Gibbs-Thomson effect

If the size dependence of CB by the Gibbs-Thomson effect can be ignored, k is a constant for all particles in a system, and dr/dt increases linearly with r. From Eq. (12),... 

The experimental results obtained from balanced double-jet precipitations of AgBr crystals can thus be qualitatively explained reasonably well by the dynamic model of nucleation which includes both diffusion and the Gibbs-Thomson effect. 

For a very soluble organic compound such as sucrose (M = 342kgkmol u=l, p= 1590kgm , 7=10 Jm ) the effect is similar 1pm (0.4% increase), 0.1 pm (4%), 0.01 pm (40%). All such calculated values, however, should be treated with caution, not only because of the unreliability of 7 values but also because the Gibbs-Thomson effect may cease to be influential at extremely small crystal sizes (see Figure 3.4). 

Crystalline fragments smaller than about 1 pm probably do not survive in an agitated crystallizer where fluctuations of both temperature and supersaturation commonly occur. The so-called survival theory (Garabedian and Strick-land-Constable, 1972) is based on the Gibbs-Thomson effect (section 3.7) which suggests that microcrystals can dissolve in solutions that are supersaturated with respect to macrocrystals. 

Another, and often more powerful, effect of crystal size may be exhibited at sizes smaller than a few micrometres, and is caused by the Gibbs Thomson effect (section 3.7). Crystals of near-nucleic size may grow at extremely slow rates because of the lower supersaturation they experience owing to their higher solubility. Henee the smaller the crystals, in the size range below say 1 or 2 pm, the lower their growth rate. 

The main conclusion of Paciejewska s thesis is the necessity to consider the specific kinetics of interfacial phenomena when evaluating the stability of colloidal suspensions. This applies not only to binary, but to all kinds of colloidal suspensions. A major factor is the dissolution of the dispersed phase(s)—in particular if the solubility and the intrinsic dissolution rate are relatively large. Its relevance is especially pronounced for a large total surface area, which depends on the particle concentration and the specific surface of the particles and which determines the amount of substance that can be dissolved in a given period of time. For many nanoparticle (x < 100 nm) systems (e.g. additives for paints and coatings), it will not be permissible to ignore the influence of dissolution on the interfacial properties and even on suspension stability—independent from the Gibbs-Thomson effect, which becomes relevant at particle sizes below 10 nm (cf. Sect. 3.1.4). 

The mechanism of shrinkage is related to the Gibbs-Thomson effect (effect of Laplace pressure on the vacancy concentration) the vacancy concentration on... 

The proposed atomistic mechanism of shrinkage is the vacancy flux from the internal surface (with radius q) to the external surface (with radius Tg). The driving force of the vacancy flux is the difference in vacancy/atoms chemical potentials and the corresponding difference in equilibrium vacancy concentrations at the curved interfaces Cv(ri) > cy(re). This Gibbs-Thomson effect can be expressed, in a linear approximation so far, as... 

As already mentioned in the previous section, any hollow nanoparticle should shrink. The general driving force of shrinkage is the same for a pure component shell (Model 1) and for an IMC shell (Models 2-4) - a decrease in the total surface energy (in other formulation - Gibbs-Thomson effect). Yet, the kinetics are different. 

As mentioned above, in a hollow nanoshell formation, we have an almost pure Frenkel effect with fuUy or partially suppressed Kirkendall shift In [10], we analyzed the formation of a hollow compound nanoshell. We demonstrated that the Gibbs-Thomson effect, leading to the shrinkage of ready compound shells, should influence the formation stage as well. Sometimes it may even suppress the nanoshell formation. 

We consider the interdiffusion of A and B in a two-layer nanosheU structure, as shown in Figure 7.13 (actually, the enveloping layer A may just represent the medium in which the B particles are immersed). In this case, both the Kirkendall effect and the inverse Kirkendall effect coexist, and how they interact with each other is not completely clear. If the flux of B, jb. is bigger than the flux of A, j a, the balancing vacancy flux jV difiuses inward, which counters the vacancy flux due to the Gibbs-Thomson effect. On the other hand, if js vacancy fluxes move in the same direction, i.e. outwards. 

The Laplace tension and compression of the compound layer due to curvatures of internal and outer interfaces have been taken into account in the analysis. However, vacancy supersaturation is assumed to be outside the compound layer (in the B-core) at the initial stage of reaction, so voids can be nucleated. Curvature effects on vacancy concentration exist, so the difference of vacancy concentrations at the internal and external boundaries of the compound cannot be neglected. On the basis of the Gibbs-Thomson effect, the equilibrium vacancy concentration at the internal boundary of the compound layer is higher than that at the planar free surface... 

Note that in the above equations the values of vacancy concentration at the external and internal boundaries can be very different, due to the Gibbs-Thomson effect, and the vacancy gradient (and the cross terms in Equations 7.92-7.93 and Equations 7.95-7.96) do not tend to zero. At the same time, the concentrations of the main components at the external and internal boundaries remain close to constant because of the narrow homogeneity range of the compound. 

This equation differs from a similar equation derived by Alivisatos et al. [5] by the last term containing G 0 (responsible for Laplace pressure and Gibbs-Thomson effect both for vacancies and for main components). When both radii and n are large, i.e. 

---