# Polymer **Polymer** is a substance whose molecules are very large and built by repeating one or a few small units, the monomers, many times over. The class is defined by that architecture rather than by chemistry, so it spans proteins, DNA, [[Natural_rubber|natural rubber]], cellulose and starch as well as [[Polyethylene|polyethylene]], [[Nylon|nylon]] and epoxy resin. Chain length is the property that makes a polymer a material: the same carbon and hydrogen that give a gas at twenty atoms give a wax at a thousand and a tough solid at a hundred thousand, because long chains entangle, and entanglement lets a solid deform without the chains sliding apart. In the microsim below the reader grows a single chain as a three-dimensional random walk, changing the number of segments *N* from 10 to 10,000 on a logarithmic control and regrowing it from a seed. Two exact results for the ideal chain are drawn with it: the root-mean-square end-to-end distance `R_rms = b·√N`, shown as a ghost sphere around the coil, and the radius of gyration `R_g = R_rms/√6`. The readouts convert *N* into a [[Degree_of_polymerization|degree of polymerization]] and a molar mass at 28 g/mol per ethylene repeat unit. The point the sphere makes is the square root: a chain of 10,000 segments has a contour length of 10,000 b but spans only 100 b, so it occupies about a millionth of the volume its length would suggest, and the space it does occupy is mostly other chains. On the [[Materials_science|Materials science]] flagship this article serves the *Polymers* section of Part VIII, and it is shared with the Chemistry flagship's synthesis spine; [[Ideal_chain|ideal chain]], [[Step-growth_polymerization|step-growth polymerization]] and [[Polyethylene|polyethylene]] reuse the same walk with their own readouts. ## Etymology The word comes from the Greek *polus*, many, and *meros*, part, and was used by Berzelius in the 1830s for compounds sharing an empirical formula but differing in molecular weight — ethylene and butylene, on his usage, were polymers of one another. The modern meaning, a molecule genuinely built of many covalently linked repeat units, is Staudinger's. Against the prevailing view that rubber and cellulose were colloidal aggregates of small molecules held by weak forces, he argued from 1920 that they were single long chains joined by ordinary [[Covalent_bond|covalent bonds]], and spent a decade proving it.[^staudinger1920] ## Common examples Polymers are more of the material world than any other class, once the biological ones are counted. Convention divides them by origin, though the division is one of history rather than of physics. ### Natural Cellulose, the most abundant organic polymer on Earth, is a chain of glucose units whose flat, hydrogen-bonded ribbons make wood and cotton stiff. Starch is the same sugar linked differently, and is therefore food rather than structure. Proteins are copolymers of twenty amino acids whose sequence folds them into catalysts, fibres and membranes; DNA stores information in the sequence of four units. [[Natural_rubber|Natural rubber]] is *cis*-polyisoprene tapped from a tree, useless until [[Vulcanization|vulcanization]] cross-links it. Silk, wool, collagen, chitin and lignin complete the load-bearing biopolymers. ### Synthetic The commodity plastics are five: polyethylene, polypropylene, poly(vinyl chloride), polystyrene and poly(ethylene terephthalate), together most of the [[Plastic|plastic]] made. Engineering polymers — polyamides such as [[Nylon|nylon]], polycarbonate, acetal, PEEK — pay more for stiffness, toughness and heat resistance. Thermosets such as epoxy, phenolic and unsaturated polyester cure into one cross-linked network that cannot be melted again, which makes them the matrices of [[Composite_material|composite materials]]. Elastomers, from styrene–butadiene rubber to silicones, are lightly cross-linked networks used above their glass transition. ## Synthesis Polymerisation joins monomers into chains, and the two great mechanisms differ in how the chain grows. In chain-growth polymerisation an active centre — a radical, an ion or a metal complex — adds monomer one unit at a time and the chain reaches full length in under a second; monomer concentration falls steadily, and high polymer is present from the start. In step-growth polymerisation any two species with reactive ends can join, so dimers, trimers and oligomers accumulate first and high molar mass appears only at the very end of the reaction. The Carothers relation makes that vivid: the number-average degree of polymerisation is `X_n = 1/(1 − p)` with *p* the fraction of functional groups reacted, so 99 % conversion is needed for a chain of only 100 units.[^carothers1931][^ball-ch16] Step-growth chemistry demands exact stoichiometry and very pure monomer for that reason; chain-growth chemistry does not. Control over the product came in stages. Free-radical polymerisation gives branched, broadly distributed chains. Coordination catalysts introduced in the 1950s controlled both branching and stereochemistry, turning polyethylene from a soft branched solid into a linear, highly crystalline one and making isotactic polypropylene possible at all; Ziegler and Natta shared the 1963 Nobel Prize in Chemistry for the work.[^nobel1963] Living polymerisations, whose chains neither terminate nor transfer, give narrow distributions and block architectures. ### Biological synthesis Living cells polymerise with an accuracy no industrial process approaches. Nucleic acids and proteins are made on a template, one unit at a time, with proofreading, so every molecule of a given protein has the same length and the same sequence — a dispersity of exactly 1. Polysaccharides and polyesters such as the bacterial PHAs are made without a template and are polydisperse like synthetic polymers. The contrast is the reason biological polymers can fold into a unique structure and synthetic ones cannot. ### Modification of natural polymers The first commercial plastics were modified naturals. Treating cellulose with nitric acid gives cellulose nitrate, the celluloid of early film; with acetic anhydride, cellulose acetate; dissolving and regenerating it gives viscose rayon and cellophane. Vulcanising natural rubber with sulfur, patented in the 1840s, converts a thermoplastic gum into an elastic network and is the oldest deliberate cross-linking. These routes remain important wherever a renewable feedstock is wanted. ## Structure A polymer's properties follow from structure at three scales: the chemistry of the repeat unit, the way units are joined along and between chains, and the arrangement of whole chains in the solid. ### Monomers and repeat units The repeat unit is what remains of the monomer in the chain, and it is not always the monomer itself: the ethylene repeat unit is –CH₂CH₂–, 28 g/mol, the same atoms as the [[Molecule|molecule]], but a polyamide repeat unit is the monomer minus the water eliminated when the amide bond formed. Molar mass is a distribution rather than a number, summarised by the number-average `M_n` and the mass-average `M_w`, whose ratio `Đ = M_w/M_n` is the dispersity — 1 for a protein, near 2 for an ideal step-growth product, and from 2 to above 20 for radical and coordination products. Many properties depend on `M_n`, but melt viscosity and toughness depend on the high-mass tail, so the whole distribution matters. ### Microstructure Along the chain, the choices are configuration and architecture. Tacticity — whether substituents on successive backbone carbons are arranged regularly or at random — decides whether a chain can pack into a crystal: isotactic polypropylene is a stiff engineering plastic, atactic polypropylene a tacky gum of identical composition. Branching interferes with packing, which is the whole difference between low- and high-density polyethylene. Copolymers can be random, alternating, block or graft, and incompatible blocks microphase-separate into ordered nanostructures. Cross-links convert the sample into one molecule, and their density separates a rubber from an unworkable thermoset. ### Morphology Most polymer solids are wholly or partly amorphous, and the amorphous state is exactly the random coil the microsim draws. For an ideal chain of *N* freely jointed segments of length *b*, the end-to-end vector is a sum of *N* independent random steps, so its mean is zero, its mean square is `N·b²`, and the distribution is Gaussian — the same [[Random_walk|random walk]] statistics that govern [[Diffusion|diffusion]].[^likharev-sm5][^kuhn1934] Hence `R_rms = b·√N` and `R_g = b·√(N/6)`. At *N* = 10,000 the coil spans 100 *b* against a contour length of 10,000 *b*, a ratio of `1/√N` = 1 % (derived). Real chains are stiffer than freely jointed ones, so *b* is taken as a Kuhn length of order one to two nanometres rather than a bond length; with that substitution the same square-root law holds, and it is why a polyethylene molecule of 280 kg/mol, some 2.6 µm long if pulled straight, forms a coil a few tens of nanometres across.[^rubinstein-colby] Where the chain is regular enough, part of it crystallises. Chains fold back and forth into lamellae about ten nanometres thick, which grow radially from a nucleus into spherulites tens of micrometres across, with amorphous material trapped between; tie molecules running from one lamella to the next carry load and supply toughness. No polymer crystallises completely, and the degree of crystallinity, typically 30–80 %, is the most useful single number for predicting stiffness, density and permeability. ## Properties Polymer properties are dominated by two temperatures — the [[Glass_transition|glass transition]] and, for crystallisable polymers, the melting point — and by the fact that both the modulus and the strength depend on how fast and how long the load is applied. ### Mechanical properties Below its glass transition a polymer is a glass of a few gigapascals; above it, uncross-linked and amorphous, it flows; above it, cross-linked, it is a rubber of a few megapascals. The modulus falls about three decades across the transition. Rubber elasticity is entropic, and a direct corollary of the microsim's statistics: stretching a coil reduces the configurations available to it, so the restoring force comes from the fall in entropy, the chain behaves as a spring of stiffness `3·k·T/(N·b²)`, and the modulus rises with temperature rather than falling.[^rubinstein-colby] Above the entanglement molar mass, chains thread through one another and melt viscosity acquires a steep dependence on chain length — what makes high-mass polymers tough and hard to process at once. All polymers creep, so a design stress is a stress at a stated time and temperature. ### Transport properties Small molecules dissolve in the amorphous phase and diffuse through it; crystals are impermeable and force a longer path. Permeability is therefore the product of a solubility and a diffusivity, both of which rise steeply above the glass transition, and it falls with crystallinity and with orientation. This is the physics of food packaging, of fuel tanks and of the barrier layers in medical devices. ### Phase behavior Polymers mix badly. The entropy of mixing per unit volume falls as 1/N, so the small positive enthalpy that most pairs of chemically different chains have is enough to make them separate; miscible blends are rare and usually depend on a specific interaction. The same arithmetic explains why block copolymers, unable to separate macroscopically, form ordered microphases instead, and why polymer solutions show upper and lower critical solution temperatures. ### Chemical properties Chain chemistry sets resistance. Polyolefins have no polar groups and resist acids, bases and most solvents but swell in hydrocarbons; polyesters and polyamides hydrolyse at their backbone linkages, particularly in hot water; PTFE resists nearly everything. Solvent resistance is a matter of degree rather than kind, because a solvent that cannot dissolve a polymer may still swell it enough to halve its strength or to crack it under stress. ### Optical properties Amorphous polymers with no absorbing groups are transparent, which is why polycarbonate and PMMA glaze aircraft and museums. Semicrystalline polymers scatter at the boundaries between crystalline and amorphous regions and are translucent to opaque, unless the crystals are kept far below the wavelength of light. Orientation makes a polymer birefringent, which is why frozen-in stress in a moulding shows as coloured fringes between crossed polarisers. ### Electrical properties Conventional polymers are excellent insulators, with the low dielectric loss that makes them cable and capacitor dielectrics, and their failure mode is electrical treeing rather than conduction. Conjugated polymers, whose backbones carry alternating single and double bonds, conduct when doped; their discovery and development won the 2000 Nobel Prize in Chemistry,[^nobel2000] and they are now used in displays, sensors and printed electronics. ## Applications Polymers displaced other materials wherever low density, formability and corrosion resistance mattered more than stiffness. Packaging is the largest use by mass, then building products — pipe, insulation, window frames, membranes — then automotive and electrical components, textiles, adhesives, coatings and medical devices. The argument is the one the [[Material_selection|material selection]] charts make: a polymer is a tenth as stiff as a metal and a fifth as dense, a losing trade for a tie and a much better one for a panel, and it can be moulded in one shot into a shape that would take a metal a dozen operations. ## Standardized nomenclature Two naming systems coexist. Source-based names take the monomer: polyethylene, polystyrene, poly(vinyl chloride), with parentheses when the monomer's name is more than one word. Structure-based names, defined by IUPAC, take the constitutional repeating unit: poly(1-chloroethylene) for PVC.[^iupac] Industry mostly uses source-based names and abbreviations, standardised so that PE, PP, PVC, PS, PET, PA and PC mean the same thing in every supplier's datasheet, together with the resin identification codes moulded into packaging. ## Characterization The three questions asked of an unknown polymer are what it is, how long its chains are, and what state it is in. Chemical identity comes from infrared and nuclear magnetic resonance spectroscopy. Molar mass and dispersity come from size-exclusion chromatography, which separates by hydrodynamic volume and so needs calibration, with light scattering or viscometry giving absolute values; dilute-solution viscosity relates to molar mass through the Mark–Houwink relation `[η] = K·M^a`.[^flory1953] Thermal state comes from differential scanning calorimetry, which shows the glass transition as a step and melting as a peak whose area gives crystallinity, and from dynamic mechanical analysis. Morphology comes from microscopy and X-ray scattering, processability from a melt flow index or a rheometer. ## Degradation Polymers age by chain scission and by cross-linking, and both change properties irreversibly. The dominant mechanism outdoors is photo-oxidation: ultraviolet light generates radicals, oxygen propagates the chain reaction, and the backbone is cut, so the material yellows, embrittles and chalks. Thermal oxidation does the same more slowly at processing and service temperatures; hydrolysis attacks ester and amide linkages; ozone cracks stretched rubber. Stabiliser packages — ultraviolet absorbers, hindered-amine light stabilisers, antioxidants — intercept each step and are as important to service life as the base polymer. ### Product failure Most polymer parts fail through a slow mechanism rather than a sudden overload. Environmental stress cracking, in which a modest tensile stress and a fluid that merely swells the polymer combine to crack it although neither alone would, is the classic case and accounts for a large share of field failures. Creep rupture under sustained load, fatigue with hysteretic self-heating, weld-line weakness in mouldings and residual stress from fast cooling account for most of the rest. Each is a consequence of the same chain mobility that makes polymers processable. ## History The materials are ancient and the understanding is a century old. Rubber was used in Mesoamerica long before Goodyear's vulcanisation of the 1840s; cellulose nitrate and Bakelite, the first wholly synthetic plastic, followed in 1869 and 1907, all without any concept of a macromolecule. Staudinger's macromolecular hypothesis of 1920 supplied it, and Carothers's work at DuPont through the 1930s turned it into synthetic method, producing neoprene and then nylon.[^staudinger1920][^carothers1931] Wartime demand industrialised polyethylene and synthetic rubber. Flory's *Principles of Polymer Chemistry* of 1953 unified the statistics, thermodynamics and kinetics into a discipline,[^flory1953] coordination catalysis arrived in the same decade, and the physics of entangled chains followed in the 1970s. The current problem is the reverse of the original one: not how to make chains that last, but what to do with them when the product does not. ## See also - [[Ideal_chain]] - [[Degree_of_polymerization]] - [[Polyethylene]] - [[Nylon]] - [[Polymer_chemistry]] - [[Polymer_science]] - [[Step-growth_polymerization]] - [[Plastic]] - [[Glass_transition]] - [[Composite_material]] ## References [^flory1953]: Flory, P. J. (1953). *Principles of Polymer Chemistry*. Ithaca, New York: Cornell University Press. Not a Portal Book; chapter and page to pin (the Mark–Houwink relation and the statistics of chain dimensions). [^rubinstein-colby]: Rubinstein, M.; Colby, R. H. (2003). *Polymer Physics*. Oxford: Oxford University Press. Not a Portal Book; chapter and page to pin (ideal chains, the Kuhn length and characteristic ratio, entropic elasticity and entanglement). [^likharev-sm5]: Likharev, K. K. (2013). *Part SM: Statistical Mechanics*. Portal Book 075. Chapter 5, pp. 143–186 (page to pin) — random walks, fluctuations and the Gaussian limit that the chain statistics rest on. https://open.umn.edu/opentextbooks/textbooks/part-sm-statistical-mechanics [^ball-ch16]: Ball, D. W. (2011). *Introductory Chemistry*. Portal Book 056. Chapter 16, Organic Chemistry, pp. 765–852 (polymers and polymerisation; page to pin). https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry [^kuhn1934]: Kuhn, W. (1934). "Über die Gestalt fadenförmiger Moleküle in Lösungen." *Kolloid-Zeitschrift* 68 (1): 2–15. The equivalent freely jointed chain and its segment length. (DOI to pin.) [^staudinger1920]: Staudinger, H. (1920). "Über Polymerisation." *Berichte der deutschen chemischen Gesellschaft* 53 (6): 1073–1085. (DOI to pin.) [^carothers1931]: Carothers, W. H. (1931). "Polymerization." *Chemical Reviews* 8 (3): 353–426. The step-growth analysis behind `X_n = 1/(1 − p)`. (DOI to pin.) [^nobel1963]: The Nobel Prize in Chemistry 1963, awarded jointly to Karl Ziegler and Giulio Natta for their discoveries in the chemistry and technology of high polymers. (Citation record and URL to pin.) [^nobel2000]: The Nobel Prize in Chemistry 2000, awarded jointly to Alan J. Heeger, Alan G. MacDiarmid and Hideki Shirakawa for the discovery and development of conductive polymers. (Citation record and URL to pin.) [^iupac]: International Union of Pure and Applied Chemistry (2009). *Compendium of Polymer Terminology and Nomenclature: IUPAC Recommendations 2008*. Cambridge: RSC Publishing. Structure-based nomenclature and the constitutional repeating unit. (Page to pin.) ## Bibliography - Flory, P. J. (1953). *Principles of Polymer Chemistry*. Cornell University Press. Not a Portal Book. - Rubinstein, M.; Colby, R. H. (2003). *Polymer Physics*. Oxford University Press. Not a Portal Book. - Likharev, K. K. (2013). *Part SM: Statistical Mechanics*. Portal Book 075 — Chapter 5 for the random-walk statistics the chain model uses. https://open.umn.edu/opentextbooks/textbooks/part-sm-statistical-mechanics - Ball, D. W. (2011). *Introductory Chemistry*. Portal Book 056 — Chapter 16 for polymers within organic chemistry. https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry - Jensen, David (2024). *Introduction to Mechanical Design and Manufacturing*. Portal Book 109 — Chapter 16, Manufacturing: Plastic Processes, pp. 335–348, for extrusion, injection moulding and thermoforming. https://open.umn.edu/opentextbooks/textbooks/introduction-to-mechanical-design-and-manufacturing ## External links - [Introductory Chemistry](https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry), David Ball, via the Open Textbook Library — Chapter 16 for the organic chemistry of polymerisation. - [Part SM: Statistical Mechanics](https://open.umn.edu/opentextbooks/textbooks/part-sm-statistical-mechanics), Konstantin Likharev, via the Open Textbook Library — the random-walk and fluctuation chapters. - Further links, including the IUPAC nomenclature recommendations and the polymer property databases, are listed on the Wikipedia pair. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Polymer.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Polymer* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Polymer.html" data-title="Polymer"></div> *Built from `MICROSIM_GUIDE/specs/sims/Polymer.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Polymer) : [Wikitube](https://en.wikitube.io/wiki/Polymer) · pinned revision [1372169557](https://en.wikipedia.org/w/index.php?oldid=1372169557) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]], [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M48 · sim pending (matter/Polymer).*