Isothermal crystallisation

Logarithm of crystallisation half time vs. logarithm of molecular weight, for polyethylene crystallised isothermally at the temperatures indicated (from Mandelkern, L. J. Mater. ScL, 6,615, 1968). 

Kinetics of crystallisation of the blends have also been studied by following crystallisation isotherms using DSC. Figure 7 presents an Avrami plot (16) for PA 66 and for the nylon matrix blends containing either EPR or functionalised EPR. From these data, half-times for crystallisation at 240 deg C were calculated. For PA 66, the half time is 1.6 minutes. Unmodified EPR in the nylon lowers this to 1.4 minutes, while with functionalised EPR in the blend, the value is 1.3 minutes. As reproducibility is only +/- 0.1 minutes, the difference between the two blends may be insignificant. However, it appears that the presence of EPR may increase the crystallisation rate of the nylon matrix. 

Figure 7.2 DSC thermograms of a-trd s-polyisoprene crystals crystallised isothermally from hexane and amyl acetate at -20 °C. Scanning rate 10 °C/min.

Where substances vary little in solubility with temperature, isothermal crystallisation may sometimes be employed. This usually takes the form of a partial evaporation of a saturated solution at room temperature by leaving it under reduced pressure in a desiccator. 

A liquid solution may be separated into its constituents by crystallising out either pure solvent or pure solute, the latter process occurring only with saturated solutions. (At one special temperature, called the cryohydric temperature, both solvent and solute crystallise out side by side in unchanging proportions.) We now consider what happens when a small quantity of solute is separated from or taken up by the saturated solution by reversible processes. Let the saturated solution, with excess of solute, be placed in a cylinder closed below by a semipermeable septum, and the w7hole immersed in pure solvent. The system is in equilibrium if a pressure P, equal to the osmotic pressure of the saturated solution when the free surface of the pure solvent is under atmospheric pressure, is applied to the solution. Dissolution or precipitation of solute can now be brought about by an infinitesimal decrease or increase of the external pressure, and the processes are therefore reversible. If the infinitesimal pressure difference is maintained, and the process conducted so slowly that all changes are isothermal, the heat absorbed when a mol of solute passes into a solution kept always infinitely... 

It has to be noticed that no isothermal volume contraction on cooling or volume expansion on heating is associated with Tg, contrary to crystallisation or melting. The latter is a true first-order transition exhibiting a discontinuity in... 

The heat required when 1 kmol of MgS04.7H20 is dissolved isothermally at 291 K in a large mass of water is 13.3 MJ. What is the heat of crystallisation per unit mass of the salt ... 

A necessary preface to a description of the procedure is that the solvent and the precipitant must be purified to exhaustion by contact with successive specimens of the acid to be purified. The acid A is dissolved in the minimum amount of solvent S. The precipitant P is then added under isothermal conditions to the solution until roughly one half to three quarters of A has been precipitated. At this stage there is a three-phase system present (vapour and two liquids) with three (or more) components (A, S, and Imp where Imp denotes an impurity), and the impurities are partitioned between A and the mixture of S and P. This mixture is separated from A by decantation or syphoning, A is redissolved in S and reprecipitated by the addition of P. At all stages of this process the mixtures must be stirred efficiently but so gently that an emulsion is not formed. It happens quite often that an acid A with a melting point near or above ambient temperature will start to crystallise after the first or second extraction. 

Where substances vary little in solubility with temperature, isothermal crystallisation may sometimes be employed. 

Fig. 28 Scanning electron micrograph of high density polyethylene first isothermally crystallised at 128 °C and then rapidly cooled to room temperature. The sample was etched with hot p-xylene to remove the material crystallising in the cooling phase. Scale bar represents 20 pm. From Gedde and Jansson [154] with permission from Elsevier, UK...

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). 

According to Avrami (1939-1941) the progress of the isothermal crystallisation can be expressed by the equation ... 

In unstrained (quasi-isotropic) crystallisation processes the crystallisation starts from a number of point-nuclei, and progresses in all directions at an equal linear velocity (v). In the case of isothermal crystallisation the radius of the crystallised regions increases by an equal amount per unit of time (v = constant). The rate of growth is very much dependent, however, on the temperature of crystallisation. 

FIG. 19.8 Relationship between maximum crystalline fraction, xc max, under isothermal quiescent crystallisation and the ratio Tg/Tm. According to Eq. (19.29) Bicerano, 2002. 

In practice, many fabrication processes take place under non-isothermal, non-quiescent and high-pressure conditions. Mechanical deformation and pressure can enhance the crystallisation as well as the crystal morphology, by aligning the polymer chains. This leads to pressure-induced crystallisation and to flow-induced or stress-induced crystallisation, which in fact is the basis for fibre melt-spinning (see Sect. 19.4.1)... 

Fig. 8. Dependence of crystal thickness on molecular weight for isothermal crystallisation...

Dilworth SE, Buckton G, Gaisford S, et al. Approaches to determine the enthalpy of crystallisation, and amorphous content, of lactose from isothermal calorimetric data. Int J Pharm 2004 284 8.3-94. 

The system is isothermal There is no temperature gradient due to the furnace geometry or the holder. Cooling rate is low enough to neglect heat dissipation, due to crystallisation at the interface. 

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