Mesomorphism,isomerization, and dynamics in a new series of pyramidic liquid crystals

Nona-alkanoyloxy tribenzocyclononene (CTV-n, where n is the number of carbons in the side chains) were prepared for n = 2 to 14. The homologues of this series appear in two stable isomeric forms, rigid crown and flexible saddle. We report on their isomerization equilibria and dynamics in solution and on their mesomorphic properties in the neat state. The crown-saddle equilibrium and interconversion kinetics of the CTV-8 isomers were studied in dimethyl formamide solutions using high-resolution (1)H NMR in the temperature range from 50 to 130 degrees C. At lower temperatures, the isomerization is too slow to measure. In this range the equilibrium saddle fraction increases from approximately 0.40 to approximately 0.65, whereas the isomerization rate increases from approximately 10(-)(4) to approximately 1 s(-)(1). The saddle isomer undergoes fast pseudorotation at room temperature, but below about -50 degrees C, it becomes slow enough to affect the NMR line width. The rate parameters for this process were estimated from the carbon-13 spectra in methylene chloride solutions to be, k(p)(-100 degrees C) approximately 1.7 x 10(3) s(-)(1) and E(a) approximately 9.6 kJ/mol. The slow crown-saddle isomerization at room temperature (half-life of about one year) allows quantitative separation (by chromatography) of the two isomers and their separate investigation. When the alkanoyloxy side chains are sufficiently long both isomers are mesogenic (n >or= 4 for the saddle and n >or= 5 for the crown), exhibiting hexagonal columnar mesophases. The structure, dynamics, and mesomorphic properties of these mesophase were investigated by X-ray diffraction, optical polarizing microscopy, differential scanning calorimetry, and NMR. The lattice parameters of the crown and saddle mesophases of corresponding homologues are almost identical and increase monotonically with increasing length of the side chains. The clearing temperatures of the saddle isomers are consistently lower than those of the corresponding crowns. Within each series, the clearing temperatures are almost independent of the length of the side chains (156 to 170 degrees C for the crown and 115 to 148 degrees C for the saddle). The thermal and kinetic properties of the neat compounds lead to peculiar phase sequences, as observed in the polarizing microscope and in the DSC thermogram, involving repeated, back and forth, interconversion between the two isomers. Carbon-13 MAS NMR measurements of the crown and saddle mesophases of several homologues were carried out. The spectra of the crown mesophase exhibit dynamic features consistent with planar 3-fold molecular jumps about the column axes. A quantitative analysis for the CTV-8 crown homologue yielded the following Arrhenius parameters, A = 3.1 x 10(22)s(-)(1) and E(a) = 130.1kJ/mol. These unusually high values suggest that the barrier to the jump process is temperature dependent, decreasing with increasing temperature. The rate of this 3-fold jump process is slower for the lower homologues and faster for the higher ones. In contrast, the saddle isomers in the mesophase do not show dynamic effects in their carbon-13 MAS spectra. They do not undergo pseudorotation, and it appears that the molecules remain locked within the columns in a saddle conformation, up to the clearing temperature. However, on (super-)cooling to room temperature and below, selective line broadening is observed in their carbon-13 MAS spectra. This suggests that the saddle conformation is twisted in the mesophase and undergoes fast high-amplitude jumps between the twisted forms. On cooling, these high-amplitude librations freeze out to give an orientationally disordered state. On a very long time scale (of the order of days at 100 degrees C), the saddle mesophase transforms into that of the crown, apparently by sublimation.     

Water Solubilization in Nonionic Microemulsions Stabilized by Grafted Siliconic Emulsifiers

Microemulsions containing octanol, decanol, or dodecanol as the oil phase and oligomeric, grafted nonionic amphiphiles based on ethoxylated polymethylsiloxanes (Silwets) have been studied. It was demonstrated that significant amounts of water can be solubilized only when the hydrophobic siliconic backbone is very short (trimers). The water solubilization was evaluated using SAXS, DSC, and conductivity measurements. It was found that up to 40 wt% of water can be solubilized in dodecanol and Silwet L-7607 (MW 1000 and 75 wt% ethylene oxide (EO)). Surprisingly, no free water was detected in the aggregate core. All the solubilized water was confined in the vicinity of the interphasal region and froze at -10 degrees C and below. Up to three molecules of water can be associated with each EO headgroup. Based on SAXS measurements, the structural units of the microemulsions were interpreted to be lamellar-like, a form previously found for the related monomeric microemulsions. Copyright 2001 Academic Press.     

Markov chains on $${{\mathbb {Z}}^+}$$ Z + : analysis of stationary measure via harmonic functions approach

Queueing Systems - We suggest a method for constructing a positive harmonic function for a wide class of transition kernels on $${{\mathbb {Z}}^+}$$ . We also find natural conditions under which...     

Competitive solubilization of cholesterol and phytosterols in nonionic microemulsions

It is well documented that phytosterols inhibit the uptake of exogenic cholesterol and do not interfere with cholesterol synthesis or cause side effects. The mechanism by which phytosterols interfere with cholesterol absorption is not completely clear and there are at least three hypotheses for their beneficial activity. Among these is that of competitive solubilization of phytosterols and cholesterol in dietary mixed micelles. In the present study we investigated the competitive solubilization of phytosterols (approximately 50% beta-sitosterol) and cholesterol in a nonionic microemulsion system constructed as a model for the dietary mixed micelles. We studied the effect of the competitive solubilization of cholesterol and phytosterols on the structural transformations and physical properties of the microemulsion and evaluated the locus of the solubilizates within the nanodroplets of each sterol separately and when they are loaded together at different weight ratios along one dilution line. Our results show that chemical and structural differences between cholesterol and phytosterols significantly influence the solubilization capacity of the nonionic microemulsion. Cholesterol, being more amphiphilic, is solubilized more efficiently at the W/O microemulsion interface, while in the O/W microemulsion phytosterols are dissolved somewhat more efficiently in the droplet core.     

Local limit theorem for the maximum of asymptotically stable random walks

Let {S _n ; n?≥?0} be an asymptotically stable random walk and let M _n denote it’s maximum in the first n steps. We show that the asymptotic behaviour of local probabilities for M _n can be approximated by the density of the maximum of the corresponding stable process if and only if the renewal mass-function based on ascending ladder heights is regularly varying at infinity. We also give some conditions on the random walk, which guarantee the desired regularity of the renewal mass-function. Finally, we give an example of a random walk, for which the local limit theorem for M _n does not hold.     

Local probabilities for random walks conditioned to stay positive

Let S ₀ = 0, {S _n , n ≥ 1} be a random walk generated by a sequence of i.i.d. random variables X ₁, X ₂, . . . and let $\tau ^{-}={\rm min} \{ n \geq 1:S_{n}\leq 0 \}$ and $\tau ^{+}={\rm min}\{n\geq1:S_{n} > 0\} $ . Assuming that the distribution of X ₁ belongs to the domain of attraction of an α-stable law we study the asymptotic behavior, as ${n\rightarrow \infty }$ , of the local probabilities ${\bf P}{(\tau ^{\pm }=n)}$ and prove the Gnedenko and Stone type conditional local limit theorems for the probabilities ${\bf P}{(S_{n} \in [x,x+\Delta )|\tau^{-} > n)}$ with fixed Δ and ${x=x(n)\in (0,\infty )}$ .     

Titanium phosphonate porous materials constructed from dendritic tetraphosphonates

An organic-inorganic hybrid material, TPPhA-Ti, was constructed by non-hydrolytic condensation of a dendritic tetrakis-1,3,5,7-(4-phosphonatophenyl)adamantane precursor and titanium(IV) isopropoxide. One preparative pathway yielded insoluble materials with a Ti/P ratio of approximately 1 which was confirmed by a combination of FT-IR, TGA, and EDS measurements. N2 sorption experiments showed that TPPhA-Ti is a porous solid (micropores approximately 13 A; mesopores approximately 38 A) with a high surface area, approximately 550 m2 g(-1). The structure and morphology of the TPPhA-Ti as investigated by transmission and scanning electron microscopy showed a layered-type material. Additional X-ray diffraction data suggest a paracrystalline material; an optimization of possible molecular arrangements of TPPhA-Ti was simulated that was in agreement with the experimental data. A second preparative pathway yielded a Ti oxide-phosphonate with a Ti/P ratio of approximately 3.4. Both TEM and SEM revealed that hollow nanospheres were formed with diameters of approximately 180-300 nm.     

Defect structure and magnetic moments in the β-phases of CoAl and CoGa

The atomic magnetic susceptibility χ_A of homogeneous β-phases of Co?Al and Co?Ga has been measured in the temperature range from 10 to 300°K. Below 50 at.% Co, χ_A can be described adequately by a Curie law, and for higher Co concentrations a Curie-Weiss law is obeyed. The results are interpreted in terms of a defect structure based on the antistructure cobalt concentration. This treatment is shown to be superior to previous models in that it is now possible to treat the whole range of homogeneous β-phase alloys with a single model. The relationship between the effective magneton number and the Co antistructure atom concentration is linear for both the Co?Al and Co?Ga β-phase above the stoichiometric ratio of Co.