J. Phys. Chem. 1986, 90, 1232-1234
1232
but even for a radius of 4 8, the repulsion is smaller than the PB prediction. In this case, the reduced repulsion can be fitted to the PB force law by choosing an effective surface charge of 0.0088 C/m2, while the real value is 0.224 C/m2. Most of this large reduction can be described as a nonspecific “adsorption” of the ions to the surfaces caused by the electrostatic pair-correlational effect. The relationship between the reduced repulsion and the correlationally induced increase in density of the ions close to the walls is also illustrated in our study of fully adsorbed, but laterally mobile, ions on two surfaces.’ W e found that the attractive part of the force curve for pointlike divalent ions is similar whether all ions are fully adsorbed on the surfaces or free to dissociate and form a diffuse double layer (as they are in this study). This holds down to a separation of about 5 A, where, in the latter case, the double layers start to overlap strongly, making the force below 2 A turn repulsive again. A detail of the pressure calculation for the ion radius of 3 A is shown in Figure 3 as an illustration of the behavior of the different contributions to the pressure between the surfaces. The repulsive kinetic term RTp(midpoint) is the only term considered in the PB theory (but with a much higher value of the concentration than obtained here). The electrostatic pair-correlation contribution is always attractive and becomes dominant in a range of separations between about 2 and 19 A. The hard-core repulsion term (core-core contact across the midplane) becomes significant relatively suddenly and then, as the surfaces approach each other, it becomes smaller again because the total momentum transfer between the ions is increasingly taking place in the direction along ~
~~
(7) R. Kjellander and S MarEelja, Chem. Scr., 25, 112 (1985).
the surfaces. Note that the ionic radius affects all three terms via the distribution functions. Therefore, we have a size effect also at larger separations, where the core-core contact term is vanishingly small. The repulsive core-core contribution quickly becomes larger with increasing ion radius, e.g. for a 3.5-A radius it has a maximum value of approximately 5.5RT at the separation of 5 A. The sudden change in slope of the corresponding force curve in Figure 2 at the separation 13 A is due to the onset of this contribution for smaller distances. For even larger radii the core term in the pressure dominates for moderate to small wall separations. The examples discussed above show that, for primitive model electrolytes, the PB theory can often provide a remarkably good fit to the accurately calculated double-layer repulsion. However, the fitted parameters in the PB force law will not always be the real physical parameters of the system. If we restrict ourselves to larger separations, the overlap of the two double layers is small and the interaction between the surfaces is transmitted via a dilute ionic solution. Then, the PB theory constitutes a valid limiting law provided the situation near the surfaces, where the PB description breaks down, is taken into account by changing, e.g., the real surface charge to a different, “effective” charge. The surface adsorption of ions deduced on the basis of the PB theory may then partly correspond to the increase in ion density near the surfaces caused by the electrostatic ion-ion correlations rather than by some specific ion-surface interaction. Note Added in Proof. We have now extended the study to the corresponding system in equilibrium with a bulk electrolyte solution (work to be published). We found that the same mechanisms are operative in both cases, leading to the same general picture at least for moderate surface separations.
Locking of Dephasing and Energy Redistribution in Molecular Systems by Multiple-Pulse Laser Excitation Edward T. Sleva, Max Glasbeek, and Ahmed H. Zewail* Arthur Amos Noyes Laboratory of Chemical Physics,+ California Institute of Technology, Pasadena, California 91 125 (Received: January 23, 1986)
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In this paper, we report experimental results on the locking of dephasing of molecules in the gas phase. The locking of inhomogeneous dephasing of the B X transition of iodine is achieved by using multiple-pulse and phase-coherent laser excitation, instead of a single-pulse excitation. We detect the locking using echo techniques. The locking concept is extended to the problem of intramolecular dephasing, emphasizing the potential for controlling selectivity in laser chemistry.
Introduction Experimentally, it is now established that there ensues upon coherent excitation a coherent evolution of vibrational/rotational motion in large polyatomic molecules. This has been demonstrated for several large molecules on a single excited-state potential energy surface.’ Knowledge about the time scale for this coherent evolution and intramolecular vibrational energy redistribution (IVR) has suggested several schemes for controlling selectivity and “eliminating” IVR which is the source of energy scrambling and dephasing in molecules. The theoretical ideas involved in these schemes include: (a) excitation of vibrational states on a time scale shorter than the time of IVR, Le., before energy is completely randomized and coherence is lost;2 (b) the use of phase-coherent pulse sequences; e.g., by using multiple phase-coherent pulse sequences as suggested by US,^^^ or by using two-photon spec‘Contribution No. 7360.
0022-3654/86/2090-1232$01.50/0
troscopy as suggested by Tannor and Rice;4or (c) the use of strong resonant laser excitation as suggested by Yeh et al.5 and by Mukamel and Sham6 Experimentally, it is therefore important to develop methods for “inhibiting” dephasing by intra- or intermolecular effects. In this paper, we present a new experimental approach for the locking of dephasing (energy scrambling) in molecular systems. The approach is based on the use of multiple phase-coherent laser pulses (instead of one pulse) to excite the sample. Basically, a ~~~
~
(1) Felker, P. M.; Zewail, A. H. Chem. Phys. Lett. 1983,
J02,113. Felker,
P.M.; Zewail, A. H. Phys. Reu. Let?. 1984,53, 501. Felker, P. M.; Zewail, A. H. J. Chem. Phys. 1985,82,2961, 2975, 2994, 3003. (2) Zewail, A. H. Phys. Today 1980, 33,27. Bloembergen, N.;Zewail, A. H. J . Phys. Chem. 1984.88,5459. ( 3 ) Warren, W. S.; Zewail, A. H. J . Chem. Phys. 1983,78, 3583. (4) Tannor, D. J.; Rice, S.A. J. Chem. Phys. 1985,83,5013. (5) Yeh, J. J.; Bowden, C. M.; Eberly, J. H. J . Chem. Phys. 1982,76. 5936. (6) Mukamel, S.; Shan, K. Chem. Phjs. Let?. 1985,I 1 7 , 489
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 7, I986
Letters
X tT-++---T-T+.+T*Tk+T+
I
2
3
1233
Y
4
Figure 1. Pulse sequence used to lock and detect the locked coherence. The locking field is phase-shifted by 90% from the preparation pulse. The refocusing pulse (for echo detection) is in phase with the preparation pulse. The probe pulse is alternately in-phase and 180' out-of-phase with
the preparation pulse. sequence of laser pulses of well-defined phases is used for the coherent preparation and locking, and a final pulse is used to detect the remaining coherence in the system (probe pulse technique'). This locking technique, reported by Sleva et a1.,8 allows one to control selectivity just as, e.g., selective averaging of certain interactions is made in N M R using trains of rf pulse^.^ In our case, success in performing these experiments is because we are able to use the probe pulse technique' and control the phases of the optical pulses,1° as reported before from this laboratory. Here, we report new results on the locking of dephasing for the B X transition of I, gas at a pressure of -30 mTorr. Evidence for locking in I, is demonstrated here by using the four-pulse sequence XYXX(X). The results are consistent with earlier reports from this laboratory8 using three-pulse sequences (XYX(x)). Armed by these results, we extend the treatment to the case of IVR in large molecules. We are encouraged by the 1, results and believe that the approach has the potential for controlling selectivity and non-RRKM behaviors in laser chemistry.
unlocked echo
locked unlocked echo echo
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Experimental Section The pulse sequence generated in this experiment was obtained in the following manner. Modulation of a C W single-mode ring dye laser (pumped by an Ar+ laser) by a travelling-wave acousto-optic modulator was implemented for the generation of the XYXX or XYXX pulse sequence. As reported by Zewail and Orlowski,' in this probe pulse technique acoustc-optic modulation of the laser allows one to generate the pulse sequence of interest. Furthermore, by controlling the relative phases of the rf pulses fed to the A 0 modulator, one can control the phases of the light pulses.l0 In this study, the singlemode C W power was -300 mW at 589.7 nm. The modulator was driven by rf (460 MHz) pulses, and the rf source was split into the three phase components of interest (X, Y, or X),each of which was regulated by an rf switch prior to recombination with the others. The relative phases were set by using a vector voltmeter. The optical pulses with these various phases, which were detected by a fast photodiode, were used to excite I, gas at low pressure (30 mTorr). The fluorescence of I2 was detected, and the coherence was monitored by using the probe pulse technique. More details can be found in ref 7,8, 10, and 11. Locking and Detection of Locking The pulse sequence used in this study was in resonance with the B X transition of I2 at 589.7 nm. In this case, the locking serves to inhibit the Doppler dephasing of gaseous iodine. We use the first pulse to create the coherence and lock this coherence using the second pulse in the sequence. We then detect the locked coherence by simple use of a probe pulse as was done by Sleva et al.* or by using the photon echo as demonstrated here. The pulse sequence used in the experiments (Figure 1) is as follows: An initial pulse of duration T~ serves to prepare a macroscopic polarization. Immediately thereafter a locking field, phase-shifted from the preparation pulse by 90°, is applied for
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(7) Zewail, A. H.; Orlowski, T. E.; Jones, K. E.; Godar, D. E. Chem. Phys. Lett. 1977, 48, 256. Orlowski, T. E.; Jones, K. E.; Zewail, A. H. Ibid. 1978, 54, 197. (8) Sleva, E. T.; Xavier, 1. M.; Zewail, A. H. J . Opt. Soc. Am., in press. (9) See, e.g., Haeberlen, U. High Resolution N M R in Solids-Selective Averaging, Academic Press: New York, 1976. (10) Warren, W. S.; Zewail, A. H. J . Chem. Phys. 1983, 78, 2279, 2298. Warren, W. S.;Zewail, A. H. Ibid. 1981, 75, 5956. (11) Sleva, E. T.; Zewail, A. H. Chem. Phys. Lett. 1981, 110, 582.
Figure 2. Experimental results for I2 at 30 mTorr obtained by using the multiple-pulse sequence of Figure 1. The scan on the left was obtained with a three-pulse echo sequence withour the locking field pulse. All three pulses were of 50-11s duration; the first two were separated by 400 ns. The separation between the third and fourth pulses was scanned from T' = 600 ns to 7 ' = 0 ns. For the data on the right, a 200-11slocking field pulse was inserted immediately after the first pulse. The locking field causes an echo of the locked coherence to appear in addition to the coherence produced by the usual echo sequence.
a time 7*.The sample is then allowed to evolve in the absence of a laser field for a time T , A refocusing pulse of duration 73, in-phase with the preparation pulse, is then applied. The probe pulse is alternately in-phase and 180' out-of-phase with the preparation pulse and is of duration T ~ .The signal obtained with the in-phase probe is subtracted from that obtained with the out-of-phase probe to produce the signal of interest. Since the locking field has a Rabi frequency which is substantially smaller than the inhomogeneous line width, a certain fraction of the coherence that is prepared by the first pulse will not be locked. This is because the condition wR >> Aw (wR is the Rabi frequency and A w the frequency spread) must hold to be effective. Consequently, one expects that the refocusing pulse will cause two echoes to appear, one at time 7' = T and one at 7' = T
+
72.
This expectation is borne out experimentally, as Figure 2 indicates for 1, a t 30 mTorr. In this experiment of Figure 2, we scan in time the probe pulse while keeping the duration of the locking field constant. As shown in the figure, we observe two echo signals; one of them disappears when the locking field is turned off. When the experiment was repeated with a locking field that was in-phase with the preparation pulse, the echoes were almost completely attenuated. In Figure 3 we present results obtained for I2 when we varied the duration of the locking field; as the pulse width increases the two echoes become less intense and more separate in time. The above results, along with the pressure dependence data of our previous experiment ( T , = TI,): demonstrate that the intense Y pulse (aR= 20 MHz) is capable of locking the coherence of the molecular I, ensemble. The first two pulses (XU)of the "locking sequence" used in our pulse train are analogous to spin locking experiments done in magnetic resonance.I2 The echo detection is related to experiments done with echoes in a strong field in atomic systems.I3 The prescription of the phases in our (12) See, e.g., Redfield, A. G. Phys. Rev. 1955, 98,
1787.
1234 The Journal of Physical Chemistry, Vol. 90, No. 7, 1986 7
X
Y
-
I-
Letters coupling between the Is) and 11) levels. At early times, t ( Vs,-l >> a-' and the V,, can be ignored; 50% of the population is maintained in Is). At long times (t I VSl-'),coherent averaging theory may be used to demonstrate that the effect of the V,, is negligible during the locking. Let Vl(t)be Vin the interaction representation:
X
VI(7) = exp(iH0T)V exp(-iHoT)
re = 200 ns
600
0 r'(nsj
600
r' (nsj
(1)
The wave function of the system at any time t is given by allowing the time evolution operator U(t) to operate on the eigenfunction of Hoy.U ( t ) may be written by using the Magnus expansion as
U ( t ) = exp(-iH0T) exp[F(t)]
(2)
where I I 600
r'(nsl
600
(3)
r'(nsi
Figure 3. A study of the effect of locking field pulse duration on the signals obtained from the sequence. i2 is the only quantity varied from scan to scan.
experiment make it possible to control the selectivity required in all these locking experiments.
Locking of Energy Redistribution and Dephasing This locking technique holds great promise for inhibiting IVR, that is, preserving intramolecular coherence, provided that the Rabi frequency (wR a) of the transition is large compared to the energy spread of eigenstates. To demonstrate this applicability, we consider the following level structure: a ground state 18) and an optically active excited state Is); Is) is coupled to a manifold (11)) of optically inactive levels by matrix elements GI. An example of this level structure is the case of an optically active vibrational mode (which we desire to selectively excite) coupled to a manifold of other modes by anharmonicity. An intense laser field (a >> Ifsl) allows one to populate Is) while preventing population of the 11) level^;*^^^^ however, in this circumstance population cycles between lg) and Is). In the locking experiment, however, phase shifting the intense radiation source by 90' after a n / 2 pulse allows one to "inhibit" intramolecular dephasing (i.e., the coupling between Is) and 111)))without cycling population between Is) and Ig). Note that in the absence of the locking field we recover the single-pulse excitation case, in which population flows by intramolecular dephasing from the Is) to the {Il)) manifold. We now consider the influence of locking on these intramolecular processes. An x pulse of duration T = n/(2R) prepares an eigenstate of the Hamiltonian Ho,, = ipE((g) (SI- Is)(gl) + CIIl)EI(11, where g is the transition moment and E is the laser field amplitude. The total Hamiltonian, however, is H = Ho + V, where V i s the (13) Ycdh, A. G . ;Golub, J.; Carlson, N. W.; Mossberg, T.W. Phys. Reu. Lett. 1984, 53,659.
Using the eigenstates of Hoto evalute the expression in eq 1 yields VdT) =
c V s l exp(-iEIT)[ls)(l)cos ( Q T ) - Ig)(ll sin I
(QT)]
+ hc
(4)
where El is the energy of 11) with respect to Is). In the interaction representation, integrals corresponding to V in the Magnus expansion of the evolution operator have terms oscillating at the frequency Q and will vanish in the limit of large Q. Similar results were obtained when we used eq 35 in ref 10 for the expansion of Ho V. Evolution will therefore be dictated by Ho, so that coupling to the 11) levels may be ignored and locking can be achieved. The probability of finding the molecule in the Is) level is constantly =OS; Le., they pulse locks the population in the Is) level without cycling.
+
Conclusions In conclusion, we have observed a locked coherence in iodine gas using multiple laser pulse excitation and a photon echo detection scheme. The results demonstrate that inhomogeneous dephasing can be inhibited by this locking procedure. Motivated by the results of our locking experiments, we have addressed the potential applicability of the optical locking technique to inhibition of intramolecular dephasing processes. Of particular interest is the utility of locking to control selectivity and non-RRKM behavior in laser-selective chemistry. This is because locking maintains the population in the state of interest without cycling or flow to nearby states, a feature that is not possible in the conventional single pulse laser excitation approach. Finally, work on solids is currently in progress.14 Acknowledgment. This work is supported by a grant from the National Science Foundation (DMR-8521191). M.G. and A.H.Z. also greatly acknowledge support from a NATO research grant. (14) Sleva, E. T.; Glasbeek, M.; Zewail, A. H., work in progress
