NMR spin-lattice relaxation time and activation energy in some molecular systems

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1 Indian Journal of Pure & pplied Physis Vol. 45, February 7, pp 8-7 NMR spin-lattie relaxation time and ativation energy in some moleular systems jay Kumar Singh * & N K * Physis Department, Bareilly College, Bareilly 43 Physis Department, Luknow University, Luknow 7 * ajaykumar3@rediffmail.om Reeived June ; revised 8 November ; aepted Deember The experimental values of NMR spin-lattie relaxation time (T ) of N-butylamine, di-isopropylamine, N, N, N- tributylamine, N, N- dimethylformamide, N, N- dimethylaetamide have been reported. The experimental values of T have been orrelated with the alulated values of T obtained using various equations of the dieletri relaxation time (). It has been onluded that Murty s equation is a better representations of the dieletri relaxation phenomenon. The values of ativation energy ( E ) obtained using dieletri relaxation time have been orrelated with alulated values obtained using rrhenius equation of NMR spin-lattie relaxation time (T ) for these ompounds. Keywords: NMR, Spin-lattie relaxation time, tivation energy IPC Code: GJ 3/8 Introdution The dieletri investigation of relaxation and nulear magneti resonane studies of organi polar omplexes having different dipole bearing groups provides useful information about the struture of the moleules. The dieletri relaxation time is very intimately onneted with the moleular motion and intramoleular interation in moleular speies,3. NMR spin-lattie relaxation time (T ) has been used to investigate the rotational and transnational motions and their relations to moleular struture, size, shape and intramoleular fores ausing internal frition. The value of hemial shift of the proton depends on the various substituent groups at different positions and is affeted when positions of the substituents are interhanged or one polar group is replaed by another. Therefore, the measurements of hemial shift, spin-lattie relaxation time (T ) and dieletri relaxation time () are of paramount importane to study the moleular struture and intramoleular fores. Bloembergen et al 4. have derived an expression for the magneti relaxation in terms of the orrelation time ( ), whih is losely related to Debye s theory 5 of the dieletri dispersion in polar liquids, aording to whih the dieletri relaxation time is given by: 4πη a 3... () kt where η is the visosity of solvent and a is the radius of solute moleule. Many researhers -8 have evaluated the spin-lattie relaxation time (T ) from Bloembergen, Purell and Pound 4 (BPP) theory and found that the alulated values of T range from / to / times the experimental values. For narrowing the gap between the experimental and alulated values of T, we have used different models of dieletri relaxation. Writz and Sperinol, elaborating Perrin s 9 idea, modified the Debye equation to the form given by: 3 3 4πη a a a () kt a a where a i M i.55 πdi N / 3 i,... (3) where M i are moleular weight and d i are density of moleules and a and a are radius of solute and solvent moleules, respetively. Murty has found a simple empirial equation for as :

2 SINGH & MEHROTR: NMR SPIN-LTTICE RELXTION TIME 9 πη α... (4) ( ε + )kt where α is the polarizability of the solute moleule and ε is the dieletri onstant of the solvent. Theory The spin-lattie relaxation of a single nulear spin in a liquid is indued by the flutuating loal magneti field of neighbouring spins. If the spin that indues the relaxation is attahed to the same moleule as the relaxing spin, the flutuating field is produed by the moleular reorientational motion. The ontribution to this mehanism to the overall T is denoted by (T ) rot. If the relaxation ours when the relaxing spin and the spin that indue relaxation are attahed to different moleules, are denoted by (T ) trans. BPP 4 have alulated the probability of the indued transition and thus, obtained the expression. ( ) ( T ) + ( T ) T (5) where ( T ) rot rot trans 4 3γ η r + w + + 4w where γ is the gyromagneti ratio, η h π (), h is Plank s onstant, r the sum of the interproton distanes within the moleule, and ω is the resonane angular frequeny. Kubo and Tomita modified Eq.( ) and obtained : 4 3γ η rot r ( ) T (7) The orrelation time ( ) required in Eq. (7) is losely related to the dieletri relaxation time (), of Debye s theory of dieletri dispersion in a polar liquid as : (8) 3 We have alulated the orrelation time using Debye s equation 5, Perrin s modifiation to Debye s eqution 9, Writz and Sperinol equation and Murty s equation. In order to test the validity of Eqs (5,9,,), different values of (T ) rot have been obtained using different values of. ssuming that BPP model is adequate to aount for the translational ontribution to the spin-lattie relaxation time (T ), the expression for (T ) trans is given by : 9π γ η ηn T trans (9) kt ( ) 4 where N o is the number of moleules per unit volume and η is the visosity of the ompound. The molar volume V m of moleules was determined from equation: M V m () D where M and D are moleular weight and density of moleules, respetively. Debye s volume (V D ) has been alulated using the Debye equation and the experimental values of relaxation time (): 4πη a 3 kt where η is the visosity of the solvent moleule. whih gives kt V D () 3η The alulated values of free energy of ativation for dieletri relaxation ( F ) are nearly equal to free energy of ativation for visous proess ( an assume approximately, equations 3. exp T and F RT Fη RT F Fη Fη ). So we in Eyring s () η B exp (3)

3 7 INDIN J PURE & PPL PHYS, VOL 45, FEBRURY 7 Simplifying Eqs () and (3), we get: BT η hn where B Vx Therefore V X hnt (4) η From Eq.(4), V x has been alulated. In order to ollet information about the volumes taking part in dipole orientation, the molar volume V, the volume V D alulated from the Debye s equation and the volume V x whih ours in the expression of onstant B in the equation of rate proess have been alulated for some of the investigated ompounds. Dieletri relaxation mehanism an be explained in terms of absolute rate theory 3 by treating dipole orientation as a rate proess in whih the polar moleules rotate from one equilibrium position to another. This proess of rotation requires an ativation energy ( E ) suffiient to overome the potential barrier and separating the two mean equilibrium position and is given by exp( E / RT )... (5) T h where is frequeny fator. The energy of k ativation ( E ) is alulated from the slope of the plot of log T against (/T). The ativation energy ( E ) has also been evaluated using rrhenius theory of rate proess. The orrelation time ( ) for the moleular motion an be written in terms of ativation energy ( E ) whih is given as : E oexp... () RT where o is frequeny fator. The NMR theory developed by BPP shows a relation between the spin-lattie relaxation time (T ) and orrelation time ( ) as : T C for ω ο <<... (7) where C is a onstant fator, ω o πν o and ν o is the resonant frequeny. The energy of ativation ( E ) an be obtained from the temperature variation of log T and is given by 4 : logt E.33R... (8) (/ T ) On substituting value of T using Eqs (4,5 and 7) in Eq. (8), we get: E.33R 3πγ η T k αη (ε + )r πν η (9) 4 3 Experimental Details ll the ompounds used are of the pure quality LR grade and have been obtained from M/s British Drug House, England. They have been used after distillation. The solvent; deuterated benzene has been obtained from M/s British Drug House; England and are reported to be of the purest quality. They have been distilled before use. ll the NMR experiments were performed on Bruker vane DRX MHz FT-NMR spetrometer, equipped with 5mm multinulear inverse probe head with Z-shielded gradient. For normal proton experiments typial experimental onditions are follows: Flip angle 9, spetral width Hz; data size 3k; relaxation delay 5 se; number of transients 8. The FIDs were line broadened by.3 Hz prior to Fourier transformation. The sample onentration was kept in the range 3 5 m molar. For T experiments inversion reovery method (8-9 ) of Beker et al 5. was used in eah system for evaluation of spin-lattie relaxation time. The time was hosen initially for s, whih varied in graduated manner in order to obtain orret phase modulation of the series of NMR spetrum in eah system so as to alulate aurately the spin-lattie relaxation time T values. The experiments were performed in automation mode using standard pulse programme from the Bruker software library.

4 SINGH & MEHROTR: NMR SPIN-LTTICE RELXTION TIME 7 Table Dieletri relaxation time, NMR spin-lattie relaxation time and moleular volumes at 98 K N-butylamine Di-isopropyl amine NNN tributyl amine NNdimethyl formamide NNdimethyl aetamide Dieletri relaxation Expt * 53 time ( )( - se) Debye Perrin Writz Murty Spin-lattie Expt time (T )(se) Debye Perrin Writz Murty Moleular volumes Molar ( -4 ) Debye Calulated (V x ) + Ref., * Ref. 7 Table Values of ativation energy for investigated ompounds Compounds E (lit)(kal/mol) E (kal/mol) uthor s work N butylamine Di isopropyl amine N,N,N-tributylamine N, N dimethyl formamide 4.5 * 5.3 N, N dimethyl aetamide 5.3 *.5 + Ref, * Ref 7 4 Results The experimental and alulated values of NMR spin-lattie relaxation time (T ) and dieletri relaxation time () of N-butylamine, Diisopropylamine, N,N,N- tributylamine, N,N - dimethylformamide, N,N - dimethylaetamide are given in Table at 98K. Molar volume, Debye Volume and Eyring s volume of these ompounds are given in Table 3. Table 4 presents the values of ativation energy of these ompounds. 5 Disussion 5. Dieletri relaxation time From Table, it is lear that dieletri relaxation time of amines inreases from N-butylamine to N,N,N-tributylamine via Di-isopropylamine. This an be explained on the basis of greater hindrane experiened by the seondary amine moleule as ompared to primary amine moleule. This interation is still greater in the ase of a tertiary amine moleule as it ontains three interating alkyl groups resulting in the highest relaxation time of the moleule. The dieletri relaxation time of N, N-dimethylaetamide is greater than dimethylformamide whih is in onformity with Debye theory as former moleule has greater size than the later. The values of alulated using Debye equation are found to be muh greater than the experimental values. When Perrin s modifiation is used, a better orrelation has been obtained. The alulated values of using Writz and Sperinol equation are more nearer to observed values of. The values of alulated using Murty s equation are found to be in quantitative agreement with the experimental values. It is, therefore, onluded that Murty equation is a better representation to the proess of dipole orientation. 5. NMR spin-lattie relaxation time The values of NMR spin-lattie relaxation time, alulated using BPP equation are smaller than the experimental values (Table). The disrepany in the theoretial and experimental values of the spin-lattie relaxation time (T ) is due to Debye s value of used in the BPP equation, whih is valid only for the spherial moleules. The main soure of the shortoming of BPP formula lies in the evaluation of the rotational ontribution to the spin-lattie of the relaxation time, whih is muh smaller than the experimental relaxation time. Moniz 8 also agree with the view that the BPP treatment gives muh smaller value of T. However, aording to them the disrepany in the results is due to time dependene of the rotational angular auto-orrelation funtion of these moleules. They suggested that this time dependene is dominated by the dynamial oherene rather than by fritional fores, as used in the BPP theory.

5 7 INDIN J PURE & PPL PHYS, VOL 45, FEBRURY 7 When the equation of Writz and Sperinol is used, a better orrelation is obtained. This is probably due to the introdution of a mirofrition fator in the equation. However, the values of T alulated using Murty s equation are in lose agreement with the experimental values. This an be explained due to the polarizability of the moleules used to alulate the dieletri relaxation time (). 5.3 Volumes The molar volumes are nearly -3 times of the Debye volume (Table ). The disrepany between the two values of the volumes may be due to the fat that the molar volumes are different from the volumes for dipole orientation. This disrepany an be explained by onsidering the ratio (V D /V M ), whih will be same as that of the mirosopi to marosopi visosity. However, the volumes V x alulated using the rate proess equations of Eyring are found to be in better agreement with the values of molar volumes. 5.4 tivation energy From Table, it is lear that the values of ativation energy obtained using NMR spin-lattie relaxation time are found to be in good agreement with the values obtained using absolute rate theory. This shows that Murty s equation for dieletri relaxation time is the appropriate substitute for orrelation time in BPP equation for NMR spinlattie relaxation time. knowledgement The author is deeply indebted to Dr Raja Roy, Sientist in-charge, NMR unit, CDRI, Luknow, for providing the experimental faility. Referenes Madhurima V, Sobhnadri J&Murty V R K, Indian J Pure & ppl Phys, 4 (4)837. Kumar S, Sharma D R & Thakur N, Indian J Pure & ppl Phys, 44() 4. 3 garwal S & Bhatnagar D, Indian J Pure & ppl Phys, 43 (5) 4. 4 Bloembergen N, Purell B M & Pound R V, Phys Rev, 73(948) Debye P, Polar Moleules (Chemial Catalogue), 99, p- 9. Vaish S K & Mehrotra N K, sian J Phys, 9 () Singh, Singh K& Mehrotra N K, Bull Chem So Jpn, 77 (4). 8 Moniz W B, Steele W & Dixon J, J Chem Phys, 38 (93) Perrin F, J Phys Radium, 5 (934) 497. Writz K & Sperinol, Z Naturforsh, 8 (953) 5. Murty C R K, Indian J Phys, 3 (958) 58. Kubo R & Tomita K, J Phys So Jpn, 9 (954) Glasstone S, Laider K J & Eyring H, The Theory of Rate Proess, (MGraw Hill Co, In, New York), 94, p ng T T & Dunell B, Can J Chem, 5 (974) Beker E D, Ferretti J, Gupta R K & Weiss G H, J Magn Reson, 37(98) 38. Srivastava H N, Studies of relaxation times employing mirowave tehniques, Ph. D. Thesis, Luknow University, Mishra C K, Study of relaxation phenomenon and moleular motions in dilute solution under mirowave field, Ph. D. Thesis, Luknow University, (979).