R. G. d e Pena, K. Olszyna, and J. Heicklen
438
ther N2 nor PJ02l3 were produced in these experiments, further reaction of NO with the product of reaction 6 apparently does not occur. At present the nature of the reactions which result in the formation of unscavengable C3Ho a t temperatures greater than 175’ is unclear. This aspect of the work is under active investigation, however, and speculation regarding the possible results would seem to be unwarranted at present. Finally, an estiniate of the lifetime, T , of the scavengable diradical precursor to C3He can be obtained from analysis of the data in Figure 3. Considering the scavengable portion of the C3He only, a Stern-Volmer type of plot may be constructed (Figure 4). The slope of the graph gives rk = 4.3 x IO6 M - I , where k is the rate constant for
the scavenging reaction. An upper limit of k 5 3.6 x 1011
M - l sec-1 is obtained for the case in which the scavenging reaction is diffusion controlled. Thus the average lifetime of D will be greater than 1.2 x 10-5 sec at 205”. Acknowledgments. The authors would like to thank the National Research Council of Canada for financial support. Some of the equipment was purchased through a Frederick Gardner Cottrell Grant from the Research Corporation. One of us (D. R. D.) would like to thank the National Research Council €or a scholarship.
(13) 6. G . Gowenlock, Progr. React. Kinet., 3, 172 (1965)
Kinetics of Particle Growth. I. Ammonium Nitrate from the Ammonia-Ozone Reaction’ a
. de Pena,lb Kenneth Olszyna,’c and Julian Heicklen* Departments of Meteorology and Chemistry and the Center for Air Environment Studies. The Pennsylvania Stale University, University Park. Pennsylvania 76802 (Received August 28. 79721
NH4N03 particles were prepared from the reaction of NH3 and 0 3 at room temperature. The NH3 and initial Os pressures ranged from 0.034 to 2.0 and from 0.020 to 0.10 Torr, respectively, their ratio being between 2 and 21.5. In all of the experiments N2 was also present. The 0 3 decay was monitored by ultraviolet absorption and obeyed the rate law -d[Oa]/dt = k[03], where k is a function of [NHs] an8 [03]0 (the initial value of [os]). One molecule of NH4N03 was presumed to be produced for every four molecules of 0 3 consumed. The total number of particles greater than 200 or 1000 i\ diameter was monitored as a function of reaction time. Initially there is a rapid production of particles in a short period of time ( < I O min) until about IO5 particles/cc are produced. Then particle production stops, as deduced from the fact that the number of particles between 200 and 1000 A rapidly falls to zero. The larger particles grow, though the number, N , decays slowly according to the rate law N = NO exp( - k ’ t ) . The number of particles is too small for coagdation to play any role, and the decay constant k’ can be associated with diffusional loss to the wall. The number of particles a t zero time, NO, increases with the loss rate of O3 arid with the N2 pressure. The particles, Cl ( 1 = integer), grow by reaction with the monomer, the average growth rate constant being Pk[O3]/4N where @ is the fraction (-3 X of NN4N03 monomers entering the gas phase. The loss of particles is entirely by diffusion to the walls, with a pressure-dependent rate constant k2,t. For the simplified situation in which initially NO particles of r monomer units each are produced, and the particle growth rate constants are all considered identical, z.P., @k[O3]/4N(a nearly time-independent parameter since N and [03] decay at similar rates), then a simplified solution ~ N ) ~ - ~ - r ) ! *where ai = @k[O3]/ foip the particle size distribution results, [Ct] = N O ( P ~ [ O ~ ] ~ /exp(-alt)/(l .lii!{+. k z , ~This . distribution predicts a single maximum for [Ci] at T~~~ = ( I - r)/aL.
Introduction In our laboratory, we have initiated a program to examine the kinetics of particle formation, i.e., both the size distribution and growth rates, as a function of time for particles produced from gas-phase chemical reactions. As far as we know, such studies have not been made before under isothermal conditions, though particle formation has been observed in numerous laboratory studies and is important in polluted urban atmospheres. A number of studies have been made of soot formation in flames and hydrocarbon pyrolysis. Soot formation in The Journal of Ph!/sical ChQmiSfry,Vol. 77, No. 4, 1973
acetylene pyrolysis initiated a t 770-1070°K and reaching 3000°K as a maximum has been discussed by Tesner.2 He considered an initial distribution of carbon particles, corresponding to a commercial soot, and assumed that the particles grew upon every collision with a CzHz molecule until the C2Hz was exhausted. The computed growth rate was about seven times that found experimentally, which (1) ( a ) CAES Report No. 246-72. (b) Department of Meteorology. ( c ) Environmental Protection Agency air pollution trainee. (2) P. A. Tesner, D m Faraday Soc.. 3 0 , 170 (1960).
NH4N03 from the EJH3-03 Reaction
Tesner felt reflected the fact that every collision would not be effective Theoretical models have been discussed for isothermal particle growth under various conditions. Several studies have considered coagulation and wall losses,3-7 whereas GoodrickP~~ and kIudson and his coworkers10,11considered growth only by monomer interaction with the particles. A number of experimental studiesf2-17 have been reported in aging of aerosols and smokes by coagulatior , but in none of these s~utlieswere gas-phase chemical reactions involved in the formation or growth process. In this paper we experimentally follow the growth rate and size distribution of NH4;C\J03particles produced in the reactiisn of NH3 with 0 3 . A previous studyls from our laboratory characterized the kinetics of the loss of the gas-phase reactants.
xyerimentai Section
All of the gases used were from the Matheson Co. These included Extra Dry grade 0 2 , CP grade "3, and prcbpurified Nz. The nitiopen was used after passing through a glass wool fiiter at -196", the only remaining impurity being trace arnounts of 0 2 . The NI13 was purified by distillation from -98 to -196O.18 The ozone was prepared from a tesla coil discharge through 0 2 , which had been passed through traps at -196'. The ozone was distilled at -186" and collected a t -196" with continuous degassing to eliminate ;my impurities, particularly oxides of nitrogen.'R Before each experiment, N2 was passed through the reaction vessel until the number of particles >200 A in diameter was X6jcc. Samples of 0 3 in N2 and NH3 in Nz were tested periodically, and they always showed -!000 or >2M) A in diameter. In this way several runs were clone for each experiment to obtain the number of particles grea'ter than 200 and 1000 A :IS a function of reaction time. Duplicate runs in which the number of particles of the same minimum particle size were counted generally were reproducible to &200/0. For the several runs in each series the 0 3 decay was monitored. It followrd eq I, from which the values 3f k were obtained. [n the replicate runs, the values of k were reproducible to f10%1,and the average values are listed in Table I for each series. T o obtain k , corrections were made for the pressure drop due to sampling, and the values tabulated represent only chemical loss. The actual values of [Os] a t any time are smaller than computed from the tabulated values of k using eq I, and after nine samplings, may be 1:i%smaller. However this effect is relatively unimportant compared to the chemical loss in most. of the series. The particln size distribution in all series shows the same general trend. Typical results are shown in Figure 2. Initially the number density of particles >200 A rises, reaches a maximum of about 105 particles/cc, and then falls off as the reaction proceeds. The same general curve shape is observed for the number density of particles > 1000 A, but the timc! ofthe maximum, T m a x , is delayed. The most interesting (and unexpected) observation from Figure 2 is the i'act that after about 40 min, there are essentially no partic!es between 200 and 1000 diameter,
IO
30
70
9o
IIO
I30
TIME ,MINUTES
Figure 3. Semilog plots of the n u m b e r density of particles exceeding 1000 A in diameter vs. reaction time at 24" for [03], = 0.040 Torr, [NH3] = 0.8 Torr, and [N2] = 790, 500, or 117 Torr.
and presumably even smaller particles are also missing. In every series where particle size counts >200 and >lo00 A were taken, the same result was found. Thus in Tabie I we report only T~~~ and NrnaX characterizing the particles >IOOOA. The most important parameter influencing the values for both T~~~ and N m a x is the Nz pressure. This effect is shown graphically in Figure 3. As the N2 pressure is raised both NmaXand T m a x are augmented. In fact the data in Table I indicate that T~~~ depends only on the Nz pressure. It rises from 17 to 25 to 40 min as the Nz pressure is increased from 117 to 500 to 790 Torr. After Tmax has been reached, the number of particles >lo00 falls off in all the series approximately exponentially with the time, t N No e x p ( - h ' t ) (11) where N is the total number of particles >IO00 14, and for times approximately > T~~~~~~probably represents the total number of particles, since the number of small particles has nearly disappeared. NO is the extrapolated value of N to zero time. Values of No and the decay constant, k ' , are tabulated for each series in Table I. The values of NOvary between 0.40 x 105 and 1.8 x 105 particles/cc. No increases with h [ 0 3 ] 0a t any iVz pressure, but drops as the NZ pressure is lowered. The values of k' the decay constant for particle depletion, are between 0.0082 and 0.013 min 1 for the series with 790 Torr of Nz added. There appears to be no obvious correlation with any of the parameters, and the spread may just reflect uncertainty in the results. However, it is clear that k' rises noticeably as the total pressure is reduced, reaching a value of 0.064 min - I for 117 Torr of Nz.
Discussion Nucleation. The fact that 0 3 decays by first-order kinetics during the whole course of a run indicates that 0 3 consumption is not influenced by either the number or size of the particles, i.c., that the main loss of 0 3 is not The Journal of Physical Chemistry, Vo/. 77. No. 4 . 1973
R. G. de Pena, K. Olszyna, and J. Heicklen
TABLE II: Rate Constants for Various Size Particles in N2 at 760 Torr and 300°K
Di.
5,A
cm2/min
/
5.3 1 11.7 10 6.5 3.2 20 52 0.80 40 416 0.202 100 6.5 X lo3 3.28 X 200 5.2 x 104 8.4 x 10-3 4.16 x 105 2.23 x 10-3 400 1000 6.5 X lo6 4.25 X 2000 5.2 x 107 1.38 x 10-4
c$Lu,
100
200
*
,
t
300 8
I
I
,
400 I
,
2
Z
5
'
00
I
I
1
,
600
10epk [C3], , Torr/mln
Figure 4. Plot of the initial number density, No, of particles YS. the initial monomer production rate for [N2] = 790, 500, or 117 lorr.
direct chemical reaction with the particles. The main loss of 0 3 must be through chemical reaction with NH3 either in the gas phase or on the wall of the reaction vessel. Such a loss process can only lead to production of NH4N03 monomer (called C to simplify the nomenclature). The mechanism of monomer production was discussed in our previous paper.18 The monomer can disappear by three routes
c 5, c, C-
kz
I
(1)
wall
c + c,
(2)
k,
I
C1+] (3) where r and 1 are integers. C, and C1 are particles with r and 1 monomer units, respectively, and 1 > r. Reaction 1 is not a fundamental reaction, but is some representation of the nucleation process to form stable particles of critical size, i e . , containing r monomer units, which then can grow. Reaction 2 represents loss of C to the wall uia diffusional processes and reaction 3 represents loss of monomer by condensation on the particles. The rate constants for reaction 2 and 3 can be estimated from simple kinetic molecular theory considerations k2l
h,,
=
- a,D1/X2
6.9 x 10 1lT''2(n1 -t
(111) 01)z/pl,lI'2
(IV)
-
where a1 is the accommodation coefficient for monomer depositing on the wall (a1 0.1), D1 is the diffusion coefficient for monomer, X is the mean distance of travel for the monomer to reach the wall, T is the absolute temperature in "K, 01 and ul are the diameters in A of C and Ci, respectively, and pa,^ is the reduced molecular weight for C and Ci. The units of k 3 , ~are cm3/min. Values for u1 and 01 can be estimated from the specific gravity of 1.66 for NH4N03.23 This value leads to a, monomer volume of 80.5 w3.
The general expression for the diffusion coefficient, of any particle in 1atm of Nz is24 The Journal of Physical Chemistry, Vel. 77, No. 4, 1973
Dl,
k3.i.
k1.i.
cm3/min
cm3/rnin
3.0 X 8.2X 2.68 X
2.0 x 10-8 2.9 X 4.1 X
5.7 X
1.42 X
9.0 X 1 0 -
5.36x 10-6 2.1 x 10-5 1.32X 5.16 x 10--4
1.2 x 10-7 1.8x 10-7 1.06 X 6.9
x
10-7
D, = LKT(1 + 2.492b/n1 + 0 . 8 4 ( b / ~ , )x exp(-0.435o,ib)]/3nyol
(v)
where K is the Boltzmann constant, b is the mean free path, and 9 is the viscosity. For Nz at 1 atm, b =; 6.5 X 10-6 cm and = 1.78 X 10-4 P. For various values of u, the corresponding values of I, DL,and k3.1 are listed in Table 11. Since in our system X is typically 2 cm, then k 2 , 1 0.3 min-1. In the initial stages, the rate law for the production of C is d[CI/dt = Ph[OJ/4 - hz l[C] (VI ) where the loss of C due to reactions 1 and 3 have been neglected since they are small. The factor of 4 indicates that the formation rate of C is only 1/4 the loss rate of 0 3 . Since C may be produced on the wall and never enter the gas phase, the constant /3 has been introduced. It represents the fraction of monomers produced that enter the gas phase. Also for the first few minutes [Os] does not change significantly, so that eq VI can be integrated to give
(VI0 [GI = ~k[0,1[1 - exp(- k,,,t)1/4h2 Since k2,1 0.3 min-1, the steady state is reached within a few minutes. Thus the initial steady-state value for [C], called [C]O, can then be represented as @k[O3]0/ 4 k 2 , ~As . will be shown later, @ 3 x 10-3. In our experiments k[O3lO > 1013 particles/cc min, k2,1 0.3 min-I, so that [C]O> 2.5 X 1010 particles/cc. The initial production rate of particles is on the average 103, particle production ac 3 x 1010), and justifies the assumption that the rate of reaction 1 is negligible compared to reaction 2. It is reasonable to expect that NO will increase with [Clo. Since [C]o = /312[03]0/4k2,1, the values of NO were plotted us. pk[O3I0, and the results are shown in Figure 4. The plots a t each N2 pressure can reasonably be represented by straight lines which nearly pass through the origin. The slopes should be inversely proportional to kz,1. Since k 2 , l rises as the Nz pressure is dropped, the slopes of the curves fall from 1.64 X 10-6 to 1.08 X to 0.71 x 10-6 min-1 as the Nz pressure is reduced from 790 to 500 to 120 Torr. N
-
-
-
(24) N. A. Fuchs, "Mechanics of Aerosols," Pergamon Press, New York, N. Y . , 1964, p 27.
NH4N03from t h e
Reaction
"3-03
443
Particle Groroth. The possible reactions of particles are
c~ wallL c + c/-CI,,
(2)
$1 I
C/+
(3)
where the average value, k3, has been used for k 3 ~ When . large particles are present, no new particles are formed, so that [C] must be much smaller than [(>lo. This can only be if C is removed principally by condensation, reaction 3. Under these conditons
[c] = Pk[O3]j4k,N
k,
(or Cn + ~ l + m - n ) (4) Reaction 2 is the particle removal step by diffusional loss to the walls. This rate is approximately equal to the diffusion constant, which is tabulated in Table I1 for various values of 1. Reaction 3 represents particle growth terms by reaction with monomer. It should be noticed that reaction 3 does not alter the number of particles. Reaction 4 is the coagulation term. Upper limits to these rate constants can be computed from collision rates. The limiting rate is given by kinetic molecular theory Cm-C,+m
h/,rn 6.9 x 10
except for particles >500 controlling. Then
11T"2(U/ +
om)2/p/,m1~z
(\m)
Thus eq X becomes d[Crl/dt = CBh[OJ/4N([Ci-,I
urn)@, +
D,)
[CJ = f r
where a,
:IN
-
9
where p ~ . , is the reduced molecular weight between particles Cr and C, irl and gnr are their diameters in A, Dl and D , are their diffusion coefficients in cm2/min, and k l , m has the units of cm"min. Values of kl,l for various t! are tabulated in Table I1 for 300°K and 760 Torr presriure. From these values it can be seen that coagulation can play no role at. all under any of our conditions, and reaction 4 can be ignored. The only important loss process of total particles, N, is wall diffusion. The loss rate constant, k ' , is about 10-2 min--1 at 760 Torr pressure. This is about 20 times larger than the value of D, for particles of 1000-Adiameter. Apparently these large particles only travel an average distance of about, 0.2 cm before deposition. At lower pressures k' goes up, but much less slowly than inversely with the pressure. Presumably the main loss has shifted to particles of larger size. The rate law lor C, is d[C!jjdt = h,[Cl([C,.
-
[C,])- k2,/[C/]
(XI
[GI)- h2i[c/l
(~11)
-
fi
+
-
Now [Os] and N are slowly decaying functions of time, and they decay with comparable rate constants. Thus bk[03]/4N is nearly constant with time. Furthermore kz,l kz.l-1, so that eq XI1 is easily integrated to give
A at 760 Torr, where diffusion is
h,,,, = 2n x 10 '(a,
(XI)
F r exp( - a,t)
(XIII)
P~[O,l/4N+ h,, Ph[O3]fl ]/4N(L - r )
f@h[ o
~ ] / ~ N ) I - ~ ~ ( Lr ) !
-
Since C, is produced almost exclusively a t very short times, f r No. Thus [ C l ] has the solution
[C,]
=
N0@h[O,]t/4N)'.' exp( - a / f ) ' ( L- r ) !
(XIV)
This solution is strongly peaked in 1 at any time t and is strongly peaked in t for any 1. For any value of 1, a maximum occurs a t 7max = (1 - r)/aI. Furthermore for particles of 1000-A diameter, k2,l is much smaller than al, 1 r 1, and
-
Equation XV is readily solved for 13, and these values are tabulated in Table I for each series. It can be seen that 3 x 10-3 for all reaction conditions.
-
Acknowledgment. This work was supported by the Environmental Protection Agency, Office of Air Programs through Grant No. AP 00022, for which we are grateful.
The Journalot PhysicalChemistry, Val. 77, No. 4 , 1973
