View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Ion Calorimetry: Using Mass Spectrometry to Measure Melting Points Colleen M. Neal, Anne K. Starace, and Martin F. Jarrold Chemistry Department, Indiana University, Bloomington, Indiana, USA Calorimetry measurements have been used to probe the melting of aluminum cluster cations with 63 to 83 atoms. Heat capacities were determined as a function of temperature (from 150 to 1050 K) for size-selected cluster ions using an approach based on multicollision-induced dissociation. The experimental method is described in detail and the assumptions are critically evaluated. Most of the aluminum clusters in the size range examined here show a distinct peak in their heat capacities that is attributed to a melting transition (the peak is due to the latent heat). The melting temperatures are below the bulk melting point and show enormous fluctuations as a function of cluster size. Some clusters (for example, n ϭ 64, 68, and 69) do not show peaks in their heat capacities. This behavior is probably due to the clusters having a disordered solid-like phase, so that melting occurs without a latent heat. (J Am Soc Mass Spectrom 2007, 18, 74–81) © 2007 American Society for Mass Spectrometry variety of techniques have been developed to numbers to differentiate them from electronic magic examine the physical properties of ions in the gas numbers where the stability results from electronic shell Aphase[1].Interesthasfocusedmainlyonproper- closings[5].Ifthedissociatingclusterisliquid,struc- ties such as the ground state structure, chemical reactivity, tural magic numbers should not be prominent in the and dissociation energies. There has been little interest in fragmentation pattern (because stability results from a thermodynamic properties such as heat capacities. The particular geometry, and the liquid does not have an reasonforthisisprobablytwo-fold.First,therehasnot orderedstructure).If,ontheotherhand,structural been a way to measure the heat capacities of isolated ions; magic numbers are prominent in the fragmentation and second, there is an expectation that the heat capacities pattern, it implies that the fragmenting cluster is solid- will reveal little of interest. The latter is probably true for like.Dissociationfromasolid-likestatecanbethought small ions that retain the same connectivity between the of as the finite size analog of sublimation. constituent atoms as the temperature is raised to the point The melting points of small particles are depressed. where they dissociate. The heat capacities become inter- Thiswasfirstpredictedin1909[6],andhassubsequently esting for larger ions that can undergo structural transi- been confirmed many times for particles with 103 to 106 tions or phase transitions (like melting and freezing). For atoms[7–11].Itisonlyrecentlythatmethodshavebeen example, unsolvated helical peptides with 10–20 residues developed to investigate the melting of particles with less can undergo a “melting” transition as the temperature is than 103 atoms. In this size regime, where properties raised[2,3].Heatcapacitymeasurementswouldreveal change rapidly, measurements must be made on size- the nature of the transition. A first-order transition occurs selectedparticlesorclusters,whichnecessitatestheuseof with a peak in the heat capacity due to the latent heat, mass spectrometry based methods. The pioneering work whileasecond-ordertransitionshowsastepratherthana of Haberland, Schmidt and their collaborators stands out peak in the heat capacity. here[12–14].Theydevelopedanexperimentalmethod Metalclustersareexpectedtoshowmeltingtransi- based on monitoring the fragmentation pattern resulting tions. Here the transition is the finite-size analog of a from multiphoton induced dissociation of cluster ions to “real” melting transition rather than the order-disorder determine their heat capacities. While their approach has transition that occurs for helical peptides. The phase of only been applied to sodium clusters with predominantly a dissociating cluster (and indeed any ion) has some more that 100 atoms, these studies provided the first interesting[4]andperhapsunderappreciatedconse- experimental information on the melting of particles with ϩ quences. Some clusters, like C60 and (NaCl)13Na for atomic resolution. example, are particularly stable because they adopt Here we report heat capacity measurements for alumi- special geometries. We refer to these as structural magic num clusters with 63 to 83 atoms. This builds on our previous work, where we have reported heat capacities foraluminumclusterswith49to63atoms[15].We Published online September 28, 2006 provide a detailed discussion of the experimental method, Address reprint requests to Dr. M. F. Jarrold, Chemistry Department, Indiana University, 800 E. Kirkwood Ave, Bloomington, IN 47405, USA. and a discussion of the assumptions inherent in the E-mail: [email protected] approach employed here. © 2007 American Society for Mass Spectrometry. Published by Elsevier Inc. Received June 23, 2006 1044-0305/07/$32.00 Revised August 17, 2006 doi:10.1016/j.jasms.2006.08.019 Accepted August 19, 2006 J Am Soc Mass Spectrom 2007, 18, 74–81 ION CALORIMETRY 75 Dissociation Threshold Figure2showsaschematicoftheexperimental apparatus. The clusters are generated by laser vapor- ization of a liquid metal target in a helium buffer gas. The surface regeneration that occurs with a liquid target ensures that the laser always strikes a pristine surface so a) Internal Energy that the laser or target do not need to be moved to avoid Temperature boring a hole in the target. However, the principal advantage of using a liquid metal target is that it provides a signal with much better short term and Internal Energy long-term stability than obtained with a more conven- tional rod or disk target, which becomes roughened by exposure to the laser. After their formation, the cluster Heat Capacity ions are carried through the source region and into the b) Temperaturec) Temperature temperature-variable extension by a flow of helium buffer gas. The extension is 10 cm long and its temper- Figure 1. Cartoon illustrating the basic principle behind the ature is regulated by microprocessor based temperature measurements reported here. (a) and (b) show the internal energy controllers. The controllers regulate liquid nitrogen and heat capacity of a typical crystalline solid as a function of temperature. The step in the internal energy and the spike in the flow for temperatures below room temperature, and heat capacity are due to melting. (c) shows how measuring the electrical heaters for higher temperatures. The temper- energyrequiredtoreachthedissociationthresholdasafunctionof ature can be adjusted from 77 K up to around 1200 K. It temperature (the arrows) can be used to map out the internal is critical that the clusters achieve thermal equilibrium energyanddetectthemeltingtransition(thestep). with the walls of the extension. A series of tests were Experimental performed, where the length of the extension, the size of the exit and entrance apertures, and the buffer gas Figure1illustratesthebasicprinciplebehindthe pressure were adjusted to determine whether thermal method.Figure1aand1bshowtheinternalenergy(E) equilibrium had been achieved. The tests suggested that and heat capacity (C ϭ dE/dT) of a typical crystalline the exiting clusters attain the same temperature as the solid as a function of temperature (T). At low temper- extension walls. ature, the sample is solid and the increase in the internal When the clusters are in the temperature variable energy with temperature reflects the heat capacity of extension they are in a buffer gas, which provides a the solid. At the melting point there is a sudden jump in means to transfer energy into and out of their internal the internal energy due to the latent heat, which also degrees of freedom. Under these conditions the cluster causesaspikeintheheatcapacity.Abovethemelting ions form a canonical ensemble. Because the buffer gas pointtheinternalenergyincreasesduetotheheat pressure is relatively low (around 10 torr) expansion capacity of the liquid, which is expected to be slightly cooling of the cluster ions as they exit the extension is larger than for the solid. For a small particle or cluster not important. This was confirmed by doing measure- the melting transition is broadened by finite size effects ments as a function of the buffer gas pressure and the (the cluster is a small system from a thermodynamic diameter of the exit aperture. Outside the extension, the point of view). In our experiments, the melting transi- cluster ions are no longer in the buffer gas and, thus, no tion is identified by detecting the jump in the internal longer form a canonical ensemble. However, if their energy (or the peak in the heat capacity) due to the internal energy is not perturbed as they leave the latent heat. extension, the cluster’s internal energy distribution re- How we measure the internal energy is illustrated in mains canonical. The cluster ions in vacuum are essen- Figure1c.Iftheinternalenergyofaclusterisincreased tially a “frozen canonical ensemble” characterized by iteventuallydissociates.Wemeasuretheamountof energy required to dissociate the cluster—the vertical arrowsinFigure1c—asafunctionoftemperature.Less Heated High Pressure energy is required to dissociate the cluster as the Temperature Collision Cell Sample Quadrupole temperature is raised because of the