Direct Measurements of the Deliquescence Relative Humidity in Salt Mixtures Including the Contribution from Metastable Phases

Abstract

Accelerated salt-induced deterioration occurs by frequent changes across the equilibrium relative humidity (RH_eq). Therefore, knowledge of the actual RH_eq of a salt mixture has a major impact on preventive conservation to ensure that the relative humidity (RH) does not cause a salt-phase transition. In addition, knowledge of the RH_eq is essential in relation to in situ desalination as the dissolution of salt is an essential criterion to enable transport of salt (ions) in materials. For decades, it has been possible to determine the RH_eq in salt mixtures with thermodynamic-based ECOS-Runsalt software. However, the ECOS-Runsalt model is challenged by the influence of kinetics along with some limitations in regard to possible ion types and combinations. A dynamic vapor sorption (DVS) instrument is used for the direct measurement of RH_eq and to deduce knowledge on the physicochemical nonequilibrium process related to the phase changes in salt mixtures. The experimentally measured RH_eq values in this study of NaCl–Na₂SO₄–NaNO₃, NaNO₃–Na₂SO₄, NaCl–NaNO₃, NaCl–Na₂SO₄, and (NH₄)₂SO₄–Na₂SO₄ are in agreement with values from the literature. A comparison with thermodynamically calculated results makes it probable that the phase transition for some salts is significantly influenced by nonequilibrium conditions. The present work bridges some of the existing gaps in regard to improving the accuracy of ECOS-Runsalt, including the effects of kinetics and the possible ions and combinations that may be found in situ. The proposed method makes it possible to determine a more representative RH_eq in relation to real conditions for the improved treatment of salt-infected constructs.

Introduction

Natural changes in climatic conditions as a consequence of seasonal changes may promote the transport of salts (ions), and result in damaging salt-phase changes.¹⁻³ Even timely limited climatic changes (a few hours) may result in salt-phase transitions.⁴ These salt-phase changes may be avoided or reduced by preventive conservation, such as predicting the equilibrium relative humidity (RH_eq) and following the establishment of favorable climatic conditions.^1,5−7 A few examples from praxis, where favorable climatic conditions have been established in terms of climatic chambers to reduce salt-induced wall painting deterioration, can be observed in the Scrovegni Chapel in Padua, Italy, and the Kirkerup, Magleby, Rørby, and Sorø Monastary churches in Denmark.

In regard to in situ desalination campaigns, the supply of water has, in many cases, resulted in the redistribution of salt ions and their penetration to various depths,⁸ e.g., ref (9) is related to the fundamental limitation of this dissolution methodology, which prevented the desired desalination effect. Therefore, for desalination campaigns, knowledge of the RH_eq to ensure the dissolution of salts with the lowest possible water supply is desirable.¹⁰

For single salts, the RH_eq is and has been well defined for decades.¹¹ An example of direct measurements of the RH_eq for a single salt is outlined in ref (12). Here, the RH_eq of the single salt NaCl is determined with X-ray diffraction under controlled conditions of temperature and relative humidity-X-ray diffraction (RH-XRD), and the disappearance of the respective educt phase peaks in the XRD patterns is used as a criterion for the determination of RH_eq along with the reaction time until RH_eq.

Regarding salt mixtures, some RH_eq values are available in the literature, e.g., given in ref (13), and most two- and three-component salt mixtures can be thermodynamically calculated.^6,13−17 However, due to the current comprehensive possibilities, not all combinations are available in the literature. Salt mixtures typically found in historic buildings are even more complex and are not limited to three-component salt mixtures.^1,18 In the conservation science community, thermodynamically based software ECOS-Runsalt^19,20 is becoming increasingly popular to predict the RH_eq of very complex salt mixtures based on measured ionic compositions (in mole or weight) from extracted samples. ECOS-Runsalt software is very user-friendly but is also known to have some limitations in regard to possible ion combinations since it relies on equilibrium conditions that do not include metastable phases. A previous contribution to the direct measurement of the RH_eq of single- and two-salt aerosol systems was shown in ref (13) and executed in a cell that could be evacuated and backfilled with water vapor; the phase transformation of the aerosol particle was monitored by laser light scattering. The RH at the transition point was determined by direct measurement of the water vapor pressure in the cell. In addition, they developed a theoretical model for composition and temperature dependence. Another technique used to measure the RH_eq of salts is the use of a dynamic vapor sorption (DVS) instrument. In ref (21), it was made probable to determine the RH_eq of single salts with a DVS instrument by measuring mass changes during a constantly changing partial pressure across the point of zero mass changes that define RH_eq. To improve the accuracy of the RH_eq for single-salt results, a methodology was developed that took the properties of single salts into account.²² This work was extended to include salt mixtures, and some preliminary examinations were reported in ref (23).

The present work makes use of the highly accurate calibration of the DVS instrument described in ref (22) to obtain a highly accurate and direct measurement of RH_eq for salt mixtures of NaCl, NaNO₃, Na₂SO₄, and (NH₄)₂SO₄–Na₂SO₄. The determination of the RH_eq of salt mixtures of NaCl, NaNO₃, and Na₂SO₄ salts is chosen since these results can be compared with results from the literature^13,14,16,17 just as results from the thermodynamically based ECOS-Runsalt program and the improved model presented in ref (24) based on an extended Pitzer formalism on the ion interaction for calculating water activity. The salt mixture (NH₄)₂SO₄–Na₂SO₄ is studied in the present work as an example of a salt that cannot be dealt with in thermodynamically based ECOS-Runsalt software or in the improved model in ref (24) without updating the associated library, and comparisons are, therefore, only possible with experimental results.²⁵ These new measurement results, along with comparisons with previous experimental results and the results from thermodynamically based ECOS-Runsalt software and the improved model described in ref (24) form the basis for a discussion and assessment of the present suggested methodology for the direct measurement of the RH_eq in salt mixtures that includes the contribution of metastable phases.

Effect of Additional Salts on the RH_eq

Salt Mixture Behavior on an Aerosol Scale

On an aerosol scale, the resulting dried particle is composed of a pure salt core with the least soluble salt surrounded by a mixed salt coating. Thermodynamic analysis and experimental studies have shown that, in general, a salt is heterogeneous with varying thicknesses of the core and coating related to the mass fraction of each single salt, and the core composition is solely determined by the original aerosol composition, whereas the coating is identical to the eutonic composition and is independent of the original aerosol composition.²⁶ If the ambient RH increases, the size of the dried particle remains unchanged until the RH in the atmosphere becomes identical to the eutonic water activity (a_w). The solid coating with an eutonic composition at the particle surface is then dissolved in the absorbed water. Due to surface tension, the remaining pure salt solid core stays at the center of the particle and is surrounded by a saturated solution of the eutonic composition. Further increasing the RH results in more water absorption by the particle, and part of the solid core of pure salt is dissolved to maintain water equilibrium between the solution and the atmosphere. At a certain RH, which is a function of the overall composition of the original particle, the solid core of pure salt is completely dissolved into the solution and the particle becomes a pure aqueous droplet.¹⁴

Salt Mixture Behavior Linked to RH and Gravimetric Changes

In the case of at least two salts (three different ion types), a multiphase region may exist during absorption. At the deliquescence point, mutual deliquescence relative humidity (RH_Meq) is the RH at which the salt mixture starts to pick up moisture and thereby weight, and only one component in the solid mixture dissolves completely. Subsequently, the solution consists of an aqueous solution and undissolved solids following growth into a common saturated solution droplet at the second critical RH (RH_SCeq) at which the dissolution is completed with increasing water vapor condensation and thereby weight gain.

An increase in the mass after the second critical RH is a consequence of continuous water droplet growth by water vapor condensation and is limited by the contact angle between the salt solution and substrate and may continue until a relatively high weight gain has been reached compared to the necessary weight gain to ensure dissolution of the salt. See Figure 1 for a visualized example of water absorption beyond the saturated solution at RH above RH_eq.

Figure 1.

Absorption of water molecules on 25 mg of NaCl(s) followed by vapor condensation in an aluminum pan (d = 6 mm) at 95%RH and 25 °C; a 453% weight gain is observed. A weight gain of only 278% is needed to ensure the complete dissolution of NaCl.

The mass increase, which is only related to water vapor condensation, differs in its mass increase function from the previous phase until RH_SCeq, and may therefore be differentiated with another mass increase function. This observation allows for the separation of the abovementioned two phases based on the change in the mass increase function at RH_SCeq with an increasing RH.

With a decreasing RH (desorption) from RH_SCeq, evaporation from the salt mixture solution occurs simultaneously with expulsion of water, resulting in one continuously decreasing mass function until RH_Meq is reached, which is where the salt mixture solution crystallizes. However, in ref (14), it is described that some salt mixtures are much less straightforward and termed nonideal. In such cases, with two salts (A and B) and a decreasing RH, one of the salts (A) eventually becomes saturated during one continuously decreasing mass function (f(x)_A) and starts to form its crystalline phase. As the RH is further reduced, more of the solid phase of salt (A) forms at another decreasing mass function (f(x)_A–B), and the residual solution becomes more concentrated in regard to salt (B). At a certain RH, RH_Meq, the two salts (A + B) crystallize together and form a mixed solid phase with an eutonic composition (RH_Meq,(A+B)). The RH_SCeq(A+B) is always lower than the RH_eq of the individual solutes (RH_eq,(A) and RH_eq,(B)).

In the following, RH_eq refers to RH_SCeq in the case of salt mixtures.

Calculation of the Water Activity in Salt Mixtures

The presence of additional ions impacts the solubility of each salt component. The equilibrium conditions, expressed as the water activity in salt mixtures (a_w,mix), can be found by²⁵

1

where X₁ and X₃ represent the cationic strength, Y₂ and Y₄ represent the anionic strength, and a_w,12 and a_w,34 represent the water activity in each of these two single salts.

The ionic strength (1) of each ion X_i and Y_i represents the cationic and anionic fractions for each component, respectively, that is

2

3

4

5

This effect is opposite to the common ion effect and is called the “secondary salt effect”. If additional ions are dissolved, the total ionic concentration of the solution increases and interionic attractions become important. Water activities in salt mixtures are therefore reduced compared to the stoichiometrically measured concentrations in solution including only the dissolution of one salt.²⁷

RH_eq in Praxis

In relation to the determination of the water activity in a solution by measurement, just as for many practical applications, the equilibrium conditions and ideal behavior of water vapor may be assumed. The water activity may then be determined as²⁰

6

where p_w and p_w⁰ are the water vapor pressure above the solution and the saturation vapor pressure, respectively.

Therefore, to determine the water activity of an electrolyte solution, it is sufficient to directly measure the vapor pressure or the relative humidity above a solution of known composition at a constant temperature because the water activity depends on the composition and concentration of the solution.⁶

Based on examinations of the Na₂SO₄ system, it is proposed that systems including hydrated states should incorporate additional phase equilibria that include the hydration reaction with an equilibrium constant (K_AB), as shown in ref (15)

7

where RH_AB refers to the specific RH_eq for the hydration–dehydration equilibrium. According to ref (6), most salts found in building materials form different hydrates.

DVS Instrument and Determination of the RH_eq

The introduction of a material sample into a sample chamber in a DVS instrument with connected software enables us to change and program the climatic conditions (temperature, air flow, and continuously changing RH) surrounding the material sample and simultaneously monitor and record gravimetric changes (see Figure 2 for a schematic of the DVS instrument (DVS Advantage 1, Surface Measurements Systems, Alperton London, United Kingdom)).

Figure 2.

Schematic of the DVS instrument. Solid arrows show the direction of the carrier gas flow. Reprinted with permission from ref (28).

The RH can be secured and measured with two independent systems: (1) a mixture of dry and moist air through valves based on prior calibration with single salts (termed open loop) and (2) a direct measurement with a dew point analyzer within the sample chamber (termed closed loop). The accuracy of the open-loop system is checked through calibration tests and performed with single salts covering RH values from 11 to 93% (LiCl; MgCl₂; Mg(NO₃)₂; NaCl; KNO₃). The salt calibration principle is based upon the principle that the vapor pressure above a saturated salt solution is constant at a particular temperature (eq 6) and may reach equilibrium with its surroundings. For a more comprehensive description of the instrument, see ref (22).

When the actual RH approaches RH_eq, the total reaction time increases. When the total reaction time is high (shown for t > 2.5 h but dependent on salt type), the empirical kinetic equation can be linearized to interpolate the equilibrium conditions (where dm/dt = 0)²²

8

where dm is the change in the sample mass, dRH is the change in the relative humidity, and c is an experimentally determined constant.

Furthermore, since each salt differs in atomic composition, thereby resulting in different sizes, atomic structures, etc., each salt also differs in its properties, namely, its water absorption and desorption properties. Therefore, individual salt calibration tests were combined together with the specified salt preparation method in ref (22) to perform a highly accurate calibration. Among others, this takes into account variations of salt crystal size, which influence the RH_eq.^2,29

The salt calibration methods incorporate the following salt properties that influence calibration: the heat of solution, heat of condensation, and kinetics connected to the salt-phase transition. These properties influence the microclimate surrounding the salts during calibration. In addition, both systems (open and closed) are used to ensure and measure the RH within the DVS, thereby supplementing each other and making the RH measurements as accurate as possible.

To achieve a highly accurate direct determination of the RH_eq, the measured values are adjusted with an experimentally determined difference between the measured values and the well-defined reference values¹¹ for single salts, as described in ref (22).

Materials and Methods

Preparation of Salt Mixtures

The approach was to use saturated salt solutions, i.e., the solution was saturated with respect to both or all three salts. This saturation was executed by adding the amount of salt corresponding to the solubility of each single salt at 100 °C.³⁰ See Table 1 for the salts and amounts used for each salt mixture.

Table 1. Masses of Each Single Salt Added to 100 mL of Distilled Water for the Preparation of the Salt Mixture.

	NaCl (g)	NaNO3 (g)	Na2SO4 (g)	(NH4)2SO4 (g)
NaCl–Na2SO4–NaNO3	39.1	180	42.7
NaCl–NaNO3	39.1	180
NaNO3–Na2SO4		180	42.7
NaCl–Na2SO4	39.1		42.7
(NH4)2SO4–Na2SO4 (mass fraction Na2SO4 0.173)			42.7	103.8

The salt mixtures were prepared by the addition of the salts into 100 mL of distilled water in a 1 L beaker. The beaker was placed in a pot with boiling water and covered with a slightly curved transparent watch glass on the top. The solution was heated until a temperature of approximately 100 °C was obtained or until nucleation occurred at the surface of the solution, whereupon the beaker was removed from the pot. Next, a small amount of the hot solution was poured into a Petri dish and placed in a fume hood to accelerate evaporation. Over time, crystals formed at the surface and gradually fell to the bottom of the beaker. After complete evaporation of the water, the salt crystals were collected.

Measuring Methods

The measured RH_eq was influenced by kinetics and the initial state of the salt, and therefore, the measuring methodology influenced the result in terms of accuracy. The most influential measuring conditions in ref (22) were found to be the preconditioning of the salts. Preconditioning was related to the needed addition of water to the dry salt until RH_eq was obtained (see Table 2), and the reasoning was extensively described in ref (22). The initial RH interval was centered around the RH_eq found in the literature as an initial approach for the measurement. In case a nonsatisfactory fit with eq 8 was found, an RH_eq was read out of the measuring data and subsequently became the center of a new measuring interval. See Table 2 for the used salt preconditioning and measuring conditions.

Table 2. Overview of the Salt Preconditioning and Measuring Conditions.

	added water (%)	interval (% RH)	measurement duration (h)
NaCl–Na2SO4–NaNO3	24.4 ± 3.1	±5	11
NaCl–NaNO3	21.8 ± 2.1	±5	11
NaNO3–Na2SO4	27.5 ± 2.3	±5	11
NaCl–Na2SO4	25.1 ± 6.6	±5	11
(NH4)2SO4–Na2SO4¤ (mass fraction Na2SO4 0.173)	29.0 ± 5.9	±1.5	21

It should be noted that in most cases, the same measurement duration and RH interval were used. However, to obtain a satisfactory fit with the link described in eq 8, it was necessary to adjust the measurement duration and size of the RH interval in relation to the salt mixture (NH₄)₂SO₄–Na₂SO₄. Such adjustments of the measurement duration and RH interval have also been made, when relevant, in previous work.²²

Results and Discussion

Checking the Generated RH in the DVS Instrument by Single-Salt Calibration Tests

Initial salt calibration tests on well-defined single salts are used to ensure the accuracy of the results for salt mixtures. Highly accurate salt calibration tests were carried out following the procedure described in ref (22). Of special relevance are the salt calibration tests for the RH interval in which the salt mixtures are expected to have an RH_eq of 55–85% RH. Therefore, calibration tests were carried out with single salts of Mg(NO₃)₂ and NaCl (see Figure 3). The average measured difference from the reference value in ref (11) and the deviation in the identically performed experiment reveals a measuring inaccuracy between the experimentally determined values and the well-defined values in the literature. Since the single salts used for calibration purposes have well-defined RH_eq values and since the determined results in this study are found to have high accuracy, differences between the measured and reference results can be used to recalculate an accurate RH_eq (RH_{eq,(re-cal,DVS)}) with the average measured difference. This approach is used in the following. A difference of 0.77% RH and 0.72% RH is found between the well-defined reference values from ref (11) and the determined RH_eq for Mg(NO₃)₂ and NaCl in this study, respectively. Measured salt mixtures with an RH_eq of approximately 52 and 75% RH are therefore recalculated to measure the deliquescence point with an added 0.77 ± 0.15% and 0.72 ± 0.12% RH, respectively (RH_{eq,(re-cal,DVS)} = RH_{measured with DVS} + RH_{diff,relevant RH}). It should be noted that the found RH_{diff,relevant RH} differs in relation to the actual calibration of the DVS instrument.

Figure 3.

Reference RH_eq from the literature¹¹ (shaded bars) together with experimentally obtained RH_eq,DVS (solid bars) shown for (a) Mg(NO₃)₂ and (b) NaCl salts. The error bars represent the deviation of the given value: references values (on shaded bars) and deviations on experimentally obtained RH_eq,DVS (solid bars), respectively.

Determination of the RH_eq in Salt Mixtures

The general definition of RH_eq is the RH at which an absence of mass change exists, provided the temperature is constant. This criterion can and is also applied to salt mixtures since the temperature and the mass fraction of each salt in the mixture is constant.

The measured RH_eq values for NaCl–Na₂SO₄–NaNO₃, NaCl–NaNO₃, NaNO₃–Na₂SO₄, NaCl–Na₂SO₄, and (NH₄)₂SO₄–Na₂SO₄ are shown in Table 3. Each measurement was performed in triplicate, thereby allowing the calculation of an average value and deviation. The reproducibility is high for all five salt mixtures, and a standard deviation of ±0.006 to 0.08% RH is obtained (Table 3). This relatively low standard deviation is obtained by ensuring a constant mass change (dm) per change in RH (dRH), enabling the determination of the constant c in eq 8 and minimizing the experimental error in the determined RH_eq. Furthermore, the constant c enables an accurate determination of the intersection with the y-axis (see Figure 4), showing an absence of the mass change at a specific RH, which is the definition of RH_eq. An example of the measurement output data is shown in Figure 4. In Figure 5, the recalculated measured results are pictured together with results from the literature^{13,14,16,17,25} and the ECOS-Runsalt-calculated results^19,20 to obtain an overview and to clarify the differences and similarities among the various RH_eq determination methods. Meanwhile, it is essential to notice that the chosen RH interval in ECOS-Runsalt has a significant influence on the results since this model does not include kinetic effects (see the “ECOS-Runsalt and Kinetics (Influence from the Chosen RH Interval)” section). To demonstrate the ECOS-Runsalt software capacity, a comparison was made with the most accurate results following the given approach in the “ECOS-Runsalt and Kinetics (Influence from the Chosen RH Interval)” section.

Table 3. Measured and Recalculated RH_eq at 25 °C^a.

salt mixture	RHeq 1st run	RHeq 2nd run	RHeq 3rd run	RHeq average/deviation	RHeq recalculated
NaCl–Na2SO4–NaNO3	65.96 ± 0.16	65.83 ± 0.03	65.89 ± 0.01	65.89 ± 0.08	66.61
NaCl–NaNO3	66.52 ± 0.01	66.19 ± 0.11	66.35 ± 0.14	66.35 ± 0.07	67.07
NaNO3–Na2SO4	72.48 ± 0.03	72.40 ± 0.01	72.53 ± 0.06	72.47 ± 0.03	73.19
NaCl–Na2SO4	73.78 ± 0.10	73.73 ± 0.08	73.50 ± 0.05	73.67 ± 0.03	74.39
(NH4)2SO4–Na2SO4 (mass fraction = 0.173 Na2SO4)	75.72 ± 0.07	75.32 ± 0.08	75.66 ± 0.07	75.57 ± 0.006	76.29

^aRecalculated values are the average measured values ± the measured difference from the reference values (shown in Figure 3).

Figure 4.

Example of the measurement results enabling the determination of the RH_eq of the salt mixture NaCl–Na₂SO₄–NaNO₃ at 25.0 °C. Dark gray solid line: measured dm/dRH with the dew point analyzer within the sample chamber, black dotted line: fitted dm/dRH, and bright gray solid line: the change in the mass in percent.

Figure 5.

RH_eq of salt mixtures as obtained by different determination methods. (White square box) RH_{eq (re-cal,DVS)} from Table 3. (Dark gray square box) Experimental data from the literature and (bright gray square box) calculated results from the thermodynamically based ECOS-Runsalt model, with an RH interval limited to the RH_eq ±1%, based on the first scan (see the “ECOS-Runsalt and Kinetics (Influence from the Chosen RH Interval)” section).

The recalculated RH_{eq(re-cal DVS)} for NaCl–Na₂SO₄–NaNO₃ (specifically, 2/3NaCl–3/10Na₂SO₄–21/10NaNO₃) was determined to be 66.61% RH (see Table 3).

With a salt mixture consisting of the same salts, though differing in the number of moles where the amount of NaNO₃ and Na₂SO₄ corresponded to the solubility of each single salt at the eutonic composition, the RH_eq was determined to be 71.8 ± 0.5% RH in ref (13). In ref (14), they characterized salt mixtures into two groups: simple and less simple systems. The former is independent of the mole fractions of the salts in this study, which is in contrast to the latter. Additionally, in ref (6), it is shown with examples that the solubility, saturation coefficients and crystallization properties of salt mixtures are strongly dependent on the mixture composition. Since the RH_eq in ref (13) is not comparable with the measured result in this study, it is not shown in Figure 5. However, the difference between RH_{eq(re-cal DVS)} and ref (13) supports the effect of the specific number of moles on RH_eq.

With the present number of moles being 3.3880, 0.66903, 2.1178, and 0.30061 for sodium, chloride, nitrate, and sulfate, respectively, RH_{eq (ECOS-Runsalt)} was calculated to be 66.3 with an RH interval limited to the RH_eq ±1%, based on the first scanning (see the “ECOS-Runsalt and Kinetics (Influence from the Chosen RH Interval)” section). However, to obtain a full picture of the formed salt phases, an RH interval ranging between 15 and 98% was applied in ECOS-Runsalt for the NaCl–Na₂SO₄–NaNO₃ salt system, indicating formation of darapskite (NaNO₃·Na₂SO₄·H₂O), nitratine (NaNO₃), halite (NaCl), and thenardite (Na₂SO₄), as shown in Figure 6. As described in the “Effect of Additional Salts on the RH_eq” section, at RH_Meq, only one component of the solid mixture dissolved completely, being a small amount of thenardite; subsequently, the composition consisted of an aqueous solution and the undissolved solids of halite and nitratine. Following the production of a common saturated solution at the second critical RH (RH_SCeq), dissolution was completed.

Figure 6.

ECOS-Runsalt output diagram for the salt mixture NaCl–Na₂SO₄–NaNO₃ with the number of moles being 3.3880, 0.66903, 0.30061, and 2.1178 for sodium, chloride, sulfate, and nitrate, respectively, at 25 °C. The RH_{eq (ECOS-Runsalt)} was calculated to be 64.8% with an RH interval of 15–98% RH. Black indicates the content of darapskite (NaNO₃Na₂SO₄·H₂O), red indicates nitratine (NaNO₃), blue indicates halite (NaCl), and green indicates thenardite (Na₂SO₄).

RH_{eq (re-cal DVS)} for NaCl–NaNO₃ (specifically 2/3NaCl–3/10Na₂SO₄) was determined to be 67.07% RH (see Table 3). In ref (14), the RH_eq for this salt mixture was thermodynamically calculated to be 67% RH. In ref (13), the RH_eq of the NaCl–NaNO₃ salt mixture at an eutonic composition, where the composition of both salts reached their solubility limit in the solution, was measured to be 68.0 ± 0.4% RH. In ref (15), the deliquescence point was calculated for various aqueous solutions of NaCl–NaNO₃ salts. Since the above salt mixture was an aqueous solution, the results were noncomparable; however, it is noticed that the water activity was relatively strongly influenced by the molar ratio, which may also be the reason for the slightly deviating results between RH_{eq (re-cal DVS)} and ref (14). With the present number of moles being 2.7868, 0.66903, and 2.1178 for sodium, chloride, and nitrate, respectively, the RH_{eq (ECOS-Runsalt)} was calculated to be 66.6% RH. According to the ECOS-Runsalt results, only halite and nitratine were present in the salt mixture; additionally, no salt hydrates formed. With the improved thermodynamically based model described in ref (24), the RH_eq was calculated to be 66.76% (by the corresponding author of ref (24)). In short, RH_{eq (ECOS-Runsalt)} ∼ RH_{eq,litt [24]} < RH_{eq (re-cal DVS)} = RH_{eq,(litt [14])} (see Figure 5).

The RH_{eq (re-cal DVS)} was determined to be 73.19% RH for NaNO₃–Na₂SO₄ (see Table 3). In ref (13), the RH_eq for NaNO₃–Na₂SO₄ was found to be 72.2 ± 0.2%, where the number of moles of NaNO₃ and Na₂SO₄ corresponded to the solubility of each single salt at an eutonic composition. Therefore, the number of moles of the above salts was not identical between the present work and ref (13). In ref (16), it was shown that for this specific salt mixture of NaNO₃–Na₂SO₄, RH_eq is a function of the total molality of NaNO₃ and Na₂SO₄. The ratio between NO₃^– and SO₄^2– significantly affects the RH_eq; thus, the RH_eq in total may vary between 55 and 85% RH. In the present work, x_NO3 equaled 0.876. In ref (17), the RH_eq was calculated under similar (but not identical) conditions, providing x_NO3 = 0.9 at 23.5 °C and read 73.8% RH in the graph. Applying ECOS-Runsalt and the present number of moles of 2.7190, 2.1178, and 0.30061 for sodium, nitrate, and sulfate, respectively, RH_{eq (ECOS-Runsalt)} was calculated to be 73.6% RH, and formation of darapskite, nitratine, and thenardite was observed. With the more advanced thermodynamically based model described in ref (24), the RH_eq was calculated to be 73.52% (by the corresponding author of ref (24)); notably, taking into account the presence of darapskite, the relations become further complicated, and with a surplus of NaNO₃, as in this case, a mixture consisting solely of nitratine and darapskite would come into existence.¹⁷ Therefore, RH_{eq (ECOS-Runsalt)} ∼ RH_{eq,(litt[24])} > RH_{eq (re-cal DVS)}.

The recalculated RH_eq (RH_{eq (re-cal DVS)}) for NaCl–Na₂SO₄ (specifically 2/3NaCl–3/10Na₂SO₄) was determined to be 74.39% RH (see Table 3). This result was consistent with and did not significantly differ from the RH_eq found by ref (13), 74.2 ± 0.3% RH (RH_{eq,(litt[13])}). In ref (16), aqueous solutions of NaCl–Na₂SO₄ salts and their water activity were found to be relatively limited due to the molar ratios of Cl^– and SO₄^2–.

With the present number of moles of 1.2703, 0.66903, and 0.30061 for sodium, chloride, and sulfate, respectively, the RH_{eq (ECOS-Runsalt)} was calculated to be 74.3%. With the improved thermodynamically based model described in ref (24), the RH_eq was calculated to be 74.33% (by the corresponding author of ref (24)). Therefore, RH_{eq (ECOS-Runsalt)} ∼ RH_{eq (re-cal DVS)} ∼ RH_{eq,(litt[13])} ∼ RH_{eq,(litt[24])}.

Furthermore, the results for RH_{eq(re-cal DVS),NaCl–Na2SO4} and RH_{eq(re-cal DVS),NaCl} clarified that it was possible to measure a significant difference in the RH_eq between NaCl (75.29 ± 0.12% RH) and NaCl–Na₂SO₄ (74.2 ± 0.3% RH), with two salts having an RH_eq relatively close to each other. This possible differentiation between salts with RH_eq values relatively close to each other was made possible by the high reproducibility of the RH_{eq,(re-cal DVS)} results that had an accuracy of 0.12% RH (see Figure 3).

The RH_{eq,(re-cal DVS)} for (NH₄)₂SO₄–Na₂SO₄ (mass fraction of 0.173 in regard to Na₂SO₄) was determined to be 76.29% RH. In ref (25), the RH_eq for the (NH₄)₂SO₄–Na₂SO₄–H₂O system was described as being dependent on the actual ion fractions (equation I) and nonideal behavior. With a mass fraction of 0.171% with respect to Na₂SO₄, the RH_eq was estimated to be between 75.20 and 76.20% RH based on electrodynamic particle balance measurements of the water activities of highly concentrated solutions and from the phase diagram in ref (25). This result was in agreement with the RH_{eq (re-cal DVS)} of 76.29% RH with a similar mass fraction of 0.173 in regard to Na₂SO₄.

These results cannot be compared with the calculated RH_eq from ECOS-Runsalt software, as this ion-type NH₄ is not included²⁰ or used as a default in the improved model in ref (24). ECOS-Runsalt was developed using the molality-based thermodynamic approach of Pitzer^19,20 and calculates in regard to mole fractions; thus, ECOS-Runsalt is restricted to the mole fractions of salts that are most commonly encountered in conservation: Na⁺, K⁺, Mg²⁺, Ca²⁺, Cl^–, NO₃^–, SO₄^2–, and H₂O and excludes mixtures containing both Ca²⁺ and SO₄^2–. Notably, model parameters are provided and validated for the Na⁺–K⁺–Cl^––NO₃^––SO₄^2––H₂O system in the improved model in ref (24). The need to exclude mixtures containing both Ca²⁺ and SO₄^2– in ECOS-Runsalt is related to practical limitations, as one frequently comes across this combination in praxis. However, this and other limitations are reported to be caused by the fact that it was not possible to refine the system to the extent that had originally been envisaged within the project period.²⁰

Having shown consistency among the measured experimental data in this study by the use of the DVS instrument, measurements, and calculations from the literature and thermodynamically calculated values from the ECOS-Runsalt model and improved model in ref (24) for a mixture consisting of up to three salts, the determined RH_eq with the DVS instrument seemed to be generally valid. According to refs^{19, 20}, data for quaternary (four ions) or higher mixtures are not required for the parameterization of the model, as experience has shown that the modeling of the thermodynamic properties of multicomponent electrolyte mixtures only requires two or three particle interactions.

ECOS-Runsalt and Kinetics (Influence from the Chosen RH Interval)

In ECOS-Runsalt, it is assumed that the entire salt system is in equilibrium with its surroundings at all times,^19,20 and therefore does not include the effect of kinetics. However, for some salt mixtures, the kinetics significantly influence the growth of crystals. The kinetics is primarily influenced by the difference between the ambient conditions and equilibrium conditions (RH_actual – RH_eq); however, for some salts, the temperature is also of major importance. A visual example of the kinetics influence on deliquesce is shown in Figure 7.

Figure 7.

Visualization of the kinetic influence (ΔRH) on a salt (NaCl)-phase transition studied by the application of a cooling stage in an ESEM: (a) reference equilibrium conditions and (b) influence of a change of 0.1% RH for 19 h.³¹

The existence of metastable phases as a consequence of nonequilibrium conditions also influences salt formation. For example, the phase diagram for the binary system of Na₂SO₄–H₂O is significantly more complex than originally predicted. Experimental investigations can document the existence of two metastable phases, which are caused by the influence of kinetics. In equilibrium models, metastable phases are not predicted. However, in ref (15), metastable equilibrium is incorporated in the thermodynamic models to simulate the existence of metastable phases, which is a necessary part of the Na₂SO₄–H₂O system, thereby obtaining a full picture for understanding deterioration mechanisms. The phase diagram pictures both stable and metastable phases, illustrating that the metastable phases have both higher and lower RH_eq than the stable phases depending on the temperature. This result is a consequence of the precipitation sequence that is under kinetic control. The crystallization of the anhydrous phases proceeds at higher rates than the precipitation of the hydrates. Therefore, the formation of the anhydrous phase is particularly favored at low relative humidity.¹⁵ Since the contribution from metastable phases is not included in the thermodynamically based ECOS-Runsalt model,^19,20 the presence of metastable phases results in deviating results for the RH_{eq (ECOS-Runsalt)}.

To overcome the kinetic influence when using ECOS-Runsalt, it is proposed to apply the same approach, as elaborated for the high accuracy determination of the RH_eq for single salts described in ref (22). First, the widest possible RH interval is examined to obtain a rough estimate of the RH_{eq,first scan} followed by the use of the smallest possible interval around the RH_{eq, first scan} to obtain a more robust result minimizing the kinetic influence. Further it was shown that it might have a significant influence whether the RH interval is 15–98 or 15–95% RH (see Figure 8).

Figure 8.

Examination of how the chosen RH interval in ECOS-Runsalt affects the determined RH_eq. White square box: the widest possible RH interval being 15–98% (also termed the first scan), dark gray square box: the RH interval limited to 15–95%, and bright gray square box: the RH interval limited to the RH_eq ±1% based on the first scan.

Figure 8 shows a significant difference in the RH_eq between the calculated results obtained with the widest possible RH interval (15–98%) and the RH interval limited to the RH_eq ±1% based on the first scan of 1.5 and 1.2% RH for NaCl–Na₂SO₄–NaNO₃ and NaCl–Na₂SO₄, respectively. Both salt mixtures form hydrated states according to ECOS-Runsalt. These significant differences can be fully accounted for by following the approach in ref (15), and include a hydration constant of 1/RH_AB (eq 7). Thus, in the NaCl–Na₂SO₄–NaNO₃ salt mixture, a constant for the hydrated phase (caused by the presence of darapskite) was included, RH_{eq (ECOS-Runsalt including the hydrated phase)} = RH_{eq (ECOS-Runsalt)} + 1/RH_{eq (ECOS-Runsalt, NaCl–Na2SO4–NaNO3)} = 64.8% + 1/0.648 = 66.34% ∼ RH_eq ±1% = 66.3. Also, when including the hydration constant for the NaCl–Na₂SO₄ salt mixture, consistency is found between RH_{eq (ECOS-Runsalt including the hydrated phase)} = 74.47% ∼ RH_eq ±1% = 74.3.

The salt mixture NaNO₃–Na₂SO₄ also formed a hydrated salt (darapskite), and differing by 0.6% RH was dependent on if the RH interval was 15–98% or limited to RH_eq ±1%. Taking the hydration constant into account, as proposed in ref (15), as a consequence of the presence of darapskite, RH_{eq (ECOS-Runsalt including the hydrated phase)} = 74.37%. The RH_{eq (ECOS-Runsalt including the hydrated phase)} = 73.98% RH based on results obtained for the interval 15–95% RH ∼ RH_eq ±1% = 73.6%. It may be considered that the hydration constant should be related to the concentration of the solution, as this would influence the chemical potential, which again would influence the activity, a_w, as stated in ref (6). In ref (6), aqueous solutions of the salt NaNO₃–Na₂SO₄ showed that the water activity was strongly influenced by the molar ratio.

In the case of NaCl–NaNO₃, ECOS-Runsalt did not predict the formation of hydrated salts, and a hydration constant was therefore not included; and the difference between the result with the RH interval 5–98% and RH_eq ±1% was limited to 0.1% RH.

The ECOS-Runsalt model was validated with water activity measurements. Direct vapor pressure measurements were obtained above single-salt solutions (a deviation of approximately 0.2%). Attempts were also made to use standard RH and T sensors for the measurements of water activities with a sensor. A Testo 601 instrument (Testotherm) was used to test solutions of LiCl and NaCl and standard solutions of known water activity. The deviations for these measurements were approximately 3–4% RH, and the authors described that such a deviation was insufficient to obtain water activities or osmotic coefficients with the accuracy required for the determination of binary model parameters. However, they reported that this type of measurement was much less time consuming than direct measurements and might be helpful for model validation.^19,20

Therefore, it may be argued that the reason for the ECOS-Runsalt calculation of RH_eq deviating from RH_eq measured with the DVS instrument and the experimental results from the literature is caused by the following: (1) equilibrium conditions are assumed at all times and do not include hydration reactions and (2) the precision of the validation data. However, applying the presently used approach, to have a first scan of the widest possible RH interval as an input for subsequently applying the RH_eq ±1% interval, it seems feasible to minimize the kinetic influence.

The abovementioned assumptions are further supported by the fact that the improved thermodynamically based model described in ref (24) provides results that differ by only ±0.33% RH from the measured RH_{eq (re-cal DVS)} for three out of the five salt mixtures in this study; thus, it is possible to calculate with the proposed model.

Conclusions

The present work contributes to enabling a more accurate determination of RH_eq in salt mixtures, thereby preventing or minimizing accelerated salt-induced deterioration. This determination is through the direct measurement of RH_eq in salt mixtures utilizing a DVS instrument. As a consequence of using a previously developed methodology for highly accurate calibration of the equipment, it is possible to determine RH_eq with similar high accuracy (<0.2% RH).

The direct measurements of RH_eq take into account the fractioning of salts in mixtures, which has been recently reported to influence RH_eq due to metastable phases.

There was consistency among the measured experimental data in this study with the DVS instrument, experimentally measured data and thermodynamically based calculations from the literature, and thermodynamically calculated values by the ECOS-Runsalt model and an improved thermodynamically based model for a mixture consisting of two or three salts. This consistency was found for all five salt mixtures that were studied (NaCl–Na₂SO₄–NaNO₃, NaCl–NaNO₃, NaNO₃–Na₂SO₄, NaCl–Na₂SO₄, and (NH₄)₂SO₄–Na₂SO₄), and the use of the DVS instrument for the determination of RH_eq seemed to be generally valid. This result makes it possible to directly measure the RH_eq in salt mixtures with an arbitrary number of ion types, which would occur in real-world, in situ applications. Therefore, the proposed methodology could be the advancement needed for the accurate determination of RH_eq and for subsequent decisions on favorable climatic conditions to avoid or reduce phase transitions without restricting validity to specific ion types and combinations.

Through the proposed direct measurements of RH_eq of salt mixtures forming hydrates, it was identified that the use of thermodynamically based ECOS-Runsalt software, in some cases, resulted in significantly different RH_eq values, if focus on the kinetics was not included. This observation was found when comparing the experimentally determined RH_eq in this work with the experimentally determined results from previous research and with the improved thermodynamically based model described in ref (24). This result may be explained by the fact that in the ECOS-Runsalt model, equilibrium conditions were assumed at all times and did not include the contribution of metastable phases together with the precision of the validation data. Additionally, some ions (e.g., NH₄⁺) and combinations of ions (Ca²⁺ and SO₄^2–) were not included in ECOS-Runsalt software. Thus, some limitations of ECOS-Runsalt software were revealed. However, ECOS-Runsalt software provides fast results on RH_eq, creating a reasonable overview of the present phases. Further, the present direct measurement of RH_eq in salt mixtures utilizing a DVS instrument enabled to propose a new approach when using ECOS-Runsalt, which seems to result in more accurate results if focus on the kinetics is included by choosing the appropriate RH interval.

Finally, having the possibility to determine the RH_eq, including the metastable contribution in salt mixtures may be of value for obtaining new theoretical insights.

This project was financially supported by the Aage and Johanne Louis-Hansen Foundation.

The author declares no competing financial interest.