Molecular reorientation of liquid trimethylchlorosilane from 13C, 29Si and 35 Cl FT NMR relaxation studies

MOLECULAR

24 June 1983

CHEMICAL PHYSICS LETTERS

Volume 98. number 3

REORIENTATION

OF LIQUID TRIMETIIYLCHLOROSILANE

FROM *3C, 2gSi AND 3%1 FT NMR RELAXATION

STUDIES

Werner STOREK Cetttral Institute of Physical Chemistv of the Academy of Sciences of the CDR. DDR-1199 Berlin. German Democratic Republic Received 20 April 1983

13C and *‘Si spin-lattice relaxation times and nuclear Overhauser enhancement factors and 35Cl quadrupole relasation times of neat liquid trimethylchlorosilane have been measured at four different temperatures. Under the assumptions of isotropic reorientation of a spherical molecule and of the validity of the extreme narrowing condition, the results of current NMR relaxation theories and molecule reorientation models have been applied for the interpretation of the experimental data.

1_ Introduction

spin rotation relaxation time TlsR. To obtain more information on the molecular reorientation processes,

(B. = 2.35 T) equipped with a Nicolet 1085 computer for data aquisition and processing. T, was measured by the (180“- t-90”-t,,---5Ti) pulse sequence with broadband proton noise decoupling. For determination of NOE values, the normal single pulse FT and the NOE-suppress gated decoupling techniques with a minimum delay of lOT, were used. T, and NOE measurements were repeated several times for each temperature. The experimental reproducibility was t- 10% for T1 and f 15% for NOE. As impurity, small amounts of hexamethyl disiloxan (~5% by volume) were present in the sample_ Oxygen was removed by bubbling dry nitrogen gas through the liquid sample for about ten minutes and after that the sample tube (8 mm OD) was sealed. For field frequency lock the deuterium or fluorine resonance of C,D, or CF3COOH in a sealed capillary was used.

especially on activation energies EA, temperature-dependent measurements have been performed.

The measured viscosity and density data were approximated in the temperature range 287-325 K by

Nuclear-spin relaxation can be a powerful tool for the investigation of the tumbling motion and internal rotation of molecules. The molecular dynamics may be characterized by correlation times and diffusion constants. As probes for the investigation of the microdynamic behavior of liquid (CH&3iCl, the nuclear spins of 13C, 2gSi and 35C1 and their spin-lattice relaxation times TI were used. Nuclear Overhauser enhancement factor vx measurements are needed for separation of the two relaxation mechanisms, which contribute to T1 for 13C and 29Si nuclei in small molecules. These are the dipole-dipole relaxation time

TID which arises from dipole-dipole

interactions

be-

tween protons and carbon or silicon atoms, and the

the two equations 2. Experiment

log(q/mPas)

and calculations

= - 1.9857

+ 440.5

K/T

and Spin-lattice relaxation time Tl and NOE measurements on neat liquid (CH,),SiCl were performed on a JEOL PFT 100 high-resolution FT NMR spectrometer 0 009-2614/83/0000-0000/$03.00

0 1983 North-Holland

dg/cm3

= 0.8158 - 0_00194(T-

A non-linear

least-squares

program

273.15)

K-l

_

[ 1] was used for 267

Volume 96. number 3

24 June 1983

PHYSICS LETTERS

CHEMICAL

the determination of Tl from peak heights of a set of at least twelve individual measurements for different delay times t. The software for the solution of the Woessner equation for anisotropic rotational diffusion [2] and for the various least-squares procedures was written in the NIC-assembler language for the instrument c0111putcr. The temyersture was maintained to an accuracy of better than K! K within the measuring time of a full dats set for the estimation of T1. Temperature changes of the sample by radiofrequency heating from high-power proton decoupling were corrected. The temperature m the probe-head was checked with 3 Wilmad Co. thermometer inside a sample tube. which WIS filled with C,D6_ The Tlq values were estimated from the j5C1 NRlR absorption signals measured on a Bruker KR 322 s spectrometer in the FT mode at 5.7 MHz with an accurxy better thau 25%_

3. Results and discussion

peratures were calculated from the half-width Avl/z of the 35Cl absorption line T,q

= ll”AV,/z

-

(4

The values of Tla

and 7c are given in table 1_ The value of 7c = 2 ps at 298 K agrees well with the result tram infrared and Raman studies of Reich et al_ [4]. The validity of the hydrodynamic Stokes-Einstein-

Debye equation (5). modified by Gierer and Wirtz [s’] by introduction of the microviscosity factorf. = 0.14 for pure rotational reorientation, could be verified from these measurements byf, = 0.15 determined by ‘C = (4nqa3/3kT)fr

.

(5)

Here is LIthe effective molecular radius, which may be obtained from the molecular volume V, for the cubic closest-packing case. Then $‘V~n’a~ = O-741/, . where 11’~ is Avogadro’s constant, h- is the Boltzrnann constant and q is the macroscopic dynamic viscosity. The geometric parameters are given in ref. [6]. Using the x test after Wallach and Huntress [7]. it is possible to characterize

In the limit of extreme nsrrowing (OTC 4 I_ where w = 15:~~~ is the Lrnior frsquency) the 35C1 spin--13lticc relaxation time T, o for molecules with isotropic rotation is rtlatcd to the rotational correlation time TC by [3]

T;:i=

(1)

III which I = 3,P is the nuclear spin for ‘5C1. czqQ/h is the nuclear electric coupling constant and B’ is the ztsynimetry parJmcter_ The quJdrupole resonwce frequency vQ for a nucleus with I = 312 is [3] VQ = i( 1 + ;q ”-)

1!2,2yQ/I,

=

5/siT’“;)

T,()

(3

.

(3

whtxe UQ = 16.465 hlllt WJS measured j’CI in (C113)3SiCl [3]_ Un&r the assumptions

at 77 K for

that VQ does not change

with the temperature and the spin-spin relaxation time TZQ = T~Q the values of T~Q at different tem268

ertia (or in general the trace of the tensor of inertia) and the factor A (A = 1,3/5,3x/9), usually cited in the literature, depends on the method of estimation principle or other apof ‘free from the equipartition prosimation procedures for the correlation function of a free rotator. With A = 3/5, preferred by Gillen and Noggle [8] and others.

x = 7(-/7frce = (5/l 8D)(~T/Ieff)1/~

9 1,

(61

with 7C = 1/6D,

,

so

7c

roughly the molecular motion by comparing 7c with the reorientation time of the classical free rotator calculated by Tfree = A&r/kT)ljZ_ Jeff * is the effective moment of in-

(7)

where D is the isotropic rotational diffusion constant. Therefore D characterizes the tumbling motion of the whole moIecule_ The values of D determined by eqs. (3) and (7) from 35Cl NMR correspond well (see tabIe 1) to the values of II,, which were obtained from macroscopic viscosity and density data. For this purpose eqs. (5) and (7)

‘l,ff=

341.5 X 1040g:m2

was calculated for (CH,)3SiCl.

Volume 98. number 3

CHEhIICAL

PKYSICS

24 June 1983

LFTI-TERS

were used under the microdynamic approximation [81 . Further the mean angle 6 = 26.5258”/~ turned per collision was calculated [8] _The results in table 1 show that the motion of (CH,),SiCl molecule after the criteria of Wallach and Huntress [7] is not pure rotational and that at the highest temperature inertial effects dominate the motion. The activation energy EA for the molecular overall motion was estimated from an Arrhenius plot by linear regression. The result is E-4 = 7.8 i 1.3 kJ/mol_ This value may be compared with EA = 8.9 kJ/mol from Qr values. 3.2. _79Sirelaxatiolz The two most important l9Si relaxation mechanisms for small molecules like trimethylchlorosilane are characterized by TED and TlsR which can be separated by the equations

T-1

= T-1

1SR

1

_ T-1 1D

(with *pi = -2 52) from measured T1 and NOE values. The TlD and TlsR values are in table 1. The results show that spin-rotation relaxation dominates

expressions T&

for this molecule_

Hubbard

for the spin-rotation

relaxation

= 2kTZ~,,(2nC,,,)‘7,,~fi’

and a connection rSRr= = Z,,+kT,

between

[9]

derived

two

rate: (10)

TSR and TC: (11)

where TSR is the spin-rotation correlation time l_ couZeff and Ceff are the inertial and spin-rotation pling constants, for spherical molecular symmetry (or in first approximation for lower symmetry). The VaheS Of TSR calculated from eq. (11) with rc from jsC1 NMR data [eq. (3)] are in table l_ Again 7SR = 0.07 ps at 298 K is in good agreement with the value of 0.1 ps for the angular momentum correlation time obtained by Reich et al. [4] for the same molecule. Substituting TSR in eq. (10) yields 112 Ceff(Hz) = @/2’rZe,,)(3r,/T,,.) (12) l

d h

The combination of eqs. (5) and (1 I) yields TSR = Ieff/ 8aqn3fr and for fr = 1 it is possible to determine the lower limit of TSR from macroscopic viscosity measurements.

269

CHEMICAL

Volume 98. number 3

PHYSICS

For 295 I<. Cerf = 2.3 liHz. Spin-rotation coupling constants are seldom estimated. Values of C for 2gSi derived from molecularbe.nn studies or chemical shift anisotropy measurements in solid state NMR could not be found in the literature. After Flygare and Goodisman [lo] and Deverell [ 1 I] it is possible to estimate spin-rotation coupling constants from the paramagnetic part of the nucltar screening up_ For molecules with high molecular symmetry (spherical or symmetric top) UP = (A-+/~x)3zeffC0

= 3h-(X)Z&Ce

.

(13

wherr h-* = G/l ‘rmhfpp~

x 1044 kg-’ = 2.7796 and all quantities have their usual meaning. It iollows for esample i;(’ H) = 6.5295 X 1 036. K(tsC) = 2.5966 X 1037. K(2gSi) = -32864 X 1O37 and A-(“9Sn) = -1.7515 X 1O37 kg-l m-’ s. From eq_ ( 12) the sign of the spin-rotation coupling constant cannot be determined. but this is possible from ccl. (13). Usu~llv or, is neglttivc and the sign of the rigbthand side of cq. (13) is directed by the sign of K(X). which depends on the sign of the gyromagnetic ratio of nucleus S. Consequently. the sign of Ccrf for 29Si 1x1-2 T-1

must be positive. If up IS AIIOWII for any srlicon compound. then on(S) for another molecule with the same nucleus CJII Iw determined from their known 29Si NhlR chemical shifts S (ppn;) after the relation o,,(S)

+ S(S)

= ul,(reference)

+ S(reference)

.

(19

\i itb the \.~lues of u,(SiH4)

= -327.7 ppm and u,,((Cfl~)_~S1) = --32S.7 ppm from ab initio calculatmns and the 6 v.rIues cited in the review of hlsrs1ii~1111 1121. u,((CHj);SiCl) = -SSS.Z or -450.3 ppm. respectivcl> , and C, = 1.06 or 1.34 ~HL. Such dtfferenccs between the calculated spin-rotation couplmg constants after the two methods were also observed by other authors for other nuclei [ 1 I]. But wnb the published value of Briguet et al. [13] for u,,(llSiCl,) = -643 ppm. it follows that C = 2 kHz m accordance wit11 C,,,. 2%_:. l;C

relax-atiotr

13~the same procedure tion times T, D and T,,,

used for ‘gSi, were separated

the relaxaby experi-

T1 and NOE measurements (here r$ = 1.988). In this way many compounds involving a methyl group have been studied. From T,, arising from the C-H dipolar interaction

mental

in the methyl group an effective can be computed again according

correlation to

T,-d = 3010/4n)‘(ti2~~?/~~_~)~=

time rc

.

(1%

or rc = 15.526/T,,(s)

ps

(16)

for a “standard” methyl group with ‘C-H = 0.109 nm for the C-H bond length and ~,,/47r = 10m7 H/m_ Under appropriate conditions 7c can be related to the intramolecular motion of the methyl group. The methyl group must be attached to a molecule with C,, symmetry or greater and the molecular geometry

in relation to the axis of the rotational sor must be known.

diffusion

ten-

In this case the theory of Woessner [2] may be applied. Two possible mechanisms are usually discussed for the internal motion of the methyl top superimposed on the motion of the whole molecule_ One model of the methyl top reorientation is a

random jumping process among equivalent positions characterized by a number r (for example r = 3 means a jumping mechanism among three positions separated by an angle of 120”) and the jumping rate DJ _ On the other hand, a small-step brownian rotation diffusion mechanism is proposed. characterized by the inner rotation diffusion constant Oi_ The Woessner equation for the anisotropic analysis of the methyl rotation was used in the notation given by lambert et al. [ 141 with a slight modification. l/2 outside the parentheses with the nine summands was put in the angle-dependent expressions _4i. Bi and Ci (i = 1,2,3). Then these terms

The factor

agree with the notation of Collins et al_ [ 151 and the identity Cf’- t (Ai + Bi + Ci) G 1 follo\vs for all values of the angles (Yand 19. Here cos (Yis the direction cosine of the methyl top axis relative to the principal axis and cos 19 is the direction cosine of the C-H bond relative to the internal methyl top axis. For (CH,),SiCl it follows under the assumption of tetrahedral symmetry, that Q = 9 = 109.47” [6]. Further with D, = Dz = D for isotropic overall motion of the molecule, it is possible to find explicit expressions for the estimation of Di or DJ from Woessner’s

770

24 June 1983

LETTERS

equation.

It follows

that

CHEMICAL

Volume 98, number 3

24 June 1983

PHYSICS LETTERS

Table 2 13C relaxation time and NOE values and data for the characterizlltion in liquid (CHs)aSiCl

of the intramolecular

methyl group reorientational

T (I;)

TI (9

aC

TI D (s)

7.1 SR (s)

TC (PS)

10 -‘* Di

298 311 317 324

12.1 14.4 15.0 16.0

1.50 1.30 1.22 1.17

16.0 22.0 24.4 27.2

49.3 41.6 38.8 38.9

0.97 0.71 0.65 0.57

2.98 5.39 6.08 6.99

(S)

10-l’

motion

DJ (jumps/s)

4.82 a) 8.45 9.51 10.93

a) Calculated for a three-fold Jumping mechanism.

DJ = 110(1

-

6D@/r[6D~~

-(A1

+B,

+C,)]

(17)

It is easy to see from the general Woessner equation, and also from eq. (17) that rDJ is a constant for ah possibIe jumping mechanisms between equivalent sites, if all other quantities in the Woessner equation are not changed. This behavior has two consequences. Firstly, if DJ is calculated for an r-fold jumping mechanism, then 0; for an r’-fold jumping mechanism can be found. 0; = (r/r’)DJ_ Secondly, the calculated activation energy for jumping mechanisms with different r values is a constant and independent of r, if EA is estimated from a In OJ versus T-1 plot. An explicit expression for Di is more complicated and not given here, because the general Woessner equations were solved with a computer program. The estimated values of Tl. Tl D. TISR, qc, TV, Di and OJ for a three-fold jumping mechanism are given in table 2. The corresponding activation energies were estimated from an Arrhenius plot: E_~i = 27.6 i 3.8 kJ/mol and EAJ = 25.7 2 3.3 kJ/mol. These values for the two models are not very different, in accord with results of other investigations [ 141. But they are different from the values EAi = 7-S + 0.8 kJ/mol and EAJ = 6.3 + 0.8 kJ/mol, found as mean values at different temperatures from a conventional relationship of the form Di = Dioexp(-E,,/kT)

,

where Di, = (kT/Imethyl)l’Z

(18) = 5 X 10”

T1/2 was

chosen for a free rotating methyl top [ 141. After Zens and Ellis [ 161 with EAi = (Tls~ - 25.61)/2.338, it follows that at 311 K, EAi = 6.7 kJ/mol for TlsR = 41.6 s. But this estimate depends critically on the errors in the measured TlsR value.

From infrared measurements Spangenberg [ 171 found for a three-fold jumping mechanism between equivalent sites a barrier energy of EA J = 8.7 kJ/mol, which corresponds better with the value from eq. (18). From semi-empirical calculations Spangenberg [ 181 found E-4 J = 11 kJ/mol. Successive changes of the angles (+2”), of rc values (210%) and of the diffusion constants (D2 = D -t 0.1, D, = pDz with p = 0,O.S and 2) have no significant influence on the calculated activation energies_

Acknowledgement I tha;.!; Dr. S. Grande from the Sektion Physik der Karl-Mars-Universitat Leipzig, who kindly measured the 35C1 FT NMR spectra and Dr. Th. Steiger for the calculation of the tensor of inertia. The author is indebted to Mr. W. Altenburg for his technical assistance in acquisition of the experimental data and to Mr. D. ReWat for the viscosity and density data of (CH&SiCI.

References 111 XI. Sass and D. Ziessow, J _alasn. Resort. 25 (1977) 263. [2] D.E. Woessner, B.S. Snowden Jr. and C.H. Meyer, J. Chem. Phys. 50 (1969) 719. 131 E-A-C_ Lucken. Nuclear quadrupole coupling constants (Academic Press, New York, 1969). 14) P. Reich, A. Reklat, G. Seifert and Tb. Steiser, Acta Phys. Polon. A28 (1980) 665. [S ] A. Gierer and Kc. Wrtz, 2. Naturforsch. 8a (1953) 532. [6] L-E. Sutton, ed.. Tables of intemtomic distances and configuration in molecules and ions (The Chemical Society, London, 1958).

271

Volume

98. number

CHE!bllCAL

3

[ 71 D. Wallach and W.T. (1969) 1219. [ 8 ] K:T. Gillen and J Ii. 801. [9] P.S. Hubbard. PII>,. [ 101 W.H. Flygare and J. (196s) 3122.

Huntress No@,

Jr-. J. Chern.

272

50

J. Chexn. Ph) s. 53 (1970)

Rek. 131 (1963) 1155. Goodisman. J. Chem. Phgs. 49

[ 1I 1 C. De\erell. Mol. Phys. 18 (1970) 112)

Phys.

319. 11. .\l.wx~~ann. in: N.\lR basic principles and progress. \‘ol. 17,cds. P. Diehl, E. Flu& and R. Kosfcld (Springer. Berlin. 1981).

PHYSICS

LETTERS

24 June

1983

[ 131 A. Briguet. J-X_ Duplan and J. Delmsu. J. Phys. (Paris) 36 (1975) 897. [ 141 J.B. Lambert. R.J. Nienhuis and J.W. Keepers, Anger. Chem. 93 (1981) 553. [ 151 S.W. Collins, T-D. Alger, D-31. Grant. K.F. Kuhlmann and J.C. Smith. J. Phys. Chem. 79 (1975) 2031. [ 161 A.P. Zens and P.D. Ellis, J. Am. Chem. Sot. 97 (1975) 5685. [ 17 ] H.-J. Spansenbeg. 2. Physih. Chem. (Leipzg) 132 (1966) 271. [ 1 S] H.-J. Spangenberg. Thesis (Dr. SC.), HumboldtUnhersitZt Berlin (1968). _