Random versus sequential pathway of molecular self-assembly

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Two important assumptions are often made in the analysis of molecular self-assembly at equilibrium, viz., that sequential is preferred to random aggregation and that the equilibrium constants at each stage of aggregation are equal, though both assumptions have not been justified strictly. In the present work we show that molecular self-assembly leading to formation of linear polymers and proceeding in a random manner appears to be less entropically favored than sequential aggregation, which provides a physical background for assuming sequential aggregation when studying molecular self-assembly in solution. Exact equations for analysis of experimental data for molecular assembly proceeding in a sequential manner were derived by taking strict account of the profile of the equilibrium constant, which provides a physically more correct approach than that using the conventional indefinite equilibrium constant (EK) model.