Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

Cyclic and telechelic ladder polymers derived from tetrahydroxytetramethylspirobisindane and 1,4‐dicyanotetrafluorobenzene

5,5′,6,6′‐Tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was polycondensed with 1,4‐dicyanotetrafluorobenzene in four different solvents at 70 °C. In dimethylformamide, N‐methylpyrrolidone, and sulfolane exclusively, cyclic polymers were detectable by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry up to masses around 13,000 Da. In dimethyl sulfoxide, linear byproducts were also found. Higher temperatures caused degradation reactions catalyzed by potassium carbonate. Polycondensations performed with the addition of 4‐tert‐butyl catechol or 2,2′‐dihydroxy binaphthyl yielded linear telechelic oligomers. Equimolar mixtures of linear and cyclic ladder polymers were examined by MALDI‐TOF mass spectra to determine how the end groups and the cyclic structure influenced the signal‐to‐noise ratio. The results suggested a preferential detection of the linear chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5344–5352, 2006     

On the existence of equilibrium states in local quantum field theory

It is shown that any local quantum field theory admits thermodynamical equilibrium states (KMS-states) for all positive temperatures provided it satisfies a nuclearity condition, proposed by Wichmann and one of the authors, which restricts the admissible number of local degrees of freedom.Dedicated to E. H. Wichmann on the occasion of his 60th birthday     

Intercalation of Dyes Containing SO3H Groups into Zn–Al Layered Double Hydroxide

The intercalates of Naphthol Yellow S, Tropaeolin 000, and Tropaeolin 00 were prepared by heating [Zn_0.67Al_0.33(OH)₂](CO₃)_0.165 · 0.5H₂O with acidic forms of the dye solutions in an open reaction vessel. The intercalates were characterized by chemical and thermal analysis, X-ray powder diffraction and UV–VIS spectroscopy. A possible arrangement of the dye molecules in the intercalates was suggested on the basis of their chemical compositions and interlayer distances, by taking into account van der Waals dimensions of the guest molecules and by assuming that the structure of the host layers is not changed during the intercalation process.     

Intercalation of 1,2-Alkanediols into α-Zirconium Hydrogenphosphate

Intercalation compounds of α-Zr(HPO₄)₂ · H₂O with 1,2-alkanediols (from C3 to C16) have been prepared by replacing 1-propanol in α-Zr(HPO₄)₂ · 2C₃H₇OH with the desired 1,2-alkanediols by a treatment in a microwave field. It was found that the intercalates contain 1.5 molecules of diol per formula unit. The diol molecules are placed between the host layers in a bimolecular way with their aliphatic chains tilted at an angle of 51°. The diol molecules are anchored in the interlayer space by H-bonds. A mixed intercalate, containing 1,2-butanediol and 1,2-decanediol in a roughly equimolar ratio, is formed when the α-Zr(HPO₄)₂ · 2C₃H₇OH intercalate, suspended in a mixture of 1,2-butanediol and 1,2-decanediol, is exposed to microwave radiation. No new phase containing both types of the guest molecules was observed when the 1-propanol intercalate, suspended in a mixture of 1-propanol and 1,2-octanediol, is exposed to microwave radiation.