Entropic Part Research Articles

Nature of Optical Thermodynamic Pressure Exerted in Highly Multimoded Nonlinear Systems.

The theory of optical thermodynamics provides a comprehensive framework that enables a self-consistent description of the intricate dynamics of nonlinear multimoded photonic systems. This theory, among others, predicts a pressurelike intensive quantity (p[over ^]) that is conjugate to the system's total number of modes (M)-its corresponding extensive variable. Yet at this point, the nature of this intensive quantity is still nebulous. In this Letter, we elucidate the physical origin of the optical thermodynamic pressure and demonstrate its dual essence. In this context, we rigorously derive an expression that splits p[over ^] into two distinct components, a term that is explicitly tied to the electrodynamic radiation pressure and a second entropic part that is responsible for the entropy change. We utilize this result to establish a formalism that simplifies the quantification of radiation pressure under nonlinear equilibrium conditions, thus eliminating the need for a tedious evaluation of the Maxwell stress tensor. Our theoretical analysis is corroborated by numerical simulations carried out in highly multimoded nonlinear optical structures. These results may provide a novel way in predicting and controlling radiation pressure processes in a variety of nonlinear electromagnetic settings.

Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles.

By employing Tsallis' extensive but non-additive δ-entropy, we formulate the first two laws of thermodynamics for gravitating systems. By invoking Carathéodory's principle, we pay particular attention to the integrating factor for the heat one-form. We show that the latter factorizes into the product of thermal and entropic parts, where the entropic part cannot be reduced to a constant, as is the case in conventional thermodynamics, due to the non-additive nature of Sδ. The ensuing two laws of thermodynamics imply a Tsallis cosmology, which is then applied to a radiation-dominated universe to address the Big Bang nucleosynthesis and the relic abundance of cold dark matter particles. It is demonstrated that the Tsallis cosmology with the scaling exponent δ∼1.499 (or equivalently, the anomalous dimension Δ∼0.0013) consistently describes both the abundance of cold dark matter particles and the formation of primordial light elements, such as deuterium 2H and helium 4He. Salient issues, including the zeroth law of thermodynamics for the δ-entropy and the lithium 7Li problem, are also briefly discussed.

A micro-mechanically-based constitutive model for hyperelastic rubber-like materials considering the topological constraints

Hyperelastic rubber-like materials are described by their nonlinear elastic behavior subjected to large deformations. The one-dimensional strain energy function for polymeric material was introduced in Mahnken and Mirzapour (2022). This follow-up contribution presents a three-dimensional statistical micro-mechanical-based constitutive model incorporating the topological constraint’s effects. The micro strain energy corresponding to the stored energy in a single polymer chain is mainly entropic and calculated from the entropic part of the Helmholtz free energy based on the Boltzmann equation. Then, the macro strain energy corresponding to the polymer networks is obtained by homogenizing the micro strain energy over the unit volume. At the same time, it can be decomposed into cross-linked and entangled strain energies. The current model is developed on the different angles of the polymer chain. The random nature of the polymer chain’s angles is defined by proper probability distribution functions (PDFs) representing different angles’ distribution. I incorporate the entangled chains based on the statistical degree of freedom introduced as polymer angles. Numerical examples to calibrate and verify the proposed model illustrate the capability of the current proposed model to reproduce the highly nonlinear behavior of rubber-like materials under different loading conditions.

Associated Water Dynamics Might Be a Key Factor Affecting Protein Stability in the Crowded Milieu.

Over the past 20 years, the most studied and debated aspect of macromolecular crowding is how it affects protein stability. Traditionally, it is explained by a delicate balance between the stabilizing entropic effect and the stabilizing or destabilizing enthalpic effect. However, this traditional crowding theory cannot explain experimental observations like (i) negative entropic effect and (ii) entropy-enthalpy compensation. Herein, we provide experimental evidence that associated water dynamics plays a crucial role in controlling protein stability in the crowded milieu for the first time. We have correlated the modulation of associated water dynamics with the overall stability and its individual components. We showed that rigid associated water would stabilize the protein through entropy but destabilize it through enthalpy. In contrast, flexible associated water destabilizes the protein through entropy but stabilizes through enthalpy. Consideration of entropic and enthalpic modulation through crowder-induced distortion of associated water successfully explains the negative entropic part and entropy-enthalpy compensation. Furthermore, we argued that the relationship between the associated water structure and protein stability should be better understood by individual entropic and enthalpic components instead of the overall stability. Although a huge effort is necessary to generalize the mechanism, this report provides a unique way of understanding the relationship between protein stability and associated water dynamics, which might be a generic phenomenon and should trigger much research in this area.

Tsallis cosmology and its applications in dark matter physics with focus on IceCube high-energy neutrino data

In this paper we employ a recent proposal of C. Tsallis and formulate the first law of thermodynamics for gravitating systems in terms of the extensive but non-additive entropy. We pay a particular attention to an integrating factor for the heat one-form and show that in contrast to conventional thermodynamics it factorizes into thermal and entropic part. Ensuing two laws of thermodynamics imply Tsallis cosmology, which is then subsequently used to address the observed discrepancy between current bound on the Dark Matter relic abundance and present IceCube data on high-energy neutrinos. To resolve this contradiction we keep the conventional minimal Yukawa-type interaction between standard model and Dark Matter particles but replace the usual Friedmann field equations with Tsallis-cosmology-based modified Friedmann equations. We show that when the Tsallis scaling exponent delta sim 1.57 (or equivalently, the holographic scaling exponent alpha sim 3.13) the aforementioned discrepancy disappears.

Hydrophobicity of Self-Assembled Monolayers of Alkanes: Fluorination, Density, Roughness, and Lennard-Jones Cutoffs.

The interplay of fluorination and structure of alkane self-assembled monolayers and how these affect hydrophobicity are explored via molecular dynamics simulations, contact angle goniometry, and surface-enhanced infrared absorption spectroscopy. Wetting coefficients are found to grow linearly in the monolayer density for both alkane and perfluoroalkane monolayers. The larger contact angles of monolayers of perfluorinated alkanes are shown to be primarily caused by their larger molecular volume, which leads to a larger nearest-neighbor grafting distance and smaller tilt angle. Increasing the Lennard-Jones force cutoff in simulations is found to increase hydrophilicity. Specifically, wetting coefficients scale like the inverse square of the cutoff, and when extrapolated to the infinite cutoff limit, they yield contact angles that compare favorably to experimental values. Nanoscale roughness is also found to reliably increase monolayer hydrophobicity, mostly via the reduction of the entropic part of the work of adhesion. Analysis of depletion lengths shows that droplets on nanorough surfaces partially penetrate the surface, intermediate between Wenzel and Cassie-Baxter states.

Concentration Bias in Reference Potentials and the pH-Effect on the Electrocatalysis of Hydrogen and Oxygen Evolution for Water Electrolysis

The electrolysis of water at low temperatures involves the transition from the liquid to the gas phase. The reactant, liquid water, has a concentration of around 55 mol/L, whereas gases such as hydrogen and oxygen with a nearly ideal behavior correspond to a concentration of only 0.04 mol/L at standard conditions (room temperature, pressure equal to 1 bar). Moreover, the oxygen and hydrogen molecules produced during electrolysis are first formed in a dissolved state in the electrolyte before escaping to the gas phase. The saturation concentrations of these gases in liquid water are around 0.001 mol/L at standard conditions, even lower than the concentrations in the gas phase. Accordingly the water electrolysis reaction involves a concentration change from approx. 55 mol/L for the reactant down to approx. 0.001 mol/L for the products. This dramatic concentration drop strongly contributes to the entropic part of the Gibbs free energy of the water splitting reaction, and it therefore implicitly biases the equilibrium voltage.We discuss why this concentration bias can be obstructive for a clear perspective on the reaction kinetics when using the equilibrium voltage, or potentials, as a reference [1]. To provide an unbiased reference voltage, we propose a definition of reference conditions with balanced concentrations on the reactant and product side. The theoretical equilibrium voltage corresponding to such balanced reactive conditions is an unbiased intrinsic reference for kinetic analysis, for which reason we denote it the kinetic reference voltage Ukin. For the electrochemical water splitting reaction, it has a value of Ukin = 1.441 V, which is in remarkable agreement with commonly observed onset voltages for macroscopic electrolysis rates.Applying the same concept of balanced reactive conditions to half-cell reactions, we define the kinetic reference potential Ekin. For a simple electrochemical redox couple Red ↔ Ox + e− with a 1:1 stoichiometry, the kinetic reference potential Ekin is simply equal to the standard equilibrium potential, because the standard reference concentrations are already balanced (1 mol/L for dissolved species). In contrast, for the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER), the standard reference concentrations are very different for reactants and products, and the corresponding standard equilibrium potentials suffer from concentration bias. Accordingly, the unbiased kinetic reference potentials of HER and OER are shifted with respect to the standard equilibrium potentials. These shifts are different in acidic and alkaline conditions and reveal an intriguing correlation with the experimentally observed effect of the pH value on the kinetics of HER and OER.The concept of balanced reactive reference conditions thus sheds a new light on the activation overvoltage in water electrolysis and the pH-effect in the electrocatalysis of HER and OER.[1] T. Binninger, A. Heinritz, R. Mohamed, Kinetic Reference Potential, pH-Effect, and Energy Recovery in Electrolysis of Water, ChemRxiv (2020), preprint, DOI: 10.26434/chemrxiv.12739091.v1

Temperature-Responsive Peptide-Nucleotide Coacervates.

Coacervates are a type of liquid–liquid phase separated (LLPS) droplets that can serve as models of membraneless organelles (MLOs) in living cells. Peptide–nucleotide coacervates have been widely used to mimic properties of ribonucleoprotein (RNP) granules, but the thermal stability and the role of base stacking is still poorly understood. Here, we report a systematic investigation of coacervates formed by five different nucleoside triphosphates (NTPs) with poly-l-lysine and poly-l-arginine as a function of temperature. All studied combinations exhibit an upper critical solution temperature (UCST), and a temperature-dependent critical salt concentration, originating from a significant nonelectrostatic contribution to the mixing free energy. Both the enthalpic and entropic parts of this nonelectrostatic interaction decrease in the order G/A/U/C/T, in accordance with nucleobase stacking free energies. Partitioning of two dyes proves that the local hydrophobicity inside the peptide–nucleotide coacervates is different for every nucleoside triphosphate. We derive a simple relation between the temperature and salt concentration at the critical point based on a mean-field model of phase separation. Finally, when different NTPs are mixed with one common oppositely charged peptide, hybrid coacervates were formed, characterized by a single intermediate UCST and critical salt concentration. NTPs with lower critical salt concentrations can remain condensed in mixed coacervates far beyond their original critical salt concentration. Our results show that NTP-based coacervates have a strong temperature sensitivity due to base stacking interactions and that mixing NTPs can significantly influence the stability of condensates and, by extension, their bioavailability.

Binding Dynamics of siRNA with Selected Lipopeptides: A Computer-Aided Study of the Effect of Lipopeptides' Functional Groups and Stereoisomerism.

The engineering issues pertaining to nanoparticle systems toward targeted gene therapies have not been fully probed. Recent experiments have identified specific structural characteristics of a novel class of lipopeptides (LP) that may lead to potent nanocarriers intended as RNAi therapeutics, albeit the molecular mechanism that underlies their performance remains unexplored. We conducted molecular dynamics simulations in atomistic detail coupled with free energy computations to study the dynamics and thermodynamics of an acrylate- and an epoxide-derived LP, members of the aforesaid class, upon their binding to siRNA in aqueous solution aiming at examining structure-potency relations. We found that the entropic part of the free energy of binding predominates; moreover, the first LP class tends to disrupt the Watson-Crick base pairing of siRNA, whereas the latter leaves the double helix intact. Moreover, the identified tug-of-war effect between LP-water and LP-siRNA hydrogen bonding in the supramolecular complex can underpin synthesis routes toward tuning the association dynamics. Our simulations on two diastereomers of the epoxide-derived LP showed significant structural and energetics differences upon binding, as a result of steric effects imposed by the different absolute configurations at their chiral centers. These findings may serve as crucial design parameters toward modulating the interplay between complex stability and ease of releasing the nucleic acid drug into the cell.

Spontaneous translation of nanodroplet over a heterogeneous surface due to thermal cycles: role of solid–liquid interfacial fluctuations

ABSTRACTWe study the molecular-scale features of the solid surface that result in the spontaneous motion of a nanodroplet due to the periodic variation of temperature. We first employ a thermodynamic model to predict the variation of solid–fluid interfacial properties that can result in the above motion. The model identifies a composite (surface couple) made of two surfaces that are characterised by a large difference between the entropic parts of the solid–liquid interfacial free energies. In order to understand the molecular-scale features of the two surfaces that may form a surface couple, we performed grand canonical Monte Carlo simulations of Lennard Jones fluid and crystalline surfaces made of Lennard Jones-like atoms. We then used the cumulant expansions of the perturbation formulas to divide the interfacial entropy into two parts: The one that is directly affected by the solid–fluid attraction (direct part), and the other (indirect part) that is indirectly affected by the solid–fluid attraction via the alteration of interfacial fluctuations. Our results indicate that two surfaces form a surface couple if the differences between their chemical natures lead to large differences in the indirect part of the interfacial entropy, while the direct part remains relatively unaffected.

Recompression of JPEG Crypto-Compressed Images Without a Key

The rising popularity of social networks and cloud computing has greatly increased a number of JPEG compressed image exchanges. In this context, the security of the transmission channel and/or the cloud storage can be susceptible to privacy leaks. The selective encryption is an efficient tool to mask the image content and to protect confidentiality while remaining format-compliant. However, image processing in the encrypted domain is not a trivial task. In this paper, we present a JPEG crypto-compression method which allows us to recompress a JPEG crypto-compressed image several times, without any information about the secret key or the original image content. Indeed, using the proposed method in this paper, each recompression can be done directly on the JPEG bitstream by removing the last bit of the code representation of each non-zero coefficient, adapting the entropic code part, and slightly modifying the quantization table. This method is efficient to recompress JPEG crypto-compressed images in terms of compression ratio. Moreover, the decryption of the recompressed image produces an image with a very similar visual quality when compared to the original image, according to the obtained results.

Dispersion Interactions and the Stability of Amine Dimers.

Weak, intermolecular interactions in amine dimers were studied by using the combination of a dispersionless density functional and a function that describes the dispersion contribution to the interaction energy. The validity of this method was shown by comparison of structural and energetic properties with data obtained with a conventional density functional and the coupled cluster method. The stability of amine dimers was shown to depend on the size, the shape, and the relative orientation of the alkyl substituents, and it was shown that the stabilization energy for large substituents is dominated by dispersion interactions. In contrast to traditional chemical explanations that attribute stability and condensed matter properties solely to hydrogen bonding and, thus, to the properties of the atoms forming the hydrogen bridge, we show that without dispersion interactions not even the stability and structure of the ammonia dimer can be correctly described. The stability of amine dimers depends crucially on the interaction between the non‐polar alkyl groups, which is dominated by dispersion interactions. This interaction is also responsible for the energetic part of the free energy interaction used to describe hydrophobic interactions in liquid alkanes. The entropic part has its origin in the high degeneracy of the interaction energy for complexes of alkane molecules, which exist in a great variety of conformers, having their origin in internal rotations of the alkane chains.

Excess molar volumes and viscosity behaviour of binary mixtures of aniline/or N,N-dimethylaniline with imidazolium ionic liquids having triflate or bistriflamide anion

In this study, densities and viscosities of four binary systems {aniline/N,N-dimethylaniline+1-butyl-3-methylimidazolium triflate ([bmim][OTf])} and {aniline/N,N-dimethylaniline+1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([bmim][NTf2])} were measured at atmospheric pressure and within the temperature range T=(288.15 to 333.15)K. Excess molar volumes VE, viscosity deviations Δη and excess molar Gibbs energies of activation of viscous flow ∆G∗E were calculated and the results were fitted to a Redlich-Kister polynomial equation. Also, enthalpic and entropic parts of the ∆G∗E function were determined, at the same composition, for three studied systems that exhibit complete miscibility, since {aniline+[bmim][OTf]} is a partially miscible system. Considering the calculated thermodynamic properties, molecular interactions in the investigated binary systems were analysed and are discussed.

Amination of Five Families of Room-Temperature Ionic Liquids: Computational Thermodynamics and Vibrational Spectroscopy

The amino group is important to enhance carbon dioxide capture capabilities of substances, including room-temperature ionic liquids (RTILs). We report thermodynamics of amination for five organic cations representing different families of RTILs (imidazolium, pyridinium, morpholinium, pyrrolidinium, pyrazolium) and compare all prospective amination sites. We conclude that amination of the cation ring is more favorable than amination of the side chains. Redistribution of electron density due to amination partially correlates with variation of enthalpy and Gibbs free energy, whereas entropic part is similar for all cations and all amination sites. Vibrational frequencies allow for easy distinguishing amination products from reactants and simplify identification of the reaction site (ring or side chain). Formation of strong hydrogen bonds between the amino group and the anions greatly favors amination of RTILs, compared to amination of benzene.

Analysis of the end-segment distribution of a polymer at the interface of filler-filled material

Distribution of end of polymer in the filler-filled material is simulated using self-consistent field method. In our simulation results, the segregation of ends of polymer can be found at the interface of filler, though the depletion region of ends is also existed around the region in the distance of Rg from filler. Sizes and shape of filler are affected to the segregation of ends of polymer, and in the cases of smaller or spherical fillers, the density of ends of polymer near the interface of filler increases. These results can be explained by the entropic effect of polymer chain ends. The segregation of ends contributes to the stabilization of interface of filler adding the entropic part of free energy.

Self-Assembly of Asymmetrically Interacting ABC Star Triblock Copolymer Melts.

The phase behavior of asymmetrically interacting ABC star triblock copolymer melts is investigated by the self-consistent field theory (SCFT). Motivated by the experimental systems, in this study, we focus on the systems in which the Flory-Huggins interaction parameters satisfy χAC > χ BC ≈ χAB. Using various initialization strategies, a large number of periodic structures have been obtained in our calculations. A fourth-order pseudospectral algorithm combined with Anderson mixing method is used to compute the free energy of candidate structures carefully. The stability has been analyzed in detail by splitting the free energy into internal and entropic parts. A complete and complex triangular phase diagram is presented for a model with χAC > χBC = χAB in which 15 ordered phases, including two- and three-dimensional structures, have been predicted to be stable from the SCFT calculations. Generally speaking, with the asymmetrical interactions, the hierarchical structures tend to be formed near the B-rich corner of the triangular phase diagram. This work broadens the previous theoretical results from equal interaction systems to unequal interaction systems. The predicted phase behavior is in good agreement with experimental observations and previous theoretical results.

SCFT Study of Microphase Separation in Mixed Polymer Brushes Grafted on Cylindrical Surface

We report on microphase separation behaviors of mixed polymer brushes grafted onto an infinitely long cylindri- cal rod by performing polymer self-consistent field theory (SCFT) calculation with "masking" technique. The "masking" technique is especially suitable to deal with systems of confined polymers grafted onto curved surfaces. We have developed a method to solve the morphology of block copolymers confined into complicated topographic surfaces with SCFT. In this paper, this unique technique is extended to solve the SCFT for nanorod grafted by mixed polymer brushes. Furthermore, the use of simple Cartesian grids in a cubic computational cell with periodic boundary conditions makes it possible to solve dif- fusion equations in SCFT by utilizing an efficient and highly accurate pseudo-spectral method involving fast Fourier trans- form. Both parallel rippled phase and ring-shaped phase are predicted. We have investigated the influences of the cylinder radius, grafting density and interaction between the two incompatible grafting polymers on the stability of the two typical phases. Our results show that the system prefers the ring-shaped phase with the increase of the cylinder radius, grafting den- sity and interaction between the two grafting polymers. Phase diagrams involving these parameters are constructed, and we explain the reason of the transition between the parallel rippled phase and ring-shaped phase in terms of the degree of phase segregation. Again, the degree of phase segregation is higher with larger cylinder radius, grafting density and interaction between the two grafting polymers. By comparing the degree of phase segregation and free energy of the parallel rippled and ring-shaped phases at the same condition, we found that the ring-shaped phase favors the entropic part of the free energy while the parallel rippled phase significantly reduces the enthalpy. Therefore, when the degree of phase segregation is low, the free energy of the system is dominated by the enthalpy, leading to the parallel rippled phase; when the degree of phase segregation is high, the free energy of the system is dominated by the entropic part and the ring-shaped phase is stable. We also found that the domain numbers of parallel rippled phase and the period of alternating ring-shaped phase vary with the radius of cylinder. These predictions are expected to be helpful in rational design and fabrication of such novel polymer brushes.

A reconsideration of the thermodynamics of phase‐change switching

AbstractPhase‐change random access memory (PCRAM) holds great promise as a future non‐volatile memory technology. All PCRAM devices have an inextricable relationship with thermodynamics. To make a memory cell crystallize or amorphize by injecting and removing thermal energy as a repetitive memory cycle results in the generation of entropy. In the study and development of PCRAM, the entropic part in the total energy has been neglected in the thermo‐dynamical system. In this paper, we discuss entropic energy losses through simple calculations based on the Sackur–Tetrode equation and compare the results with those obtained by first‐principles computer simulations. In addition, using a structure specific entropy generation model, we verify how much input energy is wasted in phase‐change memory cells fabricated with a Ge2Sb2Te5 alloy‐layer or a simulation optimized [(GeTe)2(Sb2Te3)4]7 multilayer structure. According to a detailed analysis, the entropy derived from application of the Sackur–Tetrode equation is in good agreement with results derived from first‐principles simulations. Our experimental device fabricated using an entropy‐controlled phase‐change design resulted in significant efficiency improvements. Relative to a Ge2Sb2Te5 alloy‐layer device, the new multilayer device exhibited a 82% improvement in energy efficiency for a transition from the high‐ to the low‐resistivity state and with a 64% improvement in efficiency for a transition from the low‐ to the high‐resistivity state. This new entropic‐energy‐loss optimized device was able to return to the high‐resistivity state at approximately the same current as that required for the low‐resistivity state of the alloy device.

Relation between the change in DNA elasticity on ligand binding and the binding energetics

The widespread use of tweezers for measurement of ligand-DNA binding parameters is based on the McGhee-von Hippel treatment of the DNA contour and persistence length as a function of concentration. The McGhee-von Hippel approach contains the basic assumption that the binding constant K is independent of the number of already bound ligands. However, the change in elasticity of DNA on binding affects the entropic part of the Gibbs free energy and, hence, the K value in a concentration-dependent manner, making the whole approach inconsistent. In the present work we show that the energetic effect of DNA stiffening on noncovalent binding of small ligands is negligible with respect to the net energy of reaction, whereas the DNA stiffening on binding of large ligands must always be considered in each particular case.

Entropic part of the boundary energy in a lipid membrane

Two-phase lipid membrane is modeled with lipids of different bending rigidity of hydrophobic tails: domains consist of “rigid” lipid liquid condensed phase and are surrounded by the “flexible” lipid liquid expanded phase. Within the framework of the earlier proposed model of flexible strings, entropic contribution not including mismatch energy is calculated analytically. “Entropic” line tension is found to be weakly dependent on the domain radius. According to the model, it is shown that merely “entropic mismatch” is not enough for the domain formation. In the paper it is assumed that lipids at the boundary, on the average, have larger area than the ones in the volume. This leads to an increase of energy of boundary lipids. Cases of lipids with nearly the same bending rigidities and with strongly different ones are considered. Free energy is calculated using Taylor expansion on the difference of area of lipids at the domain’s boundary and in the volume. Based on the calculated boundary energy domain stability in the finite system is estimated.