(o-Hydroxyphenyl)methylphosphonic acids: Synthesis and potentiometric determinations of their pKa Values

(o-Hydroxyphenyl)methylphosphonic acids are readily obtained from o-(bromomethyl)- or o-(hydroxymethyl)phenols and trialkyl phosphites. Subsequent hydrolysis leads to the corresponding phosphonic acids. For a series of such compounds, the pK_a values have been determined by potentiometry. Their dependence on additional substituents in the aromatic ring is discussed in terms of electronic and steric effects.     

Electrochemical deposition of copper phosphides

Summary Methods for preparation of copper phosphides at ambient temperatures by electrodeposition are presented. From P₄/PCl₃/Acetonitrile/TBA-BF₄/Cu⁺ (solvated) Cu₃P and Cu₃P₂ can be obtained at different deposition potentials.

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Elektrochemische Abscheidung von Kupferphosphiden

Zusammenfassung Es werden Verfahren zur Herstellung von Kupferphosphiden bei ambienten Temperaturen beschrieben. Aus der Anordnung P₄/PCl₃/Acetonitril/TBA-BF₄/Cu⁺ (solvatisiert) können Cu₃P und Cu₃P₂ bei verschiedenen Abscheidungspotentialen erhalten werden.

     

Influence of molecular weight and polydispersity on phase behaviour of polyesters with laterally fixed or cross-shaped mesogens

To supplement previous studies of polyesters with laterally attached and cross-shaped mesogens the influence of molecular weight and molecular weight distribution on the phase behaviour has been investigated. For that purpose two polyesters have been fractionated by preparative gel permeation chromatography under high pressure and observed by polarizing microscopy and DSC measurements. A monotropic nematic polyester with laterally attached mesogens shows changing phase transitions up to a molecular weight of 10 000 (M_w); at higher molecular weight only the clearing transition is still slightly influenced. The molecular weight distribution at an average molecular weight of 15 000 (M_w) has no influence on the melting and clearing temperatures, but does effect recrystallization. The tendency to recrystallize decreases with increasing polydispersity, with increasing aberration from a monomodal molecular weight distribution. The recrystallization and the melting enthalpy are most distinguished at molecular weights around 12 000 (M_w) and crystallization disappears at molecular weights under about 5000 (M_w). In this way, fractions with stable nematic phases are obtained. Additionally, the broadness of the biphasic region shows a distinct dependence on molecular weight. Clearing temperatures show the most significant dependence on the molecular weight of an enantiotropic polyester with crossshaped mesogens dropping significantly below a molecular weight of about 20 000 (M_w). Oligomers with molecular weights below 10 000 (M_w) do not exhibit a mesophase. Polyesters with laterally attached mesogens as well as with crossshaped mesogens show no new liquid-crystalline phases by varying the molecular weight or the molecular weight distribution.     

Numerical computation of an analytic singular value decomposition of a matrix valued function

Summary This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) ^T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.Partial support received from SFB 343, Diskrete Strukturen in der Mathematik, Universität BielefeldPartial support received from FSP Mathematisierung, Universität BielefeldPartial support received from FSP Mathematisierung, Universität BielefeldPartial support received from National Science Foundation grant CCR-8820882. Some support was also received from the University of Kansas through International Travel Fund 560478 and General Research Allocations # 3758-20-0038 and #3692-20-0038.     

Smooth factorizations of matrix valued functions and their derivatives

Summary In this paper we study the numerical factorization of matrix valued functions in order to apply them in the numerical solution of differential algebraic equations with time varying coefficients. The main difficulty is to obtain smoothness of the factors and a numerically accessible form of their derivatives. We show how this can be achieved without numerical differentiation if the derivative of the given matrix valued function is known. These results are then applied in the numerical solution of differential algebraic Riccati equations. For this a numerical algorithm is given and its properties are demonstrated by a numerical example.