Determination of anisotropic rotational diffusion constants of cyclohexane from raman linewidths and NMR T1 data

Volume 83. number 2

DETERMINATION

CHEhIICAL

OF ANISOTROPIC

FROM RAMAN LINEWIDTHS

PHYSICS

ROTATIONAL

15 October I981

LETJO-ERS

DIFFUSION

CONSTANTS

OF CYCLOHJXANE

AND NMR T1 DATA

Kazutoslu TANABE National Ckmicai Laboratory for Industry, Tsukuba, Ibaraki 305. Japan Recened

12 June 1981

Isotropic and amsotropic Raman lmewdths of the ~2, ~3. ~3. “5 and ~6 modes of cyclohevane and cycloheuane-dlz are measured m the hquid state. RotatIonal dift’bon constants for rotations around the C2 and C3 axes are determined by combmmg Raman lmewdth and NMR Tt data. The results show fight anisotropy in the rotational motion of liquid cydoheuane.

1. Introduction RotatIonal morlon of cyclohexane molecules in the liquid state has recewed considerable attention m relation to dynamic properties III the plastic crystal phase. Numerous works hake so far been devoted to reveal the rotational motion of cyclohexane molecules m the liquid and sohd states from anayses of lineshapes or lmewidths in vi&rational, NMR or neutron scattenng spectroscopy [l-17]. Andrew and Eades [3] concluded from the measurement of the NMR spin-lattice relaxation times that, below the transition pomt (186 K), molecules rotate only about their C3 axis whrle, above the temperature, molecules are able to rotate about other axes besides the C, axIs. The rota?lonal diffusion constant IS an important quantity to identify the rotational motions of a molecule about different molecular axes. The cyclo-

In this study, for the purpose of determining D, and Dz in liquid cyclohexane, Raman linewidtts of several alg bands of cyclohexane and cyclohexaned12 have been measured at room temperature, and analysed with the aid of NMR TI data obtained previously.

2. Experimental Raman spectra were obtamed with a Japan SpecCompany model R800 laser Raman spectrophotometer and a Coherent Radiation model CR8 argon Ion laser operating at 5 14.5 run. Parallel In(v) and perpendicular I,(v) polarized components of Raman spectra were recorded wirh a C&m-Thomson pnsm as an analyser, and isotropic I,(v) and anisotropic I,#) components were obtained using troscopic

hexane molecule has a D3, symmetry, thus two kmds of rotational diffusion constats are defined in cyclohexane. D, for the rotatlonal (tumbling) motion around the C2 (x) axis, and Dz for the rotational (spinning) motion ar0ur.d the C3 (z) axis. From the

&W =~,,W -ZWJ),

fact that the plastic crystal phase IS observed in “globular” molecules [S] , isotropic rotational motion of cyclohexane has often been assumed. However, the rotational diffusion constants of cyclohexane have not been determined experientally.

where 6, IS the true (corrected) Raman linewidth (fwhh), 6, the apparent (observed) Raman linewidth (fwhh), and S the spectral slit width [ 181. Raman linewidths were measured at room tempera-

0 009-2614/81/0000-0000/S

02.75 0 1981 North-Holland

$(“)

= IL(V) -

(1)

slit width effect on the observed Raman linewdth was corrected according to The fiite

6, = b,[l

-

6/fg21 3

ture for the v2 (2852 cm-l),

(2)

v4 (1157

cm-t),

v5 397

folume 83. number 2

CHEMICAL

PHYSICS

802 cm-l) and u6 (383 cm-l) bands of cycle lexane and for the v3 (1117 cm-l), u4 (1012 cm-l), p5 (723 cm-t) and v6 (298 cm-l) bands of cyclolexane-dl,, in the liquid state. Lmewidths of the )ther alg bands could not be measured because of xtremely low intensities of their perpendicular comlonents. Sample of cyclohexanc-dt2 was purchased ‘ram Merck, Sharp and Dohme of Canada Ltd., and lsed without purification because no unpunty Raman land was observed_

1. Results

and discussion

,

T = (3 co&J - 1) 2 + 3 s&9 co& e SD, + D, 240,

(3)

(6)

(4)

sults, the followmg

pomts

may be mentloned

these rehere.

Fust, the D, and D, obtamed show shght anisotropy m the rotational motion of the cyclohexane molecules III the hquld state. The isotropic rotational

hnewdths, and calculated rotational dxffunon constants Dx of qclohexane

Molecule

Mode (cm-‘)

6, (cm-’ )

6p (cm-‘)

&

G+12

"2 (2852)

va (1157) us (802) +j (383)

9.2 1.4 1.6 9.6

f f + *

0.2 0.1 0.1 0.2

17.0 = 8.8 f 9.6 + 17.2 5

0.8 0.3 0.3 0.8

0.122 0.116 0.126 0.119

5 f * *

0.013 0.005 0.005 0.013

vg (1117) uj (1012) us (723) v6 (298)

1.9 2.4 2.5 9.1

= 2 f f

0.1 0.1 0.1 0.3

9.7 10.0 10.6 17.3

f 1.1 It 0.7 f 0.5 + 0.4

0.122 0.119 0.127 0.129

i f f +

0.017 0.011 0.008 0.008

C&E

398

By using the 7e data determmed from the NMR T1 relavation times obtamed by O’Retiy et al. [ 121, and the D, deterinmed as above, D, has been calculated. The results are green in table 2. From

0, values determined from eqs. (3) and (4) are pven m table 1. Although the observed isotropic or arusotroplc F&man Lmewldths tifer from one band to another. nearly the same values of 0, are obtamed from dlfThe

Table 1 Observed isotropic 6, and amsotrop~c 6~ Raman cyclohexane4,z

+2 Sldtl 43Wx+4Dz’

(5) where 13IS the angle between the molecular symmetry a_ws (z aus) and the prmcipal axis of the electnc field gradlent tensor at the nucleus. Smce the cyclohexane molecule has axlaI (0 = 0”) and equatorial (6 = 108.S”) protons or deuterons, the observed correlation tune m cyclohexane is given as [ 171

where the rotatlonal lmewldth 6 R u determmed from the lsotroplc 6, and amsotroplc sp Raman lmerndths (fwhb). as 5R=GP-ija.

15 October 1981

ferent Raman bands. Tlus seems to suggest that the effect of the vlbratlon-rotation couphng 1151 might be neghglble m cyclohexane, and that the obtamed values ofD, are reliable. Thus the D, has been determined from these data to be 0.121 f 0.005 ps-’ for cyclohexane and 0.124 + 0.005 ps- I for cycle+ hexane-d12. The rotational diffusion constant D, for spinrung motion around the C3 axis can be determined by using the method developed by GIlen and Cnffiths [20]. For symmetnc-top molecules where the dynamics of the molecular rotation can be described by rotational dtifuslon, the rotational correlation tune 1s gven as follows [21] -

Observed Raman hnewdths of cyclohexane and :yclohexane-dlz are gwen m table I_ Cyclohehane was a D,, symmetry, and the vlbrationa! modes of the Raman bands measured m this experiment belong to the totally symmetnc species alg_ The rotational Imewdth 6, of these Raman bands thus gives the rotatIonal diffusion constant D, for tumbhng motion around the C7 a..~ 1191 D, = i&R

LETTERS

@s-*1

and

CHFMICAL PHYSICS LEXrERs

Volume 83, number 2

Table 2 Rotational correlation time rg, tumbling Dx and spinning D, rotational dlffuson constants of cyclohevane and cyclehexane-dlz Molecule rg (ps) a) C6HlZ

CsDlz

1.27 * 0.15 1.28 + 0.08

Dx @s-l)

D, @s-l)

0.121 5 0.005 0.124 + 0.005

0.175 + 0.029 0.189 5 0.018

a) Taken from ref. [ 121. motion of cyclohexane was assumed or concluded III some of earlier studies. Egelstaff [9] assumed nearly Eotroplc rotational diffusion constants (D, = 0,) m his analysis of neutron- and light-scattering data. Bartoh and Lltovitz [ 1 I] discussed the drfference in the rotational lmewldths of cyclohexane obtained by RothscUd [22] and by Rakov [5], and showed that these results can be reconciled only by assuming that the rotatlonal motion of cyclohexane is highly anisotropic. They concluded that this assumption is however mconsistent with the data obtamed by themselves, and that the rotational diffusion III cycIohexane is appro?rimately Isotropic. Zeldler [ 141 analysed the deuteron relaxation data by assuming an isotropic rotational diffusion constant. The results obtained in the present study shed light on the confusmg situation m the anisotropy of the rotational motion of ~clohexane molecules_ That is. the rotational motion of iiqwd cyclohexane is not hi&ly but slightly anisotropic, and the amsotropy IS slgmficant beyond the experimental uncertainties. The anisotropy ratio Dz/DX (1.4 for cyclohexane, and 1.5 for cyclohexane-dl,) obtamed here seems reasonable when compared with those in other molecules (2-O for benzene [23], 10 for acetonitnle and acetorutrile-d3 [24]). Second, the results Bven in table 2 indicate that the rotational dlffuslon constants for cyclohexane and for cyclohexane-d12 are equal to each other within the experimental uncert8mties. JYhis gives support to the assumption of equal angular momentum correlation times for cyclohexane and cyclohexanedi2 employed in the paper of Amdt and McClung 1171. The NMR spin-lattice relaxation times and linewidth data obtained by Andrew and Eades [3] suggest that, below 150 K, the rotational motion of cyclohexane (solid n) is frozen, 1-e. D, = D, = 0,

15 October 198t

between 150 and 180 K, molecules rotate around the C, axis, i.e. D, = 0,0, > 0, and above 186 K, moIecules (solid I or liquid) are able to rotate around the C2 ax~s, I.e. D, > 0, and D, > 0. The abrupt changes in Raman linewidths between 78 and 193.5 K observed by Schulz [ 131 correspond to the changes in the values of these rotational diffusion constants D, and Dz. However, since the Raman bands whose linewidths showed such drastic changes in the above temperature range belong to degenerate symmetry species, D, and D, cannot be determined separately. According to the results obtamed previously for cyclohexane m the plastlc crystal or solid phase, the separate determination of D, and Dz in the temperature range between room temperature and 150 K seems of much sigmficance m the discussion of dynamic properties of plastic crystal cyclohexane in relation to the problem of the isotropy in the rotational motion of molecules. The method of determinmg Dx and Dz from Raman hnewidth and NMR Tl data as employed in the present study may reveal details on molecular levels of rotational motions for various solid molecules showmg plasticity.

References [I] G.B. Carpenter and RS. Halford. J. Chen Phyr 15 (L947) 99. [2] E.R Andrewand R.G. Eades, Proc. F’hys. Sot. Condo=) A65 (1957-j 371.

131 E-R Andrewand RG. Eades. Proc Roy. Sac. A716

(1953) 398. 141 kV. Fkkov, Opt

Specb-y_ LO (1961) 377_ 151 A-V. Rakov, Opt. Spectry. 13 (1962) 203. [61 hf. Ito. Spectrochim. Acta 21 (19637 2063. 17) Yud. Zab~yakm and N.G. BAshi&, Opt. Spectry. 24 (1968) 539. [8] L.k de Graaf, Physica 40 (1969) 497. [9] P.A. Egelstaff, J. Chen Phyr 53 (1970) 2590. [lo] W.G. Rothschild, J. Chem Phys. 53 (1970) 3265. [ 1 l] FJ. Bartoli and T.A. Litowz, J. Chem Phyr 56 (1972) 40-s. [ 121 D.E. O’ReiUy, EM. Peterson aad D.L Hogenboom, I. Chea Phys. 57 (1972) 3969. [13] J. Schulz, 2. Naturforsch. 29a (1974) 1636. [ 141 M.D. &idler, in: Molecular motions in liquids. e4 I. Lasccmbe (Reidel, Dordrecht, 197-?) p. 421. [ 151 A.M. Amorim DaCosta, hlk Norman and J.ELtR Clarke,

MoL Phys. 29 (1975) 191. [ 161 hLL_ Bansal and AP. ROY, Chem, Phys. Letters 50

(1977) 513.

Folume 83, number 2

CHEhflCAL PHYSICS LJSIERS

171 R Amdt and RE.D. h~cclung, J. Chem. Fhys. 70 (1979)

5598.

181 K- Tanabe and J. Jhxh, Speckohm. Acta 36A (1980) 341. 191 LA. Nafie and W.L. Pehcolas, J. Chem. Phys. 57 (1972) 3145. 201 K.T. Gilten and J.E. Gtiiths, Chem. Phys. Letters 17 (1972) 359.

[21 J W.-T. Hnntress

15 October Jr., Ad-.

Magn.

Resos,

[221W.G.Rothschifd, J.~e~~~s.49(~968)

4 C1970)

1981 1.

2250.

[7_3] KTanabe, Chem. Phys. Letters 63 (1979) 43. f24] K. Tanabe and J. Iiimkhi, Spectrochia Acta 36A (1980) 665.