Optical rotatory power and Raman scattering experiments on chiral liquid crys- tals belonging to a series which exhibits one or two ferrielectric phases have been performed. The results of these non-perturbative techniques show that, depending upon the aliphatic chain length, a first order transition with a jump in sign and value of the helical pitch, or a divergence and sign reversal of the pitch with no transition can occur in these systems. These observations are in agreement with a generalized Landau-de Gennes phenomenological model predicting that the ferrielectric phases, when both exist, should be isostructural.
Partition coefficients of solutes between bilayers and water are determined with a new method, using contrast variation with SANS. The isotopic composition of the solvent that annuls the contrast is shown to depend on thermodynamical quantities related to the adsorption. Experimental results are given for two organic solute molecules (lactitol and aniline) in the favorable case of the swollen lamellar phase obtained with DDAB double chain surfactant.
Nous donnons une explication du comportement critique (c-a-d. non-champ moyen) de la chaleur specifique, qui a ete observe recemment sur certains composes. Cette explication repose sur l'energie libre de Andereck et Swift qui introduit des termes couplant le parametre d'ordre avec la compression de couche et la densite. Nous montrons que le comportement de la chaleur specifique depend de l'intensite de ces couplages et que les comportements qui peuvent etre observes sont par suite de type champ moyen, gaussien ou 3DXY.
The microphase separation transition in the weakly charged polyelectrolyte gels immersed in poor solvent and undergoing collapse transition is studied in the weak crystallization approximation. The chain connectivity in the gel is taken into account ma introducing polar- ization term first proposed by de Gennes. It is shown that in this case the gel can undergo multistage jump-like collapse where the intermediate states can have regular microstructures of different symmetry,. The availability of numerous metastable states in the collapse region may lead to the pronounced hysteresis effects. These results are compared with some of the recent experimental findings.
Recent Neutron Scattering experiments by Richter et al. [1] show that the presence of coil-crystalline block copolymer (PE-PEP) micelles in a mixed alkane bath suppresses the crystallization out of solution of the long alkane component at low temperatures. Motivated by these experiments, we study theoretically the thermodynamics and kinetics of lamellar coil-crystalline block copolymer micelles in a bimodal solvent to better understand the factors determining the anti-precipitation action of coil-crystalline block copolymers. We assume an Alexander-de Gennes brush model for the strongly stretched corona chains and explicitly account for the polydispersity of the solvent chains. For the thermodynamic distribution of solvent chains in the corona, we find a predominance of short solvent chains to long solvent chains in the corona phase compared to the solvent bath; both with and without nematic interactions in the corona phase. We also calculate the rate of crystallization of the long solvent chains onto the micellar crystal core and find that the rate is sensitive to both brush and core parameters. In particular, we predict that to maximize the rate, both E-fold/kTN(A) and chi(n) need to be made as small as possible, where E-fold is the folding energy of the crystal core chains, N-A the number of statistical segments of the solvated corona chains and chi(n) parameterises the strength of nematic interactions in the micellar corona. This leads to the surprising result that for fixed E-fold, the rate of crystallization is increased when we increase the molecular weight of the corona blocks.
We consider harmonically undulating ionic surfactant membranes, calculating a general expression for the bending modulus valid for all salt and surfactant concentrations, and surface charge densities. This is achieved through a perturbative expansion of the mean-field electrostatic potential and free energy about a planar reference state, consisting of two parallel planar membranes with intervening salt solution. For a given choice of undulation mode, the result for the bending modulus is seen to be generally the same as that obtained from considerations of membranes deformed into a cylindrical geometry. Thus, we show that the bending modulus is independent of global aggregate geometry, at a general system composition. Specializing to the limit of excess added salt (equivalent to a single undulating membrane in contact with bulk electrolyte), we are able to extend the free energy calculation to fourth order in undulation amplitude, and derive the bending constants of the curvature expansion to this order. These have been suggested previously to be of importance in explaining the stability of bicontinuous crystalline and disordered phases, and the formation of passages in lamellar phases. We also discuss the breakdown of the curvature description at shorter wavelengths.
Deuterium NMR quadrupolar splittings and 2 H - 2 H dipolar couplings observed from perdeuterated 1,6-dimethoxyhexane (CD 3 O(CD 2 ) 6 OCD 3 ) dissolved in a liquid crystal 4'-methoxybenzylidene-4-η-butylaniline (MBBA) were analyzed using the single-ordering-matrix (SOM) and the Photinos-Samulski-Toriumi (P-S-T) models. Within the framework of the rotational isomeric state approximation, intramolecular interactions up to the third-order (between atoms and groups separated by five bonds) were considered. The geometrical parameters and intramolecular interaction energies determined from ab initio molecular orbital calculations were employed. The two simulation models yielded fair agreement between theory and experiment, but were found to give quite different images of the solute chain: (the SOM model), the solute becomes rigid and extended to conform itself to the nematic field; (the P-S-T model), the solute has almost the same degree of flexibility as in the free state, but populations of the anisotropic conformers are selectively enhanced. To reveal the true conformational characteristics of chain molecules in nematic fields, experimental techniques to enable direct and quantitative measurements of the bond conformations are necessary.
We study the displacement of miscible fluids of different viscosities (viscosity ratio AI) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above M +J 10, the interface becomes a well-defined finger, the reduced width of which tends to A~n = 0.56 at large AI. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman-Taylor finger.
We have measured the shear modulus of three-dimensional aqueous foam under a small oscillating stress. The foam structure has also been characterized by measurements of the optical transmission. Each of these physical properties depends on a characteristic length, related to the bubble size distribution. We have shown that both lengths follow the same evolution as a function of foam age. They grow according to a parabolic law, in agreement with theoretical predictions.
This paper describes new theoretical results and calculations concerning the recently introduced index of refraction of a gas for atomic waves. More precisely, the motion of the atoms of the gas is taken into account and the equation describing the Doppler and Fizeau effects is introduced. The case where the atoms of the wave and the gas have spin 1/2 is also discussed and the rotatory power and circular dichroism of an optically pumped gas is calculated. Finally, the index of the rare gases for sodium waves is calculated. The results show how important it is to take into account glory scattering and Doppler averaging to make a meaningful comparison with experiments. The index appears to be very sensitive to the precise value of the quantum parameter B = 2 mu D-e sigma(2) (in atomic unit). Using the available interaction potential curves, we obtained a reasonably good agreement between the measurements and the corresponding calculated values. However, some experimental results appear difficult to explain with the best available interaction potentials.
We present an experimental study of the tack of a model polymer melt by the probe tack test coupled with an optical observation of the fracture profile. This set-up allowed us to study the different processes involved in tack and to estimate their importance. We distinguished three different regimes that can be correlated to the rheological properties of the adhesive. In particular, the regime where viscoelastic losses in the bulk of the polymer are important is discussed in detail, in the frame of a recent model by de Gennes. We found, in this case, an enhancement of the energy of adhesion and put into evidence peculiar fracture profiles similar to the "trumpet" profile predicted by the model. We also studied the influences of surface roughness and polymer adsorption on the formation of the bond.
We calculate the contribution, l(PA), to the persistence length arising from charge fluctuations of an intrinsically stiff polyampholyte (PA) chain. The interaction between charges along the PA backbone is taken to be given by the Debye-Huckel potential. When the charges along the chain are uncorrelated the contribution to l(PA) comes from two sources. One of them is due to the overall charge on the PA chain for which the contribution to l(PA) proportional to kappa(-2) where kappa(-1) is the Debye screening length. Surprisingly the contribution to Ipn from charge fluctuations (delta sigma)(2), namely due to the polyampholyte effect, is proportional to -(delta sigma)(4) kappa(-1) so that there is a reduction in the total persistence length when PA chain is overall neutral. We also show that the shape of a PA chain is cylindrical with length l(p) = l(0) + l(PA) with l(0) being the bare persistence length. The diameter of an overall neutral chain can become of the order of a monomer size which is considerably smaller than that of the corresponding polyelectrolyte. As a consequence, we argue that the interaction between two neutral stiff polyampholyte chains is attractive. The implication of the effective attractive interaction is that a dilute dispersion of neutral polyampholyte PA chains mould phase separate into dense (with possible nematic order) and a rare phase. When correlations between the charges are included one gets a polyelectrolyte like behavior with l(PA) proportional to kappa(-2) even when the chain is neutral. If the range of correlation, lambda, is large compared to the screening length (usually difficult to obtain in experiments) there is a large negative contribution to l(PA) which scales as l(PA) proportional to -(delta sigma)(4) lambda/kappa(2) where l(B) is the Bjerrum length.
The precipitation in water of hydrophobic molecules has been studied in presence of added surfactants. Amorphous particles grow through aggregation of clusters of hydrophobic molecules; the growth is terminated by adsorption of surfactant. The particle sizes vary according to the concentrations of hydrophobic molecules and of surfactant molecules. Two regimes have been found for the use of surfactant molecules: at low surfactant concentrations, an efficient regime where all surfactant molecules are adsorbed on the surfaces of the growing particles; at high surfactant concentrations, a wasteful regime, where excess surfactant molecules are left in water. Attempts to reduce the particle sizes by adding increasing amounts of surfactant become inefficient at some point where most of the added surfactant remains in water. These results are explained by a kinetic aggregation model which simulates the competition between aggregation of hydrophobic molecules and adsorption of surfactant. The results of experiments are well reproduced by simulations where aggregation is allowed to proceed unimpeded for a time tau, and then adsorption of the surfactant starts. In these conditions, particle sizes are determined by the rate of aggregation and by the value of this time delay.
We investigate the closed flow between coaxial contra rotating disks, at moderate to high Reynolds numbers. We show that global (i.e. spatially averaged) quantities can be used to characterize the state of the flow and its degree of turbulence. We first report measurements on the driving torque and show how it depends on the manner momentum is imparted to the fluid. We then show that pressure measurements at the how boundary provide a good estimate of the rms velocity fluctuations in the how and that it reveals the transition to turbulence in the flow volume. Finally, we show that once the transition has occurred, the knowledge of the same global quantities allows the calculation of fundamental turbulence characteristics such as the rms velocity fluctuations, the effective integral length scale L*, Taylor's microscale lambda and Kolmogorov's dissipation length eta. That these quantities may be obtained from measuring devices removed from the bulk of the flow is of importance for the study of fluid motion in complex geometries and/or using corrosive fluids.
Simplified mean field theory for the phase behaviour of polyelectrolytes in solution is described in detail. It can be viewed as the polyelectrolyte analogue of Flory-Huggins theory. A basic model is analyzed, then extended to look at the effects of multivalent:ions (specifically divalent colons), of distinguishable counterions, and of an ionization equilibrium between counterions and polyelectrolyte. Analytic transformation of the free energy to reduce the number of extensive variables facilitates the calculation of binodal curves, tielines, spinodal curves, and the spinodal instability directions. Typical salting out behaviour and salt partitioning are seen. Unexpectedly, a small region of three phase coexistence is found: it is examined in detail for the basic model. In addition, the mean field spinodal is found to be identical to that occurring in common applications of the random phase approximation, and to have an interpretation in terms of electrostatic excluded volume, including for the ionizable polyelectrolyte case where fluctuations in the ionization equilibrium give an additional contribution to the Debye-Huckel screening length. The reasons for this are elucidated in an Appendix.
Electrostatically stabilized aqueous suspensions of bromopolystyrene particles have been studied by scattering and osmotic pressure measurements. We investigated their structure and the interparticle interactions as a function of the volume fraction at very low salinity of the order of micromole/l. At slow crystallization speed we observe perfect crystals, body centrered cubic crystals by light scattering for volume fractions between 0.04 and 0.7% and face centrered cubic crystals by Ultra Small Angle X-ray Scattering (USAXS) for higher volume fractions (2-12%). After shear the crystal displays other structures. At low volume fractions (0.1-0.3%), some reflexions disappear by light scattering whereas a strong diffuse ''prepeak'' appears before the first Bragg peak for higher concentrations (2-12%) evidenced by USAXS. This ''prepeak'' can be attributed to defects in the crystal. Osmotic pressures have been measured by difference between the hydrostatic pressure in the solution and in the reservoir separated by an hemipermeable membrane. The experimental data are very well reproduced by the Poisson Boltzmann Cell (PBC) theory which shows that the interaction between particles is purely repulsive. No attractive contribution has been experimentally detected. By calculating the mean square displacement of a particle inside its cage from the eccentric PBC model, we have verified that the Lindemann criterion for the existence of crystals (against melting) is satisfied. This study has allowed to determine the equation of state of an electrostatical colloidal crystal and is equivalent to an ultraprecise force/distance measurement between latex particles since the measured forces are of the order of 10(-12) N for distances of the order of 4000 Angstrom.
Penning ionization electron spectroscopy of the CO molecule by He*(2(1)S) metastable atoms is studied. Vibrational populations are reported for the three energetically accessible states of the CO+ ion (X-2 Sigma(+), A(2) Pi and B-2 Sigma(+)). An obvious discrepancy is observed between the excited vibrational levels of the X-2 Sigma(+) state and the calculated Franck-Condon factors. This result is attributed to an excitation transfer process via Rydberg vibrational progression converging to the CO+ (D-2 Pi) ionic state in agreement with the recent observations by fluorescence of neutral dissociate states. The presence of electrons coming from the well-known a shape resonance is not excluded.
For a two-dimensional model of pattern formation the interplay between a broken up down symmetry and a weakly broken rotational symmetry is investigated. Both symmetries may be broken, for instance, in chemical reactions with an applied electric field or in thermal convection of planarly aligned nematic liquid crystals. In a system with rotational symmetry and a broken up down symmetry hexagonal patterns are favored in a certain parameter range. With increasing values for the anisotropies, by keeping the up down symmetry broken, hexagons may be deformed to centered rectangular patterns. Hence, breaking both symmetries is an alternative mechanism leading to rectangular patterns. Finally, at larger values of the anisotropies a bifurcation to stripes takes place.
In this paper we use a simple normal form approach of scale invariant fields to investigate scaling laws of passive scalars in turbulence. The coupling equations for velocity and passive scalar moments are scale covariant. Their solution shows that passive scalars in turbulence do not generically follow a general scaling observed for velocity field because of coupling effects.
