Estimation of the refractive indices of some binary mixtures

Refractive index is a useful fluid characterization parameter with widespread industrial applications. The values for many pure liquids are known or readily available in literature. However, when experimental data are not available, the refractive indices of binary and multi-component liquids are often estimated from the pure components using mixing rules which are sometimes not accurate. This study was designed to measure the refractive indices and evaluate the accuracy of some commonly used mixing rules when applied to benzene-toluene, heptane-hexane, hexane-acetone, heptane-acetic acid and acetic acid-acetone binary mixtures at varying volume fractions and temperatures between 20 and 60°C. A simpler relation based on modified Kay or Arago-Biot mixing rule was demonstrated to have wider range of applicability because of the explicit temperature-dependence term.


INTRODUCTION
Refractive index is a fundamental physical property which measures the speed of light in a material and characterizes its optical properties (Singh, 2002).It has been used for many years for accurate identification and characterization of pure fluids and mixtures (Ebatco, 2013).Sharma et al. (2007) and Vural et al. (2011) noted that refractive index, density and viscosity are essential for the characterisation and understanding of the thermodynamic properties of fluids.The molecular interaction in a fluid mixture can also be assessed from the refractive index and density of its pure components (Leron et al., 2012;Rilo et al., 2012).
Refractive index is useful in the indirect measurement of density and salinity and in the detection of structural properties of liquid-liquid mixtures.Its application has also led to the development of alternatives in fuel substitutes, additives, and treatment of oils with chemicals (Rushton, 1955).Wankhede (2011) used mixing rule to determine the composition of an unknown mixture and the presence of molecular interactions in binary mixtures.Several researchers have noted that deviation between theoretical and experimental values of the refractive indices of mixtures can be reduced by considering the concept of excess volume (Mehra, 2003;Ali andTariq 2006, Sharma et al., 2007;Meenachi and Krishnamurthi, 2013).
The refractive indices of pure, binary and multicomponent fluids can readily be measured directly using refractometers.However, there are times when the experimental values are not available and it is desirable to estimate the refractive index of binary or multicomponent liquids from the pure components by using mixing rules.The most commonly used mixing rules are the Lorentz-Lorenz equation, Weiner relation, Heller's and Gladstone-Dale equations.These mixing rules apply the concept of excess molar properties, a measure of thermodynamic interaction changes with physical forces in polar molecules (Vural et al., 2011).They therefore require rigorous procedures.
The aim of this study was to develop an accurate mixing rule that is simpler to apply than the commonly used relations.The refractive indices of pure components and mixtures were measured at different temperatures and volume fractions and the results were used to develop a simple equation based on the modification of the Kay or Arago-Biot mixing rule.The resultant temperature-dependent relation proved accurate and easy to use.

Theoretical basis
In the process of mixing two or more components effects such as the structural re-orientation occurs due to the differences in shape and size of component molecules and the interaction between molecules (Ali et al., 2008).If we assume that volumes of the pure components can be added when analyzing fluid mixtures (Andrew et al., 1986) and using the mean polarizability which approximates the average possible orientations of a molecule, the Lorentz-Lorenz (1979) relation can be obtained which for a binary mixture is expressed as: (1) The Weiner relation is given as: (2) While Heller relation is: (3) Where, m = n 2 /n 1 And, the Gladstone-Dale equation can be expressed as: However, for most fluid mixtures, since there is volume change during mixing (Brocos et al, 2003).Therefore, adapting the method of Leron et al (2012), we propose a modified Arago-Biot equation as: Where, ( 7) i= 1, 2

MATERIALS AND METHODS
Samples of pure benzene, toluene, heptane, hexane, acetone and acetic acid manufactured by Messer Griesheim were obtained and their purity ascertained at 99.9% using standard procedures.Different binary mixtures were prepared from the pure components by mixing at varying volumes of 1 to 0 ml, 7.5 to 2.5 ml, 5 to 5 ml, 2.5 to 7.5 ml and 0 to 1 ml.The Abbe refractometer double prism system (Model 300778) with monochromatic light source of 589 nm for illumination and with accuracy of 0.0001 was used in measuring the refractive indices.The refractometer was calibrated at 20°C using distilled water as well as samples of the five pure fluids used.Using a heating water bath connected to the refractometer, the refractive indices of the pure components and binary mixtures were measured at 20, 40 and 60°C using procedures similar to Bhatia et al. (2002).Results were replicated to ensure consistency.Deviations of the measured and estimated results were determined using the following equations: Where " " is the experimental value, " " is the calculated value for point i and N is the number of points.

RESULTS AND DISCUSSION
The temperature-dependent modified Arago-Biot mixing rule, Equation ( 6), accounts for the non-ideal molecular interactions which occurs during mixing.This should represent an improvement over Gladstone-Dale, Arago-Biot and other similar relations.Table 1 gives some of the physical properties of the pure components used for the    experiments as obtained in literature and confirmed during calibration.Tables 2 to 6 and Figures 1 to 6 shows the results obtained from the experiments.A close observation of these results shows that refractive indices of the pure liquids and mixtures decreased as temperature increased.This agrees with results of previous researchers such as Bhatia et al. (2002), Mehra (2003) and Navendra et al (2011) and can be attributed to the changes in fluid density with temperature.At higher temperatures, liquid dense decreases, causing light to travel faster in the medium resulting in lower refractive index.The variation of refractive indices with temperature can also be attributed to the structural changes which occur during   Furthermore, all the mixing rules considered showed remarkable changes in refractive indices of the mixtures with increasing temperature between 20 and 40°C except the Hexane-Acetone and Heptane-Acetic Acid mixture which were almost constant.This could be as a result of vaporization of acetone and hexane at temperatures close to 56 and 69°C, their boiling points respectively.However, mixtures which contain alkanes were not expected to exhibit structural changes at elevated temperatures between 40 and 60°C, in line with the observation by Mehra (2003) that no effect of increase in chain length was observed in alkanes and alkanols.4.
Furthermore, the variation of refractive index with temperature was clearly established in this study in agreement with previous researchers (Bhatia et al., 2002).Therefore, we propose the estimation of the refractive indices of the mixtures at elevated temperatures using Equation ( 11

Conclusion
Based on this work, the following conclusion can be made: (1) The refractive indices of selected binary mixtures have been determined and presented.
(2) Refractive indices of the pure components and binary mixtures investigated in this study decrease with increasing temperature.Similar trends are expected in other similar compounds.
(3) The modified Arago-Biot mixing rule which includes temperature effects is simple to use and has wider range of application than some of the existing relations in literature.Therefore, an accurate mixing rule should not only be volume fraction-dependent, but explicit in temperature.
that there is volume additivity during mixing, we can use the simple Arago-Biot relation:

Figure 6 .
Figure 6.Refractive index versus volume fraction of acetic acid-acetone at 20°C.
Where, K = Temperature correction factor = 0.0005/°C, d = Constant as given inTable 5,= Refractive index at any temperature T °C other than base temperature.

Table 1 .
Physical properties of selected pure compounds.

Table 5 .
Predictive Refractive Index correlation at varying mole fractions.