A Thermoacoustical and DFT Exploration of Physio-chemical Properties for N,N-dimethylacetamide (DMA) with Water

For the binary mixture of water and N, N-dimethylacetamide (DMA), observations have been done of the ultrasonic velocity (u), density ( ρ ), viscosity ( η ) and refractive index ( n ) in excess of the whole composition range at various temperature. Deviation in ultrasonic velocity ( Δ u ), excess intermolecular free length (L fE ), excess acoustic impedance (Z E ), excess molar volume (V mE ), deviation in molar refraction ( Δ R m ), deviation in viscosity ( Δη ) and excess Gibbs' free energy of activation for viscous flow ( Δ G* E ) were used to investigate the intermolecular interactions present in the mixture. Derived parameters such as isoentropic compressibility ( K s ), the specific heat ratio ( γ ), and the effective Debye temperature ( q D ) at varying concentrations of DMA have also been computed using experimental data. Various semi-empirical mixing rules have also been applied to the binary mixture. Density functional theory is utilised to optimise the geometry of DMA, DMA with water, and calculation of H-bonded intermolecular interactions.


INTRODUCTION
Examining the relationships between molecules in organic binary mixtures.Alcohols are highly self-linked liquids that have a hydrogen bond network that is three dimensions in size 1 and can be related with any other group possessing some degree of polarity 2 , therefore having alcohol as one of the components is of certain relevance.Because ultrasonic velocity evaluation are extremely reactive to molecular interactions, they may offer subjective information with the kind and intensity of interaction with molecules in liquid solution [3][4][5][6][7][8] .
DMA is miscible with water in all ratios and with the majority of organic solvents, such as ethers, ketones, alcohols, and so forth.The boiling point of DMA, a dipolar aprotic solvent, is 438.2K, a dipole moment of 3.72 D, which is higher than that of water, and a medium dielectric constant of 37.78 at 298.15 K 9 .Because of its exceptional solvent power and outstanding water solubility especially for high molecular weight polymers and resins.DMA is a widely used solvent in the manufacturing of synthetic fibers and polyurethanes.It functions well as a catalyst and a result for a variety of processes.In addition, it works well as an oil and gas extraction agent and plasticizer for cosmetics and pharmaceutical intermediates.
The experimental basis for selecting the suitable solvents for specific applications is provided by the estimation of ultrasonic velocity, density, refrective index, viscosity and their fluctuation with various proportion composition of liquid and temperature and composition [10][11][12][13][14][15][16][17][18][19][20] .Thus, analysis of molecular association in system of water and N, N-dimethylacetamide (DMA) has been attempted in this work.The mixture's intermolecular interactions were examined.V m E , Δu, ΔR m , L f E , Z E , Δη and ΔG* E .The linear regression polynomial equation for Curve Expert 1.3 has been fitted with these excess parameters.Using experimental data for the system, derived parameters have also been determined, including isoentropic compressibility (k s ), specific heat ratio (γ) and the effective Debye temperature (q D ) at varying concentrations of DMA.
The binary mixture has also been subjected to a several rule and theories, including the Flory's statistical theory (FST), collision factor theory (CFT), Nomoto, Vandeal and Junjie's theories for the theoretical estimation of ultrasonic velocities.The APD (average percentage deviation) values determined from the observed values has been used to compare the comparative merits of the different mixing methods and models.Furthermore, the strength of the hydrogen bonding between molecules has been examined using density functional theory (DFT).

DFT Calculations and models
Numerous researchers [21][22][23][24] have used density functional theory to calculate molecular system properties, with remarkable understanding between experimental and theoretical results.DFT 25 has been functional to compute H-bonded intermolecular interactions using Gaussian 09W [26][27][28][29] and to optimize the geometry of DMA and DMA in relation to water.The outcomes were visualized using GaussView 5.0 software 30 .
The Natural Bond Orbital (NBO) has been utilized to quantify hyperconjugation or intermolecular delocalization 31 .The intermolecular delocalization of the DMA+water binary mixture has been studied by means of second-order perturbation theory using the Fock matrix in the NBO basis.The structure of DMA+water is given in Figure 1.

EXPERIMENTAL Apparatus and Procedure
Ultrasonic velocity has been determined using the interferometric technique.The ultrasonic velocities were reproducible within an error margin of ±0.08%.
A pycnometer with a single capillary calibration has been used to measure densities.The graduation on the pcynometer stem was 0.01 mL.The reproducibility of the densities was within ±0.01%.
The LVDVII+Pro Brookfield viscometer has been used to measure viscosity.Brookfield Rheocalc 32 Software allows for total PC control over the instrument.The equipment has a repeatability of ±0.2% and an accuracy of ±1.0% of the full-scale range.
An accurate refractive index of ±0.001 unit was obtained with a thermostated Abbe's refractometer, which had a range of 1.300 to 1.700 for the liquid mixtures.

Thermo dynamic parameters
Table 1 presents the experimentally measured values for DMA+ water solution with mole fraction (x 1 ) at varying temperatures. (1) Where γ, β T , and G T are specific heat ratio, isothermal compressibility and modulus of rigidity respectively.
It can be seen from Table 1 that at all three temperatures, ultrasonic velocity (u) attains a maxima at .0999 mole fraction.As the concentration increases we see the ultrasonic velocity decreases.In liquid mixtures, the strength of the molecular interaction become maximum at the concentration where the velocity maxima take place.These observations agree with the earlier reported data 11 .
The isoentropic compressibility (k s ) reaches a least amount and then again increases with an amplify in concentration and have an opposite relationship with the velocity.The mixture under study exhibits compressibility minima in the same concentration range as the velocity maxima, as would be predicted (Fig. 2a).At or very close to the concentrations where complex formation takes place, a decrease in ks and an increase in u are the results of the hydrogen bond formation strengthening the intermolecular forces.Similar variations in ultrasonic velocity and isoentropic compressibility have also been reported earlier 7 .
The derived parameters, viz., effective Debye temperature (q D ), and specific heat ratio (γ) provide inclusive information about the interactional and structural characteristics of the mixture at the microscopic level.It can also be seen from Fig. 2b and 2c that the variation of effective Debye temperature (q D ) and specific heat ratio (γ) with concentration is also non-linear, which further help the phenomenon of complex formation between dissimilar molecules [32][33] .For calculating isoentropic compressibility (k s ), specific heat ratio (γ) and effective Debye temperature (q D ),following relations are used, Figures 3a and 3b illustrate the deviation in ultrasonic velocity (Δu) and excess acoustic impedance (Z E ) for the system of DMA with respect to the mole fraction at varying temperatures.Analyzing the curves, it can be observed that both Δu and Z E have positive values.The strong specific interactions (hydrogen bonding between DMA and water) is present and the filling of smaller water molecules into the voids created by larger DMA molecues are likely responsible for the positive values of Δu and Z E (Figs. 3a and 3b).Fort and Moore 34 , as well as many other researchers 16,17,35 , contend that positive values of Δu and Z E signify the presence of strong intermolecular interaction between different molecules.The high positive values like Δu and Z E indicates the DMA is interactive with water.
Figures 3c, 3d, and 3e demonstrate that the values of excess parameters like L f , V m E and ΔR m are all negative at all three temperatures.The hydrogen bonds with water is thought to be the reason behind DMA's ability to take protons.The molecules in the mixture varying sizes could possibly be the cause of the reported negative values.The molar volumes of DMA and water at 298.15 K are 92.9 cc/mol and 18.06 cc/ mol respectively.The larger difference in molar volume between DMA and water would result in contraction in volume due to the component molecules need to fit with other structures.The difference in component molecules sizes was also taken into account by Ali and Nain 36 and Pikkarainen 10 to explain the negative values of V m E in binary mixtures of DMA+ethanol and DMA+methanol/ethanol/propanol, respectively.
The development of strong hydrogen bonds between DMA and water molecules is further supported by the positive values of deviation in viscosity (Δη) and excess free energy of activation for viscous flow (ΔG* E ) for the DMA+water system (Figs.3f and 3g).The values of Δη and ΔG* E extrema decrease with elevation in temperature, indicating that the interaction between molecules is temperature sensitive and weakens as temperature rises.Similar patterns in Δη and ΔG* E have also been observed in the cases of DMA + methanol 5,10 and water+sulfonane 37 .Table 2 provides the standard deviation (σ(Y E )) and coefficient ai as determined by the curve expert 1.3 software.The values of the APD (Average percentage deviation) of ultrasonic velocity (u) anticipated by different semi-empirical rules are shown in Table 3.It shows that the CFT relation gives the minimum APD and Vandeal's relation gives the maximum APD for this system.However, the APD values predicted by Nomoto, Jungie, and FST are nearly equal.Theoretical study Natural bond orbital (NBO) study NBO examination relies on technique that provide a collection of algorithms that make it possible to extract the basic bonding concept through DFT calculations 31 .NBO study is an crucial tool for evaluating the molecular interaction in molecules, in addition to given that a useful establishment for analyzing conjugative interaction or charge transfer in molecular systems.Strong electrostatic hyperconjugative interactions are revealed by the NBO study 38 .The NBO study of DMA has been already mentioned in published work 24 and for DMA+water the interaction energy of LP1(N2) with anti-bondingπ*(O1-C3) increases to 67.47 kcal/mol showing higher stabilization of the system.The interaction of LP(2) of O1 and O19 with σ*(O16-H17) and σ*(O16-H18) respectively results in similar stabilization energy of 5.45 kcal/mol.

DFT investigation of H-bonded intermolecular interaction
To compute the intermolecular hydrogen bonding strength using Bader's Atoms in Molecules (AIM) hypothesis 39 has been mentioned in published work 24 .In this work to determined the hydrogen bond strength for the DMA and water binary mixture.It was computed to be 5.79825 kcal/moland 5.78869 kcal/mol at B3LYP corresponding to two hydrogen bonds formed between water and DMA molecules.Table 4 lists the topological parameters.To depict thedistribution ofelectron densities, electron localised field (ELF) graph has been constructed, as shown in Fig. 4. The overlapping of the blue zone in Fig. 4 depicts interaction with the oxygen atom of DMA molecules and the H atoms of water molecules in the binary mixture.The figure provides sufficient theoretical support for such intermolecular bonds between DMA and water.
Although the PDOS plot shows a group's relative contributions towards each molecular orbital, the TDOS plot showing population assessment per orbital provides the allocation of molecular orbitals under a certain spectral region.HOMO and LUMO (Fig. 5) plots have been drawn using the optimized structure.HOMO has been distributed over water and DMA molecules, while LUMO is confined to DMA molecules.

Fig. 5. HOMO, LUMO of DMA+water
The total density of states (TDOS) and partial density of states (PDOS) plots seen in Fig. 6 were plotted using the Gauss-Sum 2.2 Program 40 .Excellent agreement between experimental and theoretical values can be seen in the root mean square deviations for density prediction derived from the density models.The DFT/ B3LYP method's computed data was used to confirm all of the experimental results.

Fig. 2 (
Fig. 2(a).Isentropic compressibility (k s ) of DMA+water (b) Effective Debye's temperature (q D ) of DMA+water (c) Specific heat ratio (γ) of DMA+water Excess Parameters Various forms of interactions between component molecules can account for the excess parameter values for binary mixtures.Non-specific van der Waal forces, dipole-dipole interactions, hydrogen bonding, donor-acceptor interactions between unlike molecules, and smaller molecules occupying the gaps left by larger molecules are a few examples of these interactions.The sign and magnitude of excess parameters are very important for figuring out how molecules in a liquid mixture interact with each other and cause molecules to move around.

Fig. 3 (
Fig. 3(a).Deviation in ultrasonic velocity (Δu) of DMA+water (b) Excess acoustic impedance (Z E ) of DMA+water (c) Excess intermolecular free length (Lf E ) of DMA+water (d) Excess molar volume (V m E ) of DMA+water (e) Molar refraction deviation (ΔR m ) of DMA+water (f) Deviation in viscosity (Δη) of DMA+water (g) Excess Gibbs's free energy of activation for viscous flow (ΔG* E ) of DMA+water