A molecular thermodynamic model for random copolymer solutions

A new Helmholtz energy model of mixing for random copolymer solutions based on a close-packed lattice has been developed. The model contains three terms: the contribution of the athermal mixing of polymer chain and solvent, the Helmoltz energy of mixing in a multi-component Ising lattice where the interactions between segments is accounted for, and the contribution of the dissociation of the polymer and the association of monomers. The Guggenheim model, Yang et al.'s model and the sticky-point model of Cummings, Zhou and Stell are used respectively, for the above three contributions. Comparisons between Monte Carlo simulated coexistence curves with those predicted by various theories for random copolymer solutions with various chain lengths, chain compositions and inter-segment interaction parameters show that the agreement between simulations and the predictions of this work is nearly perfect. The model can be used satisfactorily to correlate the liquid–liquid equilibria of practical random copolymer solutions.     

A molecular thermodynamic model for the swelling of thermo-sensitive hydrogels

A new molecular thermodynamic model for describing the swelling behavior of thermo-sensitive hydrogels was developed. The model consists of two terms. One is the contribution of the mixing of hydrogel network and water, which is dependent on the local polymer concentration and the interaction between polymer segment and solvent. A closed packed lattice model for polymer solution developed by Yang et al. was adopted for this term. The other is the elastic contribution derived from the network elasticity, which is dependent on the cross-linking degree of gel network. The elastic Gibbs energy model based on the Gaussian chain model developed by Flory was adopted. The model equation has two parameters. One is an energy parameter ? reflecting the interaction between water and gel network, the other is a size parameter V^* that represents the cross-linking degree of the hydrogel. When the energy parameter ? is expressed as a quadratic of inverse temperature, this model can describe the swelling equilibrium behavior of neutral thermo-sensitive hydrogels quite well. The influences of model parameters were discussed in details. The experimental swelling curves of two kinds of polyacrylamide-based gels were correlated and good agreement was obtained.     

An explicit molecular thermodynamic model for polyelectrolyte solutions

Polyelectrolyte solutions are modeled as linear tangent jointed and charged hard-sphere chains and counterions. Besides coulombic interaction, stickiness between polyions and counterions is taken into account as a short-range non-coulombic perturbation. The solvent is considered as a continuum medium with a certain permittivity. Expressions of thermodynamic properties derived in this work consist of two contributions. The first contribution responsible for the formation of polyion chains from monomers is derived by the statistical association theory that is the same as our previous work. The second contribution accounting for the additional stickiness is obtained by the same method. A molecular thermodynamic model with explicit expressions is then obtained. Thermodynamic properties for polyelectrolyte solutions can be described satisfactorily.     

A molecular model of water based on the lattice gas model

A lattice gas model is used to describe the vapor-liquid state of water molecules. The orientationally directed interaction of the water molecules via their tetrahedral structure and dipole-dipole interaction are considered in the theory, along with the Lennard-Jones contributions to the potential of molecular interaction, which stabilize the system with dipole interaction. We studied how the radius of the molecular interaction potential affects the equilibrium characteristics of the system (the phase separation curves of the vapor-liquid system, and the relationship between the fluid density and the chemical potential value).     

A simple model for multicomponent etching

We consider the situation where a multicomponent solid is etched using one or more acids. Of fundamental interest is the rate of surface etching but when this involves multicomponent surface reactions, it becomes unclear how the overall rate can be estimated. In this paper, we sketch a simple model designed to determine the effective etching rate by means of an atomic scale model of the etching process.     

A redox-driven multicomponent molecular shuttle

A multicomponent [2]rotaxane designed to operate as a molecular shuttle driven by light energy has been constructed, and its properties have been investigated. The system is composed of (1) a light-fueled power station, capable of using the photon energy to create a charge-separated state, and (2) a mechanical switch, capable of utilizing such a photochemically generated driving force to bring about controllable molecular shuttling motions. The light-fueled power station is, in turn, a dyad comprising (i) a pi-electron-accepting fullerene (C60) component and (ii) a light-harvesting porphyrin (P) unit which acts as an electron donor in the excited state. The mechanical switch is a redox-active bistable [2]rotaxane moiety that consists of (i) a tetrathiafulvalene (TTF) unit as an efficient pi-electron-donor station, (ii) a dioxynaphthalene (DNP) unit as a second pi-electron-rich station, and (iii) a tetracationic cyclobis(paraquat-p-phenylene) (CBPQT4+) pi-electron-acceptor cyclophane, which encapsulates the better pi-electron-donating TTF station. Diethylene glycol spacers were conveniently introduced between the electroactive components in the dumbbell-shaped thread to facilitate the template-directed synthesis of the [2]rotaxane. A modular synthetic approach was undertaken for the overall synthesis of this multicomponent bistable [2]rotaxane, beginning with the syntheses of the P-C60 dyad unit and the two-station TTF-DNP-based [2]rotaxane separately, using conventional synthetic methodologies. These two components were finally stitched together by an esterification to afford the target rotaxane. Its structure was characterized by 1H NMR spectroscopy and mass spectrometry as well as by UV-vis-NIR absorption spectroscopy and voltammetry. The observations reflect remarkable electronic interactions between the various units, pointing to the existence of folded conformations in solution. The redox-driven shuttling process of the CBPQT4+ ring between the two competitive electron-rich recognition units, namely, TTF and DNP, was investigated by electrochemistry and spectroelectrochemistry as a means to verify its operational behavior prior to the photophysical studies related to light-driven operation. The oxidation process of the TTF unit is dramatically hampered in the rotaxane, thereby reducing the efficiency of the shuttling motion. These results confirm that, as the structural complexity increases, the overall function of the system no longer depends simply on its "primary" structure but also on higher-level effects which are reminiscent of the secondary and tertiary structures of biomolecules.     

计算离子液体溶液汽液相平衡的分子热力学模型

用平均球近似理论、微扰理论和UNIFAC基团贡献方法分别考虑离子之间的长程静电作用、离子与溶剂之间的中程静电作用以及所有粒子之间的短程作用,本文提出了一种新的分子热力学模型,可用于离子液体溶液中溶剂活度系数的计算.通过对含烷基咪唑磷酸酯类离子液体与水、甲醇或乙醇组成的9个二元体系的饱和蒸汽压数据进行关联,获得了相关的模型参数,即溶剂的分子直径和基团之间的交互作用能参数.溶剂活度系数及饱和蒸汽压的计算结果与实验值的平均偏差为1.40%,符合良好,因此本模型可望用于含离子液体体系汽液相平衡的预测.     

A new model for the molecular conformation in polyoxymethylene crystals

Nonintegral indices are found for the extra meridional reflections in the x-ray diffraction of drawn polyoxymethylene. The index of one of the extra reflections is estimated at 00l: l = 2.830 ± 0.003. A new model for the molecular conformation which accounts for the nonintegral indices is proposed. The new model is a helix with defects at constant intervals along the helix axis. The defect is an unwinding of the helix by 20° around the helix axis. This defect is believed to be characteristic of crystals of helical polymers. The interval between the defects is estimated as 18 monomers. The crystal structure with these defects is consistent with precise measurements of the layer line positions.     

A new model for predicting thermodynamic properties of ternary metallic solution from binary components

A model has been derived to predict thermodynamic properties of ternary metallic systems from those of its three binaries. In the model, the excess Gibbs free energies and the interaction parameter ω₁₂₃ for three components of a ternary are expressed as a simple sum of those of the three sub-binaries, and the mole fractions of the components of the ternary are identical with the sub-binaries. This model is greatly simplified compared with the current symmetrical and asymmetrical models. It is able to overcome some shortcomings of the current models, such as the arrangement of the components in the Gibbs triangle, the conversion of mole fractions between ternary and corresponding binaries, and some necessary processes for optimizing the various parameters of these models. Two ternary systems, Mg–Cu–Ni and Cd–Bi–Pb are recalculated to demonstrate the validity and precision of the present model. The calculated results on the Mg–Cu–Ni system are better than those in the literature. New parameters in the Margules equations expressing the excess Gibbs free energies of three binary systems of the Cd–Bi–Pb ternary system are also given.     

Phase behavior, conformations, thermodynamic properties, and molecular motion of multicomponent paraffin waxes: A Raman spectroscopy study

Variable-temperature (72–20 °C) studies of Raman spectra (3100–800 cm⁻¹) and thermal analysis of multicomponent paraffin wax have been carried out. The disorder–order transition under liquid–solid transition was observed and their temperature ranges were obtained through the S_lateral order parameter as a function of temperature. From 56 to 43 °C, the paraffin undergoes a conformational state transition of non-extended chain state (NECS) to extended chain state (ECS). The enthalpy and entropy change for the transition obtained by van’t Hoff analysis were 214.286 ± 21 kJ/mol and 0.661 ± 0.066 kJ/mol/K, respectively. The enthalpy determined by differential scanning calorimetry (DSC) was 52.165 ± 5.2 kJ/mol, which is smaller than the van’t Hoff enthalpy due to larger effective non-extended chain state. The variation of Raman spectra with decreasing temperature presents the structure evolution and molecular motion during the crystallization of paraffin wax.     

A new parametrizable model of molecular electronic structure

A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set of orthogonalized atom-centered basis functions, the variational equations being solved formally within the minimal basis but the effect of polarization functions being included in the spirit of second-order perturbation theory. It is designed to yield good dipole polarizabilities and improved intermolecular potentials with dispersion terms. The molecular integrals include up to three-center one-electron and two-center two-electron terms, all in simple analytical forms. A method to extract the effective one-electron Hamiltonian of nonlocal-exchange Kohn-Sham theory from the coupled-cluster one-electron density matrix is designed and used to get its matrix representation in a molecule-intrinsic minimal basis as an input to the parametrization procedure--making a direct link to the correlated wavefunction theory. The model has been trained for 15 elements (H, Li-F, Na-Cl, 720 parameters) on a set of 5581 molecules (including ions, transition states, and weakly bound complexes) whose first- and second-order properties were computed by the coupled-cluster theory as a reference, and a good agreement is seen. The model looks promising for the study of large molecular systems, it is believed to be an important step forward from the traditional semiempirical models towards higher accuracy at nearly as low a computational cost.     

A new three-particle-interaction model to predict the thermodynamic properties of different electrolytes

In this study, Guggenheim charging process, which involves the radial Boltzmann distribution, was introduced to develop a new predictive model with three parameters, ion–ion distance parameter, ion–solvent parameter, and solvation parameter. In this model, the ion–ion and ion–solvent molecule interaction are all included in the charging process, and it is independent of the temperature and solvent. This new model was applied to correlate the experimental data from literatures for 208 electrolytes aqueous solution at T = 298.15 K of which the concentration range is wide. The calculated results agreed well with the experimental ones for most electrolytes, especially for the prediction in high ionic strength. The estimation of solvation parameter S also gave that the solvation tendency for cations and anions follow a trend, which is in consistent with results published in literature. Investigations were also been made in calculations for electrolytes solutions at other temperatures and non-aqueous system, which proved this model was also feasible.     

A simple thermodynamic model for quantitatively addressing cooperativity in multicomponent self-assembly processes--Part 2: Extension to multimetallic helicates possessing different binding sites

The extended site-binding model, which explicitly separates intramolecular interactions (i.e., intermetallic and interligand) from the successive binding of metal ions to polytopic receptors, is used for unravelling the self-assembly of trimetallic double-stranded Cu(I) and triple-stranded Eu(III) helicates. A thorough analysis of the available stability constants systematically shows that negatively cooperative processes operate, in strong contrast with previous reports invoking either statistical behaviours or positive cooperativity. Our results also highlight the need for combining successive generations of complexes with common binding units, but with increasing metallic nuclearities, for rationalizing and programming multicomponent supramolecular assemblies.     

A novel self-consistent-field lattice model for block copolymers

We develop a self-consistent-field lattice model for block copolymers and propose a novel and general method to solve the self-consistent-field equations. The approach involves describing the polymer chains in a lattice and employing a two-stage relaxation procedure to evolve a system as rapidly as possible to a free-energy minimum. In order to test the validity of this approach, we use the method to study the microphases of rod-coil diblock copolymers. In addition to the lamellar and cylindrical morphologies, micellar, perforated lamellar, gyroid, and zigzag structures have been identified without any prior assumption of the microphase symmetry. Furthermore, this approach can also give the possible orientation of the rods in different structures.     

A thermodynamic surface model for caesium sorption on bentonite

Caesium sorption on Wyoming bentonite MX-80 has been studied in solutions of NaCl, KCl, MgCl₂, CaCl₂, NaNO₃ and Ca (NO₃)₂ of concentrations varying between 0.025 and 1 mol/L, as well as in a weakly saline (I=0.004 ml/L) and a strongly saline (I=0.46 mol/L) natural groundwater. These experiments have been used to derive a thermodynamic model for the interaction of caesium with the bentonite surface in accordance with a surface chemical model, including acid/base reactions developed recently for montmorillonite. The sorption behaviour of caesium on bentonite can be described, within the experimental and model uncertainties, in terms of a one-site ion exchange model. The ion exchange constant obtained for the reaction NaX+Cs⁺CsX+Na⁺ (where X represents the ion exchange sites on montmorillonite) is log₁₀K⁰_ex=1.6. Impurities in the bentonite, influencing the concentrations of competing cations, such as Na⁺, K⁺, Mg²⁺ and Ca²⁺, have a crucial impact on the sorption of caesium. This impact can be adequately quantified with the present model. The model predictions compare well with sorption data published in the open literature on both Wyoming bentonite MX-80 and other types of bentonite. Distribution coefficients from the literature obtained from both batch and diffusion experiments and varying over four orders of magnitude are reproduced and explained successfully by the model.     

A thermodynamic surface model for caesium sorption on bentonite

Caesium sorption on Wyoming bentonite MX-80 has been studied in solutions of NaCl, KCl, MgCl(2), CaCl(2), NaNO(3) and Ca (NO(3))(2) of concentrations varying between 0.025 and 1 mol/L, as well as in a weakly saline (I=0.004 ml/L) and a strongly saline (I=0.46 mol/L) natural groundwater. These experiments have been used to derive a thermodynamic model for the interaction of caesium with the bentonite surface in accordance with a surface chemical model, including acid/base reactions developed recently for montmorillonite. The sorption behaviour of caesium on bentonite can be described, within the experimental and model uncertainties, in terms of a one-site ion exchange model. The ion exchange constant obtained for the reaction NaX+Cs(+) left arrow over right arrow CsX+Na(+) (where X represents the ion exchange sites on montmorillonite) is log(10) K(0)(ex)=1.6. Impurities in the bentonite, influencing the concentrations of competing cations, such as Na(+), K(+), Mg(2+) and Ca(2+), have a crucial impact on the sorption of caesium. This impact can be adequately quantified with the present model. The model predictions compare well with sorption data published in the open literature on both Wyoming bentonite MX-80 and other types of bentonite. Distribution coefficients from the literature obtained from both batch and diffusion experiments and varying over four orders of magnitude are reproduced and explained successfully by the model.     

Informational thermodynamic model for nanostructures

Nanostructures may be fabricated from metal nanoclusters such as gold or platinum, which are of interest for catalytic and structural characteristics, or from nano forms of carbon allotropes. Here, informational thermodynamic properties such as free energy, enthalpy, and entropy are calculated using a graph network model at T = 298.15 K. We calculate the partition function using Euclidean adjacency matrices from the Hamiltonian and estimated bond energies. The summed atomic displacement from the Kirchhoff index has power law behavior, while the thermodynamic properties exhibit large $N$ logarithmic behavior: however, the data shows structurally related anomalies.