**Using strings of varying lengths to represent polymers of varying degrees of polymerization, students are able to calculate the number average molecular weight, the weight average molecular weight and the polydispersity index for a "sample" with a distribution of chain lengths. **

__Materials:__

- 100 pieces of string cut into pieces as follows:
- Ruler or meter stick

Number of Pieces | Length (cm) | Number of Pieces | Length (cm) |
---|---|---|---|

1 | 80 | 13 | 45 |

3 | 75 | 10 | 40 |

5 | 70 | 8 | 35 |

8 | 65 | 5 | 30 |

10 | 60 | 3 | 25 |

13 | 55 | 1 | 20 |

__Procedure:__

Mix the strings together. Have the students pull out the strings one at a time and measure the length of each. (A group of 10 students, working in pairs, can complete the measurements in approximately 10 minutes.) Assuming that each cm of length is equal to 200 repeat units of polyethylene, the students can convert the length of each string into an "atomic mass".

The data analysis is easily accomplished using a spreadsheet. The data, in tabular form, looks like this:

Length (in cm) | # of Strings or Molecules | "Atomic Weight" of String (molecule) | Strings ("molecules") x "atomic weight" | Strings ("molecules") x "atomic weight"^{2} |

The number average molecular weight is the total weight (the sum of column 4) divided by the total number of "molecules" (the sum of column 2).

The weight average molecular weight is the sum of column 5 divided by the sum of column 4.

The polydispersity index is the number average molecular weight divided by the weight average molecular weight.

The students may also examine the molecular weight distribution by plotting the number of "molecules" vs. the molecular weight of the "molecules".

It is of interest to note that even though this distribution appears to be broad, it yields a polydispersity index very close to 1.0.

Want some general information about polymer molecular weights? Click here.

Having trouble doing the calculations? An example of the calculation of number average and weight average molecular weights can be found here.

Want to see a cool page about how the data for a real polymer is collected? Check out the discussion of Size Exclusion Chromatography.