Indian Journal of Pure & Applied Physics Vol . 4 1 . November 2003, pp. 858-862

NMR spin lattice relaxation investigation of some molecular systems

and its correlation with dielectric relaxation

S K Vaish, A K Singh, Anupam Singh & N K Mehrotra

Department of Physics, Lucknow University, Lucknow 226 007

Received 22 January 2003; revised 5 May 2003; accepted 7 August 2003

Experimental measurements of NMR spin lattice relaxation time (T1 ) of butanol- I , isopropyl alcohol. 4-bromophenol. o-cresol. m-cresol and p-cresol have been reported. These experimental values of NMR spin-lattice relaxation time (T1 ) have been correlated with the calculated values of the N M R spin lattice relaxation time obtained using various equations for calculating dielectric relaxation time (-r). The calculated values of dielectric and spin lattice relaxation time obtained by using M urty equation [Murty C R K, Indian } Phys. 32 ( 1 958) 580] are i n better agreement with the experimental values.

[Keywords: NMR spin-lattice relaxation time, Chemical shift, Dielectric relaxation time]

1 Introduction

The NMR spin lattice relaxation time of polar molecules is a quantity, which depends upon the various possible mechanisms of energy decay in the medium. NMR spin l attice relaxation time TJ .is used to investigate the rotational and trans lational motions and their relations to molecul ar structure, size, shape and intra-molecular forces causing internal friction. The value of chemical shift of the protons depends on the various substituent groups at different positions and is affected when positions of the substituents are interchanged or one polar group is repl aced by another. The process of dipole orientation is contributed by both molecular as wel l as intra-molecular rotations . S imil ar results have been recent ly observed by Dutta et al.2 and Vyas & Rana3 . Correlation times for dipole-dipole and chemical shift anisotropy relaxation have been studied by Lee & Grutzner4. The TJ studies and the motion of the -OH group in p-chlorophenol have been reported by Marino et al.s. Re-orientational dynamics of molecular l iquids using spin lattice relaxation rates have been observed by Zhang et al.b.

B loembergen et al.7 have derived an expression for the magnetic relaxation in terms of correlation time '[c which is c losely related to Debye 's theor/ of dielectric dispersion in polar l iquids as '[c = '[/3 .

To evaluate '[co they used the value of dielectric

. . 47r rya3 relaxatIOn tIme 't" = , where II i s viscosity of

kT sol vent and a is the radius of solute molecule .

Many workers9- JO have calcu l ated nuclear spin lattice relaxation time from BPP theory and found that, calculated values were ranging from J /2 to 1 1 10 times the experimental value_ The possibi l ity of narrowing the gap between the experimental and calcu lated values, stimulated the work reported here.

2 Theory

The spin l attice relaxation of a single nuclear spin i n a l iquid is induced by the fluctuating local magnetic field of neighbouring spins. If the spin which induces relaxation is attached to the molecule as rel axing spin, the fluctuating field is produced by molecular re-orientational motion _ The contribution of this mechanism to overall TJ is denoted by (TJ )'01' If the spin which induces relaxation and the relaxing spin are attached to different molecules, the contribution of this mechanism to overal l TJ is denoted by (TJ )lrans- Calculating the probabl itity of transition induced, B loembergen et al_7 obtained the expressIOn:

_ . _ ( I )

where

V AISH ef at. :CORRELA TION OF SPIN LATTICE RELAXATION WITH DIELECTRIC RELAXATION 859

. . . (2)

h · h . . tz h w ere y IS t e gyromagnetlc ratIO, = - , Tc IS

2n the correlation time, ro is the sum of inter-proton distances within the molecule and {J)o is the resonance angular frequency.

Kubo & TomitalO modified Eq. 2 and obtained:

-I 3--/tz2 (T1 ) rnt = -2 6 LC

ro . . . (3)

The authors have calculated correlation time, using Debye' s equation8, Perrin ' s modification of Oebye' s equation 1 2, Writz equation J 3 and Murty' s

. 1 d I · 1 4 equatIOn as reporte ear ler .

If it is assumed that BPP model is adequate to account for the translational contribution to the spin lattice relaxation time TI then, express ion for

(TI )��II'\ is given by :

T, -I = 9n2y4tz2T/N

( I ) ,/"{/I/, 1 0kT

where N is the number of molecules per unit volume and 11 is the viscosity of the compound.

3 Experimental Details ·

All the substances used are of pure quality LR grade and have been obtained from Mis British Drug House, England. They have been used after distil lation . The solvents deuterated chloroform and benzene have been obtained from Mis British Drug House, England, and are reported to be of purest qual ity. They were distilled before use.

All the NMR exp�riments were performed on Bruker Avance DRX 300 MHz Ff NMR spectrometer, equipped with 5 mm multinuclear inverse probe head with Z-shielded gradient. The solvents used were either deuterated chloroform or benzene. For normal proton experiments, typical experimental conditions are as follows:

Fl ip angle 900 ; spectral width 39 1 9 Hz; data size 32 k; relaxation delay 5 s; number of transients 8. The FIDs were l ine broadened by 0.3 Hz prior to Fourier transformation. The sample concentration were kept in the range of 32 to 50 m molar.

For T) , experiments inversion recovery sequence ( I 800-t-900) of Freeman & Hill 12 was used in each system for evaluation of spin lattice relaxation time. The t was chosen initially for l O s, which was varied in graduated manner in order to obtain correct phase modulation of the series of NMR spectrum in each system so as to calculate accurately, the TI values. The experiments were performed in automation mode using standard pulse programme from the Bruker pulse programme library .

4 Results and Discussion

The chemical shift positions and NMR spin­lattice relaxation time of various protons of butanol-1 , i sopropyl alcohol, 4-bromophenol, o-cresol, m­cresol and p-cresol are given in Table 1 .

Table 2 shows the experimental and calculated values of the dielectric relaxation time of these compounds at 298 K. The experimental and calculated values of statistical average of NMR spin­lattice relaxation time are given in Table 3 .

The experimental value of NMR spin-lattice relaxation time TI of butanol- l is found to be 2.66 s . By the observation of chemical shift position of each proton in butanol- I , it is observed that, the protons Hb, He and Hd of CHr group show a relaxation time of 2.57, 2.72 and 2.40 s, respectively. The He protons are surrounded by the adjacent CH2- group. S ince free rotation of -OH group hinders the motion of -CH2 group, it takes a longer relaxation time (2.72 s), to come to the state of equil ibrium. The methyl group protons Ha show a greater relaxation time of 3 .06 s. The Mz component of -OH group proton He easily comes into equil ibrium position when perturbed by an exciting field. This decrease in relaxation time of -OH group proton He with TI as 2. 1 3 s, can be attributed to the presence of oxygen atom and the intra-molecular hydrogen bonding between the oxygen and hydrogen atoms. Simi lar results have been obtained by Poschi & Hertzl6 in l iquid n-propanol.

The protons of the two CH3- groups in isopropyl alcohol show a spin-lattice relaxation time of 1 .79 s, which i mplies that, the protons of CH, group take smaller time to come into equi l ibrium posi tion, when they are in i so-configuration, as compared to n-configuration. However, the proton of -OH group shows a larger relaxation time TI of 3 .67 s, due to two adjacent CH3 groups which create h indrance to

R60 I NDIAN J PURE & APPL PHYS, VOL 4 I , NOVEMBER 2003

the -OH group exci tation. The proton He of the carbon at the intermediate position shows a relaxation t ime TI of 1 .84 s. The overall relaxation time T, comes out to be 2 .04 s, showing a decrease as compared to butanol- I .

T3ble I - Chemical shi ft position and NMR spin-lattice relaxation t ime TI of various protons

Compound

Butanol- I C H �a) - CH �)

- CHi' ) - CH�C)OH «)

I soprnpylalcohol OH(b)

'a) I (e) (a) C H,-CH-CH ,

B romophenol OH(oo)

Hlh)*'.:::: H,h,

Hk) . � H'd Br

o-Cresol OH

H(c)*= C:3(a)

H" .) (f)

H(d)

Proton Chemical shift

(ppm)

0.98

1 .47

1 .62

3 . 66

4.45

1 . 24

4.03

4.87

3 .52

5.45

6 .36

2. 1 1

6.57

6.75

6.94

2. 1 4

6.56

6.68

6.73

6.82

6.97

2. 1 8

4.78

6.70

6.95

N M R spin-lattice relaxation

time (TI ) sec 3 .06

2.57

2.71

2.40

2. 1 3

1 .79

3 .67

1 . 84

5.77

5.33

4.96

�.8 1

1 .78

4.53

4.20

2.58

4.79

4.35

4.79

4.64

4.62

3 . 2 1

4.76

5. 1 8

5 .05

It is observed that, the hydroxyl group attached to a benzene ring increases the relaxation t ime. The spin-lattice relaxation time of the protons Hh and He of benzene ring of 4-bromophenol are found to be 5 .33 and 4.96 s, respectively. The increase in relaxation t ime of the proton at the meta position is due to the presence of an electronegative atom bromine, which hinders the excitation and rotation . The phenol ic group proton H" shows a larger relaxation t ime TI = 5 .77 s . It can be attributed to the molecular group rotation .

Table 2 - Dielectric relaxation rime (,r) i n 10- 1 2 s a t 298 K

Compound 'EXP 'DEBYE 'PERRIN 'WRITZ 'MURTY

Butanol- I 5.5* 4 1 .5 1 4.8 1 6 .33 5 . 1 7 Isopropylalcohol 3 .9" 52. 1 9 1 8 .79 8 .7 1 4.32 4-Bromo-phenol 1 4.7* 83 . 2 1 29.95 1 3 .80 1 3 .42 o-Cresol 4.98+ 58.4 2 1 .04 1 0.05 4. 1 2 m-Cresol 5 .86+ 58.09 20.90 9.97 7.42 p-Cresol 7.66+ 58.99 2 1 .23 1 0. 1 8 8. 1 4

*Ref 1 6, "Ref 1 7, +Ref 1 8

Table 3 - NMR spin-lattice relaxation t ime (TI ) i n s at 298 K

Compound TIEXP TIDEDYE TI PERRIN TIWRITZ TIMURTY

B utanol- I 2.66 0.87 2. 1 4 4.02 4.57 IsopropyJalcohol 2.04 0.70 1 .76 3.26 2.33 4-Bromophenol 5.43 0.44 1 . 1 7 1.28 5 . 1 8 o-Cresol 4. 1 0 0.63 1 .62 3 .00 5 .54 m-Cresol 3.86 0.63 1 .63 3 .0 1 3 .76 p-Cresol 3 . 3 1 0.62 1 .6 1 2.98 3.53

The study of CH3- group orientation in 0-, m-, ancl p-cresol shows that, the spin lattice relaxation time of the protons of CH3 group in m-cresol i s smaller, as compared to 0 - and p-cresol . S ince the -OH group present in the benzene ring is ortho and para directing in nature, the relaxation time of the protons at these posi t ions increases. The CH3 protons of the p-cresol show a larger T, as compared to the other two posi tions, hence it can be said that, the Mz component finds itself most convenient to come in equ i l ibrium at meta position, whi le at para position the equ i l ibrium condition i s not easi ly obtained. The -OH group proton shows a relaxation time of 4.79 and 4.76 s in m- and p-cresol respectively. The overal l relaxation t ime of o-cresol 4. 1 0 s is higher, whi le that of p-cresol (3 .3 1 s) i s least, the relaxation time of m-cresol is found to be 3 .86 s. Thus, p-cresol comes very quickly to the equi l ibrium posItIon when perturbed by the magnetic field created by the radio frequency pU lse.

V AISH et al. :CORRELA nON OF SPIN LATTICE RELAXA nON WITH DIELECTRIC RELAXATION 86 1

It has been observed that, the dielectric relaxation time (t) of butanol- I is greater than isopropyl alcohol which is in accordance with the decrease in chemical shift of -OH group proton, from butanol- I to i sopropyl alcohol. Similar vanatJOn of chemical shift for CH3- protons is observed in 0-, m- and p-cresols, where the chemical shift for CH3- proton increases from 0-cresol (2. 1 1 ppm) to p-cresol (2. 1 8 ppm) via m­cresol (2. 1 4 ppm). The dielectric relaxation time 't also increases from o-cresol via m- to p-cresol indicating that, the dielectric relaxation time increases with the increase in chemical shift of the proton of group, largely responsible for dipole orientation process . Mehrotra & Mishra'7 also observed similar variation of chemical shift to the dielectric relaxation time in case of pyrrole, furan and thiophene.

Table 2 shows that, the dielectric relaxation time of cresol increases from ortho via meta to para compounds and NMR spin-lattice relaxation time TI decreases in the same order. This shows that, the freedom rotation of hydroxyl group decreases from ortho via meta to para isomers. The experimental values of dielectric relaxation t ime have been correlated with the calculated values obtained, using Debye equation8, Perrin modification to Debye equation ' 2, Writz equation 1 3 and Murty equation ' . It has been observed that, Murty equation is a better representation of dielectric relaxation phenomenon. Simi lar results were earl ier obtained by Vaish & Mehrotra' R in the case of substituted methanes.

Table 3 shows the experimental and calculated values of NMR spin-lattice relaxation time T, . It is observed that, the values of spin-lattice relaxation time calcu lated using BPP equation are smaller than the experimental values . Moniz9 also agrees with the view that, BPP treatment gives much smaller values of T" but according to them, the discrepancy in the result is due to the time dependence of rotational angu lar auto correlation functions of these molecules. They suggested that, this time dependence is dominated by dynamical coherence rather than by frictional forces as used in BPP theory.

When Perrin ' s modification IS used 111 calculation for T" a better correlation has been obtained in the case of butanol- I and isopropyl alcohol . The calculated values of T, obtained using

Writz & Sperional 1 3 equation are nearer to observed TI values for isopropyl alcohol, m-cresol and p­cresol . The values of T, calculated using Murty' s equation are i n good agreement with the experimental values except for butanol - I and 0-cresol.

However, any discrepancy which still remains between the calculated and experimental values ofT, can be explained due to the fact that, dielectric relaxation equations are valid for dilute solutions, whereas the spin-lattice relaxation t ime has been determined in pure l iquid state of these compounds.

Acknowledgement

The authors are deeply indebted to Dr G P Gupta, Professor and Head of Physics Department for the encouragement and continued interest throughout the work. Thanks are also due to Dr Raja Roy, Scientist-in-Charge, NMR Unit, CDRI, Lucknow, for providing experimental faci l ity.

One of the authors (AKS) is thankful to the University Grants Commission, New Delh i , for the award of a research fellowship during this period of research.

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