Solid surfaces nucleation

Boundary conditions of the type (2.7.12) are important in crystallization where secondary nucleation, as pointed out by Randolph and Larson (1988), may be governed by the growth rate of existing particles. For example, consider a well-mixed crystallizer where the number density is only a function of the sole internal coordinate selected as particle size x as represented by a characteristic length, which should satisfy a population balance equation of the type (2.7.6). Randolph and Larson discuss a variety of nucleation mechanisms and conclude that contact nucleation is the most significant form of nucleation. Thus, the mechanical aspects of the crystallizer equipment which provide contact surfaces contribute to increased nucleation rate. When growing crystals, containing adsorbed solute on their surfaces, come into contact with other solid surfaces, nucleation is induced. The boundary condition for the formation of new nuclei in a real crystallizer is therefore considerably more complicated than that implied by (2.7.7). Instead, the boundary condition must read as... 

The adsorption of semicrystalline polymers at the polymer melt-solid interface is another interesting question to be answered. When a monolayer of semicrystalline polymer molecules is prepared on a solid surface, nucleation and crystal growth can be very different from that found in the bulk due to confinement effects [72-78]. Polymer chains in the vicinity of the solid surface tend to crystallize into lamellar crystals with either flat-on or edge-on orientations, depending on specific interactions with solids [79-81]. Among a variety of morphologies reported in the literature, the formation of dendrites or seaweed structures via the so-called diffusion-limited aggregation (DLA) process was the most commonly observed in semicrystalline polymer monolayers [76, 82]. 

The formation of a liquid phase from the vapour at any pressure below saturation cannot occur in the absence of a solid surface which serves to nucleate the process. Within a pore, the adsorbed film acts as a nucleus upon which condensation can take place when the relative pressure reaches the figure given by the Kelvin equation. In the converse process of evaporation, the problem of nucleation does not arise the liquid phase is already present and evaporation can occur spontaneously from the meniscus as soon as the pressure is low enough. It is because the processes of condensation and evaporation do not necessarily take place as exact reverses of each other that hysteresis can arise. 

Primary nucleation is the classical form of nucleation. It occurs mainly at high levels of supersaturation and is thus most prevalent during unseeded crystallization or precipitation. This mode of nucleation may be subdivided into either homogeneous viz. spontaneously from clear solution, or heterogeneous viz. in the presence of dust particles in suspension, or solid surfaces. 

Second, the molecular orientation of the fiber and the prepolymer matrix is important. The rate of crystal nucleation at the fiber-matrix interface depends on the orientation of matrix molecules just prior to their change of phase from liquid to solid. Thus, surface-nucleated morphologies are likely to dominate the matrix stmcture. 

As shown in 4.4.1., two stages usually occur in surface nucleation, nucleation and then nuclei growth. If surface nucleation is fast (Model C) it is likely due to reaction of a gas with the solid particle. The reaction of a liquid is the other possibility, i.e.-... 

The geochemical fate of most reactive substances (trace metals, pollutants) is controlled by the reaction of solutes with solid surfaces. Simple chemical models for the residence time of reactive elements in oceans, lakes, sediment, and soil systems are based on the partitioning of chemical species between the aqueous solution and the particle surface. The rates of processes involved in precipitation (heterogeneous nucleation, crystal growth) and dissolution of mineral phases, of importance in the weathering of rocks, in the formation of soils, and sediment diagenesis, are critically dependent on surface species and their structural identity. 

Increasing the temperature or lowering the pressure on a superheated liquid will increase the probability of nucleation. Also, the presence of solid surfaces enhances the probability because it is often easier to form a critical-sized embryo at a solid-liquid interface than in the bulk of the liquid. Nucleation in the bulk is referred to as homogeneous nucleation whereas if the critical-sized embryo forms at a solid-liquid (or liquid-liquid) interface, it is termed heterogeneous nucleation. Normal boiling processes wherein heat transfer occurs through the container wall to the liquid always occur by heterogeneous nucleation. 

The growth of thin films on solid surfaces is important in technology, and nucleation is one of the keys for understanding the growth mechanism. The ability of STM to image local structures down to atomic detail makes it ideal for the study of nucleation, thin film growth, and crystal growth. 

Variation of the initial content of the Cd(OH)2 over two orders of magnitude had virtually no influence on the final particle number, suggesting that the nuclei of the CdS particles were formed only from Cd ions initially dissolved in equilibrium with Cd(OH)2 and not on the solid surfaces of Cd(OH)2 (2). It is also suggested from this fact that the nucleation has been finished when the dissolution of the Cd(OH)2 starts. 

The foregoing description assumes adsorption of colloidal metal hydroxide from solution onto the substrate as the primary nucleation step. However, hydroxides can also adsorb on solid surfaces at pH values below that of bulk hy-... 

For the ion-by-ion reaction, nucleation is generally slower and the density of nuclei smaller. Additionally, growth occurs (ideally) only at a solid surface therefore nucleation is confined to two dimensions, in contrast to three dimensions for the cluster mechanism. The crystal growth may terminate when adjacent crystals touch each other or by some other termination mechanism, e.g., adsorption of a surface-active species. These factors should be valid regardless of whether the mechanism proceeds via free chalcogenide ions or by a complex-decomposition mechanism. 

As for the work of forming a nucleus, consider the simple case of the effect of a foreign solid surface. If the vapor and the liquid both wet the foreign surface, the work will be less than for the homogeneous case. This decrease will result in an increased rate of nucleation per nucleation site at the same superheat. 

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. 

Fig. 20. Nucleation from pits on a solid surface. The foregoing bubble shapes exist if the liquid has good wetting action on the solid.

Nucleate boiling from a solid surface is possible within a certain temperature-difference range only. If the temperature difference between the hot solid and the boiling liquid is very small, heat transfer to the liquid will occur by free convection and no bubbles will be created. If the temperature difference is increased, nucleate boiling occurs. As the AT is increased, the heat transfer rate increases, up to a point. The existence of an upper limit to nucleate boiling is of extreme importance to engineers. 

Unless otherwise specified, the nucleate-boiling values presented in this section refer to liquids boiling on hot solid surfaces. The liquids are not subcooled and the agitation is caused by natural convection only. 

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is believed to occur by surface nucleation and ledge movement by face specific reactions (37). The solid-state transformation from one polytype to another is believed to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

Because of the high surface free energy at the liquid-solid interface, it is suggested that the stages of nucleation, transport of species by surface diffusion, and crystallization occur at the interface in the boundary layer. Culfaz and Sand in this volume (48) propose a mechanism with nucleation at the solid-liquid interface. This mechanism should be most evident in more concentrated gel systems where interparticle contact is maximized for aggregation, coalescence, or ripening processes. The epitaxy observed by Kerr et al. (84) in cocrystallization of zeolites L, offretite, and erionite further supports a surface nucleation mechanism. 

There is diffusion of salt away from both the solid-liquid interface and the vapor-liquid interface, in each case toward the brine. Water moves counterflow to the salt. Heat must transfer from solid to liquid to gas through stagnant films at the solid surface and through the turbulent liquid. An additional resistance to the formation of ice exists at the ice surface, where water molecules must orient themselves and find positions of low energy before being incorporated into the crystal lattice. When inadequate ice surface or foreign particles exist in the freezer, nucleation may control or affect the rate of ice production. 

Such large undercoolings are normally not observed in metals. Undercoolings are usually so small that they are not noticed. The reason for the difference between the theory and practice is that the theory assumes nucleation occurs homogeneously (i.e., randomly throughout the liquid), whereas nuclei usually form on preexisting solid surfaces. 

When nucleation of a solid, S, occurs on a preexisting solid surface, Q, the area between the solid, Q, and the liquid, L, is reduced. However, a new surface is created between S and Q. See Figure 10.3. The net effect is a reduction of the activation energy for nucleation,... 

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