## Size exclusion chromatography (SEC)

Jon Eggert Carlé

Several studies have shown that the size of the polymer (its molecular weight) can have a severe influence on the device performance. It is therefore important to be able to analytically determine this in order to fully evaluate the polymers functionality in polymer solar cells. Size exclusion chromatography (SEC) is the most used method for determining the molecular weight of polymers applied in photovoltaics. The number average molar mass ($M_n$) and the average molar mass ($M_w$) are terms normally used to describe the weight of the polymers. $M_n$ and $M_w$ are defined in the equations below where $M_i$ is the molecular weight, $N_i$ is the number of molecules and $W_i=N_iM_i$. $${M_n} = \frac{{\sum {{N_i}{M_i}} }}{{\sum {{N_i}} }}$$ $${M_w} = \frac{{\sum {{N_i}M_i^2} }}{{\sum {{N_i}} {M_i}}} = \frac{{\sum {{W_i}{M_i}} }}{{\sum {{W_i}} }}$$ By comparing the equations it can be seen that $M_w$ will always be greater than $M_n$, unless when all the polymer molecules have the same molecular weight, then $M_w$ will be equal to $M_n$. The ratio of $M_w/M_n$ is known as the polydispersity index (PDI). This can be used as an indicator of the molecular range distribution of the polymer.

Figure 1: A cartoon illustrating the theory behind size exclusions chromatography.

SEC works by loading a polymer sample, dissolved in the eluent used for moving the analytes, onto the column which consist of a porous material. The smaller size polymers are to a higher degree trap in the columns porous material and will therefore stay longer on the column compared to the larger size polymers which has a limited accessibility in the pores, as seen in figure 1. By constantly monitoring the eluate using either UV-vis or refractive index the concentration of polymer can be determined to a corresponding time. This can be converted into molecular weight using a calibration curve, normally obtained from polystyrene.

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