“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

Thermodynamics for Coulomb systems: A problem at vanishing particle densities

In this paper I combine techniques recently developed by Charles Fefferman with the well-known methods of Joel Lebowitz and Elliott Lieb to resolve some technical problems left unsettled by Lebowitz and Lieb's fundamental 1972 paper The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei.     

Fermionic perturbation theory for the statistical mechanics of the nonlinear Schrödinger model

A fermionic perturbation theory is developed for the statistical mechanics of the nonlinear Schrödinger model. The theory is based on an interacting-fermion picture of the Bethe wave function. The inner product of the Bethe wave function is explicitly evaluated, and a simple graphical representation of it is given. The basic equations obtained for the free energy agree with those of Yang and Yang. In particular, the present theory gives a clear-cut meaning to the function of Yang and Yang: It represents a fermion energy at finite temperatures.     

A new approach to the determination of the statistical segment length of wormlike polymers

The Stockmayer-Fixman-Burchard (SFB) and the Dondos-Benoit (DB) equations have been applied to determine the unperturbed dimensions parameterK of wormlike polymers. An empirical relation between the Flory's constant and the Mark-Houwink-Sakurada (MHS) exponenta has been proposed. The values found by this equation are lower than the value 2.5×10²³ used in the case of flexible polymers and this deviation is attributed to the influence of the draining effect. From theK value and the so calculated value of , we calculate the Kuhn statistical segment length of wormlike polymers. The obtained — for a great number of wormlike polymers — statistical segment lengths are almost the same as these calculated by the Yamakawa-Fujii and the Bohdanecky methods. The molecular mass regions in which the SFB, the DB, and the MHS equations are valid are explored. A criterion for the distinction between flexible and wormlike polymers is proposed based on the way of approach to the power law.     

Transition metal 1,2-bidentate thiolates as building blocks and their construction into cluster complexes

Simple fragments of transition metal 1,2-bidentate thiolates, the so-called building blocks of the general compositions ML₃, ML₂, ML, M(O)L₂, ML₂L, MLL, etc. have been proposed to constitute the di-, tri- and tetranuclear complexes concerned in this review. Structureal regularities and characteristics have been discussed and summarized according to the thiolato ligands edt and pdt, bdt and tdt, mp, and mpo, and mpp, respectively.Abbreviations H₂mpo o-mercaptophenol - Hmpo 2-mercaptopyridine-N-oxide - R₂dtc N,N-dialkyldithiocarbamate - Haet 2-aminoethanethiol - H₂bdt o-benzenedithiol - H₂pdt 1,2-propanedithiol - H₂tdt toluene-3,4-dithiol - Hmpp-mppH bis-(3-hydroxy-2-pyridyl)disulfide - Hmp-mpH bis-(2-oxyphenyl)disulfide - H₂edt 1,2-ethanedithiol - dppe 1,2-bis(diphenylphosphino)ethane - H₂tedt 3,4,5,6-tetrachlorobenzene-1,2-dithiol - H₂tpdt 3-thiapentane-1,5-dithiol - H₂mnt maleonitriledithiol - Him imidazole - Bz benzyl - py pyridine     

Darstellung, 19F-NMR-spektroskopischer Nachweis und Untersuchung zur Bildung der metallgemischten Clusteranionen [(Mo6−nWnCl)F]2−, n = 0−6

Preparation, ¹⁹F NMR Spectroscopic Evidence and Study of the Formation of Metal-Mixed Cluster Anions [(Mo_6?nW_nCl )F ]^2?, n = 0?6 The complete system of metal-mixed octahedral cluster ions [(Mo_6?nW_nCl)F]^2?, n = 0?6, is prepared by tempering Mo powder with WCl₆ at 600°C. A mixture containing inclusively the geometric isomers (n = 2, 3, 4) all ten possible species is transferred into the tetra-n-butylammonium salts (TBA)₂[(Mo_6?nW_nCl)F]. In the ¹⁹F nmr spectrum the 24 expected signals are observed, assigned on the basis of their chemical shifts, multiplicities and intensities, and confirmed by a 2D-¹⁹F-¹⁹F COSY spectrum. From the integrated intensities the distribution of the different components is derived revealing a non-statistical formation, in that isomers with Mo…?Mo or W…?W atoms in trans-positions in comparision to those with mixed Mo…?W axes are favoured, and that especially the homoleptic compounds Mo₆ and W₆ are present to an over-average extent. Evaluation of ¹⁹F chemical shifts reveals that F bound to W which is in antipodal position to Mo resonates at higher field compared to F bound to W in a W…?W arrangement, caused by an increased shielding, which is synonymous to a positive antipodal-effect by Mo. Vice versa F bound to Mo with an antipodal W resonates at lower field compared with F bound to Mo in an Mo…?Mo arrangement caused by an increased deshielding and synonymous a negative antipodal-effect by W. The chemical shifts, resulting from antipodal-effects, are different for the compounds within the [(Mo_6?nW_nCl)F]^2? - system. The difference of the antipodal effect of successive substitution products results in characteristic values designated as antipodal shift constants, depending on the kind of substituents, which is valid for other cluster systems, too.     

Multiple glass transitions and local composition effects on polymer solvent mixtures

Recent differential scanning calorimetry (DSC) results on polystyrene–solvent mixtures show two distinct glass transitions whose positions and widths vary with composition. Parallel work on the dynamic response in polymer blends has focused on how segmental mobilities are controlled by local composition variations within a “cooperative volume” containing the segment. Such variations arise from both chain connectivity and composition fluctuations. We account for both using a lattice model for polymer–solvent mixtures that yields the composition distribution around polymer and solvent segments. Insights from our lattice model lead us to simplified calculations of the mean and variance of local composition, both in good agreement with lattice results. Applying our model to compute DSC traces leads to an estimate of the cooperative volume, since a larger cooperative volume both reduces the biasing effect of connectivity, and narrows the composition distribution. Comparing our results to data, we are able to account for the composition-dependent broadening with a cooperative length scale of about 2.5 nm. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3528–3545, 2006     

Advanced statistical evaluation of the complex formation constants from electrophoretic data II: Diastereomeric ion-pairs of (R,S)-N-(3,5-dinitrobenzoyl)leucine and tert-butylcarbamoylquinine

Intermolecular association and ion-pair formation, respectively, between a cationic chiral selector, viz. o-9-(tert-butylcarbamoyl) quinine (CQN), and the both enantiomers of anionic N-(3,5-dinitrobenzoyl)leucine, (R)-DNB-Leu and (S)-DNB-Leu, were investigated by affinity capillary electrophoresis (ACE). Thus, binding constants of the both diastereomeric ion-pairs, (R) and (S)-DNB-Leu/CQN associates, were determined by different experimental setups and correction of nonlinear effects. A reciprocal setup was employed for the high-affinity (S)-enantiomer, and the experimental mobility data obtained for CQN at variable (S)-DNB-Leu concentrations in the background electrolyte were linearized and evaluated by advanced statistical model. A binding constant of K_S=125.1 l mol⁻¹ was afforded. The constant for the (R)-enantiomer, which is outside the range suitable for direct affinity CE, was obtained from indirect affinity CE utilizing the separation of the DNB-Leu racemate at a single appropriate CQN concentration in the BGE (resolution method) taking advantage of the known constant for the (S)-enantiomer yielding a binding constant of K_R=2.51 l mol⁻¹. Thereby, the so-called “constant time method” was adopted for the required precise measurement of the effective mobilities of the both enantiomers. A combined approach of reciprocal affinity CE with racemic DNB-Leu as additive and the resolution method confirmed the results. The resulting constants evidence excellent enantioselectivity of the tert-butylcarbamoyl derivative of the cinchona alkaloid quinine as chiral selector for N-(3,5-dinitrobenzoyl) derivatives of amino acids.     

Extraction of kinetic information from single-molecule experiments.

We discuss two possible approaches for extracting kinetic information from single-molecule experiments. The first approach is based on computing correlation functions from measured fluorescence signals, and the second on studying the statistics of on and off times of the same fluorescence signal. We show that in both cases it is possible to extract kinetic information about the nature of intramolecular fluctuations of the single molecule. We show that for single-molecule kinetics the intramolecular fluctuations produce stochastic memory effects which lead to new dynamic features that do not exist in traditional chemical kinetics. In particular, we investigate a new type of chemical oscillations in correlation functions observed experimentally by Edman and Rigler (Proc. Natl. Acad. Sci. USA 2000, 97, 8266).     

A study for quality evaluation of Taxilli Herba from different hosts based on fingerprint-activity relationship modeling and multivariate statistical analysis

In this study, a fingerprint-activity relationship modeling between chemical fingerprints and antirheumatic activity was established, and multivariate statistical analysis was used to evaluate the quality of Taxilli Herba (TH) from different hosts. Characteristic fingerprints of 20 batches of TH samples were generated by high-performance liquid chromatography coupled with triple quadrupole-time of flight tandem mass spectrometry (HPLC-Triple TOF-MS/MS), and the similarity analysis was calculated based on thirteen common characteristic peaks by hierarchical clustering analysis (HCA). Subsequently, nine efficacy markers were discovered by combining fingerprints and antirheumatic activity through grey correlation analysis (GCA) and bivariate correlation analysis (BCA). Meanwhile, the content of 5 constituents in 9 markers was determined by high-performance liquid chromatography coupled with triple quadrupole-linear ion trap tandem mass spectrometry (HPLC-QTRAP-MS/MS). The comprehensive quality of TH was assessed using multivariate statistical analysis, including principal components analysis (PCA) and technique for order preference by similarity to ideal solution (TOPSIS). The results showed that a high dose of TH extract could markedly ameliorate arthritis damage compared to other doses, with flavonoids playing an important role in the antirheumatic activity. The comprehensive quality of samples from Morus alba L. (SS) was superior to those from Liquidambar formosana Hance (FXS). The present study will demonstrate the markers associated with efficacy, and provide an applicable strategy for more comprehensive quality control and evaluation of TH.