Scattering Wave Vector Research Articles

Phonon Propagation in Ordered Diblock Copolymer Solutions

High-resolution inelastic light scattering was employed to measure the dispersion relations for the acoustic excitations in ordered concentrated solutions of poly(styrene)-block-poly(isoprene) copolymers with both symmetric and asymmetric composition and large spacing (220−415 nm). The morphology is manifested in the rich phonon spectrum recorded for different scattering wave vectors q in the range 0.003−0.034 nm-1. The experimental ωs(q) of the sth branch is directly compared with the theoretical dispersion from band structure calculations performed for different directions of q in the reciprocal lattice of lamellar and cylindrical periodic structures. The dispersion relations turn out to be a sensitive index of the microphase morphology and the grain orientation.

The Packing of Triacylglycerols from SAXS Measurements: Application to the Structure of 1,3-Distearoyl-2-oleoyl-sn-glycerol Crystal Phases

An approach by which electron density profiles of triacylglycerols (TAGs) can be reconstructed from X-ray diffraction data has been applied to analyze lamellar structures formed by 1,3-distearoyl-2-oleoyl-sn-glycerol (StOSt). The method is analogous to one previously used to analyze lipid bilayer structures. Based on the structure of tristearin molecules crystallized in the β phase, the projection of the electron density profile along the layer normal in structures with a lamellar packing of the TAG has been calculated for both tilted and nontilted arrangements of the molecules. This enables the position of glycerol groups to be identified in the electron density profile reconstructed from the first few 00l lamellar peaks measured by small-angle X-ray scattering (SAXS). It is demonstrated that structure amplitudes of both two-chain- and three-chain-length layers formed by the same equally tilted TAG molecules follow a unique curve on a plot of the structure amplitudes versus the scattering wave vector. The approach is applied to examine the complex polymorphism of StOSt during crystallization. Time-resolved SAXS/WAXS measurements have been performed during isothermal crystallization (from the liquid phase at 55 °C) at different temperatures (0−22.5 °C), followed by annealing at 30 °C. It is concluded that six phases (α2, α1, γ, β‘, β1, and β2) and one metastable structure can be formed by StOSt molecules through polymorphic transformations. Fourier reconstructed projections of the electron density profile along the layer normal show that symmetry-related pairs of StOSt molecules adopt a two-chain packing motif in the α1 phase and a three-chain packing motif in the more stable γ, β‘, and β phases of StOSt. In accordance with the electron density profile, the unstable α2 phase appearing at the initial stage of the crystallization can be ascribed to three-chain packing, which is probably the result of the twisted acyl chains of StOSt molecules. A combination of structural parameters obtained in the study, together with models for terrace-like arrangements of terminal methyl groups developed by de Jong et al., allowed the structure of γ and β phases to be clarified. The driving forces for the polymorphic transformations taking place during crystallization and a schematic diagram of phase transitions are discussed.

KWS-3, the new focusing-mirror ultra small-angle neutron scattering instrument and reflectometer at Jülich

In Jülich, a new high-resolution small-angle neutron scattering (SANS) instrument and reflectometer has been built. The principle of this instrument is a one-to-one image of an entrance aperture on a 2D position-sensitive detector by neutron reflection on a double-focusing toroidal mirror. It permits to perform SANS studies with a scattering wave vector resolution between 10 −3 and 10 −4 A ̊ −1 with considerable intensity advantages over pinhole-SANS instruments. To date, KWS-3 is the worldwide unique SANS instrument running on this principle. We present here the characterization of the image produced by the mirror and a measurement of the scattering from a diffraction grating.

An investigation of a sol-gel/melt transition: the poly(ethylene oxide)/methanol/LiClO4 system.

The crossover behavior of 50 000 molar mass poly(ethylene oxide)/methanol solutions from dilute solution to the melt/gel was examined. At first this behavior was investigated without LiClO(4) and then reexamined with LiClO(4). To better understand this behavior, the dependencies of dynamic light scattering (specifically, photon correlation spectroscopy) measurement results on polymer concentration, on the scattering wave vector and on temperature, and the dependence of static light scattering results on the scattering wave vector were studied. This study produced interesting and important results about network structure and behavior in poly(ethylene oxide) solutions and melts generally and about the effects of LiClO(4) on this structure and behavior more particularly.

Relaxation processes in mixtures of liquid crystals and polymers near phase boundaries and during phase separation.

We present experimental studies of the relaxation of concentration fluctuations in a semidilute solution of polystyrene (PS) (30% by weight) in 4-cyano-4'-n-octyl-biphenyl (8CB) (70% by weight) using the photon correlation spectroscopy (PCS). In the homogeneous phase there are two modes of relaxation. The slow one (typical time scale is taus = 0.001 s) is due to the diffusion of polymer chains (of molecular mass 65,000) in the LC matrix (of molecular mass 290), while the fast one has the time scale of the order of tauf approximately 0.00001 s. The amplitude of the fast mode is much weaker than the one for the slow mode. Moreover it does not depend on the scattering wave vector, q. The value of the diffusion coefficient, Dc = 1/(tausq2) for the slow mode decreases with temperature according to the Arhenius law until we reach the coexistence curve. Its value close to the coexistence is Dc = 4 x 10(5) nm2/s and the activation energy in the homogeneous mixture is Ec=127 kJ/mol. If we gradually undercool the mixture below the coexistence into the metastable two-phase region without inducing the phase separation we find unexpectedly that Dc does not change with temperature even 4 degrees below the coexistence curve. The characteristic time of the fast mode does not depend on the scattering wave vector indicating that it is related to the transient gel structure. We have shown that it is possible to measure the short time relaxation of concentration fluctuations during the phase separation in the mixture. At low temperature close to the isotropic-nematic phase transition we have observed that the relaxation is well separated in time from the typical time of the domain growth. This relaxation mode is characterized by the large diffusion coefficient D = 2 x 10(8) nm2/s. The mode probably comes from the coupling between the orientational dynamics of liquid crystals and the transient gel structure of polymers.

Power spectrum of many impurities in ad-wave superconductor

Recently the structure of the measured local density of states power spectrum of a small area of the \BSCCO (BSCCO) surface has been interpreted in terms of peaks at an "octet" of scattering wave vectors determined assuming weak, noninterfering scattering centers. Using analytical arguments and numerical solutions of the Bogoliubov-de Gennes equations, we discuss how the interference between many impurities in a d-wave superconductor alters this scenario. We propose that the peaks observed in the power spectrum are not the features identified in the simpler analyses, but rather "background" structures which disperse along with the octet vectors. We further consider how our results constrain the form of the actual disorder potential found in this material.

Phase separation of off‐critical polymer blends of poly(styrene‐co‐maleic anhydride) and poly(methyl methacrylate). I. Kinetics of spinodal decomposition

AbstractThe kinetics of phase separation via the spinodal decomposition of poly(styrene‐co‐maleic anhydride)/poly(methyl methacrylate) from a delay time period to late stages were investigated with a light scattering technique. The standard procedure for identifying four stages of spinodal decomposition, based on the characteristics of concentration fluctuations, was clearly introduced with the light scattering method. The spinodal limits were divided into four stages: the delay time, the early stage, the intermediate stage, and the late stage. The validity of the linearized theory was reviewed because it was used as an indicator of the limit of the early stage of spinodal decomposition, which divided the delay time period from the early stage and the early stage from the intermediate stage. The linearized theory fit the experimental results very well after the delay time. The scaled structure function of the melt‐mixed blend was analyzed. The universality of the scale structure function, F(x) = S(q,t)qm3(t) (where S is the structure function, x is equal to q/qm, q is the scattering wave vector, qm is the maximum wave vector, and t is the time in seconds), indicated the late stage of phase separation and divided the late stage from the intermediate stage. The simple normalized scaling function profile for the cluster region proposed by Furukawa described the experimental data very well, whereas the profile for deep quenching, which was recently suggested, showed some discrepancies. As a result of the phase separation, the processing of this blend may be able to be developed to provide the most suitable morphology. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 871–885, 2004

Small angle neutron scattering from single-wall carbon nanotube suspensions: evidence for isolated rigid rods and rod networks

We report small angle neutron scattering (SANS) from dilute suspensions of purified individual single wall carbon nanotubes (SWNTs) in D 2O with added sodium dodecylbenzene sulfonate ionic surfactant. The scattered intensity scales as Q −1 for scattered wave vector, Q, in the range 0.005< Q<0.02 A ̊ −1 . The Q −1 behavior is characteristic of isolated rigid rods. A crossover of the scattered intensity power law dependence from Q −1 to Q −2 is observed at ∼0.004 A ̊ −1 , suggesting the SWNTs form a loose network at 0.1 wt% with a mesh size of ∼160 nm. SANS profiles from several other dispersions of SWNTs do not exhibit isolated rigid rod behavior; evidently the SWNTs in these systems are not isolated and form aggregates.

Scaling of light scattered from fractal aggregates at resonance

Due to the scale invariance of fractal aggregates, light scattered from them often decays as a power of the scattering wave vector. The exponent in this power law has been usually interpreted as the geometrical fractal dimension. However, the validity of this interpretation is questionable for frequencies close to the resonances of the system, for which multiple scattering becomes important. In this work we calculate the dipole moments optically induced in fractal aggregates and the corresponding self-consistent field, as well as the electromagnetic normal modes. To this end, we develop a multiresolution hierarchical representation of the aggregate that allows the study of large systems taking fully into account the long range of the interactions. We analyze the scaling properties of the dynamically induced dipolar distribution. We find that under resonant conditions, scaling with the geometric fractal dimension is only observed for systems much larger than a length scale that is related to the linewidth of each individual resonance. The relevance to this result for the interpretation of light scattering experiments is discussed.

Time-resolved x-ray Raman spectroscopy of photoexcited polydiacetylene oligomer: A simulation study

Off-resonant x-ray diffraction provides a novel real-space and real-time probe of electronic and vibrational dynamics in optically excited molecules. The entire manifold of valence electronic excitations may be monitored through the dependence of the x-ray Raman peaks on the scattering wave vector Δk and energy Δω. The electronic excitation energies and transition density matrices of a polydiacetylene oligomer, computed using the time-dependent Hartree–Fock collective electronic oscillator algorithm, are used to simulate the Raman signals and illustrate their information content.

Acoustic scattering measurement and processing for determining variances in multiple features

A method is provided for determining multiple feature variances in a medium. Acoustic sources are positioned on one side of a selected scattering direction. Acoustic receivers are positioned on an opposite side of the selected scattering direction such that, for each acoustic source, there is a corresponding acoustic receiver located at a mirror-imaged position relative to the selected scattering direction, and such that a Bragg scattering wave vector associated with each acoustic source/receiver pair is parallel to the selected scattering direction. Each acoustic source is operated at a unique time to direct a broadband ultrasonic pulse at the region of interest. An acoustic scattered wave reflects from the region of interest and is detected as a waveform at the pair's acoustic receiver. Each waveform is converted to the frequency domain to form a spectral waveform. A band of Bragg wave numbers is determined for each spectral waveform. Variations in multiple features of the medium are then determined by solving a complex acoustic scatter relationship as a function of the band of Bragg wave numbers associated with the particular source/receiver pair.

Heterodyne near-field scattering

We describe an optical technique based on the statistical analysis of the random intensity distribution due to the interference of the near-field scattered light with the strong transmitted beam. It is shown that, from the study of the two-dimensional power spectrum of the intensity, one derives the scattered intensity as a function of the scattering wave vector. Near-field conditions are specified and discussed. The substantial advantages over traditional scattering technique are pointed out, and is indicated that the technique could be of interest for wavelengths other than visible light.

Optimization of neutron scattering instrumentation using neutron spin echo: Application to the discrimination of diffuse scattering in neutron reflectivity experiments

We describe a method, based on the neutron spin-echo technique, to achieve good resolution in many neutron-scattering experiments, without sacrificing signal intensity. By “good resolution” we do not mean the ∼10−6 energy resolution usually associated with neutron spin-echo spectrometers, but rather the level of resolution traditionally obtained by collimation or monochromatization of neutron beams, often on specialized instruments, and almost always at some penalty in measured intensity. The method we discuss allows good resolution to be achieved in any chosen direction in the vector space defined by the neutron scattering wave vector, Q, and the energy transfer, E. Although the method has general applicability to many neutron scattering measurements, we discuss in detail its application to the problem of separating diffuse scattering from specular reflection in neutron reflectometry. The technological basis of the method is the availability of thin films of magnetic or easily magnetizable material that are very smooth and of uniform thickness and that do not depolarize neutrons. Enhancing resolution using this method can be as simple as adding a few such films to a spectrometer that already provides polarized neutrons. We have tested magnetizable permalloy films for this application and our experimental results show that components work as intended, although some further work is needed to optimize them. The apparatus we have used, which is inexpensive and simple to construct, will allow both in-plane and out-of-plane diffuse scattering to be effectively removed from the measurement of specular reflectivity with an accuracy comparable to that achievable with milliradian collimation. In contrast to traditional methods of achieving this level of resolution, however, the spin echo method permits the use of relatively poorly collimated beams and hence can provide substantial gains in signal intensity.

Quench–jump sequence in phase separation in polymer blends

A two-step process of phase separation–mixing is analyzed for binary mixtures. The system is first quenched into the thermodynamical instability region (temperature T), where the mixture undergoes a process of spinodal decomposition, characterized for short times by the growth of the Cahn peak of a scattered intensity at fixed scattering wave vector. Next we heat up a system (make a temperature jump to temperature T1) above the spinodal line (temperature Ts) and compute the decay of this peak. The peak intensity decreases and the peak position moves toward short wave vectors. The integrated peak intensity decreases exponentially at short times with a characteristic decay time that depends on T, T1, and Ts. The increase of the Euler characteristic from large negative values toward zero suggests that the shift of the peak toward short wave vectors is associated with the disappearance of small connections in a bicontinuous structure formed in the early stages of spinodal decomposition. Slow decay of the surface area indicates that the domains keep their shape for a long time, despite the fast decay of the saturation of the concentration field inside them.

Absolute small angle light scattering measurements from weakly scattering systems in a shear flow apparatus

We describe an optical detection layout that allows absolute small angle light scattering measurements on samples sheared in a concentric cylinders geometry. The two main features are the use of a focused incident beam and of a spatial filter that minimize the problem of stray light arising from digs and scratches in the optical path. The scattering intensity is imaged directly onto a cooled 12 bits charge-coupled device sensor. We are thus able to measure scattering intensities as low as about 4×10−4 cm−1 (about ten times the intensity scattered from a toluene standard) for scattering wave vector values between 5×10−5 and 3.5×10−4 Å−1. Some preliminary results of experiments on dilute surfactant solutions are given to demonstrate the performance of the instrument.

Microphase separation in weakly charged hydrophobic polyelectrolytes

Aqueous solutions of a well-defined poly(N-isopropylacrylamide-co-sodium 2-acrylamido-methylpropanesulfonate) (NIPAM/NaAMPS in a 95/5 molar ratio) have been investigated by means of small-angle neutron scattering (SANS) and rheological experiments as a function of temperature ( 25°C\(\)T\(\) 60°C) and polymer concentration ( 0.5wt% \(\)C\(\) 12wt%). The solutions remain optically transparent and isotropic over the whole temperature range, in contrast with the homopolyNIPAM which precipitates above its lower critical solution temperature (LCST = 32°C). Upon addition of salt, the systems undergo a micro-macrophase separation. At temperatures above 45°C, the SANS spectra exhibit a sharp peak at a scattering wave vector, qmax, which increases slightly with temperature. At high temperature ( T∼ 60°C), the scattered intensity follows a power law I(q) ∼q-4 in the asymptotic regime, characteristic of two-density media with sharp interfaces, and qmax is found to vary with polymer concentration as qmax∼C0.22. Estimates of the typical sizes give values between 40 A and 200 A. These results provide a strong evidence of a thermally induced microphase separation, which is corroborated by the very sharp increases of the viscosity (over 2 decades) and of the stress relaxation time of the solutions, occurring in the temperature range where the scattering peak is observed. The results are discussed and compared with the theoretical models proposed for weakly charged polyelectrolytes in a poor solvent.

A dynamic light scattering study of the viscoelastic twist mode in cholesteric liquid crystals

Although viscoelastic properties of liquid crystals are very important for applications like display technology, there are not many direct techniques to study them. We have used dynamic light scattering to obtain dispersion curves for the twist mode of director fluctuations in a thermotropic cholesteric liquid crystal (cholesteric) mixture, in a wave vector range comparable to the inverse pitch of the cholesteric. In the experiment, light scattered in the vicinity of Bragg reflection is investigated using a hitherto unused scattering geometry where the scattering wave vector q is parallel to the cholesteric helix axis. By fitting the experimental data to a parabolic function of the scattering wave vector, we have determined the twist viscoelastic coefficient k 22/γ 1. We have studied the temperature dependence of k 22/γ 1 and found that the viscoelastic coefficient increases rapidly as the cholesteric-to-isotropic transition temperature is approached.

Time-Resolved SAXS Study of Nucleation and Growth of Silica Colloids

This paper reports a time-resolved small-angle X-ray scattering study of in situ Stöber silica synthesis. The hydrolysis reaction is initiated by rapidly mixing equal amounts of alcoholic solutions of ammonia and tetraethyl orthosilicate, using a stopped-flow device coupled to a flow-through capillary cell. Measurements covered the scattering wave vector (q) range of 0.02 ≤ q ≤ 6 nm-1 and time (t) range of 0.1 ≤ t ≤ 1000 s. The combination of high sensitivity, low background, and high dynamic range of the experimental setup permitted observation of the primary particles of nucleation. During the entire growth process, the measured scattered intensity can be adequately described by a sphere scattering function weighted by a Schultz size distribution function. At the early stages of growth, the fitted radius increased linearly with time, subsequently crossing over to a smaller exponent of between 1/3 and 1/2. The observed behavior is consistent with an aggregation process involving primary particles of a few nanometers in size.

Glasslike character of molecular ordering in discotic lyomesophases.

We studied dynamic light scattering from isotropic solutions of triphenylene derivative in dodecane at concentrations close to the isotropic-cholesteric phase transition that takes place at c=25 wt. % at room temperature. The correlation decay g((2))(t) reveals the presence of three dynamic modes, from which two appear in polarized (VV) and one in depolarized (VH) scattering. The VH mode, which is independent of the scattering wave vector q, exhibits an Arrhenius type temperature dependence and shows a strong deviation from the exponential relaxation associated with the stretching-exponent parameter beta(VH) approximately 0.5 for all the investigated concentrations. The VV modes both exhibit a quadratic dispersion of the inverse relaxation time 1/tau on the scattering wave vector q. For concentrations 5 wt. %<c<25 wt. % the temperature dependence of the fast VV mode obeys the Vogel-Fulcher-Tamman relation that is correlated with the nonexponential character of the relaxation. The corresponding stretching-exponent parameter beta(fast) decreases by increasing concentration and decreasing temperature. The slow VV mode, on the contrary, is always close to exponential behavior and shows an Arrhenius type temperature dependence, but it exhibits strong variations in relation with sample annealing and preparation procedures. The relaxation rates of all the modes strongly decrease with increasing triphenylene concentration. The observed dynamical properties suggests on the glasslike structure of large columnar aggregates formed in the pretransitional phase.

Dynamic Light-Scattering Study of Aggregating and Gelling Colloidal Disks

We have studied the relaxation of the concentration fluctuations of gelling disk-like clay particles (Laponite) in water containing 5 mM NaCl. At a Laponite concentration of 10 g/l a gel is formed that does not flow when tilted. The comparison of dynamic light scattering and dynamic mechanical measurements shows that the terminal relaxation time of concentration fluctuations diverges not at the gel point, but only when the gel is sufficiently dense to inhibit motion over the length scale on the order of the inverse scattering wave vector. The initial decay of the concentration fluctuations is due to cooperative diffusion and is insensitive to the gel formation. At a concentration of 1 g/L, large aggregates that slowly precipitate are formed. The scattering wave vector dependence of the decay of the concentration fluctuations shows that the aggregates are semi-flexible.