From polymers to plasticswww.ebook3000.comwww.ebook3000.comFrom polymers to plasticsA.K. van der VegtDUP Blue Printwww.ebook3000.com VSSD 2002DUP Blue Print is an imprint of:Delft University PressP.O. Box 98, 2600 MGDelft, The Netherlandstel. +31 15 27 85678, telefax +31 15 27 85706, e-mail info@library.tudelft.nlinternet: http://www.library.tudelft.nl/dupPublished on behalf of:Vereniging voor Studie- en Studentenbelangen te DelftPoortlandplein 6, 2628 BM Delft, The Netherlandstel. +31 15 27 82124, telefax +31 15 27 87585, e-mail: hlf@vssd.nlinternet: http://www.vssd.nl/hlfURL on this book: http://www.vssd.nl/hlf/m008.htmAcollectionofdigitalpictures,printedinthebook,canbemadeavailableforlecturers who adopt this book. Please send an e-mail to hlf@vssd.nl.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photo-copying,recording,orotherwise,withoutthepriorwrittenpermission of the publisher.Printed in The Netherlands.Internet editionNUGI 831Key word: polymerswww.ebook3000.com5PrefaceThetwowordsinthetitleofthisbook,polymersandplastics,couldbeconsidered as referring to two different worlds.Intheworldofpolymers,thepropertiesofchainmoleculesareinthefocusofattention, and are subject of thorough theoretical studies.In the world of plastics, the end-use performance of the technically used materialscounts, as well as their behaviour in the various processing operations in which theyare transformed into finished articles.Nevertheless,thesetwoworldsarecloselyrelatedtoeachother.Thetypicalbehaviour of plastics materials, strongly deviating from other materials, can only beunderstood on the basis of the chain properties.In this book an attempt has been made to give a survey of polymer properties, and ofthe way these are, on the one hand, governed by their molecular structure, and are,on the other hand, responsible for the technological behaviour of plastics materials.As a result of this intention, cross-references are given throughout the whole book:everyaspectofpolymerscienceandofplasticstechnologyiscloselyrelatedtopractically every other aspect!ThisbookoriginatesfromseveralseriesoflecturesattheDelftUniversityofTechnology during the years 1978 - 1988, later on integrated into a number of post-graduateandothercourses.Sinceonlyafirstintroductionisgiven,moredetailedtreatmentandmorescientificdepthhavebeensacrificedtothestrivingforsurveyand integration.Delft, May 1999A.K. van der Vegtwww.ebook3000.com7ContentsPREFACE 51. INTRODUCTION 111.1. Origin of plastics / polymers 111.2. Main categories 141.3. The most important plastics 151.3.1. Thermoplastics 151.3.2. Thermosets 181.3.3. Synthetic elastomers 191.3.4. Composite plastics 202. MOLECULAR COMPOSITION 222.1. Chain structure 222.1.1. Main chain222.1.2. Side groups 252.1.3. Copolymers 262.2. Chain length and distribution 262.2.1. Averages 262.2.2. Example of a chain length distribution 312.2.3. Measuring methods 332.3. Chain regularity 382.4. Chain conformations 412.5. Chain flexibility 472.6. Chain interactions 482.7. Cross-linking 493. GLASSY STATE AND GLASS-RUBBER TRANSITION 523.1. Glassy state 523.2. Molecular picture 543.3. Thermodynamics of the glass-rubber transition 563.4. Factors governing Tg593.4.1. Chain flexibility 603.4.2. Chain interactions 613.4.3. Chain length 623.4.4. Effect of time scale 623.5. Glass-rubber transition of blends 633.6. Methods of measuring Tg64www.ebook3000.com8 From polymers to plastics4. CRYSTALLINE POLYMERS 654.1. Conditions for crystallization 654.2. The melting point 674.3. The crystallization process 724.3.1. Nucleus formation and crystal growth 724.3.2. Isothermal crystallization 754.4. Crystalline structure 784.4.1. Crystalline fraction 784.4.2. Crystal morphology 794.5. Effect on properties 814.6. Liquid-crystalline polymers 845. RUBBERY AND LIQUID PHASES 865.1. Rubbery phase 865.2. Transition of rubber to fluid 915.3. Fluid condition 925.3.1. Viscosity 925.3.2. Non-Newtonian behaviour 935.3.3. Melt elasticity 975.4. Some consequences for processing 976. VISCO-ELASTICITY 1026.1. Models 1026.2. Dynamic mechanial behaviour 1106.3. Integration 1127. MECHANICAL PROPERTIES 1177.1. Stress-strain diagram 1177.2. Stiffness and creep 1187.2.1. Modulus of elasticity 1187.2.2. Creep 1207.2.3. Non-linearity 1227.2.4. Physical ageing 1247.3. Damping 1267.4. Strength 1307.4.1. Tensile strength 1307.4.2. Long term strength 1317.4.3. Impact strength 1367.5. Surface properties 1387.5.1. Hardness 1387.5.2. Friction 1397.5.3. Abrasion 142www.ebook3000.comContents 98. FURTHER PROPERTIES 1448.1. Thermal properties 1448.1.1. Brittleness temperature 1448.1.2. Softening 1458.1.3. Thermal expansion 1478.1.4. Thermal conduction 1488.1.5. Maximum temperature of use 1508.1.6. Burning behaviour 1508.2. Electrical properties 1518.2.1. Electric resistance 1518.2.2. Dielectric properties 1548.2.3. Electric strength 1558.3. Optical properties 1558.4. Effects of environment 1568.5. Stress corrosion 1588.6. Diffusion and permeability 1599. POLYMERIC COMPOUNDS AND COMPOSITES 1619.1. Polymer blends 1619.1.1. General 1619.1.2. Miscibility of polymers 1619.1.3. Detection of miscibility 1649.1.4. Block copolymers 1659.1.5. The formation of dispersions 1689.1.6. Properties of blends 1719.2. Reinforcement by particles 1769.3. Short fibres 1779.4. Long fibres 18110. DATA ON MATERIALS 18410.1. Thermoplastics 18510.2. Thermosets 18910.3. Elastomers 19011. PROCESSING TECHNIQUES 19311.1. Principles of processing 19311.1.1. General 19311.1.2. Production cost 19511.1.3. Compounding 19711.2. Casting and compression moulding 19811.2.1. Casting 19811.2.2. Rotational moulding 199www.ebook3000.com10 From polymers to plastics11.2.3. Compression moulding 20111.3. Injection moulding 20511.3.1. General 20511.3.2. Limitations 20811.3.3. Defects 20911.3.4. Foam 21311.4. Calendering and extrusion 21311.4.1. Calendering 21311.4.2. Extrusion 21511.4.3. Film blowing 21911.4.3. Bottle blowing 22011.5. Secondary shaping 22211.5.1. Thermoforming 22211.5.2. Cold sheet forming 22411.5.3. Forging 22411.5.4. Bending 22511.5.5. Machining 22611.5.6. Welding 22611.5.7. Gluing 22811.5.8. Surface coating 22911.6. Processing of composites 23011.6.1. General 23011.6.2. Impregnating 23011.6.3. Foaming 232LITERATURE 236INDEX 237111Introduction1.1. Origin of plastics / polymersThemaincharacteristicofpolymersis,thattheyarecomposedofextremelylargemolecules; their molecular mass ranges from 10.000 to more than 1.000.000 g/mol,in contradiction to normal low-molecular substances, which in general are in theorder of 100 g/mol (water 18, sugar 342). Polymer molecules are often long, thread-like chains, which are sometimes branched, sometimes chemically cross-linked witheach other so that they form a network.Polymers are abundantly present in nature, in vegetable and animal tissues (mainlyas cellulose and proteins). Several technically used polymers have a natural origin;theyarebeingusedastechnicalmaterialsastheyareharvestedfromnaturalmaterials (natural polymers).Other polymers are partly from a natural origin; the chain molecule has grown in aliving tissue, but has been chemically modified into a half-synthetic polymer.Agrowingnumberofpolymersiswhollysynthetic;thechainmoleculeorthenetwork is being built up from small molecules (monomers) in a chemical process.Some examples of these categories are given below:Natural polymers:vegetable: timber, cotton, jute, sisal, hemp, cork, etc.animal : wool, silk, fur, etc.Half-synthetic polymers:from wood: celluloid, cellophane, viscose-rayon, cellulose plastics,from milk: casein, from which casein plastics, from hides, via a tanning process: leather,from rubber latex, via i.a. vulcanization: technical rubber.Synthetic polymers:These are synthesized from low-molecular components, mostly organic monomers.Mostofthemonomersarepreparedfromfossilfuels;herewecandistinguishbetween two main categories: carbochemistry (from coal) petrochemistry (from petroleum or natural gas).12 From polymers to plasticsCarbochemistry Coal can be pyrolysed above 800 C into coke, tar and a series of hydrocarbons. Gasification of coal with steam and air results in, a.o., a series of hydrocarbons.PetrochemistryFromdistillationofcrudeoilanumberoffuelsareobtained(kerosine,petrol,gasoline,etc.)andaresidue.Thelattercanbetransformedintoaseriesoflightercomponentsbyvacuumdistillationandthermalcracking.Alsolighterfuels(naphtha) can be converted to a series of various hydrocarbons by thermal crackingandfractionation.Naturalgascansupplyarangeofothercomponentsbysteamconversionorpartialoxidation.Itisimportantthatthermalcrackingofsaturatedhydrocarbonsresultsinunsaturatedones,containingoneofmoredoublebondsbetweentheC-atoms.Thisrendersthesemoleculesverysuitabletobeusedasmonomers in polymerisation reactions. A long saturated chain is, for instance, splitup into a number of shorter molecules which are unsaturated due to a shortage of H-atoms; they contain, therefore, one ore more double bonds:CCCCCCCCCCCCCCCCCC=CCC=CC=CC=CC=CCCC=CC=CCSome of these molecules, such as the first and the second (ethylene and propylene)can be used to build saturated chains (PE and PP). Other ones, such as the third one(butadiene)formunsaturatedchains,whichcanreactwithsulphurtoformvulcanized rubbers. (See Qu. 1.3, 1.4 and 1.5).Polymer synthesisFromthemonomersobtainedfromcarbochemicalorpetrochemicalsourcespolymerscanbebuiltup.Asmentionedabove,doublebondscantherebyplayanimportant role. Some simple examples:HCH=HCH ethylene HCHHCHHCHHCH polyethylene, PEHCH=HC HC =HCH butadiene HCHHC =HC HCH polybutadienePolymers can also be synthesized from saturated monomers, e.g. by condensationofanorganicacidwithanalcoholintoanesterwiththeformationofwater.Simplealcoholesandfattyacids,suchasethylalcohol(C2H5OH)andaceticacid(C2H5COOH)resultinalow-molecularester,ethylacetate,butwhenbifunctionalIntroduction 13molecules are used, a polymer chain (a polyester) is formed:HOOCR1COOH + HOR2OH COR1COOR2O + H2OWhen the alcohol is trifunctional (a triol), the result is a network:.Figure 1.1.PlasticsPlasticsastechnicalmaterialsarebasedonpolymers(ormacromolecularsubstances), but in most cases they contain a number of added components. Such anaddedmaterialmaybeanotherpolymer;inthiscasewehaveapolymerblend.Moreover,thereisalargevarietyofadditivesandfillers,compoundedintothepolymer for various purposes, which are roughly categorized below: in behalf of processing:lubricants for the transportation in the processing machine, antioxydantsforprotectionofthepolymeragainstoxydativedegradationduring processing, sulphur, for the vulcanization of rubbers, accelerators, for speeding up the network forming reaction with rubbers andthermosets, blowing agents, for producing foams, etc. in behalf of mechanical properties: plasticizers, e.g. in PVC, to obtain flexibility, quartz powder, mica, talcum etc. to improve the stiffness. short glass fibres, to improve stiffness and strength, rubber particles, to improve impact strength, etc. in behalf of other properties: ultraviolet stabilizers, to protect the polymer against degradation in sunlight, antioxydants,forprotectionagainstdegradationduringuseatelevatedtemperatures, antistatic agents, to reduce electrostatic charging, pigments, cheap fillers such as wood flour, for price reduction, flame retarding additives, etc14 From polymers to plastics1.2. Main categoriesTaking the chain structure as a criterion, polymers can be subdivided into two maincategories, viz. single chains and networks.Singlechainsarelinearmacromolecules,thoughthechainsmaybebranched.Anaveragescalemodelforsuchapolymerchainisahumanhairwithalengthofametre. Normally, chains are not present in this extended shape, but rather as dilutedcoils, which may, in the scale model, have a diameter of a few cm.Thecoilsaremutuallyentangled;thisfactislargelyresponsibleforthespecialbehaviour of polymers! Between chain segments relatively weakinteraction forcesare present; chain segments can move with respect to each other under the influenceof relatively small external stresses. Consequently, the stiffness of polymers is ratherlow.Flow, on the contrary, is strongly hindered by the entanglements between the coils;this is why fluid polymers show excessively highviscosities, which necessitate theuse of heavy processing machines.In networks the molecular chains are connected by strong primary chemical links; infact a network is a single gigantic molecule. Networks can be formed in two differentways:a.by forming bridges between single chains; this is the case with the vulcanizationof rubbers, mostly by sulphur bridges. But also curing of unsaturated polyesterresins is a matter of forming bridges between chains, in this case with the aid of(poly)styrene.b.byreactingbivalent with tri-(ormore)-valentmolecules,e.g.insynthesizingformaldehyde resins.Innetworkschainentanglementsandlocalmovementsofchainsegmentswithrespect to each other also occur, but flow is not possible.From the foregoing we can divide the field of macromolecular materials into threemain categories:Thermoplasticsarenon-crosslinkedsystems,whichflowatelevatedtemperaturesand which, upon cooling, return to the solid state.Syntheticelastomersareanalogoustothermoplastics,buttheyareinasoftenedcondition. As such they show flow, but after the formation of a network (by cross-linking) they are no longer fluid but retain their shape.Thermosets owetheirnametothefactthattheformationofanetwork,thecuringreaction, in many (but not in all) cases occurs at elevated temperature. The networkisconsiderablytighterthaninvulcanizedrubbers.Aformedthermosetdoesnotincreaseinhardnessorstiffnessupontemperatureincrease,but,onthecontrary,shows softening, but no flow.Introduction 15Withineachofthesethreecategoriesalargenumberofmaintypesexists,eachcharacterized by a a specific structure of the macromolecule. Within each main typeseveralvariationsoccur,e.g.concerningchainlength,chainregularity,copoly-merisation (presence of more than one monomer in the chain), etc.In the assortment of technically used materials we also meet a broad variability ofadditives and fillers, added by the manufacturer.Inthenextsectionan(incomplete)surveyisgivenofanumberofpolymers,asafirst orientation in the field of plastics materials.1.3. The most important plastics(See Qu. 1.14 1.20).1.3.1. ThermoplasticsPolyethylene (PE)isarathersoftandtough,crystallinepolymer,whichisbeingmanufacturedinthreemaintypes:LDPE(low-densityPE0.92g/cm3), HDPE(high-density PE 0.95 g/cm3), and, more recently, LLDPE (linear-low-density PE, 0.92 0.95 g/cm3). The stiffness of PE increases strongly with increasing density.All types gradually lose their properties upon temperature increase, and they melt at105 to 130 C, respectively. Principal applications are: packaging film, bags, pipes,crates,pails,bottles,etc.Specialgradesaremadeinsmallerquantities,suchasUHMPE (ultra-high-molecular), which is extremely tough and abrasion resistant, andwhich is, moreover, used for making super-strong PE-fibres. A new development is aseries of PE with very low density (.86 to .90 g/cm3), a series which extends into theregion of rubbers.Polypropylene (PP) resembles PE, but is somewhat harder and stiffer than HDPE. Itis crystalline as well, and melts at 165 C. Its impact strength at lower temperaturesis quite poor; therefore PP is often modified with a certain amount of rubber (mostlybuilt-inasacopolymer).Mainapplicationsare:filmforpackaging,fibres,crates,pipes, automotive parts (often with reinforcing fillers). A special feature of PP is itsability to form integral hinges with a practically unlimited resistance against repeatedbending.Polyvinylchloride (PVC) is a hard, amorphous polymer which softens at about 85 C.Also in PVC rubbers are sometimes added in order to improve the impact strength.The main applications of PVC are: pipes, gutters, front panels of buildings, cables,bottles, floor tiles. A much softer and more flexible material is obtained by blendingwith plasticizers: soft or plasticized PVC is being used in artificial leather, tubes andhoses, footwear, films, etc.Polystyrene(PS)isanamorphous,verybrittle,hardpolymerwithasofteningtemperature of about 90 C. Improvement of its impact strength is again obtained by16 From polymers to plasticsblendingwithrubber(inmostcasesbutadienerubber),whichgoesatthecostofstiffness. Unmodified PS is being largely applied as foam for packaging and thermalinsulation. High-impact PS (TPS or HIPS) is used for coffee cups, household wareetc.Styrene-Acrylonitrile (SAN) is somewhat stiffer than TPS, and has a better resistanceagainstimpactandtemperature.Itismainlyusedinpartsofhousehold-andelectrical appliances, battery houses etc.Acrylonitrile-Butadiene-Styrene(ABS)issometimesaterpolymerofthreemono-mers,butinmostcasesablendoftwocopolymers.ABShasanexcellentimpactstrength and a relatively high softening temperature (about 110 C). Its stiffness isonlymarginallylowerthanthatofPS.Itfindslarge-scaleapplicationsintheautomotive industry, in toys, telephones, TV-housings, etc.Polymethylmethacrylate(PMMA),carryingtradenamessuchasPerspexandPlexiglass, is an amorphous, relatively hard and transparent polymer. Its stiffness isretained until near its softening temperature (110 C). Most applications are based onits superior optical qualities: safety glass, decoration material, traffic signs, etc.Polyamide (PA)isgenerallyknownasnylon.Thisisacollectionofpolymers,whichdifferinchainstructure,andwhichare,accordingtothenumbersofconsecutive C-atoms in the chain, designated as (a.o.) PA-6, PA-6,6, PA-11, PA-4,6and PA-12. Initially PAs were only used as fibre materials, but later on they found apositionundertheengineeringplastics.Polyamidesarecrystallinepolymerswithrelatively high melting points (between about 200 and 300 C). They possess a goodimpact strength, due to the fact that they absorb several percents of water from theatmosphere.Moreover,agoodabrasionresistanceandalowfrictionmakethemsuitablefortechnicaluse,suchasinbearingsandgearwheels.Quiteoftenpolyamides are reinforced with short glass fibres to improve their stiffness.Polyoxymethylene (POM)is,again,acrystallinepolymer,withameltingpointofabout180C.Itsmechanicalpropertiesenableittograduallyreplacemetalsinanumberofapplications.ManytechnicalpartsarebeingmadefromPOM,suchasgear wheels, bars, automotive accessories, parts of several apparatuses and machines.Thepolymerisusedassuch(e.g.Delrin),butalsoasacopolymerwithasmallamount of ethylene oxide (e.g. Celcon and Hostaform).Polycarbonate (PC) is, up to about 140 C, an amorphous glassy transparent polymerwithexcellentmechanicalproperties,inparticularasregardsitsimpactstrength.This renders it very suitable for substitution of glass, but also for a series of technicalapplications in which it replaces metals. For the latter, reinforcement with short glassfibres opens further possibilities. A weak point of PC is its poor resistance againstenvironmental stress cracking in contact with a number of organic liquids.Introduction 17Polyethylene terephtalate (PETP) is a (saturated) polyester and is, like nylon, knownfor its large-scale use as a textile fibre. Moreover it is being applied at an increasingscale as a plastic, viz. in films, bottles (the PET-bottle) and injection-mouldings.Though its stiffness decreases significantly above 70 C, it remains a solid up to itsmelting point (255 C).Polybutylene terephtalate (PBTP) differs in its chemical structure only slightly fromPETP;itsmeltingpointissomewhatloweranditsprocessabilityisbetter.Theapplications in injection moulded articles are similar to those for PETP.Polyphenylene oxide (PPO) or Polyphenylene ether(PPE) is an amorphous polymerwithasofteningtemperatureofabout210C.Toimproveitsprocessabilityitismostly blended with PS (modified PPE, e.g.Noryl), which is at the cost of its heatdistortiontemperature.Thepropertiesareexcellent;theapplicationsaremainlyinfine-mechanical construction, in automotive parts, in household equipment etc.Polysulphone (PSU)isahigh-performancepolymerwithsuperiormechanical,electrical and thermal properties in a temperature region from 100 up to 180 C. Itis mainly used in exacting mechanical and electrical applications.Polyphenylene sulphide(PPS)(e.g.Ryton)isahighlycrystallinepolymerwithameltingpointof290 C.Itcombinesgoodmechanicalpropertieswithveryhighthermal and chemical resistance; it is, moreover, self-extinguishing. It is, i.a., used asprotective coating on metal surfaces.Polyimide (PI) caps all other polymers in its temperature range of use (200 to 260Cinair;short-timeevenupto500 C).Becauseofitshighprice,itisusedinspecial cases only, such as space vehicles, nuclear reactors and some electronic parts.Newer developments, related to polyimide, are the polyether imides (e.g. Ultem),polyesterimidesandpolyamideimides(e.g.Torlon),allwithverygoodmechanical, thermal and electrical properties and self-extinguishing.Polytetrafluoroethylene (PTFE), mostly known as Teflon, has as special propertiesitshighmeltingpoint(327C),itsverygoodresistanceagainstchemicalsanditsextremely low friction. though the polymer is mechanically weak and shows a strongtendency to creep, though processing is very difficult (only possible via a sinteringprocess) and though it is very expensive, it is being used in a number of applicationssuch as bearings, pipes, sealing rings, electrical insulation and coatings on kitchenpans. Often the polymer is reinforced with fillers.Tetrafluoroethylene-perfluoropropylene (FEP) resembles PTFE in its properties, butcan be processed as a thermoplastic polymer.Polyvinylidene fluoride (PVDF) and Ethylene tetrafluoroethylene copolymer (ETFE)can be considered as diluted PTFEs, which in their structure and their properties18 From polymers to plasticsare in between PTFE and the polyolefins PE and PP. They are processable with thenormal techniques and find similar applications as PTFE.Cellulose acetate(CA) and Celluloseacetatebutyrate(CAB)are,contrarytothepolymers mentioned so far, not fully synthetic, but derivates of vegetable cellulose.They are strong, tough and well processable materials, used in many household- andtechnicalapplications,suchashammerheads,magnetictape,toysetc.CABhasahigher form stability than CA, and is used in automotive accessories and in pipes.Polybutylene (PB) belongs to the family of polyolefins (PE and PP), but is much lessusedbecauseofitshigherprice.ThoughitdoesnotdifferverymuchfromPEinstiffness and melting point, it has a better resistance against creep and environmentalstresscrackingthanPEandPPandahighertoughnessandtearresistance.Itsapplications are mainly in film for heavy-duty bags and in hot water transport pipes.Polymethylenepentylene (PMP)is,again,apolyolefin,butwithamuchhighermelting point than the other ones (240 C). Despite its crystalline nature PMP can bewelltransparent.Itisuseda.o.inlaboratorybottles.OneofitstradenamesisTPX.Polyetheretherketone (PEEK)andPolyether sulphone(PES)belongtothemostrecentdevelopmentsinthefieldoftechnicalhigh-performancepolymers.Bothpossess very good thermal and mechanical properties, which can be further improvedby reinforcing fibres. Their application is mainly in aircraft and space vehicles.Polyketone (PK) (CARILON) is a new polymer with an attractive combination ofproperties (very tough, high abrasion resistance, high temperature resistance, easy toprocess, good chemical resistance and barrier properties). It is trying to find its wayin various potential applications.1.3.2. ThermosetsPhenol-formaldehyde(PF)wasthefirstfullysyntheticmacromolecularmaterial(Bakelite, 1907). In a slightly precured condition and provided with fillers, it is, asamouldingpowder,availableforprocessingintoend-usearticlessuchasbulbfittings, switch housings, coils, laminated wood and foam for thermal insulation.Ureum-formaldehyde (UF)iscomparabletoPF,butissomewhatstifferandhas,becauseofitscolourlessnessandgloss,amoreattractiveappearance.Theapplications are in the same fields as PF.Melamine-formaldehyde (MF) is qualitatively better than UF. It is, therefore, used inmore demanding applications such as crockery, various electrotechnical articles anddecorative panels.Unsaturated polyesters(UP)can,withasecondcomponent,e.g.styrene,andwithIntroduction 19initiators and accelerators be cured into a network structure. The reaction can takeplaceatroomtemperature.UPis,inmostcases,usedincombinationwithglassfibres, and finds its applications in pipes, vessels, boat building etc.Epoxyresin(EP)hastobemixedwithasecondcomponent,thecuringagent,toundergothecuringreaction,which,aswithUP,cantakeplaceatambienttemperatures.Epoxy/fibrecomposites(withglass,carbonoraramidfibres)findsimilar applications as UP/glass, but are being applied more selectively because oftheirhigherpriceandbetterproperties.Besides,epoxiesareusedinlacquersandadhesives and as casting resins in electrotechnical applications.Polyurethanes (PU).Thethermosettingtypeofthislargefamilyofpolymersismainly used as foam. A mixture of two components with a foaming agent forms alight, hard foam, which is a superior thermal insulator.1.3.3. Synthetic elastomersStyrenebutadienerubber (SBR)is,quantitatively,themostimportantsyntheticrubber.Itisacopolymerofstyreneandbutadieneinsucharatiothatitsrubberynaturepredominates.vulcanizationiscarriedoutwithsulphur,reinforcementwithcarbon black. It is used at a very large scale in tyres for passenger cars, thanks to itsexcellent combination of abrasion resistance and friction on the road. In large tyres itcan not replace natural rubber because of its heat development (hysteresis losses).Butadiene rubber (BR) or Polybutadiene has an excellent abrasion resistance and averylowdamping,butis,undiluted,toojumpyforuseintyres.InblendswithSBR or natural rubber a good compromise of properties can be obtained.Isoprene rubber (IR) or Polyisoprene is a synthetic copy of natural rubber (NR) andapproachesNRinitsproperties.Besidesfortyres,IRis,becauseofitsgoodflowproperties, suitable for injection moulding.Butylrubber (IIR) is derived from polyisobutylene, a polymer which is not furthermentionedinthischapter,whichhasarubberynature,butwhichcannotbevulcanisedintheconventionalwaywithsulphur.Thisobjectionistakenawaybycopolymerisationwithasmallamountofisoprene.Butylrubberhasaverylowresilience,butoutrivalsallotherrubbersinresistancetogaspermeation;forthatreason it is generally used for tyre inner tubes.Chloroprene rubber (CR) is a synthetic rubber with very high chemical resistance,and is, therefore, applied in cable protection, oil transport tubes etc.Nitrile rubber (NBR), a copolymer of butadiene and acrylonitrile, is characterized byits high resistance against light and oxygen, thus against ageing. Moreover it is notattacked by oil and several organic solvents. For these reasons, it finds its place indemanding applications.20 From polymers to plasticsEthylene-propylenerubber (EPRorEPDM)is,basically,acopolymerofethyleneand propylene. Because of the random arrangement of the monomers in the chain,crystallizationdoesnotoccur,andthematerialbehavesasarubber.Justaswithpolyisobutylene,vulcanizationwithsulphurisimpossible(thechainissaturated).Alsohere,asmallamountofanothermonomerisincorporated,whichenablesthevulcanizationandthustheuseasatechnicalelastomer.EPRhasahighresistanceagainst ageing and chemical attack, and is, compared with other specialty rubbers,relatively cheap.Silicone rubbers have, contrary to all other polymers, no carbon atoms in their mainchain,butsiliciumandoxygenatomsonly.Theycanbeuseduptoveryhightemperatures (250 C) and are highly resistant against ageing, so that, despite of theirhigh price, they are frequently used in demanding applications.Thermoplastic elastomers (TPEs) are characterized by the exceptional property that,withoutvulcanization,theybehaveascross-linkedrubbers.Theyareblock-copolymers, in which blocks of the same nature assemble in hard domains, acting ascross-linksbetweentherubberypartsofthechain.Theseharddomainslosetheirfunction when they reach their softening temperature, so that the material can then beprocessed as a thermoplast. One of the oldest member of the family of TPEs is SBS(styrene-butadiene-styreneblockcopolymer),butseveralotherTPEshavebeendeveloped,i.a.onthebasisofpolyesters,polyurethanesandpolyolefins.Intheirproperties these polymers cover a broad range between conventional rubbers and softthermoplastics.Polyurethane rubber (PUR). Not only in the thermosets (and the thermoplastics), butalso in the field of synthetic elastomers polyurethanes have found a position, namelyasasoftertype.Itis,again,formedfromtwocomponentsandis,withablowingagent, processed into a foam. Polyether mattresses belong to this category, but alsomicrocellular structural foams, used in bumpers, head- and arm-rests in motorcars,etc.1.3.4. Composite plasticsBlendsofpolymersaremanufacturedandappliedatanincreasingscale.Onlyinexceptional cases are polymers soluble in each other and can form a homogeneousblend (an example: PPE + PS, a blend known as Noryl). In most cases blends are,therefore, dispersions. Rubber particles are dispersed in brittle polymers to improvetheir impact strength (toughened PS and PP, ABS etc.), but also hard polymers arecombined to reach a favourable compromise between properties (and price).Reinforcementwithparticlessuchaschalk,quartz,micaandglassspheres,isfrequently carried out with thermoplastics and thermosets to obtain a higher stiffness(and sometimes a higher strength). There is a gradual transition from high-quality toIntroduction 21cheap fillers, the latter being mainly used as price reducing agents, but also for. e.g.reducing shrinkage in processing. Rubber vulcanisates gain considerably in strengthand abrasion resistance by the incorporation of carbon black (up to 40 weight %)Reinforcement with short fibres is important for thermoplasts and thermosets. Withthe former, very short fibres (glass or other) are blended into the polymer; the latterallow the use of longer fibres. The effect is a 3- to 5-fold increase of the stiffness anda 1.5 to 3-fold increase in strength.Foams can be made from thermoplastics, thermosets and rubbers. Densities can beobtained from nearly solid down to 200 times diluted. Structural (or integral) foamshaveasolidskin.Thebestknownfoammaterialsarepolystyrenefoam,polyurethane foam and polyether foam.Reinforcement with continuous fibres. In this case the fibres, as strands or cloth, arelargely responsible for the mechanical properties. Traditionally, thermosetting resinsare used in this case, because of the ease of impregnating fibre bundles or cloth withthe low-viscosity uncured resin. Recently however, techniques have been developedtoalsoreinforcethermoplasticswithlongfibres.Conventionalcombinationsarepolyester/glass(GF-UP)andepoxy/glass(GF-EP),butalsohigh-qualityfibresascarbonandaramide,andthermoplasticmatricessuchasPEEKarebeingusedforspecial applications.222Molecular composition2.1. Chain structureAlinearchainconsistsofabackbone,themainchain,atwhichsidegroupsareattached.Inthissectionasimpleclassificationofthevarioustypesofmainchainwill be given, followed by a survey of frequently occurring side groups.2.1.1. Main chain (Qu. 2.1 and 2.2)Carbon atoms only: saturated:CCCCCCexample: polyethylene (PE)[HCHHCH]nalso PP, PS, PVC, PB, PMMA, PTFE, etc. (see 2.1.2) unsaturated:CC=CCCC=CCexample: polybutadiene[HCH CH= CHHCH]nalso IR, CR, etc. (see 2.1.2) more unsaturated:C=CC=CC=Cexample: polyacetylene.[ CH= CH]nCarbon and oxygen atoms:COCOCOCOMolecular composition 23example: polyoxymethylene (POM) :[HCHO]nalsoCCOCCOCCOexample polyethyleneoxyde (PEO)[HCHHCHO]nCarbon and nitrogen atoms:CCCNCCexample: various types of PA (nylon):[C||O(CH2)pC||ON|H(CH2)qN|H]nCarbon, oxygen and nitrogen atoms:CCNCOCCexample: various types of polyurethanes:[(CH2)pOC||ON|H(CH2)qN|HC||OO]nCarbon rings: example: polycarbonate (PC):[O CH3|C|CH3 OC||O]nother example: polyethylene terephtalate (PETP):[C||O C||OOCH2CH2O]n24 From polymers to plasticsalso PBTP, with four instead of two CH2 groups,[C||O C||OO(CH2)4O]npolyetherether ketone, PEEK:[O O C||O ]npolyphenylene ether, PPE:[CH3

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CH3O]nCombination with sulphur atoms:examples:polyphenylene sulphide (PPS):[ S]npolysulphone (PSU[ CH3|C|CH3 O O||S||O O]npolyether sulphone, PES:[O O||S||O ]nSilicium and oxygen atoms only:example: polydimethylsiloxane (silicone rubber):[CH3|Si|CH3O]nMolecular composition 25Multiple rings:example: polyimide (PI):[NCOCOCOCON O ]n2.1.2. Side groups The most frequently occurring side group is the hydrogen atom; it is the only onewith polyethylene, polybutadiene and polyoxymethylene. Other arrangements often met are: vinyl polymers[HCHHCR]with: R = CH3polypropylpene (PP)R = Cl polyvinylchloride (PVC)R = C6H5 = polystyrene (PS)R = CH2CH3polybutylene (PB)R = CN polyacrylonitrile (PAN) vinylidene polymers[HCHRCR]with: R = Cl polyvinylidenechloride (PVDC)R = F polyvinylidenefluoride (PVDF)R = CH3polyisobutene (PIB) polytetrafluorethylene (PTFE)[RCRRCR]with: R = F polymethylmethacrylate (PMMA)[HCHR1CR2]with: R1 = CH3 and R2 = COOCH326 From polymers to plastics polydienes[HCHHC =RC HCH]with: (R = H polybutadiene (BR) R = CH3polyisoprene (IR) R = Cl polychloroprene (CR) etc. etc.2.1.3. CopolymersCopolymer chains are built up from more than one type of monomeric units. Someexamples::ethylene + propylene: EPRstyrene + butadiene: SBR or SBS (see 2.3)styrene + acrylonitrile: SANisobutylene + isoprene: IIR (butyl rubber)etc.Also terpolymers (with three monomers) are made:ethylene + propylene + a diene: EPDMacrylonitrile + styrene + acrylic ester: ASAethylene + CO + propylene:PK, poly ketone (Carilon).(see further 2.3)2.2. Chain length and distribution2.2.1. AveragesThechainlengthcanbeexpressedasdegreeofpolymerisationP(numberofmonomericunitsinthechain),or,inmostcases,asmolarmass(ormolecularweight)ing/mol.Sometimesthebetterunit,kg/molisused;thedifferenceisafactor of 1000. In this book the older unit, g/mol, will mostly be used.An example: PE with a degree of polymerisation P of 5000 has a molar mass:M = 5,000(2C + 4H) = 5,000(24 + 4) = 140,000Of most polymers various types exist, which differ in molecular mass. The strongestexampleisPE,whichismadeatmorethan10differentlevelsof M, the extremesdiffering by a factor of 20. But also within each type the chains may largely differ inlength, namely by a factor of 100 or even 1000. Therefore every statement about amolar mass indicates an average.Molecular composition 27Averages can be defined in several ways, for example after number or after weight.A simple example:1 chain with mass 100 and1 chain with mass 10then the number average is:12 100 + 12 10= 55since the numbers are equal, and the number fractions n1 and n2 are both12.Now consider a system with:1 chain with mass 100 (total mass 100)and10 chains with mass 10 (total mass 100)then the weight average is:12 100 + 12 10= 55because now the weight fractions are equal (w1 en w2 both 12).Expressed in a formula:number average Mn = niMiin which ni is the number fraction of the chains with massMi, and ni = 1.The weight fraction is Wi = niMi; now however, Wi is not equal to 1; the fractionsWi must, consequently, be reduced (normalized) to wi, so that wi = 1:wi = niMi niMi= Wi WiThe weight average is now:Mw = wiMiAlso valid is:Mw = niMi2 niMi= niMi2MnIn most cases it is necessary to work backward from the weight fractions wi:Ni = wiMibut28 From polymers to plastics Ni 1so Ni has to be normalized to ni with:ni = Ni Ni= wi/Mi (wi/Mi)Now ni = 1 , and Mn follows from Mn = niMi.The calculation of Mn is easier with:Mn = niMi = wi (wi/Mi)= 1 (wi/Mi)Also higher averages are used:Mz = ziMiin whichzi = wiMi wiMi (normalized)soMz = wiMi2 wiMi= niMi3 niMi2This is the so-calledz-average. A further step in the same direction gives the (z+1)-average:Mz+1 = niMi4 niMi3We apply the formulae for Mn. Mw and Mz to the simple example given above:A 100 10 (100 + 10)B 100 10 (100 + 10 10)A BM1= mass chain 1 100 100M2= mass chain2 10 10n1= number fraction 1 1/2 1/11n2= number fraction 2 1/2 10/11Mn= niMi55 18.2w1= weight fraction 1 = n1M1/ niMi10/11 1/2w2= weight fraction 2 = n2M2/ niMi1/11 1/2Mw= wiMi91.8 55z1= z-fraction 1 = w1M1/ wiMi100/101 10/11z2= z-fraction 2 = w2M2/ wiMi1/101 1/11Molecular composition 29Mz= ziMi99.1 91.8Another,morerealisticexample:Ablendismadeofthreemonodispersefractions(i.e. in each fraction all chains have the same length), with masses of 20, 50 and 30grammes and molar masses of 20,000, 100,000 and 300,000 g/mol, respectively. Themass fractions are now:w1 = 20100 = 0.2w2 = 50100 = 0.5w3 = 30100 = 0.3( wi = 1)This leads to:Mw = 0.220000 + 0.5100000 + 0.3300000 = 144000Mn can be calculated with:N1 = 0.220000 , N2 = 0.5100 000 , N3 =0.3300 000 , Ni =4.8300 000After normalization we find: n1 = 10/16, n2 = 5/16, n3 = 1/16.Mn = (10/16)20000 + (5/16)100000 + (1/16)300000 = 62.500(The calculation is simpler with Mn = 1/(wi/Mi)).The z-fractions are, unnormalized:Z1 = 0.220000 Z2 = 0.5100000 Z3 = 0.3300000and normalized:z1 = 4144z2 = 50144z3 = 90144It simply follows now that:Mz = 222,778Theexamplesshowclearlythatin Mn, Mwand Mzinthisorderofsequence,thelonger chains play an increasingly dominant part.In most casesMw is used for general characterization of the molar mass besides D =Mw/Mn, the heterogeneity index, is of importance as a simple measure for the spreadin chain length. In the first exampleD=1.67forAand3.03forB.Inthesecondexample D = 2.3. For technical polymers D can have values from 1.1 up to 30.30 From polymers to plasticsAn even more realistic question is, how the averages change when two polydispersepolymersofthesametypearebeingblended.Supposetwobatches,AandB,areavailable with weight average molar masses (Mw)A and (Mw)B anda blend is madeof a weight fraction of A with a weight fraction (1 ) of B. For the blend C theweight average is now:(Mw)C = (Mw)A + (1 )(Mw)B. The number of chains in 1 gramme of polymer is N/Mn (N is the Avogadro number).In 1 gramme of the blend C, grammes of A and 1 grammes of B are present,so).N/(Mn)C = N/(Mn)A + (1 )N/(Mn)B, or:/(Mn)C = 1/(Mn)A + (1 )/(Mn)BHow broad is now the distribution of the blend C? We find DC by multiplying theexpressions for (Mw)C and 1/(Mn)C.A much simpler expression is found when weconsider a special case, viz. two components with the same degree of dispersion D,in which (Mw)A = (Mw)B (and, therefore, (Mn)A = (Mn)B). Some calculation leadstoDC = (Mw)C(Mn)C = D[(1 ) ( 1)2 + 1].Anexample:=4, MwofA(e.g.60,000)isfourtimesgreaterthan MwofB(15,000). We choose = 12, so we blend equal masses, and the blend has an Mw of37.500. When now, for instance, D = 6, so that theMns of both components are sixtimes smaller than the Mws (10,000 en 2,500, respectively), thenDC = 6[ 12 12 94 + 1] = 6 2516 = 9.375 ;the distribution width is increased by more than a factor 1.5. Mn of the blend is now37,500 / 9.375 = 4,000.This simple rule, though based on the assumption that the molar mass distributionsare similar, has practical significance because polymers made in one and the sameprocess, do in general not differ much in their heterogeneity index.So far, we have considered the magnitudes of several types of average molar masses.The question may arise what the use is of these different averages; the attention paidto them might look a bit artificial. Well, it is easy to understand that various polymerpropertiesareinfluencedbythemolarmass.Moreover,itappearsthatdifferentphysicalpropertiesofpolymersarecontrolledbydifferenttypesofaverage molarmass. A few examples:Molecular composition 31 Thenumberaverage, Mn,isproportionaltothemassofonegrammeofthepolymerdividedbythenumberofchains.Itis,therefore,afunctionofthenumber of chains, and thus of the number of chain ends (apart from branching).Nowsupposethatacrackwithasharptippropagatesthroughapieceofthepolymer, then this propagation is easier as less chains have to be broken, and itmeets more chain ends on its way. This means that all properties in which crackpropagation plays a role, such as impact strength, tear strength and environmentalstress cracking are governed by Mn.- Theweightaverage, Mw,isthemostpracticalone.Ifyoublend,forinstance,equalquantities(inkg)oftwobatcheswithmolarmasseM1 and M2,thenyouwould expect the average (M1 + M2) / 2. And this is, of course, a weight average,for nobody would consider to blend equal nunbers of chains with each others!Inaddition, Mwisspeciallyresponsibleforthe viscosity of the polymer in moltencondition,and,therefore,fortheprocessability.Thisholds,however,onlyasafirst approximation, as we will see later in 5.3. As a third example we look at the z-average, Mz. In the foregoing we have seenthat Mz (and, in particular, Mz+1), are governed by the longest cahains, while thesort chains have hardly any effect. A property in which the longest chains have apredominant effect, is the melt elasticity. This is a rather unexpected expression,because a fluid is, in general, not an elastic substance. Yes, but for polymers, it is!Letusconsiderapolymer,consistingforthelargerpartofshortchains,withasingle very long chain. When this polymer is deformed in a flow field, the longchain will, as a tracking-thread, keep the short chains together, and force them toreturn to the most probable conformation, so to return back. This is further treatedin 5.3.2. This melt-elasticityis of major importance for practical processingtechnology and for some other properties. It is clear that we cannot neglect higheraverages, such as Mz and Mz+12.2.2. Example of a chain length distributionIn a polymerization process the chain length distribution ormolar mass distribution(MMD) is influenced by a large number of factors and conditions; the kinetics of thereaction plays a very important role. The calculation of the resulting MMD is thusverycomplicated.Foroneofthesimplestcases,astepreactionwithpolycondensation,afirst-orderapproachisgivenhere.Asanexamplewetakeahydroxy acid HORCOOH, which, upon condensation, forms the chain [ORCO]n.With each step a COOH and an OH group react with each other, forming an estergroup and a water molecule. If we denote the numbers of COOH and OH groupsboth by U, then at the start of the reaction U = U0 = the total number of hydroxy acidmolecules.32 From polymers to plasticsAfter some time t, U = U(t); the number of COOH and OH groups disappeared is(U0 U), which also is the number of ester groups formed. We define the conversiongrade p as the fraction of the number of groups which have reacted:p = U0 UU0or U = (1 p)U0Now there are U molecules, containing together U0 basic units; the number of unitsper chain, the average degree of polymerizationP, is, therefore:P = U0(1 p)U0= 11 pAn example: With a conversion grade of 0,99 P = 100. Evidently, this P is a numberaverage degree of polymerization, Pn.Thequestionisnow,howthedistributionofP(andthusofM)lookslike.Weconsider,duringthereaction,whentheconversiongradeisp,asingleCOOHgroup.ThechancethattheOHgroupofthismonomerhasreactedwithanotherCOOH group, is p; the chance that it has not reacted, is (1 p).The chance of HOOCROH thus is (1 p)The chance of HOOCROOCR is pThe chance of HOOCROOCROH is p(1 p)The chance of HOOCROOC-ROOCR is p2etc.The chance of (i 1) times addition is pi 1the chance of not reacting with the ith monomer is (1 p)the chance of both events, so the chance of the occurrence of a chain of i units,is the product pi 1 (1 p). This is, therefore the number fraction, ni.NiN= ni = pi 1 (1 p)It follows easily that:1 ni = 1With this formula the value of the number average, found before, can be checked:Pn = _i = nii ni= 1 p1 p 1 + 2p + 3p2 + 1 + p + p2 + = 11 pThe weight average degree of polymerization is:Molecular composition 33Pw= Wii Wi= nii2 nii= pi 1 (1 p)i2 pi 1 (1 p)i= 1 + 4p + 9p2 + 16p3 + 1 + 2p + 3p2 + 4p3 + = 1 + p(1 p)3 1(1 p)2= 1 + p1 pThe ratioD = Pw/Pn, theheterogeneityindex, is D = (1 + p).Fortheusuallyhighconversion rates (e.g. p = .995), D 2.The chain length distribution can be represented graphically in several ways, e.g. asnumber fractions or as weight fractions. In Figure 2.1 both cases are given (togetherwiththez-fractions)forap-valueof0.99.Fromthegraphofnumberfractionsitappears that the monomer has, numerically, the highest fraction! The distribution oftheweightfractionswihasitsmaximumatthenumberaveragedegreeofpolymerization, Pn = 100, while Pw = 199. Further calculation gives: Pz = 299.p = 0.990.0040.0020.0100.0050100 200 300 400 500iniwiziPnPwPzwiniFigure 2.1. Chain length distribution of a polycondensate.2.2.3. Measuring methodsThe number average Mn can, in principle, be determined by counting the moleculesin a gramme of polymer. This is possible by measuring colligative properties of thepolymer in solution; these are properties which are strictly dependent on the numberof molecules per unit volume of the solution, and independent of their nature or size.Colligative properties are:34 From polymers to plastics-vapour pressure reduction,-freezing point reduction,-boiling point increase,-osmotic pressureForpolymerswithnormal,highmolarmassestheosmoticpressureistheonlypossibility; the other methods give a too small effect because of the relatively smallnumber of molecules.Theosmoticpressure,,isthepressuredifferencebetweensolutionandpuresolventwhentheseareseparatedbyasemipermeablemembrane(seeFigure2.2).For very dilute solutions the osmotic pressure is given by (see Qu. 2.35 and 2.36): = kT NVin which N is the number of molecules in a volume V, k is Boltzmanns constant andT the absolute temperature. N can, via the molar fraction and the weight fraction, beexpressed in the concentration c (g/dl) and the molar mass M; the formula then reads: = RT cMnHowever,/c does not automatically lead to the correct value ofMn, since /c isstill slightlydependent on c. Measurements are, therefore, carried out at a number ofdifferent concentrations and a plot of /c against c is extrapolated to c = 0.solvent solutionFigure 2.2. Principle of osmometry.Forthedeterminationoftheweightaverage, Mw,aboutlightscattering isthestandardmethod.Thisisbasedonthefactthatadensityfluctuationinasolution,brought awayby the presence of a coil molecule, causes a deviation of a ray of light.The amplitude of the scattered waves is proportional to the mass of the particle; theintensity is proportional to the square of the amplitude and thus to the square of themass.Fromthissimplereasoningitcanbeintuitivelyunderstood(thoughnotproven), that the total amount of scattered light from all molecules present is relatedto the weight average molar mass.A strict condition is, that the scattered waves do not interfere with each other so thatthe concentration must be very low. Light scattering is a very laborious and difficultmethod;minorcontaminationsaredisastrousfortheresult.ItisonlyusedwhenMolecular composition 35h1h2c[]redFigure 2.3. Principles of measuring intrinsic viscosityabsolute determinations of Mw are necessary.Higher averages can be obtained by measuring the rate of sedimentation in solventswiththeaidofanultracentrifuge.Thisisbasedonthefactthattherateofsedimentation depends on the molar mass. The measurements supply Mwand Mz,,sometimes Mz+1.Theviscosityaverage, Mv,doesnotbelongtotheseries Mn, Mw, Mzetc.Themeasurementdoesnotsupplyanabsolutevalueofthemolarmass,butcan,bycontrast with the other methods mentioned so far, be carried out in an easy way. Itsprincipleis,thatapolymer,evenatverylowconcentrations,bringsaboutasignificant viscosity increase of the solvent. This increase is not only dependent ontheconcentrationbutalsoonthemolarmass.Themeasurementiscarriedoutasfollows (see alsoQu. 2.14 - 2.18 and 2.31 - 2.34):In a capillary viscometer the time is determined in which the liquid has dropped fromthe initial level h1 toh2 (see Figure 2.3); this time is proportional to the viscosity ofthe liquid. When we denote the viscosity of the solvent by 0 and that of the solutionby , then the specific viscosity is defined as:sp = 00This is the relative increase in viscosity, which, in a first approximation, appears tobe proportional to the concentration c. A better measure is, therefore :spc= 00c= red,the reduced viscosity.This red is still somewhat dependent on the concentration. It is, therefore, measuredatanumberof(low)concentrations;thevaluesfoundareextrapolatedtoc = 0,where the intrinsic viscosity is read off, which is denoted by []:36 From polymers to plastics[] = limc0 red = limc0 00c[] does not have the dimension of a viscosity, but of c1; in most cases it is given indl/g.A strongly schematized example:For a certain polymer in a certain solvent, times offlowthroughthecapillaryatseveralconcentrationsarefoundasindicatedinthetable. The specific viscosities ( 0)/0can now be calculated as (t t0)/t0; fromthese values the reduced viscosities follow, and extrapolation to c = 0(in this casevery simple, because the relation is linear) leads to:[] = 1.525 dl/gc (g/dl) t (sec) sp () red (dl/g)0 100.2 13.3 0.33 1.650.4 17.1 0.71 1.7750.6 21.4 1.14 1.90The intrinsic viscosity appears to depend on the molar mass according to the Mark-Houwink relation:[] = kMainwhichken aareconstantsforagivencombinationofpolymer,solventandtemperature. k is in the order of magnitude of 10-3 when [] is expressed in dl/g;a ismostly in between 0.5 and 1. The measurement of the molar mass is not an absoluteone; for each combinationk and a have to be determined in an empirical way withthehelpofabsolutecharacterizationmethodssuchaslightscattering.Valuesofkand a are amply being supplied in handbooks.Thequestionisnow,whatkindofaveragemolarmassisfoundfromtheintrinsicviscosity and the Mark-Houwink equation. To answer this question, we imagine thepolymertobesplit-upintoanumberofmonodispersefractions.Eachofthisfractions brings about a viscosity increase, which for the ith fraction amounts to:sp,i = (i 0)/0.We assume that the total increase in viscosity is, simply, the sum of the contributionof all fractions, while the concentration of the ith fraction is ci. Thenred = spi ci= (red,ici) ciMolecular composition 37When the limit to c 0is taken, this becomes:[] = []ici ci= {[]i ci ci } = wi[]isinceci ci= wi[] = (wikMia) = k (wiMia) k(Mv)aIn this way the average Mv is defined asMv = [ wiMia]1/aSo, for a = 1, Mv = Mw; for usual values of a, such as 0.8, Mv is situated between Mnand Mw,butmorecloselyto Mw.Inpracticethefullprocedureofmeasuringatdifferent concentrations and extrapolation to zero concentration, is often replaced byasimplerstandardmethod;foragivenpolymerinagivensolvent,onlyoneconcentration is taken. Optionally, a correction factor can be applied to obtain fromred the best estimate of [].Sometimes,fromsuchasingle-pointmeasurementofthesolutionviscosity,anarbitrarymeasurehasbeendefined,whichforagivenpolymersuppliesausefulmeasure for comparing levels of the molar mass. An example is the so-called k-valuefor PVC;k values of 55, 60, 65 and 70 denote grades of increasing M. (see Qu. 2.40and 2.41).Themelt index m.i. (or melt flow index m.f.i.) is a rough empirical measure of themolarmassofsomepolymers.Itis,again,basedonaviscositymeasurement,butnow not of a solution, but of the molten polymer. Through a standard capillary thepolymer moves under a standard pressure at a standard temperature. The number ofgrammestransportedin10minutesisdefinedasthemeltindex(indg/min).Themethod is frequently applied to e.g. PE and PP, and results in some measure for themolar mass. The m.i. values range from 0.1 (high M) to 80 (low M) dg/min. In fact areciprocal melt viscosity is determined. In a first approximation this depends on Mw,viz according to (:) Mw3,4(see 5.3).In a certain sense this characterization of themolarmassisfunctional,sincetheprocessabilityisoneofthemostimportantcriteria for the selection from a number of grades of the same type of polymer (see 5.4).Molar mass distribution MMDThe oldest method to determine the whole molar mass distribution is fractionation.Thismethodisbasedonthefactthatinsomesolventstheshortchainsarebettersoluble than the long ones. The polymer is precipitated onto a column, e.g. on small38 From polymers to plasticsglass spheres, over which a mixture of solvent and non-solvent is passed while theconcentrationofthesolventincreaseswithtime.Firstthesmallermoleculesaretaken away from the column, later on the bigger ones. The fractions are collectedandcharacterizedastotheirconcentrationandmolarmass(e.g.byaviscositymeasurement). From this procedure the MMD can be derived in a number (e.g. 20)ofdifferentfractions.ThisBaker-Williamsmethodisverytime-consuming:fractionation and characterization of a sample takes, in total, about a week.A more modern method to determine the MMD is GPC, gel permeation chromato-graphy,alsonamedsize-exclusionchromatography, SEC.Apolymersolutionispassed over a column with a porous structure. The residence time of the chains onthe column depends on the diameter of the coiled chain: smaller chains can migratethrough more pores (they can also enter into the smaller ones), and it takes a longertime for them to pass along the column. The bigger ones cannot enter into any of theside-pores and pass in the shortest time.The concentration of the eluted solution is continuously measured as a function oftime (or of eluted volume), e.g. via its refractive index, in comparison to that of thepure solvent.This procedure results in a concentration - volume curve, from which, after previouscalibration, the molar mass distribution can be derived. Calibration can be carried outwith known monodisperse polymers, and is needed only once for a certain type ofpolymeronacertaincolumn.Themeasurementtakesonlyafewhours.Fromthemeasured MMD the various averages can be computed easily. It is also possible tocharacterise the eluted polymer solution not only on concentration, but also on molarmass, e.g. by laser light scattering. In this way the calibration can be avoided.2.3. Chain regularityPolymer chains are, in general, regularly built-up, but a few variations are possible.We shall, successively, consider: arrangement of monomers, situation of side groups,arrangement round a double bond, branching, and copolymer structure. monomer arrangement is, in principle, possible as head-tail or as a head-head(or tail-tail) i.e. for a vinyl polymer CH2CHR:CH2CHRCH2CHRCH2CHRor:CH2CHRCHRCH2CH2CHRPracticallyalwaysthehead-tailconnectionisformed.Oneoftheexceptionsispolyvinylalcohol, in which between 1.5 and 2 % head-to-head sequences occur. situation of side groups;the chain CH2 CHRcan be regular or irregular:Molecular composition 39HCHHCRHCHHCRHCHHCRHCHHCRregular; all Rs are at one side:isotactic.HCHHCRHCHRCHHCHHCRHCHRCHregular; the position of the Rs isalternating: syndiotactic.irregular: atactic.This can, more clearly, be seen in a three-dimensional representation, in view ofthe actual valency angles (tetraedic, 109); the CC main chain is situated inthe plane of drawing (Figure 2.4), while the side groups protrude at the front sideor the backside. (syndiotactic configuration)H HCCCCCCCCCCH HHRH H H HHRH H H HHRR RFigure 2.4. Syndiotactic chain.Withconventionalpolymerizationprocesses,atacticchainsarepredominantlyformed;fortheformationofisotacticandsyndiotacticchainsaspecialcatalystsystemisrequired,e.g.Ziegler-Nattacatalysts.Suchaprocessiscalled:stereospecificpolymerization.Itenablesthemanufactureof,i.a.,technicallyusablePPandalsounbranchedPE(see4.1).Thenewestdevelopmentisthemetallocene katalyst; it enables the building-up of chains-to-measure with veryhigh degrees of chain regularity; also the manufacture of syndiotactic polystyreneis technically possible in this way(see Qu. 2.47). Round adouble bondthe main chain can show two different configurations,e.g. withpolybutadiene and polyisoprene (Figure 2.5):CC CCtransC CC CcisFigure 2.5. Cis- and trans-configuration. E.g. polybutadiene and polyisoprene40 From polymers to plasticsCis-1,4 polyisoprene (natural rubber or synthetic isoprene rubber) and trans-1,4polyisoprene (balata or guttah-percha) show strongly different properties.Within a single chain cis- and trans configuration can also both occur in a randomsequence;thechainisthanirregular(somekindsofpolybutadiene).Thishasconsequences for the occurrence of strain-induced crystallization (see Chapter 4). Branchingdisturbsthechainregularityifthebranchesaresituatedatrandompositionsalongthechain.InparticularwithPEanumberofbranchingtypesare present (see Figure 2.6):a. strongly branched with irregular branches: low-density PE LDPE)b.little branched: high-density PE, (HDPE)c. strongly branched, but more regularly: linear-low-density PE (LLDPE)The names reflect the effect of the branches on the crystallinity and thus on thedensity and the stiffness.abcFiguur 2.6. Three types of branching for PE. Withcopolymerization irregularchainsareformedwhenthesequenceofthemonomers is random::AABABBBABAAABBAThisiscalledarandom-copolymer. An example is styrene - butadiene rubber,SBR.A more regular chain structure is the block copolymer:(AAAA)(BBBB)(AAAA)(BBBB)examplesarethethermoplasticelastomerSBS(see9.1.4)andthegraftcopolymer:AABBBAAAAABBBAAABBBAAAABBBAAAand, in particular, the alternating copolymer:ABABABABABABABMolecular composition 41Strictly speaking, condensation polymers such as polyesters could be considered tobelong to this category. Also polyketone (Carilon) would be a strictly alternatingcopolymer, if the regularity would not have been disturbed by a third comonomer,propylene.2.4. Chain conformationsPolymer chains are hardly ever met in a totally stretched condition, but are, becauseoftheirmobilityandflexibility,presentascoils.Thecoilcanshowallkindsofshape,asdictatedbychance;asafirstapproximationwemayassumeasphericalshape. The diameter of this sphere is hard to define; the density in the coil decreasesfromthecentretotheouterboundary.Theeasiestcriterionistheend-to-enddistance,r0;thisisastronglyfluctuatingstatisticalquantity,ofwhichwemust,therefore, try to define some kind of average. This average has some relation with theeffective coil diameter.In order to estimate the end-to-end distance r0 we assume, as a first approximation,that the chain segments can move freely with respect to each other in all directions.The chain contains n segments, each with a length b0. The next simplification is, thatweconsiderthechainintwodimensions.Wenowhaveasimplerandomwalk(drunkmanswalk)problem.Wesituateonechainendintheoriginofanx-ycoordinate system and we build the chain step by step with randomly chosen angles (see Figure 2.7). The position of the other end is than given byx = b0cos 1 + b0cos 2 + + b0cos ny = b0sin 1 + b0sin 2 + + b0sin nor:x = b0i=1n cos i;y = b0i=1n sin iYX1234b0Figure 2.7. Random walk.42 From polymers to plasticsThe end-to-end distance is r0 = x2+y2.r02 = x2 + y2 = b02( cos i)2 + b02( sin i)2r02b02= i cos2i + ij cos icos j + i sin2i + ij sin i sin j ==1ni (cos2i + sin2i) + ij cos(i j) == n1 + 0 = nThe second sum is 0 because i jis distributed at random.The statistical value (the average) of the square of the end-to-end distance is givenby:r02 = nb02 orr02 = b0nFurther calculation shows that for a three-dimensional random walk the same resultis obtained.In a second approximation we have to introduce a fixed value for the angle betweentwolinksofthechain;since,e.g.,theanglebetweentwovalencybondsoftheC-atom is always = 109.5. (Figure 2.8). For the time being, we suppose free rotationaround this angle. The approach is similar to the previous case (of course now three-dimensional), and results in:r02 = nb02 1 cos 1 + cos Figure 2.8. Free rotation with fixed valency angle.This formula is not valid when is close to 0 or 180. It appears that the correctionfactorMolecular composition 43= 1 for = 90< 1 for < 90> 1 for > 90= 2 for = 109,5In a third approximation we also limit the freedom of rotation. This can be illustratedwith ethane CH3CH3; when this molecule is rotated around the CC bond, potentialbarriers have to be overcome as a result of the interaction between the H-atoms (seeFigure2.9).ForPEasimilarpotentialcurvecanbecalculated;thishasamorecomplicated shape as also indicated in Figure 2.9.180 120 60 0 60 120 180 potentialPEethaneFigure 2.9. Potential curve for rotationThe hindering in rotation necessitates the introduction of an extra correction factor inthe formula for r02. This factor contains the quantity cos , which is the averagecosineoftherotationangles.Forfreerotationcos=0(allvaluesforareequally probable), but it differs from 0 when potential barriers are present. It can becalculated from the potential curves. The formula becomes nowr02 = nb02 1 cos 1 + cos 1 + cos 1 cos A simplified formula is:r02 = nb2in which b is the effective bond distance, i.e. the length of the fictitious link, whichbehaveswithoutrestrictionsasarandomwalk.Wemaintainnasthenumberofprimary links (sometimes n is taken as the number of fictitious links), and we defineb/b0 as the characteristicchainstiffness.Thisquantityis,therefore= 2foraCC- chain with unrestricted rotation; b/b0 > 2 with hindered rotation.Still further approximations are required to account for the excluded volume: the44 From polymers to plasticschain parts cannot coincide. An important complication is met when the side groupsare big enough to hinder each other during chain rotations (see 2.5). In all cases theformula r02 = nb2remains valid, though b/b0 increases as a result of these effects.Some estimated values:PE PVC PMMA PVAc PS(b/b0) 2.50 2.61 2.97 3.00 3.29We can now ask the question: What is the magnitude of the coil density? How far isthe statistical coil, which we have considered so far, diluted? How many monomerunitsarepresentinaunitvolume?Itispossibletocalculatehowthedensity,,dependsonthedistancetothecentreofgravityandonthenumberoflinksn.Itappears that the volume fraction in the centre equalsf0 = 1/n, i.e.:for n = 1,000 f0 = 0.03for n = 1,0000 f0 = 0.01in other words: the coils are, even in their centre, highly diluted!A rough estimate can also be made without much theory, namely from r02 = nb2,for example for PE with M = 140,000. A chain contains 10,000 CH2links,son =10,000.The length of a link is b0 = 0.154 nm, and we simply assume unrestrictedrotation, so that b = b02 = 0.218 nm. We then find:r02 = 10,000(0.218109)2 m2If we, loosely, think of a sphere with radius r0, then the volume of this sphere is:V = 43 r023/2 = 0.4331022 m3The mass is m = 140.000 g / 61023 = 2.31022 kg. The specific mass of the coil is: = m/V = 5.3 kg/m3WhenwecomparethisvaluewiththedensityofamorphousPE(=855kg/m3),then the polymer in the coil appears to be 160 times diluted. If we choose the valueforb/b0asgivenabove,thentheresultisadilutionfactorof890.Takingintoaccountthattheformulaf0=1/ nholdsforthetightestpackedcentre,thentheresults are in the same order of magnitude.Coiledchains,are,therefore,stronglyinterwoven;ineachvolumeelementofthesize of a coil, parts of hundreds of separate chains are present!The reasoning followed so far is based on the assumption that chains, in finding theirmostprobablecoildimensions,arenotaffectedbytheirenvironment;inotherwords, that no special interactions, either attractive or repulsive, with neighbouringMolecular composition 45moleculesarepresent.Thisholds,therefore,foranundilutedpolymer,inwhichachaindoesnotundergointeractionsfromthesurroundingchainsotherthanthosefrom parts of the chain under consideration itself.If we now look at polymer solutions, then there are three possibilities (see also Qu.2.20 2.23): A very good solvent; this means that there is an extra interaction between parts ofthe chain andthe molecules of the solvent, so that the chain segments prefer tobesurroundedbymoresolventmolecules.Thecoilwillthenbecomemoreexpanded.Apoorsolvent;partsofthechainfeelbetterinanenvironmentconsistingofsimilar chain segments; the coil will become more compact.In between these cases we can define a so-called theta-solvent,which,asfarasinteractions are concerned, behaves, at a certain temperature, like the polymer.Ourcalculationofr02istherefore,forpolymersolutions,onlyvalidforthetaconditions. We shall consider this case in somewhat more detail. We have seen thatforthedeterminationoftheviscosityaveragemolarmass,theMark-Houwinkequation is valid[] = kMainwhich,ingeneral,aisinbetween0.5and1.Moreover,itisknownthatundertheta conditions a = 0.5.Wehavealsoseenthatwehavetoextrapolatetoconcentrationzerotoobtaintheintrinsic viscosity[] = lim red.Considering the calculation of coil density, this is not surprising. A concentration of1%inasolutionseemssmall,butwhenthecoilismorethan100timesdiluted,considerable mutual penetrations of the coils can be expected, and, therefore, strongdeviations from the behaviour of single, separate coils.Only at very low concentrations can the coils be considered as separate spheres. Inthat case Einsteins relation for the viscosity of suspensions can be applied: = 0(1 + 2.5) ,in which is the volume concentration and 0 the viscosity of the liquid. Then:sp = 00 = 2.5 en red = 2.5/c = 2.5/in which is the specific mass of the coil, or: = MV46 From polymers to plasticswith M the molar mass and V the volume of the coil.This, combined with the Mark-Houwink equation, yields:[] (:) Ma (:) VMorV (:) M1+aIf, as above, we express V as:V (:) r023/2andr02 (:) number of links,so(:) Mthen:V (:) M3/2 (:) M1+aso: a = 0.5.This (too) simple derivation confirms that for theta conditions: a = 0.5!When another type of solvent is chosen, a higher value for a can be found, e.g. a = 1;in this case:r02 (:) M4/3 instead of (:) Mor a lower a, e.g. 0.35; then r02 (:) M0,9.Deviations of r02 (:) M can also be brought about by other causes, for example bychainbranching;asanextremecasewecanthinkofahighlycomplexbranchedstructureinwhichthemanybranchesareagainbranched,sothatitcanhardlybedefined as a chain. The conformation statistics is then no longer applicable, and forsuch polymers a value of a near to 0 has even be found; this means that V (:) M, justaswithsmallmolecules.ViscosimetricdeterminationofMisthennolongerapplicable, since [] is independent of M.A deviation in the other direction occurs with super-stiff chains, in the extreme casewith rigid rods. The end-to-end distance then equals the whole chain length, so:r02 (:) M2which means a = 2.This value is, therefore, mentioned as the theoretical maximum of a; it remains anopen question what the significance of V is in such a case, thinking of our spheres!For liquid-crystalline polymers values round a = 1.5 are indeed being found.Molecular composition 472.5. Chain flexibilityThe flexibility of chains is governed by the freedom of rotation of the main chain,andalsobytheeffectofsidegroups.Firstweconsiderthemainchain.Intheforegoing we have already seen that the possibilities for rotation of the main chainare restricted by potential barriers. Some examples for simple compounds are:CH3(CH3) 2.8 kcal/molCH3(CH2CH3) 3.3CH3(CH.CH3CH3) 3.9CH3(OH) 1.0CH3(OCH3) 2.7CH3(COH) 1.0CH3(CC) 0.5Double(C=C)andtriple(CC)bondscannotrotate;theeaseofrotationoftheneighbouring bonds is, however, increased.The series shown below represents a number of types of main chains with decreasingflexibility:COC e.g. POM, polyoxymethyleneCNC e.g.PA, polyamide, nylonC=CC e.g.BR, butadienerubberCCC e.g.PE, polyethene C e.g.PC, polycarbonate PI, polyimideladderpolymersSidegroupsmainlyaffectchainflexibilitywhenthemainchainisflexible.Anexample is steric hindrance with (see Figure 2.10)CCHH HCCHH HRXRX0.252 nmFiguur 2.10. Steric hindrance.48 From polymers to plasticsX = H: R = 0.09 nm, little hindranceX = F: R = 0.14 nm, some hindranceX = Cl: R = 0.18 nm, considerable hindranceX = CH3: R = 0.20 nm, considerable hindranceThe situation sketched above is not quite exact, since the substitution of a side groupalso causes a slight change of .When the sterical hindrance is considerable, no zig-zag conformation of the chain ispossible; the number of conformations is then drastically reduced.Theeffectofarestrictioninrotationisanincreaseofb/b0,and,therefore,oftheeffective coil diameter r02.Thechainflexibilityhas,a.o.,alargeinfluenceontheglass-rubbertransitiontemperature, and (if applicable) on the melting point.2.6. Chain interactionsBetweenpartsofthechainsinteractionforcesareactive,the secondarybindingforces,whicharemuchsmallerthantheprimarychemicalbondsbywhichthechains are held together. Several kinds of secondary binding forces exist: dipole forces; here the distribution of electrical charges within an atom or groupofatomsisasymmetricwithrespecttothecentreofgravity(seeFigure2.11).Polargroupsformpermanentdipoles,whichalignintheelectricfieldoftheirneighbours;thisresultsinanelectricalattractionforce.Theinteractionisproportional to 1/r3 (r = distance), and is slightly dependent on the temperature asa result of the thermal motion of the dipoles. A measure for the interaction forceis thedipolemoment, the value of which is, for a few groups, given in the tablebelow.+ + + ++++permanent dipole induced dipoleFiguur 2.11. Permanent and induced dipoles.induceddipole;thisisformedwhenaneutralgroupisbeingpolarizedbyinduction from a neighbouring permanent dipole. The attraction force is proport-ional to 1/r6 and is slightly temperature dependent.Molecular composition 49CH3CH2XX dipolemoment X dipolemomentCH30 COOH 1.73OCH31.2 COOCH31.76NH21.2 COCH32.78OH 1.69 NO23.68Cl 2.05 CN 4.0 dispersion forces originate from random fluctuations in the charge distribution ofanapolargroupasaresultoftherevolutionofelectrons.Afluctuatingdipoleinduces another one; the net result is an attraction force. Dispersion forces, alsocalledLondon-VanderWaalsforces,areindependentoftemperatureandproportional to 1/r6 They form the most important class of interaction forces, asfor instance in hydrocarbons.hydrogen bridgesoccurbetweenchainsine.g.thefollowingsituations(Figure2.12):OCOHOCNHFiguur 2.12. Hydrogen bridges.The H-valency is being shared with the neighbouring atom, e.g.:NHOThisleadstorelativelystrongbonds,asinnylonandcellulose.Thehydrogenbondsarealsoresponsibleforthestronglinkbetweenwatermolecules;thatiswhy water, as a very small molecule, has a high boiling point!Consequences of chain interactions for the behaviour of a polymer are, just as withchainflexibility,mainlytheheightoftheglass-rubber transitionandthemeltingpoint.2.7. Cross-linkingThe most important characteristic of a network is the tightness, the spacing betweencross-links. Some quantities frequently used will be elucidated in a simple schematicexample:Supposethatwehavetwochains,eachof20links,whichare,atequaldistances,connected by cross-links, as illustrated in Figure 2.13.50 From polymers to plasticsFigure 2.13. Cross-links.The cross-link density is defined as: = number of units connectedtotal number of units= 640= 0.15The quantity is between 0 and 1; is low for vulcanized rubbers, namely 0.01 0.02, and much higher for thermosets.We further define:M0= molar mass of the monomer (here e.g.M = 50)Mc= molar mass between cross-links (here 5 50 = 250)M = molar mass of the whole chain (here 20 50 = 1000) = a number of chain elements, separated by cross-links (here = 8)e= effective number of chain parts, contributing to the coherence andthe elasticity of the network (here e = 4).e is related to , M and Mc according toe = [1 2McM]since the chain is divided into n = M/Mc parts, two of which are always loose,sothat the effective fraction is (n 2)/n = 1 2/n.In our case e = 8(1 2 250/1000) = 4.Inthisexampleonlyonehalfofthechainpartsareeffectivelycontributingtothenetwork properties; the remaining part, the loose ends, are not being deformed whenthe material is strained.Thevariousparameterscanbedeterminedfrommeasurementsofthemodulusofelasticity (see 5.1) and from swelling in solvents.In most cases, cross-linking is effected by the formation of chemical bonds betweenthe chains; the network is then stable, such as with: sulphur bridges with rubbers, polystyrene chains with unsaturated polyesters, bivalent with three- (or more-)valent reacting components, cross-linking by irradiation; via radical formation achemical link between chainsis formed. other cross-linking agents such as peroxides.Molecular composition 51Also physical cross-linking occurs with: crystallization (see 4.5 and 7.2.1), domainformationinblockcopolymers,self-vulcanizingrubberorthermo-plastic elastomer (see 9.1.4), temporaryentanglements,causingrubberybehaviourinunvulcanizedrubbersand in molten thermoplastics.523Glassy state and glass-rubbertransition3.1. Glassy stateIn the usual schedule solid - liquid the solid is crystalline and passes into the liquidstate at the melting point, Tm. This transition is, in nearly all cases, accompanied byan increase in volume (one of the exceptions is water!), and with an increase in theheat content (enthalpy), the heat of melting.ThejumpinvolumeisillustratedinFigure3.1;theslopeofthelineFCisthethermalexpansioncoefficientofthecrystallinephase;atthemeltingpointthevolumejumpsfromCtoB,andthehigherslopeofBAdenotestheexpansioncoefficient of the liquid phase.Some substances are, however, not able to crystallize, for instance normal glass, as aresult of a too irregular molecular structure. When such a substance is cooled downfromtheliquidstate,andfollowsthelineAB,thenfromBtoDitstillremainsafluid,whichsolidifiesatDwithoutshowingajumpinvolume.Thelinethencontinues as DE, with about the same slope as CF; the matter is, however, not in acrystallinecondition,butinanunordered,amorphous,glassystate,andhas,therefore, a greater volume.ATBCDEFglassfluidcrystallineVTgTmFigure 3.1. Volume as a function of temperature.ThetransitionatDiscalledtheglasstransition, occurring at the glasstransitiontemperature, Tg. It follows thatTg is always lower than the melting point, Tm. It isvery important to distinguish very carefully between Tgand Tm !!Glassy state en glass-rubber transition 53Polymers are sometimes wholly amorphous and non-crystallizable; they then followthe line ABDE. However, when such a polymer is heated up to above its Tg it is notimmediately transferred into a liquid state, but first into a rubbery state, which, uponfurther heating, gradually passes into a fluid. Tg is, therefore, called the glass-rubbertransition temperature.A more realistic representation of the phases is given by the stiffness of the material,which falls down to zero when the liquid state is reached. This is illustrated in Figure3.2; for a low-molecular matter the E-modulus (a measure of the stiffness) decreasestozeroattheglasstransitiontemperature(thoughmoregraduallythanforacrystalline substance at Tm). A polymer shows, above Tg, after a decrease in E by afactorof1,000to10,000,arubberyregion,which,onthetemperaturescale,islonger as the chains are longer.TgTmTE109108107106105Figure 3.2. Rubbery region with polymers.Sometimes crystallization is possible; in the solid state polymers are, however, nevertotally crystalline, but are still partly amorphous. The amorphous part may be aboveor below Tg, i.e. in the rubbery or in the glassy condition.The nature and the properties of polymers are, therefore, governed bytwo differentschedules, which are sometimes superimposed:1. glass rubber liquid2. crystalline liquid.First of all we shall consider the glassy condition.In the glassy state the molecular structure is disorderly, and comparable to that of aliquid.ThisisclearlydemonstratedbyX-raydiffractionpatterns,inwhichonlyadiffuse ring is visible, which indicates some short-distance order; in contrast to to thesharp reflections found with crystals as a result of long-distance order.Thedisorderedstateoccupiesalargervolumethanacrystal,whichexplainsthedistancebetweenthelinesEDandFCinFigure3.1,theso-calledfreevolume.54 From polymers to plasticsBelow Tg the free volume, Vf, is about constant; above Tg it increases strongly withincreasing temperature.The free volume in the glassy state allows some minor movements for small chainparts or for side groups. These movements are possible from a certain temperature;theyareapparentfromarelativelysmalldecreaseinstiffnessatthattemperature.Becausesuchadecreaseismuchlessthanintheglass-rubbertransition,thetemperatureatwhichitoccursiscalledasecondaryglasstransition.Besidesthemodulus, E, also the mechanical damping is a good criterion for the transitions. Thedamping is defined as the tangent of the loss angle in vibration experiments, or, also,as the rate of damping in a free vibration (see 6.2). The damping, tan , shows astrongmaximumatTg,andlesspronouncedmaximaatthesecondaryglasstransitions Tsec (see Figure 3.3.).Asecondaryglasstransitionis,ingeneral,importantfortheimpact strengthofapolymer; it creates the possibility to dissipate energy in situations of shock loading,so that the polymer is less brittle.Tlog Etan TsecTgFigure 3.3. A secondary glass transition.Besides by motions of chain parts or side groups (see 3.4), a secondary transitioncanalsoresultfromthepresenceofasecondpolymer,whichhasbeenaddedinasmall quantity by blending, or which has, as tails, be copolymerized with the mainpolymer. Such a second polymer then has its glass transition at Tsec. Both cases occurwhen the impact strength of a polymer has been improved, either by blending withsomerubber,orbycopolymerization.Asimilarsituationisfoundwithblockcopolymers. In 3.5 these cases are dealt with in more detail.3.2. Molecular pictureBeforelookingcloserattheglassrubbertransition,weshalltrytovisualizewhathappens on a molecular scale when a polymer is heated, starting from zero Kelvin.At T = 0 K the chains are at absolute rest. No thermal motions occur; everything isGlassy state en glass-rubber transition 55completelyfrozen-in.Thechainpartsareboundtogetherbysecondaryinteractionforces, as discussed in 2.6.WhenthetemperatureisincreasedfromT=0,thethermalmotionincreasesand,gradually, short parts of the chain or side groups may obtain some mobility, which,within the very restricted free volume, gives rise to small changes in conformation.Whether or not this occurs, is a matter of competition between the thermal energy ofa group (kT) and its interaction with neighbouring groups.The interaction can be expressed as a potential barrier which has to be overcome inordertorealizeachangeinposition.Sincethethermalenergyisstatisticallydistributed, a fraction of the groups will be able to overcome the barrier; this fractionstronglyincreaseswhenthetemperatureisraised.Hence,thereisacharacteristictransition temperature for such a specific molecular motion.This is illustrated in Figure 3.4. The potential barrier for passing from state 1 to state2, is U; the distribution of the thermal energy has been sketched schematically forthree temperature levels. At T1 only a small number of groups have enough energy toovercomethebarrier,atT2muchmore,andatT3nearlyall.ThusT2is,forthatdisplacement,thetransitiontemperature.ForT T2 the motion is free.UU1 2nnnU UT1T2> T1T3> T2Figure 3.4. Potential barrier for changing position.We should realize, that this is always a matter of probability, and that the time, i.e.thepatiencewehavetowaitforachange,playsanimportantrole.Therefore,weshouldconsiderthefrequencyatwhichjumpsfromstate1tostate2occur.Thisfrequency, , can be expressed by the the Arrhenius equation: = 0 exp(U/kT)Inthisequation0 is the natural frequency of the vibrations about the equilibriumposition.Thejumpfrequencygovernsthetimescale,,atwhichthetransitionoccurs; is namely inversely proportional to :56 From polymers to plastics = A exp(U/kT) .This equation provides a fundamental relationship between the effects of time andtemperatureonatransitionmechanism.Timeandtemperatureappeartobeequivalent in their effect on the behaviour. At a fixed time scale, 1, e.g. 1 sec, thetransitiontemperature,T1,isproportionaltotheenergyofactivation,U.Thetransition temperature can be expressed in the time scale by:ln = c + UkTConsequently. for low-temperature transitions with a low energy of activation, suchas secondary glass transitions, the transition temperature is stronger time dependentthan, e.g. the main glass-rubber transition.Anexampleofasecondarytransitionisthesidegrouprotation-CO-O-CH3withPMMA, which is set free at about 25 C on a time scale round 1 sec. PVC shows aweak transition at 30 C as a result of freedom of rotation for the Cl atoms. A veryelegantillustrationisgivenbypolycyclohexylmethacrylateincomparisonwithpolyphenylmethacrylate (Heijboer). The polymers are nearly identical; the differenceisthatthefirsthasasaturatedringasasidegroup,andthesecondanunsaturatedone:The saturated ring is able to undergo a flipping motion (chair-chair transition) at80 C, which, in contrast to the rigid ring in PCHMA, results in a strong secondarytransition (see Figure 3.5). With further increase of the temperature, bigger parts ofthe chain can move freely. About Tg the mobility increases drastically, so that coilscanfreelybetransformedtootherconformations,withoutbeinghinderedbyinteractions: the polymer shows rubbery behaviour. This is the case for free mobilityofchainpartswith,onaverage,20to70monomericunits.Chainentanglementsprevent whole chains to move relatively to each other.3.3. Thermodynamics of the glass-rubber transitionTo consider the nature of the glass rubber transition on a thermodynamic basis, weshould first compare this transition with melting. The melting point is afirst-ordertransition; Tg could be mentioned a second-order transition.ThequantityG,the(Gibbs)freeenthalpy,playsapredominantroleinthethermodynamic treatment of transitions.G = U TS + pV = H TS = F + pVin whichGlassy state en glass-rubber transition 57C OOCH3CHPCHMAPPhMAC OOCH3 Figure3.5.Effectofthenatureofthesidegrouponthesecondaryglasstransition(J.Heijboer, Mechanical properties of glassy polymers containing saturated rings, dissertationRU-Leiden, Waltman, Delft, 1972).U = internal energy, e.g. as a result of the attraction forces between moleculesT = absolute temperature,S = entropy, a measure for the disorder in the system,p = pressure,V = volume,H = U + pV = enthalpy or heat content= internal energy + work exerted on the environment,F = U TS = (Helmholtz) free energy.With each type of transition, G = 0, in other words: the G(T) curves for both phasesintersect, and slightly below and above the transition temperature the free enthalpiesareequal.Thevariousderivativesofthefreeenthalpymay,howevershowdiscontinuities. With a first-order transition such as melting, this is the case with withthe first derivatives like V and S and also with H.58 From polymers to plastics[Gp ]T = VWithmeltingthevolumediffersatbothsidesofthemeltingpoint;ajumpVinvolume occurs, which is a jump in the first derivative of G after p at constant T. AlsoajumpHoccursintheenthalpy(theheatofmelting),aswellasajumpSinentropy.The glass-rubber transition, on the contrary, does not show jumps in V, S and H (novolume change, no discontinuous change in the state of order and no heat effects).However,jumpsoccurinthederivativesofthesequantities,suchasthermalexpansion coefficient, specific heat and compressibility. Some examples:[Gp ]T = V, Vglas = Vrubber, V = 0[ 2Gp T ] = [VT ]p = V, glass rubberthe coefficient of expansion shows a jump .SotherearejumpsinthesecondderivativesofthefreeenthalpyG,and,forthatreason,theglass-rubbertransitionmightbedenotedasasecond-ordertransition.However, this appears not to be the case; the dependence of the various parameters ata real second-order transition strongly differs from what happens at Tg, which willnot be further shown here.A second argument is the time dependency: the transition from a supercooled liquidorrubbertotheglassystateisclearlydependentontherateofcooling;thelinerepresenting the liquid behaviour continues further to lower temperatures as the rateofcoolingislower;theglasstransitiontemperatureisthenlowerandthespecificvolume reaches a lower value (see Figure 3.6).Athermodynamicequilibriumis,therefore,notreached;ifsuchanequilibriumwouldexistitwouldbeatamuchlowertemperature.Onthebasisoftheoreticalcalculations it has been supposed that a real second-order transition could occur at atemperature which is 50 to 60 K below the observed value of Tg, and which would bereachedafterextremelylowratesofcooling.EstimationsonthebasisoftheempiricallyfoundrelationbetweenTgandtherateofcoolingindicatethattherequired cooling time would be of the order of 1017 years!Experimentshavealsobeencarriedoutonpolystyrenewithvariousamountsofplasticizers;extrapolationtozeroplasticizercontentprovidedaninsightintothecourseofthevolume-temperaturerelationbelowTg.Evenat(Tg 70K)noindication of a transition was found.Glassy state en glass-rubber transition 59It thus seems that the glass transition, even with infinitely low cooling rate, is not arealthermodynamictransition,butisonlygovernedbykinetics,asafreezing-inphenomenon.slow coolingrapidcoolingAAVTFigure 3.6. Effect of the time scale on the glass transition.Acloselyrelatedphenomenonisthevolumeretardationintheglassycondition.When, after rapid cooling, point A has been reached (Figure 3.6), the volume will, ataconstanttemperature,graduallydecreasetoe.g.A.Possibilitiesformotionofchainparts,thoughonaverylimitedscale,causethefreevolumetodecreasegradually, though, as we now know, an equilibrium will never be reached. The rateof volume retardation is, as a matter of fact, smaller as the temperature is lower.Thisphenomenon,alsocalledphysicalageing,isnotverysignificantintermsofvolume,but,asweshallseelateron(7.2.4.),itisveryimportantforthecreepbehaviour of polymers.3.4. Factors governing TgTheheightoftheglass-rubbertransitiontemperatureis,inthefirstinstance,governedbythecompetitionbetweenthermalmotionandtheattractionforcesbetween the chains.The thermal motion is dependent on the freedom of the chain to undergo changes inconformation.Whenthisfreedomishigher,thechainissubjectedtoastrongerthermal motion than a chain which, e.g. as a result of hindrance in rotation, is morerigid. The chain stiffness, as discussed in 2.4, plays, therefore, an important role.The primary criteria are thus: chain flexibility chain interactions.We shall consider some examples of both criteria. In doing so, besides amorphous,also crystalline polymers will be taken into account, since the latter always contain60 From polymers to plasticsan amorphous fraction, which is subject to a glass transition.3.4.1. Chain flexibilityHigherchainstiffnessresultsfromasmallernumberofpossiblechainconformations; this can be caused by: greater stiffness of the main chain, bigger side groups, cross links.First a few examples of chain stiffness differences in the main chain; the examplesarenotveryexact,becausesidegroupsmayalsoplayaroleastoflexibilityorinteractions, but they represent a global trend.[CH2CH2] PE, polyethylene, Tg = 120 C[CH2CH2OCO COO] PETP, polyethyleneterephtalate, Tg = 70C[S ] PPS, polyphenylenesulfide, Tg = 85 C[O CH3|C|CH3 OCO] PC, polycarbonate, Tg = 150 C[NCOCOCOCON O ] PI, polyimide, Tg > 400 C.Now we look at some examples of the effect of side groups on the chain flexibility:[CH2CH2] PE, polyethylene, Tg = 120 C[CH2 C|CH3H] PP, polypropylene, Tg = 15 C[CH2CH] PS, polystyrene, Tg = 100 C[CH2C|NH] PVK, polyvinylcarbazole, Tg = 210 CTheincreasingsizeofthesidegroupeffectsadecreaseofchainflexibilityandanincrease of Tg.Glassy state en glass-rubber transition 61Cross-linkslimitthemobilityofmacromolecularchains,andthusgiverisetoanincreaseinTg.Withaverylowconcentrationofcross-linksthiseffectishardlydetectable. Experiments with the system polystyrene + divinyl benzene showed thatat a concentration of 0.4 % of DVB and higher a detectable increase of Tg occurred.Withrubbers,vulcanizedwithsulphur,thedetectionlimitforanincreaseofTgappeared to be at 1 to 2 % of sulphur, so that for a technically vulcanized rubber thelevel of Tg is hardly influenced by the vulcanization process.Higherdegreesofcross-linkinghaveaasignificanteffect;foranunsaturatedpolyester resin with short and stiff cross-links, Tg appeared to be increased by 21 Cwhen the number of atoms between cross-links amounted to 50, while with 24 atomsbetweencross-linkstheincreasewas93C.So,withthermosetsthecross-linkdensityhasalargeeffectonTg,and,consequently,ontheusabilityathighertemperatures.3.4.2. Chain interactionsIn 2.6 we have looked at the types of interaction forces which can occur betweenchains. The strongest of these are the dipole forces. Their effect on Tg is illustratedby the series PP, PVC and PAN, in which the chain mobility hardly varies becausethesidegroupsareofaboutequalsize,butinwhich,intheorderofsequencementioned, the dipole interactions increase.[CH2 C|CH3H] PP, polypropylene, Tg = 15 C[CH2 C|ClH] PVC, polyvinylchloride, Tg = 90 C[CH2 C|CNH] PAN, polyacrylonitrile, Tg = 120 C(see also Qu. 3.7).Interactionscanbedecreasedbyincreasingthedistancebetweenthechains,forinstance with long side chains, which lower Tg. This effect appears to be greater thanthe increase of chain stiffness, as shown in the examples below; with PMP the morecompactstructureofthesidegroupgivesrisetoadifferentbalanceofthesecounteracting effects.[CC|C] PP, polypropylene, Tg = 15 C62 From polymers to plastics[CC|C|C] PB, polybutylene-1, Tg = 25 C[CC|C|C|C|C] polyhexene-1 , Tg = 50 C[CC|C|C/ \C C] polymethylpentene, Tg = 30 CIncreaseofthedistancebetweenchainsandshieldingofinteractionsplayaveryimportant role in plasticizing of, e.g., PVC:PVC Tg = 90 CPVC + 30% dioctylphtalate (DOP) Tg =0 C3.4.3. Chain lengthAn empirical relation for the effect of the molar mass M on Tg is:Tg = Tg K/Min which Tg is the value of Tg for infinitely long chains and K is a constant which is,e.g., about 105. Consequently, for practically used polymers Tg can, at the most, varybyafewdegreesC.ItcanbearguedthattheeffectofMonTgisrelatedtothenumberofchainends.Therefore,Intheaboveformula,Mdenotesthenumber-average molar mass, Mn. For branched polymers we meet the complication that eachchain has more than two chain ends; a large number of lon