# Recent advances in synchrotron scattering methods for probing the structure and dynamics of colloids

Theyencheri Narayanan

► To cite this version:

Theyencheri Narayanan. Recent advances in synchrotron scattering methods for probing the structure and dynamics of colloids. Advances in Colloid and Interface Science, 2024, 325, pp.103114. 10.1016/j.cis.2024.103114. hal-05099511

HAL Id: hal-05099511

https://hal.science/hal-05099511v1

Submitted on 5 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Recent advances in synchrotron scattering methods for probing the structure and dynamics of colloids

Theyencheri Narayanan

ESRF – The European Synchrotron, Grenoble 38043, France

## ARTICLE INFO

**Keywords:**

- Small-angle X-ray scattering
- Ultrasmall-angle X-ray scattering
- X-ray photon correlation spectroscopy
- Colloid microstructure and dynamics
- Self-assembly pathways

## ABSTRACT

Recent progress in synchrotron based X-ray scattering methods applied to colloid science is reviewed. An important figure of merit of these techniques is that they enable in situ investigations of colloidal systems under the desired thermophysical and rheological conditions. An ensemble averaged simultaneous structural and dynamical information can be derived albeit in reciprocal space. Significant improvements in X-ray source brilliance and advances in detector technology have overcome some of the limitations in the past. Notably coherent X-ray scattering techniques have become more competitive and they provide complementary information to laboratory based real space methods. For a system with sufficient scattering contrast, size ranges from nm to several µm and time scales down to µs are now amenable to X-ray scattering investigations. A wide variety of sample environments can be combined with scattering experiments further enriching the science that could be pursued by means of advanced X-ray scattering instruments. Some of these recent progresses are illustrated via representative examples. To derive quantitative information from the scattering data, rigorous data analysis or modeling is required. Development of powerful computational tools including the use of artificial intelligence have become the emerging trend.

## 1. Introduction

The small-angle X-ray scattering (SAXS) is a well established method to elucidate the nanoscale structure and interactions in colloidal systems [1–3]. The X-ray scattering contrast originates from the spatial fluctuations of electron density ($ρ_e$), and it is proportional to the difference in $ρ_e$ of the colloids and the surrounding medium. Typically, the electronic contrast increases linearly with the atomic number of the constituent elements and usually it is much weaker compared to the dielectric polarizability - the contrast mechanism in the optical region. Nevertheless, advances in synchrotron X-ray sources and detector technology [4] enable to overcome the limitation imposed by the lower contrast. Notably, the advent of high brilliance third-generation synchrotron sources in the nineties significantly enhanced the performance of SAXS and allied methods both in terms of accessible size range and detection limit [5,6]. Moreover, X-ray scattering experiments can be combined with a variety of thermophysical, rheological, and optical techniques. This aspect is particularly useful for probing the transient dynamics of colloidal systems driven out-of-equilibrium. Perhaps, a unique feature of synchrotron SAXS is the nanometric spatial and millisecond range temporal resolution that may not be readily accessible by other

structural methods [2]. The lower contrast becomes an advantage for studying concentrated systems as the contribution from multiple scattering is significantly smaller.

Typical information that can be derived from static SAXS experiments include the mean size, shape and size distribution of particles. When the volume fraction of particles ($φ_p$) is high enough, the interactions between particles and the corresponding potential of mean force can be determined via quantitative analysis [3,7]. Eventually at close-packing values of $φ_p$, the crystalline or glass-like order can be elucidated. Many of the colloidal systems of contemporary interest are themselves formed by the self-assembly of smaller sub-units. In such cases, not only their multiscale structure but also the pathway of the self-assembly may be explored by SAXS. The nucleation and growth of particles from a solution of the precursors is one such example where SAXS can probe the very early stages until the maturation of particles. SAXS offers a convenient means to investigate colloids subjected to different external fields such as shear flow, electric or magnetic fields [1]. The use of a two-dimensional (2D) detector directly reveals a possible distortion of the microstructure by the applied field [8]. The complementary method of X-ray photon correlation spectroscopy (XPCS), which is analogous to dynamic light scattering (DLS) with X-

<figure><img src="image_3.png" /></figure>

<footnote>E-mail address: narayan@esrf.fr.</footnote>
rays, enables probing the equilibrium dynamics of colloids for systems with sufficient scattering power. XPCS measurements using a 2D detector (multispeckle XPCS) readily yields the ensemble averaged dynamics of a suspension [9–11].

The third-generation generation synchrotron storage rings [4] provided highly intense and collimated X-ray beams well-suited for scattering experiments. These source properties together with advances in instrumentation and data analysis methods have significantly broadened the scope of SAXS in the investigation of soft matter [2] and biological macromolecules in solution [12]. The new fourth-generation sources [13–15] offer even more attractive features for scattering experiments. As compared to the former generation sources, these new storage rings have increased the brilliance and the degree of transverse coherence of X-ray beams by more than an order of magnitude [14]. The higher brilliance and coherence are very beneficial for both SAXS and XPCS techniques. In conventional SAXS measurements, typically the X-ray beam is large encompassing multiple coherent areas while XPCS ideally requires a single (or a few) coherent area that is usually selected by an aperture. As a result, the main advantage of the new sources for SAXS experiments is the higher angular resolution due to the smaller beam cross-section and lower divergence [16]. The higher degree of coherence allows multispeckle XPCS measurements even with dilute suspensions having sufficient scattering power [17] or concentrated samples of low scattering contrast [18] and probe the equilibrium dynamics down to the microsecond range. The availability of high frame rate photon counting detectors is key to the exploitation of the new source properties in SAXS and XPCS [11,16,19,20].

The main purpose of this review is to give a broad overview of new possibilities offered by the fourth-generation synchrotron sources for colloid science. Technically, all the relevant size scales and time ranges can now be accessed by X-ray scattering methods [5]. Indeed, the X-ray free-electron laser (XFEL) sources offer even higher brightness and access to much shorter time ranges [11,21]. However, the cost-effectiveness of the XFEL facilities for studying colloids is perhaps debatable and synchrotrons enable a much wider range of experiments [5,6]. Representative cases of these broad range of investigations are illustrated here. Nevertheless, due to the burgeoning publications, the literature covered is not exhaustive but more representative of the capabilities. Moreover, the discussion is primarily limited to bulk studies.

## 2. Synchrotron X-ray scattering techniques

This section briefly describes the different X-ray scattering methods employed for probing the microstructure and dynamics of colloidal systems. The extent of information derived depends strongly on the depth of data analysis. This can be a few structural or dynamical parameters or very detailed microscopic model.

### 2.1. Small-angle X-ray scattering

SAXS is the most widely used X-ray scattering method in colloid science, especially for particle size determination [3,7]. Typical scattering geometry as shown in Fig. 1 involves a highly collimated and monochromatic X-ray beam of wavelength, $\lambda$, impinging on a sample and the scattered intensity in the forward direction is recorded by a 2D detector. A beamstop in front of the detector blocks the direct beam and monitors the transmitted X-ray intensity. The flight paths before and after the sample are in vacuum to avoid absorption and scattering by air. The 2D detector records the number of photons scattered as a function of the scattering angle, $\theta$. Since the scattering is fully elastic, the magnitudes of incident and scattered wave vectors ($\mathbf{k}_i$ and $\mathbf{k}_s$, respectively) are equal to $2\pi/\lambda$. The scattering vector, $\mathbf{q} = \mathbf{k}_s - \mathbf{k}_i$, and its magnitude ($q$) is given by $q = (4\pi/\lambda)\sin(\theta/2)$. The ratio $2\pi/q$ is indicative of the nominal size scale probed by the measurement. Furthermore, from the solid angle ($\Omega$) subtended by the detector pixels and transmitted beam intensity, the measured 2D detector counts can be normalized to an absolute scale to obtain the differential scattering cross-section per unit volume ($d\Sigma/d\Omega$) [7]. The $d\Sigma/d\Omega$ that is in units of reciprocal length per solid angle ($\text{mm}^{-1}\text{sterad}^{-1}$) but usually represented by $I(q)$ in reciprocal length.

In the case of low polydispersity and isotropic interactions, the normalized $I(q)$ can be written as;

$$I(q) = N_p V_p^2 \Delta\rho_p^2 P(q)S(q) \quad (1)$$

where $N_p$, $V_p$ and $\Delta\rho_p$ are the number density, volume and scattering contrast of particles in the scattering volume, respectively. The quantity $\Delta\rho_p$ is given by the difference of scattering length density (SLD) of the particles and the surrounding medium, and SLD is a product of $\rho_e$ and $r_e$, the classical radius of an electron ($2.82 \times 10^{-15}$ m). The $P(q)$ is the form factor that contains information on the size, shape and size distribution of particles. The $S(q)$ is the structure factor of interaction, which is related to the mean separation and interaction potential between particles [3,7]. The analysis of $S(q)$ is based on liquid-state theories or computer simulations. The $I(q)$ in turn can be used to estimate the particle volume fraction, $\phi_p = N_p V_p$, provided that the mean density of particles is known independently. The SLD of self-assembled colloids is not a constant and it varies according to the distribution of constituent molecules within the particle. A quantitative analysis of $I(q)$ data from a dilute suspension yields this critical information [22–24].

Key advantages of using a synchrotron X-ray source for performing SAXS experiments are the high resolution of $q$, short duration of acquisition that allows time-resolved (TR) measurements down to the sub-millisecond range and tunability of $\lambda$ that aids to optimize the sample transmission. In combination with the complementary methods of wide-angle X-ray scattering (WAXS) and ultrasmall-angle X-ray scattering (USAXS), the nominal size range spanned is from sub-nanometer to several microns [25,26]. This range covers the molecular scale up to

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Schematic representation of a SAXS experiment setup depicting the incident, scattered and transmitted beams, the beamstop and the 2D detector. The inset shows the definition of the scattering vector ($q$) in terms of the incident and scattered wave vectors, $\mathbf{k}_i$ and $\mathbf{k}_s$, respectively. Adapted from [5] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>
the upper limit of colloidal scale for conventional particles. The tunability of $\lambda$ further enables limited contrast variation, especially in the vicinity of an atomic absorption edge of a constituent element [7] and this method is called anomalous SAXS (ASAXS). Since only a few atomic absorption edges are located in the typical $\lambda$ range used for SAXS, the application of ASAXS is not widespread in colloid science. When there is a higher degree of order within the sample, such as colloidal crystals [27], instead of the diffuse intensity distribution on the detector, sharply defined diffraction peaks appear, which can be interpreted in terms of Bragg's law. This method is usually referred to as small-angle X-ray diffraction (SAXD) and the corresponding analysis methods become based on X-ray crystallography instead of liquid-state theories.

## 2.2. Ultra-small-angle X-ray scattering

USAXS is an extension of SAXS to the ultrasmall angles ca. 10 µrad, which is useful in the investigation of larger colloids of µm size or aggregates of smaller colloidal particles. Traditionally, this requires a special setup involving highly optimized collimation and analyzer crystals known as Bonse-Hart camera [7,25]. This is a scanning method that essentially measures the 1D scattering profile superimposed on the analyzer crystal rocking curve and therefore not ideally suited for measuring an anisotropic scattering pattern. The high degree of collimation provided by the modern synchrotron beam together with a high resolution detector now enable to cover the same q-range of a Bonse-Hart camera with a pinhole instrument similar to that used for SAXS but with a long sample-to-detector distance [26,28]. This has opened the possibility for performing time-resolved USAXS and XPCS in the ultrasmall-angle region [20,26]. The best q-resolution ($\Delta q$) obtained with a sample-to-detector distance of 31 m and $\lambda$ of 0.1 nm is about $2 \times 10^{-4}$ nm$^{-1}$ [29].

## 2.3. X-ray photon correlation spectroscopy

The instrument setup for XPCS measurements is similar to SAXS and USAXS but a single coherent fraction or patch of the incident beam is selected by small slits or apertures of size $10-20 \mu m$. Then the measured scattering patterns display speckles, which represent the diffraction-limited structure function of the scattering units in the medium. In a multispeckle XPCS measurement, a sequence of 2D speckle patterns are recorded with acquisition and lag time between frames much shorter than the typical relaxation times probed in the sample as depicted in Fig. 2(a). The observed temporal fluctuations of the speckles can be quantified in terms of the intensity-intensity autocorrelation function,

$g_2(q, t)$, which is computed pixel by pixel.

$$g_2(q, t) = \frac{\langle I_p(q, t_0)I_p(q, t_0 + t) \rangle}{\langle I_p(q, t_0) \rangle^2} \qquad (2)$$

where $I_p(q, t)$ being the scattered intensity in a pixel at a given q and lag time, $t$, and $\langle \cdot \rangle$ denotes the time average. To obtain the ensemble averaged $g_2(q, t)$, the individual pixel $g_2(q, t)$s corresponding to the same q are averaged. The $g_2(q, t)$ is then related to the corresponding electric field-field autocorrelation function or intermediate scattering function, $g_1(q, t)$, via the Siegert relation, $g_2(q, t) = 1 + g_0|g_1(q, t)|^2$ where $g_0$ is the amplitude of $g_2(q, t)$ at $t = 0$ related to the speckle contrast. In the ideal case of a fully coherent beam and speckle size much larger than the detector pixel size, $g_0 \approx 1$. However, due to the limited coherence of the synchrotron beam and larger pixel size, this factor is usually smaller than one as displayed in Fig. 2(b). $g_1(q, t)$ manifests the particular dynamics within the suspension and decays exponentially with time in the simple case of Brownian motion [see Fig. 2(b)].

Many colloidal systems of contemporary interest are out-of-equilibrium and therefore exhibit non-stationary dynamics. In such cases, the time averaged $g_2(q, t)$ is inadequate and the underlying dynamics can be characterized by the normalized ensemble-averaged two-time correlation function [TTCF, $C_I(q, t, \tau)$] [11]:

$$C_I(q, t, \tau) = \frac{\langle I_p(q, t_1)I_p(q, t_2) \rangle_p}{\langle I(t_1, p) \rangle_p \langle I(t_2, p) \rangle_p} \qquad (3)$$

where $t_1, t_2$ are the time of frame 1 and 2, respectively. $t = t_2 - t_1$ is the lag time, $\tau = (t_1 + t_2)/2$ is the age, $\langle \cdot \rangle_p$ is the average over all pixels corresponding to the same q. For a stationary system, $g_2(q, t) = \langle C_I(q, t, \tau) \rangle_\tau$, i.e. the average over all ages. The steadiness of the system over the measurement time is characterized by the dynamical susceptibility, $\chi_4(q, t)$, which is given by the normalized variance of $C_I(q, t, \tau)$, a quantity that can be directly compared with computer simulations [10,30]. A key advantage of multispeckle XPCS is in the characterization of out-of-equilibrium systems via $C_I(q, t, \tau)$ and $\chi_4(q, t)$. In addition, it enables direction-dependent analyses when the dynamics is anisotropic [31,32].

# 3. Advances in instrumentation and data analysis

This Section briefly describes key developments in terms of X-ray scattering instrumentation and new approaches for data analysis.

<figure><img src="image_5.png" /><figcaption>Fig. 2. Multispeckle XPCS from a dilute colloidal suspension of silica particles (radius ~ 300 nm) in water. (a) Representative 2D speckle patterns recorded in the USAXS range and the white circle indicating a given q. (b) Typical ensemble averaged intensity-intensity autocorrelation functions [$g_2(q, t)$] with $g_0 \approx 0.4$. Continuous lines are fits to an exponential decay with rate, $\Gamma = D_0q^2$, and $D_0 \sim 0.6 \ \mu m^2 \ s^{-1}$, as expected for dilute Brownian particles. Adapted from [16] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>
### 3.1. Fourth-generation synchrotron X-ray sources

The synchrotron radiation is produced by the deflection of high energy particles, typically electrons with an energy ($E_e$) of many GeV, by a magnetic field of strength ca. 1 T [4,33]. The spectral properties of emitted radiation critically depend on the electron beam characteristics as well as the strength of the magnetic field. The electron beam is characterized by the emittance ($\epsilon$), which is a product of its size and divergence usually expressed in units of picometer times radian (pm rad). The third-generation synchrotron storage rings enabled the use of a special magnetic device called the undulator and obtain high brightness of emitted X-rays [4]. The undulator generates a sinusoidal magnetic field and therefore the high energy electron beam passing through that device experiences a sinusoidal force perpendicular to the magnetic field. The period of the sinusoidal field and its peak value are adjusted such that electron beam takes only small deflections enabling the emitted radiation to undergo constructive interference in the far field. The resulting radiation spectrum is sharply peaked at the fundamental energy ($E_0$) and its harmonics, defined by the undulator parameters and $E_e$. These sharp peaks offer the high brightness that can be further monochromatized for scattering experiments. The vertical emittance of the electron beam is typically in the range of 5–10 pm rad and the emitted X-ray source is already diffraction-limited vertically at the typical wavelength used for X-ray scattering.

The difference between third and fourth generation sources is in the horizontal emittance ($\epsilon_h$). The former based on double-bend achromat electron optics [4] has $\epsilon_h$ in the range of several thousand of pm rad, ca. 4 nm rad. The fourth-generation sources are based on the multi-bend achromat storage ring lattice concept [13]. The improvement stems from the relation, $\epsilon_h \propto E_e^2 / (N_{cell}N_{dipole})^3$, where $N_{cell}$ and $N_{dipole}$ are the number of sections in the storage ring given by its circumference and number of dipoles per section, respectively [34]. Therefore, for a given $E_e$ and $N_{cell}$, $\epsilon_h$ can be decreased by changing from double-bend to multi-bend and the advances in magnet fabrication technology enabled such compact designs [13,14]. Several orders of magnitude gain in brilliance is essentially due to the corresponding reduction in $\epsilon_h$. For example, the Extremely Brilliant Source (EBS) at the ESRF is based on the hybrid seven-bend achromat design, operating at $E_e = 6$ GeV [14]. With respect to the former double-bend achromat design, root mean square $\epsilon_h$ diminished from 4 nm rad to about 130 pm rad, corresponding to a factor 30 increase in brilliance and concomitant gain in the degree of coherence.

### 3.2. Hybrid pixel-array detectors

Although, the third-generation synchrotron sources became available in the nineties, their full exploitation for SAXS and XPCS techniques were primarily limited by the available 2D detectors. In particular, multispeckle XPCS has been restricted to relatively slow dynamics [35]. However, this scenario has been dramatically improved with the availability of hybrid photon counting (HPC) pixel array detectors with high frame rate [19,20]. In this semiconductor sensor architecture, each pixel is an independent detector with own readout electronics. The small pixel size (ca. 55–75 µm), high efficiency and dynamic range make these detectors very attractive for scattering experiments [36–38]. Moreover, they have become commercially available offering high frame rates capable of µs range time resolution [36,38]. As a result, real time SAXS and multispeckle XPCS in the µs range have become technically feasible. With the higher brightness of fourth-generation sources, the maximum count rate (ca. several $10^6$ counts/s) is a limitation for strongly scattering samples [39]. The future generation detectors are expected to improve the count rate capability and the spatial resolution in terms of the pixel size.

### 3.3. Sample environments

These are essential ancillaries for performing in situ scattering experiments [1,40]. Since the data acquisition times are relatively short, automatic change of samples enable higher throughput of the measurements [6]. In addition, for weakly scattering samples, it is essential that sample and the corresponding background are measured with the same container to preserve the exact sample thickness and background scattering. This is often facilitated by means of a flow-through capillary cell that can be coupled to an automatic sample changer or any other injection system [41]. Variations in thermodynamic parameters such as temperature, pressure, etc. are very commonly involved in scattering measurements [29,40,42]. The microstructure of colloidal systems is often very sensitive to the applied stress or shear and variety of specialized devices have been developed for this purpose [1,8]. Coupling a high resolution rheometer to the shear geometry has become the standard practice [8]. For probing kinetics in solution, stopped-flow rapid mixing is a convenient approach and generally applicable to a broad class of systems [41]. This has enabled probing self-assembly processes in the millisecond range in a wide range of amphiphilic systems [5,41].

Microfluidic devices are also used to manipulate samples and observe flow-induced orientation in many soft and biological colloids [43–45]. These devices are also useful for investigating slower kinetics with lower sample consumption and to obtain more homogeneous microstructure [45–47]. By introducing chaotic mixing, the time resolution can be improved to reach the millisecond range [48]. For many soft matter systems, decoupling the kinetics and shear effects is essential in time-resolved experiments, which can be realized by a flow-focusing scheme of mixing [49]. Apart from kinetics and shear effects, another interest of milli and microfluidic systems is in minimizing the beam damage with low sample consumption. For example, a capillary coflow scheme has been developed, where the sample flows through the centre of the cell surrounded by a flow of matched solvent, which significantly reduces the fouling effect on the capillary walls and resulting radiation damage [50]. Containerless droplet microfluidics is another approach to avoid wall-effects [51] but potential artefacts due to refraction effect needs to be considered.

More complex sample environments are involved when in situ/operando type of experiments are performed [52–54]. The flexibility, high degree of collimation and time-resolution, and small beam size offered by synchrotron SAXS instruments are key factors in such studies.

### 3.4. Data analysis methods

Most synchrotron SAXS/XPCS instruments offer software tools for reducing the measured scattering patterns to a form that can be compared to a theoretical or computational model [25,29,55,56]. This can be normalized $I(q)$ profiles as a function of $q$ and other variables. Or $g_2(q, t)$ and $C_l(q, t, \tau)$ functions in the case of XPCS [39,57]. To progress beyond the qualitative evaluation and derive quantitative information from the scattering data, advanced data analysis is an essential step.

With dilute suspensions, the main information that can be obtained from SAXS is the mean size, shape and size distribution. If the scattering contrast is sufficient, XPCS measures the Brownian diffusion coefficient ($D_0$) and the corresponding hydrodynamic radius ($R_H$) via the Stokes-Einstein relation. The analysis of $P(q)$ is usually performed via a geometrical shape while treatment of $S(q)$ involves approximations or closure relations from liquid state theory [7]. Phenomenological modeling approaches still remain useful for hierarchically assembled systems [58]. By now, many program suits such as SASfit [59], SASView [60], Irena [25], jscatter [61], GENFIT [62], etc. are available for the analysis of $P(q)$ and $S(q)$ from colloidal systems. More specialized software suits developed for biophysical structural analysis like ATSAS [55], D+ [63], etc. can reach atomic level resolution of the model. For $S(q)$ modeling, most advanced method is based on Polymer Reference
Interaction Site Model (PRISM), in particular for obtaining self-
consistent structural and thermodynamic properties [64]. In addition,
the traditional model-independent analysis and pair-distribution func-
tion are also useful for the analysis of non-interacting systems [25].

The PRISM formalism can also be used for coarse-graining of atom-
istic simulation force fields, which is essential for studying larger sys-
tems [64]. The Computational Reverse-Engineering Analysis of
Scattering Experiments (CREASE) is an even more powerful approach
for deriving the morphology and the structure from experimental I(q)
data without the use of analytical models [65,66]. The CREASE origi-
nally developed for the analysis of self-assembled micelles is a top-down
approach involving a genetic algorithm step to define the overall micelle
shape based on the experimental input and then use coarse-grained
molecular dynamics (MD) simulations to optimize the monomer level
nanostructure [65]. This approach works for not only spherical objects
but also for elongated morphologies such as cylindrical and fibrillar
assemblies [67].

While modeling relied on analytical functions still remain very
practical and useful for microstructural studies, more advanced methods
are emerging based on machine learning (ML) [66,68,69]. For instance,
the accuracy of the potential of mean force deduced via analytical liquid
state theories is usually limited but that can be overcame by an inversion
scheme using a large set of computed S(q)s [68]. This has been
demonstrated in the case of particles interacting via a screened-Coulomb
repulsive potential. The original CREASE was restricted to P(q) analysis
but ML enhanced CREASE has been shown to be more powerful and
efficient for the first step [66] and can also incorporate S(q) when P(q) is
a priori known. Until now, the success of these advanced computational
approaches have been proven primarily by means of in silico data and it
will be interesting to apply these methods to real scattering data.

4. Colloid microstructure and interactions

There are myriad of examples of nanostructures and interactions
probed by SAXS, which are covered by many reviews and book chapters
[1,3,5,7,22,45,70]. Here only some examples exploiting the high reso-
lution features of SAXS are described [16,27]. In particular, in the
USAXS range there is an overlap with the confocal microscopy and
therefore allowing to derive complementary information in the bulk
without the influence of a substrate.

4.1. Large scale microstructures

A direct benefit of the reduced source emittance (lower divergence and smaller size of the beam) is in obtaining a higher degree of colli- mation with minimal optical components. This in turn helps to preserve the spectral properties of the X-ray beam and at the same time minimizes the parasitic background. These improvements may not make a big difference in the conventional SAXS range but become significant in the USAXS region [16,71]. The classical USAXS is performed using a Bonse- Hart instrument consisting of collimator and analyzer crystals [25,72] and in this case the beam divergence is controlled by the width of the rocking curve of the crystals [7]. To take advantage of the smaller divergence and size of the beam, USAXS needs to be performed in the pinhole collimation using a high resolution 2D detector placed farther from the sample (ca. 30 m). This scheme has many advantages notably in time-resolved studies, and for the investigation of weakly scattering and radiation sensitive samples [26,28]. In addition, oriented specimens require 2D detection for more complete information [27,73]. Fig. 3 il- lustrates the typical resolution that can be obtained and the limit of detection for relatively weak scattering features over the USAXS range. The first sample is a dilute suspension (φ~p~ ~ 0.01) of polystyrene (PS) microspheres with a low polydispersity that displays fine features of the scattering form factor of uniform spheres.

The second sample in Fig. 3 is an aqueous mixture (7 wt%) of sodium dodecyl sulfate (SDS) and β-cyclodextrin (β-CD) in 1:2 molar (M) ratio,

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Normalized scattering profiles from suspensions of dilute polystyrene (PS) spherical colloids and self-assembled microtubes of sodium dodecyl sulfate (SDS) and β-cyclodextrin (β-CD) in 1:2 M ratio. The continuous curves depict corresponding models, polydisperse spheres (mean radius, R<sub>S</sub> ≃ 1.015 µm and standard deviation, σ<sub>R</sub> ≃ 7 nm) and hollow cylinders (mean radius, R<sub>C</sub> ≃ 585 nm, wall thickness, t<sub>W</sub> ≃ 74 nm and radius and thickness polydispersities 0.08 and 0.6, respectively) scattering functions. For clarity, the lower profile has been shifted down by a factor 100. The full-width at half-maximum (FWHM) q-resolution (Δq) of the setup was 2.4 × 10<sup>-4</sup> nm<sup>-1</sup>. Reproduced from [16] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>

which forms relatively long uniform microtubes at room temperature
[74]. This system exhibits the so called lattice self-assembly of CD
complexes incorporating SDS molecules in 2:1 ratio, forming a crystal-
line membrane [75]. The SAXS/USAXS data spanning over a broad
range of *q* revealed that the microtubes have a multilamellar hierar-
chical architecture built up of a membrane consisting of 2D rhombic
lattice of *β*-CD-SDS-*β*-CD complexes [74]. Furthermore, TR-SAXS/
USAXS following a temperature-jump enabled to identify an inward
growth mechanism of these microtubes subsequent to the initial nucle-
ation [76]. Fig. 4 presents the evolution of SAXS and USAXS profiles
during this hierarchical self-assembly process of microtubes initiated by
a temperature quench. From the changes in the scattering features, the
sequence of events can be easily identified and further quantified by
model analysis [76].

Structural studies exploiting the access to very low *q* region can be extended to cellular systems such as bacterial suspensions [23,77]. USAXS together with constraints from the contrast variation small-angle neutron scattering (SANS) enabled to derive a quantitative model for the in vivo ultrastructure of *Escherichia coli* [23,78]. This colloidal modeling approach has been applied to probe transient structural evolution during the action of antimicrobial peptides on the bacterial cell and derive crucial information on the time scale and efficacy of these peptides for inactivating the cells [79]. In principle, this method can be extended to other systems of immediate clinical interest but the biosafety is the limiting factor for a more widespread application.

4.2. Growth processes

The development of time-resolved USAXS found immediate appli-
cations in studies of a variety of growth processes involving relatively
fast kinetics occurring over the micron scale [5]. For example, the as-
sembly pathways in the formation of polyelectrolyte coacervates were
probed by TR-USAXS combined with stopped-flow mixing of equimolar
sodium polyacrylate (SPA) and polyallylamine hydrochloride (PAH)
monomers in aqueous solution from 0 to 1 M NaCl concentration [80].
Fig. 5 summarizes the main results of this study. Within the mixing dead
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** (a) The evolution of SAXS and USAXS profiles during the hierarchical self-assembly of SDS and β-CD complexes to form microtubes upon cooling a 10 wt% solution from 75 °C to 25 °C. (b) a 2D SAXS pattern from an oriented sample in the final state depicting the S(q) and P(q) of the multilamellar architecture of microtubes and the sawtooth Bragg peaks from 2D rhombic crystalline order within the curved membrane. (c) A cartoon of the sequence of events involved in the assembly process revealed by the data in panel (a). Reproduced from [76] distributed under Creative Commons Attribution Non Commercial (CC-BY-NC) licence.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (a) Typical time evolution of the normalized USAXS intensities upon mixing anionic sodium polyacrylate (SPA) and cationic polyallylamine hydrochloride (PAH) at different NaCl concentrations ($C_s$) and their modeling in terms of polycondensates (complexes) with spherical subunits. Inset depicts a cartoon of the complex formed during the mixing process. Parameters derived from the modeling of the USAXS profiles; (b) mean molar mass of the complexes and number of subunits within, and (c) evolution of their fractal dimension. Filled and unfilled symbols represent mass and surface fractal dimensions ($D_f$ and $D_s$), respectively. (d) Schematic representations of the morphologies of complexes at the initial and final stages at low and high salt concentrations. Reproduced with permission from [80] © the American Chemical Society 2017.</figcaption></figure>

time (~ 2.5 ms), percolated clusters were formed suggesting that the initially formed small charge neutral subunits further assembled to form higher order structures. In addition, more compact complexes were formed at higher salinity. The early stage time evolution of the molar mass of the large globular complexes was found to be comparable with the Brownian-coagulation rate [80].

Another interesting application of TR-USAXS was for investigating the kinetics of liquid-liquid phase-separation (LLPS) via spinodal

decomposition (SD) in a variety of protein systems such as bovine serum albumin [81,82], gluten [83], γ-globulin [82,84], etc. The late stage coarsening in these systems followed the classical $t^{1/3}$ behavior corresponding to a diffusive mechanism for smaller temperature quenches into the two-phase region. Deeper quenches showed a weaker t-dependence signifying an arrested phase separation with a strong interplay of the thermodynamics and viscoelasticity of the system [83,84]. It is likely that the strength of the short-range attractive interaction between
proteins is the determining factor for this kinetic arrest behavior.

Colloidal gels are another class of systems where USAXS elucidated certain unique features, especially in samples which are opaque to light [85–87]. E.g. the evolution of the fractal morphology during ultrasound assisted fluidization of carbon black based rheo-acoustic gels was elucidated [85]. In the same system, USAXS combined with rheology uncovered the structural origin of gel elasticity in terms of the cluster interpenetration as opposed to connectivity [87]. USAXS allowed a microstructural investigation of poly(vinyl alcohol) based cryogel used in cultural heritage conservation [88].

When the structural evolution is slower Bonse-Hart USAXS can be used for probing gelation process but special attention needs to be paid for possible radiation damage since it is a scanning method involving a separate X-ray exposure for each *q* point. For example, the thermally controlled gelation of pea and whey proteins was investigated by this method and results revealed the key difference in the morphology of these hydrogels [89]. Similarly, the morphology of equilibrium gel formed by model patchy particles involving metallic nanoparticles with telechelic polymer links was studied using Bonse-Hart USAXS [90]. TR-USAXS combined with computer simulations revealed a two-stage kinetics in the collapse transition of PNIPAM microgel particles, involving a fast process in that the collapsed clusters form at the periphery (hollow core-shell) and a slower process in which the hollow core-shell structure transforms to a globular particle [91].

### 4.3. Structural evolution in external fields

2D USAXS becomes indispensable for studying oriented samples, especially when coupling with rheological tools [8]. Well-known cases are different types of colloidal crystals [27]. For example, using molded films of single-component polymer-grafted particles, the elastic and plastic deformations of colloidal crystals subjected to uniaxial strains were observed in situ USAXS [73]. In another study, the degree of orientational ordering of cellulose nanocrystals in their cholesteric liquid crystalline phase up on the combined action of ultrasound and shear flow was investigated [53]. Here, depending on the strength of ultrasound and shear, different orientation paradigms were unveiled. Bonse-Hart USAXS enabled the identification of acoustic cavitation as the mechanism in ultrasound driven formation of Pickering emulsions [92]. In this case, 2D USAXS would have been beneficial for deciphering

the different steps in the emulsification process.

In lyotropic systems, rheo-SAXS is useful for discriminating possible ambiguities in the structure determination. For example, high resolution rheo-SAXS enabled to resolve the contradiction with respect to the structural organization of extremely swollen microemulsion phases consisting of SDS, brine, decane and octanol [93]. An emulsified microemulsion phase [94] composed of 2D hexagonally packed cylinders has been identified as the origin of the structural colors exhibited by this system. Fig. 6 presents the main result of this work, which revealed an hexagonal order as opposed to a previously reported cubic order in these samples. Somewhat similar oil-in-water emulsions prepared using block copolymers can be exploited to design wavelength tunable photonic spheres and their structure has been elucidated by USAXS [95]. In another work involving an historical saponified oil (lead soaps in oil), oscillatory shear revealed an unexpected transformation from lamellar to unilamellar cylinder-like morphology oriented along the neutral direction of the flow [96].

Rheo-SAXS is a powerful approach for probing the relationship between the microstructure and rheological properties, in particular for identifying the shear induced structures. For example, transformation between different liquid crystalline organization of cellulose nanocrystals associated with the three-regime rheological behavior was elucidated [97]. Rheo-SAXS probed the alignment quality and its relation to apparent improvement in mechanical properties of graphene oxide sheets [98]. Furthermore, rheo-SAXS enabled the observation of anisotropic structure during shear thickening transition in a colloidal-polymer mixture [99] and butterfly-like USAXS pattern during the yielding in a thermoreversible colloidal gel [8].

## 5. TR-SAXS studies of self-assembly processes

This Section presents some representative examples of time-resolved structural investigations, which shed light on the pathways of the self-assembly processes. These studies include both model systems from a fundamental point of view and functional systems of practical relevance.

### 5.1. Amphiphilic self-assembly

These studies present prototypical cases of self-assembly processes investigated by TR-SAXS to elucidate the underlying structural

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Evolution of the SAXS patterns upon shear cessation of a swelling microemulsion phase along (a) the flow direction and (b) the velocity gradient direction. Patterns reveal an hexagonal ordering of cylindrical microemulsion droplets as schematically represented in the cartoons (c) and (d). Reproduced from [93] © Elsevier Inc. 2021.</figcaption></figure>
pathways. These include the assembly from a pool of amphiphiles such as surfactants or block copolymers to form spherical micelles or other structures like cylindrical micelles or unilamellar vesicles as well as transformation between different morphologies by changing the ionic strength, pH, or temperature [100,101]. Up on mixing two different surfactant micelles, depending on the nature of surfactants, unilamellar vesicles [100] or cylindrical micelles [102] are formed over the millisecond time range. The transformation from micelles to unilamellar vesicles involved transient disk-like or cylinder-like mixed micelles [100]. TR-SAXS combined with stopped-flow mixing turned out to be a powerful approach to follow the underlying structural kinetics and capture the transient nanostructures. On the other hand, mixing cationic and anionic surfactants below their individual critical micellar concentrations led to the formation of nanotube-like structures [41]. Fig. 7 demonstrates the quality of TR-SAXS profiles that can be measured upon mixing 25 mM cationic decyltrimethylammonium bromide (DTAB) and anionic lithium perfluorooctanoate surfactants with 2 ms time resolution in one-shot. Here, tube-like structures are formed within the mixing time, which grow in length and diameter with time.

A similar transformation from surfactant monomers to nanotubes has been observed in bolaamphiphiles consisting of a sugar residue, an alkyl chain, and an amino group upon a pH change [103]. TR-SAXS enabled identification of the intermediate structures and underlying mechanism of self-assembly via folding of membranes. Another prototypical example is the transformation of spherical micelles to ‘wormlike’ micelles up on the addition of NaCl to an SDS micellar solution [104]. The initial spherical micelles first transformed to elongated structures and then fused together to form long flexible cylinders (‘worms’) roughly following a step-like polymerization type kinetics in the millisecond time scale. By combining SAXS, theoretical modeling, and computer simulations, it was recognized that transient SDS dimers formed via the mediation of counterions promote the stabilization of cylindrical instead of spherical micelles at higher ionic strengths [105].

In the case of surfactant micellar self-assembly, TR-SAXS revealed a single step kinetics involving insertion of unimers similar to nucleation and growth [106]. The block copolymer micellization with millisecond range time resolution also showed a similar behavior but the insertion/ expulsion step persists for a much longer time [107]. A similar study has been carried out using a microfluidic mixer combined with SAXS, which confirmed this type of micellization kinetics [108]. Polymerization- induced self-assembly is a powerful method for rational design of block copolymer nanostructures such as spheres, worms, vesicles, etc. [109]. The underlying kinetics is much slower compared to micellization but the polymerization conditions make in situ SAXS observation

very challenging. Detailed morphological evolution during reversible addition-fragmentation chain transfer emulsion polymerization reaction was monitored by SAXS, which enabled the identification of a nucleation step and subsequent growth process [110].

Similar to the complexation of homopolymer polyelectrolytes presented in the previous Section [80], polyelectrolyte complex micelles are related self-assembled nanostructures formed with a core of associated polyanions and polycations microphase-separated from neutral hydrophilic coronas of the constituent block copolymers in an aqueous solution [111]. TR-SAXS enabled to identify possible pathways of their formation or coacervation process upon mixing the oppositely charged blocks [112,113]. The results suggested a two-step kinetic process in which oppositely charged polyelectrolyte chains pair to form nascent charge neutral aggregates and in a second step they microphase-separate to form well-defined spherical micelles with a core-corona morphology [112,113]. Further growth of these complexes take place via polypair exchange into larger micellar entities. Different micellar morphologies such as cylinders or spheres can be obtained by varying the mixing ratio of the copolymers and the transformation between these morphologies can be followed by TR-SAXS [114]. Time-scale of these transformations are much longer as compared to that in surfactant or neutral block copolymer solutions. These cylinder-like or sphere-like complex micelles can be transformed to vesicles by changing the ionic strength or a combination of copolymer ratio and ionic strength, respectively [115]. In this case, TR-SAXS revealed disk-like or bowl-like transient structures, somewhat analogous to surfactant systems but without their growth, which gradually bend and fuse to form vesicles.

TR-SAXS is also useful to follow the opposite process of disassembly or dissolution. For example, the solubilization of model lipid membranes by different surfactants has been investigated in great detail [116,117]. The nonionic surfactants are found to be more efficient in the solubilization leading to different mixed lipid-surfactant morphologies depending on the bilayer rigidity [116]. In particular, a novel rippled bilamellar nanodisk structure has been identified upon the collapse of lipid vesicles by the incorporation of Triton X-100 nonionic surfactant molecules at lower temperatures [117]. A SAXS analysis elucidated the temperature-dependent reorganization and reshaping of the lipid nanoparticles formed by a phospholipid (DMPC) and a natural surfactant (saponin β-aescin) from nanodiscs to ribbons and finally sheet-like morphologies [118]. Finally, using photosensitive surfactants, micellar transformations can also be induced by light illumination and follow the underlying kinetics by TR-SAXS [119].

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** (a) An isometric plot of the normalized and background-subtracted TR-SAXS profiles following the rapid mixing of 25 mM solutions of cationic DTAB and anionic LPFO surfactants. The scattering features correspond to mixed unilamellar tubes, which are formed spontaneously during the mixing process. Each profile was integrated for 1.8 ms, comparable to the dead time of mixing (ca. 2 ms) and the dashed line represents the growth of tube radius by an exponential function. (b) Modeling of the initial and final profiles in terms of polydisperse hollow cylinders with radius, $R_c$, shell thickness, $t_s$ and length, $L_c$ values listed in the legend. Adapted from [29] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>
## 5.2. Biomolecular assemblies of colloidal dimension

As an outcome of the developments over the last several decades, SAXS has made significant inroads in structural biology research [12,120–122]. SAXS can probe macromolecular structural dynamics in solution, down to sub-nanometer spatial and sub-millisecond temporal resolutions. For example, SAXS can be used to investigate kinetics and thermodynamics of viruses at different stages of their life cycle in vitro [122]. For simplicity, viruses may be considered as biologically functional perfectly monodisperse colloids self-assembled from copies of a few components held together by weak protein-protein interactions. While their icosahedral structure can be solved by high resolution methods, the assembly process of these capsids is not easy to capture. Stopped-flow mixing combined with TR-SAXS has become a powerful approach for probing this self-assembly from their constituent proteins to form viral capsids without or with the genetic material [123–126]. Fig. 8 presents an example of the sequence of structural events, that can be captured by TR-SAXS together with advanced modeling method involving the maximum informational entropy optimization, during the assembly process of Hepatitis B virus capsid proteins [123]. The key finding of this study was that small changes in the dimer-dimer association free energy control the earliest steps of the reaction, which dictate the subsequent assembly pathway. These results may provide strategies for understanding, regulating, and designing assembly of protein cages [123].

Another interesting example is the assembly of tubulin, an essential cytoskeletal protein, into microtubules consisting of helical filamentous superstructures containing thousands of identical copies of αβ-tubulin-dimer subunits [127]. TR-SAXS elucidated the assembly pathways after rapid mixing of tubulin with spermine to form hierarchical architectures based on tubulin conical-spirals, which eventually transformed to inverted tubules at higher spermine concentration. The dynamic and reversible nature of the equilibrium between tubulin dimers, oligomers and rings at lower temperature was also uncovered by TR-SAXS [128]. Overall, the tubulin self-assembly differs from the classical route involving twisted-ribbon, helical and tubular structures, and reveals a

fascinating means to design and create a wide range of building blocks for biomaterials.

Self-assembly of amphiphilic peptides to form well-defined nano-tubes is another example of slow kinetics where SAXS and WAXS elucidate structural organization from the molecular scale to the dimension of nanotubes [129,130]. Not only the self-assembly of pure peptides but peptide-membrane interaction is another case that can be probed by TR-SAXS [22]. In particular, this topic is relevant to both the molecular mechanism of many diseases and design of drugs. The underlying dynamics can become fast as mentioned earlier [79]. TR-SAXS combined with stopped-flow mixing enabled to obtain a deeper insight into the pathways of anionic surfactant SDS induced unfolding of globular proteins (e.g. β-sheet-rich globular protein β-lactoglobulin) [131]. The reverse process of refolding aided by a nonionic surfactant octaethyleneglycol monododecyl ether ($C_{12}E_8$) is a much slower process that was also studied by TR-SAXS [131].

## 5.3. Nucleation and growth of nanoparticles

Time-resolved simultaneous SAXS and WAXS technique is a powerful method for elucidating the early stages of nucleation and growth in a wide range of systems [2,3,7]. Here only some recent works are reviewed, mainly related to the non-classical features of the growth process. In most of these cases, the reaction proceeds much slower in minutes scale but the detection of the weak scattering signal over the background due to the reaction cell and the medium is the challenge. Often these in situ experiments are also coupled to optical or X-ray spectroscopy that can probe the chemical changes prior to the nucleation [132,133]. The nucleation and growth of semiconductor nanocrystals or quantum dots (e.g. CdSe and PbS) are one of the most widely studied systems owing to their immense practical interest. An important finding of these studies is the deviation from the classical picture involving short nucleation burst and long growth phase. Instead, a long or extended nucleation phase and a sharpening of the size distribution have been observed [132,133]. The diffusion in the bulk is no longer the rate limiting step but the surface addition or reactivity as these particles

<figure><img src="image_11.png" /><figcaption>Fig. 8. (a) Time evolution of SAXS profiles during the self-assembly of Hepatitis B virus capsid proteins and the reconstructed kinetic model fits. For clarity, successive scattering profiles have been offset by a decade. (b) Mass fractions of the three main species as a function of time derived from the kinetic model. (c) Kinetic scheme of the capsid assembly under mild (physiological) and aggressive conditions. Reproduced from [123] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>
are stabilized by organic ligands. The larger reactivity of smaller parti-
cles compensates the broadening of the size distribution induced by the
extended nucleation phase, eventually leading to low dispersity of par-
ticle size. Fig. 9 depicts the typical evolution of SAXS and WAXS and
corresponding modeling in the case of persistent nucleation and growth
of PbS nanocrystals [133]. For multicomponent particles, variations in
the reactivity of particles may also arise from the differences in stoi-
chiometry among the particles [134].

A well-known example of non-classical crystallization is the precip-
itation of CaCO₃, which occurs via a metastable amorphous intermedi-
ate that dissolves and recrystallize to a more stable polymorph [7]. In
contrast, an amorphous to crystal conversion has been noticed in the
case of rare-earth oxide nanoparticles [135]. SAXS investigation of
crystallization of cerium oxalate reported a metastable chemical equi-
librium between transient liquid droplets and solid amorphous particles,
and reactant-rich droplets do not transform to amorphous particles
[136]. In the case of non-classical crystallization of zirconia nano-
crystals, SAXS and pair distribution function analysis of WAXS data
revealed the formation of small amorphous particles (less than 2 nm in
diameter) from the precursor conversion [137]. The nanocrystals
nucleated within the amorphous particles in a much slower process and
their further growth led to well-defined particles. Non-classical nucle-
ation pathway is also known in protein crystallization, where a meta-
stable intermediate phase has been detected between the initial
supersaturated solution and the final crystals by SAXS [138]. Depending
on the exact form of the free energy landscape, the metastable in-
termediates can be a dense liquid phase, mesoscopic clusters, or a semi-
crystalline state.

The high brilliance SAXS has also enabled studies of nucleation and
growth during pyrolysis [7]. In situ formation and growth of palladium
nanoparticles in an ethylene flame has been studied [139], which found
homogeneous nucleation and coalescence of these nuclei as mechanisms
for particle formation and growth. One of the challenges in this type of
studies is distinguishing the gas phase scattering and nanoparticle con-
tributions to the measured SAXS profiles [140]. Nevertheless, im-
provements in source brilliance and detectors facilitate investigations of
extremely dilute systems such as aerosol suspensions [141], dusty
plasmas [142], etc.

5.4. Self-assembled colloidal structures

High resolution SAXS or SAXD is a powerful method for elucidating the crystalline structure and long-range order in colloidal crystals [27]. Crystallization of spherical colloids usually show more conventional crystal structures [3,27]. For example, crystallization of nanoparticles grafted with a thick polymer brush in ionic liquids led to face-centered cubic and random close packed structures [143]. Using coherent diffractive imaging (CDI) method, the 3D structure of a colloidal crystal grain was reconstructed and positions of individual particles were resolved [144]. As a result, an exact stacking sequence of hexagonal close-packed layers including planar and linear defects could be identified. X-ray ptychographic tomography is an emerging method to image defects inside the colloidal crystals as shown in the case of supercrystals of DNA-functionalized nanoparticles [145]. The self-organization of anisotropic colloidal suspensions usually leads to more fascinating range of crystalline and liquid crystalline phases driven by the shape asymmetry [146,147]. High resolution SAXS revealed two different rhombohedral stackings in a sediment of superball particles having shape in between spheres and cubes [146]. In a dilute aqueous suspension of highly anisotropic synthetic Sb₃P₂O₁₄ nanosheets (diameter approximately 100 nm to 1 µm and thickness ~ 1 nm), high resolution Bragg profile analysis identified two coexisting mesophases consisting of a columnar nematic and a lamellar phase with domain sizes of about 20 µm, corresponding to about 600 nanosheets [147].

The structural paradigm becomes even more complex in the presence
of an external field such as electric or magnetic field. Orientation
ordering of spindle-shaped hematite particles in a magnetic field was
studied by combined SAXS and WAXS [148]. This work showed that the
magnetic and orientation order parameters of magnetic single-domain
nanospindles can be described by an oriented ellipsoid with the easy
axis of magnetization lying in the equatorial plane of the particle.
Texture analysis of the WAXS data further confirmed that the magnetic
easy axis is located in the basal plane of the hematite crystal lattice
[148]. In a magnetic field assisted self-assembly of hematite-silica core-
shell prolate colloids, SAXD revealed a rather counterintuitive oblate
liquid crystalline phases and an unexpected smectic phase [149]. TR-
SAXS was used to follow the rotational dynamics of anisotropic mag-
netic particles (e.g. hexaferrite platelets) in an alternating magnetic field

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** (a) SAXS profiles and corresponding modeling results; (b) radius and (c) polydispersity during extended nucleation and growth of PbS nanocrystals. (d) Simultaneous WAXS profiles recorded with SAXS and corresponding analysis results (e) intensity of [022] reflection and (f) polydispersity of nanocrystals deduced using the Scherrer equation. Scattering profiles have been shifted for the clarity of presentation. Reproduced from [133] distributed under Creative Commons Attribution Non-Commercial (CC-BY-NC) licence licence.</figcaption></figure>
[150] and explore the magneto-optical properties of the system.

An important asset of different X-ray scattering methods is that they allow probing intermediate structures during the self-assembly of colloids [151]. For instance, the sequence of phase transformations during evaporation-induced superlattice formation of PbS nanocrystals was elucidated using SAXS/WAXS and X-ray cross-correlation analysis (XCCA) [151,152]. Containerless investigation is often critical for eliminating the role of the substrate, and controlling defect formation during the assembly of nanoparticles that can be achieved using acoustically levitated drops [52]. Performing SAXS measurements with a droplet is challenging due to potential artefacts from refraction and reflection effects but the strong scattering by the particles likely submerges such contributions. This enabled probing the temporal evolution of strain and lattice contraction during evaporation-induced self-assembly of oleate-capped iron oxide nanocubes, and detect the formation of defects upon the solvent evaporation [52]. The same approach was used to probe the co-assembly of amphiphilic organo-functionalized polyoxometalate (POM) clusters with pluronic block copolymers (P123) in an aqueous solvent over a wide concentration range [153]. TR-SAXS analysis revealed the formation of a variety of morphologies; vesicles, a lamellar phase, cubic phases and eventually an hexagonal phase as the concentration is systematically increased. Fig. 10 depicts the schematic of the experiment setup and the sequence of structural evolution observed during the co-assembly process.

## 5.5. Functional colloids

SAXS can provide key structural insight in the development of nanostructured dispersions for drug delivery applications and characterization of biocolloids [24,154,155]. The lipid-based nanocarriers can encapsulate small molecular weight phytochemical drugs as well as macromolecular small interfering RNA (siRNA), plasmid DNA (pDNA), peptide and protein pharmaceuticals [154,156]. These nanocarriers may provide efficient intracellular delivery and triggered drug release.

Underlying processes are associated with a variety of lyotropic phase transitions driven by changes in the membrane curvature or changes in lipid membrane structure, which can be probed in vitro using SAXS and related methods [154,157–159]. For example, SAXS combined with a microfluidic device elucidated the structural sequence involved in cationic-lipid/siRNA complexation in lipid nanoparticles specifically designed to deliver siRNA [160]. Another fascinating case is the pH dependent self-assembly of ionizable lipids used in Covid-19 vaccine formulations and the complexation of these lipids with nucleic acids [messenger RNA (mRNA) and pDNA] probed by TR-SAXS combined with stopped-flow mixing [159]. Fig. 11 displays the evolution of TR-SAXS profiles during the complexation of one of the ionizable lipids (SM102) and a helper lipid monoolein (MO) with mRNA. The final structure in this case is multilamellar vesicles as schematically depicted in the inset (a), which are formed over the millisecond time scale.

Small-angle scattering methods are widely used for the characterization of food colloids over a broad size scales from nm to µm [161]. SAXS has been identified as a practical tool for investigating the structure-function relationship of biomacromolecules in food science and technology [162]. Casein micelles (milk proteins) are one of the widely studied example where both the interactions [163] and changes in internal structure with different chelation agents [164] have been investigated.

# 6. Probing colloid dynamics by XPCS

The XPCS method emerged with the third-generation sources but was limited to relatively slow dynamics due to low coherent photon flux and available detectors [10,11]. Several orders of magnitude increase in the degree of coherence with the fourth-generation sources and availability of fast photon counting detectors have provided a major boost for this technique [16,165].

<figure><img src="image_13.png" /><figcaption>Fig. 10. TR-SAXS/WAXS experiments on levitating POM-2C12 and pluronic P123 aqueous drops. (a) Experimental setup for simultaneous measurements of SAXS, WAXS and droplet size. (b) Image of a levitating drop and TR-SAXS patterns. (c) Volume and concentration of the shrinking levitating drop with time. (d) Scattering invariant $[Q_m(t)]$ as a function of time and identification of five growth regimes: $t_1$ to $t_5$ for a mixing ratio of 1:3. (e) Time-resolved SAXS profiles colored according to the morphology of nanostructures. Reproduced from [153] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** (a) Time evolution of the multilamellar peaks during the complexation of SM/MO lipids with mRNA. The inset shows a cartoon of the multilamellar vesicles complexed with mRNA (b) Peak profiles of three complexes in the final state taken after 120 ms after mixing. (c) Area of the main Bragg peak, A(t), as a function of time during the complexation of polyadenylic acid (polyA), mRNA, and pDNA with lipids (SM102/MO) suggesting an exponential growth kinetics. Reproduced from [159] distributed under Creative Commons Attribution NonCommercial-NoDerivs (CC-BY-NC-ND) licence.</figcaption></figure>

## 6.1. Equilibrium dynamics

In the studies of equilibrium dynamics, the new sources aid both in terms of the speckle contrast and the fastest dynamics that can be probed with a suitable detector. For dilute systems, DLS is usually much superior in terms of statistics due to larger scattering contrast but the XPCS becomes better for optically opaque concentrated samples and access to higher *q* ranges. The higher *q* values are more relevant for smaller particles like proteins but the low scattering contrast and radiation damage are the limiting factors [18,166]. Nevertheless, it has become possible to investigate dense protein (α-crystallin) solutions [18,166], dilute gold [19,167] and silica [21] colloids, virus suspensions [168], dense microemulsions [169], etc. The obtained results are generally in agreement with the theoretical expectations but an important effect that needs to be discriminated is the dynamics induced by the X-ray beam [18,21]. This can be simple heating of the suspension [21] or more complicated changes due to creation of radicals [18,29] by the X-ray beam. In the case of dense protein solutions, XPCS essentially measures the long time diffusion coefficient corresponding to protein molecules escaping the cage formed by their nearest neighbors. The intrinsic protein (α-crystallin) cage dynamics was deduced by extrapolating the apparent relaxation rates as a function of absorbed dose rate to zero. The results were found to be in good agreement with the dynamic arrest scenario similar to dense colloids [18].

As compared to the literature on dynamics of spherical colloids, studies of suspensions of anisotropic particles are somewhat scanty. XPCS enabled investigations of a variety of nonspherical colloids and probe their orientation-dependent dynamics at higher $\phi_p$. For example, peanut-shaped magnetic particles showed strong anisotropy in their collective dynamics even in a weak magnetic field prior to the formation of chain-like configurations [31]. A similar anisotropy in the effective diffusion coefficient [$D_{eff}(q)$] was noticed with cube-like magnetic particles [170]. In all these particles, the core contained hematite with an outer silica coating. A systematic investigation of the dynamics at the nearest neighbor distance of ellipsoidal particles as a function of $\phi_p$ revealed a scaling behavior of $D_{eff}(q)$ with the inverse of effective structure factor [$S_{eff}(q)$], which allowed to deduce their effective hydrodynamic function [171]. As shown in Fig. 12, $D_{eff}$ at the peak of $S_{eff}(q)$ ($q_m$) followed the Vogel-Fulcher-Tammann (VFT) equation with an arrest transition at $\phi_p$ of about 0.47, which is above the isotropic-nematic transition of ellipsoids. Moreover, the dynamics at the nearest neighbor distance became anisotropic with the application of a magnetic field. But the arrest transition seemingly taking place at the same $\phi_p$ as presented in Fig. 12 [172].

The anisotropy in the dynamics may not be very striking at very low $\phi_p$. For example, dilute suspensions of magnetic Janus particles displayed nearly isotropic dynamics, even with significant alignment of particles, until the formation of chain-like aggregates [173]. With faster detectors [37], it is likely that XPCS method will be able to probe short-

<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Left: variation of the normalized diffusion coefficient, $D_{eff}(q_m)/D_0$, with volume fraction, $\phi_p$, without and with an applied magnetic field, $\vec{B}$, both along parallel and perpendicular directions of $\vec{B}$. The inset illustrates the orientation of ellipsoids in the magnetic field. Right panels show 2D USAXS patterns observed at different $\phi_p$. Adapted from Reference [172] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>

time self-diffusion in dense colloidal suspensions composed of nanometer sized particles.

## 6.2. Out-of-equilibrium dynamics

Much of the published literature on XPCS over the last decade deals with slow dynamics in arrested colloidal systems such as gels and glasses [10,11]. These arrested systems are also intrinsically more prone to radiation damage due to the accumulation of byproducts of beam interactions in the scattering volume. As a result, such systems may not directly benefit from the higher coherent flux as the beam needs to be significantly attenuated or faster detectors since the dynamics is relatively slow. A common feature among these systems is the compressed exponential decay of $g_2(q, t)$ and weaker $q$-dependence of the relaxation rate corresponding to a hyperdiffusive dynamics, which is often interpreted in terms of dynamical heterogeneities and an internal stress relaxation process [11,31,174–177].

In thermoreversible gelation of colloids consisting of stearyl silica particles in decalin, where particles remain hard-sphere repulsive above a certain temperature and short-range attractive below, a peculiar kinetics was revealed [178]. The gelation time was found to be exponentially dependent on the quench-depth into the attractive regime though the strength of the attraction is nearly the same. This behavior has been attributed to an additional barrier for the gel formation. However, in this interpretation authors have not considered the growth of larger scale domains as a function of the quench-depth [7]. TTCF, $C_I(q, t, \tau)$, and dynamical susceptibility, $\chi_4(q, t)$, form a powerful tool for
the characterization of dynamically arrested systems [10,11]. A controlled study of stress-induced dynamics in a model repulsive colloidal glass found evidence for domains of mobile regions of the order of $10^4$ particles, which move cooperatively displaying an overall stationary dynamics but locally ballistic dynamics [179]. Fig. 13 presents the main results of this study depicting the behavior of $C_I(q, t, \tau)$ and $\chi_4(q, t)$.

Another interesting example is the dynamics during thermally induced gelation of egg-white proteins, which was analyzed by means of $C_I(q, t, \tau)$ and $\chi_4(q, t)$ [176]. The derived relaxation times increased exponentially with time until a steady state characterized by ballistic and heterogeneous dynamics, which was discussed within the framework of a stress-activated process. In another study by the same team, the out-of-equilibrium dynamics during SD of $\gamma$-globulin in a concentrated aqueous polyethylene glycol solution was probed [84]. This system exhibits an arrested-phase separation at deeper temperature quenches manifested by significant slowing down of the dynamics. Once again, an hyperdiffusive dynamics with two relaxation modes was observed, which was interpreted in terms of Cahn-Hilliard simulations. Nevertheless, the simulations did not reproduce the ballistic type dynamics, and it was attributed to the viscoelastic behavior of the system. In a phase separating system, it may be important to consider the advective contribution to the measured $C_I(q, t, \tau)$ [32].

Apart from dynamically arrested suspensions, driven colloids form another class of out-of-equilibrium systems. In this case, the advection becomes more important than diffusion or the dimensionless Peclet number, $Pe \gg 1$. Studies of these systems clearly benefit from higher coherent flux and rapid detectors. Simple examples are colloids subjected to a shear flow and even at a low shear rate, the decay of $g_2(q, t)$ becomes dominated by the Doppler shifts caused by the flow and $g_1(q, t)$ can be factorized in the following form [35],

$$|g_1(\vec{q}, t)|^2 = |g_{1,D}(\vec{q}, t)|^2 |g_{1,T}(\vec{q}, t)|^2 |g_{1,A}(\vec{q}, t)|^2 \quad (4)$$

Where the first term represents diffusive motions, the second term accounts for the transit effect of particles across the beam related to their mean velocity, $v$, and the last term is the advective term due to differences in the Doppler shifts of all particle pairs in the scattering volume, which is determined by the average velocity differences between all particle pairs, $\delta v$ [32]. In principle, Eq. (4) enables to deduce $D_{eff}$, $v$ and $\delta v$. In the case of well-defined shear flows such as in a Couette flow within the annular gap of two concentric cylinders, the exact form of $g_{1,A}(\vec{q}, t)$ can be calculated and good agreement is found with measurements [8,35]. Therefore, XPCS analysis enables to decouple the change in the intrinsic dynamics of the sample from the Doppler shifts

caused by the shear flow (velocity differences) in the measured $g_2(q, t)$. This approach has also been used to probe the evolution of colloid dynamics during sedimentation [180]. The advective term contains information about the homogeneity of the flow and can be used to identify the non-uniformities in the flow-field [181].

Self-propelled colloids are another class of driven systems where the particles derive energy from the surrounding medium and perform directed motion [182]. Different phoretic effects can be used to design self-propelled or active colloids and the diffusiophoresis involving Janus colloids is the most commonly used method. As compared to conventional passive colloids, active colloids execute directed motion in addition to their Brownian diffusion. This enhanced dynamics can be probed by XPCS when the active motion is switched on by a suitable means. A relatively simple case is colloids suspended in a binary liquid mixture where the suspending medium can be made to phase separate and then one of the phases preferentially wets on the particles [32]. This type of phoretic dynamics has been studied in the case of silica and silica-nickel Janus particles suspended in binary mixtures of 3-methylpyridine, water and heavy water [32,183]. In these cases, particle dynamics changed from diffusive to ballistic during the phase separation and then back to diffusive upon coarsening of the phases. The decomposition of $g_2(q, t)$ function enabled to extract $D_{eff}$ and $\delta v$, and dissect the underlying anomalous dynamics [32].

Another convenient method to realize self-propelled motion is by means of Janus particles with a catalytic subunit, which when suspended in a reaction medium display autonomous motion induced by the chemical gradient generated around each particle [182]. Using Janus particles composed of silica spheres with a hemispherical titania (anatase) cap suspended in hydrogen peroxide ($H_2O_2$) solution, the self-phoretic motion can be induced by illumination of ultraviolet (UV) light [182]. XPCS enabled to probe the emergence of this dynamics and derive quantities such as the enhanced diffusion coefficient, $D_e$, $v$, and $\delta v$ depending on both the UV power and the concentration of $H_2O_2$ (fuel) [17]. Fig. 14 presents the steady state dynamics of silica-titania Janus particles dispersed in $H_2O_2$ solution before and after turning on the UV light [17]. In the absence of UV illumination, Fig. 14(a), particles behave as purely Brownian (passive) with an exponential decay of $g_2(q, t)$. Upon UV illumination, the dynamics became much faster (active) with a weaker $q$-dependence as indicated by the compression of the curves in Fig. 14(b) into a narrower time range and the corresponding $g_1(q, t)$ functions are described by Eq. (4).

The above example also illustrates the ability to probe fast dynamics in a dilute sample ($\phi_p \approx 0.0003$) with sufficient scattering contrast. The availability of fast 2D detectors and higher coherent flux enhanced the

<figure><img src="image_16.png" /><figcaption>Fig. 13. (a) The $C_I(q, t, \tau)$ calculated at the peak of S(q) along a narrow horizontal sector. The fluctuations along the diagonal are signs of heterogeneous dynamics. (b) The normalized $g_2(q, t)$ and corresponding $\chi_4(q, t)$ at the peak of S(q). Here $\chi_4(q, t)$ can be related to the fraction of particles moving cooperatively. (c) The $q$-dependence of $\chi_4(q, t)$ displaying a maximum at the peak of S(q), that led to an estimation of number of particles participating in a correlated ballistic motion to be about $10^4$. Reproduced from [179] distributed under Creative Commons Attribution NonCommercial (CC-BY-NC) licence.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Fig. 14.** Typical ensemble averaged $g_1(q, t)$ functions at different $q$ values from silica-titania Janus particles ($R_s \simeq 260$ nm and $\phi_p \simeq 0.0003$) suspended in 8% $H_2O_2$ solution (a) before and (b) after turning on the UV light. The continuous lines are fit curves using Eq. (4) with only the Brownian diffusion term (a) and including the Gaussian distribution of $\delta v$ (b). The main parameters (c) - (e) derived from the analysis. Adapted from Reference [17] distributed under Creative Commons Attribution (CC-BY) licence.</figcaption></figure>

performance of rheo-XPCS [16]. In particular, this offers a renewed perspective for the combination of large amplitude oscillatory shear and XPCS [35] to perform XPCS-echo measurements. The higher time resolution is a major advantage for the analysis of the line shape of the echoes in the measured $g_2(q, t)$ functions and further developing XPCS-echo towards a matured technique for probing the intrinsic dynamics in viscoelastic samples.

## 7. Summary and outlook

The examples presented in the previous sections clearly illustrate that X-ray scattering methods are very powerful to address a variety of issues in colloid science. Since colloidal materials are involved in a large fraction of consumer products in everyday life and industrial processes, a deeper understanding of the interactions and dynamics is important for the rational design and manufacturing of new functional materials with longer-term sustainability. In addition to their significant practical applications, colloids occupy an important role in the broader picture of complex systems as models for fundamental investigations. Indeed, colloids are also very relevant to better understanding of many biological processes, and development of new methodologies in biophysical and medical research. X-ray scattering methods can provide crucial input over a broad range of size and time scales.

The specific cases described in this review mainly comprised bulk studies using X-ray scattering methods. Indeed, analogous grazing-incidence scattering methods can be used to probe colloids at surfaces and interfaces [184]. In particular, for probing in situ assembly and growth processes at buried interfaces [185,186]. These methods also benefit from the advances in synchrotron source brightness and X-ray detector technology [5]. For example, µm scale spatial and millisecond range time resolved X-ray reflectivity measurement from a convexly bent substrate has been demonstrated recently [187]. Similarly, equilibrium dynamics at the interfaces can be probed by XPCS in grazing incidence [9]. This approach enables investigation of particle dynamics

and aging process at buried interfaces such as that between oil and water [188].

Although, real space imaging techniques are fast advancing, scattering methods remain relevant for investigations under in situ and appropriate thermodynamic conditions. Furthermore, the ensemble averaged information is readily obtained, which is important for predicting the macroscopic behavior on the basis of microstructural models. By exploiting the coherence properties of the X-rays, it is also possible to reconstruct the real space images by means of CDI method in limited cases [189]. This technique is useful for obtaining the real space internal structure of particles non-destructively when there is sufficient contrast. However, a serious obstacle for employing high brilliance X-rays is the associated radiation damage that is inherent with many soft and biological materials, especially with imaging methods, which require higher levels of dose than scattering measurements. Nevertheless, the rapid advances in detector technology together with optimized data acquisition strategies help to overcome this limitation and obtain good scattering data prior to the onset of radiation damage in many cases.

The new generation synchrotrons based on multi-bend achromat storage ring lattices (such as the ESRF EBS, APS-U, etc.) have enhanced the brightness by about two orders of magnitude while XFELs have 4–6 orders of magnitude higher peak brightness as compared to the third-generation synchrotrons. The broad range of issues in colloid science may not justify the access to XFEL instruments. As a result, synchrotron facilities are likely to remain the main centers for X-ray investigations of colloidal systems. With extremely brilliant synchrotron sources, the coherent flux at high energies is significantly higher, which is beneficial for probing the dynamics both in the bulk and at buried interfaces by XPCS.

The advances in X-ray instrumentation must be complemented by development of advanced software tools. For instance, scattering experiments are becoming more sophisticated with autonomous control [190,191]. Advanced modeling and computer simulations are indispensable for deriving quantitative structural and dynamical information
from scattering experiments. In this respect, machine learning techniques are likely to be more exploited in the analysis of scattering data in the future [66,69]. In particular, the modern tools in computer science may enable circumventing the limitations imposed by both the “inverse scattering problem” for deriving real space information and approximations involved in liquid-state theories when deducing thermodynamically self-consistent microstructural properties of colloidal suspensions.

### CRediT authorship contribution statement

**Theyencheri Narayanan:** Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing.

### Declaration of competing interest

Author declares that he has no conflict of interest.

### Data availability

Data will be made available on request.

### Acknowledgements

Author is grateful to colleagues A.V. Petukhov, T. Zinn, R. Takahashi, J. Landman, L. Matthews, W. Chevremont, A. Pal and many others whose works have been reproduced here. The ESRF is acknowledged for the financial support and provision of synchrotron beam time. ID02 beamline staff is thanked for technical support.

### References

[1] Hamley IW. Small-angle scattering: Theory, instrumentation, data, and applications. John Wiley & Sons; 2021.

[2] Narayanan T, Wacklin H, Konovalov O, Lund R. Recent applications of synchrotron radiation and neutrons in the study of soft matter. Crystallogr Rev 2017;23(3):160–226.

[3] Li T, Senesi AJ, Lee B. Small angle x-ray scattering for nanoparticle research. Chem Rev 2016;116(18):11128–80.

[4] Willmott P. An introduction to synchrotron radiation: Techniques and applications. John Wiley & Sons; 2019.

[5] Narayanan T, Konovalov O. Synchrotron scattering methods for nanomaterials and soft matter research. Materials 2020;13(3):752.

[6] Jeffries CM, Ilavsky J, Martel A, Hinrichs S, Meyer A, Pedersen JS, et al. Small-angle x-ray and neutron scattering. Nat Rev Methods Prim 2021;1(1):1–39.

[7] Narayanan T. Structure from Diffraction Methods. Wiley Online Library. Small-Angle Scattering 2014:259–324.

[8] Narayanan T, Dattani R, Möller J, Kwaśniewski P. A microvolume shear cell for combined rheology and x-ray scattering experiments. Rev Sci Instrum 2020;91 (8):085102.

[9] Sinha SK, Jiang Z, Lurio LB. X-ray photon correlation spectroscopy studies of surfaces and thin films. Adv Mater 2014;26(46):7764–85.

[10] Madsen A, Fluerasu A, Ruta B. Structural dynamics of materials probed by x-ray photon correlation spectroscopy, in Synchrotron light sources and free-Electron lasers: accelerator physics, instrumentation and science applications. 2020. p. 1989–2018.

[11] Lehmkühler F, Roseker W, Grübel G. From femtoseconds to hours—measuring dynamics over 18 orders of magnitude with coherent x-rays. Appl Sci 2021;11 (13):6179.

[12] Tuukkanen AT, Spilotros A, Svergun DI. Progress in small-angle scattering from biological solutions at high-brilliance synchrotrons. IUCrJ 2017;4(5):518–28.

[13] Eriksson M, Van der Veen JF, Quitmann C. Diffraction-limited storage rings: a window to the science of tomorrow. J Synchrotron Rad 2014;21(5):837–42.

[14] Raimondi P, Carmignani N, Carver L, Chavanne J, Farvacque L, Le Bec G, et al. Commissioning of the hybrid multiband achromat lattice at the European synchrotron radiation facility. Phys Rev Acceler Beams 2021;24(11):110701.

[15] Liu L, Alves M, de Sá F, Farias R, Marques S, Oliveira A, et al. Status of SIRIUS operation. In: 13th international particle accelerator conference (IPAC’22), Bangkok, Thailand; 2022. p. 1385–8.

[16] Narayanan T, Chêvremont W, Zinn T. Small-angle x-ray scattering in the era of fourth-generation light sources. J Appl Cryst 2023;56(4):939–46.

[17] Zinn T, Narayanan T, Kottapalli SN, Sachs J, Sottmann T, Fischer P. Emergent dynamics of light-induced active colloids probed by XPCS. New J Phys 2022;24 (9):093007.

[18] Chushkin Y, Gulotta A, Roosen-Runge F, Pal A, Stradner A, Schurtenberger P. Probing cage relaxation in concentrated protein solutions by x-ray photon correlation spectroscopy. Phys Rev Lett 2022;129(23):238001.

[19] Zhang Q, Dufresne EM, Narayanan S, Maj P, Koziol A, Szczygiel R, et al. Sub-microsecond-resolved multi-speckle x-ray photon correlation spectroscopy with a pixel array detector. J Synchrotron Rad 2018;25(5):1408–16.

[20] Zinn T, Homs A, Sharpnack L, Tinti G, Fröjdh E, Douissard P-A, et al. Ultra-small-angle x-ray photon correlation spectroscopy using the Eiger detector. J Synchrotron Rad 2018;25(6):1753–9.

[21] Dallari F, Jain A, Sikorski M, Möller J, Bean R, Bösenberg U, et al. Microsecond hydrodynamic interactions in dense colloidal dispersions probed at the European XFEL. IUCrJ 2021;8(5):775–83.

[22] Nielsen JE, Koynarev VR, Lund R. Peptide meets membrane: investigating peptide-lipid interactions using small-angle scattering techniques. Curr Opin Colloid Interface Sci 2023;101709.

[23] Semeraro EF, Devos JM, Porcar L, Forsyth VT, Narayanan T. In vivo analysis of the escherichia coli ultrastructure by small-angle scattering. IUCrJ 2017;4(6): 751–7.

[24] Akiba I, Sakurai K. Characterizing block-copolymer micelles used in nanomedicines via solution static scattering techniques. Polym J 2021;53(9): 951–73.

[25] Ilavsky J, Zhang F, Andrews RN, Kuzmenko I, Jemian PR, Levine LE, et al. Development of combined microstructure and structure characterization facility for in situ and operando studies at the advanced photon source. J Appl Cryst 2018;51(3):867–82.

[26] Narayanan T, Sztucki M, Van Vaerenbergh P, Léonardon J, Gorini J, Claustre L, et al. A multipurpose instrument for time-resolved ultra-small-angle and coherent x-ray scattering. J Appl Cryst 2018;51(6):1511–24.

[27] Petukhov AV, Meijer J-M, Vroege GJ. Particle shape effects in colloidal crystals and colloidal liquid crystals: small-angle x-ray scattering studies with microradiorial resolution. Curr Opin Colloid Interface Sci 2015;20(4):272–81.

[28] Kishimoto H, Shinohara Y, Suzuki Y, Takeuchi A, Yagi N, Amemiya Y. Pinhole-type two-dimensional ultra-small-angle x-ray scattering on the micrometer scale. J Synchrotron Rad 2014;21(1):1–4.

[29] Narayanan T, Sztucki M, Zinn T, Kieffer J, Homs-Puron A, Gorini J, et al. Performance of the time-resolved ultra-small-angle x-ray scattering beamline with the extremely brilliant source. J Appl Cryst 2022;55(1):98–111.

[30] Cristofolini L. Synchrotron x-ray techniques for the investigation of structures and dynamics in interfacial systems. Curr Opin Colloid Interface Sci 2014;19(3): 228–41.

[31] Pal A, Zinn T, Kamal MA, Narayanan T, Schurtenberger P. Anomalous dynamics of magnetic anisotropic colloids studied by XPCS. Small 2018;14(46):1802233.

[32] Zinn T, Sharpnack L, Narayanan T. Phoretic dynamics of colloids in a phase separating critical liquid mixture. Phys Rev Res 2020;2(3):033177.

[33] Weckert E. The potential of future light sources to explore the structure and function of matter. IUCrJ 2015;2(2):230–45.

[34] Raimondi P, Liuzzo SM. Toward a diffraction limited light source. Phys Rev Acceler Beams 2023;26(2):021601.

[35] Leheny RL, Rogers MC, Chen K, Narayanan S, Harden JL. Rheo-XPCS. Curr Opin Colloid Interface Sci 2015;20(4):261–71.

[36] Nakaye Y, Sakumura T, Sakuma Y, Mikusu S, Dawiec A, Orsini F, et al. Characterization and performance evaluation of the XSPA-500k detector using synchrotron radiation. J Synchrotron Rad 2021;28(2):439–47.

[37] Llopart X, Alozy J, Ballabriga R, Campbell M, Casanova R, Gromov V, et al. Timepix4, a large area pixel detector readout chip which can be tiled on 4 sides providing sub-200 ps timestamp binning. J Instrum 2022;17(01):C01044.

[38] Donath T, Síšak Jung D, Burian M, Radicci V, Zambon P, Fitch AN, et al. EIGER2 hybrid-photon-counting x-ray detectors for advanced synchrotron diffraction experiments. J Synchrotron Rad 2023;30(4).

[39] Chêvremont W, Zinn T, Narayanan T. Improvement of ultra-small-angle XPCS with the extremely brilliant source. J Synchrotron Rad 2024;31(1):65–76.

[40] Feng J, Kriechbaum M, Liu L. In situ capabilities of small angle x-ray scattering. Nanotechnol Rev 2019;8(1):352–69.

[41] Matthews L, Narayanan T. Advances in synchrotron scattering methods for probing the self-assembly pathways in dilute surfactant solutions. Colloid Polym Sci 2023;301:721–8.

[42] Brooks NJ, Seddon JM. High pressure x-ray studies of lipid membranes and lipid phase transitions. Z Phys Chem 2014;228(10–12):987–1004.

[43] Ghazal A, Lafleur JP, Mortensen K, Kutter JP, Arleth L, Jensen GV. Recent advances in x-ray compatible microfluidics for applications in soft materials and life sciences. Lab Chip 2016;16(22):4263–95.

[44] Silva BF. SAXS on a chip: from dynamics of phase transitions to alignment phenomena at interfaces studied with microfluidic devices. Phys Chem Chem Phys 2017;19(35):23690–703.

[45] Yaghmur A, Hamad I. Microfluidic nanomaterial synthesis and in situ SAXS, WAXS, or SANS characterization: manipulation of size characteristics and online elucidation of dynamic structural transitions. Molecules 2022;27(14):4602.

[46] Hong L, Sesen M, Hawley A, Neild A, Spicer PT, Boyd BJ. Comparison of bulk and microfluidic methods to monitor the phase behaviour of nanoparticles during digestion of lipid-based drug formulations using in situ x-ray scattering. Soft Matter 2019;15(46):9565–78.

[47] Merkens S, Vakili M, Sánchez-Iglesias A, Litti L, Gao Y, Gwodz PV, et al. Time-resolved analysis of the structural dynamics of assembling gold nanoparticles. ACS Nano 2019;13(6):6596–604.

[48] Zielinski KA, Katz AM, Calvey GD, Pabit SA, Milano SK, Aplin C, et al. Chaotic advection mixer for capturing transient states of diverse biological
macromolecular systems with time-resolved small-angle x-ray scattering. *IUCrJ* 2023;10(3):363–75.

[49] Rosén T, Wang R, He H, Zhan C, Chodankar S, Hsiao BS. Shear-free mixing to achieve accurate temporospatial nanoscale kinetics through scanning-SAXS: ion-induced phase transition of dispersed cellulose nanocrystals. Lab Chip 2021;21 (6):1084–95.

[50] Kirby N, Cowieson N, Hawley AM, Mudie ST, McGillray DJ, Kusel M, et al. Improved radiation dose efficiency in solution SAXS using a sheath flow sample environment. Acta Cryst Sect D: Struct Biol 2016;72(12):1254–66.

[51] Marinaro G, Graceffa R, Riekel C. Wall-free droplet microfluidics for probing biological processes by high-brilliance x-ray scattering techniques. Front Mol Biosci 2022;9:1049327.

[52] Kapuscinski M, Agthe M, Lv Z-P, Liu Y, Segad M, Bergström L. Temporal evolution of superlattice contraction and defect-induced strain anisotropy in mesocrystals during nanocube self-assembly. ACS Nano 2020;14(5):5337–47.

[53] Pignon F, Semeraro EF, Chèvremont W, Bodiguel H, Hengl N, Karrouch M, et al. Orientation of cellulose nanocrystals controlled in perpendicular directions by combined shear flow and ultrasound waves studied by small-angle x-ray scattering. J Phys Chem C 2021;125(33):18409–19.

[54] Wieser PA, Moser D, Gollas B, Amenitsch H. Monitoring of pore orientation by in operando grazing incidence small-angle x-ray scattering during templated electrodeposition of mesoporous pt films. ACS Appl Mater Interfaces 2023;15 (40):47604–14.

[55] Franke D, Petoukhov M, Konarev P, Panjkovich A, Tuukkanen A, Mertens H, et al. ATAS 2.8: a comprehensive data analysis suite for small-angle scattering from macromolecular solutions. J Appl Cryst 2017;50(4):1212–25.

[56] Shih O, Liao K-F, Yeh Y-Q, Su C-J, Wang C-A, Chang J-W, et al. Performance of the new biological small-and wide-angle x-ray scattering beamline 13A at the Taiwan photon source. J Appl Cryst 2022;55(2):340–52.

[57] Zhang Q, Dufresne EM, Nakaye Y, Jemian PR, Sakumura T, Sakuma Y, et al. 20 µs-resolved high-throughput x-ray photon correlation spectroscopy on a 500k pixel detector enabled by data-management workflow. J Synchrotron Rad 2021; 28(1):259–65.

[58] Vogt K, Beaucage G, Rishi K, Jiang H, Mulderig A. Hierarchical approach to aggregate equilibria. Phys Rev Res 2019;1(3):033081.

[59] Kohlbrecher J, Breßler I. Updates in SASfit for fitting analytical expressions and numerical models to small-angle scattering patterns. J Appl Cryst 2022;55(6): 1677–88.

[60] Doucet M, Cho J, Alina G, Bakker J, Bouwman W, Butler P, et al. SasView. https://www.sasview.org/; 2018.

[61] Biehl R. Jscatter, a program for evaluation and analysis of experimental data. PLoS One 2019;14(6):e0218789.

[62] Spinozzi F, Ferrero C, Ortove MG, De Maria Antolinos A, Mariani P. GENFIT: software for the analysis of small-angle x-ray and neutron scattering data of macromolecules in solution. J Appl Cryst 2014;47(3):1132–9.

[63] Ginsburg A, Ben-Nun T, Asor R, Shemesh A, Fink L, Tekoah R, et al. D+: software for high-resolution hierarchical modeling of solution x-ray scattering from complex structures. J Appl Cryst 2019;52(1):219–42.

[64] Martin TB, Gartner III TE, Jones RL, Snyder CR, Jayaraman A. pyPRISM: a computational tool for liquid-state theory calculations of macromolecular materials. Macromolecules 2018;51(8):2906–22.

[65] Beltran-Villegas DJ, Wessels MG, Lee JY, Song Y, Wooley KL, Pochan DJ, et al. Computational reverse-engineering analysis for scattering experiments on amphipathic block polymer solutions. J Am Chem Soc 2019;141(37):14916–30.

[66] Wessels MG, Jayaraman A. Machine learning enhanced computational reverse engineering analysis for scattering experiments (CREASE) to determine structures in amphipathic polymer solutions. ACS Polym Au 2021;1(3):153–64.

[67] Wessels MG, Jayaraman A. Computational reverse-engineering analysis of scattering experiments (CREASE) on amphipathic block polymer solutions: cylindrical and fibrillar assembly. Macromolecules 2021;54(2):783–96.

[68] Chang M-C, Tung C-H, Chang S-Y, Carrillo JM, Wang Y, Sumpter BG, et al. A machine learning inversion scheme for determining interaction from scattering. Commun Phys 2022;5(1):46.

[69] Heil CM, Ma Y, Bharti B, Jayaraman A. Computational reverse-engineering analysis for scattering experiments for form factor and structure factor determination (“P(q) and S(q) CREASE”). JACS Au 2023;3(3):889–904.

[70] Lombardo D, Calandra P, Kiselev MA. Structural characterization of biomaterials by means of small angle x-rays and neutron scattering (SAXS and SANS), and light scattering experiments. Molecules 2020;25(23):5624.

[71] Allen AJ. Selected advances in small-angle scattering and applications they serve in manufacturing, energy and climate change. J Appl Cryst 2023;56(3):787–800.

[72] Pauw BR, Smith AJ, Snow T, Shebanova O, Sutter JP, Ilavsky J, et al. Extending synchrotron SAXS instrument ranges through addition of a portable, inexpensive USAXS module with vertical rotation axes. J Synchrotron Rad 2021;28(3): 824–33.

[73] Ishige R, Williams GA, Higaki Y, Ohta N, Sato M, Takahara A, et al. In situ ultra-small-angle x-ray scattering study under uniaxial stretching of colloidal crystals prepared by silica nanoparticles bearing hydrogen-bonding polymer grafts. *IUCrJ* 2016;3(3):211–8.

[74] Ouhajji S, Landman J, Prévost S, Jiang L, Philipse AP, Petukhov AV. In situ observation of self-assembly of sugars and surfactants from nanometres to microns. Soft Matter 2017;13(13):2421–5.

[75] Wu C, Xie Q, Xu W, Tu M, Jiang L. Lattice self-assembly of cyclodextrin complexes and beyond. Curr Opin Colloid Interface Sci 2019;39:76–85.

[76] Landman J, Ouhajji S, Prévost S, Narayanan T, Groenewold J, Philipse AP, et al. Inward growth by nucleation: multiscale self-assembly of ordered membranes, Sci. Adv 2018;4(6):eaat1817.

[77] Duarte H, Gummel J, Robles E, Berti D, Fratini E. Ultra-/small angle x-ray scattering (USAXS/SAXS) and static light scattering (SLS) modeling as a tool to determine structural changes and effect on growth in s. epidermidis. ACS Appl Bio Mater 2022;5(8):3703–12.

[78] Semeraro EF, Marx L, Mandl J, Frewein MP, Scott HL, Prévost S, et al. Evolution of the analytical scattering model of live escherichia coli. J Appl Cryst 2021;54 (2):473–85.

[79] Semeraro EF, Marx L, Mandl J, Letofsky-Papst I, Mayrhofer C, Frewein MP, et al. Lactoferricins impair the cytosolic membrane of escherichia coli within a few seconds and accumulate inside the cell. Elife 2022;11:e72850.

[80] Takahashi R, Narayanan T, Sato T. Growth kinetics of polyelectrolyte complexes formed from oppositely-charged homopolymers studied by time-resolved ultra-small-angle x-ray scattering. J Phys Chem Lett 2017;8(4):737–41.

[81] Matsarskaia O, Da Vela S, Mariani A, Fu Z, Zhang F, Schreiber F. Phase-separation kinetics in protein-salt mixtures with compositionally tuned interactions. J Phys Chem B 2019;123(9):1913–9.

[82] Da Vela S, Begam N, Dyachok D, Schäuferle RS, Matsarskaia O, Braun MK, et al. Interplay between glass formation and liquid-liquid phase separation revealed by the scattering invariant. J Phys Chem Lett 2020;11(17):7273–8.

[83] Banc A, Pincemaille J, Costanzo S, Chauveau E, Appavou M-S, Morel M-H, et al. Phase separation dynamics of gluten protein mixtures. Soft Matter 2019;15(30): 6160–70.

[84] Girelli A, Rahmann H, Begam N, Ragulskaya A, Reiser M, Chandran S, et al. Microscopic dynamics of liquid-liquid phase separation and domain coarsening in a protein solution revealed by x-ray photon correlation spectroscopy. Phys Rev Lett 2021;126(13):138004.

[85] Gibaud T, Dagès N, Lidon P, Jung G, Ahouré LC, Sztucki M, et al. Rheoacoustic gels: tuning mechanical and flow properties of colloidal gels with ultrasonic vibrations. Phys Rev X 2020;10(1):011028.

[86] Keshavarz B, Rodrigues DG, Champenois J-B, Frith MG, Ilavsky J, Geri M, et al. Time-connectivity superposition and the gel/glass duality of weak colloidal gels. Proc Natl Acad Sci 2021;118(15). e202239118.

[87] Dagès N, Bouthier LV, Matthews L, Manneville S, Divoux T, Poulesquen A, et al. Interpenetration of fractal clusters drives elasticity in colloidal gels formed upon flow cessation. Soft Matter 2022;18(35):6645–59.

[88] Baglioni M, Mastrangelo R, Tempesti P, Ogura T, Baglioni P. Cryogels loaded with nanostructured fluids studied by ultra-small-angle x-ray scattering. Colloids Surf A Physicochem Eng Asp 2023;660:130857.

[89] Chen D, Kuzmenko I, Ilavsky J, Pinho L, Campanella O. Structural evolution during gelation of pea and whey proteins envisaged by time-resolved ultra-small-angle x-ray scattering (USAXS). Food Hydrocol 2022;126:107449.

[90] Song J, Rizvi MH, Lynch BB, Ilavsky J, Mankus D, Tracy JB, et al. Programmable anisotropy and percolation in supramolecular patchy particle gels. ACS Nano 2020;14(12):17018–27.

[91] Keidel R, Ghavami A, Lugo DM, Lotze G, Virtanen O, Beumers P, et al. Time-resolved structural evolution during the collapse of responsive hydrogels: the microgel-to-particle transition, Sci. Adv 2018;4(4):eaa07086.

[92] Lee Y-T, Li DS, Ilavsky J, Kuzmenko I, Jeng G-S, O'Donnell M, et al. Ultrasound-based formation of nano-Pickering emulsions investigated via in-situ SAXS. J Colloid Interface Sci 2019;536:281–90.

[93] Matthews L, Narayanan T. High-resolution structural elucidation of extremely swollen lyotropic phases. J Colloid Interface Sci 2022;610:359–67.

[94] Gradzielski M, Duvail M, de Molina PM, Simon M, Talmon Y, Zemb T. Using microemulsions: formulation based on knowledge of their mesostructure. Chem Rev 2021;121(10):5671–740.

[95] Dodero A, Djeghdi K, Bauernfeind V, Airoldi M, Wilts BD, Weder C, et al. Robust full-spectral color tuning of photonic colloids. Small 2023;19(6):2205438.

[96] Laporte L, Ducouret G, Gobeaux F, Lesaine A, Hotton C, Bizien T, et al. Rheo-SAXS characterization of lead-treated oils: understanding the influence of lead driers on artistic oil paint's flow properties. J Colloid Interface Sci 2023;633: 566–74.

[97] Pignon F, Challamel M, De Geyer A, Elchamaa M, Semeraro EF, Hengl N, et al. Breakdown and buildup mechanisms of cellulose nanocrystal suspensions under shear and upon relaxation probed by SAXS and SALS. Carbohydr Polym 2021; 260:117751.

[98] Shim YH, Ahn H, Lee S, Kim SO, Kim SY. Universal alignment of graphene oxide in suspensions and fibers. ACS Nano 2021;15(8):13453–62.

[99] Akada K, Okubo S, Yamada T, Tokuda K, Yamaguchi K, Uemura S, et al. Anisotropic flocculation in shear thickening colloid-polymer suspension via simultaneous observation of rheology and x-ray scattering. Colloids Surf A Physicochem Eng Asp 2023;658:130727.

[100] Narayanan T, Gummel J, Gradzielski M. Probing the self-assembly of unilamellar vesicles using time-resolved SAXS. In: Advances in planar lipid bilayers and liposomes. vol. 20. Elsevier; 2014. p. 171–96.

[101] Fan Y, Wang Y. Applications of small-angle x-ray scattering/small-angle neutron scattering and cryogenic transmission electron microscopy to understand self-assembly of surfactants. Curr Opin Colloid Interface Sci 2019;42:1–16.

[102] Jensen GV, Lund R, Narayanan T, Pedersen JS. Transformation from globular to cylindrical mixed micelles through molecular exchange that induces micelle fusion. J Phys Chem Lett 2016;7(11):2039–43.

[103] Takahashi R, Kawauchi H, Kameta N, Lee JH, Fujii S, Shimizu T, et al. Observing the kinetic pathway of nanotube formation from bolaamphiphiles by time-resolved small-angle x-ray scattering. J Phys Chem B 2019;123(19):4340–5.
[104] Jensen GV, Lund R, Gummel J, Narayanan T, Pedersen JS. Monitoring the transition from spherical to polymer-like surfactant micelles using small-angle x-ray scattering. Angew Chem 2014;126(43):11708-12.

[105] Schäfer K, Kolli HB, Killingmoe Christensen M, Bore SL, Diezemann G, Gauss J, et al. Supramolecular packing drives morphological transitions of charged surfactant micelles. Angew Chem 2020;132(42):18750-7.

[106] Jensen GV, Lund R, Gummel J, Monkenbusch M, Narayanan T, Pedersen JS. Direct observation of the formation of surfactant micelles under nonisothermal conditions by synchrotron SAXS. J Am Chem Soc 2013;135(19):7214-22.

[107] Lund R, Willner L, Richter D. Kinetics of Block Copolymer Micelles Studied by Small-angle Scattering Methods, Controlled Polymerization and Polymeric Structures: Flow Microreactor polymerization, Micelles Kinetics, Polypeptide Ordering, Light emitting Nanostructures. 2013. p. 51-158.

[108] Kalkowski J, Liu C, Leon-Plata P, Szymusiak M, Zhang P, Irving T, et al. In situ measurements of polymer micellization kinetics with millisecond temporal resolution. Macromolecules 2019;52(9):3151-7.

[109] Brotherton EE, Hatton FL, Cockram AA, Derry MJ, Czajka A, Cornel EJ, et al. In situ small-angle x-ray scattering studies during reversible addition-fragmentation chain transfer aqueous emulsion polymerization. J Am Chem Soc 2019;141(34): 13664-75.

[110] Czajka A, Armes SP. Time-resolved small-angle x-ray scattering studies during aqueous emulsion polymerization. J Am Chem Soc 2021;143(3):1474-84.

[111] Marras AE, Ting JM, Stevens KC, Tirrell MV. Advances in the structural design of polyelectrolyte complex micelles. J Phys Chem B 2021;125(26):7076-89.

[112] Amann M, Diget JS, Lyngsø J, Pedersen JS, Narayanan T, Lund R. Kinetic pathways for polyelectrolyte coacervate micelle formation revealed by time-resolved synchrotron SAXS. Macromolecules 2019;52:8227-37.

[113] Wu H, Ting JM, Yu B, Jackson NE, Meng S, De Pablo JJ, et al. Spatiotemporal formation and growth kinetics of polyelectrolyte complex micelles with millisecond resolution. ACS Macro Lett 2020;9(11):1674-80.

[114] Takahashi R, Narayanan T, Yusa S-I, Sato T. Kinetics of morphological transition between cylindrical and spherical micelles in a mixture of anionic-neutral and cationic-neutral block copolymers studied by time-resolved SAXS and USAXS. Macromolecules 2018;51(10):3654-62.

[115] Takahashi R, Narayanan T, Yusa S-I, Sato T. Formation kinetics of polymer vesicles from spherical and cylindrical micelles bearing the polyelectrolyte complex core studied by time-resolved USAXS and SAXS. Macromolecules 2022; 55(2):684-95.

[116] Bjornestad VA, Lund R. Pathways of membrane solubilization: a structural study of model lipid vesicles exposed to classical detergents. Langmuir 2023;39(11): 3914-33.

[117] Bjornestad VA, Soto-Bustamante F, Tria G, Laurati M, Lund R. Beyond the standard model of solubilization: non-ionic surfactants induce collapse of lipid vesicles into rippled bilamellar nanodiscs. J Colloid Interface Sci 2023;641: 553-67.

[118] Geisler R, Pedersen MC, Preisig N, Hannappel Y, Prévost S, Dattani R, et al. Aescin—a natural soap for the formation of lipid nanodiscs with tunable size. Soft Matter 2021;17(7):1888-900.

[119] Royes J, Bjornestad V, Brun G, Narayanan T, Lund R, Tribet C. Transition kinetics of mixed lipid: photosurfactant assemblies studied by time-resolved small angle x-ray scattering. J Colloid Interface Sci 2022;610:830-41.

[120] Trewella J. Recent advances in small-angle scattering and its expanding impact in structural biology. Structure 2022;30(1):15-23.

[121] Tants J-N, Schlundt A. Advances, applications, and perspectives in small-angle x-ray scattering of RNA. ChemBioChem 2023;24:e202300110.

[122] Raviv U, Asor R, Shemesh A, Ginsburg A, Ben-Nun T, Schilt Y, et al. Insight into structural biophysics from solution x-ray scattering. J Struct Biol 2023;215: 108029.

[123] Asor R, Schlicksup CJ, Zhao Z, Zlotnick A, Raviv U. Rapidly forming early intermediate structures dictate the pathway of capsid assembly. J Am Chem Soc 2020;142(17):7868-82.

[124] Chevreuil M, Lecoq L, Wang S, Gargowitsch L, Nhiri N, Jacquet E, et al. Nonsymmetrical dynamics of the HBV capsid assembly and disassembly evidenced by their transient species. J Phys Chem B 2020;124(45):9987-95.

[125] Oliver RC, Potrzebowski W, Najibi SM, Pedersen MN, Arleth L, Mahmoudi N, et al. Assembly of capsids from hepatitis B virus core protein progresses through highly populated intermediates in the presence and absence of RNA. ACS Nano 2020;14(8):10226-38.

[126] Kra K, Li S, Gargowitsch L, Degrouard J, Pérez J, Zandi R, et al. Energetics and kinetic assembly pathways of hepatitis B virus capsids in the presence of antivirals. ACS Nano 2023;17:12723-33.

[127] Dharan R, Shemesh A, Millgram A, Zalk R, Frank GA, Levi-Kalisman Y, et al. Hierarchical assembly pathways of spermine-induced tubulin conical-spiral architectures. ACS Nano 2021;15(5):8836-47.

[128] Shemesh A, Ginsburg A, Dharan R, Levi-Kalisman Y, Ringel I, Raviv U. Mechanism of tubulin oligomers and single-ring disassembly catastrophe. J Phys Chem Lett 2022;13(23):5246-52.

[129] Narayanan T, Rüter A, Olsson U. Multiscale structural elucidation of peptide nanotubes by x-ray scattering methods. Front Bioeng Biotechnol 2021;9:654339.

[130] Hamley IW, Castelletto V. Small-angle scattering techniques for peptide and peptide hybrid nanostructures and peptide-based biomaterials. Adv Colloid Interf Sci 2023;318:102959.

[131] Pedersen JN, Lyngsø J, Zinn T, Otzen DE, Pedersen JS. A complete picture of protein unfolding and refolding in surfactants. Chem Sci 2020;11(3):699-712.

[132] Prins PT, Montanarella F, Dümbgen K, Justo Y, Van Der Bok JC, Hinterding SO, et al. Extended nucleation and superfocusing in colloidal semiconductor nanocrystal synthesis. Nano Lett 2021;21(6):2487-96.

[133] Abécassis B, Greenberg MW, Bal V, McMurtry BM, Campos MP, Guillemeny L, et al. Persistent nucleation and size dependent attachment kinetics produce monodisperse PbS nanocrystals. Chem Soc 2022;13(17):4977-83.

[134] Prins PT, van Der Bok JC, van Swieten TP, Hinterding SO, Smith AJ, Petukhov AV, et al. The formation of NaYF₄: Er³⁺, Yb³⁺ nanocrystals studied by in situ x-ray scattering: phase transition and size focusing. Angew Chem Int Ed 2023;62(28):e202305086.

[135] Fleury B, Neouze M-A, Guigner J-M, Menguy N, Spalla O, Gacoin T, et al. Amorphous to crystal conversion as a mechanism governing the structure of luminescent YVO₄: Eu nanoparticles. ACS Nano 2014;8(3):2602-8.

[136] Durelle M, Charton S, Gobeaux F, Chevallard C, Belloni L, Testard F, et al. Coexistence of transient liquid droplets and amorphous solid particles in nonclassical crystallization of cerium oxalate. J Phys Chem Lett 2022;13(36): 8502-8.

[137] Pokratath R, Lermusiaux L, Checchia S, Mathew JP, Cooper SR, Mathiesen JK, et al. An amorphous phase precedes crystallization: unraveling the colloidal synthesis of zirconium oxide nanocrystals. ACS Nano 2023;17(9):8796-806.

[138] Zhang F. Nonclassical nucleation pathways in protein crystallization. J Phys Condens Matter 2017;29(44):443002.

[139] Wang J, Seifert S, Winans RE, Tolmachoff E, Xin Y, Chen D, et al. In situ x-ray scattering and dynamical modeling of pd catalyst nanoparticles formed in flames. J Phys Chem C 2015;119(33):19073-82.

[140] Michelsen HA, Campbell MF, Tran IC, Johansson KO, Schrader PE, Bambha RP, et al. Distinguishing gas-phase and nanoparticle contributions to small-angle x-ray scattering in reacting aerosol flows. Chem Eur J 2022;126(19):3015-26.

[141] Bauer P, Amenitsch H, Baumgartner B, Köberl G, Rentenberger C, Winkler P. In-situ aerosol nanoparticle characterization by small angle x-ray scattering at ultra-low volume fraction. Nat Commun 2019;10(1):1122.

[142] Shoshani Y, Jerby E. Microwave-ignited dc-plasma ejection from basalt: powder-generation and lightning-like effects. Appl Phys Lett 2022;120(26):264101.

[143] Nakanishi Y, Ishige R, Ogawa H, Sakakibara K, Ohno K, Morinaga T, et al. USAXS analysis of concentration-dependent self-assembling of polymer-brush-modified nanoparticles in ionic liquid: [I] concentrated-brush regime. J Chem Phys 2018; 148(12):124902.

[144] Shabalin A, Meijer J-M, Dronyak R, Yefanov O, Singer A, Kurta R, et al. Revealing three-dimensional structure of an individual colloidal crystal grain by coherent x-ray diffractive imaging. Phys Rev Lett 2016;117(13):138002.

[145] Calcaterra HA, Zheng CY, Seifert S, Yao Y, Jiang Y, Mirkin CA, et al. Hints of growth mechanism left in supercrystals. ACS Nano 2023;17(16):15999-6007.

[146] Meijer J-M, Pal A, Ouhajji S, Lekkerkerker HN, Philipse AP, Petukhov AV. Observation of solid-solid transitions in 3d crystals of colloidal superballs. Nat Commun 2017;8:14352.

[147] Davidson P, Penisson C, Constantin D, Gabriel J-CP. Isotropic, nematic, and lamellar phases in colloidal suspensions of nanosheets. Proc Natl Acad Sci 2018; 115(26):6662-7.

[148] Zákučná D, Falke Y, Dresen D, Prévost S, Bender P, Honecker D, et al. Morphological and crystallographic orientation of hematite spindles in an applied magnetic field. Nanoscale 2019;11(15):7149-56.

[149] Pal A, De Filippo CA, Ito T, Kamal MA, Petukhov AV, De Michele C, et al. Shape matters in magnetic-field-assisted assembly of prolate colloids. ACS Nano 2022;16 (2):2558-68.

[150] Eliseev AA, Eliseev AA, Trusov LA, Chumakov AP, Boeseck P, Anokhin EO, et al. Rotational dynamics of colloidal hexaferrite nanoplates. Appl Phys Lett 2018;113(11):113106.

[151] Schulz F, Lokteva I, Parak WJ, Lehmkühler F. Recent notable approaches to study self-assembly of nanoparticles with x-ray scattering and electron microscopy. Part Part Syst Charact 2021;38(9):2100087.

[152] Lokteva I, Koof M, Walther M, Grübel G, Lehmkühler F. Coexistence of hcp and bct phases during in situ superlattice assembly from faceted colloidal nanocrystals. J Phys Chem Lett 2019;10(20):6331-8.

[153] Di A, Xu J, Zinn T, Sztucki M, Deng W, Ashok A, et al. Tunable ordered nanostructured phases by co-assembly of amphiphilic polyoxometalates and pluronic block copolymers. Nano Lett 2023;23(5):1645-51.

[154] Angelova A, Garamus VM, Angelov B, Tian Z, Li Y, Zou A. Advances in structural design of lipid-based nanoparticle carriers for delivery of macromolecular drugs, phytochemicals and anti-tumor agents. Adv Colloid Interf Sci 2017;249:331-45.

[155] Ghezzi M, Pescina S, Padula C, Santi P, Del Favero E, Cantù L, et al. Polymeric micelles in drug delivery: an insight of the techniques for their characterization and assessment in biorelevant conditions. J Control Release 2021;332:312-36.

[156] Cheung E, Xia Y, Caporini MA, Gilmore JL. Tools shaping drug discovery and development. Biophys Rev 2022;3(3):031301.

[157] Kulkarni CV, Yaghmur A, Steinhart M, Kriechbaum M, Rappolt M. Effects of high pressure on internally self-assembled lipid nanoparticles: a synchrotron small-angle x-ray scattering (SAXS) study. Langmuir 2016;32(45):11907-17.

[158] Sreij R, Prévost S, Dargel C, Dattani R, Hertle Y, Wrede O, et al. Interaction of the saponin aescin with ibuprofen in dmpc model membranes. Mol Pharm 2018;15 (10):4446-61.

[159] Yu H, Angelova A, Angelov B, Dyett B, Matthews L, Zhang Y, et al. Real-time pH-dependent self-assembly of ionisable lipids from COVID-19 vaccines and in situ nucleic acid complexation. Angew Chem 2023;135:e202304977.

[160] Aburai K, Hatanaka K, Takano S, Fujii S, Sakurai K. Characterizing an sirna-containing lipid-nanoparticle prepared by a microfluidic reactor: small-angle x-
ray scattering and cryotransmission electron microscopic studies. Langmuir 2020; 36(42):12545-54.

[161] Gilbert EP. Small-angle x-ray and neutron scattering in food colloids. Curr Opin Colloid Interface Sci 2019;42:55-72.

[162] Sun Y, Li X, Chen R, Liu F, Wei S. Recent advances in structural characterization of biomacromolecules in foods via small-angle x-ray scattering. Front Nutr 2022; 9:1039762.

[163] Smith GN, Brok E, Christiansen MV, Ahrné L. Casein micelles in milk as sticky spheres. Soft Matter 2020;16(43):9955-63.

[164] Day L, Raynes J, Leis A, Liu L, Williams R. Probing the internal and external micelle structures of differently sized casein micelles from individual cows milk by dynamic light and small-angle x-ray scattering. Food Hydrocoll 2017;69: 150-63.

[165] Berkowicz S, Das S, Reiser M, Filianina M, Bin M, Crevatin G, et al. Nanofocused x-ray photon correlation spectroscopy. Phys Rev Res 2022;4(3):L032012.

[166] Vodnala P, Karunaratne N, Lurio L, Thurston GM, Vega M, Gaillard E, et al. Hard-sphere-like dynamics in highly concentrated alpha-crystallin suspensions. Phys Rev E 2018;97(2):020601.

[167] Otto F, Sun X, Schulz F, Sanchez-Cano C, Feliu N, Westermeier F, et al. X-ray photon correlation spectroscopy towards measuring nanoparticle diameters in biological environments allowing for the in situ analysis of their bio-nano interface. Small 2022;18(37):2201324.

[168] Switalski K, Fan J, Li L, Chu M, Sarnello E, Jemian P, et al. Direct measurement of stokes-einstein diffusion of cowpea mosaic virus with 19 µs-resolved XPCS. J Synchrotron Rad 2022;29(6):1429-35.

[169] Matthews L, Narayanan T. Structural and dynamical aspects of extremely swollen lyotropic phases. Colloids Surf A Physicochem Eng Asp 2022;649:129409.

[170] Pal A, Kamal MA, Zinn T, Dhont JK, Schurtenberger P. Anisotropic dynamics of magnetic colloidal cubes studied by x-ray photon correlation spectroscopy. Phys Rev Mater 2021;5(3):035603.

[171] Pal A, Kamal MA, Holmqvist P, Schurtenberger P. Structure and dynamics of dense colloidal ellipsoids at the nearest-neighbor length scale. Phys Rev Res 2021; 3(2):023254.

[172] Pal A, Kamal MA, Schurtenberger P. Structure and anisotropic dynamics of stimuli responsive colloidal ellipsoids at the nearest neighbor length scale. J Colloid Interface Sci 2022;621:352-9.

[173] Zinn T, Sharpnack L, Narayanan T. Dynamics of magnetic janus colloids studied by ultra small-angle x-ray photon correlation spectroscopy. Soft Matter 2023;19 (13):2311-8.

[174] Chen Y, Rogers SA, Narayanan S, Harden JL, Leheny RL. Microscopic dynamics of stress relaxation in a nanocolloidal soft glass. Phys Rev Mater 2020;4(3):035602.

[175] Jain A, Schulz F, Lokteva I, Frenzel L, Grübel G, Lehmkuhler F. Anisotropic and heterogeneous dynamics in an aging colloidal gel. Soft Matter 2020;16(11): 2864-72.

[176] Begam N, Ragulskaya A, Girelli A, Rahmann H, Chandran S, Westermeier F, et al. Kinetics of network formation and heterogeneous dynamics of an egg white gel revealed by coherent x-ray scattering. Phys Rev Lett 2021;126(9):098001.

[177] Xi Y, Murphy RP, Zhang Q, Zemborain A, Narayanan S, Chae J, et al. Rheology and dynamics of a solvent segregation driven gel (seedgel). Soft Matter 2023;19 (2):233-44.

[178] Zhang Q, Bahadur D, Dufresne EM, Grybos P, Kmon P, Leheny RL, et al. Dynamic scaling of colloidal gel formation at intermediate concentrations. Phys Rev Lett 2017;119(17):178006.

[179] Dallari F, Martinelli A, Caporaletti F, Sprung M, Grübel G, Monaco G. Microscopic pathways for stress relaxation in repulsive colloidal glasses, Sci. Adv 2020;6(12): eaaz2982.

[180] Möller J, Narayanan T. Velocity fluctuations in sedimenting brownian particles. Phys Rev Lett 2017;118(19):198001.

[181] Sun Y, Carini G, Chollet M, Decker F-J, Dunne M, Fuoss P, et al. Nonuniform flow dynamics probed by nanosecond x-ray speckle visibility spectroscopy. Phys Rev Lett 2021;127(5):058001.

[182] Gibbs JG. Shape-and material-dependent self-propulsion of photocatalytic active colloids, interfacial effects, and dynamic interparticle interactions. Langmuir 2020;36(25):6938-47.

[183] Dattani R, Semeraro EF, Narayanan T. Phoretic motion of colloids in a phase separating medium. Soft Matter 2017;13(15):2817-22.

[184] Bu W, Schlossman ML. Synchrotron x-ray scattering from liquid surfaces and interfaces, in Synchrotron light sources and free-electron lasers: accelerator physics instrumentation and science applications. 2020. p. 1897-933.

[185] Geuchies JJ, Van Overbeek C, Evers WH, Goris B, De Backer A, Gantapara AP, et al. In situ study of the formation mechanism of two-dimensional superlattices from PbSe nanocrystals. Nat Mater 2016;15(12):1248.

[186] Jankowski M, Saedi M, La Porta F, Manikas AC, Tsakonas C, Cingolani JS, et al. Real-time multiscale monitoring and tailoring of graphene growth on liquid copper. ACS Nano 2021;15(6):9638-48.

[187] Belova V, Jankowski M, Saedi M, Groot IM, Renaud G, Konovalov OV. Employing surface curvature for spatially resolved x-ray reflectivity: graphene domains on liquid copper. Adv Mater Interfaces 2023;10:2300053.

[188] Kim PY, Fink Z, Zhang Q, Dufresne EM, Narayanan S, Russell TP. Relaxation and aging of nanosphere assemblies at a water-oil interface. ACS Nano 2022;16(6): 8967-73.

[189] Beuvier T, Chushkin Y, Zontone F, Gibaud A, Cherkas O, Da Silva J, et al. Self-transformation of solid CaCO₃ microspheres into core-shell and hollow hierarchical structures revealed by coherent x-ray diffraction imaging. IUCRJ 2022;9(5):580-93.

[190] Yager KG, Majewski PW, Noack MM, Fukuto M. Autonomous x-ray scattering. Nanotechnology 2023;34(32):322001.

[191] Beaucage PA, Martin TB. The autonomous formulation laboratory: an open liquid handling platform for formulation discovery using x-ray and neutron scattering. Chem Mater 2023;35(3):846-52.