Aggregation and nucleation

Structure, or in the case of polymorphs, with a limited number of well-defined structures. Those structures are invariant across a wide variety of conditions, in some cases almost under any conditions for which crystals form. Two of the principal questions to be asked for such a process is how it begins and how it proceeds, especially in the context of polymorphic systems. A great deal of work has been devoted to attempts to answer these questions, and in spite of considerable progress especially on experimental and empirical fronts, there is still much to be learnt in developing current models. Historical treatments of the classic notions of crystallization and recrystallization, including many important references, have been given by Tipson (1956) and van Hook (1961). A more recent thorough account may be found in Mullin s book (1993). 

In an attempt to avoid some of the confusion extant in the current literature on the nature of nucleation, Mullin has provided a useful schematic classification for various terms in use  

Primary nucleation refers to those systems that do not contain crystalline matter. When no foreign bodies are present (i.e. the crystallization results from the spontaneous formation of nuclei of the crystallizing material) the process is referred to as homogeneous. The presence (intentional or unintentional) of foreign particles can also induce nucleation, which is then termed heterogeneous. 

Secondary nucleation deals with the situation in which nuclei are generated in the vicinity of crystals of the solute already present in a supersaturated solution. The solute crystals may have resulted from primary nucleation or may be deliberately added. This subject has also been covered by Mullin, as well as in a number of reviews (Strickland-Constable 1968 Botsaris 1976 DeJong 1979 Garside and Davey 1980 Garside 1985 Nyvlt etal. 1985). 

Mullin has argued that the minimum number of molecules in a stable crystal nucleus can vary from about ten to several thousand. A model based on the simultaneous collision of this number of molecules with the degree of order required for it to be recognized by additional molecules as a crystal is highly unlikely. A more likely scenario is that the nucleus would be generated by a sequence of bimolecular additions in which the so-called critical cluster would be built up stepwise  

Martin, this volume Waychunas, this volume) lead to the speculation that nanoparticle aggregation is a pathway for crystal growth from molecules to microcrystals in many systems under some conditions. However, processes involving particles with sizes between those of molecules and 2 nm are very difficult to study with the level of detail needed to clearly resolve reaction mechanisms (though, of course, the existence of particle aggregates can be documented fairly easily). 

Luther et al. (1999) suggested that Zn clusters form an amorphous precipitate that develops long-range order with further cross-linking. However, as noted above, biogenic 

ZnS occurs as very small, crystalline nanoparticles and oriented aggregation-based crystal growth involving few nanometer-diameter ZnS nanoparticles occurs. Thus, we postulate that sphalerite nanoparticles form due to the aggregation of sphalerite-like Zri4S6(H20)4 clusters whereas wurtzite nanoparticles form by oriented aggregation of wurtzite-like Zn6S6(H20)9 clusters. These consideration may be relevant to many important minerals that are isostructural with sphalerite and wurtzite. 

The particle-size dependence of electrochemical interactions is a potentially very important, but largely unstudied, aspect of geochemically-significant mineral reactivity. 

Whether a mineral undergoes oxidation or reduction is determined by the rest potential if there is only one pair of redox process occurring on a mineral surface (the rest potential is the potential an electrochemical system will naturally approach if no external voltage is applied). The redox behavior will be determined by the mixed potential if there 

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A—Single crystal aggregates and nucleated against etched aluminum O—Nucleated against gold... 

CrystaUisation of biliary cholesterol monohydrate is a multiphase process not yet fuUy understood [60]. Bile is normally supersaturated with respect to cholesterol [61] which is solubilised by bile salts (the soluble end product of cholesterol metabolism, such as sodium glycocholate and sodium taurocholate [9]) within micelles, whose solubilising capacity is considerably increased by the incorporation of phosphohpid molecules such as lecithin [62]. Biliary vesicles contain virtually no bile salts but may accumulate cholesterol up to a cholesterol/phosphohpid ratio of 2 1 (by phospholipid transfer to micelles) [63]. These thermodynamically unstable (but kinetically stabilised) vesicles then aggregate and nucleate cholesterol crystals [64,65]. The mechanism of this crucial miceUe-to-vesicle transition has been the subject of various physicochemical studies, including, e.g. calorimetric, turbidimetric, dynamic light and neutron scattering methods [66-69]. 

Thus under ideal circumstances the modes of aggregation can be discriminated by such plots. Deviations below the expected slopes are usually attributed to collision inefficiency leading to imperfect aggregation. In a crystallization or precipitation process, of course, deviations may also occur due to growth and nucleation unless properly accounted for. 

Low-frequency conductivity data [37] obtained along this 45°C isotherm are illustrated in Fig 2. The initial oscillatory variation in the conductivity for a > 0.9 can be assigned to variations in AOT partitioning among dimers and other low aggregates and reverse micelles, as reverse micelles are nucleated by added water (brine). These variations will be discussed in greater detail in another publication. The key behavior for the purposes of this exposition is the onset of the electrical conductivity percolation at a = 0.85. The conductivity increases two orders as a decreases from 0.85 to 0.70, and as shown in the inset, the conductivity increases another two orders as a a decreases from 0.7 to 0.3. 

All of the chemical species, except one, will be assumed to be completely soluble. The one partially insoluble species will nucleate and grow a solid phase. A typical example is A + B ->P where P is a sparingly soluble compound. The rates of nucleation J and molecular surface growth G can be functions of the local concentration vector c, the particle size l, and the local turbulence properties. Neglecting aggregation and breakage processes, a microscopic PBE for this system can be written as follows ... 

We now turn to the question of developing a CFD model for fine-particle production that includes nucleation, growth, aggregation, and breakage. Applying QMOM to Eq. (114) leads to a closed set of moment equations as follows ... 

Von Gunten, U., and W. Schneider (1991), "Primary Products of the Oxygenation of Iron(II) at an Oxic-Anoxic Boundary Nucleation, Aggregation, and Aging", J. Colloid and Interface Science 145, 127-139. 

A structure formed by the reversible association of am-phiphiles in apolar solvents. In inverted micelles, the polar portion of the amphiphile is concentrated in the interior of the macrostructure. Such association usually occurs with aggregation and is not typically characterized by a definite nucleation stage. Thus, inverted micelles (also referred to as inverse or reverse micelles) often fail to exhibit critical micelle concentration behavior. See Micelle... 

We thus ask What causes CS planes to nucleate (i.e. what are the reasons for anion vacancy aggregation and collapse in an oxide catalyst) and grow. We examine the response of defects in oxidizing atmospheres and, in particular, the role of anion vacancy concentrations in catalytic oxides. The EM results have led to novel concepts in oxidation catalysis (Gai 1981, 1992-1993, Gai et al 1982). 

The detailed mechanisms of nanoparticle formation (nucleation, growth, aggregation, and ripening) are understood only in qualitative detail so there are no reliable process models available... 

According to the aggregative and coagulative nucleation mechanisms which have been derived originally from the homogeneous nucleation theory of Fitch and Tsai [128], the most important point in the reaction is the instant at which colloidally stabilized particles form. After this point, coagulation between similar-sized particles no longer occurs, and the number of particles present in the reaction is constant. As shown in Fig. 6, the dispersion copolymerization with macromonomers is considered to proceed as follows. (1) Before polymerization, the monomer, macromonomer, and initiator dissolve completely into the... 

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