Introduction

Nanocapsules have physical properties that differ from those of bulk materials. One of the main origins of such differences is the discreteness of the energy levels in the limited systems. According to the energy band theory, the energy levels of a bulk metal are in general continuum (or so-called quasi-continuum) because the number of electrons in the bulk is infinite. For limited systems, like clusters, nanoparticles, and nanocapsules, the limited number of electrons leads directly to the discreteness of the energy levels. When the energy gap is larger than the thermal, magne-tostatic, electrostatic, photon, or condensation energy of the superconductivity, the quantum size effect would result correspondingly in different (thermal, magnetic, electronic, photon, or superconducting) behavior of the limited systems. In bulk materials, the cyclic condition and the translation symmetry in three dimensions lead to the plane wave character of electrons. When the size of limited systems is comparable to or even less than the optical wavelength, the de Broglie wavelength, the free path length of electrons, or the coherence length of the Cooper pair, the cyclic condition and the translation symmetry would be broken down, which also affects the physical properties of the systems. The quantum interference of electrons in the confined states could become more pronounced in the nanocapsule systems. The magic number effect is a character observed in the small systems, like clusters, nanoparticles, and nano-capsules. The lack of symmetry of the atoms located at the surfaces/interfaces affects the chemical and physical properties of nanocapsules. The typical core/shell structure could also contribute to the behavior of nanocapsules. Furthermore, the metastable phases could exist in nanocapsules, which could result in different properties of nanocapsules. In this section, we introduce several concepts and topics, such energy levels, quantum effects, magic effects, surfaces/interfaces, and metastable phases, which are particular for the nanoparticles/nanocapsules. Understanding these topics and their differences from those of bulk materials is extremely important for studying the properties of nanocapsules.

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