Nearest-neighbor distribution functions in many-body systems

Conformational and static properties of tagged chains in solvents: effect of chain connectivity in solvent molecules

Polymer chains immersed in different solvent molecules exhibit diverse properties due to multiple spatiotemporal scales and complex interactions. Using molecular dynamics simulations, we study the conformational and static properties of tagged chains in different solvent molecules. Two types of solvent molecules were examined: one type consisted of chain molecules connected by bonds, while the other type consisted of individual bead molecules without any bonds. The only difference between the two solvent molecules lies in the chain connectivity. Our results show a compression of the tagged chains with the addition of bead or chain molecules. Chain molecule confinement induces a stronger compression compared to bead molecule confinement. In chain solvent molecules, the tagged chain's radius of gyration reached a minimum at a monomer volume fraction of ∼0.3. Notably, the probability distributions of chain size remain unchanged at different solvent densities, irrespective of whether the solvent consists of beads or polymers. Furthermore, as solvent density increases, a crossover from a unimodal to a bimodal distribution of bond angles is observed, indicating the presence of both compressed and expanded regions within the chain. The effective monomer-solvent interaction is obtained by calculating the partial radial distribution function and the potential of the mean force. In chain solvents, the correlation hole effect results in a reduced number of nearest neighbors around tagged monomers compared to bead solvents. The calculation of pore size distribution reveals that the solvent nonhomogeneity induced by chain connectivity leads to a broader distribution of pore sizes and larger pore dimensions at low volume fractions. These findings provide a deeper understanding of the conformational behavior of polymer chains in different solvent environments.

Dilute gel networks vs. clumpy gels in colloidal systems with a competition between repulsive and attractive interactions

Using Brownian dynamics simulations we study gel-forming colloidal systems. The focus of this article lies on the differences of dense and dilute gel networks in terms of structure formation both on a local and a global level. We apply reduction algorithms and observe that dilute networks and dense gels differ in the way structural properties like the thickness of strands emerge. We also analyze the percolation behavior and find that two different regimes of percolation exist which might be responsible for structural differences. In dilute networks we confirm that solidity is mainly a consequence of pentagonal bipyramids forming in the network. In dense gels, tetrahedral structures also influence solidity.

Unified description over time of heterogeneous condensation with quenched disorder

We report experimental results on breath figures (BFs) observed on substrates with quenched disorder. The evolution of BFs is found to be primarily influenced by global parameters associated with boundary conditions. We investigate classical statistical measures and explore topological properties using persistent homology techniques based on a modified Vietoris-Rips complex. Our findings reveal that the evolution of the number surface density of condensed droplets plays a crucial role in determining various condensation stages previously considered distinct. This evolution is significantly influenced by the distribution of nucleation sites and the individual growth law governing water droplets when coalescence does not occur. Ultimately, we demonstrate the capability to predict coalescence events based on the topological characteristics of BFs at a given point in time.

Observation of Weibull, Lognormal, and Gamma Distributions in Electrodeposited Cu and Cu-Ag Particles

In this work, the nearest-neighbor distances and Voronoi cell features of Cu-Ag deposits were analyzed and fitted with Lognormal, Weibull, and Gamma distributions. The nearest-neighbor distance distributions of the samples were compared with those of complete spatially random points, showing spatial inhomogeneity due to the nucleation exclusion effect. The radial distribution function was calculated, showing both influences from the grain size and the nucleation exclusion effect. Voronoi cells were generated based on the shape of the grains. The size, occupancy, and coordination of the Voronoi cells were examined and fitted. The results show that although the Cu-Ag deposits seemed to be governed by the instantaneous nucleation mode, the spatial distribution of the nuclei was more impacted by the nucleation exclusion effect than the Cu-only samples. This behavior is also justified by the grain size distribution generated with Voronoi cell size and occupancy distributions.

Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics

The Zhang-Torquato conjecture [G. Zhang and S. Torquato, Phys. Rev. E, 2020, 101, 032124.] states that any realizable pair correlation function g₂(r) or structure factor S(k) of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions. To further test and study this conjecture, we consider two singular nonequilibrium models of recent interest that also have the exotic hyperuniformity property: a 2D "perfect glass" and a 3D critical absorbing-state model. We find that each nonequilibrium target can be achieved accurately by equilibrium states with effective one- and two-body potentials, lending further support to the conjecture. To characterize the structural degeneracy of such a nonequilibrium-equilibrium correspondence, we compute higher-order statistics for both models, as well as those for a hyperuniform 3D uniformly randomized lattice (URL), whose higher-order statistics can be very precisely ascertained. Interestingly, we find that the differences in the higher-order statistics between nonequilibrium and equilibrium systems with matching pair statistics, as measured by the "hole" probability distribution, provide measures of the degree to which a system is out of equilibrium. We show that all three systems studied possess the bounded-hole property and that holes near the maximum hole size in the URL are much rarer than those in the underlying simple cubic lattice. Remarkably, upon quenching, the effective potentials for all three systems possess local energy minima (i.e., inherent structures) with stronger forms of hyperuniformity compared to their target counterparts. Our methods are expected to facilitate the self-assembly of tunable hyperuniform soft-matter systems.

Voronoi tessellation-based algorithm for determining rigorously defined classical and generalized geometric pore size distributions

The geometric pore size distribution (PSD) P(r) as function of pore radius r is an important characteristic of porous structures, including particle-based systems, because it allows us to analyze adsorption behavior, the strength of materials, etc. Multiple definitions and corresponding algorithms, particularly in the context of computational approaches, exist that aim at calculating a PSD, often without mentioning the employed definition and therefore leading to qualitatively very different and apparently incompatible results. Here, we analyze the differences between the PSDs introduced by Torquato et al. and the more widely accepted one provided by Gelb and Gubbins, here denoted as T-PSD and G-PSD, respectively, and provide rigorous mathematical definitions that allow us to quantify the qualitative differences. We then extend G-PSD to incorporate the ideas of coating, which is significant for nanoparticle-based systems, and of finite probe particles, which is crucial to micro and mesoporous particles. We derive how the extended and classical versions are interrelated and how to calculate them properly. We next analyze various numerical approaches used to calculate classical G-PSDs and may be used to calculate the generalized G-PSD. To this end, we propose a simple yet sufficiently complicated benchmark for which we calculate the different PSDs analytically. This approach allows us to completely rule out a recently proposed algorithm based on radical Voronoi tessellation. Instead, we find and prove that the output of a grid-free classical Voronoi tessellation, namely, the properties of its triangulated faces, can be used to formulate an algorithm, which is capable of calculating the generalized G-PSD for a system of monodisperse spherical particles (or points) to any precision, using analytical expressions. The Voronoi-based algorithm developed and provided here has optimal scaling behavior and outperforms grid-based approaches.

Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c}. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δ_{c} is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.

Structural and dynamical properties of dilute gel networks in colloid-polymer mixtures

The competition of short-ranged depletion attraction and long-ranged repulsion between colloidal particles in colloid-polymer mixtures leads to the formation of heterogeneous gel-like structures. Our special focus will be on the states where the colloids arrange in thin strands that span the whole system and that we will refer to as dilute gel networks. These states occur at low packing fractions for attractions that are stronger than those at both the binodal line of the equilibrium gas-liquid phase separation and the directed percolation transition line. By using Brownian dynamics simulations, we explore the formation, structure, and aging dynamics of dilute gel networks. The essential connections in a dilute gel network are determined by constructing reduced networks. We compare the observed properties to those of clumpy gels or cluster fluids. Our results demonstrate that both the structure and the (often slow) dynamics of the stable or meta-stable heterogeneous states in colloid-polymer mixtures possess distinct features on various length and time scales and thus are richly diverse.

Sensitivity of pair statistics on pair potentials in many-body systems

We study the sensitivity and practicality of Henderson's theorem in classical statistical mechanics, which states that the pair potential v(r) that gives rise to a given pair correlation function g₂(r) [or equivalently, the structure factor S(k)] in a classical many-body system at number density ρ and temperature T is unique up to an additive constant. While widely invoked in inverse-problem studies, the utility of the theorem has not been quantitatively scrutinized to any large degree. We show that Henderson's theorem has practical shortcomings for disordered and ordered phases for certain densities and temperatures. Using proposed sensitivity metrics, we identify illustrative cases in which distinctly different potential functions give very similar pair correlation functions and/or structure factors up to their corresponding correlation lengths. Our results reveal that due to a limited range and precision of pair information in either direct or reciprocal space, there is effective ambiguity of solutions to inverse problems that utilize pair information only, and more caution must be exercised when one claims the uniqueness of any resulting effective pair potential found in practice. We have also identified systems that possess virtually identical pair statistics but have distinctly different higher-order correlations. Such differences should be reflected in their individually distinct dynamics (e.g., glassy behaviors). Finally, we prove a more general version of Henderson's theorem that extends the uniqueness statement to include potentials that involve two- and higher-body interactions.

Continuum percolation expressed in terms of density distributions

We present an approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors. For one-dimensional systems with nearest-neighbor interactions, the nearest-neighbor distribution is in turn related to the pair-correlation function g through a simple integral equation. As a consequence, for those systems, we arrive at an integral equation relating g to the pair connectedness, which is readily solved even analytically if g is specified analytically. We demonstrate the procedure for a variety of pair potentials including fully penetrable spheres as well as impenetrable spheres, the only two systems for which analytical results for the pair connectedness exist. However, the approach is not limited to nearest-neighbor interactions in one dimension. Hence, we also outline the treatment of external fields and long-range interactions and we illustrate how the formalism can applied to higher-dimensional systems using the three-dimensional ideal gas as an example.

Depletion force between disordered linear macromolecules

When two macromolecules come very near in a fluid, the surrounding molecules, having finite volume, are less likely to get in between. This leads to a pressure difference manifesting as an entropic attraction, called depletion force. Here we calculate the density profile of liquid molecules surrounding a disordered rigid macromolecules modeled as a random arrangement of hard spheres on a linear backbone. We analytically determine the position dependence of the depletion force between two such disordered molecules by calculating the free energy of the system. We then use molecular dynamics simulations to obtain the depletion force between stiff disordered polymers as well as flexible ones and compare the two against each other. We also show how the disorder averaging can be handled starting from the inhomogenous reference interaction site model equations.

Polymer dynamics under confinement

We review recent neutron scattering work and related results from simulation and complementary techniques focusing on the microscopic dynamics of polymers under confinement. Confinement is either realized in model porous materials or in polymer nanocomposites (PNC). The dynamics of such confined polymers is affected on the local segmental level, the level of entanglements as well as on global levels: (i) at the segmental level the interaction with the surface is of key importance. At locally repulsive surfaces compared to the bulk the segmental dynamics is not altered. Attractive surfaces slow down the segmental dynamics in their neighborhood but do not give rise to dead, glassy layers. (ii) Confinement generally has little effect on the inter-chain entanglements: both for weakly as well as for marginally confined polymers the reptation tube size is not changed. Only for strongly confined polymers disentanglement takes place. Similarly, in PNC at higher NP loading disentanglement phenomena are observed; in addition, at very high loading a transition from polymer caused topological constraints to purely geometrical constraints is observed. (iii) On the more global scale NSE experiments revealed important information on the nature of the interphase between adsorbed layer and bulk polymer. (iv) Polymer grafts at NP mutually confine each other, an effect that is most pronounced for one component NP. (v) Global diffusion of entangled polymers both in weakly and strongly attractive PNC is governed by the ratio of bottle-neck to chain size that characterizes the 'entropic barrier' for global diffusion.

Improving Conductivity in Nano-Conduit Flows by Using Thermal Pulse-Induced Brownian Motion: A Spectral Impulse Intensity Approach

Inter-particle and particle-wall connectivity in suspension flow has profound effects on thermal and electrical conductivity. The spectral impulse generation and the imparting of kinetic energy on the particles is shown through a mathematical analysis to be effective as a means of achieving an approximate equivalent of a Langevin thermostat. However, with dilute suspensions, the quadratic form of the thermal pulse spectra is modified with a damping coefficient to achieve the desired Langevin value. With the dense suspension system, the relaxation time is calculated from the non-linear differential equation, and the fluid properties were supported by the viscosity coefficient. A “smoothed” pulse is used for each time-step of the flow simulation to take care of the near-neighbor interactions of the adjacent particles. An approximate optimal thermostat is achieved when the number of extra pulses introduced within each time step is found to be nearly equal to the co-ordination number of each particle within the assembly. Furthermore, the ratio of the particle kinetic energy and the thermal energy imparted is found to be never quite equal to unity, as they both depend upon the finite values of the pulse duration and the relaxation time.

Spectroscopic Analysis of Protein-Crowded Environments Using the Charge-Transfer Fluorescence Probe 8-Anilino-1-Naphthalenesulfonic Acid

The molecular behaviors of proteins under crowding conditions are crucial for understanding the protein actions in intracellular environments. Under a crowded environment, the distance between protein molecules is almost the same size as the molecular level, thus, both the excluded volume effect and short ranged soft chemical interaction on protein surface could induce the complicated influence on the protein behavior cooperatively. Recently, various kinds of analytical approaches from macroscopic to microscopic aspects have been made to evaluate the crowding effect. The method, however, has not been established to evaluate the surface specific interactions on protein surface. In this study, the analytical method to evaluate the crowding effect has been suggested by using a charge-transfer fluorescence probe, ANS. By employing the unique property of ANS attaching to charged residues on the surface of lysozyme, the crowding effect was focused, while the case was compared as a reference, in which ANS is confined in hydrophobic pockets of BSA. Consequently, the surface specific changes of fluorescence spectra were readily observed under the crowded environment, whereas the fluorescence spectra of ANS in protein inside did not change. This result suggests the fluorescence spectra of ANS binding to protein surface have the capability to estimate the crowding effect of proteins.

Spatially Adaptive Colocalization Analysis in Dual-Color Fluorescence Microscopy

Colocalization analysis aims to study complex spatial associations between bio-molecules via optical imaging techniques. However, existing colocalization analysis workflows only assess an average degree of colocalization within a certain region of interest and ignore the unique and valuable spatial information offered by microscopy. In the current work, we introduce a new framework for colocalization analysis that allows us to quantify colocalization levels at each individual location and automatically identify pixels or regions where colocalization occurs. The framework, referred to as spatially adaptive colocalization analysis (SACA), integrates a pixel-wise local kernel model for colocalization quantification and a multi-scale adaptive propagation-separation strategy for utilizing spatial information to detect colocalization in a spatially adaptive fashion. Applications to simulated and real biological datasets demonstrate the practical merits of SACA in what we hope to be an easily applicable and robust colocalization analysis method. In addition, theoretical properties of SACA are investigated to provide rigorous statistical justification.

Clustering and assembly dynamics of a one-dimensional microphase former

Both ordered and disordered microphases ubiquitously form in suspensions of particles that interact through competing short-range attraction and long-range repulsion (SALR). While ordered microphases are more appealing materials targets, understanding the rich structural and dynamical properties of their disordered counterparts is essential to controlling their mesoscale assembly. Here, we study the disordered regime of a one-dimensional (1D) SALR model, whose simplicity enables detailed analysis by transfer matrices and Monte Carlo simulations. We first characterize the signature of the clustering process on macroscopic observables, and then assess the equilibration dynamics of various simulation algorithms. We notably find that cluster moves markedly accelerate the mixing time, but that event chains are of limited help in the clustering regime. These insights will inspire further study of three-dimensional microphase formers.

LSPR Coupling and Distribution of Interparticle Distances between Nanoparticles in Hydrogel on Optical Fiber End Face

We report on a new localized surface plasmon resonance (LSPR)-based optical fiber (OF) architecture with a potential in sensor applications. The LSPR-OF system is fabricated by immobilizing gold nanoparticles (GNPs) in a hydrogel droplet polymerized on the fiber end face. This design has several advantages over earlier designs. It dramatically increase the number nanoparticles (NP) available for sensing, it offers precise control over the NP density, and the NPs are positioned in a true 3D aqueous environment. The OF-hydrogel design is also compatible with low-cost manufacturing. The LSPR-OF platform can measure volumetric changes in a stimuli-responsive hydrogel or measure binding to receptors on the NP surface. It can also be used as a two-parameter sensor by utilizing both effects. We present results from proof-of-concept experiments exploring the properties of LSPR and interparticle distances of the GNP-hydrogel OF design by characterizing the distribution of distances between NPs in the hydrogel, the refractive index of the hydrogel and the LSPR attributes of peak position, amplitude and linewidth for hydrogel deswelling controlled with pH solutions.

Can exotic disordered "stealthy" particle configurations tolerate arbitrarily large holes?

The probability of finding a spherical cavity or "hole" of arbitrarily large size in typical disordered many-particle systems in the infinite-system-size limit (e.g., equilibrium liquid states) is non-zero. Such "hole" statistics are intimately linked to the thermodynamic and nonequilibrium physical properties of the system. Disordered "stealthy" many-particle configurations in d-dimensional Euclidean space [Doublestruck R]^d are exotic amorphous states of matter that lie between a liquid and crystal that prohibit single-scattering events for a range of wave vectors and possess no Bragg peaks [Torquato et al., Phys. Rev. X, 2015, 5, 021020]. In this paper, we provide strong numerical evidence that disordered stealthy configurations across the first three space dimensions cannot tolerate arbitrarily large holes in the infinite-system-size limit, i.e., the hole probability has compact support. This structural "rigidity" property apparently endows disordered stealthy systems with novel thermodynamic and physical properties, including desirable band-gap, optical and transport characteristics. We also determine the maximum hole size that any stealthy system can possess across the first three space dimensions.

Determining Number Concentrations and Diameters of Polystyrene Particles by Measuring the Effective Refractive Index of Colloids Using Surface Plasmon Resonance

The capabilities of surface plasmon resonance (SPR) for characterization of colloidal particles were evaluated for 100, 300, and 460 nm nominal diameter polystyrene (PS) latexes. First the accuracy of measuring the effective refractive index (n_eff) of turbid colloids using SPR was quantified. It was concluded that for submicrometer sized PS particles the accuracy is limited by the reproducibility between replicate injections of samples. An SPR method was developed for obtaining the particle mean diameter (d_part) and the particle number concentration (c_p) by fitting the measured n_eff of polystyrene (PS) colloids diluted in series with theoretical values calculated using the coherent scattering theory (CST). The d_part and c_p determined using SPR agreed with reference values obtained from size distributions measured by scanning electron microscopy (SEM), and the mass concentrations stated by the manufacturer. The 100 nm particles adsorbed on the sensing surface, which hampered the analysis. Once the adsorption problem has been overcome, the developed SPR method has potential to become a versatile tool for characterization of colloidal particles. In particular, SPR could form the basis of rapid and accurate methods for measuring the c_p of submicrometer particles in dispersion.

Noncovalent Dimerization after Enediyne Cyclization on Au(111)

We investigate the thermally induced cyclization of 1,2-bis(2-phenylethynyl)benzene on Au(111) using scanning tunneling microscopy and computer simulations. Cyclization of sterically hindered enediynes is known to proceed via two competing mechanisms in solution: a classic C(1)-C(6) (Bergman) or a C(1)-C(5) cyclization pathway. On Au(111), we find that the C(1)-C(5) cyclization is suppressed and that the C(1)-C(6) cyclization yields a highly strained bicyclic olefin whose surface chemistry was hitherto unknown. The C(1)-C(6) product self-assembles into discrete noncovalently bound dimers on the surface. The reaction mechanism and driving forces behind noncovalent association are discussed in light of density functional theory calculations.

Characterization of maximally random jammed sphere packings. II. Correlation functions and density fluctuations

In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g_{2}(r) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the structural characteristics analyzed in this paper.

Kinetic instability, symmetry breaking and role of geometric constraints on the upper bounds of disorder in two dimensional packings

Although the energetics of grain boundaries are more or less understood, their mechanical description remains challenging primarily because of very fast dynamics in the atomic length scale. By contrast, granular dynamics are extraordinarily sluggish. In this study, two dimensional centripetal packings of macroscopic granular particles are employed to investigate the role of geometric aspects of grain boundary formation. Using a novel sampling scheme, the extensive configuration space is well represented by a few prominent structures. Our results suggest that cohesive effects “iron out” any disorder present and enforce a transition towards a “fixed point” basin associated with a universal high density jammed hexagonal structure. Two main conjectures are advanced: (i) the appearance of grain boundary like structures is the manifestation of the kinetic instabilities of the densification process and has its origin in the structural rearrangement and (ii) the departure from six-fold coordination in the final packing is bounded from above by a sixth of the angular dispersion present in the initial configuration. If similar predictive consequences are further developed for three dimensional cases, this may have far reaching consequences in many areas of science and technology.

The molecular interaction of a protein in highly concentrated solution investigated by Raman spectroscopy

We used Raman spectroscopy to investigate the structure and interactions of lysozyme molecules in solution over a wide range of concentrations (2.5-300 mg ml(-1)). No changes in the amide-I band were observed as the concentration was increased, but the width of the Trp band at 1555 cm(-1) and the ratios of the intensities of the Tyr bands at 856 and 837 cm(-1), the Trp bands at 870 and 877 cm(-1), and the bands at 2940 (CH stretching) and 3420 cm(-1) (OH stretching) changed as the concentration was changed. These results reveal that although the distance between lysozyme molecules changed by more than an order of magnitude over the tested concentration range, the secondary structure of the protein did not change. The changes in the molecular interactions occurred in a stepwise process as the order of magnitude of the distance between molecules changed. These results suggest that Raman bands can be used as markers to investigate the behavior of high-concentration solutions of proteins and that the use of Raman spectroscopy will lead to progress in our understanding not only of the basic science of protein behavior under concentrated (i.e., crowded) conditions but also of practical processes involving proteins, such as in the field of biopharmaceuticals.

Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings

We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions φ in the range 0.551-0.65. We find that sub has a maximum in the vicinity of the Random Loose Packing Limit φRLP = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, sub does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on φ, but it decreases strongly with the contact number.

Insight into interfacial effect on effective physical properties of fibrous materials. I. The volume fraction of soft interfaces around anisotropic fibers

With advances in interfacial properties characterization technologies, the interfacial volume fraction is a feasible parameter for evaluating effective physical properties of materials. However, there is a need to determine the interfacial volume fraction around anisotropic fibers and a need to assess the influence of such the interfacial property on effective properties of fibrous materials. Either ways, the accurate prediction of interfacial volume fraction is required. Towards this end, we put forward both theoretical and numerical schemes to determine the interfacial volume fraction in fibrous materials, which are considered as a three-phase composite structure consisting of matrix, anisotropic hard spherocylinder fibers, and soft interfacial layers with a constant dimension coated on the surface of each fiber. The interfacial volume fraction actually represents the fraction of space not occupied by all hard fibers and matrix. The theoretical scheme that adopts statistical geometry and stereological theories is essentially an analytic continuation from spherical inclusions. By simulating such three-phase chopped fibrous materials, we numerically derive the interfacial volume fraction. The theoretical and numerical schemes provide a quantitative insight that the interfacial volume fraction depends strongly on the fiber geometries like fiber shape, geometric size factor, and fiber size distribution. As a critical interfacial property, the present contribution can be further drawn into assessing effective physical properties of fibrous materials, which will be demonstrated in another paper (Part II) of this series.

Nonequilibrium structure in sequential assembly

The assembly of monomeric constituents into molecular superstructures through sequential-arrival processes has been simulated and theoretically characterized. When the energetic interactions allow for complete overlap of the particles, the model is equivalent to that of the sequential absorption of soft particles on a surface. In the present work, we consider more general cases by including arbitrary aggregating geometries and varying prescriptions of the connectivity network. The resulting theory accounts for the evolution and final-state configurations through a system of equations governing structural generation. We find that particle geometries differ significantly from those in equilibrium. In particular, variations of structural rigidity and morphology tune particle energetics and result in significant variation in the nonequilibrium distributions of the assembly in comparison to the corresponding equilibrium case.

Mechanical Reinforcement of Polymer Nanocomposites from Percolation of a Nanoparticle Network

Nanometer-sized particles that are well dispersed in a polymer melt, presumably due to strongly favorable particle-polymer interactions, can form fractal structures via polymer bridging, leading ultimately to a nanoparticle (NP) network analogous to a colloidal gel. The linear viscoelastic response of polymer nanocomposites can be quantitatively predicted by a parameter-free model in which the stress is a simple sum of contributions from the polymer matrix and the fractal NP structure linked by bridging polymer chains. The NP contribution is modeled using critical percolation, while the polymer part is enhanced by the presence of particles, owing to hydrodynamic interactions. The phase diagram at the right shows that small NPs are needed to achieve the stronger reinforcement from glassy bridges at reasonable particle loadings.

Statistical analysis of molecule colocalization in bioimaging

The quantitative analysis of molecule interactions in bioimaging is key for understanding the molecular orchestration of cellular processes and is generally achieved through the study of the spatial colocalization between the different populations of molecules. Colocalization methods are traditionally divided into pixel-based methods that measure global correlation coefficients from the overlap between pixel intensities in different color channels, and object-based methods that first segment molecule spots and then analyze their spatial distributions with second-order statistics. Here, we present a review of such colocalization methods and give a quantitative comparison of their relative merits in different types of biological applications and contexts. We show on synthetic and biological images that object-based methods are more robust statistically than pixel-based methods, and allow moreover to quantify accurately the number of colocalized molecules.

Liquid–solid transition in mesophase separated olefin multiblock copolymers during crystallization

A delayed liquid–solid transition has been found in strongly segregated olefin multiblock copolymers, compared to that in weakly segregated systems.

Bio-optimized energy transfer in densely packed fluorescent protein enables near-maximal luminescence and solid-state lasers

Bioluminescent organisms are likely to have an evolutionary drive towards high radiance. As such, bio-optimized materials derived from them hold great promise for photonic applications. Here, we show that biologically produced fluorescent proteins retain their high brightness even at the maximum density in solid state through a special molecular structure that provides optimal balance between high protein concentration and low resonance energy transfer self-quenching. Dried films of green fluorescent protein show low fluorescence quenching (-7 dB) and support strong optical amplification (gnet=22 cm(-1); 96 dB cm(-1)). Using these properties, we demonstrate vertical cavity surface emitting micro-lasers with low threshold (<100 pJ, outperforming organic semiconductor lasers) and self-assembled all-protein ring lasers. Moreover, solid-state blends of different proteins support efficient Förster resonance energy transfer, with sensitivity to intermolecular distance thus allowing all-optical sensing. The design of fluorescent proteins may be exploited for bio-inspired solid-state luminescent molecules or nanoparticles.

Structure of a tractable stochastic mimic of soft particles

The structure and assembly of soft particles is difficult to characterize because their interpenetrability allows them to be packed at ever higher density albeit with an increasing penalty in energy and/or pressure. Alternatively, the use of impenetrable particles (such as hard spheres) as a reference model for soft particles can fail because the packing densities are limited by the impossibility of complete space filling. We recently introduced the stochastic penetration algorithm (SPA) so as to allow for the computationally efficient integration of hard sphere models while including overlaps seen in soft interactions [Craven et al., J. Chem. Phys., 2013, 138, 244901]. Moving beyond the initial one-dimensional case studied earlier, we now consider the spatial properties of systems of stochastically penetrable spheres in dimensions d≤ 3 through the use of molecular dynamics simulations and analytic methods. The stochastic potential allows spheres to either interpenetrate with a probability δ or collide elastically otherwise. For δ > 0 the particles interpenetrate (overlap), reducing the effective volume occupied by the particles in the system. We find that the occupied volume can be accurately predicted using analytic expressions derived from mean field arguments for the particle overlap probabilities with the exception of an observed clustering regime. This anomalous clustering behavior occurs at high densities and small δ. We find that this regime is coincident with that observed in deterministic penetrable models. The behavior of the stochastic penetrable particles also indicates that soft particles would be characterizable through a single reduced parameter that captures their overlap probability.