2012.09.22

IntroductionNucleation & Growth Kinetics Crystal Products

MaterialsMolecular structure of PDI 747.X-ray diffraction pattern of PDI 747.Optical Photographs of PDI747.

In Situ Monitoring TechniquesFBRM (Focused Bea Reflectance Measurement)

Schematic of the 500 mL batch reactor combining the different in situ process analytical technologies of FBRM and ATR-FTIR spectroscopy.ATR-FTIR (Attenuated Total Reflection Flourier Transformed Infrared Spectroscopy)

In Situ Monitoring TechniquesCalibration data for the absorbance values at 1245 and 1654 cm-1 at 25 that correspond to the concentrations of dissolved PDI 747 and the antisolvent water.

Solubility and Supersaturation

where c is calculated using the IR band of the solute at 1245 cm-1 and c* is the solubility value of PDI 747, corresponding to the actual solute free methanol mass fraction MeOH in the liquid phase.Growth KineticsGravimetrically determined solubility data of PDI 747 as a function of solvent composition at 25C.

Solubility and SupersaturationPreparation and Characterization of Seed Crystals.F2F1Experimental PSDs of the two seed fractions F1 and F2. The inset displays the corresponding SEM microphotograph. It can be readily observed that both fractions consist of needle-shaped crystals and small agglomerates.

Population Balance EquationsThe population balance equations (PBE) for size-independent growth, with neither agglomeration nor breakage, is as follows:

The molar concentration c of the solute in the liquid-phase fulfills the following material balance:

Mthe molar mass of the solutec solid density 1187kg/m3 kv=V/L3 volume shape factor, 0.01Initial and boundary conditions:

Population Balance Equationsassume a constant supersaturation level during the induction time, this results in constant rates of primary nucleation and growth during the induction time:

m0 and mk denote the zeroth and kth moment of the PSDJ and G are constantk=3kvm3=V

Growth KineticsPreparation and Characterization of Seed Crystals.F2F1Experimental PSDs of the two seed fractions F1 and F2. The inset displays the corresponding SEM microphotograph. It can be readily observed that both fractions consist of needle-shaped crystals and small agglomerates.FBRM data of run 4. It can be easily observed that no significant nucleation occurred over the course of the experiment since the counts of small chords remain at a constant low level.

Growth KineticsThis mass transfer coefficient was used with the following equation to calculate diffusion controlled crystal growth rates:

D diffusivity, D=3.5110-10m2/s in water; D=7.3610-10m2/s in methanol viscosity,=110-6m2/s in water; =6.9110-7m2/s in methanol the average power input, 5.910-2W/kgL= the mean particle size ,110-4m Sc=/Dkd=1.0710-4m/s in water; kd=5.7910-5m/s in methanol a needle-like shapedcrystalka=0.42 kV=0.01Gdif=5.510-7-5.510-5m/s(S=1.1-11)

Growth KineticsTo estimate the growth kinetics in the case of integration controlled growth, two different growth mechanisms were compared, the surface nucleation based birth and spread (B+S) mechanism and the screw dislocation mechanism described by Burton, Cabrera and Frank (BCF).

Experimental desupersaturation data+PBE model

Growth KineticsF1:64~125 mF2:125~355 m

Nucleation KineticsInduction time the period of time between the attainment of the nominal supersaturation and the detection of particles in the given system with a specific in-situ instrument.Nucleation KineticsTime evolution of the ATR-FTIR and FBRM signal at a supersaturation of S=6.2.Measured induction times as a function of supersaturation.

Nucleation KineticsVkv0.01Scanning electron microphotograph of the final PDI 747 particles precipitated at two different initial supersaturation values of S=5.5 and S=6.3.Experimental final PSD of the antisolvent precipitation of PDI 747 at an initial supersaturation of S=6.3. The solid, dashed, and dotted lines represent the simulated final PSDs calculated with nucleation rates obtained with different values for the detectable volume fraction =110-3,510-3,110-2 ,respectively.

Nucleation Kinetics classical nucleation theory+interpolationunder the assumption of V=510-3

The overall nucleation rate is the sum of these two contributions at any supersaturation level :Nucleation rate of PDI 747 as a function of supersaturation plotted as (ln(J) vs ln-2(S)). The different nucleation regimes are highlighted, and the corresponding kinetic parameters are indicated.

ConclusionsThe solute concentration was measured using ATR-FTIR spectroscopy.

The induction time was measured as a function of supersaturation using ATR-FTIR and FBRM.

nucleation and growthDisadvantage: