Thermodynamics of Mixing Primary Alkanolamines with Water

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Thermodynamics of Mixing Primary Alkanolamines with Water Abdenacer Idrissi, and Pal Jedlovszky J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01052 • Publication Date (Web): 17 May 2018 Downloaded from http://pubs.acs.org on May 18, 2018

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The Journal of Physical Chemistry

Thermodynamics of Mixing Primary Alkanolamines with Water Abdenacer Idrissi1 and Pál Jedlovszky2* 1

Laboratoire de Spectrochimie Infrarouge et Raman (UMR CNRS 8516), University of Lille Nord de France, 59655 Villeneuve d’Ascq Cedex, France 2

Department of Chemistry, Eszterházy Károly University, Leányka utca 6, H3300 Eger, Hungary

Abstract The volume, energy, entropy, and Helmholtz free energy of mixing of the seven simplest primary alkanolamine molecules, i.e., MEA, MIPA, 2A1P, ABU, AMP, AMP2, and 1A2B with water is investigated by extensive computer simulations and thermodynamic integration. To check the force field dependence of the results, all calculations are repeated with two commonly used water models, namely SPC/E and TIP4P. The obtained results show that the thermodynamics of mixing of alkanolamines and water is largely independent from the type of the alkanolamine molecule. The Helmholtz free energy of mixing is found to be negative for all alkanolamines at every composition, in accordance with the experimentally known full miscibility of these molecules and water. This free energy decrease occurring upon mixing is found to be clearly of energetic origin, as the energy of mixing always turns out to be negative in the entire composition range, while the entropy of mixing is also negative up to high alkanolamine mole fractions. The obtained results suggest that alkanolamines form, on average, stronger hydrogen bonds with water than what is formed by two water molecules, and they induce some ordering of the hydrating water molecules both through the hydrophobic hydration of their side chains and through the strong hydrogen bonding.

*

Electronic mail: [email protected]

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1. Introduction Alkanolamines, i.e., small organic molecules having both alcoholic and amine functional groups, are widely used in several fields of chemical engineering, such as in the cosmetic1 and pharmaceutical industry.2 Further, primary alkanolamines are widely used as natural gas sweeteners, as they are very effective adsorbents of mildly acidic gases, such as CO2 and H2S.3,4 For the same reason, aqueous solutions of alkanolamines are also extensively used for post-combustion capture of CO2.5,6 Basically, these processes involve CO2 absorption into the solution at ambient temperature, and a subsequent solvent regeneration by high temperature (i.e., 100-120 °C) treatments.5,7,8 Alkanolamines, known to be present in the prebiotic Earth,9,10 are also thought to play an important role in the prebiotic evolution of several amino acids through their reactions with CO2 and O2. To investigate these processes in detail as well as to improve the efficiency of the above industrial applications, the interaction of alkanolamines with water, and hence the thermodynamic properties of the aqueous solutions of alkanolamines are needed to be better understood. Clearly, this should be the starting point of any further analysis of these systems, concerning among others, hydrogen bonding, transport properties, and molecular level structure, and hence it can be a basis of a better understanding of even their industrial applications in the future. In particular, the development of more efficient absorbers and the optimization of the operating conditions require a deep knowledge of the complex mechanisms responsible for overall absorption process, which involves both physical dissolution of the gas and chemical reaction with the solvent.11 Process reversibility is an additional fundamental issue, and a reduction of the energy cost of the regeneration step is required to make the process more efficient. In this respect, among different absorbers, tertiary amines present lower desorption energies, while primary alkanolamines seem to show better kinetics.11 It is clear that specific interactions involving water, amine and alcohol functional groups are central in determining the kinetic and thermodynamic properties of these mixtures.7 Nevertheless, several fundamental issues are still needed to be clarified, especially in connection with the role played by the solvent. In this context, it is important to reach a molecular-level description of the reacting medium, and possibly to explain how the specific chemical character and molecular topology of a given alkanolamine would influence intra- and inter-molecular arrangements in the aqueous solution, modulating microscopic and macroscopic properties of the absorbent medium.8

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A molecular-based knowledge of these mixtures can be used to improve the predictive capabilities of thermodynamic models for the calculation of quantities of engineering interest.7,11 In investigating this problem, computer simulation methods can provide a very useful tool. However, not many simulation studies concerning the properties of either neat alkanolamines or their aqueous solutions have been reported so far. Further, many of these studies considers only the simplest alkanolamine molecule, namely monoethanolamine (MEA), due both to its simplicity and to the fact that in gas sweetening processes MEA is considered as the reference adsorbent of sour gases. The first simulation of alkanolamine was reported by Button et al., who simulated the bulk liquid phase of neat MEA.12 Later, Gubskaya and Kusalik studied, among other molecules containing two alcoholic or two amine groups, also the neat liquid phase13 and aqueous solutions14 of MEA. Da Silva calculated the hydration free energy of MEA at infinite dilution using free energy perturbation.15 In all of these simulations, MEA was described by the OPLS force field.16,17 Ab initio-based potential models were developed by Alejandre et al.18 and by da Silva et al.19 for MEA, and by Bringas et al. for the tertiary alkanolamine 2-(dimethylamino)ethanol (DMEA).20 These models were, however, not always successful in reproducing the basic thermodynamic properties of alkanolamines, such as their density or heat of vaporization.13,19 Later, López-Rendón et al. improved the potential model of Alejandre et al, and developed also a force field for the secondary alkanolamine diethanolamine (DEA) and for the tertiary alkanolamines methyldiethanolamine (MDEA) and triethanolamine (TEA).21 Orozco et al. proposed a transferable potential, belonging to the AUA4 force field, for primary, secondary, and tertiary alkanolamines, tested, among others, for MEA, DEA, MDEA, TEA, 2-amino-2-methylpropan-1-ol (AMP) and diisopropanolamine (DIPA).22 Simond et al. developed an extendable force field for primary alkanolamines by calculating the fractional atomic charges by ab initio methods, taking also into account the polarizing effect of the nearby molecules, adjusting the torsional parameters to these sets of charges, and taking the other parameters from the AMBER23 and OPLS-AA17,24 force fields.25 In most of these studies, only the bulk liquid phase or the liquid-vapor interface of neat alkanolamines was considered.12,13,18,20-22,25 Structural properties of water-alkanolamine mixtures were only investigated a handful of times.7,14,19,26 These studies led to the general conclusions that alkanolamine molecules are preferentially solvated by water, there is a competition between intramolecular, N-donated hydrogen bonds of alkanolamines and intermolecular hydrogen bonds between alkanolamines and hydrating water molecules, and the strongest intermolecular hydrogen bonds are formed by the OH groups of the



alkanolamine molecules. Recently, Hwang et al studied some of the fundamental aspects of the MEA-CO2 reaction mechanism using quantum chemical and molecular dynamics simualtions. These calculations have clearly suggesed that a deep characterization of the intermolecular structure and dynamics is crucial to achieve a complete comprehension of the CO2 reactivity in amine-water solutions. In particular, it has been emphasized that the local arrangement of water molecules plays a relevant role for proton transfers, and the relevance of intra- and intermolecular H-bonding has been also pointed out.8 Concerning the thermodynamics of aqueous alkanolamine solutions, only the volume26 and enthalpy of mixing7,22 were calculated. However, to characterize the thermodynamics of mixing of two components, the determination of the free energy and also the entropy of mixing is of key importance, as these quantities not only show the composition range of miscibility of the components, but also provide information on the thermodynamic origin (i.e., energetic vs. entropic) of their miscibility.27,28 The calculation of the free energy of a bulk liquid (and, hence, also that of the free energy of mixing of two liquid components) is, however, a computationally far more demanding task than that of the internal energy. The reason for this is that free energy is directly proportional to the logarithm of the entire partition function, and hence its accurate determination requires the sampling of the entire configurational space rather than only its lowest energy domains. As a consequence, the calculation of only the free energy difference of two states (i.e., when only those domains of the configurational space have to be sampled that are markedly different in the two states) is a computationally feasible task. Some time ago we proposed a method, based on a suitably chosen thermodynamic cycle, to calculate the free energy of mixing of two neat components in computer simulation.29 This method was later applied to a number of binary systems.27-33 In the present paper, we report the computer simulation of the volume, energy, entropy, and Helmholtz free energy of mixing of the seven simplest primary alkanolamines, namely MEA, monoisopropanolamine (MIPA), 2-amino-propan-1-ol (2A1P), AMP, 1-amino-2-methylpropan-2-ol (AMP2), 2-amino-butan-1-ol (ABU), and 1-amino-butan-2-ol (1A2B), with water. (It should be noted that the 1-amino-2-methyl-propan-2-ol molecule, abbreviated here as well as in a large part of the literature as AMP2, is also referred to as AMP in the field of gas treating and post-combustion CO2 capture.) The schematic structure the alkanolamine molecules considered here are shown in Figure 1. To describe the interaction of alkanolamines, the potential model proposed by Simond et al.25 was used. In order to test the


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force field dependence of the results, the calculations were repeated with two different water models, namely SPC/E34 and TIP4P.35 The rest of the paper is organized as follows. In section 2, the used methods, including the thermodynamic cycle utilized in the calculation29,33 and the method of thermodynamic integration36,37 are described, and details of the simulations performed are presented. The results of the calculations are discussed in detail in section 3. Finally, in section 4, the main conclusions of this work are summarized.

2. Methods 2.1. Calculation of the Thermodynamic Quantities of Mixing. The change of a general, extensive thermodynamic quantity, Y, upon mixing two neat components α and β can be calculated as ∆Y mix = Yαβ − xα Yα − xβYβ + ∆Y id ,

(1)

where Yα, Yβ, and Yαβ are the molar values of the quantity Y in neat α, in neat β, an in the mixture of α and β, respectively, xα and xβ are the mole fractions of the components α and β, respectively, and ∆Yid is the change of the quantity Y in ideal mixing (i.e., when the neat components are mixed in the ideal gas state). Therefore, since neither the volume, V, nor the internal energy, U, of an ideal gas changes when two components are mixed, the volume and internal energy of mixing can simply be given as ∆V mix = Vαβ − xαVα − xβVβ

(2)

∆U mix = U αβ − xαU α − xβU β .

(3)

and

Further, the entropy of ideal mixing is ∆Sid = –R Σxi lnxi, thus, ∆S mix = S αβ − xα S α − xβ S β − R ( xα ln xα + xβ ln xβ ) ,

(4)

where R is the gas constant. Finally, considering the thermodynamic identity of F = U-TS (F and T being the Helmholtz free energy and temperature, respectively), and using eqs. 3 and 4, the Helmholtz free energy of mixing can be given as



∆F mix = Fαβ − xα Fα − xβ Fβ + RT ( xα ln xα + xβ ln xβ ) ,

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(5)

Clearly, ∆Vmix and ∆Umix can easily be calculated by computer simulation, as they only require the evaluation of the (molar) volume and internal energy, respectively, of the two neat components and their mixture. The calculation of the Helmholtz free energy of mixing, on the other hand, requires the evaluation of the free energy difference between the neat and mixed systems and the respective ideal gases, which can be done using the method of thermodynamic integration (TI). Thus, the calculation of ∆Fmix according to eq. 5 can be associated with the utilization of the following fictitious thermodynamic path.29,33 In the first step, the neat components are brought to the ideal gas state; the corresponding Helmholtz free energy change, i.e., xαFα + xβFβ can be calculated by TI. In the second step, the neat components are mixed in the ideal gas state; the corresponding change of the Helmholtz free energy of RT (xα lnxα + xβ lnxβ) can simply be evaluated. Finally, the mixture is brought back from the ideal gas state, and the accompanying change of the Helmholtz free energy of Fαβ can again be determined by TI.36,37 Finally, having ∆Fmix and ∆Umix already been calculated, ∆Smix can simply be calculated as

∆S

mix

=

∆U mix − ∆F mix . T

(6)

2.2. Thermodynamic Integration. The Helmholtz free energy difference of two states, marked here by A and B, is calculated by the method of thermodynamic integration36,37 as 1

 ∂F (λ )  ∆F = FB − FA = ∫   dλ , ∂λ  0

(7)

where λ is a coupling parameter changing between 0 and 1, which describes the (fictitious) thermodynamic path along which the system is brought from state A to B. Using the well known relations of statistical mechanics that F = -kTlnQ and Q = ∫exp(-U/kT)dqN, where Q is the configurational integral, qN denotes the 3N coordinates of all the N particles present in the system, and k is the Boltzmann constant, the integrand of eq. 7 can be written as


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 ∂U (λ )  N  exp(−U (λ ) / kT ) dq ∂F (λ ) − kT ∂Q(λ ) ∂U (λ ) ∂λ  = = = , (8) N Q(λ ) ∂λ ∂λ ∂λ λ ∫ exp(−U (λ ) / kT ) dq

∫ 

where the brackets λ denote ensemble averaging in the state corresponding to the given λ value. Conventionally, the transformation of the system from state A to B is done along a polynomial path, i.e., the function of U(λ) is given as U (λ ) = λκ U B + (1 − λ ) κ U A ,

(9)

where UA and UB denote the energies of states A and B, respectively. Since in systems in which (i) the energy is pairwise additive, and (ii) the leading term of the pair interaction energy decays with r-12, the value of κ in eq. 9 has to be at least 4 to avoid divergence of U(λ) at the λ = 0 point,36 here we set the value of κ to be 4. Further, in our case state A corresponds to an ideal gas, and thus UA = 0. Considering this, and using also eqs. 8 and 9, eq. 7 can be written as 1

∆F = ∫ 4λ3 U B λ dλ .

(10)

0

Thus, in calculating ∆F, the ensemble average of the quantity UB has to be evaluated at states corresponding to given values of λ, which can be done by performing Monte Carlo simulations at these λ values. However, the Boltzmann factor used in such simulations can be easily rewritten as

(

)

(

)

(

)

exp (− U (λ ) / kT ) = exp − λ 4U B / kT = exp − U B / k (T / λ 4 ) = exp − U B / kT * , (11)

where T* = T/ λ4. This means that a simulation performed at a given λ value at the temperature T is formally equivalent with that performed at λ = 1 (i.e., in state B) at the virtual temperature T*. This way, the ideal gas state is reached by gradually increasing the kinetic energy of the particles to infinity rather than gradually decreasing their potential energy to zero. Therefore, in calculating the value of ∆F, the integrand of eq. 10 has to be evaluated at several values of λ, which can simply be done by performing Monte Carlo simulations with the full potential functions at several virtual temperatures T*, and only the internal energy of the system is needed to be evaluated in these simulations. The integration in eq. 10 can then be performed numerically.



In calculating the values of Fα, Fβ, and Fαβ, used in eq. 5, Monte Carlo simulations of neat water, neat alkanolamines, and their mixtures have been performed at the virtual temperatures corresponding to the λ values of 0.046911, 0230765, 0.5, 0.769235, and 0.953089, chosen according to the 5-point Gaussian quadrature.38 This way, the integrand of eq. 10 has been evaluated at five different points per system. In addition, to evaluate Uα, Uβ, and Uαβ (eq. 3), the simulations have also been performed at λ = 1 (i.e., at the real temperature of the system). To perform the integration, a fourth order polynomial has been fitted to these points, and the integral of this fitted polynomial function has been calculated analytically. The values of the integrand at these points as well as the polynomial fitted to them are shown in Figure 2 for selected systems. Finally, to evaluate Vα, Vβ, and Vαβ (eq. 2) simple Monte Carlo simulations have been performed at constant pressure. 2.3. Monte Carlo Simulations. 2.3.1. (N,p,T) Ensemble. To evaluate the molar volume of the various systems simulated as well as the volume of mixing of alkanolamines and water, Monte Carlo simulations of neat water, neat alkanolamines, and their mixtures corresponding to the alkanolamine mole fraction (xaa) values of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9, respectively, have been performed on the isothermal-isobaric (N,p,T) ensemble at 298 K and 1 bar. The cubic basic simulation box has contained 512 molecules, among which 51, 102, 154, 205, 256, 307, 358, 410, and 461 have been alkanolamine at the above respective xaa values. Alkanolamine molecules have been described by the force field proposed by Simond 25

et al. This model was shown to well reproduce the density and heat of vaporization of neat alkanolamines25 as well as the heat of mixing with water.7 In order to check how the thermodynamics of mixing this model of alkanolamines with water depends on the particular water model chosen, we have repeated all the simulations employing two widely used water models, namely SPC/E34 and TIP4P.35 According to these potential models, the total energy of the system has been pairwise additive, i.e., it has been calculated as the sum of the intramolecular terms and interaction energies of all molecule pairs, where the interaction energy of a molecule pair is the sum of the Lennard-Jones and charge-charge Coulomb contributions of all pairs of their interaction sites. All bonds lengths and bond angles have been kept fixed at their equilibrium values. All interactions have been truncated to zero beyond the center-center cut off distance of 12.5 Å. The long range part of the electrostatic


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interaction has been accounted for by the method of reaction field correction39-41 under conducting boundary conditions. The simulations have been performed by the code MMC.42 In the simulations, every 512 particle move was followed by a volume change step. In a particle move, a molecule was randomly chosen for move. In cases when this selected molecule was water, it was randomly translated and rotated by no more than 0.25 Å and 10o, respectively. In cases when an alkanolamine molecule was picked for the move, it was either translated and rotated in the same way, or one of its torsional angles was randomly changed by no more than 30o. Torsional angles were selected for move in a shuffled cyclic way.43 Alkanolamine translationrotation and torsional rotation moves were done with equal probabilities. Finally, in the volume change steps the volume of the basic box was randomly changed by no more than 300 Å3 in an isotropic way. All moves were accepted or rejected according to the standard criteria.41 The ratio of the accepted and tried moves of different types in the different systems scattered between 0.1 and 0.5 The simulations were started from random arrangements of the molecules. The systems have been equilibrated by performing 108 Monte Carlo steps. Then, the average edge length of the basic simulation box and the molar volume of the systems have been determined by averaging over 108 Monte Carlo steps long equilibrium trajectories. 2.3.2. (N,V,T) Ensemble. To evaluate the energy, entropy, and Helmholtz free energy of mixing alkanolamines with water, Monte Carlo simulations have been performed on the canonical (N,V,T) ensemble the in the same way as described at the (N,p,T) ensemble simulations. The edge length of the cubic basic box, L, has been determined by the preceding simulation of the same system on the (N,p,T) ensemble, as described above. Further, as it has already been discussed, besides T = 298 K, (N,V,T) ensemble simulations have also been performed at the five virtual temperatures corresponding to the λ values described in the previous subsection. The 298 K run of each system have been started form the final configuration of the corresponding (N,p,T) ensemble simulation, the molecules being rescaled to a cubic basic box the edge length of which was the average value resulted from the preceding (N,p,T) run. Virtual temperature runs have then been performed in the order of increasing virtual temperature (decreasing λ) values; each such run has been started from the final configuration of the simulation performed at the previous temperature. The systems have been equilibrated over 5 × 107 Monte Carlo steps. The potential energy of the systems has then been evaluated over the 108 Monte Carlo steps long production phase of the simulations. Equilibrium snapshots of the systems containing MEA, 2A1P, and 1A2B together with SPC/E water at xaa = 0.2 are shown in Figure 3.



3. Results and Discussion The composition dependence of the molar volume of the various alkanolamine-water mixtures is shown in Figure 4 as obtained from our (N,p,T) ensemble simulations; the inset of the figure compares the density of the MIPA-water and AMP-water mixtures with available experimental data.44-46 As is seen, although the potential models used reproduce the experimental densities of neat alkanolamines rather accurately (as it resulted in 0.99, 0.96, 0.94, and 0.93 g/cm3 for MEA, MIPA, ABU, and AMP, respectively, whereas the corresponding experimental values are 1.0121 g/cm3 for MEA,47 0.9565 g/cm3 for MIPA,45,46 0.9467 g/cm3 for ABU,25 and 0.9235 g/cm3 (at 308 K) for AMP44), it somewhat overestimates those of the aqueous mixtures. On the other hand, the experimentally observed maximum behavior of the density vs. composition data is clearly reproduced for both alkanolamines. It is also seen that the V(xaa) curves corresponding to alkanolamines of the same size, i.e., having the same number of side C atoms (such as MIPA and 2A1P, or ABU, AMP, AMP2, and 1A2B) are almost indistinguishable from each other. Further, the difference between the molar volume of aqueous solutions of MEA (having no side C atoms) and those of MIPA or 2A1P (having one side C atom) is roughly the same at every composition than that between the aqueous mixtures of MIPA or 2A1P and ABU, AMP, AMP2, and 1A2B, i.e., alkanolamines having two side C atoms. This finding as well as the fact that the V(xaa) curve is of nearly linear shape indicates that the molar volume of these mixtures is primarily determined by the size and number of the alkanolamine molecules they contain. In other words, the contraction of the mixed systems due to the alkanolamine-water interaction is expected to be small and insensitive to the type of the alkanolamine molecule. The composition dependence of the volume of mixing of the different systems considered, shown in Figure 5, fully confirms this expectation. For the majority of the alkanolamines, the ∆Vmix(xaa) curve is either symmetric or only slightly asymmetric, having its minimum at xaa = 0.4, and its minimum value falls between -2 and -3 cm3/mol. The only exception in this respect is MEA, for which ∆Vmix never falls below -1.5 cm3/mol. The majority of the differences seen between the ∆Vmix(xaa) curves corresponding to different alkanolamines are in the order of the estimated uncertainty of the data of about ±0.5 cm3/mol. Similarly, although the ∆Vmix values corresponding to the TIP4P water model are typically slightly lower (i.e., higher in magnitude) than those corresponding to SPC/E water, this


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difference usually remains below the estimated uncertainty of the data. It should also be noted that – consistently with the aforementioned overestimation of the density of the real systems (see Fig. 4) – the model used somewhat overestimates the magnitude of the change of the volume upon mixing the two components (see Fig. 5). The molar Helmholtz free energy, energy, and entropy of the systems simulated are shown in Figure 6. As is seen, the increase of the alkanolamine mole fraction leads to a decrease of the Helmholtz free energy, and this free energy decrease is clearly of energetic origin, as both the energy and the entropy decreases with increasing alkanolamine content. The Helmholtz free energy, energy, and entropy of mixing of the seven alkanolamines considered with the SPC/E and TIP4P models of water are shown in Figures 7, 8, and 9, respectively. The somewhat larger noise of the data corresponding to the systems containing AMP originates from the larger noise obtained already in the molar volumes of these systems. As is expected, the free energy of mixing is found to be negative in every case, in accordance with the known full miscibility of alkanolamines and water. Similarly to ∆Vmix, the obtained ∆Fmix(xaa) curves (Fig. 7) are also rather insensitive to the type of the alkanolamine molecule. The curves are typically rather symmetric, their minimum falling between -2 and -2.5 kJ/mol. This value is rather small, being comparable (although exceeding, in magnitude) the average kinetic energy of the molecules along one degree of freedom of RT/2, indicating that the thermodynamic driving force of the aforementioned full miscibility is small. The obtained results show again no sensitivity to the water model used. The separation of the energetic and entropic contributions of ∆Fmix reveals that the obtained negative free energy of mixing values of alkanolamines and water are clearly of energetic origin. Thus, the energy of mixing (Fig. 8) is negative practically in the entire composition range (its value turns out to be positive only in a few systems of 80% or 90% alkanolamine content, but this positive value always remains smaller than the estimated uncertainty of the data). Further, in the xaa range between 0.2 and 0.7 the obtained ∆Umix values well exceed, in magnitude, the mean kinetic energy of the molecules along one degree of freedom of RT/2. On the other hand, the entropy of mixing of these systems is negative up to the xaa value of roughly 0.7-0.8, and turns out to be slightly positive only at high alkanolamine concentrations. Thus, unlike ∆Fmix, the ∆Umix(xaa) and ∆Smix(xaa) curves are not symmetric: both the energetic driving force and entropic hindrance of the miscibility is stronger in systems of low alkanolamine content. Thus, the minimum of the ∆Umix(xaa) data is



always located around 0.3-0.4, while that of ∆Smix(xaa) around 0.2-0.3; this latter curve is even changing sign at high xaa values. The observed entropy loss shows again a very weak dependence on the type of the alkanolamine molecule. Therefore, it cannot simply be explained by the well known water ordering effect of hydrophobic solutes, such as the CH3 and CH2-CH3 side chains of the various alkanolamine molecules. Our finding suggests that, besides this entropy loss due to the hydrophobic hydration of the side chains, the NH2 and OH groups of the alkanolamine molecules induce some additional ordering of the water molecules that are hydrogen bonded to them. The loss of entropy upon mixing suggests that this ordering of the water molecules through their hydrogen bonding to the alkanolamines should be stronger than the similar ordering effect of the water-water hydrogen bonds in neat water. This can be the consequence of either a synergistic effect of the nearby NH2 and OH groups on the water ordering, or that of the possibly stronger H-bonds formed by an alkanolamine and a water molecule than by two water molecules. Although the possibility of such a synergistic effect cannot be excluded,48 the latter explanation is clearly supported by the obtained negative values of ∆Umix. Finally, attributing the observed entropy loss to the water molecules hydrating the alkanolamines is supported by the fact that this entropy loss vanishes at high enough alkanolamine mole fraction, when the number of the water molecules, and hence also the entropy contribution of their additional ordering is small, and thus the entropy term corresponding to the ideal mixing, i.e., the entropy increase coming simply from the fact that two compounds are mixed together, compensates this entropy loss.

4. Summary and Conclusions In this study, the change of various thermodynamic quantities, such as the volume, energy, entropy, and Helmholtz free energy, occurring upon mixing the seven simplest alkanolamines with water at various compositions has been investigated by means of extensive Monte Carlo computer simulations and thermodynamic integration. The obtained results revealed that the molar volume of these mixtures is primarily determined by the number of the alkanolamine side chain C atoms, i.e., the size of the alkanolamine molecules. Consequently, the obtained volume of mixing values turned out to be largely independent from he type of the alkanolamine molecule at every composition. The Helmholtz free energy of mixing was negative in every case, in accordance with the experimentally known full miscibility of alkanolamines and water. The negative Helmholtz free energy of mixing was


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found to be clearly of energetic origin, as both the energy and entropy of mixing was found to be negative, with the exception of the entropy of mixing at very high alkanolamine mole fractions. These results suggest that (i) the hydrogen bonds formed by an alkanolamine and a water molecule are likely to be stronger, on average, than a water-water hydrogen bond, (ii) both the hydrocarbon side chains and the polar NH2 and OH groups of the alkanolamine molecules induce some additional ordering of the hydrating water molecules; in the former case this ordering is induced by hydrophobic hydration, while in the latter case by the strong alkanolamine-water hydrogen bonds, (iii) a synergistic effect of the polar NH2 and OH groups of the alkanolamine molecules on the ordering of the nearby water molecules cannot be excluded, and (iv) the entropy loss resulted from this water ordering is always overcompensated by the energy decrease, and the entropy gain corresponding simply to the ideal mixing. To check the suggested structural consequences of the present results and to understand the relation of the local structure and thermodynamics in these mixtures, further studies concerning the detailed local structure of alkanolamine-water mixtures are needed to be done. Work in this direction is currently in progress.

Acknowledgements. The authors acknowledge financial support from the NKFIH Foundation, Hungary (project number 119732), and from the Hungarian-French TéT (PHC Balaton) program under project Nos. 36402ND (France) and TÉT_15-1-2016-0029 (Hungary). The authors are very grateful to Prof. Mihaly Mezei for modifying the code MMC according to the requirements of this project and for useful discussions.

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Figure legends Figure 1. Schematic structure of the seven alkanolamine molecules considered.. Figure 2. Integrand of the thermodynamic integration (eq. 10), obtained at six λ points (full circles) in the systems containing MEA (top panel), MIPA (middle panel), and ABU (bottom panel) with SPC/E water at the alkanolamine mole fraction values of 0.0 (black), 0.2 (red), 0.4 (green), 0.6 (blue), 0.8 (orange), and 1.0 (magenta). The dashed lines show the fourth order polynomials fitted to these data points. Figure 3. Equilibrium snapshots of the systems containing MEA (top panel), 2A1P (middle panel) and 1A2B (bottom panel) with SPC/E water at the alkanolamine mole fraction of xaa = 0.2, as taken out from the constant volume simulations at T = 298 K. Alkanolamines are shown by blue sticks, water molecules are represented by red balls. Figure 4. Molar volume of the mixtures of MEA (black), MIPA (red), 2A1P (green), ABU (blue), AMP (orange), AMP2 (magenta), and 1A2B (brown) with the SPC/E (full circles) and TIP4P (open circles) models of water, as obtained from the isothermal-isobaric ensemble simulations. The lines connecting the points are just guides to the eye. The inset compares the simulated densities of the MIPA-water and AMP-water mixtures with experimental data (red dashed line: MIPA, Ref. 45, red solid line: MIPA, Ref. 46, orange line: AMP, Ref. 44, measured at 308 K). Figure 5. Volume of mixing of MEA (black), MIPA (red), 2A1P (green), ABU (blue), AMP (orange), AMP2 (magenta), and 1A2B (brown) with the SPC/E (full circles) and TIP4P (open circles) models of water, as obtained from the isothermal-isobaric ensemble simulations. The lines connecting the points are just guides to the eye. Error bars are typically below ±0.5 cm3/mol. The results corresponding to MIPA, 2A1P, ABU, AMP, AMP2, and 1A2B are shifted up by 2, 4, 6, 8, 10, and 12 cm3/mol, for clarity. The dashed lines mark the zero value of ∆Vmix for the different alkanolamines. Thick solid lines correspond to experimental data (red line: MIPA, Ref. 45, orange line: AMP, Ref. 44, measured at 308 K).


Page 18 of 29

Page 19 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. Molar Helmholtz free energy (top panel), energy (middle panel), and entropy (bottom panel) of the mixtures of MEA (black), MIPA (red), 2A1P (green), ABU (blue), AMP (orange), AMP2 (magenta), and 1A2B (brown) with the SPC/E (full circles) and TIP4P (open circles) models of water, as obtained from the simulations. The lines connecting the points are just guides to the eye. Figure 7. Helmholtz free energy of mixing of MEA (black), MIPA (red), 2A1P (green), ABU (blue), AMP (orange), AMP2 (magenta), and 1A2B (brown) with the SPC/E (full circles) and TIP4P (open circles) models of water, as obtained from the simulations. The lines connecting the points are just guides to the eye. Error bars are typically below ±0.3 kJ/mol. The results corresponding to MIPA, 2A1P, ABU, AMP, AMP2, and 1A2B are shifted up by 2, 4, 6, 8, 10, and 12 kJ/mol, for clarity. The dashed lines mark the zero value of ∆Fmix for the different alkanolamines. The average kinetic energy of the molecules along one degree of freedom of RT/2 is also shown, for reference, by bars. Figure 8. Energy of mixing of MEA (black), MIPA (red), 2A1P (green), ABU (blue), AMP (orange), AMP2 (magenta), and 1A2B (brown) with the SPC/E (full circles) and TIP4P (open circles) models of water, as obtained from the simulations. The lines connecting the points are just guides to the eye. Error bars are typically below ±0.5 kJ/mol. The results corresponding to MIPA, 2A1P, ABU, AMP, AMP2, and 1A2B are shifted up by 2, 4, 6, 8, 10, and 12 kJ/mol, for clarity. The dashed lines mark the zero value of ∆Umix for the different alkanolamines. The average kinetic energy of the molecules along one degree of freedom of RT/2 is also shown, for reference, by bars. Figure 9. Entropy of mixing of MEA (black), MIPA (red), 2A1P (green), ABU (blue), AMP (orange), AMP2 (magenta), and 1A2B (brown) with the SPC/E (full circles) and TIP4P (open circles) models of water, as obtained from the simulations. The lines connecting the points are just guides to the eye. Error bars are typically below ±2 J/mol K The results corresponding to MIPA, 2A1P, ABU, AMP, AMP2, and 1A2B are shifted up by 8, 16, 24, 32, 40, and 48 J/mol K, for clarity. The dashed lines mark the zero value of ∆Smix for the different alkanolamines. The entropy corresponding to the average kinetic energy of the molecules along one degree of freedom of R/2 is also shown, for reference, by bars.



Page 20 of 29

Figure 1. Idrissi and Jedlovszky

MEA

CH2

CH3

OH

2A1P

CH2

NH2

OH

CH2 NH2

OH

CH

CH MIPA

CH2

NH2 CH3

CH3 CH3

CH3

CH2 ABU

OH

CH NH2

NH2

NH2

CH2

OH

CH2 CH

C

NH2 CH2

CH3 CH3


CH2 AMP

OH

CH2

1A2B

OH

C

AMP2

CH3

Page 21 of 29

Figure 2.

-1

Idrissi and Jedlovszky

0 -200 -400

MEA

-600

3

4λ λ / kJ mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-800 0 -200 -400 -600 -800

xaa = 0.0 xaa = 0.2 xaa = 0.4 xaa = 0.6 xaa = 0.8 xaa = 1.0

MIPA

0 -200 -400

ABU

-600 -800 0.00

0.25

0.50


0.75

λ

1.00


Page 22 of 29


MEA-SPC/E

2A1P-SPC/E

1A2B-SPC/E


Page 23 of 29


3

-3

100

ρ /g cm

-1

1.1

V / cm mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


AMP2 AMP

1.0

80

60

1A2B ABU

0.9 0.0

0.2

0.4

0.6

xaa 0.8

2A1P

1.0

MIPA

MEA

40

20 0.0

0.2

0.4

0.6


0.8

xaa

1.0



12 1A2B

mix

3

/ cm mol

-1

10

∆V

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 29

AMP2

8 AMP

6

ABU

4 2A1P

2 MIPA

0 MEA

-2 0.0

0.2

0.4


0.6

0.8

xaa

1.0

Page 25 of 29


F / kJ mol

-1

0

-100

-200

U / kJ mol

-1

-3000 -100 -200 MEA-SPC/E MIPA-SPC/E 2A1P-SPC/E ABU-SPC/E AMP-SPC/E AMP2-SPC/E 1A2B-SPC/E

-300 -1

-50 -1

S / J mol K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


MEA-TIP4P MIPA-TIP4P 2A1P-TIP4P ABU-TIP4P AMP-TIP4P AMP2-TIP4P 1A2B-TIP4P

-100

-150

-200 0.0

0.2

0.4

0.6


0.8

xaa

1.0



12 1A2B

10 -1

/ kJ mol

mix

0

0

AMP2

8

AMP 0

6

∆F

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 29

ABU

4

0

0

1

0

1

2A1P

2

MIPA

0 MEA

-2 0.0

0.2

0.4

0.6


0.8

xaa

1.0

Page 27 of 29


12 1A2B

0

10

mix

/ kJ mol

-1

AMP2

∆U

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8 AMP

0

6 ABU

4 2A1P 0

2

MIPA 0

1

0

1

0 MEA

-2 -4 0.0

0.2

0.4

0.6


0.8

xaa

1.0



48

32

24

AMP2

-1 mix

0

40

/ J mol K

-1

1A2B

∆S

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 29

0

AMP

0

0

ABU

16 2A1P

0

8 MIPA

0

0 0

MEA

-8 0.0

0.2

0.4

0.6


0.8

xaa

1.0

1

Page 29 of 29

TOC Graphics:

OH

CR2 CR2

+

H2O

mix

NH2

∆F

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

xaa


Thermodynamics of Mixing Primary Alkanolamines with Water

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