3.2 Methods for determining molecular weight

Polymer scientists use various methods to determine molecular weight, a crucial property affecting material behavior. Size exclusion chromatography, light scattering, and mass spectrometry each offer unique insights into polymer structure and composition.

These techniques provide complementary information about molecular weight distribution, size, and exact mass. Understanding their principles and limitations helps researchers choose the most appropriate method for characterizing different polymer systems and applications.

Molecular Weight Determination Methods

Principles of size exclusion chromatography

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• Separates polymer molecules based on their hydrodynamic volume larger molecules elute first, while smaller molecules elute later
• Polymer solution passed through a column packed with porous beads molecules too large to enter pores elute first
• Smaller molecules enter pores have a longer path through the column, eluting later
• Determines molecular weight distribution of polymers by calculating number average molecular weight ($M_n$) and weight average molecular weight ($M_w$)
• Assesses polydispersity index (PDI) of a polymer sample, given by $PDI = M_w / M_n$ (polyethylene, polystyrene)

Light scattering for molecular weights

• Determines molecular weight and size of polymers in solution using static light scattering (SLS) and dynamic light scattering (DLS)
• SLS measures intensity of scattered light at different angles provides information about weight average molecular weight ($M_w$) and radius of gyration ($R_g$)
  • Requires knowledge of specific refractive index increment (dn/dc) of polymer-solvent system (polystyrene in toluene)
• DLS measures fluctuations in scattered light intensity over time provides information about hydrodynamic radius ($R_h$) of polymer molecules
  • Estimates molecular weight by relating $R_h$ to $M_w$ through scaling relationships (polyethylene glycol in water)

Mass spectrometry in polymer characterization

• Measures mass-to-charge ratio (m/z) of ionized molecules sample ionized using electrospray ionization (ESI) or matrix-assisted laser desorption/ionization (MALDI)
• Ions separated based on m/z ratio in mass analyzer detector records abundance of each m/z ratio, generating mass spectrum
• Determines exact molecular weight of oligomers and low molecular weight polymers (polyethylene glycol, polypropylene glycol)
• Provides information about end groups and repeat units of polymer identifies impurities or byproducts in polymer sample

Comparison of molecular weight methods

• Size exclusion chromatography (SEC)
  • Advantages: Rapid analysis, provides molecular weight distribution, widely available
  • Limitations: Requires calibration with standards, limited to polymers soluble in mobile phase (tetrahydrofuran, chloroform)
• Light scattering techniques (SLS and DLS)
  • Advantages: Absolute method, does not require calibration, provides size information
  • Limitations: Requires precise sample preparation, sensitive to dust and aggregates, limited to dilute solutions
• Mass spectrometry (MS)
  • Advantages: Provides exact molecular weights, can identify end groups and repeat units
  • Limitations: Limited to low molecular weight polymers, requires ionization of sample, can be affected by sample purity (salt contamination)