The Physical State of Clusters . An Infra-red Laser Study of Small Cyclopropane and Dimethylcyclopropane Clusters

Infrared absorption profiles have been measured for cyclopropane and 1,1-dimethylcyclopropane 
clusters by monitoring the depletion of signal intensity in a mass spectrometer 
as a function of laser wavelength. Data have been obtained for (C3H6)n+ with n 
in the range 2–15, and for (C5H10)n+ with n equal to 2 and 5. A comparison between the 
cluster results and available infrared data on the various bulk-phase states of both 
cyclopropane and 1,1-dimethylcyclopropane, suggests that the clusters are liquid-like.


INTRODUCTION
Much of the recent interest in clusters has been concerned with the possibility that their physical state may take the form of a microscopic component of bulk material.Under such circumstances, it might be appropriate to use clusters as models for bulk behaviour, and at the same time arrive at a molecular picture of such phenomena as nucle- ation or catalysis.Of equal interest, but not necessarily pertinent to macroscopic phenomena, is the possibility that small clusters may adopt structures which do not scale up to the bulk.For example, simple systems, such as small argon clusters appear to prefer icosahe- dral symmetry, rather than the face-centered-cubic structure char- acteristic of the bulk material. 2Most of the results to date on the physical state of clusters have come from electron diffraction experiments.2-4 From such experiments it has been possible not only to distinguish between liquid-like and solid-like clusters, 4 but also to identify different symmetries in the solid forms, i.e. icosahedral and face-centered-cubic in the case of argon clusters. 2r intention in this paper is to show that similar information on the physical state of clusters can be derived from their infrared photodissociation spectra.In the present experiments, the photodissociation technique has been used to determine infrared absorption profiles which are then compared with those measured for the same IR active mode in the bulk state.We shall show that, through the selection of an appropriate vibrational mode, the IR photodissociation technique has the potential to provide detailed information concerning the temperature(s) of the clusters.
The results presented are mainly from a detailed study of small cyclopropane clusters; however, some data recorded for dimethylcy- clopropane clusters are also discussed.Data have been obtained by monitoring the depletion of ion cluster signals in a mass spectrometer as a function of radiation wavelength.Signal depletion arises from infrared vibrational predissociation of neutral clusters.In view of the extensive fragmentation which results from electron impact ioni- zation, the relationship between an ion cluster under consideration and its neutral precursor(s) is not obvious.The only fact we can be certain of is that the sizes of the neutral clusters are larger than those of the ions being monitored.In the interpretation of these and other results, 5 we have therefore adopted the philosophy that the absorption profiles measured for small ions reflect the properties of small neutral clusters, and that as the size of the ion increases, so there is a corresponding increase in the size of the neutral clusters undergoing photodissociation.

EXPERIMENTAL SECTION
Neutral clusters are generated by the adiabatic expansion of either cyclopropane or dimethylcyclopropane seeded in argon, through a 100 #m pulsed nozzle operating at approximately 20 Hz.The cluster beam is collimated by a 0.5 mm diameter skimmer situated 2 cm from the nozzle.In almost all the experiments the stagnation pressure behind the nozzle was 760 torr.Approximately 20 cm downstream from the skimmer the cluster beam is crossed with infrared radiation from a line-tunable CO2 laser (Edinburgh Instruments Model PL 4).The laser beam is focused to a 1 mm diameter spot using a 50 cm focal length zinc selenide lens, and enters and leaves the vacuum system via two zinc selenide windows.A further 20 cm downstream from the laser excitation point, the cluster beam enters the ion source of a mass spectrometer.The mass spectrometer (AEI MS12) has been modified to facilitate the unimpeded entry of a cluster beam into the ion source.With an accelerating potential of 8 kV in the ion source, the MS12 is capable of detecting clusters with masses up to 1000 amu.Because the signal intensities from individual ion clusters are often very low, the mass spectrometer is operated with both the source and collector slits set to their maximum values.Under such conditions the instrument only has a resolution of 1000.
With the pulsed nozzle operating at a frequency, f, a reference pulse from the nozzle control unit is fed into a signal generator (Global 4001) which in turn pulses the laser at a frequency f/2.Photodissociation is detected by correlating an f/2 reference signal with the ion signal from the mass spectrometer.A phase-sensitive detector (Brookdeal Model 9502SC) is used for this purpose.By utilizing the second harmonic control on the lock-in amplifier, it is possible to switch directly from the mass spectrum of a cluster to its depletion spectrum.Figure I shows a schematic diagram of the apparatus.In a typical experiment the mass spectrometer is tuned to a particular ion cluster and the depletion signal is then monitored as a function of laser wavelength.The laser fluence throughout was held constant at 60 mJ cm-2.Laser power dependence studies showed that at this fluence, all the ion depletion signals are due to single photon absorption.To obtain the complete absorption profile for the cyclopropane clusters it was necessary to extend the range of IR radiation typically available from the 001-020 band of the CO2 laser.This was achieved by replacing the 75% reflecting output coupler, used in previous experiments, with one of 85% reflectance.The resultant slight drop in power had no effect on the measurements.

RESULTS AND DISCUSSION
Cyclopropane Figure 2 shows absorption profiles measured by monitoring ion signal depletion due to the infra-red photodissociation of the neutral precursors of the clusters (c3n6)n + for n 2, 5, 10 and 15.The spectra cover the range 1016-1036 cm -, and maximum signal depletion occurs for the P(44) band of the CO 001-020 band.When fitted to a Lorentzian, (see Figure 3) all the clusters gave a full width at half maximum (FWHM) of 10 cm -1 at a central frequency of 1024 cm-.The binding energy between cyclopropane molecules is thought to be of the order of 150 cm -1 6 therefore, each incident photon has more than enough energy to induce vibrational predissociation.
In the gas phase, the vibrational mode coincident with CO laser E' radiation in the 1016-1036 cm -1 region is the Vl0 out-of-plane C-H bend.7 Infra-red and Raman studies of the lattice vibrational spectra of cyclopropane belongs to the space group Cmc2 with two molecules in a primitive cell, each occupying a site with C symmetry.Under such circumstances, the degenerate E' gas-phase vibrational mode becomes four unit cell vibrations, three of which are infra-red active.A group site interaction produces a doublet, and a correlation interaction then splits the A' component into a further doublet to give three separate infra-red active vibrational modes.Figure 3 compares the depletion spectrum measured in the present experiments for (C3H6)10 + with the corresponding infra-red spectrum for the crystalline state of cyclopropane in the 1016-1036 cm -1 region. 1 Also shown in Figure 3 is the position of the absorption intensity maximum for the v0 mode in liquid cyclopropane at =213 K.A comparison of the three absorption features dearly suggests that the clusters are more liquid-like than solid-like.In particular, if the clusters had any crystalline characteris- tics, then strong photodissociation spectra would have been expected only from the three laser lines at 1019, 1025 and 1029 cm-.Instead, the single broad photodissociation maximum appears to coincide with the centre of the infra-red absorption profile for liquid cyclopropane.In a recent experiment, Bartell et al. 4'2 used electron diffraction in association with a supersonic nozzle to study cyclopropane clusters.They concluded that, with an initial vapour temperature of 293 K, the clusters appeared to be liquid-like under all expansion conditions.The observations of Bartell et al. 4'12 together with the present results, CH6(I/) ld16 1020 102Z, 1028 1032 frequency(cm4) Figure 3 Comparison between the photodissociation spectrum recorded from the neutral precursors of (C3H6)1o and the infrared spectrum of crystalline and liquid cyclopropane.The cluster result is shown as a Lorentzian fitted to the experimental data.The three triangles signify the splittings of the degenerate vl0 in the crystal, and the position of the absorption intensity maximum for the v0 mode in liquid cyclopropane at "--213 K is shown as a line.
suggest that the internal temperature of cyclopropane clusters is sufficiently high as to allow individual molecules to rotate about their inertial axes.
There is no direct evidence to suggest that the linewidths we observe, for example in Figure 3, are due to homogeneous broaden- ing; however, it is instructive to consider the possibility that the complete width might be associated with the decay of an excited state via a single relaxation step.The linewidth of 10 cm -1 recorded for all the spectra represents an excited state lifetime of =0.5 ps.Given the considerable difference in densities of rotational and vibrational energy states between (C3H6)2 + and (C3H6)15 + it seems unlikely that the neutral precursors of both these clusters would predissociate on the same timescale.This leads to the proposal that the lifetimes could be determined by microscopic dynamics rather than statistical theories. 13f the alternative relaxation process available, the most obvious are vibrational dephasing and vibrational relaxation.Available data for the vibrational relaxation of the vlo mode in helium, 14,5 suggests that collisional de-excitation requires of the order of 100 collisions.There- fore, even in the comparatively dense environment of a cluster such a process could take =10 ps.The dephasing of a molecular vibration corresponds to a loss of phase coherence by the excited quantum state through reorientation as the result of elastic collisions, t6 Dephasing is a T2-type process, 16 and under conditions where vibrational relaxation is very inefficient, the FWHM of a Lorentzian lineshape gives the timescale for dephasing as 2/T2.Besnard et al. 17 have used Raman spectroscopy to measure reorientation times from the v3 mode at 1188 cm-1, in liquid cyclopropane over a range of temperatures.They found that T2 varied from 0.42 ps at 298 K to 1.42 ps at 172 K; t7 our relaxation time of 0.5 ps from the FWHM of the cluster absorption profiles is consistent with the above range for liquid cyclopropane.Similar agreement has been found between the line shapes taken from ben- zene cluster absorption profiles and the reorientation times of mole- cules in liquid benzene.frequency(cm -) Figure 5 As for Figure 4, but for (C5H10)5+.
The vibrational mode coincident with the 001-100 band of the CO2 laser is an al CH3 rock (vlo). 19'2 From the heat of vaporization, 6 we estimate the binding energy of an individual molecule to be of the order of 250 cm-1.As with cyclopropane, this energy is significantly less than that of the incident infrared photons.When fitted to a Lorentzian, both the absorption profiles in Figure 4 give a FWHM of 6 cm -1 centered on a frequency of 930.5 cm-1.This frequency is closer to the liquid phase value for the Vl0 mode (931 cm-1) m than it is to the corresponding value for the crystalline phase (928 cm-1). 22

CONCLUSION
The electron diffraction experiments of Bartell et al. 4'12 have shown that cyclopropane clusters appear to be liquid-like, and that their vibrational temperature is in the range 120-150 K.In the present experiments, where the expansion conditions are not as extreme as those of Bartell et al. ,4,12 a comparison between the measured absorp- tion profiles and reorientation times taken from Raman experiments, suggests a temperature in the region of 200 K.The above values are to be compared with the bulk melting and boiling points of 145.4 K and 240.3 K, respectively.
The ability to probe the spectral properties of cydopropane dusters via the excitation of a degenerate vibrational mode, offers the possi- bility of observing the onset of solid-like behaviour.If clusters can be generated which are both sufficiently cold and large as to adopt microcrystalline forms, then any resultant unit cell formation will lift the degeneracy of the mode.It can be seen in Figure 3 that the splittings in the crystal are such that even the comparatively low resolution of a line-tunable CO2 laser would be capable of detecting the separation between the unit cell modes.Hence, the presence of microcrystallites could be detected if the expansion conditions can be controlled to a point where the degree of cooling is extreme; but that the rate of cooling is sufficiently slow as to prevent the formation of, for example, a super-cooled liquid.

Figure 1
Figure1Schematic diagram of the apparatus; f and 2f denote the frequencies of the pulses used to drive the laser and the nozzle, respectively.

Figure 2
Figure2Photodissociation spectra measured from the depletion of signal intensity for cyclopropane ion clusters (C3H6)n+, for n 2, 5, 10 and 15, as a function of laser frequency.

Figure 4
Figure4Lorentzian curve fitted to the photodissociation spectrum measured from the depletion of signal intensity for the 1,1-dimethylcyclopropane ion cluster (C5H10)2+.