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A molecular dynamics study on interaction contributions of components in liquid-vapor systems between LiBr aqueous solutions and air during absorption
Journal Pre-proofs A molecular dynamics study on interaction contributions of components in liquid-vapor systems between LiBr aqueous solutions and air during absorption Tingting Chen, Yonggao Yin, Yuwen Zhang, Xiaosong Zhang PII: DOI: Reference:
S1359-4311(19)33336-8 https://doi.org/10.1016/j.applthermaleng.2019.114732 ATE 114732
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Please cite this article as: T. Chen, Y. Yin, Y. Zhang, X. Zhang, A molecular dynamics study on interaction contributions of components in liquid-vapor systems between LiBr aqueous solutions and air during absorption, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114732
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A molecular dynamics study on interaction contributions of components in liquid-vapor systems between LiBr aqueous solutions and air during absorption Tingting Chena, Yonggao Yina,b,*, Yuwen Zhangc, Xiaosong Zhanga,b a School of Energy and Environment, Southeast University, Nanjing 210096, China b Ministry of Education of Key Laboratory of Energy Thermal Conversion and Control, Southeast University, Nanjing 210096, China c Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA *Corresponding author: Yonggao Yin Email: [email protected] Abstract: Liquid desiccant dehumidification has been prevalent for many years to remove moisture in the air. The application and enhancement of the involved absorption processes depend on the understanding of heat and mass transfer between liquid desiccants and air. In order to unravel the mystery of energy and mass transport during dehumidification, vapor absorption processes were simulated by molecular dynamics under different solution concentrations and temperatures. Energy characteristics and interaction components were further analyzed to obtain dominant particles in LiBr solutions during absorption. It is found Br- contributes the most in terms of the accumulated interactions when the water vapor molecule just enters into the interface for within 10 ps. This can be attributed to the occurrence of a OH bond directing to the liquid bulk with a high possibility of about 80%. However, after the absorbed water molecule entering into the interface for a longer time about 250 ps, the accumulated interactions caused by Li+ will be the largest under conditions with low concentrations and high temperatures. This is because the absorbed water molecule will gradually diffuse close to Li+ in the liquid desiccants and adjust the orientation around Li+. This study helps understand the absorption from microscopic level. Keywords: LiBr aqueous solution; Molecular dynamics; Interaction; Orientation angle; Liquid-vapor
system 1 Introduction Liquid desiccants such as LiBr aqueous solution have been widely used to remove moisture in the air, which could fully exploit high-temperature cooling sources, solar energy and waste heat to achieve suitable indoor atmosphere [1–4]. Therefore, liquid desiccant dehumidification has aroused much attention due to the prominent energy-saving potential [5,6]. As a crucial process, heat and mass transfer between the liquid desiccant and air has been attached with great significance by several researchers [7,8]. Velocity and physical properties were usually taken as the dominant factors which affected the intensity of dehumidification from the aspects of turbulence, surface tension and viscosity [9,10]. Consequently, based on experiments, transfer coefficients were associated with the flow and thermodynamics parameters for the purpose of practical application [9,11–14]. In general, the solution concentration, liquid-air ratio, vapor pressure ratio, dimensionless number Re and Sc were correlated. Nonetheless, most correlation equations only work perfectly in the limited investigation conditions. This is because the mechanism of heat and mass transfer between the liquid desiccant and air remains unclear, leading to the non-universality of correlation forms and parameters. In recent years, efforts were also made to optimize systems as well as operation parameters through experiments and simulations [7,15,16]. It is noticeable that the intensification of dehumidification is also restricted by the cognition of transfer phenomena between the liquid desiccant and air inevitably. Hence, investigating the mechanism of heat and mass transfer during dehumidification seems extremely important. But extensive macroscopic experiments only reflect the macroscopic results, failing to catch details of molecular scale [17–19]. Microscopic methods should be relied on to unravel the mystery of energy and mass transport. In the past few years, molecular dynamics (MD) has been demonstrated as a reliable measure to estimate physical properties
and disclose mechanisms of chemical engineering processes [20–23]. Based on molecular dynamics, investigators have conducted researches on interfaces of pure water and aqueous solutions [24–27], evaporation and condensation mechanisms [28, 29] and solution absorption processes [30]. Taylor et al. simulated the liquid-vapor interface of SPC/E water [24]. Orientation of water molecules were analyzed and they implied that free OH bonds at the interface would have an impact on absorbing particles. By observing the trajectory of water molecules, Nagata et al. simulated the evaporation of pure water [28]. It was found that the high kinetic energy of the evaporated water molecule was obtained by the making and breaking of hydrogen bonds involving at least three water molecules at the interface. After employing aqueous droplets of NaCl, KCl or LiCl, effects of the electric field intensity on the water evaporation rate were discussed by Wang et al. [29]. They attributed the evaporation enhancement under an electric field to the stretched transfer area and the directional arrangement of water molecules. Daiguji and Hihara firstly applied molecular dynamics into LiBr absorption refrigeration to reproduce the dynamic absorption process of water molecules [30]. According to the survey above, most literatures focus on the interfaces and evaporation mechanism of water and few literatures are concerned with aqueous solution absorption. The liquid-vapor systems between the liquid desiccant and air consist of diversified particles, which govern the absorption and release of water molecules through the interface. The dehumidification process deserves further exploration to find out the dominant particles and interactions when water vapor molecules move near and further enter into the liquid-vapor interface. In order to solve this problem and provide microscopic details, the vapor absorption (or dehumidification) processes of LiBr aqueous solution were simulated by molecular dynamics under different solution mass concentrations and temperatures. Kinetic and potential energy characteristics were presented subsequently. Furthermore, interactions on the absorbed
water vapor molecule caused by all components in LiBr solutions were compared and elaborated. Orientations of water were also summarized in this paper for explaining the magnitude and variation of interaction contributions. This study offers useful insight into liquid desiccant dehumidification from the perspective of microscopic level and could also inspire relevant workers to develop effective methods for intensifying absorption. 2 Method As shown in Fig.1, the simulated system was composed by the air box and the solution-air box. The air box was 7.5 nm in both width and length, which was the same as that of the solution-air box. In addition, the height of the air box was 8 nm and the height of the solution-air box was kept as 11 nm to obtain the air space of a similar size. It is notable that the height of the gas phase is usually over two times that of the liquid phase [30] and must ensure particles at one liquid-vapor interface will not interact with molecules at the other interface. Air was represented by the mixture of nitrogen molecules, oxygen molecules and water vapor molecules. The lithium bromide aqueous solution consisted of 4000 water molecules, 829 Br- and 829 Li+ ions, yielding the mass concentration of 50% in salt. For convenience of investigating the absorbed water vapor molecules, the air containing plentiful water molecules were expected in this paper, although aforementioned states may not exist in daily life. So, the air box was set to contain 6 water molecules, 8 nitrogen molecules and 2 oxygen molecules. To ensure the air state still existed (not in the condensed state) when the number of water molecules was large, the air box was firstly run in a NVT ensemble with the high temperature of 370 K for 5000 ps. Since water vapor densities are smaller than that under saturation conditions, above conditions are available. In the gas phase of the solution-air boxes, the numbers of nitrogen and oxygen molecules were the same with air boxes while the numbers of water vapor molecules were determined by MD simulations. The solution-air box was
run in a NVT ensemble of 300 K for 5000 ps to reach the equilibrium state before simulating dehumidification processes. Subsequently, the pre-equilibrated air box and the solution-air box were connected to carry out the microscopic absorption process in a NVE ensemble. Coordinates, velocities and energies of particles were output every 100 fs during the production run of 300 ps. All simulations were performed using GROMACS 5.1.1 by applying periodic boundary conditions in all directions. Non-polarizable force fields parameterized by Koneshan et al. were used to describe interactions between particles [31]. All atoms or ions were considered as Lennard-Jones (LJ) particles with charges. The intermolecular potentials between two particles were correlated by the summation of LJ potentials and electrostatic (Coulomb) potentials as follows:
U ij
4 ij ij rij
12
ij rij
6
qq f i j rij
(1)
Where lowercase subscripts i and j denote different two particles (atoms/ions), ε and σ represent energy and length parameters in LJ potentials, q and r mean charges on particles and distance between particles and f is the electric conversion factor with the value of 138.9354578 kJ·mol-1·nm·e-2. Force field parameters used in this paper are listed in Table 1. ε and σ between different kinds of atoms were produced by Lorentz-Berthelot combination rules for LJ interactions. Bonds and angles of water molecules were constrained by SETTLE algorithm [32]. The cutoff distance was set as 12 Å for Lennard-Jones potential [33–35] and short-range electrostatic interactions with potentials switching smoothly to 0 between 10 Å and 12 Å. PME solver was used to deal with long-range electrostatic interactions [36]. Newtonian equations of motion were solved by leap-frog algorithm with a time step of 1 fs. Nosé–Hoover thermostat [37] was used to keep the system at the target temperature during pre-equilibrium period. The potential energy of the water molecule was gained based on energy groups set in input files and analysis programs in GROMACS software according to Eq. (1). Moreover, the kinetic energy of the water molecule was also obtained from the analysis programs provided by GROMACS software and was
calculated by：
Ek
1 2
miv i
2
(2)
Where i, m and v represent atoms in the water molecule, masses and velocities of atoms, respectively. For analyzing the orientation of water molecules, several crucial angles are defined as shown in Fig. 2. θ represents the angle between the water dipole moment and the interface normal direction (towards air sides). For most conditions, φ1 and φ2 denote the angles of the upper OH bond and the other OH bond in H2O with respect to interface normal direction, respectively. But for water molecules at or below the lower interface in Fig. 1, φ1 and φ2 mean the angles of the lower OH bond and the other OH bond in H2O versus the interface normal direction towards air sides. For the sake of investigating the dominant particles, interactions between absorbed water vapor molecules and different particles in initial LiBr aqueous solutions were calculated, including interactions caused by water molecules, Br- and Li+. Above interactions were extracted from energy information and then was divided by the number of particles to get the interaction which a single particle imposes averagely. Therefore, the single particle interaction produced by H2O, Br- and Li+ in the initial aqueous solution could be obtained. As listed in Table 2 and Table 3, in order to study effects, the microscopic absorption processes were also studied under different solution mass concentrations between 40% and 60% by changing the number of Br- and Li+ and under different solution temperatures between 280 K and 360 K. 3 Results and discussion 3.1 Energy characteristics during absorption Taking 50% LiBr aqueous solution at 300K as an example, energy change with the simulation time was studied as the water vapor molecule in the air entered into the liquid-vapor interface and was
absorbed afterwards. Kinetic energies of 6 water vapor molecules in the air are illustrated in Fig. 3 for a typical simulation of absorption phenomena. The time range of the horizontal axis in Fig. 3 is the time period during which the water vapor molecule moves near the interface and further is absorbed. So, they may be not same since different water vapor molecules enter into interfaces at different times. The instant abrupt change of the kinetic energy means that the water vapor molecule collides with other molecules in air. And the continuous fluctuation of the kinetic energy occurs in the interface or the liquid bulk of LiBr aqueous solutions because of denser particles. It is apparent that the kinetic energy of the water vapor molecule may gain or decline after absorption. This depends on the initial kinetic energy of the molecule which follows the Maxwell distribution for the ideal gas. The average kinetic energy of water molecules after absorption is about 3.73 kJ/mol. So, if the previous kinetic energy is lower than the average value, the kinetic energy will rise. According to Fig. 3, the change of kinetic energy for every water molecule is mostly less than 10 kJ/mol. Fig. 4 gives the potential energy change corresponding to water vapor molecules in Fig. 3. The Lennard-Jones potential is represented by the open circles while the Coulomb potential is represented by the open triangles. It can be seen that the LJ potential caused by surrounding particles is embodied as the repulsive interaction synthetically with the absorption process proceeding. This is due to the fact that with a decrease in distance between the water vapor molecule and the other particle, the repulsive part in LJ potential goes up significantly but the attractive part increases relatively slowly. Once a particle is quite near the water vapor molecule, the synthetic interaction will be repulsive basically. The Coulomb potential is embodied as the attractive interaction and reduces rapidly when the water vapor molecule enters into the interface and then becomes liquid. Similar to the Coulomb potential, the total potential is characterized by a sharp drop during absorption at the interface. The average decrease of potential energy
is about 80 kJ/mol for every water molecule to achieve the phase change from gas to liquid. Compared with the kinetic energy change, the potential energy change is much larger with the dominant part of Coulomb interaction. 3.2 Interaction contributions under different concentrations The initial solution temperature was kept as 300 K and the mass concentration of LiBr solution ranges from 40% to 60% as listed in Table 2. To ensure reliable statistics of the simulation results, every condition was simulated for 20 times by using different initial microscopic states (configurations) of the system. Fig. 5(a) shows the calculated single particle interactions on a water vapor molecule caused by different particles for instance. Obviously, the single particle interactions change as the simulation goes on, resulting in comparing relative magnitudes difficultly. Thus, the accumulated interaction is proposed here which means the single particle interaction is integrated over the time. Accumulated interactions on the water vapor molecule caused by the single H2O, Br- and Li+ are shown in Fig. 5(b) where the value of various interactions could be identified simply. Due to the different trajectories of the water vapor molecules entering into the interface and the discrepant surrounding particles, the relative magnitude of various particle interactions may not be constant. The accumulated interactions between the absorbed water molecule and other components in LiBr solution were further analyzed. After obtaining accumulated interactions on water vapor molecules in all simulations, the probabilities of three following conditions were calculated. Effects of the solution concentration were discussed afterwards. The first condition is that a single Br- accumulated interaction on the water vapor molecule is higher than a single H2O accumulated interaction. The second condition is that the accumulated interaction of a single Li+ is higher than that of a single H2O. And the last condition is that the accumulated interaction of a single Br- is higher than that of a single Li+. It must be
pointed out that three conditions aforementioned are not mutually exclusive for the studied water vapor molecules in the initial air. The probabilities were calculated after the water vapor molecule entering into the interface for 2 ps, 5 ps and 10 ps, respectively. Fig. 6(a) shows the probability that the single Braccumulation interaction on the absorbed water vapor molecule is higher than the single H2O accumulation interaction during the initial absorption period. In this paper, the initial absorption period is within 10 ps after the water vapor molecule entering into the interface from the air side. With an increase in the concentration, the probability of having larger Br- interaction goes up remarkably, which indicates that the higher concentration promotes effects of Br- compared with that of H2O at the initial period of absorption. Furthermore, as the time becomes longer after capturing the water vapor, the effects of Br- are also boosted. For the studied concentration range, all probabilities of larger Br- effects are more than 59%. This implies overall, the condition that a single Br- shows larger interaction on the absorbed water than a single H2O makes up the majority. In contrast, during the initial absorption period within 10 ps, a single H2O in initial LiBr solutions plays a more important role than a single Li+ on account of all probabilities lower than 50% as depicted in Fig. 6(b). And it seems that effect of a single Li+ becomes weaker compared with a single H2O with an increase in the solution concentration. As shown in Fig. 6(c), the accumulated interaction caused by Br- is often more than that by Li+ during the initial absorption period, which is consistent with results in Fig. 6(a) and Fig. 6(b). In conclusion, at the initial absorption period within 10 ps, Br- ranks first in terms of the single particle accumulated interaction on the absorbed water vapor, followed by H2O and Li+. Above probabilities were also calculated at the final time of simulation and the probabilities of three conditions were described by open diamonds in all graphs of Fig. 6. Most water vapor molecules in air enter into the interface within 50 ps according to statistics. So the final time of simulation means about
250 ps after the water vapor molecules going into the interface. It is clear that effects of Br- and Li+ are improved significantly compared with the initial absorption period. Noticeably, the accumulated interactions caused by a single Br- are absolutely higher than that caused by a single H2O regardless of the concentration. When the concentrations are less than 53%, the accumulated interactions caused by a single Li+ are often higher than that caused by a single H2O. The rise of concentration also depresses the interaction of a single Li+ on the absorbed water molecule compared with the single H2O in liquid. The interactions caused by a single Br- are often more than that by a single Li+. It is clear that at the final time of simulation, a single Br- contributes the most, followed by a single Li+ and simultaneously, a single H2O provides the least interaction. According to results of Section 3.1, the most important is the Coulomb interaction which involves distance and charge quantity on particles. In order to explain the interaction contributions of different components to the absorption processes, water molecule orientations in the air, interface and liquid bulk were analyzed. The bin width of 0.05 (interval of cosine range) is used here for cosine statistics of angles (θ, φ1 and φ2). Fig. 7 shows the probability distribution of three important angles of water vapor molecules including the angle of the dipole moment versus the normal direction (θ), the angle of the upper OH bond versus the normal direction (φ1) and the angle of the lower OH bond versus the normal direction (φ2) for water vapor molecules in the air. The distribution probability of θ seems constant at every degree, which means in the air, the water molecule bisector has no obvious preferred direction. It can also be seen that there is no possibility of φ1 to be more than 128o or of φ2 to be less than 51o. The percentage that φ1 is less than 90o is the summation of all percentages in Fig. 7 with the horizontal axis less than 90o. According to Fig.7, most of φ1 is less than 90o with the percentage of 82.2 while most of φ2 is more than 90o with the percentage of 81.8. This indicates the existence possibility of an upward OH bond in the
water vapor molecule is about 82.2% and the existence possibility of a downward OH bond is about 81.8%. Both proportions approximate to the theoretical value of 80.4% calculated according to the water bond angle. When the water vapor molecule moves to the interface gradually from the air, the probability that a hydrogen atom in H2O is closest to the interface is very large. Hence, it is no wonder that the interaction caused by Li+ may be repulsive just as in Fig. 5, which also accounts for the weaker effects of Li+ during the initial absorption period. The simulated system was divided into slices with a thickness of 1 Å along the normal direction of the interface where the system density changes continuously from the density of the gas phase to that of the liquid phase. Fig. 8(a), Fig. 8(b) and Fig. 8(c) present the probability distribution of θ, φ1 and φ2 at different angles for water molecules at the liquid-vapor interfaces and in the liquid bulk. The solid circles represent results for water in the liquid bulk and the other symbols represent results for water at the interfaces. In terms of their representative slices, the open circles (water in the slice between 6.8 and 6.9 nm in z direction defined in Fig. 1), solid squares (water in the slice between 7.0 and 7.1 nm in z direction) and open squares (water in the slice between 7.2 and 7.3 nm in z direction) deviate from the liquid bulk farther and farther. According to Fig. 8(a), for water molecules in the liquid bulk, θ show a random distribution with almost equal possibility, similar to the angle distribution of water vapor molecules in the air. But a preferred orientation appears for water at the interfaces. With an increase in the distance from the liquid bulk, the preferred θ becomes smaller. Moreover, at the outermost layer of the interface, the average θ reduces with the concentration of LiBr aqueous solution. When the concentration increases from 40% to 60%, the average θ decreases from 82.4o to 72.2o. According to Fig. 8(b), as the distance from the interface is enlarged, more water molecules have an upward OH bond approaching the normal direction. The probability of the upper OH bond directing to the air side is more than 80% and 92% for
water in the liquid bulk and at the interfaces respectively. This may explain the weaker interaction of the single H2O than that of Br- during absorption besides the effect of the charge magnitude. As illustrated in Fig. 8(c), the lower OH bond in H2O directing to the liquid bulk also occupies the majority, agreeing well with the results of that in the air. Fig. 9(a) and Fig. 9(b) shows the water orientation around interface Br- and Li+, respectively. The water orientation angle around ions means the angle between the vector from the ion to the oxygen atom and the dipole moment of water. The water orientation angle around interface Br- reaches the maximum probability at 126.5o and the peak probability falls with larger distance from Br- because of exceeding the coordination location in the first solvation shell. The probability distribution of the water orientation angle around Br- in the liquid bulk is similar to the open square part in Fig. 9(a). This manifests in either the interface or the liquid bulk, numerous Br- particles are close to one hydrogen atom of the water molecule under equilibrium states. The water orientation angle around the interface Li+ reaches the peak probability at about 5o, which means numerous Li+ particles are close to the oxygen atom and nearly on the bisector of the water molecule under equilibrium states. Fig. 10 also verifies the particle location distribution under different mass concentrations of LiBr aqueous solution, which is similar to the radial distribution function. The first solvation shell of Li+ is closer than that of Br- and the peak number of surrounding water molecules are also larger for Li+. From this aspect, during absorption, the interaction variation under different concentrations caused by Li+ at the final simulation time may be attributed to the following two factors. On the one hand, Li+ particles produce stronger interaction due to the closer hydration shell and greater charge quantity under equilibrium conditions. As the absorption goes on, the absorbed water vapor molecule diffuses and may be captured by Li+. So, the effect of Li+ will be enhanced compared with the initial absorption period. On the other hand, with an increase in
concentration, Li+ particles are bound with previous water molecules more tightly under the strong interaction. It is also harder for the absorbed water vapor molecule to diffuse and displace the initial water around Li+. Therefore, within the same time of the whole simulation, the interaction of Li+ on the absorbed water molecule will be weaken compared with Br- and H2O when the concentration is amplified. 3.3 Interaction contributions under different temperatures Effects of the solution temperature were also researched as illustrated in Fig.11. The initial solution mass concentration in all simulations were set as 50%. Fig. 11(a) presents the probability that the accumulated interaction derived from the single Br- is stronger than that from the single H2O in liquid. It is found that when the water vapor molecule in air just moves near or into the interface, the dominant particles are Br-, followed by H2O and Li+ in terms of the interaction contributions. This can be explained by an OH bond of water in the air directing to the liquid bulk with a high possibility over 80%. But at the final simulation time, the accumulated interaction derives from the single Li+ may exceed the interaction from the single H2O. This is due to the fact that after the water vapor molecule entering into the interface, when the time is long enough, the absorbed water vapor molecule moves close to Li+ likely. And the water orientation around Li+ could be adjusted to about 5o. It can also be reflected by Fig. 11(b) and Fig. 11(c), where the rise of temperature dramatically promotes the effect of Li+ compared with Brand H2O. When the solution temperature reaches 300 K, the accumulated interaction of Li+ will exceed that of H2O. And when the solution temperature is over 340 K, the accumulated interaction of Li+ will exceed that of Br-. The faster diffusion of the absorbed water under high temperature may account for this phenomenon. Although water molecules are polar, the SPC/E water model used here is one of the most reputational models with good performance and low computation, which uses self-polarization correction
accounting for the dipole moment change. Many researchers have employed the SPC/E model to investigate the water evaporation phenomena or liquid-vapor systems [20–22, 24, 29]. And it is also demonstrated that the observables from snapshots of evaporation simulation are universal when using non-polarizable SPC/E and polarizable water models [28]. Moreover, in our previous study [19], the force fields used here have been demonstrated to reproduce physical properties with the acceptable accuracy and the change trends of the net absorption rate of water molecules under different solution temperatures agree well with the macro experiments. This could guarantee the reliability of the simulation here in some degree. The application of polarizable force fields in vapor absorption deserves further study. And the simulated phenomena may be visualized based on micro measures like neutron scattering, x-ray reflection and vibrational sum frequency spectroscopy [26], which also deserves further investigation in the future. 4 Conclusions In order to seek dominant particles in the LiBr aqueous solution during the process of liquid desiccant dehumidification, absorption phenomena were simulated by molecular dynamics under different solution mass concentrations and temperatures. The energy characteristics during absorption were provided and the single particle interactions on the absorbed water vapor molecule were further analyzed. The orientation of water molecules in the air, interface and liquid bulk were also discussed. Main conclusions are drawn as follows: (1) When the water vapor molecule in the air is transported to the LiBr aqueous solution, the kinetic energy of the water molecule may increase or decrease according to the initial value. But meanwhile, a dramatic drop occurs necessarily for the potential energy which is mainly determined by the Coulomb potential. The change of potential energy is much higher than that
of kinetic energy. (2) For the air and liquid bulk, the diploe moment direction of water is random, and the probability of having an upward OH bond or a downward OH bond is more than 80%. However, for the water molecules at the interface, an obvious preference exists as to the angle between the dipole moment and the normal direction, which reduces with an increase in the distance from the liquid bulk and the concentration of LiBr aqueous solutions. (3) The accumulated interaction was proposed to easily estimate the dominant interaction between various components in LiBr solutions and the absorbed water vapor molecule. At the initial absorption period within 10 ps, Br- usually ranks first in terms of the single particle accumulated interaction on the absorbed water vapor molecule, followed by H2O and Li+. This is quite different from the pure liquid of LiBr solutions, where the Li+ particles show the strongest interaction on water due to the ionic hydration energy. The aforementioned difference may be attributed to the existence of an OH bond directing to the liquid bulk when the water vapor molecule moves to or just enters into the liquid-vapor interface. (4) At the final simulation time, the water vapor molecule was absorbed by the liquid desiccant for a long time, bringing about a higher possibility to diffuse close to Li+ and adjust the orientation around Li+. As a result, the effect of Li+ increases compared with the initial period. It is clear that the interaction contribution caused by Li+ is enhanced by the solution temperature but depressed by the solution concentration in the investigated range. When the LiBr solution of 50% reaches 300 K or more, the interaction contribution of the single Li+ is only second to that of the single Br-. When the LiBr solution of 50% is over 340 K, the interaction contribution of the single Li+ will be the largest among all particles.
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W. Jorgensen, J. Chandrasekhar, J. Madura, R. Impey, M. Klein, et al., Comparison of simple potential functions for simulating liquid water, J. Chem. Phys. 79 (1983) 926.
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T. Darden, D. York, L. Pedersen, T. Darden, D. York, et al., particle mesh ewald : An N -log ( N ) method for ewald sums in large systems, J. Chem. Phys. 98 (1993) 10089.
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P. Hünenberger, Thermostat algorithms for molecular dynamics simulations, Adv. Polym. Sci.
173 (2005) 105–149. Nomenclature E
energy
m
mass
q
charge
r
distance from the particle
Re
Reynolds number
Sc
Schmidt number
T
temperature
U
potential function
v
velocity
X
mass concentration
Greek letters ε
energy parameter in LJ
σ
length parameter in LJ
θ
angle between the dipole moment and the interface normal direction
φ1
angle between the upper OH bond and the interface normal direction
φ2
angle between the lower OH bond and the interface normal direction
Subscripts s
solution
k
kinetic
Abbreviations LiBr
lithium bromide
LJ
Lennard-Jones
MD
molecular dynamics
NVT
canonical ensemble
NVE
microcanonical ensemble
SPC/E
extended simple point charge
Figure Captions: Fig. 1. Simulation systems and processes Fig. 2. Angles for orientations of water molecules Fig. 3. Kinetic energy change of absorbed water molecules Fig. 4. Potential energy change of absorbed water molecules Fig. 5. Particle interactions on the water vapor molecule: (a) single; (b) single accumulation Fig. 6. Effect of Xs on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+ Fig. 7. Orientation probability distribution of water vapor molecules in air Fig. 8. Probability distribution of water orientations for liquid bulk and interface: (a) θ; (b) φ1; (c) φ2 Fig. 9. Water orientation around interface ions: (a) Br-; (b) Li+ Fig. 10. Number of H2O around interface ions: (a) 40% LiBr; (b) 50% LiBr; (c) 60% LiBr Fig. 11. Effect of Ts on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+
Fig.1. Simulation systems and processes
Fig. 2. Angles for orientations of water molecules
Fig. 3. Kinetic energy change of absorbed water molecules
Fig. 4. Potential energy change of absorbed water molecules
Fig. 5. Particle interactions on the water vapor molecule: (a) single; (b) single accumulation
Fig. 6. Effect of Xs on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+
Fig. 7. Orientation probability distribution of water vapor molecules in air
Fig. 8. Probability distribution of water orientations for liquid bulk and interface: (a) θ; (b) φ1; (c) φ2
Fig. 9. Water orientation around interface ions: (a) Br-; (b) Li+
Fig. 10. Number of H2O around interface ions: (a) 40% LiBr; (b) 50% LiBr; (c) 60% LiBr
Fig. 11. Effect of Ts on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+
Table Titles:
Table 1 Parameters of atom/ion models used in this paper Table 2 Simulated conditions under different mass concentrations and temperatures Table 3 Numbers of molecules/ions corresponding to solution mass concentrations Table 1 Parameters of atom/ion models used in this paper θHOH, °
Atoms/Ions
ε, kcal/mol
σ, Å
q,e
r, Å
Li+
0.1649
1.505
1
Br-
0.1
4.539
-1
N(N2)
0.1629
3.738
0
N-N: 1.098
O(O2)
0.2014
3.480
0
O-O: 1.017
O(H2O)
0.1553
3.166
-0.8476
O-H: 1
-
109.47
Table 2 Simulated conditions under different mass concentrations and temperatures Cases
Different solution concentrations
Different solution temperatures
Solution
Solution
Number of
concentrations, %
temperatures, K
simulation runs
40
20
45
20
50
300
20
55
20
60
20
50
280
20
300
20
330
20
360
20
Table 3 Numbers of molecules/ions corresponding to solution mass concentrations Concentrations, %
Number of H2O
Number of Br-
Number of Li+
40
4000
553
553
45
4000
678
678
50
4000
829
829
55
4000
1014
1014
60
4000
1245
1245
Highlights
The single particle accumulated interaction was proposed for easy comparison. The existence possibility of a downward OH bond is over 80% for water in air. Br- contributes the most to the absorption process, followed by Li+ and H2O. The concentration and temperature affect interactions caused by Li+ markedly.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S1359-4311(19)33336-8 https://doi.org/10.1016/j.applthermaleng.2019.114732 ATE 114732
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
15 May 2019 21 October 2019 28 November 2019
Please cite this article as: T. Chen, Y. Yin, Y. Zhang, X. Zhang, A molecular dynamics study on interaction contributions of components in liquid-vapor systems between LiBr aqueous solutions and air during absorption, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114732
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A molecular dynamics study on interaction contributions of components in liquid-vapor systems between LiBr aqueous solutions and air during absorption Tingting Chena, Yonggao Yina,b,*, Yuwen Zhangc, Xiaosong Zhanga,b a School of Energy and Environment, Southeast University, Nanjing 210096, China b Ministry of Education of Key Laboratory of Energy Thermal Conversion and Control, Southeast University, Nanjing 210096, China c Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA *Corresponding author: Yonggao Yin Email: [email protected] Abstract: Liquid desiccant dehumidification has been prevalent for many years to remove moisture in the air. The application and enhancement of the involved absorption processes depend on the understanding of heat and mass transfer between liquid desiccants and air. In order to unravel the mystery of energy and mass transport during dehumidification, vapor absorption processes were simulated by molecular dynamics under different solution concentrations and temperatures. Energy characteristics and interaction components were further analyzed to obtain dominant particles in LiBr solutions during absorption. It is found Br- contributes the most in terms of the accumulated interactions when the water vapor molecule just enters into the interface for within 10 ps. This can be attributed to the occurrence of a OH bond directing to the liquid bulk with a high possibility of about 80%. However, after the absorbed water molecule entering into the interface for a longer time about 250 ps, the accumulated interactions caused by Li+ will be the largest under conditions with low concentrations and high temperatures. This is because the absorbed water molecule will gradually diffuse close to Li+ in the liquid desiccants and adjust the orientation around Li+. This study helps understand the absorption from microscopic level. Keywords: LiBr aqueous solution; Molecular dynamics; Interaction; Orientation angle; Liquid-vapor
system 1 Introduction Liquid desiccants such as LiBr aqueous solution have been widely used to remove moisture in the air, which could fully exploit high-temperature cooling sources, solar energy and waste heat to achieve suitable indoor atmosphere [1–4]. Therefore, liquid desiccant dehumidification has aroused much attention due to the prominent energy-saving potential [5,6]. As a crucial process, heat and mass transfer between the liquid desiccant and air has been attached with great significance by several researchers [7,8]. Velocity and physical properties were usually taken as the dominant factors which affected the intensity of dehumidification from the aspects of turbulence, surface tension and viscosity [9,10]. Consequently, based on experiments, transfer coefficients were associated with the flow and thermodynamics parameters for the purpose of practical application [9,11–14]. In general, the solution concentration, liquid-air ratio, vapor pressure ratio, dimensionless number Re and Sc were correlated. Nonetheless, most correlation equations only work perfectly in the limited investigation conditions. This is because the mechanism of heat and mass transfer between the liquid desiccant and air remains unclear, leading to the non-universality of correlation forms and parameters. In recent years, efforts were also made to optimize systems as well as operation parameters through experiments and simulations [7,15,16]. It is noticeable that the intensification of dehumidification is also restricted by the cognition of transfer phenomena between the liquid desiccant and air inevitably. Hence, investigating the mechanism of heat and mass transfer during dehumidification seems extremely important. But extensive macroscopic experiments only reflect the macroscopic results, failing to catch details of molecular scale [17–19]. Microscopic methods should be relied on to unravel the mystery of energy and mass transport. In the past few years, molecular dynamics (MD) has been demonstrated as a reliable measure to estimate physical properties
and disclose mechanisms of chemical engineering processes [20–23]. Based on molecular dynamics, investigators have conducted researches on interfaces of pure water and aqueous solutions [24–27], evaporation and condensation mechanisms [28, 29] and solution absorption processes [30]. Taylor et al. simulated the liquid-vapor interface of SPC/E water [24]. Orientation of water molecules were analyzed and they implied that free OH bonds at the interface would have an impact on absorbing particles. By observing the trajectory of water molecules, Nagata et al. simulated the evaporation of pure water [28]. It was found that the high kinetic energy of the evaporated water molecule was obtained by the making and breaking of hydrogen bonds involving at least three water molecules at the interface. After employing aqueous droplets of NaCl, KCl or LiCl, effects of the electric field intensity on the water evaporation rate were discussed by Wang et al. [29]. They attributed the evaporation enhancement under an electric field to the stretched transfer area and the directional arrangement of water molecules. Daiguji and Hihara firstly applied molecular dynamics into LiBr absorption refrigeration to reproduce the dynamic absorption process of water molecules [30]. According to the survey above, most literatures focus on the interfaces and evaporation mechanism of water and few literatures are concerned with aqueous solution absorption. The liquid-vapor systems between the liquid desiccant and air consist of diversified particles, which govern the absorption and release of water molecules through the interface. The dehumidification process deserves further exploration to find out the dominant particles and interactions when water vapor molecules move near and further enter into the liquid-vapor interface. In order to solve this problem and provide microscopic details, the vapor absorption (or dehumidification) processes of LiBr aqueous solution were simulated by molecular dynamics under different solution mass concentrations and temperatures. Kinetic and potential energy characteristics were presented subsequently. Furthermore, interactions on the absorbed
water vapor molecule caused by all components in LiBr solutions were compared and elaborated. Orientations of water were also summarized in this paper for explaining the magnitude and variation of interaction contributions. This study offers useful insight into liquid desiccant dehumidification from the perspective of microscopic level and could also inspire relevant workers to develop effective methods for intensifying absorption. 2 Method As shown in Fig.1, the simulated system was composed by the air box and the solution-air box. The air box was 7.5 nm in both width and length, which was the same as that of the solution-air box. In addition, the height of the air box was 8 nm and the height of the solution-air box was kept as 11 nm to obtain the air space of a similar size. It is notable that the height of the gas phase is usually over two times that of the liquid phase [30] and must ensure particles at one liquid-vapor interface will not interact with molecules at the other interface. Air was represented by the mixture of nitrogen molecules, oxygen molecules and water vapor molecules. The lithium bromide aqueous solution consisted of 4000 water molecules, 829 Br- and 829 Li+ ions, yielding the mass concentration of 50% in salt. For convenience of investigating the absorbed water vapor molecules, the air containing plentiful water molecules were expected in this paper, although aforementioned states may not exist in daily life. So, the air box was set to contain 6 water molecules, 8 nitrogen molecules and 2 oxygen molecules. To ensure the air state still existed (not in the condensed state) when the number of water molecules was large, the air box was firstly run in a NVT ensemble with the high temperature of 370 K for 5000 ps. Since water vapor densities are smaller than that under saturation conditions, above conditions are available. In the gas phase of the solution-air boxes, the numbers of nitrogen and oxygen molecules were the same with air boxes while the numbers of water vapor molecules were determined by MD simulations. The solution-air box was
run in a NVT ensemble of 300 K for 5000 ps to reach the equilibrium state before simulating dehumidification processes. Subsequently, the pre-equilibrated air box and the solution-air box were connected to carry out the microscopic absorption process in a NVE ensemble. Coordinates, velocities and energies of particles were output every 100 fs during the production run of 300 ps. All simulations were performed using GROMACS 5.1.1 by applying periodic boundary conditions in all directions. Non-polarizable force fields parameterized by Koneshan et al. were used to describe interactions between particles [31]. All atoms or ions were considered as Lennard-Jones (LJ) particles with charges. The intermolecular potentials between two particles were correlated by the summation of LJ potentials and electrostatic (Coulomb) potentials as follows:
U ij
4 ij ij rij
12
ij rij
6
qq f i j rij
(1)
Where lowercase subscripts i and j denote different two particles (atoms/ions), ε and σ represent energy and length parameters in LJ potentials, q and r mean charges on particles and distance between particles and f is the electric conversion factor with the value of 138.9354578 kJ·mol-1·nm·e-2. Force field parameters used in this paper are listed in Table 1. ε and σ between different kinds of atoms were produced by Lorentz-Berthelot combination rules for LJ interactions. Bonds and angles of water molecules were constrained by SETTLE algorithm [32]. The cutoff distance was set as 12 Å for Lennard-Jones potential [33–35] and short-range electrostatic interactions with potentials switching smoothly to 0 between 10 Å and 12 Å. PME solver was used to deal with long-range electrostatic interactions [36]. Newtonian equations of motion were solved by leap-frog algorithm with a time step of 1 fs. Nosé–Hoover thermostat [37] was used to keep the system at the target temperature during pre-equilibrium period. The potential energy of the water molecule was gained based on energy groups set in input files and analysis programs in GROMACS software according to Eq. (1). Moreover, the kinetic energy of the water molecule was also obtained from the analysis programs provided by GROMACS software and was
calculated by：
Ek
1 2
miv i
2
(2)
Where i, m and v represent atoms in the water molecule, masses and velocities of atoms, respectively. For analyzing the orientation of water molecules, several crucial angles are defined as shown in Fig. 2. θ represents the angle between the water dipole moment and the interface normal direction (towards air sides). For most conditions, φ1 and φ2 denote the angles of the upper OH bond and the other OH bond in H2O with respect to interface normal direction, respectively. But for water molecules at or below the lower interface in Fig. 1, φ1 and φ2 mean the angles of the lower OH bond and the other OH bond in H2O versus the interface normal direction towards air sides. For the sake of investigating the dominant particles, interactions between absorbed water vapor molecules and different particles in initial LiBr aqueous solutions were calculated, including interactions caused by water molecules, Br- and Li+. Above interactions were extracted from energy information and then was divided by the number of particles to get the interaction which a single particle imposes averagely. Therefore, the single particle interaction produced by H2O, Br- and Li+ in the initial aqueous solution could be obtained. As listed in Table 2 and Table 3, in order to study effects, the microscopic absorption processes were also studied under different solution mass concentrations between 40% and 60% by changing the number of Br- and Li+ and under different solution temperatures between 280 K and 360 K. 3 Results and discussion 3.1 Energy characteristics during absorption Taking 50% LiBr aqueous solution at 300K as an example, energy change with the simulation time was studied as the water vapor molecule in the air entered into the liquid-vapor interface and was
absorbed afterwards. Kinetic energies of 6 water vapor molecules in the air are illustrated in Fig. 3 for a typical simulation of absorption phenomena. The time range of the horizontal axis in Fig. 3 is the time period during which the water vapor molecule moves near the interface and further is absorbed. So, they may be not same since different water vapor molecules enter into interfaces at different times. The instant abrupt change of the kinetic energy means that the water vapor molecule collides with other molecules in air. And the continuous fluctuation of the kinetic energy occurs in the interface or the liquid bulk of LiBr aqueous solutions because of denser particles. It is apparent that the kinetic energy of the water vapor molecule may gain or decline after absorption. This depends on the initial kinetic energy of the molecule which follows the Maxwell distribution for the ideal gas. The average kinetic energy of water molecules after absorption is about 3.73 kJ/mol. So, if the previous kinetic energy is lower than the average value, the kinetic energy will rise. According to Fig. 3, the change of kinetic energy for every water molecule is mostly less than 10 kJ/mol. Fig. 4 gives the potential energy change corresponding to water vapor molecules in Fig. 3. The Lennard-Jones potential is represented by the open circles while the Coulomb potential is represented by the open triangles. It can be seen that the LJ potential caused by surrounding particles is embodied as the repulsive interaction synthetically with the absorption process proceeding. This is due to the fact that with a decrease in distance between the water vapor molecule and the other particle, the repulsive part in LJ potential goes up significantly but the attractive part increases relatively slowly. Once a particle is quite near the water vapor molecule, the synthetic interaction will be repulsive basically. The Coulomb potential is embodied as the attractive interaction and reduces rapidly when the water vapor molecule enters into the interface and then becomes liquid. Similar to the Coulomb potential, the total potential is characterized by a sharp drop during absorption at the interface. The average decrease of potential energy
is about 80 kJ/mol for every water molecule to achieve the phase change from gas to liquid. Compared with the kinetic energy change, the potential energy change is much larger with the dominant part of Coulomb interaction. 3.2 Interaction contributions under different concentrations The initial solution temperature was kept as 300 K and the mass concentration of LiBr solution ranges from 40% to 60% as listed in Table 2. To ensure reliable statistics of the simulation results, every condition was simulated for 20 times by using different initial microscopic states (configurations) of the system. Fig. 5(a) shows the calculated single particle interactions on a water vapor molecule caused by different particles for instance. Obviously, the single particle interactions change as the simulation goes on, resulting in comparing relative magnitudes difficultly. Thus, the accumulated interaction is proposed here which means the single particle interaction is integrated over the time. Accumulated interactions on the water vapor molecule caused by the single H2O, Br- and Li+ are shown in Fig. 5(b) where the value of various interactions could be identified simply. Due to the different trajectories of the water vapor molecules entering into the interface and the discrepant surrounding particles, the relative magnitude of various particle interactions may not be constant. The accumulated interactions between the absorbed water molecule and other components in LiBr solution were further analyzed. After obtaining accumulated interactions on water vapor molecules in all simulations, the probabilities of three following conditions were calculated. Effects of the solution concentration were discussed afterwards. The first condition is that a single Br- accumulated interaction on the water vapor molecule is higher than a single H2O accumulated interaction. The second condition is that the accumulated interaction of a single Li+ is higher than that of a single H2O. And the last condition is that the accumulated interaction of a single Br- is higher than that of a single Li+. It must be
pointed out that three conditions aforementioned are not mutually exclusive for the studied water vapor molecules in the initial air. The probabilities were calculated after the water vapor molecule entering into the interface for 2 ps, 5 ps and 10 ps, respectively. Fig. 6(a) shows the probability that the single Braccumulation interaction on the absorbed water vapor molecule is higher than the single H2O accumulation interaction during the initial absorption period. In this paper, the initial absorption period is within 10 ps after the water vapor molecule entering into the interface from the air side. With an increase in the concentration, the probability of having larger Br- interaction goes up remarkably, which indicates that the higher concentration promotes effects of Br- compared with that of H2O at the initial period of absorption. Furthermore, as the time becomes longer after capturing the water vapor, the effects of Br- are also boosted. For the studied concentration range, all probabilities of larger Br- effects are more than 59%. This implies overall, the condition that a single Br- shows larger interaction on the absorbed water than a single H2O makes up the majority. In contrast, during the initial absorption period within 10 ps, a single H2O in initial LiBr solutions plays a more important role than a single Li+ on account of all probabilities lower than 50% as depicted in Fig. 6(b). And it seems that effect of a single Li+ becomes weaker compared with a single H2O with an increase in the solution concentration. As shown in Fig. 6(c), the accumulated interaction caused by Br- is often more than that by Li+ during the initial absorption period, which is consistent with results in Fig. 6(a) and Fig. 6(b). In conclusion, at the initial absorption period within 10 ps, Br- ranks first in terms of the single particle accumulated interaction on the absorbed water vapor, followed by H2O and Li+. Above probabilities were also calculated at the final time of simulation and the probabilities of three conditions were described by open diamonds in all graphs of Fig. 6. Most water vapor molecules in air enter into the interface within 50 ps according to statistics. So the final time of simulation means about
250 ps after the water vapor molecules going into the interface. It is clear that effects of Br- and Li+ are improved significantly compared with the initial absorption period. Noticeably, the accumulated interactions caused by a single Br- are absolutely higher than that caused by a single H2O regardless of the concentration. When the concentrations are less than 53%, the accumulated interactions caused by a single Li+ are often higher than that caused by a single H2O. The rise of concentration also depresses the interaction of a single Li+ on the absorbed water molecule compared with the single H2O in liquid. The interactions caused by a single Br- are often more than that by a single Li+. It is clear that at the final time of simulation, a single Br- contributes the most, followed by a single Li+ and simultaneously, a single H2O provides the least interaction. According to results of Section 3.1, the most important is the Coulomb interaction which involves distance and charge quantity on particles. In order to explain the interaction contributions of different components to the absorption processes, water molecule orientations in the air, interface and liquid bulk were analyzed. The bin width of 0.05 (interval of cosine range) is used here for cosine statistics of angles (θ, φ1 and φ2). Fig. 7 shows the probability distribution of three important angles of water vapor molecules including the angle of the dipole moment versus the normal direction (θ), the angle of the upper OH bond versus the normal direction (φ1) and the angle of the lower OH bond versus the normal direction (φ2) for water vapor molecules in the air. The distribution probability of θ seems constant at every degree, which means in the air, the water molecule bisector has no obvious preferred direction. It can also be seen that there is no possibility of φ1 to be more than 128o or of φ2 to be less than 51o. The percentage that φ1 is less than 90o is the summation of all percentages in Fig. 7 with the horizontal axis less than 90o. According to Fig.7, most of φ1 is less than 90o with the percentage of 82.2 while most of φ2 is more than 90o with the percentage of 81.8. This indicates the existence possibility of an upward OH bond in the
water vapor molecule is about 82.2% and the existence possibility of a downward OH bond is about 81.8%. Both proportions approximate to the theoretical value of 80.4% calculated according to the water bond angle. When the water vapor molecule moves to the interface gradually from the air, the probability that a hydrogen atom in H2O is closest to the interface is very large. Hence, it is no wonder that the interaction caused by Li+ may be repulsive just as in Fig. 5, which also accounts for the weaker effects of Li+ during the initial absorption period. The simulated system was divided into slices with a thickness of 1 Å along the normal direction of the interface where the system density changes continuously from the density of the gas phase to that of the liquid phase. Fig. 8(a), Fig. 8(b) and Fig. 8(c) present the probability distribution of θ, φ1 and φ2 at different angles for water molecules at the liquid-vapor interfaces and in the liquid bulk. The solid circles represent results for water in the liquid bulk and the other symbols represent results for water at the interfaces. In terms of their representative slices, the open circles (water in the slice between 6.8 and 6.9 nm in z direction defined in Fig. 1), solid squares (water in the slice between 7.0 and 7.1 nm in z direction) and open squares (water in the slice between 7.2 and 7.3 nm in z direction) deviate from the liquid bulk farther and farther. According to Fig. 8(a), for water molecules in the liquid bulk, θ show a random distribution with almost equal possibility, similar to the angle distribution of water vapor molecules in the air. But a preferred orientation appears for water at the interfaces. With an increase in the distance from the liquid bulk, the preferred θ becomes smaller. Moreover, at the outermost layer of the interface, the average θ reduces with the concentration of LiBr aqueous solution. When the concentration increases from 40% to 60%, the average θ decreases from 82.4o to 72.2o. According to Fig. 8(b), as the distance from the interface is enlarged, more water molecules have an upward OH bond approaching the normal direction. The probability of the upper OH bond directing to the air side is more than 80% and 92% for
water in the liquid bulk and at the interfaces respectively. This may explain the weaker interaction of the single H2O than that of Br- during absorption besides the effect of the charge magnitude. As illustrated in Fig. 8(c), the lower OH bond in H2O directing to the liquid bulk also occupies the majority, agreeing well with the results of that in the air. Fig. 9(a) and Fig. 9(b) shows the water orientation around interface Br- and Li+, respectively. The water orientation angle around ions means the angle between the vector from the ion to the oxygen atom and the dipole moment of water. The water orientation angle around interface Br- reaches the maximum probability at 126.5o and the peak probability falls with larger distance from Br- because of exceeding the coordination location in the first solvation shell. The probability distribution of the water orientation angle around Br- in the liquid bulk is similar to the open square part in Fig. 9(a). This manifests in either the interface or the liquid bulk, numerous Br- particles are close to one hydrogen atom of the water molecule under equilibrium states. The water orientation angle around the interface Li+ reaches the peak probability at about 5o, which means numerous Li+ particles are close to the oxygen atom and nearly on the bisector of the water molecule under equilibrium states. Fig. 10 also verifies the particle location distribution under different mass concentrations of LiBr aqueous solution, which is similar to the radial distribution function. The first solvation shell of Li+ is closer than that of Br- and the peak number of surrounding water molecules are also larger for Li+. From this aspect, during absorption, the interaction variation under different concentrations caused by Li+ at the final simulation time may be attributed to the following two factors. On the one hand, Li+ particles produce stronger interaction due to the closer hydration shell and greater charge quantity under equilibrium conditions. As the absorption goes on, the absorbed water vapor molecule diffuses and may be captured by Li+. So, the effect of Li+ will be enhanced compared with the initial absorption period. On the other hand, with an increase in
concentration, Li+ particles are bound with previous water molecules more tightly under the strong interaction. It is also harder for the absorbed water vapor molecule to diffuse and displace the initial water around Li+. Therefore, within the same time of the whole simulation, the interaction of Li+ on the absorbed water molecule will be weaken compared with Br- and H2O when the concentration is amplified. 3.3 Interaction contributions under different temperatures Effects of the solution temperature were also researched as illustrated in Fig.11. The initial solution mass concentration in all simulations were set as 50%. Fig. 11(a) presents the probability that the accumulated interaction derived from the single Br- is stronger than that from the single H2O in liquid. It is found that when the water vapor molecule in air just moves near or into the interface, the dominant particles are Br-, followed by H2O and Li+ in terms of the interaction contributions. This can be explained by an OH bond of water in the air directing to the liquid bulk with a high possibility over 80%. But at the final simulation time, the accumulated interaction derives from the single Li+ may exceed the interaction from the single H2O. This is due to the fact that after the water vapor molecule entering into the interface, when the time is long enough, the absorbed water vapor molecule moves close to Li+ likely. And the water orientation around Li+ could be adjusted to about 5o. It can also be reflected by Fig. 11(b) and Fig. 11(c), where the rise of temperature dramatically promotes the effect of Li+ compared with Brand H2O. When the solution temperature reaches 300 K, the accumulated interaction of Li+ will exceed that of H2O. And when the solution temperature is over 340 K, the accumulated interaction of Li+ will exceed that of Br-. The faster diffusion of the absorbed water under high temperature may account for this phenomenon. Although water molecules are polar, the SPC/E water model used here is one of the most reputational models with good performance and low computation, which uses self-polarization correction
accounting for the dipole moment change. Many researchers have employed the SPC/E model to investigate the water evaporation phenomena or liquid-vapor systems [20–22, 24, 29]. And it is also demonstrated that the observables from snapshots of evaporation simulation are universal when using non-polarizable SPC/E and polarizable water models [28]. Moreover, in our previous study [19], the force fields used here have been demonstrated to reproduce physical properties with the acceptable accuracy and the change trends of the net absorption rate of water molecules under different solution temperatures agree well with the macro experiments. This could guarantee the reliability of the simulation here in some degree. The application of polarizable force fields in vapor absorption deserves further study. And the simulated phenomena may be visualized based on micro measures like neutron scattering, x-ray reflection and vibrational sum frequency spectroscopy [26], which also deserves further investigation in the future. 4 Conclusions In order to seek dominant particles in the LiBr aqueous solution during the process of liquid desiccant dehumidification, absorption phenomena were simulated by molecular dynamics under different solution mass concentrations and temperatures. The energy characteristics during absorption were provided and the single particle interactions on the absorbed water vapor molecule were further analyzed. The orientation of water molecules in the air, interface and liquid bulk were also discussed. Main conclusions are drawn as follows: (1) When the water vapor molecule in the air is transported to the LiBr aqueous solution, the kinetic energy of the water molecule may increase or decrease according to the initial value. But meanwhile, a dramatic drop occurs necessarily for the potential energy which is mainly determined by the Coulomb potential. The change of potential energy is much higher than that
of kinetic energy. (2) For the air and liquid bulk, the diploe moment direction of water is random, and the probability of having an upward OH bond or a downward OH bond is more than 80%. However, for the water molecules at the interface, an obvious preference exists as to the angle between the dipole moment and the normal direction, which reduces with an increase in the distance from the liquid bulk and the concentration of LiBr aqueous solutions. (3) The accumulated interaction was proposed to easily estimate the dominant interaction between various components in LiBr solutions and the absorbed water vapor molecule. At the initial absorption period within 10 ps, Br- usually ranks first in terms of the single particle accumulated interaction on the absorbed water vapor molecule, followed by H2O and Li+. This is quite different from the pure liquid of LiBr solutions, where the Li+ particles show the strongest interaction on water due to the ionic hydration energy. The aforementioned difference may be attributed to the existence of an OH bond directing to the liquid bulk when the water vapor molecule moves to or just enters into the liquid-vapor interface. (4) At the final simulation time, the water vapor molecule was absorbed by the liquid desiccant for a long time, bringing about a higher possibility to diffuse close to Li+ and adjust the orientation around Li+. As a result, the effect of Li+ increases compared with the initial period. It is clear that the interaction contribution caused by Li+ is enhanced by the solution temperature but depressed by the solution concentration in the investigated range. When the LiBr solution of 50% reaches 300 K or more, the interaction contribution of the single Li+ is only second to that of the single Br-. When the LiBr solution of 50% is over 340 K, the interaction contribution of the single Li+ will be the largest among all particles.
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173 (2005) 105–149. Nomenclature E
energy
m
mass
q
charge
r
distance from the particle
Re
Reynolds number
Sc
Schmidt number
T
temperature
U
potential function
v
velocity
X
mass concentration
Greek letters ε
energy parameter in LJ
σ
length parameter in LJ
θ
angle between the dipole moment and the interface normal direction
φ1
angle between the upper OH bond and the interface normal direction
φ2
angle between the lower OH bond and the interface normal direction
Subscripts s
solution
k
kinetic
Abbreviations LiBr
lithium bromide
LJ
Lennard-Jones
MD
molecular dynamics
NVT
canonical ensemble
NVE
microcanonical ensemble
SPC/E
extended simple point charge
Figure Captions: Fig. 1. Simulation systems and processes Fig. 2. Angles for orientations of water molecules Fig. 3. Kinetic energy change of absorbed water molecules Fig. 4. Potential energy change of absorbed water molecules Fig. 5. Particle interactions on the water vapor molecule: (a) single; (b) single accumulation Fig. 6. Effect of Xs on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+ Fig. 7. Orientation probability distribution of water vapor molecules in air Fig. 8. Probability distribution of water orientations for liquid bulk and interface: (a) θ; (b) φ1; (c) φ2 Fig. 9. Water orientation around interface ions: (a) Br-; (b) Li+ Fig. 10. Number of H2O around interface ions: (a) 40% LiBr; (b) 50% LiBr; (c) 60% LiBr Fig. 11. Effect of Ts on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+
Fig.1. Simulation systems and processes
Fig. 2. Angles for orientations of water molecules
Fig. 3. Kinetic energy change of absorbed water molecules
Fig. 4. Potential energy change of absorbed water molecules
Fig. 5. Particle interactions on the water vapor molecule: (a) single; (b) single accumulation
Fig. 6. Effect of Xs on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+
Fig. 7. Orientation probability distribution of water vapor molecules in air
Fig. 8. Probability distribution of water orientations for liquid bulk and interface: (a) θ; (b) φ1; (c) φ2
Fig. 9. Water orientation around interface ions: (a) Br-; (b) Li+
Fig. 10. Number of H2O around interface ions: (a) 40% LiBr; (b) 50% LiBr; (c) 60% LiBr
Fig. 11. Effect of Ts on probabilities: (a) Br->H2O; (b) Li+>H2O; (c) Br->Li+
Table Titles:
Table 1 Parameters of atom/ion models used in this paper Table 2 Simulated conditions under different mass concentrations and temperatures Table 3 Numbers of molecules/ions corresponding to solution mass concentrations Table 1 Parameters of atom/ion models used in this paper θHOH, °
Atoms/Ions
ε, kcal/mol
σ, Å
q,e
r, Å
Li+
0.1649
1.505
1
Br-
0.1
4.539
-1
N(N2)
0.1629
3.738
0
N-N: 1.098
O(O2)
0.2014
3.480
0
O-O: 1.017
O(H2O)
0.1553
3.166
-0.8476
O-H: 1
-
109.47
Table 2 Simulated conditions under different mass concentrations and temperatures Cases
Different solution concentrations
Different solution temperatures
Solution
Solution
Number of
concentrations, %
temperatures, K
simulation runs
40
20
45
20
50
300
20
55
20
60
20
50
280
20
300
20
330
20
360
20
Table 3 Numbers of molecules/ions corresponding to solution mass concentrations Concentrations, %
Number of H2O
Number of Br-
Number of Li+
40
4000
553
553
45
4000
678
678
50
4000
829
829
55
4000
1014
1014
60
4000
1245
1245
Highlights
The single particle accumulated interaction was proposed for easy comparison. The existence possibility of a downward OH bond is over 80% for water in air. Br- contributes the most to the absorption process, followed by Li+ and H2O. The concentration and temperature affect interactions caused by Li+ markedly.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: