Reference isotherms for water vapor sorption on nanoporous carbon: results of an interlaboratory study

This paper reports the results of an international interlaboratory study sponsored by the Versailles Project on Advanced Materials and Standards (VAMAS) and led by the National Institute of Standards and Technology (NIST) on the measurement of water vapor sorption isotherms at 25 °C on a pelletized nanoporous carbon (BAM-P109, a certified reference material). Thirteen laboratories participated in the study and contributed nine pure water vapor isotherms and four relative humidity isotherms, using nitrogen as the carrier gas. From these data, reference isotherms, along with the 95% uncertainty interval (Uk=2), were determined and are reported in a tabular format.


Introduction
Water covers most of the Earth's surfaces, largely as a liquid in lakes, seas, oceans, and as a solid in polar ice caps. Furthermore, water is found as vapor, droplets, and ice crystals in the atmosphere and is found in living organisms. The ubiquitous nature of water makes understanding its effects on the chemical structure and properties of materials important to the development, processing, and applications of materials associated with food production (Rückold et al. 2000;Schmidt and Lee 2012), pharmaceuticals (Levogeur and Williams 2006), construction (Benavente et al. 2021), separation processes (Mokhatab et al. 2019;Wang 2020), sorbent-based industries (Dawson et al. 2012;Lawrence and Katz 2022), and emerging water sorption applications such as water harvesting (Ejeian and Wang 2021) and thermal energy storage (Carrier et al. 2021). A primary way to characterize water and materials interactions is by measuring a water vapor sorption isotherm. A water vapor sorption isotherm is a measure of water content as a function of relative pressure (P/P 0 ) for pure water measurements or relative humidity (RH), when water is entrained in another gas. By providing the water content of a material, the effect of water uptake on the chemical structure and properties of materials can be investigated. In addition, a water vapor sorption isotherm can also be used to determine the stability, porosity, and hygroscopicity of a material. Given the ubiquity of water uptake processes, it is important to have reference data, reference materials and standardized protocols for water uptake measurements.
One way water vapor sorption isotherms are determined is by the tedious and time-consuming static desiccator method. In this method, a dry sample is placed in a desiccator at a fixed temperature with a salt slurry to create a given RH. The sample is repeatedly removed and weighed until the mass reading between successive weighing is nearly constant, thus determining the equilibrium water uptake at that temperature and RH. Repeating this at multiple RHs allows for an isotherm to be constructed. This method is prone to error due to disturbance of equilibrium by the opening and closing of the desiccator during weighing, and the uptake/release of water in the mass measurement environment (Lewicki and Pomaranska-Lazuka 2003). The use of salt slurry also limits which RH levels can be obtained. Using climate chambers, the RH can be generated at any desired levels by mixing wet and dry streams in different ratios to generate different RHs. In an alternative early method developed by McBain and Bakr, a helical quartz spring sorption balance is placed inside a vacuum tube, allowing a whole isotherm to be obtained without having to remove the sample between experiments and thus never exposing the sample to foreign gases or vapors (McBain and Bakr 1926;McBain et al. 1933). In this method, a bucket with sample is attached to a calibrated quartz fiber spring in the top part of a self-contained vacuum tube with the vapor generating liquid at the bottom, and two separate thermostats. The top thermostat controls the analysis temperature, and the bottom thermostat controls the vapor pressure. The system is sealed off after the sample is outgassed and the system is placed under vacuum, and then the liquid, which had been sealed off, is released into the system. The uptake mass is determined from the displacement of the spring.
Automated instruments for measuring vapor sorption isotherms were later developed and commercialized, (Benham and Ross 1989;Bergren 1994;Buckton et al. 2011;Czanderna and Vasofsky 1979;Dienstmaier 2014;Marshall et al. 1994;Rasmussen and Akinc 1983;Sandstede and Robens 1962;Williams et al. 2005) eliminating issues related to the desiccator method, and making it easier to measure vapor sorption isotherms. Common automated techniques include the following: dynamic vapor sorption (DVS), which combines continuous flow climate control with continuous mass measurements; automated vacuum sorption balances, which control water vapor pressure in an evacuated system and use an electronic microbalance; and automated manometric systems, which also control the water vapor pressure in an evacuated system and rely on pressure transducers to monitor changes in vapor pressure and determine uptake.
With the large number of isotherms generated by automated instrumentation, there is an increasing need for standardized measurement protocols, reference materials, and reference data to ensure reliable and reproducible data. The National Institute of Standards and Technology (NIST), in partnership with the Department of Energy's Advanced Research Projects Agency (ARPA-E), initiated a program to develop reference materials, reference data, and measurement protocols to improve adsorption metrology. In consultation with the International Adsorption Society, NIST has identified the most important gases and parameters the community is interested in, which includes water vapor at ambient temperatures. The NIST Facility for Adsorbent Characterization and Testing (FACT Lab) has led two interlaboratory studies (ILSs) to develop reference isotherms. One study determined a reference high-pressure surface excess isotherm for adsorption of carbon dioxide on NIST Reference Material 8852 (ammonium ZSM-5 zeolite) at 20 °C up to 4.5 MPa (Nguyen et al. 2018). A second study, sponsored through Technical Working Area 39 of the Versailles Project on Advanced Materials and Standards (VAMAS), reported a reference surface excess isotherm for methane adsorption on NIST Reference Material 8850 (sodium zeolite Y) up to 7.5 MPa (Nguyen et al. 2020).
This paper reports a third ILS, also organized through VAMAS, investigating water vapor sorption on a pelletized nanoporous carbon at 25 °C as a function of relative pressure (P/P 0 ) for pure water measurements and relative humidity, when a carrier gas is used. Interest in the effect of atmospheric water on carbon has been dated to the early twentieth century in the rubber industry (Dewey et al. 1932). In addition to practical applications of water sorption on carbon materials, the surface functionality of carbons and their pore structures can lead to complex water adsorption, and this has been the subject of many fundamental studies (Liu et al. 2017). The sorbent used in this study is a certified reference material (CRM) with a BET specific surface area of 1396 ± 24 m 2 /g, produced by the German Federal Institute for Materials Research and Testing (Bundesanstalt für Materialforschung und prüfung or BAM) and is known as BAM-P109 (Panne and Thünemann 2010). It was chosen because it is a widely available commercial nanoporous carbonaceous CRM. Although a water vapor sorption isotherm on this material has been reported, the measurement was made at 20 °C and only as a function of P/P 0 (Ross et al. 2016). Given that 25 °C is a more common temperature for water vapor sorption isotherms, 25 °C was chosen as the sorption temperature in this study. Whereas the two previous studies coordinated by the FACT Lab only looked at static measurements, the current study examines both static and dynamic measurements. While the previous studies focused on high-pressure measurements, the measurements in the current study are at subatmospheric and atmospheric pressures, because the saturation pressure of water at 25 °C is only 3.17 kPa (Wagner and Pruß 2002). Although the effects of water sorption on the stability and proper use of biological reference materials and food CRMs have been studied and reported (Rückold et al. 2001;Rückold et al. 2003;Yazgan et al. 2006), this study is the first ILS to report reference data for a water vapor sorption isotherm using a CRM.

Methods
The ILS involved measurement of water vapor isotherms at 25 °C up to a relative pressure (P/P 0 ) of 0.95 or 95% relative humidity. BAM generously donated five bottles of BAM-P109, each containing ≈ 10 g of material, for the study. The five bottles were combined and divided through a spinning riffler into sixteen units of ≈ 3.1 g each. These units were distributed to the study participants. Thirteen laboratories participated in the ILS. The measurement capabilities of these laboratories included both manometric and gravimetric instruments and encompassed both static and dynamic measurements.
The measurement protocol instructions for the ILS were minimal. The protocol specified the use of liquid chromatography-mass spectrometry (LC-MS) grade water and that the carrier gas (N 2 ) for dynamic measurements have a minimum purity of 99.999%. Nitrogen was chosen as the carrier gas because standard humidity generators typically use carbondioxide free air, whose main component is nitrogen (Carroll et al. 2015;Hasegawa and Little 1977;Hyland and Wexler 1973;Scace et al. 1997). Enhancement effects were taken to be minimal (Hyland and Wexler 1973). Sample activation was to be heating over a period of 1 h to 200 °C and holding at that temperature for 3 h under vacuum with continuous pumping to a final pressure < 0.1 Pa. If the outgassing was performed in a separate manifold, exposure to air was to be minimized when transferring to the analysis port and the sample was to be reoutgassed in the instrument to 140 °C for at least 6 h to remove any adsorbed gases. The pressure range was from dry to 95% RH or P/P 0 = 0.95; twenty recommended equilibrium pressure points were provided. Measurements were to be conducted at 25 °C, which is nominally room temperature and is used in many practical applications. It was requested that a complete isotherm (with adsorption and desorption) be measured on two separate aliquots. It was recommended to perform a blank run (i.e., an isotherm in the absence of the adsorbent) to subtract from the isotherm measured with the adsorbent present (Nguyen et al. 2017). Participants were asked to submit an experimental report, which detailed their experimental procedures and data processing steps and to submit the isotherms in units of millimoles of adsorbed fluid per gram of activated carbon (mmol/g). Details of the experimental parameters and procedures employed by each of the study participants can be found in Table 1. Certain commercial items are identified in this paper. This identification does In-situ outgassing is unavailable in the instrument. Exposure to air was minimized during sample transfer to the measuring station. The sample mass was measured statically before and after the ex-situ activation with the sample cell backfilled with N 2 . (25 ± 0.1) °C 0.01 µg, n/a Yes a, a* The absolute pressure was measured by pressure transducers accurate to ± 0.05% of full scale (F.S.). P 0 at 25 °C was set to 3.17 kPa using NIST Chemistry Webbook, SRD 69, Thermophysical Properties of Fluid Systems ). Equilibrium criteria: sorption rate change less than 1.33 Pa/min (calculated over 10 equilibrium points with sampling every 60 s).

Yes b
The absolute pressure was measured by two pressure transducers (1.33 kPa and 133 kPa) with resolution of 0.01% F.S., and accuracy of 0.5% of reading. The relative pressure was determined by dividing measured absolute pressure by a fixed P 0 value of 3.17 kPa obtained from Dortmund Data Bank (DDBST). Mass equilibration criteria: dm/dt < 0.005%/min.
(25 ± 0.2) °C 0.1 µg, 0.1 µg Yes c Absolute pressure measurement with piezoresistive transducer with a 16 bit A/D converter. The P 0 was set as the vapor pressure of the sample temperature at each point using NIST REFPROP (Lemmon et al. 2018) and the equation of state from Wagner and Pruß (Wagner and Pruß 2002). The average P 0 = (3.17 ± 0.003) kPa. Mass equilibration criteria: dm/dt < 50 µg/min.
(25 ± 0.1) °C 1 µg, 3 µg Yes not imply recommendation by NIST, nor does it imply that these items are the best available for the purposes described.

Data submission
Nine pure water datasets (a*, a to i) and four RH datasets (1 to 4) were submitted. A dataset is composed of two isotherms total from two aliquots of sorbent. Each isotherm measurement consists of the adsorption branch and then the desorption branch. Dataset a* is a high-resolution version of dataset a; while both are displayed, only dataset a was used in the statistical analyses.

Dataset display
To display clearly a plot including datasets from all participants, both isotherms for each dataset were plotted. These are shown in the figures in the text. The individual plots for each dataset can be found in the Supplementary Information. The number of each dataset is random and does not correspond to the listing of authors.

Reference isotherm determination
The individual datasets (P/P 0 adsorption, P/P 0 desorption, RH adsorption, and RH desorption) were subdivided into 20 groups according to the intended relative pressure (P/ P 0 × 100) or relative humidity, to wit: 0,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95. In each of these subsets the quantity of adsorbed water was determined using either a linear regression or a simple mean function, as deemed appropriate, for the collective set of the binned data. For the P/P 0 desorption data set, the subsets for 70, 75, 80, 85, and 90 were combined and a single linear regression was fitted. This produced a smoother function in this region. An uncertainty evaluation and 95% intervals were determined for each set of binned data. The calculations were done using the R function lm() (Chambers et al. 1992). See Section S6 in Supplementary Information for equations.

Results and discussions
In total, nine pure H 2 O/BAM-P109 datasets were submitted. The as-submitted H 2 O/BAM-P109 datasets for pure water isotherms are plotted together in Fig. 1. The isotherms exhibit Type V isotherm shape (Ross et al. 2016;Thommes et al. 2015), with little uptake until P/P 0 × 100 ≈ 40, suggesting the material to be hydrophobic in nature (Ross et al. 2016). The hysteresis loop in the water vapor isotherm is attributed to different mechanisms of adsorption/cluster formation and desorption/pore emptying (Ross et al. 2016;Thommes et al. 2012;Thommes et al. 2015). Preliminary analysis of the pure water datasets identified three datasets Fig. 2 a Pure water sorption isotherms at 25 °C for BAM-P109 used to determine the reference isotherm, along with the reference isotherm itself and the 95% uncertainty intervals. The lines through the reference data solely serve to guide the eye. b Residuals (referencemeasured) for adsorption branch of isotherms. c Residuals for desorption branch of isotherms. The uncertainty associated with each data point is taken from uncertainty data in panel a. Note the difference in the scale in b and c. The legend is the same for a, b, and c. Dataset a* is a high-resolution version of dataset a. While both are displayed, only dataset a was used in the statistical analyses. See Fig. S9 for isotherms in absolute pressure Fig. 3 As-submitted water sorption isotherms at 25 °C for BAM-P109 up to 95% RH using molecular nitrogen as the carrier gas. For individual datasets, see Fig. S3 (c, g, and h) as statistical outliers (see Fig. S5). Participant c reported that condensation had occurred before the saturation pressure and, therefore, stopped measuring at 0.85 P/P 0 . Condensation at 0.85 P/P 0 suggests the employed pressure sensor of participant c requires recalibration. Datasets g and h have lower adsorbed water amounts compared to the other datasets. Participant g reported transfer in air after ex-situ activation of the sample, which could not be re-outgassed after being attached to the instrument. Participant h reported activation at vacuum levels higher than that prescribed in Fig. 4 a Water sorption isotherms at 25 °C for BAM-P109 up to 95% RH using molecular nitrogen as carrier gas used to determine the reference isotherm, along with the reference isotherm itself and 95% uncertainty interval. The lines through the reference data solely serve to guide the eye. b Residuals (reference -measured) for adsorption branch of isotherms. c Residuals for desorption branch of isotherms. The uncertainty associated with each data point is taken from uncertainty data in panel a Note the difference in the scale in b and c. The legend is the same for a, b, and c  Figure 3 shows the four RH datasets, which are relatively in good agreement, with only minor variability in the high RH region and some spread in the region of rapid uptake/release. All four RH datasets were used in the determination of the RH reference isotherm. A series of reference values was determined for P/P 0 × 100 up to 95 and RH up to 95% in intervals of 5/5%. These data are also shown in Figs. 2 and 4. Figures 2 and 4 also show the residuals of the datasets to the reference values. There is relatively good agreement at the low and high RH and P/P 0 regions, with more variability in the region of rapid uptake/release. This greater variability could potentially be attributed to uncertainties in RH, P, P 0 , T, V, and equilibrium criteria having larger effects on the adsorbed amount due to the greater uptake or release per RH or P/P 0 , i.e., larger derivative of the sorption isotherm in this area. For example, the "steeper" desorption compared to the adsorption in the region of rapid uptake/release leads to larger uncertainties in the desorption branch. The slightly larger uncertainties in the P/P 0 desorption branch throughout may be due to accumulated uncertainties, particularly in the manometric measurements. The reference isotherms for both the pure water (P/P 0 ) and the water in N 2 carrier gas (RH) measurements show closure of the hysteresis loop, as the desorption and adsorption branches are indistinguishable at the low P/P 0 and RH within the uncertainty bounds. The reference data values and the expanded uncertainties, U k=2, are given in Tables 2 and 3, for P/P 0 and RH data, respectively. The datasets and the reference isotherm Table 3 The reference isotherm for water in nitrogen/ BAM-P109 relative humidity measurements derived from the data presented in Fig. 4 (Siderius et al. 2020).
Comparing the pure water and RH reference isotherms, it can be seen that uptake is slightly higher in the pure water isotherm compared to the RH isotherm (see Fig.  S10). This observation suggests that some of the carrier gas is adsorbed in the RH measurements. A study by Fletcher et al. in which water vapor isotherms on an activated carbon material were measured under dynamic conditions using helium as the carrier gas found no significant difference in water uptake compared to that measured under static conditions (Fletcher et al. 2002).
To determine if the lower uptake for RH measurements was due to the preadsorption and competing adsorption of the N 2 carrier gas, an experiment using helium as the carrier gas was performed (dataset 5, see Fig. S11). This yielded RH results with higher uptake compared to using molecular nitrogen as the carrier gas and matches well with P/P 0 data (see Figs. 5 and S11), indicating that some nitrogen may be adsorbed when used as the carrier gas with this material. The visible effect of adsorbed nitrogen on the water uptake could be attributed to the high surface area (1396 m 2 /g) of the material, a nanoporous carbon, as well as its hydrophobic nature. The N 2 sorption isotherm on BAM-P109 at 25 °C (Fig. S12) confirmed that indeed BAM-P109 adsorbs N 2 (≈ 0.43 mmol/g) near ambient pressure (0.1 MPa). Given that the mass of the sample in the dynamic experiments is measured in N 2 flow throughout, the measured dry sample mass at RH = 0 (and throughout) includes preadsorbed N 2 . From the N 2 sorption isotherm, the sample mass in N 2 is estimated to be slightly higher than in vacuum by around up to 0.012 g/g of sample, which equates to ≈ 1.2% mass. Thus, from this study it is recommended to use helium as a carrier gas for dynamic measurements when a like-pure water vapor sorption isotherm is desired. This is a significant outcome of the study in light that the two measurements (RH and P/P 0 ) can be fundamentally different or converge depending on the choice of the carrier gas in the dynamic measurement. The choice of the carrier gas, therefore, should be reported and would depend on the application.

Conclusions and outlook
This work provides reference sorption isotherm data for H 2 O on a pelletized nanoporous carbon (BAM-P109) at 25 °C as a function of pure water vapor (P/P 0 ) and as a function of relative humidity with molecular nitrogen as the carrier gas. This work has also shown that when helium is used as the carrier gas, dynamic RH measurements match well with pure water vapor measurements. These reference isotherms should prove useful for researchers interested in working with water as well as applications where the presence of water may play a significant role in the performance of materials.