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The Polydispersity Index (PDI) Calculator determines the breadth of a polymer's molecular weight distribution by computing the ratio of weight average to number average molecular weight. PDI is one of the most important parameters in polymer characterization because it reveals the heterogeneity of chain lengths and directly influences processing behavior and final material properties.
A PDI of exactly 1.0 represents a perfectly monodisperse sample where every chain has the same length. Real polymers always have PDI greater than 1.0, with the value depending on the polymerization mechanism. Living anionic polymerization can achieve PDI as low as 1.01, while conventional free radical polymerization typically yields PDI between 1.5 and 2.5.
The polydispersity index (also called dispersity, Đ, by IUPAC recommendation) is calculated as:
$$\text{PDI} = \frac{M_w}{M_n}$$
Where $$M_w$$ is the weight average molecular weight and $$M_n$$ is the number average molecular weight. Since Mw weights molecules by their mass while Mn weights them by number, Mw ≥ Mn always holds, and therefore PDI ≥ 1.
For specific polymerization mechanisms, theoretical PDI values are well-known:
$$\text{Step-growth: PDI} \to 2.0 \text{ at high conversion}$$
$$\text{Free radical: PDI} = 1.5 \text{ (termination by combination)} \text{ or } 2.0 \text{ (disproportionation)}$$
$$\text{Living polymerization: PDI} = 1 + \frac{1}{\text{DP}} \approx 1.0$$
The calculator classifies the PDI result into categories from monodisperse through very broad to help interpret the distribution quality immediately.
PDI below 1.1 indicates excellent molecular weight control, typically from living or controlled radical polymerization (ATRP, RAFT, NMP). Values between 1.1 and 1.5 are considered narrow and are achievable with careful reaction control. PDI of 1.5 to 2.0 is typical for conventional free radical polymerization. Values from 2.0 to 3.0 suggest broad distributions from step-growth polymerization or blending. PDI above 3.0 indicates very broad distributions, possibly from branching, degradation, or blending of distinct polymer populations.
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Results
PDI = 120,000 / 60,000 = 2.0, characteristic of free radical polymerization with termination by disproportionation
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Results
PDI = 51,200 / 50,000 = 1.024, indicating excellent molecular weight control
PDI measures the breadth of the molecular weight distribution in a polymer sample. It is the ratio of weight average (Mw) to number average (Mn) molecular weight. A PDI of 1.0 means all chains are identical in length; higher values indicate greater variation in chain lengths.
IUPAC has recommended replacing "polydispersity index" with "dispersity" (symbol Đ) to standardize nomenclature. The term "polydispersity" implies the sample is polydisperse, which is a tautology since PDI > 1 for all real samples. However, PDI remains widely used in literature and industry.
No. By mathematical definition, Mw ≥ Mn always holds, so PDI ≥ 1. If a measured PDI appears below 1, it indicates experimental error, such as incorrect calibration of GPC columns or band broadening artifacts. Some GPC software corrections can produce apparent PDI < 1 for very narrow standards.
Step-growth (condensation) polymerization produces PDI approaching 2.0 at high conversion. The Flory distribution predicts PDI = 1 + p, where p is the extent of reaction. At near-complete conversion (p → 1), PDI → 2. This theoretical limit assumes equal reactivity of all functional groups.
Polymers with broader PDI (higher values) have lower melt viscosity at high shear rates, making them easier to process by injection molding or extrusion. However, narrow PDI gives better control over mechanical properties, more uniform crystallization, and sharper melting points, which is desirable for precision applications.
Atom transfer radical polymerization (ATRP) typically achieves PDI of 1.05 to 1.30, depending on monomer type, catalyst system, and reaction conditions. Well-optimized ATRP of methyl methacrylate or styrene can reach PDI below 1.10. RAFT and NMP controlled radical techniques achieve similar results.
GPC (gel permeation chromatography) separates polymer chains by hydrodynamic volume. The elution curve is converted to a molecular weight distribution using calibration standards or MALLS/viscometry detection. Software then computes Mn and Mw from the distribution, and PDI is their ratio.
Yes. Blending two polymers with different molecular weights increases PDI significantly. If two monodisperse samples (PDI = 1) with different molecular weights are mixed, the blend will have PDI > 1. This is why post-polymerization blending is used to tailor molecular weight distributions for specific processing requirements.
Most natural polymers have narrow distributions. Proteins have PDI = 1.0 since every molecule is identical (same amino acid sequence). DNA and RNA are also monodisperse for a given gene. Natural rubber has PDI of approximately 2.0–5.0 depending on source and processing, while cellulose PDI varies from 1.5 to 10 depending on isolation method.
Broader distributions (higher PDI) tend to lower zero-shear viscosity compared to narrow distributions at the same Mw, because the low-MW fraction acts as a plasticizer. However, the high-MW tail contributes to elastic behavior and shear-thinning. The Mark-Houwink-Sakurada viscosity analysis uses Mv (viscosity average MW), which falls between Mn and Mw.
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