Adsorption Isotherms
====================

.. module:: microscopic_gating.adsorption

This module implements adsorption isotherms that describe how surface occupancy
depends on bulk concentration.

Langmuir Isotherm
-----------------

.. autoclass:: LangmuirIsotherm
   :members:
   :member-order: bysource
   :show-inheritance:

Hill Isotherm
-------------

.. autoclass:: HillIsotherm
   :members:
   :member-order: bysource
   :show-inheritance:

Theory Background
-----------------

The Langmuir isotherm derives from a grand canonical two-state site model:

.. math::

   \theta(\phi) = \frac{\phi/K}{1+\phi/K}

where :math:`K` is the dissociation constant and :math:`\phi` is the bulk concentration.

The Hill isotherm extends this with an effective cooperativity parameter:

.. math::

   \theta(\phi) = \frac{(\phi/K)^n}{1+(\phi/K)^n}

where :math:`n` is the Hill coefficient (n=1 reduces to Langmuir).