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The mechanism of bromine exchange in the bromine-graphite lamellar compounds
J. inorg, nucl. Chem., 1966, Vol. 28, pp. 1343 to 1353. Pergamon Press Ltd. Printed in Northern Ireland
THE MECHANISM OF BROMINE EXCHANGE IN THE BROMINE-GRAPHITE LAMELLAR COMPOUNDS* F. J. SALZANO and S. ARONSON Brookhaven National Laboratory, Upton, New York (Received 30 August 1965; in revised form 29 October 1965)
Almtraet--The rates of exchange of normal and radioactive bromine in bromine-graphitewere studied at temperatures of 20-45°C. A range of natural graphite flake sizes from 50-2000/z were used to prepare the compounds. The dependence of the rate of exchange on particle size, a, changed abruptly from 1/a at large particle sizes to 1/a2at small particle sizes. The apparent activation energy varied by a factor of three over the temperature range investigated. A mechanism of exchange is proposed which explains the observed particle size dependence, temperature dependence and the form of the rate curves in terms of two consecutive surface processes and the structural features of the natural graphite flakes. GRAPmTE reacts with gaseous and liquid bromine at ambient temperatures to form compounds in which the bromine penetrates between the carbon layers, while the graphific character of the layer planes is preserved, cl-4~ I f the graphite is highly graphitic, the compound CsBr is formed in saturated bromine vapour. A t lower pressures, above a threshold value, ~'s~ a continuous range of compositions are formed. In the compound CsBr, bromine occupies every other interplanar space in the graphite lattice i.e. one bromine layer for every two carbon planes. The layer plane spacing between the occupied carbon layers is the same as in graphite, 3.35/~. The distance between the filled carbon layers is 7.05/~.~2~ The bromine-graphite compounds are readily decomposed in vacuo, but it is found that some "residue" bromine always remains in the graphite, m In some graphites the concentration of residue is as high as 30 per cent of the total bromine that can be intercalated. The formation of bromine-graphite lamellar compounds involves an electron transfer mechanism, m although the degree of ionization of the reactant remains uncertain. Based on electrical measurements, HENNIGtl} believes the bromine t o be one-third ionized. The bonding between the bromine and graphite in the compounds is believed to involve ionic and van der Waals forces. ARONSONm studied the exchange of normal and radioactive bromine in b r o m i n e graphite lamellar compounds prepared from natural and synthetic graphite powders. * This work was performed under the auspices of the U.S. Atomic Energy Commission. m G. R. H E N N I G , Interstitial Compounds of Graphite, Progress in Inorganic Chemistry (Edited by F. A. COTTON)Vol. 1. Interscience, New York (1959). ~2)W. RUDORFF,Graphite Intercalation Compounds, Advances in Inorganic Chemistry and Radiochemistry (Edited by H. J. EMELEUSand A. G. SHARP~)Vol. 1. Academic Press, New York (1959). ~3)A. R. UBBELOHDEand F. A. L~wIs, Graphite andlts Crystal Compounds. Clarendon Press, Oxford (1960). "~ R. C. CRor'r, Lamellar Compounds of Graphite, Q. Rev. chem. Soc. 14 (1960). ts) j. G. HOOLEY,Canad. J. Chem. 37, 899 (1959). ~e~j. G. HOOLE~',Canad. J. Chem. 40, 745 (1962). m S. ARONSON,J. inorg, nucL Chem. 25, 907 (1963). 1343
1344
F . J . SAI.,ZANOand S. ARONSON
He measured the rates of bromine exchange on samples with particle sizes from 15 to 177/z, at temperatures from 30 to 48°C. The analysis of his data in terms of a diffusion mechanism was based on the particle size dependence and the form of the rate curves. He reported the activation energy for the exchange process to be 11-14 kcal/g-mole. Due to experimental limitations, only the last 30--40 per cent of the exchange reaction was studied in detail. The object of the present work was to extend the work of ARONSONto a greater range of particle sizes and temperatures and to extend the measurements to include the initial rates of exchange. The experiments were facilitated by the use of a more refined experimental technique which allowed continuous measurements of the concentration of radioactive bromine in the bromine-graphite lamellar compounds. The present results indicate that diffusion is not an important mechanism in the exchange reaction. EXPERIMENTAL Materials The graphite used in this study was a Madagascar natural graphite flake. It was supplied by the Asbury Graphite Mills, Inc. in 20 lb kegs and designated as grade #3045. The carbon content was specified to be 99.9 per cent. This purity was confirmed by ashing tests. The material was sieved into six fractions using the following range of sieve screens: 37-53, 88-105, 149-177, 297-354, 710-1190 and 2000-2380/~. Microscopic examination revealed the average particle size to be 1.5 x times larger than the average screen size. This is due to the fact that the particles are thin flakes and during sieving the majority of flakes pass through the diagonals of the square openings in the sieve screens. In this work we will discuss particle size in terms of the average screen size. Reagent grade bromine was purchased from the Fisher Scientific Co. The radioactive bromine was prepared by irradiating approximately I a n 8 of bromine sealed in a quartz capsule in the Brookhaven Graphite Research Reactor at a neutron flux of 7 x 10x~ neutrons/cms per see for 10 min. Both the radioactive and normal bromine were transferred into the system by distillation from a reservoir at room temperature to a reservoir at 0°C
Procedure The rates of exchange of normal and radioactive bromine in the bromine-graphite lamellar compounds were measured in a pyrex glass circulation loop shown schematically in Fig. 1. The circulation system was fabricated from 4 m m dia. tubing and contained the following components: (1) a small pyrex glass cell which contained a fritted platform on which the graphite sample was placed, (2) a large and a small storage vessel for the storage of normal and radioactive bromine respectively, (3) a liquid bromine trap, (4) a water cooled condenser in which the cold water section was insulated by means of a vacuum jacket, and four Pyrex-Viton diaphragm valves. The whole apparatus was immersed in a thermostated water bath and the valves were manipulated by handles extending above the bath. External to the water bath, a sodium iodide scintillation scanning probe was used to monitor the activity of bromine-82 in the graphite. The detection system utilized conventional scintillationcounting electronics and was biased to count the integral gamma spectrum of bromine-82 above 0.4 meV. The scintillation detector was shielded and aligned to measure only the radiation emitted from the bromine-graphite compound in the pyrex cell. A description of the detector and measuring technique has been given previously. ~8~ Approximately 1 cm 3 of radioactive and 100 cm 3 of normal bromine were loaded into the respective storage vessels. A graphite sample weighing 0"25 g was loaded into the pyrex cell. The system was then evacuated to below 5/z Hg. The bromine-graphite compound, CsBr, was formed at 45°C by equilibration of the graphite with radioactive bromine for 2-3 hr, depending on the particle size of the graphite. The scintillation detector was used to follow the course of the formation reaction. When no further change in the activity on the graphite was detected over a period of 1 hr the water bath was cooled to the desired temperature and the exchange experiment started. ts) F. J. SALZANOand S. ARONSON,J. chem. Phys. 42, 1323 (1965).
The mechanism of bromine exchange in the bromine-graphite lamellar compounds
1345
The absolute concentration of bromine in the graphite was determined for several samples by a combination of gravimetric and tracer techniques. The exchange between the normal and the radioactive bromine was initiated by first starting the flow of cold water (15°C) to the condenser. The condenser, and the inlet and outlet cold water lines attached to it, were insulated to prevent excessive heat transfer from the thermosttated water bath. The valve on the storage reservoir containing the radioactive bromine was closed and the exit valve of the normal bromine reservoir was opened. The flow of normal bromine vapour over the sample was started by opening the inlet valve to the condenser. Bromine vapour was condensed and flowed into the trap below the condenser. When the trap was filledwith liquid bromine, the inlet valve to the normal bromine reservoir was opened and the liquid overflow from the trap returned continuously to the
f
/ ~
\
GRAPHITEPOWD~ .~
~~
/~//
VACUUM JACKET WATERCOOLED CONDENSER
~ / ~P/ L I Q U/P/ ID
[ELECTRONICS ] \'\ LEADS ELDING I I ~SODIUM IOD,DECRYSTAL ~ ~--PHOTOMULTI PLIERTUBE
~
~/
BROMINER TA P
NORMALBROMINE RESERVOIR
FIG. 1.--Apparatus for the study of bromine exchange in the bromine-graphite lamellar compounds. reservoir. Thus, the small quantity of radioactive bromine was diluted in the large volume of normal bromine in the storage vessel. As long as no foreign gases leaked into the system, the flow of normal bromine continued indefinitely in this cyclic manner. During the circulation of normal bromine, the concentration of radioactive bromine in the bromine-graphite compound was continuously measured by monitoring the activity of bromine-82 remaining in the sample. The circulation of normal bromine was continued until the desired fraction of the active bromine in the solid was exchanged or the rate of exchange became too slow to measure. Each subsequent exchange experiment was done with a new graphite sample. RESULTS T h e rates o f exchange o f n o r m a l a n d r a d i o a c t i v e b r o m i n e in b r o m i n e - g r a p h i t e l a m e l l a r c o m p o u n d s were studied in the t e m p e r a t u r e range 20-45°C. T h e concent r a t i o n o f b r o m i n e in the c o m p o u n d s studied c o r r e s p o n d e d to the a p p r o x i m a t e c o m p o s i t i o n s C10Br to Ca.4Br. T h e final c o m p o s i t i o n o b t a i n e d for each s a m p l e d e p e n d e d o n the particle size a n d length o f e x p o s u r e to b r o m i n e v a p o u r . T h e rates o f exchange were n o t affected b y these v a r i a t i o n s in c o m p o s i t i o n . Several typical rate curves are s h o w n in Fig. 2. T h e f r a c t i o n o f r a d i o a c t i v e b r o m i n e r e m a i n i n g in the s a m p l e is p l o t t e d on a l o g scale vs. the r e a c t i o n time in
1346
F.J. SALZANOand S. ARONSON
minutes. In all cases the slope of the rate curve decreased continuously as the concentration of radioactive bromine in the solid diminished. The forms of all the rate curves are similar. Since the mathematical form of the function which determines the rate of exchange is unknown, it is convenient to compare the rate curves obtained for the different particle sizes and temperatures in terms of the reciprocal time to reach a given composition. I.O
i(
~( I
I
I
r
I
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I
(.9 Z
LU fig LLI
Z
~J>tu 0 IO "r " L.)
--
×
8= t~ ,¢ fig I.E. 0
0 2 0 0 0 - 2 3 8 0 ~ AT 45* C Cl 2 9 7 - - 354~. AT 39"C
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A
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I--L.) fig
"
8 8 - - 1051~ AT 2 0 " C 1 4 9 - - 177/J- AT 45°C 88105F~ AT 4 5 * C
o
0.01 0
l
I
I
I0
20
50
E 40
I 50
l I I I 60 70 80 90 TIME, MINUTES
I
I
I
I
I00
I10
120
150
140
FIG. 2.--Rates of bromine exchange in the bromine-graphite lamellar compounds. The temperature dependence of the rate of exchange is shown in Fig. 3. The ratio of the reciprocal time to exchange half the bromine at any temperature to the reciprocal time to exchange half the bromine at 35°C is plotted on a log scale vs. the reciprocal temperature. The data are normalized in this manner to facilitate a comparison of the data from each particle size. In the case of a simple reaction mechanism, such a plot is linear and the slope is proportional to the activation energy for the reaction. The data from all the particle sizes investigated fall on one curve. Thus, the temperature dependence of the rates of exchange of all the particle sizes investigated is the same. At the highest temperature (45°C) the slope is lowest and corresponds to an activation energy of 7 kcal/g-mole. The slope at the lowest temperature (20°C) corresponds t ° an activation energy of 22 kcal/g-mole. The variation of the rate of exchange with particle size at 20°C is shown in Fig. 4. It is evident that the dependence on particle size changes abruptly at about 300 FIn the range of 2200-300 F, the rate of exchange is proportional to 1/a. Below 300 F the rate of exchange is proportional to 1/a 2. Since the temperature dependence is the same for all particle sizes, the variation of the rate of exchange with particle size is the same at all temperatures.
B
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o 710-1190 j..t ZX 297- 554 /z
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FiG. 3.--The temperature dependence of the rate of bromine exchange.
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400 600 I000 2000 4000
I I IIIJlJ
i IIIIt I
AVERAGE SIEVE SCREEN SIZE,MICRONS
40 60
J IllllJ
i I liill I
F[c. 4.--The particle size dependence of the rate of bromine exchange.
0.1
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--
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1348
F.J. SALZANOand S. AI~ONSON
DISCUSSION The mechanism proposed to explain the kinetics of bromine exchange in the bromine-graphite lamellar compounds must account for the following observations: (1) the continuous change in the slope of the rate curves shown in Fig. 2, (2) the large variation in the activation energy over the temperature range 20-45°C, (3) the abrupt change in the particle size dependence from 1/a to 1/a ~. Furthermore, the proposed mechanism must be consistent with the known structural features of natural graphite flakes. The mechanism of bromine exchange in the bromine-graphite lameUar compounds is complex and is not immediately obvious from the data. We have carefully considered the following mechanisms: (1) one step surface processes, (2) simple and complex bulk diffusion processes ~9) and (3) a combination of bulk diffusion and surface processesJ 9) These mechanisms were eliminated on the basis of the form of the rate curves, the temperature and (or) particle size dependence of the rate of exchange. A mechanism of bromine exchange in the bromine-graphite lamellar compounds can be formulated which accounts for the experimental observations. In this explanation, the structure of the bromine-graphite flakes is an important factor in the exchange mechanism. Although the graphite flakes are delaminated during the formation of the compound, the original diameters of the flakes are unaltered and the original c-axis of the graphite remains perpendicular to the plane of the flakes. We propose that the bromine-graphite flakes larger than 300/~ in diameter consist of a mosaic structure of smaller units or crystallites. We will call the interracial boundaries between crystallites "grain boundaries." These crystallites are assumed to contain no "grain boundaries," but may contain other defects. The c-axes of all the crystallites are approximately parallel. In the large flakes which contain "grain boundaries," the average diameter of the crystallites parallel to the basal planes is approximately 300/~. Flakes smaller than 300 # contain no "grain boundaries." The proposed structure of the bromine-graphite flakes is depicted schematically in Fig. 5. For the sake of simplicity, we have shown the flakes and crystallites as squares and the crystallites as uniform in size. In order to account for the variation in the apparent activation energy with temperature, the exchange mechanism must consist of at least two consecutive steps which control the rate of exchange. Both steps occur at surfaces i.e. at the solid-gas interface and at the interracial boundaries of the crystallites. The first step in the exchange mechanism is the transfer of bromine from the bulk i.e. between the layer planes, to a surface adsorbed state at the edge surfaces of the crystallites. In the case of flakes smaller than 300/~, the radioactive bromine is transferred from the bulk directly to the periphery of the flakes. In flakes larger than 300/z, the bromine from the bulk is transferred into "grain boundaries" as well as to the edge surface at the periphery of the flakes. The bromine is able to move rapidly through the "grain boundaries" and from the periphery of the flakes to the exposed basal plane surfaces. In those regions of the basal planes where the bromine emerges from the edges of the flakes and grain boundaries, the bromine begins to diffuse along the basal plane surface in the adsorbed layer of bromine present on (9) j. CRANK, The Mathematics of Diffusion. Clarendon Press, Oxford (1956).
The mechanism of bromine exchange in the bromine-graphite lamellar compounds
1349
that surface. Before the radioactive bromine can diffuse over an appreciable area of the exposed basal planes, it evaporates. The amount of evaporation from the edge surfaces which are parallel to the c-axis is assumed to be small, either because the total surface area contributed by the edges is small or because the bromine is bonded more strongly at the edge surfaces than on the basal planes. During the evaporation of radioactive bromine the adsorbed bromine layer is continuously replaced by normal bromine from the gas phase. It is further assumed that the flow-rate of normal bromine over the flakes is sufficiently rapid to maintain the concentration of active bromine in the gas phase, in the vicinity of the flakes, at a negligible level. The fact that
*
L-
[,
•
/
a
"1
°
i
*EVAPORATION OF BROMINE MOLECULES IS LIMITED TO THE PERIPHERAL REGION OF EACH CRYSTALLITE • ~ LARGE FLAKES, o • d • ~ SMALL FLAKES, o = d
FIG. 5.--A model of the structures of bromine-graphite flakes of various sizes.
the rates of exchange were independent of flow-rate supports this assumption. Thus, the last rate controlling step is the evaporation of radioactive bromine from the adsorbed layer of bromine on the exposed basal plane surfaces. The net flux from the surface is proportional to the surface concentration of radioactive bromine which is continuously decreasing as the bulk concentration decreases.
Particle size dependence We can account for the particle size dependence of the rates of exchange in terms of the surface evaporation step and the proposed mosaic structure of the flakes. Since the last step in the exchange mechanism is evaporation from the basal plane surface, the rates of exchange will be proportional to the surface to volume ratio of the bromine-graphite flakes. We assume that the average thickness of the brominegraphite flakes is proportional to the average a-axis diameter of the flakes, as was found in the case of pure graphite. ~lm In the case of large flakes i.e. greater than 300 #, it is reasonable to suppose that the average size of the small crystallites which make up the mosaic structures is the same in all sieve fractions. ~xo~
F. J. SALZANOand S. ARONSON,Carbon 3, 213 (1965).
1350
F . J . SALZANOand S. ARONSON
The change in the particle size dependence of the rates of exchange from 1/a for large flakes to 1/a S for small flakes can be explained if the radioactive bromine does not migrate very far over the basal plane surface before it evaporates, but rather evaporates from a small area adjacent to the edges of the crystallites as shown in Fig. 5. We assume the crystallites to be squares with sides equal to d and also assume the thickness of the flakes, t, is given by the relation, t =
Ka,
(1)
where K is the same constant for all the flake sizes. The effective evaporation surface per unit volume, Sv, is therefore given by, 4l 1 Sv . . . . , dK a
(2)
where l is the average distance over which the radioactive bromine migrates before evaporation. This is assumed to be small compared to the smallest flake size studied. In the case of the small flakes, each of which consists of a single crystallite, d is equal to a and 41 1 Sv = ~ - a ~ . (3) Thus, in the case of small flakes the rate of exchange will be proportional to 1/a S and in the case of large flakes to 1/a. The f o r m o f the rate curves
The mechanism of bromine exchange in the bromine-graphite lamellar compounds requires at least two consecutive reactions to account for the observed temperature dependence. In the most simple case the following reactions apply: /¢
CB ~
fl
C x- ~• Gas phase
(a)
where C~ is the concentration of radioactive bromine in an individual crystallite, CA is the surface concentration of radioactive bromine on the basal planes at the gas-solid interface and k, fl and ~ are the rate constants for the reactions shown. Assuming all the reactions are first order we can write two differential equations which express the rate of removal of bromine from the bulk solid and from the exposed basal plane surfaces of a crystallite. dCB dt -- flCa -- kCB
(4)
dC~ dt
(5)
-
kCB -- (fl + ~)C~.
A solution to the above set of differential equations can be obtained by the method of the Laplace-Carson transformation, m~ The results can be expressed in terms of m) N. M. RODIGUIN and E. N. RODIGUINA, Consecutive Chemical Reactions (Translated from the Russian by Scipta Technica, Inc. Edited by R. F. SCHNEIDER). Van Nostrand, Princeton, New Jersey (1964).
The mechanism of bromine exchange in the bromine-graphite lamellar compounds
1351
the fraction of radioactive bromine, f, remaining in the crystaUite at time t as
f_
b -- y________e-r~ L t -k b -- Y__._.~e_e~t 2 ' Y2
-- ?i
Yi
--
(6)
Y~
where y~ and Y2 are the roots of the quadratic y z + (k ~- fl + ~)y q- ko:, taken with the opposite sign and
( 1 + cA°
(7)
(8)
where CA° and CB° are the respective concentrations of radioactive bromine at t = 0. In order to account for the continuously decreasing slope of the rate curve shown in Fig. 2 it is necessary to postulate the existence of a number of regions in each crystallite. The rates of transfer of bromine from the bulk to the edge surfaces is different in each region. We conceive of these regions as sections which are perpendicular to the c-axis. The edges of the regions in each crystallite are the edge surfaces of the crystallites. The rate of transfer of radioactive bromine from some regions to the exposed basal plane surface is rapid, while other regions lose bromine more slowly. This may be due to blocking of some graphitic layers at the edge surfaces. MMl~ and MEI~ING(12) indicate that the failure of certain graphites to form the limiting composition CsBr may be due to a similar blocking which closes off whole regions. Equation (6) applies to crystallites which contain one region. In the case of multiple regions we can express the exchange mechanism in an individual crystallite by the following parallel and consecutive reactions: kt ~,
CBI ~
CB~ ,(
)"
82
Ce~ ~
~ CA
) Gas phase
(b)
83
k. CB. <
>
where CB1, CB,, CB3 • • • C~. represent the respective concentrations of bromine in the n regions of a crystallite. We can obtain an expression for the overall rate of exchange which is a sum of n ~ 1 exponential terms and fit the experimental data by a proper choice of rate constants and distribution of bromine in the various regions in the crystallite. Because of the complexity of this mechanism, it is not possible to obtain quantitative information about the individual rate constants. cx~ j. MArRE and J. MERINO, Proceedings of the Third Conference on Carbon, pp. 337. Pergamon Press, London (1959).
1352
F.J. SALZANOand S. ARONSON
The temperature dependence In the case of a crystallite containing multiple regions (reaction (b)) we can write the differential equation which expresses the rate of change of the surface concentration with time, n dCA-- ~'knCB"-1 (~ + ~'fln) 1 (9) In order to demonstrate that the temperature dependence of this mechanism conforms to the experimental results, it is convenient to regard the amount of bromine in the bulk of each crystallite as large relative to the amount adsorbed on the surface. Therefore, a short time after the exchange reaction has begun the surface concentration will be changing slowly and the approximate steady state condition, dCA/dt = O, can be assumed. Equation (9) can be written, "k
Ca=
1 ~+~.
CB..
(10)
1
The flux, F, from the solid to the gas phase is
F = ~ca.
(11)
Substituting for Ca from Equation (10) into Equation (11) we obtain, n
F=
~,,
.CB.
(12)
~ +Z/~. 1
We will assume that the activation energies for the rate constants corresponding to similar reactions in the different regions of the crystallite are equal. The temperature dependence of each rate constant is given by _~. ~o e-Q~IRT, k n = kn ° e-Qdl~T,
(13) (14)
(15) where T is the absolute temperature, R is the gas constant kn°, fin° are constants which are different in each region of the crystallite, s ° is a constant and Q~, Qa and Q~ are the respective activation energies for the forward reactions, the back reactions and the surface evaporation step. n kn If we let ~ ]~ K --
1
,
(16)
1
substitute Equation (13), (14) and (15) and differentiate, we obtain
dOlT) =
R Qk q- (Q~ - Qa)
1 q- ~--~° 1 e-t°~-% )rot
(17)
The mechanismof bromine exchangein the bromine-graphitelamellarcompounds
1353
Examination of Equation (17) shows that the model gives the correct form for the temperature dependence. Irrespective of the relative values of Qk, Q~ and Qa, a plot of In K vs. 1IT will be curved. At high temperatures, the curve will have the smallest negative slope and at low temperatures it will have a larger negative slope. Consideration of the proposed mechanism and Equation (17) indicates that under certain conditions the limiting activation energy observed at low temperatures, 22 kcal/g-mole may correspond to the bond energy between bromine and graphite.
Comparison to previous investigation It is of interest to compare the results of this study with the previous investigation of the exchange kinetics. The results of the two studies are similar in several respects. The activation energies observed in the previous work, 11-14 kcal/mole at 30--48°C are similar to those observed in this study in the same temperature range. The dependence of the rate of exchange on particle size, approximately l[a ~ for particle sizes of 15-110/z, is in agreement with the present data for small particle sizes. The large continuous decrease in the rate of exchange with time is similar in both studies. The use of a bulk diffusion model in the previous study was based on information obtained on a limited range of particle sizes and is probably not correct. The complex, yet consistent, dependence of exchange rate on particle size and temperature observed in the present study can only be explained by a surface exchange mechanism.
Acknowledgement--This is to acknowledgethe contributionsof Mr. W. KALINOWSKIwho performed the measurementsand contributedto the modificationsof the experimentalapparatusand Mr. J. DAvis who constructedthe experimentalapparatus and prepared the brominecapsules for irradiation.
THE MECHANISM OF BROMINE EXCHANGE IN THE BROMINE-GRAPHITE LAMELLAR COMPOUNDS* F. J. SALZANO and S. ARONSON Brookhaven National Laboratory, Upton, New York (Received 30 August 1965; in revised form 29 October 1965)
Almtraet--The rates of exchange of normal and radioactive bromine in bromine-graphitewere studied at temperatures of 20-45°C. A range of natural graphite flake sizes from 50-2000/z were used to prepare the compounds. The dependence of the rate of exchange on particle size, a, changed abruptly from 1/a at large particle sizes to 1/a2at small particle sizes. The apparent activation energy varied by a factor of three over the temperature range investigated. A mechanism of exchange is proposed which explains the observed particle size dependence, temperature dependence and the form of the rate curves in terms of two consecutive surface processes and the structural features of the natural graphite flakes. GRAPmTE reacts with gaseous and liquid bromine at ambient temperatures to form compounds in which the bromine penetrates between the carbon layers, while the graphific character of the layer planes is preserved, cl-4~ I f the graphite is highly graphitic, the compound CsBr is formed in saturated bromine vapour. A t lower pressures, above a threshold value, ~'s~ a continuous range of compositions are formed. In the compound CsBr, bromine occupies every other interplanar space in the graphite lattice i.e. one bromine layer for every two carbon planes. The layer plane spacing between the occupied carbon layers is the same as in graphite, 3.35/~. The distance between the filled carbon layers is 7.05/~.~2~ The bromine-graphite compounds are readily decomposed in vacuo, but it is found that some "residue" bromine always remains in the graphite, m In some graphites the concentration of residue is as high as 30 per cent of the total bromine that can be intercalated. The formation of bromine-graphite lamellar compounds involves an electron transfer mechanism, m although the degree of ionization of the reactant remains uncertain. Based on electrical measurements, HENNIGtl} believes the bromine t o be one-third ionized. The bonding between the bromine and graphite in the compounds is believed to involve ionic and van der Waals forces. ARONSONm studied the exchange of normal and radioactive bromine in b r o m i n e graphite lamellar compounds prepared from natural and synthetic graphite powders. * This work was performed under the auspices of the U.S. Atomic Energy Commission. m G. R. H E N N I G , Interstitial Compounds of Graphite, Progress in Inorganic Chemistry (Edited by F. A. COTTON)Vol. 1. Interscience, New York (1959). ~2)W. RUDORFF,Graphite Intercalation Compounds, Advances in Inorganic Chemistry and Radiochemistry (Edited by H. J. EMELEUSand A. G. SHARP~)Vol. 1. Academic Press, New York (1959). ~3)A. R. UBBELOHDEand F. A. L~wIs, Graphite andlts Crystal Compounds. Clarendon Press, Oxford (1960). "~ R. C. CRor'r, Lamellar Compounds of Graphite, Q. Rev. chem. Soc. 14 (1960). ts) j. G. HOOLEY,Canad. J. Chem. 37, 899 (1959). ~e~j. G. HOOLE~',Canad. J. Chem. 40, 745 (1962). m S. ARONSON,J. inorg, nucL Chem. 25, 907 (1963). 1343
1344
F . J . SAI.,ZANOand S. ARONSON
He measured the rates of bromine exchange on samples with particle sizes from 15 to 177/z, at temperatures from 30 to 48°C. The analysis of his data in terms of a diffusion mechanism was based on the particle size dependence and the form of the rate curves. He reported the activation energy for the exchange process to be 11-14 kcal/g-mole. Due to experimental limitations, only the last 30--40 per cent of the exchange reaction was studied in detail. The object of the present work was to extend the work of ARONSONto a greater range of particle sizes and temperatures and to extend the measurements to include the initial rates of exchange. The experiments were facilitated by the use of a more refined experimental technique which allowed continuous measurements of the concentration of radioactive bromine in the bromine-graphite lamellar compounds. The present results indicate that diffusion is not an important mechanism in the exchange reaction. EXPERIMENTAL Materials The graphite used in this study was a Madagascar natural graphite flake. It was supplied by the Asbury Graphite Mills, Inc. in 20 lb kegs and designated as grade #3045. The carbon content was specified to be 99.9 per cent. This purity was confirmed by ashing tests. The material was sieved into six fractions using the following range of sieve screens: 37-53, 88-105, 149-177, 297-354, 710-1190 and 2000-2380/~. Microscopic examination revealed the average particle size to be 1.5 x times larger than the average screen size. This is due to the fact that the particles are thin flakes and during sieving the majority of flakes pass through the diagonals of the square openings in the sieve screens. In this work we will discuss particle size in terms of the average screen size. Reagent grade bromine was purchased from the Fisher Scientific Co. The radioactive bromine was prepared by irradiating approximately I a n 8 of bromine sealed in a quartz capsule in the Brookhaven Graphite Research Reactor at a neutron flux of 7 x 10x~ neutrons/cms per see for 10 min. Both the radioactive and normal bromine were transferred into the system by distillation from a reservoir at room temperature to a reservoir at 0°C
Procedure The rates of exchange of normal and radioactive bromine in the bromine-graphite lamellar compounds were measured in a pyrex glass circulation loop shown schematically in Fig. 1. The circulation system was fabricated from 4 m m dia. tubing and contained the following components: (1) a small pyrex glass cell which contained a fritted platform on which the graphite sample was placed, (2) a large and a small storage vessel for the storage of normal and radioactive bromine respectively, (3) a liquid bromine trap, (4) a water cooled condenser in which the cold water section was insulated by means of a vacuum jacket, and four Pyrex-Viton diaphragm valves. The whole apparatus was immersed in a thermostated water bath and the valves were manipulated by handles extending above the bath. External to the water bath, a sodium iodide scintillation scanning probe was used to monitor the activity of bromine-82 in the graphite. The detection system utilized conventional scintillationcounting electronics and was biased to count the integral gamma spectrum of bromine-82 above 0.4 meV. The scintillation detector was shielded and aligned to measure only the radiation emitted from the bromine-graphite compound in the pyrex cell. A description of the detector and measuring technique has been given previously. ~8~ Approximately 1 cm 3 of radioactive and 100 cm 3 of normal bromine were loaded into the respective storage vessels. A graphite sample weighing 0"25 g was loaded into the pyrex cell. The system was then evacuated to below 5/z Hg. The bromine-graphite compound, CsBr, was formed at 45°C by equilibration of the graphite with radioactive bromine for 2-3 hr, depending on the particle size of the graphite. The scintillation detector was used to follow the course of the formation reaction. When no further change in the activity on the graphite was detected over a period of 1 hr the water bath was cooled to the desired temperature and the exchange experiment started. ts) F. J. SALZANOand S. ARONSON,J. chem. Phys. 42, 1323 (1965).
The mechanism of bromine exchange in the bromine-graphite lamellar compounds
1345
The absolute concentration of bromine in the graphite was determined for several samples by a combination of gravimetric and tracer techniques. The exchange between the normal and the radioactive bromine was initiated by first starting the flow of cold water (15°C) to the condenser. The condenser, and the inlet and outlet cold water lines attached to it, were insulated to prevent excessive heat transfer from the thermosttated water bath. The valve on the storage reservoir containing the radioactive bromine was closed and the exit valve of the normal bromine reservoir was opened. The flow of normal bromine vapour over the sample was started by opening the inlet valve to the condenser. Bromine vapour was condensed and flowed into the trap below the condenser. When the trap was filledwith liquid bromine, the inlet valve to the normal bromine reservoir was opened and the liquid overflow from the trap returned continuously to the
f
/ ~
\
GRAPHITEPOWD~ .~
~~
/~//
VACUUM JACKET WATERCOOLED CONDENSER
~ / ~P/ L I Q U/P/ ID
[ELECTRONICS ] \'\ LEADS ELDING I I ~SODIUM IOD,DECRYSTAL ~ ~--PHOTOMULTI PLIERTUBE
~
~/
BROMINER TA P
NORMALBROMINE RESERVOIR
FIG. 1.--Apparatus for the study of bromine exchange in the bromine-graphite lamellar compounds. reservoir. Thus, the small quantity of radioactive bromine was diluted in the large volume of normal bromine in the storage vessel. As long as no foreign gases leaked into the system, the flow of normal bromine continued indefinitely in this cyclic manner. During the circulation of normal bromine, the concentration of radioactive bromine in the bromine-graphite compound was continuously measured by monitoring the activity of bromine-82 remaining in the sample. The circulation of normal bromine was continued until the desired fraction of the active bromine in the solid was exchanged or the rate of exchange became too slow to measure. Each subsequent exchange experiment was done with a new graphite sample. RESULTS T h e rates o f exchange o f n o r m a l a n d r a d i o a c t i v e b r o m i n e in b r o m i n e - g r a p h i t e l a m e l l a r c o m p o u n d s were studied in the t e m p e r a t u r e range 20-45°C. T h e concent r a t i o n o f b r o m i n e in the c o m p o u n d s studied c o r r e s p o n d e d to the a p p r o x i m a t e c o m p o s i t i o n s C10Br to Ca.4Br. T h e final c o m p o s i t i o n o b t a i n e d for each s a m p l e d e p e n d e d o n the particle size a n d length o f e x p o s u r e to b r o m i n e v a p o u r . T h e rates o f exchange were n o t affected b y these v a r i a t i o n s in c o m p o s i t i o n . Several typical rate curves are s h o w n in Fig. 2. T h e f r a c t i o n o f r a d i o a c t i v e b r o m i n e r e m a i n i n g in the s a m p l e is p l o t t e d on a l o g scale vs. the r e a c t i o n time in
1346
F.J. SALZANOand S. ARONSON
minutes. In all cases the slope of the rate curve decreased continuously as the concentration of radioactive bromine in the solid diminished. The forms of all the rate curves are similar. Since the mathematical form of the function which determines the rate of exchange is unknown, it is convenient to compare the rate curves obtained for the different particle sizes and temperatures in terms of the reciprocal time to reach a given composition. I.O
i(
~( I
I
I
r
I
I
I
(.9 Z
LU fig LLI
Z
~J>tu 0 IO "r " L.)
--
×
8= t~ ,¢ fig I.E. 0
0 2 0 0 0 - 2 3 8 0 ~ AT 45* C Cl 2 9 7 - - 354~. AT 39"C
Z
A
O
V
I--L.) fig
"
8 8 - - 1051~ AT 2 0 " C 1 4 9 - - 177/J- AT 45°C 88105F~ AT 4 5 * C
o
0.01 0
l
I
I
I0
20
50
E 40
I 50
l I I I 60 70 80 90 TIME, MINUTES
I
I
I
I
I00
I10
120
150
140
FIG. 2.--Rates of bromine exchange in the bromine-graphite lamellar compounds. The temperature dependence of the rate of exchange is shown in Fig. 3. The ratio of the reciprocal time to exchange half the bromine at any temperature to the reciprocal time to exchange half the bromine at 35°C is plotted on a log scale vs. the reciprocal temperature. The data are normalized in this manner to facilitate a comparison of the data from each particle size. In the case of a simple reaction mechanism, such a plot is linear and the slope is proportional to the activation energy for the reaction. The data from all the particle sizes investigated fall on one curve. Thus, the temperature dependence of the rates of exchange of all the particle sizes investigated is the same. At the highest temperature (45°C) the slope is lowest and corresponds to an activation energy of 7 kcal/g-mole. The slope at the lowest temperature (20°C) corresponds t ° an activation energy of 22 kcal/g-mole. The variation of the rate of exchange with particle size at 20°C is shown in Fig. 4. It is evident that the dependence on particle size changes abruptly at about 300 FIn the range of 2200-300 F, the rate of exchange is proportional to 1/a. Below 300 F the rate of exchange is proportional to 1/a 2. Since the temperature dependence is the same for all particle sizes, the variation of the rate of exchange with particle size is the same at all temperatures.
B
5.10
.a0
I.O
3.15
I
3.20
i
1
I
I / T *K x 103
3.25
i
5.50
i
0 8 8 - io5 F
n 149- 177/u.
o 710-1190 j..t ZX 297- 554 /z
I
5.35
i
1
5.40
I
I
FiG. 3.--The temperature dependence of the rate of bromine exchange.
8
..J
Z 0
W
I,I
13-
0 0
W
0
Z
hl
O
LU
rl
0
..--I
Z 0 I.< hl
I--
IM
¢j,
I0
20
I
]
I
I00
200
I
-~i
I
\ \
I I IJIJJ,
-
_
7- i I ~Ili±
400 600 I000 2000 4000
I I IIIJlJ
i IIIIt I
AVERAGE SIEVE SCREEN SIZE,MICRONS
40 60
J IllllJ
i I liill I
F[c. 4.--The particle size dependence of the rate of bromine exchange.
0.1
1.0--
I0--
--
I00 - -
I000
--4
O
O
O
t~
O
1348
F.J. SALZANOand S. AI~ONSON
DISCUSSION The mechanism proposed to explain the kinetics of bromine exchange in the bromine-graphite lamellar compounds must account for the following observations: (1) the continuous change in the slope of the rate curves shown in Fig. 2, (2) the large variation in the activation energy over the temperature range 20-45°C, (3) the abrupt change in the particle size dependence from 1/a to 1/a ~. Furthermore, the proposed mechanism must be consistent with the known structural features of natural graphite flakes. The mechanism of bromine exchange in the bromine-graphite lameUar compounds is complex and is not immediately obvious from the data. We have carefully considered the following mechanisms: (1) one step surface processes, (2) simple and complex bulk diffusion processes ~9) and (3) a combination of bulk diffusion and surface processesJ 9) These mechanisms were eliminated on the basis of the form of the rate curves, the temperature and (or) particle size dependence of the rate of exchange. A mechanism of bromine exchange in the bromine-graphite lamellar compounds can be formulated which accounts for the experimental observations. In this explanation, the structure of the bromine-graphite flakes is an important factor in the exchange mechanism. Although the graphite flakes are delaminated during the formation of the compound, the original diameters of the flakes are unaltered and the original c-axis of the graphite remains perpendicular to the plane of the flakes. We propose that the bromine-graphite flakes larger than 300/~ in diameter consist of a mosaic structure of smaller units or crystallites. We will call the interracial boundaries between crystallites "grain boundaries." These crystallites are assumed to contain no "grain boundaries," but may contain other defects. The c-axes of all the crystallites are approximately parallel. In the large flakes which contain "grain boundaries," the average diameter of the crystallites parallel to the basal planes is approximately 300/~. Flakes smaller than 300 # contain no "grain boundaries." The proposed structure of the bromine-graphite flakes is depicted schematically in Fig. 5. For the sake of simplicity, we have shown the flakes and crystallites as squares and the crystallites as uniform in size. In order to account for the variation in the apparent activation energy with temperature, the exchange mechanism must consist of at least two consecutive steps which control the rate of exchange. Both steps occur at surfaces i.e. at the solid-gas interface and at the interracial boundaries of the crystallites. The first step in the exchange mechanism is the transfer of bromine from the bulk i.e. between the layer planes, to a surface adsorbed state at the edge surfaces of the crystallites. In the case of flakes smaller than 300/~, the radioactive bromine is transferred from the bulk directly to the periphery of the flakes. In flakes larger than 300/z, the bromine from the bulk is transferred into "grain boundaries" as well as to the edge surface at the periphery of the flakes. The bromine is able to move rapidly through the "grain boundaries" and from the periphery of the flakes to the exposed basal plane surfaces. In those regions of the basal planes where the bromine emerges from the edges of the flakes and grain boundaries, the bromine begins to diffuse along the basal plane surface in the adsorbed layer of bromine present on (9) j. CRANK, The Mathematics of Diffusion. Clarendon Press, Oxford (1956).
The mechanism of bromine exchange in the bromine-graphite lamellar compounds
1349
that surface. Before the radioactive bromine can diffuse over an appreciable area of the exposed basal planes, it evaporates. The amount of evaporation from the edge surfaces which are parallel to the c-axis is assumed to be small, either because the total surface area contributed by the edges is small or because the bromine is bonded more strongly at the edge surfaces than on the basal planes. During the evaporation of radioactive bromine the adsorbed bromine layer is continuously replaced by normal bromine from the gas phase. It is further assumed that the flow-rate of normal bromine over the flakes is sufficiently rapid to maintain the concentration of active bromine in the gas phase, in the vicinity of the flakes, at a negligible level. The fact that
*
L-
[,
•
/
a
"1
°
i
*EVAPORATION OF BROMINE MOLECULES IS LIMITED TO THE PERIPHERAL REGION OF EACH CRYSTALLITE • ~ LARGE FLAKES, o • d • ~ SMALL FLAKES, o = d
FIG. 5.--A model of the structures of bromine-graphite flakes of various sizes.
the rates of exchange were independent of flow-rate supports this assumption. Thus, the last rate controlling step is the evaporation of radioactive bromine from the adsorbed layer of bromine on the exposed basal plane surfaces. The net flux from the surface is proportional to the surface concentration of radioactive bromine which is continuously decreasing as the bulk concentration decreases.
Particle size dependence We can account for the particle size dependence of the rates of exchange in terms of the surface evaporation step and the proposed mosaic structure of the flakes. Since the last step in the exchange mechanism is evaporation from the basal plane surface, the rates of exchange will be proportional to the surface to volume ratio of the bromine-graphite flakes. We assume that the average thickness of the brominegraphite flakes is proportional to the average a-axis diameter of the flakes, as was found in the case of pure graphite. ~lm In the case of large flakes i.e. greater than 300 #, it is reasonable to suppose that the average size of the small crystallites which make up the mosaic structures is the same in all sieve fractions. ~xo~
F. J. SALZANOand S. ARONSON,Carbon 3, 213 (1965).
1350
F . J . SALZANOand S. ARONSON
The change in the particle size dependence of the rates of exchange from 1/a for large flakes to 1/a S for small flakes can be explained if the radioactive bromine does not migrate very far over the basal plane surface before it evaporates, but rather evaporates from a small area adjacent to the edges of the crystallites as shown in Fig. 5. We assume the crystallites to be squares with sides equal to d and also assume the thickness of the flakes, t, is given by the relation, t =
Ka,
(1)
where K is the same constant for all the flake sizes. The effective evaporation surface per unit volume, Sv, is therefore given by, 4l 1 Sv . . . . , dK a
(2)
where l is the average distance over which the radioactive bromine migrates before evaporation. This is assumed to be small compared to the smallest flake size studied. In the case of the small flakes, each of which consists of a single crystallite, d is equal to a and 41 1 Sv = ~ - a ~ . (3) Thus, in the case of small flakes the rate of exchange will be proportional to 1/a S and in the case of large flakes to 1/a. The f o r m o f the rate curves
The mechanism of bromine exchange in the bromine-graphite lamellar compounds requires at least two consecutive reactions to account for the observed temperature dependence. In the most simple case the following reactions apply: /¢
CB ~
fl
C x- ~• Gas phase
(a)
where C~ is the concentration of radioactive bromine in an individual crystallite, CA is the surface concentration of radioactive bromine on the basal planes at the gas-solid interface and k, fl and ~ are the rate constants for the reactions shown. Assuming all the reactions are first order we can write two differential equations which express the rate of removal of bromine from the bulk solid and from the exposed basal plane surfaces of a crystallite. dCB dt -- flCa -- kCB
(4)
dC~ dt
(5)
-
kCB -- (fl + ~)C~.
A solution to the above set of differential equations can be obtained by the method of the Laplace-Carson transformation, m~ The results can be expressed in terms of m) N. M. RODIGUIN and E. N. RODIGUINA, Consecutive Chemical Reactions (Translated from the Russian by Scipta Technica, Inc. Edited by R. F. SCHNEIDER). Van Nostrand, Princeton, New Jersey (1964).
The mechanism of bromine exchange in the bromine-graphite lamellar compounds
1351
the fraction of radioactive bromine, f, remaining in the crystaUite at time t as
f_
b -- y________e-r~ L t -k b -- Y__._.~e_e~t 2 ' Y2
-- ?i
Yi
--
(6)
Y~
where y~ and Y2 are the roots of the quadratic y z + (k ~- fl + ~)y q- ko:, taken with the opposite sign and
( 1 + cA°
(7)
(8)
where CA° and CB° are the respective concentrations of radioactive bromine at t = 0. In order to account for the continuously decreasing slope of the rate curve shown in Fig. 2 it is necessary to postulate the existence of a number of regions in each crystallite. The rates of transfer of bromine from the bulk to the edge surfaces is different in each region. We conceive of these regions as sections which are perpendicular to the c-axis. The edges of the regions in each crystallite are the edge surfaces of the crystallites. The rate of transfer of radioactive bromine from some regions to the exposed basal plane surface is rapid, while other regions lose bromine more slowly. This may be due to blocking of some graphitic layers at the edge surfaces. MMl~ and MEI~ING(12) indicate that the failure of certain graphites to form the limiting composition CsBr may be due to a similar blocking which closes off whole regions. Equation (6) applies to crystallites which contain one region. In the case of multiple regions we can express the exchange mechanism in an individual crystallite by the following parallel and consecutive reactions: kt ~,
CBI ~
CB~ ,(
)"
82
Ce~ ~
~ CA
) Gas phase
(b)
83
k. CB. <
>
where CB1, CB,, CB3 • • • C~. represent the respective concentrations of bromine in the n regions of a crystallite. We can obtain an expression for the overall rate of exchange which is a sum of n ~ 1 exponential terms and fit the experimental data by a proper choice of rate constants and distribution of bromine in the various regions in the crystallite. Because of the complexity of this mechanism, it is not possible to obtain quantitative information about the individual rate constants. cx~ j. MArRE and J. MERINO, Proceedings of the Third Conference on Carbon, pp. 337. Pergamon Press, London (1959).
1352
F.J. SALZANOand S. ARONSON
The temperature dependence In the case of a crystallite containing multiple regions (reaction (b)) we can write the differential equation which expresses the rate of change of the surface concentration with time, n dCA-- ~'knCB"-1 (~ + ~'fln) 1 (9) In order to demonstrate that the temperature dependence of this mechanism conforms to the experimental results, it is convenient to regard the amount of bromine in the bulk of each crystallite as large relative to the amount adsorbed on the surface. Therefore, a short time after the exchange reaction has begun the surface concentration will be changing slowly and the approximate steady state condition, dCA/dt = O, can be assumed. Equation (9) can be written, "k
Ca=
1 ~+~.
CB..
(10)
1
The flux, F, from the solid to the gas phase is
F = ~ca.
(11)
Substituting for Ca from Equation (10) into Equation (11) we obtain, n
F=
~,,
.CB.
(12)
~ +Z/~. 1
We will assume that the activation energies for the rate constants corresponding to similar reactions in the different regions of the crystallite are equal. The temperature dependence of each rate constant is given by _~. ~o e-Q~IRT, k n = kn ° e-Qdl~T,
(13) (14)
(15) where T is the absolute temperature, R is the gas constant kn°, fin° are constants which are different in each region of the crystallite, s ° is a constant and Q~, Qa and Q~ are the respective activation energies for the forward reactions, the back reactions and the surface evaporation step. n kn If we let ~ ]~ K --
1
,
(16)
1
substitute Equation (13), (14) and (15) and differentiate, we obtain
dOlT) =
R Qk q- (Q~ - Qa)
1 q- ~--~° 1 e-t°~-% )rot
(17)
The mechanismof bromine exchangein the bromine-graphitelamellarcompounds
1353
Examination of Equation (17) shows that the model gives the correct form for the temperature dependence. Irrespective of the relative values of Qk, Q~ and Qa, a plot of In K vs. 1IT will be curved. At high temperatures, the curve will have the smallest negative slope and at low temperatures it will have a larger negative slope. Consideration of the proposed mechanism and Equation (17) indicates that under certain conditions the limiting activation energy observed at low temperatures, 22 kcal/g-mole may correspond to the bond energy between bromine and graphite.
Comparison to previous investigation It is of interest to compare the results of this study with the previous investigation of the exchange kinetics. The results of the two studies are similar in several respects. The activation energies observed in the previous work, 11-14 kcal/mole at 30--48°C are similar to those observed in this study in the same temperature range. The dependence of the rate of exchange on particle size, approximately l[a ~ for particle sizes of 15-110/z, is in agreement with the present data for small particle sizes. The large continuous decrease in the rate of exchange with time is similar in both studies. The use of a bulk diffusion model in the previous study was based on information obtained on a limited range of particle sizes and is probably not correct. The complex, yet consistent, dependence of exchange rate on particle size and temperature observed in the present study can only be explained by a surface exchange mechanism.
Acknowledgement--This is to acknowledgethe contributionsof Mr. W. KALINOWSKIwho performed the measurementsand contributedto the modificationsof the experimentalapparatusand Mr. J. DAvis who constructedthe experimentalapparatus and prepared the brominecapsules for irradiation.