Heterogeneous nucleation contact angles

Material Homogeneous nucleation Heterogeneous nucleation contact angle (degrees) ... 

Heterogeneous nucleation is most likely to occur when there is a strong tendency for the crystal to stick to the surface of the catalyst. This sticking tendency can be described by the angle of contact, 6, shown in Fig. 7.3 the smaller 6, the better the adhesion. Anyone who has tried to get electronic solder to stick to a strip of copper will understand this well. If the copper is tarnished the solder will just roll around as a molten blob with 6 = 180°, and will not stick to the surface at all. If the tarnished... 

It is easy to estimate the undercooling that we would need to get heterogeneous nucleation with a 10° contact angle. From eqns (7.11) and (7.3) we have... 

This question is about heterogeneous nucleation of orthopyroxene on olivine-melt interface in a basaltic melt. Suppose Oopx/meit = 0-35 J/m, Ooiiv/meit = 0-3 J/m, and Ooiiv/opx = 0-05 J/m. Find the contact angle and the modified interface energy o. ... 

Figure 3.13 Schematic diagram of contact angle formed at three phase intersection during heterogeneous nucleation. From K. M. Ralls, T. H. Courtney, and 1. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission John Wiley Sons, Inc.

The rates here are number of nuclei appearing per unit time. The symbol Xht refers to the number of sites available for heterogeneous nucleation and Nhm is the number for homogeneous nucleation. The first is proportional to solid surface area, the second to liquid volume. The value 0 depends only on the contact angle for wetting. 

When the concentration is closer to the supersaturation limit, heterogeneous nucleation occurs most often. The nucleus develops onto the substrate, with which it makes a contact angle a. Solution of the equations for the nucleus size and activation energy imply that the critical radius is the same as for homonuclear... 

Much of the treatment of nucleation catalysis in the literature is still qualitative, especially analysis of influences such as mechanical shock and ultrasonic vibrations. Heterogeneous nucleation (i.e., catalytic effects of foreign nuclei), however, has received some theoretical attention, building on the early work of Volmer (V6). Considering vapor condensation on a catalyst surface, he proposed using an interfacial contact angle as a mathematical parameter, defined by the equation... 

Turnbull has extended the classical theory of homogeneous nucleation to heterogeneous processes. In doing so he relied on the existence of an equilibrium contact angle 6 when two phases (crystal and liquid) are in contact with a solid substrate (see Fig. 1). In such a situation three different surface free energies play a role. There is first of all the crystal-liquid surface free energy a, which we have considered already. In addition, there are the surface... 

Figure 1. Contact angle of two phases a and jS with substrate. In case of heterogeneous nucleation (Section II.B), a is liquid, P crystal, and s substrate. In case of liquid-solid interfacial tension measurements (Section III.A), a is vapor, P liquid, and s crystal. (From Turnbull. )...

The presence of a foreign surface, specifically a polymeric membrane, decreases the work required to create critical nuclei and will increase locally the probability of nucleation with respect to other locations in the system this phenomenon is known as heterogeneous nucleation. The reduction of AG due to heterogeneous nucleation (AG ) compared to a homogeneous one (AG °" ) is related to the contact angle (0) between solution and solid substrate (Equation 4.1) ... 

FIGURE 14.5 Homogeneous and heterogeneous nucleation. Embryos (radius r) of phase p formed from phase a (a) in the absence of foreign particles, and (b) at the surface of foreign particles of material k1 or k2 in frames 2-5, the contact angle 0 = 45 degrees. 

In thermodynamic theory of heterogeneous nucleation of solid from vapor,P a nucleus on a substrate is considered to be cap-shaped with a contact angle to the substrate. Young s equation dictates the relationship among the surface and interfacial energies as ... 

In order to investigate heterogeneous nucleation at the existing interface one needs to analyze the conditions of equilibrium of such a nucleus with the medium. In the simplest case of non-crystalline nuclei (vapor or liquid), their shape is defined by the contact angle, 0 (Fig. IV-6). In agreement with the Young equation... 

Figure 5.8. Ratio of free energies of homogeneous and heterogeneous nucleation as a function of the contact angle...

Similar to the homogeneous nucleation, there is a threshold temperature, at which the number of embryos increases rapidly. This is referred to as the heterogeneous nucleation temperature. Equatimi 10.18 represents the number of embryos formed close to an interface. It indicates that the threshold temperature depends on the contact angle of the liquid and sohd wall ... 

Therefore, because of the dependence of the energy barrier on the contact angle, heterogeneous nucleation rate can be controlled by modulating the interaction between the crystallizing solution and the membrane. 

FIGURE 10.16 Zeldovich factor for heterogeneous and homogeneous nucleation versus contact angle at different membrane porosity. (Adapted from Journal of Crystal Growth, 310, Curcio, E., Di Profio, G., and Drioli, E., Prohahilistic aspects of polymorph selection by heterogeneous nucleation on microporous hydrophobic membrane surfaces, 5364-5369, Copyright (2008), with permission from Elsevier.)... 

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