Journal of Chromatography A, 1365 (2014) 156–163 Contents lists available at ScienceDirect Journal of Chromatography A jo ur nal ho me pag e: www.elsevier.com/locate/chroma Polydispersity in size-exclusion chromatography: A stochastic approach  Annamária Sepsey a , Ivett Bacskay b , Attila Felinger a,b,∗ a MTA–PTE Molecular Interactions in Separation Science Research Group, Ifjúság útja 6, H–7624 Pécs, Hungary b Department of Analytical and Environmental Chemistry and Szentágothai Research Center, University of Pécs, Ifjúság útja 6, H–7624 Pécs, Hungary a r t i c l e i n f o Article history: Received 15 July 2014 Received in revised form 5 September 2014 Accepted 8 September 2014 Available online 17 September 2014 Keywords: Polydispersity Stochastic theory Size-exclusion chromatography a b s t r a c t We investigate the impact of polydispersity of the sample molecules on the separation process and on the efficiency of size-exclusion chromatography. Polydispersity was integrated into the molecular (stochastic) model of chromatography; the characteristic function, the band profile and the most impor- tant moments of the elution profiles were calculated for several kind of pore structures. We investigated the parameters affected by polydispersity on the separation for a number of pore shapes. Our results demonstrate that even a small distribution in the molecular size (i.e. polydispersity) can contribute sub- stantially to the total width of the chromatographic peak. The pure effect of polydispersity can only be investigated via mathematical modeling, because its contribution to an experimental chromatogram cannot be separated from other band-broadening effects. © 2014 Elsevier B.V. All rights reserved. 1. Introduction Size-exclusion chromatography (SEC) is often used for deter- mining the molecular size or molecular weight on the basis of the retention of the molecules in porous stationary phases, than for separating polymers from each other [1]. SEC is defined as the dif- ferential elution of solutes from the porous stationary phase caused by different degrees of steric exclusion of the solutes from the pore volume due to the differential molecular size of solutes [2]. The determination of the molecular weight (M w ) can be achieved by a calibration process, where a number of special standard polymers with well-known molecular weight and size are eluted, when an accurate calibration curve is drawn by their retention volume or retention time (ln M w vs. K, where K is the partition coefficient). The retention properties of the unknown sample are then com- pared with the calibration data to determine the size or weight of the investigated molecule. Even though the standards used for the calibration process have well-defined molecular weights, they do have a distribu- tion in their molecular weight and manufacturers use a quantity  Presented at the 41st International Symposium on High Performance Liquid Phase Separations – HPLC 2014, 10–15 May 2014, New Orleans, Louisiana, USA. ∗ Corresponding author at: Department of Analytical and Environmental Chem- istry and Szentágothai Research Center, University of Pécs, Ifjúság útja 6, H–7624 Pécs, Hungary. Tel.: +36 72 501500x24582; fax: +36 72 501518. E-mail address: felinger@ttk.pte.hu (A. Felinger). to characterize the fitness-to-purpose of these polymers, polydis- persity (P). The polydispersity of a polymer sample is defined as the ratio of the weight- and number-averaged relative molecular weights of the polymer sample; P = M w /M n [3]. Although there is a new recommended IUPAC terminology for polydispersity [4] where ‘degree-of-polymerization dispersity’ and shortly the word ‘dispersity’ is recommended for use, we rather use the term poly- dispersity because this is still the common way polymer scientist refer to the distribution of polymer molecules. The knowledge and the effect of polydispersity – that it increases the peak width and leads to an apparent increase in the height equivalent to a theoretical plate (HETP) and a decrease in the num- ber of theoretical plates (N) – is almost of the same age as SEC [5–8]. It is very difficult, if feasible at all, to obtain experimentally the real polydispersity by size-exclusion chromatography. However, the first equations that described the contribution of polydispersity to the HETP value greatly underestimated the effect of polydisper- sity [5,6], it was proven that similarly to a new equation given by Knox [3], the data given by the manufacturers overestimate it as well [9,10]. The reduced plate height (h = H/d p , where H is the height equiv- alent to a theoretical plate and d p is the diameter of a particle) is a measure of the column zone-broadening and therefore of the chromatographic efficiency. Due to the additivity of variances it is possible to divide the plate height into contributors as h = h kin + h P , (1) http://dx.doi.org/10.1016/j.chroma.2014.09.023 0021-9673/© 2014 Elsevier B.V. All rights reserved.