1. Introduction

The volumetric and acoustic properties of binary mixtures would be a great importance in processing the engineering designs and also helpful in getting information about the molecular structure and intermolecular forces in liquid mixtures, which can be very helpful in making the choice of solvent in various applications [1, 2]. The thermodynamic properties of binary liquid mixtures containing protic, aprotic, and associated liquids have been studied previously [3-7].

N,N-dimethylformamide (DMF) is a colorless, non-hydrogen bonded, high-boiling, mobile, highly polar liquid with a faint, characteristic odor. DMF does not decompose at distilling at low pressure and is freely miscible with water, alcohols, ethers, ketones, esters, carbon disulfide, and chlorinated and aromatic hydrocarbons. Molecular interactions of DMF with some solvents reported by various thermodynamic and thermophysical measurements [8]. DMF is aprotic and unassociated [9] in its pure liquid state. It belongs to the so-called super solvents, owing to its miscibility with almost all common polar and no polar solvents [10], probably due to its high polarity with large dipole moment (μ = 3.8D) and moderately high dielectric constant (ε = 36.76) [11]. Several topics and examples of thermodynamic studies are depicted on the basis of the structural behavior of DMF for binary mixtures of non-electrolytes [12].

Alkanols are interesting versatile solvents, used in chemical and technological processes which are inexpensive and easily available at high purity. These polar liquids are self-associated through hydrogen bonding, creating multimers of different degrees [13, 14] whether association is disturbed when they are mixed with another solvent [15]. Alkanols are the -OH functional group containing compounds bonded to a carbon atom. Alkanols of short chain length have a greater proton-donor capacity, so the strength of bonding is expected to decrease with an increase in their chain lengths. Moreover, because of the steric hindrance of alkyl groups, hydrogen bonds are weakened for higher length alkanols [12, 16]. Alkanols are also of interest in their own right and serve as simple examples of biologically and industrially important amphiphilic materials [17]. Additionally, these solvents (amides and alkanols) and their mixtures are used as reaction solvents and find applications in many chemical and industrial processes [18].

Recently, the substantial research work has been reported on the excess properties of N, N-dimethylformamide +2-alkanols [19], formamide+2-alkanols [20], N,N-dimethylformamide+1-alkanols [21-25] acetophenone +2-alkanols [26] ethylmethylketone+2-alkanols [27], N, N-dimethylaniline+1-alkanols,+2-alkanols,+2-methyl-1-propanol,+2-methyl-2-propanol [28]. Though a number of studies have been carried out on the physical properties of DMF, the reported results are not so sufficient with the existence of some discrepancies. The study of this work is a part of an ongoing research effort to measure and characterize the binary mixtures containing 2-alkanols [29, 30].

The densities, ultrasonic velocity and excess properties of the binary blends of these compounds have important impact on the injection process. In order to gain a better understanding of the competitive role of H-bonds associations, the nature and dynamics of the molecular structures in these mixtures, we report the consequences of volumetric and acoustic investigations of 2-butanol and 2-pentanol within the temperature range at T= (298.15, 303.15, 308.15, 313.15 and 318.15) and at atmospheric pressure.

Hence, in this paper, we reported the volumetric properties like densities, ρ, excess molar volume, V^E, partial molar volume, V, and acoustic properties like ultrasonic velocity, u, excess ultrasonic velocity, u^E, excess isentropic compressibility, K_S^E, excess acoustic impedance, Z^E, of the binary systems of N,N-dimethylformamide with two positional isomeric alkanols, such as, 2-butanol and 2-pentanol. These results have been used to discuss the nature of interaction between unlike molecules in terms of hydrogen bonding, dipole-dipole interaction, proton-acceptor interaction and dispersive forces, and also used to analyze the effect of branching in the alkanol and position of the hydroxyl group in the interaction with the N,N-dimethylformamide.

Previously, a large number of researchers have demonstrated that in addition to dipole-dipole and Van der Waals interactions, alcohols are strongly self-associated through H-bonding (O-H•••••O-H) interaction. As the liquid they form clusters or networks with restricted rotations about the H-bonds, and hence show variable degrees of polymeric aggregates. The molecular interactions in the present mixtures are also controlled through the formation of the hydrogen bonds of the type C=O•••••H-O, between unlike molecules [31]. In addition, the effects of difference in shape and steric factors on molecular interactions were observed. The results of the present work were found very much similar with the literatures published previously with a few differences. The findings of this study can be utilized in having a better insight into molecular interactions between the components of the systems. It also helps in understanding the biological systems, synthesis of various compounds, process designing in chemical, petrochemical, pharmaceutical industries, paints, inks as well as in other prospects.

2. Experimental Section

2.1. Materials and Method

DMF (Aldrich, purity HPLC grade 99.9+ %), 2-BuOH (Aldrich, purity 99+%) and 2-PnOH (Aldrich, purity 98%) were used without further treatment which is shown in Fig. 1. The densities and ultrasonic velocity of pure chemicals were compared with literature values, which show satisfactory agreements as shown in Table 1.

Table 1. Experimental (bold letter) and Literature Values of Densities, ρ/(Kg.m-3) and ultrasonic velocity, u/(ms-1) of the pure N,N-dimethylformamide (DMF), 2-Butanol (2-BuOH) and 2-Pentanol (2-PnOH) at different temperatures

Figure 1. Chemical structures of the compounds used in the experiments

All of the measurements on densities, ρ, and ultrasonic velocity, u, were carried out on an Anton Paar DSA 5000 (Austria-Europe) densimeter. The mixtures samples were prepared by mixing the pure components at different proportions up to ±0.0001g, which was then converted into mole fraction. All molar quantities used in this paper were based on the IUPAC relative atomic mass table [32].

3. Results and Discussion

3.1. Densities and Excess Molar Volumes

The experimental results of the density, ρ, measurements of binary mixtures of DMF with 2-BuOH, and DMF with 2-PnOH as a common component, over the whole composition range expressed as mole fractions, x₁, of DMF (0 ≤ x₁ ≤ 1) at different temperatures are listed in Table 2. The excess molar volumes, V^E, were calculated by using the following relation

(1)

Where, ρ₁, and ρ₂ represent the densities and M₁ and M₂ the molar volume of component 1 & 2 respectively.

Table 2. Experimental densities (ρ), excess molar volume (VE), ultrasonic velocity (u), excess ultrasonic velocity (uE), excess isentropic compressibility values (KSE), acoustical impedance (ZE) of the systems DMF (x1) + 2-BuOH (x2) and + 2-PnOH (x2) for different molar ratios at different temperatures

Excess ultrasonic velocities, u^E, from their values in an ideal mixture were calculated from the equation:

(2)

Where, and , u₁ and u₂ are the volume fraction and ultrasonic velocity of component 1 and component 2, respectively.

Excess values of acoustic impedance, (Z^E) were calculated by the following equation:

(3)

Densities, ρ, and ultrasonic velocity, u, were represented by a polynomial equation,

(4)

Where, x₁ is the mole fraction of DMF, a_i is the regression coefficient and n is the degree of polynomial. The values of ρ and u fitted to equation (4) well for n = 4. The coefficients a_i of Equation (4) and relevant values of r² are listed in Table 3.

Table 3. Fitting coefficients ai of polynomial Equation (4) and the value of r2 for the systems DMF (x1) + 2-BuOH (x2) and + 2-PnOH (x2) at different temperatures

The excess values were fitted by the Redlich-Kister type [59] polynomial equation,

(5)

Where, A_i is the i^th fitting coefficient of the Redlich-Kister polynomial equation and all the other terms has their usual significance.

The relevant standard deviations, σ, were calculated by using the relation.

(6)

Where, n and p are the number of experimental points and number of parameters retained respectively.

All the coefficients, A_i, of Equation (5) and their relevant σ values by using Equation (6) are listed in Table 4 and Table 5.

Table 4. Fitting coefficients, Ai, of Redlich-Kister polynomial Equation (5) and the values of standard deviation, σ(VE) for the systems DMF (x1) + 2-BuOH (x2), + 2-PnOH (x2) at different temperatures

Table 5. Fitting coefficients, Ai, of Redlich-Kister polynomial Equation (5) and the values of standard deviation, σ(κSE) for the systems DMF (x1) + 2-BuOH (x2), + 2-PnOH (x2) at different temperatures

The densities of the systems DMF + 2-BuOH and DMF + 2-PnOH in the whole range of composition at 5 different temperatures (between 298.15 and 318.15 K) are displayed as in Table 2. The values of V^E, (calc.) were obtained from Equation (5) by using the best-fit values of Ai coefficients. The variations of V^E with mole fraction x₁, of DMF at various temperatures, along with the smoothed V^E values by using Equation (5), are presented graphically in Fig. 2 and Fig. 3.

Figure 2. Density (ρ) of DMF(x1) + 2-BuOH(x2) system for different molar ratios at different temperatures

Figure 3. Density (ρ) of DMF(x1) + 2-PnOH(x2) system for different molar ratios at different temperatures

The calculated values of V^E are presented in Table 2 and Figure 4 and Figure 5 also.

Figure 4. Excess Molar Volume (VE) of DMF (x1) + 2-BuOH (x2) system for different molar ratios at different temperatures

Figure 5. Excess Molar Volume (VE) of DMF (x1) + 2-PnOH (x2) system for different molar ratios at different temperatures

For both systems excess molar volume, V^E, versus mole fraction, x₁, curves were found as sigmoid at all temperatures. In the system of 2-BuOH + DMF, the V^E values initially increases forming a small maximum in the alcohol-rich region nearly at x₁ = 0.05 - 0.30 and V^E then decreases and made a deep negative lobe with minimum nearly at x₁ = 0.70 at all temperatures. Likewise, V^E versus x₁ curves showed maxima at x₂ = 0.05 - 0.10 and minima nearly at x = 0.55 for the system 2-PnOH + DMF.

The order of positive excess molar volumes, V^E, follows as 2-BuOH + DMF > 2-PnOH + DMF. For both systems, as T rises, the magnitude of the positive V^E increases but that of negative V^E decreases, that means, dV^E/dT is positive. The sign of V^E of solutions depends upon the relative magnitude of expansion and contraction on mixing up of the components. If the factors causing expansion outweigh the factors causing contraction, the values of V^E becomes positive. But when the contractive factors are dominant over the expansive factors, the overall V^E becomes negative.

3.2. Partial Molar Volumes

In addition to other volumetric properties, partial molar volumes ( and ) and excess partial molar volumes ( and ), of DMF, alkanols over the entire composition range were determined using Equation (7) and Equation (8)

(7)

(8)

Here, V1^* and V2^* are the molar volumes of pure components 1 and 2. Following the procedures of Maham et al. [60] the partial derivatives were obtained.

Accordingly, by differentiating Equation (5) for V^E with respect to x₁ and x₂ subsequently, substituting of its value in Equation (7) and Equation (8) lead to the following Equation (9) and Equation (10):

(9)

(10)

Again, partial molar volumes at infinite dilution V^1o and V^2o for component 1 and 2 were obtained from Equation (4) and Equation (5) at the limit of x₂ → 0 and x₁ → 0, respectively. These were further used to calculate excess partial molar volumes at infinite dilution V₁^oE and V₂^oE by using the following relations

(11)

(12)

It is concluded from the Fig. 6 and Fig. 7 that, the partial molar volumes, of 2-PnOH was slightly risen in the DMF-poor region, but rapidly decreased in the DMF-rich region at lower temperatures. Considering, the significances of , the falling of 2-PnOH and also to form the minimum at x₂ ≈ 0.85 reveals that in the overall volume expansion, the alkanol contributes slightly but in contraction 2-PnOH contributes quite significantly making the corresponding V^E values negative in the DMF-rich region.

This is just in accordance to the result that, in the stated region above (x₂ = 0.30) the value of (V₁ – V₁) falls to be negative with minimum near x₂ = 0.80 for the system of 2-PnOH + DMF. Likewise, the partial molar volume of 2-BuOH () though apparently changes very small in the whole range of concentration, ( – V₁) values are all quite large, being positive in the region 0 < x₂ < 0.65 and sharp negative above x₂ > 0.65. This clearly signifies that, contribution of 2-BuOH towards V^E is positive in the former region, while it is negative above x₂ > 0.65. However, the magnitudes of V^E, whether positive or negative are greater for 2-BuOH + DMF than that for 2-PnOH + DMF.

Figure 6. Partial molar volume of 2-BuOH in 2-BuOH(x2) + DMF(x1) system for different molar ratios at different temperatures

Figure 7. Partial molar volume of 2-PnOH in 2-PnOH (x2) + DMF (x1) system for different molar ratios at different temperatures

3.3. Excess Isentropic Compressibility

The isentropic compressibility, K_S, was calculated from density, ρ, and ultrasonic velocity, u, assuming that ultrasonic absorption is negligible, using the Newton-Laplace equation, K_S =1/ρu².

Then, the excess isentropic compressibility, K_S^E, (±10⁻¹ TPa⁻¹) can be determined according to the following equation:

(13)

where, ϕ₁ and ϕ₂, are the volume fraction of component 1 and 2.

The excess isentropic compressibility, K_S^E, for both the binary systems is plotted as a function of the mole fraction in Fig. 8 and Fig. 9. The K_S^E values are negative at all temperatures, and they are more negative for the mixture containing 2-pentanol mixture. The K_S^E minimum value occurs at x₁ ≈ 0.55 for DMF + 2-butanol system and at x₁ ≈ 0.50 for DMF + 2-pentanol system. On the other hand, when temperature increases the K_S^E values decrease, in other words, they are more negative.

Figure 8. Excess isentropic compressibilities (KsE), for N,N-dimethylformamide (X2) + 2-BuOH (X1) system at different molar ratios at different temperatures

Figure 9. Excess isentropic compressibilities, (KsE), for N,N-dimethylformamide (X2) + 2-PnOH (X1) system at different molar ratios at different temperatures

However, values of K_S showed an inverse behavior as compared to ultrasonic velocity u; K_S was decreased with increasing concentration of DMF. It is primarily the compressibility that decreases due to structural changes of molecules in the mixture leading to an increase in ultrasonic velocity. Again, the negative K_S^E and V^E values were found to follow the order: 2-PnOH + DMF > 2-BuOH + DMF, i.e. K_S^E and V^E values became more negative as the chain length of alcohol molecules increases. This may be explained by considering the electron-repelling tendency (+ I effect) of -CH₃ group(s). The presence of three methyl groups at the α- and γ-carbons in 2-PnOH and at the α- and β-positions in 2-BuOH increase the electron density at the O of -OH group of alcohol molecules that overall sequence follows: 2-BuOH < 2-PnOH. So that, the proton-accepting ability of oxygen atom of -OH group also should be in the same sequence. As a result, the extent of negative deviations in K_S^E and V^E clearly indicates that the strength of interaction between DMF and alcohol molecules should follow the order: 2-PnOH + DMF > 2-BuOH + DMF.

4. Conclusions

The density, ultrasonic velocity and some excess volumetric and acoustic properties of binary mixtures of N,N dimethylformamide with 2-butanol and 2-pentanol have been measured over the entire range of composition at T= (298.15, 303.15, 308.15, 313.15 and 318.15) K and at atmospheric pressure. The Redlich-Kister polynomial equation was used to correlate the results. From the experimental data, the positive V^E suggests that, DMF-alkanol interaction (structure making effect) is weaker than that of DMF-DMF and alkanol-alkanol interactions (structure breaking effect) and vice-versa for the negative V^E. Dissociation of H-bonded structures of 2-alkanols results into positive V^E, whereas, dissociation/formation of weak H-bonds between DMF and 2-alkanols leads to negative V^E. In applications, this study would be helpful in understanding the physical properties as well as chemical properties of mixtures between DMF and other solvents.

ACKNOWLEDGEMENTS

The authors are grateful to the Department of Chemistry, University of Chittagong, Chittagong-4331, Bangladesh.