Homogeneous nucleation, crystallization

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

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... 

If mechanisms one and two do not act, then under stress, a two-dimensional homogeneous nucleation would be needed. Just as with three-dimensional nucleation of phase change (e.g., condensation or crystallization) homogeneous nucleation of bare regions can be expected to be a slow, and hence rate-limiting, process. If the solid surface is rough, then stress concentrations around asperities might accelerate this nucleation process. 

Nucleation The mechanism of crystal nucleation from solution has been studied by many scientists, and recent work suggests that—in commercial crystallization equipment, at least—the nucleation rate is the sum of contributions by (1) homogeneous nucleation and (2) nucleation due to contaci between crystals and a) other crystals, h) the walls of the container, and (c) the pump impeller. If is the net number of new crystals formed in a unit volume of solution per unit of time. 

In this chapter we have shown that diffusive transformations can only take place if nuclei of the new phase can form to begin with. Nuclei form because random atomic vibrations are continually making tiny crystals of the new phase and if the temperature is low enough these tiny crystals are thermodynamically stable and will grow. In homogeneous nucleation the nuclei form as spheres within the bulk of the material. In... 

Here our interest is in the application of homogeneous nucleation theory to produce the comprehensive plots of meta-stable crystallization. Fig. 1 illustrates the meta-stable efflorescence paths(solid lines) of (NH4)2S04 and (NH4)3H(S04)2 particles as a function of RH with the decreasing rate of ARH = 0.005 min with the deliquescence paths(O). Fig. 2 shows the expectation time of the aqueous particle composed of (NH4)2S04 and H2SO4... 

From the initial state, chains which are close to the growth front are pulled in and rapidly crystallized, adding one layer to it. Chains which are far from the attractive influence of the growth front undergo homogeneous nucleation. 

Burke and Lindow [1.13] showed, that certain bacteria (e. g. Pseudomonas syringae) can act as nuclei for crystallization if their surface qualities and their geometric dimensions are close to those of ice. Rassmussen and Luyet [1.14] developed a connection for solutions of water with ethyleneglycol (EG), glycerol (GL) and polyvinylpyrrolidone (PVP) between the subcooling down to the heterogeneous and homogeneous nucleation of ice. 

The important consequence of eq. (6.60) is that the solubility of the solid increases with decreasing radius of crystal. Although the effect is small this illustrates the need for super-saturation on homogeneous nucleation in a liquid. Super-saturation is necessary in order to obtain nucleation since the solubility of the nuclei is higher... 

The homogeneous nucleation phenomenon was first studied by droplet crystallization experiments performed on metals [57-60], alkanes [61] and polymers [62-66] when dispersed in inert low molecular weight media. The idea was that when the polymer in the bulk is subdivided into a number of droplets that is larger than the number of active heterogeneities present in the polymer, there should be a certain number of droplets without any active heterogeneity. 

Turnbull and Cech [58] analyzed the solidification of small metal droplets in sizes ranging from 10 to 300 xm and concluded that in a wide selection of metals the minimum isothermal crystallization temperature was only a function of supercooling and not of droplet size. Later, it was found that the frequency of droplet nucleation was indeed a function of not only crystallization temperature but also of droplet size, since the probability of nucleation increases with the dimension of the droplet [76]. However, for low molecular weight substances the size dependence of the homogeneous nucleation temperature is very weak [77-80]. 

Fig. 2 Optical microscopy image of a small section of a poly(ethylene oxide) (PEO) droplet dispersion sample, see text (1000-mm wide) obtained at Tc = - 2.6 °C. Amorphous droplets appear dark and semicrystalline droplets appear white under nearly crossed polarizers. The plot shows the fraction of crystallized droplets as a function of temperature upon cooling (0.4 °C min-1) for homogeneous nucleation. (Reprinted with permission from [84], Copyright 2004 by the American Physical Society)...

Another interesting implication of the data compiled in Fig. 4 is that when Tc is plotted as a function of the inverse of the sphere diameter, the limit where the sphere diameter tends to infinity should correspond to the crystallization temperature of homogeneously nucleated PEO in the bulk. In other words, this would be the maximum temperature at which homogeneous nucleation for PEO could ever be observed, for very large heterogeneity-free PEO phases or even bulk PEO. Such a temperature depends on the fitting expression employed however, it should correspond to a crystallization temperature close to - 5 °C or between - 10 and 0 °C. 

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