Equivalence between particles and fields: A general statistical mechanics theory for short and long range many‐body forces

Abstract

While in vacuum fundamental and dispersion inter‐molecular forces can be in principle of infinite range, in the bulk, however, they are of rather short‐range, typically between a few angstroms to a few hundreds of angstroms. Yet colloidal particles, nano‐particles, and supramolecules, like enzymes, thousand or hundreds of thousands of angstroms apart, seem to recognize each other and self‐assembly, according with their shapes and sizes, in a wide variety of complex structures. In this paper we discuss this long‐range molecular recognition mechanism through a general liquid theory, based on the recognition of the equivalence between particles and fields, and molecular simulations. In particular we show results of a counter‐intuitive attraction between like‐charged colloidal particles and compare them with experimental results.

Very long-range attractive and repulsive forces in model colloidal dispersions

“…, n, and ρ l is the number density, of species l. h ij (r 21 ) ≡ g ij (r 22 ) − 1 is the total correlation functions for two particles at r 2 and r 1 , of species i and j, respectively, with r 21 = r 2 − r 1 , such that g ij (r 21 ) is the pair correlation function, also referred to as the radial distribution function (RDF), which gives the probability density of finding a particle 1, of species j, at the distance r 21 , from the central particle 2, of species i. The OZ equation is a probability balance, that guaranties a constant chemical potential in the whole system [50]. To solve it, closure relations for the direct correlation functions, c ij (r 21 ) and c lj (r 31 ), are needed.…”

Propiedades de transporte de co-solutos en hidrogeles termosensibles

“…Un sistema análogo podría ser la atmósfera terrestre, donde la presencia de la Tierra genera un campo externo -el campo gravitatorioque induce un perfil de concentración logarítmico de todas y cada una de las sustancias atmosféricas (nitrógeno y oxígeno, principalmente). Lo mismo -o algo muy similar dado que el campo externo no tiene la misma forma-ocurre con nuestro microgel, donde es posible, desde el punto de vista teórico, reemplazarlo por un campo externo generando así la misma respuesta del cosoluto como si la partícula polimérica estuviera presente [41]. De hecho, esta es la base de la teoría que utilizaremos para resolver la dinámica de los tiempos de carga y descarga del material.…”