Scattering by inhomogeneous systems with rough internal surfaces: Porous solids and random-field Ising systems

Inner structure and dynamics of microgels with low and medium crosslinker content prepared via surfactant-free precipitation polymerization and continuous monomer feeding approach

The preparation of poly(N-isopropylacrylamide) microgels via classical precipitation polymerization (batch method) and a continuous monomer feeding approach (feeding method) leads to different internal crosslinker distributions, i.e., from core-shell-like to a more homogeneous one. The internal structure and dynamics of these microgels with low and medium crosslinker concentrations are studied with dynamic light scattering and small-angle neutron scattering in a wide q-range below and above the volume phase transition temperature. The influence of the preparation method, and crosslinker and initiator concentration on the internal structure of the microgels is investigated. In contrast to the classical conception where polymer microgels possess a core-shell structure with the averaged internal polymer density distribution within the core part, a detailed view of the internal inhomogeneities of the PNIPAM microgels and the presence of internal domains even above the volume phase transition temperature, when polymer microgels are in the deswollen state, are presented. The correlation between initiator concentration and the size of internal domains that appear inside the microgel with temperature increase is demonstrated. Moreover, the influence of internal inhomogeneities on the dynamics of the batch- and feeding-microgels studied with neutron spin-echo spectroscopy is reported.

An in-situ small angle x ray scattering analysis of nanopore formation during thermally induced chemical dealloying of brass thin foils

The development of non-noble nano-porous metal materials is hindered by surface oxidation reactions and from the difficulty to generate long range order pore arrays. Dealloying is a promising route to generate such materials by selective chemical etching of metal alloy materials. This process can generate nano-metal materials with superior plasmonic, catalytic and adsorptive surface properties. Here, the impact of properties of the etching solution on the dealloying process to generate nano-pores across thin film alloys was investigated by in-situ SAXS dealloying experiments. Single phase CuZn alloys were used as model materials to evaluate the influence of the solution temperature on the pore formation kinetics. This novel analysis allowed to visualize the change in surface properties of the materials over time, including their surface area as well as their pore and ligament sizes. The dealloying kinetics at the very early stage of the process were found to be critical to both stable pore formation and stabilization. SAXS in-situ data were correlated to the morphological properties of the materials obtained from ex-situ samples by Rutherford back scattering and scanning electron microscopy.

Temperature-dependent structure and dynamics of highly-branched poly(N-isopropylacrylamide) in aqueous solution

Small-angle neutron scattering (SANS) and neutron spin-echo (NSE) have been used to investigate the temperature-dependent solution behaviour of highly-branched poly(N-isopropylacrylamide) (HB-PNIPAM). SANS experiments have shown that water is a good solvent for both HB-PNIPAM and a linear PNIPAM control at low temperatures where the small angle scattering is described by a single correlation length model. Increasing the temperature leads to a gradual collapse of HB-PNIPAM until above the lower critical solution temperature (LCST), at which point aggregation occurs, forming disperse spherical particles of up to 60 nm in diameter, independent of the degree of branching. However, SANS from linear PNIPAM above the LCST is described by a model that combines particulate structure and a contribution from solvated chains. NSE was used to study the internal and translational solution dynamics of HB-PNIPAM chains below the LCST. Internal HB-PNIPAM dynamics is described well by the Rouse model for non-entangled chains.

Random field Ising model in a uniform magnetic field: Ground states, pinned clusters and scaling laws

In this paper, we study the random field Ising model (RFIM) in an external magnetic field h . A computationally efficient graph-cut method is used to study ground state (GS) morphologies in this system for three different disorder types: Gaussian, uniform and bimodal. We obtain the critical properties of this system and find that they are independent of the disorder type. We also study GS morphologies via pinned-cluster distributions, which are scale-free at criticality. The spin-spin correlation functions (and structure factors) are characterized by a roughness exponent [Formula: see text]. The corresponding scaling function is universal for all disorder types and independent of h.

Random-field Ising model on isometric lattices: Ground states and non-Porod scattering

We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δ_{c} at zero temperature with high accuracy. For the SC lattice, our estimate (Δ_{c}=2.278±0.002) is consistent with earlier reports. For the BCC and FCC lattices, Δ_{c}=3.316±0.002 and 5.160±0.002, respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α=0.5±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy E_{i}(L) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.

Order-parameter scaling in fluctuation-dominated phase ordering

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile, which capture the breakup and remerging of particle-rich regions. We study both static and dynamic scaling laws obeyed by the Fourier modes Q_{mL} and find that the mean value obeys the static scaling law 〈Q_{mL}〉∼L^{-ϕ}f(m/L) with ϕ≃2/3 and ϕ≃3/5 for Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution, respectively, and ϕ≃3/4 for the CD model. The full probability distribution P(Q_{mL}) exhibits scaling as well. Further, time-dependent correlation functions such as the steady-state autocorrelation and cross-correlations of order-parameter components are scaling functions of t/L^{z}, where L is the system size and z is the dynamic exponent, with z=2 for EW and z=3/2 for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and the weak divergence of the flatness as the scaled time approaches 0.

Plasmonic gold–poly(N-isopropylacrylamide) core–shell colloids with homogeneous density profiles: a small angle scattering study

Four scattering methods covering nearly three orders of magnitude in momentum transfer verify homogeneous network structures in gold–PNIPAM core–shell colloids.

Phase separation of fluids in porous media: a molecular dynamics study

We present comprehensive molecular dynamics results for phase-separation kinetics of fluids in a porous medium. This system is modeled by a symmetric Lennard-Jones fluid mixture with a quenched random field. The presence of disorder slows down domain growth from power-law to a logarithmic form. It also modifies the correlation functions and structure factors which characterize the morphology. In particular, the structure-factor tail shows a non-Porod behavior, which is the consequence of scattering from rough interfaces.

Non-Porod behavior in systems with rough morphologies

Many experiments yield multi-scale morphologies which are smooth on some length scales and fractal on others. Accurate statements about morphological properties, e.g., roughness exponent, fractal dimension, domain size, interfacial width, etc. are obtained from the correlation function and structure factor. In this paper, we present structure factor data for two systems: (a) droplet-in-droplet morphologies of double-phase-separating mixtures; and (b) ground-state morphologies in dilute anti-ferromagnets. An important characteristic of the scattering data is a non-Porod tail, which is associated with scattering off rough domains and interfaces.

Ground-state morphologies in the random-field Ising model: scaling properties and non-Porod behavior

We use a computationally efficient graph-cut method (GCM) to obtain the ground-state morphologies (at zero temperature) of the random-field Ising model in d=2,3. The GCM enables us to obtain comprehensive numerical results on large-scale systems. We analyze the morphologies by computing correlation functions and structure factors. These quantities enable us to precisely evaluate characteristic properties, e.g., domain sizes, scaling functions, roughness exponents, fractal dimensions, etc.

Stabilization of TiO2 nanoparticles in complex medium through a pH adjustment protocol

Preparing TiO(2) nanoparticle (NP) suspensions displaying well-defined and reproducible dispersion state is a key feature to perform relevant toxicity experiments for environmental, animal, or human concerns. Relying on the evolution of surface charge with pH, and interactions between nanoparticles in their medium, we developed an optimized dispersion protocol involving a pH adjustment before addition of bovine serum albumin (BSA). It yielded highly dispersed and stable concentrated stock suspensions of TiO(2) NP at pH 7. It was designed for four kinds of manufactured TiO(2) nanomaterials and can be extended to a wide range of TiO(2) NP. The suspensions studied here were characterized by small-angle X-ray scattering (SAXS), using a model quantitatively describing fractal aggregates. Results were correlated with dynamic light scattering (DLS) measurements. Moreover, the stability in a typical biological medium was assessed by diluting stock suspensions in Luria-Bertani (LB) medium. It resulted in highly dispersed and stable working suspensions. No sedimentation, followed by in situ DLS, was observed over 17 h for both the concentrated stock suspensions prepared according to the pH adjusted-BSA protocol and their dilution into LB medium.

Small-angle X-ray scattering analysis of porous powders of CaCO3

The results of small-angle and ultra-small-angle X-ray scattering on porous CaCO3microparticles of pulverulent vaterite made by a conventional chemical route and by using supercritical CO2are presented. The scattering curves are analysed in the framework of the Guinier–Porod model, which gives the radii of gyration of the scattering objects and their fractal dimension. In addition, the porosity and the specific surface area are determined by using the Porod invariant, which is modified to take into account the effective thickness of the pellet. The results of this analysis are compared with those obtained by nitrogen adsorption.

Fractal Aspects of Ceramic Synthesis

The concept of fractal geometry is used to describe the structure of silica polymers, colloidal aggregates, and critical systems. We illustrate the interpretation of scattering curves (X-ray, neutron and light) for fractal systems, and review simple growth models which generate fractal structures. We describe the polymerization of silica under various conditions and demonstrate that, depending on chemical conditions, polymerization maps onto simple fractal growth processes. The key factors which control growth are monomer-cluster vs. cluster-cluster growth, and reaction-limited vs. diffusion-limited growth.

Tracing X-rays through an L-shaped laterally graded multilayer mirror: a synchrotron application

A theoretical model to trace X-rays through an L-shaped (nested or Montel Kirkpatrick-Baez mirrors) laterally graded multilayer mirror to be used in a synchrotron application is presented. The model includes source parameters (size and divergence), mirror figure (parabolic and elliptic), multilayer parameters (reflectivity, which depends on layer material, thickness and number of layers) and figure errors (slope error, roughness, layer thickness fluctuation Deltad/d and imperfection in the corners). The model was implemented through MATLAB/OCTAVE scripts, and was employed to study the performance of a multilayer mirror designed for the analyzer system of an ultrahigh-resolution inelastic X-ray scattering spectrometer at National Synchrotron Light Source II. The results are presented and discussed.

Structural modifications in the swelling of inhomogeneous microgels by light and neutron scattering

Small-angle neutron scattering and dynamic light scattering have been used to study the thermodynamics of swelling and the associated structure modifications of highly cross-linked temperature-sensitive poly (N-isopropylacrylamide) [poly(NIPAM)] microgels in D2O. A particle core-shell model is proposed, with the core containing most of the cross-linker molecules. The Flory-Rehner theory, with the inclusion of a concentration dependent Flory solvency parameter, successfully describes the experimental swelling, despite the inhomogeneous character of the particles. Interestingly, the shell evolution with temperature controls the whole particle swelling, exerting an external pressure over the core, which in turn influences its size during the swelling process. Scaling laws for the correlation lengths were found with respect to temperature and polymer concentration. Finally, it has been encountered that for the collapsed microgel states, the particle surface seems to have a fractal character.

Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications

Based on the fact that the half-width of the Fourier transform is inversely proportional to that of a symmetrical primary decay function, the half-width of the intensity profiles of light scattered from self-affine fractal random surfaces in the whole k( perpendicular ) region is studied. The primary function, whose Fourier transform is the intensity profile, is approximated with a simple mathematical decay function by equating their half-widths and maximums. The expression obtained for the half-width of the scattered intensity profiles reduces to the present results in the two extreme cases with the scattering roughness factors being either very small or very large. For a complete verification, we perform a simulation of the light scattering, in which self-affine fractal random surfaces are generated with an algorithm that is an analogy to the formation of laser speckles. The simulated and theoretical results conform well.