Adsorption chillers are an environmentally friendly solution for the valorisation of waste 12 or solar heat for cooling demands. A recent application is high efficiency data centre cooling where 13 heat from CPUs is used to drive the process providing cold for auxiliary loads. The metal organic 14 framework aluminium fumarate with water is potenti ally a suitable material pair for this low 15 temperature driven application. A targeted heat exchanger design is a prerequisite for 16 competitiveness requiring , amongst others, a sound understanding of adsorption equilibria and 17 adsorption enthalpy. A novel met hod is used for their determination based on small isothermal 18 and isochoric state changes applied with an apparatus developed initially for volume swing 19 frequency response measurement to samples with a binder based adsorbent coating. The 20 adsorption enthalp y is calculated through the Clausius -Clapeyron equation from the obtained 21 slopes of the isotherm and isobar, while the absolute uptake is determined volumetrically. The 22 isotherm confirms the step -like form know n for aluminium fumarate with a temperature 23 dependent inflection point at 𝑝𝑝rel≈ 0.25, 0.28 and 0.33 for 30, 40 and 60 °C. The calculated 24 differential enthalpy of adsorption is 2.90 ±0.05 MJ/kg (52.2 ±1.0 kJ/mol) on average which is about 25 10–15% higher than expected by a simple Dubinin approximation. 26 Keywords: adsorption equilibrium; adsorption enthalpy; heat of adsorption; metal organic 27 framework; aluminum fumarate; coating; adsorption ; cooling ; heat pump; heat transformation 28 29 1. Introduction 30 Adsorption chillers are an environmentally friendly solution for the valorisation of waste or 31 solar heat for cooling demands. The working principle allows a simple, robust and scalable design. 32 Adsorption chillers and heat pumps have been applied successful ly for different applications like 33 solar thermal cooling of buildings [1], gas adsorption heat pumps [2,3] and more [4,5]. A possible 34 application that has attracted rising interest in recent years is the provision of data centre coo ling 35 driven by heat yielded from water cooled CPUs. Current high performance CPUs allow cooling 36 water temperatures of up to 60 °C or more [6,7] that can be used to drive adsorption chillers. 37 An adsorption chiller ( Figure 1) consist s of two adsorption heat exchangers, a condenser and an 38 evaporator in a pure working fluid atmosphere. If temperatures below 0 °C can be excluded, usually 39 water is used as working fluid due to its high evaporation enthalpy. The adsorption heat exchangers 40 (Ad-HX) have a heat transfer fluid on the primary and a stationary adsorbent material or composite 41 on the secondary side. The process is cyclic: In the first half -cycle the CPU’s waste heat is used to 42 regenerate the first Ad -HX. The desorbed working fluid i s condensed in the condenser which is 43 Energies 2020, 13, x FOR PEER REVIEW 2 of 11 cooled to the ambient at e.g. 30 °C. In the second half -cycle working fluid is adsorbed on the Ad- HX 44 which is again cooled to the ambient. The resulting pressure drop induces the evaporation in the 45 evaporator at about 20 °C. For continuous provision of cold, two Ad -HXs are operated alternately. 46 Figure 1: Working principle of an adsorption chiller for data centre cooling Development of new a dsorbent materials has been a research interest for m any years [8]. 47 Aluminium fumarate, a metal -organic framework (MOF) that attracted increasing interest for 48 thermal applications in recent years, exhibits adsorption equilibrium properties that fit well to the 49 boundary conditions of this cycle [9]. Due to its beneficial stepwise isotherm [8] it can allow 50 considerably more efficient cycles compared to the state of the art material silica gel with a good 51 hydrothermal cycle stability [10,11] . The material is potentially a low cost material due to widely 52 available educts (Al- salts and fumaric acid) and water based synthesis route [12]. 53 The increase of volume specific cooling power (VSCP) – thus reduction of specific costs – while 54 keeping a reasonably high COP is one of the major development challenges for adsorption chillers 55 [13]. Typical values for COPs of market available adsorption chillers are in the order of 0.5 to 0.65 56 [14]. In the case of data centre cooling the target COP is determined by the ratio of low temperature 57 cooling demand and available waste heat from CPUs which typically is in the same range [6] . A 58 promising approach to increase VSCP is to use binder based adsorbent coatings to a llow for a 59 substantially better heat transfer to the heat exchanger structure in comparison to loose grain bed, 60 the state of the art solution [15] . Further performance increase can be reached through model based 61 design and optimization which is more cost -effective than empiric trial -and-error prototyping as 62 shown recently in a comprehensive overview on designing strategies for Ad -HX by Graf et al. [16]. 63 However, model based design requires detailed knowledge of a) the adsorption equilibria, b ) the 64 adsor ption enthalpy , c) relevant physical heat and mass mechanisms and the corresponding transfer 65 coefficients, and d) the specific heat capacities, allowing for models with explicit dependency on 66 design parameters like heat exchanger geometry, layer thicknesses and particle sizes. We developed 67 a comprehensive approach to gain most of this data , i.e. a) –c), from small representative Ad -HX 68 cutouts in a single measurement procedure based on 69 1. volumetric uptake measurement, 70 2. stepwise volume & temperature perturbation and 71 3. frequency response analysis . 72 Energies 2020, 13, x FOR PEER REVIEW 3 of 11 In this paper we will focus on the first two steps for evaluating adsorption equilibrium and 73 adsorption enthalpy . The frequency response analysis (FRA) for the investigation of heat and mass 74 transfer processes builds upon this and will be dealt with in a following publication. 75 An apparatus developed initially for volume swing frequency response measurement also 76 allows for measurements of the differential adsorption equilibrium, i.e. the slopes of the isotherm 77 and the isoba r, through the equilibrium response for small step experiments. Earlier the FR A setups 78 were used for volume step experiments to evaluate sorption dynamics using a numerical non -linear 79 transport model in the time domain [17] comparable to pressure jump [18,19] or temperature jump 80 [20–22] experiments. We extend this approach to measuring the isobar slope with small temperature 81 steps. Both slopes can be directly combined to determine the differential adsorption enthalpy at a 82 specific thermodynamic state, i.e. adsorbent loading, temperature and pressure. Together with a 83 calibrated dosing volume for the volumetric uptake measurement this allows for a comprehens ive 84 determination of sorption equilibrium, enthalpy and dynamics in a single automated measurement 85 procedure. 86 87 2. Materials and Methods 88 2.1. Material 89 An aqueous dispersion (26.8 wt% aluminium fumarate (a.k.a. MIL -53(Al) -FA) Basolite® A520, 90 BASF; 17.9 wt% SilRes® MP50E, Wacker Silicones) was processed by a knife coating applicator on 91 50x50x2 mm AlMg3 sample plates ( Table 1). The wet film thickness was varied by an octagonal 92 stainless steel mask with a defined thickness (200, 350, 600 µm) and constant coating surface 𝐴𝐴ct 93 (18.7 cm2). Samples were oven dried at 200 °C for 3 h before measuring coating thicknesses 𝑑𝑑ct of 94 final samples (Table 1, Figure 2) at five points with a probe indicator. The sample dry mass was 95 determined by quickly ( 𝑇𝑇≥160 °C) weighing the hot samples under lab atmosphere after oven 96 drying. Total dry adsorbent content 𝑤𝑤s,dry were first calculated from the suspension composition 97 based on experimentally determined dry masses of different components as shown by Kummer et 98 al. [23], and later cross checked by comparing the samples’ upt ake to the uptake of pure adsorbent 99 powder measured volumetrically (AUTOSORB®, Quantachrome). 100 Figure 2: Sample Ct_610 with 0.61 mm coating thickness 101 Energies 2020, 13, x FOR PEER REVIEW 4 of 11 Table 1: Sample mass and geometry, the adsorbent content was estimated when mixing the coating suspension and confirmed later by comparing the sample’s uptake with the pure adsorbent powder isotherm (c.f. 3.1 ) By suspension composition By comparison to pure adsorbent uptake Sample 𝑚𝑚cmp (mg) 𝑑𝑑ct (mm) 𝜌𝜌cmp (g/cm3) 𝑤𝑤s,dry (-) 𝑤𝑤bnd (-) 𝑤𝑤s,dry (-) 𝑤𝑤bnd (-) Ct_140 134±3 0.14±0.04 0.51±0.15 0.75 0.25 0.72 0.28 Ct_240 217±4 0.24±0.05 0.48±0.10 0.75 0.25 0.79 0.21 Ct_610 563±11 0.61±0.07 0.49±0.06 0.75 0.25 0.80 0.20 2.2. Apparatus 102 Measurements are done with a custom setup ( Figure 3) under pure water vapour atmosphere 103 allowing vapour dosing as well as small volume and temperature steps . Moreover, the setup allows 104 frequency response (FR), large temperature jump (LTJ), larg e pressure jump (LPJ) and small 105 pressure jump (SPJ) experiments with water. Details on jump experiments with the setup have been 106 reported extensively before [20,24,25] , FR experiments will be published elsewhere. 107 The volume of the dosing chamber is constant ( 𝑉𝑉D=41.815 ±0.021 l) while the measurement 108 chamber volume ( 𝑉𝑉�M=885 .4±1.3 ml) can be varied by 4.12% through a mechanically driven 109 vacuum bel low, while the bellow position is recorded with a vacuum stable linear variable 110 differential tran sformer (Schreiber Messtechnik ). The bellow position has been calibrated with a 111 second order polynomial to the chamber volume by filling the evacuated and thermosta ted chamber 112 with water of known mass. The sample is thermally well connected (thermal grease TG20032) to the 113 cold plate kept isothermal ( ± 0.01 K) by two switchable external circuit s. The cold plate temperature 114 is precisely measured with a 4 -wired Pt100 sensor embedded in a bore. The chamber pressure is 115 measured with a capacitive pressure transducer (MKS Baratron 627B , 0–100 mbar) . Additionally, the 116 sample’s surface temperature is recorded using an IR temperature sensor (Heitronics KT15) through 117 a ZnSe vacu um viewport with a noise equivalent temperature difference of 25 mK at 1 s response 118 time . The measurement spot has a diameter of 6 mm (95%) and the detector’s spectral response 119 maximum is between 8 and 14 µm fitting to the transmissivity of the ZnSe viewpo rt and the aimed 120 sample temperature (20–80 °C). To minimise temperature gradients the whole vacuum setup is 121 encapsulated in a temperature controlled cabinet ( ±0.1 K) set to the mean cold plate temperature. 122 Data acquisition is done with a high precision dig ital multi meter (Agilent 34970A). 123 Energies 2020, 13, x FOR PEER REVIEW 5 of 11 Figure 3: Sorption kinetic setup for frequency response, large temperature jump and large pressure jump experiments with absolute and differential equilibrium measurement. Absolute sorption equilibria are measured volumetrically by dosing in from the dosing chamber, differential equilibria by small temperature and pressure steps around equilibrium. 2.3. Procedure 124 The measurement procedure consists of two steps: pre -conditioning to the desired state and 125 determination of equilibrium slopes. Throughout the measurement the temperature controlled 126 cabinet is kept at the measurement mean temperature 𝑇𝑇0. 127 Initially, samples w ere desorbed against a rotary vane pump ( 𝑝𝑝<0.01 mbar) at 95 °C over night 128 to remove any co- adsorbed impurities. For aluminium fumarate this ensures an initial loading 𝑋𝑋init 129 of 0 kg/kg. After cooling down the closed chamber to 𝑇𝑇0 the sample is pre- conditioned to a desired 130 loading 𝑋𝑋0 by dosing in vapour from the dos ing chamber. 𝑋𝑋0 is calculated volumetrically from the 131 mass balance of both chambers and the adsorbent dry mass 𝑚𝑚𝑠𝑠 following the ideal gas law which is 132 a very good approximation for water in the pressure and temperature region of the measurements: 133 𝑋𝑋0=𝑋𝑋init+1 𝑇𝑇0𝑅𝑅w𝑚𝑚s[𝑉𝑉D𝑝𝑝D1 +𝑉𝑉M1𝑝𝑝M1−(𝑉𝑉M2𝑝𝑝M2+𝑉𝑉D𝑝𝑝D2)]. (1) Here the indexes D and M denote the dosing and the measurement chamber where the volume 134 depends on the bellow position. The pressures 𝑝𝑝D,1 and 𝑝𝑝D,2 are calculated beforehand based on 135 the isotherm of the pure adsorbent powder to approximately reach the set point for 𝑋𝑋0. The 136 equilibrium pressure of the sample 𝑝𝑝0=𝑝𝑝M,2 will follow the equilibrium of the sorbent at 𝑇𝑇0 and 137 𝑋𝑋0 yielding a point on the 𝑇𝑇0-isotherm. 138 To determine the equilibrium slopes at the pre- conditioned sample state, the sample is exposed 139 to small volume and temperature jumps symmetrically around 𝑉𝑉0 and 𝑇𝑇0 first by Δ𝑉𝑉=2𝑉𝑉� with 140 constant temperature and then by Δ𝑇𝑇=4 K with constant volume. This allows determining the 141 differential equilibrium, i.e. the slopes of the isotherm d𝑋𝑋/d𝑝𝑝≈(Δ𝑋𝑋/Δ𝑝𝑝)𝑇𝑇 and the isobar d𝑋𝑋/d𝑇𝑇≈ 142 �(Δ𝑋𝑋−d𝑋𝑋/d𝑝𝑝Δ𝑝𝑝)/Δ𝑇𝑇�𝑉𝑉 from the equilibrium pressure difference Δ𝑝𝑝 and loading change Δ 𝑋𝑋 143 measured for the isothermal and the isochoric jump, respectively. A very slow drift in the pressure 144 which is due to parasitic effects of the setup already reported before [24,25] is corrected by fitting 145 linear models to equilibrium sections before and after the jum p and using the extrapolated values at 146 V2V3 V4Vacuum pump Dosing chamberMeasuring chamber Thermostated cabinetVapor generatorMExcenterMotorBellow T3PT L V1SampleT2 T1HV2HV1 Energies 2020, 13, x FOR PEER REVIEW 6 of 11 the centre. Finally, w ith both slopes the differential enthalpy of adsorption at 𝑋𝑋0 and 𝑇𝑇0 can be 147 calculated based on Clausius Clapeyron’s equation assuming ideal gas behaviour: 148 Δℎ𝑠𝑠≈𝑅𝑅𝑇𝑇2 𝑝𝑝d𝑝𝑝 d𝑇𝑇=−𝑅𝑅𝑇𝑇2 𝑝𝑝d𝑋𝑋 d𝑇𝑇�d𝑋𝑋 d𝑝𝑝�−1 (2) Loading, differential equilibrium and adsorption enthalpy are important input parameters for a 149 subsequent FR A reported elsewhere. Integration in a single measurement routine allows for 150 measurement under exactly the sam e conditions (in -situ). As the sample is pre -conditioned only 151 once this eliminates the need for time consuming external measurements and possibly error prone 152 transfer to the measurement conditions. 153 To exclude a local hysteresis of the adsorption equilibrium , an important pre-requisite for FRA, 154 a further test is included in the routine: The same equilibrium state 𝑋𝑋0,𝑇𝑇0 is reached coming from a 155 small and from a larger volume at constant temperature and vice versa. The equilibrium loading is 156 then compared and a “hysteresis -free” behaviour assumed if the loading difference between the two 157 directions is below th e measurement uncertainty. 158 2.4. Uncertainty evaluation 159 Uncertainty analysis has been carried out based on [26] including uncertainty from sample 160 variance (type A) and uncertainties from imperfect calibration and correction (type B). 161 The uncertainty of the mean values are between 0.4 ml (20 °C) and 1.3 ml (80 °C) for 𝑉𝑉0, 162 between 0.05 mbar (𝑝𝑝0=5 mbar) and 0.15 mbar (𝑝𝑝0=100 mbar) for the chamber pressure and 163 about 0.1 K for the mean sample temperature 𝑇𝑇0. Typical uncertainties for vapou r dosing are in the 164 order of 1 to 4 mg influenced mainly by 𝑝𝑝0 for 10 to 60 mbar. Thus, uncertainties for the loading are 165 smaller for higher sample dry mass given constant dry mass uncertainty . 166 167 3. Results and Discussion 168 Results are reported for five different loadings at 40 °C and one loading at 30 and 60 °C, 169 respectively. 170 Energies 2020, 13, x FOR PEER REVIEW 7 of 11 3.1. Adsorption equilibrium 171 Figure 4: Equilibrium points measured for Ct_140 (▲ ), Ct_240 (■ ) and Ct_610 (●) at 30, 40 and 60 °C in comparison with the 40 °C isotherm of the initial pure adsorbent powder ( +), based on total sample dry mass (left) and adsorbent mass determined by uptake correction (right); the grey lines indicate the local equilibrium slope measured by small volume jumps The water isotherm of the adsorbent powder at 40 °C ( Figure 4) show s the characteristic 172 step-like uptake to a plateau at 0.32 kg/kg and is in line with [11] or slightly lower than [10,27] 173 previous results. The position of the step is temperature dependent with an inflection point at 𝑝𝑝rel≈ 174 0.25, 0.28 and 0.33 for 30, 40 and 60 °C. Measured local isotherm slopes are in agreement with the 175 tangent for 40 °C. The position of the uptake step is reproducibl e within the samples and shows a 176 strong temperature dependency that persists when applying a Dubinin transformation [28] . Hence, 177 the assumption of a temperature invariant characteristic curve is a strong simplification for 178 aluminium fumarate and should be applied with care. The exact position of the uptake step is an 179 important information for application as it determines th e available driving forces and finally the 180 resulting equipment power [3]. 181 No significant hysteresis was observed, neither locally by the procedure explained b efore ( 2.3) 182 nor globally. For the later the vapour dosing procedure was modified starting with saturated sample 183 (𝑝𝑝rel=0.5, 𝑇𝑇=40 °C, 𝑋𝑋=0.33 kg/kg s) and desorbing i nto the dosing chamber. Probably, the 184 hysteresis found in previous results was due to incomplete equilibrium and/or pore condensation 185 occurring at 𝑝𝑝rel≫0.5 which was disregarded here due to the limited relevance for heat 186 transformation applications. 187 The a dsorbent content calculated by comparing the uptake of sample to the powder ( Figure 4, 188 right) fits on average the values calculated at sample preparatio n (Table 1) showing that the binder 189 has no significant influence on adsorption equilibrium. The results show good agreement between 190 the two thicker sampl es and a slight deviation of the thinnest sample Ct_140, which could be 191 explained by a slightly lower adsorbent content of the coating. The difference to the uptake of the 192 pure adsorbent can be explained by the inert binder/loss due to the coating process, differences in 193 the production process and measurement uncertainty of the volumetric adsorption measurement. 194 A general description of the measured sorption equilibrium for modelling purposes is given in 195 the supplement (S1) . 196 Energies 2020, 13, x FOR PEER REVIEW 8 of 11 3.2. Adsorption enthalpy 197 Figure 5: Left: Clausius -Clapeyron plot ( 𝑝𝑝0=1 bar) with measured equilibrium points for different samples ( ▲ Ct_140, ■ Ct_240, ● Ct_610) and isostere slope calculated from measured local deviations (short grey lines) and linear fit of po ints with 𝑋𝑋 eff≈ 0.16 kg/kg (- - -), uncertainties of 𝑇𝑇 and 𝑝𝑝 are bellow point size; Right: d ifferential adsorption enthalpy calculated from isostere slopes of local equilibria and 0.2-k g/kg-fit over corrected loading with the evaporation enthalpy of water ( - - -) The calculated differential enthalpy of adsorption is 2.90 ±0.05 MJ/kg (52.2 ±1.0 kJ/mol) on 198 average. The calculation with Eq. ( 2) is based on either the local equilibrium slope indicated in 199 Figure 5 or on a linear fit of the quasi -isosteric points ( 𝑋𝑋eff≈ 0.16 kg/kg) measured at 30, 40 and 200 60 °C. The Clausius -Clapeyron plot show s that local slopes coincide well with the multi -temperature 201 fit, and so do the calculated enthalpies. Temperature and loading dependencies are negligible in the 202 parameter range evaluated. The adsorption enthalpy is about 10 –15% higher than expected by a 203 simple Dubinin approximation (sum of evaporation enthalpy at t he same temperature and the 204 adsorption potential 𝐴𝐴=−𝑅𝑅𝑇𝑇ln(𝑝𝑝rel), [28]) which is in qualitative accordance to the observed 205 temperature variance of the isotherm. Thus, the application of the concepts of a characteristic curve 206 for the description of the sorption equilibrium and of the adsorption potential for the sorption 207 enthalpy result in a crude approximation for the case of aluminium fumarate. 208 4. Conclusions 209 In this work we developed a novel m ethod for in -situ measurements of sorption equilibria and 210 enthalpy in an apparatus dedicated to the sorption dynamic measurement. The method, based on 211 dosing vapour from calibrated volumes and small temperature and volume steps around an 212 equilibrium point, allows for direct measurements of the isobar’s and isotherm’s slope tightly 213 around a specific thermodynamic state. This allows extracting the loading and temperature 214 dependency of the isostere’s slope and thus the sorption enthalpy. 215 The method was tested on samples coated with a composite of aluminium fumarate particles 216 with Silres® as a binder in different thicknesses (140 –610 µm) at 30 –60 °C and the entire loading 217 range . The measured sorption equilibrium fits expectations from the pure adsorbent powder’s 218 isotherm and the coating composition. The coating procedure did not alter the adsorption 219 properties. 220 The measurement of the differential adsorption enthalpy was successfully verified by 221 comparing the local slope of the isostere to the linear regression ov er the whole temperature range. 222 The sorption enthalpy is 2.90 ±0.05 MJ/kg (52.2 ±1.0 kJ/mol) on average with no significant 223 dependency with either loading or temperature. 224 Energies 2020, 13, x FOR PEER REVIEW 9 of 11 Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1 , Section S1: 225 General description of the sorption equilibrium of aluminium fumarate. 226 Author Contributions: Conceptualization , E.L. and G.F.; methodology, E.L.; software, E.L .; validation, G.F. and 227 L.S.; formal analysis, E .L.; investigation, E.L.; resources , E.L.; data curation, E.L.; writing —original draft 228 preparation , E.L.; writing —review and editing, G.F., L.S. and G.S.; visualization, E .L.; supervision, G.F., L.S. 229 and G.S.; project administration, G.F.; funding acquisition, E.L., G.F ., L.S. and G.S. All authors have read and 230 agreed to the published version of the manuscript. 231 Funding: This work result s widely from the PhD project of Eric Laurenz for which funding by Heinrich Böll 232 Stiftung is gratefully acknowledged. In addition, funding by BMBF for projec t WasserMod2 (FKZ 03ET1554A) 233 is gratefully acknowledged. 234 Acknowledgments: The authors would like to thank Harry Kummer for supervising and Raffael Wolf for 235 carrying out the sample preparation, Phillip Hügenell for performing the AUTOSORB® measurement, and 236 Florian Tönnies for implementing parts of the data processing program. 237 Conflicts of Interest: The authors declare no conflict of interest. 238 5. Nomenclature 239 5.1. Abbreviations 240 Ad-HX Adsorber heat exchanger 5.2. Variables 241 𝑇𝑇 Temperature (K) 𝑝𝑝 Pressure (Pa) 𝑋𝑋 Loading (kg adsorbed /kg sorbent,dry ) 𝑋𝑋eff Effective loading (kg adsorbed /kg composite,dry ) 𝑉𝑉 Volume (m3) 𝐴𝐴 Surface area (m2), adsorption potential (J/kg), Amplitude (any unit) 𝑅𝑅 Universal gas constant (J/(mol K)) 𝑅𝑅w Specific gas constant of water (J/(kg K)) 𝑚𝑚 Mass (kg) 𝑡𝑡 Time (s) 𝑀𝑀 Molar mass (kg/mol) Δℎs Differential adsorption enthalpy (J/kg adsorbed ) 5.3. Indices 242 w Water s (Ad)sorbent, (ad)sorption 0 Temporal mean value D Dosing chamber M Measurement chamber 𝑉𝑉 At constant volume 𝑇𝑇 At constant temperature ch (Measurement) chamber cmp Composite ct Coating rel Relative 6.