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Dielectric relaxation studies of dilute solutions of amides
Materials Science and Engineering B104 (2003) 1–4
Dielectric relaxation studies of dilute solutions of amides M. Malathi b,∗ , R. Sabesan a , S. Krishnan a a
b
Department of Physics, Annamalai University, Annamalainagar, India Department of Physics, Vellore Institute of Technology, Tamil Nadu, India Received 22 April 2003; accepted 22 April 2003
Abstract The dielectric constants and dielectric losses of formamide, acetamide, N-methyl acetamide, acetanilide and N,N-dimethyl acetamide in dilute solutions of 1,4-dioxan/benzene have been measured at 308 K using 9.37 GHz, dielectric relaxation set up. The relaxation time for the over all rotation τ (1) and that for the group rotation τ (2) of (the molecules were determined using Higasi’s method. The activation energies for the processes of dielectric relaxation and viscous flow were determined by using Eyring’s rate theory. From relaxation time behaviour of amides in non-polar solvent, solute–solvent and solute–solute type of molecular association is proposed. © 2003 Published by Elsevier B.V. Keywords: Amides; Dielectric constant; Dielectric loss; Dielectric relaxation; X-band microwave
1. Introduction The influence; of association through hydrogen bonds on the structure of liquids and their relaxation behaviour has been studied for a long time. The formation of hydrogen bonds leads to associate with restricted number of molecules, called multimers. The dynamic properties of such liquids are often interpreted in terms of the duration of life and the motions of the multimers. The primary amides like formamide and acetamide are excellent proton donors as well as proton acceptors and hence are strongly associated through intermolecular H-bonds. Consequently they exhibit physical properties, which show strong dependence on solvent environment temperature and concentration. The secondary amides like N-methyl acetamide also exhibit similar proportions. On the other hand the tertiary amides like DMP and DMA are poorly self associated. At least three types of multimers can occur in the case of monosubstituted amides namely the ␣-multimers, the -multimers and the ␥-multimers. The relaxation times of such species are far and wide. Dielectric relaxation of dilute solutions of alcohols are well studied by Smyth et al. [1,2]. An excellent review of the recent work on the dielectric relax-
∗
Corresponding author E-mail address: malathi [email protected] (M. Malathi).
0921-5107/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/S0921-5107(03)00141-7
ation of alcohols was made by Smyth [3] and Iiigasi [4]. Recently extensive dielectric relaxation studies of alcohols, and glycols have been carried out [5–7]. The dielectric relaxation behaviour of amides is expected to be similar to that of n-alcohols [8,9]. Wassink and Bovdewijk [10] compared the dielectric relaxation behaviour of solutions of n-alcohols in non-polar solvents with that of amides and observed that the mechanism of the dielectric relaxation in both are similar. As far the pure amides are concerned there are few important studies. Barthel et al. [11] reported the dielectric spectra of several amides in the frequency range of 1–90 GHz at 25 ◦ C. Bass et al. [8] have reported the dielectric properties of alkyl amides in the frequency region of 1–250 MHz. Puranik et al. [12] have reported the permittivity data and relaxation time of formamide, N-methyl formamide and N,N-dimethyl formamide in the frequency range of 10 MHz–10 GHz using time domain reflectometry. The question of whether the dielectric relaxation of these liquids and the dilute solutions of these liquids obey the simple Debye equation was studied by several other workers in the earlier period [13,14]. But definite conclusions were not arrived. Srivastava et al. [15] have investigated N,N-dimethyl formamide in solvent mixture of high viscosity and concluded that the molecule obeys the Debye equation. Similar observations were made by Itoh et al. [9] in the case of N-methyl acetamide.
2
M. Malathi et al. / Materials Science and Engineering B104 (2003) 1–4
The Debye equation interms of a0 , a1 , a11 and a∞ yields two independent equations [16]
2. Experimental E. Merck variety of amides were used without further purification. The dielectric constant ε1 and dielectric loss ε11 have been measured X-band microwave bench. The static dielectric constant ε0 at 2 MHz has been measured by “WTW Dipolemeter DM01” based on the principle of heterodyne beat method. The refractive index nD of all the solutions have been measured by an Abbe’s refractometer. The measurements for ε1 and ε11 are accurate to ±1 and ±5%, respectively. It seemed, therefore, appropriate to carry out dielectric investigations on amides such as formamide, acetamide, N-methyl acetamide, acetanilide, and N,N-dimethyl acetamide using microwave bench.
3. Results The dielectric relaxation time τ have been calculated by Iligasi’s method. Assuming ε1 , ε0 ε∞ and ε11 vary linearly with weight fraction W2 of the solute, we have
τ(1) =
a11 ω (a1 − a∞ )
τ(2) =
a0 − a1 ωa11
τ (1) may be described as the relaxation time for overall rotation of the molecules and τ (2) as a sort of average dielectric relaxation time. √ τ(1) τ(2) − τ0 may be called mean relaxation time. The free energy of activation for dielectric relaxation Fτ and viscous flow F have been calculated using Eyring’s equations [17]. Fη h Fτ NA h τ= exp and η = exp kT RT V RT The values of relaxation time and activation energies are given in Table 1.
ε0 = ε1 + a0 W2 ε1 = ε1 + a1 W2
4. Discussion
ε11 = a11 W2
Our results of τ Higasi show that it increases with increasing amide concentration. This can be explained from the viewpoint of resonance structures that contribute to the
ε∞ = ε1∞ + a∞ W2 Table 1 Values of dielectric constants, relaxation time and activation energies at 308 K Mole fraction
ε0
ε∞
ε1
ε11
Relaxation time (ps) τ (1)
τ (2)
Activation energies τ (0)
Fτ (kJ mol−1 )
Fη (kJ mol−1 )
System: formamide in 1,4-dioxan 0.009 2.392 1.998 0.013 2.473 1.999 0.021 2.658 2.000
2.38 2.43 2.52
0.06 0.14 0.31
6.1 10.6 17.0
4.4 4.9 7.8
5.2 7.2 11.5
9.0 9.8 11.0
14.4 14.4 14.5
System: acetamide; in 1,4-dioxan 0.004 2.294 1.997 0.009 2.378 1.998 0.013 2.464 1.999
2.26 2.30 2.33
0.04 0.09 0.17
13.5 16.6 23.7
14.4 15.0 13.6
13.9 15.8 17.9
11.5 11.8 12.1
14.3 14.4 14.4
System: N-methyl acetamide: in benzene 0.009 2.410 2.217 0.019 2.819 2.216 0.022 3.052 2.215 0.028 3.410 2.213
2.34 2.49 2.53 2.55
0.06 0.20 0.24 0.32
11.2 14.0 16.9 18.3
21.2 27.1 31.9 45.7
15.4 19.5 23.2 28.9
11.8 12.4 12.8 13.4
13.0 13.0 13.0 13.1
System: acetanilide in 1,4-dioxan 0.004 2.298 2.000 0.013 2.474 2.007 0.017 2.577 2.009 0.021 2.678 2.012
2.28 2.26 2.27 2.27
0.06 0.13 0.20 0.24
16.2 54.4 80.4 81.6
5.1 29.3 26.1 29.1
9.1 39.9 45.8 48.7
10.4 14.2 14.5 14.7
14.5 14.6 14.7 14.7
in 1,4-dioxane 2.220 2.38 2.220 2.49 2.219 2.55
0.09 0.19 0.32
11.3 13.7 18.4
5.6 7.9 11.9
7.9 10.4 14.9
10.1 10.8 11.7
12.9 12.9 13.0
System: N,N-dimethyl acetamide 0.009 2.410 0.018 2.578 0.026 2.772
M. Malathi et al. / Materials Science and Engineering B104 (2003) 1–4
stabilisation of the planar structure of the unsubstituted amides. The free rotation of C=O and N–H in formamide and acetamide must be restricted due to this resonance structure as pointed out by Thompson and Laplanche [18]. As the concentration of the unsubstituted amide is further diluted, the H-bonded complexes stabilised by resonance structure break. This process is assisted by the solvent effect of dioxan, which is having a better H-bonding ability with amides than the self-associated H-bonding strength of the amides themselves. Acetamide is a stronger proton donor than formamide and is hence more solvated in dioxan than formamide. This explains the higher relaxation time of acetamide at a given concentration in dioxan than that for formamide. Higasi’s τ (2) values which are related to the internal rotation of the molecule decrease with increase of concentration of acetamide, even though the average relaxation time τ 0 increases with concentration. This is again due to the better solvation of acetamide in dioxan. Acetanilide in dioxan solution τ values increase with increase of concentration. It may be due to the formation of multimers in higher concentration. Hence, relaxation time increases with increase of concentration. In N-methyl acetamide and N,N-dimethyl acetamide, the relaxation time increases with increase of concentration in benzene. It is due to solute–solvent interaction that takes place between π-electron cloud of the benzene ring with the fractional positive charge of the nitrogen. The relaxation time for N-methyl acetamide is very high compared with other amides. It has two types of interactions, i.e. solute–solute and solute–solvent. The lowering of the relaxation time for a non-rigid molecule below the value expected for a rigid molecule of similar size of shape has been attributed to the intramolecular rotations. This behaviour can be interpreted from Higasi’s theory, where two relaxation times are invoked. It has been shown by several workers [19,20] that τ (2) calculated using the Higasi’s equation leads to the Cole–Cole molecular relaxation time τ; whereas τ (1) is an explicit function of the group relaxation time τ (2) τ(1) = Aτ(2) where A is a constant. For a rigid molecule, Chitoku and Higasi [19] observed that τ (1) =τ (2) . For non-rigid molecules, like amides the relation between the relaxation time obtained from Cole–Cole plot and that obtained from Higasi’s τ (1) and τ (2) namely √ τ = τ(1) τ(2) as suggested by Crossley and Walker [21] may not be valid. The values obtained from Cole–Cole plot are always less than that obtained by the method of Higasi. The discrepancy of the relaxation time obtained by the two methods here, is attributed to this non-rigid behaviour of the amides. Eyring [17] treated the dipolar rotation on the basis of a chemical rate process. The molecules are assumed to jump from one equilibrium position to another, depending on the following factors:
3
1. The number of collisions that it makes with the neighbouring molecules, 2. The entropy Sτ which describes the disturbance of the local structure of the medium during orientation; and 3. The heat of activation Hτ , which is equal to the potential barrier separating the successive equilibrium positions. Using this concept a relation between the microscopic relaxation time and the free energy of activation is given as, h Hτ Sτ h Fτ τ= exp exp = exp kT RT R kT R It was suggested by Bauer et al. [22] that the activation energy is nearly equal to the energy necessary to break the H-bonds. The results of Middelhoek and Bottcher [23] for structurally similar systems of alcohols could not explain Bauer’s theory. Hence Dannhauser et al. [24] and Malathi et al. [25] presumed that the rupture of hydrogen bonds is not the rate determining step, but it is the co-operative process of molecular reorientation of the temporarily unbonded molecule with its surroundings that determines the relaxation times. The viscosity of a liquid can be given by a similar rate process, Hη Sη Fη NA h NA h ηs = exp exp = exp V RT R V RT where V is the molar volume of the liquid. The entropy and enthalpy of activation for viscous flow, namely Sη and Hη need not necessarily be the same as those of dipolar processes. It is evident from our data that the molar free energy of activation for viscous flow Fη is greater than Fτ , the free energy of activation for dielectric relaxation. This is in agreement with the fact that the process of viscous flow involved greater interference by neighbours than does dielectric relaxation, as the latter takes place by rotation only, whereas the viscous flow involved both the rotational and translational forms of motion. It is further suggested that for non-associated polar liquids the free energy of activation for rotation and for viscous flow would be F < 0.5F In the present study Fτ is larger than expected. This suggests that the aggregates of amides can no longer be considered as spherical and the rotation necessarily requires a translational motion of the neighbours.
References [1] S.K. Gerg, H. Kilp, C.P. Smyth, J. Chem. Phys. 43 (1965) 396, 1294. [2] F.K. Fong, C.P. Smyth, J. Am. Chem. Soc. 85 (1963) 1565. [3] C.P. Smyth, in: H. Ratajezak, W.J. Orville-Thomas (Eds.), Molecular Interactions, vol. 2, Wiley, New York, 1981, p. 305. [4] K. Higasi, Bull. Chem. Soc. Jpn. 54 (1981) 1320. [5] H.D. Purohit, R.J. Sengwa, J. Mol. Liquids 39 (1988) 43. [6] N. Chelliah, R. Sabesan, Phys. Chem. Liquids 28 (1994) 49.
4
M. Malathi et al. / Materials Science and Engineering B104 (2003) 1–4
[7] C. Magallanes, A. Catenaccio, H. Mechetti, J. Mol. Liquids 40 (1989) 53. [8] S.J. Bass, W.I. Nathan, R.M. Meigham, R.H. Cole, J. Phys. Chem. 68 (1964) 509. [9] K. Itoh, H. Sato, H. Jakahasi, K. Higasi, Bull. Chem. Soc. Jpn. 49 (1976) 329. [10] G. Wassink, P. Bovdewijk, Adv. Mol. Relax. Int. Processes 13 (1978) 299. [11] J. Barthel, K. Bachhuber, R. Buchner, G.B. Gill, M. Klee bauer, Chem. Phys. Lett. 167 (1990) 62. [12] P.G. Puranik, S.M. Puranik, A.C. Kumbharkhane, S.C. Mehrotra, Ind. J. Chem. 32A (1993) 613. [13] R.Y. Lin, W. Dannhauser, J. Phys. Chem. 67 (1963) 1805. [14] G.P. Johari, P.N. Tiwari, J. Phys. Chem. 69 (1965) 3167; 68, (1966) 117. [15] G.P. Srivastava, P.C. Mathur, K.N. Tripathi, Ind. J. Pure Appl. Phys. 6 (1968) 113, 561.
[16] S.M. Khameshara, M.L. Sisodia, Adv. Mol. Relax. Int. Processes 9 (1976) 63. [17] H. Eyring, F. Cernuschi, J. Chem. Phys. 7 (1639) 547; 4 (1636) 283. [18] H.B. Thompson, L. Laplanche, J. Am. Chem. Soc. 67 (1963) 2230. [19] K. Chitoku, K. Higasi, Bull. Chem. Soc. Jpn. 44 (1971) 992. [20] A. Singh, S.K. Saxena, M.C. Saxena, Ind. J. Pure Appl. Phys. 20 (1982) 276. [21] J. Crossley, S.P. Tay, S. Walker, Adv. Mol. Relax. Processes 6 (1964) 691. [22] E. Bauer, M. Magat, Bull. Soc. Chim. France D (1949) 341. [23] J. Middlehoek, C.J.F. Botteher, Mol. Relax. Process Chem. Soc. Spec. Pub., 20 Academic Press, London, 1966, pp. 69. [24] W. Dannhauser, A.F. Flueckinger, Phys. Chem. Liquids 2 (1970) 37. [25] M. Malathi, R. Sabesan, S. Krishnan, Mater. Sci. Eng. B, in press.
Dielectric relaxation studies of dilute solutions of amides M. Malathi b,∗ , R. Sabesan a , S. Krishnan a a
b
Department of Physics, Annamalai University, Annamalainagar, India Department of Physics, Vellore Institute of Technology, Tamil Nadu, India Received 22 April 2003; accepted 22 April 2003
Abstract The dielectric constants and dielectric losses of formamide, acetamide, N-methyl acetamide, acetanilide and N,N-dimethyl acetamide in dilute solutions of 1,4-dioxan/benzene have been measured at 308 K using 9.37 GHz, dielectric relaxation set up. The relaxation time for the over all rotation τ (1) and that for the group rotation τ (2) of (the molecules were determined using Higasi’s method. The activation energies for the processes of dielectric relaxation and viscous flow were determined by using Eyring’s rate theory. From relaxation time behaviour of amides in non-polar solvent, solute–solvent and solute–solute type of molecular association is proposed. © 2003 Published by Elsevier B.V. Keywords: Amides; Dielectric constant; Dielectric loss; Dielectric relaxation; X-band microwave
1. Introduction The influence; of association through hydrogen bonds on the structure of liquids and their relaxation behaviour has been studied for a long time. The formation of hydrogen bonds leads to associate with restricted number of molecules, called multimers. The dynamic properties of such liquids are often interpreted in terms of the duration of life and the motions of the multimers. The primary amides like formamide and acetamide are excellent proton donors as well as proton acceptors and hence are strongly associated through intermolecular H-bonds. Consequently they exhibit physical properties, which show strong dependence on solvent environment temperature and concentration. The secondary amides like N-methyl acetamide also exhibit similar proportions. On the other hand the tertiary amides like DMP and DMA are poorly self associated. At least three types of multimers can occur in the case of monosubstituted amides namely the ␣-multimers, the -multimers and the ␥-multimers. The relaxation times of such species are far and wide. Dielectric relaxation of dilute solutions of alcohols are well studied by Smyth et al. [1,2]. An excellent review of the recent work on the dielectric relax-
∗
Corresponding author E-mail address: malathi [email protected] (M. Malathi).
0921-5107/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/S0921-5107(03)00141-7
ation of alcohols was made by Smyth [3] and Iiigasi [4]. Recently extensive dielectric relaxation studies of alcohols, and glycols have been carried out [5–7]. The dielectric relaxation behaviour of amides is expected to be similar to that of n-alcohols [8,9]. Wassink and Bovdewijk [10] compared the dielectric relaxation behaviour of solutions of n-alcohols in non-polar solvents with that of amides and observed that the mechanism of the dielectric relaxation in both are similar. As far the pure amides are concerned there are few important studies. Barthel et al. [11] reported the dielectric spectra of several amides in the frequency range of 1–90 GHz at 25 ◦ C. Bass et al. [8] have reported the dielectric properties of alkyl amides in the frequency region of 1–250 MHz. Puranik et al. [12] have reported the permittivity data and relaxation time of formamide, N-methyl formamide and N,N-dimethyl formamide in the frequency range of 10 MHz–10 GHz using time domain reflectometry. The question of whether the dielectric relaxation of these liquids and the dilute solutions of these liquids obey the simple Debye equation was studied by several other workers in the earlier period [13,14]. But definite conclusions were not arrived. Srivastava et al. [15] have investigated N,N-dimethyl formamide in solvent mixture of high viscosity and concluded that the molecule obeys the Debye equation. Similar observations were made by Itoh et al. [9] in the case of N-methyl acetamide.
2
M. Malathi et al. / Materials Science and Engineering B104 (2003) 1–4
The Debye equation interms of a0 , a1 , a11 and a∞ yields two independent equations [16]
2. Experimental E. Merck variety of amides were used without further purification. The dielectric constant ε1 and dielectric loss ε11 have been measured X-band microwave bench. The static dielectric constant ε0 at 2 MHz has been measured by “WTW Dipolemeter DM01” based on the principle of heterodyne beat method. The refractive index nD of all the solutions have been measured by an Abbe’s refractometer. The measurements for ε1 and ε11 are accurate to ±1 and ±5%, respectively. It seemed, therefore, appropriate to carry out dielectric investigations on amides such as formamide, acetamide, N-methyl acetamide, acetanilide, and N,N-dimethyl acetamide using microwave bench.
3. Results The dielectric relaxation time τ have been calculated by Iligasi’s method. Assuming ε1 , ε0 ε∞ and ε11 vary linearly with weight fraction W2 of the solute, we have
τ(1) =
a11 ω (a1 − a∞ )
τ(2) =
a0 − a1 ωa11
τ (1) may be described as the relaxation time for overall rotation of the molecules and τ (2) as a sort of average dielectric relaxation time. √ τ(1) τ(2) − τ0 may be called mean relaxation time. The free energy of activation for dielectric relaxation Fτ and viscous flow F have been calculated using Eyring’s equations [17]. Fη h Fτ NA h τ= exp and η = exp kT RT V RT The values of relaxation time and activation energies are given in Table 1.
ε0 = ε1 + a0 W2 ε1 = ε1 + a1 W2
4. Discussion
ε11 = a11 W2
Our results of τ Higasi show that it increases with increasing amide concentration. This can be explained from the viewpoint of resonance structures that contribute to the
ε∞ = ε1∞ + a∞ W2 Table 1 Values of dielectric constants, relaxation time and activation energies at 308 K Mole fraction
ε0
ε∞
ε1
ε11
Relaxation time (ps) τ (1)
τ (2)
Activation energies τ (0)
Fτ (kJ mol−1 )
Fη (kJ mol−1 )
System: formamide in 1,4-dioxan 0.009 2.392 1.998 0.013 2.473 1.999 0.021 2.658 2.000
2.38 2.43 2.52
0.06 0.14 0.31
6.1 10.6 17.0
4.4 4.9 7.8
5.2 7.2 11.5
9.0 9.8 11.0
14.4 14.4 14.5
System: acetamide; in 1,4-dioxan 0.004 2.294 1.997 0.009 2.378 1.998 0.013 2.464 1.999
2.26 2.30 2.33
0.04 0.09 0.17
13.5 16.6 23.7
14.4 15.0 13.6
13.9 15.8 17.9
11.5 11.8 12.1
14.3 14.4 14.4
System: N-methyl acetamide: in benzene 0.009 2.410 2.217 0.019 2.819 2.216 0.022 3.052 2.215 0.028 3.410 2.213
2.34 2.49 2.53 2.55
0.06 0.20 0.24 0.32
11.2 14.0 16.9 18.3
21.2 27.1 31.9 45.7
15.4 19.5 23.2 28.9
11.8 12.4 12.8 13.4
13.0 13.0 13.0 13.1
System: acetanilide in 1,4-dioxan 0.004 2.298 2.000 0.013 2.474 2.007 0.017 2.577 2.009 0.021 2.678 2.012
2.28 2.26 2.27 2.27
0.06 0.13 0.20 0.24
16.2 54.4 80.4 81.6
5.1 29.3 26.1 29.1
9.1 39.9 45.8 48.7
10.4 14.2 14.5 14.7
14.5 14.6 14.7 14.7
in 1,4-dioxane 2.220 2.38 2.220 2.49 2.219 2.55
0.09 0.19 0.32
11.3 13.7 18.4
5.6 7.9 11.9
7.9 10.4 14.9
10.1 10.8 11.7
12.9 12.9 13.0
System: N,N-dimethyl acetamide 0.009 2.410 0.018 2.578 0.026 2.772
M. Malathi et al. / Materials Science and Engineering B104 (2003) 1–4
stabilisation of the planar structure of the unsubstituted amides. The free rotation of C=O and N–H in formamide and acetamide must be restricted due to this resonance structure as pointed out by Thompson and Laplanche [18]. As the concentration of the unsubstituted amide is further diluted, the H-bonded complexes stabilised by resonance structure break. This process is assisted by the solvent effect of dioxan, which is having a better H-bonding ability with amides than the self-associated H-bonding strength of the amides themselves. Acetamide is a stronger proton donor than formamide and is hence more solvated in dioxan than formamide. This explains the higher relaxation time of acetamide at a given concentration in dioxan than that for formamide. Higasi’s τ (2) values which are related to the internal rotation of the molecule decrease with increase of concentration of acetamide, even though the average relaxation time τ 0 increases with concentration. This is again due to the better solvation of acetamide in dioxan. Acetanilide in dioxan solution τ values increase with increase of concentration. It may be due to the formation of multimers in higher concentration. Hence, relaxation time increases with increase of concentration. In N-methyl acetamide and N,N-dimethyl acetamide, the relaxation time increases with increase of concentration in benzene. It is due to solute–solvent interaction that takes place between π-electron cloud of the benzene ring with the fractional positive charge of the nitrogen. The relaxation time for N-methyl acetamide is very high compared with other amides. It has two types of interactions, i.e. solute–solute and solute–solvent. The lowering of the relaxation time for a non-rigid molecule below the value expected for a rigid molecule of similar size of shape has been attributed to the intramolecular rotations. This behaviour can be interpreted from Higasi’s theory, where two relaxation times are invoked. It has been shown by several workers [19,20] that τ (2) calculated using the Higasi’s equation leads to the Cole–Cole molecular relaxation time τ; whereas τ (1) is an explicit function of the group relaxation time τ (2) τ(1) = Aτ(2) where A is a constant. For a rigid molecule, Chitoku and Higasi [19] observed that τ (1) =τ (2) . For non-rigid molecules, like amides the relation between the relaxation time obtained from Cole–Cole plot and that obtained from Higasi’s τ (1) and τ (2) namely √ τ = τ(1) τ(2) as suggested by Crossley and Walker [21] may not be valid. The values obtained from Cole–Cole plot are always less than that obtained by the method of Higasi. The discrepancy of the relaxation time obtained by the two methods here, is attributed to this non-rigid behaviour of the amides. Eyring [17] treated the dipolar rotation on the basis of a chemical rate process. The molecules are assumed to jump from one equilibrium position to another, depending on the following factors:
3
1. The number of collisions that it makes with the neighbouring molecules, 2. The entropy Sτ which describes the disturbance of the local structure of the medium during orientation; and 3. The heat of activation Hτ , which is equal to the potential barrier separating the successive equilibrium positions. Using this concept a relation between the microscopic relaxation time and the free energy of activation is given as, h Hτ Sτ h Fτ τ= exp exp = exp kT RT R kT R It was suggested by Bauer et al. [22] that the activation energy is nearly equal to the energy necessary to break the H-bonds. The results of Middelhoek and Bottcher [23] for structurally similar systems of alcohols could not explain Bauer’s theory. Hence Dannhauser et al. [24] and Malathi et al. [25] presumed that the rupture of hydrogen bonds is not the rate determining step, but it is the co-operative process of molecular reorientation of the temporarily unbonded molecule with its surroundings that determines the relaxation times. The viscosity of a liquid can be given by a similar rate process, Hη Sη Fη NA h NA h ηs = exp exp = exp V RT R V RT where V is the molar volume of the liquid. The entropy and enthalpy of activation for viscous flow, namely Sη and Hη need not necessarily be the same as those of dipolar processes. It is evident from our data that the molar free energy of activation for viscous flow Fη is greater than Fτ , the free energy of activation for dielectric relaxation. This is in agreement with the fact that the process of viscous flow involved greater interference by neighbours than does dielectric relaxation, as the latter takes place by rotation only, whereas the viscous flow involved both the rotational and translational forms of motion. It is further suggested that for non-associated polar liquids the free energy of activation for rotation and for viscous flow would be F < 0.5F In the present study Fτ is larger than expected. This suggests that the aggregates of amides can no longer be considered as spherical and the rotation necessarily requires a translational motion of the neighbours.
References [1] S.K. Gerg, H. Kilp, C.P. Smyth, J. Chem. Phys. 43 (1965) 396, 1294. [2] F.K. Fong, C.P. Smyth, J. Am. Chem. Soc. 85 (1963) 1565. [3] C.P. Smyth, in: H. Ratajezak, W.J. Orville-Thomas (Eds.), Molecular Interactions, vol. 2, Wiley, New York, 1981, p. 305. [4] K. Higasi, Bull. Chem. Soc. Jpn. 54 (1981) 1320. [5] H.D. Purohit, R.J. Sengwa, J. Mol. Liquids 39 (1988) 43. [6] N. Chelliah, R. Sabesan, Phys. Chem. Liquids 28 (1994) 49.
4
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[7] C. Magallanes, A. Catenaccio, H. Mechetti, J. Mol. Liquids 40 (1989) 53. [8] S.J. Bass, W.I. Nathan, R.M. Meigham, R.H. Cole, J. Phys. Chem. 68 (1964) 509. [9] K. Itoh, H. Sato, H. Jakahasi, K. Higasi, Bull. Chem. Soc. Jpn. 49 (1976) 329. [10] G. Wassink, P. Bovdewijk, Adv. Mol. Relax. Int. Processes 13 (1978) 299. [11] J. Barthel, K. Bachhuber, R. Buchner, G.B. Gill, M. Klee bauer, Chem. Phys. Lett. 167 (1990) 62. [12] P.G. Puranik, S.M. Puranik, A.C. Kumbharkhane, S.C. Mehrotra, Ind. J. Chem. 32A (1993) 613. [13] R.Y. Lin, W. Dannhauser, J. Phys. Chem. 67 (1963) 1805. [14] G.P. Johari, P.N. Tiwari, J. Phys. Chem. 69 (1965) 3167; 68, (1966) 117. [15] G.P. Srivastava, P.C. Mathur, K.N. Tripathi, Ind. J. Pure Appl. Phys. 6 (1968) 113, 561.
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