1. Introduction

Research activities in our laboratory consist of systematic measurements of physicochemical properties of non-aqueous binary mixtures in which difuryl methane (DFM) is one of the two components [1-4]. Studies of thermodynamic properties such as excess molar volumes contribute to understanding the nature of molecular interactions in liquid mixtures. It has been reported that DFM comprise of polar molecules and its liquid structure is determined by the dipole-dipole interactions [4].

On the other hand for pure n-alkanes, the intermolecular interactions in part comprise of van der Waals forces. In addition, thermodynamic evidence obtained from Depolarized Raleigh Scattering studies on pure n-alkanes, indicates that there is short range orientational order between chains of molecules in the pure state which increases with the carbon chain length [5, 6].

The objective of the present study is to obtain information on intermolecular interactions in the binary mixtures of DFM with n-pentane or n-hexane or n-heptane or n-octane. We herewith report densities, ρ, excess molar volumes, and excess partial molar volumes, for (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary mixtures at (T = 293.15, 298.15 and 303.15) K and atmospheric pressure. The data of the binary mixtures have been fitted to the Redlich – Kister equation [7] to allow determination of the fitting parameters. The results obtained have been used to interpret intermolecular interactions that exist in these binary mixtures. A survey of the literature has indicated that there has been no reported study on volumetric properties for (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary mixtures at (T = 293.15, 298.15 and 303.15) K.

2. Experimental

2.1. Materials and Purification of Solvents

The following chemicals were used: n-pentane (Fluka, analytical reagent ≥ 99.8%), n-hexane (Merck Co., ≥ 98.0%), n- heptane (Merck Co., ≥ 99.0%), n-octane (Saarchem chemicals, 99.0%), furfuryl alcohol (Merck Co., 98.0%), borontrifluoride-dietherate, BF₃(OEt₂)₂, (Sigma-Aldrich Chemicals Co., 99.0%). Each of (C₅ - C₈) n-alkanes was purified by distillation using 1m fractionation column fitted with glass beads. DFM was prepared as described elsewhere [8], and its purity was confirmed by ¹H-NMR and density measurements. The elemental analysis of DFM was found to be as follows: Calcd for C₉H₈O₂: C, 72.96; H, 5.44; O, 21.60. Found: C, 73.02; H, 5.46; O, 21.52%. The percentage carbon and hydrogen content of DFM were each slightly higher, while that for oxygen was lower than the expected values. This difference was attributed to a low contamination level of n-hexane solvent used in the DFM purification process.

All purified organic liquids were stored in brown glass bottles and fractionally distilled just before use. The purity of each (C₅ - C₈) n-alkanes and DFM was tested by density measurement which was compared to literature values. Measured densities for pure components at various temperatures together with corresponding literature data are listed in Table 1. Ultrapure water required for the calibration of the densimeter was obtained as follows. Distilled water was first refluxed over KMnO₄ and finally doubly distilled under nitrogen flow using a two-stage Heraeus-Destamat quartz still instrument. The conductivity of water was always less than 1.0x10^-6 S-cm^-1.

Table 1. Densities, ρ (kg-m-3) of pure components at (T = 293.15, 298.15 and 303.15) K

2.2. Apparatus and Procedure

Each one of the (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary mixtures was prepared by weighing appropriate amounts of DFM and the corresponding n-alkane co-solvent on an analytical balance (∆m = ±0.0001 g), by syringing each component into a stoppered flask. Pure components were first separately degassed in an ultrasonic bath shortly before sample preparations. All binary mixtures were completely miscible over the entire composition range. Solution density measurements were performed at atmospheric pressure with an Anton Paar DMA 4500 vibrating-tube densimeter at the experimental temperature. The densimeter was first calibrated with pure water and benzene as reference liquids. A sample volume of not more than 1.0 cm³ was needed to fill the densimeter cell and thermal equilibrium was attained quickly. The temperature of the sample was controlled electronically by means of a built-in thermostat (a semiconductor Peltier element and a resistance thermometer temperature control system) and was measured with an accuracy of ±0.01 K. The densimeter was calibrated after each set of four density measurements to offset possible instrument drift. A linear relation between the density of the fluid and the square of the vibrating period τ, (ρ = A + Bτ²), was assumed. Buoyancy corrections were made by taking into account of the air density at each of the three temperatures, the barometric pressure, and the relative humidity. Under such conditions triplet density measurements of each sample were reproducible to within ±0.01 kg-m^-3. The reliability of density measurements was ascertained by comparing the experimental density of pure liquids with the corresponding literature values (Table 1) at the studied temperatures.

3. Results and Discussion

Excess molar volumes were calculated from density measurements for each of [DFM + n-pentane or n-hexane or n-heptane or n-octane) binary systems using equation (1) [13-15];

(1)

where M is the molar mass of the mixture, which is the mole fraction weighted adduct of the molar masses of the two pure components in each binary mixture, i.e. (M = M₁ x₁ + M₂ x₂). is the ideal molar volume, ρ is the density of the mixture, and x_i, M_i and ρ_i are respectively the mole fraction, the molar mass and the density of the pure liquid component i. The Redlich-Kister polynomial equation (2) [7] in which all points are weighted equally was least-square fitted to the data (Table 2) for each binary system:

(2)

where n is the order of the polynomial, x₁ is the mole fractions of the n-alkane co-solvent and x₂ is the mole fraction of DFM. For each binary system at a specific temperature, the degree of the polynomial and the number of regression coefficients A_k, in equation (2) were fixed by testing the statistical significance of including each further term using an F-test at a 99.5% confidence level [16]. The optimized number of regression coefficients for each of the four binary systems are listed in Table 3 along with the corresponding standard deviation calculated from equation (3):

(3)

where N is the number of data points and n represents number of regression coefficients.

Table 2. Experimental densities ρ (kg m-3), excess molar volume,       and excess partial molar volumes       (cm3 mol-1) for (DFM + n-Pentane or n-Hexane or n-Heptane or n-Octane) binary mixtures at (T = 293.15, 298.15 and 303.15) K

Table 3. Least square fitted (Ak) coefficients of Equation (34) and corresponding standard deviation of fit σ(VEm) for the [DFM + (n-Pentane or n-Hexane or n-Heptane or n-Octane)]

Figure 1 presents vs x₂ data for each of the (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary mixtures at 298.15 K. For each binary mixture, the fitted curve was calculated by using the corresponding Redlich-Kister polynomial regression coefficients (Table 3). Figure 1 shows that the vs x₂ isotherms for (DFM + n-pentane or n-hexane or n-heptane) binary mixtures exhibited sigmoidal-shaped behavior, with positive deviations limited to 0.00 ≤ x₂ ≤ 0.039, 0.00 ≤ x₂ ≤ 0.39 and 0.00 ≤ x₂ ≤ 0.64 respectively, and negative deviations over the remaining x₂ - ranges. It has been suggested that the sigmoidal-shaped behavior for the vs x₂ isotherm arises from opposing effects which result from differences in energies of interaction between molecules in solution and packing effects [17, 18]. When DFM is added to the n-alkane, the mixing process may lead to a net destruction of the weak intermolecular interactions in the n-alkane and partial disruption of the dipole-dipole interactions in DFM liquid structure. In the low-x₂ compositions, positive values indicate dominance of the entropy increasing dispersive intermolecular interactions due to possible loosening of the n-alkane molecular parking and the partial disruption of the dipole-dipole liquid structure in DFM which results in the observed volume expansion for each of the three binary systems. The sequence for the positive values is in the order: n-heptane > n-hexane > n-pentane and were: +0.188 cm³ mol^-1 (at x₂ = 0.254), +0.062 cm³ mol^-1 (at x₂ = 0.236) and+0.0474cm³ mol^-1 (at x₂ = 0.022), respectively. The inflection points for n-pentane, n-hexane and n-heptane occur at x₂ = 0.039, x₂ = 0.39 and x₂ = 0.64 respectively. Thus, the DFM mole fraction at which the transition from a positive to negative values occurs increases with the increase in the n-alkane chain length. Since weak van der Waals intermolecular interactions exist between n-alkane and DFM molecules, the negative values observed for (DFM +n-pentane or n-hexane or n-heptane) binary mixtures may be arising from geometrical interstitial accommodation effects which result from the free volume differences between the unlike components in each the three binary mixtures [19]. The magnitude of values is in the order: n-pentane > n-hexane > n-heptane and were -0.812 cm³ mol^-1 (at x₂ = 0.504), -0.075 cm³ mol^-1 (at x₂ = 0.680) and -0.039 cm³ mol^-1 (at x₂ = 0.848) respectively. It is possible that DFM component in each binary mixture, forms a relatively open liquid structure with sufficiently large cavities for the n-alkane molecular interstitial accommodation resulting in closer molecular packing which is reflected in negative values for n-pentane or n-hexane or n-heptane in the x₂ - range: 0.039 ≤ x₂ ≤ 1.00 , 0.39 ≤ x₂ ≤ 1.00 and 0.64 ≤ x₂ ≤ 1.00 respectively. The trend in the values suggest that the geometrical interstitial accommodation of the n-alkane molecules into the DFM liquid structure becomes less efficient as the n-alkane chain length increases. It can also be noticed that the (DFM + n-pentane) binary system exhibits a comparatively large in comparison to the (DFM + n-hexane n-heptane) binary systems. The contributing factors to this behavior is the difference in molecular shape and size between DFM and n-pentane or n-hexane n-heptane. DFM being a polar molecule, would tend to remain self-associated in the binary solution. It is possible that the smaller n-pentane molecules are more efficiently accommodated into voids of DFM liquid structure in comparison with either n-hexane or n-heptane molecules causing more negative values for (DFM + n-pentane) binary system at each temperature investigated. For the (DFM + n-octane) binary system, positive values were observed over the entire x₂ range suggesting the dominance of the dispersive intermolecular interactions over the geometrical effects.

Figure 1. Excess molar volume, vs x2 for the [DFM (2) + n-alkane (1)] binary mixtures: (◊) n- pentane; (○) n-hexane; (∆) n-heptane and (□) n-octane at 298.15 K. The solid lines are from the appropriate Redlich-Kister fitting equations

The temperature dependent measurements of in general are of interest for better understanding of the structural behavior between molecules of components in a binary mixture. Figures 2, 3, 4 and 5 represent the temperature effect on vs x₂ isotherms for each of (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary systems. It was observed that for each of the four binary systems, the algebraic magnitude of the function over the entire composition range decreases with temperature rise. It was also observed that as temperature is raised, the vs x₂ isotherm for each of (DFM + n-pentane or n-hexane or n-heptane) systems maintains the sigmoidal behavior, but exhibited a diminished region for positive values and an enhanced region for negative values. In general the increase in temperature would promote increased molecular motion which would result in a decrease in close molecular packing leading to a positive increase in values. The experimentally observed volume contraction in each case may suggest that the volume expansion caused by temperature increase, results in a more favourable geometrical interstitial accommodation of n-alkane molecules into the expanded cavities in the DFM liquid structures. Similar temperature effect on binary systems containing n-alkanes has been reported elsewhere [12].

Figure 2. Excess molar volume, vs x2 for the [DFM (2) + n-pentane (1)] binary mixtures at (◊) 293.15 K; (○) 298.15 K. The solid lines are from the appropriate Redlich-Kister fitting equations

Figure 3. Excess molar volume, vs x2 for the [DFM (2) + n -hexane (1)] binary mixtures at (◊) 293.15 K; (○) 298.15 K, and (∆) 303.15 K. The solid lines are from the appropriate Redlich-Kister fitting equations

Figure 4. Excess molar volume, vs x2 for the [DFM (2) + n -heptane (1)] binary mixtures at (◊) 293.15 K; (○) 298.15 K, and (∆) 303.15 K. The solid lines are from the appropriate Redlich-Kister fitting equations

Figure 5. Excess molar volume, vs x2 for the [DFM (2) + n-octane (1)] binary mixtures at (◊) 293.15 K; (○) 298.15 K, and (∆) 303.15 K. The solid lines are from the appropriate Redlich-Kister fitting equations

Excess partial molar volumes, are more sensitive to changes in the aggregation schemes arising from the mixing process. The values of component i in a mixture describe the rate of change of the excess molar volume with composition, and represent the individual component response to the overall intermolecular interactions. Excess partial molar volumes for components in each binary system have been calculated in accordance with Equations (4) and (5) [14, 20];

(4)

(5)

The Redlich-Kister polynomial equation (2) of an appropriate degree for each (DFM + n-alkane) binary system was used to obtain values of the derivative over the entire concentration range. Table 2 shows the calculated excess partial molar volumes, for components in each of the four binary systems at (T = 293.15, 298.15 and 303.15) K. Figures 6 (a) and 6 (b) depict the excess partial molar volumes of the components in each of (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary systems at 298.15K. The vs x₂ isotherm for (DFM + n-pentane) binary system in the n-pentane rich region (0.00 < x₂ < 0.017) (Figure 6 b) is characterized by a steep positive variation in values, which may have resulted from the predominance of dispersive intermolecular interactions over the geometrical effects in this region. Thereafter the values are negative in the mole fraction range; (0.017 < x₂ < 1.00), with a sharp minimum centred at x₂ ≈ 0.06 and broadened minimum at x₂ ≈ 0.25 It is also observed that the variation with composition of values for n-pentane (Figure 6 a) in this system revealed a small positive in the mole fraction range: 0.00 < x₂ < 0.02 which may be due to dispersive interactions. Negative values for composition in the mole fraction range: (0.02 < x₂ < 1.00) were observed for this system. Negative values for and may be a result of geometrical effects in which the small n-pentane molecules are interstitially accommodated into the DFM liquid structure. The sharp negative variation of values in the DFM-rich region (low n-pentane concentrations) suggested enhanced structural effects when the n-pentane molecules are completely dispersed into the DFM liquid structure. The isotherms for (DFM + n-hexane or n-heptane or n-octane) systems exhibit sigmoidal behaviour (Figure 6 b), in which the positive magnitude of values increase with the n-alkane chain length in the order: n-octane > n-heptane > n-hexane. The values for n-alkane components in each of (DFM + n-hexane or n-heptane or n-octane) systems exhibited a similar trend to or at a specified temperature. Thus at each temperature investigated, the magnitude of values was in the order: n-hexane < n-heptane < n-octane respectively. The increase in the positive magnitude for is further evidence of the increase in dominance of dispersive intermolecular interactions with increase of n-alkane chain-length. Figures 7 – 10 represent the effect of temperature on data for the two components in each of (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary systems, at 293.15 and 303.15K. The positive magnitude of and data in each binary system decreased with temperature rise. It was observed that the magnitude of the contraction in decreased with the n-alkane chain-length for the same temperature increase. The decrease in magnitude of values with temperature rise corroborated the corresponding vs x₂ isotherms (Figures 2-5) and suggested an increase in effectiveness of the geometrical interstitial accommodation effects with temperature rise.

Figure 6. Excess partial molar volumes, vs x2 for the [DFM (2) + n-alkane (1)] binary mixtures: ( ) n-pentane; () n-hexane; () n-heptane; () n-octane; at 298.15 K

Figure 7. Excess partial molar volume, vs x2 for the [DFM (2) + n-pentane (1)] binary mixtures at temperatures: () 293.15; () 298.15 K

Figure 8. Excess partial molar volume, vs x2 for the [DFM (2) + n-hexane (1)] binary mixtures at temperatures: () 293.15 and () 303.15K

Figure 9. Excess partial molar volume, vs x2 for the [DFM (2) + n-heptane (1)] binary mixtures at temperatures: () 293.15 and () 303.15K

Figure 10. Excess partial molar volume, vs x2 for the [DFM (2) + n-octane (1)] binary mixtures at temperatures: () 293.15 and () 303.15K

Information about the solute-solvent intermolecular interactions can be obtained from the limiting excess partial molar volumes data for components in the mixture [21, 22]. The optimized Redlich - Kister least squares fitting correlation coefficients for each (FM + n-pentane or n-hexane or n-heptane or n-octane) binary systems at the three temperatures investigated have been used to calculate values of the limiting excess partial molar volumes for n-alkanes and using equations (6) and (7) [21-23] respectively,

(6)

(7)

The calculated values are listed in Table 4. For all (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary systems, values were positive at the three temperatures investigated (293.15, 298.15 and 303.15) K, due to an expansion in volume. This suggests that in the low x₂ region, the molar volume of DFM in the mixture is greater than its molar volume in the pure state. The observed positive values for DFM in each binary system at the three temperatures investigated may be evidence for possible presence of DFM-DFM associate species in the infinite dilute solutions (low x₂ region). The values for (C₅-C₈) n-alkane components in the binary mixtures were negative at the three temperatures investigated. Negative values in the high x₂ range (low x₁) suggest possible enhancement of the DFM-n-alkane molecular packing arising from the geometrical interstitial accommodation of n-alkane molecules into the bulk DFM-DFM, dipole-dipole liquid structure. The more negative values observed for (DFM n-pentane) binary system at the two temperatures investigated suggested a efficient structural accommodation of n-pentane molecules into the DFM liquid structure.

Table 4. Limiting excess molar volumes       for the components in [DFM + (C5-C8) n-alkane] binary systems at experimental temperatures

4. Conclusions

In this study, measured densities on pure DFM, n-pentane, n-hexane, n-heptane and n-octane) as well as their binary mixtures, (DFM + n-pentane or n-hexane or n-heptane or n-octane), are reported at (T =293.15, 298.15 and 303.15) K. For each binary mixture, the density data were used to derive the excess molar volumes, and excess partial molar volumes The vs x₂ isotherms for the (DFM + n-pentane or n-hexane or n-heptane) binary mixtures exhibit a sigmoidal behavior while for the (DFM + n-octane) binary system, positive deviation of the function was observed over the entire composition range. For each binary mixture, the magnitude of excess molar volume, for mixture and exhibited a decrease with rise in temperature. The decrease in the positive magnitude of or with increase in temperature was attributed to the enhancement of geometrical interstitial accommodation of n-alkane molecules into the expanded DFM liquid structure. The estimated excess partial molar volumes and limiting excess partial molar volumes complimented the data for each of (DFM + n-pentane or n-hexane or n-heptane or n-octane) binary mixtures at each temperature investigated.

ACKNOWLEDGEMENTS

The financial support by the University of Botswana is gratefully acknowledged.