**6. Summary**

In this chapter, several topics on the thermodynamics of nanoparticles formation under laser ablation were explored.

Firstly, thermodynamics related to some general aspects of nanoparticle formation in the gas phase and the principles behind of pulsed laser ablation (PLA) was explained. We divided the problem into the following parts for simplicity: (i) nanoparticle nucleation and growth, (ii) melting and evaporation by laser irradiation, and (iii) Knudsen layer formation. All these considerations were then used to build a model of nanoparticle formation into fluid dynamics equations.

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Secondly, fluid dynamics concerning nanoparticle formation in a high speed flow was developed. Interactions between the shock waves and plume, generation of nuclei, and growth of nanoparticles could all be treated with a single calculation. We conducted onedimensional calculations with the equation, and found conditions wherein the timing of the nucleation and growth processes could be separated based on interactions between the shock wave and plume. The existence of certain conditions for nanoparticle formation in the narrow region between the plume and the buffer gas were confirmed from the numerical results. In addition, reflected shock waves substantially contribute to the growth of nanoparticles by increasing particle radius, but do not contribute to the increase of nanoparticle numbers by promoting nucleation.

A new model of nanoparticle generator, employing an ellipsoidal cell, was then formulated based on the results of the one-dimensional calculations. To evaluate the performance of the cell, axi-symmetric two-dimensional calculations were conducted using Navier-Stokes equations without nanoparticle formation. The behavior of shock wave and plume became clear with the use of density contour maps. The reflection and conversion of shock waves, the interaction between shock wave and plume, and ejection of gas through the cell exit were clearly illustrated.

The ellipsoidal cell was manufactured and PLA process was experimentally carried out in the cell. Cu nanoparticles formed in the experiment were typically of uniform size, under 10 nm in diameter, and had a narrow size distribution, with a standard deviation around 1.1 for the lognormal distribution. The narrow distribution of nanoparticle size possibly originated from the effect of ellipsoidal cell, because the fine, uniform nano-sized particles could not be obtained unless the direction of plume ejection was coincident with the focal point of the ellipsoidal cell. Such uniformly sized nanoparticles are important for practical use as indicated by the following example.

Finally, the thermodynamics of nanoparticle sintering was explored, in particular the transition of nanoparticle appearance with changes in temperature, as well as the possibility of low temperature bonding. Since the melting point of nanoparticles sensitively depends on size, it is important to prepare uniformly sized nanoparticles for bonding at low temperatures.
