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Water Adsorption on AQSOA-FAM-Z02 Beads
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Adsorption and Diffusion in Porous Materials

Water Adsorption on AQSOA-FAM-Z02 Beads
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Journal of Chemical & Engineering Data

Cite this: J. Chem. Eng. Data 2022, 67, 7, 1723–1731
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https://doi.org/10.1021/acs.jced.1c00942
Published June 7, 2022

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Abstract

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Water/AQSOA-FAM-Z02 adsorption equilibrium data have been measured using two gravimetric systems at 30 °C, 50 °C, and 70 °C in the range 1–90% relative humidity (RH). The data were found to conform to a type IV adsorption isotherm and have been correlated with the Rigid Adsorbent Lattice Fluid dual site model in the range 1–50% RH, which has been shown to reproduce the experimental results with an average absolute deviation in line with uncertainties measured from duplicate and replicate experiments. The adsorption and desorption data were found not to overlap even at 1% RH, resulting in an open hysteresis under the experimental conditions studied. The Rigid Adsorbent Lattice Fluid dual site model adapted to take into account a nondesorbing fraction of pores reproduced the experimental desorption curves providing an overall description of the system for use in adsorption process simulations. The isosteric heats of adsorption obtained show a complex concentration dependence with a local maximum (84.2 kJ mol–1) and minimum (55.8 kJ mol–1) which are values consistent with the ranges found in the literature.

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Copyright © 2022 The Authors. Published by American Chemical Society

SPECIAL ISSUE

This article is part of the Equilibrium Adsorption Data for Energy and Environmental Applications special issue.

1. Introduction

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Due to global warming, there is an ever-present need to increase the world’s renewable energy share. The current trends in electrification of heating and transportation along with deployment of carbon capture processes depict a future in which the renewable electricity generation will not be enough to match all the users. (1) Processes that turn low temperature waste heat into useful outputs are pivotal for mitigating the future energy shortage. (2) In the family of low-temperature-heat-driven technologies, temperature swing sorption (TSS) processes stand out in terms of temperature level required. Presently, TSS can suit a wide range of diverse applications such as desalination, (3) drying, (4) heating and cooling, (5) heat storage, (6) electricity generation, (7) and greenhouse gas capture. (8) In each application, the thermodynamic and kinetic properties of the nanoporous material are the foremost features that position the performance of the technology at viable values, as reflected by the intensive activity of development in recent years of advanced zeolites, (9) zeotypes, (10) silica gels, (11) activated carbons, (12) metal organic frameworks, (13) and composites. (14) However, only a small number of materials succeeded in the path to commercialization. Among commercial materials for heating and cooling applications, the Functional Adsorbent Material Zeolite (FAM Z) series from Mitsubishi Plastics Inc. are still unrivalled when paired with water due to the stepwise change of equilibrium uptake at precise values of the relative humidity. This investigation focused on AQSOA-FAM-Z02, based on the (silico)aluminophosphate SAPO-34 zeotype with CHA-structure, (15,16) hereafter referred to as AQSOA-Z02, with an adsorption isotherm that a number of studies (17−19) have approximated to type V at relative humidity <30% across a range of temperatures from ambient to ∼80 °C. The stepwise change in adsorbed water at low relative humidity sparked theoretical and experimental activities to assess its suitability for cooling, (20) heat pumping, (21) drying, (22) desiccation, (23) desalination, (24) and CO2 capture from humid air streams, (25) with improvements over benchmarking material in most of the cases. However, all studies neglected the strong hysteresis that the AQSOA-Z02/water pair shows (19) up to temperatures of 100 °C where it disappears, (17) leading often to incorrect conclusions, especially when they are from the only utilization of adsorption data. Through thermogravimetric analysis and density functional theory, Fan and Chakraborty (15) first, and Kayal et al. (18) afterward, hypothesized the presence of two adsorption modes. In the first mode, water binds externally to the AQSOA-Z02 system of cages, while in the second mode water vapor binds in the inner cages. The hysteresis of the AQSOA-Z02/water pair originates from the difference between the ways in which this second retained amount adsorbs and desorbs. In this work, we carried out an experimental study of the water sorption and desorption equilibrium on grains of commercial AQSOA-Z02 in two distinct gravimetric apparatuses. We also show how the rigid adsorbent lattice fluid (RALF) model (26) provides a comprehensive theoretical interpretation of the adsorption and desorption equilibrium data.

2. Experimental Methods and Materials

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The primary measurements were carried out using deionized water and a Quantachrome Aquadyne DVS dual gravimetric system with a resolution of 0.1 μg, equipped with a Rotronic HC2-SM humidity probe with an accuracy of ±0.8% RH.
The AQSOA-Z02 material was in the form of spherical beads, previously tested in our laboratory. (25) The bead density, 1081 kg m–3, was determined using a Quantachrome PoreMaster mercury porosimetry. The pore size distribution obtained is shown in Figure 1, and only pores below 100 nm were found to be present. From the mercury intrusion measurements the volume accessible was determined, 98 × 10–6 m3 kg–1. The skeletal density, 2256 kg m–3, was determined using a Quantachrome Ultrapyc 1200e, and the total bead pore volume was found to be 482 × 10–6 m3 kg–1.

Figure 1

Figure 1. Pore size distribution measured by mercury porosimetry.

The pore size distribution below 10 nm was determined using a Quantachrome Autosorb iQ2 apparatus. Figure S1 in the Supporting Information shows the argon adsorption isotherm at 87 K along with the pore size distribution obtained using the software that is provided with the Autosorb and a DFT match of the adsorption branch. The results indicate a cumulative pore volume of 298 × 10–6 m3 kg–1cc/g, 279 × 10–6 m3 kg–1cc/g of which are in the micropore range.
As the Aquadyne DVS does not allow in situ regeneration, a procedure similar to that of Hampson and Rees (27) was followed to determine the dry mass of the sample. Beads of AQSOA-Z02 were equilibrated in a glass bell-jar with a saturated solution of water and NaCl, which provides a stable 75–76 RH% at or near to room temperature. (28) After 48 h of equilibration five beads were placed in a Setaram Sensys-Evo TG-DSC, and the sample mass vs temperature curve was obtained from room temperature to 160 °C. The resulting weight loss of 25.4% was determined and used to calculate the dry mass of the beads taken from the glass bell-jar.
Prior to each set of experiments 44.44 mg (dry mass) of AQSOA-Z02 beads (six in total) were regenerated in helium flow following the sequence: from room temperature 1 °C min–1 up to 110 °C; temperature held for 1 h; further temperature ramp of 1 °C min–1 up to 160 °C; temperature held for at least 8 h. After performing the zeroing and calibration of the two microbalances, the sample was weighed rapidly on a Mettler Toledo XS205 balance (guaranteed repeatability of ±0.05 mg) to measure the sample weight, which was then converted to dry mass based on the TGA measurement. Even with rapid cooling and transfer of sample to the Aquadyne DVS, some water uptake was present before the start of the isotherm measurements (approximately 3% in weight). The beads were then placed, three each, on the balances of the Aquadyne apparatus, and the cell was purged for 30 min prior to commencing the first step of the adsorption measurements. As the Aquadyne is a flow system, it is not possible to achieve a purely dry gas feed, and as a result the observed mass of a hydrophilic material will slowly increase even with a nominal dry gas. The data reported are the average of the two measurements at 30 and 50 °C along with the uncertainty at each point. At 70 °C one of the balances could not operate reliably and therefore only one measurement was possible. Figure 2 shows the dynamic response of one of the balances at 50 °C. The trends are similar at the other temperatures and the corresponding figures are included in the Supporting Information. Desorption is clearly slower than adsorption and longer equilibration times are needed at the lower concentrations.

Figure 2

Figure 2. Dynamic response of the Aquadyne system at 50 °C.

An additional set of adsorption measurements were obtained using a dynamic vapor sorption Adventure system (DVS Adventure) from Surface Measurement Systems, which has been described in detail elsewhere. (29,30) These measurements were intended for a kinetic study and only one bead (8.15 mg dry mass) was used. Only the data where equilibration was achieved are included in order to provide a further comparison of results from two instruments, primarily to show similarity between the results at 50 and 70 °C where the additional result on the Aquadyne system was not available.

3. Isotherm Model

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Water adsorption on AQSOA-Z02 is complex, and data reported in the literature tend to indicate that the isotherms have a type IV shape in the IUPAC classification. (31) The most comprehensive set of data for this system was produced by Goldsworthy (17) who correlated the data using a statistical thermodynamic isotherm modified to allow varying the site interaction energy arbitrarily. (32,33) To achieve a good match, 11 distinct site energies were used with a total of 13 adjustable parameters. To derive isosteric heats, a separate spline-fit was performed on the data; therefore, two formulations for this quantity are available. While such an approach provided a fairly accurate regression of the data, here the intent was to obtain a good match to the data with the Rigid Adsorbent Lattice Fluid (RALF) model, (26) which has been shown to represent correctly type V stepped isotherms (34) as well as stepped isotherms resulting from structural changes upon adsorption. (35)
As this system is known to exhibit an initially favorable isotherm followed by a step (type IV) a RALF dual site (RALF-DS) model was considered. This was found to be consistent with the observation that the pore volume accessible to helium but not to mercury was 384 × 10–6 m3 kg–1 while the micropore volume for this material was found to be 279 × 10–6 m3 kg–1 in close agreement with the reported value of 277 × 10–6 m3 kg–1. (18) The argon measurement at 87 K indicates that the sample used includes a mesopore volume of 19 × 10–6 m3 kg–1. The substantial difference between the pore volume accessible to argon and helium would indicate that some porosity has to be present with very small pores or that large pores exist inside the microporous structure and this could explain the presence of a hysteresis in desorption even at low %RH. (36) Given the uncertainty in the actual pore volume available for adsorption, also in view of the fact that water is smaller than argon and can therefore potentially access the same volume as helium, this quantity was considered to be an adjustable value, Vm, varying between 270 × 10–6 and 400 × 10–6 m3 kg–1.
The two types of site are independent of one another, and as a result the adsorbed amounts can be determined applying the equilibrium relationship to each site. Table 1 provides a summary of the equations needed. (26)
Table 1. RALF Calculation Sequence for a Single Site and Adsorbate
sequenceeq i = 1; j and k include the solid, therefore sums are up to 2
1specify parameters: Ti*; Pi*; ρi*; Mwi; TS*; PS*; ρS*; ξiA and κij
2specify variables: T; P; ni; ms
3set: ; ; ; ;
4mi = niMwi; mT = ∑jmj ; ; ; ;
5 with and κkk = 0
6; ; ; ; and
7; ; ;
The physical parameters of the Sanchez–Lacombe equation of state for water are TH2O* = 670 K; PH2O* = 2400 MPa; ρH2O* = 1050 kg m–3. (37) This leaves for each site the need to specify TS*; PS*; ρS* as well as the density of the solid ρS. For the single site, RALF ρS* can be taken as the skeletal density of the material. In order to keep the adjustable parameters to a minimum, ρSa* = ρSb* = ρS* = 2256 kg m–3 was chosen, as the skeletal density of the sites should be the same or nearly the same for a given material. ρS can be obtained from the additional knowledge of the volume, Vm.
In a RALF-DS model it is necessary to specify the mass fraction of site a, wa, and the fraction of pore volume corresponding to site a, fva. Then the density of the solid for each site can be calculated from
(1)
The parameter ξH2O represents the extent to which a confined molecule cannot reach its close-packed density. As the pore volume has been allowed to vary and given that water is a small molecule for both sites ξH2O = 0 was set.
With the constraints outlined above, three structural parameters, wa, fva, and Vm, and six site parameters, TSa*, PSa*, TSb*, PSb*, κH2Oa, and κH2Ob, remain to be determined. It is useful to point out that, for comparison, a multisite Langmuir model would require three parameters for each site and could not describe a type IV isotherm. Assuming an ideal gas phase and mS = 1 kg, the adsorbed amount, nH2O can be obtained solving for each site
(2)
and
(3)
The isosteric heat at zero coverage for each site can be obtained from (26)
(4)
(5)
which gives the following expression for RALF-DS
(6)
Finally, given that the vapor phase can be assumed to be ideal, the isosteric heat as a function of concentration can be obtained by numerical differentiation using
(7)
solving eq 3 for the pressure at a given total amount adsorbed.

4. Results and Discussion

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In the Aquadyne DVS system the two sample holders are approximately 50 mm apart. Given that the balances are identical, the observed variability in the measured amounts can be taken as an estimate of the point uncertainty, including any internal temperature and concentration gradients. As a result Table 2 reports the average measured isotherms along with the point uncertainties where measurements with both balances were performed. There was excellent reproducibility at 30 °C, with an average uncertainty of ±0.0022 kg kg–1. At 50 °C this increased to ±0.0074 kg kg–1, consistent with the fact that it is more difficult to control tightly the instrument set points (balance head, sample cell, and evaporator temperatures) further from room temperature. The comparison between the two instruments at 70 °C is similar to that at 50 °C and would suggest a similar uncertainty at this temperature. An uncertainty analysis based on the instrument’s known parameters is included in the Supporting Information along with results in Table S3.Figure 3 shows all the data measured where equilibrium conditions were achieved. The Supporting Information includes Table S2 with all the data obtained from the Aquadyne DVS. As with all automated devices, the Aquadyne DVS system comes with a software that determines when equilibrium has been reached and especially at the lower concentrations there was the need to extend the minimum time for each step to be closer to equilibration.
Table 2. Water/AQSOA-Z02 Adsorption and Desorption Data at 30 °C, 50 °C, and 70 °C
30 °C50 °C70 °C
%RHm kg kg–1±kg kg–1%RHm kg kg–1±kg kg–1%RHm kg kg–1
20.12450.005520.0880.009520.075
40.15300.001040.1100.009040.093
60.1910 60.1330.008560.109
80.24850.000580.1640.008080.125
100.25530.0033200.2350.0060100.143
200.27030.0024300.2460.0060200.217
300.28000.0014500.2630.0065300.231
500.29500.0019700.2780.0070500.247
700.31080.0022900.2990.0090700.264
900.33180.0025700.2890.0075900.283
700.32200.0019500.2740.0060700.272
500.30550.0018300.2600.0060500.258
300.29150.0022200.2520.0060300.245
200.28280.0023100.2340.0060200.235
100.26780.002360.2090.0060100.206
7.50.26000.002030.1320.008560.137
50.24900.002010.0980.010030.104
60.25850.0015   10.084
30.22700.0030     
10.1500      
Adventure
1.90.120 0.680.095 2.50.098
5.00.170 2.160.112 4.70.117
7.00.214 4.390.131 6.90.133
9.90.237 6.630.148 9.10.148
20.10.271 8.740.169 18.30.210
30.40.281 15.260.213   
50.10.294      
59.70.299      

Figure 3

Figure 3. Experimental data at 30 °C (a); 50 °C (b); and 70 °C (c). These include replicate runs and values from the two balances where available. Lines are to guide the eye based on the average value measured using the Aquadyne DVS.

Desorption was generally much slower than adsorption, but even allowing for extended equilibration times it was not possible to determine where the desorption branch rejoined the adsorption isotherm. The fact that this may be below RH% 1 would indicate that part of the porosity in the material is encapsulated by microporous material. As a result the desorption branch is affected by pore connectivity and a more sophisticated model taking this into account should be developed, but this is beyond the scope of this contribution as the aim is to obtain a model that can be used in adsorption process simulations which can be extended reliably to multicomponent systems.
As the adsorption and desorption data were different, the method adopted to correlate the data was to consider first the adsorption isotherms given that these data would allow direct comparisons with results reported in the literature. Regression of the data with the RALF-DS model was applied only to the adsorption data up to RH% 50 as above this value would require an additional site to account for additional condensation in the mesopores. As the number of parameters was significant, a nonlinear regression was carried out using MINUIT (38) by fixing Vm and allowing the software to determine the optimal values of the remaining eight parameters. An overall minimum was found for Vm = 400 × 10–6 m3 kg–1 and the parameters in Table 3. The average absolute deviation on 23 data points was 0.0054 kg kg–1, which is within the range of average uncertainty in the data of 0.0022 and 0.0074 kg kg–1 at 30 and 50 °C, respectively. The model reproduces the data with an average absolute percent deviation of 3.2%. Values reported include also the parameter uncertainties determined by MINUIT using a 95% confidence interval. The uncertainties for site b (type I) are larger and PSb* had a strong correlation with κH2Ob, therefore the second parameter was fixed to zero in order to arrive at a final set of reliable parameters. All the remaining model parameters are fairly well-defined indicating that there is enough information in the experimental data to characterize the parameters for both sites. Site a was the type V site as can be seen in Figure 4.
Table 3. RALF-DS Parameters and 95% Confidence Interval Uncertainties
parametervalue± uncertainty
wa, –0.5060.030
fva, –0.4910.0214
TSa*, K4403
PSa*, MPa237232
TSb*, K49015
PSb*, MPa6697924
κH2Oa, –0.02040.0002
κH2Ob, –0

Figure 4

Figure 4. Semilog (left) and linear (right) comparison of RALF-DS and experimental average adsorption data (squares) at 30 °C, 50 °C, and 70 °C. Empty squares not included in the regression. Dashed lines correspond to the statistical isotherm of Goldsworthy. (17) The linear plot includes the separate contributions of site a (full line) and site b (dash-dot line) at 70 °C.

Figure 4 shows the RALF-DS isotherms along with the isotherms from Goldsworthy. (17) From this comparison it is clear that the steps in the isotherms are at the same RH% but there are significant differences. In particular the low concentration uptake appears higher, while the overall capacity is lower. These differences can be attributed to the fact that Goldsworthy (17) performed experiments using the original powder of the material and not formed beads. Both Teo et al. (19) and Kayal et al. (18) report maximum values close to or slightly below 0.30 kg kg–1, but it is not clear if they used pure powder or beaded materials.
Figure 5 shows the comparison of the isosteric heat of adsorption at 323.15 K obtained from the RALF-DS model in comparison with the two approaches used by Goldsworthy. (17) The zero-coverage isosteric heat was found to be 73.1 kJ mol–1. The trend in concentration calculated from the RALF-DS model shows the filling of site b at low adsorbed amounts, resulting in an increasing trend corresponding to the additional water–water interactions. Once the type V filling of site a becomes significant the isosteric heat drops to a minimum followed again by an increasing trend corresponding to additional water–water interactions.

Figure 5

Figure 5. Comparison of isosteric heats obtained from the RALF-DS model and the statistical isotherm and spline fit of the data by Goldsworthy. (17)

The statistical isotherm used by Goldsworthy (17) assumes no interactions between adsorbed molecules and as a result starts with a zero coverage value of 70.2 kJ mol–1, which corresponds to the first site, remains approximately constant up to 0.03 kg kg–1 and abruptly drops to approximately 58.4 kJ mol–1. The second method based on spline fits appears to give values of the isosteric heat that are too high below 0.03 kg kg–1, but then gives similar values to the first approach. Independent measurements of the zero coverage isosteric heat from Fan and Chakraborty, (15) 55.2 kJ mol–1, provide a validation to the results obtained from the RALF-DS fit. The local maximum and minimum, respectively 84.2 kJ mol–1 and 55.8 kJ mol–1, are in excellent agreement with the limiting values of Goldsworthy (17) and provide further confirmation that the second site interactions are of a similar nature, and the observed deviations are most likely due to the differences due to the use of beaded material and not powder.
As discussed by Verbraeken and Brandani (34) the location of the step in the RALF representation of a type V isotherm (site a) depends strongly on the value of the parameter κH2Oa. Therefore to represent the desorption branch it is possible to use this parameter to shift the step to a lower pressure. While this is a purely empirical approximation, it does retain all the main interaction terms and provides a straightforward method to calculate both adsorption and desorption curves. From the observation that the desorption curves never join the adsorption ones, a further assumption is made that 25% of site a does not desorb within the pressure range used in the experiments. The desorption branch is therefore calculated using
(8)
A value of was found to provide a good representation of the desorption branch at all temperatures. Note that with the switch in the value of the parameter there is a small difference between the value of nH2Oa and nH2Oad at the end of the adsorption step and the start of desorption that is compensated by .
Figure 6 shows the final comparison between adsorption and desorption data along with the calculated RALF-DS curves. This is plotted versus pressure to avoid overlaps between the adsorption and desorption branches at the different temperatures. Considering the complexity of this system the model agrees well with all the data and can be used for process calculations involving both adsorption and desorption steps.

Figure 6

Figure 6. Comparison of RALF-DS adsorption (full line) and desorption (dashed line) curves and experimental average adsorption (squares) and desorption (circles) at 30 °C, 50 °C, and 70 °C.

Conclusions

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Water/AQSOA-Z02 adsorption equilibrium data have been measured using two gravimetric systems at 30 °C, 50 °C, and 70 °C in the range 1–90% RH. The data were found to conform to a type IV adsorption isotherm and have been correlated with the RALF-DS model in the range 1–50% RH, which has been shown to reproduce the experimental results with an average absolute deviation in line with uncertainties measured from experiments in the Aquadyne DVS dual balance system. The two sites of the RALF-DS model correspond to type I and type V isotherms, which when combined lead to the observed type IV behavior.
The adsorption and desorption data were found not to overlap even at 1% RH, suggesting that the material may be composed of a mixture of micropores and mesopores, some of which are encapsulated by the microporous phase. An empirical modification of the RALF-DS model with 25% of the pores of the type V site occluded reproduced the experimental desorption curves with the use of only one model parameter.
The isosteric heats of adsorption obtained from the RALF-DS model show a complex concentration dependence with a local maximum (84.2 kJ mol–1) and minimum (55.8 kJ mol–1) which are values consistent with the range of values found in the literature. This was seen to confirm that the base material for different batches of AQSOA-Z02 is consistent, but there appears to be variability in the mesoporosity of the material as a result of the difference between powder and beaded forms. This combined with the very interesting hysteresis observed with water would suggest the need to investigate the structure of this material using adsorption of argon at cryogenic conditions, which could provide further insight into the properties of the beaded material.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.1c00942.

  • Ar isotherm at 87 K and corresponding pore size distribution; dynamic responses of the Aquadyne system at 30 and 70 °C; detailed uncertainty analysis; tabulated values of data not included in Table 3; summary table of the isotherm data with uncertainties included (PDF)

  • Isotherm data (ZIP)

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Author Information

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  • Corresponding Author
  • Authors
    • Enzo Mangano - School of Engineering, University of Edinburgh, Edinburgh, EH9 3FB, U.K.
    • Giulio Santori - School of Engineering, University of Edinburgh, Edinburgh, EH9 3FB, U.K.Orcidhttps://orcid.org/0000-0003-2156-6647
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.

Notation

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fva

fraction of pore volume in site a (−)

K

dimensionless Henry law constant (−)

ni

adsorbed amount (mol kg–1)

nH2OT

total water adsorbed (mol kg–1)

nH2OTd

total water adsorbed in desorption, eq 8 (mol kg–1)

mj

mass of species j (kg)

ms

mass of solid (kg)

Mwi

molecular mass of species i (kg mol–1)

P

pressure (Pa)

Pmax

maximum pressure in adsorption (Pa)

reduced pressure (−)

P*

characteristic pressure of the mixture (Pa)

Pi*

characteristic pressure of component i pure (Pa)

PiA*

characteristic pressure of component i in the adsorbed phase (Pa)

PS*

characteristic pressure of the solid (Pa)

Pij*

pair characteristic pressure

r

average number of mers in a molecule (−)

rj

number of mers in molecule j in the mixture (−)

rj0

number of mers in molecule j pure (−)

R

ideal gas constant (J mol–1 K–1)

T

temperature (K)

reduced temperature (−)

T*

characteristic temperature of the mixture (K)

Ti*

characteristic temperature of component i pure (K)

TS*

characteristic temperature of the solid (K)

reduced molar volume (−)

v*

average close-packed volume of mers in a mixture (m3 mer-mol–1)

vj*

close-packed volume of mers molecule j pure (m3 mer-mol–1)

vjA*

close-packed volume of mers molecule j in the adsorbed phase (m3 mer-mol–1)

Vm

specific volume of the pores (m3 kg–1)

wa

mass fraction of site a (−)

z

compressibility factor (−)

zEoS

compressibility factor derived from the Helmholtz energy (−)

Greek letters
δ

difference between adsorbed amounts of site a at the start of desorption and the end of the adsorption step, nH2Oad (Pmax) – nH2Oa (Pmax) (mol kg–1)

ΔH0

adsorption enthalpy at zero coverage (J mol–1)

ΔU0

adsorption energy at zero coverage (J mol–1)

ϕj

volume fraction in the lattice occupied by species j at close-packing (−)

ϕs

volume fraction in the lattice occupied by the solid at close-packing (−)

κjk

pair interaction coefficient (−)

μiR

residual chemical potential of species i in the adsorbed phase (J mol–1)

ρ̃

reduced mass density (−)

ρ*

average close-packed mass density in a mixture (kg m–3)

ρj*

close-packed mass density of molecule j (kg m–3)

ρjA*

close-packed mass density of molecule j in the adsorbed phase (kg m–3)

ρS

mass density of the solid (kg m–3)

ξiA

volume correction due to confinement constraints (−)

References

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    Askalany, A. A.; Freni, A.; Santori, G. Supported Ionic Liquid Water Sorbent for High Throughput Desalination and Drying. Desalination 2019, 452, 258264,  DOI: 10.1016/j.desal.2018.11.002
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    Santori, G.; Di Santis, C. Optimal Fluids for Adsorptive Cooling and Heating. Sustain. Mater. Technol. 2017, 12, 5261,  DOI: 10.1016/j.susmat.2017.04.005
  6. 6
    Zhang, Y.; Wang, R. Sorption Thermal Energy Storage: Concept, Process, Applications and Perspectives. Energy Storage Mater. 2020, 27, 352369,  DOI: 10.1016/j.ensm.2020.02.024
  7. 7
    Olkis, C.; Brandani, S.; Santori, G. Adsorption Reverse Electrodialysis Driven by Power Plant Waste Heat to Generate Electricity and Provide Cooling. Int. J. Energy Res. 2021, 45, 19711987,  DOI: 10.1002/er.5891
  8. 8
    Santori, G.; Charalambous, C.; Ferrari, M. C.; Brandani, S. Adsorption Artificial Tree for Atmospheric Carbon Dioxide Capture, Purification and Compression. Energy 2018, 162, 11581168,  DOI: 10.1016/j.energy.2018.08.090
  9. 9
    Ristić, A.; Fischer, F.; Hauer, A.; Zabukovec Logar, N. Improved Performance of Binder-Free Zeolite Y for Low-Temperature Sorption Heat Storage. J. Mater. Chem. A 2018, 6, 1152111530,  DOI: 10.1039/C8TA00827B
  10. 10
    Krajnc, A.; Varlec, J.; Mazaj, M.; Ristić, A.; Logar, N. Z.; Mali, G. Superior Performance of Microporous Aluminophosphate with LTA Topology in Solar-Energy Storage and Heat Reallocation. Adv. Energy Mater. 2017, 7, 1601815,  DOI: 10.1002/aenm.201601815
  11. 11
    Sapienza, A.; Velte, A.; Girnik, I.; Frazzica, A.; Füldner, G.; Schnabel, L.; Aristov, Y. Water - Silica Siogel” Working Pair for Adsorption Chillers: Adsorption Equilibrium and Dynamics. Renew. Energy 2017, 110, 4046,  DOI: 10.1016/j.renene.2016.09.065
  12. 12
    Palash, M. L.; Rupam, T. H.; Pal, A.; Chakraborty, A.; Saha, B. B.; Wang, R. Design Principles for Synthesizing High Grade Activated Carbons for Adsorption Heat Pumps. Chem. Eng. J. Adv. 2021, 6, 100086,  DOI: 10.1016/j.ceja.2021.100086
  13. 13
    Liu, X.; Wang, X.; Kapteijn, F. Water and Metal-Organic Frameworks: From Interaction toward Utilization. Chem. Rev. 2020, 120, 83038377,  DOI: 10.1021/acs.chemrev.9b00746
  14. 14
    Frazzica, A.; Brancato, V.; Caprì, A.; Cannilla, C.; Gordeeva, L. G.; Aristov, Y. I. Development of “Salt in Porous Matrix” Composites Based on LiCl for Sorption Thermal Energy Storage. Energy 2020, 208, 118338,  DOI: 10.1016/j.energy.2020.118338
  15. 15
    Fan, W.; Chakraborty, A. Isosteric Heat of Adsorption at Zero Coverage for AQSOA-Z01/Z02/Z05 Zeolites and Water Systems. Microporous Mesoporous Mater. 2018, 260, 201207,  DOI: 10.1016/j.micromeso.2017.10.039
  16. 16
    Sun, B.; Chakraborty, A. Thermodynamic Formalism of Water Uptakes on Solid Porous Adsorbents for Adsorption Cooling Applications. Appl. Phys. Lett. 2014, 104, 201901,  DOI: 10.1063/1.4876922
  17. 17
    Goldsworthy, M. J. Measurements of Water Vapour Sorption Isotherms for RD Silica Gel, AQSOA-Z01, AQSOA-Z02, AQSOA-Z05 and CECA Zeolite 3A. Microporous Mesoporous Mater. 2014, 196, 5967,  DOI: 10.1016/j.micromeso.2014.04.046
  18. 18
    Kayal, S.; Baichuan, S.; Saha, B. B. Adsorption Characteristics of AQSOA Zeolites and Water for Adsorption Chillers. Int. J. Heat Mass Transfer 2016, 92, 11201127,  DOI: 10.1016/j.ijheatmasstransfer.2015.09.060
  19. 19
    Wei Benjamin Teo, H.; Chakraborty, A.; Fan, W. Improved Adsorption Characteristics Data for AQSOA Types Zeolites and Water Systems under Static and Dynamic Conditions. Microporous Mesoporous Mater. 2017, 242, 109117,  DOI: 10.1016/j.micromeso.2017.01.015
  20. 20
    Aristov, Y. Concept of Adsorbent Optimal for Adsorptive Cooling/Heating. Appl. Therm. Eng. 2014, 72, 166175,  DOI: 10.1016/j.applthermaleng.2014.04.077
  21. 21
    Dawoud, B. Water Vapor Adsorption Kinetics on Small and Full Scale Zeolite Coated Adsorbers; A Comparison. Appl. Therm. Eng. 2013, 50, 16451651,  DOI: 10.1016/j.applthermaleng.2011.07.013
  22. 22
    Santori, G.; Frazzica, A.; Freni, A.; Galieni, M.; Bonaccorsi, L.; Polonara, F.; Restuccia, G. Optimization and Testing on an Adsorption Dishwasher. Energy 2013, 50, 170176,  DOI: 10.1016/j.energy.2012.11.031
  23. 23
    Intini, M.; Goldsworthy, M.; White, S.; Joppolo, C. M. Experimental Analysis and Numerical Modelling of an AQSOA Zeolite Desiccant Wheel. Appl. Therm. Eng. 2015, 80, 2030,  DOI: 10.1016/j.applthermaleng.2015.01.036
  24. 24
    Youssef, P. G.; Mahmoud, S. M.; AL-Dadah, R. K. Performance Analysis of Four Bed Adsorption Water Desalination/Refrigeration System, Comparison of AQSOA-Z02 to Silica-Gel. Desalination 2015, 375, 100107,  DOI: 10.1016/j.desal.2015.08.002
  25. 25
    Charalambous, C.; Santori, G.; Vilarrasa-Garcia, E.; Bastos-Neto, M.; Cavalcante, C. L.; Brandani, S. Pure and Binary Adsorption of Carbon Dioxide and Nitrogen on AQSOA FAM Z02. J. Chem. Eng. Data 2018, 63, 661670,  DOI: 10.1021/acs.jced.7b00864
  26. 26
    Brandani, S. The Rigid Adsorbent Lattice Fluid Model for Pure and Mixed Gas Adsorption. AIChE J. 2019, 65, 13041314,  DOI: 10.1002/aic.16504
  27. 27
    Hampson, J. A.; Rees, L. V. C. Adsorption of Ethane and Propane in Silicalite-1 and Zeolite NaY: Determination of Single Components, Mixture and Partial Adsorption Data Using an Isosteric System. J. Chem. Soc. Faraday Trans. 1993, 89, 31693176,  DOI: 10.1039/ft9938903169
  28. 28
    Greenspan, L. Humidity Fixed Points of Binary Saturated Aqueous Solutions. J. Res. Natl. Bur. Stand. - A. Phys. Chem. 1977, 81A, 8996,  DOI: 10.6028/jres.081A.011
  29. 29
    Luberti, M.; Olkis, C.; Bensted, G.; Santori, G. Water Sorption Equilibrium on 2-Hydroxyethyl-Trimethylammonium Acetate in the Temperature Range 298.25–349.55K. Fluid Phase Equilib. 2020, 522, 112758,  DOI: 10.1016/j.fluid.2020.112758
  30. 30
    Askalany, A. A.; Freni, A.; Santori, G. Supported Ionic Liquid Water Sorbent for High Throughput Desalination and Drying. Desalination 2019, 452, 258264,  DOI: 10.1016/j.desal.2018.11.002
  31. 31
    Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Reporting Physisorption Data for Gas/Solid Systems with Special Reference to the Determination of Surface Area and Porosity. Pure Appl. Chem. 1985, 57, 603619,  DOI: 10.1351/pac198557040603
  32. 32
    Mosquera, M. A. Simple Isotherm Equations to Fit Type I Adsorption Data. Fluid Phase Equilib. 2013, 337, 174182,  DOI: 10.1016/j.fluid.2012.09.010
  33. 33
    Ruthven, D. M. Simple Theoretical Adsorption Isotherm for Zeolites. Nat. Phys. Sci. 1971, 232, 7071,  DOI: 10.1038/physci232070a0
  34. 34
    Verbraeken, M. C.; Brandani, S. A Priori Predictions of Type I and Type V Isotherms by the Rigid Adsorbent Lattice Fluid. Adsorption 2020, 26, 9891000,  DOI: 10.1007/s10450-019-00174-7
  35. 35
    Verbraeken, M. C.; Brandani, S. Predictions of Stepped Isotherms in Breathing Adsorbents by the Rigid Adsorbent Lattice Fluid. J. Phys. Chem. C 2019, 123, 1451714529,  DOI: 10.1021/acs.jpcc.9b02977
  36. 36
    Thommes, M.; Kaneko, K.; Neimark, A. V.; Olivier, J. P.; Rodriguez-Reinoso, F.; Rouquerol, J.; Sing, K. S. W. Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report). Pure Appl. Chem. 2015, 87, 10511069,  DOI: 10.1515/pac-2014-1117
  37. 37
    De Angelis, M. G.; Sarti, G. C. Solubility of Gases and Liquids in Glassy Polymers. Annu. Rev. Chem. Biomol. Eng. 2011, 2, 97120,  DOI: 10.1146/annurev-chembioeng-061010-114247
  38. 38
    James, F. Function Minimization and Error Analysis. CERN Program Library Long Writeup D506; CERN: Geneva, Switzerland, 1998. https://cdsweb.cern.ch/record/2296388/files/minuit.pdf.

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  • Abstract

    Figure 1

    Figure 1. Pore size distribution measured by mercury porosimetry.

    Figure 2

    Figure 2. Dynamic response of the Aquadyne system at 50 °C.

    Figure 3

    Figure 3. Experimental data at 30 °C (a); 50 °C (b); and 70 °C (c). These include replicate runs and values from the two balances where available. Lines are to guide the eye based on the average value measured using the Aquadyne DVS.

    Figure 4

    Figure 4. Semilog (left) and linear (right) comparison of RALF-DS and experimental average adsorption data (squares) at 30 °C, 50 °C, and 70 °C. Empty squares not included in the regression. Dashed lines correspond to the statistical isotherm of Goldsworthy. (17) The linear plot includes the separate contributions of site a (full line) and site b (dash-dot line) at 70 °C.

    Figure 5

    Figure 5. Comparison of isosteric heats obtained from the RALF-DS model and the statistical isotherm and spline fit of the data by Goldsworthy. (17)

    Figure 6

    Figure 6. Comparison of RALF-DS adsorption (full line) and desorption (dashed line) curves and experimental average adsorption (squares) and desorption (circles) at 30 °C, 50 °C, and 70 °C.

  • References


    This article references 38 other publications.

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      Krajnc, A.; Varlec, J.; Mazaj, M.; Ristić, A.; Logar, N. Z.; Mali, G. Superior Performance of Microporous Aluminophosphate with LTA Topology in Solar-Energy Storage and Heat Reallocation. Adv. Energy Mater. 2017, 7, 1601815,  DOI: 10.1002/aenm.201601815
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      Sapienza, A.; Velte, A.; Girnik, I.; Frazzica, A.; Füldner, G.; Schnabel, L.; Aristov, Y. Water - Silica Siogel” Working Pair for Adsorption Chillers: Adsorption Equilibrium and Dynamics. Renew. Energy 2017, 110, 4046,  DOI: 10.1016/j.renene.2016.09.065
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      Palash, M. L.; Rupam, T. H.; Pal, A.; Chakraborty, A.; Saha, B. B.; Wang, R. Design Principles for Synthesizing High Grade Activated Carbons for Adsorption Heat Pumps. Chem. Eng. J. Adv. 2021, 6, 100086,  DOI: 10.1016/j.ceja.2021.100086
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      Liu, X.; Wang, X.; Kapteijn, F. Water and Metal-Organic Frameworks: From Interaction toward Utilization. Chem. Rev. 2020, 120, 83038377,  DOI: 10.1021/acs.chemrev.9b00746
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      Frazzica, A.; Brancato, V.; Caprì, A.; Cannilla, C.; Gordeeva, L. G.; Aristov, Y. I. Development of “Salt in Porous Matrix” Composites Based on LiCl for Sorption Thermal Energy Storage. Energy 2020, 208, 118338,  DOI: 10.1016/j.energy.2020.118338
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      Fan, W.; Chakraborty, A. Isosteric Heat of Adsorption at Zero Coverage for AQSOA-Z01/Z02/Z05 Zeolites and Water Systems. Microporous Mesoporous Mater. 2018, 260, 201207,  DOI: 10.1016/j.micromeso.2017.10.039
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      Sun, B.; Chakraborty, A. Thermodynamic Formalism of Water Uptakes on Solid Porous Adsorbents for Adsorption Cooling Applications. Appl. Phys. Lett. 2014, 104, 201901,  DOI: 10.1063/1.4876922
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      Goldsworthy, M. J. Measurements of Water Vapour Sorption Isotherms for RD Silica Gel, AQSOA-Z01, AQSOA-Z02, AQSOA-Z05 and CECA Zeolite 3A. Microporous Mesoporous Mater. 2014, 196, 5967,  DOI: 10.1016/j.micromeso.2014.04.046
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      Kayal, S.; Baichuan, S.; Saha, B. B. Adsorption Characteristics of AQSOA Zeolites and Water for Adsorption Chillers. Int. J. Heat Mass Transfer 2016, 92, 11201127,  DOI: 10.1016/j.ijheatmasstransfer.2015.09.060
    19. 19
      Wei Benjamin Teo, H.; Chakraborty, A.; Fan, W. Improved Adsorption Characteristics Data for AQSOA Types Zeolites and Water Systems under Static and Dynamic Conditions. Microporous Mesoporous Mater. 2017, 242, 109117,  DOI: 10.1016/j.micromeso.2017.01.015
    20. 20
      Aristov, Y. Concept of Adsorbent Optimal for Adsorptive Cooling/Heating. Appl. Therm. Eng. 2014, 72, 166175,  DOI: 10.1016/j.applthermaleng.2014.04.077
    21. 21
      Dawoud, B. Water Vapor Adsorption Kinetics on Small and Full Scale Zeolite Coated Adsorbers; A Comparison. Appl. Therm. Eng. 2013, 50, 16451651,  DOI: 10.1016/j.applthermaleng.2011.07.013
    22. 22
      Santori, G.; Frazzica, A.; Freni, A.; Galieni, M.; Bonaccorsi, L.; Polonara, F.; Restuccia, G. Optimization and Testing on an Adsorption Dishwasher. Energy 2013, 50, 170176,  DOI: 10.1016/j.energy.2012.11.031
    23. 23
      Intini, M.; Goldsworthy, M.; White, S.; Joppolo, C. M. Experimental Analysis and Numerical Modelling of an AQSOA Zeolite Desiccant Wheel. Appl. Therm. Eng. 2015, 80, 2030,  DOI: 10.1016/j.applthermaleng.2015.01.036
    24. 24
      Youssef, P. G.; Mahmoud, S. M.; AL-Dadah, R. K. Performance Analysis of Four Bed Adsorption Water Desalination/Refrigeration System, Comparison of AQSOA-Z02 to Silica-Gel. Desalination 2015, 375, 100107,  DOI: 10.1016/j.desal.2015.08.002
    25. 25
      Charalambous, C.; Santori, G.; Vilarrasa-Garcia, E.; Bastos-Neto, M.; Cavalcante, C. L.; Brandani, S. Pure and Binary Adsorption of Carbon Dioxide and Nitrogen on AQSOA FAM Z02. J. Chem. Eng. Data 2018, 63, 661670,  DOI: 10.1021/acs.jced.7b00864
    26. 26
      Brandani, S. The Rigid Adsorbent Lattice Fluid Model for Pure and Mixed Gas Adsorption. AIChE J. 2019, 65, 13041314,  DOI: 10.1002/aic.16504
    27. 27
      Hampson, J. A.; Rees, L. V. C. Adsorption of Ethane and Propane in Silicalite-1 and Zeolite NaY: Determination of Single Components, Mixture and Partial Adsorption Data Using an Isosteric System. J. Chem. Soc. Faraday Trans. 1993, 89, 31693176,  DOI: 10.1039/ft9938903169
    28. 28
      Greenspan, L. Humidity Fixed Points of Binary Saturated Aqueous Solutions. J. Res. Natl. Bur. Stand. - A. Phys. Chem. 1977, 81A, 8996,  DOI: 10.6028/jres.081A.011
    29. 29
      Luberti, M.; Olkis, C.; Bensted, G.; Santori, G. Water Sorption Equilibrium on 2-Hydroxyethyl-Trimethylammonium Acetate in the Temperature Range 298.25–349.55K. Fluid Phase Equilib. 2020, 522, 112758,  DOI: 10.1016/j.fluid.2020.112758
    30. 30
      Askalany, A. A.; Freni, A.; Santori, G. Supported Ionic Liquid Water Sorbent for High Throughput Desalination and Drying. Desalination 2019, 452, 258264,  DOI: 10.1016/j.desal.2018.11.002
    31. 31
      Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Reporting Physisorption Data for Gas/Solid Systems with Special Reference to the Determination of Surface Area and Porosity. Pure Appl. Chem. 1985, 57, 603619,  DOI: 10.1351/pac198557040603
    32. 32
      Mosquera, M. A. Simple Isotherm Equations to Fit Type I Adsorption Data. Fluid Phase Equilib. 2013, 337, 174182,  DOI: 10.1016/j.fluid.2012.09.010
    33. 33
      Ruthven, D. M. Simple Theoretical Adsorption Isotherm for Zeolites. Nat. Phys. Sci. 1971, 232, 7071,  DOI: 10.1038/physci232070a0
    34. 34
      Verbraeken, M. C.; Brandani, S. A Priori Predictions of Type I and Type V Isotherms by the Rigid Adsorbent Lattice Fluid. Adsorption 2020, 26, 9891000,  DOI: 10.1007/s10450-019-00174-7
    35. 35
      Verbraeken, M. C.; Brandani, S. Predictions of Stepped Isotherms in Breathing Adsorbents by the Rigid Adsorbent Lattice Fluid. J. Phys. Chem. C 2019, 123, 1451714529,  DOI: 10.1021/acs.jpcc.9b02977
    36. 36
      Thommes, M.; Kaneko, K.; Neimark, A. V.; Olivier, J. P.; Rodriguez-Reinoso, F.; Rouquerol, J.; Sing, K. S. W. Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report). Pure Appl. Chem. 2015, 87, 10511069,  DOI: 10.1515/pac-2014-1117
    37. 37
      De Angelis, M. G.; Sarti, G. C. Solubility of Gases and Liquids in Glassy Polymers. Annu. Rev. Chem. Biomol. Eng. 2011, 2, 97120,  DOI: 10.1146/annurev-chembioeng-061010-114247
    38. 38
      James, F. Function Minimization and Error Analysis. CERN Program Library Long Writeup D506; CERN: Geneva, Switzerland, 1998. https://cdsweb.cern.ch/record/2296388/files/minuit.pdf.
  • Supporting Information

    Supporting Information


    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.1c00942.

    • Ar isotherm at 87 K and corresponding pore size distribution; dynamic responses of the Aquadyne system at 30 and 70 °C; detailed uncertainty analysis; tabulated values of data not included in Table 3; summary table of the isotherm data with uncertainties included (PDF)

    • Isotherm data (ZIP)


    Terms & Conditions

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