Predicting Deliquescence Relative Humidities of Crystals and Crystal Mixtures

Abstract

The presence of water in the form of relative humidity (RH) may lead to deliquescence of crystalline components above a certain RH, the deliquescence RH (DRH). Knowing the DRH values is essential, e.g., for the agrochemical industry, food industry, and pharmaceutical industry to identify stability windows for their crystalline products. This work applies the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) to purely predict the DRH of single components (organic acids, sugars, artificial sweeteners, and amides) and multicomponent crystal mixtures thereof only based on aqueous solubility data of the pure components. The predicted DRH values very well agree with the experimental ones. In addition, the temperature influence on the DRH value could be successfully predicted with PC-SAFT. The DRH prediction also differentiates between formation of hydrates and anhydrates. PC-SAFT-predicted phase diagrams of hydrate-forming components illustrate the influence of additional components on the hydrate formation as a function of RH. The DRH prediction via PC-SAFT allows for the determining of the stability of crystals and crystal mixtures without the need for time-consuming experiments.

Keywords: PC-SAFT; crystal; crystal mixture; deliquescence; thermodynamics; vapor sorption.

Figure 1

Temperature-dependent binary-phase diagrams indicating (a) the solubility of crystalline fructose in water and (b) the DRH of fructose. The solid line is the PC-SAFT-predicted equilibrium solubility of fructose in water (a) and the dotted line is the PC-SAFT-predicted DRH of fructose as a function of temperature (b). Darker-shaded regions indicate higher RH values, whereas brighter-shaded regions indicate lower RH regions. The squares in (a) are experimental data for fructose solubility [43]. The stars in (b) are DRH values measured via vapor-sorption measurement [44] and the circle is the measured equilibrium water activity of a saturated solution [14].

Figure 2

PC-SAFT-predicted water sorption of fructose as a function of RH at 298.15 K. Grey stars [45] and white stars [14] represent sorption data from literature. Equilibrium water activity measurements of fructose solutions obtained from the literature are shown as circles [46]. The thick line is the PC-SAFT-predicted water sorption in thermodynamic equilibrium. Experimental errors for the measurements are indicated or are smaller than symbol size.

Figure 3

Predicted phase diagrams indicating the water deliquescence behavior of a glucose/fructose crystal mixture at 298.15 K. (a) Ternary-phase diagram indicating the PC-SAFT-predicted solubilities of glucose and fructose in water as thick solid lines and (b) PC-SAFT-predicted DRH as a function of fructose content in the fructose/glucose mixture shown as dotted lines. Darker shaded regions represent higher RH values (58.1–99% RH). The dashed lines represent the compositions investigated for water sorption in Figure 4.

Figure 4

PC-SAFT-predicted water sorption of crystal mixtures with different fructose/glucose ratios as a function of RH at 298.15 K. The dashed lines are the PC-SAFT predicted water-sorption curves. Black dashed line is for w_fructose = 0.85; grey dashed lines is for w_fructose = 0.5; and white dashed line is for w_fructose = 0.3.

Figure 5

Predicted temperature-dependent DRH of (a) CA and for mixtures of (b) AA/CA, (c) CA/fructose, (d) AA/fructose, (e) fructose/sucrose, and (f) AA/CA/fructose. The equilibrium water-activity data (a) of CA hydrate are shown as squares; CA anhydrate are shown as circles [33]. Gravimetric vapor-sorption measurements of CA anhydrate in (a) are shown as stars [44]. The triangles in (a) indicate data from Reference [33] showing the solid–solid transformation of CA anhydrate to hydrate. Gravimetric vapor-sorption measurements of crystal mixtures in (b–f) are shown as half-filled stars [44]. The solid lines in (a–f) show the predicted DRHs of the anhydrate, whereas the dashed lines show the predicted DRHs of the hydrate (where applicable). The dash-dotted lines mark the predicted solid–solid transformation from anhydrate to hydrate.