Schematic experimental setup: Water vapor clusters in a liquid nitrogen (77 K) cooled helium atmosphere of the aggregation chamber (a). A discharge ionizes the clusters in the aggregation region (b). The thermalization chamber (c) serves to regulate the cluster temperature between 77 and 250 K. After removing the He by differential pumping, the clusters are accelerated and pass through the collision cell with ion guide (d), before they enter the time-of-flight mass spectrometer (e).
Mass spectrum of H+(H2O)70 with and without the fragment from H+(H2O)71 → H+(H2O)70 + H2O. For the best resolution, the clusters need 21.9 eV kinetic energy at the entrance of the spectrometer.
The fragmentation ratio R of protonated clusters with 70 water molecules for the heat-bath temperatures T th = 80 K and 132 K. The data points are fitted by χ2 distribution functions (gray lines). The clusters show the same fragmentation ratio of 50% at both temperatures, when collisions add 620 meV of heat to the originally colder clusters. The internal energy therefore differs by this amount between the two temperatures.
The internal energy of the clusters depending on the temperature of the heat bath. In order to minimize the statistical error, the curve is calculated based on the overall sum of mass peaks in the studied size range from 60 to 80. Open and full symbols indicate two independent data sets. The data is fitted to bulk ice (gray, solid line) in the temperature range of 80 to 120 K. Above 155 K, the cluster temperatures start to fall below those of the heat bath due to evaporative cooling. The curves therefore deviate from the caloric curve and level off towards the internal energy of the evaporative ensemble. The gray circle at 29 meV and 163 K indicates the evaporative ensemble resulting from the extrapolation of the caloric curve, using the heat capacity at the evaporative ensemble temperature deduced by Sundén et al. 23 At 133 K, the slope of the caloric curves increases, indicating the phase transition. The dotted line corresponds to (H2O)48 − resulting from photofragmentation calorimetry.18
The individual caloric curves of H+(H2O) n with n = 60–79. Circles and triangles indicate the two independent data sets. The solid gray curves stand for bulk ice. The vertical line connects the transition temperatures (T tr).
The size dependence of the transition temperatures: full symbols represent experimental data on water clusters charged by protons and by excess electrons. Open symbols are simulations by different methods and models on neutral35 and on protonated water clusters.39 The x-axis is proportional to −n −1/3 and the dotted, straight line represents a droplet model fit through the TIP4P data of neutral water.
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