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Jovanović (1969) Monolayer & Multilayer Adsorption Isotherm Formula: Mechanical Contact Model
Calculate equilibrium adsorption with mechanical bulk-molecule collision knock-off corrections using Dušan S. Jovanović’s (1969) monolayer isotherm q_e = q_max * (1 - EXP(-K_J * C_e)) and multilayer extension.
How Jovanović’s (1969) collision-desorption probability corrects Langmuir’s instantaneous-evaporation assumption!
Deriving adsorption equilibrium from statistical residence-time mechanics rather than Langmuir’s idealized non-colliding kinetics, Dušan S. Jovanović (1969, Kolloid-Zeitschrift und Zeitschrift für Polymere) accounted for mechanical collisions between incoming bulk-phase molecules and already-adsorbed surface molecules during finite vibrational residence time tau! This yields the remarkably clean exponential monolayer isotherm: q_e = q_max * (1 - EXP(-K_J * C_e))!
Like Langmuir, Jovanović’s monolayer equation obeys Henry’s Law q_e ≈ (q_max * K_J) * C_e at low concentration (since 1 - EXP(-x) ≈ x) and saturates at q_max—but approaches saturation faster than Langmuir at intermediate concentrations! In preparative HPLC chromatography and gas-solid sorption with mobile-layer build-up (bulk factor K_L * C_e), Jovanović’s multilayer equation multiplies the monolayer term by EXP(K_L * C_e): q_multi = q_max * (1 - EXP(-K_J * C_e)) * EXP(K_L * C_e)!
| Isotherm Model (q_max = 95 mg/g, K_J = 0.06 L/mg, C_e = 30 mg/L) | Equation | Equilibrium Uptake q_e (mg/g) |
|---|---|---|
| Jovanović Monolayer (K_L = 0) | q_max * (1 - EXP(-K_J * C_e)) | 79.2966 mg/g (83.47% Fractional Coverage) |
| Same-K Langmuir Comparison | q_max * K_J * C_e / (1 + K_J * C_e) | 61.0714 mg/g (Slower Approach to Plateau) |
| Jovanović Multilayer (K_L = 0.004 L/mg) | q_max * (1 - EXP(-K_J * C_e)) * EXP(K_L * C_e) | 89.4067 mg/g |
Jovanović (1969) Monolayer Equilibrium Uptake q_e = q_max * (1 - EXP(-K_J * C_e))
Evaluates monolayer equilibrium sorption q_e (mg/g) from q_max (B2), Jovanović constant K_J (B3, L/mg), and equilibrium concentration C_e (B4, mg/L).
=IF(OR(B2 <= 0, B3 <= 0, B4 < 0), "Invalid Jovanovic Isotherm Parameters", ROUND(B2 * (1 - EXP(-B3 * B4)), 4))Jovanović Multilayer Isotherm Uptake q_multi = q_max * (1 - EXP(-K_J * C_e)) * EXP(K_L * C_e)
Incorporates secondary-layer association constant K_L >= 0 (B5) for mobile multilayer sorption.
=IF(OR(B2 <= 0, B3 <= 0, B4 < 0, B5 < 0, B5 >= B3), "Invalid Multilayer Parameters (Requires 0 <= KL < KJ)", ROUND(B2 * (1 - EXP(-B3 * B4)) * EXP(B5 * B4), 4))Try the example
Use the original values or change them to test your understanding.