Weight Average Molecular Weight Calculator

Mw is measured primarily by static light scattering (SLS) or multi-angle laser light scattering (MALLS). The intensity of scattered light is proportional to M², making light scattering inherently sensitive to Mw. Analytical ultracentrifugation and GPC with MALLS detection also provide Mw values.

In the Mw calculation, molecules are weighted by their mass (M²/M = M), giving heavy chains more influence. In Mn, all molecules are weighted equally. Since squaring amplifies larger values, the mass-weighted average always exceeds or equals the number-weighted average. They are equal only for perfectly monodisperse samples.

Mw correlates with melt viscosity, tensile strength, impact resistance, glass transition temperature, and elastic modulus. Chain entanglements, which govern many mechanical properties, depend on the longest chains in the distribution and thus scale with Mw or even higher averages like Mz.

The polydispersity index (PDI = Mw/Mn) quantifies distribution breadth. PDI = 1 means monodisperse. Living polymerization typically achieves PDI of 1.01–1.10. Conventional free radical polymerization gives PDI of 1.5–2.0, step-growth polymerization approaches PDI = 2.0, and branched or degraded polymers may have PDI exceeding 5.

Mz (z-average molecular weight) uses M³ weighting: Mz = ΣNiMi³/ΣNiMi². It is even more sensitive to high-molecular-weight tails. Mz influences melt elasticity and die swell in processing. The hierarchy is always Mn ≤ Mw ≤ Mz for polydisperse samples.

Yes. If weight fractions (wi) are known instead of number fractions, Mw = Σ(wi × Mi). This is computationally simpler and is the form most directly obtained from GPC chromatograms where the detector response is proportional to mass concentration.

Engineering thermoplastics typically have Mw from 50,000 to 300,000 g/mol. Polyethylene for film applications ranges from 100,000 to 500,000 g/mol. Ultra-high molecular weight polyethylene (UHMWPE) used in joint implants has Mw exceeding 3,000,000 g/mol.

Long-chain branching increases Mw because branched molecules have larger total mass than linear chains with the same backbone length. However, branched polymers have smaller hydrodynamic volume than linear polymers of equal mass, so GPC calibrated with linear standards will underestimate Mw for branched polymers unless corrected with MALLS detection.

Three fractions approximate a real molecular weight distribution while keeping the calculation transparent. In practice, GPC divides the elution curve into hundreds of slices. The three-fraction model is ideal for classroom exercises, quick estimates, and understanding how different subpopulations contribute to Mn and Mw.