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Classical Nucleation Theory
Classical nucleation theory (CNT) is the most common theoretical model used to quantitatively study the kinetics of nucleation.H. R. Pruppacher and J. D. Klett, ''Microphysics of Clouds and Precipitation'', Kluwer (1997)P.G. Debenedetti, ''Metastable Liquids: Concepts and Principles'', Princeton University Press (1997) Nucleation is the first step in the spontaneous formation of a new thermodynamic phase or a new structure, starting from a state of metastability. The kinetics of formation of the new phase is frequently dominated by nucleation, such that the time to nucleate determines how long it will take for the new phase to appear. The time to nucleate can vary by orders of magnitude, from negligible to exceedingly large, far beyond reach of experimental timescales. One of the key achievements of classical nucleation theory is to explain and quantify this immense variation. Description The central result of classical nucleation theory is a prediction for the ''rate of nucleati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nucleation
In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled (at atmospheric pressure) below 0°C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0°C often stay completely free of ice for long periods (supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay. Nucleation is a common mechanism which generates first-order phase transitions, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immedi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Water Model
In computational chemistry, a water model is used to simulate and thermodynamically calculate water clusters, liquid water, and aqueous solutions with explicit solvent. The models are determined from quantum mechanics, molecular mechanics, experimental results, and these combinations. To imitate a specific nature of molecules, many types of models have been developed. In general, these can be classified by the following three points; (i) the number of interaction points called ''site'', (ii) whether the model is rigid or flexible, (iii) whether the model includes polarization effects. An alternative to the explicit water models is to use an implicit solvation model, also termed a continuum model, an example of which would be the COSMO solvation model or the polarizable continuum model (PCM) or a hybrid solvation model. Simple water models The rigid models are considered the simplest water models and rely on non-bonded interactions. In these models, bonding interactions are imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colloids
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend the definition to include substances like aerosols and gels. The term colloidal suspension refers unambiguously to the overall mixture (although a narrower sense of the word ''suspension'' is distinguished from colloids by larger particle size). A colloid has a dispersed phase (the suspended particles) and a continuous phase (the medium of suspension). The dispersed phase particles have a diameter of approximately 1 nanometre to 1 micrometre. Some colloids are translucent because of the Tyndall effect, which is the scattering of light by particles in the colloid. Other colloids may be opaque or have a slight color. Colloidal suspensions are the subject of interface and colloid science. This field of study was introduced in 1845 by Italian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Point (thermodynamics)
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a ''critical temperature'' ''T''c and a ''critical pressure'' ''p''c, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures, and the ferromagnet–paramagnet transition (Curie temperature) in the absence of an external magnetic field. Liquid–vapor critical point Overview For simplicity and clarity, the generic notion of ''critical point'' is best introduced by discussing a specific example, the vapor–liquid critical point. This was the first critical point to be discovered, and it is still the best known and most studied one. The figu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binding Energy
In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly used in condensed matter physics, atomic physics, and chemistry, whereas in nuclear physics the term ''separation energy'' is used. A bound system is typically at a lower energy level than its unbound constituents. According to relativity theory, a decrease in the total energy of a system is accompanied by a decrease in the total mass, where . Types of binding energy There are several types of binding energy, each operating over a different distance and energy scale. The smaller the size of a bound system, the higher its associated binding energy. Mass–energy relation A bound system is typically at a lower energy level than its unbound constituents because its mass must be less than the total mass of its unbound constituents. For sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grand Potential
The grand potential is a quantity used in statistical mechanics, especially for irreversible processes in open systems. The grand potential is the characteristic state function for the grand canonical ensemble. Definition Grand potential is defined by : \Phi_ \ \stackrel\ U - T S - \mu N where ''U'' is the internal energy, ''T'' is the temperature of the system, ''S'' is the entropy, μ is the chemical potential, and ''N'' is the number of particles in the system. The change in the grand potential is given by : \begin d\Phi_ & = dU - TdS - SdT - \mu dN - Nd\mu \\ & = - P dV - S dT - N d\mu \end where ''P'' is pressure and ''V'' is volume, using the fundamental thermodynamic relation (combined first and second thermodynamic laws); :dU = TdS - PdV + \mu dN When the system is in thermodynamic equilibrium, ΦG is a minimum. This can be seen by considering that dΦG is zero if the volume is fixed and the temperature and chemical potential have stopped evolving. Landau free ene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorials
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the exponential function and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal De Broglie Wavelength
In physics, the thermal de Broglie wavelength (\lambda_, sometimes also denoted by \Lambda) is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature. We can take the average interparticle spacing in the gas to be approximately where is the volume and is the number of particles. When the thermal de Broglie wavelength is much smaller than the interparticle distance, the gas can be considered to be a classical or Maxwell–Boltzmann gas. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this critical temperature, the thermal wavelength will be approximately equal to the interparticle distance. That is, the quantum nature of the gas will be evident for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Configuration Integral
In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the environment at fixed temperature, volume, and number of particles. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microstate (statistical Mechanics)
In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density. Treatments on statistical mechanics define a macrostate as follows: a particular set of values of energy, the number of particles, and the volume of an isolated thermodynamic system is said to specify a particular macrostate of it. In this description, microstates appear as different possible ways the system can achieve a particular macrostate. A macrostate is characterized by a probability distribution of possible states across a certain statistical ensemble of all microstates. This distribution describes the probability of finding the system in a certain microstate. In the thermodynamic limit, the microstates visited by a macroscopic system during ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grand Partition Function
In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the environment at fixed temperature, volume, and number of particles. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
