Role of Racemization Kinetics in the Deracemization Process via

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The role of racemisation kinetics in the deracemisation process via temperature cycles Francesca Breveglieri, and Marco Mazzotti Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.9b00410 • Publication Date (Web): 18 Apr 2019 Downloaded from http://pubs.acs.org on April 19, 2019

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Crystal Growth & Design

The role of racemisation kinetics in the deracemisation process via temperature cycles Francesca Breveglieri and Marco Mazzotti∗ 1

Separation Processes Laboratory, ETH Zurich, Zurich E-mail: [email protected] Phone: +41 44 632 24 56. Fax: +41 44 632 11 41

2

Abstract

3

18th April 2019

4

A suspension of crystals of both enantiomers of a conglomerate forming chiral

5

compound can be deracemised by applying temperature cycles in the presence of a

6

racemising catalyst that enables in solution the conversion of the undesired enan-

7

tiomer into the desired one. We aim at showing through experiments that, seemingly

8

paradoxically, accelerating the racemisation reaction by increasing the catalyst con-

9

centration speeds up the deracemisation process, if all the other parameters are left

10

unchanged. We prove this by deracemising, via temperature cycles, crystals of N-(2-

11

methyl-benzylidene)-phenylglycine amide (NMPA) suspended in either pure ACN or a

12

mixture of IPA/ACN (95/5 w/w) in the presence of different concentrations of the base

13

catalyst 1,8-diazabicyclo-[5.4.0]undec-7-ene (DBU). The applied periodic temperature

14

cycles follow a rather standard protocol. Prior to that we have fully characterized the

15

racemisation reaction rate, as a function of enantiomers' concentration, catalyst con-

16

centration and temperature, thus proving that the reaction is second order in NMPA

17

and DBU, and estimating the Arrhenius parameters for the two solvent systems.

1

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1

Introduction

19

Solid-state deracemisation (via attrition or temperature cycles) is a widely studied tech-

20

nique to attain enantiopurity, starting from a suspension of crystals of both enantiomers

21

of a conglomerate forming compound 1,2 . The suspended solid has, initially, a racemic (or

22

slightly enantiomerically enriched) composition, and during the process, it evolves towards

23

one handedness through crystal growth, agglomeration, breakage, dissolution, and through

24

racemisation in solution (Fig. 1).

25

Since during deracemisation the fraction of one enantiomer in the solid phase gradually in-

26

creases, its concentration in solution would decrease, if not restored through the racemisation

27

reaction. If such reaction is too slow, the concentration of the counter enantiomer builds up,

28

thus hindering chiral resolution, as discussed recently in the literature where racemisation

29

and deracemisation rates were compared 3 . The authors of that paper performed deracemisa-

30

tion with a simple two component system: a solvent and an atropisomer as model compound,

31

racemising spontaneously at different rates depending on the solvent chosen. Deracemisa-

32

tion was carried out under conditions where the racemisation reaction was the rate limiting

33

mechanism. They observed that a slower racemisation led to a longer deracemisation pro-

34

cess, thus concluding that the former was the rate controlling mechanism when performing

35

deracemisation through temperature cycles. This is certainly true, when the operating con-

36

ditions are such that the other phenomena, i.e. growth and dissolution, are faster than the

37

reaction. However, their investigation only focused on a simple reaction kinetic, while in

38

this paper we aim at extending the observations to the case when the reaction occurs in the

39

presence of a racemising agent, thus looking at how this additional parameter can be tuned

40

to improve the deracemisation process.

41

Since Viedma and coworkers demonstrated that the intrinsic racemisation rate constant

42

does not vary in the presence of the enantiomerically enriched solid phase 4 , by simply

43

measuring the reaction kinetic in solution one can estimate the rate constant experienced

44

in a deracemisation experiment. To this aim, we carried out the racemisation of N-(22


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45

methylbenzylidene)-phenylglycine amide (NMPA) in the presence of a base catalyst at dif-

46

ferent reagents concentration and temperature (Fig. 1). Note that deracemisation via tem-

47

perature cycles has been demonstrated also for sodium chlorate crystals 5,6 . Since this com-

48

pound is not chiral in solution, in the context of this study, it corresponds to the case of

49

infinite rate of racemisation.

50

The paper is organised as follows. First, we discuss the experimental materials and meth-

51

ods and the modelling approach utilized to evaluate the racemisation experiments. Then we

52

present and analyse the results of a comprehensive kinetic study of the racemisation reaction

53

of NMPA in the presence of DBU under different operating conditions, namely different over-

54

all enantiomers concentration, catalyst concentration and temperature, and in two different

55

solvent systems. Finally, we report the results of a series of deracemisation experiments of

56

NMPA under different operating conditions, and we conceptualise the effects observed.

Figure 1: The phenomena in deracemisation via temperature cycles with focus on the racemisation reaction at the experimental conditions investigated in this contribution.

57

3



58

2

Experimental

59

2.1

60

The experiments were performed using the following chemicals: N-(2-methylbenzylidene)-

61

phenylglycine amide (NMPA) dissolved in acetonitrile (ACN) or in the solvent mixture,

62

isopropanol and acetonitrile (IPA/ACN, 95/5 w/w), in the presence of 1,8-diazabicyclo-

63

[5.4.0]undec-7-ene (DBU) as racemisation catalyst (Fig. 1). The racemising agent and the

64

solvents were purchased from Sigma-Aldrich and used as received. The racemic NMPA

65

was first synthesised and then deracemised as reported elsewhere 7,8 to obtain the pure S-

66

enantiomer.

67

The optical rotation measurements were performed in a polarimeter Jasco P-2000, equipped

68

with a mercury lamp and a 365 nm filter. A thermostat was connected to the polarimeter

69

cell to maintain the solution at the desired temperature during the analysis.

70

The deracemisation experiments were performed in a customised version of Crystal16 (Tech-

71

nobis): the device consists of 16 independent vials of ca. 1.8 mL, each equipped with a

72

thermocouple to monitor the temperature. Rare Earth cylindrical PTFE stirring bars (8×3

73

mm) were used to stir the suspension at 1250 rpm. The vials used as crystallisers were

74

32×10 mm standard glass chromatographic vials.

75

HPLC measurements to monitor deracemisation were conducted in a DIONEX UltiMate

76

3000 HPLC series equipped with a quaternary pump and a DAD detector (Thermo Sci-

77

entific, Reinach, Switzerland). Measurements of 5 µL injections were carried out at 213 nm

78

on a CHIRALCEL OJ-H (250 × 4.6 mm) column. As mobile phase, a mixture of n-hexane

79

and isopropanol (60:40 v/v) was used with a flow rate of 1 mL/min. Retention times were

80

found to be 6.5 and 9.0 min for S-NMPA and R-NMPA, respectively. The enantiomeric

81

excess, E, was calculated using the HPLC peak area for each enantiomer.

Materials and experimental setup

4


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2.2

Experimental Procedures

83

Racemisation experiments The pseudo-first order kinetic rate constant, k 0 , was meas-

84

ured by carring out the racemisation reaction directly within the polarimeter cell. The

85

polarimeter cell was filled with a solution of pure NMPA and DBU at the desired temper-

86

ature and the optical rotation was monitored over time. To perform the experiments, we

87

prepared separatly bulk solutions of NMPA (2.9 and 5.6 g/L in IPA/ACN, 5.6 g/L in ACN)

88

and DBU in the desired solvent. Before each experiment, we mixed the two bulk solutions

89

so as to reach the desired DBU concentration (24, 12, 11, 9, 6, 3, 1 mM). The mixture was

90

quickly loaded into the polarimeter cell, and the optical rotation measurement was started

91

immediately.

92

The reference value of the rotation of the pure enantiomer, α0 , was measured for the two

93

NMPA concentrations considered in each solvent. These values were used to calculate the

94

enantiomeric excess, E, as the ratio between the observed rotation at a specific time t,

95

α(t), representing the excess of S-NMPA in solution, i.e. the difference between the concen-

96

trations of the two enantiomers (cS − cR ), and the α0 of the corresponding total (initial)

97

concentration 9,10 : E(t) =

α(t) α0

(1)

98

For each experiment, we estimated the value of the pseudo-first order rate constant k 0 from

99

the decay of the enantiomeric excess over time (see Eq. 7 in Section 3).

100

Deracemisation experiments The deracemisation experiments were carried out, as in

101

our previous work 8 , according to the following protocol.

102

To obtain a solid mixture with initial enantiomeric excess of ca. 20%, we wet-ground a solid

103

racemic mixture of NMPA powder with a powder of the desired enantiomer (in this work

104

S-NMPA) and a few µL of pure acetonitrile, which then evaporated. The desired amount of

105

DBU was added to a filtered saturated solution of racemic NMPA in the specified solvent.

106

Finally, the vials containing the solids were filled with the saturated solution, to produce a 5



107

suspension of the desired density, ρ. The suspension was stirred at 30 ◦ C for ten minutes,

108

then the first sample was taken and the temperature cycles started. The experiments ran

109

until the enantiomeric excess was at least 98%. The final product was collected by vacuum

110

filtration and washed with MTBE (tert-butylmethylether), to remove the residual solution.

111

The temperature cycle applied was the same for all experimental runs. It consists of four

112

steps: a heating ramp (1.30 ◦ C/min, i.e. 8.5 min), an isothermal step at the maximum

113

temperature (41 ◦ C), a cooling ramp (1.30 ◦ C/min), and a second isothermal step at the

114

minimum temperature (30 ◦ C).

115

The operating conditions are indicated in Section 5 for each experiment and chosen to ensure

116

that 30% of the solids are dissolved at every cycle in the experiments with the two different

117

solvents. Each experiment at a given set of operating conditions was repeated three times,

118

to assess the reproduciblity of the results.

119

The evolution of the enantiomeric excess over time was monitored by sampling the suspension

120

(7-9 µL) at the end of the isothermal step at the low temperature. The suspension was filtered

121

and washed with MTBE. The dry powder was then dissolved in IPA and its composition

122

was determined through HPLC analisys.

123

3

Modeling the racemisation reaction

The racemisation reaction consists in the reversible transformation of one enantiomer into the other:

S− )− −* −R

124

where, for symmetry, the equilibrium constant is one at every temperature.

125

This reversible reaction is responsible for the observed decay of the enantiomeric excess in

126

solution towards equilibrium, i.e. the racemic composition 11,12 . We assume that the ra-

127

cemisation reaction in both directions is first order in the catalyst concentration and in the 6


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128


concentration of the relevant enantiomer, i, hence, its reaction rate is given by:

r = k cb ci = k 0 ci

i = S, R

(2)

129

where cb is the DBU concentration, and ci is the concentration of the ith enantiomer, k is

130

the second order rate constant, and k 0 is the pseudo-first order rate constant. For the sake

131

of symmetry, rate constants are the same in both directions 9,10,13,14 . In a batch reactor,

132

the evolution of the concentration of the two species in solution is, hence, described by the

133

following rate equations: dcS = −k 0 (cS − cR ) dt dcR = k 0 (cS − cR ) dt

(3) (4)

where cS and cR are the concentrations of the S and R enantiomer, respectively. By summing and subtracting Eqs. 3 and 4 one obtains:

cS + cR = const

(5)

dE = −2k 0 E dt

(6)

134

where E = (cS − cR ) / (cS + cR ) is the enantiomeric excess. Integrating Eq. 6 with E(0) = E0

135

and linearising yields:

ln E(t) = ln E0 − 2k 0 t

(7)

136

From the optical measurements, we obtained the experimental evolution of the enantiomeric

137

excess over time (Eq. 1). By fitting Eq. 7 to the experimental measurements, using linear

138

regression, for each experiment we determined the pseudo-first rate constant, k 0 , and from

7



139

it the second order rate constant, k, as:

k=

140

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k0 cb

(8)

The obtained rate constant is a function of temperature, according to the Arrhenius law:

Ea k = k0 exp − RT

(9)

141

where R is the universal gas constant (8.31 J K−1 mol−1 ), T the absolute temperature, k0

142

and Ea are the prexponential factor and the activation energy, respectively.

143

4

144

4.1

145

We performed racemisation experiments aimed at assessing the reaction kinetic presented

146

in Section 3 and at estimating the rate constant k 0 , and consequently k, at different exper-

147

imental conditions. During these experiments, we observed the decay of the enantiomeric

148

excess over time and we estimated the rate constant, k 0 , from Eq. 7 for each operating con-

149

dition. The measurements recorded during four selected experiments are shown in Fig. 2,

150

where the colour code refers to the overall variation of the enantiomeric excess observed

151

during each experiment, ∆E: the faster the reaction, the larger the drop of the enantio-

152

meric excess in a given time. It is worth noting that this quantity gives an indication of

153

the reliability of the estimated rate constant. The linear regression of Eq. 7 is obviously

154

more representative if the experiment on which it is based spans a larger variation of the en-

155

antiomeric excess, E. Accordingly, the larger ∆E, the more reliable the estimated value of k 0 .

Racemisation reaction Racemisation reaction rate

156

157

8


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Figure 2: Racemisation experiments in the IPA/ACN mixture: the exponential decay of the enantiomeric excess over time. The colour code indicates the difference of enantiomeric excess observed during each experiment: blue and yellow shades correspond to large and small ∆E, respectively. For each experiment, the corresponding operating conditions are indicated: temperature, DBU, and NMPA concentrations. 158

For the 23 experiments performed, the values of the rate constant, k computed from the

159

corresponding k 0 -values (Eq. 8) are reported in Table 1 for the solvent mixture IPA/ACN

160

(top) and for pure ACN (only one series of experiments, reported at the bottom). Once

161

again, the colour of each cell in the table corresponds to the associated value of ∆E, so as

162

to highlight the differences in data accuracy among the different experiments. The table

163

allows analysing the dependence of the rate constant on DBU concentration, cb , and on total 9



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164

NMPA concentration, cN , (rows), as well as on temperature (columns). Considering the data

165

measured in IPA/ACN, the measured rate constants are grouped in the different columns,

166

according to the temperature at which they are estimated (22 ◦ C, 25 ◦ C, and 30 ◦ C). As a

167

consequence, the k-values should be constant along each column, whereas, they should differ

168

from one column to the next, because of their temperature dependence. This is indeed what

169

we can qualitatively observe in the table, with k-values (in min−1 M−1 ) clustering around

170

0.5 at 22 ◦ C, 0.63 at 25 ◦ C, and 1.1 at 30 ◦ C. The variability is within a band of 10%

171

for the values in the darker cells (fast, more reliable experiments), whereas experiments in

172

yellow, green, and light blue cells deviate much more, but they are also less reliable. Note

173

that increasing temperature (from left to right in Table 1) leads to an increase in the rate

174

constant as expected according to the Arrhenius law of Eq. 9. Table 1: Estimation of the second order rate constant, k [min−1 M−1 ]: experimental conditions (solvent, concentration of base and NMPA, and temperature) and corresponding measured values. The boxes are coloured according to the ∆E observed in each experiment, i.e. increasing from yellow to blue. (? in this experiment the temperature is 21.5◦ C.) cb [mM]

T [◦ C]

cN [g/L] IPA/ACN (95/5 w/w) 1 2.9 5.6 3 2.9 6 2.9 2.9 9 5.6 11 2.9 5.6 12 2.9 2.9 5.6 5.6 5.6 24 5.6 ACN 1 5.6

20

22

25

30

0.430

0.484 0.834

0.796

0.398? 0.606 0.494

1.118 1.136

0.433 0.657

0.345

0.595 0.528 0.506 0.476 0.466 0.513

7.040

10


0.602

1.115 1.070

0.629

1.038

9.439 14.851

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175

Based on this qualitative observation, we have confirmed the applicability of the kinetic

176

law of Eq. 2 and we have used the Arrhenius plot (Fig. 3) to plot the experimental data

177

(coloured symbols) utilised for the estimation of the kinetic parameters; the same colour-

178

code as in Fig. 2 and in Table 1 has been used.

179

For a good estimation of the parameters, we have reduced the unbalance in the effect of the

180

two parameters (a small variation of the slope induces a large variation of the intercept) by

181

reparametrising the Arrhenius law in its linear form, as follows 15 : Ea ln k = β − R

1 1 − T Tav

(10)

182

where β = ln k0 − Ea/RTav and Tav is the average temperature (Tav = 298 K in this case). Since

183

the reference axis is moved, the intercept is less sensitive to the variation of the slope, even if

184

the data are collected in a narrow temperature range, which is upper bounded by the solvent

185

volatility and lower bounded by the compound solubility. We computed the parameters β

186

and Ea with the method of the weighted least squares, hence, by minimising the weighted

187

residual sum of the square errors of the logarithm of k, by means of the f minsearch algorithm

188

of the MATLAB optimisation toolbox:

RSS =

n X

2 wi ln kî − ln ki

(11)

i=1

189

where n is the number of experiments, wi is the weighting factor, which is defined as

190

wi = ∆Ei , i.e. it weights more the error of the experiments with the larger variation of

191

the enantiomeric excess during experiment itself, kî is the experimentally measured value of

192

the rate constant from Table 1, and ki is its value computed using Eq. 10 at the relevant tem-

193

perature. By weighing the errors in Eq. 11 according to the reliablity of the corresponding

194

experiment (as discussed above), we have let the more reliable experiments play a larger role

195

in contributing to the estimantion of the model parameters. The parameter values obtained

196

from the regression in the case of the IPA/ACN solvent system are β = −0.422 ± 0.043 11



197

min−1 M−1 and Ea = 7.379 ± 0.918 × 104 J mol−1 , indicated with the corresponding confid-

198

ence intervals, at 95% confidence level (see Appendix A for the calculations). These values

199

result in k0 = 5.648 × 1012 min−1 M−1 .

200

The regression line of Eq. 10 is also plotted in Fig. 3. It is worth noting that experimental

201

points far from it correspond indeed to the slowest and least reliable experiments, with pos-

202

sibly the exception of the single experiment carried out at 20 ◦ C (light blue point in the

203

bottom right corner of the figure).

204

In Appendix B the reader can find a discussion about the dependence of the reaction rate

205

on the concentration of the catalyst.

206

12


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Figure 3: Temperature dependence of the second order rate constant, k, in the IPA/ACN solvent mixture. The solid line corresponds to the regression line according to Eq. 10, with β = −0.422 ± 0.043 min−1 M−1 and Ea = 7.379 ± 0.918 × 104 J mol−1 , at 95% confidence level. The colour code indicates the difference in enantiomeric excess observed during the experiments: blue and yellow shades for large and small ∆E, respectively. 207

4.2

Role of the solvent

208

We performed additional experiments to verify how a different solvent system may affect the

209

racemisation reaction and, consequently, the deracemisation process. We have performed

210

racemisation in pure ACN at three different temperatures and we have estimated the para-

211

meters in the Arrhenius law also for this solvent, thus obtaining the experimental points and

13



212

the regression line plotted in Fig. 5 (together with points and line for IPA/ACN from Fig.

213

3).

214

Despite the smaller number of data points, it is strikingly obvious that the racemisation is

215

much faster in pure ACN than in the IPA/ACN mixture (with 95% IPA).

216

In the following we discuss how to rationalise such difference based on the different physico

217

chemical properties of the two solvent systems 16,17 .

218

1. The reaction mechanism

219

The reaction occurs through the formation of an anionic transition state (Fig. 4),

220

which is stabilised by the resonance of the negative charge on the Schiff base and the

221

carbonyl group, but also by the electron withdrawing aromatic ring 18,19 . According to

222

the Hughes-Ingold rules, when this transition state is further stabilised by the solvent,

223

the reaction is accelerated, because the formation of the ion, i.e. the highest energy

224

transition state, is the rate limiting step (it is slower than the following protonation) 20 .

Figure 4: The stabilisation of the anionic transition state, thanks to the resonance of the negative charge on the carbonyl and on the Schiff base.

225

226

2. Solvent polarity

227

Since ACN is more polar than IPA 21 , it solvates the transition state better, thus

228

lowering its energy and stabilizing it. Additionally, in a more polar solvent all the ions

229

are available to the reaction, because they are better solubilised and less hindered by

230

the counter-ion. For these two reasons only, the reaction proceeds faster in ACN than

231

in the IPA/ACN 95/5 mixture. 14


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232


3. Solvent proticity and basicity

233

IPA is a protic solvent and it is more basic than ACN. Therefore, the former can

234

dissociate, thus forming isopropoxide ions. This may have a twofold effect on the

235

reaction. On the one hand, the isopropoxide ion could stabilise the reactive ions of the

236

base and of the substrate thanks to ion-ion interactions, thus reducing their reactivity.

237

On the other hand, IPA could serve as ”proton shuttle”, promoting the reaction thanks

238

to the proton transfer among the reactants 22 .

239

4. Solvent viscosity

240

In ACN, the reactants can interact more freely, thanks to ACN low viscosity, thus

241

resulting in a faster reaction, than in the case of the more viscous IPA-rich solvent 23 .

242

This analysis on the solvent properties suggests that those described in points 2 and 4 are

243

mainly responsible for the solvent effects on the racemisation reaction rate, which is ten

244

times faster in ACN than in IPA/ACN. To reinforce this conclusion, a detailed model of the

245

solute-solvent interaction should be developed and utilised, especially to confirm the stabil-

246

isation of the transition state by a polar solvent. However, such a study is beyond the scope

247

of this paper.

248

These findings point at the importance of the solvent selection in the context of the dera-

249

cemisation processes. It is however very difficult to predict such effects, because the phenom-

250

ena and mechanisms present are numerous and different solvents have different advantages

251

and disadvantages in relation to such phenomena and mechanisms.

252

15



Figure 5: Comparision of rate constants, experimental data and regression line (Eq. 10), for pure ACN (diamonds) and the solvent mixture IPA/ACN (circles). The estimated parameter values are indicated for the two solvent systems with the corresponding confidence interval at 95% confidence level. The colour code, as in Figs. 2 and 3, indicates the difference in enantiomeric excess observed during the experiments: blue and yellow shades for large and small ∆E, respectively. 253

5

Deracemisation via temperature cycles

254

In the previous section we discussed the racemisation kinetic of NMPA at different operating

255

conditions; we now examine how operating conditions, namely racemising agent concentra-

256

tion and solvent system, affect the deracemisation process, in an on-going effort to define

257

guidelines that help identifying optimal operating conditions for deracemisation via temper-

258

ature cycles.

259

Before looking at these results, we would like to underline that the accurate execution of

260

a precisely defined experimental protocol is required to obtain well reproducible results.

261

Repetitions of the same experiment may yield results that vary among each other, either be-

16


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262

cause of small differences in the composition and in the particle size distribution of the seed

263

crystals or due to fluctuations in the suspension density, that cannot be exactly controlled

264

during the experiments and their preparation. Moreover, the measurements presented here

265

are obtained through HPLC analysis, whose accuracy strongly depends on the quality and

266

preparation of the samples used. In some cases, the sample might not be representative of

267

the suspension as a whole, due to non homogeneous mixing, or small temperature variations,

268

that can promote dissolution, thus variation of the solid phase composition. A similar effect

269

is due to the sampling time: if thermodynamic equilibrium is not attained, samples taken

270

one after the other turn out to be different. In other cases, the amount of sampled powder

271

can be too little to well represent the suspension composition. However, the sample has to

272

be as small as possible not to spoil the deracemisation process. Another important step of

273

the sampling procedure is the drying of the sampled powder after filtration and washing,

274

for an effective removal of the residual solution, that might influence the observed sample

275

composition. Due to the complex phenomena occurring during the process (agglomeration,

276

breakage, primary and secondary nucleation), a special attention in carrying out the exper-

277

iments is, nevertheless, not always sufficient to extract accurate quantitative information.

278

As mentioned in the Introduction, a recent study, focused on racemisation occurring without

279

a catalyst, shows the increase of the deracemisation rate with increasing racemisation rate 3 .

280

A similar conclusion was drawn in our previous contribution on deracemisation via temperat-

281

ure cycles (see Section 3.3 of the previous work), where NMPA was deracemised in different

282

temperature ranges 8 . We observed faster deracemisation with increasing minimum temper-

283

ature, likely due to the temperature dependence of the kinetic parameters (racemisation

284

and growth). Assuming that the growth is not the limiting step, the deracemisation time

285

is controlled by the racemisation kinetic: the slow conversion of the undesired enantiomer

286

into the target enantiomer in solution leads to a higher supersaturation of the former, that

287

could grow and potentially nucleate. Such undesired particles have afterwards to dissolve,

288

before they can be converted into the desired enantiomer; such combination of events leads

17



289

obviously to increasing deracemisation time.

290

The effect of faster or slower racemisation on the deracemisation process can be assessed

291

by varying the catalyst concentration. To verify this hypothesis, we have performed dera-

292

cemisation via temperature cycles with increasing DBU concentration (namely 15, 20, and

293

30 mM), which corresponds to doubling the racemisation reaction rate. The results of the

294

experiments are illustrated in Fig. 6, where the three repetitions at each catalyst concen-

295

tration are presented in Fig. 6a, 6b, and 6c, respectively (using boxes, circles, and triangles

296

as symbols). Although the three repetitions are not overlapping exactly, most likely for the

297

reasons mentioned at the beginning of this section, the trends are clear, as highlighted by

298

the lines connecting the experimental points. Increasing the catalyst concentration speeds

299

up not only the racemisation reaction, but also the whole deracemisation process: almost

300

complete resolution is attained within ca. 15, 12, and 10 cycles when increasing DBU con-

301

centration from 15 to 20 to 30 mM.

302

When using pure ACN instead of the IPA/ACN mixture as solvent system, the racemisation

303

kinetic constant, k, at 30 ◦ C is about 13 times larger. Then, we have performed three re-

304

petitions of a deracemisation experiment in pure ACN at the same experimental conditions.

305

To do that, we measured gravimetrically the solubility of NMPA in ACN (see Table 2) and

306

we varied the suspension density, ρ, accordingly, to ensure that 30% of the suspended solid

307

is dissolved at every cycle. The results are plotted in Fig. 6d, where it is readily seen that

308

the deracemisation has not accelerated significantly: it is only slightly faster (10 cycles) in

309

ACN than in the IPA/ACN mixture (12 cycles) (compare Figs. 6b and 6d).

310

311

18


Page 18 of 27

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Table 2: The gravimetric solubility of racemic NMPA measured in IPA/ACN 8 and in pure ACN as a function of temperature. The results are reported as mean value of three sample, with the associated standard deviation. T [◦ C] 20 30 40 50

c∗ [mg/g] IPA/ACN ACN 11.9 ± 0.2 20.2 ± 0.4 16.1 ± 0.1 23 ± 1 48.0 ± 0.9 80.9 ± 0.9

19



Page 20 of 27

(a)

(b)

(c)

(d)

Figure 6: Deracemisation of NMPA via temperature cycles: evolution of the enantiomeric excess versus number of cycles. In the solvent mixture IPA/ACN with increasing DBU concentration: 15 (a), 20 (b), and 30 (c) mM; (d) in pure ACN with 20 mM DBU. For each set of experimental conditions, indicated in the corresponding plot, three repetitions have been performed (triangles, circles, and boxes, open and closed symbols for visualisation purposes).

20


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312

6

Conclusions

313

The results presented above clarify that the rate of the racemisation reaction affects directly

314

the rate of the overall deracemisation process via temperature cycles. This can be shown

315

when only the racemisation catalyst concentration is varied, whereas all the other operating

316

conditions remain unchanged, as we have done in this work in the case of the experiments

317

in the solvent system consisting of a mixture of IPA and ACN. Such effect was not obvious

318

in experiments reported in our previous paper 8 , where we had varied the interval where the

319

temperature cycles were operated, because by doing this the kinetics of all the phenomena

320

involved, i.e. not only racemisation but also growth and dissolution are affected.

321

The fact that all phenomena and mechanisms involved in the deracemisation process have an

322

important effect is demonstrated once more in this paper when deracemisation in IPA:ACN

323

is compared with deracemisation in pure ACN, i.e. a solvent where racemisation is more

324

than ten times faster. Contrary to the expectation, deracemisation is only marginally faster

325

in ACN, most likely because the new solvent affects all the other phenomena involved, and

326

not only racemisation.

327

Such observation leads to the conclusion that the choice of the solvent system has an import-

328

ant effect on the deracemisation process, though in ways that might be difficult to predict

329

a priori, indeed because of the complexity of the deracemisation process itself. However,

330

preliminary information on the rate limiting step of the deracemisation process can guide

331

the solvent choice, thus promoting a successful process design and optimisation.

332

Acknowledgements

333

This research received funding as part of the CORE project (October 2016-September 2020)

334

from the European Union's Horizon 2020 research and innovation programme under the

335

Marie Sklodowska-Curie grant agreement No 722456 CORE ITN.

336

The authors thank Ryusei Oketani (University of Rouen) and Francesca Cascella (Max Plank 21



Page 22 of 27

337

Institute, Magdeburg) for the fruitful discussions, Gérard Coquerel (University of Rouen)

338

and Erik M. Carreira (ETH Zurich) for allowing one of us, FB, to carry out part of the

339

racemisation experiments in their laboratories.

340

Appendix A

341

When estimating the Arrhenius parameters we computed the confidence intervals 15,24 , as the

342

diagonal elements of the matrix, C:

C = tN 1−α/2

343

344

p

(GT G−1 ) σw2

(12)

where tN 1−α/2 is the t-statistics with N = n − 2 (since we estimate 2 parameters) degrees of freedom and at confidence level α, and V{p} = GT G−1 σw2 is the covariance matrix of the

345

parameters, p, which is computed from the sensitivity matrix, G, and the weighted variance,

346

σw2 . The matrix G is defined as the matrix of the partial derivatives of the model function, f

347

(Eq. 10), with respect to the parameters, p:

∂f (x,p) . ∂pi

The variance σw2 is calculated as follows:

2 ˆ w ln k − ln k i i i=1 i Pn i=1 wi

Pn σw2 =

(13)

348

where n is the number of experiments, wi is the weight associated to each measurement,

349

kî and ki are the experimental value and the computed estimation of the rate constant,

350

respectively.

351

Appendix B

352

The effect of the catalyst was assessed at three different temperatures (22, 25, 30 ◦ C) and it

353

was proved that the rate constant, k 0 , is directly proportional to the DBU concentration (Fig.

354

7), as assumed in Section 3 13 . For each temperature, we computed a regression line, and we 22


Page 23 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


355

evaluated the results by performing a statistical t-test, with the hypothesis that the intercept

356

is equal to zero. At a confidence level of 95% (α = 0.05), the values of the t-statistic and

357

the corresponding significance level, in brackets, are the following: - 0.1109 (0.91), -0.0237

358

(0.98), and 2.115 (0.10), for T = 22, 25, 30 ◦ C, respectively. Since the significance level is

359

always larger then the chosen values of α, the tested hypothesis cannot be rejected, meaning

360

that the intercept-values do not significantly differ from zero. These results confirm the

361

assumption that the catalyst is primarily responsible for the reaction, i.e. that the reaction

362

rate in the absence of the catalyst is negligible with respect to that of the catalysed reaction.

363

Therefore, the second order kinetic constant can be computed using Eq. 8.

Figure 7: The pseudo-first order rate constant, k 0 , in function of DBU concentration, cb , at 30, 25, and 22 ◦ C (dots, diamonds, and squares, respectively). The the regression line with Eq. 8 is reported for every temperature as a dashed line with lighter shades of grey from 30 to 22 ◦ C; The colour code indicates the difference in enantiomeric excess observed during the experiments: blue and yellow shades for large and small ∆E, respectively.

364

23



365

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For Table of Contents Use Only

428

The role of racemisation kinetics in the deracemisation process via temperature cycles

429

Francesca Breveglieri and Marco Mazzotti

430

431

We show that a faster racemisation reaction leads to a faster deracemisation process via

432

temperature cycles. By performing racemisation experiments at different operating condi-

433

tions, we describe the racemisation rate according to a second order kinetic model and to the

434

Arrhenuis law. We, then, analyse the deracemisation experiments, performed at different

435

racemisation rates, obtained by changing the racemisation catalyst concentration.

27


Role of Racemization Kinetics in the Deracemization Process via

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