Dynamical derivation of Eyring equation and the second‐order kinetic law

Elementary gas‐phase reactions of the bimolecular type A + B → Products are characterized by the second‐order kinetic law , where [A] and [B] are the concentrations of A and B species, t is the time, and k is the rate constant, usually estimated by means of Eyring equation. Here, we show that its dynamical derivation, as such, is not consistent with the second‐order law. This contradiction is however removed by introducing a correlation between what we call potentially reactive pairs. A new presentation of the dynamical derivation of Eyring equation is finally proposed on the basis of the previous findings. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2355–2359, 2010     

On the relation between positron annihilation lifetime spectroscopy and lattice‐hole‐theory free volume

A coincidence between the temperature‐dependent hole (free volume) fraction h above the glass transition temperature, derived from lattice‐hole theory, and the corresponding function h_Ps obtained from positronium lifetime spectroscopy has been previously observed for four polystyrene fractions ranging from 4000 to 400,000 in molar mass. This result was based on the assumed proportionality of h_Ps and the product of the orthopositronium intensity I₃ and the mean cavity volume, the proportionality constant C being molar mass dependent. However, a recent analysis of the data based on volume arguments by Olson and Jamieson revealed systematic departures between the two sets of free volume functions. We reexamine the situation by departing from the customary assumption of spherical cavities, and allowing for nonspherical geometries represented by prismatic or cylindrical disks. Agreement between spectroscopic and thermodynamic functions ensues with fixed, temperature‐independent asymmetry factors decreasing with increasing molar mass. These tentative findings suggest that systematic studies of melts with varying chain flexibility and molar mass should be attempted. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2225–2229, 2005     

Phase equilibrium and diffusion of solvents in polybutadiene: A capillary‐column inverse gas chromatography study

The capillary‐column inverse gas chromatography method was used to measure the diffusion and partition coefficients of ethylbenzene, styrene, and acrylonitrile in polybutadiene (PBD) at infinite dilution of the solvents. Experiments were performed over a temperature range of 50–125 °C. At temperatures well above the glass‐transition temperature of PBD, the diffusivities were correlated using an Arrhenius expression. The Arrhenius parameters in turn were intercorrelated and shown to be a function of the occupied volume, thus providing a method for predicting the diffusion of other solvents in the same polymer. Further, the activation energy was predicted using the Duda‐Vrentas free‐volume approach. The activation energy thus obtained was compared with the activation energy of the Arrhenius approach. The weight‐fraction activity coefficient data were compared to the predictions of the group contribution, lattice‐fluid equation‐of‐state, and the UNIquac Functional‐group Activity Coefficient (UNIFAC) free‐volume models. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1046–1055, 2002     

Assessing the transport properties of organic penetrants in low‐density polyethylene using free volume models

Three models, two of them relying on free volume—the Cohen–Turnbull–Fujita (CTF) model and the Vrentas–Duda (VD) model, and the third being empirical using an exponential concentration dependence of the diffusivity, were applied to desorption data for a series of alkane penetrants (2,2‐dimethylbutane, cyclohexane, n‐hexane, n‐decane, and n‐tetradecane) in low‐density polyethylene. The CTF model described the desorption data very well and better than the exponential diffusion law. The VD model with the attractive feature of being based on independently determined parameters was unsuccessful in describing the desorption data. Diffusivity data indicated that the three components outside the crystal core were less accessible to n‐tetradecane than to the other penetrants. This indication was further substantiated by solubility data. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 723–734, 2007     

Prediction of solvent diffusion coefficient in amorphous polymers based on an equation‐of‐state

This study develops a modified free‐volume model to predict solvent diffusion coefficients in amorphous polymers by combining the Vrentas–Duda model with the Simha–Somcynsky (S‐S) equation‐of‐state (EOS), and all the original parameters can be used in the modified model. The free volume of the polymer is estimated from the S‐S EOS together with the Williams‐Landel‐Ferry fractional free volume, and the complex process of determining polymer free‐volume parameters in the Vrentas–Duda model and measuring polymer viscoelasticity can be avoided. Moreover, the modified model includes the influence of not only temperature but also pressure on solvent diffusivity. Three common polymers and four solvents are employed to demonstrate the predictions of the modified model. The calculation results are generally consistent with the experimental values. It is reasonable to expect that the modified free‐volume model will become a useful tool in polymer process development. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1000–1009, 2006     

Intramolecular screening effects in nondilute polymer solutions: An equation‐of‐state approach

In a previous article, we presented a simple modification of the traditional Flory–Huggins theory that took intramolecular screening effects (or same chain contacts) into account. In this article, we present a natural extension of that work, in which free‐volume effects are also explained with an equation‐of‐state model. The predictions of the interaction parameter, χ, for several polymer–solvent systems are presented, over the entire concentration range, in θ solvents and good solvents. A geometric mean assumption is applied to the calculation of an exchange energy interaction term. The predictions of χ are successful to various degrees when internal pressures are used, whereas the use of solubility parameters in most cases produces fairly good agreement with experimental results. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2911–2922, 2003     

Constraints and thermal expansion of the free volume in a micro‐phase separated poly(ester‐adipate)urethane

The free volume behavior of a thermoplastic polyesterurethane (TPU) versus temperature is investigated by positron annihilation lifetime spectroscopy and dilatometry. A discrepancy with the free volume predicted by the lattice‐hole theory is found. The agreement is restored by assuming anisotropic expansion of the free volume holes, which in fact results in expansion mainly in two dimensions. This finding is perfectly compatible with a polymer structure based on rheological, thermal, and TEM data which envisage TPU as formed by short soft segments limited in their movements by chain connectivity and confined by physical crosslinks due to the hard segments. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2104–2109     

Effect of thermal history on the free volume properties of semi‐crystalline poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) membranes by positron annihilation lifetime spectroscopy

Free volume properties of a series of poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) (PHBV) membranes, which were produced by various nonisothermal crystallization processes (rapid‐, step‐, and slow‐cooling processes), were investigated using positron annihilation lifetime (PAL) spectroscopy over a temperature range of 25–90 °C. From the annihilation lifetime parameters, the temperature dependence of free volume size, amount, size distribution, and fractional free volume and thermal expansion properties of free volume were discussed. A model which assumed that amorphous phase was subdivided into mobile and rigid amorphous fractions (MAF and RAF) in the semicrystalline polymer was considered to interpret the temperature dependence of those free volume properties. Morphological observation of the semicrystalline polymer by small‐angle X‐ray scattering (SAXS) indicated that the rapid‐cooled (cold‐crystallized) membranes showed a much thinner thickness of the repeating lamellar/amorphous layers and most likely higher amount of RAF, which restrained the chain motion, than the step‐ and slow‐cooled (melt‐crystallized) membranes. The difference of free volume properties among various PHBV membranes was created according to the crystalline structure of the polymer from different thermal history. The polymer crystallized with slower cooling rate induced higher crystallinity and resulted in less free volume amount and lower fractional free volume. In addition, the thermal expansion coefficients of free volume size were affected by the crystallization rate of PHBV polymer. Larger distribution of the free volume size of melt‐crystallized membranes was observed as a result of the bimodal distribution of the lamellar periodicity and less amount of RAF than that of the cold‐crystallized membranes. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 855–865, 2009     

Pressure–volume–temperature of molten and glassy polymers

The pressure–volume–temperature (PVT) dependencies of several amorphous polymers (PS, PC, PPE, and PPE/PS 1:1 blend) in the glassy and molten state were studied. The Simha–Somcynsky (S–S) lattice‐hole equation of state (EOS) was used. Fitting the PVT data in the molten state to the EOS yielded the free volume quantity, h = h(T, P), and the characteristic reducing parameters, P*, V*, and T*. The data within the glassy region were interpreted assuming that the latter parameters are valid in the molten and vitreous state, than calculating h = h(T, P) from the experimental values of V = V(T, P). Next, the frozen free volume fraction in the glass was computed as FF = FF(P). The FF values of polystyrene (PS) resins at ambient pressure showed little scattering (FF_P=1 = 0.691 ± 0.008), while their P‐dependencies varied, reflecting the thermodynamic history of the glass formation as well as the PVT measurements protocol. The pressure gradient of T_g was compared with the Ehrenfest relation for the second‐order transition; here also agreement depended on the method of vitrification. The experimental values of FF at ambient pressure decreased with increasing values of the characteristic temperature reducing parameter, T*. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 270–285, 2007.     

Free volume and water vapor transport properties of temperature‐sensitive polyurethanes

Segmented polyurethanes (PU) with crystalline soft segments were prepared with different crystalline polyols as soft segments. Morphology and microstructure of the PUs were investigated using Differential Scanning Calorimetry (DSC), Wide‐angle X‐ray Diffraction (WAXD), and Positron Annihilation Lifetime Spectra (PALS). Water vapor transport properties of the PU membranes were measured in the temperature range of crystal melting of their soft segments. Dependence of free volume of the PUs on temperature and the relationship between the free volume and water vapor permeability of the PU membranes were investigated. The results show that the mean free volume size and fractional free volume increase more rapidly in the temperature range of crystal melting than in other temperature intervals. In the specified temperature range, water vapor permeability of the polyester based PU membranes increases significantly, caused by the steep increase in free volume, due to crystal melting of the soft segments. Water vapor permeability of the polyester based PUs exhibits approximately direct correlation with the fractional free volume within the temperature range of crystal melting. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1865–1872, 2005     

Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets

Given a set of spherical balls, called atoms, in three‐dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well‐solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta‐decomposition, based on the recent theory of the beta‐complex. Given the beta‐complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta‐complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta‐complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ?³ that m = O(n) on average for biomolecules and m = O(n²) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ?² and extended to ?³. The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site. © 2012 Wiley Periodicals, Inc.     

Tuning the energy level of TAPC: crystal structure and photophysical and electrochemical properties of 4,4′‐(cyclohexane‐1,1‐diyl)bis[N,N‐bis(4‐methoxyphenyl)aniline]

The energy level of a hole‐transporting material (HTM) in organic electronics, such as organic light‐emitting diodes (OLEDs) and perovskite solar cells (PSCs), is important for device efficiency. In this regard, we prepared 4,4′‐(cyclohexane‐1,1‐diyl)bis[N,N‐bis(4‐methoxyphenyl)aniline] ( TAPC‐OMe ), C₄₆H₄₆N₂O₄, to tune the energy level of 4,4′‐(cyclohexane‐1,1‐diyl)bis[N,N‐bis(4‐methylphenyl)aniline] ( TAPC ), which is a well‐known HTM commonly used in OLED applications. A systematic characterization of TAPC‐OMe , including ¹H and ¹³C NMR, elemental analysis, UV–Vis absorption, fluorescence emission, density functional theory (DFT) calculations and single‐crystal X‐ray diffraction, was performed. TAPC‐OMe crystallized in the triclinic space group P, with two molecules in the asymmetric unit. The dihedral angles between the central amine triangular planes and those of the phenyl groups varied from 26.56 (9) to 60.34 (8)° due to the steric hindrance of the central cyclohexyl ring. This arrangement might be induced by weak hydrogen bonds and C—H…π(Ph) interactions in the extended structure. The emission maxima of TAPC‐OMe showed a significant bathochomic shift compared to that of TAPC . A strong dependency of the oxidation potentials on the nature of the electron‐donating ability of substituents was confirmed by comparing oxidation potentials with known Hammett parameters (σ).     

Modeling of the linear viscoelastic behavior of low‐density polyethylene

We predict the linear viscoelastic behavior of low‐density polyethylene from both the molecular‐weight distribution and the individual structure of each species in the sample. The “structure map” of the samples was derived from SEC measurements. This map is a three‐dimensional representation of the seniority distribution, and represents the probability of existence of a segment with seniority i in a molecule of molecular weight M. Moreover, results from the kinetics of the free radical polymerization of polyethylene show that the molecular weight of the segments increases according to their seniority. Finally, tube dilatation was generalized to the case of polydisperse samples. The solvent behavior of the relaxed segments was included through a continuous function of time that describes the instantaneous state of the entanglement network in the sample. The comparison between the theoretical predictions and the experimental data shows a good agreement over the whole experimental frequency range. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43:1973–1985, 2005     

Comparison of PARAFAC and PARALIND in modeling three‐way fluorescence data array with special linear dependences in three modes: a case study in 2‐naphthol

Owing to excited‐state proton transfer in 2‐naphthol solutions, the fluorescence excitation–emission matrices (EEMs) have factors that are highly dependent in three modes. For the first time such EEMs are used to compare the capability of PARALIND (PARAFAC with linear dependence) and conventional PARAFAC in modeling three‐way EEMs having linearly dependent factors in three modes. Two primary conclusions have been drawn. First, the results indicate that a 3‐factor PARAFAC model fit the data better than two PARALIND models (type 1 and 2) in this case while equally well with a specially PARALIND model (type 3); second, a negative core consistency (CC) in the 3‐factor PARAFAC model is reported but the type 3 PARALIND model reports a nearly 100 CC. This work has demonstrated that a properly constrained PARALIND can fit the very special EEMs of 2‐naphthol. The presence of negative CC associated with a perfect PARAFAC model would imply the presence of very special linear dependences in EEMs, which would be used as an “alarm” for the investigators to interpret the data more carefully when dealing with complicated environmental EEMs in the absence of a priori knowledge. Copyright © 2010 John Wiley & Sons, Ltd.     

The general setting for the zero‐flux condition: The lagrangian and zero‐flux conditions that give the heisenberg equation of motion

Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero‐flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, “reasonable”). For any reasonable Lagrangian for the electronic wave function and any two‐component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc.     

ChemInform Abstract: An ab‐initio Study of the Role of Ione Pairs in the Structure and Insulator‐Metal Transition in SnO and PbO

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

An Experimental and Theoretical Investigation into the Diffusion of Olefins in Semi‐Crystalline Polymers: The Influence of Swelling in Polymer‐Penetrant Systems

A comprehensive dynamic diffusion model is developed to calculate the diffusion coefficients of low molecular weight penetrants (i.e., α‐olefins) in semi‐crystalline polyolefins from dynamic sorption measurements. The model also takes into account the extent of polymer swelling on the penetrant diffusion flux, resulting in a moving boundary value problem. The free volume theory is employed to calculate the dependence of the diffusion coefficient on the penetrant concentration. The solubilities and diffusivities of ethylene and propylene in semi‐crystalline high density polyethylene films were measured at different temperatures and pressures, using a Rubotherm® magnetic suspension microbalance operated in series with an optical view cell for the measurement of the degree of polymer swelling. It is shown that model predictions are in excellent agreement with the experimental dynamic measurements on the mass uptake of the sorbed species. Moreover, it is shown that the proposed model can predict correctly the diffusion coefficient of α‐olefins in semi‐crystalline polyolefins.