Conformation of poly(L-lysine)-graft-poly(ethylene glycol) molecular brushes in aqueous solution studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) has been employed for the analysis of conformations of poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g -PEG) molecular bottle brushes in aqueous solutions. The degree of polymerisation of the PEG chains was systematically varied in order to unravel dependence of the conformational properties of the bottle brushes on the molecular weight of the grafted chains. The grafting density was kept constant and high enough to ensure strong overlap of the PEG chains. The scattering spectra were fitted on the basis of the model of an effective worm-like chain with the account of average radial distribution and local fluctuations of the PEG density in the bottle brush. The results of the fits indicate that molecular brushes retain weakly bent configuration on the length scale of the order of (or larger than) the brush thickness. This finding is in agreement with earlier simulation and recent theoretical results.     

Silver-island films probed by hyper-Rayleigh scattering and atomic force microscopy

Incoherent second-harmonic generation, or hyper-Rayleigh scattering (HRS), and atomic force microscopy (AFM) are proposed as a combined probe of nonlinear optical and structural properties of silver-island films. HRS and linear (Rayleigh) scattering indicatrices are measured. The correlation function, deduced from the HRS indicatrices and characterising spatial fluctuations of the total polarisation at second-harmonic frequency, has a length scale significantly larger than that of the correlation functions that are obtained from the AFM data and characterise spatial fluctuations of quadratic optical susceptibilities of the dipole and quadrupole types. This difference is interpreted as indicating that the HRS indicatrix shape is determined by the long-range fluctuations of the local-field factors. Received: 16 October 2001 / Revised version: 16 April 2002 / Published online: 6 June 2002     

Solitary wave dynamics in shallow water over periodic topography

The problem of long-wave scattering by piecewise-constant periodic topography is studied both for a linear solitary-like wave pulse, and for a weakly nonlinear solitary wave [Korteweg-de Vries (KdV) soliton]. If the characteristic length of the topographic irregularities is larger than the pulse length, the solution of the scattering problem is obtained analytically for a leading wave in the framework of linear shallow-water theory. The wave decrement in the case of the small height of the topographic irregularities is proportional to delta2, where delta is the relative height of the topographic obstacles. An analytical approximate solution is also obtained for the weakly nonlinear problem when the length of the irregularities is larger than the characteristic nonlinear length scale. In this case, the Korteweg-de Vries equation is solved for each piece of constant depth by using the inverse scattering technique; the solutions are matched at each step by using linear shallow-water theory. The weakly nonlinear solitary wave decays more significantly than the linear solitary pulse. Solitary wave dynamics above a random seabed is also discussed, and the results obtained for random topography (including experimental data) are in reasonable agreement with the calculations for piecewise topography.     

Liquid–gas critical phenomena under confinement: small-angle neutron scattering studies of CO2 in aerogel

Small angle neutron scattering (SANS) is a well-established technique for investigating the behavior of confined binary liquid solutions, as it can probe the correlation length and susceptibility in pores on length scales 1 – 100 nm. We applied SANS to explore the influence of confinement on critical behavior of an individual fluid carbon dioxide (CO₂) in a highly porous aerogel. The results demonstrate that quenched disorder induced by aerogel significantly depresses density fluctuations. Despite the negligible volume occupied by aerogel (< 4%), the macroscopic phase separation of confined CO₂ into coexisting liquid and gaseous phases is suppressed and below the critical temperature of the bulk fluid frozen methastable microdomains are formed. Experimental data show that critical adsorption is as important as the effect of confinement in defining the behavior of confined fluids.     

Stabilization of stokes pulse energies in the nonlinear regime of stimulated Raman scattering

An experimental study of quantum mechanical pulse energy fluctuations in stimulated Raman scattering from hydrogen is presented. The probability density function P(W) for Stokes pulse energy W is measured for highly transient scattering in both the linear and nonlinear gain regimes. While large pulse energy fluctuations (100%) occur in the linear gain regime, the fluctuations are reduced to about 20% in the nonlinear regime where the laser pulse is depleted significantly. The results are in excellent agreement with the theoretical predictions of Lewenstein.     

De-mixing dynamics of a binary liquid system in a controlled-pore glass. A neutron spin-echo spectroscopy and small angle neutron scattering study

The temperature-induced microphase separation of the binary liquid system iso-butyric acid+heavy water (iBA + D(2)O) in a mesoporous silica glass (CPG-10-75) of nominal pore width 7.5 nm was investigated by neutron spin-echo spectroscopy (NSE) and neutron small-angle scattering (SANS). Two mixtures of different composition were studied at different scattering angles at temperatures above and below the bulk phase transition temperature. The phase separation in the pore space is found to occur at a lower temperature than the bulk transition and extends over a significant temperature range. The effective diffusion coefficient derived from NSE at low scattering angles is found to decrease by one order of magnitude from 70 degrees C to 20 degrees C. This observation is attributed to the growing size of concentration fluctuations having a cut-off at ca. 8 nm, which corresponds to the mean pore size. The dynamics of the concentration fluctuations appears to be strongly influenced by the confinement in the pores, as it differs strongly from the bulk behaviour. These results are consistent with the preliminary results of the SANS study.     

Small-angle neutron and dynamic light scattering study of gelatin coacervates

The state of intermolecular aggregates and that of folded gelatin molecules could be characterized by dynamic laser light and small-angle neutron scattering experiments, which implied spontaneous segregation of particle sizes preceding coacervation, which is a liquid-liquid phase transition phenomenon. Dynamic light scattering (DLS) data analysis revealed two particle sizes until precipitation was reached. The smaller particles having a diameter of ～50 nm (stable nanoparticles prepared by coacervation method) were detected in the supernatant, whereas the inter-molecular aggregates having a diameter of ～400 nm gave rise to coacervation. Small-angle neutron scattering (SANS) experiments revealed that typical mesh size of the networks exist in polymer dense phase (coacervates) [1]. Analysis of the SANS structure factor showed the presence of two length scales associated with this system that were identified as the correlation length or mesh size, ξ = 10.6 Å of the network and the other is the size of inhomogeneities = 21.4 Å. Observations were discussed based on the results obtained from SANS experiments performed in 5% (w/v) gelatin solution at 60°C (ξ = 50 Å, ζ = 113 Å) and 5% (w/v) gel at 28°C (ξ = 47 Å, ζ = 115 Å) in aqueous phase [2] indicating smaller length scales in coacervate as compared to sol and gel.     

Time-resolved nuclear spin-dependent small-angle neutron scattering from polarised proton domains in deuterated solutions

We have investigated the process of dynamic proton polarisation by means of time-resolved polarised small-angle neutron scattering (SANS) on frozen solutions of EHBA-Cr^V molecules in glycerol-water mixtures as a function of the concentration of EHBA-Cr^V and for different degrees of deuteration of the solvent. In the EHBA-Cr^V complex, the spins of the 20 protons which surround the paramagnetic Cr^V can be oriented using the method of dynamic nuclear polarisation (DNP), thereby offering the possibility to create locally a nuclear spin-dependent contrast for SANS. The time constants which describe the build-up of polarisation around the paramagnetic centre and the subsequent diffusion of polarisation in the solvent were determined by analysing the temporal evolution of the nuclear polarisation, which in turn was obtained by fitting a core-shell model to the time-dependent SANS curves. The results on the spin dynamics obtained using the scattering function of a core-shell could be independently confirmed by evaluating the integrated SANS intensity. A thermodynamic one-centre model is presented which is able to reproduce the observed dependence of the proton polarisation times on the proton concentration of the solvent.     

Nano-meter-sized domain formation in lipid membranes observed by small angle neutron scattering

Using a contrast matching technique of small angle neutron scattering (SANS), we have investigated a phase separation to liquid-disordered and liquid-ordered phases on ternary small unilamellar vesicles (SUVs) composed of deuterated-saturated, hydrogenated-unsaturated phosphatidylcholine lipids and cholesterol, where the equilibrium size of these domains is constrained to less than 10nm by the system size. Below a miscibility temperature, we observed characteristic scattering profiles with a maximum, indicating the formation of nano-meter-sized domains on the SUVs. The observed profiles can be described by a multi-domain model rather than a mono-domain model. The nano-meter-sized domain is agitated by thermal fluctuations and eventually ruptured, which may result in the multi-domain state. The kinetically trapped nano-meter-sized domains grow to a mono-domain state by decreasing temperature. Furthermore, between the miscibility and disorder-order transition temperature of saturated lipid, the integrated SANS intensity increased slightly, indicating the formation of nano-meter-sized heterogeneity prior to the domain nucleation.     

Structural investigation on gamma-irradiated polyacrylamide hydrogels using small-angle neutron scattering and ultraviolet–visible spectroscopy

Small-angle neutron scattering (SANS) and ultraviolet (UV)–visible spectroscopic techniques are used to investigate the microstructural changes in polyacrylamide (PAAm) hydrogels on gamma irradiation. SANS measurements have revealed the presence of inhomogeneities in nanometre scale and reduction of their size with increase in dose. Analysis of SANS data also revealed the increase in the correlation length with increase in dose. The extinction coefficient obtained from the UV–visible spectroscopic studies exhibited λ^?β dependence between 500 and 700 nm and is understood to arise from the existence of scatterers (inhomogeneities) in submicron scale in PAAm hydrogels. The increase in value of exponent β with increase in dose indicates that the size of scatterers decrease with increase in dose.     

Prebifurcational noise rise in nonlinear systems

The phenomenon of prebifurcational noise increase in nonlinear systems in the process of period-doubling bifurcation is investigated. The study is conducted for a discrete system (quadratic mapping); how-ever, many of the laws discovered apply to more general systems. Estimates of the fluctuation variance are obtained both for the linear (away from the bifurcation threshold) and for the nonlinear mode (in the vicinity of the bifurcation threshold). It is shown that the variance of forced fluctuations in the strongly nonlinear mode is proportional to the root-mean-square of the noise intensity rather than to the variance. The possibility of measuring the noise in nonlinear systems on the basis of the prebifurcational noise amplification factor is demonstrated.     

Peak effect in polycrystalline vortex matter

We report a study of the peak-effect phase diagram of a strongly disordered type-II superconductor V-21 at. %Ti using ac magnetic susceptibility and small-angle neutron scattering (SANS). In this system, the peak effect appears only at fields higher than 3.4 T. The sample is characterized by strong atomic disorder. Vortex states with field-cooled thermal histories show that both deep in the mixed state, as well as close to the peak effect, there exist no long-range orientationally ordered vortex lattices. The SANS scattering radial widths reveal vortex states ordered in the sub-mum scale. We conjecture that the peak effect in this system is a remnant of the Bragg glass disordering transition, but occurs on submicron length scales due to the presence of strong atomic disorder on larger length scales.     

Form-factors for different aggregation models of micelles

Spherical micelles in ionic micellar solutions, often aggregate to form spherical, cylindrical or chain-like aggregates on addition of salt to the solution. It is known that the technique of small angle neutron scattering (SANS) can be used to distinguish spherical and cylindrical aggregates. To examine if SANS can be used to distinguish the latter two aggregation processes, we have calculated the angular distribution of scattered neutrons from 0.002 M CTAB solutions. These calculations show that aggregation of CTAB micelles results in large changes in SANS spectra. The shapes of SANS spectra are different for the above three types of aggregates, suggesting that technique of SANS can indeed be used to distinguish the three aggregation processes. The size of the aggregate can also be obtained from such studies.     

Measurements of bubbles in sea water by nonstationary sound scattering

Methods for the characterization of bubbles in sea water by acoustic scattering are analyzed. Nonstationary linear and nonlinear sound scattering methods are proposed. The transient linear and nonlinear sound scattering allows the scattering by resonant gas bubbles to be distinguished from the scattering by other microinhomogeneities. The application of parametric arrays in oceanic experiments, together with the broadband frequency analysis of the backscattering coefficient, allows information about bubbles in sea water to be obtained. Experimental results on sound scattering and gas bubble distribution functions are presented for different conditions in the ocean.     

Structure determination of AgPO3 and (AgPO3)0.5(AgI)0.5 glasses by neutron diffraction and small angle neutron scattering

Neutron diffraction and small angle neutron scattering (SANS) were performed on AgPO₃ and (AgPO₃)_0.5(AgI)_0.5 glasses. AgPO₃ glass is made up of long chains of PO₄ tetrahedra joined together by Ag atoms. When silver iodide is added, the radial distribution function shows a large peak at 2.83 Å, due to AgI interactions. AgI does not modify the network forming unit. The existence of small clusters is confirmed by analysing the coordination number of AgI pairs obtained by subtracting the experimental structure function of the AgPO₃ glass from that of the corresponding AgI-doped glasses. A rough estimation of their size is given by SANS experiments. Not all the AgI pairs are involved in AgI cluster units. The compatibility of the results obtained with recent structural investigations by non diffractometric techniques is examined.     

Period-adding bifurcations and chaos in a bubble column

We obtained period-adding bifurcations in a bubble formation experiment. Using the air flow rate as the control parameter in this experiment, the bubble emission from the nozzle in a viscous fluid undergoes from single bubbling to a sequence of periodic bifurcations of k to k+1 periods, occasionally interspersed with some chaotic regions. Our main assumption is that this period-adding bifurcation in bubble formation depends on flow rate variations in the chamber under the nozzle. This assumption was experimentally tested by placing a tube between the air reservoir and the chamber under the nozzle in the bubble column experiment. By increasing the tube length, more period-adding bifurcations were observed. We associated two main types of bubble growth to the flow rate fluctuations inside the chamber for different bubbling regimes. We also studied the properties of piecewise nonlinear maps obtained from the experimental reconstructed attractors, and we concluded that this experiment is a spatially extended system.     

Small angle neutron scattering from micellar solutions

Small angle neutron scattering (SANS) is an ideal tool for studying structures of macromolecules and colloidal solutions. A number of micellar solutions have been studied in our laboratory using a home built SANS spectrometer. This paper gives an introduction to the technique of SANS and gives a brief survey of the results obtained at Trombay.     

Diffuse scattering in RHEED induced by linear disorders of sulphur segregated on nickel (111) surface

RHEED diffuse scattering intensity is related to the growth of one-dimensional sulphur chains segregated on a nickel (111) surface. These linear disorders lead to wall domains in the reciprocal lattice which give the well-known “arching” phenomenon in RHEED patterns. The diffuse scattering process disappears when the (5√3 × 2)R30° superstructure is obtained. Knowing the absolute coverage of sulphur by calibrated Auger spectroscopy, it is possible to give a new high symmetry model for this superstructure.     

Trapping of discrete solitons by defects in nonlinear waveguide arrays

We study the trapping process of moving discrete solitons by linear and nonlinear impurities embedded in a one-dimensional nonlinear cubic array. We show that there exist specific values for the strength of the impurity and for the angle where a strong trapping is obtained. We introduce a criterion for studying the scattering dynamics of localized waves in nonlinear extended systems where the trapping of energy takes place.