Low frequency relaxation in liquid crystals in relation to structural relaxation in glass-formers

Liquid crystals (LC) are the state of matter intermediate between isotropic liquids and the crystalline state. LC-forming molecules have strongly anisotropic shapes (rod-like in most cases). This leads to an interaction potential that consists of distance-dependent and orientation-dependent parts. Rotational dynamics of LC molecules falls into two frequency regions. Rotations about the short axes are strongly hindered by the potential barrier and thus coupled to fluctuations of the molecular centers of mass. This in turn causes these longitudinal or “flip-flop” motions, characterized by a relatively large relaxation time τ_||, to exhibit considerable temperature, pressure and volume dependences. Experimental relaxation times determined to date for various LC phases (nematic, smectic A, C, and E) for different thermodynamic conditions (isobaric, isothermal and isochoric) are discussed herein, adopting the formulae applied for characterization of the structural relaxation times of glass-formers (GF). This analysis appears fruitful; in particular, the strength parameter characterizing the steepness of the interaction potential can be determined from the relaxation times, and τ_|| is independent of temperature and pressure along the nematic-isotropic transition line, similar to the behavior of the structural relaxation time along certain transitions in GFs.     

The styrylpyridine dye for the silane sol-gel transition studies by time-dependent fluorescence

A trans-4-(p-N,N-dimethylaminostyryl)-N-vinylbenzylpyridinium chloride (vbDMASP) fluorescence probe was optimized in ground and excited state as a function of change in the microenvironment polarity, using the Amsol HyperChem program package. In the calculations, protic and aprotic solvents were used. On this basis a change in the molecule geometry after excitation, depending on the surrounding solvent, was determined. Absorption and steady-state fluorescence spectra of vbDMASP in the solvent of different polarity and in the model water-glycerol solutions were also recorded. On the basis of Stokes' shift change with the Onsager polarity scale a change in the dipole moment of the probe during transition from ground to excited state, in protic and aprotic solvents was determined. Since during the sol-gel transition of tetraethylorthosilane in the acidic environment both polarity and viscosity of the microenvironment change the vbDMASP probe was applied and fluorescence time-resolved measurements were done. On this basis the correlations between the results of time-resolved measurements for the multichromophoric probe applied in the gelation process and molecular optimization data are discussed.     

The influence of the cyclopeptide sequence on its coordination abilities towards Cu(II)

The binding abilities of three novel cyclohexapeptides with three histidyl residues are presented. The analysis of the potentiometric and spectroscopic results, together with the theoretical calculations, allow the characterization of the coordination abilities of c(GlyHisArgHisHisGly), c(GlyHisArgHisGlyHis), c(GlyHisArgGlyHisHis) towards copper(II) ions and the impact of the peptide sequence on the efficiency in Cu(II) binding, and the type of formed complexes is also presented.     

Solvability of dynamic antiplane frictional contact problems for viscoelastic cylinders

We study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation. The process is dynamic, the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition. We derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field. Then we prove the existence of a weak solution to the model. The proof is based on an abstract result for second order evolutionary inclusions in Banach spaces. Also, we prove that, under additional assumptions, the weak solution to the model is unique. We complete our results with concrete examples of friction laws for which our results are valid.     

Weight choosability of graphs

Suppose the edges of a graph G are assigned 3‐element lists of real weights. Is it possible to choose a weight for each edge from its list so that the sums of weights around adjacent vertices were different? We prove that the answer is positive for several classes of graphs, including complete graphs, complete bipartite graphs, and trees (except K₂). The argument is algebraic and uses permanents of matrices and Combinatorial Nullstellensatz. We also consider a directed version of the problem. We prove by an elementary argument that for digraphs the answer to the above question is positive even with lists of size two. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 242–256, 2009     

Polynomial approximation of rational Bézier curves with constraints

We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the polynomial Bézier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, and exploits their recursive properties. Examples are given, showing the effectiveness of the algorithm.     

Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.     

Kinetics of refractive index changes in polymeric photochromic films

Methacrylate copolymers containing, in side chain azobenzene groupings with heterocyclic sulfonamide substituents: N-(2,6-dimethylpyrimidin-4-yl)sulfamoyl (sulfisomidine) and N-(5-methylisoxazol-3-yl) sulfamoyl (sulfamethoxazole) were investigated. The materials undergo reversible trans-cis isomerisation during illumination with light. This results in changes of dipole moment, polarizability and refractive index. Ellipsometric measurements showed a distinct decreasing refractive index during illumination with light corresponding to absorption band (ca. 450 nm). Depending on the polymer, the change of real part of refractive index in spin-coated films was between 0.016 and 0.031. The dynamics of growth and decay of refractive index changes, was described by biexponential function approach.