Minimum crystallization temperature

As compared to ECC produced under equilibrium conditions, ECC formed af a considerable supercooling are at thermodynamic equilibrium only from the standpoint of thermokinetics60). Indeed, under chosen conditions (fi and crystallization temperatures), these crystals exhibit some equilibrium degree of crystallinity at which a minimum free energy of the system is attained compared to all other possible states. In this sense, the system is in a state of thermodynamic equilibrium and is stable, i.e. it will maintain this state for any period of time after the field is removed. However, with respect to crystals with completely extended chains obtained under equilibrium conditions, this system corresponds only to a relative minimum of free energy, i.e. its state is metastable from the standpoint of equilibrium thermodynamics60,61). 

Substantial evidence in a number of existing experimental studies can be easily reconciled with the models discussed in the present contribution. For example segregation of short chains reported during crystal growth [1] may be thought to arise with chains which are too short to form bundles and are thus unable to provide a sufficient amount of simultaneous attractive interactions with the crystal to yield stable adsorption. We recall in this respect that one of us obtained the correct trend of the minimum chain length of PE for crystal inclusion vs. the crystallization temperature, using the bundle approach [8]. 

Turnbull and Cech [58] analyzed the solidification of small metal droplets in sizes ranging from 10 to 300 xm and concluded that in a wide selection of metals the minimum isothermal crystallization temperature was only a function of supercooling and not of droplet size. Later, it was found that the frequency of droplet nucleation was indeed a function of not only crystallization temperature but also of droplet size, since the probability of nucleation increases with the dimension of the droplet [76]. However, for low molecular weight substances the size dependence of the homogeneous nucleation temperature is very weak [77-80]. 

In Ref. 30, small increases in bandgap (up to a bandgap of 2.6 eV) were obtained for CdS deposited in the presence of a magnetic field. The main factor determining the higher bandgap was a lower deposition temperature (65°C). However, since the minimum crystal size, measmed by XRD, was at least 20 nm, and... 

Cocoa butter NF is defined as the fat obtained from the seed of Theobroma Cacao Linne (Family Sterculiaceae) (44). Cocoa butter softens at 30°C and melts at 34°C. It contains four different forms alpha, beta, beta prime, and gamma with melting points of 22°C, 34°C to 35°C, 28°C and 18°C, respectively. The beta form is the most stable and is desired for suppositories. The biggest challenge with the polymorphism of cocoa butter is the impact of the manufacturing process on the characteristics of the suppository itself. When cocoa butter is hastily melted at a temperature greatly exceeding the minimum required temperature and then quickly chilled, the result is metastable crystalline form (a crystals), which may not even... 

Figures 9 and 15 show the conspicuous changes in crystal habit occurring within rather narrow intervals of crystallization temperature and concentration, particularly around the self-poisoning minimum. Similar diversity of shape is observed in melt crystallization [30]. In addition to the morphologies...

A minimum in growth rate occurs as a function of either crystallization temperature or solution concentration at all growth transitions b etween successive integer folded forms. The latter results in negative-order kinetics, the dilution wave effect, and autocatalytic crystallization. 

Analyze the liquid conditions. Obtain complete data on the liquid pumped. These data should include the name and chemical formula of the liquid, maximum and minimum pumping temperature, corresponding vapor pressure at these temperatures, specific gravity, viscosity at the pumping temperature, pH, flash point, ignition temperature, unusual characteristics (such as tendency to foam, curd, crystallize, become gelatinous or tacky), solids content, type of solids and their size, and variation in the chemical analysis of the liquid. 

Unfortunately, the presence of the term in Eq. (5) makes it much more difficult to extract the equilibrium S J) behavior than it was to find (p T) for an Ising magnet. However, the general approach is the same— fmd the S value at which dQdS= 0 and G is a global minimum. The temperature dependence of 5arising from Eq. (5) for a nematic liquid crystal turns out to be quite complicated since there is no analytic solution to the quartic equation arising from 5 QdS = 0. However, the behavior of 5( 7) for 7 < 7j can still be very well approximated by a power-law expression ... 

A temperature 85°C is higher than the critical crystallization temperature [33] of n-octadecanol monolayer. This means that the highest surface concentration of the monolayer, irrespective of the amount of n-octadecanol deposited on silica gel, is equal to 0.27 nm per molecule. The run of Vs vs r diagram for n-octane is slightly different from that at 40°C. The retention volumes increase with r up to a surfaee concentration 0.57 nm, but without a noticeable effect of silica gel surface deactivation, and next decrease to a minimum at r corresponding to 0.27 nm per n-octadecanol molecule, i.e. at the surface concentration characteristic for LE phase. The Vs increase beginning from this value is the result of n-octane dissolution in liquid threedimensional n-octadecanol. 

The temperature for salting out need be only as high as is required to prevent crystallization of the salt (R16). For 1.8 M sodiiun sulfate and 2.1 Af sodium sulfite the minimum working temperature is 25°C. A mixture of sulfate and sulfite has been proposed (R7), but solubility is not appreciably increased and the mixture still requires storing in a warm place, i.e., above 25°C, to prevent crystallization. In practice, sulfite holds no advantage over sulfate when a 37 C incubator for storing the concentrated solution is available. Warm sulfite solutions also deteriorate and must be made fresh every week (L8). Furthermore, sulfite increases the danger of albumin denaturation by ether, while sulfate has a protective influence (B31, S4). 

The influence of the SAN copolymer composition on the spherulitic growth rate of PCL has been studied at a hxed crystallization temperature by Kressler et al. [1992, 1993]. A minimum has been observed at about 20 wt% AN in SAN for several compositions (see Figure 3.9), due to a minimum in the value of the interaction parameter, at the same copolymer composition that is responsible for a reduced chain mobility. 

Maximum temperature of feed in evaporative crystallizer Minimum operating temperature in evaporative crystallizer Maximum evaporation rate based on heat transfer area or liquid droplet entrainment limitation Maximum residence time at design capacity... 

The mixed rare earth bromates are obtained in the form of colorless or faint-pink needlelike or feathery crystals. They are moderately soluble in cold water and very soluble in hot. The minimum in solubility among the various earths occurs at europium although the position of this minimum depends upon the crystallization temperature. 

Draft tube baffte DTB or draft tube, DT (either adiabatic cooling or evaporative type also called flash growth or Pachuca) MSMPR. Mother liquor is pumped up a vertical central draft tube liquor overflow and flows down the atmulus. Limits the amount of supersaturation created per pass past the heating surface to 1 °C and therefore limits the nucleation rate to very low values. Operates with a suspension of soUds that is 25-50% apparent settled volume. Used where solute solubility is temperature independent or moderately dependent and where excess nudeation makes it difficult to achieve crystals in the size 0.6-2 mm. Minimum crystallization buildup on walls no places with dose dearances (as in Oslo). 

Ammonium chloride, which is contained in the green mixture, also affects aluminum nitride particle morphology. The influence of ammonium chloride on AIN particle shape and size is well seen at high content of NH4CI (10 mass%) and minimum combustion temperature, that is, at combustion under the conditions close to threshold [34]. In Figure 1.11b, we can see the general view of aluminum nitride powder obtained at F = 4 MPa and = 1890 K. It is obvious that thread-hke crystals exist along with spherical particles. It supports the idea that... 

The kinetics of melt-crystallization of PLA has been analyzed by a number of research groups [14, 35, 39, 71-75]. Isothermal bulk crystallization rates were determined in a wide temperature range from 70 to 165 C [71,72]. The maximum crystaUization rate is observed around 100 C, and the most peculiar behavior is a discontinuity in the phase change kinetics around 110-120°C, an example of which is shown in Figure 5.10. Figure 5.10a reports the half-time of crystallization of PLA as function of the isothermal crystallization temperature. The data set shows a broad minimum around 108 C and a step/discontinuity around 116-118°C, indicated by the arrow. The sudden variation in crystallization rate... 

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