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As shown in Figure 8C, the plot did not pass through the origin; instead, three linear portions were obtained, which suggested that the adsorption occurred in all three phases/stages including the external diffusion, intra-mat diffusion, and the internal diffusion stage.

Here, we established the 'intra-mat diffusion model' and identified the rate-controlling step in order to more clearly describe the adsorption process.

where q t is the adsorption capacity at time t (mg/g), K m is the adsorption rate constants of intra-mat diffusion model (mg/g/min1/2) and C is the intercept which is related to the thickness of the boundary layer.

The plot of q t versus t 1/2 gives a straight line with a slope of K m and an intercept of C. Based on this model, the plot should be linear if the intra-mat diffusion is involved in the adsorption process and the plot passes through the origin then intra-mat diffusion is the sole rate-controlling step [19].

These results indicated that intra-mat diffusion was not the only rate-limiting step.

According to this model, the adsorption process for nanofibers mat can be divided into three stages, including the diffusion from the bulk solution to the external surface of nanofibers mat (called 'external diffusion'), pore diffusion inside the nanofibers mat (called 'intra-mat diffusion'), and the 'internal diffusion' to the adsorption sites.

Diffusion and resistivity.

Diffusion and ion implantation.

Distribution, diffusion and significance of the dirty joke.

Diffusion topics: Fick's laws, atomic theory of diffusion, and diffusion in alloys.

They are: Discovery, Development, Diffusion and Disruption.

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