Electric field light scattering by flexible linear polyelectrolytes in aqueous solution

Electric field light scattering results on aqueous solutions of linear, flexible NaPSS at minimal ionic strength are reported. Samples of molecular weights between 356 kg/mol and 2870 kg/mol were investigated. With increasing field strength the intensity as a function of wavenumber develops a pronounced oscillating behaviour. Besides the well-known first peak a second maximum is observed at the position at which a weak maximum for some samples already occurs at zero field. The overall intensity strongly depends on the frequency of the electric field. The electro-optical effect shows a maximum at 300 kHz. Increasing the particle concentration gives a large increase of the peak maximum, normalized to concentration. If plotted versus scattering angle the relative intensity increase is maximum for samples of medium molecular weight. The results strongly indicate a stretching and alignment of the chains, thus leading to or enlarging the short range order of the chains. Received 9 April 1999 and Received in final form 18 August 1999     

Hypersonic wave anomalies in Cs3H(SeO4)2 at the transitions above room temperature

The elastic properties of Cs3H ( SeO4 ) ₂ are investigated by Brillouin spectroscopy in the temperature range 20-220 covering the two transitions III II and II I occurring at and , respectively. Phase I is known to be a protonic conductive one. Discontinuities of elastic constants are generally observed at both transitions, implying first orderness. In phases II and I, a slight broadening of the Brillouin lines is detected. The results are discussed in comparison with compounds of the families XHSeO4 (X = NH4, Rb and Cs) and CsH2BO4 (B = As and P) which also undergo a transition to a superionic phase. In the conductive phase, it appears that the lattice anharmonicity is weaker in Cs3H ( SeO4 ) ₂ than in these other compounds. Received 16 October 1998     

Light scattering by transverse waves in supercooled liquids and application to metatoluidine

We discuss the hydrodynamic equations which describe the shear dynamics of a liquid composed of anisotropic molecules, both in its normal and its supercooled phases. We use these equations to analyze 90 depolarized light scattering experiments performed in the supercooled phase of a glass forming liquid, metatoluidine, and show that the information extracted from this analysis is consistent with independent shear viscosity measurements performed on that liquid in the same temperature range. Received 28 April 1998     

Elastic anomalies and orientational glass transition in Na(CN) Cl mixed crystals. A Brillouin spectroscopic study

High performance Brillouin spectroscopy (BS) has been used to study the elastic properties (static and dynamic) of the orientational glassy state of Na(CN)_xCl_1-x samples ). The temperature behaviour of the elastic properties reveals a more complex scenario for the orientational glass transition than generally believed. The shear elastic constant shows the well-known c ₄₄ ( T ) anomaly, indicated by a minimum, found in other cyanide mixed crystals. The results obtained for the hypersonic attenuation are in clear contradiction with the dynamic character of the c ₄₄ ( T )-minimum. The temperature behaviour of the longitudinal elastic constant c₁₁ of very dilute Na(CN)_xCl_1-x samples shows two striking features: i) Similar to the anomalous temperature behaviour of c ₄₄ ( T ), lowering the temperature c ₁₁ ( T ) first decreases, goes through a minimum and then rises again. The minimum takes place at a temperature above the temperature, , where c ₄₄ ( T ) reaches its minimum value. ii) A kink-like anomaly of c ₁₁ ( T ) is observed at lower temperatures. This second anomaly is similar to the classical one observed in canonical glasses at their glass transition temperature . Received 8 April 1999 and Received in final form 3 June 1999     

Light scattering with swollen hexagonal phases

We investigate, using quasi-elastic light scattering, some features of the long-wavelength, low-frequency modes of the hexagonal phase often encountered in the study of lyotropic (surfactant-solvent) systems. The hexagonal phase is swollen by an oil-based ferrofluid, allowing magnetically aligned samples to be prepared. We show experimentally the anisotropy of the two lowest-frequency modes. We develop a model which predicts that these slow modes are associated to particle diffusion and tube motion. With the help of microscopic as well as phenomenological analyses, we suggest that the latter presumably corresponds to a peristaltic mode. Confinement effects on the one-dimensional, Brownian diffusion of the colloids along the tube axis together with the coupling between the two modes are studied experimentally, varying the tube diameter to particle size ratio. Received 7 July 1999     

Brillouin scattering study of transverse elastic waves in the α, incommensurate and β phases of AlPO4

Transverse and pseudo-transverse elastic waves have been studied in several scattering geometries in order to investigate the temperature dependences of C E ₆₆ and C E ₁₄ over the range 300-1100 K, including the transitions near 860 K. These results complete those on C E ₄₄ we have obtained in a previous work. All these constants display discontinuities at the lock-in transition. In the phase, the results are analysed in term of lowest order couplings between strains (e) and the order parameter (Q). The main features are described by the lowest order biquadratic e2Q2 coupling, in particular for C E ₄₄ in a large temperature range. However, it appears that a contribution of the next coupling term arises for C E ₆₆ below K and that the first two lowest order terms have to be taken into account even just below the lock-in transition in the case of C E ₁₄ . The temperature dependence of Q has been deduced and it can be well described in the framework of Landau's theory. Received: 2 October 1997 / Received in final form: 3 December 1997 / Accepted: 29 January 1998     

Transport properties of high temperature air in local thermodynamic equilibrium

In the paper new calculated transport coefficients of air in the temperature range 50-100 000 K are presented. The results have been obtained by means of the perturbative Chapman-Enskog method, assuming that the plasma is in local thermodynamic equilibrium (LTE). The calculations include viscosity, thermal conductivity, electric conductivity and multicomponent diffusion coefficients. For the calculation, a recent compilation of collision integrals obtained by Capitelli et al. [1] has been utilized. Analytical expression for all transport coefficients and thermodynamic parameters of the air plasma are also reported. Received 17 November 1999     

The origin of the redshift in Brillouin spectra of silica films containing tin nanoparticles

The abrupt change of velocity in surface acoustic waves in thin films of amorphous SiO_x containing nanometre scale -Sn crystals is shown to be directly associated with the size-dependent melting of the nanoparticles, confirming preliminary experiments. High resolution thin film powder diffraction using synchrotron radiation shows that the abrupt redshift in the Brillouin spectra satellites occurs at the same temperature as the melting of the nanoparticles, evident for the loss of the Bragg peaks. Effective medium theory is used to explain the origin of the anomaly. A central peak in the Brillouin spectrum, the intensity of which shows a maximum at the melting temperature, can be interpreted in terms of overdamped fluctuations in the dielectric function. The melting temperature as a function of particle size is in agreement with theoretical predictions. No evidence for strain could be found on the X-ray diffraction profiles; the a- and c-axis thermal expansion coefficients are the same as those in bulk tin. Received 30 March 2000 and Received in final form 24 July 2000     

Aqueous mixtures of spherical and rodlike (flexible) macroparticles: structure and dynamics of latex spheres in saltfree solutions

This paper resumes light scattering investigations of saltfree aqueous solutions of two component mixtures of charged spheres by extending those measurements to systems in which one component is replaced by essentially stiff rodlike particles. In a second step of investigations these were replaced by linear flexible particles. Fd-virus particles (length l=883 nm) or macromolecules of NaPSS of four different contour lengths have been used as representatives. Mostly the concentration of latex spheres was fixed at 0.02 Vol%. The concentration of the other component was varied over a wide range. Concerning the scattering intensity, the contribution of the latex spheres dominates, in particular in the systems containing NaPSS particles. This simplifies the interpretation of data considerably. A rearrangement of the spheres is observed, depending on the shape of the other sort of particles. These conclusions can be drawn from the shift of measured static structure factor with concentration c. A power law is found for the q-value of the maximum. The exponent depends on the properties of the second component. For the lower molecular weight (MW) samples of NaPSS below a critical concentration, the exponent is smaller than 1/3, decreasing the more the smaller the MW of the samples is. A tentative explanation in terms of charge number of NaPSS particles is given. The short time dynamics has been explored too. From the data a “dynamically determined structure factor” can be derived, that can be compared with the measured static structure factor. Good (fd) and fair (NaPSS) agreement is obtained respectively. Only at small wavenumbers below the maximum of deviations occur which increase with concentration; they are consistent with hydrodynamic interaction. Received 30 July 1998 and Received in final form 14 December 1998     

Pressure and temperature variation of the depolarized light scattering spectra of the fragile glass-former liquid salol

The pressure and temperature dependences of the depolarized light scattering spectra of salol have been measured at isobaric condition P = 1 bar for T between 328 and 393 K, and at isothermal condition T = 343 K for P between 1 and 625 bar, i.e. outside the metastable liquid region. The experimental results for both the α- and β-relaxations can be well described by the Mode Coupling Theory. The independence of the power-law parameters a, and consequently b and γ, from the thermodynamic variables T and P is demonstrated.The critical temperature T _c at 1 bar and the critical pressure P _c at T = 343 K have been determined from the normal liquid state. Received 2 May 2000     

Mode-coupling crossover in viscous toluene revealed by neutron and light scattering

The dynamics of supercooled toluene, studied in a GHz-THz range by incoherent neutron and depolarized light scattering, is found to be in full accord with mode coupling predictions. Around the susceptibility minimum, neutron spectra are wavenumber independent and proportional to light scattering data; the fast -relaxation scaling law applies; amplitude and frequency diverge with power laws that extrapolate towards a crossover temperature K. Received: 20 June 1997 / Accepted: 3 November 1997     

Orientational diffusivities measured by Rayleigh scattering in a lyotropic calamitic nematic () liquid crystal phase: the backflow problem revisited

Using a light-beating technique we have measured the damping time of thermal fluctuations of the nematic director for the so called cylindrical or calamitic nematic (N_C) phase of the lyotropic system K-laurate/decanol/. By varying the scattering angle in suitable geometries, we have been able to estimate the orientational diffusivities associated to the three pure deformations of splay, twist and bend. A former measurement made in the disk-like N_D phase of the same system yielded a large deviation between the splay and twist diffusivities. The effect was then attributed to induced flows, or backflow, which could be responsible for the reduction of the splay viscosity. In fact, this is the analogous effect, for disks, to the one recognized since long time ago arriving for rod-like molecules in a classical nematic, though in this case it is associated with bend deformations. The analogy comes about thanks to the interchange of the role played by disks and cylinders for, respectively, splay and bend fluctuations.The measurements reported here provide a new test on the applicability of the backflow model to a nematic system composed of micelles, that is, aggregates made of amphiphilic (surfactant) molecules, in its cylindrical-like variant, i.e. the N_C phase. In addition, the comparative study made here with the previous results existing in the literature for the N_D phase, allows us to conjecture on structural issues concerning lyotropic nematics. Received: 29 April 1998 / Revised: 19 August 1998 / Accepted: 31 August 1998     

Shrinking of anionic polyacrylate coils induced by Ca2+, Sr2+ and Ba2+: A combined light scattering and ASAXS study

Anionic polyacrylate chains (NaPA) form precipitates if alkaline earth cations are added in stoichiometric amounts. Accordingly, precipitation thresholds were established for three different alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Close to the precipitation threshold, the NaPA chains significantly decrease in size. This shrinking process was followed by means of combined static and dynamic light scattering. Intermediates were generated by varying the ratio [MCl₂]/[NaPA] with M denoting the respective alkaline earth cation. All experiments were performed at an inert salt level of 0.01M NaCl. Similar coil-to-sphere transitions could be observed with all three alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Based on these findings, supplementary conventional and anomalous small-angle X-ray scattering experiments using selected intermediates close to the precipitation threshold of SrPA were performed. The distribution of Sr counterions around the polyacrylate chains in aqueous solution provided the desired scattering contrast. Energy-dependent scattering experiments enabled successful separation of the pure-resonant terms, which solely stem from the counterions. The Sr²⁺ scattering roughly reflects the monomer distribution of the polyacrylate chains. Different ratios of the concentrations of [ SrCl₂]/[NaPA] revealed dramatic changes in the scattering curves. The scattering curve at the lowest ratio indicated an almost coil-like behaviour, while at the higher ratios the scattering curves supported the model of highly contracted polymer chains. Most of X-ray scattering experiments on intermediate states revealed compact structural elements which were significantly smaller than the respective overall size of the NaPA particles.     

Thermodynamic and transport properties in equilibrium air plasmas in a wide pressure and temperature range

Thermodynamic and transport properties of high temperature equilibrium air plasmas have been calculated in a wide pressure ( atm) and temperature range ( K). The results have been obtained by using a self-consistent approach for the thermodynamic properties and higher order approximation of the Chapman-Enskog method for the transport coefficients. Debye-Hükel corrections have been considered in the thermodynamic properties while collision integrals of charge-charge interactions have been obtained by using a screened Coulomb potential. Calculated values have been fitted by closed forms ready to be inserted in fluid dynamic codes.     

Longitudinal and bulk viscosities of binary fluid mixtures

Expressions for zeroth, second and fourth sum rules of longitudinal and bulk stress auto correlation functions have been derived for binary fluid mixtures. Longitudinal and bulk viscosities of an Ar–Kr mixture have been calculated using Mori's memory function formalism coupled with the sum rules of longitudinal and bulk stress auto correlation functions. The results obtained are compared with the molecular dynamics simulation. Mass dependence of the longitudinal and bulk viscosities has been studied for different compositions of an isotopic mixture at different densities and temperatures. For very large mass ratio, the longitudinal and bulk viscosities of the isotopic mixture are more dependent on mole fraction than on mass.     

Light scattering by longitudinal acoustic modes in supercooled molecular liquids II: microscopic derivation of the phenomenological equations

The constitutive equations for the orientational dynamics of a liquid formed of linear molecules are derived microscopically. The resulting generalised Langevin equations coincide with the phenomenological approach of Dreyfus et al. [1]. Formally exact expressions are given for the phenomenological coefficients and various constraints are shown to be consequences of this microscopic approach. Received 14 August 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: franosch@hmi.de     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Light scattering by longitudinal acoustic modes in molecular supercooled liquids I: phenomenological approach

We derive expressions for the intensity of the Brillouin polarized spectrum of a molecular liquid formed of axially symmetric molecules. These expressions take into account both the molecular dielectric anisotropy and the modulation of the local polarisability by density fluctuations. They also incorporate all the retardation effects which occur in such liquids. We show that the spectrum splits into a q-independent rotational contribution and q-dependent term, which reflects the propagation of longitudinal acoustic modes. In the latter, the two light scattering mechanisms enter on an equal footing and generate three scattering channels. We study the influence of the two new channels and show that they may substantially modify the Brillouin line-shape when the relaxation time of the supercooled liquid and the period of the acoustic excitation are of the same order of magnitude. Received 14 August 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: franosch@hmi.de     

Application of the Sherman-Morisson formula to scattering problems by multi-component systems

The scattering matrix for multi-component systems is recalculated using the extended form of the Sherman-Morisson formula. The matrix elements are given explicitly in closed form. The Gibbs-Duhem relation separates the density and composition contributions. Received 5 April 2002     

Diffusive Wave Spectroscopy of a random close packing of spheres

We are interested in the propagation of light in a random packing of dielectric spheres within the geometrical optics approximation. Numerical simulations are performed using a ray tracing algorithm. The effective refractive indexes and the transport mean free path are computed for different refractive indexes of spheres and intersticial media. The variations of the optical path length under small deformations of the spheres assembly are also computed and compared to the results of Diffusive Wave Spectroscopy experiments. Finally, we propose a measure of the transport mean free path and a Diffusive Wave Spectroscopy experiment on a packing of glass spheres. The results of those experiments agree with the predictions of this ray tracing approach.