On the electrostatic interaction of dielectric particles in an electrolyte solution in the strong screening regime

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

The electrostatic interaction between two identical charged dielectric spherical particles in a symmetric electrolyte solution is studied based on the Poisson-Boltzmann equation. Particular attention is paid to the case of high surface potentials of particles, whose radii are significantly larger than the Debye radius. Using the finite element method, the interaction forces between the particles are calculated under the assumption of a uniform charge distribution on their surfaces and in the absence of an external electric field. This study demonstrates that accounting for the nonlinearity of the Poisson-Boltzmann equation may be essential, even when the surface potentials of particles are sufficiently small, allowing for the formal application of the linearized Poisson-Boltzmann equation. The results obtained can be useful for understanding processes in colloidal systems and analyzing experiments on the interaction of micron-sized particles in electrolyte solutions.

Толық мәтін

Рұқсат жабық

Авторлар туралы

S. Grashchenkov

Псковский государственный университет

Хат алмасуға жауапты Автор.
Email: grasi@mail.ru
Ресей, Псков

Әдебиет тізімі

  1. Israelachvili J.N. Intermolecular and surface forces. San Diego: Academic press, 2011.
  2. Ledbetter J.E., Croxton T.L., McQuarrie D.A. The interaction of two charged spheres in the Poisson-Boltzmann equation // Can. J. Chem. 1981. V. 59. № 13. P. 1860–1864. https://doi.org/10.1139/v81-277
  3. Gouy M. Sur la constitution de la charge électrique à la surface d’un électrolyte // J. Phys. Theor. Appl. 1910. V. 9. № 1. P. 457–468. https://doi.org/10.1051/jphystap:019100090045700
  4. Huckel E., Debye P. Zur theorie der elektrolyte. I. Gefrierpunktserniedrigung und verwandte erscheinungen // Phys. Z. 1923. V. 24. P. 185–206.
  5. Lamm G. The Poisson-Boltzmann equation // Reviews in computational chemistry. 2003. V. 19. P. 147–365. https://doi.org/10.1002/0471466638.ch4
  6. Budkov Y.A., Kalikin N.N. Statistical field theory of ion-molecular fluids: fundamentals and applications in physical chemistry and electrochemistry. Springer Nature, 2024.
  7. Derjaguin B., Landau L. Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes // Prog. Surf. Sci. 1993.V. 43. № 1–4. P. 30−59. https://doi.org/10.1016/0079-6816(93)90013-L
  8. Ether D.S. et al. Double-layer force suppression between charged microspheres // Phys. Rev. E. 2018. V. 97. № 2. P. 022611. https://doi.org/10.1103/PhysRevE.97.022611
  9. Derjaguin B. On the repulsive forces between charged colloid particles and on the theory of slow coagulation and stability of lyophobe sols // Prog. Surf. Sci. 1993. V. 43. № 1–4. P. 15–27. https://doi.org/10.1016/0079-6816(93)90011-J
  10. Carnie S.L., Chan D.Y.C., Stankovich J. Computation of forces between spherical colloidal particles: nonlinear Poisson-Boltzmann theory // J. Colloid Int. Sci. 1994. V. 165. № 1. P. 116–128. https://doi.org/10.1006/jcis.1994.1212
  11. Lima E.R.A., Tavares F.W., Biscaia Jr E.C. Finite volume solution of the modified Poisson-Boltzmann equation for two colloidal particles // Phys. Chem. Chem. Phys. 2007. V. 9. № 24. P. 3174–3180. https://doi.org/10.1039/b701170a
  12. Russ C. et al. Three-body forces between charged colloidal particles // Phys. Rev. E. 2002. V. 66. № 1. P. 011402 https://doi.org/10.1103/PhysRevE.66.011402
  13. Warszyński P., Adamczyk Z. Calculations of double-layer electrostatic interactions for the sphere/plane geometry // J. Colloid Int. Sci. 1997. V. 187. № 2. P. 283–295. https://doi.org/10.1006/jcis.1996.4671
  14. Гращенков С.И. Электростатическое взаимодействие диэлектрических частиц в растворе электролита // Коллоидный журнал. 2024. Т. 86. № 5. С. 561–570. https://doi.org/10.31857/S0023291224050045
  15. Schnitzer O., Morozov M. A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations // J. Chem. Phys. 2015. V. 142. № 24. P. 244102. https://doi.org/10.1063/1.4922546
  16. Фортов В.Е. , Храпак А.Г., Храпак С.А., Молотков В.И., Петров О.Ф. Пылевая плазма // УФН. 2004. Т. 174. № 5. С. 495–544. https://doi.org/10.3367/UFNr.0174.200405b.0495
  17. Griffiths M.R. et al. Measuring the interaction between a pair of emulsion droplets using dual-trap optical tweezers // RSC advances. 2016. V. 6. № 18. P. 14538–14546. https://doi.org/10.1039/C5RA25073K
  18. Chen A. et al. In situ measurements of interactions between switchable surface-active colloid particles using optical tweezers // Langmuir. 2020. V. 36. №. 17. P. 4664–4670. https://doi.org/10.1021/acs.langmuir.0c00398
  19. Liu S. et al. In situ measurement of depletion caused by SDBS micelles on the surface of silica particles using optical tweezers // Langmuir. 2019. V. 35. № 42. P. 13536–13542. https://doi.org/10.1021/acs.langmuir.9b02041
  20. Vugrin K.W. et al. Confidence region estimation techniques for nonlinear regression in groundwater flow: Three case studies // Water Resources Research. 2007. V. 43. № 3. P. W03423. https://doi.org/10.1029/2005WR004804

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу
2. Fig. 1. Structure of the original computational domain.

Жүктеу (42KB)
Метадеректер
3. Fig. 2. Dependence of the normalized force of electrostatic interaction of particles on the normalized distance between the surfaces of particles for k = 10. Solid lines are the condition of constant uniform surface charge distribution: 1 – f = 10, ε = 0.1; 2 – f = 10, ε = 1; 3 – f = 10, ε = 10; 4 – f = 50, ε = 0.1; 5 – f = 50, ε = 1; 6 – f = 50, ε = 10. Dashed lines are the condition of constant potential corresponding to the value of f for a single particle: 7 – k = 10, 8 – f = 50.

Жүктеу (191KB)
Метадеректер
4. Fig. 3. Dependence of the normalized potential u on the surface of a single isolated particle on the normalized surface charge density f: 1 – k = 10, 2 – k = 50.

Жүктеу (54KB)
Метадеректер
5. Fig. 4. Dependence of the normalized force of interaction of particles on the normalized surface charge density at a distance between the particle surfaces equal to the Debye radius. Solid lines are the condition of constant uniform surface charge distribution: 1 – k = 10, ε = 0.1; 2 – k = 10, ε = 1; 3 – k = 10, ε = 10; 4 – k = 50, ε = 0.1; 5 – k = 50, ε = 1; 6 – k = 50, ε = 10. Dashed lines are the condition of constant potential corresponding to the value of f for a single particle: 7 – k = 10, 8 – k = 50.

Жүктеу (227KB)
Метадеректер
6. Fig. 5. Comparison of the dependences of the normalized force of electrostatic interaction of particles on the normalized distance between the surfaces of particles. Solid lines are the condition of constant homogeneous surface charge distribution at ε = 0.05. Dashed lines are the use of formula (8). Calculation parameters: 1 – k = 10, f = 140; 2 – k = 10, f = 32.5; 3 – k = 30, f = 30; 4 – k = 30.8, f = 28.8; 5 – k = 70, f = 25; 6 – k = 72.2, f = 26.4.

Жүктеу (205KB)
Метадеректер

© Russian Academy of Sciences, 2025