Showing papers by "Wolfgang Linert published in 2012"

The Law of Mass Action

Abstract: 1 Maxwell - Boltzmann Statitics.- 1.1 Thermodynamics and probab ility. The Boltzmann - Planck theorem.- 1.1.1 The Boltzmann - Planck theorem 5.- 1.2 The Maxwell - Boltzmann distribution law.- 1.2.1 Contin uous Maxwell - Boltzmann distribution.- 1.3 Calculation of most probable and mean values.- 1.4 Indistinguishable molecules. The Gibbs' paradox.- 1.5 Phase volume and the number of quantum states.- 1.6 Quantum statistics.- 1.6.1 Bose - Einstein statistics.- 1.6.2 Ferm i - Dirac statistics.- 1.6.3 Comparison of the three types of statis tics.- 1.6.4 Degenera te ideal gas.- 1.6.5 App lications of Bose - Einstein statistics: black-body radiation.- 1.6.6 Applications of Bose - Einstein statistics: heat capacity of solids.- 2 Ensembles, Partition Functions, and Thermodynamic Functions.- 2.1 Gibbs- approach, or how to avoid molecular interactions.- 2.2 The process of equilibration and increasing entropy.- 2.3 Microcanonical distribution.- 2.4. Canonical distribution.- 2.5 The probability of a macrostate.- 2.6 Thermodynamic functions derived from a canonical distribution.- 2.7 Some molecular partition functions.- 2.7.1 Degeneracy.- 2.7.2 Translational motion.- 2.7.3 Free rotation.- 2.7.4 Vibrational motion: linear harmonic oscillator.- 2.7.5 Total parti tion function of an ideal system.- 2.8 Fluctuations.- 2.9 Conclusions.- 3 The Law of Mass Action for Ideal Systems.- 3.1 The law of mass action, its origin and formal thermodynamic derivation.- 3.2 Statistical formulae for free energy.- 3.3 Statis tical formul ae for ideal sys tems.- 3.4 The law of mass action for ideal gases.- 3.4.1 Conversion to molar concent rations.- 3.4.2 Conversion to mole fractions.- 3.4.3 Standard sta tes and standard free energies of reaction.- 3.5 The law of mass act ion for an ideal crys tal. Spin crossover equilibria.- 3.6 Liquids.- 3.6.1 The law of mass action for an 'ideal liquid'.- 3.7 'Breakdown' of the law of mass action.- 3.8 Conclusions.- 4 Reactions in Imperfect Condensed Systems. Free Volume.- 4.1 Additive volume: a semi-empirical model of repulsive interactions.- 4.1.1 Binary equilibrium in a liquid with repul sive interactions.- 4.1.1 Non-isomolar equilibrium in a liquid with repulsive interactions.- 4.2. Lattice theories of the liquid state.- 4.3 The Lennard-Jones and Devonshir e model.- 4.4 Chemica l equi libria in Lennard-Jones and Devon shire liquids.- 4.5 The non-id eal law of mass action, activities, and standard states.- 4.6 Kinetic law of mass action.- 4.7 Conclusions.- 5 Molecular Interactions.- 5.1 Introduction.- 5.2 Empirical binary potentials.- 5.3 Taking into account nearest, next nearest, and longer range interactions in the conde nsed phase.- 5.4 Frequency of vibrations.- 5.5 The shape of the potential wcll in a cell.- 5.6 Free volume of a Lennard-Jones and Devons hire liquid.- 5.7 Experimental determ ination of parameters of the Lennard-Jones potential.- 5.7.1 Compressibility: thc Born' Lande method.- 5.7.2 Acoustical meas urements: the B.B. Kudryavtsev method.- 5.7.3 Viscosity of gases: the Rayleigh' Chapman method.- 5.8 Conclusions.- 6 Imperfect Gases..- 6.1 Introduction. The Virial Theorem.- 6.2 The Rayleigh equation.- 6.2.1 Virial coefficients: the Lennard-Jones method for the determination of the parameters of a binary potential.- 6.2.2 Free energy der ived from the Rayleigh equation of state.- 6.3 A gas with weak binary interactions: a statistical thermodynamics approach.- 6.4 Van der Waals equation of state.- 6.5 Chemical equilibria in imperfect gases.- 6.5.1 Isomolar equilibria in imperfect gases.- 6.5.2 A non-isomolar reaction in an imperfect gas.- 6.5.3 Separate conditions of ideal behaviour for attractive and repul sive molecular interactions.- 6.5.4 Associat ive equilibria in the gaseous phase.- 6.5.5 Mole cular interaction via a chemical reaction.- 6.6 Conclusions.- 7 Reactions in Imperferct Condensed Systems. Lattice Energy.- 7.1 Exchange energy 203.- 7.2 Non-ideality as a result of dependence of the partition function on the nature of the surroundings.- 7.3 Exchange free energy.- 7.4 Phase separations in binary mixtures.- 7.5 The law of mass action for an imperfect mixture in the condensed state.- 7.6 The regular solut ion model of steep spin crossover.- 7.7 Heat capacity changes in spin crossover.- 7.8 Negative exchange energy. Ordering . The Bragg - approach, or how to avoid molecular interactions.- 2.2 The process of equilibration and increasing entropy.- 2.3 Microcanonical distribution.- 2.4. Canonical distribution.- 2.5 The probability of a macrostate.- 2.6 Thermodynamic functions derived from a canonical distribution.- 2.7 Some molecular partition functions.- 2.7.1 Degeneracy.- 2.7.2 Translational motion.- 2.7.3 Free rotation.- 2.7.4 Vibrational motion: linear harmonic oscillator.- 2.7.5 Total parti tion function of an ideal system.- 2.8 Fluctuations.- 2.9 Conclusions.- 3 The Law of Mass Action for Ideal Systems.- 3.1 The law of mass action, its origin and formal thermodynamic derivation.- 3.2 Statistical formulae for free energy.- 3.3 Statis tical formul ae for ideal sys tems.- 3.4 The law of mass action for ideal gases.- 3.4.1 Conversion to molar concent rations.- 3.4.2 Conversion to mole fractions.- 3.4.3 Standard sta tes and standard free energies of reaction.- 3.5 The law of mass act ion for an ideal crys tal. Spin crossover equilibria.- 3.6 Liquids.- 3.6.1 The law of mass action for an 'ideal liquid'.- 3.7 'Breakdown' of the law of mass action.- 3.8 Conclusions.- 4 Reactions in Imperfect Condensed Systems. Free Volume.- 4.1 Additive volume: a semi-empirical model of repulsive interactions.- 4.1.1 Binary equilibrium in a liquid with repul sive interactions.- 4.1.1 Non-isomolar equilibrium in a liquid with repulsive interactions.- 4.2. Lattice theories of the liquid state.- 4.3 The Lennard-Jones and Devonshir e model.- 4.4 Chemica l equi libria in Lennard-Jones and Devon shire liquids.- 4.5 The non-id eal law of mass action, activities, and standard states.- 4.6 Kinetic law of mass action.- 4.7 Conclusions.- 5 Molecular Interactions.- 5.1 Introduction.- 5.2 Empirical binary potentials.- 5.3 Taking into account nearest, next nearest, and longer range interactions in the conde nsed phase.- 5.4 Frequency of vibrations.- 5.5 The shape of the potential wcll in a cell.- 5.6 Free volume of a Lennard-Jones and Devons hire liquid.- 5.7 Experimental determ ination of parameters of the Lennard-Jones potential.- 5.7.1 Compressibility: thc Born' Lande method.- 5.7.2 Acoustical meas urements: the B.B. Kudryavtsev method.- 5.7.3 Viscosity of gases: the Rayleigh' Chapman method.- 5.8 Conclusions.- 6 Imperfect Gases..- 6.1 Introduction. The Virial Theorem.- 6.2 The Rayleigh equation.- 6.2.1 Virial coefficients: the Lennard-Jones method for the determination of the parameters of a binary potential.- 6.2.2 Free energy der ived from the Rayleigh equation of state.- 6.3 A gas with weak binary interactions: a statistical thermodynamics approach.- 6.4 Van der Waals equation of state.- 6.5 Chemical equilibria in imperfect gases.- 6.5.1 Isomolar equilibria in imperfect gases.- 6.5.2 A non-isomolar reaction in an imperfect gas.- 6.5.3 Separate conditions of ideal behaviour for attractive and repul sive molecular interactions.- 6.5.4 Associat ive equilibria in the gaseous phase.- 6.5.5 Mole cular interaction via a chemical reaction.- 6.6 Conclusions.- 7 Reactions in Imperferct Condensed Systems. Lattice Energy.- 7.1 Exchange energy 203.- 7.2 Non-ideality as a result of dependence of the partition function on the nature of the surroundings.- 7.3 Exchange free energy.- 7.4 Phase separations in binary mixtures.- 7.5 The law of mass action for an imperfect mixture in the condensed state.- 7.6 The regular solut ion model of steep spin crossover.- 7.7 Heat capacity changes in spin crossover.- 7.8 Negative exchange energy. Ordering . The Bragg - Williams approximation.- 7.9. Description of order ing taking into account triple interactions.- 7.10 Chemica l equilibrium in ordered systems. Two-step spin crossover.- 7.11 Diluted systems.- 7.12 Conclusions.- 8 Chemical Correlations.- 8.1 Studies of variations of chemical reactivity.- 8.1.1 Molecular parameters governing variations of chemical reactivity.- 8.1.2. Solvent effects.- 8.1.3. Kinetic studies.- 8.1.4. Multidimensionality of var iations. Reference reactions.- 8.2 Linear free energy relationship. Modification of reactants.- 8.3 Linear free energy relationship. Variation of solvent.- 8.4 Isoequilibrium and isokinetic relationships.- 8.4.1 Statistical-mechanical model of the IER in ideal systems.- 8.4.2 The IER in gas-phase reactions.- 8.4.3 lsokinetic relationships.- 8.4.4 Non-ideality as a source of an IER.- 8.4.5 lER and exchange energy.- 8.5 Conclusions.- 9 Concluding Remarks.- 10 Appendices.- 10.1 Lagrange equations and Hamilt on (canonical) equations.- 10.2 Phase space.- 10.2.1 The phase space of a harmonic oscillator.- 10.2.2 The phase space of an ideal gas.- 10.3 Derivation of the canonical distribution.- 10.4 Free volume assoc iated with vibrations.- 10.5 Rotational con tribution to the equilibrium constant of the ionisation of water.- 10.6 Forms of the law of mass action employing the function approximation of the factorial.- 10.7 Derivation of the van der Waals equation of state.- 10.8 Exchange energy.- 10.9 Activity coefficients derived from the non-ideality resulting from triple interactions.- 10.10 The law of mass action for a binary equilibrium in a sys tem with non- additive volume and lattice energy.- 10.11 Physico-chemical constants and units of energy.

Comment on “The mathematical origins of the kinetic compensation effect” Parts 1 and 2 by P. J. Barrie, Phys. Chem. Chem. Phys., 2012, 14, 318 and 327

Abstract: The concept of kinetic compensation and the associated isokinetic relation continue to be subject to debate, despite the fact that the conditions under which they are to be expected are now well established, and the criteria for deciding that they have been observed are known. We present these conditions and criteria, and the reality of these relations, and stress their importance for catalysis. We then discuss the fact that statistical arguments against their reality continue to be presented. Recently two articles, based upon the statistical point of view have been published in this Journal. We show that, despite the fact that the mathematics of these articles is error free, they present a distorted image of the present understanding of the subject.

Anion driven modulation of magnetic intermolecular interactions and spin crossover properties in an isomorphous series of mononuclear iron(III) complexes with a hexadentate Schiff base ligand

Abstract: A series of spin crossover iron(III) complexes with the general composition [Fe(4OH-L6)]X (H2-4OH-L6 = 1,8-bis(4-hydroxysalicylaldiminato)-3,6-diazaoctane; X = Cl, 1a; Br, 1b; I, 1c) was prepared. A combination of the results following the single crystal X-ray analysis, infrared and EPR spectroscopy, and temperature dependent magnetic experiments revealed that the Fe(III) atoms occur in the low-spin state below room temperature and the crystal structures of the complexes involve rich networks of non-covalent intermolecular contacts resulting in two-dimensional supramolecular structures. Alterations in the halide anions influence the strength of the non-covalent contacts and affect the magnetic properties of the studied complexes. The antiferromagnetic exchange interaction between the non-covalently bound cations is the most obvious in the case of 1a and it weakens with the growing anionic volume of X. The 1D and 2D spin Hamiltonian models were applied to quantitatively extract the information about the intermolecular magnetic exchange (fit on 1D infinite chain gives J(1a) = −2.86 cm−1, J(1b) = −2.02 cm−1, J(1c) = −1.16 cm−1). Furthermore, gradual spin crossover behaviour for all of the compounds of the series was observed above room temperature in the solid state. Spin crossover accompanied by thermochromism was also demonstrated by EPR experiments in solution.

Metal ions in neurological systems

Abstract: 1. R.R. Crichton, D.T. Dexter, R.J. Ward: Brain iron metabolism and its perturbation in neurological diseases.- 2. E. Milward et al.: Brain changes in iron loading disorders.- 3. I. Paris, J. Segura-Aguilar: The role of metal ions in dopaminergic neuron degeneration in Parkinsonism and Parkinson's disease.- 4. E. Siakkou, G.N.L. Jameson: Iron, cysteine and neurodegeneration during Parkinson's disease.- 5. G. Crisponi et al.: Copper uptake and trafficking in the brain.- 6. Y. Nishida: Prion diseases and manganism.- 7. A. Granzotto, P. Zatta: Metal ions and beta-amyloid: conformational modifications and biological aspects.- 8. A. Granzotto et al.: Beta-amyloid toxicity increases with hydrophobicity in the presence of metal ions.- 9. Ch. Exley, E.R. House: Aluminium in the human brain.- 10. V.M. Nurchi, G. Crisponi, V. Bertolasi, G. Faa, M. Remelli: Aluminium dependent human diseases and chelating properties of aluminium chelatots for bio-medical applications.-11. M. Suwalsky P.L. Henrnandez, C.P. Sotomayor: Aluminum increases toxic effects of amyloid beta-peptides on human erythrocyte membrane and molecular models.- 12. E. Gaggelli, G. Valensin: Oxidative stress in neurodegeneration: targeting mitochondria as a therapeutic aid.- 13. Y. Nishsida: The chemical process of oxidative stress by copper(II) and iron(III) ions in several neurodegenerative disorders.- 14. O.G. Tsay, K. Kim, D.G. Churchil: Metal ion role in the CNS under toxic organophosphonate exposure: Traces of understanding and various open questions.- 15. S. Casito, M. Aschner: Heavy metals, behavior and neurodegeneration: Using C elegans to untangle a can of warms.- 16. C. Kallay et al.: The effect of point mutations on copper(II) complexes with peptide fragments encompassin the 106-114 region of human prion protein.- 17. E. Sija et al.: Interactions of pyridinecarboxylix acid chelators with brain metal ions: Cu(II), Zn(II), Al(III).- 18. S. Bohic et al.: Spatially resolved imaging methods to probe metals in brain.- 19. Y. Ha, O. Tsay, D.G. Churchil: ICP-MS for the neurodegenerative and brain sciences.

Superparamagnetic CoFe2O4 prepared via a modified oxalate method

Abstract: The modified oxalate precursor method was used for the preparation of nanocrystalline CoFe2O4. Structural investigations of as-produced powders performed by means of high-resolution transmission electron microscopy and X-ray diffraction revealed an average particle size of 8 nm. The nanocrystallites are pure CoFe2O4 and present a well crystallized spinel structure with lattice constant of 8.3583 A. The particles are superparamagnetic exhibiting a blocking temperature around room temperature. The magnetization and the coercive field values obtained at 9 T are 56.8 emu · g−1 and 17.0 kOe (at 4.2 K), respectively. The crystalline anisotropy determined from the coercive field as a function of temperature is 8.0 × 105 J · m−3, which is much higher than that of bulk materials.

1-(2,2-Diphenyl-eth-yl)-1H-tetra-zole.

Abstract: The crystal structure of the title compound, C15H14N4, contains chains of coplanar tetra­zole rings with the chain direction along b. These are formed through weak hydrogen bonds, donated by the tetra­zole H atoms and by one of the H atoms of the methyl­ene group, and accepted by two neighbouring N atoms of the adjacent tetra­zole ring. The chains are connected to each other in a staircase-like manner via weak hydrogen bonds, donated from the second H atom of the methyl­ene group and accepted by the N atom next to the C atom in the tetra­zole ring. The resulting layers are parallel to the bc plane.