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Microenvironment dependence of vibrational relaxation in p-methyl acetophenone
Spectrochimica Acta Part A 54 (1998) 793 – 798
Microenvironment dependence of vibrational relaxation in p-methyl acetophenone Arpita Das, Kamal Kumar * Department of Physics, North Eastern Hill Uni6ersity, Shillong-793022, India Received 27 May 1997; accepted 18 November 1997
Abstract The Raman band shape analysis and vibrational relaxation studies of the CO stretching mode of vibration of p-methyl acetophenone reveals that macroscopic considerations are not sufficient to analyse the Raman anisotropy shift and the linewidth of the isotropic component observed in complex molecular systems. The band shape analysis was therefore attempted at a microscopic level by taking into account the concept of microenvironment. The solvent dependent study of the anisotropy shift shows that the repulsive potential may be playing a major role in the vibrational relaxation process. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Vibrational relaxation; Microenvironment; Non-coincidence effect; p-Methyl acetophenone; Solvent dependent studies
1. Introduction The vibrational relaxation in molecular liquids has been the subject of many theoretical and experimental studies. Although considerable progress has been made towards a deeper understanding regarding the vibrational relaxation process in recent years, a detailed study is required to account for the discrete nature of the solute-solvent system at the microscopic level. The Raman band analysis especially the dependence of linewidth on environment may provide useful information regarding the intermolecular forces. The vibrational relaxation process which is re* Corresponding author. Tel.: + 91 364 250035; fax: + 91 364 250076.
sponsible for the line broadening of the isotropic Raman component may be due to the contribution from vibrational dephasing, population relaxation and resonant energy transfer via transition-dipole transition-dipole (TD–TD) interaction [1–4]. Moreover, the microscopic environment affects the behaviour of a reference molecule. In a liquid mixture the lineshape of the reference mode is influenced by the concentration fluctuation of the environment. In some liquids, the anisotropy shift where the peak frequencies of isotropic and anisotropic components differ from each other, has been found sometimes, to be [4] as large as 10 cm − 1, or even more. This phenomenon, termed as non-coincidence effect may be interpreted as being due to the coupling between vibrations of neighbouring molecules with
1386-1425/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S1386-1425(97)00276-X
794
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
strongly polar modes by intermolecular dipole interactions in the liquid phase [5 – 8]. The theoretical explanation for the vibrational relaxation may be given by correlating the vibra1 tional relaxation rate (t − V ) with some molecular parameter [9–11] which takes into account the effect of reaction field (solvent electric field) on the solute, and using the basic concepts of dielectric relaxation processes. To have a better picture of the solute-solvent system one may consider the so called ‘solvent cage effect’ where the molecules of a liquid are confined in a potential well. The molecule is considered to be vibrating against the walls of the cage, that is against its immediate neighbours, with an occasional escape to its adjacent position. However, the explanation for the vibrational relaxation process for complex molecular systems, sometimes cannot be understood on the basis of a macroscopic perception of the solutesolvent system. A marked difference is likely between the interaction situations in the pure solute and when it is dissolved in solvents, especially at high dilution. In order to understand more clearly the complicated nature of the processes involved, a detailed study is, therefore, required at the microscopic level, which may be performed by considering the effect of microenvironment. In an attempt to provide further support to the previous findings of Purkayastha and Kumar [11,12], and to have detailed information about the processes involved in complex molecular systems, p-Methyl acetophenone (PMA) has been chosen using its CO stretching vibration as the reference mode. The present work deals with the solvent dependent studies on the Raman band corresponding to CO stretching vibration of PMA. The CO stretching vibration of PMA is well isolated from other modes of vibration and the dipole moment of PMA is probably concentrated on the CO bond of the molecule.
2. Experimental Raman spectral measurements were made for the CO stretching band of PMA in CHCl3, CCl4, CH2Cl2, CH3CN and C6H6 solvents using a SPEX RAMALOG 1403 double monochromator spectrometer equipped with a Datamate. The sample of
PMA and the solvents were obtained commercially and were used without further purification. The laser Raman spectra were recorded using the 4880 ˚ line from the Spectra-Physics model 165 Ar + A ˚ line was laser as the excitation source. The 4880 A used with a power of 350 mW and the slitwidth was kept at 2 cm − 1. The isotropic component was obtained by using the formula Iiso(n¯ )= IVV(n¯ )− 4/3IVH(n¯ )
and
Ianiso(n¯ )= IVH(n¯ ) where IVV(n¯ ), and IVH(n¯ ) represent the polarised and depolarised Raman spectra respectively. n¯ is the frequency in wavenumbers. The accuracy of measurements is believed to be 9 0.5 cm − 1. 3. Results and discussion The laser Raman spectrum of pure PMA shows the IVV and IVH components with the peak of IVH component shifted to a higher frequency position. The non-coincidence of the isotropic and anisotropic frequency maxima may be explained by taking into consideration the resonant coupling due to TD–TD interactions [4,13] of the vibrations of two adjacent molecules. The study of the non-coincidence effect needs considerations of the influence of the intermolecular forces, viz. dispersion forces, induction forces, and multipole–multipole interactions on the vibrational transitions.The dispersion type interactions usually explain the general additive attractions between arbitrary atoms and molecules. The dispersion energy has high values even in the case of solvent molecules having a dipole moment, which is mainly because of the o 2 dependence of the dipole–dipole and dipole-induced dipole type of interactions for the solvents of high dielectric constant. The contributions to the observation due to induction forces are assumed to be present in both types of systems as a result of the dipolarity of the solute molecule under investigation, even though some of the solvent molecules have no dipole moment. The polarity of the solvent is also an important factor which contributes to the potential field perturbing the vibration, when the solute has a solvent molecule in the neighbourhood of the vibration. This is particularly true at high dilution. The explanation that the anisotropy
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
795
Fig. 1. The variation of the quantity F as a function of the solute concentration (F): (a) CCl4; (b) CH2Cl2; (c) CHCl3; (d) C6H6; (e) CH3CN.
shift is an effect due to resonant coupling is supported by the experimental data related to the effect of solvent on the Raman band of PMA molecule. This effect tends to vanish at high concentration of the solvents. The separation between the isotropic and anisotropic maxima of the Raman bands in different solvents varies with the concentration of the active substance. It was shown by McHale that the anisotropy shift dn can be expressed by the relation [14]
dn=
2m 2(dm/dQ)20N0
FS
(1)
2552 c 2n0kTd 3Vm where N0 is Avogadro’s number, F is the volume fraction of the solute, n0 is the vibrational frequency of the isolated molecule, d is the minimum intermolecular distance, Vm is the molar volume of the solute, kT is the thermal energy, m is the dipole moment, Q is the mass weighted normal
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
796 Table 1 Molecular parameters Solvents
Density (r)
Dielectric constant (o)
R.I. (n)
Dynamic viscosity (h) (cp)
CHCl3 CCl4 CH2Cl2 CH3CN C6H6
1.479 1.548 1.319 0.776 0.873
4.77 2.23 9.14 37.5 2.28
1.45 1.46 1.42 1.34 1.50
0.542 0.843 0.393 0.345 0.564
coordinate and (dm/dQ)0 is the transition moment. S is the screening factor, S comprises two factors, Sp and St related respectively to the interactions of permanent and transition dipoles. Following the dielectric model given by ONSAGER-FROHLICH (hereafter referred to as the O-F model), which treats the dielectric as continuum, the above equation takes the form dn(2o +n 2)2o − 1 =
2m 2(dm/dQ)20(n 2 +2)2N0
F
2552 c 2n0kTd 3Vm (2) The quantity [F =dn(2o +n 2)2o − 1] was plotted as a function of the volume fraction (F) in different solvents. The dielectric constant of PMA was experimentally measured and found to be 16.25. The dielectric constant of the solution was calculated by using the relation osolution =F · osolute +(1 −F)osolvent where F is the volume fraction of the solute. Fig. 1 clearly shows that the data points [dn(2o + n 2)2o − 1] do not lie on the correlation line for the entire range of dilution. A closer look reveals the fact that the data points fit rather well in two straight lines with a sharp discontinuity at around F = 0.5. The splitting given by Eq. (2) was predicted by the TD coupling model and this expression was expected to be valid only for dilute solution [15,16]. Below 50% dilution, the interactions were expected to occur more among solute molecules than solute – solvent interactions [12]. The present study indicates that to explain the non-coincidence effect in case of complex molecular systems like PMA, where the effects of dispersion, induction, multipolar interaction, etc. are likely to vary from solvent to solvent, the screening effect may not be as effective as
envisaged by the O-F model. However, the plot of the quantity ln F vs. F shows a linear graph indicating a better fit. This kind of relationship whereby a ln F vs. F graph has been found to be linear may be indicative of the repulsive potential function of the type e − aR playing an important role, (the R being the appropriate radius related to the distance of closest approach which will depend upon the fraction of solute present)(Tables 1 and 2). Detailed work is, however, required in this connection to establish the empirical relationship so obtained (Fig. 2). Experimentally measured lineshapes of the isotropic and anisotropic components of Raman bands help us to know more about the spherically symmetric part of the intermolecular forces and anisotropic forces respectively. The vibrational relaxation may be explained on the basis of life-time broadening, environmental broadening and resonance transfer. The inhomogeneous and homogeneous contributions to the linewidth, which is of great importance in understanding the molecular dynamics, may be separated by time-dependent techniques. The lineshape is Lorentzian for homogeneous broadening (Dv/t 1), Dv and 1/t denote the frequency shift and the rate of change between various inhomogeneous components. Table 2 Relaxation rate (t−1 V ) and the function fm for various molecular systems Molecular system
Giso (cm−1)
fm
−1 t−1 V (ps)
PMA-CHCl3 PMA-CCl4 PMA-CH2Cl2 PMA-CH3CN PMA-C6H6
16 12 10 9 15
3.90 2.20 1.44 1.00 3.30
1.51 1.13 0.94 0.84 1.40
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
797
Fig. 2. The variation of the quantity ln F as a function of the solute concentration (F): (a) CCl4; (b) CH2Cl2; (c) CHCl3; (d) C6H6; (e) CH3CN.
In the present work, the linewidth of the isotropic components Giso (FWHM) of the Raman band corresponding to the CO stretching mode of the PMA molecule were measured in various polar as well as nonpolar solvents at 80% concentrations. At this concentration, the Raman band was found to be Lorentzian and, therefore, vibrational relax1 ation rates (t − V ) were calculated from the isotropic linewidth (Giso) using the equation
1 t− V = 5 cGiso
The experimental results have been presented as 1 the plot of the vibrational relaxation rate (t − v ) as a function of the P–K parameter [9,10] fm (Fig. 3). The parameter fm was calculated for various solvents using the relation fm = f(r, hm, n)= rhm[(n 2 − 1)/(2n 2 + 1)] − 1
798
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
Here, hm is given by, hm = hg and g = [0.16 +0.4(a/b)] where g is the microfriction factor which takes care of the noncontinuous nature of the viscoelastic medium. a and b are the radii of the solute and the solvent molecules, respectively. The CHCl3 molecule has the tendency to form hydrogen bond due to the presence of acidic hydrogen. Therefore, hydrogen bonding is likely to be present between PMA and CHCl3 molecules. In such hydrogen bonded systems, the layers of CHCl3 molecules may be formed over PMA molecules. Due to the C–H bond of CHCl3 being oriented towards CO bond of PMA, the solute radius in this case is taken as the sum of van der Waals radius ˚ ) and the CO bond distance [18] of O atom (1.4 A ˚ ). The solvent radius in this case is taken as (1.2 A ˚ ) if H the van der Waals radius of H atom (1.2 A atom is considered to be fluctuating between C and O atoms. In CH3CN-PMA system, CH3CN may be regarded as a cylindrical like structure so far as C – CN portion is concerned. The molecular radius is chosen as the van der Waals radius of nitrogen ˚ ). In the case of CH2Cl2-PMA system atom (1.5 A the C–Cl van der Waals radius is responsible for the distance of closest approach, so the molecular radius is chosen as the Cl atom van der Waals ˚ ). For C6H6-PMA system the solvent radius (1.8 A radius is taken as the H atom van der Waals radius ˚ ). In the case of CCl4-PMA molecular system, (1.0 A ˚ ) and van der Waals the C–Cl bond distance (1.7 A ˚ radius for Cl atom (1.8 A) are added up to find the molecular radius due to the spherical nature of the molecule. The solute radius in these cases is taken as the van der Waals radius [17] of benzene (1.77
1 Fig. 3. The variation of the vibrational relaxation rate (t − V ) as function of fm.
˚ ) as the interactions are possible at benzene A moiety. The plot of vibrational relaxation rate 1 (t − V ) as a function of the parameter fm is clearly a linear plot. It is, therefore, probable that the discreteness of the medium due to the solvents may be playing a major role. Therefore, the concept of microenvironment has to be taken into account for better fitting of data points.
4. Conclusion The solvent dependent study of anisotropy Raman shift indicates that the repulsive potential may be playing a major role in the relaxation process when concentrated solution is diluted with different 1 solvents. The plot of t − vs. fm is linear which V indicates the fact that the solvent microviscosity effect plays an important role in case of complex molecular systems containing a benzene ring.
References [1] S. Tarulli, E.J. Baran, J. Raman Spectrosc. 26 (1995) 139. [2] Z. Kecki, A. Sokolowska, J. Raman Spectrosc. 27 (1996) 429. [3] D.E. Logan, Chem. Phys. 103 (1986) 215. [4] G. Do¨ge, R. Arndt, J. Yarwood, Mol. Phys. 52 (1984) 399. [5] G. Fini, P. Mirone, S. Fortunato, J. Chem. Soc.: Faraday Trans. 269 (1973) 1243. [6] G. Fini, P. Mirone, J. Chem. Soc.: Faraday Trans. 270 (1974) 1776. [7] A. Purkayastha, K. Kumar, Spectrochim. Acta Part A 42A (1986) 1379. [8] A.A. Roduguez, M. Schwartz, Chem. Phys. Lett. 129 (1986) 458. [9] A. Purkayastha, R. Das, K. Kumar, J. Raman. Spectrosc. 21 (1990) 227. [10] A. Purkayastha, R. Das, K. Kumar, Spectrochim. Acta Part A 46A (1990) 1545. [11] A. Purkayastha, R. Das, K. Kumar, Spectrochim. Acta Part A 47A (1991) 525. [12] A. Purkayastha, K. Kumar, J. Raman Spectrosc. 22 (1991) 721. [13] J. Jonas, Acc. Chem. Res. 17 (1983) 74. [14] J.L. McHale, J. Chem. Phys. 75 (1981) 30. [15] P. Mirone, J. Chem. Phys. 77 (1982) 2704. [16] M.G. Giorgini, G. Fini, P. Mirone, J. Chem. Phys. 79 (1983) 639. [17] A. Bondi, J. Phys. Chem. 68 (1964) 441. [18] M.F.C. Ladd, Structure and Bonding in Solid State Chemistry, Ellis Horwood, Chichester, 1979, pp. 251 – 253.
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798 [4] G. Do¨ge, R. Arndt, J. Yarwood, Mol. Phys. 52 (1984) 399. [5] G. Fini, P. Mirone, S. Fortunato, J. Chem. Soc.: Faraday Trans. 269 (1973) 1243. [6] G. Fini, P. Mirone, J. Chem. Soc.: Faraday Trans. 270 (1974) 1776. [7] A. Purkayastha, K. Kumar, Spectrochim. Acta Part A 42A (1986) 1379. [8] A.A. Roduguez, M. Schwartz, Chem. Phys. Lett. 129 (1986) 458. [9] A. Purkayastha, R. Das, K. Kumar, J. Raman. Spectrosc. 21 (1990) 227. [10] A. Purkayastha, R. Das, K. Kumar, Spectrochim. Acta Part A 46A (1990) 1545.
.
799
[11] A. Purkayastha, R. Das, K. Kumar, Spectrochim. Acta Part A 47A (1991) 525. [12] A. Purkayastha, K. Kumar, J. Raman Spectrosc. 22 (1991) 721. [13] J. Jonas, Acc. Chem. Res. 17 (1983) 74. [14] J.L. McHale, J. Chem. Phys. 75 (1981) 30. [15] P. Mirone, J. Chem. Phys. 77 (1982) 2704. [16] M.G. Giorgini, G. Fini, P. Mirone, J. Chem. Phys. 79 (1983) 639. [17] A. Bondi, J. Phys. Chem. 68 (1964) 441. [18] M.F.C. Ladd, Structure and Bonding in Solid State Chemistry, Ellis Horwood, Chichester, 1979, pp. 251 – 253.
Microenvironment dependence of vibrational relaxation in p-methyl acetophenone Arpita Das, Kamal Kumar * Department of Physics, North Eastern Hill Uni6ersity, Shillong-793022, India Received 27 May 1997; accepted 18 November 1997
Abstract The Raman band shape analysis and vibrational relaxation studies of the CO stretching mode of vibration of p-methyl acetophenone reveals that macroscopic considerations are not sufficient to analyse the Raman anisotropy shift and the linewidth of the isotropic component observed in complex molecular systems. The band shape analysis was therefore attempted at a microscopic level by taking into account the concept of microenvironment. The solvent dependent study of the anisotropy shift shows that the repulsive potential may be playing a major role in the vibrational relaxation process. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Vibrational relaxation; Microenvironment; Non-coincidence effect; p-Methyl acetophenone; Solvent dependent studies
1. Introduction The vibrational relaxation in molecular liquids has been the subject of many theoretical and experimental studies. Although considerable progress has been made towards a deeper understanding regarding the vibrational relaxation process in recent years, a detailed study is required to account for the discrete nature of the solute-solvent system at the microscopic level. The Raman band analysis especially the dependence of linewidth on environment may provide useful information regarding the intermolecular forces. The vibrational relaxation process which is re* Corresponding author. Tel.: + 91 364 250035; fax: + 91 364 250076.
sponsible for the line broadening of the isotropic Raman component may be due to the contribution from vibrational dephasing, population relaxation and resonant energy transfer via transition-dipole transition-dipole (TD–TD) interaction [1–4]. Moreover, the microscopic environment affects the behaviour of a reference molecule. In a liquid mixture the lineshape of the reference mode is influenced by the concentration fluctuation of the environment. In some liquids, the anisotropy shift where the peak frequencies of isotropic and anisotropic components differ from each other, has been found sometimes, to be [4] as large as 10 cm − 1, or even more. This phenomenon, termed as non-coincidence effect may be interpreted as being due to the coupling between vibrations of neighbouring molecules with
1386-1425/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S1386-1425(97)00276-X
794
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
strongly polar modes by intermolecular dipole interactions in the liquid phase [5 – 8]. The theoretical explanation for the vibrational relaxation may be given by correlating the vibra1 tional relaxation rate (t − V ) with some molecular parameter [9–11] which takes into account the effect of reaction field (solvent electric field) on the solute, and using the basic concepts of dielectric relaxation processes. To have a better picture of the solute-solvent system one may consider the so called ‘solvent cage effect’ where the molecules of a liquid are confined in a potential well. The molecule is considered to be vibrating against the walls of the cage, that is against its immediate neighbours, with an occasional escape to its adjacent position. However, the explanation for the vibrational relaxation process for complex molecular systems, sometimes cannot be understood on the basis of a macroscopic perception of the solutesolvent system. A marked difference is likely between the interaction situations in the pure solute and when it is dissolved in solvents, especially at high dilution. In order to understand more clearly the complicated nature of the processes involved, a detailed study is, therefore, required at the microscopic level, which may be performed by considering the effect of microenvironment. In an attempt to provide further support to the previous findings of Purkayastha and Kumar [11,12], and to have detailed information about the processes involved in complex molecular systems, p-Methyl acetophenone (PMA) has been chosen using its CO stretching vibration as the reference mode. The present work deals with the solvent dependent studies on the Raman band corresponding to CO stretching vibration of PMA. The CO stretching vibration of PMA is well isolated from other modes of vibration and the dipole moment of PMA is probably concentrated on the CO bond of the molecule.
2. Experimental Raman spectral measurements were made for the CO stretching band of PMA in CHCl3, CCl4, CH2Cl2, CH3CN and C6H6 solvents using a SPEX RAMALOG 1403 double monochromator spectrometer equipped with a Datamate. The sample of
PMA and the solvents were obtained commercially and were used without further purification. The laser Raman spectra were recorded using the 4880 ˚ line from the Spectra-Physics model 165 Ar + A ˚ line was laser as the excitation source. The 4880 A used with a power of 350 mW and the slitwidth was kept at 2 cm − 1. The isotropic component was obtained by using the formula Iiso(n¯ )= IVV(n¯ )− 4/3IVH(n¯ )
and
Ianiso(n¯ )= IVH(n¯ ) where IVV(n¯ ), and IVH(n¯ ) represent the polarised and depolarised Raman spectra respectively. n¯ is the frequency in wavenumbers. The accuracy of measurements is believed to be 9 0.5 cm − 1. 3. Results and discussion The laser Raman spectrum of pure PMA shows the IVV and IVH components with the peak of IVH component shifted to a higher frequency position. The non-coincidence of the isotropic and anisotropic frequency maxima may be explained by taking into consideration the resonant coupling due to TD–TD interactions [4,13] of the vibrations of two adjacent molecules. The study of the non-coincidence effect needs considerations of the influence of the intermolecular forces, viz. dispersion forces, induction forces, and multipole–multipole interactions on the vibrational transitions.The dispersion type interactions usually explain the general additive attractions between arbitrary atoms and molecules. The dispersion energy has high values even in the case of solvent molecules having a dipole moment, which is mainly because of the o 2 dependence of the dipole–dipole and dipole-induced dipole type of interactions for the solvents of high dielectric constant. The contributions to the observation due to induction forces are assumed to be present in both types of systems as a result of the dipolarity of the solute molecule under investigation, even though some of the solvent molecules have no dipole moment. The polarity of the solvent is also an important factor which contributes to the potential field perturbing the vibration, when the solute has a solvent molecule in the neighbourhood of the vibration. This is particularly true at high dilution. The explanation that the anisotropy
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
795
Fig. 1. The variation of the quantity F as a function of the solute concentration (F): (a) CCl4; (b) CH2Cl2; (c) CHCl3; (d) C6H6; (e) CH3CN.
shift is an effect due to resonant coupling is supported by the experimental data related to the effect of solvent on the Raman band of PMA molecule. This effect tends to vanish at high concentration of the solvents. The separation between the isotropic and anisotropic maxima of the Raman bands in different solvents varies with the concentration of the active substance. It was shown by McHale that the anisotropy shift dn can be expressed by the relation [14]
dn=
2m 2(dm/dQ)20N0
FS
(1)
2552 c 2n0kTd 3Vm where N0 is Avogadro’s number, F is the volume fraction of the solute, n0 is the vibrational frequency of the isolated molecule, d is the minimum intermolecular distance, Vm is the molar volume of the solute, kT is the thermal energy, m is the dipole moment, Q is the mass weighted normal
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
796 Table 1 Molecular parameters Solvents
Density (r)
Dielectric constant (o)
R.I. (n)
Dynamic viscosity (h) (cp)
CHCl3 CCl4 CH2Cl2 CH3CN C6H6
1.479 1.548 1.319 0.776 0.873
4.77 2.23 9.14 37.5 2.28
1.45 1.46 1.42 1.34 1.50
0.542 0.843 0.393 0.345 0.564
coordinate and (dm/dQ)0 is the transition moment. S is the screening factor, S comprises two factors, Sp and St related respectively to the interactions of permanent and transition dipoles. Following the dielectric model given by ONSAGER-FROHLICH (hereafter referred to as the O-F model), which treats the dielectric as continuum, the above equation takes the form dn(2o +n 2)2o − 1 =
2m 2(dm/dQ)20(n 2 +2)2N0
F
2552 c 2n0kTd 3Vm (2) The quantity [F =dn(2o +n 2)2o − 1] was plotted as a function of the volume fraction (F) in different solvents. The dielectric constant of PMA was experimentally measured and found to be 16.25. The dielectric constant of the solution was calculated by using the relation osolution =F · osolute +(1 −F)osolvent where F is the volume fraction of the solute. Fig. 1 clearly shows that the data points [dn(2o + n 2)2o − 1] do not lie on the correlation line for the entire range of dilution. A closer look reveals the fact that the data points fit rather well in two straight lines with a sharp discontinuity at around F = 0.5. The splitting given by Eq. (2) was predicted by the TD coupling model and this expression was expected to be valid only for dilute solution [15,16]. Below 50% dilution, the interactions were expected to occur more among solute molecules than solute – solvent interactions [12]. The present study indicates that to explain the non-coincidence effect in case of complex molecular systems like PMA, where the effects of dispersion, induction, multipolar interaction, etc. are likely to vary from solvent to solvent, the screening effect may not be as effective as
envisaged by the O-F model. However, the plot of the quantity ln F vs. F shows a linear graph indicating a better fit. This kind of relationship whereby a ln F vs. F graph has been found to be linear may be indicative of the repulsive potential function of the type e − aR playing an important role, (the R being the appropriate radius related to the distance of closest approach which will depend upon the fraction of solute present)(Tables 1 and 2). Detailed work is, however, required in this connection to establish the empirical relationship so obtained (Fig. 2). Experimentally measured lineshapes of the isotropic and anisotropic components of Raman bands help us to know more about the spherically symmetric part of the intermolecular forces and anisotropic forces respectively. The vibrational relaxation may be explained on the basis of life-time broadening, environmental broadening and resonance transfer. The inhomogeneous and homogeneous contributions to the linewidth, which is of great importance in understanding the molecular dynamics, may be separated by time-dependent techniques. The lineshape is Lorentzian for homogeneous broadening (Dv/t 1), Dv and 1/t denote the frequency shift and the rate of change between various inhomogeneous components. Table 2 Relaxation rate (t−1 V ) and the function fm for various molecular systems Molecular system
Giso (cm−1)
fm
−1 t−1 V (ps)
PMA-CHCl3 PMA-CCl4 PMA-CH2Cl2 PMA-CH3CN PMA-C6H6
16 12 10 9 15
3.90 2.20 1.44 1.00 3.30
1.51 1.13 0.94 0.84 1.40
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
797
Fig. 2. The variation of the quantity ln F as a function of the solute concentration (F): (a) CCl4; (b) CH2Cl2; (c) CHCl3; (d) C6H6; (e) CH3CN.
In the present work, the linewidth of the isotropic components Giso (FWHM) of the Raman band corresponding to the CO stretching mode of the PMA molecule were measured in various polar as well as nonpolar solvents at 80% concentrations. At this concentration, the Raman band was found to be Lorentzian and, therefore, vibrational relax1 ation rates (t − V ) were calculated from the isotropic linewidth (Giso) using the equation
1 t− V = 5 cGiso
The experimental results have been presented as 1 the plot of the vibrational relaxation rate (t − v ) as a function of the P–K parameter [9,10] fm (Fig. 3). The parameter fm was calculated for various solvents using the relation fm = f(r, hm, n)= rhm[(n 2 − 1)/(2n 2 + 1)] − 1
798
A. Das, K. Kumar / Spectrochimica Acta Part A 54 (1998) 793–798
Here, hm is given by, hm = hg and g = [0.16 +0.4(a/b)] where g is the microfriction factor which takes care of the noncontinuous nature of the viscoelastic medium. a and b are the radii of the solute and the solvent molecules, respectively. The CHCl3 molecule has the tendency to form hydrogen bond due to the presence of acidic hydrogen. Therefore, hydrogen bonding is likely to be present between PMA and CHCl3 molecules. In such hydrogen bonded systems, the layers of CHCl3 molecules may be formed over PMA molecules. Due to the C–H bond of CHCl3 being oriented towards CO bond of PMA, the solute radius in this case is taken as the sum of van der Waals radius ˚ ) and the CO bond distance [18] of O atom (1.4 A ˚ ). The solvent radius in this case is taken as (1.2 A ˚ ) if H the van der Waals radius of H atom (1.2 A atom is considered to be fluctuating between C and O atoms. In CH3CN-PMA system, CH3CN may be regarded as a cylindrical like structure so far as C – CN portion is concerned. The molecular radius is chosen as the van der Waals radius of nitrogen ˚ ). In the case of CH2Cl2-PMA system atom (1.5 A the C–Cl van der Waals radius is responsible for the distance of closest approach, so the molecular radius is chosen as the Cl atom van der Waals ˚ ). For C6H6-PMA system the solvent radius (1.8 A radius is taken as the H atom van der Waals radius ˚ ). In the case of CCl4-PMA molecular system, (1.0 A ˚ ) and van der Waals the C–Cl bond distance (1.7 A ˚ radius for Cl atom (1.8 A) are added up to find the molecular radius due to the spherical nature of the molecule. The solute radius in these cases is taken as the van der Waals radius [17] of benzene (1.77
1 Fig. 3. The variation of the vibrational relaxation rate (t − V ) as function of fm.
˚ ) as the interactions are possible at benzene A moiety. The plot of vibrational relaxation rate 1 (t − V ) as a function of the parameter fm is clearly a linear plot. It is, therefore, probable that the discreteness of the medium due to the solvents may be playing a major role. Therefore, the concept of microenvironment has to be taken into account for better fitting of data points.
4. Conclusion The solvent dependent study of anisotropy Raman shift indicates that the repulsive potential may be playing a major role in the relaxation process when concentrated solution is diluted with different 1 solvents. The plot of t − vs. fm is linear which V indicates the fact that the solvent microviscosity effect plays an important role in case of complex molecular systems containing a benzene ring.
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