Interactions in reentrant phase behavior of a charged nanoparticle solution by multivalent ions

Abstract

The interactions following a reentrant phase transition of charged silica nanoparticles from one phase to two phases and back to one phase by varying the concentration of multivalent counterions have been examined. The observations are far beyond the framework of Debye-Hückel or even nonlinear Poisson-Boltzmann equations and demonstrate the universal behavior of multivalent counterion-driven charge inversion. We show that the interplay of multivalent counterion-induced short-range attraction and long-range electrostatic repulsion between nanoparticles results in reentrant phase behavior.

Electrostatic correlation induced ion condensation and charge inversion in multivalent electrolytes

“…Similar non-monotonic dependence of charge inversion on the salt concentration has been observed in computer simulations on electrophoresis of polyelectrolytes [15,16]. Furthermore, recent experiments show that although the initial addition of multivalent ions leads to aggregation of like-charged colloids, the aggregates redissolve on continued addition of salts [17,18]. This phenomenon of precipitation and resolubilization on adding multivalent salts has also been seen in polymeric systems and is commonly known as "reentrant condensation" [19,20].…”

Structure and Interaction of Nanoparticle–Protein Complexes

“…It may be observed in Figure a that the addition of small amounts of lysozyme with silica nanoparticles gives scattering buildup in the low- Q region with almost no changes in the intermediate and high- Q values. Similar to the variations in autocorrelation functions, such scattering buildup in the SANS data also originates from the evolution of attraction between nanoparticles and/or from the formation of larger structures. , Being oppositely charged in nature, lysozyme immediately adsorbs on nanoparticles and therefore mediates an attraction between them, leading to their aggregation. ,, In the low protein concentration (≤0.02 wt %) regime, the system is characterized by the nanoparticles experiencing the protein-induced attraction (Figure a), and hence the corresponding S ( Q ) has been modeled by the two-Yukawa (2Y) potential. , The fitted potentials (the details of which are provided in the next paragraph) give a signature for the existence of short-range attractive interaction in the system . The fitted parameters are given in Table a.…”

“…On the other hand, SANS can separate these two contributions because the scattering cross-section in SANS is proportional to the form factor and structure factor, providing information on the structure and interaction, respectively. 90,100 Therefore, to unfold these two contributions, SANS measurements were carried out on nanoparticle− lysozyme protein systems at pH 7 (Figure 6). 74 The important features of the data can be seen in three concentration regimes, similar to phase behavior: (i) the low protein concentration (0.0−0.02 wt %) regime (Figure 6a) corresponding to data also originates from the evolution of attraction between nanoparticles and/or from the formation of larger structures.…”

“…However, by DLS, it is difficult to disintegrate the contributions of structure and interaction because both of these influence the data in the same manner. On the other hand, SANS can separate these two contributions because the scattering cross-section in SANS is proportional to the form factor and structure factor, providing information on the structure and interaction, respectively. , Therefore, to unfold these two contributions, SANS measurements were carried out on nanoparticle–lysozyme protein systems at pH 7 (Figure ). The important features of the data can be seen in three concentration regimes, similar to phase behavior: (i) the low protein concentration (0.0–0.02 wt %) regime (Figure a) corresponding to Figure (b-II), (ii) the intermediate protein concentration (0.05–0.2 wt %) regime (Figure b) where the DLS data shows a bimodal distribution [Figure (b-III)], and (iii) the higher protein concentration (0.5–5 wt %) regime (Figure c) where the DLS size distribution shows the presence of large structures [Figure (b-IV)].…”

“…The two-Yukawa (2Y) potential disintegrates the attractive and repulsive parts of the total interaction potential, which allows the determination of the magnitude and range of the respective parts of the potential without any predefined assumption or limitations. Moreover, the present system is primarily governed by the electrostatic interactions, hence the choice of the 2Y potential is expected to present the system in its most suitable physical manner. ,,, Furthermore, it has been shown that the 2Y potential is also able to take account of the most popular theory of colloidal stability, i.e., DLVO theory, by simulating the van der Waals potential by a short-range attractive Yukawa potential. , Considering all of these points, we believe that the 2Y potential could be a proficient option for representing such systems without losing generality.…”