Estimation of Nanoparticle’s Surface Electrostatic Potential in Solution Using Acid–Base Molecular Probes I: In Silico Implementation for Surfactant Micelles

Abstract

Surface electrostatic potential Ψ is a key characteristic of colloid particles. Since the surface of the particles adsorbs various compounds and facilitates chemical reactions between them, Ψ largely affects the properties of adsorbed reactants and governs the flow of chemical reactions occurring between them. One of the most popular methods for estimating Ψ in hydrophilic colloids, such as micellar surfactant solutions and related systems, is the application of molecular probes, predominantly acid−base indicator dyes. The Ψ value is calculated from the difference of the probe's indices of the apparent acidity constant between the examined colloid solution and, usually, some other colloid solution with noncharged particles. Here, we show how to implement this method in silico using alchemical free energy calculations within the framework of molecular dynamics simulations. The proposed implementation is tested on surfactant micelles and is shown to predict experimental Ψ values with quantitative accuracy depending on the kind of surfactant. The sources of errors in the method are discussed, and recommendations for its application are given.

Solvatochromic and Acid–Base Molecular Probes in Surfactant Micelles: Comparison of Molecular Dynamics Simulation with the Experiment

“…In total, seventeen molecular probes were examined mainly in SDS and CTAB micellar solutions. The results of our research group have been reported in seventeen articles from 2016 to the present [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69]. We thought it is expedient to summarize the data obtained and the regularities found.…”

Estimation of Nanoparticle’s Surface Electrostatic Potential in Solution Using Acid–Base Molecular Probes II: Insight from Atomistic Simulations of Micelles

“…In Table , they are shown together with several metrics of the indicator’s hydration: the molar fractions of water χ(water) in the local environment of either the whole molecule (except hydrocarbon tails) or the O atom(s) of its ionizing OH or COOH group(s) of acidic and basic forms. The p K a shifts were calculated via eq (the protocol for finding χ(water) is described in the Supporting Information): normalΔ normalp K normala calc app = normalΔ G deprot ( m ) − normalΔ G deprot ( w ) R T .25em ln nobreak0em.25em⁡ 10 . Here, Δ G deprot(m) and Δ G deprot(w) are the free energies of deprotonation of the indicator in TX-100 micelles and in water, respectively, which were taken from preceding studies. , …”

“…Correspondence between the Ψ values found with the indicator method in vitro and in silico (adapted from Paper I, copyright 2022 American Chemical Society). Black squares: DDP, green diamonds: HHC, red circles: DF (filled for neutral, hollow for cationic), and brown triangles: DODR.…”

“…Here, ΔG deprot(m) and ΔG deprot(w) are the free energies of deprotonation of the indicator in TX-100 micelles and in water, respectively, which were taken from preceding studies. 21,23 For the case of water fraction around the ionizing groups of the basic forms, a monotonic dependence is observed (Figure 4, eq 5): on average, reducing water content by 10% makes the calculated pK a more negative by ≈0.6 units. The relevance of this metric has a clear physical explanation: within the entire compound, the strongest interaction with water molecules is formed by the charged O − or COO − groups, and these groups are present in the basic forms (the acidic forms have electroneutral OH or COOH groups).…”

“…In our recent work, we implemented the described method in silico (we will refer to it as Paper I below in the text). 21 There, we recreated a unique situation: both the "instrumental" parameter (Ψ calc ) and its microscopic origins (the MD trajectories of the systems' evolution in time) belong to the same simulated system and are available at the same time. Hence, they can be matched safely, and the trends discovered in the model systems may then be extrapolated to the real ones.…”