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Electrostatic Force Between Two Colloidal Spheres

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Daniel Martínez Tibaduiza

Soft Condensed Matter · Submitted 26 Feb 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We obtained an analytical solution from the LPBE for the electrostatic interaction via multipole expansion, considering a uniform and fixed surface charge density on the spheres.

how it is stated · asserted 1.00 read the record →

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arXiv ID1602.09074 (version 1)
Pith ID3MFBPTNN, Pith's permanent record of this paper and its review
CitationDaniel Mart\'inez Tibaduiza. "Electrostatic Force Between Two Colloidal Spheres." arXiv:1602.09074 (2016). https://pith.science/paper/3MFBPTNN
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,407 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.73 · human participants 0.02 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.91 · mentions code or data availability 0.08.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this dissertation we analyzed the double-layer force interaction between two dielectric charged colloidal spheres of different radii immersed in a solution of ions in water and in thermal equilibrium. In the limit of low electrostatic potential the interaction is governed by the Linearized Poisson-Boltzmann Equation (LPBE). We obtained an analytical solution from the LPBE for the electrostatic interaction via multipole expansion, considering a uniform and fixed surface charge density on the spheres. A code in the Mathematica platform was developed, allowing us to calculate the force between the spheres as a function of their separation. In order to validate the code, we compared our numerical results with the analytical ones in the limits of Linear Superposition Approximation (LSA) (valid for sphere separations much greater than the Debye length) and Proximity Force Approximation (PFA) (valid for sphere separations and Debye length much smaller than the radii of the spheres).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this dissertation we analyzed the double-layer force interaction between two dielectric charged colloidal spheres of different radii immersed in a solution of ions in water and in thermal equilibrium. contribution 0.89 0.93 0.05 asserted 0.99
s1 In the limit of low electrostatic potential the interaction is governed by the Linearized Poisson-Boltzmann Equation (LPBE). background 0.75 0.13 0.05 asserted 1.00
s2 We obtained an analytical solution from the LPBE for the electrostatic interaction via multipole expansion, considering a uniform and fixed surface charge density on the spheres. method 0.59 0.96 0.16 asserted 1.00
s3 A code in the Mathematica platform was developed, allowing us to calculate the force between the spheres as a function of their separation. method 0.95 0.96 0.04 asserted 1.00
s4 In order to validate the code, we compared our numerical results with the analytical ones in the limits of Linear Superposition Approximation (LSA) (valid for sphere separations much greater than the Debye length) and Proximity Force Approximation (PFA) (valid for sphere separations and Debye length much smaller than the radii of the spheres). method 0.99 0.95 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.85 · evidence from proof or derivation 0.61.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this dissertation we analyzed the double-layer force interaction between two dielectric charged colloidal spheres of different radii immersed in a solution of ions in water and in thermal equilibrium. In the limit of low electrostatic potential the interaction is governed by the Linearized Poisson-Boltzmann Equation (LPBE). We obtained an analytical solution from the LPBE for the electrostatic interaction via multipole expansion, considering a uniform and fixed surface charge density on the spheres. A code in the Mathematica platform was developed, allowing us to calculate the force between the spheres as a function of their separation. In order to validate the code, we compared our numerical results with the analytical ones in the limits of Linear Superposition Approximation (LSA) (valid for sphere separations much greater than the Debye length) and Proximity Force Approximation (PFA) (valid for sphere separations and Debye length much smaller than the radii of the spheres).

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