Thermally driven refrigeration by methanol adsorption

ESI - Thermally driven refrigeration by methanol adsorption on coatings of MIL-101(Cr) and HKUST-1

Electronic supplementary information for journal article:

Thermally driven refrigeration by methanol adsorption on coatings of MIL-101(Cr) and HKUST-1 a,b

a

a

a

Harry Kummer , Max Baumgartner , Philipp Hügenell , Dominik Fröhlich , a b Stefan K. Henninger and Roger Gläser

This contribution presents new and versatile binder-based metal organic framework- (MOF-) coatings for the use in fast-cycle adsorption chillers for cooling and refrigeration applications. Two different adsorbents, HKUST-1 and Mil-101 (Cr) were used, showing promising methanol adsorption characteristics with loading capacities up to 1.22 gg-1. Polysiloxane-based coatings with adsorbent contents of 65 and 80 wt% were produced and the adsorption characteristics were tested before and after a cyclic thermal treatment over 1000 cycles between 20 °C and 130 °C under methanol atmosphere by thermogravimetric analysis and X-ray diffractometry. The adsorption properties were transformed according to the Dubinin-Astakhov approach to quantify the possible methanol loading lifts in a refrigeration process under different application conditions.

a. b.

Fraunhofer Institute for Solar Energy Systems, Heidenhofstr. 2, 79110 Freiburg. University of Leipzig, Linnéstr. 3-4, 04103 Leipzig.

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ESI01: Dubinin-Astakhov model and Calculation of the loading uptake under different boundary conditions Within the Dubinin approach, the adsorbed volume can be described by the Dubinin-Astakhov (DA) equation: 𝑨 𝒏 ]

𝑾 = 𝑾𝟎 𝒆−[(𝑬)

ESI01-(1)

𝑬 = 𝜷𝑬𝟎

ESI01-(2)

W0 is the total adsorbed volume, A the differential adsorption potential and E is the characteristic energy of the working pair. To separate the effects from adsorbent and adsorbed phase, E can also be described as

In this case, E0 is the characteristic adsorption enthalpy of the adsorbent. The affinity coefficient of the adsorptive β is referenced to benzene (β = 1) and can be found tabulated for various adsorptives[1]. The adsorbed volume W is temperature dependent due to the temperature dependency of the adsorptive density. The liquid density ρliq is taken as a good first approximation for the adsorbed phase. For methanol as the adsorptive, W is calculated as 𝑾=

𝒙

ESI01-(3)

𝝆𝒍𝒍𝒍,𝑴𝑴𝑴𝑴 (𝑻)

3

-1

with W given in cm g . The differential adsorption potential A may be defined as the difference between the chemical potential of the adsorbed phase and the liquid phase and can be calculated for methanol as the adsorptive 𝑨 = −∆𝑮𝒈 = (𝝁𝒂𝒂 − 𝝁𝜷 ) =

−𝑹𝑹 𝐥𝐥(𝒑𝒓𝒓𝒓 )

ESI01-(4)

𝑴(𝑴𝑴𝑴𝑴)

The representation of the adsorbed volume versus the adsorption potential generally gives a smooth curve, the so-called characteristic curve, which can be approximated by the exponential DA function. However, as shown previously, an arbitrary function may be used to minimize the deviation, but preserving the thermodynamic validity of the Dubinin [2] approach. In a first step, the measured adsorption equilibrium data (prel vs. loading x) of the volumetric and gravimetrically measurements were transformed in the specific adsorbed volume W and the adsorption potential A by the equations (3) and (4) of the main text. The transformed data can be fitted close to a DA approach with the following formula: 𝒏

𝑾 = 𝑾𝟎 𝒆−[(𝒃 𝑨) ] + 𝑪 [𝐜𝐜³𝐠 −𝟏 ]

(2)

Factor b is defined as b = (1/E0β) and C is an offset correction factor.

As reported before by Núñez et al[2] it is also possible to fit the DA-plot with user-defined equations and keep the thermodynamic validity. In case of HKUST-1 the DA equation fits the data quite well. For the MIL-101(Cr) a two stage isotherm exists, referring to two defined pore sizes in the crystalline structure.[3] For Methanol these two pore sizes seems -1 to adsorbed almost independently, forming a plateau with almost no uptake in the range of A ~ 250 J g or at a prel ~ 0.09. Therefore both pore sizes were fitted independently by a DA approach. The correction factor C for the large pores takes into account that a part of the total pore volume is already blocked and the DA fit doesn’t converge to 0. Therefore C is corresponding to the total accessible volume of the small pores. The data for both pore sizes were fitted independently for two valid ranges, taking a measurement point as cut. For the -1 larger pores the fit is valid from W smaller than and equal to 246.5628 J g and for the small pore size it is valid from bigger -1 than 246.5628 to 1300 J g . The whole fit equation has to be continuous but not differentiable in the whole range. The resulting fit parameters can be found in the main text in table 3. In a second step the boundary conditions for three different refrigerant cases demanding evaporating temperatures Tev of +8 °C, -5 °C and -10 °C was calculated. The condenser and the heat rejection temperature were set equal, holds true for common setups. The condenser and heat rejection temperature Tcond was varied from 10 °C to 60 °C in steps of 5 K and the heat source temperature Theat was varied from 60 °C to 150 °C in steps of 10 K. The adsorption potential boundaries were calculated from these temperatures for ad- and desorption as followed:

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𝑨𝑨𝑨𝑨 = 𝑨𝑫𝑫𝑫 =

−𝑹𝑹 𝐥𝐥( −𝑹𝑹

𝒑𝑺𝑺𝑺,𝑴𝑴𝑴𝑴 (𝑻𝒆𝒆) ) 𝒑𝑺𝑺𝑺,𝑴𝑴𝑴𝑴 (𝑻𝒄𝒄𝒄𝒄 )


𝒑𝑺𝑺𝑺,𝑴𝑴𝑴𝑴 (𝑻𝒄𝒄𝒄𝒄) 𝐥𝐥( ) 𝒑𝑺𝑺𝑺,𝑴𝑴𝑴𝑴 (𝑻𝒉𝒉𝒉𝒉 )


[𝐉 𝐠 −𝟏 ]

ESI01-(5)

[𝐉 𝐠 −𝟏 ]

ESI01-(6)

With these parameters the equilibrium loading point vcalc,Ads/Des for the adsorption and desorption case was calculated with fit equation (2) and the difference between the adsorption and desorption loading is the calculated uptake for the MOF powders vcalc,AdM at these boundary conditions. In a last step the calculated uptake as specific volume was transformed back to a calculated loading lift for the adsorption material with the following equation: 𝒙𝒄𝒄𝒄𝒄,𝑨𝑨𝑨 = 𝑾𝒄𝒄𝒄𝒄,𝑨𝑨𝑨 𝝆𝒍𝒍𝒍,𝑴𝑴𝑴𝑴 (𝑻𝒄𝒄𝒄𝒄 ) − 𝑾 𝒄𝒄𝒄𝒄,𝑫𝑫𝑫 𝝆𝒍𝒍𝒍,𝑴𝑴𝑴𝑴 (𝑻𝒉𝒉𝒉𝒉 )

ESI01-(7)

𝒙𝒄𝒄𝒄𝒄,𝒄𝒄𝒄𝒄 = 𝒙𝒄𝒄𝒄𝒄,𝑨𝑨𝑨 𝒘𝑨𝑨𝑨

ESI01-(8)

The equilibrium loading points for the coatings were also calculated according to equation ESI01-(7) but have to be corrected by the adsorbent content wAdM of the coating.

ESI02:

ESI02: Methanol adsorption of HKUST-1. Volumetric isotherms measured at 25°C (olive squares) and at 40°C (blue triangles); gravimetrical isobar measured at 7.3 kPa (brown spheres). Adsorption is depicted by full symbols, desorption by empty symbols. Calculated isotherms by fit equation (2), calculated for temperatures from -5 °C to 150°C.

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ESI03:

ESI03: Methanol adsorption of MIL-101(Cr). Volumetric isotherms measured at 25°C (olive squares) and at 40°C (blue triangles); gravimetrical isobar measured at 7.3 kPa (brown spheres). Adsorption is depicted by full symbols, desorption by empty symbols. Calculated isotherms by fit equation (5), calculated for temperatures from -5 °C to 150°C.

ESI04:

ESI04: XRD pattern of HKUST-1: powder (black), simulated diffractogram by CIF-File CCDC 112954 [4] (grey), coating fresh (blue) and coating after solvothermal cycling (red).

ESI05:

ESI05: XRD pattern of MIL-101(Cr): powder (black), simulated diffractogram by CIF-file COD 4000663 [3] (grey), coating fresh (blue) and coating after solvothermal cycling (red).

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ESI06:

ESI06: Calculated uptake capacities xcalc,AdM of HKUST-1_powder at Tev=+8 °C. The loading performance is shown in blue, big bars with grey contour. The colour also indicates the loading value: brighter values means higher loading capacities.

ESI07:

ESI07: Calculated uptake capacities xcalc,AdM of HKUST-1_powder at Tev=-5 °C. The loading performance is shown in blue, big bars with grey contour. The colour also indicates the loading value: brighter values means higher loading capacities.

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ESI08:

ESI08: Calculated uptake capacities xcalc,AdM of HKUST-1_powder at Tev=-10 °C. The loading performance is shown in blue, big bars with grey contour. The colour also indicates the loading value: brighter values means higher loading capacities.

ESI09:

ESI09: Calculated uptake capacities xcalc,AdM of MIL-101(Cr)_powder at Tev=+8 °C. The loading performance is shown in green, small bars with black contour. The colour also indicates the loading value: brighter values means higher loading capacities.

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ESI10:

ESI10: Calculated uptake capacities xcalc,AdM of MIL-101(Cr)_powder at Tev=-5 °C. The loading performance is shown in green, small bars with black contour. The colour also indicates the loading value: brighter values means higher loading capacities.

ESI11:

ESI11: Calculated uptake capacities xcalc,AdM of MIL-101(Cr)_powder at Tev=-10 °C. The loading performance is shown in green, small bars with black contour. The colour also indicates the loading value: brighter values means higher loading capacities.

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ESI12: Table - comparison between different known ACs, HKUST-1 and MIL-101(Cr) for two working points: 95°C_29°C_7°C and 120°C_35°C_-5°C

Working point 95°C_29°C_7°C

Working point 120°C_35°C_-5°C

Source:

HKUST-1

0.188

0.175

*

HKUST-1_coat

0.148

0.138

*

MIL-101(Cr)

0.508

0.045

*

MIL-101(Cr)_coat

0.328

0.029

*

G32-H

0.164

0.249

[5]

RÜTGERS CG1-3

0.169

0.183

[5]

Norit R 1 Extra

0.181

0.238

[5]

Norit RX 3 Extra

0.183

0.233

[5]

CarboTech C40/1

0.201

0.185

[5]

CarboTech A35/1

0.234

0.206

[5]

* own work

ESI13:

ESI13: N2 Isotherms of of MIL-101(Cr)_powd (blue squares) and MIL-101(Cr)_coat (red circles). Full symbols indicate adsorption, empty symbols desorption points. The maximum accessible pore volume by nitrogen is reduced by 61%.

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ESI14:

ESI14: Calculated cumulative pore volume by DFT (bla---) of MIL-101(Cr)_powd (blue squares) and MIL-101(Cr)_coat (red circles). DFT reveals micro pores between 9 to 20 Å and the larger pores between 29 and 34 Å. The coating lost about 60 vol-% of the micro pore volume and about 65 vol-% of the meso pore volume.

References [1] [2]

[3] [4] [5]

G.O. Wood, Affinity coefficients of the Polanyi/Dubinin adsorption isotherm equations. A review with compilations and correlations, Carbon 39 (2001) 343–356. T. Núñez, H.M. Henning, W. Mittelbach, Adsorption cycle modeling: Characterization and comparison of materials, in: C. Schweigler (Ed.), Proceedings of the International Sorption Heat Pump Conference: March 24-26, 1999, Munich, Germany, ZAE Bayern, Munich, Germany, 1999, pp. 209–217. G. Ferey, A Chromium Terephthalate-Based Solid with Unusually Large Pore Volumes and Surface Area, Science 309 (2005) 2040–2042. S.S. Chui, A Chemically Functionalizable Nanoporous Material [Cu3(TMA)2(H2O)3]n, Science 283 (1999) 1148–1150. S. Henninger, M. Schicktanz, P. Hügenell, H. Sievers, H.-M. Henning, Evaluation of methanol adsorption on activated carbons for thermally driven chillers part I: Thermophysical characterisation, Int. J. Refrig. 35 (2012) 543–553.

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