A Multipole Method for the Rapid Solution of the Stationary Linearized Stokes System

Here we will show how the multipole method can be used for the questions connected with the hydrodynamical potentials. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Normal and Lateral Deformation of Lyotropically Ordered Polymer Brush

Summary: Planar polymer brush formed by semirigid chains of freely jointed rigid segments and immersed into a solvent is considered. Brush collapse induced by deterioration of the solvent quality and its deformation by external normal or lateral force is studied. It is demonstrated that these three different situations can be described in the framework of the common approach. It is shown that the collapse is accompanied by liquid‐crystalline (LC) ordering within the brush. The LC transition can be jump‐like (the first order) or continuous, depending on the segment's aspect ratio and grafting density. Transition point is investigated in detail, the corresponding phase diagrams are calculated. It is shown that the phase diagrams of a normally deformed brush have different structures, with a narrow ‘leg’ in the good solvent region for sparsely grafted brush, with two coexistence regions and a triple point, in addition, for shorter segment length or without these features if the chains are densely grafted. For the laterally deformed brush, phase diagrams have similar structures with a critical point in the good solvent regime.

Polymer brush subjected to deformation by normal (top) and lateral (bottom) external force.     

Phase transitions in polymer brushes

Liquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self-consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump-wise first order phase transition for a finite chain length (N). The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞ since this transition occurs only in a vanishingly small part (∝ N^−1/2) of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.     

The effect of tethered polymers on the conformation of a lipid membrane

We consider the effect of tethered macromolecules on the stability of the flat conformation of a lipid bilayer in a dense brush regime when anchored chains are significantly overlapped. On the basis of a scaling approach we have shown that redistribution of polymer chains from inner to outer layers reduces the free energy of the system and stabilizes spherically bent configurations of the membrane.     

Mixed supercrystalline structures in mixtures of ABC‐triblock and AB(BC)‐diblock copolymers, 1. Lamellar structures in bicomponent mixtures

The theory of lamellar superstructures in binary mixtures of AB diblock and linear ABC triblock copolymers under the condition of strong segregation between chemically different blocks is developed. This system is considered using Alexander‐de Gennes (box‐model) and self‐consistent field (SCF) models. The formation of a mixed lamellar superstructure comprising both mixture components is proved. It is shown that a mixed lamella may be the only type of lamellae in the mixture, or it may coexist with pure diblock lamellae, depending on the mixture composition, local characteristics of blocks (thickness and Kuhn segment length), and surface tension coefficients at the A/B and B/C interfaces. Preliminary experimental results provide support of these theoretical estimations. The formation of mixed lamellae in a mixture of linear ABC and branched (AB)₂C block copolymers is also considered.     

Microphase segregation in bridging polymeric brushes: Regular and singular phase diagrams

A mean-field theory of deformation-induced microphase segregation in bridging polymeric brushes anchored to two parallel surfaces is presented. Models with isotropic and orientation-dependent liquid-crystalline interactions between segments are considered. For the first model, the problem is similar to that of classical liquid-vapor phase separation, and the phase diagram in the P-T plane has a line of first-order transitions terminating at the critical point. We show that the critical pressure is negative implying that a free brush tethered only to one surface always exists at supercritical conditions and hence cannot undergo the collapse phase transition. In the second model, the free energy density depends on two coupled order parameters, one related to segment density and the other to the orientational order, which strongly modifies the phase behavior. Depending on the grafting density the system is described by a phase diagram of a regular or a singular type. In the regular phase diagram the first-order transition line terminates at the critical point. In a singular diagram, the first-order transition line extends to infinity; the critical point corresponds to infinite pressure so that the system undergoes the phase transition at arbitrary external pressures. Regular phase diagrams correspond to dense grafting, and singular ones to sparse grafting. The change from a regular phase behavior to another occurs at a certain marginal value of the grafting density. On approaching this value the critical point on the regular diagram moves to infinity, logarithmically with the deviation from the critical grafting density. We relate the analytical properties of the free energy density as a function of the segment concentration to the type of the phase diagram and the shape of the coexistence curve in the temperature- concentration plane.     

3,5‐Bis­[4‐(diethyl­amino)­benzyl­idene]‐1‐methyl‐4‐piperidone and 3,5‐bis[4‐(diethyl­amino)­cinnamyl­idene]‐1‐methyl‐4‐piperidone: prospective biophotonic materials

The structures of 3,5‐bis­[4‐(diethyl­amino)­benzyl­idene]‐1‐methyl‐4‐piperidone, C₂₈H₃₇N₃O, (I), and 3,5‐bis­[4‐(diethyl­amino)­cinnamyl­idene]‐1‐methyl‐4‐piperidone, C₃₂H₄₁N₃O, (II), have been characterized. Because of conjugation between donor and acceptor parts, the central heterocycles (including the carbonyl group) in (I) and (II) are flattened and exhibit a `sofa' conformation, with a deviation of the N atom from the planar fragment. The dihedral angles between the planar part of the heterocycle and the two almost flat fragments that include a phenyl ring and bridging atoms are 23.2 (1) and 11.2 (1)° in (I), and 11.8 (1) and 8.7 (2)° in (II). One‐ and two‐photon absorption of light and the fluorescence of (I) and (II) have also been characterized.     

Di­chloro­bis­(imidazolidin‐2‐one‐κO)­zinc(II) at 150 K

In the title compound, [ZnCl₂(C₃H₆N₂O)₂], the zinc(II) cation is surrounded by a distorted tetrahedral environment consisting of two Cl anions and two imidazolidin‐2‐one mol­ecules, the latter bound to the metal through their carbonyl O atoms. All atoms that are able to participate in hydrogen bonding are involved in such interactions. A hydrogen‐bonding network mediates the formation of mol­ecular columns parallel to the a axis. Neighboring columns are not bound by significant non‐covalent interactions; the result is an extended pattern of supramolecular aggregation that is intermediate in completeness between the situations observed in two related complexes of cobalt that have been studied previously.     

1,3-Phosphorotropic rearrangement of pyridyl phosphates to hydroxypyridyl phosphonates

The lithium diisopropylamide (LDA) induced regioselective 1,3-rearrangement of 3- and 2- pyridyl phosphates into the corresponding 3-hydroxy-4-pyridyl-and 2-hydroxy-3-pyridylphosphonates has been observed and investigated. The rearrangement is proposed as a useful method for a directed introduction of a phosphoryl group into a hydroxypyridine nucleus.