Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N₂ atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Graphical Abstract

     

A perimeter-based angle measure in Minkowski planes

Measuring angles in the Euclidean plane is a well-known topic, but for general normed planes there exists a variety of different concepts. These can be of a special kind, e.g. also preserving special orthogonality types. But these concepts are no angle measures in the sense of measure theory since they are not additive. This motivates us to define a new angle measure for normed planes that is in fact a measure in the sense of measure theory. Furthermore, we look at related types of rotation and reflection.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Parametrix for the localization of the Bergman metric on strictly pseudoconvex domains

We give the parameter version of a localization theorem for the Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of Graham-Kerzman is proved in the hereby paper, as well.     

An enriched damage-frictional cohesive-zone model incorporating stress multi-axiality

The paper presents an interphase cohesive zone model (CZM) incorporating stress multi-axiality devised to capture, by simplified micro-modeling, the influence of the in-plane strain and stress state in the mechanical response of the CZM. Moreover, the model is able to account for the Poisson-related effect in the interphase, which can play an important role in the modeling of heterogeneous masonry elements. From the constitutive point of view, the proposed formulation couples damage and friction by addressing a smooth transition from a quasi-brittle response to a residual frictional behavior described by a Coulomb law with unilateral contact. As in-plane stresses are accounted for, damage activation and evolution are governed by a Drucker–Prager law with linear softening. A predictor-corrector procedure based on a backward Euler scheme is detailed for integrating the nonlinear evolutive problem together with the related tangent operator which consistently linearizes the algorithmic strategy. This framework is embedded into a kinematically-enriched finite element interphase formulation incorporating stress multi-axiality. The modeling features of the resulting numerical tool are tested both at the local level, for the typical interphase point, and in meso-structural tests consisting of brick-mortar triplets, investigating the capability of the proposed model and numerical procedure to simulate the brick-mortar decohesion mechanism during confined slip tests.     

Static Charge Susceptibility in the <Emphasis Type="Italic">t-J-V</Emphasis> Model

We describe the static charge susceptibility and correlation function of the charge density in the twodimensional t-J-V model based on the method of equations of motion for the relaxation functions of the Hubbard operators. We obtain the dependence of the susceptibility and correlation function on the hole concentration and temperature. Charge density waves can develop if the intersite Coulomb interaction is sufficiently strong.     

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic non-Newtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption (Stokes flow) and lubrication theory approximations (large wavelength). Small ionic Peclét number and Debye–Hückel linearization (i.e. wall zeta potential ≤ 25 mV) are also considered to simplify the Nernst–Planck and Poisson–Boltzmann equations. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design.     

A Framework for Characterizing Structural Uncertainty in Large-Eddy Simulation Closures

Motivated by the sizable increase of available computing resources, large-eddy simulation of complex turbulent flow is becoming increasingly popular. The underlying filtering operation of this approach enables to represent only large-scale motions. However, the small-scale fluctuations and their effects on the resolved flow field require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of incertitude that can impact the quantities of interest. The objective of this work is to introduce a framework for the systematic estimation of structural uncertainty in large-eddy simulation closures. In particular, the methodology proposed is independent of the initial model form, computationally efficient, and suitable to general flow solvers. The approach is based on introducing controlled perturbations to the turbulent stress tensor in terms of magnitude, shape and orientation, such that propagation of their effects can be assessed. The framework is rigorously described, and physically plausible bounds for the perturbations are proposed. As a means to test its performance, a comprehensive set of numerical experiments are reported for which physical interpretation of the deviations in the quantities of interest are discussed.     

Multi-scale Fractured Coal Gas–Solid Coupling Model and Its Applications in Engineering Projects

With coal mining entering the geological environment of “high stress, rich gas, strong adsorption and low permeability,” the difficulty of joint coal and gas extraction clearly augments, the risk of solid–gas coupling dynamic disasters greatly increases, and the underlying mechanisms become more complex. In this paper, based on the characteristics of coal’s multi-scale structure and spatiotemporal variation, the multi-scale fractured coal gas–solid coupling model (MSFM) was built. In this model, the interaction between coal matrix and its fractures and the mechanical characteristics of gas-bearing coal were considered, as well as their coupling relationship. By MATLAB software, the stress–damage–seepage numerical computation programs were developed, which were applied into Comsol Multiphysics to simulate gas flow caused by coal mining. The simulation results showed the spatial variability of coal elastic modulus and cross-flow behaviors of coal seam gas, which were superior to the results of traditional gas–solid coupling model. And the numerical results obtained from MSFM were closer to the measured results in field, while the computation results of traditional model were slightly higher than the measured results. Furthermore, the MSFM in a large scale was verified by field engineering project.