ids 133 (2007) 17–21www.elsevier.com/locate/molliq

Journal of Molecular Liqu

Study of activation parameters and NMR spin-lattice relaxation timein some substituted amines

Anupam Singh ⁎, N.K. Mehrotra

Department of Physics, Lucknow University, Lucknow-226007, India

Received 26 October 2005; accepted 10 May 2006Available online 18 September 2006

Abstract

The present communication reports the experimental values of NMR spin-lattice relaxation time (T1) and dielectric relaxation time (τ) ofpiperidine, pyrrole, pyridine, diethylamine, triethylamine and pyrrolidine. The values of activation energy (ΔEA) obtained using dielectricrelaxation time, have been correlated with calculated values of ΔEA obtained using Arrhenius equation of NMR relaxation time (T1) for pyridine,diethylamine and pyrrole. Authors have also established a correlation between the experimental values of NMR spin-relaxation time (T1) with itscalculated values obtained using different equations of dielectric relaxation time (τ).© 2006 Published by Elsevier B.V.

Keywords: NMR spin-lattice relaxation time (T1); Dielectric relaxation time (τ); Activation parameters (ΔEA)

1. Introduction

NMR spin-lattice relaxation investigation of organic polarcompounds provide valuable information about the dipole–dipole interaction, spin rotational interaction between thenuclear magnetic moments and the magnetic fields producedat the positions of the nuclei by the rotation of the molecule.Both rotational and translational motion arise due to perturba-tion of collisions from time to time. Many collisions take placeduring the time a molecule takes to turn around or move througha distance.

Bloembergen et al. [1] have derived an expression for thenuclear magnetic relaxation which is closely related to Debye'stheory [2] of dielectric dispersion in polar liquids as reported inour earlier paper [3].

Many workers [4,5] have calculated nuclear spin-latticerelaxation time from the BPP theory and found that thecalculated values were ranging from 1/2 to 1/10 times of theexperimental values. In the present work the authors havemodified the BPP equation by using Murty's equation in placeof Debye equation. We also wish to find out for these molecular

⁎ Corresponding author.E-mail address: ajaykumar301@rediffmail.com (A. Singh).

0167-7322/$ - see front matter © 2006 Published by Elsevier B.V.doi:10.1016/j.molliq.2006.05.002

systems whether the dipole orientation process is contributed byoverall molecular rotations [6,7].

2. Experimental

NMR spectra were recorded in deuterated benzene anddioxane at 20 °C temperature using a Bruker Avance DRX200 MHz FT-NMR spectrometer equipped with a 5 mmmultinuclear inverse probe head with Z-shielded gradient.Chemical shifts are measured on the δ-scale.

1H NMR spectrum was recorded with flip angle 90°, spectralwidth 4139.07 Hz; Data size 32 K; relaxation delay 5 s; numberof transients 8. The FIDs were line broadened by 0.3 Hz prior toFourier transformation. The sample concentrations were kept inthe range of 32 to 50 mM.

For T1 experiments the inversion recovery method (180°–τ–90°) ofBecker et al. [12]was used in each system for evaluation ofthe spin-lattice relaxation time. The time was chosen initially for10 s which varied in graduated manner in order to obtain correctphase modulation of the series of NMR spectra in each system soas to calculate accurately the spin-lattice relaxation timeT1 values.The experiments were performed in automation mode using thestandard pulse programme from the Bruker software library.

All the compounds used are of pure quality obtained fromM/s British Drug House Ltd. England. The percentage purity of the

Table 1Chemical shift position (δ) and NMR spin-lattice relaxation time (T1) of various protons

Polarcompound

Proton Chemical shift (δ) ppm The statistical average of NMR spin-lattice relaxation time T1 (s) Structure

Piperidine Ha 3.90 1.04

Pyrrole Ha 6.60 3.50

Hb 6.09

Pyridine Ha 8.29 3.86

Hb 6.77Hc 7.15

Pyrrolidine Ha 4.49 5.94

Hb 0.96

Diethyl amineHa 2.58 3.76

Hb 1.08

Triethyl-amineHa 2.42 6.64

Hb 0.95

18 A. Singh, N.K. Mehrotra / Journal of Molecular Liquids 133 (2007) 17–21

Table 3Values of dielectric relaxation time (τ) (in 10−12 s) at 293 K for compoundstudies

Polar compounds τ

Exp Debye Perrin Writz Murty

Pyrrole 5.98 76.69 17.61 12.50 6.02Pyridine 7.30+++ 72.20 25.99 11.11 7.32Diethylamine 2.50⁎⁎⁎ 54.90 19.70 8.80 4.30Triethylamine 9.20oo 82.60 29.74 19.10 9.30Piperidine 5.19⁎⁎ 105.99 38.16 15.53 5.20Pyrrolidine 12.43⁎⁎⁎ 89.04 32.18 13.05 12.53

+++ Ref. [18].⁎⁎⁎ Ref. [20].oo Ref. [19].⁎⁎ Ref. [21].

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compounds investigated ranged from 99.8% to 99.9%. Purestquality of deuterated benzene and dioxane obtained fromM/s B.D.H. was distilled before use.

3. Theory

Dielectric relaxation mechanism may be explained in terms ofabsolute rate theory [9] by treating dipole orientation as a rateprocess in which the polar molecules rotate from one equilibriumposition to another. This process of rotation requires an activationenergy (ΔEA) sufficient to overcome the energy barrier separatingthe two mean equilibrium positions and is given by

s ¼ ATexp

DEA

RT

� �ð1Þ

where A=h /k is the frequency factor.The activation of energy has also been evaluated using Arrhe-

nius's theory [10] of rate process. The energy of activationΔEA is

sc ¼ soexpþDEA

RT

� �ð2Þ

Here τc is correlation time and τo is frequency factor.On rearrangement the Eq. (2) yields

DEA ¼ 2:303RT logsosc

� �ð3Þ

Kubo and Tomita [10] established a relation betweencorrelation time (τc) and NMR spin-lattice relaxation time (T1)

ðT1Þ−1 ¼ 3g4Qh2

2r60sc

� �rot

þ 9k2g4Qh2g2N10kT

� �ð4Þ

where correlation time τc is related to dielectric relaxation timeτ by the expression

sc ¼ s3

ð5Þ

Murty [11] has derived an equation for dielectric relaxationtime (τ) which is given by

s ¼ 6kg1aðeþ 2ÞkT ð6Þ

hence

sc ¼ 2kg1aðεþ 2ÞkT ð7Þ

where symbols have their usual meaning.

Table 2Activation parameters for investigated compounds

Polar compound ΔEA (lit)(kcal/mol)kK/mol) ΔEA Author's work(kcal/mol)

Pyridine 3.02+ 3.41Diethylamine 2.63o 1.71Pyrrole 2.20⁎ 1.77

⁎ Ref. [17].+ Ref. [15].o Ref. [16].

The energy of activation ΔEA can be obtained from thetemperature variation of log T1 with absolute temperature T asgiven below.

DEA ¼ 2:303RBlogT1Bð1=TÞ

� �ð8Þ

On substituting the value of T1, Eq. (8) yields

DEA ¼ 2:303RT1

d3kg4Qh2

kag1

ðeþ 2Þr60þ kNg2

5

� �ð9Þ

where γ is the gyromagnetic ratio and r0 is the sum of theinterproton distances within the molecules. α is the polariz-ability of the compound and ε is dielectric constant of thesolvent. N is the number of molecules per unit of volume. η1and η2 are the coefficient of viscosity of solvent and solute,respectively.

4. Results

The chemical shift position and NMR spin-lattice re-laxation time of various protons of piperidine, pyrrole, py-ridine, diethylamine, triethylamine and pyrrolidone are givenin Table 1. Table 2 shows the values of activation energy(ΔEA). The experimental and calculated values of dielectricrelaxation time (τ) and NMR spin-lattice relaxation time (T1)of these compounds at 293 K are given in Tables 3 and 4,respectively.

Table 4Values of NMR spin-lattice relaxation time T1 (in s) at 293 k

Polar compounds T1 Exp T1 Debye T1 Perrin T1 Writz T1 Murty

Pyrrole 3.50 2.77 9.06 10.50 3.48Pyridine 3.86 2.35 3.25 3.72 3.75Diethylamine 3.76 0.67 1.73 3.38 5.57Triethylamine 6.54 2.92 4.86 5.60 6.53Piperidine 1.04 3.29 4.34 4.37 1.02Pyrrolidine 5.94 3.12 3.87 3.89 5.91

20 A. Singh, N.K. Mehrotra / Journal of Molecular Liquids 133 (2007) 17–21

5. Discussion

5.1. Chemical shift

The NMR spectrum of piperidine gives a multiplet signal. Thenitrogen atom attached to the ring of piperidine is influenced byother hydrogen nuclei. So, Hc proton resonates at lower fieldregion.The spin-lattice relaxation time (T1) is the statistical averageof overall relaxation time. The Hb proton of pyrrole is resonated atlower field region. The peak multiplicity of Hb is multiplet, due toquadrupole broadening effects associatedwith nitrogen atom causethe NH absorption band. The low field shift of the Hc proton ofpyridine has been explained in terms of the magnetic anisotropiceffects of nitrogen atom and intramolecular electric field effectassociated with the local dipole moment from the nitrogen lonepair. The peak multiplicity of remaining protons is multiplet in thehigher field region. Similarly the two ethyl groups Hb proton ofdiethylamine have the same chemical environment and hence theyresonate at lower field region. The remaining six Hb protons of themethyl group give a resonance signal at higher field region. Hb

protons of triethylamine are resonated at lower field region. Hence,we obtain a triplet signal, due to (n+1) rule. The remaining Ha

methyl protons are resonated at higher field region. In pyrrolidine,the singlet of theHa proton resonates at lower field region, which iseffected by the nitrogen atom. The meta Hb proton resonates athigher field region, due to ortho coupling with neighbouringprotons. The statistical average of overall relaxation time forobtaining NMR relaxation time for pyrrole, pyridine, diethyla-mine, triethylmaine and pyrrolidine can be explained similarly.

5.2. Activation parameters

Activation energies and enthalpies of activation calculatedusing NMR spin-lattice relaxation time are found to be in goodagreement with the values obtained using absolute rate theory.This shows that Murty equation for dielectric relaxation time isthe appropriate substitute for correlation time τc in BPP equationfor NMR spin-lattice relaxation time. Pyridine has the highestvalue for the free energy of activation for both dielectric re-laxation and NMR relaxation mechanisms and pyrrole exhibitsthe lowest value. This can be attributed to the fact that the formermolecule experiences the maximum resistance in dipolarrotation, whereas the latter experiences the least steric hindrance.It has been observed from Table 2 that activation energy fordipole orientation increases with size and shape of moleculeswhich is in accordance with the results obtained by Smyth andGrub [13]. The most probable enthalpies of activation are lessthan the corresponding free activation energies.

5.3. Dielectric relaxation time

It is observed from Table 3 that the dielectric relaxation time τof pyridine is be larger than that of pyrrole which is in accordancewith the increase of its molecular size. Similarly the relaxationtime (τ) of triethylamine is greater than that of diethylaminewhichshows that the former molecule experiences greater sterichindrance in rotation. This also shows that the process of dipole

orientation in most of the molecular species investigated iscontributed by the overall molecular rotation only.

5.4. NMR spin-lattice relaxation time

It is evident from Table 4 that the values of spin-latticerelaxation time calculated using the BPP equation are smaller thanthe experimental values. Moniz [4] also agrees with the view thatthe BPP treatment gives much smaller values of T1, but accordingto them the discrepancy in results is due to the time dependence ofthe rotational angular auto-correlation function of these mole-cules. They suggested that this time dependence is dominated bydynamical coherence rather than by frictional forces as used in theBPP theory; when Writz and Sperinol equation [14] is used abetter correlation is obtained. This is probably due to theintroduction of the microfriction factor in the equation.

However, the values of T1 calculated using Murty's equationand the experimental values of τ are in quantitative agreementwith the experimental values. This is probably due to thepolarizability of molecules used for the calculation of dielectricrelaxation time.

6. Conclusions

The close agreement between the experimental and calcu-lated values of activation energy confirms our assessment thatthe Murty equation is a better substitute for correlation time (τc)in the BPP equation for NMR spin-lattice relaxation time (T1). Ithas been observed from the structural studies of these molecularspecies that the process of dipole orientation is contributed byoverall molecular rotations.

Acknowledgements

The authors are deeply indebted to Dr. G.P. Gupta, Professorand Head, Physics Department, for the encouragement and keeninterest throughout the progress of the work. Thanks are alsodue to Dr. Raja Roy, Scientist In charge, NMR Unit, CDRI,Lucknow, for providing the experimental facility.

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