Nucleation steady period

The primary nucleation process is divided into two periods in CNT one is the so called induction period and the other is the steady (or stationary) nucleation period (Fig. 2) [16,17]. It has been proposed by CNT that small (nanometer scale) nuclei will be formed spontaneously by thermal fluctuation after quenching into the supercooled melt, some of the nuclei could grow into a critical nucleus , and some of the critical nuclei will finally survive into macroscopic crystals. The induction period is defined as the period where the nucleation rate (I) increases with time f, whereas the steady period is that where I nearly saturates to a constant rate (fst). It should be noted that I is a function of N and t,I = I(N, t). In Fig. 2, N and N mean the size of a nucleus and that of the critical nucleus, respectively. The size N is defined... 

The purpose of this section is to present direct evidence of nucleation during the induction period by means of synchrotron small angle X-ray scattering (SAXS). In the classical nucleation theory (CNT), the number density distribution function of nuclei of size N at time t, f(N, t), is expected to increase with an increase of t during the induction period and saturates to a steady f(N, t),fst(N) in the steady period. The change off(N, t) should correspond to that of the scattering intensity of SAXS. 

Crystallization from the melt (or gas) is one of the most predominant and well-known phenomena in any material. Nucleation is the early stage of crystallization and significantly controls the structure and physical properties of materials. Described by the classical nucleation theory (CNT) proposed by Becker and Dbring,Turnbull and Fisher, and Frenkel in the 1930s [1-3], nucleation has an induction and a steady peri<. The induction period leads to the steady period when the nuclei are steadily generated. 

The rate of polymerization with styrene-type monomers is directly proportional to the number of particles formed. In batch reactors most of the particles are nucleated early in the reaction and the number formed depends on the emulsifier available to stabilize these small particles. In a CSTR operating at steady-state the rate of nucleation of new particles depends on the concentration of free emulsifier, i.e. the emulsifier not adsorbed on other surfaces. Since the average particle size in a CSTR is larger than the average size at the end of the batch nucleation period, fewer particles are formed in a CSTR than if the same recipe were used in a batch reactor. Since rate is proportional to the number of particles for styrene-type monomers, the rate per unit volume in a CSTR will be less than the interval-two rate in a batch reactor. In fact, the maximum CSTR rate will be about 60 to 70 percent the batch rate for such monomers. Monomers for which the rate is not as strongly dependent on the number of particles will display less of a difference between batch and continuous reactors. Also, continuous reactors with a particle seed in the feed may be capable of higher rates. 

Fig. 2 Illustration of the induction and the steady (stationary) periods during the nucleation process. Small clusters exist in the supercooled melt at t = 0. During the induction period (t < r,), isolated nuclei of size N, smaller than the critical nuclei (named nanonuclei or embryo), are formed. The nuclei grow larger and larger with increase of time and some of them attain a much larger size than the critical size, N ...

The prediction of transformation diagrams after Bhadeshia (1982). Later work by Bhadeshia (1982) noted that the approach of Kirkaldy et al. (1978) could not predict the appearance of the bay in the experimentally observed TTT diagrams of many steels, and he proposed that the onset of transformation was governed by nucleation. He considered that the time period before the onset of a detectable amount of isodiermal transformation, r, could be reasonably defined as the incubation period, r necessary to establish a steady-state nucleation rate. The following expression for r, was then utilised... 

Stage II is the quasi-steady-state nucleation regime. During this period, the distribution of clusters has built up into a quasi-steady state and stable nuclei are being produced at a constant rate. 

Non-Steady-State Nucleation The Incubation Time. Although in principle, non-steady-state nucleation in single-component systems can be analyzed by solving the time-dependent nucleation equation (Eq. 19.10) under appropriate initial and boundary conditions, no exact solutions employing this approach have been obtained. Instead, various approximate solution have been derived, several of which have been reviewed by Christian [3]. Of particular interest is the incubation time described in Fig. 19.1. During this period, clusters will grow from some initial distribution, usually essentially free of nuclei, to a final steady-state distribution as illustrated in Fig. 19.5. 

Figure 11 is a schematic summary of the nucleation process. Region I on the plot represents the induction period, region II the period of rapid nucleation and partial relief of supersolubility, and region III the period of steady growth on a constant number of nuclei. 

Polymerization of G-actin in vitro Is marked by a lag period during which nucleation occurs. Eventually, a polymerization reaction reaches a steady state In which the rates of addition and loss of subunits are equal (see Figure 19-10). 

Equation (11.2) provides the basis for studying transient nucleation. For example, if the monomer concentration is abruptly increased at t = 0, what is the time-dependent development of the cluster distribution Physically, in such a case there is a transient period over which the cluster concentrations adjust to the perturbation in monomer concentration, followed eventually by the establishment of a pseudo-steady-state cluster distribution. Since the characteristic time needed to establish the steady-state cluster distribution is generally short compared to the timescale over which typical monomer concentrations might be changing in the atmosphere, we can assume that the distribution of clusters is always at a steady state corresponding to the instantaneous monomer concentration. There are instances, generally in liquid-to-solid phase transitions, where transient nucleation can be quite important (Shi et al. 1990), although we do not pursue this aspect here. 

The existence of an induction period in a supersaturated system is contrary to expectations from the classical theory of homogeneous nucleation (section 5.1.1), which assumes ideal steady-state conditions and predicts immediate nucleation once supersaturation is achieved. The induction period may therefore be considered as being made up of several parts. For example, a certain relaxation time , c, is required for this system to achieve a quasi-steady-state distribution of molecular clusters. Time is also required for the formation of a stable nucleus, and then for the nucleus to grow to a detectable size, tg. So the induction period, tmd, may be written. 

The flow in the final stages of large steam turbines is transonic with maximum Mach numbers of about 2 and shock waves are always present. The flow may not always be steady relative to the blades and periodically oscillating waves of the type observed in nozzles by Barschdorff [1] and Skillings [2] may be the norm rather than the exception. The three-dimensional geometry of turbine blading is complex and most attempts to calculate nucleating and wet steam flows have adopted numerical rather than analytical methods. Because of this. 

Figure 22 shows experimental plots of the number of nuclei vs. time (i.e., vs. the nucleation pulse duration) at different overpotentials in the electrodeposition of mercury on platinum. The steady state nucleation rate dN/dt = const) is clearly attained only after an induction period of time. This induction period has been treated in terms of nonstationary effects connected with the readjustment of the surface to the new overpotential conditions. A detailed mathematical analysis based on the Zeldovich-Frenkel formulation of the nucleation kinetics has been given by Kashchiev and Toshev. ... 

The formation of whisker carbon cannot be tolerated in a tubular reformer. The important question is whether or not carbon is formed, and not the rate at which it may be formed. In terms of the growth mechanism, it means to extend the induction period (to in Equation 5.1) to infinity. This is achieved by keeping the steady-state activity of carbon smaller than one (refer to Section 5.2.4). The carbon formation depends on the kinetic balance between the surface reaction of the adsorbed hydrocarbon with oxygen species and the further dissociation of the hydrocarbon into adsorbed carbon atoms, which can nucleate to whisker carbon. However, this approach is complex and there is a need for simple guidelines using simple thermodynamic calculations. 

Particle formation in a steady-state CSTR, however, depends on the amount of free emulsifier within the CSTR and, thus, in the effluent stream. The average particle size will be larger than that of the particles in a batch reactor at the end of the nucleation period. Also these larger particles will be saturated with... 

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