Electric Dipole Moments of Water Clusters from a Beam Deflection Measurement

The response of $({\mathrm{H}}_2\mathrm{O}{)}_{n=3–18}$ clusters to an electric field is studied by beam deflection. All clusters deflect uniformly, behaving as polarizable particles. The effective polarizabilities exceed the electronic component and increase as the clusters are cooled, revealing a large permanent dipole contribution. The results resolve a discrepancy concerning the polarity of water clusters and show that all species access conformations with moments exceeding 1 D. The data show no evidence for a freezing transition down to $\sim 120\mathrm{K}$, but suggest a shift in the conformer arrangement at $n=8–9$.

Figure 1

An outline of the experimental arrangement. A supersonic beam of water clusters is formed by expanding water vapor, either neat or with helium carrier gas, through a $75\mu \mathrm{m}$ nozzle. The jet passes through a 0.3 mm skimmer and is collimated by a $0.25\mathrm{mm}\times 2.5\mathrm{mm}$ slit just before entering the deflecting field region. The inhomogeneous field is created by 152 mm long asymmetric aluminum plates with a “two-wire” cross section and a 2.49 mm gap at the center [15, 16]. The deflected clusters travel 709 mm to a 0.25 mm wide slit scanned by a stepper motor (shown rotated by 90° in the figure for clarity), and then enter a quadrupole mass spectrometer (UTI-100, 300 amu range) equipped with an electron-impact ionizer set to 70 eV. Chopping the beam at a frequency of 114.8 Hz and feeding the mass spectrometer output and the chopper pulses into a lock-in amplifier removes the background gas signal as well as determines the cluster speed from the phase difference.

Figure 2

(a) Beam profiles of $({\mathrm{H}}_2\mathrm{O}{)}_9$ at zero field (dashed line) and with 25 kV on the plates (field of $79.4\mathrm{kV}/\mathrm{cm}$ and a gradient of $375\mathrm{kV}/{\mathrm{cm}}^2$, solid line), yielding a deflection of $46.1\pm 5.0\mu \mathrm{m}$. (b) $({\mathrm{H}}_2\mathrm{O}{)}_9$ deflections for several plate voltages.

Figure 3

Solid circles: Measured effective polarizabilities of water clusters (prepared by supersonic expansion of neat water vapor) minus the theoretical electronic contribution ${\alpha }^{\mathrm{el}}\approx n\times (1.2{\AA }^3)$ [4]. These residual values are the contribution of permanent dipoles. Dotted line: Langevin formula, Eq. (2), with $T\approx 200\mathrm{K}$. The full effective polarizabilities are shown in Fig. 4.

Figure 4

Squares: Effective polarizabilities of cooled water clusters prepared by expanding a mixture of helium and water vapor into vacuum ($P_{\mathrm{He}}=670\mathrm{Torr}$, $T_{\mathrm{source}}=343\mathrm{K}$, $P_{{\mathrm{H}}_2\mathrm{O}}=233\mathrm{Torr}$, $T_{\mathrm{nozzle}}=353\mathrm{K}$). Circles: Full effective polarizabilities for the hotter clusters (from which Fig. 3, which includes the error bars, was derived). Dashed line: rescaling of the latter values using Eq. (2) with $T=120\mathrm{K}$.

Figure 5

Effective polarizabilities of $({\mathrm{H}}_2\mathrm{O}{)}_3$ under different source conditions. For the seeded expansion, $P_{\mathrm{He}}$ was kept at 670 Torr and the water vapor pressure varied. The data point for neat vapor expansion is also shown.