Small-angle X-ray Scattering Patterns Research Articles

Determination of Reaction Kinetics by Time‐Resolved Small‐Angle X‐ray Scattering during Polymerization‐Induced Self‐Assembly: Direct Evidence for Monomer‐Swollen Nanoparticles

AbstractThe kinetics of heterogeneous polymerization is determined directly using small‐angle X‐ray scattering (SAXS). This important advancement is exemplified for the synthesis of sterically‐stabilized diblock copolymer nanoparticles by reversible addition‐fragmentation chain transfer (RAFT) dispersion polymerization of benzyl methacrylate (BzMA) in mineral oil at 90 °C. The principle of mass balance is invoked to derive a series of equations for the analysis of the resulting time‐resolved SAXS patterns. Importantly, there is a continuous change in the X‐ray scattering length density for the various components within the reaction mixture. This enables the volume fraction of unreacted BzMA monomer to be calculated at any given time point, which enables the polymerization kinetics to be monitored in situ directly without relying on supplementary characterization techniques. Moreover, SAXS enables the local concentration of both monomer and solvent within the growing swollen nanoparticles to be determined during the polymerization. Data analysis reveals that the instantaneous rate of BzMA polymerization is proportional to the local monomer concentration within the nanoparticles. In principle, this powerful new time‐resolved SAXS approach can be applicable to other heterogeneous polymerization formulations.

Determination of Reaction Kinetics by Time-Resolved Small-Angle X-ray Scattering during Polymerization-Induced Self-Assembly: Direct Evidence for Monomer-Swollen Nanoparticles.

The kinetics of heterogeneous polymerization is determined directly using small-angle X-ray scattering (SAXS). This important advancement is exemplified for the synthesis of sterically-stabilized diblock copolymer nanoparticles by reversible addition-fragmentation chain transfer (RAFT) dispersion polymerization of benzyl methacrylate (BzMA) in mineral oil at 90 °C. The principle of mass balance is invoked to derive a series of equations for the analysis of the resulting time-resolved SAXS patterns. Importantly, there is a continuous change in the X-ray scattering length density for the various components within the reaction mixture. This enables the volume fraction of unreacted BzMA monomer to be calculated at any given time point, which enables the polymerization kinetics to be monitored in situ directly without relying on supplementary characterization techniques. Moreover, SAXS enables the local concentration of both monomer and solvent within the growing swollen nanoparticles to be determined during the polymerization. Data analysis reveals that the instantaneous rate of BzMA polymerization is proportional to the local monomer concentration within the nanoparticles. In principle, this powerful new time-resolved SAXS approach can be applicable to other heterogeneous polymerization formulations.

Small Angle X‐Ray Scattering Study for Investigating the 3D Packing Structure of Pt Catalysts on Gd‐Doped CeO2 Supports for Fuel Cells

AbstractA 3D structural model for fuel cell catalysis systems is constructed, which consist primarily of Pt and CeO2 nanoparticles, to fit observed small angle X‐ray scattering (SAXS) patterns by using the reverse Monte–Carlo (RMC) method. The observed SAXS patterns are well reproduced by those of the simulations. Pore size distributions using the obtained structure models are compared with the Barrett–Joyner–Halenda (BJH) analysis for the nitrogen gas adsorption data, and the lower quartiles and medians of the pore diameters are reasonably consistent. In addition, analysis of the SAXS patterns indicates that the number of nanometer‐size Pt particles is much smaller than that of the introduced amount. This suggests that most Pt particles are not uniformly distributed in the catalysis system.

Pair-Variational Autoencoders for Linking and Cross-Reconstruction of Characterization Data from Complementary Structural Characterization Techniques.

In materials research, structural characterization often requires multiple complementary techniques to obtain a holistic morphological view of a synthesized material. Depending on the availability and accessibility of the different characterization techniques (e.g., scattering, microscopy, spectroscopy), each research facility or academic research lab may have access to high-throughput capability in one technique but face limitations (sample preparation, resolution, access time) with other technique(s). Furthermore, one type of structural characterization data may be easier to interpret than another (e.g., microscopy images are easier to interpret than small-angle scattering profiles). Thus, it is useful to have machine learning models that can be trained on paired structural characterization data from multiple techniques (easy and difficult to interpret, fast and slow in data collection or sample preparation) so that the model can generate one set of characterization data from the other. In this paper we demonstrate one such machine learning workflow, Pair-Variational Autoencoders (PairVAE), that works with data from small-angle X-ray scattering (SAXS) that present information about bulk morphology and images from scanning electron microscopy (SEM) that present two-dimensional local structural information on the sample. Using paired SAXS and SEM data of newly observed block copolymer assembled morphologies [open access data from Doerk G. S.; et al. Sci. Adv.2023, 9 ( (2), ), eadd3687], we train our PairVAE. After successful training, we demonstrate that the PairVAE can generate SEM images of the block copolymer morphology when it takes as input that sample's corresponding SAXS 2D pattern and vice versa. This method can be extended to other soft material morphologies as well and serves as a valuable tool for easy interpretation of 2D SAXS patterns as well as an engine for generating ensembles of similar microscopy images to create a database for other downstream calculations of structure-property relationships.

Insights into the precipitation kinetics of CaCO3 particles in the presence of polystyrene sulfonate using in situ small-angle X-ray scattering.

The formation of calcium carbonate (CaCO3) nanoparticles (NPs) in the presence of polystyrene sulfonate (PSS) as an additive was examined by time-resolved small-angle X-ray scattering (SAXS) in a flow system that mimics experimental conditions used at home facilities where the precipitation can be achieved in a beaker. The experiments were carried out at low concentrations to remain in the dilute regime. A model-independent analysis was performed using the Porod invariant which defines the scale factor, leaving only the distribution of radii as the adjustable parameter. The presence of the PSS additive strongly retards the precipitation of CaCO3 NPs. The formation of NPs reaches a state of equilibrium after a few minutes. Here, it is shown that the concentration of precursors at a fixed PSS concentration plays a key role in determining the size of the NPs obtained. A full analysis of the SAXS patterns was carried out using the Hurd-Flower model to account for the weaker intensity decay than the classical Porod behaviour. The temporal evolution of the particle radii was determined. Wide-angle X-ray scattering experiments carried out simultaneously show that the particles formed have the structure of vaterite with growth consistent with the evolution of the Porod invariant.

Relationships between Chemical Composition, Asphaltene Nanostructures, and Thermochemical Properties of Bitumen before and after Accelerated Oxidative Aging

An oxidative aging treatment in the laboratory by a pressure aging vessel (PAV) is applied on fresh 10/20 and 35/50 bitumens with different thermomechanical properties, in order to simulate long-term aging of bitumen on road pavements. The influence of the aging treatment on bitumen properties is studied as a function of the aging time. Combining Fourier transform infrared spectroscopy (FTIR), the saturate, aromatic, and resin-asphaltene determinator (SAR-AD), and small-angle X-ray scattering (SAXS) techniques allows us to confirm that less polar aromatic species are oxidized onto more polar content, and the asphaltene family content is found to increase significantly for more than 75% after a 45 h PAV treatment. SAXS patterns exhibit a progressive increase in the average size of nanoaggregates (from ∼1.8 to 2.3 nm) and primary clusters (from ∼4.7 to 5.4 nm) after such aging treatment. This is coherent with both the size increase of smaller asphaltene nanoaggregates and the formation of new nanoaggregates by auto-association of new oxidized asphaltene monomers. As expected, such evolutions of both the asphaltene content and its nanostructure have an influence on macroscopic rheological properties. An analysis of black diagrams and bending beam rheometer (BBR) measurements show that aging induces a shift toward higher moduli at low frequencies coupled with a loss of curvature at intermediate frequencies, meaning lesser susceptibility of aged bitumens regarding thermomechanical solicitation, a loss of viscous behavior at the profit of elastic behavior, and a decrease of the ability to relax stress at low temperatures.

Studies on Morphological Parameters, Radius of Gyration, Correlation Length and Invariant of HPMC Polymer Doped with Ferrous (II) Oxide Using SAXS Method

It shed light on morphological parameters which influence radius of gyration, correlation length and invariant of Hydroxy Propyl Methyl Cellulose (HPMC) polymer doped with ferrous (II) oxide (FeO) using small angle X-ray scattering (SAXS) method. SAXS patterns have been recorded for different composition and gives an information about the structure of the polymer on a scale of about 800Ǻ, in which the variation of scattered intensity with angles from 0o to 2.5o has been measured for different composition of FeO with host polymer of HPMC. Employing para-crystalline model and exponential distribution function of phase lengths (amorphous and crystalline), we find a good agreement between the measured and predicted scattering 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. A stepping procedure has been employed to compute the final parameters which gave the best fit between the calculated and experimental data. This was done by minimizing the statistical goodness-of-fit parameter chi-square. It is observed that there are significant changes in distribution of phase lengths due to different percentage weight of FeO in HPMC contents. Additionally, SAXS data has been used to estimate (i) radius of gyration (Rg), ii) correlation length (Lcor) and (iii) invariant (Q) parameters. A functional representation of the long period and also radius of gyration at different dopant concentrations is adopted by viewing them as realizations of a continuous-time stochastic process observed with measurement error. This allows one to estimate the mean functional relationship between long period and the dopant concentration.

Visualization of small-angle X-ray scattering datasets and processing-structure mapping of isotactic polypropylene films by machine learning

With the rapid development of the synchrotron radiation X-ray characterization techniques, the preprocessing of large small-angle X-ray scattering (SAXS) datasets and the data mining become urgent requirements for researchers. In this work, we apply the variational autoencoder (VAE) and the conditional variational autoencoder (cVAE) to visualize a large SAXS dataset of hard-elastic isotactic polypropylene (iPP) films in 2- and 1-dimensional latent spaces. The low-dimensional representations enable us to capture key features of the dataset rapidly, such as the similarity among SAXS patterns and the structural evolution trends. The preprocessing of the dataset points out the further direction of data analysis so that researchers can focus on the most valued regions in the dataset. Then, we develop a hybrid VAE-multilayer perceptron (MLP) neural network to realize the processing-structure mapping of iPP films. The robustness of the hybrid VAE-MLP network is verified. Finally, SAXS patterns in the temperature-strain space are generated, which allows us to explore the processing parameter space not involved by previous experiments. These capabilities indicate that the developed machine-learning methods are valuable artificial intelligence toolset to assist in the preprocessing of large-scale SAXS datasets and the establishment of comprehensive processing-structure relationship of hard-elastic iPP films.

Reversed thermal stability between stress-induced melting and recrystallized crystallites and original inclined ones in moderately stretched ultra high molecular weight polyethylene and high density polyethylene

The structural evolution of tensile stretched ultra high molecular weight polyethylene (UHMWPE) and high density polyethylene (HDPE) samples to an intermediate strain before the completion of fibrillation upon heating was investigated by means of small-angle X-ray scattering (SAXS) and wide angle X-ray diffraction techniques (WAXD). Six-point SAXS patterns illustrated the existence of two populations of lamellae, one at the inclined direction belonging to the original lamellae experienced deformation of slip processes and another at the tensile direction (meridional lamellae) which were newly formed ones due to fibrillation (stress induced melting-recrystallization). Surprisingly, the inclined lamellae exhibit better thermal stability compared to meridional lamellae in UHMWPE sample, whereas in the HDPE sample the situation is opposite. It turns out that this higher stability of original deformed lamellae at the inclined direction is due to the much higher number of tie chains and more stable entangled amorphous network in UHMWPE which minimizes the surface free energy of those lamellae during heating.

Estimation of the fiber orientation distribution of carbon fiber–reinforced plastics using small-angle X-ray scattering

• Carbon fiber orientation distributions in the CFRP were determined using their SAXS analysis. • Fast evaluation was achieved by introducing a calibration curve for integral width of the azimuthal direction. • Similar orientation distribution compared those obtained with X-ray CT could be obtained. The orientation of discontinuous carbon fibers (CFs) in CF-reinforced plastics (CFRPs) determines their properties, necessitating convenient evaluation methods. Herein, a fast and non-destructive method is proposed for the evaluation of the orientation distribution of CFs in CFRPs based on small-angle X-ray scattering (SAXS). The width of the equatorial streak in the SAXS pattern of (or azimuthal intensity distribution of scattering from) a CFRP depends on the orientation distribution of its CFs; a calibration curve for this relationship was derived by assuming the orientation distribution to be Gaussian. This calibration curve was used to determine the orientation distributions of CFRPs featuring CFs with different orientation distributions, which correspond well with the orientation distributions determined by X-ray computed tomography. Thus, the proposed method can be used to conveniently and quantitatively evaluate the orientation distribution of discontinuous CFs in CFRPs. Because this method is based on scattering from elongated nanovoids in CFs, it can be used to evaluate composite materials in which reinforcing fibers containing elongated scattering bodies, e.g., high-strength organic fibers containing fibrils, are preferentially oriented.

Fatigue Characteristics of Poly(ether-b-amide) Elastomers during Cyclic Dynamic Tests and the Underlying Microstructural Evolution

The dynamic fatigue behavior of the poly(ether-b-amide) (PEBA) elastomers was characterized by a combination of step increase load test (SILT), step increase strain test (SIST), and single load dynamic creep (SLDC). PEBA had crystalline hard segments of polyamide 12 (PA12) and soft segments of poly(tetramethylene oxide) (PTMO). The crystalline morphologies before and after the tests were studied by ex situ wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS). Fast stress relaxation can be seen under the applied strain well below than the elongation at break. Remarkable dynamic creep can be observed under the applied load triggering yielding of the specimen, which is substantially less than the ultimate tensile strength. Although the presence of high content of amorphous PTMO renders high entropic elasticity, the disintegration of the crystalline hard domains of PA12 is expected to determine the relaxation rate, creep rate, and modulus, as strain-induced crystallization in soft domains did not occur and no trace was found by WAXD. SAXS patterns showed that the orientation of the PA12 lamellae at lower stresses or strains can largely be restored. However, the fractured and highly aligned PA12 lamellae resulted in classic four-point or two-lobe SAXS patterns, which implied the underlying microstructural changes after the cyclic dynamic tests.

Small-angle X-ray scattering: characterization of cubic Au nanoparticles using Debye's scattering formula.

A versatile software package in the form of a Python extension, named CDEF (computing Debye's scattering formula for extraordinary form factors), is proposed to calculate approximate scattering profiles of arbitrarily shaped nanoparticles for small-angle X-ray scattering (SAXS). CDEF generates a quasi-randomly distributed point cloud in the desired particle shape and then applies the open-source software DEBYER for efficient evaluation of Debye's scattering formula to calculate the SAXS pattern (https://github.com/j-from-b/CDEF). If self-correlation of the scattering signal is not omitted, the quasi-random distribution provides faster convergence compared with a true-random distribution of the scatterers, especially at higher momentum transfer. The usage of the software is demonstrated for the evaluation of scattering data of Au nanocubes with rounded edges, which were measured at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II in Berlin. The implementation is fast enough to run on a single desktop computer and perform model fits within minutes. The accuracy of the method was analyzed by comparison with analytically known form factors and verified with another implementation, the SPONGE, based on a similar principle with fewer approximations. Additionally, the SPONGE coupled to McSAS3 allows one to retrieve information on the uncertainty of the size distribution using a Monte Carlo uncertainty estimation algorithm.

Mold temperature- and molar mass-dependent structural formation in micro-injection molding of isotactic polypropylene

The structural formation and development of isotactic polypropylene (iPP) upon the micro-injection molding process was investigated at different mold temperatures and molecular weights utilizing a real-time synchrotron radiation small angle X-ray scattering (SAXS) technique combined with a customized micro-injection molding apparatus. Shish-kebab structure and parent-daughter lamellae were found to be formed during micro-injection molding for all iPP samples. In the case of kebab lamellae, a considerable growth in the long period and in the average thickness of lamellar crystallites and amorphous domains is observed at initial stages of crystallization for samples molded at varying temperatures. This effect is caused by the successive formation of thin lamellae in the outer layer and thick lamellae in the inner layer during the manufacturing process as evidenced by the spatial distribution of the crystalline lamellae across the thickness. In addition, the length of the shish formation increases remarkably at the onset of crystallization, the extent of which is dependent on the mold temperature. Despite the large changes of the lamellar stacks and the shish misorientation, the final length of the shish remains essentially unchanged when varying mold temperature. Since there is a critical orientation molecular weight above which the chains are stretched and oriented to form stable shish, the iPP sample with a low molar mass exhibits an overall decrease in the scattering intensity of SAXS patterns compared to the high molecular weight polypropylene. • The structural formation of iPP is investigated utilizing a customized micro-injection molding device. • Shish-kebab and parent-daughter lamellae are formed during micro-injection molding. • A considerable increase in the long period is observed at initial stages of crystallization. • The length of the shish formation increases remarkably at the onset of crystallization. • The final shish length remains essentially unchanged when varying mold temperature.

Fractal features of dual temperature/pH-sensitive poly(N-isopropylacrylamide-co-acrylic acid) hydrogels and resultant effects on the controlled drug delivery performances

Using acrylic acid (AA) as pH-responsive monomer, and N-isopropyl acrylamide (NIPAM) as temperature-responsive monomer, the stimuli-responsive P(NIPAM-co-AA) copolymers were prepared via soap-free emulsion polymerization. Their constructed porous structures, swelling-shrinking behaviors, and controlled drug delivery performances were systematically demonstrated via various characterizations. Particularly, the small-angle X-ray scattering (SAXS) method was employed to elucidate their fractal features and the structural evolutions with increasing AA content, showing the occurrences from dense aggregates (mass fractal (Dm) value of 2.92) to loose networks (surface fractal (Ds) value of 2.18) with statistical self-similarity. Meanwhile, the ibuprofen (IBU) was used as a model drug, their temperature/pH-dual sensitive delivery and related mechanism were discussed on the basis of the fractal demonstrations. The results showed that the cross-linking networks with an interconnected open-cell skeleton and abundant large pores were beneficial to improve the adsorption-diffusion performances of the drug delivery, while the drug-releasing kinetics of P(NIPAM-co-AA)-30 followed a non-Fickian diffusion mechanism. Specially, the fractal evolutions of the obtained copolymers along with the drug loading and releasing behaviors were evaluated via SAXS patterns. In which, the drug-loaded copolymers presented the Ds characteristics with the increased amounts of monomer AA added. While, the fractal features varied from Ds value of 2.40 to Dm value of 2.76 along with sustained drug releasing in pH 2.0 at 25 °C, indicating that the structural transformation of the used copolymers occurred from dense (Dm value of 2.86) to loose (Dm value of 2.76) with the extension of release time. These demonstrations suggested that the resultant P(NIPAM-co-AA) hydrogel is a potential intelligent-responsive drug carrier for targeted delivery.

Artificial neural networks for solution scattering data analysis

Small-angle X-ray scattering (SAXS) experiments are widely used for the characterization of biological macromolecules in solution. SAXS patterns contain information on the size and shape of dissolved particles in nanometer resolution. Here we propose a method for primary SAXS data analysis based on the application of artificial neural networks (NNs). Trained on synthetic SAXS data, the feedforward NNs are able to reliably predict molecular weight and maximum intraparticle distance (Dmax) directly from the experimental data. The method is applicable to data from monodisperse solutions of folded proteins, intrinsically disordered proteins, and nucleic acids. Extensive tests on synthetic SAXS data generated in various angular ranges with varying levels of noise demonstrated a higher accuracy and better robustness of the NN approach compared to the existing methods.

Effects of beam divergence and polychromaticity on small angle x-ray scattering measurements with laser plasma sources

We explore the feasibility of small angle x-ray scattering (SAXS) measurements with intense laser-induced plasma sources. Such x-ray sources are inherently polychromatic and divergent. We simulate SAXS patterns using monochromatic and polychromatic x-ray sources with different divergences of polydisperse particle systems with different size distributions. The beam divergence is adjusted via varying x-ray source size, pinhole size, and the source-to-pinhole distance. Three typical laser plasma He-α sources (Fe, Cu, and Ge) are considered. The scattering curves are analyzed using the modified Guinier approach and the total non-negative least squares method. We demonstrate certain feasibility of SAXS measurements using laser plasma sources with a finite size, without a monochromator and additional software desmearing.

Highly oriented NiSi2@Si thin-nanocomposite produced by solid state diffusion: Morphological and crystallographic characterization

This article describes a morphological and crystallographic multi-technique characterization of a 2D-nanocomposite consisting of highly oriented NiSi2 nanoplates endotaxially grown inside a single-crystalline Si(001) wafer close to its external surface. This nanostructured material is prepared using a novel procedure which promotes the diffusion of Ni atoms from a deposited Ni-dopped-SiO2 thin film into the volume of a Si(001) flat wafer under controlled thermodynamic conditions. High Resolution Scanning Transmission Electron Microscopy images reveal the formations of well oriented thin hexagonal nanoplates totally buried inside a Si(001) wafer and randomly oriented nearly spherical Ni nanocrystals located inside the Ni-doped SiO2 thin film and also inside a thin layer close to external surface of the Si(001) wafer. The NiSi2 nanoplates formed by endotaxial growth have their large hexagonal flat surfaces parallel to one of the four Si{111} crystallographic planes and exhibit coherent 7A-type interfaces with the host Si matrix. Additional analyses of Grazing-Incidence Small-Angle X-ray Scattering patterns - which probe a high number of nanoparticles - indicated that the average thickness and maximum diameter of NiSi2 nanoplates are 12 nm and 118 nm, respectively, and the average radius of Ni nanocrystals is 1.7 nm. The described process for obtaining 2D-NiSi2@Si nanocomposites opens new possibilities for exploiting the structural features of these materials for use in devices requiring anisotropic electrical transport properties.

Synthesis and aggregation behavior of novel biosurfactants choline cholate and choline deoxy cholate

Herein, we report the synthesis and interfacial properties of cholesterol based biocompatible surface-active biosurfactant choline cholate (CC) and choline deoxy cholate (CDC) surfactants, prepared through salt metathesis reaction. The surface activity and aggregation behavior of these surfactants were investigated by surface tension measurements and small angle X-ray scattering (SAXS) technique. CC and CDC both formed well-defined micelles with distinct CMC values as indicated by tensiometry, while the SAXS patterns can be well described by the polydisperse ellipsoid model. Furthermore, it was observed that both CC and CDC showed good foamability ascribed to the foam film rigidity which could be highly beneficial. Also, CC and CDC showed sphere-to rod micellar transition in the presence of CTAB. The study reported here may prove to be highly beneficial for pharmaceutical and personal care product formulations.

Small-angle X-ray scattering to quantify the incorporation and analyze the disposition of magnetic nanoparticles inside cells

Access to detailed information on cells loaded with nanoparticles with nanoscale precision is of a long-standing interest in many areas of nanomedicine. In this context, designing a single experiment able to provide statistical mean data from a large number of living unsectioned cells concerning information on the nanoparticle size and aggregation inside cell endosomes and accurate nanoparticle cell up-take is of paramount importance. Small-angle X-ray scattering (SAXS) is presented here as a tool to achieve such relevant data. Experiments were carried out in cultures of B16F0 murine melanoma and A549 human lung adenocarcinoma cell lines loaded with various iron oxide nanostructures displaying distinctive structural characteristics. Five systems of water-dispersible magnetic nanoparticles (MNP) of different size, polydispersity and morphology were analyzed, namely, nearly monodisperse MNP with 11 and 13 nm mean size coated with meso-2,3-dimercaptosuccinic acid, more polydisperse 6 nm colloids coated with citric acid and two nanoflowers (NF) systems of 24 and 27 nm in size resulting from the aggregation of 8 nm MNP. Up-take was determined for each system using B16F0 cells. Here we show that SAXS pattern provides high resolution information on nanoparticles disposition inside endosomes of the cytoplasm through the structure factor analysis, on nanoparticles size and dispersity after their incorporation by the cell and on up-take quantification from the extrapolation of the intensity in absolute scale to null scattering vector. We also report on the cell culture preparation to reach sensitivity for the observation of MNP inside cell endosomes using high brightness SAXS synchrotron source. Our results show that SAXS can become a valuable tool for analyzing MNP in cells and tissues.

Quantification of Starch Order in Physically Modified Rice Flours Using Small-Angle X-ray Scattering (SAXS) and Fourier Transform Infrared (FT-IR) Spectroscopy.

The purpose of this study was to understand the ordered structure of starch in rice flour based on a physical modification with non-heating, milling, and water sorption through the structural evaluation of rice flour using small-angle X-ray scattering (SAXS) and infrared spectroscopy within the 4000-100 cm-1 region. The SAXS pattern of the samples with low moisture contents subjected to milling yield a band within the 0.4-0.9 nm-1 of the q range owing to a lamellar repeat of starch with an ordered structure in rice flour. We proposed an order parameter using the intensity of the SAXS band to quantify the order structure of starch in rice flour, and the true density was negatively correlated with the order parameter. Infrared band at 990 cm-1 in COH bending mode applied to the hydroxyl group of C6 shifted to a low wavenumber corresponding to the order parameter. A linear correlation was found between the order parameter and the 990 cm-1 and band at 861 cm-1 owing to COC symmetrical stretching of glycoside bond and CH2 deformation of the glucose unit of starch, 572, 472, and 436 cm-1, owing to the pyranose ring in the glucose unit of starch. The identified infrared bands are effective for quantifying the ordered structure of starch at the lamellar level. When subjected to water sorption, the band position at 990 cm-1 shifted to a higher wavenumber above a water activity of 0.7. This result revealed that the water-induced transition of glass to rubber of starch in rice flour can be clearly evaluated through infrared spectroscopy using the band at 990 cm-1. In addition, the band at 861 cm-1 also shifted to a higher wavenumber, whereas those at 572 and 436 cm-1 did not show a significant shift. These results indicate that water sorption slightly affects the internal structure and may mainly affect the surface of starch.