2D Ising Model for Enantiomer Adsorption on Achiral Surfaces: L- and D-Aspartic Acid on Cu(111)

Abstract

The 2D Ising model is well-formulated to address problems in adsorption thermodynamics. It is particularly well-suited to describing the adsorption isotherms predicting the surface enantiomeric excess, ees, observed during competitive co-adsorption of enantiomers onto achiral surfaces. Herein, we make the direct one-to-one correspondence between the 2D Ising model Hamiltonian and the Hamiltonian used to describe competitive enantiomer adsorption on achiral surfaces. We then demonstrate that adsorption from racemic mixtures of enantiomers and adsorption of prochiral molecules are directly analogous to the Ising model with no applied magnetic field, i.e., the enantiomeric excess on chiral surfaces can be predicted using Onsager’s solution to the 2D Ising model. The implication is that enantiomeric purity on the surface can be achieved during equilibrium exposure of prochiral compounds or racemic mixtures of enantiomers to achiral surfaces.

Molecular Origins of Chiral Amplification on an Achiral Surface: 2D Monolayers of Aspartic Acid on Cu(111)

“…This autoamplification of ee s can result from enantiospecific interactions between adsorbed Asp enantiomers, in particular, attractive homochiral interactions . Recently, we have demonstrated that this behavior is well-described by the 2D Ising model. , …”

“…The example that serves as the focus of this work is the equilibrium coadsorption of d - and l -aspartic acid (Asp, HO 2 CCH(NH 2 )CH 2 CO 2 H) on the Cu(111) surface. 26 − 28 Figure 1 plots the equilibrium adsorption isotherms for three systems exhibiting different behaviors: d -/ l -alanine on Cu(3,1,17) R&S , 29 d -/ l -Asp on Cu(3,1,17) R&S , 30 and d -/ l -Asp on Cu(111). 27 Note that, in our notation, d -/ l - refers to enantiomer mixtures of arbitrary composition, distinct from dl - that commonly refers to a racemic mixture.…”

“… 29 Recently, we have demonstrated that this behavior is well-described by the 2D Ising model. 26 , 28 …”

Homochirality and chiral-induced spin selectivity: A new spin on the origin of life

“…It is important to appreciate that the enantioselectivity arising from the spin-polarized electrons need not be 100%, as experiments have shown that nonlinear amplification schemes can lead to homochirality from a relatively small chiral bias, or enantiomeric excess. The time evolution of a small initial excess of one molecular handedness toward a much larger excess is thought to be possible through autocatalytic processes ( 18 , 19 ), as well as other nonlinear processes ( 1 , 20 ). Along similar lines, CISS-based processes could reinforce and propagate the benefit of homochirality in biology; CISS has been shown to manifest in biomolecules and biochemical mechanisms; see Fig.…”

Ising Model: Recent Developments and Exotic Applications

“…Up and down spins in the Ising models can be also interpreted as left and right enantiomers of chiral molecules. Using such an analogy, Dutta and Gellman developed adsorption thermodynamics of chiral molecules [ 13 ]. They argue that adsorption from racemic mixtures of enantiomers is directly analogous to the Ising model’s behaviour.…”