Homogeneous and inhomogeneous distributions of correlation times. Lineshapes for chemical exchange

Abstract

Molecular motions, especially in polymers, can be described in terms of a broad distribution of correlation times. In principle, these distributions can arise in two fundamentally different ways. There may be an inhomogeneous spatial distribution of processes individually characterized by a single correlation time and each with an exponentially decaying autocorrelation function. Alternatively one can imagine an autocorrelation function identical for all common molecular processes but one which is inherently nonexponential. This nonexponential autocorrelation function can also be expressed mathematically as a probability distribution of exponential autocorrelation functions. The latter is called a homogeneous distribution. It is shown that NMR lineshape analysis can distinguish between the two forms of distributions. For simplicity the lineshape expected for two-site chemical exchange driven by homogeneous and inhomogeneous distributions is treated theoretically. Computer simulations of the expected lineshapes are presented for a distribution whose autocorrelation function is exp[ −( t τ p ) α ], where 0 < α ≥ 1. For a broad distribution, the correlation time τ p inferred from the coalescence point depends critically on whether the distribution is homogeneous or inhomogeneous.