A.1 Physical and Chemical Properties of Model Systems

Transcription

1 175 Appendix A.1 Physical and Chemical Properties of Model Systems Within this work the following substances were used: Ammonium chloride (Carl Roth GmbH + Co. KG, > 99.5% Ph. Eur., USP, BP) Ascorbic acid (KMF-optiChem, L(±)-Ascorbic Acid, crystalline, pure) Glycine (Carl Roth GmbH + Co. KG, > 99%, for synthesis, α-aminoacetic acid) Manganese chloride, tetrahydrate (Merck KGaA, p.a.) Distilled water Figure A-1 shows the respective solubility of the investigated model systems. Solubility [kg/kg Water] H Ammonium Chloride Ascorbic Acid Ascorbic Acid (max-min) α-glycine γ-glycine H N H + - HO H Cl Ammonium Chloride (NH 4 Cl, M mol = g/mol, ρ Crystal = 153 kg/m³) OH HO O O OH Ascorbic Acid (C 6 H 8 O 6, M mol = g/mol, ρ Crystal = 165 kg/m³) H 2 N OH O α-glycine (C 2 H 5 NO 2, M mol = 75.7 g/mol, ρ Crystal = 159 kg/m³) Temperatuer [ C] Figure A-1: Solubility data for the investigated model systems [Mul1, Par3, Oma6b] By comparing literature references (see table A-1), a significant scattering of the solubility values for ascorbic acid was found. The bars are indicating the respective maximum and minimum values. Within this work, the data from Apelblat et al. [Ape89] and Omar et al. [Oma6a] were found to be applicable. Although the solubility for glycine is often reported in literature, it is sometimes not mentioned to which polymorph the solubility data belongs. However, only a minor scattering of the α-glycine solubility data from different authors was found. Within this work the solubility data by Park et al. [Par3] was used. Table A-1 summarises the empirical constants that were derived to predict the solubility using equation A.1 (c eq [kg solute/kg water], T [ C]).

2 176 Appendix c eq a + = ( A.1 ) 2 1 T + a2 T a3 Table A-1: Empirical constants for equation A.1 (solubility) Substance a 1 a 2 a 3 Valid Range Ammonium Chloride 1.25E E E-1 3 C [Mul1] Ascorbic Acid E E E C α-glycine E E E-1 3 C References for Solubility Data [Ape89, Hal93, Mat99, Bod99, Oma6a] [Dal33, Sak92, Par3, Iga3, Yi6, Che7] The liquid density of the saturated solution was calculated using equation A.2 (ρ eq [kg/m³], T [ C]) with empirical constants given in table A-2 ρ ( A.2 ) 2 eq = a1 T + a2 T + a3 Table A-2: Empirical constants for equation A.2 (liquid density of a saturated solution) Valid References for Substance a 1 a 2 a 3 Range Liquid Density Data Ammonium Chloride -5.E-3 6.1E E+3 3 C [Mul1] Ascorbic Acid E E E C [Ape7] α-glycine (ideal solution) E E E C [Dal33], T=25 C, ρ eq = [Gin92], T=25 C, ρ eq = 171. Experimental data for the heat of crystallization or solution and the interfacial tension are given in table A-3. Table A-3: Heat of crystallization or solution and interfacial tension for model systems Substance Data Reference Heat of Crystallization/Solution [kj/mol] Ammonium Chloride 15.9 (heat of solution, dilute solution, 25 C) [Mul1] 23. (heat of solution, dilute solution, 25 C) Ascorbic Acid (heat of solution, saturated solution, 25 C) (-) (-)31. (heat of crystallization, 25 C) Interfacial Tension (γ CL [J/m²]), Solvent: Water Ammonium Chloride.27 [Mer9] Glycine.4 [Bla88] [Ape89] [Dal98, Oma6a] [Dal98, Che] Figure A-2 shows the ratio of the activity coefficients (γ/γ eq ) as a function of the supersaturation for all investigated substances. The arrows highlighting the individual supersaturation range studied (zone two).

3 Appendix Ammonium Chloride Glycine Ascorbic Acid 1.2 γ/γ eq [-] 1. Ammonium Chloride Ascorbic Acid Glycine Supersaturation lns [-] Figure A-2: Ratio of activity coefficients as a function of supersaturation at 25 C [Moh2, Oma6b], arrows are indicating the experimental range (see chapter 1) The use of activity coefficients was neglected for ammonium chloride and glycine. The extrapolation of the activity coefficient for ascorbic acid derived by Omar [Oma6b] seemed to be too uncertain. Figure A-3 shows the binary diffusion coefficient for ammonium chloride [Hal53, Oht98] and glycine [Gin92] versus the concentration. For ascorbic acid, a diffusion coefficient of m²/s was determined by Robinson et al. [Rob9] at a concentration of.9 kg/kg water. 3.E-9 NH4Cl Glycine 1.2E-9 D AB NH 4 Cl [m²/s] 2.5E-9 2.E-9 saturated (5) saturated (.39) 8.E-1 4.E-1 D AB Glycine [m²/s] 1.5E Concentration [kg/kg Water].E+ Figure A-3: Diffusion coefficient as a function of concentration at 25 C [Hal53, Gin92] The diffusion coefficient tends to decrease rapidly within the supersaturated regime [Gin92, Mye2].

4 178 Appendix A.2 Comparison between Laser Scanner and Laser Diffraction Instruments From round robin studies it is known that a "single" particle analyser is generally capable of measuring the size distribution with a high precision [Jim92, Hay95a, Hay95b, Mer95b, Hay98]. Often the median particle size between duplicates or replicates differ only in the range of L 5 = ±2 to 3% [Mer95b]. However, by comparing the same instrument class from different vendors (for example all laser diffraction and scattering instruments) a variation within the median particle size in the range of L 5 = ±25% to 5% is observed [Mer95b, Hay98, Hay95a]. The variation can mainly be attributed to different instrument designs, if applicable, different deconvolution algorithms and individual operators using different instrument settings and sample preparation procedures. The results are dependent on the particle shape and if a narrow or wide particle size distribution is investigated. The variations of the respective measurements tend to be larger at the upper and lower end of the particle size distribution [Jim92, Hay95b]. By comparing different instrument classes of particle analysers, it must be distinguished if spherical or non-spherical particles are investigated. For spherical particles, the result does not depend on the orientation of the particle. Additionally, only one "characteristic length", the diameter, can be defined. Hayakawa et al. [Hay95a] investigated various distributions of spherical particles using different instrument principles. It was found out that the median particle size, between different instrument classes, differs in the range of ±5% to 1%, depending if a narrow or wide particle size distribution was studied. Within crystallization processes, generally, non-spherical (irregular) particles are observed. Thereby, each instrument class responses different to particles that deviate from sphere and/or show non-ideal optical conditions [Nai98, Pat6]. Additionally, if a deconvolution of the raw measured data is applicable, spherical particle are generally assumed regardless the actual morphology [Neu2]. By comparing instruments based on different physical principles, the variation within the median particle sizes for non-spherical particles can become intolerable high (L 5 > ±1%) [Jim92, Hay95a, Hay95b, Mer95b, Bar96, Hay98, Nai98, Pat6]. Besides various distributions (for example: Q, Q 1, Q 2, Q 3 ) and mean sizes (for example: L median, L mode, L mean ) different characteristic sizes that describe a non-spherical particle can be defined. It can be distinguished between geometrical lengths (for example: L length, L width, L diagonal ), geometrical equivalent diameters (for example: L volume, L surface, L projected area ) and physical equivalent diameters corresponding to an individual equipment class (for example: L sieve, L settling, L stokes, L scattering ). A relation between these characteristic sizes is necessary to complement any comparison among instruments. In general, the interrelation is given by the relation L char-1 f(shape) L char-2 [Les84, Les2, Gar2, Li5a, Pat6]. For further details it is referred to the following references [Sca85, Sca96, Les2, Sca3] and figure A-4(b). Randolph and Larson [Ran88] proposed to choose the characteristic length for any crystal shape in such a way that the relation between the surface (k A ) and volume shape factor (k V ) is

5 Appendix 179 equal to 6. For a detailed discussion on the characteristic length measured by the laser scanner instrument it is referred to Vaccaro et al. [Vac6a]. Various studies have been made that compare the FBRM with other sizing techniques [Dow1, Hea2, Abb2, Tei5, Li5a, Pat8]. Thereby, often glass, ceramic beads, Duke standards, BCR quartz powders, PVC, silica and emulsion drops are taken as particulate systems. For the comparison, however, only the chord length distribution (or some weighted form) without any deconvolution, is used. The results are ranging from oversizing, undersizing, poor performance in differentiating median sizes up to a good agreement. A good agreement of the deconvoluted FBRM signal to other sizing techniques was found by Worlitschek et al. [Wor5] and Li et al. [Li5c]. Figure A-4(a) compares the 3D-ORM measurement with laser diffraction. The result shown in figure A-4(a) is typical for all substances and individual sieve cuts studied within this work. For a thorough comparison it is referred to figure A-5. The chord length distribution was converted to a particle size distribution using the method described in chapter The volume distribution was subsequently obtained by weighting. The distribution refers to a suspension density of 11 kg/m³ Susp and a measuring time of 12 minutes. To ease the comparison, the number of channels of the distribution measured by the 3D-ORM was changed to number of the laser diffraction device. (a) 1. Glycine (Laser Backscattering) Glycine (Laser Diffraction) Sieve Cut: 9-16 µm (b) q ln,psd,3 [-] Shape of Crystals 4 µm Particle Size [µm] Figure A-4: (a) Comparison between a laser scanner and a laser diffraction device (sieve cut: 9-16 µm), (b) illustration of various characteristic lengths [Mül1] Both measurement principles are not in good agreement with the respective sieve cut of 9 16 µm. The laser diffraction device measured particles up to 4 µm. Additionally, tails towards smaller sizes were observed for α-glycine and ascorbic acid (see figure A-5). According to Neumann et al. [Neu2] these tails are typical for flakes and tablet like particles. Teipel [Tei2] showed that those tails could also be caused by transparent crystals. An evaluation using the Mie-theory instead, as suggested by Teipel [Tei2], led to no significant changes.

6 18 Appendix In comparison, the laser scanner showed a clear undersizing of the respective sieve cut, as also observed by various other authors [Hea2, Li5a, Pat8, Hu8]. Patchigolla et al. [Pat8] reported differences within the median size of up to 2 µm. The systematic undersizing can be cause by several non-ideal conditions that are described in detail in chapter Contrary, Chew et al. [Che7a] found the square weighted chord length distribution of α-glycine crystals to be in close agreement with image analysis. Figure A-5 shows the particle size measurement using the laser scanner and laser diffraction device for different sieve cuts. The capability to distinguish between different particle sizes depends on the substance and instrument (see chapter 8.2.2). Both instrument therefore record different particle size distributions that would lead to different crystal growth kinetics.

7 Appendix 181 Ammonium Chloride Laser Scanner (at 1 kg/m³ Susp ) Laser Diffraction 1 Sieve Cut: <63 µm Sieve Cut: 63-9 µm Sieve Cut: 9-16 µm Sieve Cut: µm 1. Sieve Cut: <63 µm Sieve Cut: 63-9 µm Sieve Cut: 9-16 µm Sieve Cut: µm Q PSD,3 [-] Q PSD,3 [-] Particle Size [µm] Particle Size [µm] Ascorbic Acid Laser Scanner (at 11 kg/m³ Susp ) Laser Diffraction Q PSD,3 [-] 1 Sieve Cut: <9 µm Sieve Cut: 9-16 µm Sieve Cut: µm Sieve Cut: µm Sieve Cut: µm Q PSD,3 [-] 1. Sieve Cut: 9-16 µm Sieve Cut: µm Sieve Cut: µm Sieve Cut: µm Particle Size [µm] Particle Size [µm] α-glycine Laser Scanner (at 11 kg/m³ Susp ) Laser Diffraction 1 Sieve Cut: <9 µm Sieve Cut: 9-16 µm Sieve Cut: µm Sieve Cut: µm Sieve Cut: µm 1. Sieve Cut: < 9 µm Sieve Cut: 9-16 µm Sieve Cut: µm Sieve Cut: µm Sieve Cut: µm Q PSD,3 [-] Q PSD,3 [-] Particle Size [µm] Particle Size [µm] Figure A-5: Comparison between laser scanner and laser diffraction instruments; the chord length distribution of the laser scanner was converted using the method described in chapter and subsequently weighted to a Q PSD,3 distribution, the laser diffraction data was evaluated using the Fraunhofer diffraction theory* *sieve cuts vary between the individual model substances

8 182 Appendix A.3 Additional Data for Chapter 8.1 Ammonium Chloride (a) (b) Ascorbic Acid (a) (b) Glycine (a) (b) Figure A-6: Calibration of the ultrasound probe (a) Comparision between experimental data (black dots) and model prediction (shaded surface) using equation 8.3, (b) residuals between experimental data and prediction

9 Appendix 183 A.4 Additional Data for Chapter Ammonium Chloride (Experimental Range: 1-3 kg/m³ Susp ) 8 Counts [#/s] Suspension Density m T [kg/m³ Susp ] Ascorbic Acid (Experimental Range: 1-1 kg/m³ Susp ) Sieve Cut: < 63 μm Sieve Cut: 63-9 μm Sieve Cut: 9-16 μm Sieve Cut: μm Non-Sieved Material Counts [#/s] Sieve Cut: < 9 μm Sieve Cut: 9-16 μm Sieve Cut: μm Sieve Cut: μm Sieve Cut: μm Non-Sieved Material Suspension Density m T [kg/m³ Susp ] α-glycine (Experimental Range: 8-4 kg/m³ Susp ) Counts [#/s] Sieve Cut: < 9 μm Sieve Cut: 9-16 μm Sieve Cut: μm Sieve Cut: μm Sieve Cut: μm Non-Sieved Material Suspension Density m T [kg/m³ Susp ] Figure A-7: The effect of the suspension density on the measured "counts"* *sieve cuts vary between the individual model substances

10 184 Appendix A.5 Additional Data for Chapter Ammonium Chloride Sieve Cut: 63-9 µm LCLD,5, (Sieve Cut: 63-9 µm).55 Q CLD, [-] I. at mt = 1 kg/m³susp II. at mt = 22 kg/m³susp III. at mt = 35 kg/m³susp IV. at mt = 44 kg/m³susp II. - I. III. - I. IV. - I Difference [-] L CLD,5, [µm] CV (QCLD,) (Sieve Cut: 63-9 µm).5 5 CV (Q CLD, ) [-] Chord Length [µm] Suspension Density m T [kg/m³ Susp ].35 Sieve Cut: 9-16 µm LCLD,5, (Sieve Cut: 9-16 µm).55 Q CLD, [-] I. at mt = 1 kg/m³susp II. at mt = 22 kg/m³susp III. at mt = 35 kg/m³susp IV. at mt = 44 kg/m³susp II. - I. III. - I. IV. - I Difference [-] L CLD,5, [µm] CV (QCLD,) (Sieve Cut: 9-16 µm).5 5 CV (Q CLD, ) [-] Chord Length [µm] Suspension Density m T [kg/m³ Susp ].35 Non-Sieved Material LCLD,5, (non-sieved material).55 Q CLD, [-] I. at mt = 1 kg/m³susp II. at mt = 22 kg/m³susp III. at mt = 35 kg/m³susp IV. at mt = 44 kg/m³susp II. - I. III. - I. IV. - I Difference [-] L CLD,5, [µm] CV (QCLD,) (non-sieved material).5 5 CV (Q CLD, ) [-] Chord Length [µm] Suspension Density m T [kg/m³ Susp ].35 Figure A-8: The effect of the suspension density on the cumulative distribution (Q CLD, ), the median chord length and on the CV-value of the Q CLD, distribution* *all other sieve cuts (< 63 µm, µm) showed similar results

11 Appendix 185 Ascorbic Acid Sieve Cut: < 9 µm LCLD,5, (Sieve Cut: < 9 µm) Q CLD, [-]. I. at mt = 11 kg/m³susp II. at mt = 18 kg/m³susp III. at mt = 25 kg/m³susp IV. at mt = 36 kg/m³susp Chord Length [µm] L CLD,5, [µm] CV (QCLD,) (Sieve Cut: < 9 µm) Suspension Density m T [kg/m³ Susp ].7.5 CV (Q CLD, ) [-] Sieve Cut: 9-16 µm LCLD,5, (Sieve Cut: 9-16 µm) Q CLD, [-]. I. at mt = 11 kg/m³susp II. at mt = 25 kg/m³susp III. at mt = 4 kg/m³susp IV. at mt = 53 kg/m³susp Chord Length [µm] L CLD,5, [µm] CV (QCLD,) (Sieve Cut: 9-16 µm) Suspension Density m T [kg/m³ Susp ].7.5 CV (Q CLD, ) [-] Non-Sieved Material Q CLD, [-]. I. at mt = 11 kg/m³susp II. at mt = 25 kg/m³susp III. at mt = 4 kg/m³susp IV. at mt = 53 kg/m³susp II. - I III. - I IV. - I Chord Length [µm] Difference [-] L CLD,5, [µm] LCLD,5, (non-sieved material) CV (QCLD,) (non-sieved material) Suspension Density m T [kg/m³ Susp ].7.5 CV (Q CLD, ) [-] Figure A-9: The effect of the suspension density on the cumulative distribution (Q CLD, ), the median chord length and on the CV-value of the Q CLD, distribution* *all other sieve cuts (16-25 µm, µm, µm) showed similar results

12 186 Appendix α-glycine Sieve Cut: < 9 µm Q CLD, [-] 1 I. at mt = 11 kg/m³susp II. at mt = 25 kg/m³susp III. at mt = 4 kg/m³susp IV. at mt = 54 kg/m³susp Chord Length [µm] L CLD,5, [µm] LCLD,5, (Sieve Cut: < 9 µm) CV (QCLD,) (Sieve Cut: < 9 µm) Suspension Density m T [kg/m³ Susp ] CV (Q CLD, ) [-] Sieve Cut: 9-16 µm Q CLD, [-] I. at mt = 11 kg/m³susp II. at mt = 25 kg/m³susp III. at mt = 4 kg/m³susp IV. at mt = 54 kg/m³susp Chord Length [µm] L CLD,5, [µm] LCLD,5, (Sieve Cut: 9-16 µm) CV (QCLD,) (Sieve Cut: 9-16 µm) Suspension Density m T [kg/m³ Susp ] CV (Q CLD, ) [-] Non-Sieved Material Q CLD, [-] I. at mt = 11 kg/m³susp II. at mt = 25 kg/m³susp III. at mt = 4 kg/m³susp IV. at mt = 54 kg/m³susp Chord Length [µm] L CLD,5, [µm] LCLD,5, (non-sieved material) CV (QCLD,) (non-sieved material) Suspension Density m T [kg/m³ Susp ] CV (Q CLD, ) [-] Figure A-1: The effect of the suspension density on the cumulative distribution (Q CLD, ), the median chord length and on the CV-value of the Q CLD, distribution* *all other sieve cuts (16-25 µm, µm, µm) showed similar results

13 Appendix 187 A.6 Additional Data for Chapter Ammonium Chloride (Experiment 1) Temperature [ C] Ascorbic Acid (Experiment 1) 8 4 Temperature (Reactor) mt (Solubility) mt (koptical = 9.5) mt (koptical = 4.75) Data used for Kinetics Sensitivity decreases Influence of k optical Suspension Density [kg/m³ Susp ] Temperature [ C] Temperature (Reactor) mt (Solubility) mt (koptical = 13) mt (koptical = 65) 1 g Seeds Data used for Kinetics Sensitivity decreases Influence of k optical Suspension Density [kg/m³ Susp ] 2 α-glycine (Experiment 4) Temperature [ C] Temperature (Reactor) mt (Solubility) mt (koptical = 1) mt (koptical = 5) Data used for Kinetics Sensitivity decreases Influence of k optical Suspension Density [kg/m³ Susp ] Figure A-11: Influence of the optical factor on the calculated suspension density (m T ) in comparison to the suspension density calculated via the solubility and supersaturation measurement (m T(Solubility) ) (not every measurement point is shown)

14 188 Appendix A.7 Additional Data for Chapter Ammonium Chloride (Experiment 1) CV (Q PSD, ) [-] Ascorbic Acid (Experiment 1) Data used for Kinetics CV (QPSD,) (measured) CV (QPSD,) (reconciled) LPSD,[3,2] (measured) LPSD,[3,2] (reconciled) L PSD,[3,2] [µm] 1..9 Data used for Kinetics 5 4 CV (Q PSD, ) [-] α-glycine (Experiment 4).7.5 CV (QPSD,) (measured) CV (QPSD,) (reconciled) LPSD,[3,2] (measured) LPSD,[3,2] (reconciled) L PSD,[3,2] [µm] CV (Q PSD, ) [-] Data used for Kinetics CV (QPSD,) (measured) CV (QPSD,) (reconciled) LPSD,[3,2] (measured) LPSD,[3,2] (reconciled) L PSD,[3,2] [µm] Figure A-12: Effect of data reconciliation on the Sauter diameter and CV-value (not every measurement point is shown)

15 A.8 Additional Data for Chapter 1 (Ascorbic Acid) 189

16 19 Appendix Temperature [ C] Temperature (Reactor) Temperature (Thermostat) Supersaturation S-1 Supersaturation S-1 [-] L PSD,[3,2] [µm], CV (Q PSD, ) 2 [-] LPSD,[3,2] 2.4E CV (QPSD,) 2 NTotal 1.6E+13 8.E+12 N Total [#/m³] Growth Rate [nm/s] E Growth Rate Growth Rate, unfiltered Nucleation Rate Nucleation Rate, unfiltered.e+ 1.E+9 1.E+8 1.E Figure A-13: Experimental data and calculated parameters for the crystallization of ascorbic acid (experiment 1, zone 2: from 1 to 2 min) Nucleation Rate [#/(m³ s)]

17 Figure A-14: Comparison between experimental data (circles) and simulation (line) (experiment 1, zone 2: 1 min, every third measurement point) Appendix 191

18 192 Appendix Temperature [ C] Temperature (Reactor) Temperature (Thermostat) Supersaturation Supersaturation S-1 [-] L PSD,[3,2] [µm], CV (Q PSD, ) 2 [-] LPSD,[3,2] 3.2E CV (QPSD,) 2 NTotal 2.4E E+13 8.E+12 N Total [#/m³] Growth Rate [nm/s] Growth Rate Growth Rate, unfiltered Nucleation Rate Nucleation Rate, unfiltered.e+ 1.E+1 1.E+9 1.E+8 1.E Figure A-15: Experimental data and calculated parameters for the crystallization of ascorbic acid (experiment 3, zone 2: from 25 to 125 min) Nucleation Rate [#/(m³ s)]

19 Figure A-16: Comparison between experimental data (circles) and simulation (line) (experiment 3, zone 2: 1 min, every third measurement point) Appendix 193

20 194 Appendix Temperature [ C] Temperature (Reactor) Temperature (Thermostat) Supersaturation.3.1 Supersaturation S-1 [-] E+13 L PSD,[3,2] [µm], CV (Q PSD, ) 2 [-] Growth Rate [nm/s] Growth Rate 1.E+1 Growth Rate, unfiltered Nucleation Rate Nucleation Rate, unfiltered 4 1.E+9 2 LPSD,[3,2] CV (QPSD,) 2 NTotal 1.2E+13 6.E+12.E+ 1.E+8 1.E Figure A-17: Experimental data and calculated parameters for the crystallization of ascorbic acid (experiment 4, zone 2: from 1 to 1 min) N Total [#/m³] Nucleation Rate [#/(m³ s)]

21 Figure A-18: Comparison between experimental data (circles) and simulation (line) (experiment 4, zone 2: 9 min, every third measurement point) Appendix 195

22 196 Appendix Temperature [ C] Temperature (Reactor) Temperature (Thermostat) Supersaturation Supersaturation S-1 [-] L PSD,[3,2] [µm], CV (Q PSD, ) 2 [-] E+13 LPSD,[3,2] 3 2 CV (QPSD,) 2 NTotal 1.6E+13 8.E+12 N Total [#/m³] Growth Rate [nm/s] Growth Rate 1.E+1 Growth Rate, unfiltered 8 Nucleation Rate Nucleation Rate, unfiltered E+ 1.E+9 1.E+8 Figure A-19: Experimental data and calculated parameters for the crystallization of ascorbic acid (experiment 5, zone 2: from 8 to 14 min) Nucleation Rate [#/(m³ s)]

23 Figure A-2: Comparison between experimental data (circles) and simulation (line) (experiment 5, zone 2: 6 min, every third measurement point) Appendix 197

24 198 Appendix

25 A.9 Additional Data for Chapter 1.3 (α-glycine) 199

26 2 Appendix 2 L PSD,[3,2] [µm], CV (Q PSD, ) 2 [-] Temperature [ C] Temperature (Reactor) Temperature (Thermostat) Supersaturation LPSD,[3,2] CV (QPSD,) 2 NTotal Supersaturation S-1 [-] 6.E+12 4.E+12 2.E+12 N Total [#/m³] Growth Rate [nm/s] Growth Rate Growth Rate, unfiltered Nucleation Rate Nucleation Rate, unfiltered.e+ 1.E+1 1.E+9 1.E+8 Nucleation Rate [#/(m³ s)] E+7 Figure A-21: Experimental data and calculated parameters for the crystallization of α- glycine (experiment 1, zone 2: from 125 to 15 min)

27 Figure A-22: Comparison between experimental data (circles) and simulation (line) (experiment 1, zone 2: 25 min) Appendix 21

28 22 Appendix Temperature [ C] Temperature (Reactor) Temperature (Thermostat) Supersaturation Supersaturation S-1 [-] E+12 L PSD,[3,2] [µm], CV (Q PSD, ) 2 [-] Growth Rate [nm/s] LPSD,[3,2] CV (QPSD,) 2 NTotal E+1 Growth Rate Growth Rate, unfiltered Nucleation Rate Nucleation Rate, unfiltered E+12 1.E+12.E+ 1.E+9 1.E+8 1.E+7 Figure A-23: Experimental data and calculated parameters for the crystallization of α- glycine (experiment 2, zone 2: from 25 to 5 min) Nucleation Rate [#/(m³ s)] N Total [#/m³]

29 Figure A-24: Comparison between experimental data (circles) and simulation (line) (experiment 2, zone 2: 25 min) Appendix 23

30 24 Appendix Temperature [ C] Temperature (Reactor) Temperature (Thermostat) Supersaturation Supersaturation S-1 [-] E+12 L PSD,[3,2] [µm], CV (Q PSD, ) 2 [-] Growth Rate [nm/s] LPSD,[3,2] CV (QPSD,) 2 NTotal E+1 Growth Rate Growth Rate, unfiltered Nucleation Rate Nucleation Rate, unfiltered 4.E+12 2.E+12.E+ 1.E+9 1.E+8 1.E Figure A-25: Experimental data and calculated parameters for the crystallization of α- glycine (experiment 3, zone 2: from 3 to 55 min) N Total [#/m³] Nucleation Rate [#/(m³ s)]

31 Figure A-26: Comparison between experimental data (circles) and simulation (line) (experiment 3, zone 2: 25 min) Appendix 25

32 26 Appendix