Rotational Relaxation and Chemical Exchange

Anderson, James E.; Fryer, Peter A.

doi:10.1063/1.1671627

Cited by 50 publications

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“…This approach is applied to the derivation of equation (1) and its analogue for T~. Some of the results of [2][3][4][5] are re-derived and in some cases made more general. Finally we consider case (iv) above in some detail.…”

Section: Introductionmentioning

confidence: 99%

“…In a number of papers [2][3][4][5] it has been pointed out that in deriving (1) the presence of chemical exchange of the same order of magnitude in rate as the diffusional motion has been neglected. Such a fast chemical exchange has the potential for shortening the correlation times in the expression for Tll , since if exchange occurs before rotation of the molecule has taken place a speeding up of the interaction causing relaxation is obtained.…”

Section: Introductionmentioning

confidence: 99%

“…Case (i) was considered by Marshall [2] under the condition that there is no correlation between sites on exchange; (ii) was treated by Anderson and Fryer [3] under the assumption of complete correlation on exchange; (iii)was considered first by Beckert and Pfeifer [4] and more thoroughly by Hertz [5], in both cases under rather general conditions. All these derivations [2][3][4][5] start from the assumption that the relaxation time is inversly proportional to an integral over a correlation function, and the effect of chemical exchange is introduced implicitly in this correlation function. In the present paper a different method of handling the chemical exchange is proposed.…”

Section: Introductionmentioning

confidence: 99%

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Nuclear magnetic relaxation induced by chemical exchange

Wennerström¹

1972

Molecular Physics

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A new method of treating chemical exchange in nuclear magnetic relaxation theory is proposed. The essence of the method is to introduce the exchange in the spin hamiltonian by writing H=;f~(t)H~, where ft(t) is a function of time and has the value unity if the nucleus considered is at site i at time t, and zero otherwise. The method is applied to cases where the chemical exchange is faster than the relaxation. Some previously derived results are re-derived and in some cases made more general. The case of very fast intramolecular exchange is also considered. l. INTRODUCTIONNuclear magnetic relaxation is an important technique for obtaining a detailed picture of the microdynamic properties of fluid systems. Many problems of chemical significance, such as association phenomena and exchange processes, have been treated successfully with this method. It is assumed that the relaxation is caused by a time-dependent interaction, with zero time average, between the nuclear spin system and the lattice. The relaxation in a liquid phase is usually caused by a time-dependent brownian diffusional motion. In the standard derivations of relaxation times it is found that the spin-lattice relaxation time T 1 is inversly proportional to a correlation time of molecular motion in the case of extreme narrowing. It has also been found [1] that if the nuclei studied exchange between different sites much faster than the rate of nuclear magnetic relaxation in each site, the observed relaxation time is given bywhere Pi is the equilibrium fraction of the nuclei in site i and Tli is the relaxation time in site i in the absence of exchange. In a number of papers [2][3][4][5] it has been pointed out that in deriving (1) the presence of chemical exchange of the same order of magnitude in rate as the diffusional motion has been neglected. Such a fast chemical exchange has the potential for shortening the correlation times in the expression for Tll , since if exchange occurs before rotation of the molecule has taken place a speeding up of the interaction causing relaxation is obtained.Examples of cases when a fast chemical exchange can be expected to be of practical importance are :(i) The quadrupolar relaxation of ions such as asCl-, SlBr-or 2aNa+ exchanging between aqueous surroundings and attachment to a macromolecule or micelle.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nuclear magnetic relaxation induced by chemical exchange

Wennerström¹

1972

Molecular Physics

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“…A simplification in eq. [5] also occurs (5) in the limiting case for fast exchange relative to the rates of reorientation (k,, k4 k l , kz). The results in Table 5 show that the system under investigation is best defined as having an intermediate rate of exchange relative to kl and k2.…”

Section: Effect Of Complex Formationmentioning

confidence: 99%

“…In the limiting case for slow exchange relative to the rates of molecular reoriention in the free and complexed environments (k3, k4 << k l , k2), eq. [5] simplifies to (5)…”

Section: Effect Of Complex Formationmentioning

confidence: 99%

A spin-lattice relaxation study of the molecular reorientation of 2-methylindole as a function of viscosity and complex formation

Friesen¹,

Blackburn²

1984

Can. J. Chem.

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. Can. J. Chem. 62, 1618 (1984).The viscosity (q) dependence of the I3C spin-lattice relaxation time (TI) of C-3 of 2-methylindole was investigated by changing the temperature (T) and by changing the solvent system. The observed q / T dependence of the effective reorientation correlation time (calculated from T I ) is compared with those derived from theory based on hydrodynamic rotation with "stick" and with "slip" boundary conditions. This data implies that the reorientation of 2-methylindole obeys a near-slip condition in 1,2-dichloroethane. The I3C T I of C-3 of 2-methylindole was also determined as a function of the fraction complexed with 1,3,5-trinitrobenzene (TNB) at 3S°C in 1,2-dichloroethane. The observed TI, in this case, depends on the rates of reorientation of the molecule in the free and the bound states, the rate of association of the molecules, the rate of dissociation of the complex, as well as increases in viscosity brought about by increases in the concentration of TNB. Analysis of the data, by application of the Anderson-Fryer formulation, gives a rate of reorientation in the bound state of 55 ns-I at 3S°C and 0.69 cP as compared to a value of 150 ns-' in the free state under the same conditions. KENNETH J. FRIESEN et BARRY J . BLACKBURN. Can. J. Chem. 62, 1618Chem. 62, (1984.Faisant varier la temperature (T) et le systkme de solvant, on a CtudiC l'effet de la viscositt (q) sur le temps de relaxation spin-rtseau (TI) du I3C du carbone en position 3 du methyl-2 indole. La valeur observCe pour la dtpendance q / T du temps de corrtlation effectif de la rkorientation (calculee a partir de TI) a CtC comparCe aux valeurs que l'on peut deriver en se basant sur une rotation hydrodynamique dans des conditions ou les limites sont fixees par des "tiges" et des "lamelles". Ces donnCs impliquent que, dans le dichloro-1,2 Cthane, la reorientation du mCthyl-2 indole obCit une condition quasilamelaire. Operant h 3S°C, dans le dichloro-1,2 ethane, on a tgalement dCtermint la valeur TI du "C pour le carbone en position 3 du methyl-2 indole en fonction de la fraction complexee avec le trinitro-l,3,5 benzkne (TNB). Dans ce cas, la valeur observCe pour T, depend des vitesses de rkorientation de la molCcule dans les Ctats libre et lie, de la vitesse d'association des moltcules, de la vitesse de dissociation du complexe ainsi que des augmentations de viscositi, dues aux augmentations de concentration dans le TNB. L'analyse des donnCes, i l'aide de la formulation de Anderson-Fryer, conduit h une vitesse de rkorientation de 1'Ctat liC de 55 ns-I, a 35°C et 0,69 cP, qui se compare h une valeur de 150 ns-' pour l'ttat libre dans les mCmes conditions.[Traduit par le journal]

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Some Structural Aspects of the Rotational and Translational Diffusion in Liquids

Hertz

1970

Ber Bunsenges Phys Chem

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An interconnection between the rotational correlation time of a molecule and the structure of the liquid is demonstrated. For this purpose the angular velocity correlation function is constructed by taking account of fluctuating effective moments of inertia of aggregates due to molecular association. From this correlation function the rotational diffusion coefficient or rotational correlation time is obtained. The probabilities for the occurence of various aggregates which appear in this treatment are expressed in terms of integrals, containing the orientation dependent pair distribution function and a function describing the chance that the aggregate is sufficiently long‐lived. The reorientation time increases with increasing degree of structure. A numerical example for water is presented. The situation in mixtures and the occurence of intramolecular motions is discussed. The analogous treatment for the translational self‐diffusion coefficient is sketched.

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Rotational Relaxation and Chemical Exchange

Cited by 50 publications

References 10 publications

Nuclear magnetic relaxation induced by chemical exchange

Nuclear magnetic relaxation induced by chemical exchange

A spin-lattice relaxation study of the molecular reorientation of 2-methylindole as a function of viscosity and complex formation

Some Structural Aspects of the Rotational and Translational Diffusion in Liquids

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