Lindemann index

Lindemann index

The Lindemann Index is a simple measure of thermally driven disorder. The local Lindemann index is defined as: [Melting and premelting of carbon nanotubes; Nanotechnology 18 (2007) 285703; Kaiwang Zhang, G Malcolm Stocks and Jianxin Zhong]

q_i = frac{1}{N - 1} sum_{j eq i} frac{sqrt{langle r_{ij}^2 angle - langle r_{ij} angle^2 {langle r_{ij} angle}

Where angle brackets indicate a time average. The global Lindemann index is a system average of this quantity.

;In condensed matter physics

A departure from linearity in the behaviour of the global Lindemann index or an increase above a threshold value related to the spacing between atoms ( or micelles, particles, globules... ) is often taken as the indication that a solid-liquid phase transition has taken place.

;In Biomolecules

Biomolecules often possess separate regions with different order characteristics. In order to quantify or illustrate local disorder, the local Lindemann index can be used. [A Consensus View of Protein Dynamics; PNAS 104 (2007) 796; Manuel Rueda, Carles Ferrer-Costa, Tim Meyer, Alberto Perez, Jordi Camps, Adam Hospital, Josep Lluis Gelpi and Modesto Orozco]

Care must be taken if the molecule possesses globally defined dynamics, such as about a hinge or pivot, because these motions will obscure the local motions which the Lindemann index is designed to quantify. An appropriate tactic in this circumstance is to sum the rij only over a small number of neighbouring atoms to arrive at each qi. A further variety of such modifications to the Lindemann index are available and have different merits, eg for the study of glassy vs crystalline materials. [The distance fluctuation criterion for melting: Comparison of square-well and Morse potential models for clusters and homopolymers;J Chem Phys 116 5 (2002) 2323;Yaoqi Zhou, Martin Karplus, Keith D. Ball and R. Stephen Berry]


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