  To explore charge regulation (CR) in physicochemical and biophysical systems,
we present a model of colloidal particles with sticky adsorption sites which
account for the formation of covalent bonds between the hydronium ions and the
surface functional groups. Using this model and Monte Carlo simulations, we
find that the standard Ninham and Parsegian (NP) theory of CR leads to results
which deviate significantly from computer simulations. The problem of NP
approach is traced back to the use of bulk equilibrium constant to account for
surface chemical reactions. To resolve this difficulty we present a new theory
of CR. The fundamental ingredient of the new approach is the sticky length,
which is non-trivially related with the bulk equilibrium constant. The theory
is found to be in excellent agreement with computer simulations, without any
adjustable parameters. As an application of the theory we calculate the
effective charge of colloidal particles containing carboxyl groups, as a
function of pH and salt concentration.
