Nucleation, crystal homogeneous

Keywords ABC triblock copolymers Block Copolymers Crystallization Homogeneous nucleation... 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

In the nucleation step, there must be sites upon which the crystals can form. This is similar to seeding the clouds to cause water to precipitate (rain). There are two sources for these nucleating particles homogeneous and heterogeneous agents. 

Whether nucleation is homogeneous, heterogeneous or both there is strong evidence that in subsequent crystal growth the gel, if present, progressively dissolves and that the dissolved material then feeds the growing crystals. This also applies in successive transformations such as ( ) ... 

The existence of the phase boundary between the solid and liquid phase complicates matters, since a phase boundary is associated with an increase in free energy of the system which must be offset by the overall loss of free energy. For this reason the magnitudes of the activated barriers are dependent on the size (i.e. the surface to volume ratio of the new phase) of the supramolecular assembly (crystal nucleus). This was recognized in 1939 by Volmer in his development of the kinetic theory of nucleation from homogeneous solutions and remains our best model today (Volmer 1939). 

There are two approaches to nucleation kinetics that have been utilized to explain intraglobular fat crystallization—homogeneous and heterogeneous nucleation. During homogeneous nucleation, there are no impurities present to act as nucleation catalysts (6). Heterogeneous nucleation involves the presence of impu-... 

There are several other points of view regarding the definition of the nucleus of zeolite. For example, it was suggested that some primary structural units of the framework, such as rings and basic cages, could be defined as the nucleus of zeolites and other microporous crystals. It was also proposed that the nucleus of zeolite could be defined as particles with critical size. These particles should be stable under crystallization conditions. Compared with the classical theory of nucleation from homogeneous solution, the theory developed by Pope could well explain the significant decrease of the free-energy barrier of nucleation for zeolites and other microporous compounds.[43] This... 

The homogenization could be effectively coupled with nucleation/crystallization to allow in-unit separation and phase transfer catalysis. 

The crystallization of dilferent polymorphs and crystal forms is best understood in terms of nucleation, which is often the rate-determining step (16). In the absence of foreign particles for inducing heterogeneous nucleation, spontaneous homogeneous nucleation can be assumed to occur as a first step in the crystallization process. The rate of homogeneous nucleation J can be expressed as... 

Nucleation is homogeneous. This is very seldom the case. As discussed below, crystal nucleation occurs almost always heterogeneously on impurity particles or container walls at relatively low undercoolings. 

In simple liquids studied by computer simulation the problem of glass formation through structural arrest cannot be dissociated from the problem of nonequilibrium crystallization (homogeneous nucleation), since under many conditions the time scales for the two processes are comparable. A broad review emphasizing phase changes has recently been given by Frenkel and McTague, to which we refer the interested reader for a more... 

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