Viedma deracemization converts a racemic suspension of conglomerate-forming crystals into a single enantiomer by combining mechanical attrition (grinding) with racemization in the surrounding solution, and is a canonical experimental realization of spontaneous mirror symmetry breaking (SMSB). A thermodynamically consistent kinetic model of the process (Blanco et al., ChemPhysChem 2013) reproduces its qualitative features but leaves its quantitative core undetermined: the numerical ranges of physical parameters — interfacial free energies, capillary lengths, size-dependent solubility functions, cluster-to-cluster versus monomer-to-cluster rate constants, and attrition kernels — that place a real, experimentally studied compound inside or outside the SMSB domain are unknown; the effect of realistic geometry- and size-dependent aggregation rules on the domain boundaries is unquantified; and no direct quantitative comparison to time-resolved experimental data has been performed. Later work has fitted effective parameters of population-balance or microreversible-network models to enantiomeric-excess trajectories, derived an exact deracemization condition for the temperature-cycling class, and extended the theory to crystal-size distributions and to polymerization analogues, but the mapping from independently measured material properties to the SMSB domain and full multi-observable time-resolved validation remain open. The problem is to make the SMSB model of Viedma deracemization quantitative and predictive for specific compounds, and to give the proposed polymerization SMSB network a quantitative theoretical realization.

Background

Many chiral molecules crystallize as conglomerates: each crystal contains only one enantiomer (one of the two mirror-image molecular forms), so a racemic batch consists of a physical mixture of left- and right-handed crystals. The enantiomeric excess, ee, measures the composition imbalance, (NL−NR)/(NL+NR)(N_L-N_R)/(N_L+N_R). In 2005 Viedma showed that vigorously grinding such a racemic suspension in a saturated solution — with a fast racemization reaction in solution that interconverts the two molecular enantiomers — drives the solid phase to a single hand (100% ee), a process now called Viedma deracemization or Viedma ripening. Attrition continually fragments crystals into small pieces; smaller crystals are more soluble (the Gibbs–Thomson effect, i.e., size-dependent solubility controlled by the crystal–solution interfacial free energy and a capillary length), so material dissolves from fragments and regrows on larger crystals; solution racemization recycles the unwanted enantiomer. A key theoretical question is whether the observed amplification is genuine spontaneous mirror symmetry breaking (SMSB): a bifurcation in which a stationary state with a large ee is intrinsically more stable than the racemic one, rather than a merely kinetic, transient outcome.

Blanco, Crusats, El-Hachemi, Moyano, Veintemillas-Verdaguer, Hochberg and Ribó (ChemPhysChem 2013) built the most detailed thermodynamically consistent kinetic model of this process. They translated the free-energy landscape of classical primary nucleation theory — in which clusters below a critical size are unstable and shrink while larger ones grow — into a chemical kinetics network of monomer–cluster and cluster–cluster steps. The defining feature is microreversibility: every forward step has a backward step whose rate constant is fixed by detailed balance, so the network cannot violate thermodynamics and produce artificial in-silico symmetry breaking. Two motifs emerge: enantioselective (homochiral) cluster-to-cluster aggregation acts as the autocatalytic stage, and the back-flow of chiral clusters toward small, effectively achiral clusters acts as mutual inhibition. Cluster-size dependence was treated with piecewise isodesmic approximations (isodesmic meaning each aggregation step of a given range is assigned the same equilibrium constant), and attrition enters as an irreversible fragmentation step with a chosen kernel, i.e., a rule for the rate and fragment-size distribution of breakage events.

That model reproduces the qualitative features of deracemization under both mechanical attrition and imposed temperature gradients, but — as its authors state — it does not determine the actual numerical parameter ranges. The unknowns are physical: interfacial free energies (surface tensions) and capillary lengths that set size-dependent solubilities via the functions sis_i for clusters of size ii; the absolute magnitudes of cluster-to-cluster versus monomer-to-cluster rate constants; and realistic attrition kernels. In parallel, a complementary modeling tradition uses population balance equations (PBMs), which evolve the crystal-size distributions of both enantiomers under growth, dissolution, agglomeration, breakage, and solution racemization (Iggland and Mazzotti 2011; Bodák, Maggioni and Mazzotti 2018; Vetter 2020). These models deracemize in simulation but contain many parameters — agglomeration, breakage, and ripening rate expressions — that are difficult to measure or uniquely estimate, so their fit constants do not constitute a mapping from measured material properties to behavior.

Later work has advanced pieces of the problem. A successor microreversible network by Noble-Terán, Cruz, Cruz-Rosas, Buhse and Micheau (2023) was parametrized on a real sodium chlorate deracemization experiment and found a window of grinding intensities (with lower and upper limits and a minimum deracemization time) inside which SMSB occurs; a minimalist kinetic model by Micheau, Buhse, Cintas, Ortiz, Ribó and Viedma (2026) was parametrized on the ee amplification of an aspartic acid deracemization; and Deck, Hosseinalipour and Mazzotti (2024) proved, within a reduced population-balance model of temperature-cycle deracemization validated by experiment, an exact and general condition (crystal dissolution faster than crystal growth) — while explicitly acknowledging that the rate expressions of full mechanistic models remain inaccessible to measurement and theory. Uwaha and Katsuno have analyzed crystal-size distributions and chirality conversion with Becker–Döring-type models (stepwise cluster attachment/detachment kinetics). In all of this, however, the parameters fitted to enantiomeric-excess trajectories are effective constants, not values derived from independently measured surface tensions, solubilities, and attrition kernels; no multi-observable, time-resolved quantitative validation exists; and the 2013 paper's proposed extension of the same network motif to enantioselective polymerization (template-cooperative growth of homochiral chains with externally driven depolymerization as the recycling step) remains a theoretical construction.

Problem Statement

Derived from the stated open questions of the 2013 microreversible SMSB model of Viedma deracemization (Blanco et al., ChemPhysChem 2013), the problem is to make that model quantitative, physically parameterized, and experimentally validated. Its common objective is a predictive theory that states, before the experiment, whether a given racemizable conglomerate-forming compound under specified grinding and racemization conditions will undergo spontaneous mirror symmetry breaking, at what rate, and through which measurable time-resolved signatures, together with the corresponding quantitative theoretical realization of the polymerization analogue. All four items enumerated below are required for completion; resolving only a subset of them does not complete the task. Concretely, for a thermodynamically consistent (microreversible) kinetic network of Viedma deracemization:

  1. Parameter mapping: determine, for specific experimentally studied compounds, the numerical ranges of the physical parameters — crystal–solution interfacial free energies (surface tensions) and capillary lengths, the size-dependent solubility functions sis_i for clusters of size ii, the absolute magnitudes of cluster-to-cluster versus monomer-to-cluster rate constants, and realistic attrition (fragmentation) kernels — as obtained from measurements or calculations independent of the deracemization experiments used for validation, rather than effective constants fitted to deracemization trajectories, and thereby locate those compounds inside or outside the SMSB parameter domain.
  2. Domain-boundary robustness: quantify how the boundaries of the SMSB domain shift when the simplifications of the original model — piecewise isodesmic cluster-size dependence and isodesmic cluster-to-cluster aggregation — are replaced by detailed geometry- and size-dependent aggregation rules, within the source's conglomerate setting (enantiopure crystals as the more stable solid phase).
  3. Time-resolved validation: demonstrate quantitative agreement between model predictions and time-resolved experimental data under mechanical attrition (and, where applicable, temperature gradients), encompassing measured crystal/cluster-size distributions, time-dependent solution- and solid-phase enantiomeric excess, and attrition-rate measurements, for the same compound and conditions as the parameterization.
  4. Polymerization analogue (a theoretical extension discussed by the source): give the proposed polymerization SMSB network — enantioselective template-cooperative growth of homochiral chains, externally driven depolymerization as the recycling step, and monomer racemization — a quantitative theoretical (in-silico) realization for a specific covalent polymer system (cooperativity parameters, depolymerization stoichiometry and kinetics, racemization rates).

References

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