Effect of Polymer Aging on Uptake/Release Kinetics of Metal Ions and Organic Molecules by Micro- and Nanoplastics: Implications for the Bioavailability of the Associated Compounds.

The main driver of the potential toxicity of micro- and nanoplastics toward biota is often the release of compounds initially present in the plastic, i.e., polymer additives, as well as environmentally acquired metals and/or organic contaminants. Plastic particles degrade in the environment via various mechanisms and at different rates depending on the particle size/geometry, polymer type, and the prevailing physical and chemical conditions. The rate and extent of polymer degradation have obvious consequences for the uptake/release kinetics and, thus, the bioavailability of compounds associated with plastic particles. Herein, we develop a theoretical framework to describe the uptake and release kinetics of metal ions and organic compounds by plastic particles and apply it to the analysis of experimental data for pristine and aged micro- and nanoplastics. In particular, we elucidate the contribution of transient processes to the overall kinetics of plastic reactivity toward aquatic contaminants and demonstrate the paramount importance of intraparticulate contaminant diffusion.

Kinetics of metal detection by luminescence-based whole-cell biosensors: connecting biosensor response to metal bioavailability, speciation and cell metabolism.

Luminescent whole-cell metal biosensors are genetically engineered cells used for the detection of metals in e.g. aqueous solutions. Herein, we detail the quantitative connections between time-response of luminescent bacterial metal sensors and the bioavailability of free and complexed metal species. To that end, we formulate the biophysicochemical dynamics of metal partitioning at a biosensor/solution interface and integrate the required metabolism contribution to cell response. The formalism explains the ways in which cell signal depends on: coupled Eigen kinetics of metal complexation and diffusion of metal species to/from the interface; kinetics of metal excretion, Michaelis-Menten bioaccumulation and ensuing metal depletion from bulk solution; and kinetics of bioluminescence production following intracellular metal sequestration by regulatory metalloproteins. In turn, an expression is derived for the time-dependent cell signal as a function of interrelated (bioavai)lability of metal species and (thermo)dynamic descriptors of extra/intracellular metal complexation. Quantitative criteria are elaborated to identify scenarios where equilibrium modeling of metal speciation is incorrect, bulk metal depletion is operative, metal biouptake kinetics is governed by metal diffusion, or labile metal complexes fully contribute to cell response. Remarkably, in agreement with experiments, the theory predicts time-shifts of bioluminescence peaks with increasing concentration of biosensor and/or metal ligand in solution. We show that these shifts originate from the crosstalk between activation kinetics of cell photoactivity and speciation-dependent kinetics of bulk metal depletion. Overall, the work paves the way for the elaboration of new strategies to exploit the bioluminescence response of metal lux-biosensors at a dynamic level and evaluate metal bioavailability properties in environmental or biological aqueous samples.

Absolute and Relative Positioning of Natural Organic Matter Acid-Base Potentiometric Titration Curves: Implications for the Evaluation of the Density of Charged Reactive Sites.

Potentiometric acid-base titration curves collected on humic (nano)particles as a function of pH and salt concentration reflect the electrostatics of the particles and the amount of chemical charges (Q) they carry. In turn, the interpretation of titration data helps quantify their reactivity toward metals provided that both intrinsic chemical and nonspecific electrostatic contributions to proton binding are correctly unraveled. Establishing a titration curve requires several steps, i.e., blank subtraction, relative curve positioning with respect to the electrolyte concentration, and absolute curve positioning achieved by the estimation of particle charge Q0 at low pH. Failure to properly establish each step may lead to the misevaluation of nanoparticle charging behavior. Here, we report (i) a simple procedure to measure and position titration curves for humic substances (HS) versus salt concentration and (ii) an original approach for absolute curve positioning upon the exploitation of proton affinity spectra. The latter do not depend on Q0 and they thus constrain the titration data analysis using the soft Poisson-Boltzmann-based titration (SPBT) formalism for nanoparticles in the thick electric double-layer regime. We illustrate the benefits of our approach by analyzing titration measurements for a large range of humic nanoparticles and by comparing the outcome with results from the literature.

Rigorous Physicochemical Framework for Metal Ion Binding by Aqueous Nanoparticulate Humic Substances: Implications for Speciation Modeling by the NICA-Donnan and WHAM Codes.

Latest knowledge on the reactivity of charged nanoparticulate complexants toward aqueous metal ions is discussed in mechanistic detail. We present a rigorous generic description of electrostatic and chemical contributions to metal ion binding by nanoparticulate complexants, and their dependence on particle size, particle type (i.e., reactive sites distributed within the particle body or confined to the surface), ionic strength of the aqueous medium, and the nature of the metal ion. For the example case of soft environmental particles such as fulvic and humic acids, practical strategies are delineated for determining intraparticulate metal ion speciation, and for evaluating intrinsic chemical binding affinities and heterogeneity. The results are compared with those obtained by popular codes for equilibrium speciation modeling (namely NICA-Donnan and WHAM). Physicochemical analysis of the discrepancies generated by these codes reveals the a priori hypotheses adopted therein and the inappropriateness of some of their key parameters. The significance of the characteristic time scales governing the formation and dissociation rates of metal-nanoparticle complexes in defining the relaxation properties and the complete equilibration of the metal-nanoparticulate complex dispersion is described. The dynamic features of nanoparticulate complexes are also discussed in the context of predictions of the labilities and bioavailabilities of the metal species.

The Intrinsic Stability of Metal Ion Complexes with Nanoparticulate Fulvic Acids.

The electrostatic contributions to metal ion binding by fulvic acids (FAs) are characterized in light of recent theoretical developments on description of the net charge density of soft nanoparticles. Under practical electrolyte concentrations, the radius of the small, highly charged soft nanoparticulate FAs is comparable to the electrostatic screening length and their electric potential profile has a bell shape that extends into the surrounding aqueous medium. Consequently, accumulation of counterions in the extraparticulate zone can be significant. By comparison of experimentally derived Boltzmann partitioning coefficients with those computed on the basis of (i) the structural FA particle charge and (ii) the potential profile for a nanoparticulate FA entity equilibrated with indifferent electrolyte, we identify the thickness of the extraparticulate counter charge accumulation shell in 1-1 and 2-1 electrolytes. The results point to the involvement of counterion condensation phenomena and call into question the approaches for modeling electrostatic contributions to ion binding that are invoked by popular equilibrium speciation codes. Overall, the electrostatic contributions to Cdaq2+ and Cuaq2+ association with FA are weaker than those previously found for much larger humic acids (HA). The intrinsic chemical binding strength of CdFA is comparable to that of CdHA, whereas CuFA complexes are weaker than CuHA ones.

Carbonate Disequilibrium in the External Boundary Layer of Freshwater Chrysophytes: Implications for Contaminant Uptake.

The interplay between biological and chemical reactions in the freshwater phytoplankton phycosphere and the resulting modulations of contaminant speciation and uptake is poorly characterized. Here we modeled the effect of algal C and N uptake on carbonate cycling and speciation of selected contaminants in the phycosphere (external boundary layer) of chrysophytes, a key phytoplankton group in oligotrophic systems. We calculated an enrichment in H+ concentration relative to that in the bulk solution (pH 7.0) of approximately 40% or a depletion of approximately 30% for NH4+ or NO3--grown cells, respectively, at the algal membrane surface of a 5-µm radius cell. Such changes are mainly due to direct H+ uptake or release at the plasmalemma if NO3- or NH4+ is the N source, respectively. Due to these pH changes in the external boundary layer, competition between H+ and metals for uptake is enhanced, for NH4+-grown cells which contributes to a decrease in potential metal uptake. Our model suggests that the uptake of protonated weakly acidic organic acids (HA) is greater in NH4+-grown cells compared to that in NO3--grown cells. The account of chemical reactions in the algal external boundary layer could improve ecological risk assessments for a wide range of contaminants.

Chemodynamics of metal ion complexation by charged nanoparticles: a dimensionless rationale for soft, core-shell and hard particle types.

Soft nanoparticulate complexants are defined by a spatial confinement of reactive sites and electric charges inside their 3D body. In turn, their reactivity with metal ions differs significantly from that of simple molecular ligands. A revisited form of the Eigen mechanism recently elucidated the processes leading to metal/soft particle pair formation. Depending on e.g. particle size and metal ion nature, chemodynamics of nanoparticulate metal complexes is controlled by metal conductive diffusion to/from the particles, by intraparticulate complex formation/dissociation kinetics, or by both. In this study, a formalism is elaborated to achieve a comprehensive and systematic identification of the rate-limiting step governing the overall formation and dissociation of nanoparticulate metal complexes. The theory covers the different types of spherical particulate complexants, i.e. 3D soft/permeable and core-shell particles, and hard particles with reactive sites at the surface. The nature of the rate-limiting step is formulated by a dynamical criterion involving a power law function of the ratio between particle radius and an intraparticulate reaction layer thickness defined by the key electrostatic, diffusional and kinetic components of metal complex formation/dissociation. The analysis clarifies the intertwined contributions of particle properties (size, soft or hard type, charge, density or number of reactive sites) and aqueous metal ion dehydration kinetics in defining the chemodynamic behavior of nanoparticulate metal complexes. For that purpose, fully parameterized chemodynamic portraits involving the defining features of particulate ligand and metal ion as well as the physicochemical conditions in the local intraparticulate environment, are constructed and thoroughly discussed under conditions of practical interest.

Impact of intracellular metallothionein on metal biouptake and partitioning dynamics at bacterial interfaces.

Genetically engineered microorganisms are alternatives to physicochemical methods for remediation of metal-contaminated aquifers due to their remarkable bioaccumulation capacities. The design of such biosystems would benefit from the elaboration of a sound quantitative connection between performance in terms of metal removal from aqueous solution and dynamics of the multiscale processes leading to metal biouptake. In this work, this elaboration is reported for Escherichia coli cells modified to overexpress intracellular metallothionein (MTc), a strong proteinaceous metal chelator. Depletion kinetics of Cd(ii) from bulk solution following biouptake and intracellular accumulation is addressed as a function of cell volume fraction using electroanalytical probes and ligand exchange-based analyses. It is shown that metal biouptake in the absence and presence of MTc is successfully interpreted on the basis of a formalism recently developed for metal partitioning dynamics at biointerfaces with integration of intracellular metal speciation. The analysis demonstrates how fast sequestration of metals by intracellular MTc bypasses metal excretion (efflux) and enhances the rate of metal depletion to an extent such that complete removal is achieved at sufficiently large cell volume fractions. The magnitude of the stability constant of nanoparticulate metal-MTc complexes, as derived from refined analysis of macroscopic bulk metal depletion data, is further confirmed by independent electrochemical measurement of metal binding by purified MTc extracts.

Atomic force microscopy analysis of IgG films at hydrophobic surfaces: a promising method to probe IgG orientations and optimize ELISA tests performance.

IgG films are widely used in the field of immunoassays, especially in (double) antibody-sandwich ELISA tests where capture antibodies are coated on surfaces like polystyrene or hydrophobic self-assembled monolayers (h-SAMs). It is critical to analyze-at a molecular scale and under liquid conditions-the structure of the deposited IgG film in order to quantitatively address the efficiency of the ELISA test in terms of antigen detection. In this communication, we report an atomic force microscopy (AFM) analysis evidencing a strong relationship between immunological activities of mouse monoclonal anti-human interleukin-2 (IL-2) and 6 (IL-6) antibodies, thickness and roughness of the IgG monolayer adsorbed onto h-SAMs, and surface concentration of IgG molecules. Indirect information may be further obtained on antibody orientation. Collating the results obtained by AFM and those from ELISA tests leads us to conclude that antibodies like anti-IL-6 forming flat monolayers should be more efficient under ELISA detection conditions. In addition, the concentration of IgG in the coating suspension should be optimized to obtain a monolayer heavily populated by "end-on" adsorbed molecules, an orientation that is desirable for enhancing ELISA tests performance.

Coupled metal partitioning dynamics and toxicodynamics at biointerfaces: a theory beyond the biotic ligand model framework.

A mechanistic understanding of the processes governing metal toxicity to microorganisms (bacteria, algae) calls for an adequate formulation of metal partitioning at biointerfaces during cell exposure. This includes the account of metal transport dynamics from bulk solution to biomembrane and the kinetics of metal internalisation, both potentially controlling the intracellular and surface metal fractions that originate cell growth inhibition. A theoretical rationale is developed here for such coupled toxicodynamics and interfacial metal partitioning dynamics under non-complexing medium conditions with integration of the defining cell electrostatic properties. The formalism explicitly considers intertwined metal adsorption at the biointerface, intracellular metal excretion, cell growth and metal depletion from bulk solution. The theory is derived under relevant steady-state metal transport conditions on the basis of coupled Nernst-Planck equation and continuous logistic equation modified to include metal-induced cell growth inhibition and cell size changes. Computational examples are discussed to identify limitations of the classical Biotic Ligand Model (BLM) in evaluating metal toxicity over time. In particular, BLM is shown to severely underestimate metal toxicity depending on cell exposure time, metal internalisation kinetics, cell surface electrostatics and initial cell density. Analytical expressions are provided for the interfacial metal concentration profiles in the limit where cell-growth is completely inhibited. A rigorous relationship between time-dependent cell density and metal concentrations at the biosurface and in bulk solution is further provided, which unifies previous equations formulated by Best and Duval under constant cell density and cell size conditions. The theory is sufficiently flexible to adapt to toxicity scenarios with involved cell survival-death processes.

Kinetic and thermodynamic determinants of trace metal partitioning at biointerphases: the role of intracellular speciation dynamics.

There is a large body of work evidencing the necessity to evaluate chemical speciation dynamics of trace metals in solution for an accurate definition of their bioavailability to microorganisms. In contrast, the integration of intracellular metal speciation dynamics in biouptake formalisms is still in its early stages. Accordingly, we elaborate here a rationale for the interplay between chemodynamics of intracellular metal complexes and dynamics of processes governing metal biouptake under non-complexing outer medium conditions. These processes include the conductive diffusion of metal ions to the charged soft biointerphase, metal internalisation, excretion of intracellular free metal species and metal depletion from bulk solution. The theory is formulated from Nernst-Planck equations corrected for electrostatic and reaction kinetic terms applied at the biosurface and in the intracellular volume. Computational illustrations demonstrate how biointerfacial metal distribution dynamics inherently reflects the chemodynamic properties of intracellular complexes. In the practical limits of high and weak metal affinity to biosurface internalisation sites, the metal concentration profile is explicitly solved under conditions of strong intracellular complexing agents. Exact analytical expression is further developed for metal partitioning at equilibrium. This provides a way to evaluate the metal biopartition coefficient from refined analysis of bulk metal depletion measured at various cell concentrations. Depending on here-defined dimensionless parameters involving rates of metal internalisation-excretion and complex formation, the formalism defines the nature of the different kinetic regimes governing bulk metal depletion and biouptake. In particular, the conditions leading to an internalisation flux limited by diffusion as a result of demanding intracellular metal complexation are identified.

Structural effects of soft nanoparticulate ligands on trace metal complexation thermodynamics.

Metal binding to natural soft colloids is difficult to address due to the inherent heterogeneity of their reactive polyelectrolytic volume and the modifications of their shell structure following changes in e.g. solution pH, salinity or temperature. In this work, we investigate the impacts of temperature- and salinity-mediated modifications of the shell structure of polymeric ligand nanoparticles on the thermodynamics of divalent metal ions Cd(ii)-complexation. The adopted particles consist of a glassy core decorated by a fine-tunable poly(N-isopropylacrylamide) anionic corona. According to synthesis, the charges originating from the metal binding carboxylic moieties supported by the corona chains are located preferentially either in the vicinity of the core or at the outer shell periphery (p(MA-N) and p(N-AA) particles, respectively). Stability constants (KML) of cadmium-nanoparticle complexes are measured under different temperature and salinity conditions using electroanalytical techniques. The obtained KML is clearly impacted by the location of the carboxylic functional groups within the shell as p(MA-N) leads to stronger nanoparticulate Cd complexes than p(N-AA). The dependence of KML on solution salinity for p(N-AA) is shown to be consistent with a binding of Cd to peripheral carboxylic groups driven by Coulombic interactions (Eigen-Fuoss mechanism for ions-pairing) or with particle electrostatic features operating at the edge of the shell Donnan volume. For p(MA-N) particulate ligands, a scenario where metal binding occurs within the intraparticulate Donnan phase correctly reproduces the experimental findings. Careful analysis of electroanalytical data further evidences that complexation of metal ions by core-shell particles significantly differ according to the location and distribution of the metal-binding sites throughout the reactive shell. This complexation heterogeneity is basically enhanced with increasing temperature i.e. upon significant increase of particle shell shrinking, which suggests that the contraction of the reactive phase volume of the particulate ligands promotes cooperative metal binding effects.

Remarkable electrokinetic features of charge-stratified soft nanoparticles: mobility reversal in monovalent aqueous electrolyte.

The electrokinetic behavior of G6.5 carboxylate-terminated poly(amidoamine) (PAMAM) starburst dendrimers (8 ± 1 nm diameter) is investigated over a broad range of pH values (3-9) and NaNO3 concentrations (c(∞ )= 2-200 mM). The dependence of nanodendrimer electrophoretic mobility µ on pH and c(∞) is marked by an unconventional decrease of the point of zero mobility (PZM) from 5.4 to 5.5 to 3.8 upon increase in salt concentration, with PZM defined as the pH value at which a reversal of the mobility sign is reached. The existence of a common intersection point is further evidenced for series of mobility versus pH curves measured at different NaNO3 concentrations. Using soft particle electrokinetic theory, this remarkable behavior is shown to originate from the zwitterionic functionality of the PAMAM-COOH particles. The dependence of PZM on c(∞) results from the coupling between electroosmotic flow and dendrimeric interphase defined by a nonuniform distribution of amine and carboxylic functional groups. In turn, µ reflects the sign and distribution of particle charges located within an electrokinetically active region, the dimension of which is determined by the Debye length, varied here in the range 0.7-6.8 nm. In agreement with theory, the electrokinetics of smaller G4.5 PAMAM-COOH nanoparticles (5 ± 0.5 nm diameter) further confirms that the PZM is shifted to higher pH with decreasing dendrimer size. Depending on pH, a mobility extremum is obtained under conditions where the Debye length and the particle radius are comparable. This results from changes in particle structure compactness following salt- and pH-mediated modulations of intraparticle Coulombic interactions. The findings solidly evidence the possible occurrence of particle mobility reversal in monovalent salt solution suggested by recent molecular dynamic simulations and anticipated from earlier mean-field electrokinetic theory.

Structure of Multiresponsive Brush-Decorated Nanoparticles: A Combined Electrokinetic, DLS, and SANS Study.

Particles consisting of a glassy poly(methyl methacrylate) core (ca. 40 nm in radius) decorated with a poly(N-isopropylacrylamide) anionic corona are synthesized using either methacrylic acid (MA) or acrylic acid (AA) as reactive comonomers in the shell. The different reactivity ratios of MA and AA toward N-isopropylacrylamide originates p(MA-N) and p(N-AA) particles with carboxylate charges supposedly located, preferentially, in the close vicinity of the core and at the shell periphery, respectively. The corresponding swelling features of these nanoparticles are addressed over a broad range of pH values (4 to 7.5), NaNO3 concentrations (3 to 200 mM), and temperatures (15 to 45 °C) by dynamic light scattering (DLS) and small angle neutron scattering (SANS). DLS shows that the swelling of the particle shells increases their thickness from ∼10 to 90 nm with decreasing temperature, ionic strength, or increasing pH, with the effect being more pronounced for p(N-AA) whose lower critical solution temperature is shifted to higher values compared to that of p(MA-N). Potentiometric titration and electrokinetic results further reflect the easier dissociation of carboxyl groups in p(N-AA) and a marked heterogeneous interfacial swelling of the latter with decreasing solution salt content. The DLS response of both particles is attributed to the multiresponsive nature of a peripheral dilute shell, while SANS only probes the presence of a quasi-solvent-free dense polymer layer, condensed on the core surface. The thickness of that layer slightly increases from ∼6 to 9.5 nm with increasing temperature from 15 to 45 °C (at 15 mM NaNO3 and pH 5) due to the collapse of the outer dilute shell layer. Overall, results evidence a nonideal brush behavior of p(MA-N) and p(N-AA) and their microphase segregated shell structure, which supports some of the conclusions recently formulated from approximate self-consistent mean-field computations.

Dynamics of Metal Partitioning at the Cell-Solution Interface: Implications for Toxicity Assessment under Growth-Inhibiting Conditions.

Metal toxicity toward microorganisms is usually evaluated by determining growth inhibition. To achieve a mechanistic interpretation of such toxic effects, the intricate coupling between cell growth kinetics and metal partitioning dynamics at the cell-solution interface over time must be considered on a quantitative level. A formalism is elaborated to evaluate cell-surface-bound, internalized, and extracellular metal fractions in the limit where metal uptake kinetics is controlled by internalization under noncomplexing medium conditions. Cell growth kinetics is tackled using the continuous logistic equation modified to include growth inhibition by metal accumulation to intracellular or cell surface sites. The theory further includes metal-proton competition for adsorption at cell-surface binding sites, as well as possible variation of cell size during exposure to metal ions. The formalism elucidates the dramatic impacts of initial cell concentration on metal bioavailability and toxicity over time, in agreement with reported algae bioassays. It further highlights that appropriate definition of toxicity endpoints requires careful inspection of the ratio between exposure time scale and time scale of metal depletion from bulk solution. The latter depends on metal internalization-excretion rate constants, microorganism growth, and the extent of metal adsorption on nonspecific, transporter, and growth inhibitory sites. As an application of the theory, Cd toxicity in the algae Pseudokirchneriella subcapitata is interpreted from constrained modeling of cell growth kinetics and of interfacial Cd-partitioning dynamics measured under various exposure conditions.

Evaluation of metal biouptake from the analysis of bulk metal depletion kinetics at various cell concentrations: theory and application.

Bioavailability of trace metals is a key parameter for assessment of toxicity on living organisms. Proper evaluation of metal bioavailability requires monitoring the various interfacial processes that control metal partitioning dynamics at the biointerface, which includes metal transport from solution to cell membrane, adsorption at the biosurface, internalization, and possible excretion. In this work, a methodology is proposed to quantitatively describe the dynamics of Cd(II) uptake by Pseudomonas putida. The analysis is based on the kinetic measurement of Cd(II) depletion from bulk solution at various initial cell concentrations using electroanalytical probes. On the basis of a recent formalism on the dynamics of metal uptake by complex biointerphases, the cell concentration-dependent depletion time scales and plateau values reached by metal concentrations at long exposure times (>3 h) are successfully rationalized in terms of limiting metal uptake flux, rate of excretion, and metal affinity to internalization sites. The analysis shows the limits of approximate depletion models valid in the extremes of high and weak metal affinities. The contribution of conductive diffusion transfer of metals from the solution to the cell membrane in governing the rate of Cd(II) uptake is further discussed on the basis of estimated resistances for metal membrane transfer and extracellular mass transport.

Electrokinetics as an alternative to neutron reflectivity for evaluation of segment density distribution in PEO brushes.

Unravelling details of charge, structure and molecular interactions of functional polymer coatings defines an important analytical challenge that requires the extension of current methodologies. In this article we demonstrate how streaming current measurements interpreted with combined self consistent field (SCF) and soft surface electrokinetic theories allow the evaluation of the segment distribution within poly(ethylene oxide) (PEO) brushes beyond the resolution limits of neutron reflectivity technique.

Dynamics of metal uptake by charged soft biointerphases: impacts of depletion, internalisation, adsorption and excretion.

A comprehensive theory is elaborated for the dynamics of metal ion uptake by charged spherical microorganisms. The formalism integrates the interplay over time between bulk metal depletion, metal adsorption, metal excretion (efflux) and transport of metals by conductive diffusion toward the metal-consuming biomembrane. The model further involves the basic physicochemical features of the microbial interphase in terms of size, distribution of electrostatic charges and thickness of peripheral soft surface appendage. A generalization of the Best equation is proposed and leads to the expression of the time-dependent concentration of metal ions at the active membrane surface as a function of bulk metal concentration. Combination of this equation with the metal conservation condition over the sample volume allows a full evaluation of bulk metal depletion kinetics and the accompanying time-dependent uptake and excretion fluxes as a function of metal-microorganism electrostatic interaction, microbe concentration and relevant biophysicochemical features of the interphase. Practically tractable expressions are derived in the limit where the Biotic Ligand Model (BLM) is obeyed and in situations where conductive diffusion transport of metals significantly determines the rate of biouptake. In particular, the plateau value reached at sufficiently long times by bulk metal concentration is rigorously expressed in terms of the key parameters pertaining to the adsorption process and to the kinetics of metal uptake and excretion. The theory extends and unifies previous approximate models where the impacts of extracellular metal transport and/or metal efflux on the overall rate of uptake were ignored.

Electrodynamics of soft multilayered particles dispersions: dielectric permittivity and dynamic mobility.

We report a theory for the evaluation of the electrodynamics of dispersions of spherical soft multilayered (bio)particles, with microorganisms and polyelectrolyte multilayers-coated particles as illustrative paradigms. These particles generally consist of a hard (ion- and water-impermeable) core component supporting a succession of step-function or diffuse-like concentric soft (permeable) polymeric layers defined by distinct electrostatic, hydrodynamic and structural properties. The formalism is based on a rigorous numerical resolution of the coupled Navier-Stokes-Brinkman equation, continuity equations for the flow and for the ionic species present in solution, and the non-linear Poisson equation corrected for the multilayered nature of the soft interphase. The frequency-dependent dynamic mobility and dielectric permittivity of such soft particles suspensions are discussed as a function of the key electrohydrodynamic features of the constituting particulate peripheral layers and solution salinity. It is shown that the frequency dependent permittivity is mostly affected by the total charge carried by the overall soft interphase. In contrast, the dynamic mobility is mainly determined by the charge and friction characteristics of the layers located within an electrokinetically-active outer particle region whose extension is defined by the electric double layer thickness and the Brinkman length. Results highlight that under particular electrolyte concentration and layer-to-layer thickness ratio conditions, the dynamic mobility may reflect the physico-chemical and structural properties of the only innermost layers of the soft particle coating.

Speciation dynamics of metals in dispersion of nanoparticles with discrete distribution of charged binding sites.

We report a comprehensive theory to evaluate the kinetics of complex formation between metal ions and charged spherical nanoparticles. The latter consist of an ion-impermeable core surrounded by a soft shell layer characterized by a discrete axisymmetric 2D distribution of charged sites that bind metal ions. The theory explicitly integrates the conductive diffusion of metal ions from bulk solution toward the respective locations of the reactive sites within the particle shell volume. The kinetic constant k for outer-sphere nanoparticle-metal association is obtained from the sum of the contributions stemming from all reactive sites, each evaluated from the corresponding incoming flux of metal ions derived from steady-state Poisson-Nernst-Planck equations. Illustrations are provided to capture the basic intertwined impacts of particle size, overall particle charge, spatial heterogeneity in site distribution, type of particle (hard, core-shell or porous) and concentration of the background electrolyte on k. As a limit, k converges with predictions from previously reported analytical expressions derived for porous particles with low and high charge density, cases that correspond to coulombic and mean-field (smeared-out) electrostatic treatments, respectively. The conditions underlying the applicability of these latter approaches are rigorously identified in terms of (i) the extent of overlap between electric double layers around charged neighbouring sites, and (ii) the magnitude of the intraparticulate metal concentration gradient. For the first time, the proposed theory integrates the differentiated impact of the local potential around the charged binding sites amidst the overall particle field, together with that of the so-far discarded intraparticulate flux of metal ions.