Proceedings of the 3rd Annual ISC Research Symposium ISCRS 9 April 14, 9, Rolla, Missouri PHOTO-DISSOCIATION OF CO GAS BY USING TWO LASERS Zhi Liang MAE department/zlch5@mst.edu Dr. Hai-Lung Tsai MAE department/tsai@mst.edu ABSTRACT The objective of ab initio calculations of photo-dissociation of molecules is to determine the optimized laser parameters so that the desired free radicals (CO, CH, ) and conditions can be produced. These free radicals and conditions may facilitate the formation of diamond or diamond-like thin films. In order to efficiently produce the desired free radicals, one needs to either choose appropriate laser frequency (one-laser-dissociation case) or involve a proper intermediate state (multi-laser-dissociation case). In this paper, we use an ab initio model of two-laser dissociation of CO molecules to show the influences of different combinations of laser parameters (laser intensity, laser pulse duration, and time lag between two laser pulses) on the population of free radicals. The optimized laser parameters will be used as reference parameters in the experiments. 1. INTRODUCTION It is well-known, the natural conditions of diamond formation require extremely high pressure (4.5 ~ 6 GPa) and high temperature (1 ~ 16 K) [1]. When high temperature and high pressure (HTHP) techniques were used to produce diamond, the growth speed is about 1μm/hr. However, the HTHP condition is not the unique condition under which diamond grows. Over the past tens of years, a lot of research groups such as Y.F. Lu s group found diamond particles on a copper substrate as a result of interactions between the substrate and a C H /C H 4 /O combustion-flame []. Although the real mechanism for the diamond formation in this condition is still unclear, it was found from the spectrometer that free radicals such as CO, CH, and OH exist in the flame. The diamonds may come from the interactions between these active free radicals. The growing speed of diamond by this mechanism is supposed to be much faster (~1μm/s) than the traditional HTHP techniques if a large population of those desired free radicals can be sustained for a period of time. In addition to using a flame to produce free radicals, the desired free radicals can be also obtained from precursor gases like CO, C H 4 by photodissociations at room temperature and atmospheric pressure. In an ongoing research project on diamond thin film coating by using multiple lasers, we propose to produce those free radicals by photo-dissociation of molecules. To produce desired free radicals, a particular bond in the molecule should be broken by lasers. Hence, bond-selective fragmentation is important in producing desired free radicals. It is proved that one-laser dissociation is not able to effectively enhance the population of desired free radical. While bond-selective fragmentation is controllable by two-laser dissociations if an infrared laser is firstly applied to excite the molecule to a particular vibrational energy state, and then a UV laser is applied to dissociate the molecule [3-5]. In order to efficiently produce the desired free radicals, we use an ab initio model to study the influence of laser parameters on the population of the desired free radicals in two-laser dissociation case. This model is based on the theory of Shapiro [6]. The model of photo-dissociation of molecules by two lasers is introduced in section. Use this model, we will show the influences of laser intensity, pulse durations and time lag between two laser pulses on the population of free radicals in section 3. Conclusions are drawn in section 4.. AB INITIO MODEL FOR PHOTO-DISSOCIATIONS At room temperature and atmospheric pressure, most of molecules are on their ground energy states. To simplify our calculation, we consider a molecule initially on its ground energy state ψ is broken apart into two fragments as a result of s irradiation of two lasers. Lasers are considered as classical electro-magnetic waves. ε( t) = ˆ εε 1 1( t) cos( ω1t) + ˆ εε ( t) cos( ωt) (1) In Eq. (1), ˆε and 1 ˆε are polarizations of two lasers, ω and 1 ω are laser frequencies, ε 1 ( t ) and ε ( t) are magnitudes of laser electric fields. Fig. 1 two-laser dissociation diagram Fig. 1 shows a two-laser dissociation diagram. Assume that the first laser is in near resonance with the transition from the ground energy state ψ to the intermediate energy state s ψ and 1
the second laser is near resonance with the transition from the intermediate state ψ to final continuum states ψ ( E,n ) (where n incorporates the identity of the free radicals and their electronic, vibrational, rotational, etc. quantum numbers), the full time-dependent wave functions can be expanded as Eq. (). ( ) s s( ) ψs ( ) + E,n ψ n E E i t i t ψ E i t Ψ t = b t e + b t e ( ) (,n ) de b t E e In order to produce a large population of desired free radicals, short-pulse lasers with high laser intensities are used. Both laser pulses are assumed to be a Gaussian function of time. ε tt c 1 α1 ( t) = ε e, ε ( t) 1 L1 tt c α εle () = (3) In Eq. (3), each of expression contains three adjustable parameters, i.e. pulse center t c, pulse durationα, and magnitude of electric field at the pulse centerε. When two lasers are L involved in the dissociation process, there is one more parameter to be considered, i.e. time lag between two laser pulses t = tc t. 1 c The populations of molecules at different energy states as b t functions of time are determined by coefficients ( ) s and be,n ( t ) in Eq. (). ( ) ( ), ( ) ( ) ( ) ( ),,, In Eq. (4), Ps ( t ), P ( t ) and PEn, ( ) s s En En b t, ( ) P t = b t P t = b t P t = b t (4) t represent the populations at the ground energy state, the intermediate energy state and the continuum state as functions of time, respectively. We assume that initially all molecules are on their ground energy state. Hence, P s ( ) = 1 and P ( ) = P En, ( ) =. In order to determine the variations of populations on different energy states as a result of irradiation of lasers, Eq. () is substituted into the time-dependent Schrödinger equation Ψ i = Hˆ totalψ where Hˆ ˆ total = H µ ε ( t) t (5) In Eq. (5), Ĥ is the radiation-free molecular Hamiltonian and µ is the transition dipole moment operator. bs ( t ), b ( t ) and be,n ( t ) are determined by solving Eq. 6(a) through Eq. 6(c) simultaneously. dbs i =µ s,ε1 ( t) exp ( i 1t) b ( t) (6a) dt db i =µ s,ε1 ( t) exp ( i 1t) bs() t i ε ( t) µ ( ω ) b () t (6b) dt 1 t ben, ( t) = µ ( E, n ) dt ' ε( t ') exp ( i ') Et b( t ') (6c) i In Eq. (6), 1 and are the deviations of laser frequencies E from the resonant frequencies for the corresponding transitions. In the calculation we set the deviations to a minimal detuning.1 cm -1. In Eq. (6), µ and s, µ ( E,n ) represent transition dipole moments of the transition from the ground energy state ψ to the intermediate energy state s ψ and the transition from the intermediate state ψ E,n, respectively. ( ) ( ) ψ to final continuum state ( ) µ ω = π µ En, is the sum of the n transition dipole moments. The quantities mentioned above are all molecular related parameters. They are independent of laser parameters. For a specific molecule, these quantities are all constants. They can be determined by ab initio calculations or by experiments. We have shown how to determine these constants by ab initio method in ISC Symposium of last year. The details are shown in our paper [7] published last year. In the current paper, we use these calculated constants in our model to do calculations. We will use CO molecules as an example to study variation of population of free radicals produced by two- laser dissociations under different combinations of laser parameters. For CO molecules, the following molecular properties are used. TABLE 1 transition energy and dipole moment of CO Transitions Properties Ground state Intermediate state Intermediate state Continuum state Energy (cm -1 ) 349 53 dipole moment (a.u.).13 13. We will optimize the laser parameters to obtain the maximum population of desired free radicals. 3. CALCULATION RESULTS For the reaction 1 1 1 349 53 () cm ω = ω = cm CO CO(1) CO( n) + O We firstly use an infrared laser to excite the CO molecule from ground energy state to the first excited state of asymmetric stretching vibration mode, and then dissociate the CO molecule by an UV laser. 3.1. Influences of laser intensities and time lag between two laser pulses In the first step, we fix the pulse durations of both lasers to 16 ps. The maximum laser intensity of the nd laser (UV laser) is 19 fixed at I = 1.6 1 W cm which is almost the maximal intensity that can be obtained from a pico-second laser. The maximum laser intensity of the 1 st laser (infrared) varies. For different combinations of laser intensities, we calculated the variation of total population of free radicals as a function of time lag between two laser pulses. The results are shown in Fig. 17. The red solid curves correspond to I1 =.6 1 W cm, the
18 green dashed curves correspond to I1 = 1.4 1 W cm, the 18 blue dash-dot curves correspond to I1 = 4.16 1 W cm. I1 = 4.16 1 W cm 18 sensitive to the time lag between two laser pulses. It is not easy to make two laser pulses reach the same point simultaneously with a time error of only several picoseconds. Hence larger pulse duration makes the experiment more controllable. However, the maximum population of free radicals is insensitive to the variation of pulse duration of the infrared laser. With the increase of the pulse duration, the maximum population only increases with a small percentage. I1 = 1.4 1 W cm 18 I1 =.6 1 W cm 17 Fig. population of free radical CO vs. time lag between two 19 laser pulses if I = 1.6 1 W cm. From Fig. we can see if the intensity of laser pulse (UV laser) is constant, the population of free radicals always increase with the intensity of laser pulse 1 (infrared laser). This is because an infrared laser with higher intensity excites the molecule more efficiently from the ground state to the intermediate vibrational state. The molecules at the intermediate state will be dissociated directly by laser pulse. The population of the free radical strongly depends on the time lag between two laser pulses (negative time lag means the infrared laser is applied earlier than the UV laser, positive time lag means the infrared laser is applied later than the UV laser). From Fig., we can see when the intensity of the infrared laser is relatively low (red curve), the maximum population of free radicals is obtained when the infrared laser is applied about 3ps earlier than the UV laser. If the intensity of the infrared laser is high (green and blue curve), the maximum population of free radicals is obtained when two laser pulses are applied simultaneously. 3.. Influence of pulse duration In the second step, we fix the maximum laser intensities of the 18 infrared laser to I 1 = 1.4 1 W cm and UV laser to 19 I = 1.6 1 W cm. The pulse duration of the UV laser is fixed to 16 ps. The pulse duration of the infrared laser varies. For different combinations of pulse durations, we calculated the variation of total population of free radicals as a function of time lag between two laser pulses. The results are shown in Fig. 3. In Fig. 3 α=7,9,11,13,15ps describe the different pulse durations of the infrared laser. From Fig. 3 we can see when pulse duration of the UV laser is a constant, with the increase of pulse duration of the infrared laser, the population of free radicals becomes less Fig. 3 influence of pulse duration on free radical populations 3.3. Photo-dissociation by two nano-second lasers The laser parameters used in the above calculations are all chosen for calculation convenience. However, due to the limitation of laser facilities, laser parameters in the calculations should be more consistent with the existing lasers. The two short-pulse lasers available in our laser micro-machining lab are a nano-second laser whose pulse duration varies from 3ns to 9ns and a femto-second laser whose pulse duration varies from 4fs to 1 fs. Using the parameters of existing lasers, we firstly try to dissociate the CO molecule with two nano-second laser. The pulse durations of both lasers are fixed at 3. ns. The peak intensities of the 1 st nano-second laser (infrared laser) and nd 13 nano-second laser (UV laser) are fixed at1.66 1 W cm 14 and.1 1 W cm, respectively. These two laser intensities are almost the maximum laser intensity that can be obtained by a nano-second laser. Obviously, the peak laser intensity of a nano-second laser is much lower than a pico-second laser and a femto-second laser. Under this combination of laser parameters, the populations of the CO molecule at different energy states as function of time are shown in Fig. 4(a) through 4(c). In the application of two laser pulses, the center of pulse is fixed at 5ns. The center of pulse 1 varies so that we can study the influence of time lag between two laser pulses on the population of free radicals. In Fig. 4(a), the nd nano-second laser (UV laser) is applied 1ns earlier than the 1 st nano-second laser 3
(a) (b) (c) Fig. 4 Populations of molecules at different states vs. time, Red solid curve shows the population on the ground energy state, green dashed curve shows the population on the excited vibrational state, the blue dash-dot curve shows the total population of free radicals (infrared laser). In Fig. 4(b), two laser pulses are applied simultaneously. In Fig. 4(c), the UV laser is applied 1ns later than the infrared laser. From Fig. 4 we can see the intensity of the infrared laser pulse is strong enough to excite molecules from the ground state to the intermediate state. The maximum population of molecules at the intermediate state (green dashed curve) could reach more than 9%. Consistent with the previous results, the maximum population of free radicals is obtained when two lasers are applied simultaneously. The problem is the intensity of UV laser is too weak to dissociate molecules from the intermediate state efficiently even though we have chosen the largest possible intensity of the nano-second laser. The maximal population of free radicals is very small (~.1). To solve this problem, we replace the nd nano-second laser pulse (UV laser) by a high-intensity femto-second laser pulse. 3.4. Photo-dissociation by a combination of a nanosecond laser and a femto-second laser In this part of calculation, the pulse duration of 1 st laser (infrared laser) is still fixed at 3. ns. The laser pulse has peak intensity at 5ns. The pulse duration of the nd laser (UV laser) is fixed at 1 fs. The problem is when we should apply the femto-second laser to the molecules. The femto-second laser is used to dissociate the molecules from the intermediate state. Hence, we should apply the femto-second laser when the population at the intermediate state reaches the maximum. Fig. 5 shows variation of population of the ground energy state and the intermediate state with time if only the infrared laser is applied to excite molecule from ground state to intermediate state. Fig. 5 variation of populations on ground and intermediate state as a result of one laser excitation From Fig. 5 we can see population of the intermediate state reaches the maximum at the center (t=5ns) of the nano-second laser pulse. Hence, femto-second laser should be applied at the center of the nano-second laser. Since a nano-second laser with laser intensity 13 1.66 1 W cm is strong enough to efficiently populate the molecule from the ground energy state to the intermediate state, we fix the intensity of the nano-second laser to this value and vary the intensity of the femto-second laser from.1 1 W cm to 4.4 1 W cm. Fig. 6(a) and 6(c) show the variation of populations at different combinations of laser intensities. Fig. 6(b) and 6(d) show the details of variation of populations when the femto-second laser is applied. Note Fig. 6(b) and (d) have different time scales from Fig. 6(a) and Fig. 6(c). 4
From Fig. 6 we can see during the application of the femtosecond laser pulse, a large population of molecules is pumped from the intermediate state to continuum states, the population on the ground energy state is almost unaffected during this process. The final populations of free radicals increase with the intensity of femto-second laser. Some populations at continuum states gradually flow back to the ground and the intermediate state due to the spontaneous emission after femto-second laser is applied. I =.1 1 W cm Fig. 6(a) Populations on different states vs. time I = 4.4 1 W cm Fig. 6(b) variation of populations when fs laser is applied Fig. 6(c) Populations on different states vs. time Fig. 6(d) variation of populations when fs laser is applied 4. CONCLUSIONS The influences of laser parameters on the population of free radicals are discussed by using an ab initio model. In two-laser dissociation of molecules, it is found the maximum free radical population is obtained if two lasers are applied simultaneously. With the increase of pulse duration of the infrared laser, the population of free radicals becomes less sensitive to the time lag between two laser pulses. But the maximum population of free radicals is almost not affected. Using existing laser parameters, it is not possible to dissociate a CO molecule efficiently by using a combination of two nano-second lasers. In order to make the two-laser dissociation process more controllable and efficient, it is necessary to use the combination of one nano-second laser and one femto-second laser. The femto-second laser should be applied at the center of the nano-second laser pulse in order to obtain the maximum population of free radicals. The current model can be extended to photo-dissociation of other molecules if the molecular properties like transition dipole moments and transition energies for the corresponding 5
molecules are available from either ab initio calculations or experiments. 8. ACKNOWLEDGMENTS This project is supported by ISC and ONR. Thanks to Dr. Tsai for giving me instructions in my research. 9. REFERENCES [1] Diamonds and Diamond Grading: Lesson 4 How diamonds form. Gemological Institute of America, Calsbad, California,. [] Han, Y.X., Ling, H., Sun, J., Zhao, M., Gebre, T. and Lu, Y.F., 8, Enhanced diamond nucleation and growth on copper substrates by laser assisted combustion- flame method, Appl. Surf. Sci., 54, pp. 54-58 [3] Amstrup, B., Henriksen, N.E., 1996, Two-pulse laser control of bond-selective fragmentation, J. Chem. Phys., 15, pp. 9115-91. [4] Rozgonyi, T., Gonzalez, L., 8, Control of photodissociation of CH BrCl using a few-cycle IR driving laser pulse and a UV control pulse, Chem. Phys. Lett., 459, pp. 39-43. [5] Wal, R.L. V., Scott, J.L., and Crim, F.F., 199, An experimental and theoretical study of the bond selected photodissociation of HOD, J. Chem. Phys., 94, pp. 3548-3555. [6] Shapiro, M., 1994, Theory of one- and two-photon dissociation with strong laser pulses, J. Chem. Phys. 11, pp. 3844-3851 [7] Liang, Z., Tsai, H.L., 8, Determinations of vibrational energy levels and transition dipole moments of CO molecules by density functional theory, J. Mol. Spect., 5, pp. 18-114 6