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Nanodrops on the Solid surface Contact Angle, Sticking Force
Published in Eli Ruckenstein, Gersh Berim, Wetting Theory, 2018
The dependence of the contact angles of nanodrops of Lennard-Jones type fluids in nanocavities on their sizes are calculated using a nonlocal density functional theory in a canonical ensemble. Cavities of various radii and depths, various temperatures, as well as various values of the energy parameter of the fluid-solid interactions were considered. It is argued that this dependence might affect strongly, for instance, the rate of heterogeneous nucleation on rough surfaces, which is usually calculated under the assumption of constant contact angle. In the framework of the classical nucleation theory, this assumption essentially simplifies the calculation of the free-energy barrier for nucleation, which is a function of the unique contact angle given by the Young equation. The obtained results show that the contact angle that a nanodrop makes with the surface of a cavity depends on the size Nd of the drop.
Surface Energy and Nucleation Modes
Published in Ion N. Mihailescu, Anna Paola Caricato, Pulsed Laser Ablation, 2018
To summarize the classic thermodynamic picture, clusters smaller than a critical size appear and disappear spontaneously through thermal fluctuations. A transient regime, lasting a time termed “incubation time,” exists before the nucleation rate reaches its stationary value [55, 58–60]. In the case of a nucleation barrier comparable to or higher than the thermal energy kBT, metastable clusters may overcome the critical size and from there on continue to grow and become more and more stable. Classical nucleation theory assumes that the steady-state distribution of a nucleating system slightly deviates from the equilibrium distribution around the critical size. Cluster random size fluctuations around the critical size may cause disintegration of a stable nucleus [52] and only the critical clusters reaching a size large enough to enter the steady-state regime fall in the stable region and can continuously grow (supercritical nuclei). Definitively, the steady state can be reached once the cluster size increases far enough away from the critical size.
Phase Change Memory and Its Applications in Hardware Security
Published in Mark Tehranipoor, Domenic Forte, Garrett S. Rose, Swarup Bhunia, Security Opportunities in Nano Devices and Emerging Technologies, 2017
Raihan Sayeed Khan, Nafisa Noor, Chenglu Jin, Jake Scoggin, Zachary Woods, Sadid Muneer, Aaron Ciardullo, Phuong Ha Nguyen, Ali Gokirmak, Marten van Dijk, Helena Silva
Classical nucleation theory uses thermodynamic properties to model crystallization dynamics. The energy associated with a grain is approximated as the sum of a positive component (associated with the surface area of the grain) and a negative component (associated with the volume of the grain): $$ \Delta G(r) = 4\pi r^2\sigma - \frac{4}{3}\pi r^3 \Delta g $$ΔG(r)=4πr2σ−43πr3Δg where ΔG(r) is the free energy of a crystal with radius r, σ is the surface tension between the amorphous and crystalline phases, and Δg is the energy difference per unit volume between the amorphous and crystalline phases. There is a critical grain size at the maximum of ΔG: crystal grains smaller than the critical size can reduce their energy by shrinking, while crystal grains larger than the critical size reduce their energy by growing (Figure 6.2). While it is energetically unfavorable for subcritical nuclei to form and grow, thermal energy in the system makes it possible. In a material with no subcritical nuclei (i.e., no atoms in the material are associated with a crystal), subcritical nuclei form and grow due to thermal energy until a steady-state Boltzmann distribution is reached. The experimentally observed incubation time (time before steady-state crystallization begins) is captured by classical nucleation theory as the time for this steady-state subcritical nuclei distribution to form [25]. σ and Δg can be approximated from material viscosity and the heat of fusion at melt. Kalb uses classical nucleation theory to extract nucleation and growth parameters from experimental data of GexSbyTez compounds and Ag5In5Sb60Te30 (AIST) [26,27]. Burr models crystallization in GST by tracking a large 3D matrix of GST atoms with probabilistic association and dissociation rate equations based on classical nucleation theory and extracts temperature-dependent nucleation and growth rates [28]. Nucleation and growth rates extracted from classical nucleation theory can then be used in less computationally expensive models (e.g., JMAK), but typically at the expense of physical relevance and accuracy.
Microstructural evolution and phase transformation in the liquid-solid Al/Ni diffusion couple
Published in Philosophical Magazine, 2019
Z.X. Zhang, H. Jiang, A.M. Russell, W. Skrotzki, E. Müller, R. Schneider, D. Gerthsen, G.H. Cao
The precipitation of the γ′ phase from the supersaturated γ-Ni(Al) solid solution is divided into three stages: (i) nucleation of the γ′ phase, (ii) growth of the nuclei and accompanying depletion of the solutes from γ-Ni(Al), and (iii) coarsening of the precipitates of the γ′ phase, operating in isolation or concurrently. According to the classical nucleation theory, the nucleation rate I (per unit volume) in a homogeneous nucleation process is given by Equation (1) for the steady state [39]:Here, n0 is the number of atomic nucleation sites per unit volume, Z is the Zeldovich factor, β* is the rate at which atoms are added to the critical nucleus, k is Boltzmann’s constant and T is the absolute temperature. ΔG* stands for the Gibbs free energy of forming a critical nucleus of the precipitate, which is given by Equation (2) [40]:where σ is the free energy of the precipitate/matrix interface and is the molar volume of the precipitate. represents the molar free energy of formation of the precipitate being the driving force associated with the nucleation event, which is proportional to the degree of supersaturation and undercooling () below the equilibrium solvus temperature.
On aerosol formation by condensation of oil vapor in the crankcase of combustion engines
Published in Aerosol Science and Technology, 2022
N. Nowak, T. Sinn, K. Scheiber, C. Straube, J. Pfeil, J. Meyer, T. Koch, G. Kasper, A. Dittler
Figure 13 indicates that the surface tension has a minor impact on aerosol formation when cooling down saturated oil vapor. This was unexpected as classical nucleation theory suggests a major negative influence of surface tension on nucleation rates (see Equation (4)). The simulations have shown however, that higher surface tensions also delay the start of nucleation during cool-down, thus, permitting the build-up of higher peak saturations before the on-set of particle formation. (In our simulation, the delay was from about 14 ms to 20 ms, leading to an increase in S from 40 to 383!) Ultimately both factors seem to neutralize each other resulting in similar aerosol nucleation rates, number concentrations and diameters after cool-down.
Surface tension data of n-propane, n-octane and n-dodecane from nucleation simulations
Published in Tellus B: Chemical and Physical Meteorology, 2018
Zamantha Nadir Z. Martin, Imee Su Martinez, Ricky B. Nellas
Our current understanding of nucleation has been enriched by a number of theories (Kathmann et al., 2009; Karthika et al., 2016), the most dominant of which is the Classical Nucleation Theory (CNT) (Volmer and Weber, 1926; Becker and Döring, 1935; Frenkel, 1939). While it generally predicts erroneous nucleation rates and critical supersaturations at extreme temperatures, CNT predictions for most gases have been within reasonable error (Cohen, 1970; Laaksonen et al., 1995).