Effective Structure Factor Research Articles

Rescaled mode-coupling scheme for the quantitative description of experimentally observed colloid dynamics.

We describe experimentally observed collective dynamics in colloidal suspensions of model hard-sphere particles using a modified mode coupling theory (MCT). This rescaled MCT is capable of describing quantitatively the wave-vector and time-dependent diffusion in these systems. Intermediate scattering functions of liquidlike structured dispersions are determined by means of static and dynamic light-scattering experiments. The structure and short-time dynamics of the systems can be described quantitatively employing a multicomponent Percus-Yevick ansatz for the partial structure factors and an effective, one-component description of hydrodynamic interactions based on the semianalytical δγ expansion. Combined with a recently proposed empirical modification of MCT in which memory functions are calculated using effective structure factors at rescaled number densities, the scheme is able to model the collective dynamics over the entire accessible time and wave-vector range and predicts the volume-fraction-dependence of long-time self-diffusion coefficients and the zero-shear viscosity quantitatively. This highlights the potential of MCT as a practical tool for the quantitative analysis and prediction of experimental observations.

Arrested spinodal decomposition of the screened symmetric restricted primitive model.

Amorphous solids, such as glasses and gels, arise as the asymptotic limit of non-equilibrium and irreversible relaxation aging processes. These amorphous solids form when the system is suddenly and deeply quenched in the dynamic arrest region. We use the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory to investigate the formation of such structures via arrested spinodal decomposition in the screened symmetric restricted primitive model. We propose a direct correlation function that allows us to derive an expression for the functional derivative of the chemical potential, which serves as the necessary input in the NE-SCGLE theory. By analyzing the asymptotic localization length and the asymptotic characteristic length, we identify different classes of dynamic arrest states as a function of the density and the final quench temperature. The system features simultaneously attractive and repulsive interactions, resulting in different arrested regions in the non-equilibrium phase diagram for a given screened parameter: (i) ionic glasses, (ii) electrostatic gels, and (iii) attractive glasses. Finally, by collapsing the asymptotic effective structure factors at a typical fractal dimension of df = 3, we confirm the formation of gels slightly above the glass-gel transition in the arrested phase diagram.

Calculation of diffusion coefficient of liquid less simple metals

Diffusion coefficient of liquid less simple metals has been studied using linear trajectory (LT) and small-step (SS) diffusion theories of liquid metals with Carnahan–Stirling (CS) approximation. Friction coefficients, the key ingredients of this study, are calculated using effective pair potentials, v(r), and static structure factors, S(q). For v(r), Brettonet–Silbert pseudopotential model has been chosen whereas for S(q), both variational modified hypernetted chain (VMHNC) integral equation and linearized Weeks–Chandler–Andersen (LWCA) perturbation theory have been employed. Calculated friction coefficients are found comparable to the available simulated data. Inclusion of CS approximation increases the value of friction coefficient obtained from hard part which dominates over rest of the coefficients. Applied LWCA theory provides slightly larger values of diffusion coefficients than those obtained from VMHNC. Comparing with literature values, calculated results suggest that the combination of LWCA theory along with LT and SS theories with CS approximation is excellent for calculation of diffusion coefficient.

Universal effective interactions of globular proteins close to liquid-liquid phase separation: Corresponding-states behavior reflected in the structure factor.

Intermolecular interactions in protein solutions, in general, contain many contributions. If short-range attractions dominate, the state diagram exhibits liquid-liquid phase separation (LLPS) that is metastable with respect to crystallization. In this case, the extended law of corresponding states (ELCS) suggests that thermodynamic properties are insensitive to details of the underlying interaction potential. Using lysozyme solutions, we investigate the applicability of the ELCS to the static structure factor and how far effective colloidal interaction models can help to rationalize the phase behavior and interactions of protein solutions in the vicinity of the LLPS binodal. The (effective) structure factor has been determined by small-angle x-ray scattering. It can be described by Baxter's adhesive hard-sphere model, which implies a single fit parameter from which the normalized second virial coefficient b2 is inferred and found to quantitatively agree with previous results from static light scattering. The b2 values are independent of protein concentration but systematically vary with temperature and solution composition, i.e., salt and additive content. If plotted as a function of temperature normalized by the critical temperature, the values of b2 follow a universal behavior. These findings validate the applicability of the ELCS to globular protein solutions and indicate that the ELCS can also be reflected in the structure factor.

Effects of Monovalent Salt on Protein-Protein Interactions of Dilute and Concentrated Monoclonal Antibody Formulations.

In this study, we used sodium chloride (NaCl) to extensively modulate non-specific protein-protein interactions (PPI) of a humanized anti-streptavidin monoclonal antibody class 2 molecule (ASA-IgG2). The changes in PPI with varying NaCl (CNaCl) and monoclonal antibody (mAb) concentration (CmAb) were assessed using the diffusion interaction parameter kD and second virial coefficient B22 measured from solutions with low to moderate CmAb. The effective structure factor S(q)eff measured from concentrated mAb solutions using small-angle X-ray and neutron scattering (SAXS/SANS) was also used to characterize the PPI. Our results found that the nature of net PPI changed not only with CNaCl, but also with increasing CmAb. As a result, parameters measured from dilute and concentrated mAb samples could lead to different predictions on the stability of mAb formulations. We also compared experimentally determined viscosity results with those predicted from interaction parameters, including kD and S(q)eff. The lack of a clear correlation between interaction parameters and measured viscosity values indicates that the relationship between viscosity and PPI is concentration-dependent. Collectively, the behavior of flexible mAb molecules in concentrated solutions may not be correctly predicted using models where proteins are considered to be uniform colloid particles defined by parameters derived from low CmAb.

Structure and dynamics of dense colloidal ellipsoids at the nearest-neighbor length scale

Anisotropic particles are known to exhibit a richer and more complex phase behavior in comparison to their spherical counterpart. While the majority of the existing studies address structural properties, the dynamic behavior of anisotropic particles is a relatively lesser explored avenue. Using multispeckle ultra-small-angle x-ray photon correlation spectroscopy (USA-XPCS), we have carried out a systematic investigation of the structural and dynamic properties of colloidal ellipsoids at the nearest-neighbor length scale. The USA-XPCS measurements have allowed us to probe, as a function of the volume fraction, the q-dependent effective structure factor, Seff(q), along with the effective long time diffusion coefficient, Deff(q), for this anisotropic system. Our results indicate a scaling behavior of Deff(q) with 1/Seff(q) from which we have estimated the effective amplitude function Aeff(q), which can be directly related to the effective hydrodynamic function Heff(q). Aeff(q) shows a similar q dependence to that of S(q). Our investigation also allows for the precise determination of the volume fraction corresponding to the arrest transition.

Equilibrium field theory of magnetic monopoles in degenerate square spin ice: Correlations, entropic interactions, and charge screening regimes

We describe degenerate square spin as an ensemble of magnetic monopoles coupled via an emergent entropic field that subsumes the effect of the underlying spin vacuum. We compute their effective free energy, entropic interaction, correlations, screening, and structure factors that coincide with the experimental ones. Unlike in pyrochlore ices, a dimensional mismatch between real and entropic interactions leads to weak singularities at the pinch points and algebraic correlations at long distance. This algebraic screening can be, however, camouflaged by a pseudo-screening regime.

Investigation of Gas Transport Properties of PEMFC Catalyst Layers Using a Microfluidic Device

The effective gas diffusivity, porous structure, and tortuosity factor of catalyst layers used in proton exchange membrane fuel cells were evaluated using a microfluidic device. Sufficient gas transport properties of the catalyst layers are a key factor for achieving high-performance catalyst layers and fuel cells. In the present study, catalyst layers with different thicknesses and different carbon supports were evaluated. Stand-alone carbon black and multi-walled carbon nanotubes were blended into the catalyst layers as the support. The all-carbon-black-based catalyst layer contained some volume of isolated pores and some amount of microcracks, which depended on its thickness. The tortuosity factor was evaluated considering the effects of the isolated pores and microcracks. However, the tortuosity factor of the all-carbon-black-based catalyst layer was larger than the well-known Bruggeman-correlated tortuosity factor. When carbon nanotubes were blended into the catalyst layer, the tortuosity factor was drastically decreased to less than one-half that of the carbon-black-based catalyst layers. A change in the number of straight pores formed by the fibrous support and variation of the ionomer distribution can affect the tortuosity factor.

Studying Excipient Modulated Physical Stability and Viscosity of Monoclonal Antibody Formulations Using Small-Angle Scattering.

Excipients are substances that are added to therapeutic products to improve stability, bioavailability, and manufacturability. Undesirable protein-protein interactions (PPI) can lead to self-association and/or high solution viscosity in concentrated protein formulations that are typically greater than 50 mg/mL. Therefore, understanding the effects of excipients on nonspecific PPI is important for more efficient formulation development. In this study, we used National Institute of Standards and Technology monoclonal antibody (NISTmAb) reference material as a model antibody protein to examine the physical stability and viscosity of concentrated formulations using a series of excipients, by varying pH, salt composition, and the presence of cosolutes including amino acids, sugars, and nonionic surfactants. Small angle X-ray scattering (SAXS) together with differential scanning calorimetry (DSC), dynamic light scattering (DLS), and viscosity measurements were used to obtain various experimental parameters to characterize excipient modulated PPI and bulk solution viscosities. In particular, a good correlation was found between SAXS and DLS/SLS results, suggesting that the use of DLS/SLS is valid for predicting the colloidal stability of NISTmAb in concentrated solutions. Moreover, further analysis of effective structure factor S(q)eff measured from SAXS enabled the dissection of net PPI into hydrodynamic forces due to excluded volume as well as any additional attractive or repulsive interactions with the presence of excipients. It was found that although no denaturation or aggregation of NISTmAb was observed and that the net PPI were repulsive, the use of ionic excipients such as pH and salts leads to increased short-range attraction, whereas the nonionic excipients including sugars, amino acids, and polysorbate surfactants lead to increased repulsive PPI with increasing protein concentration. Results obtained from viscosity measurements showed that the use of excipients can lead to increased solution viscosities at high protein concentrations. The use of S(q)eff, interaction parameter kD, and second virial coefficient B22 as predictors for solution viscosity was also evaluated by comparing the predicted results with the measured viscosities. Although B22 and S(q)eff appeared to be better predictors than kD, disagreement between the predicted and measured results suggests other factors apart from PPI contribute to the bulk rheological properties of concentrated protein solutions.

Self-Interaction of Human Serum Albumin: A Formulation Perspective.

In the present study, small-angle X-ray scattering (SAXS) and static light scattering (SLS) have been used to study the solution properties and self-interaction of recombinant human serum albumin (rHSA) molecules in three pharmaceutically relevant buffer systems. Measurements are carried out up to high protein concentrations and as a function of ionic strength by adding sodium chloride to probe the role of electrostatic interactions. The effective structure factors (Seff) as a function of the scattering vector magnitude q have been extracted from the scattering profiles and fit to the solution of the Ornstein–Zernike equation using a screened Yukawa potential to describe the double-layer force. Although only a limited q range is used, accurate fits required including an electrostatic repulsion element in the model at low ionic strength, while only a hard sphere model with a tunable diameter is necessary for fitting to high-ionic-strength data. The fit values of net charge agree with available data from potentiometric titrations. Osmotic compressibility data obtained by extrapolating the SAXS profiles or directly from SLS measurements has been fit to a 10-term virial expansion for hard spheres and an equation of state for hard biaxial ellipsoids. We show that modeling rHSA as an ellipsoid, rather than a sphere, provides a much more accurate fit for the thermodynamic data over the entire concentration range. Osmotic virial coefficient data, derived at low protein concentration, can be used to parameterize the model for predicting the behavior up to concentrations as high as 450 g/L. The findings are especially important for the biopharmaceutical sector, which require approaches for predicting concentrated protein solution behavior using minimal sample consumption.

Small-angle neutron scattering and molecular dynamics structural study of gelling DNA nanostars.

DNA oligomers with properly designed sequences self-assemble into well defined constructs. Here, we exploit this methodology to produce bulk quantities of tetravalent DNA nanostars (each one composed of 196 nucleotides) and to explore the structural signatures of their aggregation process. We report small-angle neutron scattering experiments focused on the evaluation of both the form factor and the temperature evolution of the scattered intensity at a nanostar concentration where the system forms a tetravalent equilibrium gel. We also perform molecular dynamics simulations of one isolated tetramer to evaluate the form factor numerically, without resorting to any approximate shape. The numerical form factor is found to be in very good agreement with the experimental one. Simulations predict an essentially temperature-independent form factor, offering the possibility to extract the effective structure factor and its evolution during the equilibrium gelation.

Concentration-Induced Association in a Protein System Caused by a Highly Directional Patch Attraction

Self-association of the protein lactoferrin is studied in solution using small-angle X-ray scattering techniques. Effective static structure factors have been shown to exhibit either a monotonic or a nonmonotonic dependence on protein concentration in the small wavevector limit, depending on salt concentration. The behavior correlates with a nonmonotonic dependence of the second virial coefficient on salt concentration, such that a maximum appears in the structure factor at a low protein concentration when the second virial coefficient is negative and close to a minimum. The results are interpreted in terms of an integral equation theory with explicit dimers, formulated by Wertheim, which provides a consistent framework able to explain the behavior in terms of a monomer-dimer equilibrium that appears because of a highly directional patch attraction. Short attraction ranges preclude trimer formation, which explains why the protein system behaves as if it were subject to a concentration-dependent isotropic protein-protein attraction. Superimposing an isotropic interaction, comprising screened Coulomb repulsion and van der Waals attraction, on the patch attraction allows for a semiquantitative modeling of the complete transition pathway from monomers in the dilute limit to monomer-dimer systems at somewhat higher protein concentrations.

Structure of alumina-silica nanoparticles grafted with alkylphosphonic acids in poly(ethylacrylate) nanocomposites

Alumina-coated silica nanoparticles (NPs) grafted with phosphonic acids of different hydrophobicity were used as filler in poly(ethylacrylate) nanocomposites. Phosphonic acids bearing short alkyl chains or a diethylene glycol group have been grafted at densities up to 3.2 P/nm2 on NPs (20 nm) dispersed in water. Nanocomposites at particle fractions up to 10 vol% have been formulated by casting from the colloidal mixtures of modified NPs and nanolatex in water. The dispersion of the NPs in the polymer matrix has been studied by TEM combined with small-angle scattering, evidencing aggregation of NPs. TEM shows micrometer-scale inhomogeneities depending on the surface/polymer matrix compatibility. For the local interparticle correlations, a quantitative analysis of the intensity based on the mapping onto the effective structure factor of polydisperse hard spheres is developed. This mapping allows the model-free determination of the internal volume fraction of aggregates, termed compacity κ, to between 10% and 30%, compatible with the TEM analysis. κ is found to increase for the higher particle volume fractions, to decrease with grafting density, and to be mostly independent of the nature and mass of the graft. Preliminary evidence for an improved compatibility of grafted with respect to bare NPs is found, as opposed to their aqueous precursor suspensions where some pre-aggregation is induced by grafting.

Designing disordered materials using DNA-coated colloids of bacteriophage fd and gold.

DNA has emerged as an exciting binding agent for programmable colloidal self-assembly. Its popularity derives from its unique properties: it provides highly specific short-ranged interactions and at the same time it acts as a steric stabilizer against non-specific van der Waals and Coulomb interactions. Because complementary DNA strands are linked only via hydrogen bonds, DNA-mediated binding is thermally reversible: it provides an effective attraction that can be switched off by raising the temperature only by a few degrees. In this article we introduce a new binary system made of DNA-functionalized filamentous fd viruses of ∼880 nm length with an aspect ratio of ∼100, and 50 nm gold nanoparticles (gold NPs) coated with the complementary DNA strands. When quenching mixtures below the melt temperature Tm, at which the attraction is switched on, we observe aggregation. Conversely, above Tm the system melts into a homogenous particulate 'gas'. We present the aggregation behavior of three different gold NP to virus ratios and compare them to a gel made solely of gold NPs. In particular, we have investigated the aggregate structures as a function of cooling rate and determine how they evolve as function of time for given quench depths, employing fluorescence microscopy. Structural information was extracted in the form of an effective structure factor and chord length distributions. Rapid cooling rates lead to open aggregates, while slower controlled cooling rates closer to equilibrium DNA hybridization lead to more fine-stranded gels. Despite the different structures we find that for both cooling rates the quench into the two-phase region leads to initial spinodal decomposition, which becomes arrested. Surprisingly, although the fine-stranded gel is disordered, the overall structure and the corresponding length scale distributions in the system are remarkably reproducible. Such highly porous systems can be developed into new functional materials.

Analysis of dielectric function and dynamic structure factor of a multi-component plasma in a wurtzite GaN

We investigated dielectric responses of a multi-component plasma at finite temperature and applied the results to spectral analysis of dynamic structure factor of a photo-generated high density plasma in a wurtzite GaN. The behavior of effective dielectric function and dynamic structure factor in energy loss measurement are examined focusing to the effects of dynamic screening of carriers in the plasma. Features of their spectral behavior are illustrated including the roles of various elementary excitations in the three-component solid state plasma.

Small-angle X-ray scattering probe of intermolecular interaction in red blood cells**Supported by National Basic Research Program of China (2009CB918600) and National Natural Science Foundation of China (10979005)

With high concentrations of hemoglobin (Hb) in red blood cells, self-interactions among these molecules could increase the propensities of their polymerization and aggregation. In the present work, high concentration Hb in solution and red blood cells were analyzed by small-angle X-ray scattering. Calculation of the effective structure factor indicates that the interaction of Hb molecules is the same when they are crowded together in both the cell and physiological saline. The Hb molecules stay individual without the formation of aggregates and clusters in cells.

Intermolecular interactions and molecular dynamics in bovine serum albumin solutions studied by small angle X-ray scattering and dielectric relaxation spectroscopy

We used small angle X-ray scattering (SAXS) and dielectric relaxation spectroscopy (DRS) to clarify static structure and molecular dynamics of bovine serum albumin (BSA) in solution. SAXS allowed us to access spatial correlations of the protein molecules in concentrated solutions at different ionic strength. Using a well-established Fourier inversion technique, called SQ-IFT, we deduced the effective pair correlation functions, g(r)eff, from the effective (or experimental) structure factors, S(q)eff, without assuming any potential models for protein–protein interactions. In terms of S(q)eff and g(r)eff, the mean nearest-neighbor distance, d⁎, the osmotic compressibility, κosm, and the coordination number, NC, were evaluated.The complex dielectric spectra of aqueous BSA solutions measured in the frequency range from 1MHz to 10GHz were able to be decomposed into three relaxation processes having different physical origins. The highest frequency process, whose relaxation time was ca. 8ps, was assigned to cooperative rearrangement of H-bond network of bulk-water. We evaluated the effective hydration number of a BSA molecule, Zhyd, using the bulk-water relaxation amplitude. This approach yielded ca. 1200 hydrated water molecules per a BSA molecule, corresponding to ca. 0.3g hydrated water per 1g protein. The lowest frequency process having a relaxation time of ca. 50ns was assigned to rotational diffusion of the BSA molecule. We confirmed that an effective molar volume of BSA calculated with Stokes–Einstein–Debye equation was identical to that predicted from its molecular weight and specific density. According to the Kirkwood relationship, the dipole–dipole orientational correlation factor decreased with an increase of protein concentration, which indicated the operation of BSA–BSA interaction and favored antiparallel dipolar correlation between the protein molecules.

Effects of water chemistry on structure and performance of polyamide composite membranes

The effects of feed solution ionic strength, pH and divalent cation content on NF/RO membrane structure and performance were elucidated experimentally and fitted with a modified solution–diffusion transport model that describes polyamide thin film free volume through an effective pore radius and structure factor. All the membranes tested became more hydrophilic and swollen with increasing feed solution ionic strength, pH, and divalent cation concentrations. Generally, water permeabilities of all three membranes decreased with ionic strength and divalent cation content, but increased with pH. For RO membranes, neutral solute rejection decreased with pH and divalent cation content, but increased with ionic strength and the salt rejection remained independent with water chemistry except for very low pH of 3; for a NF membrane, solute rejection was more sensitive to water chemistry and neutral solute rejection decreased with ionic strength and pH, but increased with divalent cation content. The results presented herein provide new insight into the fundamental relationship between changes in NF/RO membrane structure and performance. Ultimately, these new insights may be useful in selection of already commercial or design of new NF/RO membranes for removal of chemicals of emerging concern in water treatment.

Fast-SAXS-pro: A unified approach to computing SAXS profiles of DNA, RNA, protein, and their complexes

A generalized method, termed Fast-SAXS-pro, for computing small angle x-ray scattering (SAXS) profiles of proteins, nucleic acids, and their complexes is presented. First, effective coarse-grained structure factors of DNA nucleotides are derived using a simplified two-particle-per-nucleotide representation. Second, SAXS data of a 18-bp double-stranded DNA are measured and used for the calibration of the scattering contribution from excess electron density in the DNA solvation layer. Additional test on a 25-bp DNA duplex validates this SAXS computational method and suggests that DNA has a different contribution from its hydration surface to the total scattering compared to RNA and protein. To account for such a difference, a sigmoidal function is implemented for the treatment of non-uniform electron density across the surface of a protein/nucleic-acid complex. This treatment allows differential scattering from the solvation layer surrounding protein/nucleic-acid complexes. Finally, the applications of this Fast-SAXS-pro method are demonstrated for protein/DNA and protein/RNA complexes.

Concentration induced ordering of microemulsion droplets in bulk and near the liquid–air interface

The structure of the air interface of water–AOT (sodium bis(2-ethyl hexyl) sulfosuccinate)–decane microemulsions in the droplet phase with ω = 20, 30, 40 is studied in a range of compositions with droplet volume fractions of ϕ = 0.2 to 0.7. A combination of small angle X-ray scattering (SAXS) and X-ray reflectometry (XR) reveals a detailed image of the morphology in the bulk and at the microemulsion–air interface. The structure of the volume is described in terms of effective structure factors to obtain the bulk droplet structure and correlations. With increasing droplet density ϕ the droplets remain unchanged in their size and show an increase in the local order. The reflectivity behaviour of the samples can be consistently explained by bulk small angle scattering and specular reflectivity at the surface. The microemulsion–air interface consists of droplets with the same ϕ-dependent local order as in the bulk, e.g. we found a droplet volume fraction induced ordering of droplets.