Measurement of the Surface Energy of Unsupported Nanocrystals

A novel method to study the evaporation kinetics of nanocrystals (NC) is developed. Direct in situ measurement of mass change using a tandem ion-mobility size and mass spectrometers is used to determine the size dependent evaporation rate. A kinetic model is used to relate the evaporation rate to the temperature dependent surface energy. We report measurements for Zn NC surface energies of 9.0 and 13.6 J/m 2 at 375 0 C and 350 0 C, respectively. We also observed using electron microscopy the crystal edge effects which lead to an evaporation anisotropy for Zn NCs. Nanoparticles, due to their large surface-to-volume ratio, and finite number of atoms, have demonstrated many physical and chemical properties which significantly differ from the respective bulk material. For example, particle size dependent physical processes such as melting point depression [1-3] (one of the oldest areas of small particle research), size dependent structural transformations [4, 5], increased surface energy [6] and band gap have generated considerable interest in both scientific and technological communities. The starting point for understanding the novel properties of NCs is to study their atomic structure, and one of the fundamental physical quantities in determining the mesoscopic structure is surface energy. The surface energy is defined as the energy required to create a unit area of new surface. It plays an essential role in nanoparticle processes such as melting, coalescence and evaporation. It also determines the equilibrium shape, faceting and crystal growth of NCs. During the last decade, many theoretical studies on surface energy of metals and semiconductors employing either first-principles or semi-empirical methods have been published [7, 8]. While there exists a fairly broad literature for bulk material, there are only a few experimental studies that report surface energy of NCs. Even for bulk material, most experimental data stems from the liquid phase surface tension measurements, which are extrapolated to the solid [7]. Direct experimental measurement of surface energy for NC’s has proven to be difficult due to the obvious size issues and because of the interference between the NC’s with its supporting environment. In a recent studies, however, Nanda et al. [6, 9] reported on measurements of surface energies of free (unsupported) Ag, Au, and PbS nanoparticles based on a size dependent evaporation study. Nanda et al. found that using the Kelvin equation [10], the surface energy was fund to be significantly higher than their bulk counterparts. In the interpretation of their results they assumed that the surface energy is not dependent on the particle size and temperature. However, theoretical considerations show that the surface energy is both temperature and particle size dependent [11]. In this study we employ both the size selection and subsequent monitoring of the mass changes using tandem gas-phase ion-mobility methods. Because of the polyhedron shape of NCs and the fact that particle size can change due to density change in the processes such as melting and re-crystalization, direct mass measurement promises to be a more accurate analysis than monitoring particle size change during evaporation. The experimental measurements are conducted for Zn nanocrystals, but the method is generic. In this way we are able to characterize surface energy without the need for collecting particles and imaging them with a TEM. The experiment system consists of three components. Preparation of monodisperse Zn particles, exposure of size selected Zn particles into a controlled temperature region, and finally, measurement of the mass change resulting from evaporation. Our experiment consists of two different ion-mobility schemes in series. The first mobility characterization is to size select particles with a differential mobility analyzer (DMA) [12]. The second mobility characterization employs an aerosol particle mass analyzer (APM) [13] and measures changes in mass resulting from a controlled evaporation of the NCs. Since we are employing ion-mobility methods, particles are first charged with a Boltzmann charge distribution by exposing the nanoparticle aerosol to a Po-210 source, before the DMA. The average charge state of sample particles under Boltzmann distribution is roughly neutral, with most of particles uncharged and equal amount of particles carry +/1 charge and +/-2 charges, etc. For example, in case of 50 nm particles, 60.2% particles will be neutral, 19.3% carry +/-1 charge, 0.6% carry +/2 charges, and higher charge state would be even less. Considering the small percentage in the multiple charged states, we ignore multiple charged particles. Both the DMA and APM are configured to classify positively charge particles for these experiments. The DMA, used in this experiment for size selection, consists of an annular region between two concentric cylinders, with the center cylinder held at high voltage and the outer one at ground [12]. Charged particles of the right polarity feel an attractive force toward the center electrode and move radically inward at an electrophoretic velocity determined by the particle charge, and drag force which is a function of particle size. When charged particles flow between the cylinders the electric force on the particle is balanced by the drag force, and at a fixed voltage all particle exiting the instrument have (to the resolution of the instrument) equivalent mobility sizes. In the size range of consideration here, the DMA functions as a source of mono-area particles [14]. The APM can determine the particle mass distribution based on particle mass to charge ratio, and is used in our experiment to monitor changes to the particle mass resulting from evaporation. The APM consists of two concentric cylindrical electrodes that rotate together at a controlled speed. An electrical field is created by applying high voltage on the inner electrode while the outer one is held at ground. Charged particles flowing within the concentric cylinders experience opposing centrifugal and electrostatic forces and as a result particles exiting the instrument at fixed voltage and rotation speed all have the same nominal mass. By scanning either the voltage or the rotation speed, the particle mass distribution (independent of particle shape) can be determined. APM mass measurements are independent of particle morphology because the centrifugal force is directly proportional to the mass. Our previous experiments have used the DMA-APM technique to measure the inherent density of nanoparticles, as well as to study the mechanism of aluminum and nickel oxidation [15]. Based on operating conditions for the DMA and APM, we estimate uncertainties as follows. For the DMA operating conditions the uncertainty is based on the theoretical transfer function which will give an uncertainly in the peak particle size of +/4 %. We then use Gaussian fit to determine the peak size which would have a precision uncertainty of no more than 1%. A similar result can be obtained for the APM however the uncertainties are not due to the transfer function but uncertainties in the step voltage which has a resolution of only +/-0.5V, which gives an uncertainty in mass of ~4%. Using the root-sum-square (RSS) method, we can estimate the uncertainty of density calculation ~5%. This is consistent with prior work (unpublished) using combined DMA/APM on reference aerosols (NaCl and DOP) which gave an experimentally determined uncertainly in density of 4%. In our study Zn NCs are generated using an evaporation/condensation method in argon. Zn vapor is generated from granular Zn (purity, ≥99.99% from Sigma-Aldrich) by evaporation in a tube furnace at 0 550 C with a flow of argon. Unagglomerated single crystal Zn NCs are formed at the exit of the flow tube by empirical adjustment of the furnace temperature and the argon carrier gas flow rate. In our experiment, Zn NCs of ion-mobility sizes of 50nm, 70nm, 100nm and 150nm were selected in sequential experiments to study the size-dependent evaporation. After size classification, a second tube furnace enables the controlled evaporation of the NCs. The residence time of the aerosol in this furnace is about 5 seconds at a flow rate of carrier gas of 0.5 SLPM. To monitor the small mass change of the NCs due to evaporation, an aerosol particle mass analyzer is placed downstream. Particles exiting the APM will be selected on the basis of mass and are counted using standard particle counting methods using a condensation particle counter. In the experiment, the temperature in the evaporation furnace was set between 250 400 C in increments of 25 C . The particle mass distribution was then measured for each furnace temperature after the system reached steady state. The room temperature particle mass distribution was also taken, and set as the base of the mass measurement. Samples for electron-microscopic analysis were collected exiting the evaporation furnace by electrostatically precipitating the aerosol onto a TEM grid. Zn has a hexagonal close-packed crystal structure. Figure 1(a) shows SEM images of two single Zn NCs which clearly exhibit the shape of perfect hexagonal prism. EDS spectra obtained from the NCs in SEM confirmed that the composition as Zn. Selected area electron diffraction analysis indicated that the Zn NCs have top surfaces of {0001} crystal planes and side surfaces of _ {1100}planes. A typical plot of normalized mass distributions of Zn NCs classified by the DMA operated at a fixed mobility size at different evaporation temperature is shown in the Figure 2(a). To study the size-dependent evaporation behavior of Zn NCs, the peak mass in Figure 2(a) is plotted against the temperature. The plots is shown in Figure 2(b) and can be categorized as falling into two regions, which can be represented by the best linear fits to the data. The near horizontal line represents the un-evaporated case, in whi