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A new far-infrared broadband absorption in non-rigid polar molecules
Volume 139, number 1
CHEMICAL PHYSICS LETTERS
14August 1987
A NEW FAR-INFRARED BROADBAND ABSORPTION IN NON-BIGID POLAR MOLECULES J.K. VIJ Departmentof Microelectronicsand Efectncal Engineering, TrinityColfege,Dublin 2, Ireland
and F. HUFNAGEL Instrtutftir Physik,Johannes Gutenberg Universit&D-6500 Maim, Federaf Republicof Germany Received 24 March 1987; in final form 4 June 1987
A new far-infrared broadband absorption has been observed for non-rigid ketone molecules in the frequency range 220 to 340 cm - ‘. It has been found that the amplitude of this absorption increases with an increase in the flexibility of the molecule. Such an increase in the amplitude of this absorption is accompanied by a corresponding reduction in that of the Poley absorption.
It has been known for sometime [ l-4 ] that nonrigid molecules possess more than one discrete relaxation time even when dipole-dipole coupling is neglected. Such a phenomenon arises because different parts of the molecule, if it contains polar groups, may rotate at different rates. It may also arise due to the shape of the molecule. It is however difficult to separate these relaxation times when they differ from each other by a factor [ 5 ] less than 10. Then the dist~bution of the dielectric relaxation times is expressed in terms of a Cole-Cole [6] distribution parameter. In yet other cases, the microwave dielectric e-e” data are analysed in terms of two discrete relaxation times: (i) an intramolecular process, in which a part of the molecule involving either a component of or the entire dipole moment is rotating within the molecule; (ii) an intermolecular process with a relatively long relaxation time involving an overall rotation of the molecule with this rotation being affected by the neighbouring molecules. In view of the foregoing, we were prompted to investigate the far-infrared spectrum of some well known non-rigid molecules over a wide frequency range than has hitherto been attempted. The reason
behind this is that the presence of even weak dipole-dipole coupling between different parts of the molecule or with other molecules would manifest itself in the form of a far-infrared absorption peak whose position would depend on the configuration of the groups in the molecule and/or on the neigbbouring molecules, the dipole-dipole coupling and the moment of inertia for the relaxation process. To explain the microwave and FIR absorption of dipolar fluids, Coffey et al. [ 7,8] have derived a formula for the frequency of maximum power absorption, &rR, which is &&fR=(4&jYrz,-t/J”>“*.
(1)
The model is that of two dipoles which rotate in a plane; dipole-dipole coupling between them is fully included. This system possesses only one natural frequency of oscillation, !&ii+ which is the frequency of torsional oscillations of the two dipoles relative to each other. Eq. (1) has been derived on the assumption that the potential well is much deeper compared with the kinetic energy of a dipolar molecule and that escape of the dipole to a nei~~u~ng well can be neglected. Furthermore, the derivation is based on the small-~plitude approximation. If a large number of dipoles, say three, were constrained to rotate
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
77
Volume 139, number
1
CHEMICAL
PHYSICS
in the plane, one would expect a number of natural frequencies of oscillation connected with the relative angular motions of the dipoles. This behaviour is likely to manifest itself in the FIR region as a peak structure. We return to this later. For the case of two dipoles in the model equal in all respects, Marchesoni et al. [ 91 have attempted to include the effect of the dipole jumping over the potential barrier due to its finite height. For the present discussion, however, eq. (1) is much more general as it is applicable to that of unequal dipoles. The parameters in this equation are defined as follows: &=(kT/Z,)“2,
~=l/o/Z,&,
LETTERS
14 August
1987
mole fraction of the dipolar fluid in the solvent. For f2 upto say 0.015, 1-fix 1 within an error of 1.5%. Eq. (4) can therefore be written as A,(B)=[A(~)-A,(~)]/J;=~(~)/fZ,
(5)
where AA( rr) is the increment in the absorption coefficient of the solution over the solvent. Developments in the dielectric measuring techniques in the frequency range l-300 GHz have been described before [ lo]. E”(V) is converted to A ( P) using the Maxwell relation A(V)=OC(V)IIZ(r+z,
(6)
Aliphatic ketones are selected due to their large dipole moment (x2.80 D) and for their FIR spectrum to be free from proper modes, i.e. vibrational or vibrational-mode-difference frequencies for these molecules. Acetone as a representative of aliphatic ketones is found to be an almost transparent liquid in the wavenumber range between 220 and 400 cm- I.
where n(r) is the real part of the refractive index and c is the velocity of light in vacua. For signal frequencies above 150 GHz, Golay cell or triglycine sulphate or InSb type bolometric detectors can normally be used. For a number of frequencies in the range 239 GHz to 3.1 THz (7.97 to 103.6 cm- ’ ), we used a molecular laser [ 111 as source and a Golay cell as detector. The measurements in the wavenumber range 80-400 cm- ’ were made using a Briiker 113~ interferometer. The frequency range of this interferometer depends on the beam splitter and the detector system used. A polyethylene film of thickness 6 urn is used for the beam splitter and a triglycinesulphate bolometer as detector. Fixed path length cells of 5 and 10 mm pathlengths are used. The windows of these cells are made up of TPX (polymetylpentene teraphthalate) which is coated with a thin layer of teflon. For the six ketones studied, the average of A,~(v)& versus B at 20°C are shown in figs. l-5; AA(@/f2 is the absorption coefficient of the solute extrapolated from dilute solution to full concentration.
2. Experimental and results
3. Discussion
Ketones are studied in dilute solutions of cyclohexane in the concentration range 0.5 to 1.5 moleoh. The power absorption coefficient of the solution A( rr) can be expressed as
We note from fig. 1 that acetone which may be regarded as an almost rigid molecule of spherical shape, shows the main far-infrared spectrum in a single absorption profile. This is identified as the Poley [ 121 absorption of the dipolar fluid. The half-width of the absorption profile, compared to the rest of the fluids of this class, is relatively small. The next bigger molecule studied, hexanone-2, shows a secondary
a, ‘212/(Z, +I,).
(2)
/3is the friction coefficient acting on the dipoles under discussion. I, and Z2 are the moments of inertia of the molecule and its cage. The second dipole in the model is regarded as the cage which simulates the nearest neighbours of the molecule and practically Z2z+ I,. 2 V, is the amplitude of the potential energy of interaction between the dipole moments of the molecule and that of the cage. For a given molecular system, it is reasonable to assume that the parameters V, and j3 are fixed and with a, x 2, eq. ( 1) reduces to QFIR=(2VJz, -tfi”)“‘.
A(~)=A,(~)(l-f,)+f,Az(~),
(3)
(4)
where A, (P) and A2( fl) are the absorption coefficients of the solvent and solute respectively. f2 is the 78
Volume 139, number I 160r
14 August 1987
CHEMICAL PHYSICS LETTERS I
I,
Fig. 1.Power absorption coefftcient AA(Y)lf (neper cm- ’ ) versus wavenumber Y (cm-‘) for acetone in the frequency range O-400 cm-‘; swept frequency (in the microwave range) and Brtiker interferometer results (80-400 cm- ’ ), 0 molecular laser results; # # hexanone-2, x molecular laser results.
Fig. 4. Same as fig. I for nonanone-5, 0 molecular laser results.
1
0
100
*cm
JOCI
4M)
Fig. 5. Same as fig. 1for undecanone-6, 0 molecular laser results.
Fig. 2. Same as fig. 1for heptanone-2, 0 molecular laser results.
Fig. 3. Same as fig. 1for heptanone-4, 0 molecular laser results.
absorption profile (fig. 1) in addition to its usual primary profile. The secondary profile is observed to be relatively broad. A significant secondary absorption profile is also observed for heptanone4 (fig. 3) which is centred at the wavenumber of 304 cm-‘. The amplitude of its primary profile has correspondingly been seen to be reduced. Another isomer of heptanone, i.e. heptanone-2, shows similar features (fig. 2) for the secondary absorption profile but less spectacularly than heptanone-4. The secondary absorption profiles for the big molecules nonanone5 (fig. 4) and undecanone-6 (fig. 5) are almost as significant as their primary absorption counterparts. From these observations, it would appear as if the secondary absorption was caused by an increase in the flexibility of the ketone molecule. This absorption profile is too broad to be characterised by the vibrational or the difference between the vibrational 79
Volume 139, number
1
CHEMICAL
PHYSICS
modes of the atoms in these molecules. It may be helpful to recall that in the analysis of the power absorption/dielectric loss data from radio to farinfrared frequencies, three main types of power absorption mechanisms have so far been identified in terms of a two-particle itinerant oscillator [ 131 type model. The main relaxation mode in the microwave range arises from the overall rotation of the dipoles as a unit; the far-infrared absorption arises mainly from the orientations of the dipoles resulting from their librations in the potential troughs or wells. These troughs of potential are created by the strength of the dipole-dipole coupling (2u,,) between the molecule and its surroundings. For the case of two dipoles involved in the coupling, this is given by Y(r~)= - 2v, cos 255where 2rl is the angle between the two dipoles. A third relaxation mechanism discovered recently by Gerschel et al. [ 141 and confirmed in our earlier papers [ 10,131 has been suggested to arise from the jumping of the dipoles [ 13,15,16] from one well into another. In this paper we report still another power absorption mechanism. From the analysis so far it would appear that this mechanism is the libration counterpart of the intramolecular relaxation mechanism for these molecules. The results on the dielectric relaxation time for these ketones which have already been discussed [ 10,171 lead us to the conclusion that the various segments of the longer chain length (or bigger) ketone molecules coil up together to form a sponge-like ellipsoidal-shaped structure. The results suggest that the flexibility of the various molecular segments increases with an increase in the number of methyl groups on each side of the ketone group. It follows therefrom that the major contributor to the intermolecular relaxation mechanism for these molecules is the rotational diffusion of the molecule along the major axis of the ellipse. This axis is perpendicular to the direction of the dipole moment. The intramolecular relaxation amplitude which is due to motion within the molecule is likely to increase with an increase in the size of the molecule. This would happen at the expense of the intermolecular relaxation process, whose amplitude would correspondingly decrease with an increase in the size of the molecule due to the steric hindrance of the intermolecular rotation by its neighbouring molecules. The intramolecular relaxation mechanism may 80
LETTERS
14 August 1987
therefore occur in either of the following two ways. The dominance of the one type over the other is to be dependent on the chain length and consequently on the shape of the molecule. (i) The twisting of the C=O dipole moment around the two closest H2C-C bonds. This is likely to happen especially in heptanone4, nonanone-5 and undecanone-6. (ii) A terminal rotation of the acetyl group (CH,CO) around the C-C bond, which may take place in hexanone-2 and heptanone-2. In order to establish quantitatively a possible basis of this new absorption, we recall here briefly the mechanics of a two-particle itinerant oscillator model [ 8,131. A simple mechanical system of a disk and annulus concentric with the disk simulates a dipolar fluid where the molecule under discussion is surrounded by a continuum of dielectric media. The disk is assumed to be bound to the rim of the annulus through an interaction potential. Both the disk and annulus can rotate along the axis passing through the centre of the system and at right angles to it. The disk carries a dipole of moment ,u, and moment of inertia II, whereas the annulus simulating the surroundings carries a dipole of moment ,u2and moment of inertia Z2.The mechanical system is governed by the Langevin equations with stochastic noise acting on both the dipoles. In the harmonic approximation of the coupling potential, this produces one FIR absorption profile. In order to explain two FIR absorption profiles, we need to have at least three coupled equations involving a third dipole of moment p3 for the intramolecular rotation. For simplicity, this dipole is assumed to lie on the disk and making an angle d3 with the reference direction. The equations of motion for the three-dipole case with the electric field turned off at t=O are ZI$1 +PZIII
+PU12F12(@1-+2)
(7)
+/43F13(@1-@3)=r,(o,
z2~2++pz26s2+~2,~2,(~2--,)
+p23F23(@2
1363
+813h
-@3)
+p32F32(@3
+~3IF3,(9,-g),)=r3(t).
=r2(t),
(8)
-@2)
(9)
Volume 139, number 1
CHEMICAL PHYSICS LETTERS
9, and & are the angles that the dipoles pl and p2 make with the electric field direction prior to t = 0. p,2F,2(@, -qj2) is the torque due to the dipole-dipole coupling, which is a function of the angle between the dipoles 1 and 2. The other fl terms likewise are the torques between the various dipoles following this notation. r, (t), r2 and r,(t) are the random torques acting on the three dipoles. The solutions of eqs. (7) to (9) would be extremely difficult unless some assumptions could be made. Coffey [ 18 ] has shown that for the three dipoles equal in all respects, i.e. the magnitudes of the interaction potentials are the same and I, =Z2=ZJ, the torsional frequency of the third dipole relative to the second dipole, L2FIR(3_2j in the harmonic approximation is L&(3-2) =3(4&Va, -f P2)“’
(10)
14 August 1987
4. Conclusion New far-infrared broadband absorption has been observed for some dilute solutions of non-rigid ketone molecules in the wavenumber range 220 to 340 cm- I. This absorption is proposed to be the libration counterpart mechanism of the intramolecular rotational relaxation in these molecules.
Acknowledgement We thank Professors B.K.P. Scaife, W.T. Coffey and Dr. G.J. Evans for very useful discussions. Mr. M. Helker is thanked for his help in measurements on the Molecular Laser System.
for (r,(t)
T,(t))
=26,,kZjYZ,6(t),
References
i,j=2,3
[ I ] A. Bud& E. Fischer and S. Miyamoto, Z. Physik 40 (1939)
with a3
=2Z,/(Z,
+I,)
and for I, =zz
=z3
a3=al
(11)
‘I,
(12)
=I
i.e. Q FIR(3-2)
= 3GFIR(,-2)
*
(13)
From the experimental results on non-rigid polar ketone molecules, we find that the torsional frequency for the intramolecular relaxation process is approximately 4.5 times that for the intermolecular process. A possible reason for this discrepancy between theory and experiment is that in practice the three dipoles are unequal and in particular the moment of inertia of the dipole involved in the intramolecular relaxation process is much lower compared to that for the intermolecular process. It seems reasonable to expect QFiR(intramolecular) to be 4.5 &&( intermolecular) if Z3z 4 Z[.
337. [2] K. Higasi, K. Bergmann and C.P. Smyth, J. Phys. Chem. 64 (I 960) 880. [ 31 K. Higasi, Dielectric relaxation and molecular structure, Research Institute of Applied Electricity, No. 9, Hokkaido University, Sapporo, Japan ( 196 1) . [4] C.P. Smyth, Chem. Sot. Special Publication, No. 20. Molecular relaxation processes (Chem. Sot, London, 1966) pp. l-13. [ 51B.K.P. Scaife, private communication. [6] K.S. Co1eandR.H. Cole, J. Chem. Phys. 9 (1941) 341. [7] W.T. Coffey, P.M. Corcoran and J.K. Vij, Chem. Phys. Letters 129 (1986) 375. [ 81 W.T. Coffey, P.M. Corcoran and M. Evans, Proc. Roy. Sot. A410 (1987) 61. [9] F. Marchesoni, J.K. Vij and W.T. Coffey, Z. Physik B61 (1985) 357. [IO] J.K. Vij and F. Hufnagel, Advan. Chem. Phys. 63 (1985) 775. [ 111 J.K. Vij, F. Hufnagel, M. Helker and C.J. Reid, IEEE J. Quantum Electron. QE-22 (1986) 1123. [ 12 ] J.Ph. Poley, J. Appl. Sci. Res. B4 (1955) 337. [ 131 W.T. Coffey, P.M. Corcoran and J.K. Vij, Proc. Roy. Sot. A (1987), to be published. [ 141 A. Gerschel, T. Grochulski, Z. Kisiel, L. Pszeczolkowski and K. Leibler, Mol. Phys. 54 (1985) 97. [ 151 F. Marchesoni and J.K. Vij, Z. Physik B58 (1985) 187. [ 161 P.M. Corcoran and J.K. Vij, Mol. Phys., submitted for publication. [ 171 J. Crossley, J. Chem. Phys. 56 (1972) 2549. [ 181 W.T. Coffey, private communication.
81
CHEMICAL PHYSICS LETTERS
14August 1987
A NEW FAR-INFRARED BROADBAND ABSORPTION IN NON-BIGID POLAR MOLECULES J.K. VIJ Departmentof Microelectronicsand Efectncal Engineering, TrinityColfege,Dublin 2, Ireland
and F. HUFNAGEL Instrtutftir Physik,Johannes Gutenberg Universit&D-6500 Maim, Federaf Republicof Germany Received 24 March 1987; in final form 4 June 1987
A new far-infrared broadband absorption has been observed for non-rigid ketone molecules in the frequency range 220 to 340 cm - ‘. It has been found that the amplitude of this absorption increases with an increase in the flexibility of the molecule. Such an increase in the amplitude of this absorption is accompanied by a corresponding reduction in that of the Poley absorption.
It has been known for sometime [ l-4 ] that nonrigid molecules possess more than one discrete relaxation time even when dipole-dipole coupling is neglected. Such a phenomenon arises because different parts of the molecule, if it contains polar groups, may rotate at different rates. It may also arise due to the shape of the molecule. It is however difficult to separate these relaxation times when they differ from each other by a factor [ 5 ] less than 10. Then the dist~bution of the dielectric relaxation times is expressed in terms of a Cole-Cole [6] distribution parameter. In yet other cases, the microwave dielectric e-e” data are analysed in terms of two discrete relaxation times: (i) an intramolecular process, in which a part of the molecule involving either a component of or the entire dipole moment is rotating within the molecule; (ii) an intermolecular process with a relatively long relaxation time involving an overall rotation of the molecule with this rotation being affected by the neighbouring molecules. In view of the foregoing, we were prompted to investigate the far-infrared spectrum of some well known non-rigid molecules over a wide frequency range than has hitherto been attempted. The reason
behind this is that the presence of even weak dipole-dipole coupling between different parts of the molecule or with other molecules would manifest itself in the form of a far-infrared absorption peak whose position would depend on the configuration of the groups in the molecule and/or on the neigbbouring molecules, the dipole-dipole coupling and the moment of inertia for the relaxation process. To explain the microwave and FIR absorption of dipolar fluids, Coffey et al. [ 7,8] have derived a formula for the frequency of maximum power absorption, &rR, which is &&fR=(4&jYrz,-t/J”>“*.
(1)
The model is that of two dipoles which rotate in a plane; dipole-dipole coupling between them is fully included. This system possesses only one natural frequency of oscillation, !&ii+ which is the frequency of torsional oscillations of the two dipoles relative to each other. Eq. (1) has been derived on the assumption that the potential well is much deeper compared with the kinetic energy of a dipolar molecule and that escape of the dipole to a nei~~u~ng well can be neglected. Furthermore, the derivation is based on the small-~plitude approximation. If a large number of dipoles, say three, were constrained to rotate
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
77
Volume 139, number
1
CHEMICAL
PHYSICS
in the plane, one would expect a number of natural frequencies of oscillation connected with the relative angular motions of the dipoles. This behaviour is likely to manifest itself in the FIR region as a peak structure. We return to this later. For the case of two dipoles in the model equal in all respects, Marchesoni et al. [ 91 have attempted to include the effect of the dipole jumping over the potential barrier due to its finite height. For the present discussion, however, eq. (1) is much more general as it is applicable to that of unequal dipoles. The parameters in this equation are defined as follows: &=(kT/Z,)“2,
~=l/o/Z,&,
LETTERS
14 August
1987
mole fraction of the dipolar fluid in the solvent. For f2 upto say 0.015, 1-fix 1 within an error of 1.5%. Eq. (4) can therefore be written as A,(B)=[A(~)-A,(~)]/J;=~(~)/fZ,
(5)
where AA( rr) is the increment in the absorption coefficient of the solution over the solvent. Developments in the dielectric measuring techniques in the frequency range l-300 GHz have been described before [ lo]. E”(V) is converted to A ( P) using the Maxwell relation A(V)=OC(V)IIZ(r+z,
(6)
Aliphatic ketones are selected due to their large dipole moment (x2.80 D) and for their FIR spectrum to be free from proper modes, i.e. vibrational or vibrational-mode-difference frequencies for these molecules. Acetone as a representative of aliphatic ketones is found to be an almost transparent liquid in the wavenumber range between 220 and 400 cm- I.
where n(r) is the real part of the refractive index and c is the velocity of light in vacua. For signal frequencies above 150 GHz, Golay cell or triglycine sulphate or InSb type bolometric detectors can normally be used. For a number of frequencies in the range 239 GHz to 3.1 THz (7.97 to 103.6 cm- ’ ), we used a molecular laser [ 111 as source and a Golay cell as detector. The measurements in the wavenumber range 80-400 cm- ’ were made using a Briiker 113~ interferometer. The frequency range of this interferometer depends on the beam splitter and the detector system used. A polyethylene film of thickness 6 urn is used for the beam splitter and a triglycinesulphate bolometer as detector. Fixed path length cells of 5 and 10 mm pathlengths are used. The windows of these cells are made up of TPX (polymetylpentene teraphthalate) which is coated with a thin layer of teflon. For the six ketones studied, the average of A,~(v)& versus B at 20°C are shown in figs. l-5; AA(@/f2 is the absorption coefficient of the solute extrapolated from dilute solution to full concentration.
2. Experimental and results
3. Discussion
Ketones are studied in dilute solutions of cyclohexane in the concentration range 0.5 to 1.5 moleoh. The power absorption coefficient of the solution A( rr) can be expressed as
We note from fig. 1 that acetone which may be regarded as an almost rigid molecule of spherical shape, shows the main far-infrared spectrum in a single absorption profile. This is identified as the Poley [ 121 absorption of the dipolar fluid. The half-width of the absorption profile, compared to the rest of the fluids of this class, is relatively small. The next bigger molecule studied, hexanone-2, shows a secondary
a, ‘212/(Z, +I,).
(2)
/3is the friction coefficient acting on the dipoles under discussion. I, and Z2 are the moments of inertia of the molecule and its cage. The second dipole in the model is regarded as the cage which simulates the nearest neighbours of the molecule and practically Z2z+ I,. 2 V, is the amplitude of the potential energy of interaction between the dipole moments of the molecule and that of the cage. For a given molecular system, it is reasonable to assume that the parameters V, and j3 are fixed and with a, x 2, eq. ( 1) reduces to QFIR=(2VJz, -tfi”)“‘.
A(~)=A,(~)(l-f,)+f,Az(~),
(3)
(4)
where A, (P) and A2( fl) are the absorption coefficients of the solvent and solute respectively. f2 is the 78
Volume 139, number I 160r
14 August 1987
CHEMICAL PHYSICS LETTERS I
I,
Fig. 1.Power absorption coefftcient AA(Y)lf (neper cm- ’ ) versus wavenumber Y (cm-‘) for acetone in the frequency range O-400 cm-‘; swept frequency (in the microwave range) and Brtiker interferometer results (80-400 cm- ’ ), 0 molecular laser results; # # hexanone-2, x molecular laser results.
Fig. 4. Same as fig. I for nonanone-5, 0 molecular laser results.
1
0
100
*cm
JOCI
4M)
Fig. 5. Same as fig. 1for undecanone-6, 0 molecular laser results.
Fig. 2. Same as fig. 1for heptanone-2, 0 molecular laser results.
Fig. 3. Same as fig. 1for heptanone-4, 0 molecular laser results.
absorption profile (fig. 1) in addition to its usual primary profile. The secondary profile is observed to be relatively broad. A significant secondary absorption profile is also observed for heptanone4 (fig. 3) which is centred at the wavenumber of 304 cm-‘. The amplitude of its primary profile has correspondingly been seen to be reduced. Another isomer of heptanone, i.e. heptanone-2, shows similar features (fig. 2) for the secondary absorption profile but less spectacularly than heptanone-4. The secondary absorption profiles for the big molecules nonanone5 (fig. 4) and undecanone-6 (fig. 5) are almost as significant as their primary absorption counterparts. From these observations, it would appear as if the secondary absorption was caused by an increase in the flexibility of the ketone molecule. This absorption profile is too broad to be characterised by the vibrational or the difference between the vibrational 79
Volume 139, number
1
CHEMICAL
PHYSICS
modes of the atoms in these molecules. It may be helpful to recall that in the analysis of the power absorption/dielectric loss data from radio to farinfrared frequencies, three main types of power absorption mechanisms have so far been identified in terms of a two-particle itinerant oscillator [ 131 type model. The main relaxation mode in the microwave range arises from the overall rotation of the dipoles as a unit; the far-infrared absorption arises mainly from the orientations of the dipoles resulting from their librations in the potential troughs or wells. These troughs of potential are created by the strength of the dipole-dipole coupling (2u,,) between the molecule and its surroundings. For the case of two dipoles involved in the coupling, this is given by Y(r~)= - 2v, cos 255where 2rl is the angle between the two dipoles. A third relaxation mechanism discovered recently by Gerschel et al. [ 141 and confirmed in our earlier papers [ 10,131 has been suggested to arise from the jumping of the dipoles [ 13,15,16] from one well into another. In this paper we report still another power absorption mechanism. From the analysis so far it would appear that this mechanism is the libration counterpart of the intramolecular relaxation mechanism for these molecules. The results on the dielectric relaxation time for these ketones which have already been discussed [ 10,171 lead us to the conclusion that the various segments of the longer chain length (or bigger) ketone molecules coil up together to form a sponge-like ellipsoidal-shaped structure. The results suggest that the flexibility of the various molecular segments increases with an increase in the number of methyl groups on each side of the ketone group. It follows therefrom that the major contributor to the intermolecular relaxation mechanism for these molecules is the rotational diffusion of the molecule along the major axis of the ellipse. This axis is perpendicular to the direction of the dipole moment. The intramolecular relaxation amplitude which is due to motion within the molecule is likely to increase with an increase in the size of the molecule. This would happen at the expense of the intermolecular relaxation process, whose amplitude would correspondingly decrease with an increase in the size of the molecule due to the steric hindrance of the intermolecular rotation by its neighbouring molecules. The intramolecular relaxation mechanism may 80
LETTERS
14 August 1987
therefore occur in either of the following two ways. The dominance of the one type over the other is to be dependent on the chain length and consequently on the shape of the molecule. (i) The twisting of the C=O dipole moment around the two closest H2C-C bonds. This is likely to happen especially in heptanone4, nonanone-5 and undecanone-6. (ii) A terminal rotation of the acetyl group (CH,CO) around the C-C bond, which may take place in hexanone-2 and heptanone-2. In order to establish quantitatively a possible basis of this new absorption, we recall here briefly the mechanics of a two-particle itinerant oscillator model [ 8,131. A simple mechanical system of a disk and annulus concentric with the disk simulates a dipolar fluid where the molecule under discussion is surrounded by a continuum of dielectric media. The disk is assumed to be bound to the rim of the annulus through an interaction potential. Both the disk and annulus can rotate along the axis passing through the centre of the system and at right angles to it. The disk carries a dipole of moment ,u, and moment of inertia II, whereas the annulus simulating the surroundings carries a dipole of moment ,u2and moment of inertia Z2.The mechanical system is governed by the Langevin equations with stochastic noise acting on both the dipoles. In the harmonic approximation of the coupling potential, this produces one FIR absorption profile. In order to explain two FIR absorption profiles, we need to have at least three coupled equations involving a third dipole of moment p3 for the intramolecular rotation. For simplicity, this dipole is assumed to lie on the disk and making an angle d3 with the reference direction. The equations of motion for the three-dipole case with the electric field turned off at t=O are ZI$1 +PZIII
+PU12F12(@1-+2)
(7)
+/43F13(@1-@3)=r,(o,
z2~2++pz26s2+~2,~2,(~2--,)
+p23F23(@2
1363
+813h
-@3)
+p32F32(@3
+~3IF3,(9,-g),)=r3(t).
=r2(t),
(8)
-@2)
(9)
Volume 139, number 1
CHEMICAL PHYSICS LETTERS
9, and & are the angles that the dipoles pl and p2 make with the electric field direction prior to t = 0. p,2F,2(@, -qj2) is the torque due to the dipole-dipole coupling, which is a function of the angle between the dipoles 1 and 2. The other fl terms likewise are the torques between the various dipoles following this notation. r, (t), r2 and r,(t) are the random torques acting on the three dipoles. The solutions of eqs. (7) to (9) would be extremely difficult unless some assumptions could be made. Coffey [ 18 ] has shown that for the three dipoles equal in all respects, i.e. the magnitudes of the interaction potentials are the same and I, =Z2=ZJ, the torsional frequency of the third dipole relative to the second dipole, L2FIR(3_2j in the harmonic approximation is L&(3-2) =3(4&Va, -f P2)“’
(10)
14 August 1987
4. Conclusion New far-infrared broadband absorption has been observed for some dilute solutions of non-rigid ketone molecules in the wavenumber range 220 to 340 cm- I. This absorption is proposed to be the libration counterpart mechanism of the intramolecular rotational relaxation in these molecules.
Acknowledgement We thank Professors B.K.P. Scaife, W.T. Coffey and Dr. G.J. Evans for very useful discussions. Mr. M. Helker is thanked for his help in measurements on the Molecular Laser System.
for (r,(t)
T,(t))
=26,,kZjYZ,6(t),
References
i,j=2,3
[ I ] A. Bud& E. Fischer and S. Miyamoto, Z. Physik 40 (1939)
with a3
=2Z,/(Z,
+I,)
and for I, =zz
=z3
a3=al
(11)
‘I,
(12)
=I
i.e. Q FIR(3-2)
= 3GFIR(,-2)
*
(13)
From the experimental results on non-rigid polar ketone molecules, we find that the torsional frequency for the intramolecular relaxation process is approximately 4.5 times that for the intermolecular process. A possible reason for this discrepancy between theory and experiment is that in practice the three dipoles are unequal and in particular the moment of inertia of the dipole involved in the intramolecular relaxation process is much lower compared to that for the intermolecular process. It seems reasonable to expect QFiR(intramolecular) to be 4.5 &&( intermolecular) if Z3z 4 Z[.
337. [2] K. Higasi, K. Bergmann and C.P. Smyth, J. Phys. Chem. 64 (I 960) 880. [ 31 K. Higasi, Dielectric relaxation and molecular structure, Research Institute of Applied Electricity, No. 9, Hokkaido University, Sapporo, Japan ( 196 1) . [4] C.P. Smyth, Chem. Sot. Special Publication, No. 20. Molecular relaxation processes (Chem. Sot, London, 1966) pp. l-13. [ 51B.K.P. Scaife, private communication. [6] K.S. Co1eandR.H. Cole, J. Chem. Phys. 9 (1941) 341. [7] W.T. Coffey, P.M. Corcoran and J.K. Vij, Chem. Phys. Letters 129 (1986) 375. [ 81 W.T. Coffey, P.M. Corcoran and M. Evans, Proc. Roy. Sot. A410 (1987) 61. [9] F. Marchesoni, J.K. Vij and W.T. Coffey, Z. Physik B61 (1985) 357. [IO] J.K. Vij and F. Hufnagel, Advan. Chem. Phys. 63 (1985) 775. [ 111 J.K. Vij, F. Hufnagel, M. Helker and C.J. Reid, IEEE J. Quantum Electron. QE-22 (1986) 1123. [ 12 ] J.Ph. Poley, J. Appl. Sci. Res. B4 (1955) 337. [ 131 W.T. Coffey, P.M. Corcoran and J.K. Vij, Proc. Roy. Sot. A (1987), to be published. [ 141 A. Gerschel, T. Grochulski, Z. Kisiel, L. Pszeczolkowski and K. Leibler, Mol. Phys. 54 (1985) 97. [ 151 F. Marchesoni and J.K. Vij, Z. Physik B58 (1985) 187. [ 161 P.M. Corcoran and J.K. Vij, Mol. Phys., submitted for publication. [ 171 J. Crossley, J. Chem. Phys. 56 (1972) 2549. [ 181 W.T. Coffey, private communication.
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