Anomalous thermo-osmotic conversion performance of ionic covalent-organic-framework membranes in response to charge variations

Increasing the charge density of ionic membranes is believed to be beneficial for generating high output osmotic energy. Herein, we systematically investigated how the membrane charge populations affect permselectivity by decoupling their effects from the impact of the pore structure using a multivariate strategy for constructing covalent-organic-framework membranes. The thermo-osmotic energy conversion efficiency is improved by increasing the membrane charge density, affording 210 W m−2 with a temperature gradient of 40 K. However, this enhancement occurs only within a narrow window, and subsequently, the efficiency plateaued beyond a threshold density (0.04 C m−2). The complex interplay between pore-pore interactions in response to charge variations for ion transport across the upscaled nanoporous membranes helps explain the obtained results. This study has far-reaching implications for the rational design of ionic membranes to augment energy extraction rather than intuitively focusing on achieving high densities.

S2 chambers was used (4 cm 3 ), where the low concentration solution reservoirs were separated from a high concentration solution reservoir by the COF membrane and PAN, respectively (the effective testing area is 0.008 mm 2 ). The voltage was scanned with a step of 0.01 V s −1 . The ion transference number − of COF-EBxBDy/PAN was evaluated by determining the transmembrane diffusion potential (ф ). Herein, given that the redox potential of Ag/AgCl electrodes was eliminated during testing, ф is equal to .
The ion transference number − can be calculated with the following equation: where ℎ ℎ , , , , , and are the activities of ions in high concentration solution and low concentration solution, open circuit potential, Faraday constant, gas constant, and absolute temperature, respectively.

Evaluation of thermoelectric response of COF-EBxBDy/PAN
The thermoelectric response was recorded by a homemade setup ( membrane, a conductivity cell with the pierced membrane separating two chambers was used and both of the chambers were filled with 1 mM KCl solutions. A temperature gradient was induced by a brief heating of the chamber facing the COF active layer. The voltage variation relative to the initial state can be expressed as:

Osmotic energy harvesting
A pair of cation-selective membrane (Nafion ® 212) and anion-selective membrane (COF-EBxBDy/PAN) is mounted in a three-compartment conductive cell to harvest osmotic energy. The volume of each chamber is 4 cm 3 with a pore diameter of 0.1 mm. The high salinity solution (0.5 M NaCl) is placed in the middle chamber S3 and the low salinity solution (0.01 M NaCl) is set at the side chambers. Ag/AgCl electrodes were used to apply a transmembrane potential and measure the resulting current. The X-intercepts of the I-V plots represent the open-circuit voltage ( ) and the Y-intercepts of I-V plots present the short-circuit current ( ). The maximum output power can be calculated using where , , and are the maximum power, maximum power density, and the effective working area of the COF membrane, respectively.

Evaluation of the thermo-osmotic power production
The thermo-osmotic power production of COF-EBxBDy/PAN was evaluated using a homemade setup. A micro- to the initial state is dependent on both temperature and activity gradient, which can be calculated using the following equation: where ℎ ℎ , and are the temperatures of high concentration and low concentration solutions. When the temperature of low concentration solution was changed (the temperature of solution in high concentration solution remained unchanged), the voltage variation relative to the initial state can be expressed as: The maximum output power density can be calculated using equations 5 and 6.

Numerical simulations
The numerical simulation was performed based on coupled Poisson and Nernst-Planck equations by setting appropriate boundary parameters using a commercial finite-element software package COMSOL (version 5.2).
The Nernst-Planck equation (9) defines the flux of each ion species in the presence of concentration gradient, which describes the transport character of charged nanochannels. The ion concentration induced electrical potential can be described by Poisson equation (10). When the system reaches a stationary regime, the ion flux should conform to the steady-state continuity equation (11).
For simplification, a 1.5-nm-width and 200-nm-length rectangle nanochannel was used to simulate the channels inside the COF-EBxBDy/PAN. To decrease the effect of entrance/exit mass transfer resistances on the overall ionic transport, two electrolyte reservoirs are introduced. The external potential is applied on the boundary 1 , and 2 offered the reference potential. The boundary conditions for the electrical potential and ion flux are shown as below:

S5
�⃗ · = 0 (13) The physical quantity σ represents the surface charge density of the channel walls. The ionic current can be calculated by In addition to the concentration gradient, temperature gradient, as an external driving force, also drives the motion of solutes. Taking the thermal potential inside a nanochannel into account, the numerical model has to consider both mass and heat transfers. To facilitate the calculation, the diffusion coefficients of Na + and Cl − were fixed during heating. Therefore, we introduce the Nernst-Plank equation into the model to describe ion transport and concentration profiles under a temperature gradient, where is the velocity induced by thermo-osmosis and thermoelectric effect, which can be formulated as follow [1] , where is the zeta potential; is the viscosity of solvent; 0 is the bulk electric potential.
For the power generation calculations, a concentration gradient ( ℎ ℎ / = 0.5 M/0.01 M) is employed and no external potential is applied. The corresponding diffusion current can be attained by:

Ion Transmission Activation Energy Measurement
The membrane was mounted between the two chambers of a symmetric H-type electrochemical cell with a pore diameter of 0.1 mm and both chambers were filled with different concentrations of NaCl aqueous solutions (4 cm 3 for each). The COF layer was in contact with the low concentration side. Ag/AgCl electrodes were used to apply a transmembrane potential. A scanning triangle voltage signal from 0.2 V to -0.02 V with a step voltage of 0.01 V and a period of 1 s was applied to record the I-V curves. The ionic currents of the systemes at various temperatures were recorded by a CHI660E. The conductance values were derived from the slops of the resulting I-V curves. The ion transmission activation energies were calculated by the Arrhenius equation: whereby , , , R, and T represnet the conductance, preexponential factor, activation energy, gas constant, and temperature, respectively.

S7
Supplementary Because of the negligible charge screening ability of COF-BD, we assume that the charge density of COF-BD is 0 C m −2 to facilitate the calculation. The charge density of COF-EBxBDy was calculated using the following equations: