Architectural effects on the stability limits of ABC block copolymers

The random phase approximation has been used to extend the Leibler theory for the stability limit of a homogeneous melt of A–B diblock copolymers to examine the onset of microphase and macrophase separation in a variety of ABC block copolymer systems. The stability limit is located by the divergence of the collective structure factor of the melt. We introduce and analyze three models for ABC block copolymers: linear triblocks, random comb copolymers where a fixed number of A and B teeth are placed randomly along a C backbone, and statistical comb copolymers, with A or B teeth spaced regularly, but with sequences constructed using a two parameter Markov process. We compute order-disorder stability boundaries for the segregation strength parameter _χABN at threshold as a function of _χACN, _χBCN, composition, and other model parameters, and compare the results for the three different architectural models. An interesting “reentrant order-disorder transition” is located in several model phase diagrams, and is associated with a peculiar situation in which more incompatibility causes less segregation. In the case of statistical combs, macrophase separation into two liquid phases can be favored over microphase separation. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 849–864, 1997     

Optimal Domains for Kernel Operators via Interpolation

The problem of finding optimal lattice domains for kernel operators with values in rearrangement invariant spaces on the interval [0,1] is considered. The techniques used are based on interpolation theory and integration with respect to C([0, 1])–valued measures.     

Synthese,Kristallstruktur und magnetisches Verhalten von (2,4,6‐Trimethylpyridinium)10[ErCl6][ErCl5(H2O)]2Cl3

Preparation, Crystal Structure, and Magnetic Behaviour of (2,4,6‐Trimethylpyridinium)₁₀[ErCl₆][ErCl₅(H₂O)]₂Cl₃ Crystals of the complex chloride (2,4,6‐Trimethylpyridinium)₁₀[ErCl₆][ErCl₅(H₂O)]₂Cl₃ have been prepared by reaction of ErCl₃·6H₂O with 2,4,6‐Trimethylpyridiniumchloride in ethanol solution for the first time. The crystal structure has been determined from single crystal X‐ray diffraction data. The compound crystallizes monoclinically in the space group P2₁/a (Z = 2) with a = 1704.5(3) pm, b = 1696.7(2) pm, c = 1798.5(4) pm and β = 90.76(3)°. The structure contains octahedral building units [ErCl₆]^3— and [ErCl₅(H₂O)]^2—. The octahedra, the organic cations and isolated chloride anions are interconnected via hydrogen bonds forming layers parallel to the ac‐plane (0 1 0). The magnetic behaviour of (2,4,6‐Trimethylpyridinium)₁₀[ErCl₆][ErCl₅(H₂O)]₂Cl₃ has been studied. The magnetic data are interpreted by ligand field calculations applying the angular overlap model.     

Synthesen und Kristallstrukturen von Dialkylgalliumhydriden — dimere versus trimere Formeleinheiten

Syntheses and Crystal Structures of Dialkylgallium Hydrides — Dimeric versus Trimeric Formula Units Dialkylgallium hydrides (R = Me, Et, iPr, iBu, neopentyl) were obtained on two different synthetic routes. The dimethyl and diethyl compounds were formed by the reaction of LiH with the corresponding dialkylgallium chlorides via lithium dialkyldihydridogallate intermediates, which so far have not been isolated in a pure form. On the second route, trialkylgallium compounds were treated with [GaH₃·NMe₂Et] to yield the dialkylgallium hydrides by a substituent exchange reaction. The dimethyl, diethyl and diisopropyl compounds are trimeric in solution. That trimeric structure was verified for the diisopropyl derivative by a crystal structure determination. Di(neopentyl)gallium hydride has a dimeric structure in solution and in the solid state.     

Pseudo‐Isomerie durch unterschiedliche Jahn‐Teller‐Ordnung: Die Kristallstrukturen des Hemihydrats und des Monohydrats von (pyH)[MnF(H2PO4)(HPO4)]

Pseudo‐Isomerism by Different Jahn‐Teller Ordering: Crystal Structures of the Hemihydrate and the Monohydrate of (pyH)[MnF(H₂PO₄)(HPO₄)] With pyridinium counter cations (pyH⁺) the Mn^III fluoride phosphate anion [MnF(H₂PO₄)(HPO₄)]^— can be stabilized. It forms a chain structure with Mn³⁺ ions bridged by a fluoride ion and two bidentate phosphate groups. Under sleightly differing conditions either the hemihydrate (pyH)[MnF(H₂PO₄)(HPO₄)]·0.5H₂O ( 1 ) or the monohydrate (pyH)[MnF(H₂PO₄)(HPO₄)]·H₂O ( 2 ) is formed. The hemihydrate 1 crystallizes monoclinic in space group P2₁/n, Z = 8, a = 7.295(1), b = 17.052(2), c = 18.512(3) Å, β = 100.78(1)°, R = 0.033, the monohydrate triclinic in space group P1¯, Z = 2, a = 7.374(1), b = 8.628(1), c = 10.329(1) Å, α = 83.658(8)°, β = 77.833(9)°, γ = 68.544(8)°, R = 0.025. Whereas the topology of the chain anions is identical in both structures, the Jahn‐Teller effect is expressed in different ordering patterns: in 1 antiferrodistortive ordering of [MnF₂O₄] octahedra is observed, with alternating elongation of an F—Mn—F‐axis or a O—Mn—O‐axis, respectively. This leads to asymmetrical Mn—F—Mn‐bridges. In 2 ferrodistortive ordering is found, with elongation of all octahedra along the F—Mn—F‐axis. Thus, symmetrical bridges are formed with long Mn—F distances. This unusual pseudo‐isomerism is attributed to the differing influence of inter‐chain hydrogen bonds.