A statistical field theory of salt solutions of 'hairy' dielectric particles
Abstract
In this paper, we formulate a fieldtheoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a 'central' charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a pointlike test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain FisherWidom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a saltfree solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metalorganic complexes and polymeric stars.
 Publication:

Journal of Physics Condensed Matter
 Pub Date:
 January 2020
 DOI:
 10.1088/1361648X/ab4d38
 arXiv:
 arXiv:1909.02319
 Bibcode:
 2020JPCM...32e5101B
 Keywords:

 electrostatic interactions;
 manybody effects;
 electrolytes;
 statistical mechanics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 Revised version submitted to Journal of Physics: Condensed Matter 15 September 2019