Table of Contents - uni-halle.desundoc.bibliothek.uni-halle.de/diss-online/08/09H002/t16.pdf · • Ascorbic acid (KMF-optiChem, L(±)-Ascorbic Acid, crystalline, pure) ... comparison,

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.

0.1

0.3

0.5

0.7

0 10 20 30 40 50 60Temperatuer [°C]

Solu

bilit

y [k

g/kg

Wat

er]

Ammonium ChlorideAscorbic AcidAscorbic Acid (max-min)α-Glycineγ-Glycine

N

H

H

H

H Cl+ -

N

H

H

H

H Cl+ - HO

OH

HO

O

OH

O

H2N

OH

O

Ammonium Chloride (NH4Cl, Mmol = 53.49 g/mol,

ρCrystal = 1530 kg/m³)

Ascorbic Acid (C6H8O6, Mmol = 176.13 g/mol,


α-Glycine (C2H5NO2, Mmol = 75.07 g/mol,


Figure A-1: Solubility data for the investigated model systems [Mul01, Par03, Oma06b] 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. [Oma06a] 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. [Par03] was used. Table A-1 summarises the empirical constants that were derived to predict the solubility using equation A.1 (ceq [kg solute/kg water], T [°C]).

176 Appendix

322

1 aTaTaceq +⋅+⋅= ( A.1 )

Table A-1: Empirical constants for equation A.1 (solubility)

Substance a1 a2 a3Valid Range

References for Solubility Data

Ammonium Chloride 1.25000E-05 3.51500E-03 2.97150E-01 0 – 30 °C [Mul01]

Ascorbic Acid 1.53732E-04 1.85994E-03 1.95591E-01 20 – 50 °C [Ape89, Hal93, Mat99, Bod99, Oma06a]

α-Glycine 2.67480E-05 3.19730E-03 1.52109E-01 0 – 30 °C [Dal33, Sak92, Par03, Iga03, Yi06, Che07]

The liquid density of the saturated solution was calculated using equation A.2 (ρeq [kg/m³], T [°C]) with empirical constants given in table A-2

322

1 aTaTaeq +⋅+⋅=ρ ( A.2 )

Table A-2: Empirical constants for equation A.2 (liquid density of a saturated solution)

Substance a1 a2 a3Valid Range

References for Liquid Density Data

Ammonium Chloride -5.00000E-03 6.10000E-01 1.06610E+03 0 – 30 °C [Mul01]

Ascorbic Acid 8.19936E-03 1.90699E+00 1.05735E+03 15 – 45 °C [Ape07]

α-Glycine (ideal solution)

-3.90280E-03 1.61076E+00 1.04432E+03 5 – 40 °C [Dal33], T=25 °C, ρeq = 1084.5 [Gin92], T=25 °C, ρeq = 1071.0

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) [Mul01]

Ascorbic Acid 23.0 (heat of solution, dilute solution, 25 °C) 20.8-21.8 (heat of solution, saturated solution, 25 °C) (-)19.7 - (-)31.0 (heat of crystallization, 25 °C)

[Ape89] [Dal98, Oma06a] [Dal98, Che00]

Interfacial Tension (γCL [J/m²]), Solvent: Water Ammonium Chloride 0.027 [Mer90]

Glycine 0.04 [Bla88]

Figure A-2 shows the ratio of the activity coefficients (γ/γeq) as a function of the supersaturation for all investigated substances. The arrows highlighting the individual supersaturation range studied (zone two).

Appendix 177

0.6

0.8

1.0

1.2

1.4

0.001 0.01 0.1 1Supersaturation lnS [-]

γ/γ e

q [-]

Ammonium ChlorideAscorbic AcidGlycine

Ascorbic Acid

GlycineAmmonium Chloride

Figure A-2: Ratio of activity coefficients as a function of supersaturation at 25 °C [Moh02, Oma06b], arrows are indicating the experimental range (see chapter 10) The use of activity coefficients was neglected for ammonium chloride and glycine. The extrapolation of the activity coefficient for ascorbic acid derived by Omar [Oma06b] 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 5.8·10-10 m²/s was determined by Robinson et al. [Rob90] at a concentration of 0.009 kg/kg water.

1.5E-09

2.0E-09

2.5E-09

3.0E-09

0 0.1 0.2 0.3 0.4Concentration [kg/kg Water]

DA

B N

H4C

l [m

²/s]

0.0E+00

4.0E-10

8.0E-10

1.2E-09D

AB

Gly

cine

[m²/s

]NH4ClGlycine

saturated (0.25)

saturated (0.39)

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, Mye02].

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 L50 = ±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 L50 = ±25% to 50% 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 ±50% to 100%, 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, Pat06]. Additionally, if a deconvolution of the raw measured data is applicable, spherical particle are generally assumed regardless the actual morphology [Neu02]. By comparing instruments based on different physical principles, the variation within the median particle sizes for non-spherical particles can become intolerable high (L50 > ±100%) [Jim92, Hay95a, Hay95b, Mer95b, Bar96, Hay98, Nai98, Pat06]. Besides various distributions (for example: Q0, Q1, Q2, Q3) and mean sizes (for example: Lmedian, Lmode, Lmean) different characteristic sizes that describe a non-spherical particle can be defined. It can be distinguished between geometrical lengths (for example: Llength, Lwidth, Ldiagonal), geometrical equivalent diameters (for example: Lvolume, Lsurface, Lprojected area) and physical equivalent diameters corresponding to an individual equipment class (for example: Lsieve, Lsettling, Lstokes, Lscattering). A relation between these characteristic sizes is necessary to complement any comparison among instruments. In general, the interrelation is given by the relation Lchar-1 ≈ f(shape) Lchar-2 [Les84, Les02, Gar02, Li05a, Pat06]. For further details it is referred to the following references [Sca85, Sca96, Les02, Sca03] 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 (kA) and volume shape factor (kV) is

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. [Vac06a].

Various studies have been made that compare the FBRM with other sizing techniques [Dow01, Hea02, Abb02, Tei05, Li05a, Pat08]. 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. [Wor05] and Li et al. [Li05c].

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 9.2.1. The volume distribution was subsequently obtained by weighting. The distribution refers to a suspension density of 11 kg/m³Susp 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.

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100 1000Particle Size [µm]

q ln,

PSD

,3 [-

]

Glycine (Laser Backscattering)

Glycine (Laser Diffraction)Sieve Cut: 90 -160 µm

Shape of Crystals

(a) (b)

400 µm

Figure A-4: (a) Comparison between a laser scanner and a laser diffraction device (sieve cut: 90-160 µm), (b) illustration of various characteristic lengths [Mül01] Both measurement principles are not in good agreement with the respective sieve cut of 90 – 160 µm. The laser diffraction device measured particles up to 400 µm. Additionally, tails towards smaller sizes were observed for α-glycine and ascorbic acid (see figure A-5). According to Neumann et al. [Neu02] these tails are typical for flakes and tablet like particles. Teipel [Tei02] showed that those tails could also be caused by transparent crystals. An evaluation using the Mie-theory instead, as suggested by Teipel [Tei02], led to no significant changes.

180 Appendix

In comparison, the laser scanner showed a clear undersizing of the respective sieve cut, as also observed by various other authors [Hea02, Li05a, Pat08, Hu08]. Patchigolla et al. [Pat08] reported differences within the median size of up to 200 µm. The systematic undersizing can be cause by several non-ideal conditions that are described in detail in chapter 5.3.2. Contrary, Chew et al. [Che07a] 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.

Appendix 181

Ammonium Chloride Laser Scanner (at 10 kg/m³Susp) Laser Diffraction

0

0.2

0.4

0.6

0.8

1


QPS

D,3 [-

]

Sieve Cut: <63 µmSieve Cut: 63-90 µmSieve Cut: 90-160 µmSieve Cut: 160-250 µm

0.0

0.2

0.4

0.6

0.8

1.0


QPS

D,3 [-

]

Sieve Cut: <63 µmSieve Cut: 63-90 µmSieve Cut: 90-160 µmSieve Cut: 160-250 µm

Ascorbic Acid Laser Scanner (at 11 kg/m³Susp) Laser Diffraction

0.0

0.2

0.4

0.6

0.8

1.0


QPS

D,3 [-

]

Sieve Cut: 90 - 160 µmSieve Cut: 160 - 250 µmSieve Cut: 250 - 315 µmSieve Cut: 315 - 400 µm

0

0.2

0.4

0.6

0.8

1


QPS

D,3 [-

]

Sieve Cut: <90 µmSieve Cut: 90-160 µmSieve Cut: 160-250 µmSieve Cut: 250-315 µmSieve Cut: 315-400 µm

α-Glycine Laser Scanner (at 11 kg/m³Susp) Laser Diffraction

0.0

0.2

0.4

0.6

0.8

1.0


QPS

D,3 [-

]

Sieve Cut: < 90 µmSieve Cut: 90 - 160 µmSieve Cut: 160 - 250 µmSieve Cut: 250 - 315 µmSieve Cut: 315 - 400 µm

0

0.2

0.4

0.6

0.8

1


QPS

D,3 [-

]

Sieve Cut: <90 µmSieve Cut: 90-160 µmSieve Cut: 160-250 µmSieve Cut: 250-315 µmSieve Cut: 315-400 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 9.2.1 and subsequently weighted to a QPSD,3 distribution, the laser diffraction data was evaluated using the Fraunhofer diffraction theory* *sieve cuts vary between the individual model substances

182 Appendix

A.3 Additional Data for Chapter 8.1 Ammonium Chloride

Ascorbic Acid

Glycine

(a)

(a)

(a)

(b)

(b)

(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

Appendix 183

A.4 Additional Data for Chapter 8.2.1 Ammonium Chloride (Experimental Range: 10-30 kg/m³Susp)

Ascorbic Acid (Experimental Range: 10-100 kg/m³Susp)

α-Glycine (Experimental Range: 8-40 kg/m³Susp)

Figure A-7: The effect of the suspension density on the measured "counts"* *sieve cuts vary between the individual model substances

0

2000

4000

6000

8000

0 10 20 30 40 50 60Suspension Density mT [kg/m³Susp]

Cou

nts

[#/s

]

Sieve Cut: < 63 μmSieve Cut: 63-90 μmSieve Cut: 90-160 μmSieve Cut: 160-250 μmNon-Sieved Material

0

1000

2000

3000

4000

5000


Cou

nts

[#/s

]

Sieve Cut: < 90 μmSieve Cut: 90-160 μmSieve Cut: 160-250 μmSieve Cut: 250-315 μmSieve Cut: 315-400 μmNon-Sieved Material

0

2000

4000

6000


Cou

nts

[#/s

]

Sieve Cut: < 90 μmSieve Cut: 90-160 μmSieve Cut: 160-250 μmSieve Cut: 250-315 μmSieve Cut: 315-400 μmNon-Sieved Material

184 Appendix

A.5 Additional Data for Chapter 8.2.2 Ammonium Chloride Sieve Cut: 63-90 µm

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]

0

0.05

0.1

0.15

0.2

Diff

eren

ce [-

]

I. at mT = 10 kg/m³SuspII. at mT = 22 kg/m³SuspIII. at mT = 35 kg/m³SuspIV. at mT = 44 kg/m³SuspII. - I.III. - I.IV. - I.

10

14

18

22

26


L CLD

,50,

0 [µm

]

0.35

0.40

0.45

0.50

0.55

CV

(QC

LD,0) [

-]

LCLD,50,0 (Sieve Cut: 63-90 µm)

CV (QCLD,0) (Sieve Cut: 63-90 µm)

Sieve Cut: 90-160 µm

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]

0

0.05

0.1

0.15

0.2

Diff

eren

ce [-

]


10

14

18

22

26


L CLD

,50,

0 [µm

]

0.35

0.40

0.45

0.50

0.55

CV

(QC

LD,0) [

-]



Non-Sieved Material

10

14

18

22

26


L CLD

,50,

0 [µm

]

0.35

0.40

0.45

0.50

0.55C

V (Q

CLD

,0) [

-]LCLD,50,0 (non-sieved material)

CV (QCLD,0) (non-sieved material)

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]

0

0.05

0.1

0.15

0.2

Diff

eren

ce [-

]


Figure A-8: The effect of the suspension density on the cumulative distribution (QCLD,0), the median chord length and on the CV-value of the QCLD,0 distribution* *all other sieve cuts (< 63 µm, 160-250 µm) showed similar results

Appendix 185

Ascorbic Acid Sieve Cut: < 90 µm

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]

I. at mT = 11 kg/m³Susp

II. at mT = 18 kg/m³Susp

III. at mT = 25 kg/m³Susp

IV. at mT = 36 kg/m³Susp10

14

18

22

26


L CLD

,50,

0 [µm

]

0.40

0.50

0.60

0.70

0.80

CV

(QC

LD,0) [

-]

LCLD,50,0 (Sieve Cut: < 90 µm)

CV (QCLD,0) (Sieve Cut: < 90 µm)


10

14

18

22

26


L CLD

,50,

0 [µm

]

0.40

0.50

0.60

0.70

0.80

CV

(QC

LD,0) [

-]



0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]




IV. at mT = 53 kg/m³Susp

Non-Sieved Material

10

14

18

22

26


L CLD

,50,

0 [µm

]

0.40

0.50

0.60

0.70

0.80

CV

(QC

LD,0) [

-]

LCLD,50,0 (non-sieved material)CV (QCLD,0) (non-sieved material)

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]

0

0.04

0.08

0.12

0.16

0.2

Diff

eren

ce [-

]

I. at mT = 11 kg/m³SuspII. at mT = 25 kg/m³SuspIII. at mT = 40 kg/m³SuspIV. at mT = 53 kg/m³SuspII. - IIII. - IIV. - I

Figure A-9: The effect of the suspension density on the cumulative distribution (QCLD,0), the median chord length and on the CV-value of the QCLD,0 distribution* *all other sieve cuts (160-250 µm, 250-315 µm, 315-400 µm) showed similar results

186 Appendix

α-Glycine Sieve Cut: < 90 µm

6

10

14

18

22


L CLD

,50,

0 [µm

]

0.45

0.55

0.65

0.75

CV

(QC

LD,0) [

-]

LCLD,50,0 (Sieve Cut: < 90 µm)

CV (QCLD,0) (Sieve Cut: < 90 µm)

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]






6

10

14

18

22


L CLD

,50,

0 [µm

]

0.45

0.55

0.65

0.75

CV

(QC

LD,0) [

-]



0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]





Non-Sieved Material

6

10

14

18

22


L CLD

,50,

0 [µm

]

0.45

0.55

0.65

0.75C

V (Q

CLD

,0) [

-]

LCLD,50,0 (non-sieved material)

CV (QCLD,0) (non-sieved material)0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100Chord Length [µm]

QC

LD,0 [-

]





Figure A-10: The effect of the suspension density on the cumulative distribution (QCLD,0), the median chord length and on the CV-value of the QCLD,0 distribution* *all other sieve cuts (160-250 µm, 250-315 µm, 315-400 µm) showed similar results

Appendix 187

A.6 Additional Data for Chapter 8.3.1 Ammonium Chloride (Experiment 1)

4

8

12

16

20

-10 0 10 20 30 40 50 60 70Time [min]

Tem

pera

ture

[°C

]

0

10

20

30

40

50

Susp

ensi

on D

ensi

ty

[kg/

m³ S

usp]

Temperature (Reactor)mT (Solubility)mT (koptical = 9.5)mT (koptical = 4.75)

Influence of koptical

Sensitivity decreases

Data usedfor Kinetics

Ascorbic Acid (Experiment 1)

20

25

30

35

40

45

-20 40 100 160 220 280 340Time [min]

Tem

pera

ture

[°C

]

0

20

40

60

80

100

120

Susp

ensi

on D

ensi

ty

[kg/

m³ S

usp]

Temperature (Reactor)mT (Solubility)mT (koptical = 130)mT (koptical = 65)


Sensitivity decreasesData used

for Kinetics

1 g Seeds

α-Glycine (Experiment 4)

4

8

12

16

20

-20 0 20 40 60 80 100Time [min]

Tem

pera

ture

[°C

]

0

10

20

30

40

50

Susp

ensi

on D

ensi

ty

[kg/

m³ S

usp]

Temperature (Reactor)mT (Solubility)mT (koptical = 100)mT (koptical = 50)


Sensitivity decreases


Figure A-11: Influence of the optical factor on the calculated suspension density (mT) in comparison to the suspension density calculated via the solubility and supersaturation measurement (mT(Solubility)) (not every measurement point is shown)

188 Appendix

A.7 Additional Data for Chapter 8.3.2 Ammonium Chloride (Experiment 1)

0

0.3

0.6

0.9

1.2

1.5

-10 0 10 20 30 40 50 60 70Time [min]

CV

(QPS

D,0) [

-]

25

55

85

115

145

L PSD

,[3,2

] [µm

]

CV (QPSD,0) (measured)CV (QPSD,0) (reconciled)LPSD,[3,2] (measured)LPSD,[3,2] (reconciled)


Ascorbic Acid (Experiment 1)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-20 40 100 160 220 280 340Time [min]

CV

(QPS

D,0) [

-]

0

10

20

30

40

50

L PSD

,[3,2

] [µm

]CV (QPSD,0) (measured)CV (QPSD,0) (reconciled)LPSD,[3,2] (measured)LPSD,[3,2] (reconciled)


α-Glycine (Experiment 4)

0.1

0.4

0.7

1.0

1.3

1.6

-20 0 20 40 60 80 100Time [min]

CV

(QPS

D,0

) [-]

0

15

30

45

60

75

90

L PSD

,[3,2

] [µm

]

CV (QPSD,0) (measured)CV (QPSD,0) (reconciled)LPSD,[3,2] (measured)LPSD,[3,2] (reconciled)


Figure A-12: Effect of data reconciliation on the Sauter diameter and CV-value (not every measurement point is shown)

189

A.8 Additional Data for Chapter 10.2 (Ascorbic Acid)

190 Appendix

0

2

4

6

8

-20 50 120 190 260 330 400Time [min]

Gro

wth

Rat

e [n

m/s

]

1.0E+07

1.0E+08

1.0E+09

1.0E+10

Nuc

leat

ion

Rat

e [#

/(m³·s

)]

Growth RateGrowth Rate, unfilteredNucleation RateNucleation Rate, unfiltered

20

25

30

35

40

-20 50 120 190 260 330 400Time [min]

Tem

pera

ture

[°C

]

0.00

0.20

0.40

0.60

Supe

rsat

urat

ion

S-1

[-]

Temperature (Reactor)Temperature (Thermostat)Supersaturation S-1

10

20

30

40

-20 50 120 190 260 330 400Time [min]

L PSD

,[3,2

] [µm

], C

V (Q

PSD

,0)·2

0 [-]

0.0E+00

8.0E+12

1.6E+13

2.4E+13

NTo

tal [

#/m

³]

LPSD,[3,2]CV (QPSD,0)·20NTotal

Figure A-13: Experimental data and calculated parameters for the crystallization of ascorbic acid (experiment 1, zone 2: from 100 to 200 min)

Appendix

191

Figure A-14: Comparison between experimental data (circles) and simulation (line) (experiment 1, zone 2: 100 min, every third measurement point)

192 Appendix

0

2

4

6

8

10

-30 40 110 180 250 320 390Time [min]

Gro

wth

Rat

e [n

m/s

]

1.0E+07

1.0E+08

1.0E+09

1.0E+10

Nuc

leat

ion

Rat

e [#

/(m³·s

)]


20

30

40

50

-30 40 110 180 250 320 390Time [min]

Tem

pera

ture

[°C

]

0.00

0.20

0.40

0.60

Supe

rsat

urat

ion

S-1

[-]

Temperature (Reactor)Temperature (Thermostat)Supersaturation

10

20

30

40

-30 40 110 180 250 320 390Time [min]

L PSD

,[3,2

] [µm

], C

V (Q

PSD

,0)·2

0 [-]

0.0E+00

8.0E+12

1.6E+13

2.4E+13

3.2E+13

NTo

tal [

#/m

³]



Appendix

193


194 Appendix

30

35

40

45

50

-30 80 190 300 410Time [min]

Tem

pera

ture

[°C

]

0.00

0.10

0.20

0.30

Supe

rsat

urat

ion

S-1

[-]


0

2

4

6

-30 80 190 300 410Time [min]

Gro

wth

Rat

e [n

m/s

]

1.0E+07

1.0E+08

1.0E+09

1.0E+10

Nuc

leat

ion

Rat

e [#

/(m³·s

)]


10

15

20

25

30

35

-30 80 190 300 410Time [min]

L PSD

,[3,2

] [µm

], C

V (Q

PSD

,0)·2

0 [-]

0.0E+00

6.0E+12

1.2E+13

1.8E+13

NTo

tal [

#/m

³]



Appendix

195


196 Appendix

20

25

30

35

40

-15 45 105 165 225 285Time [min]

Tem

pera

ture

[°C

]

0.00

0.20

0.40

0.60

Supe

rsat

urat

ion

S-1

[-]


0

2

4

6

8

10

-15 45 105 165 225 285Time [min]

Gro

wth

Rat

e [n

m/s

]

1.0E+08

1.0E+09

1.0E+10

Nuc

leat

ion

Rat

e [#

/(m³·s

)]


10

20

30

40

-15 45 105 165 225 285Time [min]

L PSD

,[3,2

] [µm

], C

V (Q

PSD

,0)·2

0 [-]

0.0E+00

8.0E+12

1.6E+13

2.4E+13

NTo

tal [

#/m

³]



Appendix

197


198 Appendix

199

A.9 Additional Data for Chapter 10.3 (α-Glycine)

200 Appendix

0

5

10

15

20

-10 30 70 110 150 190Time [min]

Tem

pera

ture

[°C

]

0.00

0.05

0.10

0.15

0.20

Supe

rsat

urat

ion

S-1

[-]


0

10

20

30

-10 30 70 110 150 190Time [min]

Gro

wth

Rat

e [n

m/s

]

1.0E+07

1.0E+08

1.0E+09

1.0E+10

Nuc

leat

ion

Rat

e [#

/(m³·s

)]


0

15

30

45

-10 30 70 110 150 190Time [min]

L PSD

,[3,2

] [µm

], C

V (Q

PSD

,0)·2

0 [-]

0.0E+00

2.0E+12

4.0E+12

6.0E+12

NTo

tal [

#/m

³]


Figure A-21: Experimental data and calculated parameters for the crystallization of α-glycine (experiment 1, zone 2: from 125 to 150 min)

Appendix

201

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

202 Appendix

10

15

20

25

-15 5 25 45 65 85Time [min]

Tem

pera

ture

[°C

]

0.00

0.05

0.10

0.15

Supe

rsat

urat

ion

S-1

[-]


0

10

20

30

-15 5 25 45 65 85Time [min]

Gro

wth

Rat

e [n

m/s

]

1.0E+07

1.0E+08

1.0E+09

1.0E+10

Nuc

leat

ion

Rat

e [#

/(m³·s

)]


0

10

20

30

40

-15 5 25 45 65 85Time [min]

L PSD

,[3,2

] [µm

], C

V (Q

PSD

,0)·2

0 [-]

0.0E+00

1.0E+12

2.0E+12

3.0E+12

NTo

tal [

#/m

³]



Appendix

203


204 Appendix

0

5

10

15

20

-25 0 25 50 75 100 125 150Time [min]

Tem

pera

ture

[°C

]

0.00

0.05

0.10

0.15

Supe

rsat

urat

ion

S-1

[-]


0

10

20

30

-25 0 25 50 75 100 125 150Time [min]

Gro

wth

Rat

e [n

m/s

]

1.0E+07

1.0E+08

1.0E+09

1.0E+10

Nuc

leat

ion

Rat

e [#

/(m³·s

)]


0

20

40

60

-25 0 25 50 75 100 125 150Time [min]

L PSD

,[3,2

] [µm

], C

V (Q

PSD

,0)·2

0 [-]

0.0E+00

2.0E+12

4.0E+12

6.0E+12

NTo

tal [

#/m

³]



Appendix

205


206 Appendix

Documents

Table of Contents - uni-halle.desundoc.bibliothek.uni-halle.de/diss-online/08/09H002/t16.pdf · • Ascorbic acid (KMF-optiChem, L(±)-Ascorbic Acid, crystalline, pure) ... comparison,