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  • During recent years two primary types of models

    2019-11-11

    During recent years, two primary types of models have been applied for calculating various thermodynamic properties of amino Maraviroc solutions, i.e. excess Gibbs energy (gE) models used numerously to describe the solubility of amino acid solutions, and equations of state (EOS) models appropriate to obtain density, vapor Maraviroc pressure, enthalpy, etc. One of the preliminary endeavors for giving a distinguished overview of both mentioned approaches was that of Khoshkbarchi and Vera [2]. The Wilson model [3], NRTL model [4], Pitzer model [5], and UNIFAC model [6], [7] are also so illustrative among the gE models which are utilized in amino acids calculations. These models have successfully presented their ability in variety of systems containing aqueous amino acids [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. For instance, Nass [8] described the solubility of various amino acids such as l-serine, l-threonine, and l-alanine through electrolyte NRTL model [4] by introducing equilibrium constants of amino acid ionic species. Likewise, Ferreira et al. [14] optimized NRTL parameters for correlating and predicting amino acids solubility in mixed water-alcohol solutions at different temperatures. Additionally, Gupta and Heidemann [10] made an effort to present a predictive model for the activity coefficients of amino acids via modified UNIFAC group contribution model [7]. Although application of gE models is so common due to their simplicity, these models are not able to calculate the solutions density, and the pressure dependency of the activity coefficients cannot be determined directly. Since the EOSs do not have these disadvantages, and they can be calculated using the residual Helmholtz energy framework straightly, these models have drawn more attention to calculate various thermodynamic properties of solutions containing amino acids without any extra term. Most of the well-known attempts [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29] for estimating different thermodynamic properties in aqueous amino acid solutions are about different versions of Statistical Associating Fluid Theory (SAFT) [30], [31], [32] which are proposed based on Wertheim’s contribution. For illustration, Fuchs et al. [18] measured the solubility of dl-methionine in pure water in a temperature range of 293.15–353.15 K, and then modeled the solubility of three different amino acids in aqueous and alcohol solutions via PC-SAFT EOS considering the dependency of solubility on pH value. Moreover, Ji and Feng [19] used the SAFT EOS in order to describe the solubility of aqueous amino acid solutions by expanding the approach [33] previously developed to examine the SAFT parameters for amino acids. In addition, Anvari et al. [27] utilized the SAFT-VR EOS to correlate the phase behavior of simple aqueous peptides and aqueous electrolyte solutions of amino acids by taking into account the range of interaction as a variable, in addition to other substantial qualities of these bio molecules such as number and diameter of segments, interaction energy, association energy and association volume. Afterwards, they predicted the pH variation on the solubility of amino acids, and also predicted the phase behavior of mixed solutions. Beside presented efforts, Lee and Kim [23] focused on modeling the thermodynamic properties of amino acid solutions by reducing the optimized parameters of PC-SAFT EOS from five to three. They considered the effects of pH value on solubility data assuming that the association volume of amino acids can be set to a fixed number, and that segment number of these components is related with the molecular weight linearly. The proposed model calculated the density and solute activity coefficient as well. Also, the predicted values of water activity, osmotic coefficient, and solubility were in good agreement with experimental data. Furthermore, Cameretti and Sadowski [20] modeled vapor pressure, liquid density, and solubility of four amino acids and oligopeptides using PC-SAFT EOS. Afterwards, Gross et al. [24] measured the solubility of ternary mixtures l-alanine/l-valine, l-alanine/l-leucine, and l-leucine/l-valine in water at 303 and 323 K. Furthermore, they modeled the solubility of seven binary, eight ternary, and one quaternary amino acid systems applying PC-SAFT EOS without considering dissociation/association equilibria. After a while, Held et al. [25] applied PC-SAFT EOS to simultaneously evaluate different thermodynamic properties of 28 aqueous amino acid and oligopeptides solutions. Moreover, they measured, and predicted osmotic coefficients in aqueous solutions containing two amino acids in order to prove the predictive behavior of PC-SAFT EOS without dissociation/association equilibria. In their subsequent work [26], they used the parameters which were optimized in [25], and modeled pH and solubility in aqueous multi-solute amino acid solutions with different PIs [26]. Additionally, they extended their investigations to measure and model aqueous electrolyte/amino acid solutions with ePC-SAFT EOS [27]. Subsequently, osmotic coefficient and amino acid solubility of ternary electrolyte/amino acid/water systems have been predicted.