First Curl,Then Wrinkle

The excellent properties of elastomers are exploited to trigger wrinkling instabilities in curved shells. Micro‐ and nano‐fibres are produced by electrospinning and UV irradiated: each fibre consists of a soft core and a stiff outer half‐shell. Upon solvent de‐swelling, the fibres curl because the shell and the core have different natural lengths. Wrinkling only starts after the fibre has attained a well‐defined helical shape. A simple analytical model is proposed to find the curling curvature and wrinkle wavelength, as well as the transition between the “curling” and “wrinkling” regimes. This new instability resembles that found in the tendrils of climbing plants as they dry and lignify.

     

Asymptotic of grazing collisions for the spatially homogeneous Boltzmann equation for soft and Coulomb potentials

We give an explicit bound for the Wasserstein distance with quadratic cost between the solutions of the Boltzmann and Landau equations in the case of soft and Coulomb potentials. This gives an explicit rate of convergence for the grazing collisions limit. Our result is local in time for very soft and Coulomb potentials and global in time for moderately soft potentials.     

Mechanically activated cholesteric polymer dispersed liquid crystals

In this paper we deal with a cellulose derivative cholesteric dispersed liquid crystal (CCDLC) with mechanically tuneable optical properties. The composite is formed with a matrix of acetoxypropylcellulose with embedded micrometric and submicrometric droplets of a cholesteric mixture. Polarizing optical microscopy and atomic force microscopy (AFM) measurements performed on the system are reported and it is shown that the wavelength of the reflected light can be changed by a temperature variation and it is also changeable through a mechanical deformation. The pitch of the deformed droplets can be measured from AFM photographs and compared with the wavelength reflected by the CCDLC composite material.     

Optical properties of cholesteric (2-hydroxypropyl) cellulose (HPC) esters

Acetoxypropylcellulose (APC) and propionic, n-butyric, isobutyric, valeric, isovaleric, hexanionic, and heptanionic acid esters of hydroxypropylcellulose (HPC) (respectively PPC, BPC, iBPC, VPC, iVPC, HexPc, and HepPc) were prepared and characterized by differential scanning calorimetry, chromatography, polarizing microscopy, chemical methods, and spectroscopy. All these esters form thermotropic cholesteric liquid crystalline phases. The glass (T_g) and clearing (T_c) transition temperatures were determined. The stability interval of the mesophases appears to be greater in the case of longer-linear side chains. The mesophases of APC, PPC, iBPC, VPC, and iVPC exhibit reflection bands in the visible region, at wavelengths that depend on temperature, moisture content, size and number of substituents, and degree of polymerization ( \[ \overline {{\rm DP}} \] ). The pitch of the cholesteric helical structure increases with side chain length and with increasing temperature. At room temperature, a fingerprint-like pattern can be observed for HepPc. No reversal in the sense of the pitch with temperature variations was observed. The pitch of BPC increases with moisture content and with decreasing values of the degree of esterification ( \[ \overline {{\rm DE}} \] ) and \[ \overline {{\rm DP}} \] . A theory for cholesteric mesophases composed of helical rod-like species and a model of elastic bend chain have been compared to the experimentally observed changes in the pitch with temperature and with the length of the side chain substituents (for iBPC, iVPC, BPC, PPC, and APC) and \[ \overline {{\rm DE}} \] and \[ \overline {{\rm DP}} \] (for BPC). © 1994 John Wiley & Sons, Inc.     

The first normal stress difference and viscosity in shear of liquid crystalline solutions of hydroxypropylcellulose: new experimental data and theory

The constitutive equations for liquid crystalline polymers recently proposed by one of us [1] are applied here to interpret the behaviour of the shear viscosity η and the first normal stress difference N₁() measured for liquid crystalline (LC) solutions of hydroxypropylcellulose in acetic acid. N₁( ) is observed to change from positive to negative and again to positive, as the shear rate increases, at lower concentrations, in the LC phase. The -values at which N₁ changes sign depend on the molecular mass (degree of polymerization) and on the concentration. η shows a small Newtonian plateau at low shear rates and a strong shear-thinning at higher values of . The rate of decrease of η in this region shows an “hesitation” similar to one previously observed in LC solutions of poly-γ-benzyl-L-glutamate PBLG. All these observations can be rationalized within the frame-work of Martins' theory. The expressions for N₁() and η derived from this theory fit very well (quantitatively) to the experimental data and some fundamental viscoelastic parameters of the system under study are thereby obtained for the first time.     

Conditions for the Solvability of Systems of Two and Three Additive Forms Over p-Adic Fields

This paper is concerned with non-trivial solvability in p-adicintegers of systems of two and three additive forms. Assumingthat the congruence equation ax^k + by^k + cz^k d (modp) has asolution with xyz 0(modp) we have proved that any system oftwo additive forms of odd degree k with at least 6k + 1 variables,and any system of three additive forms of odd degree k withat least 14k + 1 variables always has non-trivial p-adic solutions,provided p does not divide k. The assumption of the solubilityof the congruence equation above is guaranteed for example ifp > k⁴. In the particular case of degree k = 5 we have proved the followingresults. Any system of two additive forms with at least n variablesalways has non-trivial p-adic solutions provided n 31 and p> 101 or n 36 and p > 11. Furthermore any system of threeadditive forms with at least n variables always has non-trivialp-adic solutions provided n 61 and p > 101 or n 71 andp > 11. 2000 Mathematics Subject Classification 11D72, 11D79.     

Magnetic and transport properties of transition-metal implanted ZnO single crystals

ZnO single crystals were implanted with Mn, Co and Ni with fluences between 1 × 10¹⁶ cm^-2 and 1 × 10¹⁷ cm^-2 and energy of 200 keV. Results indicate that aggregation of transition metal ions in the as implanted state occurs only in the case of Ni. After an annealing stage to recover the ZnO structure aggregation occurs for the higher fluences of all implanted species. For lower concentrations paramagnetic behaviour with magnetic moments close to those of individual ions is observed. No polarised impurity band is formed as a result of the presence of transition metal ions and all samples show electrical conduction by carriers in extended states of ZnO. Significant values of magnetoresistance are measured at low temperatures, where electrical transport is described by hopping mechanisms between localized states. The sign of the magnetoresistance is dependent of the doping ion and is correlated with the observed aggregation.     

Anisotropic hydroxypropylcellulose films as alignment layers of a bistable ferroelectric device

Hydroxypropylcellulose films are used as the alignment substrate in a liquid crystal bistable electro-optical device. These alignment films were characterized by atomic force microscopy. The electro-optical behaviour of this device, which operates in the Clark-Lagerwall mode, is identical to that observed for typical SSFLC cells. In particular the bistability of the cell was clearly observed, the threshold voltage was measured and an estimation of the anchoring energy of the LC mixture used, in this type of system, was made.     

Investigation of the iron site localization in doped ZnO

Iron doped (5%) ZnO powders were prepared by hydrothermal and combustion methods. Subsequent heating treatments on these samples were performed under air and also under a reductive atmosphere. Powder XRD, Mössbauer spectroscopy and magnetization studies were used to characterize the products and investigate the localization of iron ions in the ZnO lattice. It was shown that a mixture with a ZnFe₂O₄ type phase was obtained when the sample was prepared by the hydrothermal method, while Fe³⁺ occupy tetrahedral sites of the ZnO lattice in the case of the sample obtained by the combustion method. The magnetic measurements show that no ferromagnetism was detected in the iron doped ZnO compound, neither in the as prepared state nor after reduction.