text: The Polanyi potential adsorption theory is based on the assumption that the molecules near a surface move according to a potential, similar to that of gravity or electric fields.  This model is applicable in the case of gases at a surface at constant temperature.  Gas molecules move closer to that surface when the pressure is higher than the equilibrium vapor pressure.  The change in potential relative to the distance from the surface can be calculated using the formula for difference of the chemical potential,
  where  is the chemical potential,  is the molar entropy,  is the molar volume, and  is the molar internal energy.
  At equilibrium, the chemical potential of a gas at a distance  from a surface, , is equal to the chemical potential of the gas at an infinitely large distance from the surface, .  As a result, the integration from an infinitely far distance to r distance from the surface leads to
  where  is the partial pressure at distance r and  is the partial pressure at infinite distance from the surface.
  Since the temperature remains constant, the difference in chemical potential formula can be integrated over pressures  and 
  By setting the , the equation can be simplified to
  Using the ideal gas law, , the following formula is obtained
  Since gas condenses into a liquid on a surface when the pressure of the gas exceeds the equilibrium vapor pressure, , we can assume a liquid film forms over the surface of thickness, . The energy at  is
  Considering that the partial pressure of the gases relates to the concentration, the adsorption potential,  can be calculated as
  where  is the saturated concentration of adsorbate and  is the equilibrium concentration of the adsorbate.