Preparation and determination of the structure of high-performance polymer blends by small-angle neutron scattering

Amorphous blends from a deuterated polyaryletherketone and a polyetherimide have been prepared and investigated by neutron scattering. The used components differ remarkably in their structure and their solution properties. The blends on the other hand are combinatorial mixtures: the scattering quantity ϕ₁ϕ₂/S(q) is independent of the composition of the blends if the polymer chains have the same length.     

Quasielastic scattering of neutrons from freely jointed polymer chains in dilute solutions

Starting with Kirkwood's Fokker–Planck equation for the polymer configuration-space distribution function and using the Zwanzig–Mori projection operator technique we have calculated the scattering law S_(q,w) for a freely jointed model polymer chain in a dilute solution. When memory effects are neglected, the theory predicts a Lorentzian for S_(q,w) with a halfwidth Ω_(q), which we have determined as a function of the momentum transfer q for all values of q. The results are compared with recent neutron scattering experiments on deuterated polytetrahydrofuran and polystyrene in dilute solution in CS₂. It is found that the observed q dependence of Ω(q) is represented satisfactorily by the present theory with a bond length b of about 6.3 Å for polystyrene and 3.8 Å for polytetrahydrofuran, and a friction coefficient ζ = 4πη0b where η₀ is the viscosity of the solvent.     

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     

Characteristic lengths and the structure of salt free polyelectrolyte solutions. A small angle neutron scattering study

We have studied salt free semi dilute polyelectrolyte solutions by small angle neutron scattering. Specific labelling associated with an extrapolation method has allowed the separation of the form factor of a single polyelectrolyte chainS ₁(q) and the structure factorS ₂(q). Two lengths are deduced from these two factors: the persistence lengthb _t which characterizes the electrostatic interactions along the chain by a fitting ofS ₁(q) with calculation of the scattering function for a wormlike chain, and fromS ₂(q),q _m ^–1 which characterizes the interactions between chains. These two lengths vary in the same way with the concentration of polyions (b _t C _p ^–1/2 ,q _m ^–1 C _p ^–1/2 ) and a constant relation exists between them: only one length is then necessary to describe the structure of polyelectrolyte soltuion on this semidilute concentration range.Laboratoire Commun CEA-CNRS.     

Rheological and structural properties of aqueous solutions of a hydrophobically modified polyelectrolyte and its unmodified analogue

Rheological methods and small angle neutron scattering (SANS) were used in the characterization of dilute and semidilute aqueous solutions, both with and without added salt, of anionic poly(vinyl alcohol) (PVA⁻) and its hydrophobically modified analogue (HM-PVA⁻). The rheological measurements showed that the concentration induced viscosification effect and elastic responses are considerably stronger for solutions of HM-PVA⁻ than in solutions of the unmodified polyelectrolyte. Over the considered polymer concentration domain, the solutions of PVA⁻ exhibit virtually Newtonian behavior, whereas strong shear thinning effects are observed in the HM-PVA⁻ solutions. The SANS results for HM-PVA⁻ solutions reveal a pronounced peak in the plot of scattering intensity versus scattering wavevector q at intermediate q values and the position of the maximum scales with polymer concentration as q_max∼c^0.28±0.02. This peak is suppressed in solutions of the unmodified polyelectrolyte and merely a shoulder in the scattering curve appears. Additionally, an “upturn” in the scattered intensity is observed at small q values and the magnitude of this effect depends on polymer concentration, hydrophobicity and salt addition. At large q values, the SANS results from HM-PVA⁻ solutions suggest morphological changes, from rod-like chains to a network of semiflexible chains, as the polyelectrolyte concentration increases.     

Light,Small Angle Neutron and X-Ray Scattering from Gels

This paper gives two examples of experiments that demonstrate the power of small angle scattering techniques in the study of swollen polymer networks. First, it is shown how the partly ergodic character of these systems is directly detected by neutron spin echo experiments. The observed total field correlation function of the intensity scattered from a neutral gel allows the ergodic contribution to be directly distinguished from the non ergodic part, at values of transfer wave vector q that lie well beyond the range of dynamic light scattering. The results can be compared with those obtained at much lower q from visible light scattering. Second, a recent application of small angle X-ray (SAXS) and neutron (SANS) scattering is described for a polyelectrolyte molecule, DNA, in semi-dilute solutions under near-physiological conditions. For these observations, the divalent ion normally present, calcium, is replaced by an equivalent ion, strontium. The comparison between SANS and SAXS yields a quantitative picture of the cloud of divalent counter-ions around the central DNA core. At physiological conditions, the cloud is thinner than that predicted on the basis of the Debye screening length but thicker than if the counter-ions were condensed on the DNA chain.     

Polydispersity effects in polymer self-diffusion measured by small-angle neutron scattering

The small-angle neutron scattering (SANS) method for measuring the self-diffusion coefficient D has been analyzed for effects of polydispersity in degree of polymerization for the case of linear polymers diffusing by reptation. Polydispersities corresponding to M_w/M_n = 1.0?10 were considered. It is shown that in all cases a meaningful effective diffusion coefficient D_e can be obtained from the short time recovery of the SANS intensity. This quantity D_e ≤ 1.3 D(M_w), where D(M_w) is the diffusion coefficient of a monodisperse polymer having molecular weight M = M_w. The method relies on SANS intensities extrapolated to zero scattering angle; realistic extrapolation is shown to give rise to quite acceptable errors on the order of 0.05 D_e.     

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.     

Evidence for hydrophobic attraction between latex particles in aqueous systems as investigated by turbidimetry

We report the evidence for attractive interaction of latex particles which are covered by poly(ethylene oxide) chains. These particles are suspended in aqueous solutions of ammonium sulfate. The interaction is probed by measurements of the turbidity of the suspensions up to 70 g/l. Turbidity is insensitive to multiple scattering and allows the static structure factor, S(q) [q=(4πn ₀/λ₀)sin(θ/2), where θ is the scattering angle, n₀ is the refractive index of the medium and λ₀ is the wavelength in vacuo], to be determined at small q values. The analysis of S(q) at small q values yields information about possible attraction of the particles. The analysis of the turbidity data furthermore shows that no aggregation took place in these systems. A weak but long-range attractive interaction was found at ammonium sulfate concentrations of 0.01 and 0.1 M. The relation of this attractive force to hydrophobic forces is discussed. Received: 9 March 2000/Accepted: 28 June 2000     

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.     

Molecular dimensions and chain conformation in glassy syndiotactic polystyrene

For the first time the small-angle neutron scattering (SANS) from mixtures of protonated and totally deuterated syndiotactic polystyrene (sPS) has been studied. Two amorphous samples with similar molecular weights have been measured at various concentrations of the protonated part. All measurements were performed at room temperature using the scattering equipment of two different laboratories. The molecular weight M_w evaluated from SANS data agreed with those obtained by gel permeation analysis (GPC). In the Kratky representation the scattering contribution due to the contrast scattering shows a plateau behavior up to q = 0.45 Å^?1, where q is magnitude of the scattering vector. This observation is in evident contrast to what is expected from the rotational isomeric state (RIS) model. In addition the characteristic ratios C_∞, derived either from the plateau height or from radii of gyration of the Zimm regime and being in reasonable agreement with each other, show strong deviations from the predictions of the RIS model. © 1994 John Wiley & Sons, 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     

Microstructure and swelling behavior of ion-exchange resin

The microstructure and swelling kinetics of ion-exchange resins having sulfonic acid groups were investigated by small-angle neutron scattering (SANS) and swelling experiments as functions of the crosslinking density (CD), pH, and the salt concentration (C_salt). The swelling kinetics was analyzed on the basis of the Tanaka-Fillmore swelling equation for the cooperative diffusion of polymer gels. The swelling behavior was very sensitive to CD, but not to pH and C_salt. The SANS intensity functions, I(q), were independent of CD and well described with a power law function, I(q) ∼ q^−D, where q and D are the magnitude of the scattering vector and the mass-fractal dimension, respectively. D was estimated to be ∼2, indicating that the resin consisted of a rather coarsely interconnected domains irrespective of CD at swelling equilibrium. It was found that CD is the most important parameter determining the swelling power of ion-exchange resin. However, no remarkable variations were found in the microstructure in the order of tens to hundreds of angstrom. © 1996 John Wiley & Sons, Inc.     

Some properties of the structure factor S(q) in two-dimensional classical liquids near freezing

We explore general properties of the main peak of the structure factor S(q) near the melting temperature T _melt in liquids confined in two dimensions, especially for the one component plasma model and for monatomic liquids interacting through inverse twelfth-power potentials. Those properties are the height of the peak, S(q _m), where q _m is the position of maximum in the peak, and the ratio between S(q _m) and q _m/Δq, where 2Δq is the width of the peak. The results obtained are then compared with those for similar systems in three dimensions. Other magnitude that we use to compare two-dimensional and three-dimensional simple liquids is r _m/Δr, where r _m is the position of the main peak in the pair distribution function g(r) and 2Δr is the width of that peak.     

Water‐soluble polymer‐grafted platinum nanoparticles for the subsequent binding of enzymes. synthesis and SANS

Functionalized platinum nanoparticles (PtNPs) possess catalytic properties towards H₂0₂ oxidation, which are of great interest for the elaboration of electrochemical biosensors. To improve the understanding of phenomena involved in such systems, we designed platinum‐polymer‐enzyme model nanostructures according to a bottom–up approach. These structures have been elaborated from elementary building units based on polymer‐grafted PtNPs obtained from surface initiated‐atom transfer radical polymerization. This paper describes the polymerization of ter‐butyl methacrylate from PtNPs and its subsequent hydrolysis to obtain a water‐soluble corona, followed by an activated ester modification to introduce an enzyme (glucose oxidase). The structure of the objects, the molecular weight and the grafting density of the polymer chains were principally elucidated by small angle neutron scattering (SANS). After the grafting of the enzyme, the final hybrid structures were characterized by both microscopy and SANS to attest for the covalent grafting of the enzyme. Composition and enzyme activity of the nanohybrid objects, have also been determined by UV spectroscopy. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Structural properties of some liquid transition metals

This article addresses the computation of structural properties of liquid transition metals, namely, 3d (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn), 4d (Zr, Pd, Ag and Cd) and 5d (Pt, Au and Hg). We have calculated the structure factor S(q), pair distribution function g(r), interatomic distance r ₁, coordination number n ₁, long wavelength limit of structure factor S(0) and isothermal compressibility χ_T for liquid transition metals. To describe electron–ion interaction, we have used our own model potential along with one component plasma reference system. To see the influence of exchange and correlation effect, Sarkar et al.'s [Mod. Phys. Lett. B12, 639 (1998)] local field correlation function is used. Thus, our newly constructed model potential has successfully generated the structural properties (structure factor S(q), pair distribution function g(r), interatomic distance r ₁, coordination number n ₁, long wavelength limit of structure factor S(0) and isothermal compressibility χ_T ) for liquid transition metals.     

Small-angle neutron scattering study of sodium cholate and sodium deoxycholate interacting micelles in aqueous medium

Small angle neutron scattering (SANS) measurements of D₂O solutions (0.1 M) of sodium cholate (NaC) and sodium deoxycholate (NaDC) were carried out atT= 298 K. Under compositions very much above the critical micelle concentration (CMC), the bile salt micelle size growths were monitored by adopting Hayter-Penfold type analysis of the scattering data. NaC and NaDC solutions show presence of correlation peaks atQ = 0.12 and 0.1 ?_-1 respectively. Monodisperse ellipsoids of the micelles produce best fits. For NaC and NaDC systems, aggregation number (9.0, 16.0), fraction of the free counterions per micelle (0.79, 0.62), semi-minor (8.0 ?) and semi-major axes (18.4, 31.7 ?) values for the micelles were deduced. Extent of micellar growth was studied using ESR correlation time measurements on a suitable probe incorporating NaC and NaDC micelles. The growth parameter (axial ratio) values were found to be 2.3 and 4.0 for NaC and NaDC systems respectively. The values agree with those of SANS.     

Small angle neutron scattering study of tetramethylurea solutions

The results of small-angle neutron scattering(SANS) carried out on aqueous and CS₂ solutions of tetramethylurea(TMU) are compared. It is shown that the SANS data indicate the formation of TMU-TMU dimers in both solutions.     

Small-angle X-ray and neutron scattering studies of the morphology of ionomers

Preliminary small-angle neutron scattering (SANS) studies have been made of different ionomers in the dry state and after saturation with water. Scattering from the dry samples arises from differences in the neutron scattering cross sections of the ionic and nonionic units in the polymer. The SANS technique is complementary to previous small-angle x-ray scattering (SAXS) studies since the SANS contrast differences are generally quite different than those for SAXS. A quantitative comparison is made of SANS and SAXS intensities for a dry cesium salt of an ethylene-methacrylic acid (E-MAA) copolymer. For water-saturated samples the technique of isotopic replacement can be used in conjunction with SANS since saturation can be effected with either H₂O or D₂O. In this case information about the chemical composition of the phases is obtained from an analysis of the intensity ratio I/I. Results are consistent with the presence of a separate phase containing water molecules and ions in a matrix of the nonionic units. A Guinier analysis gives a radius of gyration of 17 Å for a water-saturated cesium salt of an E-MAA copolymer.