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Charged aggregation
Phys. Rev. E 110, 044128 – Published 21 October, 2024
DOI: https://doi.org/10.1103/PhysRevE.110.044128
Abstract
We introduce an aggregation process that begins with equal concentrations of positively and negatively “charged” monomers. Oppositely charged monomers merge to form neutral dimers. These dimers are the seeds for subsequent aggregation events in which neutral clusters of necessarily even mass join irreversibly to form neutral aggregates of ever-increasing size. In the mean-field approximation with mass independent reaction rates, we solve for the reaction kinetics and show that the concentration of clusters of mass , asymptotically scales as , with having a nontrivial dependence on . We also investigate the phenomenon of gelation in charged aggregation when the reaction rate equals the product of the two incident cluster masses. Finally, we generalize our model to the case of three and more types of monomers.
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References (28)
- P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, USA, 1953).
- S. K. Friedlander, Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics, EngineeringPro collection (Madison Avenue, New York, USA, 2000).
- M. V. Smoluchowski, Mathematical theory of the kinetics of the coagulation of colloidal solutions, Z. Phys. Chem. 92, 129 (1917).
- S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys. 15, 1 (1943).
- A. A. Ovchinnikov, S. F. Timashev, and A. A. Belyi, Kinetics of Diffusion Controlled Chemical Processes (Nova Science, Hauppage, NY, 1989).
- P. L. Krapivsky, S. Redner, and E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge University Press, Cambridge, UK, 2010).
- P. L. Krapivsky and C. Connaughton, Driven Brownian coagulation of polymers, J. Chem. Phys. 136, 204901 (2012).
- R. L. Drake, A general mathematical survey of the coagulation equation, in Topics in Current Aerosol Research, part 2, edited by G. M. Hidy and J. R. Brock (Pergamon Press, New York, 1972), pp. 201–376.
- R. M. Ziff, Kinetics of polymerization, J. Stat. Phys. 23, 241 (1980).
- F. Leyvraz, Scaling theory and exactly solved models in the kinetics of irreversible aggregation, Phys. Rep. 383, 95 (2003).
- P. G. J. van Dongen and M. H. Ernst, Dynamic scaling in the kinetics of clustering, Phys. Rev. Lett. 54, 1396 (1985).
- P. G. J. van Dongen and M. H. Ernst, Scaling solutions of Smoluchowski's coagulation equation, J. Stat. Phys. 50, 295 (1988).
- I. Ispolatov and P. L. Krapivsky, Annihilation of charged particles, Phys. Rev. E 53, 3154 (1996).
- V. V. Ginzburg, L. Radzihovsky, and N. A. Clark, Self-consistent model of an annihilation-diffusion reaction with long-range interactions, Phys. Rev. E 55, 395 (1997).
- P. Meakin and Z. B. Djordjevic, Cluster-cluster aggregation in two-monomer systems, J. Phys. A 19, 2137 (1986).
- F. Leyvraz and S. Redner, Nonuniversality and breakdown of scaling in a two-component coagulation model, Phys. Rev. Lett. 57, 163 (1986).
- D. S. Ben-Naim, E. Ben-Naim, and P. L. Krapivsky, Jamming and tiling in aggregation of rectangles, J. Phys. A 51, 455002 (2018).
- F Leyvraz, Existence and properties of post-gel solutions for the kinetic equations of coagulation, J. Phys. A: Math. Gen. 16, 2861 (1983).
- F. Leyvraz and S. Redner, Nonuniversality and breakdown of scaling in two-species aggregation, Phys. Rev. A 36, 4033 (1987).
- P. Meakin and S. Miyazima, Reaction limited aggregation with two species of monomers, J. Phys. Soc. Jpn. 57, 4439 (1988).
- P. L. Krapivsky and E. Ben-Naim, Aggregation with multiple conservation laws, Phys. Rev. E 53, 291 (1996).
- R. Normand, A model for coagulation with mating, J. Stat. Phys. 137, 343 (2009).
- J. Bertoin, Two solvable systems of coagulation equations with limited aggregations, Ann. Henri Poincaré 26, 2073 (2009).
- M. A. Ferreira, J. Lukkarinen, A. Nota, and J. J. L. Velázquez, Non-equilibrium stationary solutions for multicomponent coagulation systems with injection, J. Stat. Phys. 190, 98 (2023).
- Y. Kovchegov and P. T. Otto, Multidimensional Lambert-Euler inversion and vector-multiplicative coalescent processes, J. Stat. Phys. 190, 188 (2023).
- G. B. Field and W. C. Saslaw, A statistical model of the formation of stars and interstellar clouds, Astrophys. J. 142, 568 (1965).
- W. H. White, On the form of steady-state solutions to the coagulation equations, J. Colloid Interface Sci. 87, 204 (1982).
- C. M. Bender and S. A Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer, New York, 1999).
