Predicting how well a sorbent material will capture PFAS compounds is central to designing effective water treatment systems. The Freundlich isotherm is the mathematical workhorse scientists rely on to model this relationship, translating laboratory equilibrium data into design parameters for full-scale filters.
What the Freundlich Equation Actually Measures
The Freundlich isotherm takes the form q_e = K_F × C_e^(1/n), where q_e is the mass of PFAS adsorbed per unit mass of adsorbent at equilibrium, C_e is the equilibrium liquid-phase concentration, K_F is the Freundlich capacity coefficient, and 1/n is the heterogeneity factor. A higher K_F value indicates greater overall adsorption capacity, while 1/n below 1 signals favorable, nonlinear adsorption—typical of PFAS on carbonaceous materials.
For PFOA on granular activated carbon (GAC), experimentally derived K_F values commonly fall in the range of 50–200 (mg/g)(L/mg)^(1/n) depending on carbon type, surface chemistry, and the presence of competing organics. Short-chain compounds such as PFBS (C4) yield significantly lower K_F values, often an order of magnitude below PFOA, which explains their notoriously poor removal at GAC contactors.
Importantly, the Freundlich model assumes surface heterogeneity—the adsorbent has sites of varying energy. This is physically realistic for activated carbon, which contains a spectrum of micropores, mesopores, and surface functional groups, each contributing differently to PFAS uptake.
Applying Isotherm Data to Treatment System Design
Once K_F and 1/n are determined from batch equilibrium tests, engineers use these values to estimate the theoretical bed volumes a GAC or PFAS-selective adsorbent column can treat before breakthrough. Combined with empty bed contact time (EBCT) and pilot column data, isotherm parameters feed directly into design models such as the homogeneous surface diffusion model (HSDM).
A critical limitation of relying solely on single-compound isotherms is that real source waters contain mixtures of PFAS congeners plus natural organic matter. Competitive adsorption can reduce effective K_F by 30–60% compared to clean-water experiments. This is why pilot testing in actual source water is indispensable before committing to a full-scale installation.
PFAS-selective adsorbents engineered with fluorophilic binding sites exhibit steeper isotherms for short-chain PFAS than GAC, meaning their K_F advantage is most pronounced precisely where GAC fails most—at the C4–C6 chain length range that accounts for an increasing share of detected PFAS in treated drinking water after long-chain compound restrictions took effect.