Structure and interaction in the polymer-dependent reentrant phase behavior of a charged nanoparticle solution

Realizability of iso-g2 processes via effective pair interactions

An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function g2( r) [or equivalently, structure factor S( k)] at some number density ρ can be achieved by many-body systems in d-dimensional Euclidean space. The Zhang–Torquato conjecture states that any realizable set of pair statistics, whether from a nonequilibrium or equilibrium system, can be achieved by equilibrium systems involving up to two-body interactions. To further test this conjecture, we study the realizability problem of the nonequilibrium iso- g2 process, i.e., the determination of density-dependent effective potentials that yield equilibrium states in which g2 remains invariant for a positive range of densities. Using a precise inverse algorithm that determines effective potentials that match hypothesized functional forms of g2( r) for all r and S( k) for all k, we show that the unit-step function g2, which is the zero-density limit of the hard-sphere potential, is remarkably realizable up to the packing fraction ϕ = 0.49 for d = 1. For d = 2 and 3, it is realizable up to the maximum “terminal” packing fraction ϕ c = 1/2 d, at which the systems are hyperuniform, implying that the explicitly known necessary conditions for realizability are sufficient up through ϕ c. For ϕ near but below ϕ c, the large- r behaviors of the effective potentials are given exactly by the functional forms exp[ − κ( ϕ) r] for d = 1, r−1/2 exp[ − κ( ϕ) r] for d = 2, and r−1 exp[ − κ( ϕ) r] (Yukawa form) for d = 3, where κ−1( ϕ) is a screening length, and for ϕ = ϕ c, the potentials at large r are given by the pure Coulomb forms in the respective dimensions as predicted by Torquato and Stillinger [Phys. Rev. E 68, 041113 (2003)]. We also find that the effective potential for the pair statistics of the 3D “ghost” random sequential addition at the maximum packing fraction ϕ c = 1/8 is much shorter ranged than that for the 3D unit-step function g2 at ϕ c; thus, it does not constrain the realizability of the unit-step function g2. Our inverse methodology yields effective potentials for realizable targets, and, as expected, it does not reach convergence for a target that is known to be non-realizable, despite the fact that it satisfies all known explicit necessary conditions. Our findings demonstrate that exploring the iso- g2 process via our inverse methodology is an effective and robust means to tackle the realizability problem and is expected to facilitate the design of novel nanoparticle systems with density-dependent effective potentials, including exotic hyperuniform states of matter.

Unravelling Polyethylenimine Mediated Non-monotonic Stability Behaviour of Silica Colloids: Role of Competing Electrostatic and Entropic Interactions

Polymer-mediated interactions play an important role in the stability of the colloids and therefore, are paramount for both fundamental as well as scientific interests. The stability of the colloids in...

Oligomerization of Pharmaceutically Relevant Insulin Analogues for Varying Concentration and Salinity Revealed by Small-Angle X-ray Scattering

Two different insulin analogues, insulin degludec and lithocholyl insulin, were studied by small-angle X-ray scattering with respect to their self-assembly and interactions in solution at different concentrations of insulin and salt, NaCl. Very different behavior was observed for the two. Insulin degludec, linked to a hexadecanedioic acid, consistently formed di-hexamers, without any further oligomeric growth upon screening of electrostatic repulsions, indicating a stable di-hexamer unit without further oligomerization, as expected in the presence of phenol. The other insulin analogue, linked to the sterol lithocholic acid, formed n-hexamers with n ranging from 1 to 15, increasing with NaCl concentration and insulin concentration, indicating attractive forces in competition with the electrostatic repulsion and solution entropy. At the highest concentration of insulin and NaCl, a liquid crystal phase was observed, which has not previously been identified, featuring a quadratic structure organized into layers, which might hold interesting properties for pharmaceutical applications.

Interplay between Interparticle Potential and Adsorption Structure in Nanoparticle Dispersions with Polymer Addition as Displayed by Small-Angle Scattering

The effect of polymer adsorption on the dispersion stability of particles is an important subject applicable to various manufacturing processes. In this study, small-angle scattering was used to examine the relationship between interparticle potential and polymer adsorption in dispersions of nanoparticles with an 81 Å radius containing two types of polymers. Small-angle X-ray scattering (SAXS) measurements in a silica/polyacrylamide (PAAm) system showed an increase in interparticle attractive interactions as PAAm concentration was increased. In a silica/poly(ethylene oxide) (PEO) system, the correlation between PEO concentration and interparticle potential strength became negligible at higher concentrations. Hence, the contrast variation small-angle neutron scattering (CV-SANS) method was employed to evaluate the interparticle potential and polymer adsorption simultaneously. CV-SANS revealed that PAAm was adsorbed to silica particles with a polymer shell layer thickness of 186 Å. The attractive potential observed in the absorbed layer region can be attributed to bridging PAAm molecules between the silica particles. By contrast, CV-SANS of the silica/PEO system indicated a low-polymer-concentration layer with a thickness of 34 Å around silica particles, indicating weak adsorption of PEO molecules. Negligible interaction between PEO and silica particles was assumed to be the origin of the depletion stabilization from excess polymer addition. Thus, quantitative analyses conducted using SAXS and CV-SANS measurements for the first time clearly demonstrated a difference in the adsorption structure of the polymer, which induces changes in the interaction potential between nanoparticles.

Evolution of Interactions in the Protein Solution As Induced by Mono and Multivalent Ions

The evolution of interactions in the bovine serum albumin (BSA) protein solution on addition of mono and multivalent (di, tri and tetra) counterions has been studied using small-angle neutron scattering (SANS), dynamic light scattering (DLS) and ζ-potential measurements. It is found that in the presence of mono and divalent counterions, protein behavior can be well explained by DLVO theory, combining the contributions of screened Coulomb repulsion with the van der Waals attraction. The addition of mono or divalent salts in protein solution reduces the repulsive barrier and hence the overall interaction becomes attractive, but the system remains in one-phase for the entire concentration range of the salts, added in the system. However, contrary to DLVO theory, the protein solution undergoes a reentrant phase transition from one-phase to a two-phase system and then back to the one-phase system in the presence of tri and tetravalent counterions. The results show that tri and tetravalent (unlike mono and divalent) counterions induce short-range attraction between the protein molecules, leading to the transformation from one-phase to two-phase system. The two-phase is characterized by the fractal structure of protein aggregates. The excess condensation of these higher-valent counterions in the double layer around the BSA causes the reversal of charge of the protein molecules resulting into reentrant of the one-phase, at higher salt concentrations. The complete phase behavior with mono and multivalent ions has been explained in terms of the interplay of electrostatic repulsion and ion-induced short-range attraction between the protein molecules.

Nanoparticle self-assembly: from interactions in suspension to polymer nanocomposites

Recent experimental results using in particular small-angle scattering to characterize the self-assembly of mainly hard spherical nanoparticles into higher ordered structures ranging from fractal aggregates to ordered assemblies are reviewed. The crucial control of interparticle interactions is discussed, from chemical surface-modification, or the action of additives like depletion agents, to the generation of directional patches and the use of external fields. It is shown how the properties of interparticle interactions have been used to allow inducing and possibly controlling aggregation, opening the road to the generation of colloidal molecules or potentially metamaterials. In the last part, studies of the microstructure of polymer nanocomposites as an application of volume-spanning and stress-carrying aggregates are discussed.

Tuning Nanoparticle-Micelle Interactions and Resultant Phase Behavior

The evolution of the interaction between an anionic nanoparticle and a nonionic surfactant and their resultant phase behavior in aqueous solution in the presence of electrolyte and ionic surfactants have been studied. The mixed system of anionic silica nanoparticles (Ludox LS30) with nonionic surfactant decaethylene glycol monododecylether (C12E10) forms a highly stable clear phase over a wide concentration range of surfactant. Small-angle neutron scattering (SANS) and dynamic light scattering data show that the surfactant micelles adsorb on the surface of the nanoparticle, resulting in micellar-decorated nanoparticle structures. With the addition of a small amount of electrolyte into this system, the stability gets disturbed substantially and turns to a two-phase (turbid) system. The evolution of interaction in this system has been examined, and it was found that micelle-induced long-range depletion attraction (modeled by a double Yukawa potential) between nanoparticles leads to their aggregation. Interestingly, the addition of anionic surfactant sodium dodecyl sulfate (SDS) in this two-phase system transforms it to a transparent one-phase state, suppressing the depletion-mediated aggregation of nanoparticles. This is attributed to the formation of anionic C12E10-SDS mixed micelles, and it is their repulsive micelle-micelle interaction that disrupts the depletion phenomenon. On the other hand, the addition of cationic surfactant dodecyl trimethylammonium bromide (DTAB) to the turbid LS30-C12E10 electrolyte system shows no change in the turbidity arising from an aggregated nanoparticle system. The driving interaction, in this case, is different from that of the surfactant-mediated depletion attraction; it is due to the attraction between the nanoparticles mediated by the presence of oppositely charged DTAB micelles between them, resulting in a charge-driven bridging aggregation of nanoparticles. Each of these multicomponent systems has been investigated using contrast variation SANS measurements for different contrast conditions where the role of individual components (nanoparticle or surfactant) in the mixed system has been selectively studied. These results thus show that nanoparticle-surfactant micelle interactions can be tuned by the presence of electrolyte and/or choice of surfactant combination.

Structure and Interaction in the pH-Dependent Phase Behavior of Nanoparticle-Protein Systems

The pH-dependent structure and interaction of anionic silica nanoparticles (diameter 18 nm) with two globular model proteins, lysozyme and bovine serum albumin (BSA), have been studied. Cationic lysozyme adsorbs strongly on the nanoparticles, and the adsorption follows exponential growth as a function of lysozyme concentration, where the saturation value increases as pH approaches the isoelectric point (IEP) of lysozyme. By contrast, irrespective of pH, anionic BSA does not show any adsorption. Despite having a different nature of interactions, both proteins render a similar phase behavior where nanoparticle-protein systems transform from being one-phase (clear) to two-phase (turbid) above a critical protein concentration (CPC). The measurements have been carried out for a fixed concentration of silica nanoparticles (1 wt %) with varying protein concentrations (0-5 wt %). The CPC is found to be much higher for BSA than for lysozyme and increases for lysozyme but decreases for BSA as pH approaches their respective IEPs. The structure and interaction in these systems have been examined using dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The effective hydrodynamic size of the nanoparticles measured using DLS increases with protein concentration and is related to the aggregation of the nanoparticles above the CPC. The propensity of the nanoparticles to aggregate is suppressed for lysozyme and enhanced for BSA as pH approached their respective IEPs. This behavior is understood from SANS data through the interaction potential determined by the interplay of electrostatic repulsion with a short-range attraction for lysozyme and long-range attraction for BSA. The nanoparticle aggregation is caused by charge neutralization by the oppositely charged lysozyme and through depletion for similarly charged BSA. Lysozyme-mediated attractive interaction decreases as pH approaches the IEP because of a decrease in the charge on the protein. In the case of BSA, a decrease in the BSA-BSA repulsion enhances the depletion attraction between the nanoparticles as pH is shifted toward the IEP. The morphology of the nanoparticle aggregates is found to be mass fractal.

Small-Angle Neutron Scattering Study of Interplay of Attractive and Repulsive Interactions in Nanoparticle-Polymer System

The phase behavior of nanoparticle (silica)-polymer (polyethylene glycol) system without and with an electrolyte (NaCl) has been studied. It is observed that nanoparticle-polymer system behaves very differently in the presence of electrolyte. In the absence of electrolyte, the nanoparticle-polymer system remains in one-phase even at very high polymer concentrations. On the other hand, a re-entrant phase behavior is found in the presence of electrolyte, where one-phase (individual) system undergoes two-phase (nanoparticle aggregation) and then back to one-phase with increasing polymer concentration. The regime of two-phase system has been tuned by varying the electrolyte concentration. The polymer concentration range over which the two-phase system exists is significantly enhanced with the increase in the electrolyte concentration. These systems have been characterized by small-angle neutron scattering (SANS) experiments of contrast-marching the polymer to the solvent. The data are modeled using a two-Yukawa potential accounting for both attractive and repulsive parts of the interaction between nanoparticles. The phase behavior of nanoparticle-polymer system is explained by interplay of attractive (polymer-induced attractive depletion between nanoparticles) and repulsive (nanoparticle-nanoparticle electrostatic repulsion and polymer-polymer repulsion) interactions present in the system. In the absence of electrolyte, the strong electrostatic repulsion between nanoparticles dominates over the polymer-induced depletion attraction and the nanoparticle system remains in one-phase. With addition of electrolyte, depletion attraction overcomes electrostatic repulsion at some polymer concentration, resulting into nanoparticle aggregation and two-phase system. Further addition of polymer increases the polymer-polymer repulsion which eventually reduces the strength of depletion and hence re-entrant phase behavior. The effects of varying electrolyte concentration on the phase behavior of nanoparticle-polymer system are understood in terms of modifications in nanoparticle-nanoparticle and polymer-polymer interactions. The nanoparticle aggregates in two-phase systems are found to have surface fractal morphology.

Electrolyte effect on the phase behavior of silica nanoparticles with lysozyme and bovine-serum-albumin proteins

Small-angle neutron scattering (SANS) and dynamic light scattering (DLS) studies have been carried out to investigate the effect of an electrolyte on the phase behavior of anionic silica nanoparticles with two globular proteins-cationic lysozyme [molecular weight (MW) 14.7 kDa] and anionic bovine serum albumin (MW 66.4 kDa). The results are compared with our earlier published work on similar systems without any electrolyte [I. Yadav, S. Kumar, V. K. Aswal, and J. Kohlbrecher, Phys. Rev. E 89, 032304 (2014)]. Both the nanoparticle-protein systems transform to two phase at lower concentration of protein in the presence of an electrolyte. The autocorrelation function in DLS suggests that the diffusion coefficient (D) of a nanoparticle-protein system decreases in approaching two phase with the increase in protein concentration. This variation in D can be attributed to increase in attractive interaction and/or overall increase in the size. Further, these two contributions (interaction and structure) are determined from the SANS data. The changes in the phase behavior of nanoparticle-protein systems in the presence of an electrolyte are explained in terms of modifications in both the repulsive and attractive components of interaction between nanoparticles. In a two-phase system individual silica nanoparticles coexist along with their fractal aggregates.