## 2 Theory of the POCIS  
The POCIS, a permeation-based passive sampler, consists of a receiving phase made of solid sorbent sandwiched between two microporous diffusion-limiting membranes [34]. The passive diffusion of pollutants into the POCIS in an aquatic environment can be regarded as a multi-phase mass transfer process. As shown in Figure 2, the analytes firstly transport through the water boundary layer (WBL) from bulk water; then across biofilm, water-filled membrane pores, and the membrane matrix transfer by molecular diffusion; and finally the analytes enter the absorbent phase inside the device [35]. Several mathematical models have been proposed to describe the dynamic process of compound sorption in passive samplers, which have some differences in the composition of models [36]. Most of them are based on simplified common assumptions: the existence of steady (or pseudo-stability) state, isotropic water sampler exchange kinetics, and the linear distribution curve. In those cases, the accumulation of analytes by passive samplers typically follow first-order kinetics (Equation (1)), which is divided into dynamic and equilibrium stages with time [37].  
\[C_{s}(t)=C_{w}K_{mw}\Big{(}1-e^{-k_{e}t}\Big{)} \tag{1}\]  
where \(C_{s}(t)\) is the concentration (\(\mu\)g/g) of analyte in the sorbent; \(C_{w}\) is the TWA concentration (\(\mu\)g/L) of the analyte in water; \(K_{mw}\) (\(k_{u}\)/\(k_{e}\)) is the partition constant (L/g) of analytes in membrane water; \(k_{e}\) and \(k_{u}\) are the elimination and uptake rate constants (L/g/d), respectively; and \(t\) is exposure time (days). In the Equation (1), the \(k_{e}\) value can be defined as follows [38]:  
\[k_{e}=\frac{R_{s}}{K_{mw}M_{s}} \tag{2}\]  
where \(R_{s}\) is the sampling rate (L/d or mL/d) and \(M_{s}\) is the mass (g) of sorbent in the POCIS.  
The enrichment process of target compounds on sorbent in the POCIS can be divided into three different regimes: (a) a linear (or kinetic/integrative) regime, (b) a pseudolinear regime, and (c) an equilibrium regime. The POCIS, as an integrative sampler, generally determines TWA concentration in a linear regime by calibrated the \(R_{s}\)[39]. During a kinetic regime, the \(k_{e}\) is negligible compared to the \(k_{u}\), and thus Equation (1) is simplified to Equation (3):  
\[C_{s}(t)=C_{w}k_{u}t \tag{3}\]  
By substituting the \(k_{u}\) with the sampling rate \(R_{s}\), Equation (3) can be changed to an equivalent relationship, as expressed by Equation (4):  
\[C_{s}(t)=\frac{C_{w}R_{s}t}{M_{s}} \tag{4}\]  
The diffusion of analytes into the POCIS in an aquatic environment is a complicated mass transfer process through the WBL, biofilm, and the membrane matrix, entering the receiving absorbent (Figure 2). Under WBL control [13; 34], the \(R_{s}\) can be described by Equation (5):  
\[R_{s}=(D_{w}/\delta_{w})A \tag{5}\]  
where \(D_{w}\) is the diffusion coefficient in water; \(\delta_{w}\) is the effective thickness of the WBL, and \(A\) is the surface area of the sampler. Under membrane control, the \(R_{s}\) can be expressed by Equation (6):  
\[R_{s}=(D_{m}/\delta_{m})K_{mw}A \tag{6}\]  
where \(D_{m}\) is the diffusion coefficient in the membrane and \(\delta_{m}\) is the thickness of the membrane.  
Figure 2: Schematic diagram on multi-phase transport process of pollutants in the polar organic chemical integrative sampler (POCIS) (\(\delta\): the effective thickness of relative phases).