The Viedma Deracemization of Racemic Conglomerate Mixtures as a Paradigm of Spontaneous Mirror Symmetry Breaking in Aggregation and Polymerization

Simulations of a chemical kinetics model, based on the free‐energy relationships of classical primary nucleation theory, show that the deracemization phenomenon in systems of achiral or fast racemizing compounds yielding enantiopure crystals as the more stable solid phase is a true spontaneous mirror symmetry breaking process (SMSB). That is, the achievement of a stationary chiral state is more stable than the racemic one. The model translates the free‐energy relationships determined by the existence of a critical size cluster to a chemical kinetics model, in which the consideration of forward and backward reaction rate constants avoids the misuse of network parameters that violate thermodynamic constraints (microreversibility principle), which would lead to apparent in silico SMSB. The model provides qualitative agreement for deracemizations by mechanical attrition of visible crystals, as well as for those obtained under temperature gradients. The analysis of the effect of the system parameters to obtain a SMSB scenario shows that the network possesses the principal characteristics of SMSB networks: 1) an enantioselective autocatalytic stage, corresponding to the non‐linear kinetics of enantioselective (homochiral) cluster‐to‐cluster growth, and 2) the mutual inhibition step originating in the backward flow of chiral clusters towards smaller achiral clusters, or even to a racemizing monomer. The application of such a SMSB kinetic model to enantioselective polymerizations and to chiral biopolymers is discussed.     

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self‐diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole‐free volume variation above and below the glass‐transition temperature. Solvent mutual‐diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000     

Thermodynamic characterization of polymer‐polymer interfaces

The properties of multiphase polymer blends are determined in part by the nature of the polymer‐polymer interface. The interfacial tension, γ, influences morphology development during melt mixing while interfacial thickness, λ, is related to the adhesion between the phases in the solid blend. A quantitative relation between the thermodynamic interaction energy and these interfacial properties was first proposed in the theory of Helfand and Tagami and has since been correlated with experimental measurements with varying degrees of success. This paper demonstrates that the theory and experiment can be unified for polymer pairs of some technological importance: copolymers of styrene and acrylonitrile (SAN) with poly (2, 6‐dimethyl‐1, 4‐phenylene oxide) (PPO) and with bisphenol‐A polycarbonate (PC). For each pair, the overall interaction energy was calculated using a mean‐field binary interaction model expressed in terms of the interactions between repeat unit pairs extracted from blend phase behavior. Predictions of γ and λ as a function of copolymer composition made by combining the binary interaction model with the Helfand‐Tagami theory compare favorably with experimental measurements.     

Long‐term growth of core‐set curl in poly(ethylene terephthalate) film

Solid polymeric films (plates) commonly exhibit only partial recovery after being subjected to a bending moment for some finite duration. This phenomenon, generally called bending recovery or core‐set, has been described and successfully modeled in past studies using the viscoelastic plate bending theory. In this study, the viscoelastic theory of core‐set curl was extended to account for physical aging effects during the bending recovery test. The contribution of physical aging was incorporated into the model through the effective time theory and assuming a thermorheologically simple behavior. The model was tested against long‐term core‐set data for a biaxially oriented poly(ethylene terephthalate) (PET) film under ambient conditions and was then used to map the effect of sample age on the evolution of core‐set curl over long times. The predictions of the model agreed favorably with the data, and the results underscored the strong retarding effect of physical aging on the rate of acquisition of core‐set curl in PET film at ambient temperature. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1957–1967, 2001     

Shear‐induced Apparent Shift of Phase Boundary of Binary Polymer Blends

Summary: The combined influence of the thermodynamical and hydrodynamic effects of shear was tentatively considered for the first time, in the modeling of the shear‐induced phase behavior of binary polymer blends in this paper. In this model, the original “two‐fluid” model proposed by Onuki 1 , 2 was modified by replacing the quiescent thermodynamical term with the one defined in the frame of extended irreversible thermodynamics (EIT). 3 - 5 The stress term of the polymer blend was determined by using the mixing rule of “Double Reptation” 6 , 7 along with the Graessley's 8 functions to make the model applicable in both linear and weak non‐linear regions. Then the apparent shift of phase boundary of a model blend system was computed by using this theory. It's found that this modified theory can predict both the “miscibility gap” and anisotropical phase separation of the polymer blend, while the two different previous theories, that is the pure thermodynamical one and hydrodynamic one, could only predict one but not both of them. For example, this modified “two‐fluid” model predicts that the miscibility gap can be observable not only in vorticity direction but also in the velocity gradient direction.

The calculated reduced stored energy F_s/RT as a function of Φ_A and the temperature T (shear rate: 0.5 s⁻¹).     

A statistical/collisional approach to rates of bimolecular reactions at low pressure

An expression for the rate constant of gas‐phase bimolecular reactions at low pressure is derived in the framework of collisional theory. The key feature of the proposed model is the calculation of the energy‐dependent rate constant in terms of the collisional cross section and the probability of reaction, expressed as the ratio of the volume in phase space that leads to product over the total volume. The contribution of the internal energy of the reacting fragments is taken into account, as well as the relative translational energy. The resulting formulation is able to account for both negative and positive temperature dependences of the rate constants of neutral and charged species. The dependence of temperature of the bimolecular rate constant is given both for reactions with and without potential energy barriers. The performance of the proposed model is tested against experimental rate constant for three well‐studied reactions by fitting the parameters of the model to experimental data at various temperatures. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 233–242, 2005     

Prediction of yield and long‐term failure of oriented polypropylene: Kinetics and anisotropy

The time‐dependent yield and failure behavior of off‐axis loaded uniaxially oriented polypropylene tape is investigated. The yield and failure behavior is described with an anisotropic viscoplastic model. A viscoplastic flow rule is used with an equivalent stress, based on Hill's anisotropic yield criterion, and the Eyring flow theory combined with a critical equivalent strain definition. This model is based on factorization of the rate and draw ratio dependence and is capable of quantitatively predicting the rate, angle and draw ratio dependence of the yield stress as well as time‐to‐failure in various off‐axis tensile loading conditions characterized solely from the transverse direction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2026–2035, 2009     

A highly efficient hybrid method for calculating the hydration free energy of a protein

We develop a new method for calculating the hydration free energy (HFE) of a protein with any net charge. The polar part of the energetic component in the HFE is expressed as a linear combination of four geometric measures (GMs) of the protein structure and the generalized Born (GB) energy plus a constant. The other constituents in the HFE are expressed as linear combinations of the four GMs. The coefficients (including the constant) in the linear combinations are determined using the three‐dimensional reference interaction site model (3D‐RISM) theory applied to sufficiently many protein structures. Once the coefficients are determined, the HFE and its constituents of any other protein structure are obtained simply by calculating the four GMs and GB energy. Our method and the 3D‐RISM theory give perfectly correlated results. Nevertheless, the computation time required in our method is over four orders of magnitude shorter.     

Single‐pulse pulsed laser polymerization–electron paramagnetic resonance investigations into the termination kinetics of n‐butyl acrylate macromonomers

The termination of model mid‐chain radicals (MCRs), which mimic radicals that occur in acrylate polymerization over a broad range of reaction conditions, has been studied by single‐pulse pulsed laser polymerization (SP‐PLP) in conjunction with electron paramagnetic resonance spectroscopy. The model radicals were generated by initiator‐fragment addition to acrylic macromonomers that were preformed prior to the kinetic experiments, thus enabling separation of termination from the propagation reaction, for these model radicals propagate sparingly, if at all, on the timescale of SP‐PLP experiments. Termination rate coefficients of the MCRs were determined in the temperature range of 0–60°C in acetonitrile and butyl propionate solution as well as in bulk macromonomer over the range of 0–100 °C. Termination rate coefficients slightly below those of the corresponding secondary radicals were deduced, demonstrating the relatively high termination activity of this species, even when undergoing MCR–MCR termination. For chain length of 10, a reduction by a factor of 6 is observed. Unusually high activation energies were found for the termination rate coefficient in these systems, with 35 kJ mol^?1 being determined for bulk macromonomer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Reaction of a low‐molecular‐weight free radical with a flexible polymer chain: Kinetic studies on the OH + poly(N‐vinylpyrrolidone) model

This work addresses the issue of kinetics of diffusion‐controlled reactions of small radicals with macromolecules in solution. Attack of pulse‐generated hydroxyl radicals on poly(N‐vinylpyrrolidone)—PVP—chains of various molecular weight in water was used as the model reaction. Pulse radiolysis with spectrophotometric detection was applied to determine the rate constants by competition kinetics. The rate constant depends both on polymer concentration and on its molecular weight. In dilute solutions, a distinct dependence of the rate constant on the molecular weight is observed. In the studied range of molecular weight, the values of reaction radius, calculated using Smoluchowski equation on the basis of experimental kinetic data, are very close to the radius of gyration of polymer coils. We believe that radius of gyration, as an easily determined parameter, could possibly serve for predicting rate constants of diffusion‐controlled reactions of polymers with low‐molecular‐weight compounds in dilute solutions. With increasing polymer concentration and thus increasing spatial overlap of polymer coils the dependence of the rate constant on the molecular weight fades away, and the rate constant values increase with increasing concentration toward the value determined for low‐molecular‐weight model of PVP. Most steep increase approximately coincides with the hydrodynamic critical concentration of a given PVP sample, reflecting the change in reaction geometry from individual coils to a continuous matrix of interpenetrating chains. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 474–481, 2011     

Geometry of an Isolated Dimer of Imidazole Characterised by Rotational Spectroscopy and Ab Initio Calculations

An isolated, gas‐phase dimer of imidazole is generated through laser vaporisation of a solid rod containing a 1:1 mixture of imidazole and copper in the presence of an argon buffer gas undergoing supersonic expansion. The complex is characterised through broadband rotational spectroscopy and is shown to have a twisted, hydrogen‐bonded geometry. Calculations at the CCSD(T)(F12*)/cc‐pVDZ‐F12 level of theory confirm this to be the lowest‐energy conformer of the imidazole dimer. The distance between the respective centres of mass of the imidazole monomer subunits is determined to be 5.2751(1) Å, and the twist angle γ describing rotation of one monomer with respect to the other about a line connecting the centres of mass of the monomers is determined to be 87.9(4)°. Four out of six intermolecular parameters in the model geometry are precisely determined from the experimental rotational constants and are consistent with results calculated ab initio.     

Coupled‐cluster theory for the polarizable continuum model. III. A response theory for molecules in solution

A coupled‐cluster (CC) response functions theory for molecular solutes described with the framework of the polarizable continuum model (PCM) is presented. The theory is an extension to the dynamical molecular properties of the PCM‐CC analytic derivatives recently proposed for the calculation of static molecular properties (Cammi, Jr Chem Phys 2009, 131, 164104). The theory is presented for linear and quadratic response functions, and the operative expressions of these response functions can accurately account for the nonequilibrium solvation effects. The excitation energies and transition moments of the solvated chromophores have been determined from the linear response functions. Accurate expressions for gradients of excitation energies for the evaluation of the excited state properties have been also discussed. © 2012 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.     

Clarifying and illustrating the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria allophycocyanin within the framework of Förster theory

Within the framework of the Förster theory, the electronic excitation energy transfer pathways in the cyanobacteria allophycocyanin (APC) trimer and hexamer were studied. The associated physical quantities (i.e., excitation energy, oscillator strength, and transition dipole moments) of the phycocyanobilins (PCBs) located in APC were calculated at time‐dependent density functional theory (TDDFT) level of theory. To estimate the influence of protein environment on the preceding calculated physical quantities, the long‐range interactions were approximately considered with the polarizable continuum model at the TDDFT level of theory, and the short‐range interaction caused by surrounding aspartate residue of PCBs were taken into account as well. The shortest energy transfer time calculated in the framework of the Förster model at TDDFT/B3LYP/6–31+G* level of theory are about 0.10 ps in the APC trimer and about 170 ps in the APC monomer, which are in qualitative agreement with the experimental finding that a very fast lifetime of 0.43–0.44 ps in APC trimers, whereas its monomers lacked any corresponding lifetime. These results suggest that the lifetime of 0.43–0.44 ps in the APC trimers determined by Sharkov et al. was most likely attributed to the energy transfer of α¹‐84 ? β³‐84 (0.23 ps), β¹‐84 ? α²‐84 (0.11 ps) or β²‐84 ? α³‐84 (0.10 ps). So far, no experimental or theoretical energy transfer rates between two APC trimmers were reported, our calculations predict that the predominate energy transfer pathway between APC trimers is likely to occur from α³‐84 in one trimer to α⁵‐84 in an adjacent trimer with a rate of 32.51 ps. © 2014 Wiley Periodicals, Inc.     

The equilibrium structure of ferrocene.

The molecular structures of ferrocene in the eclipsed (equilibrium) and staggered (saddle‐point) conformations have been determined by full geometry optimizations at the levels of second‐order Møller–Plesset (MP2) theory, coupled‐cluster singles‐and‐doubles (CCSD) theory, and CCSD theory with a perturbative triples correction [CCSD(T)] in a TZV2P+f basis set. Existing experimental results are reviewed. The agreement between the CCSD(T) results and experiment is in all cases excellent; the calculated structure parameters and the barrier to internal rotation of the ligand rings differ from the most accurate experimental values by less than two estimated standard deviations. The CCSD(T) calculations for single‐configuration‐dominated transition metal complexes such as ferrocene thus appear to have an accuracy comparable to that observed for molecules containing only first‐ and second‐row atoms, and to be of a quality similar to that obtained experimentally. A comparison with previous DFT results indicates that the B3LYP model gives overall the best DFT results, with a deviation of around 2 pm for the metal–carbon distance and smaller errors for the cyclopentadienyl rings.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the C?H Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the CH Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C? H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

Diffusion-controlled reactions in vinyl chloride suspension polymerization

The vinyl chloride suspension polymerization is kinetically modeled with a general approach for the independent calculation of diffusion effects on polymerization reactions. For the initiator decomposition, propagation and termination an apparent rate coefficient is determined, built up from two contributions: the intrinsic rate coefficient and a diffusional contribution. The diffusional contribution is calculated with the Smoluchowski model, the diffusion coefficients being determined from the free volume theory. When applying the free volume theory no adjustable parameters are used. The intrinsic rate coefficients are taken from the literature. Hence, a model without any adjustable parameters is obtained. Calculations show that the glass effect appears only at (very) high conversions. Due to the cage effect the initiator efficiency decreases strongly as soon as the monomer phase has disappeared. The gel effect always occurs in the polymer-rich phase and results in a decrease of the termination rate coefficient at the start of the third stage in the polymerization process. There is a good agreement with experimental results.     

Modeling Diffusion in Foamed Polymer Nanocomposites

Two‐way multicomponent diffusion processes in polymeric nanocomposite foams, where the condensed phase is nanoscopically reinforced with impermeable fillers, are investigated. The diffusion process involves simultaneous outward permeation of the components of the dispersed gas phase and inward diffusion of atmospheric air. The transient variation in thermal conductivity of foam is used as the macroscopic property to track the compositional variations of the dispersed gases due to the diffusion process. In the continuum approach adopted, the unsteady‐state diffusion process is combined with tortuosity theory. The simulations conducted at ambient temperature reveal distinct regimes of diffusion processes in the nanocomposite foams owing to the reduction in the gas‐transport rate induced by nanofillers. Simulations at a higher temperature are also conducted and the predictions are compared with experimentally determined thermal conductivities under accelerated diffusion conditions for polyurethane foams reinforced with clay nanoplatelets of varying individual lamellar dimensions. Intermittent measurements of foam thermal conductivity are performed while the accelerated diffusion proceeded. The predictions under accelerated diffusion conditions show good agreement with experimentally measured thermal conductivities for nanocomposite foams reinforced with low and medium aspect‐ratios fillers. The model shows higher deviations for foams with fillers that have a high aspect ratio.