Ionic heat dissipation in solid-state pores

Abstract

Energy dissipation in solid-state nanopores is an important issue for their use as a sensor for detecting and analyzing individual objects in electrolyte solution by ionic current measurements. Here, we report on evaluations of heating via diffusive ion transport in the nanoscale conduits using thermocouple-embedded SiN_x pores. We found a linear rise in the nanopore temperature with the input electrical power suggestive of steady-state ionic heat dissipation in the confined nanospace. Meanwhile, the heating efficiency was elucidated to become higher in a smaller pore due to a rapid decrease in the through-water thermal conduction for cooling the fluidic channel. The scaling law suggested nonnegligible influence of the heating to raise the temperature of single-nanometer two-dimensional nanopores by a few kelvins under the standard cross-membrane voltage and ionic strength conditions. The present findings may be useful in advancing our understanding of ion and mass transport phenomena in nanopores.

Fig. 1.. Local heating in a solid-state nanopore.

(A) A schematic model depicting simultaneous measurements of ionic current I_ion and local temperature at a nanopore. Diffusive ion transport in salt solution under the applied cross-membrane voltage V_b induces energy dissipation to local heating at the nanopore, whose effect was evaluated by recording the thermovoltage change V_th at the thermocouple embedded in the vicinity of the channel. (B and C) Optical image (B) and false-colored scanning electron micrograph (C) of a 300-nm-sized thermometer-embedded nanopore. Square region in (B) is the SiO₂/SiN_x membrane. The thermometer consisted of a 100-nm-sized point contact made of Pt and Au nanowires lithographed at the side of the nanopore (C).

Fig. 2.. Simultaneous measurements of ionic current and local temperature at a nanopore.

(A) Changes in the thermovoltage ΔV_th and the corresponding local temperature T_th at the thermocouple against the voltage V_b applied across the 40-nm-thick SiO₂/SiN_x membrane holding a nanopore of 300 nm diameter. Red and blue plots are the results obtained in phosphate-buffered saline (PBS) of ion concentration 1.37 M and 137 mM, respectively. Inset is the simultaneously recorded ionic current I_ion versus V_b curves. (B) Plots of T_t of (A) as a function of the electric power P = I_ionV_b. Color code is the same as that in (A). (C) Temperature response against larger input power in a 300-nm-sized nanopore. The curve became irretraceable when excessive power was loaded over 30 μW. In contrast, the I_ion-V_b characteristics was observed to be stable as shown in the inset, indicating failure of the thermocouple under the dissipated heat at the nanopore.

Fig. 3.. Ion transport in self-heated nanopores.

(A) The ionic current I_ion (red) and the conductance G (blue) in a 300-nm-sized nanopore filled with electrolyte buffer containing 1.37 M NaCl under a voltage scan from 0 to 3 V. (B) Theoretically predicted water viscosity change η associated with the temperature increase at the nanopore. (C) Linear dependence of G on η⁻¹ revealing pronounced effects of heat dissipation–mediated viscosity change on the ionic current characteristics. Red line is a linear fit defining a slope β. (D) Linear relation between β and the pore diameter d_pore from 100 nm to 10 μm. Dashed line is a linear fitting to the plots.

Fig. 4.. Cross-membrane voltage–dependent noise spectra.

(A) Overplots of noise spectra obtained at V_b = 0.3 V (green), 0.6 V (blue), and 0.9 V (red), which showed a monotonic upward shift with increasing V_b. Dashed line indicates f = 2 kHz. (B) Plots of the noise intensity I_th at f = 2 kHz as a function of the input electrical power. Inset shows a magnified view at a low-power regime. Dashed lines are linear fits at I_ionV_b < 100 W.

Fig. 5.. Local heating in solid-state pores.

(A) T_t-P characteristics in pores of various sizes from 100 nm to 10 μm. Images are the false-colored scanning electron micrographs displaying the structure of the thermometer-embedded pores used. The local temperature tends to be raised under lower electric power for smaller channels, attributed mainly to the lower water heat capacity involved in the heating. (B) Plots of the power cost C to raise the local temperature by 1 K with respect to d_pore. The gray curve is a linear fit with zero intercept indicating C increase with d_pore. Insets are an equivalent circuit depicting steady-state heat flow under the temperature difference of T_t and the bath temperature T₀ via the thermal resistance 1/K and a magnified view at small d_pore. (C) Predicted change in the temperature ΔT at nanopores of diameter d_pore = 10 nm in a 10-nm-thick membrane (blue) and a 1-nm-sized channel mimicking a graphene nanopore structure (red) under the applied voltage V_b in 1 M KCl. A case of 4 M KCl is also shown for the 1-nm nanopore (pink).