Growth one-dimensional

The concept of the specific resistance used in equation 4 is based on the assumptions that flow is one-dimensional, growth of cake is unrestricted, only soHd and Hquid phases are present, the feed is sufficiently dilute such that the soHds are freely suspended, the filtrate is free of soHds, pressure losses in feed and filtrate piping are negligible, and flow is laminar. Laminar flow is a vaHd assumption in most cake formation operations of practical interest. 

One-dimensional growth (Lath-shaped particles of reactant) ... 

The apparent activation energy of decomposition estimated from the Arrhenius plot for gave 120 kJ/mol. Conversely, Stander noticed that if the difference between the experimental dissociation pressures (e.g., 384 kPa) and the equilibrium (plateau) dissociation pressure corresponding to T = const (e.g., 404 kPa at T = 335°C for MgH ) is relatively small, then better fits were obtained with the model of random nucleation followed by one-dimensional growth or instantaneous nucleation followed by two-dimensional growth as given by the equation ... 

All of the various methods of producing whiskers may be characterized as one-dimensional growth. The term refers to conditions that are constrained in such a way as to promote growth in one crystallographic direction. If the basic units, or crystal structure, of the phase to be made as a whisker are anisotropic, the direction of growth is influenced and possibly enhanced along certain directions by chemical affinities that lower the nu-cleation energy. A well-known example is polymerization. 

ORDER-DISORDER THEORY AND APPLICATIONS. Phase transitions in binary liquid solutions, gas condensations, order-disorder transitions in alloys, ferromagnetism, antiferromagnetism, ferroelectncity, anti-ferroelectricity, localized absorptions, helix-coil transitions in biological polymers and the one-dimensional growth of linear colloidal aggregates are all examples of transitions between an ordered and a disordered state. 

The role of surfactants in promoting one-dimensional growth from single crystal seeds has been analysed computationally and this is discussed in Section 11.4 1.2 4. 

Further suppiort for the model of one-dimensional growth being driven by preferential binding of organic species to higher energy crystal faces is provided by recent computational work. 

The ultimate particle size distribution can be calculated by simple geometry. A simple calculation is shown in Table 4-2 for growth on 5 micron cubes at different seed/nucleate levels, for three-, two-, and one-dimensional growth. As noted in the note at the bottom... 

In order to obtain one-dimensional structures, there has to be a preferential growth direction (i.e. a faster growth rate in a particular direction). Even though the exact mechanism responsible for one-dimensional growth in the vapor phase is still not clearly understood, vapor phase methods have been explored and are extensively used by many research groups to synthesize one-dimensional materials. The main advantage is its simplicity in terms of the procedure and the experimental set-up used. 

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