The rate of crystallisation

When the temperature of a melt is lowered below the melting point, crystallisation takes place at a rate that depends on the degree of supercooling, AT = T — where is the temperature at which crystallisation takes 

Assuming that the surface free energy of the fold surfaces is 93 mJ that the density of the crystallites p,. = 1-00 x 10 kg m and that the increase in enthalpy per unit mass, Ah, on melting is 2.55 x 10 J kg for an infinitely thick crystal, determine the equilibrium melting temperature. 

Hence 7 = (131.2 - 121.2)/0.0243 = 411 K = 138 °C. (In a real determination of 7 data from many samples with different values of I would be used.) 

The increase in free energy Ag per unit mass on melting is Ag = Ah — TcAs. Assuming that Ah and As are constant in the temperature range of interest, it follows from the fact that Ag is zero at the true melting point that, at any temperature of erystallisation Tc, 

More generally it can be shown that, whatever the precise nucleation and growth mechanisms, the following equation, called the Avrami equation, holds  

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Solid organic compounds when isolated from organic reactions are seldom pure they are usually contaminated with small amounts of other compounds ( impurities ) which are produced along with the desired product. Tlie purification of impure crystalline compounds is usually effected by crystallisation from a suitable solvent or mixture of solvents. Attention must, however, be drawn to the fact that direct crystallisation of a crude reaction product is not always advisable as certain impurities may retard the rate of crystallisation and, in some cases, may even prevent the formation of crystals entirely furthermore, considerable loss of... 

Chain orientation enhanees the rate of crystallisation, because every volume element in which a few ehain parts lie parallel forms a nueleus. This is the ease in fibre spitming, film stretehing and bottle blowing. 

The ratio of the crystallisation rates is 98/23 = 4.26, the ratio of the molar masses is 143/87 = 1.64. The ratio of the melt viseosities (which govern the erystal growth) amounts to 1.64 1 = 5.38. Apparently the rate of crystallisation is, next to the rate of nucleation, governed by the melt viscosity. 

In the rate of crystallisation of a substance from a supersaturated solution two independent factors have to he considered, firstly the rate of nucleus formation from which crystallisation may proceed and secondly the rate of growth of a nucleus once it is formed. 

Leuconostoc mesenteroides and Leuconostoc ssp. are found in fermented foods of plant origin [11]. The occurrence of these bacteria in sugar refineries is responsible for problems in filtration processes because of increased viscosity by the presence of soluble dextran [12,13]. Furthermore, dextran retards the rate of crystallisation of sucrose and adversely affects the crystal shape. The occurrence of dextran in the matrix of dental plaque results from certain Streptococcus strains [14]. The principle organism, Streptococcus mutans, is able to produce water-soluble glucan (named dextran) and water-insoluble... 

Tietz and Hartel (2000) studied the effects of removing or adding minor components naturally present in milk fat on the crystallization of milk fat-cocoa butter blends. They suggested that at low concentrations, minor lipids act as sites for nucleation and promote the rate of crystallisation and at higher concentrations inhibit crystallisation. They concluded that the presence of minor lipids, at the concentrations naturally occurring in milk fat, were sufficient to affect crystallisation rates, chocolate microstructure and fat bloom formation in chocolate. 

There is a striking resemblance between Permeation (Chap. 18) and Crystallisation. Just as Permeability is the product of Solubility and Diffusivity (P = SD), the rate of crystallisation is the product of Nucleability (or probability of Nucleation, also called "nucleation factor") and Transportability (Self-diffusivity of chains or chain fragments, also called "transport factor"). This statement is valid as well for the primary nucleation in melt or solution, as for the growth of the crystallites (which is a repeated sequence of surface nucleation and surface growth). 

The rate of crystallisation increases as the temperature decreases below Tm, reaching a maximum at T, and decreases again when the temperature is lowered still further. 

The usual procedure in studying the rate of crystallisation is to cool the polymer sample quickly from the molten state to the temperature of measurement and then measure the development of crystallinity at constant temperature (isothermal crystallisation). 

When the rate of crystallisation of a generalised salt is expressed in... 

Addition of starch has a nucleating effect, which increases the rate of crystallisation. The rheology of starch/PCL blends depends on the extent of starch granule destruction and the formation of thermoplastic starch during extrusion. Increasing the heat and shear intensities can reduce the melt viscosity, but enhance the extrudate-swell properties of the polymer. 

The external shape of the crystal can be described in terms of its habit, which is affected by the rate of crystallisation and by the presence of impurities, particularly surfactants. The habit of a crystal is of pharmaceutical importance, since it affects the compression characteristics and flow properties of the dmg during tableting and also the ease with which the suspensions of insoluble dmgs will pass through syringe needles. 

Polyester is not a fast crystallising polymer. The rate of crystallisation is maximum for polyester at around 180 C. The maximum crystallisation rate for polyester is about 0.016/sec, while it is 0.14/sec for nylon 6. The following changes take place as a function of increasing temperature in polyester when heat-set under free to relax conditions (i.e. free annealing) and when held taut at constant length (i.e. taut annealing) ... 

For a number of the common scale forming species such as calcium sulphate and carbonate, the rate of crystallisation follows a parabolic relationship with supersaturation, and the value of the effective order of reaction is 2. An explanation may involve the dehydration of lattice cations at the crystal surface. For other examples when the value of n > 2, i.e. where the growth rate varies more strongly with supersaturation, the explanation may involve the interaction between several nuclei and spread of growth [Nielson 1964, O Hara and Reid 1973]. 

Stabilisation is a much slower process, which occurs progressively over several months, and involves the reaction of lime with the siliceous and aluminous components of the soil. The lime raises the pH to above 12, which results in the formation of calcium silicates and aluminates. These are believed to form initially as a gel, which coats the soil particles, and which subsequently crystallises as calcium silicate/aluminate hydrates. Those hydrates are cementitious products, similar in composition to those found in cement paste. The rate of crystallisation is temperature dependant and may take many months to reach completion. The resulting gain in strength (measured by the California Bearing Ratio Test [26.11]) is progressive, as illustrated in Fig. 26.2. 

The crystallisation kinetics of PET suit the process (Fig. 3.26). A glassy preform can be injection moulded with a wall thickness of up to 4 mm. If the mould is kept at 10 °C, the inner layers of the polymer cool fast enough for the crystallinity to be negligible. High molecular weight PET, with Mn — 24 000, is used so that the rate of crystallisation is suitably low. 

For crystallisation to occur in a polymer, the requirement is that the chain should be chemically sufficiently regular. In addition, there should be sufficient chain mobility at the melting point for the actual process of crystallisation to take place. For that reason, bulky side groups reduce the rate of crystallisation. 

Precipitation of sulphates can be prevented by dosing with poly electrolyte crystaUisa-tion inhibitors such as SHMP. Its effect is to hinder the rate of crystallisation, rather than to prevent it altogether. SHMP is almost totally rejected by RO membranes and has htde or no effect on the permeate quality. The RO module feed/reject channels must be flushed before shutting the RO system down. 

It is probable that all forms of phosphorus can be melted to form what is approximately the same colourless liquid, of density 1.745 g/cc at 44.5°C. Liquid phosphorus can be readily supercooled to a state from which the rate of crystallisation of the white form is extremely rapid. The Raman spectra of the solid and solution states of white phosphorus resemble that of the liquid, indicating that the latter also contains tetrahedral P4 molecules. Recently, evidence for two different forms of liquid P has been obtained [28]. 

The rate of crystallisation increases when the difference between the temperature at which the solution is prepared and the storage temperature increases. This is because the driving force for crystallisation will increase when the temperature difference increases. Supersaturation can occur in starting materials or intermediates, but supersaturated compositions are also used in therapy. Some relevant examples will be briefly discussed below. 

Rubber incorporation into the nylon also affects crystallinity. Although the overall extent of PA 66 crystallinity is not greatly altered (15), the rate of crystallisation and final nylon spherullite size is affected by the rubber particles. Presumably due to smaller rubber particles, functionalised EPR also leads to a more refined nylon crystal structure than does unmodified EPR in the blends studied here. 

The intensity of the scattering peak increased with time in a sigmoidal manner to plateau at a value Lo, corresponding to a limiting PCL crystallisation after about 1200 s for both pure PCL and for the blend at temperatures of about 40 °C. From values of times Xy2 required to reach 1, 2 were calculated. Values of Xj/2 showed that PCL crystallisation in the blend was slower than in pure PCL and that the rates of crystallisation, as might be expected, decreased as T was approached [95]. 

Rates of radial growth of spherulites, constant with time, were highest for pure PCL and decreased with increasing SAN content and with increasing temperature in the range 34-50 C [1061 he. the presence of SAN decreased the rate of crystallisation. The variation in extent of crystallinity with time was sigmoidal and the kinetics of crystallisation were consistent with the Avrami equation (Eq. 26) with an exponent of 3 0.02, consistent with three-dimensional growth... 

In this study, Vanneste and Groeninckx investigated crystallisation and melting in blends rich in PCL (90 wt %), from which PCL could crystallise [ 149]. The presence of SAN -15 and/or SMA-14 reduced the temperature at which PCL could crystallise on cooling from the melt, compared with that for pure PCL. The SAN and SMA components also reduced the rate of crystallisation and crystallisation exotherms were broader than for pure PCL. The presence of the amorphous SAN and SMA also reduced the crystallinity of the PCL which was achieved [149]. 

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