 O , ( I A ) + I,(x)
+ 0,(3z
0,(1z
k3
0,(3z)t
1
I*
lo-"
11 12
10-17
2
(1.1 t 0.3) x 1 0 4 3
4
h - , = ( 2 . 6 * 0 . 4 ) x lo-", ( k , = ( 7 . 6 ?: 2 . 5 ) X lO-")'
2 5 , 26
Table V
this work
Table V
this work
G ( 3 . 5 r 0.5) x
2 7 , 28
Table V
this work
k
f
02(3z
t I,+
k-3 O , ( ~ A )+ I?*
11 12
(2.04 t 0.28) X 7 x 10-11 (2.0 t 0.5) x
ref
k6 -+
0 , ( 9 t 21
k
I*
+ I,(X) 2 I + I,* k-7
I**
+
k8
I* + 31
O , ( ~ Z )+ H,O
k9 -+
k
O,('Z)+ wall+ k Ira
I,* t H , O +
10
0 , ( 1 ~ , 3 t~ H,O
O , ( ' A , ~ Z ) +wall
12*+ Ar
-+
k
k
3x
10-3)e
4
I,(X) t 0,
Table V
this work
I,(X) t Ar
Table V
this work
Table V
this work
Table V
this work
12
+ wall-+ I,(x) I (I*) + wall -+ l/J,(X) I,*
(y =
this work
11C
-+
20 s-1
2,11
Table V
I,(X) t H,O
rib
I,* t 0,
( 5 . 5 t 1) x 10'''
13
t wall
a The value for h , , was calculated from the h l , / k , result from ref 12. The authors of ref 1 2 imply that k , determined in ref 11 is t o be preferred, The value of k , is calculated from h - , by statistical mechanics ( K E Q= 2.9 at T = 295 K). The reported value is the I* removal rate coefficient. e y = (2Rk1,)/cwhere E is the oxygen mean velocity and R is the tube radius.
excitation model will be formally separated. The rate processes considered in these models are summarized in Table I. A. Steady-State O2(lX)+ Iz Model. If one assumes that the products of process l b return to 12(X)in its initial distribution and that the equilibrium represented by process 4 is instantaneously established, the removal of I2 by O&Z) can be written explicitly by using definitions for [I*], RIP$(s-'), and [0z(12)],, developed in Appendix A: where
and writing down a steady-state expression for [I2$](Appendix A). At this juncture, we are only hypothesizing that I2$is in steady state:
A term in [I*I2has been neglected in the derivation of eq 15. This assumption is examined in section IV. C. Global Analytic Equation. Equations 14 and 15 can
x = KEQ[1Al/[3zl This formalism and that for sequential excitation, which follows, assume that the ['A] and [3Z]are constant during the dissociation. Both analyses allow for the presence of I atoms at t = 0. B. Sequential Model with I,$ in Steady State. The analysis of the sequential model depends upon the relative importance of processes 7 and 8. The general expression can be derived by defining the quenching term for I,*,RIzf,
be combined to give a single differential equation -(d[IJ/dt) = (a, + asQ)[I2]- ( b , + bsQ)[I2lZ(16) that can be integrated into the following expression:
2352
The Journal of Physical Chemistry, Vol. 87,No. 13, 1983
Heidner et
al.
TABLE 11: Analvtic Dissociation Model Parametersa
where a = ax + U S Q , b = b z + bsQ,and c = a / b . Because the I, decays are not exponential, it is useful to define a dissociation half-life, tl,z:
"I
1
I
.e.-
00
= a-l In ([1210/c'+ 2)
where
KZ(1) + KSQ(1) Kx(2) + KSQ(2) The parameters in eq 14-19 have been categorized in Table 11, so that they can be useful for sensitivity analysis. The strongest variation in eq 19 is in the term a, which consists of two subterms: ignoring RL: and R1,,for the moment, the first scales as [1A]2[Iz]o/[3Z] (assuming [I], > k , k , ; therefore, k , / k , = 1.8 X lo-'; assumes k, = 3.5 x l o - " cm3/(molecules) Assuming k , = 3.5 X lo-" cm3/(molecules), (Table I). k b / k l l b% 6.
to fitting the shape as well as the t1/2of the Iz dissociation curves. B. Extent of I2 Dissociation i n Steady State. The simplified model represented in Table I1 does not include I-atom recombination, so it will not account for incomplete dissociation in steady state. When I-atom recombination is treated in Appendix B, we find that the steady-state amount of Iz is given by eq B5 [Idm= -P = h , / b if asQ + a x > k13. Thus, the I-atom wall recombination coefficient is a potential source of systematic error, because it may vary from experiment to experiment (or even during an experiment) as the walls age. C. I2 Dissociation Half-Life and Extent of Dissociation. Variation with Initial Conditions (Table III). In this section, the experimental variation of tllz with the initial system densities is described. By an iterative procedure, the five data sets presented (Table 111) were fitted with the parameters k13,RIB$,Kw(l), and Kw(2). The term R12$ is not well constrained by these data. Two sets of these parameters are offered in Table V as models 1and 2. The data are compared in Figures 7, 9, 11, 13, and 15 with model 2 (analytic model fits), although model 1 gives a virtually identical set of fits. Neither model is strongly favored. The rate coefficients presented in Table VB (model 2) are consistent with the empirical parameters but are not unique. They were combined with the rate coefficients in Table I and used in a numerical modeling programls to solve for all time-dependent species densities. (18) E. B. Turner, G. Emanuel, and R. L. Wilkins, "The NEST Chemistry Computer Program", TR-0059(6240-20)-1,The Aerospace Corp., El Segundo, CA, 1970.
-3 0
'50
I
152
1 154
LOG ID^ I1-11
, 155
158
16:
motecuies,cm 3~
Flgure 8. plots of log t 1,2 vs. log ['A],,: experimental data (O),analytic fits (-), numerical fits (---). Modeling data from Tables I and V.
In these calculations (referred to in the figures as "numerical fits"),no steady-state assumptions were made. No evidence was found that suggested that processes proportional to [I*I2 were active in the dissociation mechanism (i.e., process 7 followed by process 8). This result does not eliminate the possibility of such a process. 1. Variation of tllzwith O,['A]. An examination of eq 19 reveals that the principal dependence of tllzon ['A] occurs in the denominator term a. This term is dissected in detail in Table 11. There are implicit dependences on ['A] in the term c' (in X and RI $); however, these weak dependences are further m i t i g a d by their presence in the logarithmic factor. The same logic applied to the more general eq B7 identifies the critical term as (-Q)'/2. Table I1 indicates that, if the subterm a , dominates, tl12is proportional to If asQ dominates, the dependence will fall between ['A]' and ['A]' depending on whether RIgtis proportional to ['A]. Figure 7 shows plots of [I,] vs. time as ['A], is varied with all other conditions held constant. Figure 8 summarizes these data as a plot of log t l vs. log ['A]. Within experimental error, the slope is -2 ratiher than -1, which indicates that RI : is a weak function of ['A] in this concentration range. &e demonstrate that asQ> a, later in this section. We will examine this dependence on 'A in detail, because it implies that most of the 1,' mole-
The Journal of Physical Chemistry, Vol. 87, No. 13, 1983 2355
Chain-Reaction Mechanism for I, Dissociation
10
0.8
1 00 0 00 000
0015
0045
003
006
0075
009
0105
I [sect 004
008 t
016
012 lsecl
020
024
Figure 9. Experimental data (Table 111: runs B1 (0) 83 ,(A),and 85 (0)),analytic model fits (-), and numerical model fRs (---) for I, dissociation vs. time as a function of [32]0. ['XI, variation: (1.4-7.1)
Figure 11. Experimental data (Table 111: runs C3 (0), C2 (A),and analytic model fits (-), and numerical model fits (- - -) for C1 (O)), I2 dissociation vs. time as a function of [I2lO. [I,], variation: (0.51-3.3) X 101'/cm3.
--1.0
O
-:i' ,
f
i
r
, , , , i1
-3 0
120
124
128
132
136
140
144
LOG 111210, mo~ecu~esicm';
16.2
16.4
16.6
168
170
LOG 1[02 13111moleculesic") ,
Figure 10. Plots of log t vs. log [32]~: experimental data (O), analytic fRs (-), numerical fits (- - -). Modeling data from Tables I and V.
cules are not removed by processes 6 and 8. If the dominant 12 removal process is a quenching process other than process -5, serious implications arise for loss of available 02('A) because of the inefficiency of the dissociation process. This issue is discussed within the context of the measured ['A] time profiles during I2dissociation. The data in Figures 7 and 8 are fitted by using empirically determined parameters for Kw(l), E(,(2), and k13 (Tables I and V). 2. Variation of tl with Oz(3X).Equation 19 and Table I1 show an explicit dependence of a2 on [3Z]-'. If RIzt were proportional to [3Z], tllz would be expected to be proportional to [3Z]2. In our experiments, X 4 0.3, so that the term c'is almost proportional to [3Z] ( p is concentration independent to first order). Thus, we expect that tl12 is proportional to [ 3 Z ] n In (2 + c'132]-'), where c" is a constant and 1 < n S 2. Figure 9 shows several plots of [I2]vs. time with [3Z] as a variable. Figure 10 consolidates these results into a log t,/z vs. log [3Z] plot. A serious ambiguity in these data results because total pressure is held constant by replacing 0 2 ( 3 X ) with Ar. This ambiguity was removed by studying the dissociation time as a function of [Ar] (section IV.C.5).
Figure 12. Plots of log f I l 2 vs. log [I2lO: experimental data (0), analytic fits (-), numerical fits (- - -). Modeling data from Tables I and V.
Since Ar was found to have no measurable effect on t 1 / 2 in the concentration range studied, we conclude that Figure 10 represents the dependence of a2 on [ 3 X ] with a slight dependence of RIzt on [3Z] at high ground-state O2 densities. 3. Variation of tl12with [I2lO.Analysis of eq 19 and Table I1 indicates that the predicted behavior of t1,2with [I2lOcan be quite complicated. The decay curves shown in Figure 11point to a dissociation half-life that becomes shorter as [1210is increased (Figure 12). This is the single strongest argument for I* participation in the dissociation process. If a2 > al and [I2l0/c'>> 2, eq 19 predicts that t112is proportional to [I&' In ([I2l0/c?. The slope of tllz vs. this quantity on a log-log plot is not constant; however, it is given by S = -(0.7 f 0.1) over a wide range of [I2lO if c'is chosen in a reasonable manner. This dependence occurs using either the 0 2 ( ' X ) model ( K 2 ( 2 ) )or the sequential model (Kss(2))contributions to a2. We can quantify K2(2),however, and demonstrate with the use of currently accepted values of kl,, k3, and k9 that the term a2 >> ax. 4. Variation of tlI2with HzO.The variation of t1/2with small quantities of HzO is discussed in section 1V.A. In addition to effects traceable to Oz('Z), there seems to be a secondary effect at high H 2 0 additions that can most easily be explained as a contribution to RIzt. Since k l / k , i= 4,the analytic model presented in section I11 is valid
2356
Heidner et al.
The Journal of Physical Chemistfy, Vol. 87, No. 13, 1983
I
330
LO2
104
006
008
01c
012
: isecl
Figure 13. Experimental data (Table 111: runs 0 2 (0),D4 (A),and D6 (0)), analytic fits (-), numerical fits (- - -) for I, dissociation vs. time as a function of [H,O]. [H,O] variation: (0-3.4) X 10i5/cm3.
~/
8
1 lsecl
Figure 15. Experimental data (Table 111: runs E l (O),E2 (O), E3 (0); E4 (A)),analytic fit (to run E l ) (-), numerical fits (to run E l ) (---) for I, (1.5-13.0) X 10'6/cm3.
-1 101
-1 40
U
9 i
-1 70
7
c
I -
c I
-1 85 L
i
" "
1230
1275
'350
1425
LOG 1!H201 molecules
1500
1575
'650
I
cm'i
Figure 14. Plots of log t , , , vs. log [H,OIo: experimental data (O), analytic fits (-), numerical fits (- - -). Modeling data from Tables I and V. Curves 1 and 2 refer to models 1 and 2 in Table V.
only for [H20]>> 4[1210. For the data presented in Figures 13 and 14, this implies [H,O] > 1014/cm3.We have chosen a value for klla to fit the high [H20]data points and then used The Aerospace Corp. numerical modeling code NEST)'^ to solve for the exact time dependence of I2 dissociation over the full [H20]range. These calculations are shown in Figure 14. These fits are less than satisfactory. The fault may be with the model, particularly with the competition between I2 and H 2 0 for 0 2 ( l Z ) , or it may be in the data themselves. These data were obtained with in order to avoid O2('A) deactivation caused a very low [I2lO by I* + H20. Data taken at high [IzlOand at [HzO] = 0 (Figure 18) are consistent with model 2 (Table V). 5 . Variation of t l I zwith [ A r ] . The density of Ar was varied over 1 order of magnitude while a constant initial density of all other species was maintained (Table 111). Within experimental error, we found no dependence of the dissociation rate on Ar (Figure 15). Figure 16 shows a log tllzvs. log [Ar] plot. The solid line represents the largest value of kllc consistent with our observations. Note that the lack of an Ar pressure dependence is unexpected for a vibrationally excited 12.*intermediate but is consistent with the Oz('2) mechanism. The low contrast ratio of [Ar]/ [O,]that was experimentally possible does not rule out a vibrationally excited I2 intermediate if O2 is a particularly efficient vibrational quencher.
-2001 160
, 162
1
164
166
168
I
170
172
174
LOG IIArl, moleculeslcm31 Figwe 16. Plots of log fl,, vs. log [Ar]: experimental data (O),anaiytii fit (-), numerical fit (---). Modeling data from Tables I and V.
6. Overview of the tllz us. [Ci]Data. The analytic fits to the two types of plots presented, i.e., plots of log tl12 vs. log [C,] and [I2]vs. time have identified the variables k13 and &Q(2) (E(k5k8 k6k7)/RIlt) a8 critical. Somewhat less important for the concentration ranges studied are the variables K s ~ ( 1 )( + , k 6 ) / R 1 2 $and ) kl,. The detailed analysis of Ks (2) presents a number of problems: (a) What is IJ? (by What are the important contributions to R,,? (c) What are the absolute magnitudes of RIZtand k&, k&7? Numerous workers in this field, including us, have suggested that there are two major possibilities for the identity of I,*. As suggested by Ogryzlo and co-workers,' the intermediate could be Iz(At3nzU). The other possibility for the intermediate is vibrationally excited 12.1+z1Neither of these explanations is immune to criticism. In our earlier paper on I2 dissociation,14we reiterated the suggestion that I2(At3n2,,) could be the product of process 5 and/or 7. Recently published spectroscopic analy~is'~ has identified this state as the lower level of the
+
+
(19) J. Tellinghuisen and K. Wieland, submitted for publication in J . Mol. Spectrosc. (20) G . Black, private communication, 1980. (21) P. L. Houston, private communication, 1981.
-
Chain-Reaction Mechanism for
I2 Dissociation
I2laser at 3400 A (D' A'). Tellinghuisen and Wielandlg have argued that the total of the spectroscopic data requires a T, value for A'Q2, of 10047.5 cm-'. Independent measurements by Koffend et al.= confirm this position for A'. Thus, process 5 would appear to be -2060 cm-' endoergic and process 7 would be -2340 cm-' endoergic. At T = 295 K, these processes could not occur rapidly enough to avoid limiting the rate of I2 dissociation in an unrealistic fashion. If 12 denotes vibrationally excited I,, we must assume that vibrational relaxation is rapid, although some relaxation could be tolerated and IJ would still have sufficient energy for process 6 to be energetically feasible. If this were the case, R,,, would be very large and k6 must be nearly gas kinetic to permit 02('A) to compete for 12. On the other hand, k,['A] cannot dominate R12,completely without producing a ['A]-' dependence of tl12instead of the observed ['A]-2. If we accept that R12*must be large in a vibrationally excited intermediate model, we cannot realistically expect that I* participates by energy transfer to IJ. Thus, process 8 is much less important than process 6 in producing I atoms. Of course if vibrational relaxation is slower than we expect on the basis of the work of Koffend et al.,23the reaction sequence (k5,k,) could still be possible. At present, we believe that process 6 is rapid and that it must therefore proceed on the basis of E E transfer, most probably
k22b
k,
0 2 ( l A ) + 1,+'320)
-
12f(A3111,) + 0,
21 + 0
2
which would account for the observed presence of 12(A3111,) during the dissociation process. If 121is vibrationally excited 12, increasing the total pressure of buffer gas (with ['A], [3Zl, [I&, and [H20]constant) should demonstrate some significant effects on both tl and the quantum yield of A3111,. This was not observed (Figures 15 and 16 and Table 111). Thus, Ar must be significantly less efficient than 02(3z) or H 2 0 as a vibrational relaxer of 12. Pritt24has suggested that A3111, and At3II2, may be populated below their dissociation limit by the second step of the sequential transfer and that dissociation may require the participation of a third pump species (I* or 'A). This mechanism would produce dissociation terms that are third order in 02('A) and could permit an observed second-order dependence on 'A if the final step of the dissociation, i.e.
The Journal of Physical Chemisrry, Vol. 87, No. 13, 1983 2357
'v
L
0
I
1
20 1
40 lmsecl
80
60
Flgure 17. Time profiles for 12(A-+X) and I,(B-X) relative to other measured species. Experimental data: run D3 (Table 111). The lines are empirical fits rather than theoretical.
postulated that 12(A2111,) (which they did not observe) was formed as a major product of process l b
O,('z) + I,(X)
klb
1dA3%,) + 02(32)
and that 12(B311)was formed by process 24. o,(~A)
+ I,(A~II,,) 5 02(32)+ I ~ ( B ~ I I ~ ,(24) +)
We observed a near-infrared transition analyzed to be 12(A-X) emission originating from the u' = 0 and 1 levels.', Figure 17 shows that the time dependence of both emission bands serves as a useful diagnostic for the dissociation of 12(X). Qualitatively, the data for these two band systems are consistent with the Derwent and Thrush mechanism. Because the A X and B X emission profiles are similar under all experimental conditions studied, either the A and B states have the same precursor or B311 is produced from, and maintains a steady-state relationship to, A311. A simple way to view the traces in Figure 17 is to analyze eq A4 from Appendix A with Rz constant (dominated by H20 quenching) and with ['A] constant. In that case, the ['2],, increases linearly with k23. the [I*] (see Figure 17) and the Derwent and Thrush 12(A',A) + 02(lA) 12(B3n)+ O2 mechanism (klb, k2*)A311 and B311concentration dependences can be written as follows: k23b 21 + 0 2 [I2(A)I = kA[I*I[IZI/RA (25) dominates the loss of 12(A' and A). Several other three-step where RA (s-') contains the removal terms for the A3111, models are capable of demonstrating the correct kinetic state and kA is a constant. This analysis assumes k2[lA] order for dissociation. < k3[I*]. When this simple steady-state analysis is used, D. Behauior ofl2(A3IIlu) and 12(B3110u+). In their series [12(A)]- occurs when [I2]has reached half-minimum and of papers on the 02-12 system, Derwent and T h r ~ s h ~ ~ ~ [I*] s ~ has ' ~ reached half-maximum. If ['A] remains constant invoked a mechanism for the I,(B-X) chemiluminescence during the dissociation and B311 is in steady state with that had rather significant mechanistic implications. They A311, then
-
-
-
-
(22) J. B. Koffend, R. Bacis, and A. Sebai, submitted for publication. (23) J. B. Koffend, F. J. Wodarczyk, R. Bacis, and R. W. Field, J. Chem. Phys., 72,478 (1980). (24) A. T.Pritt, Jr., private communication, 1982. (25) J. J. Deakin and D. Husain, J.Chem. SOC., Faraday Tram. 2,68, 41 (1972). (26) D. H. Burde and R. A. MacFarlane, J. Chem. Phys., 64, 1850 (1976). (27) A.J. Grimley and P. L. Houston, J. Chem. Phys., 68,3366 (1978). (28) H. Hofmann and S. R. Leone, J. Chem. Phys., 69,641 (1972).
[Iz(B)I = b [ I d A ) I['AI /RB (26) where RB represents the total removal rate of B311 state molecules. Thus, 12(B-X) emission has the same temporal profile as 12(A-+X),but scales differently with the ['A]. This temporal behavior for A311 and B311is not unique to the Derwent and Thrush mechanism. The sequential mechanism favored by this study (k7,k,) invokes a vibrationally excited 12(X)intermediate. On these flow tube
2358
The Journal of Physical Chemistry, Vol. 87, No. 13, 1983
Heldner et al.
time scales, I,$ will be held in steady state by the rapid removal rates, I?,,,, that are typical of vibrational relaxation processes in heavy diatomics. Thus, we can write [I2*],,= (k7/R~Pt)[I*l[121 [lZ(A)lss KA[l*l[I21 zz KB[I*][IZl ~~Z(B)lss
(274 (27b) (274
where KA
= [(b2ak7)/(R12*RA)I [la] KB
= (~Z~KA/RB)['AI
E. I2 Dissociation in an H,O-Free 02*System. The analytic model presented in this study requires four fundamental assumptions: (1)[lA] constant during I, dissociation; (2) 'Z in steady state and RE not a function of 1,; (3) I,t in steady state; and (4) [Izt1 10000 cm-l. This state must be collisionally and optically metastable if the sequential path (It5, kJ is followed. Vibrationally excited I2 is somewhat more tangible as an intermediate by means of sequential path (k7,k6) because I* is known to be rapidly quenched by I* When we have made the assumption that this quenching process produces 12, however, we are forced to conclude that k6 can compete against vibrational relaxation. The fact that tl is independent of [Ar] is troubling. Despite these ambiguities regarding 12, the value of the analytic model lies in identifying the parameters that permit one to model the I, dissociation data. The wall recombination rate, k13, is necessary for understanding the flow tube, although KsQ(2)(=k5ks + k6k7)/R12t)and the initiation terms kla and Ks (1)(=k5k6/RIzt)are the variables that ultimately contro the production of I atoms in the continuous-wave transfer laser. The results reported here are presented as constraints on a final set of rate coefficients employed to provide accurate numerical modeling. The rate coefficients given in Table V satisfy those constraints and are useful for modeling. Only more detailed experiments can identify 12 and provide a unique set of rate coefficients for the dissociation kinetics of I, in electronically excited 0,.
,
4
Acknowledgment. We acknowledge the continuing support of and interest in this work by Lt. Col. W. E. McDermott and the staff members of the New Laser Concepts Branch of the Air Force Weapons Laboratory. The active participation of Prof. J. V. V. Kasper was crucial to the early stages of this program. R.F.H. acknowledges the invaluable exchange of ideas with many colleagues working actively in this field. These include Drs. H. Lilenfeld (McDonnell Douglas), A. T. Pritt, Jr., and D. Benard (Rockwell Science Center), G. Fisk and G. Hays
The Journal of Physlcal Chemistry, Vol. 87, No. 13, 1983 2359
(Sandia), J. Berg (TRW), G. Black (SRI), and Profs. P. L. Houston and J. R. Wiesenfeld (Cornell University). We thank H. Michels (UTRC), Prof. J. Tellinghuisen (Vanderbilt University), and J. B. Koffend (Lyon) for recent information regarding potential energy curve calculations and spectroscopy of the A'3112u state of Iz. Many thanks are due to Mrs. Karen Foster, who performed the NEST calculations, and Ms. Lydia Hammond, who prepared the manuscript. This work was supported by the Air Force Weapons Laboratory under US.Air Force Space Division (SD) Contract No. F04701-81-C-0082.
Appendix A Definitions for Analytic Modeling. I. Iodine Mass Balance. If the steady-state concentration of intermediate I, states (12)is small compared to [I2lO,iodine mass balance can be approximated as follows: [I210 - '/([I1 + [I*])
[I21
(AI)
Earlier work has established that process 4 produces a rapid equilibrium between I(2p1/2,2p3/2)and 02('A,%), and we can write [I*]/[I] = K E Q [ ' A ] / [ ~E~ ]x (A2) The equilibrium constant, Kw k 4 / k 4 , is 2.9 at T = 295 K. Equations A1 and A2 can be combined to yield
Within that context, d[I*]/dt = -[2X/(1 + X)] d[12]/dt. II. O,(lZ) Behavior. As developed in ref 4, the steady-state concentration of O,(lE) can be represented in the general case (with I, I*, and I, present) as ['El,, = ((k2 + k3[I*l/['A1)['Al2)/Rz
(A4)
where R, = k9[H20]+ k1[12], + klo. In the dissociation region where [I,] is changing rapidly, analysis is simplified if k9[H20]+ klo >> kl[12]. III. Quenching of Izf. R I (s-l) ~ ~ = ks['A] k-6[3E] ks[I*] k-7[1] klla[H2OI + klld32:] + k11c[ArI + It12 (A5) IV. Steady-State Concentration of 12.
+
+
[I2*Is,= M 1 A 1
+
+ ~,[I*I)[I~(X)I/RI,,
(A6)
Appendix B Analytical Dissociation Model for 1,Including I-Atom Recombination. The introduction of the wall recombination process 13 into the kinetic scheme requires that the differential eq 16 be modified in the following manner: -d[Iz]/dt = a[I2] - b[I2I2- d
(B1)
where
+ asQ + k13 b = bx + bs,
a = ax
d = k13[1210 The solution of this equation is given by eq B2 (2b[Iz] - a - (-Q)1/2) (2b[I,]o - a + (-Q)1/2) (2b[Iz] - a + (-Q)'/') (2b[I,]o - u - (-Q)'12) e x ~ [ ( - Q ) ~ /(B2) ~tl where Q = 4bd - a2. The following definitions are then useful: a = [-a - (-Q)1/2]/2b
J. Phys. Chem. 1963, 87,2360-2364
2360
= [-a
+ (-Q)”2]/2b
Y = ([I210 + 4/([IZIO
[Id-
+ P)
Using these definitions, one can write the time-dependent expression for [I2] -a
[I21 =
+ Pr exp[(-Q)%]
1-
e~p[(-Q)’/~t]
(B3)
Unlike the result in eq 18, there is residual 1, at long times
[hlm
=
-P
A very useful approximation holds if [I], = 0 and U UZ
E
k13/b
(B5)
We have chosen to define a dissociation time representing the time necessary to produce one-half of the total I atoms present at t = 03, This definition is equivalent to the time necessary to reach the mean of the initial and final I2 concentrations: [I~lmean= ([IzIo+ [I~lml/2 A half-life for dissociation within that context is
(B4)
+
~ Q
Registry No. 12, 7553-56-2;I, 14362-44-8;02,1182-44-7.
> k13:
Thermodynamics of Unsymmetrical Electrolyte Mixtures. Enthalpy and Heat Capacity Kenneth S. PRzer Department of Chemistry and Lawrence Serkeley Laboratory, University of Californla, Eerkeley, California 94720 (Received: December 2, 1982)
There is a purely electrostatic contribution to the thermodynamic properties of electrolytes for the mixing of ions of different charge but the same sign. The previous treatment, which was limited to activity or osmotic coefficients,is extended to enthalpies and heat capacities and applied to the measurements of Cassel and Wood on the heat of mixing in the systems NaC1-BaC1, and NaC1-Na2S04.
Introduction For electrolytes involving unsymmetrical mixing of ions of different charges of the same sign there is a higher order limiting law. Friedman’ derived this law by the clusterintegral method which was developed for electrolytes by Mayer., A method of practical application to unsymmetrical mixtures of realistic concentration was developed by mea3 While the limiting law alone is inadequate, it was shown that one could define a new function, valid at finite molalities. With this function an anomaly in the thermodynamics of HC1-A1Cl3 was removed. This new function has the same character as the limiting law; it depends only on the charges on the ions, and solvent properties, i.e., dielectric constant and density, as well as the temperature. The Debye-Huckel limiting law has these characteristics. The new function becomes zero for mixing ions of the same charge. Cassel and Wood4 measured heats of mixing of NaCl with BaC1, and of NaCl with Na2S04in dilute aqueous solution with the intent of testing the corresponding limiting law for heat of unsymmetrical mixing. While they found a significant effect of the right sign as the ionic strength approached zero, they were unable to verify the law quantitatively. Even between ionic strengths of 0.02 and 0.05 mol kg-l their slope was less than half the theoretical limiting value. In this paper we extend to enthalpies the derivation of the unsymmetrical mixing function de-
rived earlier3 for free energy and obtain good agreement with Cassel and Wood’s measurements. Friedman and Krishnan5 have made calculations in the HNC approximation with parameters specifically chosen for the NaC1-BaC12 system and at the molalities of measurement. They obtained reasonable agreement. However, their calculations are much more complex and less general than the method presented here. The heat of mixing is, of course, related to the temperature dependence of activity and osmotic coefficients for mixed electrolytes, and in a companion paper Roy et aL6 present new and precise measurements of the activity coefficient of HCl in HC1-LaC1, mixtures at several temperatures. The appropriate equations for the heat capacity of unsymmetrical mixtures are derived, although there do not appear to be any experimental data at present for which this effect would be significant. The molecular-level implications are also discussed.
(1)H.L.Friedman, “Ionic Solution Theory”, Interscience, New York, 1962. (2)J. E.Mayer, J. Chem. Phys., 18, 1426 (1959). (3) K. S. Pitzer, J. Solution Chem., 4, 249 (1975). (4)R. B. Cassel and R. H. Wood, J. Phys. Chem., 78, 1924 (1974).
(5)H.L. Friedman, and C. W. Krishnan, J . Phys. Chem., 78, 1927 (1974). (6) R. N. Roy, J. J. Gibbons, J. C. Peiper, and K. S. Pitzer, J. Phys. Chem., following article in this issue. (7)K. S. Pitzer and J. J. Kim, J. A m . Chem. Soc., 96,5701 (1974).
Equations for Unsymmetrical Mixed Electrolytes It was shown3that this limiting law for unsymmetrical mixing could easily be incorporated into the general equations for mixed electrolytes of Pitzer and Kim; these equations comprise a Debye-Huckel term together with virial coefficients for short-range interparticle forces. In most cases it is sufficient to include only second and third
QQ22-3654/83/ 2Q87-236Q$Q1.5Q/Q 0 1983 American Chemical Society
