Entropic Barrier Research Articles

Unraveling two distinct polymorph transition mechanisms in one n-type single crystal for dynamic electronics

Cooperativity is used by living systems to circumvent energetic and entropic barriers to yield highly efficient molecular processes. Cooperative structural transitions involve the concerted displacement of molecules in a crystalline material, as opposed to typical molecule-by-molecule nucleation and growth mechanisms which often break single crystallinity. Cooperative transitions have acquired much attention for low transition barriers, ultrafast kinetics, and structural reversibility. However, cooperative transitions are rare in molecular crystals and their origin is poorly understood. Crystals of 2-dimensional quinoidal terthiophene (2DQTT-o-B), a high-performance n-type organic semiconductor, demonstrate two distinct thermally activated phase transitions following these mechanisms. Here we show reorientation of the alkyl side chains triggers cooperative behavior, tilting the molecules like dominos. Whereas, nucleation and growth transition is coincident with increasing alkyl chain disorder and driven by forming a biradical state. We establish alkyl chain engineering as integral to rationally controlling these polymorphic behaviors for novel electronic applications.

Macrocyclization Strategies Towards the Synthesis of Amphidinolide Natural Products

Abstractdinoflagellates amphidinolide group of natural products have drawn the attention of the synthetic community owing to their natural scarcity, variation in ring size (12‐ to 27‐membered), and architectural complexity. The manifold strategies for creating the unique macrocyclic framework of amphidinolides, overcoming the entropy barrier of cyclisation, in good yields and selectivity, are highly encouraging as this platform provides an opportunity to develop compounds for structure‐activity relationship studies. This review emphasizes various methods of intramolecular C−C and C−O bond‐forming reactions for constructing the macrocyclic structure of different naturally occurring molecules of amphidinolide family.

Path sampling with memory reduction and replica exchange to reach long permeation timescales

Assessing kinetics in biological processes with molecular dynamics simulations remains a computational and conceptual challenge, given the large time and length scales involved. For kinetic transport of biochemical compounds or drug molecules, the permeability through the phospholipid membranes is a key kinetic property, but long timescales are hindering the accurate computation. Technological advances in high-performance computing therefore need to be accompanied by theoretical and methodological developments. In this contribution, the replica exchange transition interface sampling (RETIS) methodology is shown to give perspective toward observing longer permeation pathways. It is first reviewed how RETIS, a path-sampling methodology that gives in principle exact kinetics, can be used to compute membrane permeability. Next, recent and current developments in three RETIS aspects are discussed: several new Monte Carlo moves in the path-sampling algorithm, memory reduction by reducing pathlengths, and exploitation of parallel computing with CPU-imbalanced replicas. Finally, the memory reduction presenting a new replica exchange implementation, coined REPPTIS, is showcased with a permeant needing to pass a membrane with two permeation channels, either representing an entropic or energetic barrier. The REPPTIS results showed clearly that inclusion of some memory and enhancing ergodic sampling via replica exchange moves are both necessary to obtain correct permeability estimates. In an additional example, ibuprofen permeation through a dipalmitoylphosphatidylcholine membrane was modeled. REPPTIS succeeded in estimating the permeability of this amphiphilic drug molecule with metastable states along the permeation pathway. In conclusion, the presented methodological advances allow for deeper insight into membrane biophysics even if the pathways are slow, as RETIS and REPPTIS push the permeability calculations to longer timescales.

Dynamics and thermodynamics of bimolecular reactions at heterogeneous biological interfaces.

The behaviors of biomolecules at heterogeneous biological aqueous-nonaqueous interfaces markedly differ from those in bulk water. We found that various biomolecular reactions, including protein unfolding, protein-ligan binding, chlorophyll demetallation, redox reactions, and crystallization, are accelerated by a factor of 103 or higher at the interface of micron-sized water droplets (microdroplets) (PNAS, 2015; QRevPhys, 2015 and 2017). The FRET analysis revealed that molecules are highly localized at the nanoscale regime near the water surface, which is in part responsible for the observed accelerated dynamics (JPCB, 2020). Besides, the thermodynamics of biomolecular reactions are also altered near the water surface. We found that molecules are in highly ordered states near the aqueous-nonaqueous interface (Sci Adv, 2020, Sci Rep, 2020). This minimized entropy lowers entropic barriers so that thermodynamically unfavorable reactions such as phosphorylation and RNA formation can proceed without any enzyme or ATP energy source at room temperature (PNAS 2017, 2018). Moreover, the charge exchange between water molecules and biomolecules spontaneously occurs at the water interface, leading to the oxidation of water molecules and the reduction of biomolecules in the Krebs cycle (JACS, 2019; Nat Commun, 2018; PNAS, 2018, 2019; Chem Sci, 2019). Vibrational Stark spectroscopy coupled with stimulated Raman excited fluorescence microscopy showed the presence of a strong intrinsic interfacial electric field formed at the surface of the microdroplet (JPCL, 2020). This strong electric field, combined with the partial desolvation effect, can be responsible for the unusual behaviors of biomolecules at the aqueous-nonaqueous interface (Annu Rev Phys Chem, 2020). These findings suggest that the dynamics and thermodynamics of biomolecular reactions occurring in cells with various aqueous-nonaqueous interfaces and compartments may significantly differ from those in bulk water.

Mechanistic insights into the crystallization of coamorphous drug systems.

In our previous study, the coamorphous formulation of lurasidone hydrochloride (LH) with saccharin (SAC) showed significantly enhanced dissolution and physical stability compared to crystalline/amorphous LH. However, the coamorphous system is still in amorphous state, and has the tendency to recrystallization, which will in turn result in the loss of above advantages. In this study, the crystallization kinetics under isothermal and non-isothermal conditions was investigated. Compared to amorphous LH, coamorphous LH-SAC showed 68.3-361.2 and 2.6-6.1 times lower crystallization rates in glassy state and supercooled liquid state, respectively. After co-amorphization, the addition of SAC changed the crystallization mechanism of amorphous LH from nucleation-controlled to diffusion-controlled manner. Amorphous LH followed the site-saturated nucleation, whereas the coamorphous system exhibited a fixed number of nuclei. The non-isothermal crystallization indicated amorphous LH and coamorphous LH-SAC showed two-dimensional (JMAEK 2) and three-dimensional (JMAEK 3) growth of nuclei, respectively. Furthermore, coamorphous LH-SAC exhibited higher molecular mobility and dynamic fragility (mD) than amorphous LH, which is kinetically unfavorable for its physical stability. However, from thermodynamic perspective, coamorphous LH-SAC had a higher configurational entropy, i.e., a higher entropy barrier for crystallization, which is beneficial to hinder its crystallization. Therefore, it was concluded that the higher configurational entropy rather than the molecular mobility was proposed to be responsible for its improved stability. In addition, molecular dynamics simulations with miscibility, radial distribution function and binding energy calculations suggested coamorphous components exhibited good miscibility and strong intermolecular interactions, which was also conductive to the enhancement in its stability. This study offers an in-depth understanding about the effect of the coformer on the crystallization kinetics of coamorphous systems, and points out the important contribution of the configurational entropy in stabilizing the coamorphous systems.

Boundary design regulates the diffusion of active matter in heterogeneous environments.

Physical boundaries play a key role in governing the overall transport properties of nearby self-propelled particles. In this work, we develop dispersion theories and conduct Brownian dynamics simulations to predict the coupling between surface accumulation and effective diffusivity of active particles in boundary-rich media. We focus on three models that are well-understood for passive systems: particle transport in (i) an array of fixed volume-excluding obstacles; (ii) a pore with spatially heterogeneous width; and (iii) a tortuous path with kinks and corners. While the impact of these entropic barriers on passive particle transport is well established, we find that these classical models of porous media flows break down due to the unique interplay between activity and the microstructure of the internal geometry. We study the activity-induced slowdown of effective diffusivity by formulating a Smoluchowski description of long-time self diffusivity which contains contributions from the density and fluctuation fields of the active particles. Particle-based and finite element simulations corroborate this perspective and reveal important nonequilibrium considerations of active transport.

Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale.

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon's needle, requires the rods to "land," with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.

On the Computability of Continuous Maximum Entropy Distributions with Applications

We initiate a study of the following problem: Given a continuous domain $\Omega$ along with its convex hull $\mathcal{K}$, a point $A \in \mathcal{K}$ and a prior measure $\mu$ on $\Omega$, find the probability density over $\Omega$ whose marginal is $A$ and that minimizes the KL-divergence to $\mu$. This framework gives rise to several extremal distributions that arise in mathematics, quantum mechanics, statistics, and theoretical computer science. Our technical contributions include a polynomial bound on the norm of the optimizer of the dual problem that holds in a very general setting and relies on a balance property of the measure $\mu$ on $\Omega$, and exact algorithms for evaluating the dual and its gradient for several interesting settings of $\Omega$ and $\mu$. Together, along with the ellipsoid method, these results imply polynomial-time algorithms to compute such KL-divergence minimizing distributions in several cases. Applications of our results include: 1) an optimization characterization of the Goemans-Williamson measure that is used to round a positive semidefinite matrix to a vector, 2) the computability of the entropic barrier for polytopes studied by Bubeck and Eldan, and 3) a polynomial-time algorithm to compute the barycentric quantum entropy of a density matrix that was proposed as an alternative to von Neumann entropy in the 1970s: this corresponds to the case when $\Omega$ is the set of rank one projections matrices and $\mu$ corresponds to the Haar measure on the unit sphere. Our techniques generalize to the setting of Hermitian rank $k$ projections using the Harish-Chandra-Itzykson-Zuber formula, and are applicable even beyond, to adjoint orbits of compact Lie groups.

Enthalpic and Entropic Contributions to Fast Lithium Ion Conduction in Solid-State Aqueous Polymer Electrolytes

Solid-state aqueous polymer electrolytes (SAPEs), a mixture of hydrophilic polymers and an appropriate amount of water, can produce high Li-ion conductivity while maintaining a solid state. Also, they can overcome the limitations of normal solid electrolytes. This study reports that the very high SAPE ionic conductivity (∼10 mS/cm at T = 298.15 K) originates from a low energy barrier (∼0.28 eV) closely correlated with water-filled ion passages in the medium. The low energy barrier is ascribed to a considerable reduction of the enthalpic barrier due to water addition despite a growth of the entropic barrier incurred by the negative nature of entropy change across water tubes. The extremely high ionic conductivity, coupled with an exceptionally low energy barrier, provides a unique advantage to SAPEs over conventional solid electrolytes.

Entropic interactions of 2D materials with cellular membranes: Parallel versus perpendicular approaching modes

Understanding the interaction of 2D materials including graphene, boron nitride and MoS2 with biological systems is a growing topic of interest to many applications such as biosensors, drug delivery, gene therapy and nano-toxicity. In this paper, we show that the interaction of 2D materials with cellular membranes at its early stage of approaching is dominantly controlled by entropic forces. Recent experiments indicate that graphene sheets, depending on their size, can either undergo a near-orthogonal cutting or a parallel attachment mode of interaction with cell membranes. Here, we perform a set of integrated theoretical statistical mechanics analysis and coarse-grained molecular dynamics simulations to quantify the entropic energy barrier for these modes of interactions. Our results indicate that micro-sized graphene sheets prefer approaching a fluctuating membrane through a sharp corner, while nano-sized sheets are more likely to adhere to the cell membrane surface due to relatively low entropic energy cost that is comparable with thermal energy from random Brownian motions.

Colloidal Stochastic Resonance in Confined Geometries.

We investigate the dynamical properties of a colloidal particle in a double cavity. Without external driving, the particle hops between two free-energy minima with transition mean time depending on the system's entropic and energetic barriers. We then drive the particle with a periodic force. When the forcing period is set at twice the transition mean time, a statistical synchronization between particle motion and forcing phase marks the onset of a stochastic resonance mechanism. Comparisons between experimental results and predictions from the Fick-Jacobs theory and Brownian dynamics simulation reveal significant hydrodynamic effects, which change both resonant amplification and noise level. We further show that hydrodynamic effects can be incorporated into existing theory and simulation by using an experimentally measured particle diffusivity.

Monte Carlo Simulation of Static and Dynamic Properties of Linear Polymer in a Crowded Environment

In this paper, we investigate the static and dynamic properties of linear polymer in the presence of obstacles. A Monte Carlo (MC) simulation method in two dimensions with a bond fluctuation model (BFM) was used to achieve this goal. To overcome the entropic barrier, we put the middle monomer of the polymer in the middle of the pore, which is placed between ordered and disordered obstacles. We probed the static properties of the polymer by calculating the mean square of the radius of gyration and the mean square end-to-end distance of the polymer, and we found that the scaling exponents of both the mean square end-to-end distance R 2 and the mean square radius of gyration R g 2 as a function of the polymer length N vary with the area fraction of crowding agents, ϕ . The dynamic properties have also been studied by exploring the translocation of the polymer. Our current research shows that the escape time τ increases as ϕ increases. Moreover, in the power-law relation of escape time τ as a function of polymer length N , the scaling exponent ( α ) changes with ϕ . Furthermore, the study has shown that the translocation of the polymer favors the disordered barriers.

Entropy reduction from strong localization – an explanation for enhanced reaction rates of organic synthesis in aqueous micelles

HypothesisThe underlying mechanism for increased reaction rates in micellar catalysis-based organic synthesis is a reduced entropy barrier for the reaction. A two-dimensional localization of reactants and catalyst in the surfactant micelle reduces the translational entropy of all components. The entropy is reduced less for the reaction intermediate than for the reactants, which leads to the lower barrier. SimulationsQuantum chemistry, the COSMO-RS implicit solvent model and statistical thermodynamics were employed to predict the stability of a range of reactants, catalysts and intermediates in a series of surfactant micelles. The localized stability in the linker region between the lipophilic and hydrophilic regions and the resulting decrease in entropy were also calculated. FindingsThe predicted reaction rates for the proposed mechanism show that the entropy reduction leads to a larger prefactor for the reaction. The resulting reaction rate can be significantly higher than conventional organic synthesis in an organic solvent even when the smaller reaction volume and lower reaction temperatures typically needed under micellar catalysis conditions are considered. The results are general across a wide range of types of reactions, reactants and catalysts and a selection of surfactants commonly used in organic synthesis, strongly supporting the hypothesis.

Limited ion-ion selectivity of salt-rejecting membranes due to enthalpy-entropy compensation

Water and ion transport in salt-rejecting membranes, such as nanofiltration (NF) and reverse osmosis (RO), are exposed to different hindrance effects that result in selectivity between species. In this study, we explored systematically the hindrance effects that govern water-salt and ion-ion selectivity in NF and RO membranes. More specifically, we measured the permeability of different species at varying temperatures and applied an Eyring-type equation to quantify the enthalpic and entropic barriers for their transport in three types of salt-rejecting membranes. We found that water-salt selectivity is entropically driven, where water molecules gain entropy in the membrane, while the salt ions face a substantial entropic barrier due to their larger size that reduces their possible configurations in the membrane. As the enthalpic barriers of the water and salt did not show a prominent difference (with minor effect on the water-salt selectivity), most ion-ion separations were restricted by an enthalpy-entropy compensation (EEC) effect; that is, an ion with a higher entropic barrier experienced a lower enthalpic barrier compared to the competing ion, resulting in minor variations in the free-energy barriers between ions that limit the ion-ion selectivity. We conclude by proposing possible mechanisms that promote EEC during ion transport in salt-rejecting membranes.

Kinetic study on the molecular mechanism of light-driven inward proton transport by schizorhodopsins

Schizorhodopsins (SzRs) are light-driven inward proton pumping membrane proteins. A H+ is released to the cytoplasmic solvent from the chromophore, retinal Schiff base (RSB), after light absorption, and then another H+ is bound to the RSB at the end of photocyclic reaction. However, the mechanistic detail of H+ transfers in SzR is almost unknown. Here we studied the deuterium isotope effect and the temperature dependence of the reaction rate constants of elementary steps in the photocycles of SzRs. The former indicated that deprotonation and reprotonation of RSB is mainly accomplished by H+ hopping between heavy atoms with similar H+ affinity. Furthermore, the temperature dependence of the rate constants revealed that most of H+ transfer events have a high entropy barrier. In contrast, the activation enthalpy and entropy of extremely thermostable SzR (MsSzR) are significantly higher than other types of SzRs (SzR1 and MtSzR) suggesting that its highly thermostable structure is optimized with at the cost of slower reaction rates at ambient temperatures.

Entropic stochastic resonance and super-harmonic stochastic resonance in a dichotomous fluctuating potential

When a Brownian particle moves in a confined space, the boundaries of the confined space can form an entropic barrier and thus induce the classical entropic stochastic resonance (ESR) phenomenon. This paper introduces a dichotomous fluctuating potential into the classical ESR model and studies the dynamics and ESR phenomena of the confined particle. It is shown that the amplitude of each harmonic component of both the horizontal and vertical displacements of the confined particle appears in various types of ESR phenomena, such as single-peak ESR, double-peak ESR, or even multi-peak ESR. This multi-peak ESR phenomenon is caused when the different dynamical states of the confined particle (under the joint action of the energy and entropy potentials) reach the optimal equilibrium. The results of this paper will help to understand the mechanism of stochastic dynamics of particles in confined spaces.

In Situ 29Si solid-state NMR study of grafting of organoalkoxysilanes to mesoporous silica nanoparticles

Since the catalytic activity and the stability of silica-bound organometallic complexes are affected by their interactions with hydroxyl groups on the surface, isolated hydroxyls are often created prior to the introduction of catalytic species. Here, we investigate a method to remove the indigenous hydroxyls and create new isolated hydroxyls by grafting organo-trimethoxysilane (R-TMS) to generate a silicon T2 site, (≡SiO‒)2SiR(‒OH). We used in situ 29Si solid-state NMR experiments to monitor the evolution of Tn sites, (≡SiO‒)nSiR(‒OH)3-n (n = 1, 2, 3). The study indicates that i) the grafting proceeds in a consecutive manner as T1 → T2 → T3, and ii) the kinetics depend on the type of functional groups in the silane. However, the rates of T1 formation and T2 → T3 conversion are also controlled to a significant extent by the entropy loss associated to the initial silane binding and the spatial arrangement of surface hydroxyls, respectively. The grafting of R-TMS with a basic functional group leads to a lower concentration of T1 sites. The nucleophilicity of the functional group facilitates the grafting process by lowering the enthalpy barrier, while the T1 formation rate is more influenced by the entropy barrier than the T1 → T2 conversion rate. Thus, the basic functional group promotes the T1 → T2 conversion more than the T1 formation, resulting in a lower concentration of T1 sites.

Mode-selective ballistic pathway to a metastable electronic phase.

Exploiting vibrational excitation for the dynamic control of material properties is an attractive goal with wide-ranging technological potential. Most metal-to-insulator transitions are mediated by few structural modes and are, thus, ideal candidates for selective driving toward a desired electronic phase. Such targeted navigation within a generally multi-dimensional potential energy landscape requires microscopic insight into the non-equilibrium pathway. However, the exact role of coherent inertial motion across the transition state has remained elusive. Here, we demonstrate mode-selective control over the metal-to-insulator phase transition of atomic indium wires on the Si(111) surface, monitored by ultrafast low-energy electron diffraction. We use tailored pulse sequences to individually enhance or suppress key phonon modes and thereby steer the collective atomic motion within the potential energy surface underlying the structural transformation. Ab initio molecular dynamics simulations demonstrate the ballistic character of the structural transition along the deformation vectors of the Peierls amplitude modes. Our work illustrates that coherent excitation of collective modes via exciton-phonon interactions evades entropic barriers and enables the dynamic control of materials functionality.

Temperature responses of two synergistic pathways for low-temperature catalytic oxidation of high-concentration NO over ACFs: Nano-confinement and nitrogen-containing groups

This study reveals for the first time that low-temperature catalytic oxidation of high-concentration NO over ACFs achieved by two synergistic paths: the quasi-homogeneous NO oxidation (path 1) and the nitrogen-containing functional groups catalysis (path 2). In path 1, the kinetic properties of reaction transition state are stabilized by ultra-micropores due to its non-specific van der Waals interaction, accelerating the transfer from gaseous reactants to the transition state 100 ∼ 1000 times. The micropore confinement effect of activation enthalpy is strongest at ambient temperature therefore the catalytic efficiency is the highest 6.89 × 10-4 mol·L-1·S-1. In path 2, extra π electrons generated by the substitution of N for C in the aromatic ring transfer to NOx and O2. Pyridine and quaternary nitrogen serve as catalytical active sites to promote the adsorption of NO and the activation of O2. Temperature increasing leads to a significant negative entropy barrier, the catalytic activity decreases accordingly, this is the main reason for the fluctuation in NO oxidation efficiency caused by temperature. The approximate proportion of the two oxidation pathways and their changes with reaction temperature are quantitatively analyzed by transition state theory calculations. Raising the reaction temperature from 25℃ to 200℃ increased the activity contribution of the active functional group catalytic pathway by about 25 %, which to some extent compensated for the negative entropy barrier effect of the quasi-homogeneous NO oxidation pathway.

Quantifying Energetic and Entropic Pathways in Molecular Systems.

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Finally, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.