Estimation of second order rate constants using chemometric methods with kinetic constraints

Several methods are described for determining rate constants for second order reactions of the form U + V --> W using chemometrics and hard modelling to analyse UV absorption spectroscopic data, where all species absorb with comparable concentrations and extinctions. An interesting feature of this type of reaction is that the number of steps in the reaction is less than the number of absorbing species, resulting in a rank-deficient response matrix. This can cause problems when using some of the methods described in the literature. The approaches discussed in the paper depend, in part, on what knowledge is available about the system, including the spectra of the reactants and product, the initial concentrations and the exact kinetics. Sometimes some of this information may not be available or may be hard to estimate. Five groups of methods are discussed, namely use of multiple linear regression to obtain concentration profiles and fit kinetics information, rank augmentation using multiple batch runs, difference spectra based approaches, mixed spectral approaches which treat the reaction as two independent pseudospecies, and principal components regression. Two datasets are simulated, one where the spectra are quite different and the other where the spectrum of one reactant and the product share a high degree of overlap. Three sources of error are considered, namely sampling error, instrumental noise and errors in initial concentrations. The relative merits of each method are discussed.     

Synthesis and characterization of platinum(II) and (IV) complexes containing hexamethyleneimine ligand: crystal structure of [Pt(hexamethyleneimine)2(cyclobutanedicarboxylato)]·H2O

A series of new platinum(II) and platinum(IV) complexes of the type [Pt^II(HMI)₂X] (where HMI=hexamethyleneimine, X=dichloro, sulfato, 1,1-cyclobutanedicarboxylato [CBDCA], oxalato, methylmalonato, or tatronato) and [Pt^IV(HMI)₂Y₂Cl₂] (where Y=hydroxo, acetato, or chloro) were synthesized and characterized by infrared (IR) spectroscopy, ¹³C and ¹⁹⁵Pt nuclear magnetic resonance (NMR) spectroscopy and elemental analysis. Among the complexes synthesized, [Pt^II(hexamethyleneimine)₂(1,1-cyclobutanedicarboxylato)]·H₂O was examined by single-crystal X-ray diffraction. The slightly distorted square planar coordination environment of the platinum metal includes the amino group of the hexamethyleneimine (HMI) molecule and the oxygen atoms of the carboxylato ligand. The cyclobutanedicarboxylic acid (CBDCA) molecule adopts six-member chelating rings with platinum. Hydrogen bonding plays an important part in holding the crystal lattice together.     

Synthesis of 1-Hydroxyoxindoles

A convenient synthesis of various substituted 1-hydroxyoxindoles is described.     

The bicritical phase diagram of two-dimensional antiferromagnets with and without random fields

Neutron scattering measurements have been made of the phase diagrams of the nearly two-demensional antiferromagnets Rb₂MnF₄ and Rb₂Mn_0.7Mg_0.3F₄ in a magnetic field applied along thec-axis. In Rb₂MnF₄ there is at low temperatures a spin-flop phase at fields above 5.5 T which has long range order. The observation of true long range order rather than the algebraic decay of the order characteristic of the two-dimensional XY model is presumably due to subtle anisotropy effects in the plane as well as weak three-dimensional coupling. The phase boundaries of the uniaxial and transverse phases are shown to be consistent with renormalization group predictions for two-dimensional systems. The two lines become exponentially close to each other at low temperatures. The weak three-dimensional coupling moves the bicritical point fromT=0 to a non-zero temperature. The situation is more complex in Rb₂Mn_0.7Mg_0.3F₄ because of Ising random field effects. At low fields we observe typical random field metastable behavior with a sharp metastability boundary and a gange of length scales which are time independent below that boundary. At higher fields there are substantial uniaxial fluctuations. The transverse phase boundary and the metastability line appear to intercept atT=0 showing that the random field fluctuations do have a large effect on the phase diagram. The theory of the phase diagrams has been extended to include the random field fluctuations and good agreement is obtained with the observed transverse phase boundary. Unfortunately, there is as yet no theory of the metastable uniaxial phase with which to compare our results.     

Some morphological observations on polycaprolactam filament

Examination of longitudinal, cross, and skew sections of extruded polycaprolactam filaments with the polarizing light microscope reveal morphological features not previously described. In cross-sectional view, three distinct layers enclose a “homogeneous” central matrix. The outermost layer is characterized by large, birefringent, truncated cones extending upward from the surface. Associated with the cones and an entity in its own right is what appears to be a second layer of ultrafibrils. Below the latter is a fine-structured layer of submicroscopic spherulites. A combination of the above features forms the transcrystalline region of stressed melts. Row nucleation is evident on the surface of the filaments.     

Synthesis of a novel C2-aryl substituted 1,2-unsaturated pyrrolobenzodiazepine

A novel C2-aryl 1,2-unsaturated PBD (14) has been prepared via an enol triflate intermediate (8). The regiochemistry of triflation is dependent upon the point at which the reaction is performed during the synthetic route.     

Viscoelastic properties of pathological synovial fluids for a wide range of oscillatory shear rates and frequencies

Summary A series of pathological synovial fluids are examined for viscoelastic properties in oscillatory shear flow at frequencies of physiological significance. When tested at varying amplitudes of shear at a frequency of 2 Hertz, the fluids show marked nonlinearity for shear rates above 10 sec^–1, the elastic component of the shear stress truncating in the range from 1 to 10 dynes/cm². At low shear rates, the fluids are linear and viscoelastic and have frequency dispersions matching the character of Gaussian chain theory for polymer solutions. Enzymatic degradation of the hyaluronate destroys the viscoelasticity, leaving a Newtonian fluid of relatively low viscosity. The concentration and molecular weight of the hyaluronate produce substantial intermolecular interaction. The relaxation times, viscosity, and elasticity of the synovial fluids are greatly increased over values expected for noninteracting molecules of hyaluronic acid in solution. While both the viscosity and elasticity vary greatly among the pathological fluids, the elasticity is the more sensitive indicator of viscoelastic properties.

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Zusammenfassung Es wird eine Serie pathologischer Synovialflüssigkeiten bezüglich ihrer viskoelastischen Eigenschaften in einer oszillatorischen Scherströmung mit physiologisch signifikanten Frequenzen untersucht. Bei einer Frequenz von 2 Hz zeigen die Flüssigkeiten eine ausgeprägte Nichtlinearität, wenn ein rms-Wert von 10 s^–1 überschritten wird: Die elastische Komponente der Schubspannung flacht im Bereich von 1–10 dyn/cm² ab. Bei niedrigen Schergeschwindigkeiten verhalten sich die Flüssigkeiten dagegen linear-viskoelastisch, und ihre Frequenzabhängigkeit läßt sich durch die Theorie der Gaußschen Netzwerk-Lösungen beschreiben. Enzymatischer Abbau des Hyaluronats zerstört die Viskoelastizität, so daß eine newtonsche Flüssigkeit mit relativ niedriger Viskosität übrig bleibt. Infolge seiner Konzentration und seines Molekulargewichts unterliegt das Hyaluronat einer erheblichen intermolekularen Wechselwirkung. Relaxationszeiten, Viskosität und Elastizität zeigen erheblich größere Werte, als sie für nicht in Wechselwirkung stehende Hyaluronsäure-Moleküle in Lösung zu erwarten wären. Obgleich bei den verschiedenen pathologischen Flüssigkeiten sowohl die Viskosität als auch die Elastizität stark schwanken, stellt sich doch die Elastizität als der von den viskoelastischen Eigenschaften empfindlichere Indikator heraus.

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List of Symbol a Tube radius (cm) - b Gaussian chain segment length (cm) - c _m Mass concentration (g/cm³) - f Frequency (Hz) - G ^* Complex shear rigidity (dynes/cm²) - h ^* Hydrodynamic interaction factor for the Gaussian chain theory - k Boltzmann's constant (ergs/deg) - M Molecular weight - N Number of Gaussian subchain segments - N _a Avogadro's number - P ^* Pressure gradient, complex form (dynes/cm³) - P, P Real and imaginary parts ofP ^* (dynes/cm³) - t Time (sec) - T Absolute temperature (K) - u Volume rate of flow (cm³/sec) - Shear rate, instantaneous value (sec^–1) - Shear rate, amplitude (sec^–1) - Critical shear rate for onset of nonlinearity (sec^–1) - _p Eigenvalue,p-th value - ^* Complex coefficient of viscosity (P) - _v Viscosity, real part of ^* (P) - _E Elasticity, imaginary part of ^* (P) - ₀ Limiting viscosity at zero frequency (P) - _s Viscosity of solvent (P) - Limiting viscosity at infinite frequency (P) - []₀ Intrinsic viscosity at zero frequency (cm³/g) - Phase angle between shear rate and shear stress (rad) - (/f) Gaussian chain theory parameter - Shear stress, instantaneous value (dynes/cm²) - _M Shear stress, amplitude (dynes/cm²) - ^* Shear stress, complex form (dynes/cm²) - _v Viscous component of the shear stress (dynes/cm²) - _E Elastic component of the shear stress (dynes/cm²) - _p Relaxation time,p-th value (sec) - ₁ Terminal (longest) relaxation time (sec) - Radian frequency (rad/sec) With 7 figures and 3 tables