Rational approach to the selection of conditions for diastereomeric ...
Rational approach to the selection of conditions for diastereomeric ...
Rational approach to the selection of conditions for diastereomeric ...
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F. C. Ferreira et al. / Tetrahedron: Asymmetry 17 (2006) 1337–1348 1343<br />
Model outputs<br />
-Yield<br />
-Solid e.e.<br />
-Mo<strong>the</strong>r liquor e.e<br />
-Mo<strong>the</strong>r liquor pH<br />
ASR<br />
R t , S t<br />
Model parameters:<br />
-K s AS , K s AR , K s AR2 , K s<br />
AS2<br />
Model input variables:<br />
[A] 0 , [S] 0 , [R] 0<br />
S t<br />
AS 2<br />
Kd 1’S<br />
2 × S t<br />
Kd 2S<br />
A t<br />
2 × R t<br />
Kd 2R<br />
R t<br />
AR 2<br />
Kd 1’R<br />
AS<br />
S t<br />
R t<br />
AR<br />
Kd 1S<br />
Kd 1R<br />
Figure 5. Equilibria considered in model I, which neglects acid–base equilibrium.<br />
ASR<br />
Model outputs<br />
Model parameters:<br />
-Yield<br />
-Kd 1 ,Kd 2<br />
-Solid e.e.<br />
-Mo<strong>the</strong>r liquor e.e<br />
-Ka 1 ,Ka 2 ,Ka amine K w<br />
-K AS s , K AR s , K AR2 AS2<br />
s , K s<br />
AS A 2- 2 AR 2<br />
SH + H + Kd 2S<br />
H + Kd 2R<br />
RH + H +<br />
pH ~ pKa 2<br />
-Mo<strong>the</strong>r liquor pH<br />
Model input variables:<br />
RH + , SH + [A] 0 , [S] 0 , [R] 0<br />
2 × SH +<br />
2 × RH +<br />
Kd 1’S SH +<br />
RH +<br />
Kd 1’R<br />
AS<br />
HA -<br />
AR<br />
Kd 1S<br />
H +<br />
Kd 1R<br />
pH ~ pKa 1<br />
H 2 A<br />
R<br />
S<br />
H + H +<br />
RH +<br />
SH +<br />
pH ~ pKa amine<br />
Figure 6. Equilibria considered in model II, which takes in<strong>to</strong> account acid–base equilibrium.<br />
3. Precipitation/crystallisation <strong>of</strong> <strong>the</strong> four <strong>diastereomeric</strong><br />
salts follows ideal behaviour and is <strong>the</strong>rmodynamically<br />
controlled, following <strong>the</strong> solubility limits <strong>of</strong> <strong>the</strong> respective<br />
<strong>diastereomeric</strong> salts (Ks AS , Ks AR , Ks AR2 and<br />
Ks AR2 ).<br />
4. The two proposed models differ in <strong>the</strong> following<br />
assumptions:<br />
(a) For model I (<strong>the</strong> simpler model) <strong>the</strong> acid–base equilibrium<br />
<strong>of</strong> <strong>the</strong> diacid resolving agent and amine<br />
enantiomers is neglected, and <strong>the</strong> <strong>diastereomeric</strong><br />
equilibrium constants are defined on <strong>the</strong> basis <strong>of</strong><br />
<strong>the</strong> <strong>to</strong>tal amount <strong>of</strong> reactants dissolved in <strong>the</strong><br />
mo<strong>the</strong>r liquor (Eqs. 8a–11a).<br />
(b) For model II (<strong>the</strong> more complex model), acid–base<br />
equilibrium are taken in<strong>to</strong> account and is assumed<br />
that <strong>the</strong> <strong>for</strong>mation <strong>of</strong> <strong>diastereomeric</strong> salts occurs<br />
through ionic bonds between <strong>the</strong> charged carboxylate<br />
groups <strong>of</strong> <strong>the</strong> diacid resolving agent and<br />
ammonium group <strong>of</strong> <strong>the</strong> amine. There<strong>for</strong>e, <strong>the</strong><br />
equilibrium constants <strong>for</strong> <strong>diastereomeric</strong> salt <strong>for</strong>mation<br />
are based only on <strong>the</strong> ionic <strong>for</strong>ms <strong>of</strong> <strong>the</strong><br />
reactants (Eqs. 8b–11b). Moreover, <strong>the</strong> acid–base<br />
equilibria <strong>for</strong> <strong>the</strong> amine and <strong>the</strong> diacid resolving<br />
agent, with <strong>the</strong> respective acid dissociation constants,<br />
are also taken in<strong>to</strong> account through Ka amine ,<br />
Ka 1 and Ka 2.<br />
5. There is no chiral recognition in solution. 16 There<strong>for</strong>e,<br />
<strong>the</strong> same value is assigned <strong>to</strong> equilibrium constants <strong>of</strong><br />
reactions in <strong>the</strong> mo<strong>the</strong>r liquid independently <strong>of</strong> <strong>the</strong><br />
enantiomer considered, that is, Kd 1S ¼ Kd 1R ¼ Kd 1 ;<br />
Kd 1 0 S ¼ Kd 1 0 R ¼ Kd 1<br />
0 and Kd 2S ¼ Kd 2R ¼ Kd 2 .<br />
6. Diastereomeric salt <strong>for</strong>mation tends <strong>to</strong>wards irreversibility<br />
and <strong>the</strong> values <strong>of</strong> <strong>the</strong> equilibrium constants were<br />
selected accordingly.<br />
7. The Gibbs free energy <strong>of</strong> bond <strong>for</strong>mation between <strong>the</strong><br />
free resolving agent and <strong>the</strong> first amine (acidic salt <strong>for</strong>mation),<br />
and <strong>the</strong> acidic salt and <strong>the</strong> second amine (<strong>for</strong>mation<br />
<strong>of</strong> <strong>the</strong> neutral salt) is <strong>the</strong> same, hence <strong>the</strong>y have<br />
<strong>the</strong> same <strong>for</strong>mation enthalpy and constants, that is,<br />
Kd 1 ¼ Kd 1<br />
0 and f = 1. Thus Kd 2 is equal <strong>to</strong> (Kd 1 ) 2 .