Degree of Polymerization
Calculate a polymer chain's degree of polymerization, DP = M_n ÷ M₀, dividing the number-average molar mass of the chain (M_n) by the molar mass of the monomer or repeat unit (M₀). The dimensionless result is the average number of monomer units in each chain. The higher the degree of polymerization, the longer the chains and the more pronounced the polymer properties: increased mechanical strength, melt viscosity, transition temperature and toughness. Below a critical value, the material lacks typical polymer properties. Enter the chain molar mass and the monomer molar mass.
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Degree of polymerization
A polymer is literally 'many parts' (from the Greek poly + meros): long chains built by repeating one small unit, the monomer. The degree of polymerization (DP) counts how many of those units, on average, make up each chain: DP = M_n ÷ M₀, the average molar mass of the chain divided by the molar mass of the repeat unit (the monomer). A polyethylene with M_n of 100,000 g/mol and a –CH₂CH₂– unit (28 g/mol) has DP ≈ 3,570 — each chain is a queue of about 3,570 units. DP is what transforms the properties: small molecules (low DP) are liquids or waxes; as DP grows, polymeric behavior emerges — mechanical strength, elasticity, film and fiber formation, high melt viscosity. There is a critical DP (typically a few hundred) below which the material has no useful strength, since the chains are too short to entangle with one another — and it is precisely entanglement between long chains that gives plastic its toughness. Above that threshold, properties such as tensile strength rise with DP until they level off. A very high DP, on the other hand, makes the melt too viscous to process. Controlling the degree of polymerization (through reaction time, temperature, initiator concentration and chain transfer agents) is one of the polymer engineer's main levers for tuning the balance between performance and processability. Enter the molar mass of the chain and that of the monomer.
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Polydispersity Index (PDI)
Calculate a polymer's polydispersity index (PDI), PDI = M_w ÷ M_n, dividing the weight-average molar mass (M_w) by the number-average molar mass (M_n). The dimensionless result (always ≥ 1) measures the breadth of the molar mass distribution: PDI = 1 means a monodisperse polymer (all chains the same size, rare, typical of living polymers); larger values mean a wide range of sizes. Commercial polymers have PDI of 2 to 20, depending on the polymerization process. PDI affects processability, strength and flow properties. Enter M_w and M_n.
Intrinsic Viscosity (Mark-Houwink)
Calculate a polymer's intrinsic viscosity by the Mark-Houwink-Sakurada equation, [η] = K·Mᵃ, from the constants K and a (specific to the polymer-solvent-temperature system) and the viscosity-average molar mass M. The result, in dL/g, relates the viscosity of a dilute polymer solution to its molar mass — the basis of molar mass determination by viscometry, a simple and cheap technique. The exponent a (between 0.5 and 0.8) reflects the chain conformation in the solvent: 0.5 for a theta solvent (coiled chain) and up to 1.0 for an extended chain in good solvent. Enter the constants K, a and the molar mass.
Crystallinity Degree (Enthalpy)
Calculate a polymer's crystallinity degree by the melting enthalpy method, X_c = (ΔH_m ÷ ΔH_m°) × 100%, dividing the melting enthalpy measured by DSC (ΔH_m) by the enthalpy of the 100% crystalline polymer (ΔH_m°, a tabulated reference). The result, in %, is the fraction of polymer mass organized in crystalline regions, as opposed to amorphous ones. Crystallinity governs key properties: higher crystallinity raises stiffness, strength, density, opacity and chemical resistance, but lowers transparency and impact resistance. Enter the measured melting enthalpy and that of the 100% crystalline material.
Molar Mass from Gas Density
Enter density in g/L, temperature in K and pressure in atm: M = ρ·R·T/P with R = 0.08206. A gas at 1.96 g/L, 273 K and 1 atm gives 43.9 g/mol.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.