Diffusion in glassy polymers. II

The Fickian diffusion coefficient of methylene chloride in a glassy epoxy polymer is calculated with the use of Crank's model of discontinuous change of D with concentration C. The diffusion constant is obtained as 1.93 × 10^?6 cm²/sec. The swollen layer behind the advancing solvent front is essentially in the rubbery state of the same polymer. The case II swelling by benzene is discussed in terms of a convective transport arising from the partial stress (internal) tensor of the penetrant. The superposition of Fickian and case II diffusion found with mixtures of methylene chloride and benzene is also discussed briefly.     

The index of ideality of correlation: improvement of models for toxicity to algae

Toxicity to algae is important characteristic of substances from ecologic point of view. The CORAL software (http://www.insilico.eu/coral) gives possibility to build up model of toxicity to algae using data on the molecular architecture and experimental toxicity, without additional data on physicochemical and/or biochemical parameters. Considerable improvement of the model is observed in the case of using the index of ideality of correlation (IIC) in the role of additional criterion of predictive potential. The IIC is calculated with using of the correlation coefficient between experimental and calculated values of endpoint for the calibration set, with taking into account the positive and negative dispersions between experimental and calculated values. The best model calculated with use the IIC is characterized (the validation set) by n?=?50, r²?=?0.947, RMSE?=?0.401 whereas, model calculated without use the IIC is characterized by n?=?50, r²?=?0.805, and RMSE?=?0.539. The suggested models are built up in accordance to five OECD principles.

     

A model for methanol transport through Nafion membrane in diffusion cell

The transport of methanol through Nafion^® membrane in diffusion cell is investigated using the open circuit potential method at different initial methanol concentration solutions. A simple mathematical model based on quasi-steady-state diffusion for the transport of methanol across the membrane in a diffusion cell is developed to simulate the experimental data in order to measure the methanol permeability. The influence of the diffusion cell parameters and thickness of the membrane on the methanol permeability measurement has been evaluated and analyzed. By means of Maclaurin expansion technique, this model can be used to predict the deviation of methanol permeability determined by steady-state diffusion model.     

SDS-Based Biomembrane Mimetic Chromatography for Prediction of Human Drug Transport as an in Vitro Technique

The main oral drug absorption barriers are fluid cell membranes, and generally drugs are absorbed by a passive diffusion mechanism. On the other hand, the blood–brain barrier (BBB) is considered to be the main barrier to drug transport into the central nervous system (CNS). The BBB restricts the passive diffusion of many drugs from blood to brain. Biopartitioning micellar chromatography (BMC), a mode of micellar liquid chromatography that uses micellar mobile phases in adequate experimental conditions, can be useful as an in vitro system in mimicking the drug partitioning process into biological systems. In this study, relationships between the BMC retention data of a heterogeneous set of 12 drugs and their pharmacokinetics parameters (human oral drug absorption and BBB penetration ability) are studied and the predictive ability of the models is evaluated. Modeling of log k _BMC of these compounds was established by multiple linear regression in two different concentrations (0.07 and 0.09 M) of sodium dodecyl sulfate (SDS). The results showed a fair correlation between human oral drug absorption and BMC retention data in 0.09 M SDS (R ² = 0.864) and a good correlation between the blood–brain distribution coefficient and BMC retention data in 0.07 M of SDS (R ² = 0.887). Application of the developed models to a prediction set demonstrated that the model is also reliable with good predictive accuracy. The external and internal validation results showed that the predicted values are in good agreement with the experimental value.

     

Polarizable empirical force field for nitrogen‐containing heteroaromatic compounds based on the classical Drude oscillator

The polarizable empirical CHARMM force field based on the classical Drude oscillator has been extended to the nitrogen‐containing heteroaromatic compounds pyridine, pyrimidine, pyrrole, imidazole, indole, and purine. Initial parameters for the six‐membered rings were based on benzene with nonbond parameter optimization focused on the nitrogen atoms and adjacent carbons and attached hydrogens. In the case of five‐member rings, parameters were first developed for imidazole and transferred to pyrrole. Optimization of all parameters was performed against an extensive set of quantum mechanical and experimental data. Ab initio data were used for the determination of initial electrostatic parameters, the vibrational analysis, and in the optimization of the relative magnitudes of the Lennard‐Jones (LJ) parameters, through computations of the interactions of dimers of model compounds, model compound‐water interactions, and interactions of rare gases with model compounds. The absolute values of the LJ parameters were determined targeting experimental heats of vaporization, molecular volumes, heats of sublimation, crystal lattice parameters, and free energies of hydration. Final scaling of the polarizabilities from the gas‐phase values by 0.85 was determined by reproduction of the dielectric constants of pyridine and pyrrole. The developed parameter set was extensively validated against additional experimental data such as diffusion constants, heat capacities, and isothermal compressibilities, including data as a function of temperature. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Removal of thorium from aqueous solutions by sodium clinoptilolite

Adsorptive behavior of natural clinoptilolite was assessed for removal of thorium from aqueous solutions. Natural zeolite was characterized by X-ray diffraction and X-ray fluorescence. The zeolite sample composed mainly of clinoptilolite. Na-exchanged form of zeolite was prepared and its sorption capacity for removal of thorium from aqueous solutions was examined. The effects of relevant parameters, including initial concentration, contact time, solid to liquid ratio, temperature and initial pH on the removal efficiency were investigated in batch studies. The pH strongly influenced thorium adsorption capacity and maximal capacity was obtained at pH 4.0. Kinetics and isotherm of adsorption were also studied. The pseudo-first-order, pseudo-second-order, Elovich and intra-particle diffusion models were used to describe the kinetic data. The pseudo-second-order kinetic model provided excellent kinetic data fitting (R ² > 0.999) with rate constant of 1.25, 1.37 and 1.44 g mmol⁻¹ min⁻¹ respectively for 25, 40 and 55 °C. The Langmuir and Freundlich models were applied to describe the equilibrium isotherms for thorium uptake and the Langmuir model agrees very well with experimental data. Thermodynamic parameters were determined and are discussed.     

Effect of microheterogeneities on the diffusion of gases through glassy polymers

The diffusion of gases through glassy polymers is studied and the effective diffusion coefficient D^eff is represented as the result of the superposition of two fundamental mechanisms, namely slipping and hopping. D^eff is calculated by a two-point correlation method. Comparisons are made with experimental data of Meares for diffusion coefficients of Kr, O₂, He, and A in poly(vinyl acetate) in the glassy state. Good fits are obtained and yield significant parameters.     

Contribution of concentration-dependent surface diffusion in ternary adsorption kinetics of ethane, propane and n-butane in activated carbon

The role of concentration-dependent surface diffusion in the adsorption kinetics of a multicomponent system is investigated in this paper. Ethane, propane and n-butane are selected as the model adsorbates and Ajax activated carbon as the model adsorbent. Adsorption equilibrium isotherm and dynamic parameters extracted from single-component systems are used to predict the ternary adsorption equilibria and kinetics. The effect of concentration-dependent surface diffusion on the adsorption kinetics predictions is studied by comparing the results of two mathematical models with the experimental data. Three diffusion mechanisms, macropore, surface and micropore diffusions are incorporated in both models. The distinction between these two models is the use of the chemical potential gradient as the driving force for the diffusion of the adsorbed species in one model and the concentration gradient in the other. It was found that the model using the chemical potential gradient provides a better prediction of the ternary adsorption kinetics data, suggesting the importance of the concentration dependency of the surface diffusion, which is implicitly reflected in the chemical potential gradient. The kinetic model predictions are also affected by the way how single-component adsorption equilibrium isotherm data are fitted.     

Electrochemical Behavior of Partially-Discharged Li x V2O5 Electrodes upon Interruption of Current

A mathematical diffusion model, which takes into account the electrochemical behavior of partially-discharged thin-layer electrodes made of intercalation materials upon interruption of circuit, is put forward. The applicability of the model is tested by the example of Li _x V₂O₅ films. According to theoretical calculations and experimental data, the equilibrium potential of the films studied depends practically linearly on the degree of intercalation with a slope of –0.8 V for intercalation degrees of 0.3–0.7. The chemical diffusion coefficient of lithium in the films is equal to 1.5 × 10^–11 cm²/s and changes insignificantly at these intercalation degrees.     

ESR and fluorescence studies of Mn-doped Na2ZnP2O7 single crystal and glasses

X-band electron spin resonance (ESR) spectra and fluorescence measurements were performed on Mn-doped Na₂ZnP₂O₇ (NZPO) single crystal synthesized by the Czochralski pulling method and glasses synthesized by the quenching process. For the single crystal, ESR angular dependences were measured in both the zx and xy plans of the NZPO lattice. The fine and hyperfine structure parameters and g-factor values were determined by modelling the experimental spectra. Using the Newman superposition model, the resonating centres in the single crystal and powder (crushed from crystals) samples are assigned to Mn²⁺ ions substituting for both zinc and sodium. For the glass sample the analysis of the ESR data shows that Mn²⁺ ions substitute for the Na⁺ ions. These interpretations are confirmed by the fluorescence measurements with a unique broad red band for the glassy compound and the presence of two emission bands (green and red) in the case of the crystal sample.     

On the diffusion of gases in partially crystalline polymers

The diffusion of gases through partially crystalline polymers is studied. The effective diffusion coefficient D^eff is obtained as the result of the averaged superposition of two fundamental mechanisms, namely, diffusion through the crystallites is considered to be zero, and diffusion through the rubbery fraction of the polymer obeys a Fujita-like free-volume theory. The predicted D^eff is compared with experimental data of Kreituss and Frisch. The behavior of the diffusion coefficient in terms of concentration and crystalline fraction is satisfactorily explained through the model.     

Density Functional Theory calculations on the magnetic properties of the model tyrosine radical-histidine complex mimicking tyrosyl radical Y<Subscript>D</Subscript><Superscript>·</Superscript> in photosystem II

Results of Density Functional Theory (DFT) theoretical investigations, which use a model tyrosyl (Tyr) radical and tyrosyl-histidine (Tyr-His) complex to mimick the Y _D ^· radical in Photosystem II (PSII) are presented and compared to experimental results from ¹⁵N Electron-Nuclear Double Resonance spectroscopy (ENDOR) studies of the τ nitrogen coupling from His-189 in the PSII Tyr-His complex. The DFT calculations are performed using an optimized geometry of the tyrosine radical and Tyr-His complex. The conformational space of the Tyr-His tandem is explored by varying the relative geometry of the two components; relevant parameters, such as the spin distribution on the phenoxy-ring carbons of the Tyr radical and the EPR hyperfine tensors, are calculated at each geometry and compared with the available experimental data. The isotropic ¹⁵N-ENDOR signal arising from spin delocalization on the His hydrogen-bonded to the PSII tyrosine radical is analyzed in terms of the DFT obtained parameters. The calculations of the g tensor using the Gauge Independent Atomic Orbital (GIAO) approach are presented and the influence of the geometry of the Tyr-His complex on the deviation of the g-tensor elements from the free electron values is discussed.     

One-dimensional models of polymer dynamics. I. Dashpot-spring models applied to a single rotor

The proposion of Clark and Zimm that a dashpot and a spring can be used in place of a set of rotational barriers in polymer dynamics is studied. The simplest possible case is examined here, that of a single rotor. Reasons for altering the Clark–Zimm diffusion equation are presented and an alternative diffusion equation is proposed. The results of both diffusion equations for the correlation function 〈exp[?iθ(0)] exp[iθ(t)]〉 (θ is the angular position of the rotor) are compared with the correlation function for a rotor in an n-fold cosine potential. Although the two diffusion equations differ, both agree well with the n-fold cosine model for barriers above a few k_BT. This agreement is obtained in the absence of adjustable parameters, and motivates the application of these two diffusion equations to polymeric systems.     

An analysis of the EPR spectral parameters and the electronic state of the low-symmetry complexes of 67Zn+, 111Cd+, and 205Tl2+ns1 ions in crystals with the potassium sulfate structure

The electronic structures of the low-symmetry complexes of 4s ¹-⁶⁷Zn⁺, 5s ¹-¹¹¹Cd⁺, and 6s ¹-²⁰⁵Tl²⁺ ions in isostructural crystals of potassium sulfate, rubidium sulfate, and potassium selenate were studied by the EPR data. The sp-mixing of the atomic orbitals of the paramagnetic ion in the molecular orbital of the ground state was established. The parameters of the EPR spectra were analyzed. The sp-mixing was shown to result in negative shifts of the Zeeman interaction parameters. The signs of components of the hyperfine coupling tensor (A tensor) were considered. The determining role of the contribution from the isotropic hyperfine coupling to the components of the A tensor was found. The anomalously low observed values of the hyperfine coupling parameters of the thallium complexes were interpreted.     

Relevance of cage recombination in the plastic deformation of polymers

For a polymer in which permanent rupture of individual molecules is the rate-limiting process for plastic deformation, the kinetics of chain-end diffusion and secondary radical reactions should be compared with the kinetics of caged radical recombination in the calculation of activation parameters for plastic deformation. If mechanisms of cage escape are slower than those for cage recombination, the activation parameters for plastic deformation will differ from those for the initial bond-breaking process. For the case of polyethylene deformed in the vicinity of 250°K, the critical thermally activated event appears to involve scission of the polymer molecule near the site of an abstracted hydrogen atom. For this system the dominant cage-escape mechanism is diffusion, which is faster than either hydrogen abstraction or unzipping to the monomer. However, at low stresses the rate of cage recombination is expected to be higher than the rate of cage escape, so that the activation parameters for deformation should be the sum of those for chain scission and diffusion. The contribution of diffusion (ca. 15 kcal/mole) to the activation energy for deformation (E^*, extrapolated to zero stress conditions) is relatively modest. However, the calculated molar activation volume for deformation V^* increases by almost an order of magnitude, i.e., from ca. 10 to ca. 76 cm³/mole when diffusion is required. Consideration of experimental values of E^* and V^* for high molecular weight polyethylene indicates that, in the regime examined, chain scission plus chain-end diffusion is required to effect plastic deformation.     

Theoretical calculations of hypersurfaces of the C chemical shift anisotropy in the COHN hydrogen bond and the benefit for the ab initio structure determination

We investigated the influence of structural changes on the anisotropic part of the carbonyl ¹³C chemical shift tensor in a model complex containing hydrogen bonded cyanuric acid and pyrrole. The model was chosen for its chemical resemblance to cyameluric acid. In the solid state this compound comprises three different hydrogen bonds which are well distinguishable based on the anisotropy parameters δ_aniso and η of the carbonyl ¹³C atoms. The variation of six relevant structural variables in the model system produced hypersurfaces for the isotropic shift, δ_aniso and η. Our goal was to investigate whether such surfaces can be used for the ab initio structure determination of hydrogen bonds. With a medium size basis set it could be shown that although the absolute values differ DFT describes the relative change in δ_aniso and η close to the quality of MP2 calculations. Due to the high dimensionality of the hypersurface we had to reduce the number of variables in our study. We systematically created subsurfaces each described by three of the six variables and investigated their isolated influence on the NMR observables. We identified the most important structure parameters and on this base built a minimal model. For a fixed NO distance the hydrogen bond arrangement was altered by two angular variations and one dihedral distortion. In this model evidence was found that the η surfaces for different NO distances exhibit a uniform shape and can be transformed into one another by a simple shift and multiplication by a mean factor. Furthermore, the experimental parameters δ_aniso and η of cyameluric acid were taken as a base for the extraction of structures from the hypersurfaces. δ_aniso and η unequivocally selected ensembles of similar structure and the COHN arrangement in two of the three cyameluric hydrogen bonds could be predicted with good quality from the theoretical model. Our results show that it is possible to predict the distance and at least qualitatively the orientation in a hydrogen bond environment from an analysis of the anisotropic part of the ¹³C chemical shift tensor.     

Density Functional Theory Calculations of 95Mo NMR Parameters in Solid‐State Compounds

The application of periodic density functional theory‐based methods to the calculation of ⁹⁵Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid‐state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented‐wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for ⁹⁵Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge‐including projector augmented‐wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition‐metal nucleus. The effects of ultra‐soft pseudo‐potential parameters, exchange‐correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.     

Reactions of photogenerated fluorine atoms with contaminant molecules trapped in solid argon 5. EPR spectroscopy of FC<Subscript>60</Subscript> · radical in solid argon

Reactions of photogenerated fluorine atoms with C₆₀ fullerene molecules isolated in solid argon were studied by EPR spectroscopy in the temperature range from 15 to 25 K. Highly resolved anisotropic EPR spectrum of the FC₆₀ ^⋅ radical was obtained for the first time. The spectrum is characterized by low anisotropy of the g-tensor and by axially symmetric HFC tensor on ¹⁹F nuclei. The parameters of the HFC tensor for ¹⁹F magnetic nuclei were determined. The isotropic HFC constant A _iso equals 202.8 MHz and the anisotropic magnetic dipole-dipole interaction constant A _dip equals 51.8 MHz. Quantum chemical calculations of FC₆₀ ^⋅ radical showed that the PBE1/Λ22m method (PBE1 functional and the correlation triple-zeta basis sets augmented with polarization functions on inner atomic shells) provides good agreement between the theoretical magnetic parameters and experimental data. Specific features of the spin density distribution in the FC₆₀ ^⋅ radical are discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 424–428, March, 2007.     

Theoretical and experimental comparison of the colloid stability of two polystyrene latexes with different sign and value of the surface charge

 The purpose of this paper is to apply the classical DLVO theory to explain the colloid stability of two model colloids with similar size and different sign and value of the surface charge. For this comparison the hydrodynamic interaction and the presence of hydration forces (extended DLVO theory) have been taken into account. The experimental stability factor and the experimental doublet rate constant in diffusion conditions were compared with those evaluated theoretically. The mathematical treatment permits an easy evaluation and interpretation of the different adjustable parameters such as the Hamaker constant, diffuse layer potential and the hydration layer thickness. The theoretical and experimental comparison shows that the “extended DLVO theory” only permits to explain the stability curves Log[W]/Log[KBr] in a semiquantitative way by using, for the evaluation of the total interaction potential V _T, a value of the Hamaker constant (A) similar to the classical theoretical one for polystyrene particles dispersed in water. In the case of the anionic latex, it was necessary to admit the presence of a hydration layer of a thickness similar to the radius of the hydrated/dehydrated counterion. On the other hand, by using the experimental doublet rate constant in diffusion conditions, we obtain a lower value of the Hamaker constant (A), but within the range of the A values usually found in previous studies. Received: 8 September 1997 Accepted: 8 January 1998     

Diffusion coefficients and activation energies of diffusion of low molecular weight migrants in Poly(ethylene terephthalate) bottles

Poly(ethylene terephthalate) (PET) is nowadays the packaging material of choice for beverages. Therefore knowledge about the diffusion coefficients at a certain temperature or activation energies of diffusion of potential migrants in the polymer is of interest, especially for the definition of the basic parameter set for migration modelling of PET. In this study, the diffusion coefficients of acetaldehyde, benzene and tetrahydrofuran in PET bottle materials were determined from kinetic migration experiments at four different temperatures. The activation energies for tetrahydrofuran and benzene were determined to be 106.8 kJ mol⁻¹ and 101.4 kJ mol⁻¹, respectively. The activation energy for acetaldehyde is significantly lower (75.7 kJ mol⁻¹) which is due to the lower molecular weight of this molecule compared to benzene and tetrahydrofuran. The results were compared with literature data of diffusion coefficients of other low molecular weight molecules in PET. From the results it is evident that the current migration model with the default modelling parameters for PET does not describe realistically the diffusion coefficients in PET. The migration of small molecules like acetaldehyde will be underestimated whereas higher molecular weight compounds will be overestimated by the current migration model. Whereas the overestimation is useful for compliance evaluation of PET bottles, for more realistic migration calculations, e.g. for exposure estimations, such overestimation is not desirable. Therefore, more accurate modelling parameters should be established. The key parameters for more realistic migration modelling are the activation energies of diffusion in the polymer.