# Polydispersity – what does it mean for DLS and chromatography?

Written by: Ulf Nobbmann

The term polydispersity (or more recently dispersity without the poly, as per IUPAC recommendation) is used to describe the degree of “non-uniformity” of a distribution. In the field of molecular/nanoparticular characterization there are in principle two different definitions of polydispersity, depending on the underlying property of interest.

In Gel Permeation Chromatography (GPC) and Size Exclusion Chromatography (SEC) we are interested in the molecular weight of the sample. The distribution obtained from GPC/SEC is typically a molecular weight distribution describing how much material there is present of the various molecular weight “slices.” The distribution is traditionally described by two numbers derived from it:

- Mw – the mass weighted molecular weight and
- Mn – the number weighted molecular weight

where one describes the average molecular weight by mass (of molecules in the different “slices”) and the other the average molecular weight by number (of molecules in the different “slices” of the distribution). For a perfectly uniform (“monodisperse”) sample consisting of exactly one and only one molecular weight both the Mw and the Mn would be the same value. For real samples, the two numbers are however not the same, and the ratio of the two can be used to describe how far away the encountered distribution is from a uniform distribution. The ratio Mw/Mn is called the **dispersity** formerly known as polydispersity index (PDI) . Recently a new symbol was assigned to the parameter, Dstroke, *Đ* to represent the newer convention of the term dispersity. For a uniform sample, *Đ* = 1.0

In Dynamic Light Scattering (DLS) the size distribution of molecules or particles is the property of interest. Here, the distribution describes how much material there is present of the different size “slices.” In DLS, the native distribution is the intensity distribution which indicates how much light is scattered from the various size “slices” or “bins.” The mean size and the standard deviation from that mean can be obtained directly from the statistics of the distribution. Here, the (absolute) width of the distribution can be compared to the mean, and a relative polydispersity = width/mean can be obtained. Historically, instead of requiring a distribution, a simpler forced single exponential fitting scheme (the cumulant method) has been used to find an overall mean size (by intensity) and an overall polydispersity (the normalized second cumulant). For a theoretical Gaussian distribution the overall polydispersity would be the relative polydispersity of the distribution. Traditionally, this overall polydispersity has also been converted into an overall polydispersity index PDI which is the square of the light scattering polydispersity. For a perfectly uniform sample, the PDI would be 0.0

The values for different classes of dispersity are listed in the table below.

Parameter | Definition | Distribution Type | |||
---|---|---|---|---|---|

“monodisperse” | “polydisperse” | ||||

uniform | narrow | moderate | broad | ||

PDI from GPC | =Mw/Mn | 1.0 | 1.0-1.1 | 1.1-2.0 | >2.0 |

PDI from DLS | =(width/mean)^2 | 0.0 | 0.0-0.1 | 0.1-0.4 | >0.4 |

where the moderate column indicates an intermediate, moderately polydisperse distribution type, where the distribution is neither extremely polydisperse, or broad, nor in any sense narrow.

**Further Resources**

- White Paper: Dynamic light scattering – common terms defined
- White Paper: Static Light Scattering Technologies for GPC/SEC Explained

**Previously**

- 5 steps to improve SEC-LS data
- Demonstration of Chromatography software (3minutes)
- Which size is right: intensity volume number distributions