Sample dimensionality: a predictor of order-disorder in component peak distribution in multidimensional separation

While the use of multiple dimensions in separation systems can create very high peak capacities, the effectiveness of the enhanced peak capacity in resolving large numbers of components depends strongly on whether the distribution of component peaks is ordered or disordered. Peak overlap is common in disordered distributions, even with a very high peak capacity. It is therefore of great importance to understand the origin of peak order/disorder in multidimensional separations and to address the question of whether any control can be exerted over observed levels of order and disorder and thus separation efficacy. It is postulated here that the underlying difference between ordered and disordered distributions of component peaks in separation systems is related to sample complexity as measured by a newly defined parameter, the sample dimensionality s, and by the derivative dimensionality s'. It is concluded that the type and degree of order and disorder is determined by the relationship of s (or s') to the dimensionality n of the separation system employed. Thus for some relatively simple samples (defined as having small s values), increased order and a consequent enhancement of resolution can be realized by increasing n. The resolution enhancement is in addition to the normal gain in resolving power resulting from the increased peak capacity of multidimensional systems. However, for other samples (having even smaller s values), an increase in n provides no additional benefit in enhancing component separability.