5:15 PM - 7:15 PM
[MIS13-P07] Conversion of stable racemic crystals into metastable chiral crystals by grinding
Keywords:Viedma ripening, Cluster incorporation, Grinding, Phase conversion
Deracemization in crystallization of chiral crystals has attracted much attention because of its simple physical methods. Continuous abrasive grinding of left- and right-handed sodium chlorate crystals in a saturated solution transforms those crystals into an enantiopure state. This method can also be applied to chiral organic crystals. The achievement of an enantiopure state by continuous grinding is now called Viedma ripening (VR).
The mechanism of deracemization in crystallization is also interesting from the viewpoint of fundamental science. The widely accepted theoretical idea is the chiral cluster incorporation mechanism for VR experiments. Recently, a surprising experiment has been reported in which the enantiopure state is obtained from a solution with a larger amount of stable racemic crystals of aspartic acid and a smaller amount of metastable chiral crystals by VR and boiling a solution without any chiral additives. In order to reproduce the result, we propose a rate equation model with a cluster reaction that takes into account the effect of VR.
The model describes the time evolution of the mass density of eight components: stable crystals Zs, metastable chiral crystals Xs and Ys, chiral molecules Xm and Ym, subcritical chiral clusters Xc, Yc, and subcritical racemic clusters Zc. The subcritical clusters contribute to the growth and the dissolution of crystals of the same type. In addition, crystals and subcritical clusters are broken at a certain rate by the effect of the grinding. The ratio of the parameters related to the growth rate and the dissolution rate in the model is chosen from the experimental result.
The time evolution of the crystal enantiomeric excess (ee) reproduces the experimental result, that is, the crystal ee increases exponentially. The behavior of the solution ee is comparable to previous theoretical and experimental results. Our result also shows that even if the initial amount of metastable crystals is smaller than that of stable crystals in a solution, only metastable chiral crystals survive if crystals are continuously ground. Their masses change during the reaction. The behavior is visualized with the projection into a two-dimentional ternay diagram. Without grinding, one fixed point, which represents a stable racemic crystals, appears in the diagram. With grinding, one unstable fixed point and three saddle points appear near points of the chiral states. When the grinding rate is large, one unstable fixed point and two saddle points move to the point of the stable racemic state. If the grinding rate is of the same order as the dissolution rate, the saddle point is located at the point where the amount of the stable crystals is equal to the amount of the metastable crystals. This result suggests that the grinding rate is sufficiently large, a small amount of metastable crystals can prevail over the stable crystals. However, this phenomenon can be seen if the amount of stable crystals is less than a critical value.
The cluster incorporation mechanism in chirality conversion by crystal grinding is effective even if there is an energetic disadvantage compared to the competing phase. This extinction of the most stable phase crystals can occur when the number of its components exceeds that of the competing metastable phase crystals.
The mechanism of deracemization in crystallization is also interesting from the viewpoint of fundamental science. The widely accepted theoretical idea is the chiral cluster incorporation mechanism for VR experiments. Recently, a surprising experiment has been reported in which the enantiopure state is obtained from a solution with a larger amount of stable racemic crystals of aspartic acid and a smaller amount of metastable chiral crystals by VR and boiling a solution without any chiral additives. In order to reproduce the result, we propose a rate equation model with a cluster reaction that takes into account the effect of VR.
The model describes the time evolution of the mass density of eight components: stable crystals Zs, metastable chiral crystals Xs and Ys, chiral molecules Xm and Ym, subcritical chiral clusters Xc, Yc, and subcritical racemic clusters Zc. The subcritical clusters contribute to the growth and the dissolution of crystals of the same type. In addition, crystals and subcritical clusters are broken at a certain rate by the effect of the grinding. The ratio of the parameters related to the growth rate and the dissolution rate in the model is chosen from the experimental result.
The time evolution of the crystal enantiomeric excess (ee) reproduces the experimental result, that is, the crystal ee increases exponentially. The behavior of the solution ee is comparable to previous theoretical and experimental results. Our result also shows that even if the initial amount of metastable crystals is smaller than that of stable crystals in a solution, only metastable chiral crystals survive if crystals are continuously ground. Their masses change during the reaction. The behavior is visualized with the projection into a two-dimentional ternay diagram. Without grinding, one fixed point, which represents a stable racemic crystals, appears in the diagram. With grinding, one unstable fixed point and three saddle points appear near points of the chiral states. When the grinding rate is large, one unstable fixed point and two saddle points move to the point of the stable racemic state. If the grinding rate is of the same order as the dissolution rate, the saddle point is located at the point where the amount of the stable crystals is equal to the amount of the metastable crystals. This result suggests that the grinding rate is sufficiently large, a small amount of metastable crystals can prevail over the stable crystals. However, this phenomenon can be seen if the amount of stable crystals is less than a critical value.
The cluster incorporation mechanism in chirality conversion by crystal grinding is effective even if there is an energetic disadvantage compared to the competing phase. This extinction of the most stable phase crystals can occur when the number of its components exceeds that of the competing metastable phase crystals.