Small-angle X-ray Scattering Intensity Research Articles

The effect of polydispersity, shape fluctuations and curvature on small unilamellar vesicle small-angle X-ray scattering curves.

Small unilamellar vesicles (20-100 nm diameter) are model systems for strongly curved lipid membranes, in particular for cell organelles. Routinely, small-angle X-ray scattering (SAXS) is employed to study their size and electron-density profile (EDP). Current SAXS analysis of small unilamellar vesicles (SUVs) often employs a factorization into the structure factor (vesicle shape) and the form factor (lipid bilayer electron-density profile) and invokes additional idealizations: (i) an effective polydispersity distribution of vesicle radii, (ii) a spherical vesicle shape and (iii) an approximate account of membrane asymmetry, a feature particularly relevant for strongly curved membranes. These idealizations do not account for thermal shape fluctuations and also break down for strong salt- or protein-induced deformations, as well as vesicle adhesion and fusion, which complicate the analysis of the lipid bilayer structure. Presented here are simulations of SAXS curves of SUVs with experimentally relevant size, shape and EDPs of the curved bilayer, inferred from coarse-grained simulations and elasticity considerations, to quantify the effects of size polydispersity, thermal fluctuations of the SUV shape and membrane asymmetry. It is observed that the factorization approximation of the scattering intensity holds even for small vesicle radii (∼30 nm). However, the simulations show that, for very small vesicles, a curvature-induced asymmetry arises in the EDP, with sizeable effects on the SAXS curve. It is also demonstrated that thermal fluctuations in shape and the size polydispersity have distinguishable signatures in the SAXS intensity. Polydispersity gives rise to low-q features, whereas thermal fluctuations predominantly affect the scattering at larger q, related to membrane bending rigidity. Finally, it is shown that simulation of fluctuating vesicle ensembles can be used for analysis of experimental SAXS curves.

Structural studies on fluid Hg and fluid Se at high temperatures and high pressures by means of X-ray diffraction and small angle X-ray scattering

Abstract X-ray diffraction (XRD) and small angle X-ray scattering (SAXS) measurements for fluid Hg and fluid Se up to the supercritical region have been carried out using synchrotron radiation at SPring-8. We obtained the structure factor, S ( Q ) $S\left(Q\right)$ , including a small angle region, and the pair distribution function, g ( r ) $g\left(r\right)$ , for both fluids from the liquid to the dense vapor region. Change of the local structure and medium-range correlations at the metal-insulator transition in fluid Hg were revealed. On the other, the average coordination number of two was preserved at the semiconductor-metal transition in fluid Se. From a SAXS experiment of fluid Se in 2012, SAXS spectra near the semiconductor-metal transition region show the Ornstein–Zernike profile and the SAXS intensity is reduced with increasing pressure. These results indicate difficulties of separating fluctuations intrinsic to the semiconductor-metal transition from those arising from the liquid-vapor critical point in fluid Se, although fluctuations intrinsic to the electronic transitions are largely expected in both fluids.

Molecular Dynamics Simulations Combined with Nuclear Magnetic Resonance and/or Small-Angle X-ray Scattering Data for Characterizing Intrinsically Disordered Protein Conformational Ensembles.

The concept of intrinsically disordered proteins (IDPs) has emerged relatively slowly, but over the past 20 years, it has become an intense research area in structural biology. Indeed, because of their considerable flexibility and structural heterogeneity, the determination of IDP conformational ensemble is particularly challenging and often requires a combination of experimental measurements and computational approaches. With the improved accuracy of all-atom force fields and the increasing computing performances, molecular dynamics (MD) simulations have become more and more reliable to generate realistic conformational ensembles. And the combination of MD simulations with experimental approaches, such as nuclear magnetic resonance (NMR) and/or small-angle X-ray scattering (SAXS) allows one to converge toward a more accurate and exhaustive description of IDP structures. In this Review, we discuss the state of the art of MD simulations of IDP conformational ensembles, with a special focus on studies that back-calculated and directly compared theoretical and experimental NMR or SAXS observables, such as chemical shifts (CS), 3J-couplings (3Jc), residual dipolar couplings (RDC), or SAXS intensities. We organize the review in three parts. In the first section, we discuss the studies which used NMR and/or SAXS data to test and validate the development of force fields or enhanced sampling techniques. In the second part, we explore different methods for the refinement of MD-derived structural ensembles, such as NMR or SAXS data-restrained MD simulations or ensemble reweighting to better fit experiments. Finally, we survey some recent studies combining MD simulations with NMR and/or SAXS measurements to investigate the relationship between IDP conformational ensemble and biological activity, as well as their implication in human diseases. From this review, we noticed that quite a few studies compared MD-generated conformational ensembles with both NMR and SAXS measurements to validate IDP structures at both local and global levels. Yet, beside the IDP propensity to form local secondary structures, their dynamic extension or compactness also appears important for their activity. Thus, we believe that a close synergy between MD simulations, NMR, and SAXS experiments would be greatly appropriate to address the challenges of characterizing the disordered structures of proteins and their complexes, relative to their biological functions.

Physical properties and morphology of crosslinked polyurethane synthesized from para‐phenylene diisocyanate and polyether polyol

ABSTRACTA series of crosslinked polyurethanes (PUs) were synthesized from para‐phenylene diisocyanate, 2‐(hydroxymethyl)‐2‐ethyl propane‐1,3‐diol (TMP), and butane‐1,4‐diol as the hard segments and poly(oxytetramethylene glycol) as the soft segments. The effects of TMP on the physical properties and microphase structure of the PUs were studied with dynamic mechanical analysis, Fourier transform infrared–attenuated total reflection spectroscopy, small‐angle X‐ray scattering (SAXS), and mechanical testing. We found that the storage modulus, hydrogen bonding with carbonyl groups, SAXS intensity, and hysteresis values decreased with increasing TMP; this indicated that the degree of microphase separation decreased with the increasing crosslinking density introduced by TMP. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 45241.

Fibrillar assembly of bacterial cellulose in the presence of wood-based hemicelluloses

Composite materials mimicking the plant cell wall structure were made by culturing cellulose-producing bacteria together with secondary-wall hemicelluloses from wood. The effects of spruce galactoglucomannan (GGM) and beech xylan on the nanoscale morphology of bacterial cellulose were studied in the original, hydrated state with small-angle X-ray scattering (SAXS). The SAXS intensities were fitted with a model covering multiple levels of the hierarchical structure. Additional information on the structure of dried samples was obtained using scanning and transmission electron microscopy and infra-red spectroscopy. Both hemicelluloses induced a partial conversion of the cellulose crystal structure from Iα to Iβ and a reduction of the cross-sectional dimensions of the cellulose microfibrils, thereby affecting also their packing into bundles. The differences were more pronounced in samples with xylan instead of GGM, and they became more significant with higher hemicellulose concentrations.

Rod-like particles growing in sol–gel processing of 1:1 molar mixtures of 3-glycidoxypropyltrimethoxysilane and tetraethoxysilane

The growth kinetics and the structure of organic/silica hybrids prepared from acid hydrolysis of 1:1 molar mixtures of 3-glycidoxypropyltrimethoxysilane and tetraethoxysilane were studied by small-angle X-ray scattering (SAXS) at 315, 325 and 335 K. The evolution of the SAXS intensity is compatible with the growth of silica-rich domains by aggregation from a fixed number of primary particles. Two distinct growth regimes could be identified by analyzing the relation I(0) ∝ R g D between the intensity extrapolated to zero I(0), the radius of gyration R g of the aggregates and the exponent D, which gives information on the geometry and the mechanism of growth of the aggregates. An initial period was attributed to the growth of rod-like particles with approximately the same radius and variable length. At more advanced degrees of aggregation the process was controlled by the growth of larger aggregates with higher-order dimensionality. A narrow distribution of cylinder lengths given by the Schulz function fitted the experimental SAXS data well during the most part of the initial regime of cylindrical particle growth. These particles were later found as rod-like subunits of the larger aggregates grown at more advanced degrees of aggregation. Some condensation possibilities yielding the formation of structures compatible with those inferred from the present study are discussed.

Coarse-Grained Molecular Modeling of the Solution Structure Ensemble of Dengue Virus Nonstructural Protein 5 with Small-Angle X-ray Scattering Intensity.

An ensemble-modeling scheme incorporating coarse-grained simulations with experimental small-angle X-ray scattering (SAXS) data is applied to dengue virus 2 (DENV2) nonstructural protein 5 (NS5). NS5 serves a key role in viral replication through its two domains that are connected by a 10-residue polypeptide segment. A set of representative structures is generated from a simulated structure pool using SAXS data fitting by the non-negativity least squares (NNLS) or standard ensemble optimization method (EOM) based on a genetic algorithm (GA). It is found that a proper low-energy threshold of the structure pool is necessary to produce a conformational ensemble of two representative structures by both NNLS and GA that agrees well with the experimental SAXS profile. The stability of the constructed ensemble is validated also by molecular dynamics simulations with an all-atom force field. The constructed ensemble successfully revealed the domain-domain orientation and domain-contacting interface of DENV2 NS5. Using experimental data fitting and additional investigations with synthesized data, it is found that energy restraint on the conformational pool is necessary to avoid overinterpretation of experimental data by spurious conformational representations.

Structural Insights into a Hemoglobin-Albumin Cluster in Aqueous Medium.

A hemoglobin (Hb) wrapped covalently by three human serum albumins (HSAs) is a triangular protein cluster designed as an artificial O2-carrier and red blood cell substitute. We report the structural insights into this Hb-HSA3 cluster in aqueous medium revealed by 3D reconstruction based on cryogenic transmission electron microscopy (cryo-TEM) data and small-angle X-ray scattering (SAXS) measurements. Cryo-TEM observations showed individual particles with approximately 15 nm diameter in the vitrified ice layer. Subsequent image processing and 3D reconstruction proved the expected spatial arrangements of an Hb in the center and three HSAs at the periphery. SAXS measurements demonstrated the monodispersity of the Hb-HSA3 cluster having a molecular mass of 270 kDa. The pair-distance distribution function suggested the existence of oblate-like particles with a maximum dimeter of ∼17 nm. The supramolecular 3D structure reconstructed from the SAXS intensity using an ab initio procedure was similar to that obtained from cryo-TEM data.

Resolving the Controversy between SAXS and FRET Measurements on Unfolded Proteins

Chemical denaturants are the most commonly used agents for unfolding proteins. An expansion of unfolded chains with increasing denaturant concentration is expected due to improved solvation. However, experiments have yielded qualitatively different results. Studies using Forster resonance energy transfer (FRET) and other methods found an increase in radius of gyration (Rg) with denaturant concentration, but most small-angle X-ray scattering (SAXS) studies found no change. This discrepancy challenges our understanding of denaturation mechanism and the accuracy of these experiments on intrinsically disordered proteins. We use all-atom molecular simulations to investigate the effect of urea and guanidinium chloride on the intrinsically disordered protein ACTR, which can be studied by both FRET and SAXS over a wide range of denaturant concentration. Using a carefully calibrated denaturant model, we find that the chain expands with increasing denaturant concentration. This is due to the favorable association of urea or guanidinium chloride with the backbone of all residues and with the side-chains of most residues. The denaturant-water transfer free energies inferred from this association are in reasonable agreement with experiment. By computing FRET efficiencies and SAXS intensities, we showed that the simulations are in accord with both experiments on this protein, demonstrating that there is no fundamental inconsistency between the two experimental methods. In addition, our simulations suggest that some potential artefacts are unlikely, i.e. the commonly used FRET chromophores do not qualitatively alter the results and that SAXS data are not distorted by preferential solvent partitioning into the interior of the chain. A careful analysis of the experimental data suggests that the discrepancy is largely related to the challenging inverse problem of inferring Rg from ensemble-averaged data. We show how this can be overcome by fitting the data to explicit molecular ensembles.

Probing the Action of Chemical Denaturant on an Intrinsically Disordered Protein by Simulation and Experiment

Chemical denaturants are the most commonly used agents for unfolding proteins and are thought to act by better solvating the unfolded state. Improved solvation is expected to lead to an expansion of unfolded chains with increasing denaturant concentration, providing a sensitive probe of the denaturant action. However, experiments have so far yielded qualitatively different results concerning the effects of chemical denaturation. Studies using Förster resonance energy transfer (FRET) and other methods found an increase in radius of gyration with denaturant concentration, but most small-angle X-ray scattering (SAXS) studies found no change. This discrepancy therefore challenges our understanding of denaturation mechanism and more generally the accuracy of these experiments as applied to unfolded or disordered proteins. Here, we use all-atom molecular simulations to investigate the effect of urea and guanidinium chloride on the structure of the intrinsically disordered protein ACTR, which can be studied by experiment over a wide range of denaturant concentration. Using unbiased molecular simulations with a carefully calibrated denaturant model, we find that the protein chain indeed swells with increasing denaturant concentration. This is due to the favorable association of urea or guanidinium chloride with the backbone of all residues and with the side-chains of almost all residues, with denaturant-water transfer free energies inferred from this association in reasonable accord with experimental estimates. Interactions of the denaturants with the backbone are dominated by hydrogen bonding, while interactions with side-chains include other contributions. By computing FRET efficiencies and SAXS intensities at each denaturant concentration, we show that the simulation trajectories are in accord with both experiments on this protein, demonstrating that there is no fundamental inconsistency between the two types of experiment. Agreement with experiment also supports the picture of chemical denaturation described in our simulations, driven by weak association of denaturant with the protein. Our simulations support some assumptions needed for each experiment to accurately reflect changes in protein size, namely, that the commonly used FRET chromophores do not qualitatively alter the results and that possible effects such as preferential solvent partitioning into the interior of the chain do not interfere with the determination of radius of gyration from the SAXS experiments.

Scattering and Spectroscopic Study on the Hydration and Phase Behavior of Aqueous Alcohol Ethoxylate and Methyl Ester Ethoxylate: Effects of Terminal Groups in Hydrophilic Chains.

Using dielectric relaxation spectroscopy (DRS), small-angle X-ray scattering (SAXS), dynamic light scattering (DLS), and viscometry, we have investigated the hydration behavior, static structures, Brownian dynamics, and mechanical properties of aqueous solutions of alcohol ethoxylate (C12E15) and methyl ester ethoxylate (C12MEE), hereafter abbreviated as AE and MEE, respectively, in which we especially focus on the effects of the endcaps of these nonionic surfactants. We find that AE and MEE exhibit fairly different phase behaviors in water: AE produces liquid crystalline phases at w (surfactant weight fraction) > 0.35, whereas MEE retains a liquid phase in an extremely wide concentration range (w < 0.7) at ambient temperature. The structure factor deduced from SAXS intensities using a generalized indirect Fourier transformation technique and the effective hydration number evaluated from the negative excess bulk water relaxation amplitude revealed by DRS unambiguously demonstrate that hydration water molecules, exhibiting about 4-times-slower collective reorientational dynamics than that of bulk water, contribute to the excluded volume of the micelles. The blocked terminal hydrogen-bond donor/acceptor site of MEE leads to smaller hydration number of MEE than compared to that of AE, and consequently the lower excluded volume of the MEE micelles. The effective micellar volume fraction, ϕ(eff), should be defined by incorporating such different hydration effects. Importantly, voluminosity, defined as the micellar volume fraction per unit mass, is clearly a decreasing function of w, demonstrating progressive dehydration at a higher w. The collective diffusion constants determined by DLS for the AE and MEE micelles show a monotonous increase up to ϕ(eff) ≈ 0.5, as expected for the hard spheres. Low-shear-rate viscosities follow a Krieger-Dougherty model in the identical micellar packing fraction range. All static, dynamic, and mechanical properties of these micellar solutions can be explained in a consistent and quantitative manner only when the excluded volume of hydration water molecules is properly taken into account.

Study of photochromic silver-containing quartz-like glass using X-ray diffraction methods

Photochromic quartz-like glassess obtained by sintering plates of porous glass, which were successively impregnated with an aqueous solution of silver nitrates with or without the presence of sensitizers (copper or cerium nitrates) and halides (NH4Cl, KBr, KI) are studied using the methods of X-ray difraction and small-angle X-ray scattering (SAXS). It is shown that the main crystalline phases in the composition of lightsensitive regions formed in quartz-like glass are AgBr and KBr in the form of nanodimensional crystals with a size of 100–130 A. The sizes of the scattering regions according to the data of small-angle scattering are amount to 250–300 A. The temperatures of melting and crystallization of light-sensitive phases are determined from the temperature dependences of the SAXS intensity.

Constrained Maximum Likelihood Estimation of Relative Abundances of Protein Conformation in a Heterogeneous Mixture from Small Angle X-Ray Scattering Intensity Measurements.

In this paper, we describe a model for maximum likelihood estimation (MLE) of the relative abundances of different conformations of a protein in a heterogeneous mixture from small angle X-ray scattering (SAXS) intensities. To consider cases where the solution includes intermediate or unknown conformations, we develop a subset selection method based on k-means clustering and the Cramér-Rao bound on the mixture coefficient estimation error to find a sparse basis set that represents the space spanned by the measured SAXS intensities of the known conformations of a protein. Then, using the selected basis set and the assumptions on the model for the intensity measurements, we show that the MLE model can be expressed as a constrained convex optimization problem. Employing the adenylate kinase (ADK) protein and its known conformations as an example, and using Monte Carlo simulations, we demonstrate the performance of the proposed estimation scheme. Here, although we use 45 crystallographically determined experimental structures and we could generate many more using, for instance, molecular dynamics calculations, the clustering technique indicates that the data cannot support the determination of relative abundances for more than 5 conformations. The estimation of this maximum number of conformations is intrinsic to the methodology we have used here.

Constrained Maximum Likelihood Estimation of the Abundances of Protein Conformation in a Heterogeneous Structural Ensemble from Small Angle X-ray Scattering Intensity Measurements

A method is described for maximum likelihood estimation (MLE) of the relative abundances of different conformations of a protein in a heterogeneous mixture based on small angle X-ray scattering (SAXS) intensities.This approach is of particular interest in situations where there are unknown, intermediate conformations, for instance, during catalytic cycling of a protein. First, an ensemble of structures is generated using molecular dynamics, crystallography or other technique. This ensemble is then clustered into sub-sets based on k-means clustering and the Cramer-Rao bound on the mixture coefficient estimation error. A sparse basis set that represents the space spanned by the measured SAXS intensities of the conformations of a protein is then generated from representative members of each cluster. Based on a statistical model for the intensity measurements, we show that the MLE approach can be expressed as a constrained convex optimization problem. Starting with a basis set generated from known conformations of the enzyme, adenylate kinase (ADK), we carried out Monte Carlo simulations to assess the performance of the proposed estimation scheme. We demonstrate the utility of the approach by identification of dominant conformations under different solution conditions and provide estimates of the abundance of minor species as a function of concentration of different ligands.

Kinetics of Water-Mediated Fluctuations in Room Temperature Ionic Liquid: N, N-Diethyl-N-methyl-N-(2-methoxyethyl) Ammonium Tetrafluoroborate

The kinetics of small-angle X-ray scattering (SAXS) was assessed in the room temperature ionic liquid (RTIL)–x mol% H2O system, where the RTIL is N,N-diethyl-N-methyl-N-(2-methoxyethyl) ammonium tetrafluoroborate, [DEME][BF4]. During equilibration of a non-equilibrium state, the largest time evolution of SAXS was observed at approximately 90 mol% H2O. Above 85 mol% (x c), the SAXS intensity increased gradually for 24 h. For the larger q region, the prepeak and principal peak in X-ray diffraction patterns have no time dependence in the water-rich region (70–91 mol%). The long time relaxation process observed in SAXS was related to the outstanding pH oscillations at 90–95 mol% over several days in the [DEME][BF4]–water system. The x c for nonequilibrium anomalies is related to the equilibrated crossover concentration from 65–85 mol% (from SAXS) to 85–95 mol% (for the prepeak in X-ray diffraction) in the [DEME][BF4]–H2O system. Inside [DEME][BF4], the dynamic and static properties of hydrogen bonding of water changed drastically at x c.

The structure of Lactobacillus brevis surface layer reassembled on liposomes differs from native structure as revealed by SAXS

The reassembly of the S-layer protein SlpA of Lactobacillus brevis ATCC 8287 on positively charged liposomes was studied by small angle X-ray scattering (SAXS) and zeta potential measurements. SlpA was reassembled on unilamellar liposomes consisting of 1-palmitoyl-2-oleyl-sn-glycero-3-phosphocholine and 1,2-dioleoyl-3-trimethylammonium-propane, prepared by extrusion through membranes with pore sizes of 50nm and 100nm. Similarly extruded samples without SlpA were used as a reference. The SlpA-containing samples showed clear diffraction peaks in their SAXS intensities. The lattice constants were calculated from the diffraction pattern and compared to those determined for SlpA on native cell wall fragments. Lattice constants for SlpA reassembled on liposomes (a=9.29nm, b=8.03nm, and γ=84.9°) showed a marked change in the lattice constants b and γ when compared to those determined for SlpA on native cell wall fragments (a=9.41nm, b=6.48nm, and γ=77.0°). The latter are in good agreement with values previously determined by electron microscopy. This indicates that the structure formed by SlpA is stable on the bacterial cell wall, but SlpA reassembles into a different structure on cationic liposomes. From the (10) reflection, the lower limit of crystallite size of SlpA on liposomes was determined to be 92nm, corresponding to approximately ten aligned lattice planes.

Studies on microwave-irradiated kopak cotton fibers (Bombax ceiba): using SAXS technique

Microwave energy at a frequency of 2450 MHz was used to irradiate Bombax ceiba cotton (kopak fibers) samples for different intervals of time. These samples were studied using small angle X-ray scattering (SAXS) method which gives information about the structure of the fiber on a scale of about 700 Ǻ. Using this method, variation in scattered intensity with angles from 0.3° to 2.5° has been measured for the fibers of cotton with and without microwave irradiation and compared with that predicted by the linear paracrystalline model. In these samples, exponential distribution of phase lengths of the measured and predicted scattering is in good agreement with each other except for a very small range of angles on the low-angle side of the peak intensity. The method enabled quantitative parameters describing morphology of the two phases, amorphous and crystalline, consistent with the SAXS intensity distribution. For a given type of distribution function, five parameters describing the model were chosen on a stepping procedure so that the final parameters give the best fit between the calculated distribution from the model and that observed experimentally. This was done by minimizing the statistical goodness-of-fit parameter chi-square. It is observed that there are significant changes in the distribution of phase lengths due to microwave irradiation of fibers.

Synchrotron Small Angle X-Ray Scattering Spectra of Iron-Based Magnetic Fluids

Magnetic fluid is a special class of materials which possesses the advantages of a liquid state of the carrier and a magnetic state of the particles. In addition to the conventional uses in mechanical engineering, magnetic fluids containing magnetite (Fe3O4) superparamagnetic nanoparticles are under research and development for drug delivery, hyperthermia and MRI contrast agents. On the other hand, iron-platinum (FePt) is investigated as materials for ultrahigh density recording. Before their assembly into patterned media, the as-synthesized FePt nanoparticles in superparamagnetic state are commonly stored in forms of magnetic fluids. In this work, iron-platinum (FePt) nanoparticles with their surface modified by oleic acid and oleyleamine were synthesized from the polyol process. The starting material was an environmental friendly iron(III) acetylacetonate and the products were dispersed in n-hexane. In small-angle X-ray scattering (SAXS) measurements at the Synchrotron Light Research Institute, Thailand, each magnetic fluid was injected into a sample cell with aluminum foil windows and the X-ray of wavelength 1.55 Å from BL2.2 was used. The measured SAXS intensity profiles as a function of the scattering vector from 0.27 to 2.30 nm-1 were fitted and compared between two different reactions. Nanoparticles synthesized by using a higher amount of Fe(acac)3 were matched with monodisperse spheres of radius 2.4±0.3 nm. The other reaction with a reducing agent gave rise to smaller nanoparticles of two size distributions. From this work, the potential of synchrotron radiation to complement conventional characterization techniques in the investigation of nanoparticles for high density recording and biomedical applications is underlined.

Structure and Growth Kinetics of 3-Glycidoxypropyltrimethoxysilane-Derived Organic/Silica Hybrids at Different Temperatures

The structure and the growth kinetics of 3-glycidoxypropyltrimethoxysilane(GPTS)-derived organic/silica hybrids have been studied in situ by small-angle X-ray scattering (SAXS) at 298, 316, and 334 K. The SAXS data were compatible with the growth of silica-rich domains from a fixed number of primary particles, with polydispersity likely increasing with time. The isothermal growth of the average radius of gyration Rg of the domains occurs in a power law with time t as Rg ∝ (t – t0)α, with t0 being a small offset time and α = 0.247 in the studied temperature range. The SAXS intensity I(0) extrapolated to q = 0 increases in a power law with time as I(0) = B(t – t0)β, where B is a function of temperature and β a constant equal to 0.443 in the studied temperature range. The activation energy was evaluated as ΔE = 67.7 ± 1.1 kJ/mol from an Arrhenius equation for the rate constant k = βB1/β. The extrapolated intensity I(0) scales with Rg as I(0) ∝ RgD with D = 1.71 ± 0.01 in the studied temperature range, in good agreement with the value β/α = 1.79 ± 0.07 from the kinetic study. This suggests that the macromolecules grow in a dimensionality ∼1.7, typical of macromolecules in good solvent conditions in diluted or semidiluted solution. A time-independent function F(qRg) = I(q,t)Rg–D/Q, where Q is the invariant, was found to hold for every time and temperature within a domain limited by a primary particle size. This finding suggests that the system exhibits primary-particle-size-limited dynamic scaling properties.

Dynamic Scaling and Growth Kinetics of 3-Glycidoxypropyltrimethoxysilane-Derived Organic/Silica Hybrids

Structural evolution and dynamic scaling properties have been probed by small-angle X-ray scattering (SAXS) in the growth kinetics of 3-glycidoxypropyltrimethoxysilane (GPTS)-derived organic/silica hybrids in basic solution. The SAXS intensity curves were found to be well described by a particle form factor valid for polydisperse coils of linear chains and for particular cases of random and nonrandom polycondensates in solution together with an interference factor accounting for very weak correlations of particles. The SAXS data are consistent with formation and growth of GPTS-derived organic/silica hybrids in solution with polydispersity increasing with time. The following properties have been found: (i) The SAXS intensities I(q,t) corresponding to different times t are given by a time-independent function F(qRg) = I(q,t)Rg–D, Rg being the average radius of gyration of the hybrid particles; (ii) the average radius of gyration grows in a power-law with time t as Rg ∝ tα, with α = 0.307 ± 0.009, suggesting...