Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh

We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m. We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.     

The Mathematical Theory of Ito Diffusions on Hypersurfaces, with Applications to NMR Relaxation Problems

A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a Rippled surface are presented.     

Accurate values for the nonrelativistic energies of the lowest singlet and triplet S-states of the4He-Isotop

Accurate lower and upper bounds for the nonrelativistic lowest energies¹ E ₀ and³ E ₀ of the singlet and triplet-system of the⁴He-Isotop are calculated with the linearized method of variance minimization. The same was done for¹ E ₁ the energy of the first excitedS-state 2¹ S. The results especially for¹ E ₀ and³ E ₀ in a.u. are −2.9033076997₅ ≤¹ E ₀ ≤ −2.9033076921₈ −2.1749324263₇ ≤³ E ₀ ≤ −2.1749324245₉ i.e. the values are determined with an absolute error smaller than 0.00167 cm⁻¹ for¹ E ₀ and 0.00039 cm⁻¹ for³ E ₀.     

THE CORRELATION EFFECT ON THE CHAIN MOTION CONTRIBUTION TO IONIC TRANSPORT IN POLYMER ELECTROLYTES

The ionic transport process in polymer electrolytes (such as polyethylene oxide) wassimulated numerically on a two dimensional square lattice where charge carriers areaccommodated by the lattice sites connected randomly with available bonds to represent theamorphous chain configuration. Following the dynamic bond percolation theory(DBPT),the chainmotion contribution to the ionic conduction was incorporated via periodical renewal of the randombond configuration. To check and extend the prediction made by DBPT employing global abruptbond renewal,spatial correlation of the bond reassignment was introduced to the system by: 1)regional bond renewal and 2) organized bond motion. It is found that the difference between thediffusivities simulated involving regional bond renewal and those of DBPT becomes negligiblewhen the bond renewal rate approaches the carrier hopping rate.     

Mixed-valence, mixed-spin-state, and heterometallic [2x2] grid-type arrays based on heteroditopic hydrazone ligands: synthesis and electrochemical features

An extended family of heterometallic [(M1)2(M2)2(L-)4](n+) [2x2] grid-type arrays 1-9 has been prepared. The three-tiered synthetic route encompasses regioselective, redox and enantioselective features and is based on the stepwise construction of heteroditopic hydrazone ligands A-C. These ligands contain ionisable NH and nonionisable NMe hydrazone units, which allows the metal redox properties to be controlled according to the charge on the ligand binding pocket. The 2-pyrimidine (R) and 6-pyridine (R') substituents have a significant effect on complex geometry and influence both the electrochemical and magnetic behaviour of the system. 1H NMR spectroscopic studies show that the Fe(II) ions in the grid can be low spin, high spin or spin crossover depending on the steric effect of substituents R and R'. This steric effect has been manipulated to construct an unusual array possessing two low-spin and two spin-crossover Fe(II) centres (grid 8). Electrochemical studies were performed for the grid-type arrays 1-9 and their respective mononuclear precursor complexes 10-13. The grids function as electron reservoirs and display up to eight monoelectronic, reversible reduction steps. These processes generally occur in pairs and are assigned to ligand-based reductions and to the Co(III)/Co(II) redox couple. Individual metal ions in the heterometallic grid motif can be selectively addressed electrochemically (e.g., either the Co(III) or Fe(II) ions can be targeted in grids 2 and 5). The Fe(II) oxidation potential is governed by the charge on the ligand binding unit, rather than the spin state, thus permitting facile electrochemical discrimination between the two types of Fe(II) centre in 7 or in 8. Such multistable heterometallic [2x2] gridlike arrays are of great interest for future supramolecular devices incorporating multilevel redox activity.     

NMR studies on solid cyclohexaamylose inclusion compounds

Orthorhombic inclusion compounds of cyclohexaamylose with methanol,n-propanol, acetic acid and water as guest molecules were studied using¹³C and²H NMR techniques.¹³C chemical shifts were correlated with structural data, whereas²H NMR lineshapes were used to derive information on guest molecule motions.Issued as NRCC No. 25568. Presented in part at the 2nd International Symposium on Clathrate Compounds and Molecular Inclusion Phenomena, Parma, Italy, 30 Aug.–3 Sept. 1982     

Heat capacities and volumes of transfer of cholesteryl oleyl carbonate into various solvents

Heat capacities C _p and volumes V have been obtained at 25°C for the transfer of cholesteryl oleyl carbonate (ChOC) from a reference solvent, the highly-branched alkane 2,2,4,4,6,8,8-heptamethylnonane into various solvents. These include normal, branched, and cyclic alkanes as well as the pure cholesteric ChOC. V and most C _p are associated with the change of environmental free volume during the transfer process and are predicted by the Prigogine-Flory theory. However, for n-alkane solvents with more than twelve carbons, C _p is large, positive, and unattributable to free volume changes. It is consistent with a restriction of alkane segmental motion by the ChOC. The same mechanism has been proposed to explain an antiplasticization effect of ChOC on transitions in polymers.     

Homo- and heterometallic [2x2] grid arrays containing RuII, OsII, and FeII subunits and their mononuclear RuII and OsII precursors: synthesis, absorption spectra, redox behavior, and luminescence properties

The absorption spectra, redox behavior, and luminescence properties (both at 77 K in rigid matrices and at room temperature in fluid solution) of a series of [2x2] molecular grids have been investigated. The latter were prepared either by means of sequential self-assembly, or by a stepwise protection/deprotection procedure, and are based on a ditopic hexadentate ligand 1 in which two terpyridine-like binding sites are fused together in a linear arrangement. The molecular grids studied include the homometallic species [[Fe(1)](4)](8+) (Fe(2)Fe(2)), and the heterometallic species [[Ru(1)](2)[Fe(1)](2)](8+) (Ru(2)Fe(2)) and [[Os(1)](2)[Fe(1)](2)](8+) (Os(2)Fe(2)). For comparison purposes, the properties of the mononuclear complexes [Ru(1)(2)](2+) (1-Ru) and [Os(1)(2)](2+) (1-Os) have been studied. All these compounds exhibit very intense absorption bands in the UV region (epsilon in the 10(5)-10(6) M(-1) cm(-1) range, attributed to spin-allowed ligand-centered (LC) transitions), as well as intense metal-to-ligand charge-transfer (MLCT) transitions (epsilon in the 10(4)-10(5) M(-1) cm(-1) range) that extend to the entire visible region. The mononuclear species 1-Ru and 1-Os exhibit relatively intense luminescence, both in acetonitrile at room temperature (tau=59 and 18 ns, respectively) and in butyronitrile rigid matrices at 77 K. In contrast, the tetranuclear molecular grids do not exhibit any luminescence, either at room temperature or at 77 K. This is attributed to fast intercomponent energy transfer from the Ru- or Os-based subunits to the low-lying metal-centered (MC) levels involving the Fe(II) centers, which leads to fast radiationless decay. The redox behavior of the compounds is characterized by several metal-centered oxidation and ligand-centered reduction processes, most of them reversible in nature (as many as twelve for Fe(2)Fe(2)). Detailed assignment of each redox process has been made, and it is apparent that these systems can be viewed as multilevel molecular electronic species capable of reversibly exchanging a number of electrons at accessible and predetermined potentials. Furthermore, it is shown that the electronic interaction between specific subunits depends on their location in the structure and on the oxidation states of the other components.     

N-苯基苯二甲酰亚胺和2-苯基喹噁啉晶态分子动力学行为研究

本文在晶体结构分析的基础上, 对二个芳香杂环高聚物模型化合物N-苯基苯二甲酰亚胺和2-苯基喹噁啉分子的原子热振动参数进行分析, 结果表明N-苯基苯二甲酰亚胺晶态分子基本上为刚性分子, 而2-苯基喹噁啉分子的热振动应包含分子内取代苯基的内旋转运动, 其平均平方振幅为53(25) deg~2。     

Dielectric and13C NMR studies of the carbon monoxide clathrate hydrate

The structure I clathrate hydrate of carbon monoxide has been studied using dielectric measurements and¹³C NMR spectroscopy. Broad, weak dielectric absorption curves with maxima at 2.2–3.8 K yieldE _a = 0.14 kJ mol^–1 for the average Arrhenius activation energy associated with the reorientation of the low polarity guest. Except for H₂S this represents the fastest reorienting polar guest known among the clathrate hydrates. The low temperature dielectric absorption curves can best be fitted with a Cole-Davidson asymmetric distribution of relaxation times and activation energies (with = 0.06 at 4 × 10⁶ Hz), which at 10⁷ Hz has been resolved into a double symmetric distribution of discrete relaxation times for CO in the small and large cages. The cross-polarization magic angle spinning¹³C NMR spectra indicate identical chemical shifts for CO in the small and large cages, in contrast to other hydrates. The static spectra show that the CO molecules undergo anisotropic reorientation in the large cages and that there is still considerable mobility at 77 K. One possible model for the anisotropic motion has the CO rapidly moving among sites over each of the 14 faces of the cage with the CO axis orientated towards the cage centre. The cage occupancy ratio at 220 K, _s/ _L = 1.11, indicates slightly greater preference of CO for the small cage.Dedicated to Dr D. W. Davidson in honor of his great contributions to the sciences of inclusion phenomena.