Polymer Chemistry: Molecular Weight of Polymers
One of the chemical properties of a molecule is its molecular weight which is unique for every molecule. However, in synthetic polymer this is a bit of problem because of the nature of polymerisation reaction which produces different lengths of polymeric chains. This means synthetic polymers are polydisperse, no unique molecular weight, unlike small molecules. Therefore, the molecular weight of polymers is measured using molecular weight distribution (MWD).
In MWD curve, there are three moments of molecular weight distribution which are mean-average, weight average and z-average molar mass. Mean-average molar mass, Mn, can be defined as the value obtained by weighting each molar mass by the number of molecules of that mass present in the sample. From the definition, Mn can be calculated using equation below
where Ni is the number of molecules with mass Mi and there are N molecules in all.
Experimentally, Mn can be measured using several methods. The first method is using end-group analysis where in this technique the concentration of end-group in known concentration of polymer. This means end-group analysis depends on the functional group at the end of polymeric chain which implies the need of polymers modification. From this technique, Mn can be calculated as
The other methods use the fact that the polymer chains are in solution system which means the measurement is based on the colligative properties of polymer solution. Common methods are ebuliometry which measures the elevation of boiling temperature and cryoscopy which measures the depression of melting temperature. Because those measurements depend on the colligative properties which means the magnitude change depends heavily on molecule present, this means a small change is observed due to the high molecular weight. Hence, a sensitive measuring device is required. The upper limit of these methods are in order of 30 000 - 40 000 g/mol. Another colligative property that can be used to measure Mn is osmotic pressure using vapour pressure osmometry or membrane osmometry which has higher limit between 20 000 - 106 g/mol.
Besides that, weight-average molar mass Mw can be defined as the average calculated by weighting the molar masses of the molecule by the mass of each present in the sample.
In the equation above, mi is the total mass of molecule with molar mass Mi and m is the total mass present in sample. Then, because mi is (NiMi)/NA, so the equation can be written as follow.
Mw can be measured using scattering technique as the long polymeric chains coils up in polymer solution. The incident radiation will be scattered by this random coils and the scattering intensity is proportional to square mass particle. The most common scattering to measure Mw is static light scattering. This method requires dust-free solution which can be achieved using ultrafiltration or ultracentrifugation method. Besides that, this method also needs the refractive index increment (dn/dc) of the polymer solution and also high dilution factor to ensure one scattering for every coil.
The results of this analysis of the scattering is plotted as Zimm plot where the data is extrapolated ot 0 angle (green line) and to 0 concentration (red line).
Furthermore, the y-intercept from Zimm plot is 1/Mw.
The last description of molecular weight of polymer is Z-average molar and this can be achieved from sedimentation experiments. The name of Z-average is derived from the z-coordinate used to depict the data in a procedure to determining the average. Z-average molecular mass turns out to be proportional to the mean cubic of molar mass.
The moments of MWD, especially Mn and Mw, are commonly used for the molecular weight analysis. The value of Mn is biased towards low molecular weight while Mw is biased toward high molecular weight. Those values are also used to measured how polydisperse the polymer is and this value is quoted as heterogeneity index of polydispersity index (PDI).
Therefore, by definition if PDI is 1.000 this means an ideal monodisperse polymer where all the polymeric chain has the same length. If PDI is less than 1.20 it can be called near monodisperse and this value is common for living anionic polymerisation. Common value of PDI of polymerisation is around 2.00.
The molecular weight of polymer also depends on how long the molecular weight which can be quoted as degree of polymerisation or Dp. Dp is the mean number of monomer units per polymer chain.
Dp is always quoted as an integer and If it is lower 10 so it is called an oligomer not polymer.
One of the methods to plot the whole MWD curve of polymer can be done by gel permeation chromatography (GPC) which is a quick, convenient and widely used method.
In this method, the molecular weight is plotted as function of elution time. The low MW polymer tends to get lost in microporous beads, so the high MWpolymer would pass the column first. This implies that the MW is inversely proportional to the elution time which means a calibration is required and this requires near-monodisperse standard.
In MWD curve, there are three moments of molecular weight distribution which are mean-average, weight average and z-average molar mass. Mean-average molar mass, Mn, can be defined as the value obtained by weighting each molar mass by the number of molecules of that mass present in the sample. From the definition, Mn can be calculated using equation below
Experimentally, Mn can be measured using several methods. The first method is using end-group analysis where in this technique the concentration of end-group in known concentration of polymer. This means end-group analysis depends on the functional group at the end of polymeric chain which implies the need of polymers modification. From this technique, Mn can be calculated as
The other methods use the fact that the polymer chains are in solution system which means the measurement is based on the colligative properties of polymer solution. Common methods are ebuliometry which measures the elevation of boiling temperature and cryoscopy which measures the depression of melting temperature. Because those measurements depend on the colligative properties which means the magnitude change depends heavily on molecule present, this means a small change is observed due to the high molecular weight. Hence, a sensitive measuring device is required. The upper limit of these methods are in order of 30 000 - 40 000 g/mol. Another colligative property that can be used to measure Mn is osmotic pressure using vapour pressure osmometry or membrane osmometry which has higher limit between 20 000 - 106 g/mol.
Besides that, weight-average molar mass Mw can be defined as the average calculated by weighting the molar masses of the molecule by the mass of each present in the sample.
Mw can be measured using scattering technique as the long polymeric chains coils up in polymer solution. The incident radiation will be scattered by this random coils and the scattering intensity is proportional to square mass particle. The most common scattering to measure Mw is static light scattering. This method requires dust-free solution which can be achieved using ultrafiltration or ultracentrifugation method. Besides that, this method also needs the refractive index increment (dn/dc) of the polymer solution and also high dilution factor to ensure one scattering for every coil.
 |
| SLS technique instrumentation |
The last description of molecular weight of polymer is Z-average molar and this can be achieved from sedimentation experiments. The name of Z-average is derived from the z-coordinate used to depict the data in a procedure to determining the average. Z-average molecular mass turns out to be proportional to the mean cubic of molar mass.
The moments of MWD, especially Mn and Mw, are commonly used for the molecular weight analysis. The value of Mn is biased towards low molecular weight while Mw is biased toward high molecular weight. Those values are also used to measured how polydisperse the polymer is and this value is quoted as heterogeneity index of polydispersity index (PDI).
The molecular weight of polymer also depends on how long the molecular weight which can be quoted as degree of polymerisation or Dp. Dp is the mean number of monomer units per polymer chain.
One of the methods to plot the whole MWD curve of polymer can be done by gel permeation chromatography (GPC) which is a quick, convenient and widely used method.
In this method, the molecular weight is plotted as function of elution time. The low MW polymer tends to get lost in microporous beads, so the high MWpolymer would pass the column first. This implies that the MW is inversely proportional to the elution time which means a calibration is required and this requires near-monodisperse standard.
Comments