Electrical Cross-Correlation Spectroscopy: Measuring Picoliter-per-Minute Flows in Nanochannels

We introduce all-electrical cross-correlation spectroscopy of molecular number fluctuations in nanofluidic channels. Our approach is based on a pair of nanogap electrochemical transducers located downstream from each other in the channel. When liquid is driven through this device, mesoscopic fluctuations in the local density of molecules are transported along the channel. We perform a time-of-flight measurement of these fluctuations by cross-correlating current-time traces obtained at the two detectors. Thereby we are able to detect ultralow liquid flow rates below $10\mathrm{pL}/\min $. This method constitutes the electrical equivalent of fluorescence cross-correlation spectroscopy.

Figure 1

(a) Schematic of the measurement concept. Fluctuations of the number of electrochemically active molecules are electrically measured at two electrodes in a nanochannel. Liquid flow velocity is determined by time-of-flight detection of these fluctuations as the molecules are transported along the channel from the upstream to the downstream transducer. (b) Raw current-time traces recorded at both electrodes at a flow rate corresponding to a time shift of approximately 0.2 s. Gray lines are guides to the eye.

Figure 2

(a) Schematic cross section of a nanofluidic device connected to a microchannel in a parallel flow control setup. (b) Equivalent fluidic circuit of the configuration. (c) Top view micrograph of a $50\mu \mathrm{m}$ long device bonded to a $100\mu \mathrm{m}$ long microchannel in PDMS.

Figure 3

(a) Cross-correlation functions of current-time traces recorded at the two $49\mu \mathrm{m}$ long top electrodes of a $100\mu \mathrm{m}$ long device for different pump flow rates. (b) Cross correlation of current-time traces generated by a one-dimensional random walk superimposed with flow for the same device geometry and diffusion coefficient. (c) Analytically derived cross-correlation functions for the same one-dimensional geometry and diffusion coefficient.

Figure 4

(a) Autocorrelation functions determined of the same traces (but only from one electrode) used for the cross-correlation analysis. The arrows indicate the corresponding cross-correlation peak times shown in Fig. 3a. (Functions for smaller flow rates are omitted because the short duration of the traces leads to excessive scatter.) (b) Analytically derived one-dimensional autocorrelation functions.

Figure 5

Nanofluidic flow rates in a nanofluidic device as a function of syringe pump flow rate. The adjusted experimental data points (black dots) include a correction for adsorption as well as for the shift of the peak times ${\tau }_{\mathrm{peak}}$. The dashed line’s slope is identical to the ratio of hydraulic resistances $2R_{\mathrm{micro}}/R_{\mathrm{nano}}=1/16000$.