Fig. 5. Thermodynamic and kinetic analyses of the MV²⁺⊂BPP34C10 complex (de)formation in SMJs at the graphene-liquid interface.

(A) Plots of the thermodynamic parameters (ln K_a versus 1000/T and ΔG^o versus 1000/T) deduced from single-molecule measurements at the SMJ device-Me₂SO interfaces at 293 K. Error bars were calculated from the data obtained from five different devices. ΔH^o and ΔS^o were obtained by using the van’t Hoff equation. (B) I-t curve (black) of a BPP34C10-SMJ device in a Me₂SO solution of 1 mM MV·2PF₆ at 293 K, and the idealized fit (orange) obtained from segmental k-means method based on hidden Markov model analysis using a QUB software (V_bias = 100 mV). (C) Plots of time intervals of the high (T_high, blue) and low (T_low, red) current states in the idealized fit in (B), and their exponential fits in which the lifetimes of two states (τ_high and τ_low) can be derived. (D) Arrhenius plots of association (k_a = 1/τ_low) and dissociation (k_d = 1/τ_high) rate constants deduced (E_a = −38.7 kJ mol⁻¹ and E_d = 31.5 kJ mol⁻¹).