Decoding Noise in Nanofluidic Systems: Adsorption versus Diffusion Signatures in Power Spectra

TL;DR

This work addresses how adsorption and diffusion shape noise signatures in nanofluidic channels by deriving a minimal 1D model that captures coupled diffusion and wall-adsorption dynamics. The authors obtain closed-form PSDs for the total, bound, and free particle numbers and validate them with Brownian-dynamics simulations, revealing robust $1/f^{3/2}$ (diffusion) and $1/f^{2}$ (adsorption) scalings. Crucially, the PSDs are non-additive due to cross-correlations, and two distinct spectral corners emerge only when diffusion and adsorption/desorption timescales are well separated, enabling a diagnostic based on PSD shape to identify the dominant transport mechanism. The results offer practical guidance for interpreting noisy signals in ion channels, nanopores, and electrochemical sensors and highlight the potential to extract microscopic adsorption properties from spectral data.

Abstract

Adsorption processes play a fundamental role in molecular transport through nanofluidic systems, but their signatures in measured signals are often hard to distinguish from other processes like diffusion. In this paper, we derive an expression for the power spectral density (PSD) of particle number fluctuations in a channel, accounting for diffusion and adsorption/desorption to a wall. Our model, validated by Brownian dynamics simulations, is set in a minimal but adaptable geometry, allowing us to eliminate the effects of specific geometries. We identify distinct signatures in the PSD as a function of frequency $f$, including a $1/f^{3/2}$ scaling related to diffusive entrance/exit effects, and a $1/f^2$ scaling associated with adsorption. These scalings appear in key predicted quantities -- the total number of particles in the channel and the number of adsorbed or unadsorbed particles -- and can dominate or combine in non-trivial ways depending on parameter values. Notably, when there is a separation of timescales between diffusion inside the channel and adsorption/desorption times, the PSD can exhibit two distinct corners with well-separated slopes in some of the predicted quantities. We provide a strategy to identify adsorption and diffusion mechanisms in the shape of the PSD of experimental systems on the nano- and micro-scale, such as ion channels, nanopores, and electrochemical sensors, potentially offering insights into noisy experimental data.

Figures (11)

• Figure 1: Adsorption and diffusion phenomena in nano- and micro- scale systems. In the schematics, particles (black) diffuse under confinement, with their relevant length scales highlighted. In these systems attractive interactions like adsorption (red) between the particles and the confining walls are also important, and add a degree of complexity.
• Figure 2: A representation of our model system of a channel connected to two reservoirs (line $P$) and adsorption on the channel wall (line $Q$). The channel has length $L_0$ while the total length of the system is $L$. Adsorption and desorption rates are set by $k_{\rm on}$ and $k_{\rm off}$, respectively.
• Figure 3: Power spectral density of number fluctuations for the purely diffusive case, with $L=20\ell_0$. Dashed lines indicate $\tau_{\rm sys}=L^2/2D$ and $\tau_{\rm cha}=L_0^2/2D$. Expected scalings for high and intermediate frequency regimes of $f^{-3/2}$ and $f^{-1/2}$ respectively are indicated. Data in purple shows the spectrum for the total number of particles from simulations. Data in green shows the corresponding spectrum for simulations in 3D, with the same parameters. The 3D result plateaus for frequencies smaller than $1/\tau_{\rm cha}=2D/L_0^2$.
• Figure 4: Power spectral density of number fluctuations with no diffusion and only adsorption/desorption processes. Spectrum for fluctuations in the number of unadsorbed particles is shown, which is equivalent to that for adsorbed particles. Dashed lines indicate $\tau_{\rm ads}=1/k_{\rm on}$ and $\tau_{\rm des}=1/k_{\rm off}$. A solid line indicates $f_0$, the corner frequency, which is the mean of the two rates $f_0=(k_{\rm on}+k_{\rm off})/2\pi$. There is a clear $1/f^2$ scaling at high frequencies and a plateau below $f_0$. In this case, $L=L_0=\ell_0$, $k_{\rm on}=0.027f_0$, and $k_{\rm off}=6.3f_0$. We use separated adsorption and desorption rates to demonstrate the dependence of the corner primarily on the faster rate (here, $k_{\rm off}$).
• Figure 5: Slow diffusion, fast adsorption/desorption: Case 1 -- $\tau_{\rm cha} \gg \tau_{\rm ads} \sim \tau_{\rm des}$. Left: total PSD. Middle: bound PSD. Right: free PSD. We use $L=2\ell_0$, $k_{\rm on}=125/\tau_0$, and $k_{\rm off}=375/\tau_0$. Note here that $k_{\rm on} \leq k_{\rm off}$. The dotted curve indicates the pure diffusive case with the same parameters (but $k_{\rm on}=0$). Similarly, the dash-dotted curve indicates the pure adsorption/desorption case with the same parameters (but $D=0$). Relevant timescales are labeled and marked with dashed vertical lines.