www.elsevier.com/locate/molliq

Journal of Molecular Liqu

Study of NMR spin-lattice relaxation mechanism and

mutual viscosity in some substituted alcohols

Anupam Singh, A.K. Singh, N.K. MehrotraT

Department of Physics, Lucknow University, Lucknow-226 007, India

Received 16 April 2003; accepted 10 October 2004

Available online 17 May 2005

Abstract

The present communication reports the experimental values of NMR spin-lattice relaxation time (T1) and dielectric relaxation time (s) ofa-naphthol, h-naphthol, o-aminophenol, benzyl alcohol, phenol, pyrogallol, catechol, and the experimental values of mutual viscosity g12 of

o-aminophenol, m-aminophenol, and p-aminophenol. The correlation of mutual viscosity with dielectric relaxation time (s) of the

compounds investigated leads to the conclusion that mutual viscosity is a better representation of the resistance to the rotation of the

individual solute molecule. The experimental values of T1 have been correlated with calculated values of T1 obtained using various equations

of dielectric relaxation time. It has been concluded that Murty’s equation is a better substitute of dielectric relaxation phenomenon.

D 2005 Elsevier B.V. All rights reserved.

Keywords: NMR spin-lattice relaxation time (T1); Mutual viscosity (g12); Dielectric relaxation time (s)

1. Introduction

The dielectric investigation of relaxation and nuclear

magnetic resonance studies of organic polar complexes

having different dipole bearing groups, provide useful

information about the structure of the molecules. The

dielectric relaxation time is very intimately connected with

the molecular motion and intramolecular interaction in

molecular species.

NMR relaxation time T1 has been used to investigate the

rotational and translational motions and their relations to

molecular structure, size, shape, and intramolecular forces

causing internal friction. The chemical shift of the proton

depends on the various substituent groups at different

positions and is affected when positions of the substituents

are interchanged or when one polar group is replaced by

another one. Therefore, the measurements of chemical shift,

spin-lattice relaxation time, dielectric relaxation time, and

mutual viscosity are important for the study of molecular

structure and intramolecular forces.

0167-7322/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.molliq.2004.10.041

T Corresponding author. Tel.: +91 522 2376230.

E-mail address: apsnmr@yahoo.co.in (N.K. Mehrotra).

Many workers [1–3] calculated the values of T1 from

BPP theory [4] and found that the calculated values ranged

from 1/2 to 1/10 of the experimental values. The possibility

of narrowing the gap between the experimental and the

calculated values stimulated the work reported in this paper.

We also wish to find out for these molecular systems that the

dipole orientation process is due either to molecular or to

both molecular as well as intramolecular rotations [5,6]. The

values of dielectric relaxation time (s) calculated using

Debye equation [7] were found to be nearly 5 to 10 times

the experimental values. This difference between the

calculated and observed values of the relaxation time was

explained by Hill [8], who suggested that the microscopic

viscosity of the solvent (g1) should be replaced by the

mutual viscosity of solute and solvent (g12) which is a

measure of solute–solvent interaction.

2. Materials and methods

The dielectric relaxation times have been determined

using the fixed frequency method of Gopal Krishna for dilute

solutions, using a microwave bench of 3.13-cm wavelength.

ids 121 (2005) 110–114

A. Singh et al. / Journal of Molecular Liquids 121 (2005) 110–114 111

The microwaves were generated by a 723 A/B Klystron and

dielectric constant eV and losses e Wwere determined using the

standing wave technique of Roberts and Von Hippel [9] and

its subsequent simplification by Dakin and workers [10]. The

accuracy in the measurement of dielectric constants and loss

tangents was F5% to F2%, respectively.

Viscosities were measured with an accuracy of F2%

with a Hoppler precision viscometer. This method requires

the determination of time of fall of a glass or a metal ball

between two marks in a glass tube filled with a liquid with

known density. Viscosity of the liquid (gm) is calculated

using the relation gm=F(SK�SF)K, where F is the time of

the fall of the ball in seconds. SK is the specific gravity of

the ball, SF is the specific gravity of the liquid, and K is the

ball constant (=0.009495).

NMR experiments were performed with a Bruker Avance

DRX 200 M Hz FT-NMR spectrometer, equipped with a 5-

mm multinuclear inverse probe head with z-shielded

gradient. For normal proton experiments, typical exper-

imental conditions are as follows.

Flip angle 908, spectral width 4139.073 Hz, data size 32

K; relaxation delay 5 sec; number of transients 8. The FIDs

were line broadened by 0.3 Hz prior to Fourier trans-

formation. The sample concentrations were kept in the range

of 32 to 50 mM.

For T1 experiments the inversion recovery method

(1808–s–908) of Freeman and Hill [11] was used in each

system for the evaluation of nuclear spin-lattice relaxation

time. The time chosen initially was 10 sec which varied in

graduated manner in order to obtain correct phase modu-

lation of the series of NMR spectra in each system so as to

calculate accurately the spin-lattice relaxation time T1

values. The experiments were performed in automation

mode using a standard pulse programme from the Bruker

software library.

All the compounds used were of pure quality obtained

from M/s British Drug House Ltd., England. The percentage

purity of the compounds investigated ranged from 99.8% to

99.9%. Purest quality of deuterated benzene, dioxane, and

heptane obtained from M/s British Drug House were

distilled before use.

3. Theory

Earlier investigations by Meakins [12] and Roberti et al.

[13] on the dielectric dispersion in a number of organic

polar compounds show that there is a big discrepancy

between observed values of relaxation time and those

calculated using Debye’s equation. This discrepancy can

be explained if we use mutual viscosity g12 representing the

interaction between both solute and solvent molecules

instead of solvent viscosity g1. The expression of g12 as

proposed by Hill is given by

gmrm ¼ X 21 r1g1 þ X 2

2 r2g2 þ 2X1X2g12r12 ð1Þ

where gm, g1 and g2 are the coefficients of viscosity of

solution, solvent, and solute, respectively. X1 and X2 are the

mole fractions of the solvent and the solute and the

quantities r represent the average intermolecular distances.

On rearrangement, the Eq. (1) yields

gmrm � X 21 g1r1

X 21 r2

¼ g2 þ 2X1

X2

�r12

r2

�g12

��ð2Þ

This equation represents a straight line, the slope of

which gives the mutual viscosity g12.Bloemberger et al. [4] have derived an expression for the

magnetic relaxation in terms of correlation time (sc) whichis closely related to Debye’s theory of the dielectric

dispersion in polar liquids as discussed in our earlier paper

[14].

NMR spin-lattice relaxation of a single nuclear spin in

a liquid is induced by the fluctuating local magnetic field

of neighbouring spins. If the spin which induces the

relaxation is attached to the same molecule as the relaxing

spin, the fluctuating field is produced by the molecular

reorientational motion. The contribution of this mecha-

nism to the overall T1 is denoted by (T1)rot. If the

relaxation which occurs when relaxing spin and spin

which induces relaxation are attached to different mole-

cules the contribution of this mechanism to overall T1 is

denoted by (T1)trans. Bloemberger et al. have calculated

the probability of induced transition and the equations

thus obtained for (T1)rot and (T1)trans are given in our

earlier paper [15].

4. Results

The chemical shift positions and NMR spin-lattice

relaxation times of various protons of pyrogallol, catechol,

a-naphthol, h-naphthol, benzyl alcohol, and phenol are

given in Table 1. Table 2 shows the values of mutual

viscosity (g12) and the ratios (s/g1) and (s/g12) of ortho-,

meta-, and para-aminophenols. The experimental and

calculated values of dielectric relaxation time s and NMR

spin-lattice relaxation (T1) of these compounds at 293 K are

given in Tables 3 and 4.

5. Discussion

5.1. Chemical shift

In the 1H spectrum of a-naphthol, the peak multiplicity

of the Ha proton is a triplet at lower field region, due to the

presence of the ortho-directing –OH group. The doublet of

the Hb proton is resonating at higher field region, due to

shielding effect. The multiplet of the Hc protons is

resonating at 7.08 ppm. The triplet of the Hd proton is

resonating at slightly lower field region, due to ortho

Table 1

Chemical shift position (d) and NMR spin-lattice relaxation time (T1) of various protons

Polar compound

β-Naphthol

O-Aminophenol

Hd

NH2

OH

Ha

Hb

HcBenzyl alcohol

Ha

C

Hb

Ha

Ha

Ha

Phenol

Hb

Hb

Pyrogallol

Ha

Hb

OH

Hb

Ha

Ha

OH

OH

OH

Hb

Ha

Hb

OH

Hc

Hc

HbHd

Hd

Ha

Hb

Hc

OH

Hc

Hc Hb

Hd

Hb

Ha

Proton Statistical average of NMRspin-lattice relaxationtime T1 (Sec)

Chemical shift(δ) ppm

HaHbHcHd

4.31

8.13 6.09 7.12 7.44

HaHbHcHd

3.79

6.87 7.61 7.35 7.01

HaHbHcHd

4.94

6.75 6.62 6.42 6.30

2.94 HaHb

6.907.15

4.79 HaHb

2.404.50

α-Naphthol

OH

3.59 HaHb

5.206.81

A. Singh et al. / Journal of Molecular Liquids 121 (2005) 110–114112

Table 2

Values of dielectric relaxation time (s), mutual viscosity (g12), and the ratio

(s/g1), (s/g12) for the investigated compounds (viscosity of dioxane at 293

K, g1=1.42 cps)

Polar compounds sExpa (s/g1)�1010 (g12) cps (s/g12)�1010

o-Aminophenol 7.47 5.270 1.469 5.98

m-Aminophenol 7.05 4.980 1.450 4.85

p-Aminophenol 6.22 4.390 1.440 4.30

a Ref. [17].

A. Singh et al. / Journal of Molecular Liquids 121 (2005) 110–114 113

coupling with neighbouring proton. So, we obtain a double

doublet at lower field region due to the increase of electron

density at orthoposition. The peak multiplicity of the Ha

proton of h-naphthol is doublet at higher field region due

to ortho coupling with neighboring proton. The triplet of

the Hd proton resonates at slightly lower field due to the

presence of the neighboring phenolic ring. Similarly, the

triplet of the Hc proton also resonates at lower field region,

which is ortho-coupled with the Hb and Hd protons. The

PMR spectrum of o-aminophenol have complex spectrum

pattern. The Ha proton of o-aminophenol resonates at lower

field region, due to the presence of the ortho-directing –

OH group. The Ha proton is ortho-coupled with neighbor-

ing protons. So, we obtain a triplet at 6.75 ppm. The triplet

of the Hb proton resonates at slightly lower field region,

due to ortho coupling with neighboring protons. The peak

multiplicity of Hd is doublet at higher field region, due to

the presence of the –NH2 group. In the 1H spectrum of

benzyl alcohol Hb protons of –CH2 are slightly shielded.

Hence, we obtain the singlet at 4.50 ppm. The protons of

the aromatic ring resonating at lower field region, due to

deshielding effect. The phenolic proton peak is usually a

sharp singlet, there is no coupling, and its range depends

on concentration dependence of the –OH peak. In the

NMR spectrum, the orthoposition Hb protons of phenol are

resonating at slightly lower field region due to the presence

of the ortho-directing –OH group. The remaining protons

of the phenol ring are resonating at 6.90 ppm. The

statistical average of the overall relaxation time for the

obtained NMR relaxation time for pyrogallol and catechol

can be explained similarly.

Table 3

Values of dielectric relaxation time (s) in 1012 sec at 293 K for compound

studied

Polar compound (s)

Exp Debye Perrin Writz Murty

Pyrogallol 18.30a 91.30 32.86 15.05 18.05

Catechol 16.40a 83.80 30.17 9.81 16.06

a-Naphthol 8.30a 59.18 21.31 8.54 8.42

h-Naphthol 6.64a 56.35 20.28 7.39 6.22

Benzyl alcohol 6.70b 46.68 16.80 7.26 5.44

o-Aminophenol 7.47a 81.24 29.24 10.38 8.12

Phenol 6.17c 25.15 9.05 8.80 7.34

a Ref. [17].b Ref. [18].c Ref. [19].

5.2. Mutual viscosity

The result tabulated in Table 2 shows that the dielectric

relaxation time (s) of aminophenols decreases from ortho

via meta to para compounds. The ratio s/g1 for these

compounds also decreases in the same order as s. But

according to Debye’s theory this ratio s/g1 should remain

constant for molecules of similar size. This anomaly can be

explained if g12, mutual viscosity of the solute and solvent,

is used in place of solvent viscosity (g?). As g12 also

decreases from ortho via meta to para compounds, the ratio

(s/g12) is almost constant. Mehrotra et al. [16] have also

found similar results in the case of some substituted

benzaldehydes.

5.3. Dielectric relaxation time

It is observed from Table 3 that the relaxation time of

phenol is found to be smaller than that of o-aminophenol.

This can be explained on the basis of the intramolecular

interaction to rotation of the –OH group by the neighbour-

ing –NH2 group in the latter molecule while in the case of

phenol the –OH group has greater freedom of rotation round

its bond with the benzene ring resulting in the decrease of its

relaxation time.

The higher value of relaxation time of pyrogallol as

compared to catechol can be attributed to the greater steric

hindrance to the intramolecular rotation of the three –OH

groups resulting in the increase of the relaxation time of the

former molecule.

The relaxation time of a-naphthol is slightly greater than

that of h-naphthol although both are of similar size. This is

probably due to the greater steric hindrance experienced by

the former molecule in molecular and intramolecular

motions.

5.4. NMR spin-lattice relaxation time

It is evident from Table 4 that the values of spin-lattice

relaxation time calculated using the BPP equation are

smaller than the experimental values. Moniz et al. [1] also

agree with the view that BPP treatment gives much smaller

values of (T1), but according to them the discrepancy in

results is due to the time dependence of the rotational

Table 4

Values of NMR spin-lattice relaxation time T1 (in sec.) of 293 K

Polar compound T1

Exp Debye Perrin Writz Murty

Pyrogallol 3.59 2.14 3.16 3.70 3.60

Catechol 3.89 2.32 3.41 4.15 3.88

a-Naphthol 4.31 3.21 4.67 5.46 4.47

h-Naphthol 3.79 3.00 4.15 4.82 3.88

Benzyl alcohol 4.79 3.22 4.19 4.76 4.87

o-Aminophenol 4.94 2.52 3.80 4.66 4.78

Phenol 2.94 2.74 3.16 3.17 2.90

A. Singh et al. / Journal of Molecular Liquids 121 (2005) 110–114114

angular auto-correlation function of these molecules. They

suggested that this time dependence is dominated by

dynamical coherence rather than by the frictional forces

as used in the BPP theory. When Writz and Perrin equation

is used, a better correlation is obtained. This is probably due

to the introduction of the microfriction factor in the

equation.

However, the values of (T1) calculated using Murty’s

equation and the experimental values of (s) are in

quantitative agreement with the experimental values. This

is probably due to the polarizability of molecule used for the

calculation of the dielectric relaxation time s.

6. Conclusion

It is concluded that Murty’s equation is a better substitute

for the correlation time in BPP equation for T1 and mutual

viscosity (g12) is a better representation for inner friction

experienced by the rotating solute molecule. It has been

observed from the structural studies of these molecular

species that the process of dipole orientation is contributed

by both molecular as well as intramolecular rotations.

Acknowledgement

The authors are deeply indebted to Dr. G.P. Gupta,

Professor and Head of the Physics Department for the

encouragement and keen interest throughout the progress of

the work. Thanks are also due to Dr. Raja Roy, Scientist

Incharge, NMR Unit, CDRI, Lucknow, for providing the

experimental facility.

One of the authors (AKS) is thankful to the University

Grants Commission, New Delhi, for the award of a

Research Fellowship during this period of research.

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