9726
J. Phys. Chem. 1996, 100, 9726-9731
Collisionally Induced Bottleneck Weakening in IR Multiphoton Dissociation J. A. Torresano* and M. Santos Instituto de Estructura de la Materia, Centro de Fı´sica “Miguel Catala´ n”, CSIC Serrano 121, 28006 Madrid, Spain ReceiVed: October 13, 1995; In Final Form: April 4, 1996X
An extension of the method of McRae et al. is proposed to quantify the contribution of the distinct collisional processes to the total yield obtained in infrared multiphoton dissociation experiments. The extension consists of the introduction of a substrate pressure dependence in the parameter representing one homogeneous collision. This allows the application of the method at a pressure where the collision time is of the order of the temporal width of the laser pulse and the discrimination between the different processes associated in a given collisional sequence. We have tested the reliability of this extended method by applying it to the multiphoton dissociation of CF2HCl, where the dependence of the dissociation yield on initial pressure and laser fluence has been investigated. We have shown that the homogeneous collisions occurring during the laser pulse may play a fundamental role in the weakening of the bottleneck absorption effects. It has been also suggested that fluence is the main excitation parameter for fixing the pressure interval along which dissociation can be regarded as collisionless.
1. Introduction Although the contribution of the different collisional processes to the enhancement or inhibition of infrared multiphoton dissociation (MPD) of polyatomic molecules has been qualitatively studied for many species,1,2 reliable quantitative conclusions from these studies are difficult to obtain. One reason pointed out by only some authors3 is that the pressure of the products formed in the dissociation process taking place in a closed cell increases as the number of pulses grows. This must be taken into account in the study of the collisional MPD process, but this is not possible with the use of the conventional methods. These either represent the yield by averaging over all the pulses used in the irradiation (e.g. the fraction of molecules dissociated per laser pulse,4 f, or the reaction volume,5 VR) or take the number of pulses as a continuous temporal variable and derive kinetic equations to represent the dissociation process.6,7 Problems with these procedures have already been pointed out elsewhere.3 Actually dissociation products may significantly affect the subsequent excitation process through their collisions with parent molecules. Although dissociation products generally increase vibrational quenching, sometimes they can help to overcome vibrational and rotational bottlenecks. In addition, if any of the reaction products absorb the infrared exciting field, they can affect dissociation by vibrational energy pooling. Recently, McRae et al.3,8,9 have put forward a method for the analysis and quantification of the contributions from different collisional processes. In this method, the dissociation probability is modeled with a two-variable power series expansion in pressures of reactant and products. Model parameters, determined from a fit to experimental data, are associated with different collisional sequences. However, the model has only been applied in experiments carried out at rather high values of pressure where the time between collisions is short compared to the pulse time width (∼10 and ∼100 ns fwhm, respectively), and it is not possible to discriminate between processes taking place during the pulse and those occurring later. X
Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(95)03031-0 CCC: $12.00
In this paper we extend the McRae model in a simple way for dissociation experiments at initial pressure conditions at which the collision time is of the order of the laser pulse temporal width. To test the reliability and applicability of the proposed extended method, we have applied it to the study of MPD of CF2HCl. For this molecule we have been able to distinguish and quantify processes that, when initiated, need further infrared excitation to be completed. We have established the important role played by homogeneous collisions in the weakening of bottleneck effects and also the influence of the laser fluence on the character of the process. Finally, we discuss the dissociation and recombination reactions taking place among the fragments formed in the multiphoton dissociation of CF2HCl. 2. Analysis Method There are two main mechanisms that hinder multiphoton excitation of a molecule in low-lying rovibrational levels: progressive detuning in the absorption of the initially resonant infrared photons, caused by the anharmonicity of the vibrational ladder, and rotational selection rules that hinder a big proportion of molecules from interacting with the radiation field. We use the label “anharmonic barrier”, BA, for the ensemble of the two above effects. That is, BA comprises all the quantum rovibrational characteristics of a molecule that tend to prevent the occurrence of a multiphoton absorption process. Clearly, collisional processes, even if they remarkably influence multiphoton absorption and dissociation, cannot be included in BA, as this is a genuine intramolecular concept. The influence of BA on the overall dissociation process can be characterized by its strength, which depends not only on the characteristics of the molecule but also on the experimental conditions used in the irradiation. Finally, we must point out that BA has to be related to the concept of effective size of the molecule, and so we may associate large and small molecules10 to molecules with weak and strong BA, respectively. In the method of McRae et al.,3 the number of parent molecules Nn left in the cell after n irradiation pulses is given by © 1996 American Chemical Society
Collisionally Induced Bottleneck Weakening n
[
Nn ) N0 ∏ 1 k)1
VI Vc
fk(φk,Rk-1,βk-1)
]
J. Phys. Chem., Vol. 100, No. 23, 1996 9727
(1)
where N0 is the initial number of parent molecules, VI and Vc are, respectively, the irradiation and the total cell volumes, and f (φ,R,β) is the single pulse decomposition probability. This is a function of the fluence, φ, and the partial pressures of parent molecule, R, and dissociation products or any other buffer gas introduced in the reaction cell, β. It is assumed a power dependence of f on partial pressures given by
f(φ,R,β) ) ∑ ∑hij(φ)Ri-1βj
(2)
Figure 1. Proposed dependence on the substrate initial pressure for the parameter representing one homogeneous collision, h20.
where the coefficients hij are associated with Lindemann-like collision reactions.11 The partial pressure of the parent molecule after n pulses can be expressed as
introduce some kind of dependence of the collisional parameters, hij, on the substrate pressure. We have introduced the above described pressure dependence in the one-homogeneous-collision parameter, h20, in the simple form (Figure 1):
i)1 j)0
Rn )
Nn R N0 0
and the accumulated partial pressure of the products after n pulses is
βn ) S(R0 - Rn) The proportionality constant S accounts for the progress of the induced chemical reaction. It depends on the stoichiometry of the dissociation reaction and, in principle, takes a different value for each possible dissociation product. This method takes into account the variation in the pulseto-pulse yield induced by the change of the partial pressures of reactant and products during the course of the experiment. From the magnitude and sign of the model parameters, hij, one may infer the different contributions to the dissociation yield coming from the direct pressure-independent process (h10) and from the mechanisms induced by homogeneous and heterogenous collisions (h20, h11, and higher order parameters). McRae et al. have been able to find hij parameters, only dependent on fluence, for a number of molecules,3,8,9,12-14 working at pressure values where there is a rather high number of collisions during the time of the laser pulse. The relation between the collision time, tc, and the temporal width of the infrared pulse, tp, determines the different processes that take place in a given collisional sequence. For example, there are at least three processes contributing to the onehomogeneous-collision parameter, h20: (a) weakening of the anharmonic barrier effect (through rotational hole filling15 and overcoming of the vibrational bottleneck16 via R-T and V-V′ intermolecular energy transfer, respectively), (b) vibrational energy pooling17 (V-V′ transfer between molecules excited to the quasicontinuum), and (c) quenching of the vibrational excitation1 (via V-T transfer). For a substrate pressure low enough, i.e. when there are no collisions during the time of the pulse, the process (a) does not contribute to the value of h20. As the initial pressure increases and tc ∼ tp, the process (a) starts to contribute and thus leads to a higher value of h20. At higher initial pressure, i.e. when there are large numbers of collisions during tp, the weakening of the anharmonic barrier produced by homogeneous collisions reaches its maximum efficiency and h20 takes its highest value. Therefore, it seems clear that to apply McRae’s method at initial pressure conditions where tc ∼ tp it is necessary to
{
ha20, if P < P′ a h20 ) h20 + m (P - P′), if P′ < P < P′′ ha20 + hb20, if P > P′′
(3)
The parameter ha20 is associated with processes taking place irrespective of the presence of the laser field; i.e. energy pooling and quenching; hb20 is related to processes which can only occur in the presence of infrared photons. So, hb20 may be interpreted as a measure of the maximum weakening that can be induced in the anharmonic barrier, BA, by means of homogeneous collisions at given irradiation conditions. The sign of ha20 is determined by the competition between energy pooling and vibrational quenching, being positive (negative) if the first (second) mechanism dominates. The sign of hb20 is always positive. P′ and P′′ are, respectively, the initial pressure at which the collisional processes associated with hb20 start to be active and that at which they saturate. The slope m gives the rate at which this saturation value is reached and can be regarded as an estimation of the effectiveness with which homogeneous collisions deactivate the effect of BA. The parameters m, P′, P′′, and hb20 are related by
m)
hb20 P′′ - P′
(4)
The value of P′ corresponds to the approximate pressure at which the number of collisions taking place in the time of the pulse becomes enough to start the deactivation of the collisional barrier. This number depends on the irradiation conditions in such a way that, for a low irradiation fluence, several collisions in the time of the pulse may be necessary for the molecule to reach the quasicontinuum. For higher fluences, fewer collisions are required to excite the molecule to this energy regime. When very low initial pressures are used, the time between collisions may be larger than the lifetimes of the excited species, making smaller the influence of both the energy pooling and the quenching of the vibrational excitation and decreasing the absolute value of ha20 down to zero (dotted line in Figure 1). A similar pressure dependence would be introduced in the parameter h11, corresponding to one heterogeneous collision, and also in other higher order parameters, hij (i + j > 2). Nevertheless, we have found in our application of the extended method to CF2HCl and C3F618 that the introduction of such
9728 J. Phys. Chem., Vol. 100, No. 23, 1996
Torresano and Santos
dependence is not necessary, so we have kept a pressure dependence only in h20. From a mathematical point of view, it is worth remarking that our proposed extended method may be reformulated so that it takes a form equivalent to the original model. However, this reformulation would give rise to the occurrence of higher order parameters in the power expansion of the decomposition probability given in eq 2, and the interpretation of the hijs in terms of collision sequences would be difficult. On the other hand, the pressure dependence in h20 that we have introduced (eq 3) retains the collisional significance in the hijs by introducing new parameters, P′, P′′, and m, which also have direct physical meanings. 3. Experimental Section A Lumonics K-103 TEA CO2 laser was employed for the irradiation of the CF2HCl samples. It was equipped with a frontal Ge multimode optics (35% reflection) and a rear diffraction grating with 135 lines/mm blazed at 10.6 µm. The laser operated with a CO2:N2:He mixture in the proportion 8:8: 84. For the irradiation we used the 9R(34) line at 9.201 µm corresponding to a maximum in the multiphoton absorption and dissociation spectra19,20 and nearly resonant with the C-F stretching mode of CF2HCl.21 The laser pulse temporal profile was monitorized with a photon drag detector (Rofin Sinar 7080) and consisted of a spike of 65 ns (fwhm), followed by a tail approximately 1 µs long. This temporal profile was constant throughout the study. Two cylindrical Pyrex cells, 8.8 and 9.5 cm long with 30.5 and 71.0 cm3 total volume, respectively, fitted with NaCl windows, contained the gas during the irradiation. We have used a near parallel irradiation geometry in which the laser beam enters the absorption cell slightly focused by a 2 m focal length NaCl lens. The laser fluence was calculated as the ratio of the pulse energy, measured with a Lumonics 20D pyroelectric detector, and the “1/e” cross-sectional beam area measured at the cell position with a pyroelectric detector array Delta Development Mark IV (these beam areas, also used for computing the irradiation volumes VIs, are given in the captions of the Figures 2 and 3). The estimated uncertainty in the absolute values of the fluence was around 8% (5% being a constant error arising from the nominal detector calibration factor). Real time absorption measurements were performed by simultaneously irradiating the cell with the IR laser beam and a CW UV beam from a 200 W Xe-Hg high-pressure discharge lamp in a crossed configuration setup described elsewhere.22 Matheson CF2HCl (99.9%) was used without further purification. Sample pressures in the cell were measured with two (0-1 and 0-10 mbar) MKS Baratron gauges. The dissociation yield was determined by infrared spectrophotometry, monitoring the change in the absorbance of the 1115 cm-1 CF2HCl band, using a Perkin Elmer FTIR spectrophotometer model 1725X. As a measure of the C2F4 proportion we have used
δ)
2[C2F4] ∆[CF2HCl]
(5)
where ∆[CF2HCl] denotes the change in the CF2HCl concentration due to the dissociation, and [C2F4] is the concentration of C2F4 also determined by infrared spectroscopy using measurements of its absorption band23 at 1189 cm-1. The parameter δ takes on a value 1 if C2F4 and HCl are the only dissociation products formed through the mechanisms given in eqs 7 and 8.
Figure 2. Fraction of CF2HCl molecules remaining in the 8.8 cm long cell after dissociation versus the number of laser pulses. Solid lines represent the fit of the experimental points to the extended method described in the text. The irradiation fluence is φ ) 2.6 J cm-2, and beam area is 0.27 ( 0.01 cm2. The ordinate average uncertainty is ≈0.01.
Figure 3. The same as in Figure 2 for φ ) 5.9 J cm-2. The beam area is 0.45 ( 0.01 cm2, and the experiments were made in the 9.5 cm long cell. The ordinate average uncertainty is ≈0.015.
4. Results and Discussion To test our extended method, we have applied it to the MPD of CF2HCl. This molecule can be regarded as a medium-size one,10 and it has been extensively studied, mainly because is a good candidate for deuterium and 13C separation24 and for its potential role in atmospheric chemistry.25 Because of its relatively simple chemistry, CF2HCl has often been chosen as a model molecule in studies of the basic properties of multiphoton dissociation.1,19,26 The multiphoton dissociation yield of CF2HCl versus the number of laser pulses used in the irradiation is shown in Figure 2 for a laser fluence φ ) 2.6 J cm-2 and in Figure 3 for φ ) 5.9 J cm-2. In both cases, results are given for several values of the initial concentration of CF2HCl. Continuous lines on the figures represent yields obtained by applying the extended method described in section 2. In the fits, each experimental point has been weighted by the inverse square of the associated error. The chi-square,27 χ2, for the best fit was 43 for 76 degrees of freedom in the experiments at the lowest fluence and 61 for 62 in the experiments at the highest one. Table 1 shows the relevant parameters of the fits and their standard deviation errors. As we cannot separate in these experiments the collisional effects of C2F4 and HCl, the parameters h11 and h21 are averaged over both dissociation products, and the proportionality constant S has been fixed to 1.
Collisionally Induced Bottleneck Weakening
J. Phys. Chem., Vol. 100, No. 23, 1996 9729
TABLE 1: The Model Parameters and Their Standard Deviations Obtained for the Fits Corresponding to Figures 2 and 3a parameter
Figure 2 (φ ) 2.6 J cm-2)
Figure 3 (φ ) 5.9 J cm-2)
h10 h11 ha20 hb20 P′ P′′ m h21
0.012 ( 0.001 0.078 ( 0.005 0.037 ( 0.003 0.149 ( 0.003 0.59 ( 0.01 1.45 ( 0.04 0.174 ( 0.003 -0.077 ( 0.003
0.052 ( 0.001 0.149 ( 0.006 0.398 ( 0.011b 0 0.73 ( 0.04 0.543 ( 0.012 -0.133 ( 0.008
a P′′ has been computed from the values of hb , P′, and m through 20 eq 4. Units are mbar for P′ and P′′, mbar-1 for h11, ha20, and hb20 and mbar-2 for h21 and m. b Value for the overall parameter h20.
We have found that the fits corresponding to the experimental points at φ ) 2.6 J cm-2 obtained with our modified model significantly improve those obtained by using the original one, even if in the latter we take into account processes associated with two molecular collisions. In this way, if we fit our data with McRae’s model, using the parameters h10, h20, h11, h30, h21, and h12, the minimum value obtained for χ2 is 1090. When we introduce the extended model parameters P′ and m instead of h30 and h12, χ2 decreases to 120. Splitting of the parameter h20 into ha20 and hb20 leads to the final result cited above. The fits of the data at φ ) 5.9 J cm-2 are also better when the modified model is applied, although in this case the improvement is not as large, probably because of the weakening of the anharmonic barrier produced by the higher fluence. In this case, the minimum value obtained for χ2 is 210 for the unextended model (using the same six parameters cited before). The parameter h10, which accounts for the contribution from the pressure independent dissociation of CF2HCl, takes on small values for both fluences. Even at the lowest initial concentration, P0 ) 0.2 mbar, h10 is smaller than the fraction of molecules dissociated per pulse (Figure 4), f, which is defined by4
γn )
(
Nn VI ) 1- f N0 Vc
)
n
(6)
This result indicates that collisional effects provide a significant contribution to the final observed yield, even within fluence and pressure ranges for which some authors claim28 that the MPD of CF2HCl is collisionless. The importance of the laser beam fluence in the weakening of the anharmonic barrier is also shown by the fact that h10 increases up to four times its original value when the fluence is doubled. A weaker BA allows the CF2HCl molecule to reach a higher excitation level, making the molecular RRKM rate faster, hence increasing the collisionless dissociation yield. A similar conclusion could be drawn from the fluence dependence of the parameters ha20, hb20, P′, and m. These results suggest that to characterize the anharmonic barrier of any molecule, a study of the dependence of the parameter h10 on the irradiation fluence should be necessary. For the lowest fluence, the model is able to discriminate between the two collisional mechanisms represented by ha20 and hb20, and so a small contribution to the yield from collisions between excited molecules in the quasicontinuum can be distinguished from the contribution due to the anharmonic barrier deactivation. The initial concentration, P′′, at which the homogeneous collisions induce the maximum weakening of the barrier is 1.45 mbar, in this case. From P′ it is possible to estimate the number of homogeneous collisions required to deactivate BA, which will be dependent on the temporal width
of the IR pulse, tp. Taking tp as the peak pulse width (66 ns in our case), a collision number of 0.4 is obtained; however, in our experiments, the pulse tail contains a relevant amount of the total pulse energy (around 27%), so, relative to the dissociation process, it is reasonable to consider an effective temporal pulse width longer than that corresponding to the peak. Taking tp ) 500 ns (corresponding to 90% of the total pulse energy), we get a maximum number of collisions of three for the obtained value of P′ (0.59 mbar). This result indicates that, even for this rather long pulse, deactivation of BA needs only a few collisions. When the beam fluence is fixed to 5.9 J cm-2, the number of collisions needed to overcome the barrier is lower, implying a smaller pressure P′. This number is so small that the method cannot in fact determine its value with enough accuracy, and it has been therefore set to 0 in the fits. In addition, at this fluence the population of molecules excited to the quasicontinuum is increased, and hence we would expect a larger contribution of energy pooling to the observed dissociation yield. In this situation, the model is able to provide a value for the overall parameter h20 but cannot distinguish between the processes associated with homogeneous collisions taking place in the time of the pulse and after it. The above results together with the smaller value for the h20 saturation pressure, P′′ ) 0.73 mbar, support the existence of a weakening of the anharmonic barrier when higher irradiation fluences are used. In the study of the MPD of CDCl3,3 the positive sign of the parameter h11 was interpreted as due to the absorption of IR laser photons by some of the dissociation products. This energy is transferred to the parent molecules via collisions, leading to an increase in the dissociation yield. In our case, this possibility seems to be unlikely because the unique polyatomic product, C2F4, has a very weak absorption band at the wavelength corresponding to the IR field23 (1087 cm-1). The positive value we obtain for the parameter h11 at both fluences may be explained assuming that heterogeneous collisions also induce a weakening of the barrier, thereby contributing positively to the dissociation process. However, by comparing the values of h11 and hb20, it seems that homogeneous collisions between CF2HCl molecules are more effective in overcoming the bottleneck and increasing the yield than the heterogeneous collisions between the parent molecules and the dissociation products. This result agrees with that obtained for MPD of CF2HCl in the presence of argon.29 Nevertheless, in that work, an [Ar]/[CF2HCl] proportion of 440/1 only produced a 10-fold increase in the yield, whereas increasing the initial parent partial pressure 14 times multiplies it by 7. This suggests a much higher effectiveness of homogeneous compared to heterogeneous collisions in deactivating BA than that implied in our results where h11 ∼ h20. The difference may be caused by the fact that in our case the buffer gases are polyatomic (e.g. C2F4). In these conditions, high amounts of energy can be exchanged between the collisional partners due to the occurrence not only of V-T but also of V-V′ transferences that are absent with monoatomic buffers. Moreover, the rotational structure of C2F4 also provides the possibility of R-R′ intermolecular relaxation. So in this case, heterogeneous collisions may induce the weakening of the two components of the anharmonic barrier, rotational and vibrational, through rotational hole filling and overcoming of the vibrational bottleneck, respectively. These arguments also explain the larger contribution of the vibrational bottleneck to the anharmonic barrier, compared to the rotational one, in the MPD of CF2HCl. The parameter h11 represents the balance between the effects produced by the heterogeneous collisions: the positive contribu-
9730 J. Phys. Chem., Vol. 100, No. 23, 1996
Torresano and Santos
Figure 4. Fraction of dissociated molecules per laser pulse, f, versus the initial CF2HCl pressure in the cell. The number of pulses is 50.
tion to the yield from the weakening of BA in molecules that are bottlenecked in the low-lying levels, and the negative effect of the quenching induced mainly in those molecules that are excited in the quasicontinuum or even above the dissociation limit. This balance is thus directly related to the distribution of the excited molecules under and above the quasicontinuum limit. This could explain the obtained negative sign of h21 (which might appear unexpected given the positive character of h11 and h20), because the homogeneous collision contained in this second-order parameter actually modifies the molecular distribution and can therefore change the balance between the processes associated with the heterogeneous collision that is also included in h21. Figure 4 shows the dependence of the fraction of molecules dissociated per laser pulse, f (eq 5), on the initial CF2HCl pressure, for several values of the laser fluence. For the lowest fluence, the curve has an initial plateau, followed by a region of increasing f. The emergence of this plateau as P0 f 0, can be used as a criterion to define the collisionless regime in multiphoton dissociation.28,30 We can in fact observe in Figure 4 how the extent of this region strongly depends on the fluence: the larger the fluence, the shorter the observed plateau. The occurrence of collisionless dissociation up to 1 mbar of initial pressure (see the plot for φ ) 1.5 J cm-2) could in principle seem somewhat striking, but this may be explained by the rather larger number of collisions needed to deactivate the anharmonic barrier. For this fluence, the number of collisions during the laser pulse is not sufficient, even at pressures of 1 mbar, to start overcoming BA. When the fluence is raised, fewer collisions are required to start the deactivation of BA, leading to a decrease of the upper limit of the observed plateau. The plateau becomes unobservable in Figure 4 at the highest value of fluence (5.9 J cm-2). A similar behavior for the f P0 dependence has been observed by changing the effective temporal pulse width.31 By FTIR spectroscopy, we have not detected dissociation products other than tetrafluoroethylene and hydrogen chlorine, in agreement with the reaction mechanism previously described in the literature32
CF2HCl + nhν f CF2 + HCl
(7)
CF2 + CF2 f C2F4
(8)
In Figure 5 we show the dependence of the proportion of C2F4, δ (eq 5), on the number of laser pulses, n, for the experiments of Figure 2 (φ ) 2.6 J cm-2). It can be seen that δ is a function of the initial pressure and the number of pulses and tends to a constant value, lower than 1, when n increases for a given P0. This saturation value increases as P0 is raised.
Figure 5. Dependence of the proportion of C2F4 formed in the dissociation of CF2HCl (δ, defined in the text) on the number of laser pulses for the same experiments as those shown in Figure 2.
For the experiments of Figure 3 (φ ) 5.9 J cm-2), we have similar results to those in Figure 5, but in this case δ varies in a narrower interval (from 0.8 to 1.0), for the same range of P0 and n. The possible occurrence of some dissociation channels other than eq 7, dependent on fluence and/or initial pressure, could provide an explanation for these plots. To check this possibility, we have carried out UV absorption experiments to detect the formation of CF2. The presence of this radical can be uncovered by measuring its absorption at 249 nm.7,28 Since we obtain a linear dependence between optical density and CF2 concentration, at least up to a pressure of 0.5 mbar, for the two fluences used in this study, eq 7 appears to be the only significant dissociation channel in the MPD of CF2HCl. Other reactions in the MPD of CF2HCl have only been observed under conditions other than those used here33 and in these other studies represented no more than 1% of the total dissociation. Thus, the lack of C2F4 observed in Figure 5 should be attributed to some processes affecting the recombination reaction (eq 8). One process could be the production of a polymer from the CF2. This has already been described in the MPD of CF2HCl induced by a CW CO2 laser,34 where a solid deposit on the cell walls, identified as polytetrafluoroethylene, (CF2-CF2)n, was obtained. We have also found this substance among the products of the MPD of C3F6, induced by pulsed CO2 laser35 (C3F6 also gives rise to CF2 as a dissociation product). The fact that the largest deficit of C2F4 (Figure 5) takes place at low pressure and/or fluence might suggest that CF2 radicals formed from less energetic parents are more likely to polymerize. At high pressures, in order to dissociate before deactivation, the RRKM lifetime needs to be short. This means the energy in the parent molecule and in the product CF2 will be large. Hot CF2 radicals should be less likely to undergo gas-solid polymerization reactions. The fluence dependence may be due to the weakening of the anharmonic barrier that allows the molecule to reach a higher excitation level. The weakening of BA produced at high initial pressure conditions could also contribute to the explanation of the pressure dependence of δ. Though we have not detected any solid deposit in the IR spectroscopic analysis of the irradiated samples of CF2HCl, this may be due to the fact that the polymer largely appears at low fluence where small amounts of dissociation products are formed. Another possibility for the fate of the “missing” C2F4 could be related to some physical interactions between the C2F4 and/ or CF2 and the “inner” cell surface, as it has been suggested in previous work.36
Collisionally Induced Bottleneck Weakening 5. Conclusions We have generalized the method of McRae et al. to quantify the contribution from the different collisional processes to the observed yield in infrared multiphoton dissociation of polyatomic molecules. The introduced modification is essential when the model is applied to experiments at pressures for which the time between collisions is comparable to the effective temporal pulse width. In this way we can distinguish the contributions to the dissociation yield coming from those mechanisms involving one homogeneous collision: i.e. the weakening of the anharmonic barrier and the energy pooling between molecules excited to the quasicontinuum. We have checked this extended method in the study of the multiphoton dissociation of CF2HCl. We have demonstrated the importance of the homogeneous collisions in the weakening of the bottleneck effects, and we have also shown how the fluence determines both the extent of the pressure-independent regime and the influence of the anharmonic barrier in the process of multiphoton dissociation of CF2HCl. The method of McRae et al. is, in our opinion, a powerful tool of easy implementation for studying the role of collisions and intermolecular vibrational energy transfer processes in multipulse dissociation experiments. When extended in the way considered in the present work, the method can provide important information not only about the collisional mechanisms involved in multiphoton dissociation but also about more intimate features of the process, such as the absorption bottleneck strength or the influence of the laser temporal profile. Acknowledgment. The authors acknowledge C. L. Sigu¨enza, P. F. Gonza´lez-Dı´az, L. Dı´az, and G. A. Mena for useful discussions. We are heartily grateful to the anonymous referee for his exhaustive reading of the manuscript and for his valuable comments and suggestions. This work has been carried out with financial support provided by the Spanish DGICYT under Project PB93-0145-C02-02. References and Notes (1) Cantrell, C. D., Ed. Multiple Photon Excitation and Dissociation of Polyatomic Molecules; Topics in Current Physics 35; Springer Verlag: Berlin and Heidelberg, 1986. (2) Letokhov, V. S., Ed. Laser Spectroscopy of Highly Vibrationally Excited Molecules; Adam Hilger: Bristol and New York, 1989. (3) McRae, G. A.; Yamashita, A. B.; Goodale, J. W. J. Chem. Phys. 1990, 92, 5997. (4) Bado, P.; van den Bergh, H. J. Chem. Phys. 1978, 68, 4188.
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