Nucleation time dependence

Qualitatively it may be noted that the constant values of n for both types of silica fillers at all experimental terperature (with the one exception) indicates a similar crystallisation mechanism by both the high and low energy surface silica conposites. For the pure polymer, there operates a different mechanism, showing either a change in heterogeneous nucleation time dependence or in growth morphology. 

The nucleation stage is followed by two different kinetic regimes of cluster growth (i) a diffusional one (occurring at the earlier stage of growth) which is characterized by a time dependence of cluster radius scaling as where... 

The model of amyloid fibril formation is a nucleation step followed by growth, where the nucleation mechanism dictates the concentration and time dependence of the aggregation (Harper and Lansbury, 1997 ... 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

The occurrence of coagulative nucleation does not alter the -power dependence of N on R,. However, the coagulative nucleation mechanism indicates a more complex dependence of N on S. The exponent of S decreases monotonically from 1.2 to 0.4 with increasing S. The concentration of polymer particles is higher and the nucleation time is longer for systems with high surfactant concentrations. Polymer particle formation becomes less efficient at longer... 

The assumption of a stationary nucleation rate is justified by the fact that in situations not too far from equilibrium the relaxation time is small compared to those timescales which determine the hydrodynamical evolution of the shell. Yet this is not true for the growth process which always has to be treated as a time dependent problem (c.f. Gail and Sedlmayr, 1987c). 

Metal oxidation is a heterogeneous solid state reaction and starts in the same way as other heterogeneous reactions with nucleation and initial growth. This was discussed in Chapter 6. A time-dependent nucleation rate may dominate the overall growth kinetics of thin Films. Even under an optical microscope (i.e., in macroscopic dimensions), preferential sites of growth can still be discerned [J. Benard (1971)). This indicates that lateral transport on the surface (e.g., at sites where screw dislocations emerge) can possibly be more important for the initial reactive growth than transport across thin oxide layers. 

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. 

Approximate solutions of the time-dependent nucleation equation discussed by Christian indicate that the time-dependent nucleation rate in Region I for a singlecomponent system may be approximated by... 

Time Cone Vc for Isotropic, Time-Dependent Growth Rate R t). The time cone s geometry is given by simple relations. For isotropic (i.e., radial) growth, at time t the radius of a transformed region nucleated at an earlier time r is given by... 

Number of Nuclei Expected in the Time Cone, (N)c. For time-dependent nucleation rates J (t) and isotropic growth rates R (t) (such as in nonisothermal transformations under conditions in which thermal gradients can be neglected), the number of nuclei in Vc is given for the d = 3 case as... 

Adamski and Klimczyk analyzed cholesteryl pelargonate36) and caproate 37) liquid crystal to fully-ordered-crystal transitions over a temperature range of about 25 K. Again, the appearance of the fully ordered crystals was that of a spherulitic superstructure. The nucleation was time dependent, and the linear growth rate of the spherulites decreased with decreasing temperature by a factor 1/2 to 1/3, in contrast to the nonanoate and acetate. The Avrami exponent was close to 4 as judged from the measurement of the crystallized volume in the field of view under the microscope. 

Chapter 3 presents the fundamentals of the time-dependent hydrate phenomena of nucleation, growth, and decomposition. These fundamentals are presented with an objective of understanding how hydrate formation and decomposition occur, such that this knowledge may be applied to a range of hydrate applications, such as flow assurance, storage, separation, or gas production from hydrate reservoirs. 

Two questions of hydrate time-dependent phenomena are essential to both industry and researcher (1) When will hydrates nucleate (2) Once nucleated, how rapidly will hydrates grow or dissociate ... 

The time-dependent phenomena of hydrate nucleation and growth are challenging to both measure and model. This is in contrast to hydrate thermodynamics that... 

Although both SH transients in Fig. 5.21 fall to a minimum at about the same time, their form is quite different and qualitative comparisons are useful. The isotropic contribution, /pp(/), decays as a single exponential, in agreement with previous measurements of submonolayer thallium deposition on polycrystalline electrodes [54]. The solid line in Fig. 5.21 a is an exponential fit with r = 10.7 msec. The exponential form suggests that the deposition occurs by an absorption, rather than a nucleation, mechanism [154]. The transient anisotropic response is not as simple. In fact, the initial fall in /ps( ) in Fig. 5.21 b is not a simple decaying exponential. The differing time dependencies for the isotropic and anisotropic responses suggests that f, the bulk anisotropic susceptibility element which is the only common element, is not the main source of the nonlinear response in either case. 

Crystallization is an inherently time-dependent process the nucleation and growth of crystalline structures, the degree of crystallinity, the phase structure and quality of crystal lamellae, and their connectedness strongly influence the mechanical properties of semi-crystalline polymers. It is for this... 

L. Demeio and B. Shizgal, /. Chem. Phys., 98, 5713 (1993). Time Dependent Nucleation. II. A Semiclassical Approach. 

It is worth noting that the condition of constancy of the dissolution rate is rather essential. If the dissolution rate decreases during the experiment, as is often the case, it may well happen that the conditions under which inequality (5.34) is satisfied, are established even before the full disappearance of the ApBq layer due to its dissolution in the liquid. Therefore, after some temporary reduction, the layer thickness will again start to increase. Both equations (5.19) and (5.27) allow such a form of the layer thickness-time dependence. Hence, under varying dissolution conditions it is not so easy to unambiguously decide whether the absence of the ApBq layer is due to the difficulties of phase nucleation or to its too high dissolution rate exceeding the rate of interfacial chemical reactions. 

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