The present invention is directed to a method of preparing compositions enriched in compounds containing carbon chains of varying degrees of unsaturation using argentation chromatography. The present method utilizes an argentized cationic resin or a conditioned argentized alumina to separate compounds containing saturated or mono-unsaturated carbon chains from compounds having polyunsaturated carbon chains present in a starting composition. The invention is particularly useful for preparing a composition enriched in polyunsaturated fatty acid alkyl esters from mixtures of fatty acid esters in a starting composition derived from vegetable oils. The present invention is also directed to a method of preparing a conditioned argentized alumina adsorbent having increased selectivity for compounds containing one or more polyunsaturated carbon chains.