1 Introduction

Carbohydrates (Syal et al., 1998) are the main key ingredients of the entire living organism in energy production and also play a crucial role in the synthesis of glycoproteins. The present study deals with lactose sugar in the mixed solvent of DMF–H₂O at different temperatures, although some work has been reported on sugars like glucose and sucrose in aqueous D-glucose and dextran solution by some researchers (Ali et al., 2006a; Samant and Ray, 2010). Some other properties like conductivity of cross-linked thorium (IV)-alginate complex is also investigated by (Zaafarany et al., 2009). Hence in order to investigate the interaction of lactose in a mixed solvent of N,N-dimethylformamide–H₂O at 298, 308 and 318 K, studies have been carried out and results are reported herein. The use of mixed solvents has attained great attention in recent years in the study of molecular interactions of biomolecules. In continuation to our work, the present study provides valuable information about solute–solute, solute–cosolvent interactions. These interactions are useful to understand the various biochemical processes of human metabolism. The influence of temperature on the interactions has also been determined.

2 Experimental

N,N-dimethylformamide and lactose were obtained from Himedia Chemicals Ltd of AR grade with purity better than 99 percent. The Doubly distilled water was used to prepare solution. The mixed solvent of DMF–H₂O has been prepared using DMF and water in 1:1 (v/v) solution. Eleven sets of solution from 0.1050 to 1.045 m concentration were prepared and used on the same day. The viscosity of the solution was determined using pre calibrated Ostwald’s viscometer (Mehra et al., 2010) having uncertainty within the order of ±0.067%. The viscosity measurements are based on the measurement of flow time of the solutions taken for the investigation with an uncertainty up to ±0.01 s. The density measurement has been done using a bicapillary pycnometer (Mehra and Gaur, 2008) with an uncertainty of ±0.06%. Sound speeds of solutions were measured using an ultrasonic interferometer (Misra et al., 1997) (Model F-81) with single frequency of 2 MHz having uncertainty within the order of ±0.056%. Refractive index has been measured using Abbe’s refractometer (Ali et al., 2006b) with an uncertainty of ±0.062%. All the instruments and apparatus were calibrated with standard liquids like benzene, cyclohexane, N,N-dimethylformamide, n-hexane and water before taking measurements. The temperature is maintained constant within ±0.1 °C by the thermostatically controlled refrigerated water bath with circulating water around the cell. The weighing was done using the Denver balance with an uncertainty of ±0.1 mg.

3 Results and discussion

The values of density (ρ), viscosity (η), sound speed (u) and refractive index (n_D) increase with an increase in the concentration of lactose in DMF–H₂O. The increase in density and sound speed may be due to the cohesive forces and thus molecular association is responsible for the observed values. The viscosity values increase with rise in concentration due to the increase of solute–solvent interactions while decrease with rise in temperature may be due to the increase in the movement of molecules and ions present in the solutions, which decrease solute–solvent interactions (Parmar et al., 2002). The experimental values of density (ρ), viscosity (η), sound speed (u), refractive index (n_D) derived parameters adiabatic compressibility (β), apparent molal volume (ϕ_v) of lactose in DMF–H₂O are given in Table 1.

The apparent molar volume of lactose in a mixed solvent of DMF–H₂O has been determined using the following equation.

The positive values of ϕ_v indicate stronger solute–solvent interactions. The ϕ_v values decrease with an increase in the concentration of solute due to the electrostriction effect. The positive values of ${\phi }_v^0$ indicate the presence of strong solute–solvent interactions. The negative values of S_v suggest weak solute–solute interactions. Solute–solvent interaction shows an increase while solute–solute interactions decrease with a rise in the temperature.

Adiabatic compressibility (β) is given by the relation;

Apparent Molal Compressibility (ϕ_k) has been calculated using the relation as:

The negative values of limiting apparent molal compressibility ${\phi }_k^0$ show weak solute–solvent interactions and increase with a rise in the temperature from 298 to 318 K. When solute is added in the solvent structural changes occur in the solvent and exhibit solute–solvent interaction in solution. The magnitude of compressibility depends upon electrostriction. The negative values indicate hydrophobic interactions and loss of structural compressibility due to increased population of H-bonded water molecules. The negative values of S_k indicate weak solute–solute interactions which decrease with a rise in the temperature.

Viscosity data were analysed using the Jones–Dole equation (Jones and Dole, 1929):

Values of limiting apparent molal volume ( ${\phi }_v^0$ ), experimental slope (S_v), limiting apparent molal compressibility ( ${\phi }_k^0$ ), experimental slope (S_K), Jones–Dole coefficient (B) and Falkenhagen coefficient (A) are given in Table 2.

The Falkenhagen coefficient (A) values are the measure of solute–solute interactions. A negative value of coefficient-A indicates weak solute–solute interactions in the system. Jones–Dole coefficient -B is highly sensitive to the nature of solute–solvent interactions. Positive values of Jones–Dole coefficient at all the temperature suggest structure making tendency of solute.

The values of derived acoustic parameters such as apparent molal compressibility (ϕ_K), acoustic impedance (Z), intermolecular free length (L_f), free volume (V_f), internal pressure (π_i) and hydration number (n_H) for lactose + (DMF–H₂O) system at 298, 308 and 318 K are given in Table 2.

Specific Acoustic Impedance (Z) is the product of density (ρ) and sound speed (u) and can be estimated as:

Intermolecular free length (L_f) is obtained using the equation:

The intermolecular free length decreases with an increase in the solute concentration indicating that there is a significant interaction between solute and solvent molecules, suggesting a structure promoting behaviour on the addition of solute and these results are also supported by the viscosity data. As the temperature increases it leads to the less ordered structure and more spacing between the molecules due to an increase in the thermal energy of the system, which causes an increase in volume expansion and hence, increase in intermolecular free length (Reddy and Reddy, 2000).

Free volume calculated from sound speed (u) and viscosity (η) of solutions using Suryanarayana relation;

Internal pressure has been calculated by using the physical properties like density, viscosity and sound speed from the free volume concept on the basis of statistical thermodynamics as given by (Suryanarayana and Kuppusami, 1976);

Internal pressure decreases with a rise in the temperature because of the thermal agitation of ions from each other due to increasing thermal energy, which reduces the possibility for interactions and reduces the cohesive forces and ultimately leads to a decrease in the internal pressure.

Intermolecular forces define the property of solution and presence of attractive and repulsive forces. The attractive forces depend on the distance between the centres of attraction of molecules, while the repulsive forces depend on the distances between the surfaces of molecules. The internal pressure is a net force of electrostatic, hydrophobic, hydrophilic, dipole, dispersion and repulsion between the molecules (Rajendran, 1994). Internal pressure is the important parameter that gives significant information about structural changes in solution. Internal pressure decreases with a rise in the temperature because of the thermal agitation of ions from each other due to increasing thermal energy, which reduces the possibility for interactions and reduces the cohesive forces and ultimately leads to a decrease in the internal pressure.

Hydration number (n_H) was calculated by the following relation:

The hydration number is the number of water molecules rigidly bound to the ions. The positive values of hydration number (Palani, 2008; Zavitas, 2005) reveal that there is a significant interaction between solute and solvent molecules due to which structural arrangement in the surrounding is affected. In the present case, hydration number increases with concentration. Lactose molecules interact with water and DMF molecules from -OH groups. It suggests that hydration sphere of solute–solvent interaction is more intensive than solvent–solvent interactions.

The derived parameters Rao’s constant (R_m), relative association (R_A), Wada’s constant (W), acoustic relaxation time (τ), absorption coefficient (α/f²), molar refractivity (R_D) and Gibbs free energy (ΔG) are given in Table 3.

Rao’s constant can be calculated using the following relation:

Relative association (R_A) can be determined as:

Acoustic relaxation time is obtained using the relation:

The molar refractivity (R_D) (Ali et al., 2006c) of the mixture can be calculated from the values of refractive indices (n_D) by using the Lorentz–Lorentz equation.

4 Conclusion

• Structure making tendency of lactose is observed in the mixed DMF–H₂O system.

• Stronger solute–solvent interactions are present may be due to the formation of hydrogen bonds among the unlike molecules viz. amide group of N,N-dimethylformamide, water molecules, and –OH group of lactose sugars.

• As the temperature increases more and more solute molecules come closer to the solvent molecules due to the increased kinetic energy and hence solute–solvent interactions increase.