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.     

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     

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.     

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.     

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.     

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.     

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.     

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.     

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     

Growth process of polymer aggregates formed by perfluorooctyltriethoxysilane. Time-resolved near-IR and two-dimensional near-IR correlation studies

The polymerization of 1H, 1H, 2H, 2H-perfluorooctyltriethoxysilane in ethanol, catalyzed by 0.5, 1.0 and 2.0 M HCl·H₂O, has been examined using time-resolved near-IR (NIR) and 2D NIR correlation techniques. The time-resolved NIR results have demonstrated that the growth of polymeric aggregates prior to the phase separation proceeds in a two-step process, which depends upon the HCl concentration. Furthermore, it has been found that the 2D NIR correlation data provide direct information on the sequence of the intricate reaction steps and interaction of participating components through hydrogen bonding in the growth process. Received: 25 July 2001 Accepted: 16 October 2001     

The exponential distribution in small angle X-ray scattering. Theory and practice

Summary From all the theoretical small-angle X-ray scattering (SAXS) curves of compact (non-particulate) systems elaborated systematically by Porod [2], we give a theoretical analysis of only one scattering curve, the corresponding correlation function of which is an exponential distribution. To obtain a correct as well as an easier determination of the zero-intensityI ₀ and the correlation lengthl _c than with the procedure usual up to now (analysis of the plotI(s)^–1/n vs.s ² withn=2 or 3/2) the classical SAXS-parameters of particle scattering will be involved in the evaluation. In this way the results get also a more useful conception for a practical application.Von den systematisch besprochenen Röntgenkleinwinkelstreukurven der dichtgepackten Systeme von Porod [2] wird nur eine Streukurve, deren Korrelationsfunktion eine exponentielle Verteilung aufweist, theoretisch analysiert und mit den klassischen Auswertungsmethoden der Partikelstreuung in Verbindung gesetzt. Dadurch werden die die Streukurve bestimmenden Parameterl _c (Kohärenzlänge) und die NullintensitätI ₀ besser erfaßt als mit der in der Literatur bisher veröffentlichten Methode (AuftragungI(s)^–1/n gegens ², mitn=2 oder 3/2). Damit erhalten außerdem die Meßergebnisse eine anschaulichere Auslegung.Dedicated to Prof. Dr. Dr. h.c. mult. Otto Kratky on the occasion of his 90th birthday     

Acrylic acid copolymer nanoparticles for drug delivery: structural characterization of nanoparticles by small-angle x-ray scattering

Nanoparticles are possible carriers for drug delivery. Copolymer nanoparticles of acrylic acid, acrylic amide, acrylic butylester, and methacrylic methylester (CAA) dispersed in water and in 0.15 M NaCl-solution were investigated by small-angle x-ray scattering (SAXS) experiments. The particles were characterized in terms of parameters relevant for the in vivo distribution: particle shape and diameter, size distribution, surface structure, and their organization within tight systems.The CAA-nanoparticles exist in at least three populations of spheres with two minor subpopulations having radii of about 32 and 66 nm and the main moiety around 45 nm. The degree of polydispersity isR _w/R _N=1.05. The subpopulations possess different hydrophobic areas on their surfaces, leading to different recognition by opsonins in vivo and different organ distribution and clearance velocity. The particles are compact without channels and holes, which is proved by low internal hydrationw=0.22 g H₂O/g polymer. Drugs and coating surfactants will interact mainly with the outer surface and not tunnel into the carriers. The surface of the nanoparticles is fractal with a dimensionD=2.3. Probe-molecules with dimensions less than 11.4 nm in diameter will find a larger contact area than expected from the sphere radius. Adsorption rate and position of the arrival of surfactants, and possibly opsonins, may be affected thereby. The negative charges on the CAA-nanoparticle surface are nearly completely screened in physiological NaCl-solutions by counter-ions. Therefore, surface charges hamper carrier-cell interaction at short distances only and do not prevent specific recognition and clearance by the reticuloendothelial system (RES).     

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.     

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.     

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.     

High-pressure small-angle neutron scattering for food studies

This article highlights contributions and the tremendous potential of high pressure (HP) small-angle neutron scattering for our understanding of biopolymer stability and phase behavior, in the context of nutrition and food properties. The use of HP processing as a nonthermal sterilization technique is well established in the food industry, and many other applications are emerging in recent years. Green chemistry, consumer preferences, and nutritional trends push for further developments, which require a database of experimental data. Unbiased studies on pressure-induced effects on colloids and amphiphiles are paramount for the development of new food molecules and methodologies. Biopolymer phase diagrams are described, with an emphasis on proteins. HP small-angle neutron scattering research capabilities and future directions are discussed.     

Time-resolved small-angle neutron scattering study of polyethylene crystallization from solution

With time-resolved small-angle neutron scattering (TR-SANS), the crystallization kinetics of polyethylene from deuterated o-xylene solutions upon a temperature jump have been investigated. On the basis of a morphological model of coexisting lamellar stacks and coil chains in solution, experimental data have been quantitatively analyzed to provide structural information, such as the lamellar long period, the lamellar crystal thickness, the thickness of the amorphous layers between lamellae, the degree of crystallinity, and the crystal growth rate at various degrees of undercooling. The viability of TR-SANS for studying polymer crystallization is demonstrated through the consistency of these measurements and well-established knowledge of polyethylene crystallization from xylene solutions. One unique feature of this experimentation is that both the growth of lamellar crystals and the condensation of coil chains from solution are monitored simultaneously. The ratio of the crystal growth to the chain consumption rate decreases rapidly with a decreasing degree of undercooling. The Avrami analysis suggests that the growth mechanism approaches two-dimensional behavior at higher temperatures, and this is consistent with the observation of an increasing ratio of the sharp-surface area to the bulk crystal growth rate with temperature. The limitations, possible remedies, and potentials of TR-SANS for studying polymer crystallization are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3133–3147, 2004     

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     

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