Fluctuation approach to the problem of thermodynamics’ applicability to nanoparticles

Fractal Nanoparticles of Phase-Separating Solid Solutions: Morphology-Dependent Phase Equilibria in Tungsten Heavy Pseudo-Alloys

“…In the case of the properties of small-volume systems being considered in the framework of the thermodynamical approach, the problem of the thermodynamics applicability at the nanoscale and its lower boundary cannot be ignored. As the authors of [23] have noted, it is the most appropriate to apply the theoretical approaches based on the fluctuation theory to determine the applicability limits of chemical thermodynamics. Indeed, spontaneous fluctuations of thermodynamical characteristics (associated with the discreteness of the atomic-molecular structure of any system, being increased with a decrease in the amount of the matter which forms the system) represent the natural limitations on the application of thermodynamical approaches: if the fluctuation values of a parameter get comparable with the values of the parameter, this fact testifies, on the one hand, to the inadequate application of the thermodynamics techniques in this case, on the other hand, to the instability of the considered system itself as well as to the tendency of its decomposition due to fluctuations.…”

“…These peculiarities manifest themselves in significant dependences of mutual solubilities of components and equilibrium volume fractions of coexisting phases on the volume [9][10][11][12][13][14][15][16][17][18][19][20], shape of a nanoparticle [12][13][14]18], thermodynamical characteristics of the surrounding environment [20] and several other factors [15,17,19]. The equilibrium phase compositions of small-volume systems are significantly different from the phase compositions of the same systems in the bulk state and can be modeled using the methods of equilibrium chemical thermodynamics [21] and several other approaches [22] (the applicability of thermodynamical methods in the analysis of phase equlibria in small-volume systems as well as their applicability limits are discussed in [23]). The experimental observations of the abovementioned effects are described, for example, in [24,25].…”

О Распределении По Размерам Дисперсных Частиц Фрактальной Формы

“…Оценки области применимости термодинамического подхода при описании структур малого объема на основе теории флуктуаций получены в [34]. Подобные результаты могут быть дополнены рассмотрением размерных зависимостей поверхностной энергии наночастиц [35], а также ряда физических и физико-химических свойств, включая обусловленные квантовыми эффектами [36].…”

“…Подобные результаты могут быть дополнены рассмотрением размерных зависимостей поверхностной энергии наночастиц [35], а также ряда физических и физико-химических свойств, включая обусловленные квантовыми эффектами [36]. В соответствии с данными [34][35][36] термодинамический подход успешно применяется для прогнозирования равновесных состояний в ансамблях нанодисперсных частиц и фазовых превращений в структурах малого объема при характерных размерах частиц вплоть до 2−5 nm (см., например, результаты [37,38]).…”

Spontaneously Generated Stress Waves inside Nanoparticles during Rapid Heating in Molecular Dynamics Simulation

“…It can be directly observed in surface tension fluctuations. The fluctuating pressure can be described by the formula ⟨ ( Δ P ) 2 ⟩ = − T false( ∂ P ∂ V false) S , where T is the temperature of the system and V is the volume of the system . The fluctuations will be around 100 MPa in 30 nm nanoparticles at 1000 K. The fluctuation intensity can be estimated by the stress tensor component σ φφ ( r ) calculated by the IKT method here.…”