Surface Tension of Simple Molten Salts: Insight from a Charged Hard Sphere Model.

Surface tension of molten salts is rooted in many important phenomena in physical chemistry. We develop an analytical theory for the surface tension of molten salts, where the molten salt is described by a restricted primitive model electrolyte consisting of charged hard spheres, and surface tension is related to the formation of a cavity in the electrolyte. The integral equation theory is applied to the restricted primitive model electrolyte to derive an analytical formula of the cavity formation energy. The scaling relation of the cavity formation energy is further combined with morphological thermodynamics theory to determine the formula for surface tension. According to our formula, surface tension consists of a positive hard sphere contribution and a negative electrostatic contribution. Using the molar mass, interionic distance, density, and temperature as the input, our theory leads to a good prediction of surface tension of more than 16 molten salts at their melting point without introducing any adjustable parameters.

Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions.

In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions.

In this work, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

Torsion Angles between Donor and Acceptor Moieties as a Descriptor for Designing Nonlinear Optics and Thermally Activated Delayed Fluorescence Materials.

The performances of nonlinear optics (NLO) and thermally activated delayed fluorescence (TADF) materials are strongly related to the torsion angles (θ) between donor (D) and acceptor (A) moieties in D-A architecture molecules. However, the underlying relationships connecting θ to the performances of NLO/TADF materials remain unclear. Herein, we present a comprehensive theoretical study on NLO/TADF materials composed of a series of D-A backbone molecules (TPAAP/TPAAQ series and AQ-DMAC/AQ-MeFAC series) to shed light on these relationships. It is found that changing θ via the intramolecular locking strategy can greatly influence values of the first hyperpolarizability (ß) and singlet-triplet energy gap (ΔEST), further leading to better/worse performances of NLO/TADF materials, respectively. Intriguingly, a more detailed analysis indicates that the variation trends between θ and ß/ΔEST are changeable in low θ regions, exhibiting volcano-like relationships. The large coefficients of determination (R2, ranging from 0.76 to 0.93) suggest that this experimentally measurable parameter (θ) can be used as a promising descriptor to evaluate the performances of related materials. Following the revealed θ-ß/θ-ΔEST correlations, the optimal/worst torsion angles for different materials are identified. These findings highlight the importance of the intrinsic structure-performance relationships, thus providing novel design strategies for high-performance NLO/TADF materials.

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions.

In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

A cavity formation energy formula for hard spheres in simple electrolyte solutions.

A formula for cavity formation energy of a hard sphere in restricted primitive electrolyte solutions is derived based on the integral equation theory. Specifically, the contact values of radial distribution functions between the hard sphere and the ionic species, determined analytically from the first-order mean spherical approximation theory, are used to evaluate the cavity formation energy. In the large solute-size limit, the scaling relation of the cavity formation energy further leads to an analytical expression for the surface tension of the electrolyte solution near a curved interface. Our theory is applied to hard spheres immersed in restricted primitive electrolyte solutions, where the good agreement of the cavity formation energy with the hyper-netted chain theory demonstrates the accuracy of our theory.

An intramolecular-locked strategy for designing nonlinear optical materials with remarkable first hyperpolarizability.

To meet the expanding demands of high performance nonlinear optical (NLO) materials, an unprecedented intramolecular-locked strategy is proposed to design NLO materials with remarkable static first hyperpolarizability (ß0). This strategy means that importing a large steric hindrance group diphenylmethane (DPM) decreases the torsion angles (θ) between the donor {triphenylamine (TPA)} and acceptor {9-H-thioxanthen-9-one-10,10-dioxide (TXO)} units, as well as between the donor (TPA) and π-bridge (benzene) fragments. The decrease of θ can accelerate the intramolecular charge transfer and enhance the contributions of the TPA, TXO and quinoxaline-6,7-dicarbo-nitrile (QCN) fragments to the axial component of the ß0 value, and then the ß0 values of TPA-TXO (ß0 = 10 762 au) and TPA-QCN (ß0 = 22 495 au) are increased by 14.9% and 34.4%, respectively. Overall, the intramolecular-locked strategy is very effective for designing high performance NLO materials.

Fast Calculation of Electrostatic Solvation Free Energy in Simple Ionic Fluids Using an Energy-Scaled Debye-Hückel Theory.

Continuum theories are useful to compute the solvation free energy in ionic fluids. Herein, the electrostatic solvation free energy (ESFE) in simple ionic fluids is studied with an energy-scaled Debye-Hückel (ESDH) theory. Given the ESFEs of simple spherical ions as input, the ESDH theory is applicable to molecules with various complex geometries and charge distributions. Specifically, the ESDH theory is applied to molecules in a molten salt system, where the predicted ESFEs are in good agreement with molecular dynamics simulation results. Our study sheds light on accurately predicting the ESFE in ionic fluids with phenomenological continuum theories.

A Systematic Way to Extend the Debye-Hückel Theory beyond Dilute Electrolyte Solutions.

An extended Debye-Hückel theory with fourth order gradient term is developed for electrolyte solutions; namely, the electric potential φ(r) of the bulk electrolyte solution can be described by ∇2φ(r) = κ2φ(r) + LQ2∇4φ(r), where the parameters κ and LQ are chosen to reproduce the first two roots of the dielectric response function of the bulk solution. Three boundary conditions for solving the electric potential problem are proposed based upon the continuity conditions of involving functions at the dielectric boundary, with which a boundary element method for the electric potential of a solute with a general geometrical shape and charge distribution is derived. Solutions for the electric potential of a spherical ion and a diatomic molecule are found and used to calculate their electrostatic solvation energies. The validity of the theory is successfully demonstrated when applied to binary as well as multicomponent primitive models of electrolyte solutions.

A molecular Debye-Hückel theory of solvation in polar fluids: An extension of the Born model.

A dielectric response theory of solvation beyond the conventional Born model for polar fluids is presented. The dielectric response of a polar fluid is described by a Born response mode and a linear combination of Debye-Hückel-like response modes that capture the nonlocal response of polar fluids. The Born mode is characterized by a bulk dielectric constant, while a Debye-Hückel mode is characterized by its corresponding Debye screening length. Both the bulk dielectric constant and the Debye screening lengths are determined from the bulk dielectric function of the polar fluid. The linear combination coefficients of the response modes are evaluated in a self-consistent way and can be used to evaluate the electrostatic contribution to the thermodynamic properties of a polar fluid. Our theory is applied to a dipolar hard sphere fluid as well as interaction site models of polar fluids such as water, where the electrostatic contribution to their thermodynamic properties can be obtained accurately.

A molecular Debye-Hückel theory and its applications to electrolyte solutions: The size asymmetric case.

A molecular Debye-Hückel theory for electrolyte solutions with size asymmetry is developed, where the dielectric response of an electrolyte solution is described by a linear combination of Debye-Hückel-like response modes. As the size asymmetry of an electrolyte solution leads to a charge imbalanced border zone around a solute, the dielectric response to the solute is characterized by two types of charge sources, namely, a bare solute charge and a charge distribution due to size asymmetry. These two kinds of charge sources are screened by the solvent differently, our theory presents a method to calculate the mean electric potential as well as the electrostatic contributions to thermodynamic properties. The theory has been successfully applied to binary as well as multi-component primitive models of electrolyte solutions.

Heat dissipation and information flow for delayed bistable Langevin systems near coherence resonance.

In this paper, stochastic thermodynamics of delayed bistable Langevin systems near coherence resonance is discussed. We calculate the heat dissipation rate and the information flow of a delayed bistable Langevin system under various noise intensities. Both the heat dissipation rate and the information flow are found to be bell-shaped functions of the noise intensity, which implies that coherence resonance manifests itself in the thermodynamic properties.

Association between mode of delivery and failure of neonatal acoustic emission test: a retrospective analysis.

BACKGROUND: Infants born by cesarean delivery (CD) appear to fail the otoacoustic emission (OAE) test more frequently than infants delivered vaginally (VD). OBJECTIVE: The present study aimed to evaluate the influence of CD on failure to the OAE test in Chinese infants. METHODS: In this retrospective study, 1460 Chinese infants were included. The OAE test was performed before hospital discharge. Modes of delivery, test time and OAE results were collected and analyzed. RESULTS: Compared with VD infants, CD infants had lower gestational age (week), were smaller for their gestational age (SGA), and presented a lower 1-min Apgar score and a younger age at first OAE. On multivariate analysis, CD and age at first OAE were significantly associated with failed OAE (both P<0.001). CD infants had a 3-fold higher rate of failure to the OAE test compared with VD infants (21% vs. 7.1%). The results of the OAE test changed with different test time regardless of the mode of delivery, and the neonatal OAE test failure rate decreased with time. The difference was not significant between CD and VD infants 42h or more after delivery. CONCLUSION: CD infants had significantly higher failure rates on first OAE test. Results suggest that the OAE test should be performed 42h after delivery so as to minimize repetition of OAE, improve the OAE test pass rate, and minimize costs and parents' anxiety.

Extended Debye-Hückel theory for studying the electrostatic solvation energy.

The electrostatic part of the solvation energy has been studied by using extended Debye-Hückel (DH) theories. Specifically, our molecular Debye-Hückel theory [J. Chem. Phys. 2011, 135, 104104] and its simplified version, an energy-scaled Debye-Hückel theory, were applied to electrolytes with strong electrostatic coupling. Our theories provide a practical methodology for calculating the electrostatic solvation free energies, and the accuracy was verified for atomic and diatomic charged solutes.

A molecular Debye-Hückel approach to the reorganization energy of electron transfer reactions in an electric cell.

Electron transfer near an electrode immersed in ionic fluids is studied using the linear response approximation, namely, mean value of the vertical energy gap can be used to evaluate the reorganization energy, and hence any linear response model that can treat Coulomb interactions successfully can be used for the reorganization energy calculation. Specifically, a molecular Debye-Hückel theory is used to calculate the reorganization energy of electron transfer reactions in an electric cell. Applications to electron transfer near an electrode in molten salts show that the reorganization energies from our molecular Debye-Hückel theory agree well with the results from MD simulations.

Reorganization energy of electron transfer processes in ionic fluids: a molecular Debye-Hückel approach.

The reorganization energy of electron transfer processes in ionic fluids is studied under the linear response approximation using a molecule Debye-Hückel theory. Reorganization energies of some model reactants of electron transfer reactions in molten salts are obtained from molecular simulations and a molecule Debye-Hückel approach. Good agreements between simulation results and the results from our theoretical calculations using the same model Hamiltonian are found. Applications of our theory to electron transfer reactions in room temperature ionic liquids further demonstrate that our theoretical approach presents a reliable and accurate methodology for the estimation of reorganization energies of electron transfer reactions in ionic fluids.

A molecular Debye-Hückel theory and its applications to electrolyte solutions.

In this report, a molecular Debye-Hückel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Hückel theory which is related to the dressed ion theory in the static case. Due to the multi-pole structure of dielectric function of ionic fluids, the electric potential around a single ion has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Hückel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to binary as well as multi-component primitive models of electrolyte solutions demonstrated the accuracy of our approach. More importantly, for electrolyte solution models with soft short-ranged interactions, it is shown that the traditional perturbation theory can be extended to ionic fluids successfully just as the perturbation theory has been successfully used for short-ranged systems.

Stochastic thermodynamics for delayed Langevin systems.

We discuss stochastic thermodynamics (ST) for delayed Langevin systems in this paper. By using the general principles of ST, the first-law-like energy balance and trajectory-dependent entropy s(t) can be well defined in a way that is similar to that in a system without delay. Because the presence of time delay brings an additional entropy flux into the system, the conventional second law (Δs(tot))≥0 no longer holds true, where Δs(tot) denotes the total entropy change along a stochastic path and (·) stands for the average over the path ensemble. With the help of a Fokker-Planck description, we introduce a delay-averaged trajectory-dependent dissipation functional η[χ(t)] which involves the work done by a delay-averaged force F(x,t) along the path χ(t) and equals the medium entropy change Δs(m)[x(t)] in the absence of delay. We show that the total dissipation functional R=Δs+η, where Δs denotes the system entropy change along a path, obeys (R)≥0, which could be viewed as the second law in the delayed system. In addition, the integral fluctuation theorem (e(-R))=1 also holds true. We apply these concepts to a linear Langevin system with time delay and periodic external force. Numerical results demonstrate that the total entropy change (Δs(tot)) could indeed be negative when the delay feedback is positive. By using an inversing-mapping approach, we are able to obtain the delay-averaged force F(x,t) from the stationary distribution and then calculate the functional R as well as its distribution. The second law (R)≥0 and the fluctuation theorem are successfully validated.

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics.

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time-averaged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation (HB). In the large system size (weak noise) limit, we find that P ∼ N(ß) with ß = 0 or 1, when the system is below or above the HB, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.

Internal noise enhanced oscillation in a delayed circadian pacemaker.

The effect of internal noise in a delayed circadian oscillator is studied by using both chemical Langevin equations and stochastic normal form theory. It is found that internal noise can induce circadian oscillation even if the delay time τ is below the deterministic Hopf bifurcation τ(h). We use signal-to-noise ratio (SNR) to quantitatively characterize the performance of such noise induced oscillations and a threshold value of SNR is introduced to define the so-called effective oscillation. Interestingly, the τ-range for effective stochastic oscillation, denoted as Δτ(EO), shows a bell-shaped dependence on the intensity of internal noise which is inversely proportional to the system size. We have also investigated how the rates of synthesis and degradation of the clock protein influence the SNR and thus Δτ(EO). The decay rate K(d) could significantly affect Δτ(EO), while varying the gene expression rate K(e) has no obvious effect if K(e) is not too small. Stochastic normal form analysis and numerical simulations are in good consistency with each other. This work provides us comprehensive understandings of how internal noise and time delay work cooperatively to influence the dynamics of circadian oscillations.