Spontaneous Mirror Symmetry Breaking Research Articles

Spontaneous chiral symmetry breaking in polar fluid–heliconical ferroelectric nematic phase

Spontaneous mirror symmetry breaking by formation of chiral structures from achiral building blocks and emergent polar order are phenomena rarely observed in fluids. Separately, they have both been found in certain nematic liquid crystalline phases; however, they have never been observed simultaneously. Here, we report a heliconical arrangement of achiral molecules in the ferroelectric nematic phase. The phase is thus spontaneously both polar and chiral. Notably, the pitch of the heliconical structure is comparable to the wavelength of visible light, giving selective reflection controllable by temperature or application of a weak electric field. Despite bearing resemblance to the heliconical twist-bend nematic phase, this chiral ferroelectric nematic phase arises from electrical interactions that induce a noncollinear orientation of electric dipoles.

The Formation of Supramolecular Chiral Materials from Achiral Molecules Using a Liquid-Crystallin System: Symmetry Breaking, Amplification, and Transfer

Recently, the formation of chiral materials by the self-organization of achiral small molecules has attracted much attention. How can we obtain chirality without a chiral source? Interesting approaches, such as mechanical rotation, circularly polarized light, and asymmetric reaction fields, have been used. We describe recent research developments in supramolecular chirality in liquid crystals, focusing primarily on our group’s experimental results. We present the following concepts in this review. Spontaneous mirror symmetry breaking in self-assembled achiral trimers induces supramolecular chirality in the soft crystalline phase. Two kinds of domains with opposite handedness exist in non-equal populations. The dominant domain is amplified to produce a homochiral state. Chirality is transferred to a polymer film during the polymerization of achiral monomers by using the homochiral state as a template. Finally, we discuss how the concepts obtained from this liquid crystal research relate to the origin of homochirality in life.

Flow-induced periodic chiral structures in an achiral nematic liquid crystal

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.

Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Homochirality, the phenomenon by which one of two virtually identical (non-superimposable mirror images) compounds is favored over the other in the chemistry of life, has been regarded as a requisite for the emergence of all living things on earth. Spontaneous mirror symmetry breaking has been proposed to produce the imbalance. Under this framework, Frank presented, in his foundational article “On spontaneous asymmetric synthesis”, a simple chemical reaction network that displays spontaneous symmetry breaking for a specific set of reaction rates. Research has since focused on finding more complex and plausible models, each one with its advantages and disadvantages. Nevertheless, finding reaction rate values that make a model exhibit spontaneous symmetry breaking is a complex task, even for specially crafted models. LInear STability ANALysis of CHEmical Mechanism, Listanalchem, is a method and software for the search for appropriate reaction rates. It includes four different algorithms inspired by the analysis of Frank's network. Two classical algorithms are also included in Listanalchem: the Trace-Determinant plane and the Stoichiometric Network Analysis by Bruce Clarke. Listanalchem reads a chemical reaction network from plain text and runs one or more of the available algorithms according to the user selection. Listanalchem is tested and verified by studying classical, modified, and recent models proposed to explain the origin of biological homochirality.•Listanalchem allows a fast and reliable search for instability behavior in chemical mechanisms that pretend to explain spontaneous mirror symmetry breaking.•Listanalchem contains several model examples, including the most cited in the related literature.•Listanalchem is a tool that tests models that pretend to explain the origin of biological homochirality, helps find errors, and aids in designing new models.

A Complex Reaction Network Model for Spontaneous Mirror Symmetry Breaking in Viedma Deracemizations.

Attrition-enhanced chiral symmetry breaking in crystals, known as Viedma deracemization, is a promising method for converting racemic solid phases into enantiomerically pure ones under non equilibrium conditions. However, many aspects of this process remain unclear. In this study, we present a new investigation into Viedma deracemization using a comprehensive kinetic rate equation continuous model based on classical primary nucleation theory, crystal growth, and Ostwald ripening. Our approach employs a fully micro-reversible kinetic scheme with a size-dependent solubility following the Gibbs-Thomson rule. To validate our model, we use data from a real NaClO3deracemization experiment. After parametrization, the model shows spontaneous mirror symmetry breaking (SMSB) under grinding. Additionally, we identify a bifurcation scenario with a lower and upper limit of the grinding intensity that leads to deracemization, including a minimum deracemization time within this window. Furthermore, this model uncovers that SMSB is caused by multiple instances of concealed high-order autocatalysis. Our findings provide new insights into attrition-enhanced deracemization and its potential applications in chiral molecule synthesis and understanding biological homochirality.

Many-Body Superradiance and Dynamical Mirror Symmetry Breaking in Waveguide QED.

The many-body decay of extended collections of two-level systems remains an open problem. Here, we investigate whether an array of emitters coupled to a one-dimensional bath undergoes Dicke superradiance. This is a process whereby a completely inverted system becomes correlated via dissipation, leading to the release of all the energy in the form of a rapid photon burst. We derive the minimal conditions for the burst to happen as a function of the number of emitters, the chirality of the waveguide, and the single-emitter optical depth, both for ordered and disordered ensembles. Many-body superradiance occurs because the initial fluctuation that triggers the emission is amplified throughout the decay process. In one-dimensional baths, this avalanchelike behavior leads to a spontaneous mirror symmetry breaking, with large shot-to-shot fluctuations in the number of photons emitted to the left and right. Superradiant bursts may thus be a smoking gun for the generation of correlated photon states of exotic quantum statistics.

Conditions for the origin of homochirality in primordial catalytic reaction networks

We study the generation of homochirality in a general chemical model (based on the homogeneous, fully connected Smoluchowski aggregation-fragmentation model) that obeys thermodynamics and can be easily mapped onto known origin of life models (e.g. autocatalytic sets, hypercycles, etc.), with essential aspects of origin of life modeling taken into consideration. Using a combination of theoretical modeling and numerical simulations, we look for minimal conditions for which our general chemical model exhibits spontaneous mirror symmetry breaking. We show that our model spontaneously breaks mirror symmetry in various catalytic configurations that only involve a small number of catalyzed reactions and nothing else. Of particular importance is that mirror symmetry breaking occurs in our model without the need for single-step autocatalytis or mutual inhibition, which may be of relevance for prebiotic chemistry.

Spontaneous mirror symmetry breaking and chiral segregation in the achiral ferronematic compound DIO.

An achiral compound, DIO, known to exhibit three nematic phases namely N, NX and NF, is studied by polarizing microscopy and electro-optics for different surface conditions in confinement. The high temperature N phase assigned initially as a conventional nematic phase, shows two additional unusual features: the optical activity and the linear electro-optic response related to the polar nature of this phase. An appearance of chiral domains is explained by the spontaneous symmetry breaking arising from the saddle-splay elasticity and followed by the formation of helical domains of the opposite chirality. This is the first example of helical segregation observed in calamitic non-chiral molecules in the nematic phase. As reported previously, the ferronematic NF shows strong polar azimuthal surface interaction energy which stabilizes a homogeneous structure in planar aligned LC cells rubbed parallel and exhibits a twisted structure in cells with antiparallel buffing. The transmission spectra are simulated using Berreman's 4 × 4 matrix method. The observed agreement between the experimental and the simulated spectra quantitatively confirms the presence of twisted structures in antiparallel rubbed cells.

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.

Spontaneous emergence of enantioenriched chiral aldol reaction products from Achiral precursors in solution and origin of biological homochirality of sugars: a first-principles study.

Experimental reports about observation of spontaneous mirror symmetry breaking and chiral amplification in stereoselective Mannich and aldol reactions, run under fully achiral initial conditions, have drawn a lot of attention, fuelled partly by the role these reactions could have played in chemical evolution as a cause for still puzzling observed homochirality of biomolecules, often considered a prerequisite for the origin of life. We have now revisited this still unresolved problem, using DFT computation of all combinatorially possible transition states and numerical solution of complete set of resulting coupled kinetic rate equations to model the aldol reaction rigorously "from the first principles" and without making any a priori assumptions. Spontaneous mirror symmetry breaking in this autocatalytic, reversible, closed and homogenous system is explained by a supercritical pitchfork bifurcation, occurring in concentrations of enantiomers due to time-delayed kinetic instability of racemic composition of reaction mixture, when reactants are initially provided in non-stoichiometric quantities. Same process, taking place under similar conditions in primordial "soup" of chemicals, might conceivably explain origin of biological homochirality of sugar molecules on early earth billions of years ago. Our results suggest that seemingly innocuous chemical reactions could exhibit unexpected and counter-intuitive emergent behaviour, when initial conditions are appropriately chosen. Chiral amplification in self-catalyzed aldol reaction occurs during approach of thermodynamic equilibrium in accord with principle of microscopic reversibility and second law of thermodynamics.

Resilience of parity-violation-induced chiral selectivity to nonequilibrium temperature fluctuations in open systems

We consider the sensitivity of chemical reactions, able to undergo spontaneous mirror symmetry breaking, to chiral bias in the presence of nonequilibrium temperature fluctuations and derive a selectivity criterion. For this, we estimate the magnitude of fluctuations $\ensuremath{\delta}k$ in chemical reaction rate constants $k$ arising from the nonequilibrium temperature fluctuations $\ensuremath{\delta}T$ about a mean value $T$. To leading order, the relative rate constant fluctuations $\ensuremath{\delta}{k}_{i}/{k}_{i}$ for each reaction $i$ are given by the product of the activation enthalpy $\mathrm{\ensuremath{\Delta}}{H}_{i}^{\ifmmode\ddagger\else\textdaggerdbl\fi{}}/RT$ for the $i\mathrm{th}$ reaction multiplied by the relative rms temperature fluctuations $\ensuremath{\delta}{T}_{\mathrm{rms}}/T$. The latter are determined by the system's specific heat at constant volume: ${C}_{V}$. We test this criterion with simulations carried out for an open-flow fully reversible Frank model, and for a range of parity-violating energy differences (PVED) within the theoretically estimated upper and lower bounds. Depending on the relative magnitudes of the deterministic PVED bias and the temperature fluctuations, the PVED bias can either (i) select the final stable chiral outcome deterministically or (ii) select one of two possible stable chiral outcomes with an asymmetric statistical weighting. For larger temperature fluctuations, the PVED bias loses its selectivity, and the final stable chiral outcomes are stochastic and equally probable. This paper points towards the possible design of small volume chemical flow reactors capable of detecting the elusive PVED bias in bulk systems, provided other sources of fluctuations can be sufficiently controlled and attenuated.

Biological homochirality and stoichiometric network analysis: Variations on Frank’s model

Biological homochirality is modelled using chemical reaction mechanisms that include autocatalytic and inhibition reactions as well as input and output flows. From the mathematical point of view, the differential equations associated with those mechanisms have to exhibit bistability. The search for those bifurcations can be carried out using stoichiometric network analysis. This algorithm simplifies the mathematical analysis and can be implemented in a computer programme, which can help us to analyse chemical networks. However, regardless of the reduction to linear polynomials, which is made possible by this algorithm, in some cases, the complexity and length of the polynomials involved make the analysis unfeasible. This problem has been partially solved by extending the stoichiometric matrix with rows that code the duality relations between the different reactions occurring in the network given as input. All these facts allow us to analyse 28 different network models, highlighting the basic requirements needed by a chemical mechanism to have spontaneous mirror symmetry breaking.

Spontaneous Emergence of Transient Chirality in Closed, Reversible Frank-like Deterministic Models.

To explore abiotic theories related to the origin of biomolecular homochirality, we analyze two entirely reversible kinetic models composed of an enantioselective autocatalysis with limited stereoselectivity that is coupled to an enantiomeric mutual inhibition (Frank-like models). The two models differ in their autocatalytic steps in respect to the formation of monomer species in one model and of dimer species in the other. While fully reversible and running in a closed system, spontaneous mirror symmetry breaking (SMSB) gives rise to transient chiral excursions, even when starting from a strictly achiral situation. Before the SMSB, the two models differ in the main dissipative processes. At the SMSB, the entropy production rate reaches its maximum in both models. Here it is the enantioselective autocatalysis with retention of the winner enantiomer that dominates. During the terminal phase, the enantioselective autocatalysis with inversion prevails, while the entropy production rate vanishes, thus fulfilling the conditions of microscopic reversibility. SMSB does not occur if the autocatalytic rate constant is too strong or too weak. However, when the autocatalysis is relatively weak, the temporary chiral excursions last for long periods of time and could be the starting point of a cascade of asymmetric reactions. The realism of such Frank-like models is discussed from the viewpoint of their relevance to prebiotic chemistry.

Spontaneous Symmetry Breaking in a Coherently Driven Nanophotonic Bose-Hubbard Dimer.

We report on the first experimental observation of spontaneous mirror symmetry breaking (SSB) in coherently driven-dissipative coupled optical cavities. SSB is observed as the breaking of the spatial or mirror Z_{2} symmetry between two symmetrically pumped and evanescently coupled photonic crystal nanocavities, and manifests itself as random intensity localization in one of the two cavities. We show that, in a system featuring repulsive boson interactions (U>0), the observation of a pure pitchfork bifurcation requires negative photon hopping energies (J<0), which we have realized in our photonic crystal molecule. SSB is observed over a wide range of the two-dimensional parameter space of driving intensity and detuning, where we also find a region that exhibits bistable symmetric behavior. Our results pave the way for the experimental study of limit cycles and deterministic chaos arising from SSB, as well as the study of nonclassical photon correlations close to SSB transitions.

Circular Dichroism of Emergent Chiral Stacking Orders in Quasi-One-Dimensional Charge Density Waves.

Chirality-driven optical properties in charge density waves are of fundamental and practical importance. Here, we investigate the interaction between circularly polarized light and emergent chiral stacking orders in quasi-one-dimensional (quasi-1D) charge-density waves (CDWs) with density-functional theory calculations. In our specific system, self-assembled In nanowires on a Si(111) surface, spontaneous mirror symmetry breaking leads to four symmetrically distinct degenerate quasi-1D CDW structures, which exhibit geometrical chirality. Such geometrical chirality may naturally induce optically active phenomena even when the quasi-1D CDW structures are stacked perpendicular to the CDW chain direction. Indeed, we find that left- and right-chiral stacking orders show distinct circular dichroism responses while a nonchiral stacking order has no circular dichroism. Such optical responses are attributed to the existence of glide mirror symmetry of the CDW stacking orders. Our findings suggest that the CDW chiral stacking orders can lead to diverse active optical phenomena such as chirality-dependent circular dichroism, which can be observed in scanning tunneling luminescence measurements with circularly polarized light.

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.

Spontaneous mirror symmetry breaking in reaction-diffusion systems: ambivalent role of the achiral precursor.

The behaviour of a Frank-like chemical network model featuring autocatalytic production of chiral enantiomers from achiral reactants is studied numerically in 1D and 2D systems using fluctuating initial conditions and accounting for diffusion processes. Our results reveal that the achiral substrate concentration can play an ambivalent role. It is shown that when the achiral reactant concentration is maintained constant and homogeneous in 1D systems, global homochirality is not systematically reached when the size of the system or the achiral reactant concentration are increased. However, with a fixed concentration gradient, coexisting homochiral domains of opposite handedness are no longer observed and homogeneous homochirality, i.e. the presence of a single stable homochiral domain, is recovered. In 2D systems, reaching global homochirality is just a matter of time. This time is dramatically increased when insufficient or excessive amount of achiral reactant is used. An optimal amount of achiral material is observed to maximise the enantiomer production rates.

Поляритонный резонанс в автомодуляции асимметричного состояния сверхизлучающего лазера

Based on the numerical solution to the semiclassical Maxwell-Bloch equations in a one-dimensional model of a superradiant laser with a low-Q symmetric Fabry-Perot cavity, a comparative analysis of the spectrum of polariton modes of the linearized problem and the discrete spectrum of the of quasi-monochromatic generation with weak self-modulation under the condition of strong spontaneous mirror symmetry breaking of the counterpropagating electromagnetic waves, population inversion and polarization of an active medium is carried out. It is shown that the main frequencies of resonant self-modulation of a steady asymmetric superradiant phase state are close to the frequencies of polariton modes that are calculated in the linearized problem for the average level of the population inversion taken from the nonlinear problem and have small decay rates.

Racemized photonic crystals for physical unclonable function.

As Internet of Things-based technologies continue to digitalize our society, the development of secure and robust identification systems against evolving adversaries remains a grave challenge. Recently, physical unclonable functions (PUFs) have garnered tremendous scientific interest due to their intrinsic randomness, which makes them difficult to counterfeit. Herein, we present a facile approach for fabricating optical PUFs using spontaneous mirror symmetry breaking of molecular self-assembly. The PUF composed of racemic helical structures that generate chiroptical signals exhibits high encoding capacity (∼1013 000), precise recognition rate, and impressive reconfigurability. The present study demonstrates that the utilization of random symmetry breaking is a promising approach to the design of high-level security systems.

Absolute Asymmetric Catalysis, from Concept to Experiment: A Narrative

AbstractThe generally accepted hypothesis to explain the origin of biological homochirality (that is to say, the fact that proteinogenic amino acids are left-handed, and carbohydrates right-handed, in all living beings) is to assume, in the course of prebiotic chemical evolution, the appearance of an initial enantiomeric excess in a set of chiral molecular entities by spontaneous mirror-symmetry breaking (SMSB), together with suitable amplification and replication mechanisms that overcome the thermodynamic drive to racemization. However, the achievement of SMSB in chemical reactions taking place in solution requires highly specific reaction networks showing nonlinear dynamics based on enantioselective autocatalysis, and examples of its experimental realization are very rare. On the other hand, emergence of net supramolecular chirality by SMSB in the self-assembly of achiral molecules has been seen to occur in several instances, and the chirality sign of the resulting supramolecular system can be controlled by the action of macroscopic chiral forces. These considerations led us to propose a new mechanism for the generation of net chirality in molecular systems, in which the SMSB takes place in the formation of chiral supramolecular dissipative structures from achiral monomers, leading to asymmetric imbalances in their composition that are subsequently transferred to a standard enantioselective catalytic reaction, dodging in this way the highly limiting requirement of finding suitable reactions in solution that show enantio­selective autocatalysis. We propose the name ‘absolute asymmetric catalysis’ for this approach, in which an achiral monomer is converted into a nonracemic chiral aggregate that is generated with SMSB and that is catalytically active.Our aim in this Account is to present a step-by-step narrative of the conceptual and experimental development of this hitherto unregarded, but prebiotically plausible, mechanism for the emergence of net chirality in molecular reactions.1 Introduction: The Origin of Biological Homochirality and Spontaneous Mirror-Symmetry Breaking2 Experimental Chemical Models for Spontaneous Mirror-Symmetry Breaking: The Soai Reaction and Beyond3 Spontaneous Mirror-Symmetry Breaking in Supramolecular Chemistry: Plenty of Room at the Top4 Absolute Asymmetric Catalysis: An Alternative Mechanism for the Emergence of Net Chirality in Molecular Systems 5 Experimental Realization of Top-Down Chirality Transfer to the Molecular Level6 Conclusions and Outlook