4284
J . Phys. Chem. 1984, 88, 4284-4287
Low-Level Vibrational Relaxation in Single Gas-Surface Encounters. Molecular Structure, Surface, and Temperature Effects V. T. Amorebieta and A. J. Colussi* Department of Chemistry, University of Mar del Plata, 7600 Mar del Plata, Argentina (Received: February 24, 1984)
Direct measurement of the vibrational temperatures attained by different gases after single encounters with hot silica or platinum surfaces at T, have been obtained by modulated-beam mass spectrometry. Vibrational energy accommodation coefficients a, for n-butane, n-octane, and 1-chlorobutane are smaller than one over both surfaces, slightly increase with molecular size or polarity, and are nearly independent of T, between 350 and 700 K. Relaxation is more efficient on platinum.
Introduction The study of gassurface internal energy relaxation has recently become an active field.’-3 It is generally assumed that basic information on the details and magnitude of the interactions involved may be valuable to control not only heat-exchange processes but the outcome of gas-solid reactions. Actually, the very possibility of observing nonequilibrium effects in these systems such as laser induction of heterogeneous reactions by excitation of either the admolecule4 or the substrate5 and, conversely, the desorption of excited species in exothermic catalytic processes6 rests upon the relative rates of chemical change and internal energy tran~fer.~ Several techniques for the fast, efficient, and selectivegeneration and detection of excited species in both phases are now available. Thus, spontaneous infrared or laser-induced fluorescence of small molecules in the gas phase are particularly informative and have been very recently applied to the study of chemiluminescent gas-solid reactioda and rotationally inelastic scattering of diatomics and triatomics.’ Optical methods, however, become progressively inapplicable for modest levels of internal excitation in the case of larger polyatomcs. In this paper we report measurements of vibrational temperature relaxation of n-butane, n-octane and 1-chlorobutane in single encounters with hot silica and platinum surfaces. Postcollision vibrational excitation is directly monitored by mass spectromety based on the sensitive temperature dependence of the fragmentation pattern of molecular ions produced by low-energy electron Modulated molecular beam samplinglo ensures that hot species reach the ionizer region in collision-free trajectories which preserve their energy content. Under these conditions, independent calibration of mass spectra of the different gases as functions of temperature provides an accurate and versatile vibrational thermometer.8 In this connection it should be pointed out that since external rotations as well as translations can be considered adiabatic modes, they will not appreciably influence (1) G. Rosenblatt, Acc. Chem. Res., 14, 42 (1981). (2) (a) J. C. Tully, Acc. Chem. Res., 14, 188 (1981); (b) J. C. Tully, C. W. Muhlhausen, and L. R. Ruby, Ber. Bunsenges. Phys. Chem., 86, 433 (1982). (3) V. P. Zhdanov and K. I . Zamarev, Catal. Rev. Sci. Eng., 24, 373 (1982). and references therein. (4) C. T. Lin and T. D. Z. Atwars, J . Chem. Phys., 68,4233 (1978). ( 5 ) F. A. Houle, IBM Research Report RJ 3661, IBM, Yorktown Heights, NY, 1982; Chem. Phys. Lett., in press. (6) (a) S. L. Bernasek and S. R. Leone, Chem. Phys. Lett., 84,401 (1981): (b) W. A. Sanders and M. C. Lin, “Laser Spectroscopy for Sensitive Detection”, Vol. 286, Society of Photo-Optical Instrumentation Engineers, Redondo Beach, CA, 1981, p 101. (7) D. Ettinger, K. Honma, M. Keil, and J. C. Polanyi, Chem. Phys. Lett., 87. 413 f1982). ‘(8) V: T. Amorebieta and A. J. Colussi, Chem. Phys. Lett., 89, 193 (1982). (9) V. T. Amorebieta and A. J. Colussi, J . Phys. Chem. 86, 2780 (1982). (10) A. J. Colussi and S. W. Benson, Int. J. Chem. Kinet., 10,1091 (1978).
branching ratios in the unimolecular decomposition of molecular ions.” The nonfixed energy in their active modes then consists of the excess energy imparted by vertical ionization plus the variable vibrational thermal energy already present in the neutral precursor.*2 Present data confirm and extend previous results regarding temperature effects obtained by the same technique.1314 Two additional facts emerge: vibrational energy accomodation coefficients a, increase somewhat with molecular size or polarity and markedly depend on surface material. A trapping mechanism in which the admolecule spends a finite time on the surface coupled to the lattice modes of the solid is consistent with these observations.’~~ On the other hand, the weak temperature dependence of a, suggests an exponential increase of vibrational exchange transition probabilities to nearly compensate for the shorter residence times attained at larger temperatures. Such is the behavior predicted by current theories of phonon-vibron relaxation in condensed phases.I5
Experimental Section The experimental setup consisted of three sections: (1) a standard gas-handling vacuum manifold, (2) the hot target surface ( S , Figure 1) contained within a molecular flow cell, plus the ancillary heating and surface temperature measurement devices, and (3) the gas-phase vibrational thermometer, realized here as a modulated-beam spectrometer (EMBA 11, Extranuclear Laboratories) (Figure 2). The cylindrical Pyrex cell (25-mm id., 42 mm long) was coupled to the differential pumping chamber of the mass spectrometer (A) by means of a small circular opening (diameter = 2 mm) drilled at the center of its front base. A clear silica window (W) covered the back of the cell, allowing full illumination of the target. Steady-state flows of the different vapors were admitted into the cell through the inlet I. The variable flow rates were determined by measuring pressure drops in a calibrated volume as a function of time with a Baratron capacitance manometer and were always kept below 10l6 molecules s-’. The operating cell pressure and the corresponding mean free paths were lower than 2 mtorr and longer than 2.5 cm, respectively. These conditions ensured molecular flow through the outlet and avoided gas scattering within the cell. We have also verified that our results were insensitive to a fourfold reduction of flow rates. The cell walls were always (11) D. W. Setser in “International Review of Science: Physical Chemistry”, Series One, Vol. 9, J. C. Polanyi, Ed., Butterworths, London, 1972. (12) M. L. Vestal in “Fundamental Processes in Radiation Chemistry”, P. Ausloos, Ed., Wiley, New York, 1968, Chapter 2. (13) V. T. Amorebieta and A. J. Colussi, J . Phys. Chem., 86, 3058 (1982). (14) V. T. Amorebieta and A. J. Colussi, Chem. Phys. Lett., 104, 221 (1984). (15) H. Eyring, S. H. Lin, and S. M. Lin, “Basic Chemical Kinetics”, Wiley, New York, 1980, p 350.
0022-3654/84/2088-4284$0 1.5010 0 1984 American Chemical Society
Low-Level Vibrational Relaxation 'I
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984 4285
I
The measured Cartesian in-phase xJ and out-of-phase yJ signal intensities corresponding to the different ions j were converted to polar coordinates: the signal amplitudes I, and their phase shifts p, Phase lags qJ,relative to the reference signal generated at the chopper, arise from the finite times, t,, that the parent neutral spends flying the distance l1between the chopper and the ionizer, plus the time ti taken by the ion to travel the length of the mass filter, 12, and are given by the expression qJ = w(t, + t,)) More explicitly
Figure 1. Target surface S is held by thermocouple wires t. Radiative heating is provided by lamp L. Typical pressures in the cell and chamber A and B are 1 X lo-*, lo4, and lod torr, respectively. Light and P h o t o d i o d e
Ionizer
-,
Modulator
Ref
Signal
Figure 2. Schematic view of the modulated-beam mass spectrometer (not to scale). The circled region is shown in Figure 1. Signal and ref signals are fed to a lock-in amplifier.
maintained at room temperature (To = 295 f 2 K). The target consisted of a small flat pellet (7 mm X 7 mm X 1 mm) of clear fused silica mounted on a small piece of folded platinum foil (0.05mm thick). The pellet faced the exit orifice at about 2-mm separation and was optically aligned with the mass spectrometer ionizer region. By removal of the pellet the bright inner surface of the mount could be exposed. The back of the mount was externally coated with carbon black deposited upon an adherent layer of WSe2 to optimize radiation absorption. Four thin (diameter = 0.1 mm) copper-constantan thermocouple wires, pressed between the mount folds, monitored the temperature and held the target in place with a minimum of heat conduction. The small assembly could be evenly heated up to 750 K by irradiation with a collimated light beam from a Schceffel illumination system. The light source was a 500-W Hg vapor lamp whose output could be conveniently attenuated with fine mesh screens. The light beam had a cross section about twice as large as that of the target. Under these conditions, only those molecules undergoing their last collision with the hot target could effuse from the cell in the forward direction. The rest was geometrically excluded from the beam by an additional collimating aperture (diameter = 1 mm) located in the wall separating chambers A and B (Figure 2)about 35 mm ahead of the cell. Moreover, since the target is convex and its overall area is about 44 times smaller than the cell walls, previous collisions with its surface were inevitably followed by many others against the cell body, a process that effectively kept the bulk of the gas at room temperature. The molecular beam produced in chamber A was mechanically chopped at w = 1 kHz and then ionized at 15 eV by electron impact.8 The mass analysis was performed by a quadrupole mass filter. Detector signals were preamplified and fed to a phasesensitive detector operating at the chopping frequency. In this manner, the recorded output only displayed the mass spectra of the species contained in the modulated molecular beam, Le., those that last collided with the hot target.g
where M and m, are the masses of the neutral parent and ion j , respectively; qJ is the ion charge, T the translational temperature of the beam, and V the potential at which the ions are created. cpo is an arbitrary instrumental constant. Equation 1 is particularly useful in the present context, since a plot of pJ vs. m,'/* at constant T and Vshould only be linear if a single neutral were present in the beam. This condition can then be used to check whether the enhancement of lighter ions in the mass spectra of heated gases is due to thermal energy effects in the decomposition of molecular ions or arises from contributions made by smaller neutral fragments produced by thermal decomposition of gases on the hot target. Also since the ZJ's are independent of q,loss of beam modulation due to broader velocity distributions at higher temperatures will affect all amplitudes to the same extent and therefore the ratios I,/Zk, on which we base our analysis, are strictly independent of translational temperatures T.8 The experiments designed to investigate the temperature dependence of dissociative ionization were carried out by flowing the gases through a uniformly heated fused silica cylinder (2-mm i.d., 10 cm long). Gas pressures inside this tube were low enough so that molecualr flow conditions prevailed throughout. Since it can be shown that molecules made about 100 collisions with the walls, it can be safely assumed that they left the tube fully thermalized. The average themperature of the beam gas was measured with a chromel-alumel thermocouple attached to the tip of the silica tube.8 n-Butane (Matheson, CP), n-octane, and 1-chlorobutane (Carlo Erba, reagent) were used as received. Their mass spectra at 70 eV coincided with literature reports. Bright platinum foil (99.9%) and clear fused silica (Heraeus) were carefully cleaned and heated under vacuum before use. Results and Discussion The mass spectra of n-butane, n-octane, and 1 -chlorobutane obtained at 15 eV still display several fragment ions in addition to the parent peaks at m / e 58, 114,and 92, respectively. We have chosen those fragments at m l e 28 and 43 for n-C4Hlo,at m l e 43 and 85 for n-C8Hla,and at m l e 41,43,and 56 for n-C,H9C1 (Figure and studied their relative signal amplitudes 1431158, 12a/158 3), 1851143 (Figure 4) and 143/156r 141/156 (Figure 5) as functions of gas temperatures (curves a). These plots represent the calibration curves of a sensitive gauge of vibrational thermal energy content. The linear dependence of phase shifts pJ on rnJij2 for n-octane, shown in Figure 6 , is typical of all experiments described in this paper. We conclude that no decomposition took place before ionization and that we are actually dealing with genuine thermal effects on ion fragmentation. The results of vibrational temperature measurements after single encounters with platinum and silica surfaces at T, are shown in curves a and b, respectively (Figures 3-5). They were quite reproducible, indicating that target surfaces were fully seasoned. Moreover, they clearly show that vibrations never reach T, in a single collision. Data for n-butane and n-octane on silica, which had been reported elsewhere, have been included here for comparison.14 In principle, level- or mode-selective vibrational excitation is possible and would produce species having characteristic dissociative ionization patterns. For n-butane and 1-chlorobutane the fact that vibrational temperatures derived from the ratios 128/158 or 14,/158 and 14i/156 or 143/156 respectively, were indentical within the limits of random experimental errors may be taken as
Amorebieta and Colussi
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984
4286
1.5
ru i4 0 N 00
00
.5
T/
K Figure 3. Ratio of ion signal amplitudes as function of surface temperature T, at 15 eV for n-butane: (a) fully thermalized after ca. 100 collisions, (b) after one collision with Pt, (c) after one collision with silica surfaces.
1.5
I
.7
0
d
2 -
1.
.5
.3 Figure 4. Ratio of ion signal amplitudes as function of surface temperature T, at 15 eV for n-octane: (a) fully thermalized after ca. 100 collisions, (b) after one collision with Pt, (c) after one collision with silica surfaces.
evicence of well-defined postcollisional temperatures T I . Vibrational energy accommodation coefficients aV,given by eq 2, can be now calculated by using available heat capacity data % = [Ev(T,) - Ev(To)I/[Ev(Ts) - EV(T0)I to evaluate the vibrational energy differences:
(2)
Our experimental results are presented as a set of aV(T,) values for each gas on both surfaces (Figure 7). It is apparent that all molecules relax more efficiently on platinum. On the other hand, when data obtained on the same surface are compared, a slight
I
I
400
I
1
600
I
I
800
T/K Figure 5. Ratio of ion signal amplitudes as functions of surface temperature T, at 15 eV for 1-chlorobutane: (a) fully thermalized after ca. 100 collisions, (b) after one collision with Pt, (c) after one collision with
silica surfaces. increase of CY, with either mass or polarity is observed. Extrapolation of present results on platinum to 300 K yields values of CY, similar to those estimated by Rosenblatt et al. from overall accommodation coefficients of hydrocarbons on metals.16 It (16) C. W. Draper and G. M. Rosenblatt, J . Chern. Phys., 69, 1465 (1978).
Low-Level Vibrational Relaxation
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984 4287 counters in the mechanism of gas-surface internal energy exchange.' This view is also consistent with kinetic and thermodynamic parameters for gassolid physical adsorption. Assuming negligible activation barriers and heats of adsorption at least as large as the enthalpies of vaporization' it is clear that the chances of sticking to the surface are controlled by the probability of transferring some of this energy to the solid during collision
lifetime^.^
7
9 [mj/wl'"
11
Figure 6. Phase shifts for the different ion fragments of n-C8Hlstas function of (ion at beam temperatures of (a) 300, (b) 344, (c) 461, and (d) 822 K. The linear plots indicate that a single neutral was present in the beam at all temperatures.
t 0.3
tc t
I
0 0 -
I
o---o-o-~--.
0
I
n-CEH18 o-o-o-o-_o~
o-o-
40.7
600
400
X/K
Figure 7. Vibrational accommodation coefficients avas function of T,: (0) on platinum, 0 on silica.
should be pointed out that internal energy relaxation data derived from high-speed vibration experiments are essentially indirect since they require additional assumptions about the extent of rotational accommodation. However, the effect of such contributions on a, becomes less important as vibrational heat capacity increases with molecular complexity. Considering the low efficiency (Pl05 of nonresonant V-V transfer in isolated gas-phase collisions17and the fact that molecular frequencies barely overlap the phonon spectra of solids, present data strongly suggest the involvement of long-live en(17) J. T. Yardley, "Introduction to Molecular Energy Transfer", Academic Press, New York, 1980, Chapter 5.
A simple model for V-V transver, similar to the one proposed by Rapp and Kassal," shows that fast deactivation of the dense upper vibrational manifold of the strongly anharmonic admolecule-substrate bond is indeed possible, mainly due to nearresonance with lattice average freq~encies.~ An extension of this model to the case of adsorption of highly excited molecules is not yet available. However, the above arguments suggest that the vibrational quasicontinuum of relatively simple molecules above 5000 cm-' may efficiently exchange energy with the newly formed bond, thereby reducing the probability of sticking. Low-level interfacial energy transfer may occur after the admolecule becomes attached to the surface. The mechanism of exchange must involve multiphonon transitions in the solid as a result of the relatively wide spacing between the lower molecular Current theories of vibrational relaxation of isolated centers in condensed phases indicate that the probability of phonon-vibron transitions, K , increases with (1) the coupling strength parameter So,(2) the reciprocal of the reduced frequency w* = wM/wL, where w M and wL are the molecular and average lattice frequencies, and (3) the reduced temperature T* = kTJhw,. Moreover, this variation becomes exponential K = KO exp(aT*) for T* > 0.3.15 According to this picture the amount of energy transferred per encounter is simply given by the product of transition probabilities times the duration of the interaction: AE = KT.Since residence times T are an inverse function of T,, r = ro exp(Eads/kTS),it follows that the weak temperature dependence of a, observed in these experiments actually implies the nearly exponential increase of K with T, predicted by theory. Thus, although theory is incapable of estimating relaxation rates a priori and, on the other hand, it is not possible to vary the relevant experimental parameters independently, we feel that the above analysis affords some useful insights into the mechanisms of vibrational energy exchange in gas-surface encounters. For the very important case of excitation of upper vibrational levels in the quasicontinuum of polyatomics, lower values of w* are possible and therefore a weaker temperature variation of K would be predicted.15 As a consequence, the exponential decrease of T will, in general, override the rise of K leading to the actual decline of a, with T,. Conflicting reports concerning the temperature dependence of a, for the population of reactive levels of cyclobutene over silica20,2'do not warrant further speculation at this time. Additional experimental tests are under way. Acknowledgment. This work was supported by grants from CIC, SUBCYT, and CONICET of Argentina. Registry No. n-C4Hlo,106-97-8; n-C8H,,, 11 1-65-9; n-C,H,Cl, 69-3; Pt, 7440-06-4;
109-
silica, 7631-86-9.
(18) D. Rapp and T. Kassal, Chem. Rev., 69, 61 (1969). (19) D. J. Diestler, J . Chem. Phys., 60, 2692 (1974). (20) D. F. Kelley, T. Kasai, and B. S. Rabinovitch, J . Phys. Chem., 85, 1100 (1981). (21) R. Arakawa and B. S. Rabinovitch, J . Phys. Chem.. 86,4772 (1982).
