Chiral Separation in Microflows

Molecules that only differ by their chirality, so-called enantiomers, often possess different properties with respect to their biological function. Therefore, the separation of enantiomers presents a prominent challenge in molecular biology and has long been a main pursuit of organic chemistry. We suggest a new separation technique for chiral molecules that is based on the transport properties in a microfluidic flow with spatially variable vorticity. Because of their size the thermal fluctuating motion of the molecules must be taken into account. These fluctuations play a decisive role in the proposed separation mechanism.

Figure 1

A chiral molecule consisting of three atoms with different friction coefficients ${\gamma }_i$ on an equilateral triangle at positions ${\mathbf{x}}_i=\mathbf{X}+{\mathbf{r}}_i(\phi )$. The mirror particle differs only in the sequence of the friction coefficients. The rigid rods (gray lines) of lengths $d$ maintain the structure.

Figure 2

The streaming pattern given by Eq. (7) is shown in one unit cell. The streamlines circulate within adjacent quarters in opposite directions.

Figure 3

The deterministic motion of chiral partner molecules (top vs bottom row) is visualized by the respective domains of attraction (left panels) and the corresponding attractors. The $(+)$ molecule in the top row has the shape of an equilateral triangle with side length $d=0.2$ and friction coefficients $({\gamma }_1,{\gamma }_2,{\gamma }_3)=(1/6,1/3,1/2)$. Its chiral $(-)$ partner in the bottom row has the sequence $({\gamma }_1,{\gamma }_2,{\gamma }_3)=(1/3,1/6,1/2)$. Their motions are determined by the deterministic parts of Eqs. (3, 4), with the velocity field (7). The left column shows cuts through the domains of attraction at $\phi =2$ within the upper right quarter of the unit cell; see Fig. 2. The respective attractors are depicted in the right panels with corresponding colors. Trajectories starting from white regions do not approach the indicated quarter. Note that the domain of attraction of the additional red attractor in the bottom row extends beyond the upper right quarter and consequently attracts trajectories starting outside of this quarter.

Figure 4

For a single chiral $(+)$ molecule with size $d=0.2$ the stationary probability density integrated over all orientations $\phi$ exhibits a pronounced asymmetry with respect to quarters of different parity. The friction coefficients are $({\gamma }_1,{\gamma }_2,{\gamma }_3)=(1/6,1/3,1/2)$ and the dimensionless noise strength is $D/L_0{V}_0={10}^{-3}$. With $x\to -x$ one obtains the density of a $(-)$ molecule.

Figure 5

The selectivity as given by the fraction of numbers of molecules with different chirality $N_{+}/N_{-}$ in the first quarter decreases with increasing noise strength $D/L_0{V}_0$. The time $\tau$ it needs to reach the stationary value increases with decreasing noise strength. For the parameters of the molecules see Fig. 3. The error bars indicate the standard deviation as it results from the numerical simulation.