Study of Thermodynamic Properties of l-Serine and l-Threonine in Aqueous Solutions of 1-(2-Carboxyethyl)-3-methylimidazolium Chloride [HOOCEMIM][Cl]

Abstract

The stability of amino acids in solutions containing electrolytes and the effect of ambient pH on their biological activity is an important research area. In this research work, the volumetric and transport properties of ionic liquid (IL) aqueous solution with special performance of 1-(2-carboxyethyl)-3-methylimidazolium chloride ([HOOCEMIM][Cl]) were studied. The selected IL acts as an electrolyte and allows the study of systems containing amino acids at acidic pH. In this work, the density, speed of sound and viscosity of binary and ternary solutions of IL in aqueous solution of amino acids in the structure of proteins, namely l-serine and l-threonine within IL molality range of (0.05, 0.07 and 0.09 mol·kg⁻¹) were measured at 298.15 K. From these quantities, apparent molar volume, limiting apparent molar volume, apparent molar isentropic compression, limiting apparent molar isentropic compression, transfer standard volumes for amino acids from water to the aqueous IL solutions and viscosity B-coefficients were calculated using the equations of Redlich–Meyer and Jones–Dole. Close examination of literature indicates that there is no data for water activity for solution of l-serine + H₂O at 308.15 and 318.15 K. In this way water activity, osmotic coefficient and vapor pressure were measured and using the interaction parameters of Wilson, NRTL, NRF-NRTL and UNIQUAC models, activity coefficient values of l-serine calculated.

1 Introduction

The advancement of biotechnology has largely led to the production of many biomolecules, which has led to the development of effective methods for the separation, concentration and purification of biomolecules. Biomolecules are complex molecules whose behavior in the mixture is affected by many factors such as pH, chemical structure, surface charge distribution, solvent properties, electrolyte type and concentration and even the presence of other biomolecules [1, 2]. Among these factors, the interaction of biomolecules with electrolytes has a potential application in the processes of separation and concentration of biomolecules [3, 4]. Many separation processes of biomolecules, such as adding electrolyte, which is one of the simplest methods of protein precipitation, are widely used in biotechnology and pharmaceutical industries [5, 6]. Also, the extraction of reverse micelles of proteins and amino acids with an electrolyte or solvents that have recently received attention is directly related to the interaction of biomolecules with electrolytes [7, 8]. Investigating the nature of these interactions is very important in designing suitable separation processes. Therefore, the interaction of biomolecules with electrolytes plays a central role in the physicochemical properties of these systems. Due to the complex three-dimensional structure of protein, which makes it difficult to investigate the effect of solvent on these macromolecules, interpreting the behavior of proteins by model compounds such as amino acids and peptides can be a valuable clue for understanding the behavior of biomolecules [9, 10].

Today, ionic liquids (ILs) as organic electrolytes and green solvents have a significant effect on many biochemical and chemical processes [11]. Therefore, due to the increasing importance and use of ILs, these compounds are a suitable option for studying the thermodynamic properties of amino acids due to their unique properties. Also, investigating and understanding the nature of the interaction of these compounds with amino acids is very important in designing suitable processes for the separation of amino acids, peptides and biomolecules. Of course, the design of these processes requires extensive and systematic studies of thermodynamic properties of these systems.

In the present work, the studied ionic liquid is functionalized by –COOH. Close examination of literature indicates that, water activity and solubility of 1-(2-carboxyethyl) -3-methylimidazolium chloride ([HOOCEMIM][Cl]) in presence of l-serine and l-threonine have been investigated in our previous work [12, 13] but no volumetric and transport data are available for these systems. However, volumetric and transport properties of l-serine and l-threonine in binary and ternary aqueous solutions of other ILs were determined in several works [14,15,16,17,18,19,20,21]. We found that, the studied ionic liquid promoted remarkable changes in the solubility of the studied amino acid by reducing the pH of the solution [12].

In this work, the density, speed of sound and viscosity of binary and ternary solutions of IL in aqueous solution of amino acids in the structure of proteins, namely l-serine and l-threonine within IL molality range of (0.05, 0.07 and 0.09 mol·kg⁻¹) were measured at 298.15. From these quantities, apparent molar volume, limiting apparent molar volume, apparent molar isentropic compression, limiting apparent molar isentropic compression, transfer standard volumes for amino acids from water to the aqueous IL solutions and viscosity B-coefficients were calculated using the equations of Redlich–Meyer [22] and Jones–Dole [23]. Close examination of literature indicates that there is no data for water activity for solution of l-serine + H₂O at 308.15 and 318.15 K. In this way water activity, osmotic coefficient and vapor pressure were measured and using the interaction parameters of Wilson [24], NRTL [25], NRF-NRTL [26] and UNIQUAC [27] models activity coefficient values of l-serine in aqueous solution were calculated.

2 Experimental Section

2.1 Materials

The TSIL has been synthesized. The synthesis method is described in detail in our previous work [12] and its specifications are given in Table 1. TSIL is a brownish yellow solid with melting point of 472.15 K. Other materials used in this research work, l-serine and l-threonine amino acids with molecular mass of 105.09 and 119.12, respectively, and in mass fraction purity > 0.99, are manufactured by Merck. These amino acids were used without further purification. Double distilled and deionized water was used.

Table 1 Characteristics of ionic liquid 1-(2-carboxyethyl)-3-methylimidazolium chloride [HOOCEMIM][Cl]

2.2 Apparatus and Procedure

Densities and sound velocities were continuously, simultaneously, automatically measured using a commercial density and sound velocity measurement apparatus (Anton Paar DSA 5000 densimeter and sound velocity analyzer). Both of speed of sound and density are extremely sensitive to temperature, so it was kept constant within ± 0.001 K using the Peltier Method. This device determines the density of solutions by electronically measuring the frequency of an oscillating system at the approximate frequency of 3 MHz. The uncertainties of density and speed of sound data measurement by this device is equal to 0.15 kg·m⁻³ and 0.5 m·s⁻¹, respectively. The apparatus was calibrated with double distilled deionized and degassed water, and dry air at atmospheric pressure. All solutions were degassed before measurement. The solutions were prepared by weighing with an analytical balance (Shimadzu, 321–34,553, Shimadzu) with an uncertainty of ± 10^–7 kg. Before each series of measurements, the device was calibrated using distilled water and dry air.

In this work, the viscosity of the solutions is measured using an Ubbelohde viscometer suspended in a water bath (Julabo, MD-18 V, Germany). This device is able to keep the temperature constant to ± 0.01 K. To make the temperature of the bath uniform and stabilize the temperature better, we connect it to another thermostat (Huber, D-77656, Germany). The dynamic viscosity, η, was calculated by the following relation of η = dK(t−θ), where t is the flow time; K is the viscometer constant; θ is the Hagenbach correction factor; and d is the density. The flow times were measured using a stopwatch. The precision of the used stopwatch was 0.01 s. The viscometer constant, K, is determined by calibrating at working temperatures with distilled water using viscosity values from the literature. The uncertainty for the dynamic viscosity determination was estimated to be ± 0.006 mPa·s. Each measurement was repeated five times.

The isopiestic method is a simple but highly accurate method for measuring the vapor pressure of a solution with a non-volatile solute, through equilibrium with a solution with a known vapor pressure (as a reference). The isopiestic device used in this research work contained two types of aqueous solution (NaCl as a reference and amino acid sample) which are in contact with each other through the vapor phase and are in thermal contact through an intermediate. The vapor space is emptied of air so that it contains only solvent vapor. Normally, the time needed to establish an equilibrium in the system is at least one week and more time is needed for dilute solutions. Equilibrium occurs when the differences between the mass fractions of each of the two repetitions is less than 0.01 %. The bath of water containing a Julabo temperature controller (Julabo, MB, Germany) was used to keep the isopiestic system at T = 308.15 and 318.15 K with an accuracy of 0.1 K. It is estimated that the standard uncertainty of solvent activity to be 0.008.

3 Results and Discussion

The measured density, speed of sound and viscosity data for binary systems of [HOOCEMIM][Cl] + H2O and ternary systems of [HOOCEMIM][Cl] +  l-serine + H₂O and [HOOCEMIM][Cl] + L-threonine + H₂O at a temperature of 298.15 K are reported in Tables 2, 3, 4 and 5. Using these data and the following relations, the apparent molar volume (${V}_{\varphi }$), isentropic compressibility (${\kappa }_{S}$) and apparent molar isentropic compression (${K}_{S,\Phi }$) of solutions considered are obtained, and the relevant results are given in these tables:

$$V_{\varphi } = \frac{M}{d} - \frac{{\left( {d - d_{0} } \right)}}{{mdd_{0} }},$$

(1)

$$\kappa_{S} = \frac{1}{{du^{2} }},$$

(2)

$$K_{S,\Phi } = \frac{{\left( {\kappa_{S} d_{0} - \kappa_{S0} d} \right)}}{{mdd_{0} }} + \frac{{\kappa_{S} M}}{d},$$

(3)

where m, M, d, d₀ and ${{\kappa }_{S}}_{0}$ are molality of solution (in mol·kg⁻¹), molar mass of the IL (in kg·mol⁻¹), densities (in kg·m⁻³) of solution and pure solvent and ${{\kappa }_{S}}_{0}$ the isentropic compressibility of pure solvent, respectively. The apparent molar volume at infinite dilution (${V}_{\varphi }^{0}$) is obtained by fitting the values of the apparent molar volume in the dilute region with the Redlich–Meyer equation [22], that is, Eq. 4. At infinite dilution, each ion is almost surrounded by solvent molecules and is separated from other ions. Therefore, the values are not affected by ion–ion interactions and this quantity will be a measure of ion–solvent interactions [28].

Table 2 Molality (m), density (d), speed of sound (u), apparent molar volume (${V}_{\varphi }$), isentropic compressibility (${\kappa }_{\mathrm{s}}$) and apparent molar isentropic compression (${{K}}_{\mathrm{S},\Phi }$) for [HOOCEMIM][Cl] + H₂O solution at 298.15 K and total experimental pressure (p_total) of 85.7 kPa

Table 3 Molarity (c_IL), density (d) and viscosity (η) for [HOOCEMIM][Cl] + H2O solution at 298.15 K and total experimental pressure (p_total) of 85.7 kPa

Table 4 Molality (m), density (d), speed of sound (u), apparent molar volume (${V}_{\varphi }$), isentropic compressibility (${\kappa }_{{s}}$) and apparent molar isentropic compression ($K_{S,\Phi}$) for [HOOCEMIM][Cl] + l-serine + H₂O and [HOOCEMIM][Cl] + l-threonine + H₂O solutions at 298.15 K and total experimental pressure (p_total) of 85.7 kPa

Table 5 Molarity (c_IL), density (d) and viscosity (η) for [HOOCEMIM][Cl] + l-serine + H₂O and [HOOCEMIM][Cl] + l-threonine + H₂O solutions at 298.15 K and total experimental pressure (p_total) of 85.7 kPa

$${V}_{\varphi }={V}_{\varphi }^{0}+{S}_{v}{m}^{1/2}+{B}_{v}m.$$

(4)

In this equation, S_v and B_v are adjustable parameters. The values of ${V}_{\varphi }^{0}$, S_v and B_v at each temperature are reported in Table 6. Apparent molar isentropic compressions in dilute region, m₁ < 0.1 mol·kg^{− 1} (${K}_{S,\Phi }^{0}$) for the studied binary and ternary systems can be obtained by fitting the apparent molar isentropic compression values for IL aqueous solutions at the studied temperature using Eq. 5. Calculated values for ${K}_{S,\Phi }^{0}$ are reported in Table 7.

$${K}_{S,\Phi }={K}_{S,\Phi }^{0}+{S}_{k}{m}^{1/2}+{B}_{k}m.$$

(5)

where ${S}_{k}$ and ${B}_{k}$ are the fitting coefficients. The experimental and calculated values of the apparent molar volume from the Redlich–Meyer equation versus the molality of the IL for the binary aqueous IL system are shown in Fig. 1 and are compared with the results of our previous work on 1-carboxymethyl-3-methylimidazolium chloride ([HOOCMMIM][Cl]) [14]. Also, to better show the effect of ILs on the studied amino acids, the experimental and calculated values of apparent molar volume from Eq. 4 were drawn according to the molality of amino acids for ternary systems [HOOCEMIM][Cl] +  l-serine + H₂O and [HOOCEMIM][Cl] + l-threonine + H₂O in different molality of the studied IL and temperature in Fig. 2. As can be seen from Table 2 and Fig. 1, the apparent molar volume increases with increasing concentration for both ionic liquids. The increase in the apparent molar volume with the increase in molality is the result of the decrease in the water molecules around the IL. The ${V}_{\varphi }$ of [HOOCEMIM][Cl] is larger than that of [HOOCMMIM][Cl], which is due to the bulkiness of the carboxyethyl group compared to carboxymethyl. Figure 2 and Table 4 show that the apparent molar volume decreases with the increase of amino acids in the IL solution. This decrease in ${V}_{\varphi }$ can be attributed to the phenomenon that the addition of amino acid to the system (IL + water) causes strong interaction between the ionic species of the IL and the dipolar ion part of amino acid molecules as well as water molecules. More information about these interactions can be obtained from the standard volumes of transfer (${\Delta }_{t}{V}^{0}$) which is calculated using the apparent molar volume at infinite dilution. The ${\Delta }_{t}{V}^{0}$ of amino acids from water to aqueous solution of IL is calculated from the following relationship:

Table 6 Limiting apparent molar volume (${V}_{\varphi }^{0}$) and adjustable parameters S_V and B_V of Eq. 4 along with standard deviations ($\sigma ({V}_{\varphi })$) for [HOOCEMIM][Cl] + H₂O, [HOOCEMIM][Cl] + L-serine + H₂O and [HOOCEMIM][Cl] + l-threonine + H₂O solutions at 298.15 K

Table 7 Limiting apparent molar isentropic compression (${K}_{S,\Phi }^{0}$) and adjustable parameters ${S}_{\kappa }$ and ${B}_{\kappa }$ of Eq. 5 along with standard deviations ($\sigma ( {K}_{S,\Phi } )$) for [HOOCEMIM][Cl] + H₂O, [HOOCEMIM][Cl] + l-serine + H₂O and [HOOCEMIM][Cl] + l-threonine + H₂O solutions at 298.15 K

Fig. 1

Experimental and calculated values of apparent molar volume (${V}_{\varphi }$) from Redlich–Meyer equation versus the IL molality for aqueous binary solutions of ILs at 298.15 K: filled triangle, [HOOCEMIM][Cl] + H₂O; filled diamond, [HOOCMMIM][Cl] + H₂O from our previous work [14]; and the lines calculated from the Redlich–Meyer (Eq. 4)

Fig. 2

Experimental and calculated values of apparent molar volume (${V}_{\varphi }$) from Redlich-Meyer equation versus the amino acid molality for aqueous ternary solutions at 298.15 K and different molality of IL (m_IL): filled diamond, m_IL = 0.05 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-serine + H₂O; × , m_IL = 0.09 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-serine + H₂O; filled circle, m_IL = 0.05 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-threonine + H₂O; filled Square, m_IL = 0.07 mol·kg.⁻¹ for [HOOCEMIM][Cl] + l-threonine + H₂O; and the lines calculated from the Redlich–Meyer (Eq. 4)

$${\Delta }_{t}{V}^{0}\left(\text{water}\to \text {aqueous} \, \text{IL}\right)={V}_{\varphi }^{0}\left(\text{in}\,\text{aqueous}\, \text{IL}\right)-{V}_{\varphi }^{0}\left(\text{in}\, \text{water}\right).$$

(6)

The values of ${V}_{\varphi }^{0}$ for amino acids l-serine and l-threonine in aqueous solution and temperature of 298.15 K are 60.6 and 76.81 cm³.mol⁻¹, respectively, which are reported in the reference [29]; the obtained results for the ${\Delta }_{t}{V}^{0}$ are given in Table 8. This Table clearly shows that ${\Delta }_{t}{V}^{0}$ is positive. Positive values ​​can be justified using the cosphere overlap model [28, 30]. Based on this model, interactions between IL and amino acids can be divided into four categories [30]:

• 1. Hydrophilic–ion interactions.

• 2. Hydrophilic–hydrophilic interactions.

• 3. Interaction between hydrophilic and hydrophobic.

• 4. Hydrophobic–hydrophobic interaction.

Table 8 Standard volumes of transfer (${\Delta }_{t}{V}^{0}$) of amino acid transfer from water to aqueous solutions of [HOOCEMIM][Cl] at 298.15 K

According to this model, the first two types of interactions lead to positive and the third and fourth types of interactions lead to negative values [30]. In general, it can be said that it will be positive when the sum of the interactions of the first and second categories are dominant compared to the interactions of the third and fourth categories. These interactions cause water molecules to be released in the solution and consequently it will be positive [30]. The positive values for the systems [HOOCEMIM][Cl] +  l-serine/ l-threonine + H₂O indicates the predominance of the first two classes of interactions to the interactions are in the third and fourth categories.

Table 2 shows that the obtained values for apparent molar isentropic compression are negative and become less negative as the concentration of IL increases. The negative values indicate that the compressibility of the hydration layer around the ions is lower than the bulk of the solvent, and this is due to the hydration of the ions at low concentrations [31]. By increasing the concentration of the IL, the ion–solvent interaction becomes weaker and the compressibility of the water molecules around the dissolved ions increases, and as a result, it becomes less negative. In Fig. 3, the experimental and calculated values of apparent molar isentropic compression from Eq. 3 are plotted versus the IL molality and compared with the results obtained from our previous work for [HOOCMMIM][Cl] [14]. This figure shows that ${K}_{S,\Phi }$ becomes less negative with increasing chain length. This issue can be attributed to the reduction of the ion–solvent interactions due to the reduction of the hydration of the IL and the electrostatic interaction with water, resulting in the release of some water molecules into the solution mass [32]. The plot of the change of ${K}_{S,\Phi }$ in different molality of IL is shown in Fig. 4 for ternary systems. In general, ${K}_{S,\Phi }^{0}$ for ionic species are large negative, positive for hydrophobic solutes, and small negative for polar species [33]. The results obtained in Table 7 show that all the values calculated for ${K}_{S,\Phi }^{0}$ are marginally negative. Negative values indicate that the water molecules surrounding the solute are more resistant to condensation than the solution [33].

Fig. 3

Experimental and calculated values of apparent molar isentropic compression (${K}_{S,\Phi }$) from Eq. 5 versus the IL molality for aqueous binary solutions of ILs at 298.15 K: filled triangle, [HOOCEMIM][Cl] + H₂O; filled diamond, [HOOCMMIM][Cl] + H₂O from our previous work [14]; and the lines calculated from the Eq. 5

Fig. 4

Experimental and calculated values of apparent molar isentropic compression (${K}_{S,\Phi }$) from Eq. 5 versus the amino acid molality for aqueous ternary solutions at 298.15 K and different molality of IL (m_IL): filled triangle, m_IL = 0.05 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-serine + H₂O; open circle, m_IL = 0.09 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-serine + H₂O; filled diamond, m_IL = 0.05 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-threonine + H₂O; × , m_IL = 0.07 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-threonine + H₂O; and the lines calculated from Eq. 5

The relative viscosity data (${\eta }_{r}$) of binary and ternary systems were fitted with the Jones–Dole model [23] of Eq. 6 in order to calculate the viscosity B-coefficients, which provides information about the solvent–solute interactions.

$${\eta }_{r}=\frac{\eta }{{\eta }_{0}}=1+Bc.$$

(7)

In this model, c and ${\eta }_{0}$ are molarity and the viscosity of pure solvent where aqueous solution of IL is considered as a solvent in ternary systems. B-coefficients values along with standard deviation values ​​are reported in Table 9. As we know, Jones–Dole B-coefficient is a measure of ion–solvent interactions, and positive Jones–Dole coefficient values ​​indicate that ion–solvent interactions are strong. In other words, the positive B-coefficient in the studied systems means that the solvent is a structure builder, i.e. solutes causes regularization of the solvent structure [33]. Also, the standard deviations obtained for viscosity in Table 9 show the efficiency of Eq. 6 for fitting the viscosity values. Figure 5 shows the changes in the viscosity of the solutions in the studied systems according to their molarity. The drawn lines show the viscosity calculated from Eq. 7 with the parameters listed in Table 9 and are in good agreement with the experimental viscosity data.

Table 9 Viscosity B coefficient along with standard deviations (σ(η)) for [HOOCEMIM][Cl] + H₂O, [HOOCEMIM][Cl] + l-serine + H₂O and [HOOCEMIM][Cl] + l-threonine + H₂O solutions at 298.15 K

Fig. 5

Experimental and calculated values of viscosity (η) from Eq. 7 versus the amino acid molarity for aqueous ternary solutions at 298.15 K and different molality of IL (m_IL): filled diamond, m_IL = 0.05 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-serine + H₂O; Δ, m_IL = 0.09 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-serine + H₂O; × , m_IL = 0.05 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-threonine + H₂O; filled circle, m_IL = 0.07 mol·kg⁻¹ for [HOOCEMIM][Cl] + l-threonine + H₂O; and the lines calculated from Eq. 6

Using the isopiestic technique and with the following equation, the partial pressure of water (p) for aqueous systems of l-serine has been calculated at 308.15 and 318.15 K [34, 35]:

$$\mathrm{ln}\left(p\right)=\mathrm{ln}({a}_{m}{p}_{m})-\frac{\left({B}_{m}-{V}_{m}\right)\left(p-{p}_{m}\right)}{RT}.$$

(8)

In this equation information of water as the second virial coefficient (${B}_{m}$) is calculated from the Rard and Platford equation [36]; the state equation of Saul and Wagner [37] is utilized to estimate the vapor pressure (${p}_{m}$) of water; density of water [38] is utilized to estimate the molar volume (${V}_{m}$) of it. R and T are, respectively, universal constant of gases and absolute temperature. ${a}_{m}$ is the water activity in the solutions studied which is calculated applying the following equation [34, 35]:

$${a}_{m}=\mathrm{exp}(-{v}_{\text {NaCl}}{m}_{\text {NaCl}}{\varphi }_{\text {NaCl}}{M}_{m}).$$

(9)

In this equation, ${\varphi }_{\text{NaCl}}$ is the osmotic coefficients of aqueous solution of NaCl which can be estimated using the following equation proposed by Colin et al. [39]:

$$\varphi_{\rm{NaCl}} = 1 - A\sqrt {m_{\rm{NaCl}} } \left( {1 + 1.2\sqrt {m_{\rm{NaCl}} } )^{ - 1} + Qm_{\rm{NaCl}} \exp ( - 2\sqrt {m_{\rm{NaCl}} } } \right) + Bm_{\rm{NaCl}} + Cm_{\rm{NaCl}}^{2} + Dm_{\rm{NaCl}}^{3} + Em_{\rm{NaCl}}^{4} .$$

(10)

In Eq. 9${v}_{\rm{NaCl}}$, m_NaCl and M_m are, respectively, total stoichiometric numbers of anions and cations in NaCl solutions, the molality of aqueous solution of NaCl and molecular mass of water. In Eq. 10, parameters adjusted by Colin et al. (A, Q, B, C, D and E) have, respectively, values of 0.391942, 0.280069, 0.079776, 1.565033 × 10^–3, − 2.048323 × 10^–4 and 8.748618 × 10^–6 at 298.15 K [39]. The experimental results of osmotic coefficient, activity and partial pressure of water for binary system l-serine + water at temperatures of 308.15 and 318.15 K were calculated and reported in Table 10. As can be seen in this table, with increase in the molality, the activity and partial pressure of water decreases. Figures 6 and 7 show the effect of temperature on the activity and vapor pressure of the solvent for the l-serine system. The water activity data for 298.15 K is taken from our previous work [12]. According to these figures and Table 10, it is clear that the activity and partial pressure of water increases with the increase in temperature. The partial pressure is directly related to the activity of the solvent, the higher the activity of the solvent in the solution, the higher the vapor pressure of the solvent. As can be seen from these figures, changes in vapor pressure due to temperature are more intense than activity.

Table 10 Molality (m), osmotic coefficient (ϕ), water activity (a_m) and partial pressure of water (p) for (l-serine + H₂O) at temperatures of 308.15 and 318.15 K and total experimental pressure (p_total) of 85.7 kPa

Fig. 6

Solvent activity according to amino acid molality (m_l-serine) for binary system (l-serine + H₂O) at different temperatures: filled square, 298.15 K [42]; open triangle, 308.15 K; × , 318.15 K; Lines calculated from the Wilson model

Fig. 7

partial pressure of water according to amino acid molality (m_l-serine) for binary system (l-serine + H₂O) at different temperatures: filled square, 298.15 K [42]; open triangle, 308.15 K; × , 318.15 K; Lines calculated from the Wilson model

Water activity data were fitted by local composition models (Wilson [24], NRTL [25], NRF-NRTL [26] and UNIQUAC [27]) using the following relation

$$\text{ln}a_{m} = \text{ln}\gamma_{m}^{cal} + \text{ln}x_{m} ,$$

(11)

where, ${x}_{m}$ and ${\gamma }_{m}^{\text{cal}}$ are respectively the water mole fraction and water activity coefficient calculated by Flory–Huggins relation (FL) [41] and aforementioned local composition-based models (LC) as ${\mathrm{ln}}{\gamma}_{{m}}^{\mathrm{cal}}={\mathrm{ln}}{\gamma}_{{m}}^{\mathrm{FL}}+{\mathrm{ln}}{\gamma}_{{m}}^{\mathrm{LC}}$. Flory–Huggins relation is as follow [41]:

$${\mathrm{ln}{\gamma }}_{m}^{\mathrm{FL}}=\mathrm{ln}\left(\frac{{X}_{m}}{{x}_{m}}\right)+1-{\sum }_{J}\frac{{X}_{J}}{{r}_{J}}$$

(12)

where r_J is the number of polymer segments, subscript J denote the component J. ${X}_{J}$ is the effective local mole fractions of species J and ${X}_{m}={x}_{m}$. The necessary equations of these models are given in the appendix. The results of fitting are given in Table 11 and the efficiency of Wilson model is shown in Figs. 6 and 7. As can be seen from these figures and Table 11, the performance of all models is good in fitting the water activity data. The activity coefficients for the studied system were calculated by the considered local combination models and the results of the NRTL model as an example are shown in Fig. 8. As seen in this figure, the activity coefficient of amino acid increases with increasing temperature. This result is in accordance with the studies conducted by Romero et al. [40] on the effect of temperature on aliphatic amino acids. But there is no interpretation about the effect of temperature on the activity coefficient. It seems that with the increase in temperature, the values of the solute activity coefficient deviate less than the ideal state due to the decrease in the solute–solute interaction.

Table 11 Parameters of local composition models obtained from fitting the experimental data of water activity for the system of l-serine + H₂O along with standard deviations (sd) at 308.15 and 318.15 K

Fig. 8

activity coefficient of l-serine (γ_m^*) calculated from NRTL model for binary system (l-serine + H₂O) at different temperatures: filled diamond, 298.15 K [42]; open square, 308.15 K; × , 318.15 K; Lines calculated from the Wilson model

4 Conclusion

The density, speed of sound and viscosity of binary and ternary solutions of (2-carboxyethyl)-3-methylimidazolium chloride ([HOOCEMIM][Cl]) in aqueous solution of amino acids in the structure of proteins, namely l-serine and l-threonine within ionic liquid (IL) molality range of (0.05, 0.07 and 0.09 mol·kg⁻¹) were measured at 298.15 K. From these quantities, apparent molar volume, limiting apparent molar volume, apparent molar isentropic compression, limiting apparent molar isentropic compression, transfer standard volumes for amino acids from water to the aqueous IL solutions and viscosity B-coefficients were calculated using the equations of Redlich–Meyer and Jones–Dole. It was found that apparent molar volume (${V}_{\varphi }$) decreases with the increase of amino acids in the IL solution. This decrease in ${V}_{\varphi }$ can be attributed to the phenomenon that the addition of amino acid to the system (IL + water) causes strong interaction between the ionic species of the IL and the dipolar ion part of amino acid molecules as well as water molecules. In the systems of [HOOCEMIM][Cl] + l-serine/l-threonine + H₂O, hydrophilic–ion interactions and hydrophilic–hydrophilic interactions are dominant compared to interactions of hydrophilic–hydrophobic and hydrophobic–hydrophobic. The compressibility of the hydration layer around the ions is lower than the bulk of the solvent, and this is due to the hydration of the ions at low concentrations. By increasing the concentration of the IL, the ion–solvent interaction becomes weaker and the compressibility of the water molecules around the dissolved ions increases. In ternary systems, the water molecules surrounding the solute are more resistant to condensation than the solution; and the solvent is a structure builder, i.e. solutes causes regularization of the solvent structure. Osmotic coefficient, water activity, vapor pressure and activity coefficient for l-serine + H₂O at 308.15 and 318.15 K were measured and correlated with Wilson, NRTL, NRF-NRTL and UNIQUAC models. It is clear that the activity and partial pressure of water increases with the increase in temperature. The partial pressure is directly related to the activity of the solvent, the higher the activity of the solvent in the solution, the higher the vapor pressure of the solvent. With the increase in temperature, the values of the solute activity coefficient deviate less than the ideal state due to the decrease in the solute–solute interaction.

Appendices

Appendix 1

1.1 Wilson Equation

The coefficient equation of the solvent for Wilson model [24] is as follow:

$$\begin{aligned} \ln \gamma_{m}^{*,\text{Wilson}} = & - C\ln (x_{m} + \exp ( - \frac{{E_{sm} }}{CRT})x_{s} + \exp ( - \frac{{E_{Em} }}{CRT})\left( {x_{a} + x_{c} } \right) \\ & - \frac{{Cx_{m} \left( {x_{a} + x_{c} + x_{s} - \exp ( - \frac{{E_{sm} }}{CRT}} \right)x_{s} - \exp ( - \frac{{E_{Em} }}{CRT})\left( {x_{a} + x_{c} } \right)}}{{x_{m} + \exp ( - \frac{{E_{sm} }}{CRT})x_{s} + \exp ( - \frac{{E_{Em} }}{CRT})\left( {x_{a} + x_{c} } \right)}} \\ & + \frac{{Cx_{s} \left( {x_{s} - \exp ( - \frac{{E_{ms} }}{CRT}} \right)\left( {x_{a} + x_{c} + x_{s} } \right) + \exp ( - \frac{{E_{Es} }}{CRT})\left( {x_{a} + x_{c} } \right)}}{{x_{s} + \exp ( - \frac{{E_{ms} }}{CRT})x_{m} + \exp ( - \frac{{E_{Es} }}{CRT})\left( {x_{a} + x_{c} } \right)}} \\ & + \frac{{Cx_{a} \left( {x_{c} + \exp ( - \frac{{E_{sE} }}{CRT}} \right)x_{s} - \exp ( - \frac{{E_{mE} }}{CRT})\left( {x_{c} + x_{s} } \right)}}{{\left( {x_{c} + x_{s} + x_{m} } \right)\left( {x_{c} + \exp ( - \frac{{E_{sE} }}{CRT}} \right)x_{s} + \exp ( - \frac{{E_{mE} }}{CRT})x_{m} }} \\ & + \frac{{Cx_{c} \left( {x_{a} - \exp ( - \frac{{E_{mE} }}{CRT}} \right)x_{a} + x_{s} \left( {\exp ( - \frac{{E_{sE} }}{CRT}} \right) - \exp ( - \frac{{E_{mE} }}{CRT}))}}{{\left( {x_{a} + x_{s} + x_{m} } \right)\left( {x_{a} + \exp ( - \frac{{E_{sE} }}{CRT}} \right)x_{s} + \exp ( - \frac{{E_{mE} }}{CRT})x_{m} }} \\ \end{aligned}$$

(13)

Here, ${E}_{mE}$, ${E}_{Em}$, ${E}_{sE}$, ${E}_{Es}$, ${E}_{sm}$ and ${E}_{ms}$ are the adjustable parameters of Wilson model; R is the universal constant of gases; C is the coordination number of the model which was set to 10.

1.2 NRTL Equation

The activity coefficient equation of the solvent for NRTL model [25] is as follow:

$$\begin{aligned} \ln \gamma_{m}^{*,\text{NRTL}} = & \frac{{\left( {\exp ( - \alpha_{sm} \tau_{sm} } \right)x_{s} + \exp ( - \alpha_{Em} \tau_{Em} )\left( {x_{a} + x_{c} } \right))\left( {\exp ( - \alpha_{sm} \tau_{sm} } \right)x_{s} \tau_{sm} + \left( {\exp ( - \alpha_{Em} \tau_{Em} } \right)\tau_{Em} \left( {x_{a} + x_{c} } \right)}}{{\left( {x_{m} + \exp ( - \alpha_{sm} \tau_{sm} } \right)x_{s} + \exp ( - \alpha_{Em} \tau_{Em} )\left( {x_{a} + x_{c} } \right))^{2} }} \\ & + \frac{{\exp ( - \alpha_{ms} \tau_{ms} )x_{s} \left( {x_{s} \tau_{ms} + \exp ( - \alpha_{Es} \tau_{Es} } \right)\left( {x_{a} + x_{c} } \right)\left( {\tau_{ms} - \tau_{Es} } \right))}}{{\left( {x_{s} + \exp ( - \alpha_{ms} \tau_{ms} } \right)x_{m} + \exp ( - \alpha_{Es} \tau_{Es} )\left( {x_{a} + x_{c} } \right))^{2} }} \\ & + \frac{{\exp ( - \alpha_{mE} \tau_{mE} )x_{a} \left( {x_{c} \tau_{mE} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} )\left( {\tau_{mE} - \tau_{sE} } \right))}}{{\left( {x_{c} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} + \exp ( - \alpha_{mE} \tau_{mE} )x_{m} )^{2} }} \\ & + \frac{{\exp ( - \alpha_{mE} \tau_{mE} )x_{c} \left( {x_{a} \tau_{mE} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} )\left( {\tau_{mE} - \tau_{sE} } \right))}}{{\left( {x_{a} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} + \exp ( - \alpha_{mE} \tau_{mE} )x_{m} )^{2} }} \\ \end{aligned}$$

(14)

Here, x is mole fraction; subscripts E, m and s denote IL, water and drug, respectively; ${\alpha }$ is non-randomness factor and in this work its values are set to 0.2 for obtaining the better fitting quality.${\tau }_{mE}$, ${\tau }_{Em}$, ${\tau }_{sE}$, ${\tau }_{Es}$, ${\tau }_{sm}$ and ${\tau }_{ms}$ are the adjustable parameters of NRTL model.

1.3 NRF-NRTL Equation

The activity coefficient equation of the solvent for NRF-NRTL model [26] is as follow:

$$\begin{aligned} \ln \gamma_{m}^{*,\text{NRF-NRTL}} = & \frac{{\left( {\exp ( - \alpha_{sm} \tau_{sm} } \right)x_{s} + \exp ( - \alpha_{Em} \tau_{Em} )x_{a} + \exp ( - \alpha_{Em} \tau_{Em} )x_{c} )\left( {\exp ( - \alpha_{sm} \tau_{sm} } \right)x_{s} \tau_{sm} + \exp ( - \alpha_{Em} \tau_{Em} )x_{a} \tau_{Em} + \exp ( - \alpha_{Em} \tau_{Em} )x_{c} \tau_{Em} )}}{{\left( {x_{m} + \exp ( - \alpha_{sm} \tau_{sm} } \right)x_{s} + \exp ( - \alpha_{Em} \tau_{Em} )x_{a} + \exp ( - \alpha_{Em} \tau_{Em} )x_{c} )^{2} }} \\ & - \frac{{\left( {x_{a} + x_{c} + x_{s} } \right)\left( {x_{s} \tau_{sm} + x_{a} \tau_{Em} + x_{c} \tau_{Em} } \right)}}{{(x_{a} + x_{c} + x_{s} + x_{m} )^{2} }} \\ & + \frac{{\left( {\exp ( - \alpha_{ms} \tau_{ms} } \right)\left( {x_{s} \tau_{ms} + \exp ( - \alpha_{Es} \tau_{Es} } \right)x_{a} \tau_{ms} + \exp ( - \alpha_{Es} \tau_{Es} )x_{c} \tau_{ms} - \exp ( - \alpha_{Es} \tau_{Es} )x_{a} \tau_{Es} - \exp ( - \alpha_{Es} \tau_{Es} )x_{c} \tau_{Es} )}}{{\left( {x_{s} + \exp ( - \alpha_{ms} \tau_{ms} } \right)x_{m} + \exp ( - \alpha_{Es} \tau_{Es} )x_{a} + \exp ( - \alpha_{Es} \tau_{Es} )x_{c} )^{2} }} \\ & - \frac{{x_{s} \left( {x_{a} \tau_{ms} + x_{c} \tau_{ms} + x_{s} \tau_{ms} - x_{a} \tau_{Es} - x_{c} \tau_{Es} } \right)}}{{(x_{a} + x_{c} + x_{s} + x_{m} )^{2} }} \\ & + \frac{{\left( {\exp ( - \alpha_{mE} \tau_{mE} x_{a} } \right)\left( {x_{c} \tau_{mE} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} \tau_{mE} - \exp ( - \alpha_{sE} \tau_{sE} )x_{s} \tau_{sE} )}}{{\left( {x_{c} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} + \exp ( - \alpha_{mE} \tau_{mE} )x_{m} )^{2} }} \\ & - \frac{{x_{a} \left( {x_{a} \tau_{mE} + x_{c} \tau_{mE} + x_{s} \tau_{mE} - x_{s} \tau_{sE} } \right)}}{{(x_{a} + x_{c} + x_{s} + x_{m} )^{2} }} \\ & + \frac{{\left( {\exp ( - \alpha_{mE} \tau_{mE} x_{c} } \right)\left( {x_{a} \tau_{mE} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} \tau_{mE} - \exp ( - \alpha_{sE} \tau_{sE} )x_{s} \tau_{sE} )}}{{\left( {x_{a} + \exp ( - \alpha_{sE} \tau_{sE} } \right)x_{s} + \exp ( - \alpha_{mE} \tau_{mE} )x_{m} )^{2} }} \\ & - \frac{{x_{c} \left( {x_{a} \tau_{mE} + x_{c} \tau_{mE} + x_{s} \tau_{mE} - x_{s} \tau_{sE} } \right)}}{{(x_{a} + x_{c} + x_{s} + x_{m} )^{2} }}, \\ \end{aligned}$$

(15)

where the nonrandomness factor values are set to 0.3 for obtaining the better fitting quality in this work.${\tau }_{mE}$, ${\tau }_{Em}$, ${\tau }_{sE}$, ${\tau }_{Es}$, ${\tau }_{sm}$ and ${\tau }_{ms}$ are the adjustable parameters of NRF-NRTL model.

1.4 UNIQUAC Equation

The activity coefficient equation of the solvent for UNIQUAC model [27] is as follow:Where

$$\begin{aligned} \ln \left( {\gamma_{m}^{*} } \right) = & \ln \left( {\frac{{\psi_{m}^{*} }}{{x_{m} }}} \right) + \frac{z}{2}q_{m} \ln \frac{{\theta_{m} }}{{\psi_{m}^{*} }} + l_{m} - \left( {\frac{{\psi_{m}^{*} }}{{x_{m} }}} \right)\left( {x_{w} l_{w} + x_{m} l_{m} + x_{ca} l_{ca} } \right) \\ & - q_{m} \ln \left( {\theta_{w}^{^{\prime}} \exp (\frac{{ - u_{w,m} }}{RT}) + \theta_{ca}^{^{\prime}} \exp (\frac{{ - u_{ca,m} }}{RT}) + \theta_{m}^{^{\prime}} } \right) + q_{m} \\ & + q_{m} - q_{m} \left[ {\left( {\frac{{\theta_{w}^{^{\prime}} \exp (\frac{{ - u_{m,w} }}{RT})}}{{\theta_{w}^{^{\prime}} + \theta_{ca}^{^{\prime}} \exp (\frac{{ - u_{ca,w} }}{RT}) + \theta_{m}^{^{\prime}} \exp (\frac{{ - u_{m,w} }}{RT})}}} \right) + \left( {\frac{{\theta_{ca}^{^{\prime}} \exp (\frac{{ - u_{m,ca} }}{RT})}}{{\theta_{w}^{^{\prime}} \exp (\frac{{ - u_{w,ca} }}{RT}) + \theta_{ca}^{^{\prime}} + \theta_{m}^{^{\prime}} \exp (\frac{{ - u_{m,ca} }}{RT})}}} \right) + \left( {\frac{{\theta_{m}^{^{\prime}} }}{{\theta_{w}^{^{\prime}} \exp (\frac{{ - u_{w,m} }}{RT}) + \theta_{ca}^{^{\prime}} \exp (\frac{{ - u_{ca,m} }}{RT}) + \theta_{m}^{^{\prime}} }}} \right)} \right] \\ & - \ln \left( {\frac{{r_{m} }}{{r_{w} }}} \right) + 1 - \left( {\frac{{r_{m} }}{{r_{w} }}} \right) - \frac{z}{2}q_{m} \left( {\ln \frac{{r_{m} }}{{r_{w} }}\frac{{q_{w} }}{{q_{m} }}} \right) + 1 - \frac{{r_{m} }}{{r_{w} }}\frac{{q_{w} }}{{q_{m} }} + q_{m} \left( {1 - \ln \left( {\exp \left( {\frac{{ - u_{w,m} }}{RT}} \right) - \exp \left( {\frac{{ - u_{m,w} }}{RT}} \right)} \right)} \right), \\ \end{aligned}$$

(16)

$$l_{i} = \frac{z}{2}\left( {r_{i} - q_{i} } \right) - \left( {r_{i} - 1} \right)$$

(17)

$z$ which is the coordination number whose value is equal to 10; and the values of r and q which are parameters related to size can be calculated by the group theory.

Data Availability

All data can be found in the current manuscript.