Rotational Entropy Research Articles

Entropy-favorable adsorption of polymer-grafted nanoparticles at fluid-fluid interfaces.

The adsorption of polymer-grafted nanoparticles at interfaces is a problem of fundamental interest in physics and soft materials. This adsorption behavior is governed by the interplay between interaction potentials and entropic effects. Here, we use molecular dynamics simulations and umbrella sampling methods to study the adsorption behavior of a Janus-like homopolymer-grafted nanoparticle at fluid-fluid interfaces. By calculating the potential of the mean force as the particle moves from fluid A to the interface, the adsorption energy Ea can be obtained. When two homopolymer chains with types A and B are grafted to the opposite poles of the particle, Ea shows a scaling behavior with respect to chain length N: Ea ∝ N0.598. This is determined by the interactions between polymers and fluids. The enthalpy dominates, and the entropy effects mainly come from the rotational entropy loss of the polymer-grafted nanoparticle at interfaces, which disfavors the stabilization of particles at interfaces. When the grafted polymer number m is large, the adsorption energy exhibits a linear dependence on m. While the enthalpy dominates the behavior, the entropy becomes significant at a larger chain length of N = 15, where the configurational entropy of the polymer chains dominates the entropy of the system. The globule-coil transition occurs when polymers move from poor solvents to good solvents, increasing the configurational entropy and favoring the stabilization of particles at interfaces. Our study provides novel insights into the stabilization mechanism of polymer-grafted nanoparticles at interfaces and reveals the stabilization mechanism favored by the configurational entropy of grafted polymer chains.

Generalized rotation sets and rotational entropy for circle maps

In this paper, we consider the generalized rotation set and rotational entropy for circle maps. Let f:S1→S1 be continuous and F be a lifting of f. In [1] a notion of F-rotation set of a point x∈S1 was given when f is homotopic to the identity. We firstly extend this notion, designated ‘generalized rotation set’ ρ(F), to the general continuous map of the circle, not necessarily homotopic to identity. We show that ρ(F) is compact and connected, i.e., a closed interval, and moreover, each of its endpoints is a generalized rotation number of a recurrent point of f. We also consider the generalized rotation set for f on its invariant sets. Secondly, we introduce a notion of generalized rotational entropy hr(f) for f, which follows the definition that Botelho proposed in [3] for the annulus, and then we show that it exactly vanishes.

Modulation of Aβ 16-22 aggregation by glucose.

The self-assembly of amyloid-beta (Aβ) peptides into fibrillar structures in the brain is a signature of Alzheimer's disease. Recent studies have reported correlations between Alzheimer's disease and type-2 diabetes. Structurally, hyperglycemia induces covalent protein crosslinkings by advanced glycation end products (AGE), which can affect the stability of Aβ oligomers. In this work, we leverage physics-based coarse-grained molecular simulations to probe alternate thermodynamic pathways that affect peptide aggregation propensities at varying concentrations of glucose molecules. Similar to previous experimental reports, our simulations show a glucose concentration-dependent increase in Aβ aggregation rates, without changes in the overall secondary structure content. We discovered that glucose molecules prefer partitioning onto the aggregate-water interface at a specific orientation, resulting in a loss of molecular rotational entropy. This effectively hastens the aggregation rates, as peptide self-assembly can reduce the available surface area for peptide-glucose interactions. This work introduces a new thermodynamic-driven pathway, beyond chemical cross-linking, that can modulate Aβ aggregation.

Rotational entropy − a homotopy invariant for torus maps

To connect topological entropy with rotation theory, Botelho [2] introduced the notion of topological rotational entropy for annulus maps which are homotopic to the identity and later Geller and Misiurewicz [5] showed that it indeed vanished. In this paper, we generalize the notion of rotational entropy to any torus map, give its calculation formula and hence show that it is a homotopy invariant. We also introduce a notion of measure-theoretic rotational entropy and show that it is always less than or equal to the rotational entropy.

Rotation sets and rotational entropy for random dynamical systems on the torus

In this paper, we consider the rotation theory for a random dynamical system φ on the m-dimensional torus Tm(m≥1). Here φ is generated by random composition of a collection of continuous maps φω, ω∈Ω, each of which is homotopic to the identity. Let Φω be the fundamental lift of φω,ω∈Ω, and assume that the periodic maps Φω−id,ω∈Ω, are uniformly bounded on Rm. Firstly, the notions of rotation set, pointwise rotation set and measure rotation set for φ are introduced and investigated. It is shown that the rotation set is a random compact and connected set. Secondly, the notion of rotational entropy, which connects the topological entropy and the rotation theory, of φ is introduced. It is shown that the rotational entropy is zero, however, it can be positive, even infinite without the above assumption.

Water-Structure-Specific Entropic Dominance in the Filling of Boron Nitride Nanotubes

The filling of nanometer and sub-nanometer channels/tubes with water governs applications ranging from desalination and filtration to nanoscale energy conversion. Here, we report the most nonintuitive entropy-dominated filling of mildly hydrophilic boron nitride nanotubes (BNNTs) with diameters ranging from 0.85 to 1.69 nm. For all the BNNT sizes, water inside the BNNT is more stable than water in the bulk. The factor dictating the favorable nature of the entropy depends on the specific-BNNT-diameter-dictated structure of the water molecules. For example, for the 0.85 nm BNNT, the rotational entropic component dominates due to the presence of a significant fraction of the dangling water OH bonds that do not participate in hydrogen bonding. The fraction of such dangling OH bonds (the average HBs per molecule) decreases (increases) with an increase in the BNNT diameter, leading to a progressively reduced contribution of the rotational entropy. For the 1 nm BNNT, the translational entropic component dominates due to the enhanced in-plane motion of the water molecules caused by the single-file nature of water molecules spanning a significant radial expanse inside the BNNT. For larger BNNTs, translational entropy decreases with an increase in the BNNT diameter, although it remains the dominant factor governing the entropy-driven filling of BNNTs. This favorable translational entropy for larger BNNTs can be associated with (1) the presence of chain-like regions formed by water in 1.13 nm BNNT and (2) the presence of a high specific water volume and reduced number of HBs per molecule (as compared with bulk water) in 1.27, 1.41, 1.55, and 1.69 nm BNNTs.

Anisotropic Metamagnetic Spin Reorientation and Rotational Magnetocaloric Effect of Single Crystal NdAlGe.

Magnetic anisotropy strongly influences the performance of the magnetocaloric effect. We investigated the magnetocaloric properties of the NdAlGe single crystal with I41md structure. The temperature-dependent magnetization revealed significant anisotropic properties; stable antiferromagnetic transition at TN = 6 K for H//a and meta-magnetic spin reorientation at low temperature (T ≤ 5 K) within an intermediate field (H = 2 T) for H//c. During the metamagnetic spin reorientation, the abrupt change of the magnetic entropy leads to a significant magnetocaloric effect with negative magnetic entropy change (∆SM) by -13.80 J kg-1 K-1 at TC = 5.5 K for H = 5 T along the H//c axis. In addition, the antiferromagnetic state for H//a shows the inverse magnetocaloric effect(I-MCE) by positive entropy change ∆SM = 2.64 J kg-1 K-1 at TN = 6 K for H = 5 T. This giant MCE accompanied by the metamagnetic transition resulted in a significantly large relative cooling power (158 J/kg at H = 5 T) for H//c. The giant MCE and I-MCE can be applied to the rotational magnetocaloric effect (R-MCE) depending on the crystal orientations. NdAlGe exhibits rotational entropy change ∆Sc-a = -12.85 J kg-1 K at Tpeak = 7.5 K, H = 5 T. With comparison to conventional MCE materials, NdAlGe is suggested as promising candidate of R-MCE, which is a novel type of magnetic refrigeration system.

Phase Transition Kinetics of MAPbI3 for Tetragonal-to-Orthorhombic Evolution.

Despite the commonly observed phase-instability-induced photovoltaic degradation of MAPbI3, the phase transition kinetics at the atomic level remains elusive. Herein, by developing a stepwise NEB method, we clarify a nonsynergistic minimum-energy pathway for the tetragonal-to-orthorhombic phase transition. It is kinetically driven by the tilting of PbI6 4- that induces a spontaneous small rotation of adjoining MA+ and ends with stepwise ∼110° reorientations of two nonadjacent MA+ enabled by the cavity expansion. Compared to the common concerted mechanism, this process gives a low barrier of 0.08 eV/unit, demonstrating the easiness of the transition at extremely low temperatures and the importance of rotational entropies in regulating transition at elevated temperatures. With an explicit phase transition mechanism, we explore the structure-induced property response and reveal that introducing even low content of large-sized organic cations could help maintain the quasi-stable low-temperature performance of MAPbI3 solar cells.

Three-dimensional critical behavior and nearly isotropic magnetic entropy change of Cr4PtGa17: A Half-Heusler-type compound with distorted Kagome planes

We performed a systematic investigation on the magnetic properties of the single crystals of Cr4PtGa17, which is a Half-Heusler-type compound with distorted Kagome planes. The measured saturated and effective moments indicate an itinerant nature of the ferromagnetism at around 58 K with a Rhode-Wohlfarth ratio (RWR) equals 1.58 (1.57) for H∕∕ab (H∕∕c). Detailed analysis on critical behavior and the scaled magnetic entropy change verify the ferromagnetic transition at Tc ∼ 58 K is of a second order. Critical exponents are generated to be β = 0.300 ± 0.002 with Tc = 58.2 ± 0.1 K, γ = 1.211 ± 0.015 with Tc = 58.0 ± 0.1 K, and δ = 5.04 ± 0.03 at Tc = 58 K, exhibiting a three-dimensional critical behavior. The magnetic exchange coupling J(r) decreases spatially as J(r) ∼ r−4.86. Furthermore, the magnetic entropy change -ΔSM(T, H) are achieved, which features a maximum close to Tc with -ΔSMmax equals 0.413 (0.405) J kg−1K−1 under H∕∕ab (H∕∕c) with a field change of 5 T. The rotational magnetic entropy change ΔSMR is ∽ 0 J kg−1 K−1 at T > Tc showing an almost isotropic behavior, and is < 0.03 J kg−1K−1 at T < Tc exhibiting very weak anisotropy.

Fingerprints of the Crossing of the Frenkel and Melting Line on the Properties of High-Pressure Supercritical Water.

Using molecular dynamics simulations in combination with the two-phase thermodynamic model, we reveal novel characteristic fingerprints of the crossing of the Frenkel and melting line on the properties of high-pressure water at a near-critical temperature (1.03Tc). The crossing of the Frenkel line at about 1.17 GPa is characterized by a crossover in the rotational and translational entropy ratio Srot/Strans, indicating a change in the coupling between translational and rotational motions which is also reflected in the shape of the rotational density of states. The observed isosbestic points in the translational and rotational density of states are also blue-shifted at density and pressure conditions higher than the ones corresponding to the Frenkel line. The first-order phase transition from a rigid liquid to a face-centered cubic plastic crystal phase at about 8.5 GPa is reflected in the discontinuous changes in the translational and rotational entropy, particularly in the significant increase of the ratio Srot/Strans. A noticeable discontinuous increase of the dielectric constant has also been revealed when crossing this melting line, which is attributed to the different arrangement of the water molecules in the plastic crystal phase. The reorientational dynamics in the plastic crystal phase is faster in comparison with the "rigid" liquid-like phase, but it remains unchanged upon a further pressure increase in the range of 8.5-11 GPa.

Rotational thermodynamic parameters for asymmetric-top molecules: classical vs. quantum approaches and new analytical partition function

We investigated classical and quantum rotational partition functions, rotational energies and rotational entropies for asymmetric-top molecules in a canonical system within a wide range of temperatures under the rigid rotor approximation. We then derived the temperature, , below which classical approach is not valid, and the complex quantum approach is strongly recommended. This temperature certainly increases with the inertia moment of the molecule and follows a power function when rotational partition functions are considered. As for linear-, spherical- and symmetric-top molecules, quantum approach is not needed at all for energetic rotational parameters, whatever the temperature for asymmetric-top molecules. Therefore, there is no real frontier between the classical and quantum approaches when energetic rotational parameters are concerned, though the frontier is naturally a bounded decreasing sequence converging to zero when rotational partition functions are rather concerned. Particularly, classical approach fails describing rotational partition functions for light molecules or molecules at low temperatures. Moreover, all the closed-form expressions proposed in the whole literature fail drastically approaching quantum and exact results for light molecules or molecules at low temperatures. In regard to the importance of partition functions in the evaluation of rate constants for chemical reactions and accurate intensities lines in spectroscopy, we proposed new accurate and simple analytic expression of the rotational partition functions of asymmetric-top molecules, valid at all temperatures.

Optimum anamorphic image generation using image rotation and relative entropy

Optimum anamorphic image generation using image rotation and relative entropy

Giant Rotational Magnetocaloric Effect in Ni(en)(H2O)4·2H2O: Experiment and Theory

An experimental study of the rotational magnetocaloric effect in Ni(en)(H2O)4SO4∙2H2O (en = ethylenediamine) single crystal is presented. The study was carried out at temperatures above 2 K and was associated with adiabatic crystal rotation between the easy plane and hard axis in magnetic fields up to 7 T. The magnetocaloric properties of the studied system were investigated by isothermal magnetization measurement. The experimental observations were completed with ab initio calculations of the anisotropy parameters. A large rotational magnetic entropy change ≈12 Jkg−1K−1 and ≈16.9 Jkg−1K−1 was achieved in 5 T and 7 T, respectively. The present study suggests a possible application of this material in low-temperature refrigeration since the adiabatic rotation of the single crystal in 7 T led to a cooldown of the sample from the initial temperature of 4.2 K down to 0.34 K. Finally, theoretical calculations show that S = 1 Ni(II)-based systems with easy-plane anisotropy can have better rotational magnetocaloric properties than costly materials containing rare-earth elements in their chemical structures.

A Bionic-Homodimerization Strategy for Optimizing Modulators of Protein-Protein Interactions: From Statistical Mechanics Theory to Potential Clinical Translation.

Emerging protein–protein interaction (PPI) modulators have brought out exciting ability as therapeutics in human diseases, but its clinical translation has been greatly hampered by the limited affinity. Inspired by the homodimerize structure of antibody, the homodimerization contributes hugely to generating the optimized affinity is conjectured. Herein, a statistical‐mechanics‐theory‐guided method is established to quantize the affinity of ligands with different topologies through analyzing the change of enthalpy and the loss of translational and rotational entropies. A peptide modulator for p53‐MDM2 termed CPAP is used to homodimerize connecting, and this simple homodimerization can significantly increase the affinity. To realize the cellular internalization and tumor accumulation, DimerCPAP and MonoCPAP are nanoengineered into gold(I)‐CPAP supermolecule by the aurophilic interaction‐driven self‐assembly. Nano‐DimerCPAP potently suppressed tumor growth in lung cancer allograft model and a patient‐derived xenograft model in more action than Nano‐MonoCPAP, while keeping a favorable drug safety profile. This work not only presents a physico‐mechanical method for calculating the affinity of PPI modulators, but also provides a simple yet robust homodimerization strategy to optimize the affinity of PPI modulators.

Origin of Ferroelectricity in Two Prototypical Hybrid Organic-Inorganic Perovskites.

Hybrid organic-inorganic perovskite (HOIP) ferroelectrics are attracting considerable interest because of their high performance, ease of synthesis, and lightweight. However, the intrinsic thermodynamic origins of their ferroelectric transitions remain insufficiently understood. Here, we identify the nature of the ferroelectric phase transitions in displacive [(CH3)2NH2][Mn(N3)3] and order-disorder type [(CH3)2NH2][Mn(HCOO)3] via spatially resolved structural analysis and ab initio lattice dynamics calculations. Our results demonstrate that the vibrational entropy change of the extended perovskite lattice drives the ferroelectric transition in the former and also contributes importantly to that of the latter along with the rotational entropy change of the A-site. This finding not only reveals the delicate atomic dynamics in ferroelectric HOIPs but also highlights that both the local and extended fluctuation of the hybrid perovskite lattice can be manipulated for creating ferroelectricity by taking advantages of their abundant atomic, electronic, and phononic degrees of freedom.

Role of entropy in determining the phase behavior of protein solutions induced by multivalent ions.

Recent experiments have reported lower critical solution temperature (LCST) phase behavior of aqueous solutions of proteins induced by multivalent ions, where the solution phase separates upon heating. This phenomenon is linked to complex hydration effects that result in a net entropy gain upon phase separation. To decipher the underlying molecular mechanism, we use all-atom molecular dynamics simulations along with the two-phase thermodynamic method for entropy calculation. Based on simulations of a single BSA protein in various salt solutions (NaCl, CaCl2, MgCl2, and YCl3) at temperatures (T) ranging 283-323 K, we find that the cation-protein binding affinity increases with T, reflecting its thermodynamic driving force to be entropic in origin. We show that in the cation binding process, many tightly bound water molecules from the solvation shells of a cation and the protein are released to the bulk, resulting in entropy gain. To rationalize the LCST behavior, we calculate the ζ-potential that shows charge inversion of the protein for solutions containing multivalent ions. The ζ-potential increases with T. Performing simulations of two BSA proteins, we demonstrate that the protein-protein binding is mediated by multiple cation bridges and involves similar dehydration effects that cause a large entropy gain which more than compensates for rotational and translational entropy losses of the proteins. Thus, the LCST behavior is entropy-driven, but the associated solvation effects are markedly different from hydrophobic hydration. Our findings have direct implications for tuning the phase behavior of biological and soft-matter systems, e.g., protein condensation and crystallization.

Benchmark ab initio proton affinity and gas-phase basicity of α-alanine based on coupled-cluster theory and statistical mechanics.

We determine the proton affinity (PA) and gas-phase basicity (GB) of amino acid α-alanine at a chemically accurate level by performing explicitly-correlated CCSD(T)-F12b/aug-cc-pVDZ geometry optimizations and normal mode vibrational frequency calculations as well as CCSD(T)-F12b/aug-cc-pVTZ energy computations at the possible neutral and protonated geometries. Temperature effects at 298.15 K considering translational, rotational, and vibrational enthalpy and entropy corrections are obtained via standard statistical mechanics utilizing the molecular geometries and the harmonic vibrational energy levels. Both the amino nitrogen (N) and the carbonyl oxygen (O) atoms are proven to be potential protonation sites and a systematic conformational search reveals 3 N- and 9 O-protonated conformers in the 0.00-7.88 and 25.43-30.43 kcal/mol energy ranges at 0K, respectively. The final computed PA and GB values at (0)298.15 K in case of N-protonation are (214.47)216.80 and 207.07 kcal/mol, respectively, whereas the corresponding values for O-protonation are (189.04)190.63 and 182.31 kcal/mol. The results of the benchmark high-level coupled-cluster computations are utilized to assess the accuracy of several lower-level cost-effective methods such as MP2 and density functional theory with various functionals (SOGGA11-X, M06-2X, PBE0, B3LYP, M06, TPSS).

First-principles calculations of precursor adsorption on substrate during atomic layer deposition: The example of SiO2 deposition using tris(dimethylamino)silane

In this study, we investigate the reaction mechanisms of precursor adsorption during the atomic layer deposition (ALD) using density functional theory (DFT) calculations and ideal-gas methods; herein, we considered adsorption of tris(dimethylamino)silane (TDMAS) on a hydroxylated SiO2 surface to be the example for our investigation. When the reaction free energy is calculated, the DFT results obtained at 0 K suggest that the dissociation of a hydrogen atom from TDMAS is favorable upon TDMAS adsorption, which is inconsistent with the experimental results where one dimethylamino group is released. The experimental results can be accurately predicted when enthalpy and entropy changes are considered at elevated temperatures, thereby indicating the significance of finite-temperature effects in free-energy changes for solid-gas reactions. We analyze the changes in enthalpy and entropy and find that dimethylamine is a more favorable gaseous product than H2 owing to its larger translational and rotational entropy.

Rotational Entropy of an Annular Iterated Functions System

In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.

Molecular dynamics of dissolution of a 36-chain cellulose Iβ microfibril at different temperatures above the critical pressure of water

The cellulose dissolution is an essential pretreatment process for the chemical conversion of lignocellulosic biomass into biofuels. Here, the dissolution of a 36-chain Iβ cellulose model with a hexagonal cross-section (M36HCS) in water is analyzed by Molecular Dynamics (MD) with CHARMM36/TIP3P (C36/TIP3P) force field using gradual heating at 25 MPa. Our simulations showed that the dissolution of M36HCS starts to occur between 560 K and 600 K, which agrees with experimental observations. In our system, conditions near the critical point of water reveal that translational and rotational entropies decrease, while the low hydration level increases vibrational entropy. This investigation theoretically shows that C36/TIP3P adequately reproduces the dissolution of M36HCS even in high-pressure water as corroborated in reactors.