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.     

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.     

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     

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     

Analysis of a polydisperse system using small-angle X-ray scattering

The small-angle X-ray data from a polydisperse solution of sodium silicate have been measured in the concentration range 3.6–169 mg/cm³ using aKratky camera. The following values of the particle parameters were obtained: the average radius of gyration =7.5 nm, the average particle weight =900 000, the average volume =671 nm³, and the average particle surface area =717 nm².From the above parameters and the apparent specific volume, analysed to be 0.422 cm³/g, the water content of the silicate particles was determined to be 3% (by weight).From small-angle X-ray measurements, performed on solutions exposed to a hydrodynamic field, it is indicated that at least the larger particles in the solution have a relatively symmetric shape. Based on this observation it was assumed that the particles in solution are spherical, and particle size distribution functions were calculated using a least-squares program. It was found that the distribution cannot be described by a simple function, such as aGaussian function; instead, the distribution follows a histogram with three local maxima.Dedicated to Prof. Dr. Dr.Otto Kratky, Graz, on the occasion of his 80th birthday.     

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.     

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.     

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     

Development of nonuniform micropore structure of carbon adsorbents during activation: adsorption and small-angle X-ray scattering studies

The development of the micropore structure of activated carbons during activation was studied by small-angle X-ray scattering and adsorption methods. A new method for the processing of experimental data was used; this method makes it possible to obtain curves of the dimension distribution of micropores from the intensities of small-angle X-ray scattering and the adsorption isotherm. In the initial stage of activation, up to burnouts 0.3, the micropore structure is uniform, micropores with radius of gyration under 0.5–0.6 nm dominate. When activation is more prolonged ( = 0.3÷0.67), a bimodal system withR ₁ ^max 0.6 nm andR ₂ ^max 0.85÷1.0 nm forms, and the volume of large micropores (supermicropores) exceeds that of small ones considerably.Deceased.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 231–235, February, 1994.     

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.     

Utilising spatial frequency filtering to extract nanoscale layer structure information from isotropic small-angle X-ray scattering data

 A separation method by spatial frequency filtering of the diffuse background of small-angle X-ray scattering (SAXS) is transferred to the case of isotropically scattering samples of polymer materials. Analysis of the residual discrete SAXS is demonstrated. Evaluations of model scattering curves from lamellar two-phase systems show that this technique, in general, results in a good separation. If samples with pure particle scattering or such with rough domain surfaces are investigated, the separation of a suitable background is possible, but is prone to some uncertainty which is estimated. In the case of particle scattering from lamellae the problem is solved by fitting a model function considering polydispersity to the Lorentz-corrected scattering intensity. After background correction the residual information on the distorted nanostructure is collected in an interface distribution function, from which topological parameters can be recovered with high accuracy. These parameters comprise average layer thicknesses and parameters of particle polydispersity. Parameter recovery is achieved by nonlinear regression with model functions describing stacking statistics. Automated versions of the technique are suited to process and analyse series of polymers collected in time-resolved synchrotron radiation experiments. Received: 24 July 2001 Accepted: 12 September 2001     

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.     

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.     

Complexation of DNA with cationic surfactants as studied by small-angle X-ray scattering

The phase behaviors of the complex formed by didodecyldimethylammonium bromide(DDAB)and cetyltrimethylammonium bromide(CTAB)interacting with three different types of DNAs,salmon testes DNA(~2000 bp),21-bp double-stranded oligonucleotides(oligo-ds DNA),and 21-nt single-stranded oligonucleotides(oligo-ss DNA)were studied by synchrotron small-angle X-ray scattering.It was found that the DNA length and flexibility,together with the positive/negative charge ratio,determined the final structure.At higher charge ratios,the DNA length exhibited negligible effect.Both oligo-ds DNA and salmon DNA formed inverted hexagonal packing of cylinders with CTAB,as well as bilayered lamella with DDAB.However,at lower charge ratios,oligo-ds DNA formed a distorted hexagonal phase with CTAB and a new structure with DDAB,which was different from the behaviors of salmon DNA.The flexible oligo-ss DNA formed rich structures that were subject to environmental disturbance.Kinetic study also indicated that the structures of the complex formed by oligo-ss DNA took much longer to mature than the structures formed by oligo-ds DNA.We attributed this result to the conformational adjustment of oligo-ss DNA in the complex.     

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     

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.     

On the interpretation of small-angle X-ray scattering during water adsorption by carbon adsorbents

Two models accounting for the changes of shape of the small-angle X-ray scattering (SAXS) curves during water adsorption by carbon adsorbents are discussed. The first model is based on the assumption of partial filling of the pore space; the second one presumes micropore swelling during water adsorption. Analysis of the results allows one to conclude that the first model is valid. This conclusion is in agreement with adsorption investigation data.Deseased 1993.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1220–1223, July, 1993.     

A small-angle X-ray scattering study of nanoparticle assembly in an aligned nematic liquid crystal

The assembly of colloidal particles in a nematic liquid crystal has been investigated using small-angle X-ray scattering. The structure and orientation of nanoparticle assemblies in bulk samples of aligned nematic liquid crystal have been determined. The method offers some advantages over optical microscopy, which is usually restricted to investigations of thin cells and micron-sized particles. The scattering from chains of particles has been calculated, and comparison with experimental results has shown that suspensions of 48 and 105 nm diameter silica nanoparticles formed highly ordered structures perpendicular to the liquid crystal director, consistent with quadrupolar defect-induced assembly.     

Effect of ultrasound on the microstructure of polystyrene in cyclohexane: a synchrotron small-angle X-ray scattering study

Synchrotron small-angle X-ray scattering technique has been used to study the effect of ultrasound on the microstructure of polystyrene (PS) in cyclohexane solutions. The results show that the intramolecular radius of gyration (R _g) decreases with ultrasound, indicating the shrinkage and collapse of PS chains. There is an exponential relationship between R _g and the molecular weight of PS (M _w), and the exponent changes from 0.5 to 0.417, as the ultrasound time is increased. This means that the shape of PS chain changes from random coil to shrunken form. The Kratky plots also confirm the shape transformation of PS chains induced by ultrasound. Moreover, the intermolecular correlation length increases with the ultrasound time, which is indicative of the entanglement of PS chains.