A discretized representation for Monte Carlo simulation of deformed semiflexible chains.

In this study, we present a novel orientation discretization approach based on the rhombic triacontahedron for Monte Carlo simulations of semiflexible polymer chains, aiming at enhancing structural analysis through rheo-small-angle scattering (rheo-SAS). Our approach provides a more accurate representation of the geometric features of semiflexible chains under deformation, surpassing the capabilities of traditional lattice structures. Validation against the Kratky-Porod chain system demonstrated superior consistency, underscoring its potential to significantly improve the precision of uncovering geometric details from rheo-SAS data.

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

Two series of hyper-coordinated halide-centered M cuboctahedral clusters, [M(μ-X){SP(OPr)}{CCPh}](PF), 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 M cage, which is stabilized by six dithiophosphate and four alkynyl ligands. Compound 2b is the first Ag(I) cluster containing a twelve-coordinated bromide.

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.

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.

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.

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.

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.

Copper Clusters Containing Hydrides in Trigonal Pyramidal Geometry.

Structurally precise copper hydrides [CuH{SP(OPr)}(C≡CR)], R = Ph (), CHF (), and CHOMe (), were first synthesized from the polyhydrido copper cluster [CuH{SP(OPr)}] with nine equivalents of terminal alkynes. Later, their isolated yields were significantly improved by direct synthesis from [Cu(CHCN)](PF), [NH][SP(OPr)], NaBH, and alkynes along with NEt in THF. , , and were fully characterized by single-crystal X-ray diffraction, ESI-MS, and multinuclear NMR spectroscopy.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.