Melting properties of amino acids and their solubility in water

The state-of-the-art unit operation for separation and purification of amino acids is still crystallization, which requires solubility data and melting properties of pure compounds. Since measuring solubility is time-consuming, prediction tools are desired. Further, melting properties are not yet available due to decomposition of amino acids upon slow heating. In this work, melting properties of twenty amino acids (except Met) were measured by Fast Scanning Calorimetry (FSC) with heating rates up to 20 000 K s−1. PC-SAFT was used to predict interactions in amino acid + water systems. Additionally, solubility, pH, and PXRD was measured. By combining FSC and PC-SAFT, the solubility of 15 amino acids was successfully predicted in a wide temperature range in good agreement with the experimental data. Thus, this work provides melting properties of amino acids for the first time and highlights the usefulness of such data to predict material properties such as aqueous solubility of amino acids.


Introduction
Commonly proteins are represented by the set of twenty "standard" a-amino acids (AA). These either exist as a monomer or they are bound as building blocks in peptides and proteins. 1 Since their isolation in the 19 th century the physical and chemical properties of AA have been widely investigated because of their crucial importance in nature and by relevance for industrial processes. 2,3 The applied separation unit of fractional crystallization is still state-of-the-art. 4,5 This requires basic understanding of the melting temperatures as well as the solubility behavior to further develop and optimize the downstream process. 6 However, consistent melting temperatures are still not available for the amino acids. Further, aqueous AA solubility studies have not been checked for consistency. Such studies were carried out in the early 20 th century focusing on AA + water. [7][8][9][10][11][12] Many of these works were performed in a narrow temperature range, without pH measurements and analysis of the crystal structure of AA between its pure component and the solid in saturated solutions.
Undoubtedly measuring solubility data is expensive. Hence, prediction of AA solubility in a wide temperature range based on physical properties such as melting properties is highly desired. Unfortunately, conventional methods, e.g. Differential Scanning Calorimetry (DSC), are not applicable to determine the melting properties of AA due to thermal decomposition upon slow heating rates. 13 Experimental melting properties is available in literature only for two AA: glycine, L-alanine 14 and L-arginine. 15 In the current study we continue this work and present the melting properties of twenty proteinogenic AA characterized with Fast Scanning Calorimetry (FSC). FSC with scanning rates up to 20 000 K s À1 has been established as a reliable device to study the melting thermodynamics of thermally labile biomolecules, e.g. bio-polymers, 16,17 low molecular mass pharmaceuticals 18 and nucleobases. 19,20 The experimental melting properties are applied as an input for the thermodynamic framework PC-SAFT to predict the aqueous AA solubility. Additionally, a solid-liquid equilibrium between solid AA and the saturated liquid aqueous phase was applied. Assuming pure solid amino-acid phase the solubility x L i is determined according to Prausnitz 21 as: Dc SL p0i ðTÞ T dT (1) (2) with g L i as the activity coefficient of AA, R the universal gas constant, Dh SL 0i the melting enthalpy at melting temperature, T SL 0i the melting temperature, and Dc SL p0i (T) the temperaturedependent difference between the heat capacities in liquid (L) and solid (S) state of a pure AA. In eqn (2), Dc SL p0i (T) was assumed to show a linear temperature dependence with a c L p0i ða c S p0i Þ and b c L p0i ðb c S p0i Þ as the slope and the intercept of the heat capacities, respectively. The solubility increase (decrease) with decrease (increase) of Dh SL 0i , while increase in T SL 0i and Dc SL p0i (T) reduces the slope of the solubility-temperature curve to less temperaturedependency. The inuence of the solvent is accounted by g L i , which describes interactions between studied compound and solvent in the liquid phase. The crystal structure of the AA was measured by Powder X-ray Diffraction (PXRD). Eqn (1) is only valid for the neutral form of the molecule, which was conrmed by pH measurements of the saturated solutions.
Detail workow of this work is illustrated in ESI Fig. S1. † The abbreviation of AA are in ESI Table S1. †

Materials and reagents
Twenty proteinogenic AA investigated in this work are listed in ESI Table S1. † All AA were of commercial origin and used without additional purication. The Millipore-Q grade water for the solubility measurements was directly taken in the lab.

Melting measurements with FSC
Experimental FSC melting properties measurements were carried out by using Flash DSC 1 (Mettler Toledo) with the calorimetric twin chip sensor UFS1. 22,23 The experimental FSC study of the AA was given in the previous works, where detailed experimental description of FSC method has been presented. 14,24 All measurements were conducted under inert atmospheres of dry nitrogen (dew point lower than 150 K) with a ow rate of 50 mL min À1 . The sensors were conditioned according to manufacturer's procedure and the temperature was calibrated with recommended calibration metals (indium, bismuth and tin).
The experimental FSC procedure consists of three measurement stages, as presented in the temperature-time prole in ESI Fig. S2. † The starting temperature is set to 303 K to reduce the measuring time, as starting temperature below 303 K requires a cooler and long system equilibration times.
For the rst stage (#1 to #4), the temperature range from 303 K to 473 K and constant scanning rate 2000 K s À1 were selected to assure the high reproducibility of the heating and cooling cycles. The reproducibility is indirect proof indicating that sample mass loss due to sublimation and decomposition has not occurred, and that volatile impurities or water were absent. It is also indicating that the sample was measured in its anhydrous form. The sample mass (without silicon oil) is determined in this stage as is the total heat capacity of the sample from the rst FSC stage and c S p0i [J mol À1 K À1 ] is specic heat capacity obtained DSC measurements (Pyris 1, Perki-nElmer, USA). 14,16,19,[24][25][26] In the second stage, the melting properties were determined in heating step #5. To improve the thermal contact between the sample and the sensor, silicon oil can be added to the sample before heating step #5. All the samples used in FSC measurements were relatively small (less than 100 ng) and for such small samples, the surface-to-volume ratio is rather high, what leads to increase in mass loss due to sublimation or evaporation at higher temperature. This effect is especially prominent for small molecules like AA. Therefore silicon oil not only improves the thermal contact but additionally coats the sample surface and suppresses the mass loss of the sample due to sublimation or evaporation. The heating rates of step #5 typically ranged from 2000 K s À1 to 10 000 K s À1 . However for a few extremely thermally labile AA, e.g. Ile, Asn, Cys, higher heating rates up to 20 000 K s À1 were applied together with silicon oil coating to further minimize the sublimation or evaporation processes. Unfortunately even with these methods, sublimation or evaporation of Met cannot be suppressed enough. The melting and evaporation process were overlapping each other which leads to an unsuccessful determination of melting properties.
In the heating step #5 the shaded grey area in Fig. 1(a) in the temperature range of the melting peak was designated as the melting enthalpy, DH SL 0i [J], while the onset of the melting peak is a scanning rate dependent melting temperature, T SL 0i (b). The specic melting enthalpy, Dh SL 0i , is dened as a ratio Dh SL 0i ¼ DH SL 0i Â M/m 0 , where M is the molar mass of AA and m 0 is the mass of the sample.
Aer heating step #5, the molten samples without silicon oil were quenched rapidly to retain the sample in the liquid state below the melting temperature without crystallization. During the heating and cooling cycles (#8 to #11) in third stage a step change in specic heat capacity corresponding to glass transition from amorphous solid of AA to liquid (supercooled) state was observed. Due to complications in avoiding sublimation or evaporation mass loss of the samples at high temperatures in the current state of FSC technique, the glass transition can be determined only for half of the 20 proteinogenic AA.

Measurement of solubility
AA are widely investigated and their aqueous solubility data are readily available in literature. Most of the studies are carried out by using the gravimetric method. However, in some cases a discrepancy between literature data and experimental values is observed. In this work an excess amount of solute is added to water till the saturated solution in equilibrium with the solid solute is formed. The compounds were shaken and equilibrated isothermally (at least 72 h) to ensure the solid-liquid equilibrium is reached. Aer this a dened amount of the saturated liquid phase is withdrawn and weighed. The sample solution is placed in a drying chamber and a vacuum chamber to ensure total evaporation of the water. The remaining solid was weighed again and thus the solubility determined. Additionally oen pH values of the saturated solutions and crystal-structure studies of solid phase are missing, which are important since the crystal structure of the pure compound and the solid compound in equilibrium state is not allowed to change during the solubility determination and solubility model. In order to complete the missing information about crystal structure and pH values, AA solubility (for all 20 AA) was determined gravimetrically at T ¼ 298.15 K in three independent unbuffered aqueous solutions. The solutions were mixed for 24 h and le without further shaking for equilibration for 48 h. Then 200 mL of the saturated liquid phase was withdrawn for the solubility determination. The pH measurement of the unbuffered saturated solutions in solid-liquid equilibrium, as well as, the crystal structure of the initial pure AA (from the supplier), and of the solid phase equilibrated with saturated liquid phase were determined using pH meter with a standard uncertainty of AE0.01 and Powder Xray Diffractometer (PXRD, Miniex 600, Rigaku, Japan, operating temperature (295.15 K) and pressure (1 atm), speed scan 5 min À1 from 2 to 35 in 0.02 steps, voltage 40 kV, current 15 mA, type of radiation Cu Ka anode), respectively. All the pH values of the saturated solutions are listed Table 3

PC-SAFT
The successful prediction of AA solubility using eqn (1) requires the corresponding activity coefficient and experimental melting properties. The activity coefficient is the ratio of the fugacity coefficient 4 L i at the solubility mole fraction to the fugacity coefficient 4 L 0i of the pure-component. In this work the PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) equation of state is used and the fugacity coefficient is expressed as follows where m res i represents the residual chemical potential and Z the compressibility. The calculation of m res i and Z requires the residual Helmholtz energy a res which is expressed in this work as where a hc , a disp and a assoc are the Helmholtz energy contributions "hard chain", "dispersion" and "association", respectively. In this work the original PC-SAFT from Gross and Sadowski 26 is used, where all required contributions have already been implemented. For mixtures (here water + AA), the conventional Berthelot-Lorentz combining rules were applied to describe the interactions between two components i and j where k ij is the binary interaction parameter to describe deviations from the geometric mean of the dispersion-energy parameters of two components i and j (i.e., water and AA). The interaction parameter k ij was tted to osmotic-coefficient data at T ¼ 298.15 K. For some AA, a linearly temperaturedependent binary interaction parameter k ij (T) was available in the literature, expressed as: In this work k ij (T) was tted to solubility data at higher temperatures.
In the current work the AA were considered as associating uids, and each one association site was assigned for the amine ) and for glass transition step of ultra-fast quenched melted His (without silicon oil) ( ) and DSC for heat capacity of solid, c S p0i ( ). The area under the melting peak ( ) indicates Dh SL 0i , while onset temperature corresponds to T SL 0i . Dc SL p0i is determined at glass transition temperature, Dc SL p0i (T G 0i ) and adjusted to melting temperature, Dc SL p0i (T SL 0i ). (b) Melting temperature vs. heating rate diagram. Red line is the linear extrapolation to zero heating rate. The uncertainty is the standard deviation of multiple measurements. (c) Enthalpy, DH SL 0i , of His with respect to sample mass, m 0 , regardless of the scanning rates b [K s À1 ]. The slope of the linear fit through zero origin (line) signifies Dh SL 0i . The applied scanning rates were 2000 K s À1 ( ), 4000 K s À1 ( up-triangles), 6000 K s À1 ( ), 8000 K s À1 ( ) and 10 000 K s À1 ( ). Solid symbols (without silicon oil), empty symbols (with silicon oil). The melting properties of all twenty proteinogenic AA are shown in ESI Fig. S3 and S4. † The T SL 0i , Dh SL 0i , Dc SL p0i (T G 0i ) and Dc SL p0i (T SL 0i ) for each AA are listed in Table 1. (d) His aqueous solubility as temperature vs. weight fraction diagram. The red area presents the solubility modeling assuming g L i ¼ 1 (eqn (1) This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 44205-44215 | 44207 group and for the carboxylic group, respectively. In case of specic side chains of the AA, additional association site were added depending on a proton donator (e.g. Glu 1 : 2) or proton acceptor (Gln 2 : 1). The PC-SAFT pure-component parameters for most of the AA are already published 11 and will be utilized in this work, except for Glu and Asp with improved parameters, and for Trp with completely new parameters (listed in Table 2). The pure-component parameters were tted to osmoticcoefficient data and density data of aqueous solutions at T ¼ 298.15 K. For some further AA new experimental data for osmotic coefficients and mixture density was added in this work. The diagrams of the tted osmotic coefficients and mixture densities are shown in Fig. S5-S24 in the ESI. † Water was modeled with the 2B association scheme with a temperature-dependent segment diameter as it was used already in our previous work. 14 The PC-SAFT pure-component parameters as well as binary interaction parameters between the AA and water according eqn (6) used in this work are listed in Table 2.

Experimental melting properties
The melting properties of 19 proteinogenic AA (except Met) were characterized experimentally with FSC. The FSC experimental results for His as a representation are presented in Fig. 1(a-c), while for all other AA in ESI Fig. S3 and S4. † Ideally, a direct determination of Dc SL p0i at T SL 0i is preferable from the melting curve. However, this is not possible for some AA due to the mass loss caused by sublimation or evaporation aer melting. The mass loss of the sample is indicated by a baseline drop below c S p0i aer the melting, even though the sample was cooled down rapidly right aer the melting to minimize the mass loss at high temperature. If complete mass loss and crystallization are avoided, a glass transition step at T G 0i from glassy to supercooled liquid AA is shown as solid green line.
For low volatile samples such His or Arg (ESI Fig. S3 †), the liquid phase immediately aer the melting (solid red line) is in accordance with the c L p0i above glass transition. This indicates that the linear extrapolation from c L p0i of the glass transition to T SL 0i is applicable. For consistency reasons this extrapolation was applied for all AA with measured glass transition. For high volatile AA (Gly, Ala, Val, Leu, Ile, Pro, Lys, Phe, Cys) without measurable glass transition, Dc SL p0i (T) was estimated as explained in the discussion.
The c L p0i of the glass transition was tted linearly with a c L p0i as slope and b c L p0i as intercept, while the c S p0i determined from DSC as solid blue line is tted linearly with a c S p0i and b c S p0i . The heat capacity of crystal and glass are assumed to be equal, especially at temperatures close to T G . This assumption is commonly accepted, e.g. indomethacin, 27 saccharides, 28 o-terphenyl, 29 selenium, 30 poly-p-dioxanone. 31 The heat capacity difference between crystal and glass of such components does not differ by more than 5 to 10%. This difference is also within the uncertainty of our investigation. Nevertheless, we have to acknowledge that there is a difference in the heat capacity, which may inuence the result of our investigation. Nevertheless, in sum the difference between heat capacity of solid and glass phases are worst-case assumed to be <10%. Thus, heat capacity of solid was set equal to the glass. This allows indirect determination of Dc SL p0i (T G 0i ) at glass transition temperature and adjustment to melting temperature, Dc SL p0i (T SL 0i ), which is required in eqn (1). 24 In Fig. 1(b), the melting temperature was determined by extrapolating the onset melting temperature at different scanning rates to zero scanning rate b, DT SL 0i (b / 0), considering the thermal lag and possible superheating. [33][34][35] The slope of the linear t through zero origin in Fig. 1(c) signies the specic melting enthalpy, Dh SL 0i , where the DH SL 0i depends linearly on the sample mass, regardless of the scanning rates. Samples were measured with and without encapsulating in silicon oil. The good agreement of melting temperatures and melting enthalpies between both samples indicates the absence of chemical interaction between AA and silicon oil.
The experimental melting properties measured by FSC are listed in Table 1.

Discussion
First, without any thermodynamic modelthe activity coefficient g L i is assumed to be one (ideal mixture); this results in direct relation between the melting properties and the solubility according to eqn (1), where low melting temperature and enthalpy correspond to high solubility. The rule is true for the series of basic AA (Arg, His, Lys) as well as for aromatic AA (Phe, Tyr, Trp). However, the rule is not valid for the acidic AA (Asp, Glu) and their amides (Asn, Gln). The amide AA are better soluble in water compared to their acidic pendants despite the fact that the latter have lower melting temperatures and enthalpies. This wrong description of solubility using ideal mixture can only lead to the conclusion that g L i has to be taken into account to describe the interactions in the liquid phase. This can be quantied by another example. The solubility of His in an ideal mixture was calculated using melting properties in the range of their uncertainties. The result is shown as red area in Fig. 1(d). The experimental data of His solubility in water are not within the red area, giving the conclusion that g L i should be lower than one to match solubility according to eqn (1).
In Fig. 1(e) the PC-SAFT predicted g L His of His of the saturated solutions are presented. This is compared with values determined by using experimental FSC melting properties and experimental solubility data solved by eqn (1) to yield g L i . It can be observed that g L His values are far away from being one, and that the results of PC-SAFT prediction agrees with the experimental values within FSC uncertainty. The activity coefficients change with the temperature till it approaches unity at the melting temperature. The PC-SAFT predicted values of g sat 298.15 K for each AA at T ¼ 298.15 K are listed in Table 2.

PXRD measurements
The hydration of AA has been widely reported in literature. [44][45][46][47][48][49] In this work the PXRD measurement lead to further investigations in terms of possible polymorphs or formation of hydrates. Unfortunately, some AA were found to form hydrates (Ser, 12 Lys, 50 Asn, Pro), which does not allow the application of eqn (1) since the solid crystal in solution as well as for the melting properties must be the same. All the PXRD measurements were performed for the saturated solutions at T ¼ 298.15 K and are shown in ESI Fig. S25-S34. †

pH measurements
The pH measurement in aqueous solution of AA was conducted in order to ensure that only one neutral species (>99%) was present in the saturated solution. Asp (z95%), Arg (z90%), Glu (z88%) have less neutral species present in the saturated solutions, but this is still sufficient for PC-SAFT modeling, unfortunately not for Lys (z70%), for which Lys was excluded from the PC-SAFT modeling. The pH values for all AA solutions are listed in Table 3.

Solubility predictions with PC-SAFT
The solubility of all AA was predicted with PC-SAFT based on the experimental melting properties measured with FSC. Prediction means that all PC-SAFT pure-component parameters were t to non-solubility properties such as osmotic coefficients and mixture densities at T ¼ 298.15 K in water. The deviations between PC-SAFT values and the experimental solubility were quantied with the absolute relative deviations (ARD) according to eqn (8) where NP is the number of the available experimental solubility points, x PC-SAFT k and x exp k are the PC-SAFT predicted and the experimental solubility, respectively.
As shown recently 12 the Dh SL 0i has the highest inuence on the solubility prediction. Unfortunately, Dh SL 0i values from FSC have rather high uncertainty up to 20%, in comparison to the Dc SL p0i (T SL 0i ) (up to 5%) and T SL 0i (up to 2%). Therefore, FSC experimental results of Dc SL p0i (T SL 0i ) and T SL 0i were utilized as input for solubility predictions with PC-SAFT directly, i.e. without varying within the experimental uncertainty. In contrast, the Dh SL 0i was adjusted (within the range of uncertainty of the FSC results) to experimental solubility data at 298.15 K. As a result, the FSC data for Dh SL 0i in (Table 1) and the PC-SAFT t for Dh SL 0i (Table 3) are nearly identical, which proves the general suitability of PC-SAFT method for the mixtures considered in the present work, where the predicted PC-SAFT solubility is in good agreement with experimental solubility Table 2.
Most of the PC-SAFT parameters were already available in the literature. 8 These are listed in Table 2 together with binary interaction parameters between water and AA. The parameter k ij (T) was applied for AA with a rather low temperature dependency of solubility. Therefore, the solubility ratio between T ¼ 323.15 K and T ¼ 298.15 K should indicate the necessity of a temperature-dependent interaction parameter. Ratio lower than (greater than) 1.5 increases (decreases) the probability of using two such parameters (one parameter).
AA with non-polar substituents From Fig. 2(a) it was observed that the solubility decreases in the following order Gly > Ala > Val > Leu for T < 450 K. However at higher temperatures, this order is disarranged. This new nding becomes possible only due to the availability of the new experimental melting data from FSC in this work. All non-polar aliphatic AA show a high tendency for sublimation/evaporation aer the melting, so no glass transition step could be measured. However, even small values for differences of heat capacities moderately inuence the slope of the solubility line. Therefore, heat capacity differences were t to experimental solubilitytemperature curves.
The aqueous AA solubility of Ile and Pro are shown in Fig. 2(b). Apparently Pro is most soluble in water among the twenty proteinogenic AA. In this case the PXRD results from the present work showed a change in the crystal structure which was referenced to the formation of a hydrate. The exact hydration is at least below T Hydration # 298.15. As the melting properties belong to the anhydrous form, eqn (1) cannot be applied. Fig. 2(c) shows that solubility of Ser is higher than of Thr. For Thr the melting properties were taken as measured and the solubility prediction is in good agreement with the literature. For Ser a crystal change was found during the solubility measurement. The crystal change can be referenced to Luk,12 which shows the formation of a hydrate (T Hydration < 312.15 K). At higher temperatures the anhydrous Ser was formed (conrmed by PXRD), which allows the application of eqn (1). Table 2 PC-SAFT pure-component parameters and binary interaction parameters used to evaluate k ij according to eqn (7). Solubility ratio of one AA at two temperatures w 323.15 K /w 298.15 K , ARD between PC-SAFT and experimental solubility for N dp data points, activity coefficients in saturated solutions at T ¼ 298.15 K, and PXRD transitions This might explain the slight kink in the solubility curve observed for Ser in Fig. 2(c). The melting properties can only be determined for the anhydrous form. For the PC-SAFT predictions melting temperature and difference in heat capacity was taken from the FSC measurements. The melting enthalpy was adjusted within FSC uncertainty to the only available experimental solubility value at T ¼ 315.15 K. A good agreement between PC-SAFT and experimental solubility-temperature data supports the proposed procedure.

AA with acidic substituents
The acid AA (Asp, Glu) are characterized by a carboxyl group in the side chain and the amides (Asn, Gln) have a primary amide group. These additional polar groups also affect the pH value of the saturated solutions, which corresponds to their isoelectric points (pI). In general, these four AA show very low solubility in water, the amide AA are slightly more soluble than their acidic pendants at their pI ( Fig. 2(e)). However, for Asn a hydrate has formed upon equilibration in water. 7,9 Unfortunately, solubility literature data of the anhydrous Asn was not available. Hence eqn (1) could not be applied for temperatures below T Hydration # 298.15 and Asn solubility cannot be predicted. For Glu, Gln and Asp eqn (1) was applied and the results are in good agreement with the literature.

AA with basic substituents
His, Arg and Lys and increase the pH value in unbuffered aqueous solution, resulting in high pI values (Table 3). For Lys the experimental solubility re-measured in this work was higher than the only available literature data, 9 see Fig. 2 For His and Arg no change in crystal structure was detected and the conventional approach was applied. The solubility prediction is in good agreement with the literature data.

AA with aromatic substituents
The aqueous solubility of the aromatic AA are very low (Fig. 2(f)) with order of Phe > Trp > Tyr. The solubility measurements from this work are in good agreement with the literature data. No crystal structure change is detected in the PXRD in aqueous solutions, which allows modeling by application of eqn (1).
Due to high sublimation/evaporation, the glass transition of Phe was unattainable, subsequently the heat capacity difference could not be determined. The heat capacity was estimated to be Dc SL p0i (T SL 0i ) ¼ 184.37 J mol À1 K À1 in order to maintain the FSC determined Dh SL 0i within its experimental uncertainty. Modeling solubility without taking into account of Dc SL p0i would predict a very low Dh SL 0i , which is inconsistent with FSC data. This shows that the heat capacity difference is a very important property, which is unfortunately oen neglected in thermodynamic modeling.
For Trp and Tyr the experimental melting properties applied in PC-SAFT are within the uncertainties of the FSC measurement. The predicted solubility of Phe, Trp and Tyr are in good agreement with the experimental solubility data.

AA with sulfuric substituents
The solubility order for sulfuric AA is Cys > Met (ESI Fig. S35 †). A crystal structure change for Cys during the measurement was observed. Hence, solubility modeling with eqn (1) was not performed.
The experimental solubility for Met is consistent with the literature data. 51 Unfortunately no melting properties could be measured using FSC. Thus solubility modeling is also not possible. No crystal change was observed for both Cys and Met.

Comparison to literature
The classical way of thermodynamic solubility model for components with inaccessible experimental melting properties are performed as follows: different g E models or equations of state were used to calculate the activity coefficients for eqn (1), while simultaneously tting the melting properties to experimental solubility data. This procedure is still state-of-the art in the literature; however, the results of this approach differ strongly from the FSC-determined melting properties. Additionally, oen applied in the literature solubility model differs from the eqn (1) used in this work. For example, the modied Apelblat equation which ts the solubility with three independent parameters A, B and C. In this case it is not possible to distinguish the proper melting properties and therefore the comparison to the FSC melting properties is not possible. For this reason the "right side" of each solubility model can be treated as the solubility product K SP , which consist of the solubility x L i and activity coefficient g L i . x K SP depends only on the absolute temperature T. This allows the comparison of different solubility models without accounting for the tting to physically meaningful melting properties or purely adjustable tting parameters (Fig. 3). In Fig. 3 the solubility product of each AA is shown at T ¼ 298.15 K and T ¼ 323.15 K. In some literature studies the melting properties were calculated by using group contribution methods without further applying it on solubility modeling. 37,55 In this case, we applied eqn (1). However, regardless of how the melting properties/adjustable parameter was achieved, it is clear that the literature data differ to the solubility product determined in the current work. The predicted solubility based on the experimental melting properties is in good agreement with the experimental solubility, therefore the solubility product is more precise in comparison to other models in literature.

Conclusions
In this work nineteen proteinogenic AA (except Met) were characterized using FSC and the melting properties were successfully determined. It was shown that the experimentally determined melting properties are indispensable parts of solubility predictions using PC-SAFT. The access to the melting properties not only allows solubility prediction but also the quantication of the activity coefficients, which will give access to future model validation. The combination of FSC and PC-SAFT opens the door to predict solubility of solid compounds that decompose before melting.

Conflicts of interest
There are no conicts to declare.