Surface crystallization kinetics

Mention was made in Section XVIII-2E of programmed desorption this technique gives specific information about both the adsorption and the desorption of specific molecular states, at least when applied to single-crystal surfaces. The kinetic theory involved is essentially that used in Section XVI-3A. It will be recalled that the adsorption rate was there taken to be simply the rate at which molecules from the gas phase would strike a site area times the fraction of unoccupied sites. If the adsorption is activated, the fraction of molecules hitting and sticking that can proceed to a chemisorbed state is given by exp(-E /RT). The adsorption rate constant of Eq. XVII-13 becomes... 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

Kinetics of Ammonia Synthesis on Re Crystal Surfaces. The kinetics of the ammonia synthesis reaction on Re were studied on the Re(ll50) surface which is composed of atoms having seven-fold coordination. The rate of production at 70 K and 20 atm. ... 

When the crystal purity is plotted against the total crystal mass in the slurry calculated from the mass balances, the purity decrease seems to start at some constant value of the crystal mass as shown in Figure 5. As mentioned earlier in the text, there are possibilities of existence of the D-enantiomer as small particles on the surface of the seed crystals. If we assume that the breeding of the D-enantiomer starts only when that enantiomer has grown to a certain size, the amount of the L-enantiomer crystals must have also increased to a certain value, the latter being proportional to the former. The crystallization kinetics of the both enantiomers are believed to be the same, the relative amounts of crystals of the both enantiomers must therefore be constant before nucleation of the D-enantiomer starts. 

Similar to chlorine and bromine, iodine may be employed as a reagent for etching semiconductor surfaces. The kinetic study of the etching of InP in iodine solutions has been reported by Vermeir et al. [185]. Single crystal surfaces in contact with iodine solution were studied and a particularly slow rate of etching at (111) surfaces was observed. An interaction of electrochemical and iodine etching processes was suggested. 

In semi-crystalline polymers the interaction of the matrix and the tiller changes both the structure and the crystallinity of the interphase. The changes induced by the interaction in bulk properties are reflected by increased nucleation or by the formation of a transcrystalline layer on the surface of anisotropic particles [48]. The structure of the interphase, however, differs drastically from that of the matrix polymer [49,50]. Because of the preferred adsorption of large molecules, the dimensions of crystalline units can change, and usually decrease. Preferential adsorption of large molecules has also been proved by GPC measurements after separation of adsorbed and non-attached molecules of the matrix [49,50]. Decreased mobility of the chains affects also the kinetics of crystallization. Kinetic hindrance leads to the development of small, imperfect crystallites, forming a crystalline phase of low heat of fusion [51]. 

It is generally considered that crystal-growth includes two steps (1) diffusion of the solute from the solution bulk towards the surface of the crystals, and (2) crystallizing reaction on the surface, the kinetics of which are represented, respectively, by... 

One of the most controversial topics in the recent literature, with regard to partition coefficients in carbonates, has been the effect of precipitation rates on values of the partition coefficients. The fact that partition coefficients can be substantially influenced by crystal growth rates has been well established for years in the chemical literature, and interesting models have been produced to explain experimental observations (e.g., for a simple summary see Ohara and Reid, 1973). The two basic modes of control postulated involve mass transport properties and surface reaction kinetics. Without getting into detailed theory, it is perhaps sufficient to point out that kinetic influences can cause both increases and decreases in partition coefficients. At high rates of precipitation, there is even a chance for the physical process of occlusion of adsorbates to occur. In summary, there is no reason to expect that partition coefficients in calcite should not be precipitation rate dependent. Two major questions are (1) how sensitive to reaction rate are the partition coefficients of interest and (2) will this variation of partition coefficients with rate be of significance to important natural processes Unless the first question is acceptably answered, it will obviously be difficult to deal with the second question. 

The lateral surface free energy a is a key parameter in polymer crystallization, and is normally derived from crystallization kinetics. In polydisperse polymers, where the supercooling dependence of growth rate is affected both by changing... 

Before we start to describe thoroughly the kinetics of mineralorganic-filled thermoplasts we would note that in Ref. [13], with the example of PE keroplasts, it was proved that kerogens only very slightly influence polymer crystallization kinetics, and, consequently can be classified as low-energy surface fillers. 

Sodium bicarbonate Sodium bicarbonate (NaHCOs) is an odorless, white crystalline powder with a saline, slightly alkaline taste. A variety of particle-size grades of powders and granules are available. The carbon dioxide yield is approximately 52% by weight. At RH below approximately 80% (at room temperature), the moisture content is less than 1%. Above 85% RH, it rapidly absorbs an excessive amount of water and may start to decompose. Its solubility in water is 1 part in 11 parts at 20°C, and it is practically insoluble in 95% ethanol at 20°C. When heated to 250-300°C, NaHCOs decomposes and is converted into anhydrous sodium carbonate. However, thisprocess is both time-and temperature-dependent, commencing at about 50°C. The reaction proceeds via surface-controlled kinetics, and when NaHCOs crystals are heated for a short period of time, very fine needle-shaped crystals of anhydrous sodium carbonate appear on the surface. ... 

Compared with the high-alumina zeolites NaCaA or NaY, the relatively low hydrothermal stability of high-silica faujasites DAY-S and DAY-Tg result from the attack of water molecules at the silanol groups and the energy-rich Si-O-Si bonds of the crystal surface. The kinetics of this dissolution is significantly more rapid than that of the hydrolysis of aluminosilicates. 

Regardless of the shear rate and temperature, only the Form V is observed at the end of crystallization. Results obtained by Ziegleder (12) for similar experiments done at 20°C are also reported in Figure 6. This author identified Form IV at the lowest shear rates and Form V at higher values. He also measured slightly slower crystallization kinetics. This is certainly due to the different experimental apparatus used in his study, since kinetics is very sensible in particular to the surface of the container in contact with the fat (13). 

Surface Reaction Kinetics-Based Models. The basic consideration in reaction kinetics models is that the reaction rate is determined by the lattice strueture on the surface. The difference in the lattice structures of various crystal planes gives rise to differences in surface bond density, electron density, surface free energy, and so on, which then determine the dissolution rate of the surface silicon atoms. All etching... 

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