High brilliance small-angle X-ray scattering applied to soft matter

This article reviews some recent applications of high brilliance small-angle X-ray scattering (SAXS) to soft matter and closely related systems in biology. Owing to the burgeoning literature in this field, examples presented are restricted to those exploiting the high brightness of the synchrotron source. Three types of experiments are discussed; (1) dynamic processes in systems driven out of equilibrium, (2) transient processes in extremely dilute systems, and (3) microbeam technique probing the local nanostructure of hierarchically organized specimens. In addition, recent advances in sample environments specifically adapted to microbeam applications are described. Present limitations and suggestions for future developments are discussed.     

Analysis to obtain precise density fluctuation of supercritical fluids by small-angle X-ray scattering

A procedure of analysis for small-angle X-ray scattering (SAXS) data has been established to obtain density fluctuation of supercritical fluids near the critical point. It is indispensable for the certain analysis to utilize both of high-quality SAXS data measured under stable thermodynamic condition and accurate P–ρ–T data in supercritical region. As a standard example, SAXS measurements have been performed for supercritical CO₂, which is a suitable sample satisfying the condition for both experiment and analysis. The measurements were carried out along four isothermal conditions at reduced temperature of T_r = T/T_c = 1.020, 1.022, 1.043 and 1.064. Comparing the experimental density fluctuation with calculated one from the most reliable equation of state, the differences are within 8% at most.     

Growth process for fractal polymer aggregates formed by perfluorooctyltrimethoxysilane. Time-resolved small-angle X-ray scattering study

The acid-catalyzed condensation reaction of perfluorooctyltrimethoxysilane (PFOS) and n-octyltrimethoxysilane (OTMS) in ethanol has been followed by time-resolved synchrotron radiation small-angle X-ray scattering (SAXS) on a short time scale. SAXS curves for PFOS and OTMS have been interpreted as arising from mass fractals with D _f=2 (PFOS) and D _f=1.7 (OTMS). The time dependence of the apparent radius of gyration, obtained from the Guinier plots, showed that the growth of fractal precursors occurs in a two-step process within 2 h for PFOS and within 1.5 h for OTMS, in which small clusters involving monomers, dimers and trimers are formed in the initial step and formation of larger clusters occurs in the second step. Furthermore, it has been suggested that the hydrophobicity and lipophobicity of the bulky alkyl groups may also contribute to the formation of these giant aggregates. Received: 13 July 1999/Accepted in revised form: 6 October 1999     

Size-exclusion chromatography combined with small-angle X-ray scattering optics

Size-exclusion chromatography with on-line synchrotron radiation solution small-angle X-ray scattering optics, absorbance and/or refractive index detectors was evaluated by protein characterizations. The radius of gyration value and zero-angle scattering intensity of protein molecules eluted from the chromatography column were estimated using this measurement system. In addition, the characterization of the conformation of the eluted proteins was demonstrated for hen egg lysozyme and bovine submaxillary mucin. The present technique will be useful for not only the determination of the radius of gyration value and molecular weight of proteins with dimensions of 1–10 nm, but also for the structural characterization of the macromolecules during the chromatography.     

Analysis of the morphology of hectorite by use of small-angle X-ray scattering

An analysis of the three-dimensional correlation function of small-angle scattering is applied for the direct determination of stereological parameters of hectorite samples. Beside characteristic lengths and volume fractions the specific order distances are given. The samples can be described by homogeneous particles of different order magnitudes up to the size of the secondary particles, which were estimated to have maximum dimensions of about 450 nm. Beside traditional stereological formulas, including the interpretation of the derivatives of the small-angle correlation function, the so-called transformed correlation function is applied in order to detect distinctive characteristic lengths. Received: 2 December 1999 Accepted: 9 March 2000     

Correlation of counterions with rodlike macroions as assessed by anomalous small-angle X-ray scattering

We consider the analysis of a rodlike synthetic polyelectrolyte in solution by anomalous small-angle X-ray scattering (ASAXS) in order to elucidate the correlation of the counterions with the highly charged macroion. ASAXS can be applied to these systems because the absorption edge of typical counterions, for example, bromine or iodine ions can be attained by synchrotron radiation. Model calculations using the Poisson–Boltzmann cell model show that ASAXS furnishes two terms caused by the anomalous dispersion of the counterions. The leading terms is a cross-term between the ordinary scattering amplitude of the polyelectrolyte and the real part of the scattering length f ′ of the counterions. A second term refers solely to the anomalous contribution of the counterions, i.e., to f ′ and f ′′ ( f ′′: imaginary part of scattering length). Preliminary data obtained from rodlike synthetic macroions having iodine counterions corroborate the theoretical deductions. They demonstrate that ASAXS is capable of furnishing information that is not available by the ordinary SAXS experiment. Received: 11 December 2000/Accepted: 22 February 2001     

Peptide meets membrane: Investigating peptide-lipid interactions using small-angle scattering techniques

Peptide–lipid interactions play an important role in defining the mode of action of drugs and the molecular mechanism associated with many diseases. Model membranes consisting of simple lipid mixtures mimicking real cell membranes can provide insight into the structural and dynamic aspects associated with these interactions. Small-angle scattering techniques based on X-rays and neutrons (SAXS/SANS) allow in situ determination of peptide partition and structural changes in lipid bilayers in vesicles with relatively high resolution between 1-100 nm. With advanced instrumentation, time-resolved SANS/SAXS can be used to track equilibrium and nonequilibrium processes such as lipid transport and morphological transitions to time scales down to a millisecond. In this review, we provide an overview of recent advances in the understanding of complex peptide–lipid membrane interactions using SAXS/SANS methods and model lipid membrane unilamellar vesicles. Particular attention will be given to the data analysis, possible pitfalls, and how to extract quantitative information using these techniques.     

Multiple small-angle X-ray scattering analyses of the structure of gold nanorods with unique end caps

Small-angle X-ray scattering (SAXS) experiments were carried out on gold nanorods generated by a seed-mediated growth method. Previous transmission electron microscopy observations suggest that the main components of nanoparticles are rod-shaped nanoparticles, but they are contaminated by other different-shaped, large-volume particles. By performing profile fitting of theoretical and experimental scattering curves, we determined and then removed from the obtained SAXS profile, the contribution of the contaminating particles. From the revised SAXS profile, we calculated the distance distribution function by Fourier transform and precisely determined the structural parameters of the nanorods and the structure of the nanorod end caps.     

Structure development during isothermal crystallisation of high-density polyethylene: Synchrotron small-angle X-ray scattering study

Isothermal melt crystallisation in high-density polyethylene (HDPE) was studied using the time-resolved SAXS method with synchrotron radiation over a wide range of crystallisation temperatures. The SAXS profile was analysed by an interface distribution function, g₁(r), which is a superposition of three contributions associated with the size distributions of crystalline (L_C) and amorphous (L_A) layers and a distribution of long period (LP). The morphological parameters extracted from the g₁(r) functions show that the lamellar thickness increases with time, obeying a logarithmic time dependence. The time evolution of L_C observed for the sample crystallised at 122 °C leads to the conclusion that crystallisation proceeds according to the mechanism of thickening growth. For samples crystallised at lower temperatures (116 °C and 118 °C), the lamellar thickening mechanism has been observed. The rate of lamellar thickening in these cases is much lower than that at 122 °C. At 40 °C, thickening of the crystalline layer does not occur. The interface distribution functions were deconvoluted, and the relative standard deviation σ_C/L_C obtained in this way is an additional parameter that is varied during crystallisation and can be used for analysis of this process. Time-dependent changes in the σ_C/L_C at large supercooling (T_C=40 °C) indicates that L_C presents a broad distribution in which the relative standard deviation increases with time. At lower supercooling (T_C=122 °C), L_C shows a much sharper distribution. In this case, the relative standard deviation decreases with time.     

Using light scattering to evaluate the separation of polydisperse nanoparticles

The analysis of natural and otherwise complex samples is challenging and yields uncertainty about the accuracy and precision of measurements. Here we present a practical tool to assess relative accuracy among separation protocols for techniques using light scattering detection. Due to the highly non-linear relationship between particle size and the intensity of scattered light, a few large particles may obfuscate greater numbers of small particles. Therefore, insufficiently separated mixtures may result in an overestimate of the average measured particle size. Complete separation of complex samples is needed to mitigate this challenge. A separation protocol can be considered improved if the average measured size is smaller than a previous separation protocol. Further, the protocol resulting in the smallest average measured particle size yields the best separation among those explored. If the differential in average measured size between protocols is less than the measurement uncertainty, then the selected protocols are of equivalent precision. As a demonstration, this assessment metric is applied to optimization of cross flow (V_x) protocols in asymmetric flow field flow fractionation (AF⁴) separation interfaced with online quasi-elastic light scattering (QELS) detection using mixtures of polystyrene beads spanning a large size range. Using this assessment metric, the V_x parameter was modulated to improve separation until the average measured size of the mixture was in statistical agreement with the calculated average size of particles in the mixture. While we demonstrate this metric by improving AF⁴V_x protocols, it can be applied to any given separation parameters for separation techniques that employ dynamic light scattering detectors.     

Electron microscopy of oriented high-density polyethylene: Comparison with small-angle X-ray scattering

The morphology of cold-drawn, rolled and annealed high-density polyethylene was investigated by transmission electron microscopy of stained sections. From the electron micrographs, a model of the structure was developed and the scattering pattern calculated. This was then compared with the corresponding small-angle X-ray scattering (SAXS) pattern, in order both to aid in the interpretation of SAXS patterns of oriented polymers, and to assess the effects of staining with chlorosulphonic acid on the morphology.     

Analysis of orientation fluctuation in fluids by small angle X-ray scattering

The small angle X-ray scattering of molecular fluids contains information on particular aspects of their orientational order. Examples are given for the case of the isotropic, nematic and cholesteric phases of mesogenic molecules. It is shown that the distribution of the molecular centers relative to the direction defined by the molecular long axes can be analysed by means of small angle X-ray scattering. An approximate expression for the circulation correlation function is given.     

Determination of the width of the domain boundaries in polymer two-phase systems by X-ray small-angle scattering

An accurate determination of the width of domain boundaries presupposes an unambigous elimination of the intensity component due to density fluctuations within the domains. The theoretical aspects of this problem are discussed and an application is demonstrated in an SAXS study of a styrene-isoprene-styrene blockcopolymer. The widths of the domain boundaries depend on the history of the sample, its values are, in general, smaller than theoretically predicted. The domain sizes correspond to the theoretical values, its variance is of the same order as the variance of the molecular weight of the domain-building blocks.Dedicated to Prof. Dr. Dr. h. c. O. Kratky on the occasion of his 80th birthday.     

Small-angle X-ray scattering study on the microstructure evolution of zirconia nanoparticles during calcination

Zirconia nanoparticles have been synthesized from zirconium hydroxide precipitates followed by a supercritical CO₂ extraction. The microstructure evolution of these zirconia nanoparticles during the calcination at the moderate temperature has been investigated. Assisted by the analyses of TEM and XRD, small-angle X-ray scattering (SAXS) study offers possibilities to a comprehensive and quantitative characterization of the structural evolution on the nanometer scales. The as-synthesized zirconia sample exhibits a mass fractal structure constructed by the surface fractal particles. Such a structure can be preserved up to 300 °C. After calcination at 400 °C, considerable structural rearrangement occurs. In the interior of nanoparticles zirconia nanocrystallites emerge. It is the scattering from such zirconia nanoparticles that give rise to the broadened crossover in the ln[J(q)] vs. ln q plot and the scattering peak in the ln[q³J(q)] vs. q² plot. With a further increase in the calcination temperature, the power-law region at large-q in ln J(q) vs. ln q plot expands, and the peak in ln[q³J(q)] vs. q² plot shifts towards lower q values, indicating size increases in both the nanocrystallites and nanoparticles. Besides, the mass fractal structure constructed by zirconia nanoparticles can be largely preserved during the moderate temperature calcination.     

Investigation of molecular order and phase transitions of smectic poly(ester imide)s by means of small-angle X-ray scattering

The molecular order and phase transitions of two smectic poly(ester imide)s based on aminobenzoic acid trimellitimide (PEI 1) or aminocinnamic acid trimellitimide (PEI 2) and α,ω-dihydroxydodecane were investigated by X-ray scattering. During cooling, the polymers pass through monotropic smectic liquid-crystalline (LC) phases (S_A, S_C), which transform into higher-ordered smectic-crystalline phases (S_E, S_H). The smectic layer structure of about 3 nm gives rise to a sharp reflection at 2θ ≅ 3°. Peak shape analysis and analysis of the interface distribution function revealed long-range longitudinal correlation among the mesogens in the LC phase but short-range lateral correlation. The development of a broad reflection in the small-angle X-ray scattering (SAXS, 2θ < 1°) indicates the formation of a lamellar two-phase system. The long-period changes reversibly between 10 and 30 nm with increasing temperature. The crystalline lamellae comprise a number of smectic-crystalline layers with packed mesogens, while the noncrystalline interlamellar regions keep their smectic-LC order. In the metastable S_B phase, formed during annealing of quenched PEI 1, the diffuse SAXS indicates a random distribution of small, probably fringed, crystals with hexagonal-packed mesogens. In the lamellar S_E and S_H phases, tie molecules play an important role, but chain folding cannot be excluded. Received: 16 July 1999/Accepted: 28 April 2000     

A small-angle X-ray scattering study of bromine-containing latex particles

A small-angle X-ray scattering (SAXS) study of two-stage latices (TSL), composed of polystyrene (PS) and polytribromostyrene (PTBrS), is presented. The analysis of the scattering curves leads to the conclusion that the TSL particles have a concentric core-shell structure. When a PTBrS latex was used as a seed, its particles were overcoated with a PS shell during the second-stage polymerization. However, only a small portion of the seed particles were overcoated with a PTBrS shell when using a PS seed. The size distributions of the TSL and the PTBrS latex particles were determined from the scattering curves, using the method of Indirect Fourier Transformation. The resulting average radii were in good agreement with the values obtained from TEM observations. © 1996 John Wiley & Sons, Inc.     

Quantitative determination of large structures by small-angle light scattering

A new small-angle light scattering camera has been developed. In contrast to conventional detection the present system is based on a recently developed two-dimensional charge-coupled-device chip made by Thomson (France). The advantage of this chip is its excellent linear response and very low dark signal even at room temperature. The best linearity was obtained by leading each pixel signal through the same amplifying system. The optical system covered a diffraction angular region from about 1° to 15° (q = 0.2–2.6 μm⁻¹). The camera was calibrated with grids and pinholes and was tested with polymer latex particles in solution and with spherulites from polymer films. Received: 06 December 1999 Accepted: 04 February 2000     

Rapid detection of compositional drift of polydisperse copolymers using thermal field-flow fractionation and multi-angle light scattering

Summary The use of thermal field-flow fractionation (ThFFF) with multi-angle light scattering (MALS) for the rapid detection of compositional heterogeneity in random copolymers is demonstrated. Soret coefficients were directly calculated from the ThFFF retention times while the MALS detector provided the polymer's radius of gyration (R _g) distribution. FromR _g, the diffusion coefficient (D) could be calculated and this allowed, in combination with the Soret coefficient, the calculation of the thermal diffusion coefficient (D _T). It was shown that theD _T distribution can serve as a measure for the chemical composition distribution of random styrene acrylonitrile copolymers. Comparison of ThFFF-MALS results with literature data from ThFFF-hydrodynamic chromatography (HDC) cross-fractionation experiments showed a fair agreement.     

Small-angle X-ray scattering studies of the open and closed conformations of aspartate aminotransferase

Summary Aspartate aminotransferase was investigated by X-ray small-angle scattering. A small difference was found between the open (active) and the closed (liganded) conformation of the enzyme. The results were compared with X-ray crystallography data.

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Untersuchungen zur Röntgenkleinwinkelstreuung der offenen und geschlossenen Konformation von Aspartat-Aminotransferase

Zusammenfassung Aspartat-Aminotransferase wurde mittels Röntgenkleinwinkelstreuung untersucht. Ein kleiner Unterschied zwischen der offenen (aktiven) und der geschlossenen (ligandierten) Konformation wurde gefunden. Die Ergebnisse wurden mit Röntgenkristallstrukturdaten verglichen.

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Abbreviations AspAT aspartate aminotransferase