Two-dimensional nucleation methods

The kinetics of formation of the condensed layer of adenosine, studied by the potential step method, is controlled by a two-dimensional nucleation and growth process as well [28]. The rate of relaxation measured is a function of the initial potential situated respectively in the low adsorption range or in the high adsorption range. The asymmetrical kinetic behaviour can be explained by the difference between the metastable states prior to the relaxation depending on the initial potential. 

Let us discuss main ideas of the above mentioned methods on an example of thin film growth kinetics for structureless gas flux under the conditions when diffusion processes are faster than those of adsorption-desorption (see. (8.3.7)). On the initial stage of film formation a role of diffusion is restricted to the promotion of two-dimensional nucleation (two-dimensional vapor of adatoms is assumed to be supersaturated). The study of growth kinetics at all stages of film formation can be done on the base of (8.3.7). On the other hand, if one is interested in the film growth description on large time scale (when nuclei are large and can be treated thermodynamically) methods of linear thermodynamics of irreversible processes can... 

Formation and stripping of a cobalt adlayer on/from a polycrystalline Au electrode have been studied [469] applying electrochemical methods under underpotential conditions. The kinetics of deposition fitted a model of a simultaneous adsorption and diffusion-controlled two-dimensional instantaneous nucleation of cobalt on the electrode surface. 

Philipp and Retter [151] have studied the formation of the first monolayer of adenine on mercury electrode in borate solutions. Applying potential-step method, they have proposed to explain the observed transients in terms of two-dimensional (2D) truncated progressive nucleation and constant growth of monolayer islands. 

The data for the isothermal crystallization of [IX-Cg] from the glassy state were analyzed by the same method as that for the polyethers. Avrami s index obtained was between 2.1 and 2.2, i.e., n = ca. 2. This value, n = 2, suggests that the crystals grow two-dimensionally, if the nucleation process is heterogeneous and the growth process is diffusion-controlled. 

The method of molecular dynamics (MD) provides a remarkable opportunity for the observation of various mechanisms of processes taking place on a micro-(nano-) level, and for the evaluation of the probability of such processes by repeating experiments dozens of times. Figure IX-37 shows the MD simulation of the deformation and fracture of a two-dimensional crystal. Plastic deformation and formation of a dislocation (AB) at elevated temperature (upper part) and the formation of a brittle crack at low temperature (lower part) are shown in Fig. IX-37, a, while simultaneous processes of crack nucleation influenced by the presence of foreign atoms, and their propagation to the tip of the crack, taking place at elevated temperature, are illustrated in both lower and upper portions of Fig. IX-37, b [40,41]. 

Kinetic of two-dimensional condensation The kinetics of nucle-ation and growth of a new phase can be observed by two different methods. The first method embodies the direct detection of isolated nucleations, and hence a statistical analysis is required (mononucle-ation regime). The second method focuses on the deterministic behavior of large numbers of nuclei (polynucleation regime) [83]. 

The general formula for the nucleation work AG(n) = -nAji +0 n) (equation (1.32)) provides the possibility to obtain explicit expressions for this quantity if the surface free energy 0(n) is evaluated accounting for the supersaturation dependence of the nucleus size MAji). To illustrate the thermodynamic method developed by Gibbs [1.2] and Volmer [1.11,1.16] we shall calculate the woik of formation of two-dimensional (2D) and three-dimensional (3D) liquid and crystalline nuclei on flat foreign substrates. For the sake of simplicity in these calculations we shall consider the idealized case of a stmctureless substrate thus neglecting any lattice mismatch between the electrode surface and the nuclei of the new phase. 

The seeding-growth procedure is a popular technique that has been used for a century to synthesize metal particles in solution. Recent studies have successfully led to control the dimensionality of the particles where the sizes can be manipulated by varying the ratio of seed to metal salt [23-25]. The step-by-step particle enlargement is more effective than a one-step seeding method to avoid secondary nucleation [26,27]. This mechanism involves a two-step process, i.e. nucleation and then successive growth of the particles as illustrated in Scheme 1. 

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