α-D-Glucose anhydrous

RH-Temperature Phase Diagrams of Hydrate Forming Deliquescent Crystalline Ingredients

Highlights
• Created RH-temperature phase diagrams of sodium sulfate, glucose, and citric acid
• Developed water activity method to measure the anhydrate-hydrate phase boundary
• Determined the peritectic temperature of sodium sulfate, glucose, and citric acid
• Anhydrates can deliquesce prior to forming hydrates at some RH-temperature conditions

Abstract
Several common deliquescent crystalline food ingredients (including glucose and citric acid) are capable of forming crystal hydrate structures. The propensity of such crystals to hydrate/dehydrate or deliquesce is dependent on the environmental temperature and relative humidity (RH). As an anhydrous crystal converts to a crystal hydrate, water molecules internalize into the crystal structure resulting in different physical properties. Deliquescence is a solid-to-solution phase transformation. RH-temperature phase diagrams of the food ingredients alpha-D-glucose and citric acid, along with sodium sulfate, were produced using established and newly developed methods. Each phase diagram included hydrate and anhydrate deliquescence boundaries, the anhydrate-hydrate phase boundary, and the peritectic temperature (above which the hydrate was no longer stable). This is the first report of RH-temperature phase diagrams of glucose and citric acid, information which is beneficial for selecting storage and processing conditions to promote or avoid hydrate formation or loss and/or deliquescence.

1. Introduction
Many food ingredients are crystalline solids, some of which are deliquescent and a subset of these are capable of forming crystalline hydrates under typical ambient conditions. Examples of deliquescent food ingredients include: salts, sugars, sugar alcohols, organic acids, and some water-soluble vitamin forms (e.g., sodium ascorbate, thiamine hydrochloride) (Mauer & Taylor, 2010). Deliquescent ingredients exhibit a first order phase transformation from a solid to a solution when a critical relative humidity at a given temperature (called the deliquescence point, or RH0) is exceeded. As temperature increases, the solubility of many deliquescent crystals also increases and their RH0s decrease (Clausius-Clapeyron relation) (Lipasek, Li, Schmidt, Taylor, & Mauer, 2013). Environments that exceed the RH0 cause undesirable physical and chemical changes in products, including caking, clumping, complete dissolution, and degradation of sensitive compounds (e.g., vitamin loss) (Hiatt, Ferruzzi, Taylor, & Mauer, 2008; Scholl & Schmidt, 2014). Storing deliquescent ingredients in environments below the deliquescence phase boundary extends shelf-life and limits interactions with water to adsorption and capillary condensation, with the potential for hydrate formation in some conditions.
Some examples of deliquescent ingredients that are also able to form crystal hydrate structures include: glucose, lactose, maltose, trehalose, citric acid, malic acid, sorbitol, and thiamine hydrochloride. A crystalline hydrate is a pseudo-polymorph that forms when the crystal lattice is altered by the internalization of water molecules, often in stoichiometric ratios (Morris & Brittain, 1999). Water molecules are stabilized in the crystal via hydrogen bonding and/or van der Waals interactions, creating different bond characteristics and unit cells within the crystal (Khankari & Grant, 1995; Liu, Chen, & Zhang, 2007; Vogt, Brum, Katrincic, Flach, Socha, Goodman, et al., 2006). These changes alter the intrinsic properties such as melting temperature, solubility, and chemical stability (Khankari & Grant, 1995; Zhu, Yuen, & Grant, 1996). There is some evidence that the RH0s of anhydrous and hydrate crystals of the same compound are different, although some measurement techniques induce crystal hydrate formation during the analysis which complicates the true measurement of the anhydrous RH0. For example, the RH0 of anhydrous citric acid measured by dynamic vapor sorption was 75%RH while that of the monohydrate was 78%RH; however, when their RH0s were determined by measuring the water activity (aw) of their saturated solutions, both RH0s were 0.78aw (Salameh, Mauer, & Taylor, 2006).
The driving forces for the transition between the anhydrate and hydrate form of a crystal are the external RH (or aw) and temperature (Vippagunta, Brittain, & Grant, 2001). As temperature and aw change, the Gibbs free energies of the hydrate and anhydrous forms shift, eventually intersecting where a conversion becomes thermodynamically favorable (Ymén, 2011). The anhydrate-hydrate phase boundary can be difficult to measure since the kinetics of hydrate formation or loss can be very slow (months to years) (Franks, 2013; Scholl & Schmidt, 2014). Even if there is a lower energy form, the activation energy of the phase change allows for metastable forms to exist, which further increases the difficulty to measure the actual anhydrate- hydrate boundary (Ymén, 2011). As temperature increases, the RH (aw) of the anhydrate-hydrate boundary increases because molecules at cooler temperatures have less molecular movement and water forms hydrogen bonds more easily with the host crystal (Krzyzaniak, Williams, & Ni, 2007). Once a boundary is crossed, there is a change of the stable state but the rate of conversion is dependent on the nature of the compound, crystal morphology, the environment, and the difference in free energy between the two states (Giron, Goldbronn, Mutz, Pfeffer, Piechon, & Schwab, 2002; Morris & Brittain, 1999; Te, Griesser, Morris, Byrn, & Stowell, 2003; Ymén, 2011). The interconversion between the anhydrate and hydrate crystal forms is typically undesirable. In the case of dehydration, the expelled water from the hydrate could interact with other ingredients and, depending on the formulation, may promote glass transition temperature lowering in amorphous solids, recrystallization of amorphous solids, increased degradation of labile ingredients, deliquescence, and/or powder clumping (Bell, 2008; Hiatt, Ferruzzi, Taylor, & Mauer, 2008; Karel, Anglea, Buera, Karmas, Levi, & Roos, 1994; Mauer & Taylor, 2010; Stoklosa, Lipasek, Taylor, & Mauer, 2012). The conversion of an anhydrous crystal to a hydrate structure lowers solubility, can cause clumping, increases shipping weight, alters solids content in formulations prepared by weight, and affects bioactivity (Pudipeddi & Serajuddin, 2005; Scholl & Schmidt, 2014). However, there may be situations wherein the internalization of water during hydrate formation could have advantageous moisture ‘scavenging’ effects.
To maintain the desired form of a deliquescent compound capable of forming hydrates, it is important to control storage environments. Storage conditions can be selected after establishing RH-temperature phase diagrams that document the thermodynamically stable form at a given RH and temperature. These phase diagrams contain three boundaries (1-anhydrate-hydrate transition, 2- hydrate deliquescence, 3- anhydrate deliquescence) that intersect at the peritectic point (Figure 1). Above the peritectic temperature, the hydrate is no longer thermodynamically stable because the vibrational energy of water is too great to be stabilized in the crystal structure (Griesser, 2006; Lafontaine, Sanselme, Cartigny, Cardinael, & Coquerel, 2013), and the RH0 boundary shifts from the hydrate to the anhydrous RH0 (Figure 1). This shift can also be observed in solubility curves, where below the peritectic temperature the solubility is of the hydrate form (less soluble, greater ∆Hs), and above the peritectic temperature the solubility is of the anhydrous form (more soluble, lower ∆Hs) (Khankari & Grant, 1995; Lafontaine, Sanselme, Cartigny, Cardinael, & Coquerel, 2013; Young, 1957). Other methods of determining the peritectic point have included x-ray diffraction, NMR, or IR spectroscopy by monitoring the peak shifts with RH and temperature (Krzyzaniak, Williams, & Ni, 2007; Lafontaine, Sanselme, Cartigny, Cardinael, & Coquerel, 2013; Linnow, Zeunert, & Steiger, 2006; Liu, Chen, & Zhang, 2007).
An RH-temperature phase diagram of a hydrate forming deliquescent crystal was established for sodium sulfate by Linnow, Zeunert, and Steiger (2006) using a novel RH-XRD method to map the stable sodium sulfate forms in ambient RH-temperature conditions. This study served as inspiration for our objective: to generate RH-temperature phase diagrams of hydrate forming deliquescent food ingredients (alpha-D glucose and citric acid).

2. Materials and methods

2.1 Materials
All compounds were reagent grade and stored in RH-controlled conditions in desiccators at ambient temperature to maintain the desired crystal states. Anhydrous glucose, glucose monohydrate, anhydrous sodium sulfate, sodium sulfate decahydrate, and citric acid monohydrate were purchased from Sigma-Aldrich Chemical Co. (St. Louis, MO) and anhydrous citric acid was purchased from J.T. Baker (Center Valley, PA). Salts used to control RH in desiccators were: lithium chloride (LiCl, 11%RH), magnesium nitrate (MgNO3, 54%RH), sodium bromide (NaBr, 58%RH), potassium iodide (KI, 69%RH), sodium chloride (NaCl, 75% RH), and potassium chloride (KCl, 84% RH) (the RHs reported are taken from Greenspan (1977) at 25˚C). All salts were obtained from Sigma-Aldrich (St. Louis, MO) except LiCl (EMD Millipore, Darmstadt, Germany) and KCl (Mallinckrodt Chemicals, Phillipsburg, NJ). The hydrate sample forms were stored at an RH just below the hydrate RH0 at 25°C to ensure all crystals maintained the hydrate state: glucose monohydrate and sodium sulfate decahydrate were stored at 84%RH and citric acid monohydrate was stored at 75%RH. The anhydrous samples were vacuum dried overnight at 60˚C and 50-10kPa to dehydrate any hydrate crystals that might have been present then stored over indicating anhydrous calcium sulfate (0%RH, Drierite™ with a vial containing LiCl crystals as a secondary desiccant. The water used in this study was processed using reverse osmosis then filtered by a Barnstead E-Pure Lab Water System (Dubuque, IA) to >17.4 milliohm-cm, and 100% ethanol was purchased from Koptec (King of Prussia, PA).

2.2 Dynamic vapor sorption (DVS) profiles
Dynamic vapor sorption profiles were collected using the SPSx-1µ by ProUmid GmbH & Co. KG (Ulm, Germany). Approximately 0.5g of each crystal form was weighed into an 18mm aluminum pan and placed onto a 23 sample holder. The RH conditions of the sorption profiles began several RHs below previously reported anhydrate-hydrate phase boundaries and ended above the hydrate RH0, generally ranging from 70-95% RH. The RH step size was 1%RH and equilibrium conditions were set as 0.01% weight change between measurements (15 min) or a maximum of 3hrs at each RH. Sorption profiles were collected from 15-50°C in 5°C increments. For each sample, data collection ended when >200% weight change occurred, likely caused by extensive deliquescence.

2.3 Deliquescence boundary measurements
Two approaches were used for determining the deliquescence (RH0) boundaries for the anhydrous and hydrate crystals. The first was applicable to all crystal forms across all temperatures: the DVS profiles as described above, where the RH0 was the RH at which a sharp upward inflection of the moisture uptake occurred (Mauer & Taylor, 2010). The DVS profiles were particularly helpful in determining the anhydrous crystal RH0 below the peritectic temperature. The second approach utilized aw measurements of saturated solutions to determine the RH0, primarily for hydrate crystals below the peritectic temperature and anhydrate crystals above the peritectic temperature, using a Decagon Devices AquaLab 4TE (Pullman, WA) (Allan & Mauer, 2016). Slurries were prepared in Decagon Devices aw cups (2g hydrate+200µL water, or 2g anhydrate+600µL water except for anhydrous sodium sulfate, where only 1g was used), capped, and stored in incubators at 20, 25, 30, 35, 40, 45, and 50℃ for 24 to 48hrs before aw measurements. A greater water-to-solid ratio was used for anhydrous forms to account for the internalization of water that may take place during equilibration at temperatures below the peritectic temperature. After equilibration, the initial aw measurement was taken at the incubation temperature, then the temperature on the AquaLab 4TE was adjusted +1˚C. The final aw at each condition was documented as the aw reading after the instrument had 5 consecutive measurements with <0.001aw variation. Equilibration at each new temperature required 30min to several hrs. This was repeated for another +1˚C increment and continued until the sample was +5˚C above the incubation temperature. The aw measurements above 50˚C were achieved by turning off the AquaLab 4TE temperature control and placing the instrument in an incubator set at 50-55˚C. To avoid damage to the device, measurements were not performed above 56℃ per manufacturer recommendations. All samples were produced and analyzed in at least duplicate. 2.3 Anhydrate-hydrate boundary measurements A modified aw measurement technique was developed to identify the anhydrate-hydrate boundary, wherein aw-controlled solutions of alcohol and water were prepared, crystals were introduced and equilibrated, and the equilibrium aw was measured. The method was adapted from Grant and others (Zhu, Khankari, Padden, Munson, Gleason, & Grant, 1996; Zhu, Yuen, & Grant, 1996) who produced a series of water-organic solvent solutions with a range of aws then equilibrated hydrate forming crystals in the solutions and observed the crystal packing structure. If the crystal structure changed, it was not stable at that starting aw, while if it did not change it was stable at that aw. Our aw measurements in the presence of volatiles were performed using the Tunable Diode Laser aw measurement device (TDL, Decagon Devices) operating with the software version S4TDL-R2-12 (Decagon Devices, 2015). Following preliminary trials using methanol, ethanol, propanol, butanol, and isopropanol as cosolvents to adjust the solution aw, we selected ethanol:water solvents for further studies. The ethanol did not form solvates with the compounds under ambient conditions, and small changes in water:ethanol ratios resulted in substantial changes in aw, important for tracking hydrate formation or loss. Ethanol:water solutions were mixed at 99:1-90:10 in 1% volumetric increments and from 90:10-10:90 in 5% volumetric ratios, then equilibrated overnight before aw measurement. These aws were plotted to generate a standard curve using Microsoft Excel 2016 (Redmond, WA), which fit well to polynomial equations (R2>0.997) with respect to the initial volumetric ratio and molar ratio (Fig. 1-3 in reference Allan and Mauer (submitted for publication)). Equation 1 was used for aw-controlled solutions below 0.75aw, and for solutions above 0.75aw equation 2 was used:
The aw-controlled solutions serve a similar purpose as desiccators for controlling environmental RH, with the advantages that solution-mediated hydrate formation kinetics exceed vapor-mediated changes and water entering or leaving the crystal alters the aw of the closed system. A conversion continued until either there was no more substrate to convert and all of the solid was in the stable form, or the aw was at the phase boundary and both the hydrate and anhydrous forms were stable (Equation 3) (Grant & Higuchi, 1990): A(solid) + mH2O ⇋ A ∙ mH2O(solid) (3) where A (solid) is the anhydrous form, mH2O is the moles of water, and the A∙mH2O(solid) is the hydrate. If this equilibrium is achieved where both forms are stable, the aw of the solution is the anhydrate-hydrate boundary at the given temperature. The anhydrate-hydrate phase boundaries were determined by mixing the anhydrous and hydrate crystal forms in a range of aw-controlled ethanol:water solutions and measuring the changes in the aw using the TDL and crystal packing structure by x-ray diffraction (PXRD). The boundaries were determined for each compound in 5˚C increments from 20˚C to the temperature just below the peritectic temperature: 32.4˚C for sodium sulfate (Okorafor, 1999), 54.7˚C for glucose (Young, 1957), and 37˚C for citric acid (Lafontaine, Sanselme, Cartigny, Cardinael, & Coquerel, 2013). Slurries were made by weighing 2.5g of each crystal form into a aw cup, to which 1.5mL (or 0.75mL for citric acid) of aw-controlled ethanol:water solution and a 2.5cm magnetic stir bar were added, and then each cup was capped and sealed with Parafilm™. Each crystal form was combined with a minimum of 5 different aw solutions in 0.05aw increments. For example, anhydrous glucose was mixed with 0.50, 0.55, 0.60, 0.65, 0.70, and 0.75aw solutions. Samples were placed onto a Variomag 15 multipoint stirrer (Daytona Beach, FL) and continuously stirred at 100-150RPM in the desired equilibration temperature chambers for 3-7 days. After equilibration, the endpoint aw was measured using the TDL set at the incubation temperature with the criteria of 2 consecutive measurements within 0.001aw of each other. The anhydrate-hydrate boundary at a specific temperature was determined by plotting the endpoint aws against the initial aws (as shown in Figure 4A). When slurries prepared at multiple starting aws equilibrated to a similar endpoint aw, the common endpoint aw was estimated to be the anhydrate-hydrate boundary point for that temperature, with further confirmation by X-ray diffraction analysis. After measuring the aw, the crystal packing structure was determined using powder X-ray diffraction (PXRD) by a Shimadzu LabX XRD-600 diffractometer (Kratos Analytical, Chestnut, NY) with a Bragg-Brentano configuration. The crystals were loaded into an aluminum sample holder with an inner diameter of 1cm and 0.5mm depth and immediately scanned from 10-40 2Θ at a continuous scan rate of 8 degrees/minute (a fast scan rate to minimize potential anhydrate-hydrate conversion that might occur at ambient conditions). The presence of both anhydrous and hydrate patterns found in PXRD diffractograms was used to confirm the anhydrate-hydrate boundary results using the TDL (e.g. Figure 4B compared to Figure 4A). Samples were prepared and analyzed in at least duplicate in all experimental conditions.

2.4 Vapor sorption techniques for the anhydrate-hydrate phase boundary
Following identification of the anhydrate-hydrate phase boundary aw at 25°C using the approach described above, anhydrous and hydrate crystal samples were placed into desiccators controlled at RHs above and below the boundary aw, and weight changes were monitored.
Samples (≈1g) were weighted into 5cm aluminum weigh pans in triplicates and stored in square 12.7cm Lock & Lock™ containers containing ≈150mL of a saturated salt solution. Sodium sulfate crystals were stored at 84%RH (KCl) and 75%RH (NaCl), glucose crystals were stored at 69%RH (KI) and 58%RH (NaBr), and citric acid crystals were stored at 69%RH (KI) and 53%RH (MgNO3). All samples were stored in a temperature controlled room at 25˚C and undisturbed except for measurements after 66 days and 195 days. An attempt to determine the anhydrate-hydrate phase boundary was also made by analyzing the DVS profiles using 3hr and 6hr equilibration periods per 1%RH step. The change in the slope of the first derivative of weight change in respect to RH was used to identify the RH where the onset of moisture uptake began to possibly identify this boundary.

2.5 Polarized light microscopy
An Omano polarizing light microscope with a λ filter (Omano, China) and a GenRH-A RH controlled microscope stage (Surface Measurement Systems Ltd., London UK) were used to observe the effects of RH on the anhydrate and hydrate crystals. Time-lapse photography was performed using Lapse It Pro software (Interactive Universe) on an Apple iPhone 6S (Cupertino, CA) attached to the microscope by an iDu LabCam Microscope Adapter (iDu Optics, New York, NY).

2.6 Graphing the RH-temperature phase diagrams
All boundary data were plotted and the polynomial equations used for peritectic temperature extrapolation were generated using Microsoft Excel 16 (Redmond, WA). The standard deviations between at least two RH0 measurements at each temperature are shown as error bars on the RH0 boundaries in the phase diagrams. The error bars for data generated using DVS measurements (DVS anhydrous RH0, Figures 3A and 5A) were calculated for each compound and temperature as the difference between the SPS measured hydrate RH0 (the SPS RH probe was calibrated only at 25°C) and the saturated solution aw measured by the Aqualab 4TE (which was verified/calibrated at different temperatures). The anhydrate-hydrate data points plotted on the phase diagrams are the averages of the endpoint aws for samples equilibrated at the same temperatures, with the standard deviation shown as the error bars. For most data points in the phase diagrams, the error bars are smaller than the data points and cannot be seen. Wolfram Alpha (wolframalpha.com) was used to calculate the peritectic temperature by the intersection of the RH0 boundaries and to calculate predicted RH0s using the polynomial equations generated form the thermodynamically stable RH0s. The phase diagram illustration (Figure 1) was drawn using Inkscape 0.91 (open source), and Figure 4B (the stacked PXRD diffractograms) was made using Origin Pro 8.6 (OriginLab, Northampton, MA). Data were extracted from the sodium sulfate RH temperature phase diagram by Linnow et al. (2006) using WebPlotDigitizer (version 3.8) and overlaid with our data in Figure 2A.

3. Results and discussion

3.1 The sodium sulfate RH-temperature phase diagram
The RH-temperature phase diagram of sodium sulfate published by Linnow et al. (2006) was used as the starting comparison point for our approaches to generate phase diagrams. To dissect the different phase boundaries, comparisons between our results (Figure 2A) and those of Linnow et al. (2006) will be broken down into the hydrate RH0, the anhydrate RH0 above the peritectic temperature, the anhydrate RH0 below the peritectic temperature, and the anhydrate- hydrate phase boundary. The hydrate RH0 boundary of sodium sulfate decahydrate decreased with increasing temperature, as measured by both DVS and aw techniques. This was also observed by others measuring the RH0 of sodium sulfate using RH controlled chambers (Linnow, Zeunert, & Steiger, 2006) and the aw of saturated solutions (Lipasek, Li, Schmidt, Taylor, & Mauer, 2013). The RH0 of the hydrate followed a clear trend line from 15 to 33˚C where it intersects with the anhydrous RH0 boundary. This intersection occurs at the peritectic temperature, above which the hydrate will dehydrate to the anhydrous form (Lafontaine, Sanselme, Cartigny, Cardinael, & Coquerel, 2013). Sodium sulfate converted relatively rapidly (minutes-hours) to the anhydrous form above the peritectic temperature. When the temperature was increased to above the peritectic temperature in a aw meter, there was an immediate endothermic response in the saturated decahydrate solution as it was releasing water from the hydrate structure to such an extent that the aw meter temperature did not exceed the peritectic temperature until a full conversion to the anhydrous form took place. The peritectic temperature of sodium sulfate in our study was determined to be 32.9˚C by extrapolating the polynomial trend lines of the deliquescence boundaries. This is comparable to the previously reported peritectic temperature of 32.4˚C (Okorafor, 1999; Van Hook, 1961; von Plessen, 2012).
Above the peritectic temperature, the anhydrous RH0 is the boundary of interest which can be measured by either aw or DVS techniques at these temperatures. The anhydrous RH0 boundary has a different slope than the hydrate RH0 (Figure 2A) because of the differences in heat of solution and solubility between the forms. Solubility differences affect the RH0 and the heat of solution influences the change in RH0 in response to temperature (Lipasek, Li, Schmidt, Taylor, & Mauer, 2013; Nicklasson & Nyqvist, 1983). Many deliquescent compounds have positive heats of solution (including the anhydrous and hydrate forms of glucose and citric acid) and their RH0s decrease with increasing temperature. Sodium sulfate is a unique example where the anhydrous form has a negative heat of solution (exothermic) and the RH0 increases as the temperature increases (Lipasek, Li, Schmidt, Taylor, & Mauer, 2013), while the hydrate form has a positive heat of solution (endothermic) and exhibits decreasing RH0 with increasing temperature. The anhydrous RH0 boundary in the phase diagram from Linnow et al. (2006) also increases with temperature, agreeing with the results from our aw measurements.
Below the peritectic temperature, the anhydrous RH0 is still of interest due to the kinetics of the different phase changes even though the anhydrate-hydrate boundary is exceeded. If anhydrous sodium sulfate is exposed to an RH above its RH0 at temperatures below the peritectic temperature, the kinetics of deliquescence can exceed those of hydrate formation. Xu and Schweiger (1999) observed anhydrous sodium sulfate deliquescence precede crystalline hydrate formation, but were unable to measure the anhydrous RH0 using single particle RH controlled in- situ Raman spectroscopy because hydrate formation occurred too quickly (Xu & Schweiger, 1999). Linnow et al. (2006) reported the anhydrous RH0 boundary below the peritectic temperature using calculated RH0s, but were also unable to experimentally measure these RH0s. Unfortunately, in our study, neither the DVS profiles nor the measurement of saturated solutions aws were able to accurately measure the RH0 of anhydrous sodium sulfate below the peritectic temperature, also due to the rapid hydrate formation kinetics. Our calculated anhydrous RH0 boundary below the peritectic temperature, based on regression of the anhydrous RH0 boundary above the peritectic temperature, was similar to that of Linnow et al. (Figure 2A). Although difficult to measure, this boundary is still important because anhydrous sodium sulfate can deliquesce when the RH is not slowly ramped. For example, when the RH was quickly increased to 95%RH at 22˚C (near the hydrate RH0), anhydrous crystals appear to deliquesce while the hydrate crystals remain essentially unchanged (Video S1).
The anhydrate-hydrate boundary of sodium sulfate determined using our aw-controlled solution approach was also similar to the boundary reported by Linnow et al. (2006): at 25˚C ours was 81.2%RH (Figure S1A), and theirs was 82-83%RH. Additionally, in the DVS profile of sodium sulfate decahydrate from 70-95%RH at 25˚C (Figure S1B), the sample lost weight until 79-81%RH (the 1st derivative reached 0). Above this RH range, the partially dehydrated sodium sulfate began to sorb moisture (hydrate formation). The behavior of not losing or gaining weight at RHs around the boundary predicted by the TDL helps validate the accuracy of this method for determining the hydrate-anhydrate boundary. The anhydrate-hydrate boundary measured by the aw-controlled method was the same when using either the anhydrate (81.8%RH±0.7%RH at 25˚C) or the hydrate (81.2%RH±1.7%RH at 25˚C) sodium sulfate form. This suggests it is possible to start with either the anhydrous or the hydrate crystal form to determine the anhydrate- hydrate phase boundary using the aw-controlled method. The boundary should be the same despite if the hydrate is dehydrating or the anhydrous form is hydrating (Equation 3), however, the kinetics of conversion can vary greatly between the two (Morris & Brittain, 1999).
The rate of anhydrate-to-hydrate conversion can also vary greatly between compounds, and between solution and vapor mediated environments. For sodium sulfate, the hydration kinetics of the anhydrous form are relatively fast, and the moisture uptake is substantial enough to be quantifiable using moisture sorption techniques. In the DVS profile at 84%RH (25˚C) (Figure 2B), which was 3% RH above its anhydrate-hydrate boundary (81.2%RH) and below its anhydrous RH0 boundary (~86%RH), anhydrous sodium sulfate exhibited 0.16±0.04%wt change per hour. Assuming this constant rate, it would take around 33 days for a full anhydrous to decahydrate conversion. This is relatively fast in comparison to the conversion of glucose in a desiccator at 25˚C and 2%RH above its anhydrate-hydrate phase boundary, where there was only a 5% conversion of the anhydrous glucose to the monohydrate after 1 year (Scholl & Schmidt, 2014). However, after 6 months in an 84%RH desiccator (25˚C), anhydrous sodium sulfate did not gain weight indicative of hydration, and the decahydrate did not lose mass indicative of dehydration at 84%RH but did dehydrate at 75%RH (Figures S1A and S1B). The lack of hydrate formation could be due to the passive moisture migration, a downfall to desiccator studies, and is a compounding factor for the slow kinetics associated with anhydrate- hydrate phase boundary measurements. This underscores the usefulness of the aw-controlled method for determining the anhydrate-hydrate boundary in a reasonable timeframe (days).
In summary, the approaches used in our study generated an RH-temperature phase diagram of sodium sulfate that was quite similar to that published by Linnow et al. (2006) using different techniques (Figure 2A). By applying DVS, aw, and aw-controlled ethanol:water solutions where relevant, it was possible to generate a complete RH-temperature phase diagram of sodium sulfate and accurately identify the peritectic temperature. We then proceeded to generate RH-temperature phase diagrams for glucose and citric acid.

3.2 The glucose RH-temperature phase diagram
To our knowledge, Figure 3A is the first reported comprehensive RH-temperature phase diagram of glucose that includes both hydrate and anhydrate RH0 boundaries and the anhydrate- hydrate phase boundary. Our peritectic temperature was 54.4˚C, and previously reported peritectic temperatures bracketed this temperature: 54.7˚C (Young, 1957), 50˚C (Goldberg & Tewari, 1989), and 52˚C (Van Hook, 1961). These studies used solubility data to determine the peritectic temperature, while ours used the intersection of the RH0 boundaries. The hydrate RH0 boundary was determined using aw measurements, and the anhydrate RH0 boundary below the peritectic temperature was determined using the DVS method. The anhydrate RH0 boundary could not be measured using the aw of the saturated solution because anhydrous glucose converted to the monohydrate during equilibration, and no measurements could be taken above the peritectic temperature due to the temperature operation limits of the aw device. Instead, the anhydrous RH0 above the peritectic temperature was extrapolated from its DVS measurements taken below the peritectic temperature. The hydrate RH0 boundary produced in this study was similar to the monohydrate RH0s reported by Scholl and Schmidt (2014) at 15, 25, and 35˚C.
The RH0 of anhydrous glucose was identified as the onset of substantial moisture uptake in its DVS moisture sorption profiles (Figures 3B and 3C). These data points are identified as the anhydrous RH0 and not hydrate formation because the initial moisture sorption kinetics resemble deliquescence, the weight change exceeds the stoichiometric hydrate ratio (10% w/w) while below the hydrate’s RH0, and microscopy observation shows the anhydrous form can deliquesce before forming a hydrate (Video S2). The slower vapor-mediated kinetics of hydrate formation compared to solution-mediated kinetics enable identification of the anhydrate RH0 using DVS techniques in conditions wherein deliquescence kinetics exceed hydrate formation kinetics. In the study by Scholl and Schmidt (2014), they attributed this onset of moisture uptake and the additional moisture content above 10%db to adsorption, capillary condensation, or the onset of hydrate formation. However, the additional 1.3% and 4.2% weight change above the monohydrate stoichiometric ratio at 25 and 30˚C (Figures 3B and 3C), respectively, is much greater than expected from adsorption or capillary condensation (often <0.1% weight change) (Stoklosa, Lipasek, Taylor, & Mauer, 2012). The onset of moisture uptake can appear to be initiated by hydrate formation because there is no visual evidence of deliquescence on a macroscopic scale and hydrate formation quickly follows deliquescence, especially near ambient temperatures. In the moisture sorption profiles at 15, 20, and 25˚C, there was a monohydrate recrystallization event taking place several RHs above the anhydrous RH0 as the moisture sorption kinetics began to slow to the point the slope approached 0 (Figures S2A, S2B, and 3B, respectively). When recrystallization is taking place, a ternary system with two crystal forms and water is present, and the moisture sorption kinetics no longer follow the kinetics of deliquescence. As the temperature increases, anhydrous deliquescence kinetics further exceed hydrate formation kinetics indicated by the additional percent weight change above the monohydrate stoichiometric ratio (e.g. 30˚C, Figure 3C). The measured RH0 of the anhydrous glucose at 25˚C was 81%RH and, to our knowledge, this is the first accurately reported RH0 of anhydrous glucose. Previous studies have incorrectly labeled the monohydrate’s RH0 as the anhydrous RH0 because the experiments started with the anhydrous form which converted to the hydrate form during analysis (Peng, Chow, & Chan, 2001; Rüegg & Blanc, 1981; Salameh, Mauer, & Taylor, 2006; Scholl & Schmidt, 2014). If water is added to anhydrous crystals, such as when forming saturated solutions for later aw measurements, the crystals can convert to the monohydrate form and the results are no longer accurate for the anhydrous form. For example, Salameh, Mauer, and Taylor (2006) reported the RH0 of anhydrous glucose at 25˚C to be the same as that of the monohydrate determined by aw measurement (0.90aw). Because the solubility of anhydrous glucose (60.7wt% at 20˚C) is higher than that of glucose monohydrate (47.3wt.% at 20˚C) (Young, 1957), the anhydrate RH0 (81%RH) is expected to be lower than that of the monohydrate (89%RH) as seen for the sodium sulfate (Nicklasson & Nyqvist, 1983). The glucose anhydrate-hydrate phase boundary is impractical to determine using moisture sorption profiles because the vapor-mediated kinetics of hydrate formation are extremely slow. The year-long desiccator study by Scholl and Schmidt (2014) determined that the anhydrate-hydrate phase boundary of glucose at 25˚C was between 58%RH and 64%RH, and only 5% of the anhydrous form had converted to the monohydrate at 64%RH. In our study, only 3.3% of anhydrous glucose converted to the monohydrate at 69%RH (25˚C) after 195 days (Figures S1C). Due to these slow kinetics, the DVS profiles could not (practically) measure the anhydrate-hydrate phase boundary. Using our aw-controlled solution mediated equilibration method, the phase boundary for glucose was determined to be 62.4±0.3%RH at 25˚C (within the range reported by Scholl and Schmidt (2014)), and additional data points were collected from 20˚C up to 50˚C. The samples starting with anhydrous glucose converted partially to the monohydrate form when the initial aw was above the phase boundary. As the anhydrous crystal hydrated, water moved into the crystal which lowered the measured aw and the hydrate formation continued until the aw was at the anhydrate-hydrate phase boundary. At this boundary, both the anhydrate and hydrate are stable (Equation 3). At 25˚C, anhydrous glucose crystals added to multiple starting aw solutions equilibrated to endpoints of 0.62aw (Figure 4A), and the initial 0.75 and 0.70aw slurries had PXRD measurable amounts of both anhydrate and hydrate forms (Figure 4B). The leveling off of the aw (Figure 4A) suggests the anhydrate-hydrate boundary is at 0.62aw, which was confirmed by the PXRD diffractograms. Slurries starting with glucose monohydrate did not dehydrate within the timeframe of the experiment. In a RH controlled environment, glucose monohydrate also did not dehydrate after 195 days at 58%RH, 25˚C (Figure S2D). Scholl and Schmidt (2014) found similar resilience of the monohydrate where there was no sign of dehydration except at 11%RH. The monohydrate is likely able to remain in a metastable state until there is a great enough driving force or energy to liberate the water from the crystalline structure. It is common for carbohydrate crystalline hydrates to not dehydrate as easily as the anhydrates will form hydrates (Franks, 2013). With the assumption that glucose anhydrate and monohydrate have the same thermodynamic anhydrate-hydrate phase boundary but different rates of transformation, only the data starting with anhydrous glucose were used to generate the anhydrate-hydrate boundary for glucose shown in Figure 3A. 3.3 The citric acid RH-temperature phase diagram The phase diagram of citric acid (Figure 5A) is also the first to our knowledge that includes both the anhydrate-hydrate phase boundary and anhydrous RH0 boundary. The citric acid monohydrate RH0 boundary decreased with temperature until it intersected with the anhydrous RH0 boundary at 36.3˚C and 71.4%RH. This peritectic temperature (36.3˚C) falls within the range of previously reported peritectic temperatures (36-38˚C) (Dalman, 1937; Lafontaine, Sanselme, Cartigny, Cardinael, & Coquerel, 2013). Unlike hydrate forms of sodium sulfate and glucose, citric acid monohydrate exhibited greater metastability above the peritectic temperature to such an extent that the aw of the hydrate saturated solution could be measured above the peritectic temperature (the crystals did not rapidly dehydrate) and followed the same slope as the hydrate RH0 boundary below the peritectic temperature. However, these metastable RH0s were not used for extrapolating the peritectic temperature. Anhydrous citric acid was also quite metastable, which facilitated measurements of the anhydrous RH0 boundary below the peritectic temperature using both DVS and saturated aw measurements. Salameh et al. (2006) measured both the anhydrate and hydrate citric acid RH0s at 25˚C using the saturated aw method, finding the anhydrate and hydrate RH0s at 75 and 78%RH, while in this study they were measured at 75.1 and 78.1%RH, respectively. The metastable anhydrous RH0 determined by the aw measurement at 25˚C (Figure 5A), is close to the RH0 measured by DVS at 74%RH (Figure 5B) and the RH0 calculated by regressing the anhydrate RH0 boundary from above the peritectic temperature (74.4%RH). The metastability of citric acid in the experimental conditions might be attributed to its low peritectic temperature and slow crystallization kinetics. The citric acid anhydrate-hydrate boundary measured using the aw-controlled technique in this study was 60.3±0.1%RH at 25˚C. In the citric acid study by Lafontaine and others (2013) the RH determined to be the boundary where the anhydrous and monohydrate forms and water vapor are in equilibrium was 73.4%RH at 25˚C (Lafontaine, Sanselme, Cartigny, Cardinael, & Coquerel, 2013). Based on the anhydrous RH0 determined by both DVS and aw measurements (74-75% RH at 25˚C), it is likely that Lafontaine et al. (2013) inadvertently reported anhydrous citric acid deliquescence instead of hydrate formation. The slow hydrate formation kinetics just above the boundary are difficult to quantitate using traditional DVS methods, which often surpass the boundary RH without substantial weight change based on the relatively short length (hours-days) of the programmed RH steps. In a longer desiccator study, anhydrous citric acid stored at 69%RH, 25˚C, had a 4% conversion (0.35% weight change) from the anhydrate to the hydrate form after 195 days, while citric acid monohydrate stored at 53%RH had around a 2% conversion (-0.14% weight change) to the anhydrate (Figures S1E and S1F). The very slow hydration of the anhydrate at 69%RH and the slow dehydration of the hydrate at 53%RH indicate that the boundary falls between these RHs, and thus the 60%RH boundary determined by the aw-controlled technique is feasible. Since the rate of hydrate formation is slow below the anhydrous RH0, in a DVS profile the RH typically continues to increase beyond the anhydrate-hydrate boundary without measurable moisture uptake until it exceeds the anhydrous RH0 (e.g. Figure 5B). Above this RH, deliquescence takes place but the solution on the surface of the crystal exceeds the solubility of the stable monohydrate form and causes the solution to quickly crystallize. Deliquescence of the anhydrous form expedites the conversion of the anhydrous form to the hydrate by breaking the bonds necessary for hydrate formation through dissolution, which can appear as the anhydrate- hydrate phase boundary. In a moisture sorption profile of anhydrous citric acid at 25˚C (Figure 5B), the onset of moisture uptake begins at the anhydrous RH0 and the first derivative continues to increase until 77%RH where there is drop in the sorption kinetics. At 30˚C, the 1st derivative of sorption kinetics continues to increase above the monohydrate RH0 but there is a shift in the 1st order deliquescence phase transformation around 74%RH (Figure 5C). The moisture sorption kinetics slow several RH above the anhydrous RH0 because the solution is supersaturated in respect to the solubility of the hydrate form and crystallization of the monohydrate is occurring. When both the monohydrate and anhydrous forms of citric acid were exposed to 78%RH, 22˚C (Video S3), the anhydrous form fully deliquesced and the monohydrate remained visibly unchanged. The monohydrate did not deliquesce because 78%RH is below the monohydrate RH0 at 22˚C (80%RH), and the anhydrous citric acid deliquesced because the anhydrous RH0 is 74%RH and the rate of deliquescence exceeded the monohydrate crystallization. 4. Conclusions It was possible to establish RH-temperature phase diagrams of sodium sulfate, glucose, and citric acid using a combination of temperature-controlled DVS profiles, saturated solution aw measurements, and water:ethanol aw-controlled TDL aw measurements. Deliquescent hydrate forming compounds that exhibit only one hydrate form have three thermodynamically important boundaries in RH temperature phase diagrams: the anhydrate-hydrate boundary, the hydrate RH0 boundary below the peritectic temperature, and the anhydrate RH0 boundary above the peritectic temperature. These three boundaries intersect at the peritectic temperature, above which the hydrate form is no longer stable. There is a fourth boundary of interest to some situations: the anhydrate RH0 below the peritectic temperature. Hydrate formation kinetics depend on the compound, but generally are very slow between the anhydrate-hydrate boundary and the anhydrous RH0. 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