Crystallization growth rate measurement

Myerson (2002), Mullin (2001), and Mersmann (2001) provide excellent descriptions of methods for crystal growth rate measurements. These methods involve measurements of either single crystals or suspensions. Much information can be gained from the traditional technique of measuring ( grab samples or in-line) solute concentration versus time in batch crystallization on a seed bed. Initial and later slopes on such a plot can provide multiple data points of growth rate versus supersaturation. 

Desupersaturation methods for crystal growth rate measurements have been reported for ammonium alum (Bujac and Mullin, 1969), potassium sulphate (Jones and Mullin, 1973a), nickel ammonium sulphate (Ang and Mullin, 1979), potassium chloride (Nyvlt, 1989) and succinic acid (Qui and Rasmuson, 1990). 

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

Bujac, P.B. and Mullin, J.W., 1969. A rapid method for the measurement of crystal growth rates in a fluidised bed crystallizer. Symposium on Industrial Crystallization. London, 1969. Rugby Institution of Chemical Engineers, pp. 121-129. 

One of the more important uses of OM is the study of crystallization growth rates. K. Cermak constructed an interference microscope with which measurements can be taken to 50° (Ref 31). This app allows for study of the decompn of the solution concentrated in close proximity to the growing crystal of material such as Amm nitrate or K chlorate. In connection with this technique, Stein and Powers (Ref 30) derived equations for growth rate data which allow for correct prediction of the effects of surface nucleation, surface truncation in thin films, and truncation by neighboring spherulites... 

Comparison of crystal growth rate coefficients measured in ISC and FBC... 

The overall rate of crystallization is determined by both the rate of nuclei formation and by the crystal growth rate. The maximum crystal growth rate lies at temperatures of between 170 and 190 °C [71, 72], as does the overall crystallization rate [51, 61, 75], The former is measured using hot stage optical microscopy while the latter is quantified by the half-time of crystallization. Both are influenced by the rate of nucleation on the crystal surface and the rate of diffusion of polymer chains to this surface. It has been shown that the spherulite growth rate decreases with increasing molecular weight due to the decrease in the rate of diffusion of molecules to this surface [46, 50, 55, 71, 74],... 

Methods used for the measurement of crystal growth rates are either a) direct measurement of the linear growth rate of a chosen crystal face or b) indirect estimation of an overall linear growth rate from mass deposition rates measured on individual crystals or on groups of freely suspended crystals 35,41,47,48). 

Therefore a particular method was chosen (4). We worked on a statistical population of crystals in order to minimize the dispersion and on simultaneous measurement of all faces in order to compare their growth rate under the same conditions of supersaturation and temperature. Therefore classical (R,o ) isotherms were obtained. Experimentally we grew at the same time and in the same solution a single crystal and twin. Whereas growth rate measurements of the forms hOL are relatively simple (thanks to the fact that the b axis is a binary axis) (Figure lb), the kinetic measurements of the p 110 and p llO forms are more difficult. 

Batch crystallization studies of D-fructose from aqueous ethanolic solutions demonstrate that crystal growth rate is dependent on supersaturation (possibly to the 1.25 power), ethanol content and temperature. It appears that solution viscosity also has an effect. Growth rates of up to 1 pm/mln were measured. 

In this study, D-SCMC seed crystals were put in a racemic SCMC supersaturated solution in a batchwise agitated vessel and growth rates in longitudinal and lateral directions and the optical purity of D-SCMC crystals were measured. The growth rates and optical purity were discussed considering surface states of grown crystal observed by a microscope. The kinetics of crystal growth were measured and a model of inclusion of impurity was proposed. 

Beers KL, Douglas JE, Amis EJ, Kaiim A (2003) Combinatorial measurements of crystallization growth rate and morphology in thin films of isotactic polystyrene. Langmuir 19 3935-3940... 

Table 4-2 Measured crystal growth rates of substances in their own melt...

Table 3-2 Diffusion coefficients of noble gases in aqueous solutions Table 3-3 Ionic porosity of some minerals Table 4-1 Steps for phase transformations Table 4-2 Measured crystal growth rates of substances in their own melt...

From the results of analysis of the structural form of quartz crystal and the growth rate measurements on synthetic quartz, it has been well established that the difference in growth rates of r 1011] and z 0111] is small,... 

No study has been made to discover which of the several resistances is important, but a simple rate equation can be written which states that the rate of the over-all process is some function of the extent of departure from equilibrium. The function is likely to be approximately linear in the departure, unless the intrinsic crystal growth rate or the nucleation rate is controlling, because the mass and heat transfer rates are usually linear over small ranges of temperature or pressure. The departure from equilibrium is the driving force and can be measured by either a temperature or a pressure difference. The temperature difference between that of the bulk slurry and the equilibrium vapor temperature is measured experimentally to 0.2° F. and lies in the range of 0.5° to 2° F. under normal operating conditions. 

On the other hand, as an implication, the equation for the diffusion rate based on Pick s law includes the assumption of the solute concentration in the liquid bulk being completely uniform, which is actually difficult to realize and thus may yield a deviation from reality. The poorer the micromixing, the larger would be the deviation. Therefore the crystal-growth rate coefficients measured in different devices with different micromixing conditions may be different from each other. 

To ensure that all the overall crystal-growth rate coefficients are measured under the conditions without nucleation, the metastable region of the solution has to be determined first and therefore the solubility and super solubility need to be measured. 

For comparison, the experiments for measuring the overall crystal-growth rate coefficient are carried out in an impinging stream crystallizer (ISC) and a fluidized bed crystallizer (FBC). 

The structure of a experimental fluidized bed crystallizer (FBC) is shown in Fig. 12.4, where the crystallizer is actually a universal equipment for the measurement of crystal-growth rate. The solution enters the FBC at its bottom, and leaves the FBC by overflow. All the other parts of the experimental system are the same as shown in Fig. 12.3, and so are not shown in Fig. 12.4. The operation procedure for the FBC is the same as for the ISC. For convenience of comparison, the corresponding conditions, temperature and concentration of the solution, operated in the ISC and the FBC are rigorously controlled to be the same, with the deviation of the operating temperature no greater than 0.05 °C. 

The values measured in the ISC for the overall crystal-growth rate coefficient of Na2HP04 are listed in Table 12.2. As can be seen, the reproducibility of the data is in a reasonable range and that of most data is very good. 

Except for a few questionable data, the values for the observed active energy measured in the two crystallizers of different types, EiS and EFB, show little difference and can be considered to be more or less identical. On the other hand, the values measured in the impinging stream crystallizer for the overall crystal-growth rate coefficient, KIS, are obviously and systematically larger than those in the fluidized bed crystallizer, A pe. Therefore it can be affirmed without the need for further analysis that, with the observed frequency factors, there must... 

In the ranges of the operating conditions tested, the overall crystal- growth rate coefficient of Na2HP04 measured in ISC, Vs. is higher systematically than that measured in FBC, Vu. by 15 to 20%, while the reaction rate constant of ethyl acetate saponification measured in the SCISR, Vs. is larger systematically than that measured in the STR, Vt> by about 20%. 

Fig. 14 Binary phase diagram for C246H494 in octacosane. The top curve shows the equilibrium liquidus for extended-chain crystals, and the bottom line the metastable liquidus for once-folded crystals. Experimental dissolution temperatures are fitted to the Flory-Huggins equation with / = 0.15 (solid lines). Vertical dotted lines (a) and (b) indicate the concentrations at which the growth rates were determined as a function of Tc in [29]. Horizontal dotted lines indicate the temperatures at which the rates were determined in [45] as a function of concentration. G(c) at Tc = 106.3 °C, measured along line (c), is shown in Fig. 12. The shading indicates schematically the crystal growth rate (black = fast), and the dashed line the position of the growth rate minimum...

Fig. 20 Crystal growth rate G of n-CiggTbgg calculated as a function of concentration at constant Tc using the model in Fig. 19. Parameters are those for C198H398 crystallization from phenyldecane at Tc = 98.0 °C, experimentally measured in [44], Compare with Fig. 12 (from [44] by permission of American Physical Society)...

Kinetic models for crystal growth usually quantify the interface velocity, which is a direct measure of the crystal growth rate. The rate of stable cluster formation on a surface is proportional to the equilibrium surface concentration of clusters (of critical radius rc), nrc, and the frequency of addition of adatoms to these clusters, va (Howe, 1997) ... 

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