Sound Velocities and Micellar Behaviour Studies of Dodecyltrimethylammonium Bromide in Aqueous Solutions at 295 . 15 , 302 . 15 and 309 . 15

Speed of sound, u, of dodecyltrimethylammonium bromide (DTAB) aqueous solutions has been determined at 295.15, 302.15 and 309.15 K. The speeds of sound, u, data have been used to estimate isentropic compressibility, Ks, apparent molal isentropic compressibility, φk(s), acoustic impedance, Z, molal sound of speed, Rm, and relative association, RA, of DTAB in aqueous solution. These parameters have been interpreted in terms of solute-solute and solute-solvent interactions and micellar behavior of DTAB.


Introduction
Surfactants are amphiphilic molecules consisting of polar (hydrophilic) and non-polar (hydrophobic) parts.Due to their dual character (hydrophilic and hydrophobic) surfactants are employed in different industrial applications (Herzog et al., 1998).In recent years, there has been growing interest in the interactions between protein and surfactant due to their many applications in biosciences, foods and cosmetics, drug delivery, detergency and biotechnological processes.Using various numbers of tools and techniques, these interactions have been studied and published in the past few years (Goddard et al., 1993, Brash et al., 1995, Sonesson et al., 2008, Mehta et al., 2008, Verdes et al., 2008, Mehta et al., 2009).Cationic surfactants are widely used in industry and have a great bearing on our day-to-day life (Rosen, 1989).The dodecyltrimethylammonium bromide (DTAB) is bio-degradable, non-toxic and is widely available material at low costs.Survey of available literature reveals that no serious attempt has been made to study the micellization phenomenon of dodecyltrimethylammonium bromide (DTAB) surfactant in aqueous solvent.The aim of the present work is to analyze the influence of the presence of dodecyltrimethylammonium bromide (DTAB) aqueous solutions upon several physical properties that allow the characterization of this kind of solutions.
Studies on sound velocities of surfactants solutions are of great use in characterizing the structure and properties of solutions.Also compressibility is a powerful thermodynamic parameter for elucidating the behaviour of a solute in a solvent.(Chalikian et al., 1994).Various types of interactions exist between the solutes in solutions, and these solute-solute and solute-solvent interactions are of current interest in all branches of chemistry.These interactions provide a better understanding of the nature of the solute and solvent, i.e., whether the solute modifies or distorts the structure of the solvent.In the present work, an attempt has been made to provide an interpretation of solutesolvent and solute-solute interactions prevailing in the studied cationic surfactant dodecyltrimethylammonium bromide (DTAB) aqueous solutions as well as findings the micellar behaviour at the temperatures T=(295.15 to 309.15) K.

Experimental
The surfactant used in this study was dodecyltrimethyammonium bromide, CH 3 (CH 2 ) 11 N + (CH 3 ) 2 CH 3 Br (molar purity  98%, Fluka AG, Switzerland ).Supplied distilled water was redistilled and deionized by passing through two ion exchange columns.The deionized water was distilled again in alkaline KMnO4 medium and used for preparation of solution.Conductivity of this deionized water was found to be about 4.00 S.The electric balance with an accuracy of  0.0001g was used for weighting.
Sound velocities of DTAB in aqueous solutions were measured using high precision vibrating tube digital density meter (DSA-5000, Anton Paar, Austria).The accuracies in sound velocity was found to be 0.1m•s -1 respectively.The method is based on the principle of time lapse measurement for certain number of oscillations of a vibrating U-shaped sample tube filled with the sample liquid.The temperature of the sample tube is controlled by two integrated in-built 100  Pt resistance thermometers to a level of highest accuracy and traceable to national standards.The temperature of the sample tube is controlled to  0.001K.The conductivity measurements were carried out on a Laboratory Conductivity Meter (Model 4310 Jenway), which based on the resistance of the solution in a conductivity cell.

Speed of Sound
Speed of sound, u, and densities, ρ, of DTAB in water have been measured at five equidistance temperatures ranging from 295.15 K to 309.15 K and given in Table 1.The variation of sound velocities of DTAB in aqueous solutions against molality is graphically shown in Figure 1.The increase or decrease in speed of sound depends on the structure properties of solute (Pandey et al., 1997).The values of sound velocities are found to increase with increases in temperature and solute concentration.The rising trend in the speed of sound is due to cohesion brought about by hydration.The water molecules are attached to solute by electrostatic effect which brings about the shrinkage in the volume of solvent caused by ionic portion of solute is increased in solvent in comparison to that of water.This implies that the system under consideration behaves like structure maker but up to a specific concentration.Such an increase may be attributed to an increase in the intermolecular interaction between the water and DTAB.

Isentropic Compressibility
Density, ρ, and Speed of sound, u, measurements are combined to calculate isentropic compressibility, K s, using the Laplace equation (Pandey et al., 2000) 2 The isentropic compressibility, K (s), against molality of DTAB are shown in Table 2 and the graphical representations K (s) versus m data are shown in figure 2 The value of isotropic compressibility decreases with increases of concentration.The decrease in isentropic compressibility is due to the increase in electrostriction compression of solvent around the molecules at which results in a large decrease in the compressibility of solvent (Riyazuddin et al., 2009) The apparent molar isentropic compressibility, φ k(s), is calculated from speed of sound measurements, Where K S and K s 0 are the isentropic compressibility of the solution and solvent, and ρ and ρ o is the density of the solution and solvent, respectively and M is the molar mass.The apparent molal isentropic compressibility, φ k(s), against molality of DTAB is shown in Table 2. Table 2 reveals that isentropic compressibility decreases but apparent molal isentropic compressibility increase with the increase in molality of DTAB.The ionic part of DTAB holds the water molecule through hydrophilic hydration, while the hydrophobic moiety of DTAB holds the water molecule through hydrophobic hydration.The hydrophilic hydration shell of ionic group of DTAB is controlled predominantly by electrostatic interactions between water molecules and the ionic group of DTAB.Strong electrostatic force between ionic group of DTAB and water causes electrostriction.The hydrophobic moiety of DTAB forms hydration shell around it through hydrophobic hydration.Thus hydrophilic as well as hydrophobic solute-solvent interactions determine the hydration sphere of DTAB.As the concentration of DTAB increases, the solute-solute interaction relaxes water molecules from both hydrophilic and hydrophobic hydration zone and hydrophobic zone to the bulk render the solution more compact and imparts a decrease in molality of DTAB.
The variation of φ k(s) with m of DTAB exhibits that at lower concentration zone φ k(s) change rapidly after that φ k(s) shows very slow changing trend with the increase in m of DTAB.This may be attributed to the CMC conformation of DTAB.After the micelle formation the solution becomes less compressible.The slow change after CMC reveals that the relaxation of water molecules from hydration spheres to the bulk due to interactions between solute and solvent.

Acoustic Impedance
Acoustic impedance is defined as (Pandey et al., 2000): 3) The acoustic impedances, Z, of aqueous DTAB solutions as a function of concentration are presented in Table 3.The variations of Z with the DTAB in aqueous solutions are shown in Figure 3.The figures demonstrate that acoustic impedance increases with the increase in molality.Acoustic impedance is a measure of resistance to the propagation of sound wave through any medium.The increase in Z with the molality indicates that as concentration increases the sound wave has to face more resistance to flow.As the concentration increases the solute-solute interactions also increase.The positive acoustic impedance is therefore an evidential parameter for solute-solvent and solute-solute interaction.The Z values indicate that there exists strong solute-solute along with solute-solvent interaction in aqueous solutions (Kannappan et al., 2008).Table 3. Acoustic impedance, Z, of aqueous DTAB solutions at T= (295.15, 302.15 and 309.15

Relative Association
The relative association is defined as a measure of the extent of interaction between the component molecules in a real mixture relative to that in an ideal one (Frank et al., 1957): where ρ, ρ o and u, u o are densities and ultrasonic speeds of the mixture and the solvent respectively.The relative associations, R A , values of DTAB are shown in

Molar Sound Velocity
Molal sound velocity indicates the presence of solvent-solvent interactions.It can be represented as (Frank et al., 1957): where V and u are the molar volume and speed of sound, respectively.The molar sound velocity, R m , shows an asymptotic increase with the increase in molality.The values of R m are presented in Table 5 and the variations of R A against molality are shown in Figure 5.The increase in R m values with molality is evident of the structure of solution due to solute-solute and solute-solvent intersections.The asymptotic nature reveals that the reinforcement of structure of solution approaches to attain a maximum value Table 5. Molal sound velocities, R m , of aqueous DTAB solutions at T= (295.15, 302.15 and 309.15  (■) 295.15 K, (•) 302.15 K, (▲) 309.15K

Micellar Behaviour
Conductivity technique has been found to be highly useful for studying the association behaviour of various system (Fujiwara et at., 1997, Moulik et al., 1996).The concentration dependence of specific conductivity of aqueous solutions of DTAB is shown in Figure 6. and the data are presented in Table 6.The specific conductance increases with increasing DTAB concentration and shows a sharp break in its value where micelle starts to form and is determined by extrapolating the specific conductivity data in the premicellar region to intersect with a straight line drawn through the data in the micellar region.The estimated CMC value thus obtained for DTAB in aqueous is 1.5210 -2 mol.kg -1 at 302 K, in good agreement with the values reported earlier in literature (Benrra et al., 2003, Jones et al., 1972, Markarian et al., 2005) as well as satisfying our different experimental CMC values.The CMC (critical micelle concentration) of aqueous solution of Dodecyltrimethylammonium bromide (DTAB) at different temperatures using different methods (sound velocities, isentropic compressibility, acoustic impedance and relative association) were found from sharp braking point, presented in Table 7.

Conclusions
In summary, we have determined speed of sound of DTAB in aqueous solutions at 295.15, 302.15 and 309.15 K.The isentropic compressibility, K s , apparent molal isentropic compressibility, φ k(s) , acoustic impedance, Z, molal sound of speed, R m , and relative association, R A , have been determined and reported.These results confirmed that strong solute-solute, solute-solvent interactions occur in the reported system.From the analysis of the experimental data, it is found that the micellar behaviour of DTAB in aqueous solution is temperature dependent.

Figure 5 .
Figure 5. Plots of molar sound velocity versus molality of aqueous DTAB solutions at studied temperatures:

Table 4 .
The graphical representations R A versus m data are shown R A influenced by two factors (i) the breaking up of solvent structure on addition of solute to it; and (ii) the salvation of solutes that are simultaneously present.Decrease in R A , is due to former and letter results in increase of R A .The relative association, R A for DTAB in aqueous shown slow initial decrease in molality then at a certain molality the R A increases with the increase in molality which indicates that solvation of DTAB predominates over the breaking of the solvent structure.The positive relative association, R A demonstrates that solute-solvent interaction causes association of DTAB, which increases with DTAB concentration.

Table 6 .
Conductance, G, Specific conductance, Қ, and Critical Micelle Concentration (CMC), m cmc , of aqueous DTAB solutions as a function of molality, m, at temperature 302.15K 1 Figure 6.Plot of Specific Conductance versus molality of aqueous DTAB solutions at 302.15 K temperature
The critical micelle concentration of DTAB in aqueous at different temperatures from this study are of the order: m cmc (309.15)> m cmc (302.15)> m cmc (295.15).This may be due to a decrease in the hydrophobic character of molecule DTAB in aqueous with the increase in temperature.