# Why Do Smaller Particle Size Columns Improve Resolution?

Particle size (*dp*), or the mean diameter of the spherical supports used to pack a column, is a physical dimension that has a significant impact on the performance of an HPLC column. Smaller particle sizes have been shown to offer higher peak efficiencies. But, how does this actually affect analyte resolution? If we consider the fundamental relationship in separation science—the resolution equation (Figure 1), we can better understand how particle size can lead to improved separations. The resolution equation comprises three terms: selectivity, retention capacity, and efficiency. Each of these terms is affected by the specific components of an analytical method. A column’s particle size, in particular, affects the efficiency term of the resolution equation.

Efficiency is ultimately derived from the *theoretical plate model of chromatography*. Conceptually, a plate refers to one complete equilibrated transfer (or partition) of a solute between the mobile and stationary phases. Efficiency is a qualitative term used to measure the *number of theoretical plates* in a given column, or the degree to which an analyte partitions between the mobile and stationary phases. In relation to particle size, efficiency is inversely proportional (Figure 2). As particle size decreases, efficiency increases, and more resolution is achieved. In contrast, efficiency is directly proportional to the column length (Figure 2); therefore, an analyst can keep the same resolution and decrease the length of the column by the same factor as the particle size, shortening the analysis time. It is also beneficial that efficiency is inversely proportional to the square of the peak width—higher efficiencies produce narrower peak widths. Narrow peak widths enhance resolution by lengthening the baseline between two adjacent peaks. (An important note—this does not imply that by simply lowering the particle size we can separate all test mixes. Stationary phase selectivity is still the driving force behind resolution.)