Effects of Temperature on the Structure and Dynamics of Aqueous

Article pubs.acs.org/jced

Effects of Temperature on the Structure and Dynamics of Aqueous Mixtures of N,N‑Dimethylformamide Sohag Biswas and Bhabani S. Mallik* Department of Chemistry, Indian Institute of Technology Hyderabad, Telangana 502 205, India ABSTRACT: The hydrogen-bonded structure and dynamics of aqueous N,N-dimethylformamide (DMF) solutions of varying compositions are investigated by means of molecular dynamics simulations at three different temperatures at ambient pressure. The dynamical aspects of the solution are investigated in terms of the single-particle and mutual diffusion coefficients, calculated from the mean square displacement, and also in terms of the lifetimes of water−water and water−DMF hydrogen bonds. The calculated densities and diffusion coefficients at different temperatures are compared with the available experimental data; it is observed that they agree qualitatively with the experimental data and reproduce the general trends within the limitations of adopted force fields. With the increase in DMF concentrations, the water−water hydrogen bonding is less preferred, facilitating the water−DMF association; the lifetimes of both type of hydrogen bonds increase due to existence of long-lived clusters of molecules. The effects of temperature on dynamics of water−DMF hydrogen bonds have significant contribution toward the microheterogeneity of the systems at higher DMF mole fractions.

1. INTRODUCTION N,N-Dimethylformamide (DMF), a polar aprotic organic solvent, is used in various applications, including organic synthesis, fibers and artificial leathers, and petroleum and pharmaceutical industries. Small amide molecules, like DMF, serve as a model of the peptide bond, due to which they are the focus of many scientific investigations. Water−DMF mixtures are known to show significant nonideality in their equilibrium and dynamical properties with a variation of composition and temperature.1,2 These mixtures are interesting not only because of their ubiquitous nature but also due to their importance as model systems for a weak hydrogen bonding environment. The presence of hydrophobic methyl groups that perturb the water structure is believed to give rise to very different water−DMF interactions in aqueous mixtures as compared to pure components. The bulk water consists of a tetrahedral threedimensional network of hydrogen bonds (H-bonds) at ambient conditions, but the formation of strong H-bonds in DMF is not possible due to the lack of a strong donor atom. The mixing of DMF with water causes structural changes in the liquid due to both hydrogen bonding and hydrophobic interactions between two molecules. The presence of weak interaction like C−H···O type may play their part in equilibrium and dynamical properties. There have been a number of experimental3−7 and theoretical studies8−18 on various structural, energetics, and dynamical aspects of the pure and aqueous solutions of DMF. The results from NMR chemical-shift measurements on pure DMF liquids and in various solvents showed no evidence for hydrogen-bonded species, and the association of DMF molecules was due to dipole−dipole interactions.6 Visser and © XXXX American Chemical Society

Somsen studied the hydrophobic interactions in the mixtures of DMF and water using alkyl ammonium salts by calculating enthalpies of the solution.19 Vitagllano and co-workers1,2 reported diffusion, viscosity, and refractivity data of these systems at various temperatures. The authors suggested the following models for the interactions exist between molecules: the presence of well-defined water complexes with single DMF molecule, and the formation of cluster like structures due to water−DMF interactions where hydrogen bonds played an important role. The associative nature of these interactions is evident in various physicochemical properties1,2,20,21 of these aqueous mixtures such as density, viscosity, compressibility, heat of mixing, and partial molar enthalpies; minima or maxima have been observed for these properties in the mole fractions 0.3−0.4 DMF. The dielectric characterization study had shown that water−DMF hydrogen bond interactions were stronger than water−alcohol, which were due to the breaking of the water tetrahedral structure.22 Yashonath and Rao12 published the first molecular dynamics study of pure liquid DMF at room temperature and normal pressure. Several simulations have been carried out on dilute solutions of DMF in water.10,23,13−15,24 In particular, we note the Monte Carlo study of Jorgensen and Swenson,9 who used optimized intermolecular potential to study the solvation of DMF in water. DMF participated in about two hydrogen bonds Special Issue: Modeling and Simulation of Real Systems Received: March 16, 2014 Accepted: September 5, 2014

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dx.doi.org/10.1021/je5002544 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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respectively. The partial charges for DMF were determined using the restrained electrostatic potential (RESP)33 protocol implemented in the ante-chamber module of AMBER1232 through fitting the electrostatic potentials calculated by Gaussian0934 at HF/6-31G* level of theory. The values of Lennard−Jones and electrostatic interaction potential for water and DMF have been presented in Table 1. To get the minimum

with the surrounding water molecules, and approximately 3.4 nearest water molecules were found around the CH groups. Subsequently, experimental studies based on FTIR spectra combined with theoretical investigations proposed the clathrate-like hydrogen-bonded cage like structure for hydrophobic hydration shell containing amides.25 There have been also a number of simulation studies on water−DMF mixtures at higher DMF concentrations in liquid phases. Monte Carlo simulations of water−DMF mixtures10 showed that the main contribution to the water−DMF interaction energy came from hydrogen-bonded dimers, which was due to the association between the oxygen of DMF and the hydrogens of water. The rigidity of peptide bond of hydrated solute was equivalent to the gas phase structure confirming the planar nature for the amide molecule. Samios and co-workers15 investigated the intermolecular interactions of the aqueous systems by exploring the effects of potential models of pure liquid water (SPC, SPC/ E, TIPS2) and DMF (CS2) in predicting several properties of the solutions. Another group23 combined OPLS and TIP5P models for DMF and water molecules, respectively, in their molecular dynamics simulations to study pure DMF and its aqueous mixtures, and they observed that the composition dependence properties were due to two reasons: the clustering feature of water, and the polarizable amide group of DMF. Perera and co-workers26 studied the concentration fluctuations and microheterogeneity of the aqueous DMF solution and found that water displayed sponge-like structure, which was insensitive to the differences between the force fields of the amide molecule. DMF was also used as a solvent to dissolve polymeric material for membrane casting with the technique of phase inversion;27,28 water was used as the nonsolvent in this process. The solvent−nonsolvent interdiffusion process affected the mechanism of membrane formation where temperature also played a vital role. Earlier computational studies on water−DMF systems were focused mostly on room temperature. In this work, we have carried out classical molecular dynamics simulations of these solutions at varying compositions and temperatures. Our main focus has been to calculate the density, single-particle and mutual diffusion coefficients, and lifetimes of water−water as well as amide−water hydrogen bonds. The details of the simulations are presented in section 2. In section 3, we have discussed the density, structure, and diffusive nature and hydrogen bond dynamics. Our conclusions are briefly summarized in section 4.

Table 1. Values of Lennard−Jones and Electrostatic Interaction Potential for Water and DMF molecule

site

σ/Å

ε/(kcal·mol−1)

charge (e)

water

OW HW O C(CO) H(CO) N C(N−CH3) H(N−CH3)

3.166 0.0 2.76 3.64 1.85 3.33 3.64 1.92

0.155 0.0 0.210 0.086 0.015 0.170 0.109 0.0157

−0.8476 +0.4238 −0.5638 0.4482 0.0359 −0.0239 −0.3304 0.1274

DMF

energy configuration, each system was minimized for 5000 steps, where first 2500 steps were in steepest descent method followed by the same number of steps in conjugate gradient method. Then, 100 ps NVT simulation was performed to heat the system up to a temperature higher than the target one, and another 200 ps NVT simulation was carried out to cool the system at the required temperature. Subsequently, the systems were equilibrated in the isothermal−isobaric (NPT) ensemble at 1 atm pressure for 12 ns. Last 10 ns trajectory was used for calculating the density of the system. The average volume and final configuration of this simulation period were used for further simulation in the canonical ensemble. Some 15 ns production runs were performed for each system for calculating structural properties. In order to calculate the diffusion coefficient, we have run another 15 ns in a microcanonical ensemble. Periodic boundary conditions were applied in all directions. A Langevin molecular dynamics method was followed to control the temperature with 1 ps−1 as the collision frequency. The time step was 2 fs, and a cutoff distance of 12.0 Å was used for all nonbonded interactions. Long-range electrostatic interactions were treated with the smooth particle mesh Ewald method.35 All of the bond lengths of water and DMF molecules involving a hydrogen atom were constrained according to the SHAKE algorithm.36 The analysis of reported properties other than the H-bond lifetimes was done by PTRAJ module available in amber tools. The analysis tool g_hbond, available in GROMACS 4.537 simulation package, was used for the calculation of H-bond lifetimes after converting the Amber trajectory to appropriate format with the help of VMD38 and an amb2gmx.pl script. The standard deviation of the density and dynamical data presented here is within 1 % and 2 % of the average values, respectively.

2. MOLECULAR MODELS AND SIMULATION METHOD We have carried out classical molecular dynamics simulations to study the effects of temperature on the density, structure, and dynamics of aqueous mixtures of DMF. Three temperatures ((278.15, 293.15, and 313.15) K) and nine mole fractions of DMF (0.00, 0.125, 0.25, 0.375, 0.50, 0.675, 0.75, 0.875, 1.00) were chosen in this study. The total number of simulated molecules was 1200, and the appropriate numbers of individual molecule were taken to generate the required mole fraction of the particular mixture. As earlier theoretical studies were mostly focused at 298 K, we have chosen the other three temperatures for the present study and compared our result with that of room temperature wherever available. The initial configurations of the systems were prepared using the PACKMOL29 program. All of the simulations were carried out with the AMBER1232 package. We have adopted an all sites general amber force field (GAFF) 30 and SPC/E 31 model for DMF and water,

3. RESULTS AND DISCUSSION The densities and diffusion coefficients for all of the systems at three temperatures were calculated from NPT and NVE simulations, respectively. The route of mean square displacement using the Einstein relation was followed to obtain the single-particle diffusion coefficients. The mutual diffusion coefficients were obtained using Darken’s relation39,40 considering corresponding self-diffusion coefficients and mole fractions. The results of the density as a function of DMF B



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mole fractions (XDMF) obtained in the present work are compared with experimental data in Figure 1. The over

Figure 1. Comparison of calculated and experimental densities in water−DMF mixtures at 278.15 (top), 293.15 (middle), and 313.15 (bottom) K temperatures. The experimental data are taken from refs 1 and 2.

Figure 2. Composition dependence of single-particle diffusion coefficients for DMF−water mixtures at various temperatures. The inset plot of bottom panel depicts the comparison of calculated diffusion coefficient of DMF with experiments. The experimental values for pure water (shown in stars in the top panel) and DMF for various temperatures are taken from refs 41 and 42, respectively.

estimation of the densities is due to the combination of force fields used in the present study, especially considering the many body nature of the investigated aqueous mixtures being modeled by interactions composed of two-body interactions; the differences are more pronounced toward the higher pure component mole fractions. This feature can be found for all the temperatures. The experimental densities1,2 of the mixtures show a maximum in the water-rich region at two lower temperatures due to the presence of hydrogen-bonded complexes between DMF and water; this maximum is not observed for our calculated values. However, we can see the closeness of the values near the region of maximum observed for experimental data. No maximum is observed in the data at highest temperature for both the calculated and experimental densities. The average density of the mixture decreases slowly with increase in temperature and DMF concentrations. The data for single-particle and mutual diffusion coefficients are presented in Figures 2 and 3, respectively. As it can be seen from the results, both of the data show a nonlinear dependence with the composition of the mixtures. The comparison of calculated mutual diffusion coefficients with experimental data is shown in Figure 3. The largest difference observed between these values is toward higher XDMF. This is due to the adopted approximate formula for the calculations that neglects the collective correlations, and they are very important for aqueous mixtures. An interesting aspect of the mutual diffusion coefficient values for all of the temperatures is the presence of a minimum near XDMF = 0.375. This feature is also clearly observed for the single-particle diffusion coefficients of water (DWAT) and DMF (DDMF); the later has been shallower than the earlier. The experimental reported1,2 minima are also

shallow and correspond to smaller mole fractions of DMF than the minima found in the present work. The single-particle diffusion data for both the molecules show that the diffusive nature of one species is slowed down by the addition of other and vice versa until the approach of minimum. DWAT values decrease sharply with the increase in XDMF, and the appearance of minimum for DDMF is shallower than DWAT; an earlier study15 has also reported the shallow minima at ambient conditions in the range of 0.3−0.4 for XDMF. After crossing the minimum, there is an increase of mobility for each species. The diffusion coefficients for pure water at all of the temperatures match well with the experimental values.41 We have compared our calculated diffusion coefficients of DMF with the available experimental data in the inset of Figure 2 (lower panel). The trend line containing single particle diffusion data of DMF has been underestimated as compared to experimental data, however within the temperature range, our data follow a similar trend as of the experiment.42 With the increase in temperature, the translational dynamics of water is much faster between XDMF = 0.0 and 0.375. There was a correspondence with the viscosity data that showed a maximum at the same position diffusion coefficients showed a minimum. However, the density results do not show well-defined maximum in this composition range. It is obvious that significant interactions, contributed by various types of forces acting between these two molecules, exist in the solution: hydrophobic nature of methyl groups, relatively strong hydrogen bonding nature of the C



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Figure 4. Snapshot of part of the simulation box corresponding to XDMF = 0.5 at 293.15 K showing DMF−water and water−water hydrogen bonding. For better visualization, one of the DMF molecules along with nearest hydrogen-bonded water molecule is shown in CPK representation; other water and DMF molecules are represented in licorice and line styles, respectively. The picture was generated with the help of VMD package.

Figure 3. Comparison of calculated (red squares) and experimental (black stars) mutual diffusion coefficients in water−DMF mixtures for various DMF mole fractions. The top, middle, and bottom panels depict data at (278.15, 293.15, and 313.15) K, respectively. The experimental data are taken from refs 1 and 2.

carbonyl group, and very weak interactions of aminic nitrogen (N-aminic) and aldehydic hydrogen (A-hydrogen) with other hydrogen bonding sites. Although hydrophobicity promotes the formation of water−water hydrogen bonds, primarily, the carbonyl group provides the stability to the hydrogen bonded well-defined (DMF)m−(H2O)n complexes; hydrogen bonds on N-aminic and A-hydrogen may be very weak to play the major role for the purpose. Because of its aprotic nature, DMF is unable to participate in N−H···OC type hydrogen bonding with dialkyl substitution at nitrogen. However, in aqueous mixtures, DMF forms hydrogen bonds with water molecules. The carbonyl oxygen (O) of DMF can accept the hydrogens (HW) from the water oxygen (OW). Figure 4 shows the snapshot of part of the simulation box corresponding to XDMF = 0.5 showing water− DMF and water−water hydrogen bonding at 293.15 K. To explore the hydrogen bonding nature of the mixtures, we have calculated the relevant radial distribution functions (RDFs) involving donor and acceptor atoms. Because of the weak hydrogen bonding nature of C−H···O W and N···H W interactions, the peaks are very weak, and the role played by these interactions, investigated in earlier studies,23 may not be so significant toward the overall hydrogen bond dynamics of the aqueous mixtures. The results obtained for O···HW and OW···HW RDFs for four DMF mole fractions are shown in Figures 5 and 6, respectively. The first peak in O···HW RDF profile occurs at 1.73 Å for almost all of the mole fractions. The position of this peak is mostly invariant to the addition of DMF. The increase in temperature results in decrease in the peak

Figure 5. Site−site radial distribution functions for carbonyl oxygen and water hydrogen atoms involved in hydrogen bonding at different temperatures for four different DMF mole fractions. The black, red, and blue solid lines depict the RDF data at (278.15, 298.15, and 313.15) K, respectively.

height. The first minimum located at 2.47 Å for the lowest mole fraction indicates strong water structuring around the carbonyl oxygen. The position of this minimum slightly moved to higher distance for higher DMF mole fractions. The depth of this minimum increases as we add more DMF to the mixtures and decrease the temperature. The heights of first and second peaks increase with higher values of XDMF; this indicates the more short-range association of water and DMF molecules, and structured solvation shell around DMF. This can be partly attributed to the combined force fields, which results in overestimation and under estimation of densities and diffusion coefficients, respectively. O···HW and OW···HW RDFs show similar behaviors as the concentrations of DMF and temperD



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dependent on the orientation of molecules. So, the H-bond dynamics of the system can be affected by diffusion as well as orientation of molecules involved in hydrogen bonded pairs. The overall balanced effects due to the increase in density and decrease in diffusion may have a role in deciding the hydrogen bond dynamics of the system. As the corresponding experimental data are not available, the quantitative comparison of hydrogen bond dynamics in these mixtures is not possible. The results of the correlation functions and the obtained lifetimes are shown in Figures 7 and 8, respectively, as a

Figure 6. Oxygen−hydrogen distribution functions of water molecules at different temperatures for four different DMF mole fractions. The designation of the black, red, and blue solid lines is according to Figure 5.

ature vary. The peak positions in OW···HW RDFs also do not vary by the change in XDMF; heights of these peaks change significantly. The differences in the heights of first and second peaks (intermolecular) of OW···HW RDFs are smaller than that of O···Hw RDF peaks with the increase in values of XDMF; overall structural changes are observed beyond the first solvation shell. A similar type of structural rearrangement obtained from molecular dynamics simulations was also reported for DMF,23 acetonitrile,43 and DMSO44 aqueous mixtures. From the RDFs, it seems that the aqueous mixture can contain two types of hydrogen bonds: water−water and water− DMF. As water molecules are loosing their three-dimensional H-bond network, there will be a competition between two hydrogen bonding environments; the stability of the mixture comes from the balance between the breaking and formation of water−water and water−DMF hydrogen bonds, respectively, with the increase in DMF concentration. From the infrared spectroscopy study of these mixtures,45 Biliškov and Baranović also noticed considerable changes in hydrogen bond network of water; a single DMF molecule binds more than one water molecule, and there is a smooth change of characteristics of microheterogeneity with mixture composition. To further explore the dynamics, the lifetimes of H-bonds were calculated by using hydrogen bond time correlation function approach.46−50 The lifetime of a particular type of H-bond was calculated from the average over autocorrelation function of the existence functions (either 0 or 1) for all hydrogen-bonded pairs. The integral of autocorrelation function gives a rough estimate of the average H-bond lifetime. For the existence of the H-bond, we adopted a standard criterion; a donor (D)− acceptor (A) distance and A−D−H angle cutoffs are 3.5 Å and 30°, respectively. We want to note that, decaying of correlation functions depends on the geometric definition adopted for the existence of a hydrogen bond, and our adopted definition is the same for all of the hydrogen-bonded pairs analyzed here. Another aspect can be noted here: the H-bond correlation functions for the water−water and water−DMF hydrogen bonds are primarily related to the interplay between diffusion and bond breaking/making processes. The later events are

Figure 7. Time dependence of the hydrogen bond time correlation function for DMF−water (left panels) and water−water (right panels) hydrogen bonds. The top, middle, and bottom panels depict the data at (278.15, 293.15, and 313.15) K temperatures, respectively. Dotted black lines are the data for water−water hydrogen bonds in bulk water.

function of XDMF. The decay of these functions for water−water hydrogen bonds is found to be slower with the addition of DMF as compared to pure water. At two lower temperatures, the decay for pure water is found to be slower than the continuous correlation function at ambient conditions;50,51 the hydrogen bond dynamics of water becomes faster with increase in temperature. On average, the dynamics for water−DMF hydrogen bonds is found to be slower than that of water−water hydrogen bonds until XDMF = 0.375; the dynamics of these two types hydrogen bonds are approximately similar for the 50:50 mixture. After this mole fraction, less cooperative nature between the molecules results in decrease of the lifetimes of water−DMF H-bonds. The longer lifetimes of water−water E



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disturbed more than the water−water pairs. The structural analysis indicates the fact that, with the concentration, the number of water−water hydrogen bonds varies inversely proportional to water−DMF hydrogen bonds; however, one can notice significant degree of hydrogen bonding represented by composition dependent small clusters, which may be the key factor for the stability of DMF rich solutions.

4. CONCLUSIONS We have investigated the structure and dynamics of aqueous solutions of DMF of different mole fractions at three temperatures. The dynamics of hydrogen bonds are also studied by estimating the lifetimes of water−DMF and water− water hydrogen bonds from hydrogen bond correlation functions. The calculations are done at (273.15, 293.15, and 313.15) K temperatures for nine different DMF mole fractions. The overestimation of density is found for all of the temperatures. The calculated values of density and mutual diffusion coefficient agree qualitatively with the experimental data and reproduce the general trends. The minima of mutual diffusion data are found near XDMF = 0.375 for all of the temperatures. The single particle diffusion coefficients of water match well with experimental observed value, but the values are underestimated for pure DMF molecules within the studied temperature range. With addition of DMF to water, the water− water hydrogen bonding is less preferred promoting the water− DMF association. The lifetimes of water−water and water− DMF hydrogen bonds increase with increase in DMF mole fractions indicating the existence of long-lived clusters formed primarily due to association of water−water and water−DMF molecules through hydrogen bonding. With the increase in temperature, hydrogen-bonded pairs correlate weakly resulting in decrease of lifetimes, and the increase in temperature has significant effects on the microheterogeneity of mixtures at higher concentrations.

Figure 8. Hydrogen bond lifetimes of water−water (top) and DMF− water (bottom) hydrogen bonds as obtained from the hydrogen bond correlation functions. The filled black circles, red squares, and blue diamonds are for (278.15, 293.15, and 313.15) K temperatures, respectively.

hydrogen bonds are due to the enhancement of short-range hydrogen bonding correlation of hydroxyl oxygen as compared to amide oxygen toward water molecules. Due to the presence of hydrophobic group, the cooperativeness of hydrogen bonded pairs gives rise to various clusters containing water and DMF or only water molecules. The formation of (DMF)m·(H2O)n type cluster depends on both the hydrogen bonding and hydrophobic interactions; however, the role of hydrophobicity of methyl groups is composition-dependent. 23 The water molecules participate in the formation of more aggregates in higher DMF concentration, where some water molecules tend to reside. This was evident from the increase in lifetimes of water−water hydrogen bonds with increase in XDMF; water molecules do not get partners to switch their hydrogen bonds. As reported earlier,23 DMF enhances the structure of water in dilute solutions of XDMF < 0.1, but at higher concentrations the breaking of water−water hydrogen bonds promotes the formation of water−DMF association. Once the clusters are formed, both water and DMF molecules do not get a switching partner so that a particular H-bond will break to initiate the formation of other. Visual observations indicate the chain-like structure for water molecules; these hydrogen-bonded water chains are trapped between hydrophobic groups of DMF. So, the lifetimes of two types of H-bonds increase with the increase of XDMF. The increase in lifetime of both types of H-bonds is very much homogeneous over all the concentration range at lowest temperature; one can notice the irregularity in lifetimes after XDMF = 0.5 at higher temperatures due to heterogeneity nature of DMF rich mixtures. With the increase in temperature, hydrogen-bonded pairs correlate weakly resulting in decrease in lifetimes. The contribution from the effects of temperature on the microheterogeneity of mixtures at higher concentration is significant; the water−DMF hydrogen-bonded pairs are

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel. no.: +914023017051. Fax no.: +914023016032. Funding

Funding from Indian Institute of Technology Hyderabad, India is acknowledged. Part of the simulations was performed in HPC facility, IIT Hyderabad and Bioinformatics Resources & Applications Facility (BRAF) at Centre for Development of Advanced Computing, Pune, India. Notes

The authors declare no competing financial interest.

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