Extended Data Fig. 11: Fitting experimental spectra with a Debye-type approximation.
From: In-plane dielectric constant and conductivity of confined water
a, Experimental data as a function of frequency (symbols) and corresponding fits (solid line) using the Debye-type MW relaxation model in equation (11) and 3D numerical simulations for our representative device with h = 30 nm. Bars are the random noise level as measured at each f. Fitted parameters: τ// = 9 × 10−5, εlf// = 2 × 104 (yielding σ// = 0.002 S m−1 using σ// = ε0εlf///τ//) and εhf// = 70. Dashed line shows the model prediction for high-f and low-f dielectric constants equal to the value of bulk water (εlf// = εhf// = εlf⊥ = εhf⊥ = εbulk). b, Same as in a but for our representative device with h = 5 nm. Fitted parameters: τ// = 2 × 10−5, εlf// = 8 × 104 (yielding σ// ≈ 0.03 S m−1) and εhf// = 100. c, Same as in a and b but our representative device with h = 1.5 nm. Fitted parameters: τ// = 8 × 10−6, εlf// = 1.5 × 106 (yielding σ// = 1.7 S m−1) and εhf// = 900. Dotted red line is the best fitting at low frequencies but imposed high-f dielectric constant equal to the bulk value (εhf// = 80), demonstrating that, for h = 1.5 nm, the experimental data at high frequencies lie well above the response expected from bulk water. Other experimental parameters used in the simulations: geometric parameters and out-of-plane dielectric constants of water (εlf⊥ = εhf⊥) are as used in Extended Data Fig. 10.
