Search NASA⌕ Search
Home/Archive/DOE OSTI

DOE OSTI · 2438334

Nonlinear Poisson–Boltzmann solutions for charged parallel plates: When opposite charges repel

Travesset, Alex
View original source ↗Read source document ↗Export metadata ↓

Abstract

I present an exact solution of the Poisson–Boltzmann equation for two parallel plates and discuss the solution properties. I discuss in more detail plates with opposite charges: In this case, there are two critical separations, L c,1 < L c,2 . For separations less than L c,1 , the force between plates is repulsive. It switches to attractive at L c,1 , but with the electric potential having the same sign on both plates. For L > L c,2 , the force remains attractive, and the potential at the plates has the same sign as the charge on each plate. I also describe charge regulation, determined by pK a , and provide formulas for both the critical distance where oppositely charged plates repel and their charging process. Finally, the implications of these results for the nanoparticle assembly, as driven by electrostatic interactions, are also discussed.

Explore related subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRYPoisson-Boltzmann equationVan der Waals forcesasymptotic analysisbiological physicscomplex functionselectrolyteselectrostaticsintegral calculusnanoparticleplasma properties and parameters

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Travesset, Alex. 2024-08-01. Nonlinear Poisson–Boltzmann solutions for charged parallel plates: When opposite charges repel. https://doi.org/10.1063/5.0221826

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

DOE OSTI2026

Frontiers in divalent $f$-block chemistry

Divalent f-block chemistry has undergone rapid expansion in recent years, driven by advances in the stabilization of low-valent lanthanide and actinide complexes. Although f-elements were historically accessed in the +3 or higher oxidation states, the isolation of +2 species has revealed unusual spectroscopic signatures, distinct bonding motifs, and multiple accessible electronic configurations that influence their chemical and physical properties. These developments have generated opportunities in areas including quantum information science, molecular magnetism, catalysis, and luminescence. Computational chemistry has played a pivotal role in interpreting the electronic structure and reactivity of these systems. However, accurately modeling divalent f-block complexes remains challenging because of strong electronic correlation, multiconfigurational character, and the presence of close-in-energy competing electronic states. As experimental capabilities and theoretical methodologies continue to advance, a comprehensive assessment of divalent chemistry is both timely and needed. In this Review, we integrate experimental and theoretical perspectives to provide a systematic analysis of divalent lanthanide and actinide complexes across the f-block series. We critically assess the role of ligands in determining competing ground-state configurations (f n d 1 vs. f n+1 ) resulting in their distinct spectroscopic, magnetic, and bonding properties. Finally, we discuss emerging strategies for predictive modeling and rational design of low-valent f-block molecular systems, with potential applications ranging from dinitrogen reduction to quantum technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Unveiling the electronic structure and chemical bonding of the deprotonated cisplatin anion [(NH 3 )(NH 2 )PtCl 2 ] − via low-temperature photoelectron spectroscopy and theoretical calculations

The dehydrogenated cisplatin anion, [(NH 3 )(NH 2 )PtCl 2 ] − , was investigated via low-temperature photoelectron spectroscopy and theoretical calculations. Seven and four spectral peaks are respectively resolved at 193 and 266 nm, yielding rich electronic structure information for both the anion and neutral. From the threshold and maximum of the lowest electron binding energy band, the experimental adiabatic (ADE) and vertical detachment energies (VDE) are determined to be 3.3 ± 0.1 and 3.525 ± 0.025 eV, respectively. Theoretical calculations indicate the dominant isomer adopting a cis-geometry, in which the platinum center is coplanar with two chlorine and two nitrogen ligands. The calculated VDE of 3.54 eV based on this structure agrees well with the experimental value. Charge analyses reveal that the excess electron in the anion is primarily localized on the Pt and Cl atoms. A suite of theoretical analysis tools was employed to elucidate the bonding characteristics and interaction strength between Pt and its ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Adsorption, charge transfer and a coverage-driven transition of alkali metals on rutile TiO 2 (110)

The interaction of alkali metals with metal oxide surfaces is central to tuning surface reactivity in heterogeneous catalysis and photocatalysis. Here we present a comprehensive DFT+U study of the adsorption of alkali metals (Li, Na, K, Rb, Cs) on the (110) surface of rutile TiO 2 . At low coverage (θ = 1/8), all alkali metals bind preferentially to bridging oxygen sites with adsorption energies in the range −4.06 to −3.33 eV, transferring nearly one full electron (0.92–0.99 |e|) to the substrate and inducing Ti 4+ → Ti 3+ reduction. The excess charge localizes preferentially at subsurface Ti sites in the form of small polarons. Diffusion barriers indicate facile motion along bridging-oxygen rows, whereas inter-row hopping is strongly hindered. Coverage effects were examined systematically for potassium: adsorption energy and charge transfer per K atom decrease monotonically with increasing θ. Strikingly, a sharp energy discontinuity occurs between θ = 4/8 and θ = 5/8 (ΔE ≈ 1 eV per atom), which we identify as a coverage-driven structural transition arising from steric packing constraints and enhanced K–K electrostatic repulsion once every (1×1) surface cell is occupied. This structural transition perfectly correlates with a dramatic drop in the work function down to an ultra-low minimum of 0.84 eV at θ=5/8, followed by a metallization- driven recovery at higher coverages. Ab initio molecular dynamics simulations confirm zigzag K arrangements at moderate coverage (θ = 1/3), while at high coverage (θ = 2/3) short-range K–K correlations emerge without long-range order. These results provide atomistic insight into the structure–activity relationships underlying alkali promotion effects on oxide-supported catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗