Comparative Study of Scattering and Osmotic Properties of Synthetic and Biopolymer Gels

Summary: The effect of monovalent/divalent cation exchange on the structure and osmotic properties of chemically cross-linked polyacrylate and DNA gels swollen in near physiological salt solutions has been investigated. Both systems exhibit a reversible volume phase transition in the presence of calcium ions. The small-angle neutron scattering spectra of these gels display qualitatively similar features. At low values of q surface scattering is observed, while in the intermediate q range the signal is characteristic of scattering from rod-like elements. At high values of q the scattering intensity is governed by the local (short-range) geometry of the polymer chains. The competition between monovalent and divalent cations has been studied by anomalous small-angle X-ray scattering (ASAXS). The ASAXS results reveal that the local concentration of the divalent counter-ions in the vicinity of the polymer chains significantly exceeds that of the monovalent counter-ions.     

Monte Carlo simulation algorithm for B‐DNA

Understanding the structure–function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small‐angle X‐ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all‐atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub‐ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B‐DNA is represented using a wormlike bead–rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse‐grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.     

Similarities between polyelectrolyte gels and biopolymer solutions

Small angle neutron scattering (SANS) measurements and osmotic swelling pressure measurements are reported for polyelectrolyte gels and solutions under nearly physiological conditions. A synthetic polymer (sodium-polyacrylate) and three biopolymers (DNA, hyaluronic acid, and polyaspartic acid) are studied. The neutron scattering response of these anionic polyelectrolytes is closely similar, indicating that at larger length scales the organization of the polymer molecules is not significantly affected by the fine details of the molecular architecture (e.g., size and chemical structure of the monomer unit, type of polymer backbone). The results suggest that specific interactions between the polyelectrolyte chains and the surrounding monovalent cations are negligible. It is found that the osmotic compression modulus of these biopolymer solutions determined from the analysis of the SANS response decreases with increasing chain persistence length. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3679–3686, 2006     

SAXS and SANS studies of polymer colloids

The analysis of latex particles by small-angle scattering (small-angle X-ray scattering, SAXS; small-angle neutron scattering, SANS) is reviewed. Small-angle scattering techniques give information on the radial structure of the particles as well as on their spatial correlation. Recent progress in instrumentation allows to extend SANS and SAXS to the q-range of light scattering. Moreover, contrast variation employed in SANS and SAXS studies may lead to an unambiguous determination of the radial scattering length density of the particles in situ, i.e. in suspension. Hence, these techniques are highly valuable for a comprehensive analysis of polymer colloids as shown by the examples discussed herein.     

Small angle X-ray scattering measurements probe water nanodroplet evolution under highly non-equilibrium conditions

Our in situ small angle X-ray scattering (SAXS) measurements yield an unprecedented and detailed view of rapidly evolving H(2)O nanodroplets formed in supersonic nozzles. The SAXS experiments produce spectra in a few seconds that are comparable to small angle neutron scattering (SANS) spectra requiring several hours of integration time and the use of deuterated compounds. These measurements now make it possible to quantitatively determine the maximum nucleation and growth rates of small droplets formed under conditions that are far from equilibrium. Particle growth is directly followed from about 10 micros to 100 micros after particle formation with growth rates of approximately 0.2 to 0.02 nm micros(-1). The peak H(2)O nucleation rates lie between 10(17) and 10(18) cm(-3) s(-1).     

Interaction of blockcopolymer micelles as probed by small-angle neutron and by small-angle X-ray scattering

 The analysis of the interaction of micelles formed by a blockcopolymer is given by means of small-angle X-ray (SAXS) and small-angle neutron scattering (SANS). The blockcopolymer consists of poly(styrene) and poly(ethylene oxide) (molecular weight of each block: 1000 g/mol) and forms well-defined micelles (weight-association number: 400, weight-average diameter: 15.4 nm) in water. The internal structure has been studied previously (Macromolecules 29:4006 (1996)) by SAXS. There it has been shown that the micelles are spherical objects. The structure factor S(q) as a function of the scattering vector q (q=(4π/λ) sin (θ/2); λ: wavelength of the radiation in the medium; θ: scattering angle) can be extracted from both sets of small-angle scattering data (SANS: q≤0.4 nm^-1; SAXS: q≤0.6 nm^-1). It is shown that particle interaction in the present system can be described by assuming soft interaction which is modeled by a square-step potential. Received: 12 May 1997 Accepted: 9 July 1997     

含C60球两亲分子有序聚集体研究

综合评述了C60两亲分子有序聚集体的形成、结构及聚集体演变规律,介绍了含C60球两亲分子有序聚集体结构的冷冻刻蚀电子显微镜和电子显微镜、小角度中子散射、小角度X光散射、激光光散射以及聚集体结构模型的研究结果.     

Crystallization and chain conformation of semicrystalline and amorphous polymer blends studied by wide‐angle and small‐angle scattering

We examine the crystallization and chain conformation behavior of semicrystalline poly(ethylene oxide) (PEO) and amorphous poly(vinyl acetate) (PVAc) mixtures with wide‐angle X‐ray diffraction (WAXD), small‐angle X‐ray scattering (SAXS), and small‐angle neutron scattering (SANS) experiments. For blends with PEO weight fractions (wt_PEO) greater than or equal to 0.3, below the melting point of PEO, the WAXD patterns reveal that crystalline PEO belongs to the monoclinic system. The unit‐cell parameters are independent of wt_PEO. However, the bulk crystallinity determined from WAXD decreases as wt_PEO decreases. The scattered intensities from SAXS experiments show that the systems form an ordered crystalline/amorphous lamellar structure. In a combination of WAXD and SAXS analysis, the related morphological parameters are assigned correctly. With the addition of amorphous PVAc, both the average amorphous layer thickness and long spacing increase, whereas the average crystalline layer thickness decreases. We find that a two‐phase analysis of the correlation function from SAXS, in which the scattering invariant is linearly proportional to the volume fraction of lamellar stacks, describes quantitatively the crystallization behavior of PEO in the presence of PVAc. When wt_PEO is close to 1, the samples are fully spaced‐filled with lamellar stacks. As wt_PEO decreases from 1.0 to 0.3, more PVAc chains are excluded from the interlamellar region into the interfibrillar region. The fraction outside the lamellar stacks, which is completely occupied with PVAc chains, increases from 0 to 58%. Because the radius of gyration of PVAc with a random‐coil configuration determined from SANS is smaller than the average amorphous layer thickness from SAXS, we believe that the amorphous PVAc chains still persist with a random‐coil configuration even when the blends form an ordered structure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2705–2715, 2001     

Volume transition and internal structures of small poly(N‐isopropylacrylamide) microgels

Monodispersed poly(N‐isopropylacrylamide) (PNIPAM) nanoparticles, with hydrodynamic radius less than 50 nm at room temperature, have been synthesized in the presence of a large amount of emulsifiers. These microgel particles undergo a swollen–collapsed volume transition in an aqueous solution when the temperature is raised to around 34 °C. The volume transition and structure changes of the microgel particles as a function of temperature are probed using laser light scattering and small angle neutron scattering (SANS) with the objective of determining the small particle internal structure and particle–particle interactions. Apart from random fluctuations in the crosslinker density below the transition temperature, we find that, within the resolution of the experiments, these particles have a uniform radial crosslinker density on either side of the transition temperature. This result is in contrast to previous reports on the heterogeneous structures of larger PNIPAM microgel particles, but in good agreement with recent reports based on computer simulations of smaller microgels. The particle interactions change across the transition temperature. At temperatures below the transition, the interactions are described by a repulsive interaction far larger than that expected for a hard sphere contact potential. Above the volume transition temperature, the potential is best described by a small, attractive interaction. Comparison of the osmotic second virial coefficient from static laser light scattering at low concentrations with similar values determined from SANS at 250‐time greater concentration suggests a strong concentration dependence of the interaction potential. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 849–860, 2005     

Ion condensation in a polyelectrolyte gel

Anomalous small angle X-ray scattering is used to determine the distribution of divalent ions in a neutralized polyelectrolyte gel of sodium polyacrylate in the vicinity of the volume transition. At the five different energies of the incident beam used to vary the contrast, the scattering curves have similar shapes, and are separated only by constant multiplying factors. This result, in conjunction with SANS results from the same sample, indicates that the divalent ion (strontium) is confined on the polymer backbone.     

Thermodynamic interaction parameters in polymer solutions and gels

Polymer-solvent interaction parameters are reported for poly(vinyl acetate)-acetone, poly(vinyl acetate)-toluene, and poly(dimethyl siloxane)-toluene systems using different techniques. Results obtained by osmotic deswelling are compared with those from quasi-elastic light scattering and small-angle neutron scattering (SANS). In gels, the latter techniques involve separation of the time-dependent from the static component of the scattered radiation+ Separation is achieved in quasi-elastic light scattering through the heterodyning properties of the light, and in SANS by subtracting an appropriate static structure factor. The interaction parameters obtained by different separation procedures are consistent with measurements using the osmotic method. © 1995 John Wiley & Sons, Inc.     

Calcium induced volume transition in polyelectrolyte gels

The osmotic properties and the small angle neutron scattering (SANS) behaviour of fully neutralized sodium polyacrylate gels are investigated in the presence of calcium ions. Analysis of the SANS response displays three characteristic length scales, two of which are of thermodynamic origin, while the third, associated with the frozen-in structural inhomogeneities, is static. The SANS results are consistent with direct osmotic observations which indicate that the thermodynamic properties cannot be adequately described by a single correlation length. The concentration dependence of the osmotic pressure displays a power law behaviour with an exponent that decreases with increasing calcium concentration.     

A hierarchical algorithm for fast debye summation with applications to small angle scattering

Debye summation, which involves the summation of sinc functions of distances between all pair of atoms in three‐dimensional space, arises in computations performed in crystallography, small/wide angle X‐ray scattering (SAXS/WAXS), and small angle neutron scattering (SANS). Direct evaluation of Debye summation has quadratic complexity, which results in computational bottleneck when determining crystal properties, or running structure refinement protocols that involve SAXS or SANS, even for moderately sized molecules. We present a fast approximation algorithm that efficiently computes the summation to any prescribed accuracy ? in linear time. The algorithm is similar to the fast multipole method (FMM), and is based on a hierarchical spatial decomposition of the molecule coupled with local harmonic expansions and translation of these expansions. An even more efficient implementation is possible when the scattering profile is all that is required, as in small angle scattering reconstruction (SAS) of macromolecules. We examine the relationship of the proposed algorithm to existing approximate methods for profile computations, and show that these methods may result in inaccurate profile computations, unless an error‐bound derived in this article is used. Our theoretical and computational results show orders of magnitude improvement in computation complexity over existing methods, while maintaining prescribed accuracy. © 2012 Wiley Periodicals, Inc.     

Observation of Ion Electrosorption in Metal–Organic Framework Micropores with In Operando Small‐Angle Neutron Scattering

A molecular‐level understanding of transport and adsorption mechanisms of electrolyte ions in nanoporous electrodes under applied potentials is essential to control the performance of double‐layer capacitors. Here, in operando small‐angle neutron scattering (SANS) is used to directly detect ion movements into the nanopores of a conductive metal–organic framework (MOF) electrode under operating conditions. Neutron‐scattering data reveals that most of the void space within the MOF is accessible to the solvent. Upon the addition of the electrolyte sodium triflate (NaOTf), the ions are adsorbed on the outer surface of the protrusions to form a 30 Å layer instead of entering the ionophobic pores in the absence of an applied charging potential. The changes in scattering intensity when potentials are applied suggests the ion rearrangement in the micropores following different mechanisms depending on the electrode polarization. These observations shed insights on ion electrosorption in electrode materials.     

Aggregation behavior of pyridinium based ionic liquids in water--surface tension, 1H NMR chemical shifts, SANS and SAXS measurements

The aggregation behavior of short alkyl chain ionic liquids (ILs), namely 1-butyl, or 1-hexyl or 1-octylpyridinium and 1-octyl-2-, or -3-, or -4-methylpyridinium chlorides, in water has been assessed using surface tension, electrical conductance, (1)H NMR, small angle neutron scattering (SANS) and small angle X-ray scattering (SAXS) measurements. Critical aggregation concentrations (CACs), adsorption (at air/water interface) and thermodynamic parameters of aggregation have been reported. The values of CAC and area per adsorbed molecule decrease with the number of carbon atoms in the alkyl chain. The aggregation process is driven by both favorable enthalpy and entropy contributions. An attempt was made to examine the morphological features of the aggregates in water using SANS and SAXS methods. SANS and SAXS curves displayed diffuse structural peaks that could not be model fitted, and therefore, we calculated the mean aggregation numbers from the Q(max) assuming that IL molecules typically order into cubic type clusters.     

SANS study of the aging of xTiO2-SiO2 gels

Silica-titania gels, prepared in acidic conditions, with contents of TiO₂ up to 6 mol%, have been studied by small angle neutron scattering (SANS) as wet gel with increasing aging times. In all samples, small primary particles have been found with a diameter of about 3 nm. At the gel point, cylindrical clusters, ca. 10 nm long, were observed as well. These grow with aging time, becoming branched. The cluster-cluster diffusion limited aggregation model is found to be consistent with the SANS results. The growth process is independent of the TiO₂ content. It is mainly influenced by the ratio of the aging time to the gelation time.     

Dynamic light scattering by weakly ionized gels: Effects of inhomogeneities and non-ergodicity

Small angle neutron scattering and light scattering experiments have been performed on partially neutralized poly(acrylic acid) solutions and gels. The structure factor obtained from small angle scattering and static light scattering reveals the absence of significant contribution from large scale inhomogeneities in the gels as soon as the ionization degree exceeds 9·10⁻³. The comparison of the time and ensemble averages of the autocorrelation function of scattered light intensity shows that the gels behave with respect to that experiment as ergodic media.     

Hydrodynamic radius of polyethylene glycol in solution obtained by dynamic light scattering

In order to compare the size characterizations in poly(ethylene glycol) (PEG) obtained by dynamic light scattering (DLS) and small angle neutron scattering (SANS), DLS experiments were performed in various PEG solutions to ascertain the hydrodynamic radius. Data from the experiments were analyzed by using a method to eliminate effects of PEG aggregation on dynamic correlation functions. The results of the analysis were then compared to the radii of gyration reported from SANS experiments. The relation between the hydrodynamic radius, obtained by DLS, and the radius of gyration, obtained by SANS, in PEG in solution was found to be in agreement with a previously obtained relation for PEG, where the radius of gyration was found by static light scattering.     

Tetraalkylammonium bromides in methanol: Small angle neutron scattering and vapor pressure measurements

Vapor pressure measurements and small angle scattering (SANS) experiments are reported and discussed for bispiperidinium (BP) bromide and n-tetrapentylammonium bromide solutions in methanol at 25°C. The BP⁺ ion which may be considered as a tetraalkylammonium (TAA) ion with pairwise connected alkyl chains, is used for the study of the effects due to flexible TAA alkyl chains. SANS intensities are calibrated with the help of the precise osmotic coefficients from the vapor pressure measurements.