THE PULSED HOMOGENEOUS LASER PYROLYSIS : DETERMINATION OF ARRHENIUS PARAMETERS OF CHCIF 2 DESTRUCTION BASING ON THE MODEL OF PHYSICAL AND CHEMICAL PROCESSES

The Pulsed Homogeneous Laser Pyrolysis (PHLP) of CHClF2 initiated by IOP(20) radiation of TEA-CO2 
laser was carried out in the presence of SF6 sensitizer with the mixture components ratio 1:1 under partial 
pressure of the reactant equal to 1 Torr and 2 Torr.To describe PHLP process in the afterpulse period we suggested a kinetic model of CHClF2 thermal 
destruction accounting for the inhomogeneity of laser heating of the reaction mixture and its further 
cooling by the heat conduction mechanism. Applying the standard mathematical procedure for matching 
the experimental results of the degree of reactant destruction, and the numeric computations of this value 
made according to the suggested model, the Arrhenius parameters of the reaction of CHClF2 monomolecular 
conversion in the temperature range of 1000–1200 K were unambiguously determined. 
The values were obtained for the activation energy E α = 52.8 ± 0.3 kcal/mol, and the pre-exponential 
factor A = (2.5 ± 1) · 1012 s−1.


INTRODUCTION
The Pulsed Homogeneous Laser Pyrolysis (PHLP) technique enables one to study the gas-phase chemical processes at high temperatures (1000 K plus) and without the catalytic effect of the reaction vessel walls. 1,2e gas thermalization time under pulse irradiation corresponds to V-T, R relaxation time of the multiphoton-excited sensitizer molecules and under the pressure of several torr is ca. 10 #s. 2 It is known 3'4 that if the irradiated area is only a small part of the reaction vessel, the main mechanism of cooling would be the adiabatic expansion.Computation of cooling due to shock waves requires creation of complex gas dynamic models that are illustrations of physical processes rather than a tool of kinetic analysis.
To assess the reaction rate constant of thermal destruction of the studied reactant under PHLP a technique of "chemical thermometer" is applied that does not require precise determination of temperature distribution in time and over reactor space.3][4] The method error depends on the differences in the activation energy (E) and pre-exponential factor (A) of these two processes.The reference reaction is not always easy to select, since there is an additional restriction of the complete mutual inertness of both the initial substances and the conversion products for both reactions.
6][7] Conversion mechanism was determined: CHC1F2 > CF2: + HC1 CF2: + CF3: The Pulsed Homogeneous Laser Pyrolysis of freon-22 was carried out in the works 1'8 '9 The TFE was found to be the main destruction product.No special kinetic studies were carried out in the mentioned works.It seems interesting to use the CHC1F2 single-channel destruction reaction with well-defined mechanism and kin- etic data as the model reaction for probation of the method suggested in the present paper for determination of the activation energy and the pre-exponential factor of reaction (1) under PHLP.
In the absence of the internal reference it is necessary to have information on the spatial and time distribution of temperature over reaction volume.The problem is greatly simplified if laser radiation fills the major part of the cell.In this case the shock waves do not cause any significant temperature changes, and heat conduction is the dominant cooling mechanism. 1 '11 Under initially uniform heating of gas the problem can be reduced to analytical calculation of gas cylinder cooling.Such calculation was made in 11 where the ozone PHLP was studied.The activation energy of 03 destruction reaction was assessed by the slope (tangent) of the experimental curve, O3 conversion degree (AC/Co) vs. maximum initial gas temperature (Tw:R), in the semilogarithmic coordinates ln(AC/Co) I/TvTR.The pre-exponential factor was determined from the correspondence of AC/C0 values obtained experimentally and those computed by the kinetic equation of 03 thermal destruction process basing on the "homogeneously-heated-reaction-mix-cooling" model.It should be noted that solving this problem in the analytical form it is practically impossible to account for the relationship of the mix components heat capacity, Cv, and gas heat The reaction (3) plays an important role only under deep conversion of freon-22 and under HC1 excess.At low degrees of conversion difluorocarbene completely recombines with tetrafluoroethylene (TFE) formation.In 5-7 the following values of the Arrhenius parameters were obtained for the first step of destruction process (1): E 55.8 kcal/mol, A 1013"84 S -1 5 E 55.0 kcal/mol, A 1013"2 S -1 6 E 55.8 kcal/mol, A 1012"6 S -1 7 conduction, A, with temperature.This, generally speaking, is incorrect because at those considerable heating levels occurring under laser action, Cv,, changes 1.5-2- fold, and , 6-7-fold.To account for these relationships the numeric methods are required.
Moreover, a really existing inhomogeneity of laser beam cross-section intensity leads to spatial distribution of IR-radiation energy absorbed by the gas mix (Eabs)   and, primordially, to inhomogeneous heating of different areas of the internal reaction cell space.The further temperature variation with time for these areas can be determined through monitoring of heat flows between them and accounting for Cv,[T(t)] and [T(t)] changes.Such calculation was made in 10, where cyclobutanone PHLP was studied under TEAoCO2 laser action.The value of AC/C0 was computed in the afterpulse period as a sum of independent conversion degrees (AC/Co)v, for each elementary volume Vi within the cell, assuming parameters Ea and A as the preset ones.The experimental and computed data were in good agreement.
The stationary longitudinal and transverse temperature profiles of SF6 and C2H5C1 under CW-CO2 laser irradiation were calculated in 12. Also, that paper presented a calculation of chloroethane conversion degree as a function of laser radiation energy for two values of E: 57.4 and 65.0 kcal/mol.The authors of 12 found that the experimental data are in better agreement with the value 57.4 kcal/mol generally accepted in the literature.
The goal of the present study was development of a method for determination of the primary elementary reaction rate constant for a reactant conversion process exemplified by CHC1F2 under pulsed homogeneous laser IR heating, via the afterpulse temperature and concentration fields modelling that enables unam- biguous determination of Arrhenius parameters of the studied reaction basing on the experimental data.

THE HEAT CONDUCTION MODEL
The model we have suggested accounts for temperature variation with time due to heat flows and changes of concentration fields under these conditions.For that purpose the entire internal volume of the cell was presented as the sum of elementary volumes, Vi, and each was assigned, according to its spatial location, the initial gas temperature, To(Vi), upon completion of V-T, R relaxation process of SF6.It was assumed that in the elementary volumes directly adjoining the reactor walls the temperature was constant throughout the entire process period and equalled to 298 K.For concentration calculations the density gradient was determined basing on that the rate of pressure equalization is considerably higher than that of temperature equalization.13 In each elementary volume Vi, the reactant concentration C(Vi), and temperature are related by the equation of the ideal gas state: Since it can be assumed that the pressure at any moment of time t is constant over the volume dp/dv O, then C(Vi) qg(t)/T(Vi), where the function qv(t) Co * Vtotal/Vi E 1/r(vi) (5)   v is obtained from the condition of substance quantity conservation in the entire volume _, [C(Vi) * Vii-" Co * Vtotal (6)   v and the ideal gas Eq. ( 4).
Chemical conversion of the reactant was studied in the selected short time intervals, At, and small volumes, Vi, isothermally and described by the general kinetic equation with the rate constant expressed in the Arrhenius form k A x exp[-Ea/RT(Vi)].Then, for a relatively short time interval At the quantity of the reacted substance can be written as" AC(V) C(Vi) * A exp[-Ea/RT(Vi)] * At (7)   under condition of independent course of chemical conversion in each elementary volume.
The heat flow between the adjacent volume elements due to temperature gradient was determined for a time period At by the formula: (8)   where Sq is the area of the boundary between subvolumes V and V; L is the length of the j-th subvolume in the direction of the heat flow from V to V; Z is the heat conduction factor.The total heat quantity, Q, transferred to the volume V was obtained by summing up those of the adjacent volumes, V.The temperature variation within the time interval At would be k where C(Vi) is the concentration of the k-th component, and Cv[T(Vi)] is its heat capacity.Temperature relationships of the components, heat capacities were calcu- lated basing on the statistical data, and the heat conduction of mix--by the standard method.4 This calculation procedure for the time period At was performed for all elementary volumes resulting in the new temperature and concentration fields obtained.Then, the calculation was repeated by sequential time intervals At throughout the entire cooling process.Summing-up the quantity of reacted substance AC(V) of all elementary volumes and over all time intervals we obtained the total conversion degree for one laser pulse.Since conversion degrees in each volume V over a time period At are very small A C(V) <_ 10-4%, and the total reactant destruction degree in one pulse normally does not exceed few per cent, the concentration variation conditioned by the chemical reaction was not accounted for in the concentration field calculations.
Let us note that in the earlier work 0 calculation was based on the prerequisites similar to those that we used.The paper, however, did not account for the concentration gradients.This, as was shown by preliminary estimations at quite real temperature difference ca. 600brings about underestimation of the reactant concentration in the "hot" region ca.50%, and in the "cold" one--almost its doubling.

EXPERIMENTAL
Pulsed heating was done by TEA-CO2 laser (CO2:N2:He:D2 in ratio 1:1:4:1) zeroed in on the IOP(20) line, 'pulse 150 ns.The laser output beam of -(2 1,6) cm 2 was diaphragmed with the 1.5-cm-diameter iris diaphragm to separate its most homo- geneous part.A sodium chloride plate was placed in the way of the laser beam to reflect ca.1% of its energy onto the calorimeter to monitor the laser output energy.The laser pulse output energy spread was never above 3% in the 100 experiment series.When required, the beam was attenuated by introduction of calibrated wedges and then channelled through a cylindrical stainless steel cell (length L 7.2 cm; internal diameter d 1.5 cm) having barium fluoride windows.Then the beam entered the second calirometric sensor measuring the value of the IR-radiation incident energy (Eo) when the cell was empty, and the transient energy E/ when the L-long cell contained a reaction mix.The laser beam energy distribution over the cell cross-section was measured with 1.1 mm orifice diaphragm moved by the microm- eter screw vertically and horizontally over the whole beam cross-section.According to this procedure the entire internal cell volume was approximated by the set of 149 equal elementary volumes (Vi) each having the cross-section S(Vi) 1 mm2; that corresponds to the diaphragm orifice size.Thus, the output laser beam energy (E0) distribution over the cell cross-section was represented by the set of Eo(Vi) values of all 149 elementary volumes.Axial inhomogeneity of the laser beam in the reaction mix containing cell was neglected, since the IR-radiation energy absorbed by gas never exceeded 10% of E0 in all experiments.The ratio of the energy flow Eo(Vi) falling onto the selected elementary volume of S(Vi) area to [Eo(Vi)] averaged by all values is 1.84 in the cell center, and up to 0.54 at the edges.
We have carried out a series of experiments in one of the central elementary volumes for each of the studied mixes to determine the relationship between the absorption cross-section SF6(aen) and the incident energy Eo(Vi); the total energy E0 was varied in the range 0.4 / 0.85 J.The SF6:CHC1F2 mix in the ratio 1" 1 under total pressure 2 and 4 torr was used.In the main experimental series with the mixes of the mentioned composition the samples were irradiated with the same levels of E0 energy.Upon irradiation the cell contents were analyzed with the "Khrom-5" chromatograph in a column with "POROPAK-T."The TFE was found to be the main (over 99.9%) product of freon-22's PHLP.The reactant conversion degrees, AC/Co, ranged in one pulse from 1.10 -2 to 6%, as a function of the laser output energy E0.RESULTS

AND DISCUSSION
1. Absorbed Energy Determination and Temperature Computations It is known, 2 that for SF6 at laser radiation energy densities (tp) from 1 10 -4 to 3 J/cm2, the mean number of absorbed IR photons with energy hto has the relation [tl] tp 2/3.Since the sensitizer-absorbed energy, Eabs htO* [n], and tp Eo/S, it may be expected that Eabs Eo 2/3.
For one of the central elementary volumes, Vi, the experimental data of the absorbed energy relation Eabs(Vi) Eo(Vi) -EL(Vi) were processed in the form of a function of the incident energy Eo(Vi) according to the equation: ln[Eabs(Vi)] A + B * ln[Eo(Vi)] (10) by the least squares method.The power exponent (B) values obtained were 0.66 + 0.02 for mix total pressure of 2 torr, and 0.55 + 0.02 for 4 torr, this is in good agreement with expected exponential relation Eabs VS.Eo for SF6.At that, the absorption cross-section, Oeff, defined as O'ef Eabs(Vi)/d(Vi), where (Vi) Eo(Vi)/ S(Vi), slightly decreases with increasing Eo(Vi) and is 3 10-19-5 * 10 -19 cm 2 (see Figure 1).These data on SF6 multiphoton absorption cross-section are in good agreement with the generally accepted, 2 and enable one to calculate, using the set of Eo(Vi) values, the absorbed energy Eabs(Vi) in each elementary volume Vi.The total IR energy Eabs(Vi) absorbed in the system for each mixture at different E0 values was determined by summing up all elementary volumes.The corresponding to this energy initial equilibrium gas temperature (TvTR) from which pyrolysis process starts was calculated in the approximation of complete thermalization of Eaus energy by the expression: TVTR Eabs 3298 k Ck * Cvk(T) * dT (11)   where Ck is the k-th component concentration, Cvk(T) is the k-th component heat capacity.
Thus introduced TVTR temperature does not account for the actually existing inhomogeneity of laser heating of a gas; this parameter, however, enables compari- son of the PHLP experimental results for mixtures of different composition and different Eabs values.F, J/cm 2 Figure 1 Effective cross-section of multiphoton absorption of SF6 mixed with CHC1F2 (1:1) vs. the laser radiation energy density. (o)----experimental data at P 2 Torr; (--)--the result of the experimental data processing in the form of exponental relation (10) by the least squares method.
(nc/c o) - It is assumed in the suggested PHLP model that chemical conversions occur in the completely thermalized system.Under pressure of 10 Torr and above in the gas system the characteristic times of V-T/R equilibrium settlement are almost one order less than the characteristic times of the reaction.In the region of low pressure (ca. 1 torr and below) under SF6 molecules multiphoton excitation (MPE) up to [n] [12][13][14][15][16] quanta per molecule there occurs on the one hand a considerable, compared to "weak" excitation, increase of V-T/R relaxation rate, 15 and on the other, even greater increase of the rate of V-V' exchange between the polyatomic molecules is expected.fTherefore, at the initial stage of collision relaxation there may occur a brief excess of the "vibration temperature" over the translatory-rotational one.Under conditions of our experiment [1 Torr < Ptotal < 10 Torr] this "break-away" of vibration temperature is apparently so brief (in the order of few microseconds) that it can be considered that the main conversion of the reactant (CF2HC1) occurred under conditions of complete thermalization of IR irradiation energy absorbed by the sensitizer, i.e. at temperature close to Tv-x/R values (11), which under our experi- mental conditions is preserved for over 100 microseconds in the process of the afterpulse gas cooling (see Figure 3).A proof of that assumption is on the one hand a good agreement between our experimentally obtained values of E and A under CF2HC1 PHLP and the literature data, and on the other hand the results of 9 Regretfully, there are no quantitative data in literature on the rates of V-V' exchange between the MFE molecules of SF6 and CF2HC1.confirming that in the absence of threshold effects, related to SiF4 electron excitation or SF6 MPD, the detected CFaHC1 destruction in the presence of sensitizers (SiF4, SF6) occurs in the thermalized systems.The work 9 studied the kinetics of real-time :CFa radical formation with high-sensitivity afterpulse LiF diagnostics.It was found that LiF signal appeared with --10 #s delay relative to the initiation pulse.This delay time, according to authors of, 9 is in good correlation with the termination of thermalization process of SF6 (1 Torr) + CFaHC1 (1 Torr) mixture.We have obtained similar results in the UV-detection of :CF radical ( 248,3 nm) formed under C3F60 PHLP (SF6 sensitizer, 2 Torr total pressure): C3F60 > :CF2 + C2F40 The signal of :CF2 absorption was observed in a thermalized system with a delay of 8-10 #s relative to the initiating laser pulse.
As has been mentioned, in the systems with pressure about 10 Torr and above, the times of the vibration temperature "break-away" from the equilibrium Tv-r/R would be so short that the contribution of the nonequilibrium mode reactant destruction to the overall destruction degree would be negligible.
Figure 2 shows in symbols the experimental data of difluorochloromethane destruction under PHLP in the coordinates ln(AC/Co) I/TvTR.In the case of homogeneous heating of the mixture, as shown in it, the slope of the straight line--plotted in the mentioned coordinates for the set of experimental datamto the I/TvTR axis corresponds to Eo,/R value of the reactant destruction reaction.For the data shown in Figure 2 it would correspond to E 48 kcal/mol of CHCIF2 destruction reaction.It was noted in t0, however, that for the inhomogeneous heating this method yields 5-10% underestimated values of the activation energy of monomolecular destruction reaction.Therefore, according to the above model, E was determined with a detailed account of contribution of all zones with different initial temperature To(Vi) to the reactant destruction total degree (AC/Co).To calculate the total conversion degree of CHC1F2 (AC/Co) after a laser pulse in each of 149 elementary volumes (Vi parallelepipeds sized [1 1 72] mm) of the set describing the reaction volume of the cell, an Eabs(Vi) magnitude was calculated by the IR-beam-spatial-energy-distribution net of Eo(Vi) values and the corresponding absorption cross-section values of SF6-mixtures with the reactant: The initial equilibrium temperature in each elementary volume To(Vi) was found Thus found initial temperature distribution of the cell reaction volume was then introduced into the above heat conduction model for numeric calculations of the concentration and temperature fields time variation, as well as for determination of the reactant destruction degree.Also, cooling at the edge windows of the cell was not accounted for, since their area comprised less than 10% of the total cell area and, as has been shown by the preliminary assessment, produced no significant effect on the cooling process and reactant destruction in general.
The calculated temperature and concentration fields are shown in Figure 3.The time pitch At, and the finite summation time tmax were 10 and 500 ps, respectively, and did not limit the calculation accuracy.The CHCIF2 destruction degrees were computed for the activation energy range of 35-70 kcal/mol and the pre-exponential factor 1010-1014 S-1.These values exceed the range of possible E and A values for HCI concerted elimination reactions. 16he least squares criterion was applied to determination of the activation energy and pre-exponential factor.A normalizing function F X [(AC/Co)exp (AC/Co)calc] 2 N make the decisive contribution to the total destruction degree of difluorochlorome- thane; this is due to the exponential relation between the rate constant and temperature.
The kinetic model suggested in this paper describes with good approximation the real PHLP process, and enables one to unambiguously determine the Arrhenius parameters of the homogeneous thermal destruction of the reactant.This method is applicable for research into pyrolytic reactions of a wide scope of reactants at higher temperatures.

Figure 3 1 10
Figure 3 Time evolution of the reactant's radial temperature (a) and concentration (b) profiles in the afterpulse period.(a) 1