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Biologically functional liquid-liquid phase separation of intrinsically disordered proteins (IDPs) is driven by interactions encoded by their amino acid sequences. Little is currently known about the molecular recognition mechanisms for distributing different IDP sequences into various cellular membraneless compartments. Pertinent physics was addressed recently by applying random-phase-approximation (RPA) polymer theory to electrostatics, which is a major energetic component governing IDP phase properties. RPA accounts for charge patterns and thus has advantages over Flory-Huggins (FH) and Overbeek-Voorn mean-field theories. To make progress toward deciphering the phase behaviors of multiple IDP sequences, the RPA formulation for one IDP species plus solvent is hereby extended to treat polyampholyte solutions containing two IDP species plus solvent. The new formulation generally allows for binary coexistence of two phases, each containing a different set of volume fractions ( φ 1 , φ 2 ) for the two different IDP sequences. The asymmetry between the two predicted coexisting phases with regard to their φ 1 φ 2 ratios for the two sequences increases with increasing mismatch between their charge patterns. This finding points to a multivalent, stochastic, 'fuzzy' mode of molecular recognition that helps populate various IDP sequences differentially into separate phase compartments. An intuitive illustration of this trend is provided by FH models, whereby a hypothetical case of ternary coexistence is also explored. Augmentations of the present RPA theory with a relative permittivity ϵ r ( φ ) that depends on IDP volume fraction φ = φ 1 + φ 2 lead to higher propensities to phase separate, in line with the case with one IDP species we studied previously. Notably, the cooperative, phase-separation-enhancing effects predicted by the prescriptions for ϵ r ( φ ) we deem physically plausible are much more prominent than that entailed by common effective medium approximations based on Maxwell Garnett and Bruggeman mixing formulas. Ramifications of our findings on further theoretical development for IDP phase separation are discussed.

Porosity, one of the important quality attributes of pharmaceutical tablets, directly affects the mechanical properties, the mass transport and hence tablet disintegration, dissolution and ultimately the bioavailability of an orally administered drug. The ability to accurately and quickly monitor the porosity of tablets during manufacture or during the manufacturing process will enable a greater assurance of product quality. This tutorial systematically outlines the steps involved in the terahertz-based measurement method that can be used to quantify the porosity of a tablet within seconds in a non-destructive and non-invasive manner. The terahertz-based porosity measurement can be performed using one of the three main methods, which are (i) the zero-porosity approximation (ZPA); (ii) the traditional Bruggeman effective medium approximation (TB-EMA); and (iii) the anisotropic Bruggeman effective medium approximation (AB-EMA). By using a set of batches of flat-faced and biconvex tablets as a case study, the three main methods are compared and contrasted. Overall, frequency-domain signal processing coupled with the AB-EMA method was found to be most suitable approach in terms of accuracy and robustness when predicting the porosity of tablets over a range of complexities and geometries. This tutorial aims to concisely outline all the necessary steps, precautions and unique advantages associated with the terahertz-based porosity measurement method.

Poly(3,4-ethylenedioxythiophene): polystyrene sulfonate (PEDOT:PSS) is a conductive water-processable polymer with many important applications in organic electronics. The electrical conductivity of PEDOT:PSS layers is very diverse and can be changed by changing the processing and post-deposition conditions, e.g., by using different solvent additives, doping or modifying the physical conditions of the layer deposition. Despite many years of intensive research on the relationship between the microstructure and properties of these layers, there are still gaps in our knowledge, especially with respect to the detailed understanding of the charge carrier transport mechanism in organic semiconductor thin films. In this work, we investigate the effect of acid doping of PEDOT:PSS thin films on the intra-chain and inter-chain conductivity by developing a model that treats PEDOT:PSS as a nanocomposite material. This model is based on the effective medium theory and uses the percolation theory equation for the electrical conductivity of a mixture of two materials. Here its implementation assumes that the role of the highly conductive material is attributed to the intra-chain conductivity of PEDOT and its quantitative contribution is determined based on the optical Drude–Lorentz model. While the weaker inter-chain conductivity is assumed to originate from the weakly conductive material and is determined based on electrical measurements using the van der Pauw method and coherent nanostructure-dependent analysis. Our studies show that doping with methanesulfonic acid significantly affects both types of conductivity. The intra-chain conductivity of PEDOT increases from 260 to almost 400 Scm−1. Meanwhile, the inter-chain conductivity increases by almost three orders of magnitude, reaching a critical state, i.e., exceeding the percolation threshold. The observed changes in electrical conductivity due to acid doping are attributed to the flattening of the PEDOT/PSS gel nanoparticles. In the model developed here, this flattening is accounted for by the inclusion shape factor.

The use of a nanolaminate metamaterial exhibiting a subwavelength periodic pattern is demonstrated to tailor a one-dimensional photonic crystal (1DPC) in such a way that both transverse electric and magnetic surface modes can be simultaneously excited in the VIS-NIR range. In this framework, we provide a detailed analysis of the structure design by means of a combined use of the effective medium approximation and three-dimensional finite element method. Fabrication feasibility and limitations are considered, particularly in keeping into account the available materials. The tunability of the design and the capability of the 1DPC platform in controlling polarization states can suggest new approaches for polarization-resolved sensing on photonic chips.

Effective-medium theory pertains to the theoretical modelling of homogenization, which aims to replace an inhomogeneous structure of subwavelength-scale constituents with a homogeneous effective medium. The effective-medium theory is fundamental to various realms, including electromagnetics and material science, since it can largely decrease the complexity in the exploration of light-matter interactions by providing simple acceptable approximation. Generally, the effective-medium theory is thought to be applicable to any all-dielectric system with deep-subwavelength constituents, under the condition that the effective medium does not have a critical angle, at which the total internal reflection occurs. Here we reveal a fundamental breakdown of the effective-medium theory that can be applied in very general conditions: showing it for deep-subwavelength all-dielectric multilayers even without a critical angle. Our finding relies on an exotic photonic spin Hall effect, which is shown to be ultrasensitive to the stacking order of deep-subwavelength dielectric layers, since the spin-orbit interaction of light is dependent on slight phase accumulations during the wave propagation. Our results indicate that the photonic spin Hall effect could provide a promising and powerful tool for measuring structural defects for all-dielectric systems even in the extreme nanometer scale.

Nonlocality is a fundamental concept in photonics. For instance, nonlocal wave-matter interactions in spatially modulated metamaterials enable novel effects, such as giant electromagnetic chirality, artificial magnetism, and negative refraction. Here, we investigate the effects induced by spatial nonlocality in metamaterials, i.e., media with a dielectric permittivity rapidly modulated in time. Via a rigorous multiscale approach, we introduce a general and compact formalism for the nonlocal effective medium theory of temporally periodic metamaterials. In particular, we study two scenarios: (i) a periodic temporal modulation, and (ii) a temporal boundary where the permittivity is abruptly changed in time and subject to periodic modulation. We show that these configurations can give rise to peculiar nonlocal effects, and we highlight the similarities and differences with respect to the spatial-metamaterial counterparts. Interestingly, by tailoring the effective boundary wave-matter interactions, we also identify an intriguing configuration for which a temporal metamaterial can perform the first-order derivative of an incident wavepacket. Our theoretical results, backed by full-wave numerical simulations, introduce key physical ingredients that may pave the way for novel applications. By fully exploiting the time-reversal symmetry breaking, nonlocal temporal metamaterials promise a great potential for efficient, tunable optical computing devices.

Thermal conductivity is a key parameter governing heat transfer in rocks and soils with applications to geothermal systems and groundwater studies. Its accurate measurement is crucial to understand energy exchange in the Earth's subsurface. This study explores the application of the percolation-based effective-medium approximation (P-EMA) model to a broad range of soil types using a database including 158 soil samples. The P-EMA model for soil thermal conductivity, introduced by Ghanbarian and Daigle, is validated through robust optimization of its parameters and by comparing with the laboratory measurements where we find an excellent match between the theory and the experiments. A regression-based model is developed to estimate the P-EMA model parameters directly from other soil properties, such as sand, clay, bulk density, and thermal conductivities at completely dry and full saturation. The proposed regression-based relationships are evaluated using unseen data from two databases: one from Kansas containing 19 soil samples and another from Canada containing 40 soil samples. These regression-based relationships offer an approximation for the P-EMA model parameters, providing a practical approach to estimate the thermal conductivity of soils. Furthermore, a curve-clustering approach is proposed to classify soil thermal conductivity curves based on their similarities, providing insights into the heterogeneity of samples. We find seven clusters for each of which the average P-EMA model parameters are reported. The classification and regression models generally extend the seamless applicability of the P-EMA model.

We propose a theoretical method for calculating the stimulated Brillouin scattering (SBS) gain coefficient in metamaterials. The presented model is based on homogenization and effective medium theories. We examined all of the optical, acoustic, and opto-acoustic parameters required to calculate SBS gain coefficient in metamaterials and proposed an approximate method for calculating each one. We have shown that the electrostriction is not the only important mechanism, and for different metamaterials, other parameters can play a significant role in the enhancement and suppression of the SBS gain coefficient. This result is consistent with previous work.

Seismic wave exhibits the characteristics of anisotropy and attenuation while propagating through the fluid-bearing fractured or layered reservoirs, such as fractured carbonate and shale bearing oil or gas. We derive a linearized reflection coefficient that simultaneously considers the effects of anisotropy and attenuation caused by fractures and fluids. Focusing on the low attenuated transversely isotropic medium with a vertical symmetry axis (Q-VTI) medium, we first express the complex stiffness tensors based on the perturbation theory and the linear constant Q model at an arbitrary reference frequency, and then we derive the linearized approximate reflection coefficient of P to P wave. It decouples the P- and S-wave inverse quality factors, and Thomsen-style attenuation-anisotropic parameters from complex P- and S-wave velocity and complex Thomsen anisotropic parameters. By evaluating the reflection coefficients around the solution point of the interface of two models, we analyze the characteristics of reflection coefficient vary with the incident angle and frequency and the effects of different Thomsen anisotropic parameters and attenuation factors. Moreover, we realize the simultaneous inversion of all parameters in the equation using an actual well log as a model. We conclude that the derived reflection coefficient may provide a theoretical tool for the seismic wave forward modeling, and again it can be implemented to predict the reservoir properties of fractures and fluids based on diverse inversion methods of seismic data.

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.