Unveiling mesoscopic structures in distorted lamellar phases through deep learning-based small angle neutron scattering analysis.

HYPOTHESIS: The formation of distorted lamellar phases, distinguished by their arrangement of crumpled, stacked layers, is frequently accompanied by the disruption of long-range order, leading to the formation of interconnected network structures commonly observed in the sponge phase. Nevertheless, traditional scattering functions grounded in deterministic modeling fall short of fully representing these intricate structural characteristics. Our hypothesis posits that a deep learning method, in conjunction with the generalized leveled wave approach used for describing structural features of distorted lamellar phases, can quantitatively unveil the inherent spatial correlations within these phases. EXPERIMENTS AND SIMULATIONS: This report outlines a novel strategy that integrates convolutional neural networks and variational autoencoders, supported by stochastically generated density fluctuations, into a regression analysis framework for extracting structural features of distorted lamellar phases from small angle neutron scattering data. To evaluate the efficacy of our proposed approach, we conducted computational accuracy assessments and applied it to the analysis of experimentally measured small angle neutron scattering spectra of AOT surfactant solutions, a frequently studied lamellar system. FINDINGS: The findings unambiguously demonstrate that deep learning provides a dependable and quantitative approach for investigating the morphology of wide variations of distorted lamellar phases. It is adaptable for deciphering structures from the lamellar to sponge phase including intermediate structures exhibiting fused topological features. This research highlights the effectiveness of deep learning methods in tackling complex issues in the field of soft matter structural analysis and beyond.

Synthesis, structural studies, and photophysical properties of heteroleptic inverse-coordination clusters.

Two series of hyper-coordinated halide-centered M12 cuboctahedral clusters, [M12(µ12-X){S2P(OnPr)2}6{CCPh}4](PF6), 1a-c and 2a-c (where M = Cu, 1; Ag, 2; X = Cl, a; Br, b; I, c), were synthesized and fully characterized by ESI-MS, multi-NMR spectroscopy, IR and UV-Vis spectroscopy, photoluminescence analysis, and single-crystal X-ray crystallography. Structures 1c, 2b, and 2c show a twelve-coordinated halide encapsulated in the M12 cage, which is stabilized by six dithiophosphate and four alkynyl ligands. Compound 2b is the first Ag(I) cluster containing a twelve-coordinated bromide. The structural features of all six clusters are highly similar, providing a comparison basis of the inverse coordination for halides. Besides, the detailed structural analysis illustrates how the inverse coordination of a halide has influenced the size of the cuboctahedral M12 framework.

Ion Atmosphere of Wormlike Micelles Profiled by Contrast Variation Small-Angle Neutron Scattering.

Structural studies of wormlike micelles have so far mostly focused on the conformational properties of surfactant aggregates. The diffuse ionic atmosphere, which has a profound influence on various micellization phenomena such as thermodynamic stability and structural polymorphism, remains largely unexplored experimentally. In this report a strategy of contrast variation small-angle neutron scattering for this crucial structural study is outlined. Underlined by a general criterion established for unbiasedly identifying the length scale relevant to charge association from the spectral evolution, our analytical framework can provide a quantitative description of counterion distribution in a mathematically tractable manner. Our method can be conveniently extended to facilitate structural studies of complex multicomponent systems using contrast variation neutron scattering.

An exact inversion method for extracting orientation ordering by small-angle scattering.

We outline a nonparametric inversion strategy for determining the orientation distribution function (ODF) of sheared interacting rods using small-angle scattering techniques. With the presence of direct inter-rod interaction and fluid mechanical forces, the scattering spectra are no longer characterized by the azimuthal symmetry in the coordinates defined by the principal directions of simple shear conditions, which severely compounds the reconstruction of ODFs based on currently available methods developed for dilute systems. Using a real spherical harmonic expansion scheme, the real-space ODFs are uniquely determined from the anisotropic scattering spectra and their numerical accuracy is verified computationally. Our method can be generalized to extract ODFs of uniaxially anisotropic objects under different flow conditions in a properly transformed reference frame with suitable basis vectors.

Determining population densities in bimodal micellar solutions using contrast-variation small angle neutron scattering.

Self-assembly of amphiphilic polymers in water is of fundamental and practical importance. Significant amounts of free unimers and associated micellar aggregates often coexist over a wide range of phase regions. The thermodynamic and kinetic properties of the microphase separation are closely related to the relative population density of unimers and micelles. Although the scattering technique has been employed to identify the structure of micellar aggregates as well as their time-evolution, the determination of the population ratio of micelles to unimers remains a challenging problem due to their difference in scattering power. Here, using small-angle neutron scattering (SANS), we present a comprehensive structural study of amphiphilic n-dodecyl-PNIPAm polymers, which shows a bimodal size distribution in water. By adjusting the deuterium/hydrogen ratio of water, the intra-micellar polymer and water distributions are obtained from the SANS spectra. The micellar size and number density are further determined, and the population densities of micelles and unimers are calculated to quantitatively address the degree of micellization at different temperatures. Our method can be used to provide an in-depth insight into the solution properties of microphase separation, which are present in many amphiphilic systems.

Spatial correlation functions of paracrystals with radial symmetry.

We develop a phenomenological model to describe the structure of radially symmetric paracrystals whose long-range order are destroyed by propagation of particle fluctuations. General expressions are derived for the spatial correlation functions in one-, two-, and three-dimensional spaces. And the spatial correlation in paracrystals in reciprocal space is further discussed and clarified. The developed method can be used to quantitatively analyze the microstructure of paracrystalline materials in both real and reciprocal spaces via scattering experiments and computer simulations.

Revealing the Influence of Salts on the Hydration Structure of Ionic SDS Micelles by Contrast-Variation Small-Angle Neutron Scattering.

The influence of lithium chloride (LiCl) on the hydration structure of anionic micelles of sodium dodecyl sulfate (SDS) in water was studied using the contrast-variation small-angle neutron scattering (SANS) technique. In the past, extensive computational studies have shown that the distribution of invasive water plays a critical role in the self-organization of SDS molecules and the stability of the assemblies. However, in past scattering studies the degree of the hydration level was not examined explicitly. Here, a series of contrast-variation SANS data was analyzed to extract the intramicellar radial distributions of invasive water and SDS molecules from the evolving spectral lineshapes caused by the varying isotopic ratios of water. By addressing the intramicellar inhomogeneous distributions of water and SDS molecules, a detailed description of how the counterion association influences the micellization behavior of SDS molecules is provided. The extension of our method can be used to provide an in-depth insight into the micellization phenomenon, which is commonly found in many soft matter systems.

Copper Clusters Containing Hydrides in Trigonal Pyramidal Geometry.

Structurally precise copper hydrides [Cu11H2{S2P(OiPr)2}6(C≡CR)3], R = Ph (1), C6H4F (2), and C6H4OMe (3), were first synthesized from the polyhydrido copper cluster [Cu20H11{S2P(OiPr)2}9] with nine equivalents of terminal alkynes. Later, their isolated yields were significantly improved by direct synthesis from [Cu(CH3CN)4](PF6), [NH4][S2P(OiPr)2], NaBH4, and alkynes along with NEt3 in THF. 1, 2, and 3 were fully characterized by single-crystal X-ray diffraction, ESI-MS, and multinuclear NMR spectroscopy. All three clustershave 11 copper atoms, adopting 3,3,4,4,4-pentacapped trigonal prismatic geometry, with two hydrides inside the Cu11 cage, the position of which was ascertained by a single-crystal neutron diffraction structure of cluster 1 co-crystallized with a [Cu7(H){S2P(OiPr)2}6] (4) cluster. Six dithiophosphate and three alkynyl ligands stabilize the Cu11H2 core in which the two hydrides adopt a trigonal pyramidal coordination mode. This coordination mode is so far unprecedented for hydride. The 1H NMR resonance frequency of the two hydrides appears at 4.8 ppm, a value further confirmed by 2H NMR spectroscopy for their deuteride derivatives [Cu11(D)2{S2P(OiPr)2}6(C≡CR)3]. A DFT investigation allows understanding the bonding within this new type of copper(I) hydrides.

Structural properties of the evolution of CTAB/NaSal micelles investigated by SANS and rheometry.

Surfactants are amphiphilic molecules that spontaneously self-assemble in aqueous solution into various ordered and disordered phases. Under certain conditions, one-dimensional structures in the form of long, flexible wormlike micelles can develop. Cetyltrimethylammonium bromide (CTAB) is one of the most widely studied surfactants, and in the presence of sodium salicylate (NaSal), wormlike micelles can form at very dilute concentrations of surfactant. We carry out a systematic study of the structures of CTAB/NaSal over a surfactant concentration range of 2.5-15 mM and at salt-to-surfactant molar ratios of 0.5-10. Using small-angle neutron scattering (SANS), we qualitatively and quantitatively characterize the equilibrium structures of CTAB/NaSal, mapping the phase behavior of CTAB/NaSal at low concentrations within the region of phase space where nascent wormlike micelles transition into long and entangled structures. Complementary rheological assessments not only demonstrate the significant influence of the inter-micellar Coulombic interaction on the micellar structure but also suggest the potential existence of a hierarchical structure which is beyond the accessibility of the SANS technique.

Determining Gyration Tensor of Orienting Macromolecules through Their Scattering Signature.

A method is presented for quantitatively evaluating the shape and size of deformed particles in dispersion from their two-dimensional anisotropic spectra by small-angle scattering. By means of real spherical harmonic expansion, we derive analytical expressions of the gyration tensor R in terms of experimentally measured anisotropic scattering functions, yielding a tensorial extension of the Guinier law. We demonstrate the usefulness of this approach by a model study of an affinely deformed Gaussian chain. We further show that radius of gyration Rg is the source term of intraparticle structure factor at the mean-field limit, and from this perspective, we address the connection between R and conformation asphericity. The developed method not only facilitates quantitative scattering studies of deforming materials, but also provides insightful information regarding their deformation behavior at the molecular level based on the symmetric properties of real spherical harmonics.

Orientational Distribution Function of Aligned Elongated Molecules and Particulates Determined from Their Scattering Signature.

We present a strategy for quantitatively evaluating the field-induced alignment of nonspherical particles using small-angle scattering techniques. The orientational distribution function (ODF) is determined from the anisotropic scattering intensity via the scheme of real spherical harmonic expansion. Our developed approach is simple and analytical and does not require a presumptive hypothesis of the ODF as an input in data analysis. A model study of aligned rigid rods demonstrates the validity of this proposed approach to facilitate the quantitative structural characterization of materials with preferred orientational states.

Local elasticity in nonlinear rheology of interacting colloidal glasses revealed by neutron scattering and rheometry.

The flow of colloidal suspensions is ubiquitous in nature and industry. Colloidal suspensions exhibit a wide range of rheological behavior, which should be closely related to the microscopic structure of the systems. With in situ small-angle neutron scattering complemented by rheological measurements, we investigated the deformation behavior of a charge-stabilized colloidal glass at particle level undergoing steady shear. A short-lived, localized elastic response at particle level, termed as the transient elasticity zone (TEZ), was identified from the neutron spectra. The existence of the TEZ, which could be promoted by the electrostatic interparticle potential, is a signature of deformation heterogeneity: the body of fluids under shear behaves like an elastic solid within the spatial range of the TEZ but like fluid outside the TEZ. The size of the TEZ shrinks as the shear rate increases in the shear thinning region, which shows that the shear thinning is accompanied by a diminishing deformation heterogeneity. More interestingly, the TEZ is found to be the structural unit that provides the resistance to the imposed shear, as evidenced by the quantitative agreement between the local elastic stress sustained by the TEZ and the macroscopic stress from rheological measurements at low and moderate shear rates. Our findings provide an understanding on the nonlinear rheology of interacting colloidal glasses from a micro-mechanical view.

Strain heterogeneity in sheared colloids revealed by neutron scattering.

Recent computational and theoretical studies have shown that the deformation of colloidal suspensions under a steady shear is highly heterogeneous at the particle level and demonstrate a critical influence on the macroscopic deformation behavior. Despite its relevance to a wide variety of industrial applications of colloidal suspensions, scattering studies focusing on addressing the heterogeneity of the non-equilibrium colloidal structure are scarce thus far. Here, we report the first experimental result using small-angle neutron scattering. From the evolution of strain heterogeneity, we conclude that the shear-induced deformation transforms from nearly affine behavior at low shear rates, to plastic rearrangements when the shear rate is high.

Characterization of microscopic deformation through two-point spatial correlation functions.

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

Accurate analytic solution of chemical master equations for gene regulation networks in a single cell.

Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method with finite-size corrections to solve such CMEs accurately at the intermediate region of switching, where switching rate is comparable to fast protein production rate. We applied this approach to a model of self-regulating proteins [H. Ge et al., Phys. Rev. Lett. 114, 078101 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.078101] and found that as a parameter related to inducer concentration increases the probability of protein production changes from unimodal to bimodal, then to unimodal, consistent with phenotype switching observed in a single cell.

Reconstruction of three-dimensional anisotropic structure from small-angle scattering experiments.

When subjected to flow, the structures of many soft-matter systems become anisotropic due to the symmetry breaking of the spatial arrangements of constituent particles at the microscopic level. At present, it is common practice to use various small-angle scattering techniques to explore flow-induced microstructural distortion. However, there has not been a thorough discussion in the literature on how a three-dimensional anisotropic structure can be faithfully reconstructed from two-dimensional small-angle scattering spectra. In this work, we address this issue rigorously from a mathematical perspective by using real spherical harmonic expansion analysis. We first show that, except for cases in which mechanical perturbation is sufficiently small, the existing small-angle scattering techniques generally do not provide complete information on structural distortion. This limitation is caused by the linear dependence of certain real spherical harmonic basis vectors on the flow-vorticity and flow-velocity gradient planes in the Couette shear cell. To circumvent the constraint imposed by this geometry, an alternative approach is proposed in which a parallel sliding plate shear cell is used with a central rotary axis along the flow direction. From the calculation of rotation of the reference frame, we demonstrate the feasibility of this experimental implementation for a fully resolved three-dimensional anisotropic structure via a case study of sheared polymers.

High Thermal Dissipation of Al Heat Sink When Inserting Ceramic Powders by Ultrasonic Mechanical Coating and Armoring.

Aluminum alloys, which serve as heat sink in light-emitting diode (LED) lighting, are often inherent with a high thermal conductivity, but poor thermal total emissivity. Thus, high emissive coatings on the Al substrate can enhance the thermal dissipation efficiency of radiation. In this study, the ultrasonic mechanical coating and armoring (UMCA) technique was used to insert various ceramic combinations, such as Al2O3, SiO2, or graphite, to enhance thermal dissipation. Analytic models have been established to couple the thermal radiation and convection on the sample surface through heat flow equations. A promising match has been reached between the theoretical predictions and experimental measurements. With the adequate insertion of ceramic powders, the temperature of the Al heat sinks can be lowered by 5-11 °C, which is highly favorable for applications requiring cooling components.

Origin of sample size effect: Stochastic dislocation formation in crystalline metals at small scales.

In crystalline metals at small scales, the dislocation density will be increased by stochastic events of dislocation network, leading to a universal power law for various material structures. In this work, we develop a model obeyed by a probability distribution of dislocation density to describe the dislocation formation in terms of a chain reaction. The leading order terms of steady-state of probability distribution gives physical and quantitative insight to the scaling exponent n values in the power law of sample size effect. This approach is found to be consistent with experimental n values in a wide range.