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 N M R 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 N M R 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: N M R 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 translational
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 replaced by another. The process of dipole
orientation is contributed by both molecular as wel l
as intra-molecular rotations. Simil ar results have
been recently 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 closely related to Debye's theor/
of dielectric dispersion in polar liquids as '[c '[/3 .
To evaluate '[co they used the value of dielectric
.
47r rya 3
, where II is viscosity of
kT
solvent and a is the radius of solute molecule.
Many workers9- J O have calcul ated nuclear spin
lattice relaxation time from B PP theory and found
that, calculated values were ranging from J /2 to
1110 times the experimental value_ The possibility of
narrowing the gap between the experimental and
calculated values, stimulated the work reported here.
relaxatIOn tIme
't" =
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 overall TJ is
denoted by (TJ )lrans- Calculating the probablitity of
transition induced, Bloembergen et al_7 obtained the
expressIOn:
_ . _( I )
=
where
V AISH ef at. :CORRELATION OF SPIN LATTICE RELAXATION WITH DIELECTRIC RELAXATION
. . . (2)
.
.
w h ere y ·IS t h e gyromagnetlc ratIO,
tz = h ,
2n
Tc
IS
the correlation time, ro is the sum of inter-proton
distances within the molecule and {J)o is the
resonance angular frequency.
Kubo & Tomita l O modified Eq. 2 and obtained:
-I
( T1 )rnt
=
3--/tz2
2 ro
6
LC
. . . (3)
The authors have calculated correlation time,
using Debye' s equation8 , Perrin ' s modification of
Oebye' s equation 12, Writz equation J 3 and Murty' s
.
1
· 1 4.
equatIOn as reported earI 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'\
T,
-
I
( I ) ,/"{/I/,
is given by :
=
9n2 y4tz2T/N
1 0k T
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
k; relaxation delay 5 s; number of transients 8.
The FIDs were line broadened b y 0.3 H z prior to
Fourier transformation. The sample concentration
were kept in the range of 32 to 50 m molar.
32
859
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 spin­
lattice relaxation time of various protons of butanol1 , isopropyl alcohol, 4-bromophenol, o-cresol, m­
cresol and p-cresol are given in Table 1 .
Table 2 shows the experimental and calculated
values of the d ielectric relaxation time of these
compounds at 298 K. The experimental and
calculated values of statistical average of NMR spin­
lattice 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 o f 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 equilibrium. 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 & Hertz l6 in
l iquid n-propanol.
The protons of the two CH3- groups in i sopropyl
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 equ i 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 hindrance to
I NDIAN J PURE & APPL PHYS, VOL
R60
the -OH group excitation. The proton He of the
carbon at the intermediate position shows a
relaxation time 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 shift position and N M R spin-lattice
relaxation time TI of various protons
Proton
Compound
Chemical
shift
(ppm)
NMR
spin-lattice
relaxation
ti me ( TI ) sec
Butanol- I
C H �a) - C H �)
0.98
3 .06
1 .47
2.57
- C H i') - C H �C)OH «)
1 . 62
2.71
3 . 66
2.40
4.45
2. 1 3
1 . 24
1 .79
4.03
3 . 67
4.87
1 . 84
3.52
5.77
5.45
5.33
6.36
4.96
I soprnpylalcohol
OH(b)
'a)
I
(e)
C H,-CH-C H ,
(a)
*
.
*= :
B romophenol
H lh)
H k)
'.::::
�
H,h,
H 'd
Br
o-Cresol
OH
H (c)
C 3( a)
H " .)
It is observed that, the hydroxyl group attached
to a benzene ring increases the relaxation time. 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 time of the proton at the meta position is
due to the presence of an electronegative atom
bromine, which hinders the excitation and rotation.
The phenolic group proton H" shows a larger
relaxation time TI 5 .77 s. It can be attributed to
the molecular group rotation.
Table 2
(f)
2. 1 1
�.8 1
6.57
1 .7 8
6.75
4.53
6.94
4.20
H (d)
2. 1 4
2.58
6.56
4.79
6.68
4.35
6.73
4.79
6.82
4.64
6.97
4.62
2. 1 8
3.2 1
4.78
4.76
6.70
5. 1 8
6.95
5 .05
-
Compound
=
Dielectric relaxation rime (,r) i n 1 0 - 1 2 s a t
Butanol- I
Isopropylalcohol
4-Bromo-phenol
o-Cresol
m-Cresol
p-Cresol
*Ref
1 6,
Table
O H (oo)
4 I , NOVEMBER 2003
3
-
298 K
'EXP
'DEBYE
5.5*
4 1 .5
1 4.8 1
6.33
5. 1 7
3 .9"
52. 1 9
1 8 .79
8.7 1
4.32
'PERRIN
'WRITZ
'MURTY
1 4. 7 *
83 . 2 1
29.95
1 3 .80
1 3 .42
4.98+
58.4
2 1 .04
1 0.05
4. 1 2
5 .86+
5 8 .09
20.90
9.97
7.42
7.66+
5 8 .99
2 1 .23
1 0. 1 8
8. 1 4
"Ref 1 7, +Ref
18
N M R spin-lattice relaxation time ( TI ) i n s at
Compound
B utanol- I
IsopropyJalcohol
4-Bromophenol
o-Cresol
m-Cresol
p-Cresol
TIEXP
298 K
TI DEDYE TI PERRIN TI WRITZ TI MURTY
2.66
0.87
2. 1 4
4.02
2.04
0.70
1 .76
3.26
2.33
5.43
0.44
1.17
1.28
5. 1 8
4. 1 0
0.63
1 . 62
3 . 00
5 . 54
3.86
0.63
1 . 63
3 .0 1
3 . 76
3.3 1
0.62
1 .6 1
2.98
3.53
4.57
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 is
smaller, as compared to 0 - and p-cresol. Since the
-OH group present in the benzene ring is ortho and
para directing in nature, the relaxation time of the
protons at these positions increases. The CH3
protons of the p-cresol show a larger T, as compared
to the other two positions, hence it can be said that,
the Mz component finds itself most convenient to
come in equilibrium at meta position, while at para
position the equilibrium condition is not easily
obtained. The -OH group proton shows a relaxation
time of 4.79 and 4.76 s in m- and p-cresol
respectively. The overall relaxation time of o-cresol
4. 1 0 s is higher, while 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
equilibrium posItIon when perturbed by the
magnetic field created by the radio frequency pUlse.
VAISH et al. :CORRELA nON OF SPIN LATTICE RELAXA nON WITH DIELECTRIC RELAXATION
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 0cresol (2. 1 1 ppm) to p-cresol (2. 1 8 ppm) via m­
cresol (2. 1 4 ppm). The dielectric relaxation time 't
also increases from o-cresol via m- to p-cresol
indicating that, the d ielectric relaxation time
increases with the increase in chemical shift of the
proton of group, largely responsible for dipole
'7
orientation process . Mehrotra & Mishra 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 time have been
correlated with the calculated values obtained, using
Debye equation 8 , Perrin modification to Debye
13
equation ' 2, Writz equation 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 &
'R
Mehrotra in the case of substituted methanes.
Tab le 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
9
the experimental values . Moniz 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
molecu les. 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 I S 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
86 1
13
Writz & Sperional equation are nearer to observed
TI values for isopropyl alcohol, m-cresol and p­
cresol . The values of T, calculated using Murty ' s
equation are i n good agreement with the
experimental values except for butanol - I and 0cresol.
However, any d iscrepancy which still remains
between the calculated and experimental values of T,
can be explained due to the fact that, dielectric
relaxation equations are valid for d ilute solutions,
whereas the spin-lattice relaxation time 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 Del h i , for the
award of a research fellowship during this period of
research.
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