Physical Chemistry Models for Chemical Research in the XXth and XXIst Centuries.

Thermodynamic hypotheses and models are the touchstone for chemical results, but the actual models based on time-invariance, which have performed efficiently in the development of chemistry, are nowadays invalid for the interpretation of the behavior of complex systems exhibiting nonlinear kinetics and with matter and energy exchange flows with the surroundings. Such fields of research will necessarily foment and drive the use of thermodynamic models based on the description of irreversibility at the macroscopic level, instead of the current models which are strongly anchored in microreversibility.

Chiral selectivity vs. noise in spontaneous mirror symmetry breaking.

Mirror symmetry breaking bifurcations, that occur in nonlinear chemical systems leading to final chiral states with very large enantiomeric excess, can be exploited as an efficient chiral signal selector for even the smallest chiral polarizations. This effect of the chiral polarization requires the system's capacity for overcoming thermal noise, which is manifested as fluctuating reaction rate constants. Therefore, we investigate the chiral selectivity across a range of tiny parity-violating energy differences (PVED) in the presence of inevitable non-equilibrium temperature fluctuations. We use a stochastic differential equation simulation methodology (Ito process) that serves as a valuable tool in open systems for identifying the thresholds at which the chiral force induces chiral selectivity in the presence of non-equilibrium temperature fluctuations. This approach enables us to include and analyze chiral selectivity in the presence of other types of fluctuations, such as perturbations in the rate of fluid flow into and out of the reactor and in the clamped input concentrations. These concepts may be of practical interest (i.e., spontaneous deracemizations) but are also useful for a better understanding of the general principles governing the emergence of biological homochirality.

Stoichiometric network analysis in reaction networks yielding spontaneous mirror symmetry breaking in a prebiotic atmosphere.

The generation of amino acid homochirality under prebiotic atmosphere conditions is a relevant issue in the study of the origin of life. This research is based on the production of amino acids via Strecker synthesis and how it is adjusted to the Kondepudi-Nelson autocatalytic model. The spontaneous mirror symmetry breaking (SMSB) of the new Kondepudi-Nelson-Strecker model, subject to two modifications (with Limited Enantioselective and Cross Inhibition), and also their combination were studied using the stoichiometric network analysis (SNA). In the calculations, the values obtained from the literature for alanine were considered. A total production of alanine of 7.56 × 109 mol year-1 was determined under prebiotic atmosphere conditions and starting from that value, the reaction rates for the models studied were estimated. Only the model with cross inhibition or achiral dimer formation is driven by stochastic fluctuations during SMSB. The stochastic fluctuation was estimated for a value of 2.619 × 10-15 mol L-1. This perturbation was sufficient to trigger SMSB. Finally, the results of SMSB were used to calculate the entropy production for the cross inhibition model.

The Coordinate Reaction Model: An Obstacle to Interpreting the Emergence of Chemical Complexity.

The way chemical transformations are described by models based on microscopic reversibility does not take into account the irreversibility of natural processes, and therefore, in complex chemical networks working in open systems, misunderstandings may arise about the origin and causes of the stability of non-equilibrium stationary states, and general constraints on evolution in systems that are far from equilibrium. In order to be correctly simulated and understood, the chemical behavior of complex systems requires time-dependent models, otherwise the irreversibility of natural phenomena is overlooked. Micro reversible models based on the reaction-coordinate model are time invariant and are therefore unable to explain the evolution of open dissipative systems. The important points necessary for improving the modeling and simulations of complex chemical systems are: a) understanding the physical potential related to the entropy production rate, which is in general an inexact differential of a state function, and b) the interpretation and application of the so-called general evolution criterion (GEC), which is the general thermodynamic constraint for the evolution of dissipative chemical systems.

Correction: Spontaneous mirror symmetry breaking: an entropy production survey of the racemate instability and the emergence of stable scalemic stationary states.

Correction for 'Spontaneous mirror symmetry breaking: an entropy production survey of the racemate instability and the emergence of stable scalemic stationary states' by Josep M. Ribó et al., Phys. Chem. Chem. Phys., 2020, 22, 14013-14025, DOI: 10.1039/D0CP02280B.

Entropic analysis of bistability and the general evolution criterion.

We present a detailed study of the entropy production, the entropy exchange and the entropy balance for the Schlögl model of chemical bi-stability for both the clamped and volumetric open-flow versions. The general evolution criterion (GEC) is validated for the transitions from the unstable to the stable non-equilibrium stationary states. The GEC is the sole theorem governing the temporal behavior of the entropy production in non-equilibrium thermodynamics, and we find no evidence for supporting a "principle" of maximum entropy production. We use stoichiometric network analysis (SNA) to calculate the distribution of the entropy production and the exchange entropy over the elementary flux modes of the clamped and open-flow models, and aim to reveal the underlying mechanisms of dissipation and entropy exchange.

Spontaneous Deracemizations.

Spontaneous deracemizations is a challenging, multidisciplinary subject in current chirality research. In the absence of any chiral inductors, an achiral substance or a racemic composition is driven into an enantioenriched or even homochiral state through a selective energy input, e.g., chemical potential, photoirradiation, mechanical grinding, ultrasound waves, thermal gradients, etc. The most prominent examples of such transformations are the Soai reaction and the Viedma deracemization. In this review, we track the most recent developments in this topic and recall that many other deracemizations have been reported for solutions from mesophases to conglomerate crystallizations. A compiled set of simply available achiral organic, inorganic, organometallic, and MOF compounds, yielding conglomerate crystals, should give the impetus to realize new experiments on spontaneous deracemizations. Taking into account thermodynamic constraints, modeling efforts have shown that structural features alone are not sufficient to describe spontaneous deracemizations. As a guideline of this review, particular attention is paid to the physicochemical origin and symmetry requirements of such processes.

Spontaneous mirror symmetry breaking: an entropy production survey of the racemate instability and the emergence of stable scalemic stationary states.

We study the emergence of both stable and unstable non-equilibrium stationary states (NESS), as well as spontaneous mirror symmetry breaking (SMSB) provoked by the destabilization of the racemic thermodynamic branch, for an enantioselective autocatalytic reaction network in an open flow system, and for a continuous range n of autocatalytic orders. The system possesses a range of double bi-stability and also tri-stability depending on the autocatalytic order. We carry out entropy production and entropy flow calculations, from simulations of ordinary differential equations, stoichiometric network analysis (SNA), and consider a stability analysis of the NESS. The simulations provide a correct description of the relationship between energy state functions, the isothermal dissipated heat, entropy production and entropy flow exchange with the surroundings, and the correct solution of the balance of the entropy currents at the NESS. The validity of the General Evolution Criterion (GEC) is in full agreement with all the dynamic simulations.

Spontaneous mirror-symmetry breaking coupled to top-bottom chirality transfer: from porphyrin self-assembly to scalemic Diels-Alder adducts.

This report shows how the net supramolecular chirality that emerged by spontaneous mirror-symmetry breaking (SMSB) at the mesoscale level can be transferred towards asymmetric solution chemistry. The J-aggregates obtained by self-assembly of an achiral porphyrin act as chiral counteranions in an iminium-promoted Diels-Alder reaction, leading to enantiomeric imbalances in the final adducts.

Diastereoisomerism, Stability, and Morphology of Substituted meso-4-Sulfonatophenylporphyrin J-Aggregates.

The comparison between nanoparticle morphologies of the J-aggregates of different meso-4-sulfonatophenylporphyrins showing non-sulfonato groups at some of the meso-positions constitutes an ultimate proof of the 2D crystal-like character of the basic self-assembly motif of this family of J-aggregates. Diastereoisomerism stemming from the tacticity of the relative configurations in relation to the J-aggregate bidimensional sheet is the key factor that determines both the striking monolayer in solution and also the hierarchical pathways leading to different nanoparticle morphologies upon further growth. The unexpected stability of such large monolayered sheets made up of porphyrin units is probably caused by the support originated at both surface faces by the double layer potentials of the peripheral ionic substituents. These double layer potentials play a driving role in the subsequent 3D growth of the monolayers, as deduced herein from the determining role of tacticity both in the stability of the J-aggregate sheet and in its evolution either to monolayered or to bilayered nanoparticles. The stabilizing role of the forces at the electrical double layer of the particle suggests a relationship between these forces and the previously reported detection of racemic biases when shear hydrodynamic forces are in action during the aggregation process.

Entropic Analysis of Mirror Symmetry Breaking in Chiral Hypercycles.

Replicators are fundamental to the origin of life and evolvability. Biology exhibits homochirality: only one of two enantiomers is used in proteins and nucleic acids. Thermodynamic studies of chemical replicators able to lead to homochirality shed valuable light on the origin of homochirality and life in conformity with the underlying mechanisms and constraints. In line with this framework, enantioselective hypercyclic replicators may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, which can be an obstacle for the emergence of evolutionary selection properties. We analyze the entropy production of a two-replicator system subject to homochiral cross-catalysis which can undergo SMSB in an open-flow reactor. The entropy exchange with the environment is provided by the input and output matter flows, and is essential for balancing the entropy production at the non-equilibrium stationary states. The partial entropy contributions, associated with the individual elementary flux modes, as defined by stoichiometric network analysis (SNA), describe how the system's internal currents evolve, maintaining the balance between entropy production and exchange, while minimizing the entropy production after the symmetry breaking transition. We validate the General Evolution Criterion, stating that the change in the chemical affinities proceeds in a way as to lower the value of the entropy production.

Stoichiometric network analysis of entropy production in chemical reactions.

We use stoichiometric network analysis (SNA) to obtain a flux-based approach for the evaluation and description of the entropy production and exchange for chemical reactions in open systems. For non-equilibrium stationary states (NESS) the production and exchange are expressed as functions over the convex cone of the stationary reaction rates, revealing the reaction pathways and elementary flux modes (EFM) responsible for both entropy production and balance. The analysis of the entropy production of EFMs leads to a unique description of the contribution of the coupling between linear or cyclic reaction network paths, and the fluxes due to the matter exchange of the system with the system's surroundings. Network stoichiometry leads to an independent proof and confirmation of Prigogine's theorem of minimum entropy production for the linear regime of non-equilibrium thermodynamics. Moreover, the non-linear thermodynamic regime allows us to test the validity of the General Evolution Criterion (GEC) for NESS in isothermal chemical networks in mechanical equilibrium.

Spontaneous mirror symmetry breaking and origin of biological homochirality.

Recent reports on both theoretical simulations and on the physical chemistry basis of spontaneous mirror symmetry breaking (SMSB), that is, asymmetric synthesis in the absence of any chiral polarizations other than those arising from the chiral recognition between enantiomers, strongly suggest that the same nonlinear dynamics acting during the crucial stages of abiotic chemical evolution leading to the formation and selection of instructed polymers and replicators, would have led to the homochirality of instructed polymers. We review, in the first instance, which reaction networks lead to the nonlinear kinetics necessary for SMSB, and the thermodynamic features of the systems where this potentiality may be realized. This could aid not only in the understanding of SMSB, but also the design of reliable scenarios in abiotic evolution where biological homochirality could have taken place. Furthermore, when the emergence of biological chirality is assumed to occur during the stages of chemical evolution leading to the selection of polymeric species, one may hypothesize on a tandem track of the decrease of symmetry order towards biological homochirality, and the transition from the simple chemistry of astrophysical scenarios to the complexity of systems chemistry yielding Darwinian evolution.

Stoichiometric network analysis of spontaneous mirror symmetry breaking in chemical reactions.

We apply stoichiometric network analysis (SNA) to study enantioselective chemical reaction schemes, subject to various thermodynamic architectures, which may lead to spontaneous mirror symmetry breaking (SMSB). Stoichiometric matrices are used to calculate extreme currents or fluxes: the vector basis for the convex polyhedral cone of all stationary reaction rates. A major emphasis is given to the constraints that the rate constants must obey and how to express these in terms of the convex parameters and stationary inverse concentrations. We evaluate the corresponding Jacobians in terms of the constrained convex parameters and the inverse stationary concentrations and carry out stability analyses for the steady-state racemic configurations. A geometric visualization of SMSB is proposed, based on the structures of the convex cones, the angles between currents, and the cone's subspaces that result from enforcing the pertinent thermodynamic and chiral constraints.

Spontaneous mirror symmetry breaking in heterocatalytically coupled enantioselective replicators.

Chiral hypercycle replicators (first-order autocatalysis together with mutual cross-catalysis) formed from achiral or racemizing resources may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, such as those of the Frank-like models, which are an obstacle for the emergence of evolutionary selection properties. The results indicate that the chemical models for the emergence of primordial autocatalytic self-reproducing systems, of and by themselves, can also explain naturally the emergence of biological homochirality.

Hydrodynamic Effects in Soft-matter Self-assembly: The Case of J-Aggregates of Amphiphilic Porphyrins.

Chiral J-aggregates of achiral amphiphilic porphyrins (4-sulfonatophenyl and aryl meso-substituted porphyrins) show several effects under the hydrodynamic forces of common stirring. These effects can be classified as pure mechanic (e. g. elasticity, plasticity and breaking of the self-assembly non-covalent bonding) and chemically selective as detected in the formation/growth of the nanoparticles. Diastereoselective, enantioselective and, depending on the sign of chiral shear forces, even enantiospecific selections have been described. Some types of these effects have been reported in other type of J-aggregates. Reversible and irreversible structural effects have been studied by atomic force imaging. The determination of the optical polarization properties (linear and circular) of their solutions is best done using Mueller matrix polarimetry methods.

Reversible and irreversible emergence of chiroptical signals in J-aggregates of achiral 4-sulfonatophenyl substituted porphyrins: intrinsic chirality vs. chiral ordering in the solution.

Mueller matrix polarimetry distinguishes the different origins of the reversible and irreversible chiroptical effects emerging in stirred solutions of J-aggregate nanoparticles: the reversible effect is due to an anisotropic ordering in the solution and the irreversible one is due to a bias from the racemic composition of intrinsically chiral structures.

Necessary conditions for the emergence of homochirality via autocatalytic self-replication.

We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the autocatalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reverse reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism.

Effect of Hydrodynamic Forces on meso-(4-Sulfonatophenyl)-Substituted Porphyrin J-Aggregate Nanoparticles: Elasticity, Plasticity and Breaking.

The J aggregates of 4-sulfonatophenyl meso-substituted porphyrins are non-covalent polymers obtained by self-assembly that form nanoparticles of different morphologies. In the case of high aspect-ratio nanoparticles (bilayered ribbons and monolayered nanotubes), shear hydrodynamic forces may modify their shape and size, as observed by peak force microscopy, transmission electron microscopy of frozen solutions, small-angle X-ray scattering measurements in a disk-plate rotational cell, and cone-plate rotational viscometry. These nanoparticles either show elastic or plastic behaviour: there is plasticity in the ribbons obtained upon nanotube collapse on solid/air interfaces and in viscous concentrated nanotube solutions, whereas elasticity occurs in the case of dilute nanotube solutions. Sonication and strong shear hydrodynamic forces lead to the breaking of the monolayered nanotubes into small particles, which then associate into large colloidal particles.