Like-Charge Attraction between Metal Nanoparticles in a 1∶1 Electrolyte Solution

Examining the Correlation between the Inorganic Nano-Fertilizer Physical Properties and Their Impact on Crop Performance and Nutrient Uptake Efficiency

The physical properties of nano-fertilizers (NFs) are important in determining their performance, efficacy, and environmental interactions. Nano-fertilizers, due to their small size and high surface area-to-volume ratio, enhance plant metabolic reactions, resulting in higher crop yields. The properties of nano-fertilizers depend on the synthesis methods used. The nanoparticle's nutrient use efficiency (NUE) varies among plant species. This review aims to analyze the relationship between the physical properties of NF and their influence on crop performance and nutrient uptake efficiency. The review focuses on the physical properties of NFs, specifically their size, shape, crystallinity, and agglomeration. This review found that smaller particle-sized nanoparticles exhibit higher nutrient use efficiency than larger particles. Nano-fertilizer-coated additives gradually release nutrients, reducing the need for frequent application and addressing limitations associated with chemical fertilizer utilization. The shapes of nano-fertilizers have varying effects on the overall performance of plants. The crystalline structure of nanoparticles promotes a slow release of nutrients. Amorphous nano-fertilizers improve the NUE and, ultimately, crop yield. Agglomeration results in nanoparticles losing their nanoscale size, accumulating on the outer surface, and becoming unavailable to plants. Understanding the physical properties of nano-fertilizers is crucial for optimizing their performance in agricultural applications.

Two-dimensional assembly of gold nanoparticles grafted with charged-end-group polymers

HYPOTHESIS

Introducing charged terminal groups to polymers that graft nanoparticles enable Coulombic control over their assembly by tuning the pH and salinity of their aqueous suspensions.

EXPERIMENTS

Gold nanoparticles (AuNPs) are grafted with poly (ethylene glycol) (PEG) terminated with (charge-neutral), (negatively charged) or groups (positively charged), and characterized with dynamic light scattering, ζ-potential, and thermal gravimetric analysis. Liquid surface X-ray reflectivity (XR) and grazing incidence small-angle X-ray scattering (GISAXS) are used to determine the density profile and in-plane structure of the AuNPs assembly at the aqueous surface.

FINDINGS

Assembly of PEG-AuNPs at the liquid/vapor interface is tunable by adjusting pH or salinity for COOH but less for terminals. The distinct assembly behaviors are attributed to the overall charge of PEG-AuNPs as well as PEG conformation. COOH-PEG corona is more compact than those of the other terminal groups, leading to a crystalline structure with a smaller superlattice. The net charge per particle depends not only on the PEG terminal groups but also on the cation sequestration of PEG and the intrinsic negative charge of the AuNP surface. [1] The closeness to overall charge neutrality, and hydrogen bonding in play, brought by -PEG, drive -PEG-AuNPs to assembly and crystallinity without additives to the suspensions.

Real Electrolyte Solutions in the Functionalized Mean Spherical Approximation: A Density Functional Theory for Simple Electrolyte Solutions

The equation of state based on the mean spherical approximation (MSA) can describe electrolyte solutions as a primitive model, where the ions are charged hard-sphere particles and the solvent is a continuum medium. In recent years, many propositions of the classical density functional theory (cDFT) for electrolyte solutions have been presented. One of these is the functionalized MSA (fMSA) which has proven to be a great functional approach of MSA to calculate the electric double layer structures. This work demonstrates how the fMSA theory can describe real electrolyte solutions (e.g., NaCl, KI, and LiBr) where hydration and solvent concentration effects are present. Experimental data of the mean activity coefficients of different simple salts were successfully reproduced. When the hydrated diameter and the electrolyte solution electric permittivity are used, the fMSA predicts a charge inversion on the electrostatic potential near a charged surface at high salt concentrations.

Impact of Charge Regulation on Self-Assembly of Zwitterionic Nanoparticles

Zwitterionic modification of colloids with weak acids and bases represents a promising strategy in creating functional materials with tunable properties and modeling the self-organization of charged proteins. However, accurate incorporation of the dynamic dissociation or association of ionization groups known as charge regulation (CR) is often intractable in theoretical and computational investigations since charge redistribution and configuration need to be evolved self-consistently. Using hybrid Monte Carlo and molecular dynamics simulations, we demonstrate that a dilute suspension of overall charge-neutral zwitterionic Janus nanoparticles shows a conformational transition from an open assembly of string or bundle to compact cluster along with the variation in pH. The behavior under CR is qualitatively different from the commonly employed constant charge condition where the transition is absent. The CR-induced clustering is due to the inhomogeneous and fluctuating charges localized near the equatorial boundary of the Janus particle. These features are enhanced particularly at low salt concentration and high electrostatic coupling strength. Our results indicate the critical role of charge regulation in the spatial self-organization of zwitterionic nanoparticles.

Thermodynamics of Electrolyte Solutions Near Charged Surfaces: Constant Surface Charge vs. Constant Surface Potential

Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational---that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson--Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

Accelerated simulation method for charge regulation effects

The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.

Nonmonotonic Pair Potentials in the Interaction of Like-Charged Objects in Solution

We consider the long-standing like-charge attraction problem, wherein under certain conditions, similarly charged spheres suspended in aqueous electrolyte have been observed to display a minimum in their interaction potential, contrary to the intuitively expected monotonically varying repulsion. Recently, we described an interfacial mechanism invoking the molecular nature of the solvent that explains this anomalous experimental observation. In our model for the interaction of negatively charged particles in water, the minimum in the pair potential results from the superposition of competing contributions to the total free energy. One of these contributions is the canonical repulsive electrostatic term, whereas the other is a solvation-induced attractive contribution. We find that whereas both contributions grow approximately exponentially with decreasing interparticle separation, the occurrence of a stable, long-ranged minimum in the pair potential arises from differences in the precise interparticle separation dependence of the two terms. Specifically, the interfacial solvation term exhibits a more gradual decay with distance than the electrostatic repulsion, permitting the attractive contribution to dominate the interaction at large distances. Importantly, these disparities become evident in quantities calculated from exact numerical solutions to the governing nonlinear Poisson-Boltzmann (PB) equation for the spatial electrical potential distribution in the system. In marked contrast, we find that the linearized PB equation, applicable in the regime of low surface electrical potentials, does not support nonmonotonic trends in the total interaction free energy within the present model. Our results point to the importance of exact descriptions of electrostatic interactions in real systems that most often do not subscribe to particular mathematical limits where analytical approximations may provide a sufficiently accurate description of the problem.

One-dimensional colloidal model with dielectric inhomogeneity

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.

Anisotropic electrostatic screening of charged colloids in nematic solvents

The physical behavior of anisotropic charged colloids is determined by their material dielectric anisotropy, affecting colloidal self-assembly, biological function, and even out-of-equilibrium behavior. However, little is known about anisotropic electrostatic screening, which underlies all electrostatic effective interactions in such soft or biological materials. In this work, we demonstrate anisotropic electrostatic screening for charged colloidal particles in a nematic electrolyte. We show that material anisotropy behaves markedly different from particle anisotropy. The electrostatic potential and pair interactions decay with an anisotropic Debye screening length, contrasting the constant screening length for isotropic electrolytes. Charged dumpling-shaped near-spherical colloidal particles in a nematic medium are used as an experimental model system to explore the effects of anisotropic screening, demonstrating competing anisotropic elastic and electrostatic effective pair interactions for colloidal surface charges tunable from neutral to high, yielding particle-separated metastable states. Generally, our work contributes to the understanding of electrostatic screening in nematic anisotropic media.

Electrolytes in regimes of strong confinement: surface charge modulations, osmotic equilibrium and electroneutrality

In the present work, we study an electrolyte solution confined between planar surfaces with nanopatterned charged domains, which has been connected to a bulk ionic reservoir. The system is investigated through an improved Monte Carlo (MC) simulation method, suitable for simulation of electrolytes in the presence of modulated surface charge distributions. We also employ a linear approach in the spirit of the classical Debye-Hückel approximation, which allows one to obtain explicit expressions for the averaged potentials, ionic profiles, effective surface interactions and the net ionic charge confined between the walls. Emphasis is placed on the limit of strongly confined electrolytes, in which case local electroneutrality in the inter-surface space might not be fulfilled. In order to access the effects of such a lack of local charge neutrality on the ion-induced interactions between surfaces with modulated charge domains, we consider two distinct model systems for the confined electrolyte: one in which a salt reservoir is explicitly taken into account via the osmotic equilibrium with an electrolyte of fixed bulk concentration, and a second one in which the equilibrium with a charge neutral ionic reservoir is implicitly considered. While in the former case the osmotic ion exchange might lead to non-vanishing net charges, in the latter model charge neutrality is enforced through the appearance of an implicit Donnan potential across the charged interfaces. A strong dependence of the ion-induced surface interactions on the employed model system is observed at all surface separations. These findings strongly suggest that due care is to be taken while choosing among different scenarios to describe the ion exchange in electrolytes confined between charged surfaces, even in cases when the monopole (non zero net charge) surface contributions are absent.

Uniform, Anticorrosive, and Antiabrasive Coatings on Metallic Surfaces for Cation-Metal and Cation-π Interactions

Metals are widely used, from daily life to modern industry. Great efforts have been made to protect the metals with various coatings. However, the well-known conventional electrochemical corrosion induced by cations and the ubiquitous nature of the coffee-ring effect make these processes very difficult. Here, a scheme by two bridges of cations and ethylenediamine (EDA) is proposed to overcome the coffee-ring effect and electrochemical corrosion and experimentally achieve uniform, anticorrosive, and antiabrasive coatings on metallic surfaces. Anticorrosive capability reaches about 26 times higher than that without cation-controlled coatings at 12 h in extremely acidic, high-temperature, and high-humidity conditions and still enhances to 2.7 times over a week. Antiabrasive capability also reaches 2.5 times. Theoretical calculations show that the suspended materials are uniformly adsorbed on the surface mediated by complexed cations through strong cation-metal and cation-π interactions. Notably, the well-known conventional electrochemical corrosion induced by cations is avoided by EDA to control cations solubility in different coating processes. These findings provide a new efficient, cost-effective, facile, and scalable method to fabricate protective coatings on metallic materials and a methodology to study metallic nanostructures in solutions, benefitting practical applications including coatings, printing, dyeing, electrochemical protection, and biosensors.

Electrostatic pair-interaction of nearby metal or metal-coated colloids at fluid interfaces

In this paper, we theoretically study the electrostatic interaction between a pair of identical colloids with constant surface potentials sitting in close vicinity next to each other at the fluid interface. By employing a simplified yet reasonable model system, the problem is solved within the framework of classical density functional theory and linearized as well as nonlinear Poisson-Boltzmann (PB) theory. Apart from providing a sound theoretical framework generally applicable to any such problem, our novel findings, all of which contradict common beliefs, include the following: first, quantitative and qualitative differences between the interactions obtained within the linear and the nonlinear PB theories; second, the importance of the electrostatic interaction between the omnipresent three-phase contact lines in interfacial systems; and, third, the occurrence of an attractive electrostatic interaction between a pair of identical metal colloids. The unusual attraction we report largely stems from an attractive line interaction, which although scales linearly with the size of the particle can compete with the surface interactions and can be strong enough to alter the nature of the total electrostatic interaction. Our results should find applications in metal or metal-coated particle-stabilized emulsions where densely packed particle arrays are not only frequently observed but also sometimes required.

Topological-Defect-Induced Surface Charge Heterogeneities in Nematic Electrolytes

We show that topological defects in an ion-doped nematic liquid crystal can be used to manipulate the surface charge distribution on chemically homogeneous, charge-regulating external surfaces, using a minimal theoretical model. In particular, the location and type of the defect encodes the precise distribution of surface charges and the effect is enhanced when the liquid crystal is flexoelectric. We demonstrate the principle for patterned surfaces and charged colloidal spheres. More generally, our results indicate an interesting approach to control surface charges on external surfaces without changing the surface chemistry.

Charge regulation radically modifies electrostatics in membrane stacks

Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, and membrane size. Our results shed light on the basic reorganization mechanism of thylakoid membrane stacks.

Interfacial solvation can explain attraction between like-charged objects in aqueous solution

Over the past few decades, the experimental literature has consistently reported observations of attraction between like-charged colloidal particles and macromolecules in aqueous solution. Examples include nucleic acids and colloidal particles in the bulk solution and under confinement, and biological liquid-liquid phase separation. This observation is at odds with the intuitive expectation of an interparticle repulsion that decays monotonically with distance. Although attraction between like-charged particles can be rationalized theoretically in the strong-coupling regime, e.g., in the presence of multivalent counterions, recurring accounts of long-range attraction in aqueous solution containing monovalent ions at low ionic strength have posed an open conundrum. Here, we show that the behavior of molecular water at an interface-traditionally disregarded in the continuum electrostatics picture-provides a mechanism to explain the attraction between like-charged objects in a broad spectrum of experiments. This basic principle will have important ramifications in the ongoing quest to better understand intermolecular interactions in solution.

Charge Regulation of Colloidal Particles: Theory and Simulations

To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem with the NP approach is traced back to the use of a bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is nontrivially related to the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.