Tunable Low‐Pressure Water Adsorption in Stable Multivariate Metal‐Organic Frameworks for Boosting Water‐Based Ultralow‐Temperature‐Driven Refrigeration

Abstract The green water‐based adsorption refrigeration is considered as a promising strategy to realize near‐zero‐carbon cooling applications. Although many metal‐organic frameworks (MOFs) have been developed as water adsorbents, their cooling performance are commonly limited by the insufficient water uptakes below P/P 0 = 0.2. Herein, the development of multivariate MOFs (MTV‐MOFs) is reported to highly modulate and boost the low‐pressure water uptake for improving coefficient of performance (COP) for refrigeration. Through ligand exchange in the pristine MIL‐125‐NH2, a series of MTV‐MOFs with bare nitrogen sites are designed and synthesized. The resulting MIL‐125‐NH2/MD‐5% exhibits the significantly improved water uptake of 0.39 g g−1 at 298 K and P/P 0 = 0.2, which is three times higher than MIL‐125‐NH2 (0.12 g g−1) and comparable to some benchmark materials including KMF‐1 (0.4 g g−1) and MIP‐200 (0.36 g g−1). Combined with its low‐temperature regeneration, fast sorption kinetics and high stability, MIL‐125‐NH2/MD‐5% achieves one of the highest COP values (0.8) and working capacities (0.24 g g−1) for refrig‐2 under an ultralow‐driven temperature of 65 °C, which are higher than some best‐performing MOFs such as MIP‐200 (0.74 and 0.11 g g−1) and KMF‐2 (0.62 and 0.16 g g−1), making it among the best adsorbents for efficient ultralow‐temperature‐driven refrigeration.


Kinetic measurement and cycle test of water adsorption/desorption
The samples used to develop the kinetic measurements and cyclability tests also need to be solvent-exchanged and activated.And this two kinds of tests were developed on TA SDT 650 thermal analyzer with a humidity generator and nitrogen stream.Different humidity atmospheres are produced by adjusting the flux of dry nitrogen and moisture, and the specific humidity values are measured by a sensitive humidity sensor.Adsorption measurements were taken up in 20% RH atmosphere at 25 °C, and desorption processes were developed at 65 °C.
And the water adsorption cycle tests were proceeded in 20% RH atmosphere at 25 °C in adsorption stages, and carried out at 65 °C in desorption stages.

Water adsorption enthalpy measurement
Netzsch STA 449F3 simultaneous thermal analyzer was used to measure the heat of water adsorption.First, the sample was heated to 423 K and purged with nitrogen to activate it.Then, when the temperature was maintained at 298 K, moisture was added to purge the sample and the change of heat flux during the adsorption process was recorded.

Chemical and thermal stability tests
Four parallel samples were placed in different environments, in pure water for five days and in solutions at pH = 1 and pH = 9 for three days, respectively.After that, all the samples were filtered or picked out, and washed with dry MeOH.The integrity of crystallinity and the stability of pore structure were confirmed by PXRD and nitrogen adsorption.The thermal stability was tested by thermogravimetric analysis and various temperature PXRD patterns.Before developing the thermogravimetric analysis, samples were heated to 423 K for activation.

Working principle of adsorption refrigeration system
In general, an adsorption refrigeration cycle consists of two segments, adsorption and desorption.And each segment consists of two steps.These are briefly depicted and explained from a thermodynamic point of view by means of the cycle diagram (Figure S13). [2,10] first, the system is at a low temperature and pressure and the adsorbent is fully saturated.
The first step is isosteric heating (Ⅰ-Ⅱ).Before desorption, the adsorbent chamber is isolated from the condenser and evaporator, and the pressure needs to be raised from Pev to Pcon, achieving by heating the adsorbent from T1 to T2.Ideally, no adsorbate is removed in this stage.
Then the second step: isobaric desorption (Ⅱ-III).In this stage, the adsorbent chamber is connected to the condenser and continuously heated.After the input of higher energy (Qdes), the water is desorbed.This process is stopped when reaching the desorption temperature (Tdes) and holding the minimal adsorbent loading (Wmin).And the adsorbent completes the regeneration process.All of the desorbed water (ΔW = Wmax−Wmin) is condensed, releasing heat at the same time (Qcon).In general, in order to save energy and protect the environment, industrial waste heat or solar energy is used as a source of thermal energy to complete the desorption process.
The third step: isosteric cooling (III-IV).Contrary to the first step, the pressure needs to be lowered to Pev by cooling the system temperature from Tdes to T3, and the adsorbent chamber is again isolated from the condenser and the evaporator.
The forth step: isobaric adsorption (IV-I).In this stage, the adsorbent chamber is connected to the evaporator, allowing water to be adsorbed.Partial water adsorbs heat from the low temperature environment through evaporation (Qev), producing useful cooling effect.The process stopped when the temperature drops to T1, the adsorbent is saturated again (Wmax), and the heat is released to the surrounding environment (Qads) during the adsorption process.

Calculation of the characteristic curves
At equilibrium, water adsorption capacity of porous materials such as MOF is a function of pressure and temperature.The water adsorption curves are tested at one or several fixed temperatures to evaluate and compare the water adsorption properties of materials.In order to character and describe conveniently, Polanyi adsorption potential is introduced to reduce the number of variables, which is the inverse of the molar Gibbs free energy of adsorption, defined as: P0 is the temperature-dependent vapor pressure of water.R is the universal gas constant.
At the same time, the adsorption amount should be expressed in terms of the volume of adsorbed water molecules, defined as: ( , ) () Here, q is the mass of the adsorbate.
In general, the adsorption data measured at different temperatures can be reduced to a characteristic curve.This means that each combination of pressure and temprature (P, T) can be converted to a single adsorption potential A, and the adsorption volume W can be easily determined by interpolating the characteristic curve.The adsorption curves of MIL-125-NH2/MD-5% were tested at 293 K, 298 K and 303 K respectively, and they were converted into characteristic curve by simple calculation, and all the characteristic curves were almost exactly coincident (Figure S14).The same is true for MIL-125-NH2 (Figure S15).

Calculation the isosteric enthalpy of adsorption
Water adsorption is an exothermic process, and the isosteric enthalpy of adsorption can be calculated using a form of the Clausius-Clapeyron equation given by [11,12] ads ln (1/ ) Here, ∆adsHW represents the isosteric enthalpy of adsorption (kJ mol -1 ), P represents pressure (bar), T represents temperature (K).
And also given by: T1 and T2 are two temperatures in isotherm, and P1 and P2 are pressures at T1 and T2 , respectively, for a given uptake.

Calculation of the coefficient of performance
The coefficient of performance for cooling (COPC), which is the commonly adopted parameter to evaluate the cooling effect, defined as the useful energy output divided by the energy required for input.It is writen as: Here, Qev is the energy taken up in the evaporator, and Qregen is the energy of adsorbents regeneration.
According to working principle, the energy required in stage I-II and stage II-III is the desorption energy (Qdes), that is, the energy required for the regeneration of the adsorbent, while the energy released in stage III-IV and satge IV-I is the adsorption energy (Qads).
The energy required for each stage is expressed in the following equations: Isosteric heating (I-II): The energy required for water evaporation in the evaporator (Qev) is calculated by: The energy released by the condenser (Qcon) is calculated by: The energy released during adsorption of the working fluid (Qsorption) can be written as:

Figure S1 .
Figure S1.Schematic diagram of working cycle (left) and regeneration cycle (right) in a waterbased adsorption refrigeration.Reproduced with permission.[2] Copyright 2013, Royal Society

Figure S2 .
Figure S2.The PXRD patterns of as-synthesized MIL-125-NH2, compared with the simulated XRD pattern from the structure of MIL-125-NH2.

Figure S13 .
Figure S13.Schematic diagram of the thermodynamic cycle of an adsorption chiller.

Figure S14 .
Figure S14.Characteristic curves of MIL-125-NH2/MD-5% at different temperatures determined using eq 1 and 2. The orange dotted line represents the optimal adsorption potential for refrig-1 cooling, the green dotted line for refrig-2 cooling, and the red dotted line for heat pump heating.

Figure S15 .
Figure S15.Characteristic curves of MIL-125-NH2 at different temperatures determined using eq 1 and 2 The orange dotted line represents the optimal adsorption potential for refrig-1 cooling, the green dotted line for refrig-2 cooling, and the red dotted line for heat pump heating.

Figure S21 .
Figure S21.The PXRD patterns of MIL-125-NH2/MD-5% before and after the water adsorption/desorption cycles compared with the simulated XRD pattern from the structure of MIL-125-NH2.

1 A 1 G 1 R
Abbreviation refrig refrigeration