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Published in Chad A. Mirkin, Spherical Nucleic Acids, 2020
Matthew N. O’Brienv, Keith A. Brown, Chad A. Mirkin
Nucleation is the universal process by which most phase transitions begin, and thus the extent to which nucleation can be controlled dictates the range of thermodynamic states that can be accessed and studied. The emergence of a new phase occurs through two primary pathways—homogeneous nucleation, in which materials spontaneously form a nucleus, or heterogeneous nucleation, where an existing surface (e.g., container wall, impurity) seeds the formation of a nucleus. To overcome the temperature-dependent activation energy associated with crystal formation, materials must be cooled below their melting temperature (Tm) by a temperature difference known as the undercooling, which results in a supersaturation that drives crystallization [1–3]. The critical undercooling at which homogeneous nucleation occurs provides the most direct thermodynamic insight into a phase transition; however, study and control of this process is experimentally challenging in many systems (e.g., atoms, polymers, proteins) due to difficulties in preventing heterogeneous nucleation [2–6].
Introduction
Published in Charles W. W. Ng, Anthony K. Leung, Junjun Ni, Plant–Soil Slope Interaction, 2019
Charles W. W. Ng, Anthony K. Leung, Junjun Ni
where Γsoil, Γplant and Γair are the heat outflux from soil, plants and the atmosphere, respectively; Fsoil is the soil heat flux, which is used for the metabolism and respiration of bacteria and fungi; and Lplant and Lsoil are the latent heat of transpiration and soil evaporation, respectively. Latent heat is the thermal energy released or absorbed by a body or a thermodynamic system during a constant-temperature process – usually a first-order phase transition. Rlr is the long-wave heat outflux from plants and the soil surface. In the equation, Lsoil and Fsoil affect the amount of water evaporation and hence soil suction. Lplant affects plant transpiration and hence suction. Different from Blight (1997), Eqs (1.4) and (1.5) consider the effects of plants on the energy balance (such as ΔSplant, ΔSreac, Lplant and Γplant).
Energy Metrics
Published in John Andraos, Synthesis Green Metrics, 2018
A phase transition corresponds to a pathway that changes the phase of a substance either by applying a change of temperature or a change of pressure. In a typical pressure–temperature (p-T) phase diagram, a phase transition occurs if a vertical or a horizontal line crosses anyone of the three boundary lines representing the boundaries between the solid, liquid, and gas phase regions of a substance. Since there are three main phases, there are six possible pairwise phase transitions that are possible as summarized in Table 5.1. Figure 5.6 shows some phase transitions depicted on a typical p-T phase diagram.
Parallel splitting solvers for the isogeometric analysis of the Cahn-Hilliard equation
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2019
Vladimir Puzyrev, Marcin Łoś, Grzegorz Gurgul, Victor Calo, Witold Dzwinel, Maciej Paszyński
Phase transition is a process through which a thermodynamic system changes from one “phase” to another. The most common phase transitions in physics are the changes between the states of matter (solid, liquid, gas, and plasma). Widely used approaches for dealing with phase transition phenomena are the sharp interface modeling and phase-field (diffuse-interface) modeling. The past two decades witnessed the rise of the phase-field approach as one of the most powerful methods for phase transition modeling. One of the main application areas is the microstructure evolution in solids which are common in many fields including biology, hydrodynamics, and chemical reactions (Fried and Gurtin 1994; Chen 2002). The phase-field method is also widely used to model solidification processes, foams, and liquid-liquid interfaces (Lowengrub and Truskinovsky 1998; Fonseca et al. 2007; Gómez et al. 2008).
State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis
Published in Molecular Physics, 2018
Max Innerbichler, Georg Menzl, Christoph Dellago
The mechanism and kinetics of first-order phase transitions can be conceptually understood in the framework of classical nucleation theory (CNT). In this model, the phase transition occurs via the formation of a small nucleus of the new, thermodynamically favoured phase within the old phase. Initially, growth of the nucleus is impeded by a free energy barrier arising from the cost of creating an interface between the two phases. For larger nuclei, however, this free energetic cost is outweighed by the favourable contribution of the new phase. As a consequence, the thermodynamically stable phase evolves to macroscopic scales only if the nucleus grows to the so-called critical size due to a rare thermal fluctuation.
Equation of State: Manhattan Project Developments and Beyond
Published in Nuclear Technology, 2021
Scott D. Crockett, Franz J. Freibert
A modern EOS model is built by leveraging data collected over experimental conditions ranging from ambient, static compression, and shock regimes, and by developing an integrated theoretical approach to ensure data set inclusion. These modern models cover compressions of 0 to 106 volumetric strains and temperatures from 0 to 109 kelvins. Once optimized across multiple data sets, the model forms naturally extend to known thermodynamic limits. We start, however, with ambient data along the 1-atm isobar. The EOS-relevant thermophysical properties data include information for the reference density, thermal expansion, specific heat, and bulk moduli. X-ray diffraction measures the initial crystal structure and density. Dilatometry measures the thermal expansion. Resonant ultrasound spectroscopy is used to measure the adiabatic bulk modulus. Calorimetry is a measurement of the enthalpy and specific heat. Experimental methods also provide the temperatures of phase transitions (solid-solid, solid-liquid, liquid-gas, solid-gas). These isobaric data provide constraints to the thermal components of an EOS model. Then theoretical calculations are used for constraining our models in regions where data are often absent. For that we rely on DFT, quantum molecular dynamics, and quantum Monte Carlo calculations. These methods are computationally intensive, but better match experimental results for most materials describable by a multiphase EOS (Ref. 24). Such a modern multiphase EOS generated at LANL for aluminum is shown in Fig. 2. Other modern EOS models include that of the Lawrence Livermore National Laboratory PURGATORIO, a novel implementation of the INFERNO EOS physical model.50