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4098 Macromol ecu l e s 1990, 23, 4098-4107Suzuki, Y. ; Miyamoto, Y.; Miyaji, H.; Asai, K. J . Polym. Sci.,Polym. Let t . Ed. 1982,20, 563.Simha, R.; Somcynsky,T. Macromolecules 1969,2, 341.Nies, E. ; Stroeks, A. Macromolecules, preceding paper in thisissue.Jain, R. K.; Simha, R. Macromolecules 1984, 17 , 2663.Prigogine, I.; Bellemans, A,; Englert-Chwoles,A . J . Chem. Phys .1956, 24, 518.Gibbs, J. W. Collected W o r k s ; Yale Univers i ty Press: N ewHaven, 1948; Vol. 1.Irvine. P. ; Gordon, M. Macromolecules 1980, 13, 761.Koningsveld, R. ; Kleintjens, L. A,; Shultz, A . R. J . Polym. Sci.,Part A 2, 1970, 8 , 1261.Saeki,S.;Kuwahara, N .; Konno, S.:Kaneko, M. Macromolecules1973, 6, 246.Quach, A,; Simha, R. J . A p p l . P hys . 1971, 42 , 4592.Jonas, J.; Hasha, D.; Huang, S. G. J . Phys. Chem. 1980,84, 109.Nies, E.; Stroeks,A, ; Simha, R.; Jain, R. K. , accepted fo r pub-lication in J . Colloid Polym. Sci.Stroeks, A. ; Nies, E. Polym. Eng. S C L 988. 28, 1347.Flory, P. J. J . Chem. P hys . 1945, 13, 453.

(26) Flory, P. J. Principles of Polymer Chemistry;Cornell UniversityPress: Ithaca, NY, 1953; Chapter VII, XII.(27) Zimm. B. H. J . Chem. Phvs. 1946. 14. 164.(28) Flory, P. J.; Krigbaum, W. R. J. Chem. Phys. 1950, 18 , 1086.(29) Casassa, E. F.; Markovitz, H. J.Chem. P hys . 1958, 29,493.(30) Yamakawa, H. Modern Theory of Polymer Solutions; Harper(31) Fixman, M. J . Chem. Phys. 1960,33, 370.(32) Fixman,M.; Peterson, J. M. J . A m . C hem. SOC. 964,86,3524.(33) Edwards, S. F. Proc. P hys . SOC. ondon 1966,88,265.(34) Koningsveld, R.; Stixkmayer,W. H.; Kennedy, J . W.; Kleintjens,( 3 5 ) De s Cloizeaux, J . P hys. (Les Ulis, Fr.) 1981, 42, 635.(36) Knoll, A.; Schafer,L.; Witten, T.A. J . Phys. (Les Ulis,Fr.) 1981,(37) Schafer, L. Macromolecules 1982, 15 , 652.(38) Ohta, T.; Oono, Y. Phys . L e t t . A 1982,89A, 460.(39) Muthukumar, M.; Edwards, S. F. J . Chem. Phys. 1982,76,2720.(40) McMaster, L. P. Macromolecules 1973, 6, 760.(41) Chandler, D. Studies in Statistical Mechanics; Montroll, E. W.,Lebowitz, J. L., Eds.; North-Holland Publishing Co.: Amster-d a m , 1982; Vol. VIII, pp 275-340.

and Row: New York, 1971; Chapter IV .

L. A. Macromolecules 1974, 7, 73 .42, 767.

A New Multiplet-Cluster Model for the Morphology of RandomIonomersA. Eisenberg,' B. Hird,t a n d R. B. MooreDepar t men t of Chemistry , McGill Univers i ty , Montreal , P.Q., 3A 2K6, C anadaReceived December 7, 1989; Revised Manu script Received February 21, 1990

ABSTRACT: A new morphological model for random ionomers is proposed which incorpora tes he findin gsof recent dynamic mechanical and X -ray scattering studies. The model is based on the existence of mu l-tiplets , which reduce the mobility of the polymer chains in their vicinity. The thickn ess of th e restrictedmobility layer surroundin g each multiple t is postulated to be of the order of the persistance length of thepolymer. Isolated multiplets act as large cross-links, hus increasing the glass transition temperature of thematerial. As the ion conten t is increased, he regions of restricted mobility surrounding each multiplet overlapto form larger contiguous regions of restricted m obility. When these regions become sufficiently large, theyexhibit phase-sep arated behavior and are termed clusters. The model is in good agreement with a very widerange of experimentally observed phenomena, especially those based on dynamic mechanical and X-ray scatteringtechniques.

1. IntroductionOver the past two decades, a considerable amount ofresearch has been devoted t o random ionomers due to theirunique physical properties.I-l3 A number of models forthe morphology of random ionomers have been proposed,none of which are completely consistent with all of the

exper imenta l observat ions on these materia ls . Thesemode ls have been reviewed recently.lOJ1 It is now generallyaccepted th at th e ion pairs aggregate to form quadruplets,sex tupl ets, and high er aggregates, collectively calledm ~ l t i p l e t s . ' ~n addition, ion-rich regions termed clustersmay also exist a t sufficiently high ion co ntent s in somesystems.14 T he clusters behave as a separate phase in tha tthey exhibit their own glass transit ion tem perature ( T g ) .However, the exa ct structures of the m ultiplets and clustershave not yet been fully elucidated. In this paper, a newmultiplet-cluster model is proposed, which is based on*To whom all correspondence should be addressed.t Presented as part of a dissertation by B. Hird in partial fulfillmentof the Ph.D. degree requirements.

restricted mobility of th e polymer chains in th e vicinityof th e multiplets andwhich reconciles some of th e appa rentinconsistencies in our current understanding of thesesystems.The f irst quali tative model for the morphologies ofrandom ionomers was developed by Bonotto and Bon-

ner in 1968.15 In th e same year, Longworth an d VaughanlGproposed a model based on th e analysis of small-angle X-ray scatter ing (SAXS) da ta for poly(ethy1ene-co-meth-acrylic acid) a nd its alkali-metal ionomer derivatives. Apeak corresponding to a Bragg spacing of ca. 50 A wasobserved in the scattering profiles. Th is "ionic" peak wasin terpre ted as be ing due to sca t ter ing f rom orderedhydrocarbon chains between ionic aggregates rath er t hanth e aggregates themselves. Th is model was shown to haveseveral shortcomings, among which are its inability toaccount for th e fact t ha t cesium salts show a much morein tense SAXS peak tha n l i th ium sa l ts , as well as th eobservation th at both the melting point and the degreeof crystallinity are approximately the same in the acidcopolymers an d th e corresponding sa lt forms.0024-9297/90/2223-4098$02.50/0 0 990 American Chemical Society


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Macromolecules,Vol. 23, No. 18, 1990In a theoretica l model presented by Eisenberg in 1970,14steric effects were postulated t o limit the n umbe r of ionpairs th at can aggregate in a spherical droplet withoutthe presence of any intervening hydrocarbon. The se smallaggregates containing only ionic m aterial a nd possessinglow m ass an d s t r o n g e l ec t r o s t a t i c i n t e r ac t io n s wer ecollectively termed m ultiplets. Electrostatic interactionsb e t w e e n m u l t i p l e t s w e r e p r o p o s ed t o f a v o r t h e i ragglomeration to form phase-separated regions termedclusters, with elas tic forces opposing cluster formation.

From the oretical evaluation of the electros tatic and elasticforces in rando m ionomers of low dielectric constant, clusterforma tion was inferred t o be energetically favorable abovea certain critical ion concentration . Th is model was notbased on a detailed analysis of X-ray scattering studiesof morphology bu t was able to account qualitatively forthe mechanical data suggesting two phases.Recent, more sophisticated theoretical approaches byForsman,17J8Dreyfus,lgand Dayte and Taylor,m based onthe same principles of electros tatic vs elastic forces dueto local chain extension on aggregation of the ion pairs,arrived a t similar conclusions to those of th e Eisenbergmodel but provided considerable additional insight. Inaddition, following the ex perimen ts by Earnest e t

Forsman suggested th at th e entire polymer coil may expandsom ewh at on ag grega tion of th e ions.17J8 However, Squir eset a1.22 ave suggested t ha t no theoretica l justification foroverall chain extension is necessary to describe ionicaggregation in ionomers with a random distribution ofaggregates.Marx et aLZ3proposed a model in 1973 in which theionic SAXS peak was ascribed to the electron densitydifference between the meta l cations and th e hydrocarbon,with the scattering moieties being treate d as points on aparacrystall ine latt ice. In this model, the size of theaggregates is postulated to be very small in all cases,amou nting to no m ore than septimers , even at relativelyhigh ion contents. Hence, only multiplets are postulatedto exist witho ut the occurrence of an y clustering or phases e p a r a t i o n . T h e m o de l d e s c ri b e s t h e S A X S p e a kq u an t i t a t i v e ly b u t can n o t acco u n t sa ti s f ac to r il y f o rmechanical measurements, which indicate a two-phasemorphology in these materials.A similar model was put forwward by Binsbergen andKroon in 197324 n which the sc atter ing m oieties areassumed to be points a t the ce nters of spheres, which arerandomly packed. Th is model has quite similar featuresto those of the paracrystalline lattice model and likewisedoes not predict two-phase behavior.In 1983, Yarusso and Cooperz5proposed a modified h ard-sphere model in which the m ultiplets are proposed to haveliquidlike order a nd to have a distan ce of closest approac hdetermine d by the layer of hydrocarbon chains attache dto and sur rounding each mul t ip le t . This model is inexcellent agreem ent with the experimentally determine dionic peak in the SAXS profiles of SPS ionomers butmakes no att em pt to a ccount for the mechanical propertiesof these materials.A recent model by Ding et a1.26based on anomalousSAXS from SPS ionomers accurately describes th e entireSAX S prof ile , inc lud ing the charac ter is t ic up tu rn inscatter ing inten sity near zero angle. Th is model alsoa t t r i b u t e s t h e S A X S i o n o m e r p ea k t o i n t e r p a r t i c lescattering of hard spheres with liquidlike order but includesthe effects of a nonrandom distribution of lone ion pairs,thereby accounting for the small-angle upturn. Again,mechanical effects are not considered.

Multiplet-Cluster Model for Random Ionomers 4099Mac Knight et al.27 proposed a model in 1974 derivedfrom the radial distribution function of the scattered X-rays for pa rtially neu tralized poly(ethy1ene-co-cesium meth -acrylate) ionomers. Th is model, known as the core-shell model, postulates the existence of clu sters with aradius of 8-10 A , each containing ca. 50 ion pairs. Th ecluster is shielded from surroundin g matrix ions by a shellof hydrocarbon chain s tha t is of the order of 20-A hick.Electrostatic attraction thu s results in a preferred distancebetween the clu ster and matrix ions, i.e. the thick ness of

the hydrocarbon shell. Th is preferred distance is assumedto be the origin of th e SA XS peak corresponding to ca.20 A. I t is important to note tha t the ionic peak is notconsidered to arise from interference between scatteringcenters bu t ra ther f rom in trapar t ic le sca t te ring . Th econsiderab le number of ions per aggregate and therelatively large dimensions of the cluste rs postulated inthis model may provide an exp lanation for the observedhigh-temperature TeI n 1 9 80 R o ch e e t a1.2 8 su g g es t ed a mo d e l t h a t i sconceptually similar to the core-shell model bu t differsin th e proposed geometry of the clusters. In this model,the central ionic core is proposed to be lamellar ins teadof spherical with a region depleted of ions on either sideof th e lamellar core. Th is depleted region defines th edistance of closest approach of other ion pairs, whichconstitute the shell. In this model, the spacing betweenthe core and shell accounts for the SA XS peak, and thesize of th e clusters may be su fficient to explain the observedtwo-phase behavior.A number of other treatments have been advanced todescribe specific ionomer systems. The se include blocki o n o m e r ~ , ~ ~equential ionomers such as polyurethane-b as ed m a t e r i a l ~ , ~ O , ~ lemicrystall ine ionomers such asSurlyn,lG n d hydrated sy stems such as the perfluorosul-fona tes, e.g., Nafion.17 As these treatments do not addressthemselves to dry, noncrystalline random ionomers, theywill not be discussed here exce pt for one th at is of particularinterest to the cu rrent system an d was developed for ha-

lato telechelics by Williams et a1.38~3~ xtensive stud ieson these materials have clearly indicated th at they containonly large m ultiplets.Two recent experimental results have cas t considerabledoub t on the models proposed to date for random iono-mers. Detailed mechanical studies on poly(styrene-co-alkali methacrylate) ionomers indicate th at the clustersbecome dominant and perhaps even continuous at a n ioncon ten t of ca. 6 mol % . 4 0 These s tud ies were basedprimarily on analysis of the loss tangent da ta ( tan 6) , whichindicate that, for this system, the area under each tan 6peak is representative of the volum e fraction of th e phaseresponsible for tha t peak. Compa rison of the relative areasof the loss tangen t peaks leads to the conclusion tha t the

volume fraction of the clusters is ca. 50% at an ion contentof 6 mol 5% . This conclusion is reinforced by the storagemo d u lu s d a t a a s we ll a s b y o th e r a b r u p t ch an g es inproperties a t approximately the same ion content, suchas th e breakdown of the t ime-temperature superposi-tion.Another recent study suggests tha t the S AXS peak inrandom ionomers is du e t o interp article interference.41Thisstudy was based on SAXS data for styrene-based iono-mers in which the ions were situa ted a t the e nds of flexibleside chains of varying length. Th ese materials show a lineardependence of the Bragg spacing, dBragg, n th e s id e-chain length, from very long side chains down t o the pointwhere the ionic group is attach ed directly to the polymerbackbone or styrene ring. Since the morphology of the


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4100 Eisenberg et al.long side-chain ionomers is very likely to be the same ast h a t o f t h e h a l a t o t e l e c h e li c s , t h i s i m p l i e s t h a tmorphological continuity extends from the telechelics torandom ionomers such as th e poly(styrene-co-alkali meth -acrylates). Extensive studie s on halato telechelics haveindicated tha t only multiplets exist in these materials andt h a t t h e S A X S p e a k i s t h u s d u e t o i n t e r p a r t i c l es ~ a t t e r i n g . ~ , ~ ~ence, it is considered highly probable th atthe SAX S peak in random ionomers is also due to int er -particle scattering an d th us represents the distance betweencenters of the scattering moieties.In order to observe a second Tg,omains must be presentthat have minimum dimensions of 50-100 A dependingon the technique used to detect the Tg.Thi s estimate wasmade on the basis of several experimental results. On theone hand, many nonionic copolymers, even those withconsiderable blockiness, show only a single T,. On theother hand, block copolymers of styrene and dimethyl-siloxane (PDMS),with PDMS block length s of 1000units,exhibit two-phase behavior.42for dry, noncrystalline random ion-omers is generally con siderably less than 50A, despite thefact tha t these materials exhibit two tan 6 peaks.25 Thi sraises an appar ent inconsistency in models th at attri but ethe SAXS peak to interparticle interference, in tha t theinterpar t ic le center- to-center scat ter ing distances aresmaller than the minimum dimensions of the clustersthemselves. Thus, if the ionic peak in th e SA XS profilesof random ionomers is interpre ted as being due to int er-multiplet scattering, the small size of th e mult iplets doesnot allow for explanation of the observed second T , indynamic mechanical measurements. On the other han d,while models th at ascribe th e ionic SAXS peak t o in-traparticle scattering may account for the second Tg,heydo not account for the proposed co ntinuity of morphologybetween halato te lechel ics and random ionomers , asdemonstrated by the linear dependence of dBraggon theside-chain length in random side-chain systems.41In this paper, we propose a new model of clustering inrandom ionom ers . T h is new approach succes s fu l lyaccounts fo r the observed ionic peak in the SA XS da ta,the high volume fraction and dominance of the clustersat re lat ively low ion contents , and the cont inui ty ofmorphology of these m aterials with t ha t of telechelics. T hemodel is also in keeping with a wide range of otherexperim ental o bservations, as will be discussed in section3.

T he observed

Macromolecules, Vol. 23, No. 18, 1990

2. The ModelIn this section, the param eters t ha t govern the formationan d charac teristics of multiplets will be discussed; this willbe followed by a description of clusters and thei r properties.2.1. Multiplets. T he formation of multiplets is a crucial

element in the current model. Th e term multiplet hasexactly the same meaning as in the original theoreticalmodel by Eisenberg,* i.e., an aggregate consisting of severalion pairs and containing only ionic material. A numberof factors govern the formation of multiplets in randomionomers, some of which are determined by the ionicspecies themselves and others by the nature of the hostpolymer.Th e most important ionic parameter th at affects mul-t ip le t fo rm at ion i s the s t r eng th of th e e lec t ros ta t i cinteractions between the ion pairs. Th is is determined bythe sizes of the ions and t he p artial covalent character ofthe ionic bond. Although none of these param eters canbe varied independently of the others, they are imp ortan tf ac to r s in m ul t ip le t fo rm at ion . If the e lec t ros ta t i c

interactions between ion pairs are too weak to overcomethe elastic forces of th e chains to which they are atta ched ,no multiplets will form. T he firmness with which the ionpairs are held together is also determined by t he stren gthof these electrostatic interactions; small highly polar ionpairs interact more strongly and thus tend to be morefirmly held tha n larger groups. T he firmness with whichthe ion pairs are held in a mult ip let is an impor tantconsideration in the current model, as will be discussedbelow.Th e ion conte nt of the ionomer is also a crucial factorin influencing multiplet formation. Th e proximity of theion pairs to one anoth er is dete rmin ed by the ion contentof th e system. If the ion pairs are very dilute, they aretoo f a r ap ar t to exper ience s ign i f i can t e lec t ros ta t i cattractions and hence do not tend to aggregate.T h e c h a r a c t e r i s t ic s o f t h e h o s t p o l y m e r a r e a l s oimpo rtant in determining the exten t of multiplet formationin a random ionomer. Low dielectric consta nt and low T gof the ho st polymer te nd to favor ionic aggregation, whilehigh dielectric constant and /or high Tg end t o inhibit mul-tip let formation . T he presence of plasticizers, as well asspecific interactions between plasticizer or backbone andt h e io nic g ro up s, a lso in fl ue nc es t h e p r o ~ e s s . ~ ~ - ~ ~In ionom ers in which ionic aggregation is energeticallyfavorable, the size of the aggregates is limited by stericfactors, barring unu sual aggregate geometries. In typicalrandom polystyrene-based ionomers such as the poly-(styrene-co-alkali methacrylates), steric factors preve ntmore tha n a small number of ion pairs from coming intodirect contact with one anot her. T he multiplets are thuspos tulated to be relat ively small and r ig id in thesei0n0 me rs.l~ n halato telechelics or ionomers in which theions are situate d a t the e nd s of long flexible side chains,there is less steric hindrance to aggregation and larger mul-ti pl et s result.38339Each ion pair in a multipl et effectively anchors thepolymer chain at the point to which it is attached. Hence,the m obility of th e polymer chain in th e immediate vicinity

of a multiplet is expected to be greatly reduced relativeto th at of a chain in the bulk polymer, with the mobilityincreasing gradually with increasing distance from the mul-tiplet. Th e firmness with which the ion pair is anchoredis importan t in de termining how effectively the mobilityof th e polyme r chain is restricted. Rigid mul tiplets restrictthe mobility of the chains more tha n mu ltiplet s in whichthe ions pairs can move relative to one an other. For rigidmultiplets t o exist, strong electrostatic interactions mu stbe operative between the ion pairs in the multiplet.Depending on the number of ion pairs per multiplet,considerable local or short-range chain extension of someof the chains is likely to occur on multiplet formation.17J8T he locally extend ed chain segm ents have fewer availableconf igura t ions an d a re thu s l es s m obi le t ha n unex-tended chains. Hence, this extension is believed to enhancethe restriction in mobility experienced by the chains inclose proximity to their point of att ach me nt to a multi-plet.T he cha ins tha t a r e anchored to the m ul t ip le t a r eexpected to have an effect opposite to t ha t of a plasticizerby effectively reducing th e mobility of neighboring nonan-chored chains in the imm ediate vicinity of the m ultipletsurface. Each mu ltiplet is therefore surrounded by a regionof restricted chain mobility or skin, as depicted in Figure1. Th ere is no definite boun dary between t he region ofrestricted mobility an d the rest of the polymer.Th e skin surrounding each multiplet is expected tobe depleted of ions, since ion pairs very close to a mul-


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Macromolecules, Vol. 23 , No. 18 , 1990

Figure 1. Schematic diagram of the region of restricted mobilitysurrounding a m ultiplet in a poly(styrene-co-sodiummethacry-late) ionomer.tiple t would experien ce relatively strong electrostatic forcesduring multiplet formation and would thus tend to beincorporated into th e multiplet itself. Furtherm ore, twoion pairs very close together o n the s ame chain w ould alsohave a very high probability of being incorporated in to thesame m u l t ip l e t , w i th t h e in t e r v en ing ch a in seg m en teffectively forming a sho rt loop emana ting from th e surfaceof th e multiplet. However, the presence of some lone ionpair s wi th in t he reg ion of res t r ic ted mobi l i ty i s no texcluded.

T he thicknes s of th e region of restr icted m obili tysurrounding each m ultiplet is determined largely by theflexibility of the polymer ba ckbon e; th e more flexible thechain, the thinner th e skin of restricted mobility. Th edistance over which polymer segments experience anappreciable restriction in mobility is difficult to ascertainexactly but may be assumed to be of the order of thepersis tenc e length of the bulk polymer. Th e persistencelength is a measure of the distance over which localinflexibility in a polymer chain persists47 and has beens h o w n t o b e r e l a t i v e l y i n s e n s i t i v e t o c h a n g e s i nt e m p e r a t ~ r e . ~ ~

A mu ltiple t consisting of only two or thre e ion pairs willhave a relatively lower mass an d will therefore be relativelymore mobi le tha n a larger mul t ip le t . Th e number ofanchored chains is also lower for small multiplets, resultingin a lower volume fraction of material with reducedmobility in a sphere of radius equal to the persistencelength surrounding the multiplet. Conversely, th e largerthe m ultiplet , the greater the number of anchored chainsand the greater the reduction in mobili ty. A multipletcontaining only two ion pairs, i.e., a quar tet, is expectedto behave in a similar ma nner t o a conventional cross-link and hence influences the properties of the materialin a similar fashion.

Multiplet-Cluster Model for Random Ionomers 4101

Average Chain MobllltyMULTIPLET

&50A JDistanceFigure 2. Schematic representation of chain mobility: (A ) inthe vicinity of an isolated multiplet; (B)n the region of clusteredmultiplets.

I

In general, the restricted mobility region surroundingan isolated m ultiplet would be too small to have its ownTg,ut the multiplet itself would increase the Tg f thepolymer by acting as a large cross-link.2.2. Clusters. As the ion content is increased, theaverage distance between multiplets decreases. Eventuallya point is reached where some overlap is encounteredamong the regions of restricted m obility surrounding eachmultiplet. It should be stressed, however, that only th eregions of restr icted mobili ty overlap; the multipletsthemselves remain intact. As this overlap becomes morefrequ ent, relatively large contiguous regions of restric tedmobility mu st form. When such a region is large enoughto have its own Tg,t constitutes a cluster and exhibitsbehavior characteristic of a phase-separa ted region. It isimportant to note that, within the framework of this m odel,cluster formation does not sim ply lead to broadening ofth e Tg f the material b ut gives rise to a new T g . This isillustrated qualitatively in Figure 2, which schematicallycompares chain m obility in the vicinity of an isolated m ul-tiplet with tha t in the region of clustered multiplets. Smallregions of restr icted mobili ty effectively act as cross-links and thus raise the T g of th e material (Figure 2A).How ever, when a sufficient num ber of multiplets are closeenough together to form a contiguous region of restrictedmobility greater tha n 50-100 8, n dimension (Figure 2B),the reg ion const i tu tes a c luster and exhib i ts i t s ownseparate T g .T he exact s ize of th e dom ains a t which two-phasebehavior becomes detectable is not well-defined, as is thecase in any microphase-separated system. T he distancebetween adjacent mu ltiplets within a cluster mu st be lessth an twice the thickness of th e restricted mobility layer.No boundaries between overlapping regions within thecluster are proposed to exist.An important feature of this model is that it does notrequire the clusters to be of any particular geom etry; infact highly irregular shape s are probable, as depicted in


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4102 Eisenberg e t ai. Macromolecules, Vol. 23, No. 18, 1990a

0 00 400a

8 0

Figure 3. Schematic representation of the morphologies ofrandom ionomers at d ifferent ion contents: (A ) low ion content;(B)ntermediate ion con tent; (C) high ion content. The shadedareas indicate regions of restricted mobility. A, B, and C areschematic represen tations of the spa tial arrangement of mul-tiple ts considering only electron densi ty factors without regardto chain mobility,Figure 3. In contrast t o othe r models, there is also no well-defined size or number of ion pairs or multiplets in acluster.Another impor tant aspect is th at i t not necessary toinvoke electrostatic interactions betwe en multiplets withina cluster. Although weak electrostatic intermultiple t forcesmay exist, they are considered t o he less impor tant thanother factors. T he multiplets thus do not condense toform the cluster bu t are close together by virtue of th eproximity of the ion pairs on the polymer chain. In thisrespect, th e model differs dramatically from previoustheories, which ascribe the driving force for clustering toelectrostatic attraction between multiplets.In random ionomers, the re is a distribution of distancesbetween ionic groups along the chain. Very short inter-group distances will probably result in bo th ions pairs beingincorporated into th e same mu ltiplet, effectively forminga short loop of polymer chain emanating from t he mul-tiplet surface. Beyond this loopback distance, the sho rterdistances between ionic species will tend to be do min antin determining th e distribution of intermultiplet distances.Th is is il lustrated schematically in Figure 4. If ion pairsA and C become incorporated into a multiplet, then forion pairs B and D to be incorporated into another mul-tiplet, the second multiplet m ust form within th e reachof th e shorte r chain segment, i.e., th e length of th e chainsegment between ion pairs A an d B. Th us intergroupdistances slightly longer tha n th e loopback distance willhe dom inant in determining intermultiplet distances andwill probably give rise to a most prevalent or preferredspacing. Th is spacing is thought to be responsible for theposition of th e ionic peak in t he SAX S profiles of thesematerials . However, i t should he stressed tha t a range ofintermultiplet spacings is expected, a s evidenced by thewidth of th e ionic SAX S peak in th ese materials.38Considering th e dimensions of polymer ch ains and tho seof multiplets and clusters, it seems reasonable th at o ne

A

Yt

Figure 4. Schematic diagram representing t h e dependence ofi n t e rm ul t i p l t t distance on the spacing of ionic groups along thepolymer chains.polymer chain may be anchored to a relatively largenum ber of different mu ltiplets and probably even passesthrough numerous clusten . Th e intercluster region consistsof nonionic chain material in the form of long nonionicsegments, loops, and c hain ends. In addition, th is regionmay con tain lone ion pairs, individual multiplets, or evensmall aggregates of multiplets with dimensions smaller thanthose needed for a second T , to he observed.I n t h e r u r r e n t m o d el , t h e p r e s e nc e of c lus te r s isdetermined by the existence of sufficiently large regionso f m a t e r i a l w i t h r e s t r i c t e d m o b i l i t y ; t h e r e is n othermodynamic driving force for phase separatio n of theclusters. Thu s, from a thermodyn amic point of view, th eterm ph ase may not be entirely appro priate to describethe clustered domains. However, the clusters exhibit theirown well-defined merhanical characteristics, which arequite reproducible and thus clearly demo nstrate phase-separated behavior. T he material may be compared to atwo-phase sys tem very c lose to i t s c r i t i ca l so lu t iontemperature. In that case, the differences in compositionan d prop erties between th e two phases would be expectedt n 1)esmall but qu ite reproducible, as is the case here. Forthese reasons, the rlu sters will be considered t o constitutea sepa rate phase for the purposes of this discussion.T he tw o-phase behavior observed in some ionomers mayalso he expected to occur in nonionic polymer networkscontaining multifunction al cross-links. However, thisshould only occur if th e m ass and rigidity of the cross-link cente r is sufficient t o cause a ppreciable immobilizationof the polymer chains in th e vicinity of the cross-link andprovided further that the distance between these cross-link cente rs is less tha n twice the pe rsistence length of thepolymer.2.3. S e m i q u a n t i t a t i v e A s p e c t s . SAXS s tudies onpoly(styrene-co-resium methacrylate) with an ion contentof 7 mol indicate an ionic- peak with a dB,= of ca. 25.&.4,49 If it is assumed for simplirity that the multipletsare uniformly distrib uted o n a cubic lattice in this ma terialwith a density of 1.0 g ~ m - ~ ,he nu mber of ion pairs permultiplet is 5.9 if all of th e ion pairs are incorporated intomultiplets , 4.4 if 75 % of the ion pairs are in multiplets ,and 2. 9 if 50$ are in multiplets.Fo r the purposes of an illustrative calculation, stericrestrictions are assumed to limit the multiplets to anaverage of ca. 5 ion pairs each, with an average volume ofca . 100 A3 in po ly t s ty rene- ro - sod ium m ethacry la te )containing 7 mol ions (S0.7MANaJ. T h e thickness ofthe region of restricted mobility surrounding each mul-tiplet is postulated to be of the ord er of the persistencelength of the polymer chain t o which th e ionic groups are


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Macromolecules, Vol. 23, N o. 18,1990 Multiplet-Cluster Model for Random Ionomers 4103dete rmin ed only by intermultiplet distances; th e relativemobility of interstitial chain ma terial has no effect on thescattering, In this regard, the current m odel is completelyconsistent with the paracrystalline or liquidlike hard-s p he re s ca tt er in g m od el s p re vio usly d i ~ c u s s e d . ~ ~ - ~ ~

The model also accounts for the weak dependence ofthe B ragg spacing on th e ion conten t of random ionomers.5lIf the multiplets are all assumed to be th e same size anduniformly d istributed in space, the n there is a cube-rootdependence of the inte rmultiplet distance, Le., dBregg, onthe inverse of the ion ~onc en tra tio n. '~ f the num ber ofion pairs per m ult ip let increases with increas ing ioncontent, th is already weak dependence of d B r q g becomeseven weaker, as discussed below. If the nu mb er of ion pairsin a multiplet is proportional to th e ion content, the n theintermultiplet distance remains constant as the ion contentis increased. It is recognized th at t he above relation is onlyvalid for a uniform distribution of multiplets thro ugh outt h e m a t e r i a l a n d t h a t t h e c u r r e n t m o d e l p ro p o se s ad i s t r ibu t ion o f in te rm ul t ip le t d i s t ances w i th a m os tprevalent spacing. Nevertheless, th e model is in qualitativeagreement with th e weak dependence of dBregg on the ionconcentration, C, observed for the polystyrene-based ion-omers.

The average dis tance between ionic groups on thepolymer chain decreases as the ion content increases, thu sfavoring the formation of mu ltiplets in closer proximityto one another . Th is is in accordance with cube-rootdependence of d B r w g on C, ssuming constant multipletsize. However, the size of each multiple t is limited onlyby steric factors.I4 At relatively high ion contents, i t isexpected that the number of ionic groups on adjacentrepeat un its along th e same chain will be higher than th atat low ion contents. For example, in perfectly random ion-omers, th e fraction of ion pairs on adjacent re peat unitsis approximately 10% for a 5 mol % sample, while ca. 20 %of ion pai rs in a 10 mol % sample are on a repeat unit th atis adjacen t to ano ther ion-containing unit. Such vicinalionic groups may allow more ion pa irs to aggregate in amultiplet by effectively reducing the amount of chainmaterial per ion p air, thereby lessening th e steric hindranceto aggregation. Hence , the average size of the mu lti-plets is expected t o increase slightly with increasing ioncontent, thus furthe r reducing the dependence of dBraggon the ion concentration expec ted from the simple cube-root dependence.

The fact that th e SAXS peak pers is ts t o temperaturesabove the T, f th e c lus te rs in som e i o n o m e r ~ ~ ~ ?sconsistent with the model in tha t th e multiplets remainintact above the clus ter Tg n most cases . Th e high-temp erature loss tangen t peak is due to the glass transitionof the non ion ic com ponen t o f the c lus te r s and no tdecomposition of th e multiplets.No maximum is evident in the SA XS profiles of somepolystyrene sulfonate ionomers cast from a 9 01 0 tetrahy-drofuran-water mixture.52 However, a typical SAXS peakappears rapidly when t he sample is heated above its TB'This pheno menon is completely consistent with the cu rrentmodel. In solution, th e ions ar e expected to be highlysolvated an d the electrostatic interactions greatly reduced.During the casting process, the most tightly bound solventmolecules, i.e., th e wate r molecules solvating th e ions, wouldbe expected to be the last to evaporate. By the time theselast water molecules are removed, there is little do ubt th atth e ionomer is below its T g . Th e individual ion pairs arethu s prevented from associating extensively to form mul-tiplets. As soon as t he material is heated above its Tg,h eions are able to associate to form multiplets, which, if

attache d. Th e persistence length of polystyrene in the bulkhas been reported as being ca. 10A, independ ent of thet e m p e r a t ~ r e . ~ ~ssuming tha t all of th e material within10A of th e surface of th e multiplet is appreciably restrictedin mobility, th e volume of immobilized material per ionpair is approximately 1800 A3. Assuming a den sity of 1g/mL , a t an ion content of 7 mol %, pproximately 72 vol% of th e materia l is restricted in mobility if all of th e ionpairs are incorporated into isolated multiplets. However,th e volume fraction of clusters is somewhat less th an thisfor several reasons. Isolated m ultiplets, or aggregates ofmultiplets less than 50-100 8, n dimension, would notcontribute t o the volume of the clustered regions. Loneion pairs, which are not considered in the above calculation,should also reduce the volume f ract ion of res tr ic tedmaterial. In add ition, a significant portion of the clusteredmateria l is comprised of overlap ping regions of restrictedmobility. The se overlapping regions occupy the sam evolume in space, thus making only a single contributionto the volume fraction of th e clusters.

T h e r e l a t iv e a r e a s of t h e l o ss t a n g e n t p e a k s f o rS.07MANa indicate tha t t he clusters occupy on the orderof 7 0 vo l % of th e material,40 which corroborate s t heconsiderations described above. These c onsiderations weret a k e n i n t o a c c o u n t i n f o r m u l a t i n g t h e s c h e m a t i creprese ntations of multiplets an d clusters in Figures 1and3 , r espec tive ly . I t shou ld be em phasized tha t theseconsiderations ar e justifiable only for th e poly(styrene-co-sodium methacrylate) ionomers . Dif ferent s ter iccons traints and/or pers is tence lengths in other iono-m ers m ay lead to qu i te d i f f e ren t m orpho logies. Forexample, in polystyrene-based ionomers with the same ionconte nt a nd functional group (i.e., carboxylates),it has beenshown th at th e size of th e ionic aggregates ranges from ca.5 to 25 A, depending on whether the ionic groups areattach ed directly to th e polymer backbone or to the endsof flexible decyl side chains. Likewise, since the ionicgroups in sulfonated polystyrene ionomers are furth er fromthe backbone and are thu s less sterically hindered t hanthose in analogous poly(s tyrene-methacry la te) iono-mers, the average numb er of ion pairs per mu ltiplet is alsoexpected to be different. Th is aspect is discussed in greaterdetail in a separate pub l i~a t io n.~ '3. Experimental Corroboration

Thi s model e i ther explains or is cons is tent with anunprecedented range of experimental da ta for random ion-omers. Although it may n ot addre ss itself to all observedphenomena, the a uthors are not aware of anything thatdirect ly contradicts the model . Mos t im po r tan t ly , i tr e c on c i le s S A X S a n d d y n a m i c m e c h a n i ca l d a t a a n daccounts for phase inversion at relatively low ion contents.In t his section, some of the specific phenomena accountedfor by the model are discussed in somewhat greater detail.3.1. S A X S Data. T he "ionic" SAXS peak is proposedto arise primarily from the most prevalent intermulti-plet distance within th e clusters. T he model allows forinterparticle bu t predominantly intracluster scattering a tthe same time. I t should be noted tha t the SAXS peaksare relatively broad25-2*@-53 and th a t a dist rib ut io n of in-t er m ul ti pl et d is ta nc es i s i n d i ~ a t e d . ~ ~ost of these in-termultiple t distances are intra cluster spacings; however,some scattering may also be due t o distances between mul-tiplets in neighboring clusters, distances between lon e mul-tiplets an d those in nearby clusters, or distances betweendifferent lone multiplets. These distances are expectedto con t r ibu te to t he observed background sca t t e r ingi n t e n s i t y . T h e SA X S prof i l e o f these m ate r ia l s i s


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4104 Eisenberg et al.prese nt in sufficiently high num bers, give rise to a SAXSpeak.3.2. Dynamic Mechanical Data. A t ion contents aslow as ca. 2 mo l %, a second loss tangent peak appearsin the dynamic mechanical data for poly(s tyrene-co-so diu m me th ac ry la te ) i o n o m e r ~ . ~ ~his peak has beenascribed to the glass transi tion of the clusters. In orderto exhibit a glass transition, th e clustered regions must haveminimum dimensions of 50-100 A. Th e average diameterof an individual mult ip le t and surrounding "skin" inS . 07MANa i s though t to be approx im ate ly 25 A , asdepict ed schematically in Figure 1. Hen ce, only very fewof the restricted mobility regions surrounding each mul-tiplet need to overlap in order t o create a region largeenough to exhibit i ts own TB 'Th e fact that two separate peaks are evident in the losstangent curves for a wide range of random ionomers3v8indicates t ha t only two dist inct morphological regions arepresent in these materials. A wide range of morphologieswould presumably lead t o a single, broad t an 6 peak. Thisis a fundam ental feature of the current model in that th eloss tang ent peaks a re postulated to arise from only twomorphological regions, viz. , unclustered material andclustered material, in which the regions of restrictedmobility are large enough to exhibit t heir own T,.As outlined above, the m ultiplets are expected to beslightly larger and some what closer togeth er a t higher ioncon ten t s . T h us , the m obi l i ty of the po lym er cha insbetween the m ultiplets may be expected t o decrease withincreasing ion conten t. Th is provides an explanation forth e observed increase in Tg f the clusters with increasingion con tent. T he growth in th e volume fraction of thecluster component a t the expense of the unclustered regionis responsible for the relative change in t he m agnitude ofthe loss tangent peaks with increasing ion content.In a previous publication, it was suggested that thecluster component becomes dominant and perhaps evencont inuous a t an ion content of ca. 6 mol 57 in poly-(styrene-co-sodium methacrylate) ionomers.@ T he curr entmodel is unique in being able t o account successfully forth i s phenom enon . As was shown in section 2.3, theclustered component occupies ca. 70 vol rL a t 7 mol 96,and , given th e highly irregular shapes of the clusters (seeFigure 3 ) , it is not surprising that phase continuity mayalready exist at ca. 6 mo l %.I t has been observed tha t ionom ers der ived f rompolymers in which t he chains are relatively inflexible donot ex hibit two-phase behavior of th e type described above.These polymers include materials such as carboxylatedphenylated phenylenes& and a numb er of other materialsMThes e materials, by virtue of their high rotational barriers,would be expected t o have very long persistence lengths.Therefore, even a t very low ion con tents, the distancebetween ionic groups is expected to be less than twice th epersistance length. If th e ion pairs associate to form mul-tiplets, the mobility of the ent ire chain would be restricted.Since there would be only negligible a mo unts of materialwith unrestricted mobility, two-phase behavior would notbe expected.Ionomers derived from polymers w ith extremely flexiblechains such as polypentenamers only exhibit two-phasebehavior at significantly higher ion contents than iono-mers derived from polymers with stiffer chains such asp o l y ~ t y r e n e . ~ ' . ~ ~mall-angle neutron-scattering studieson these materials indicate tha t the average intermulti-plet distance is also somewhat smaller at the onset ofcluster ing than that in polys tyrene i o n o m e r ~ . ~ ~ccordingto th e cu rre nt model, flexible-chain ionomers are expected

Macromolecules, Vol. 23, N o. 18 , 1990to have only a thin region of restricted mobility surroundingeach multiplet. Th e multiplets would thu s have to be invery close proximity to one another for overlap of thesurrounding "skin" to occur. T he reduced size of th e mul-tiplet p lus "skin" would necessitate larger numbe rs ofover lapp ing r eg ions in o rder to fo rm c lus te r s w i thdiscernible proper t ies . Th us , the onset of two-phasebehavior should only occur a t significantly higher ioncontents tha n tha t in ionomers with stiffer chains. Becausethe m ultiplets in t he clusters have t o be closer togetherin such flexible-chain materials, th e Bragg spacing at thepoint a t which two-phase behavior is observed should beless than t ha t in ionomers with stiffer chains at the onsetof clustering in those materials.

In ionomers derived from polymers with relativelyinflexible chains, th e Tgof the material increases withincreasing ion content a t a significantly higher rate th anin ionomers derived from polymers with more flexiblechains, provided tha t th e Tgs f the two host polymers arereasonably similar. For example, the Tg f sulfonate d poly-(a ry l e the r e ther ke tone)56 inc reases as th e inver seequivalent weight increases at a r ate of 9.4 X 104"C g mob1,while for sulfonated p olystyrene,60 he r ate is 3.4 X lo 4 "Cg mol-'. The Tgs f th e two host polymers are ca. 150 and100 " C , respectively. As descr ibed above, a t low ioncontents, the Tg f a rigid-chain ionomer is not increasedby cross-linking effects as in more flexible ionomers butby the immediate onset of c lus ter ing. Th us , it is notsurprising tha t th e T gof the mate rial increases rapidly asthe ion content is increased. It should be noted th at whenth e behavior of flexible ionomers is contra sted with morer i g i d - c h a i n i o n o m e r s , it i s e s se n t i a l n o t t o m a k ecomparisons on the basis of mole perce nt ions because therepeat units may be significantly different in size and mass.In such cases it is better to compare the ionomers on thebasis of equivalent weight.In polystyrene-based ionomers there is a range of ionconte nts over which two-p hase behavior is observable. A tvery low ion contents (15mol %) virtuallyall of the material is "overlapped" or restricted in m obilityand may therefore be cons idered to be clus tered, asevidenced by th e almost co mplete absence of a low-tem pera ture loss tang ent peak.40 Thi s illustrates one ofthe key featu res of th e model, i.e., th at app roximately twicethe persistance length between m ultiplets is required fortwo-phase behavior to be observed. At much larger in-termultiplet distances, no overlap of restricted mobilityregions occurs, thus resulting in only a single observableTg. Th is is the case for flexible-chain ionomers such aspolypentenamers a t ca. 6 mol '%.57 A t in termult ip let

distances much shorter th an twice the persistence length,the entire sample may be effectively clustered an d thu sexhibit only single-phase behavior. Th is is the case forrelatively inflexible-chain ionomers or in polystyrene ion-omers at very high ion cont ents.Th e fact tha t the loss tangent peak associated with theclusters is significantly broader t han th e low-temperaturepeak4" may be accou nted for by the rang e of mobilities ofthe polymer chains w ithin the clusters. A high degree ofoverlap of th e regions of restricted mobility surroundingeach multiplet will result in lower chain mobility than inth e case of less overlap. A range of intermultiplet distanceswithin the clusters is indicated by SA XS studies, thusgiving r ise to dif ferent extents of over lap and cha inmobilities.


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Macromolecules, Vol. 23,N o . 18, 1990Although not a feature of random ionomers, the modelalso successfully explains the absence of two-phase behaviorin noncrystalline telechelics with relatively high mo lecularmass.61 Carboxy-terminated polystyrenes with number-average molecular weight, M,, reater than 5900 do notshow any breakdown of the time-tem perature superpo-sit ion in stress-relaxation studies, thus indicating thepresenc e of only a single phase. T h e ionic aggrega tes inthese m aterials are likely to be too far apa rt for the regionof restr icted mobili ty surrounding each multiplet to

overlap. However, carboxy-term inated polystyrene tele-chelics with nu mbe r-averag e molecular weights of less th an3300 show a clear breakdown of the time-temperature su-perposition in stress-relaxation studies.61 Th is evidenceof two-phase behavior may be due to th e fact tha t, in thesematerials, the multiplets are close enough to each otherfor overlap of the restricted mobility regions to occur.Steric limitations on multiplet size are less significantin telechelics and long side-chain ionomers tha n in ran domionomers. Th is results in larger multiplets, which mu stcontain some nonionic chain material unless unusualgeometries develop. T hese large aggregates are clearly notclusters and may be thou ght of as arge multiplets, althoughthey may be slightly different from the classical multi-plet encountered in random ionomers in th at they containsome nonionic material. It should be noted in this regardth at hala to telechelics, which are widely regarded as beinggood models for multiplet formation in random iono-mers, are clearly not good models with respect to clusteringin random ionomers.3.3. Electron Microscopy. Desp i t e t h e f ac t t h a tdynamic mechanical data have indicated that the minimumdimensions of the clusters mus t be 50-100 A, extensiveelectron microscopy studies on random ionomers havefailed to det ect any evidence of fea tures of this size.13~63Th e current model provides a simple explanation for thisphenome non. Because microscopy techniques cannotdistinguish between th e regions of restricted mobility inthe ionomer from th e regions of higher mo bility, it is not

p o ss i bl e t o d e t e c t t h e c l u s t e r s w i t h t h i s a p p r o a c h .Resolution on t he o rder of a few angstroms would berequired in order to see the multiplets.Because the ionic aggregates in halato telechelics aresubstan t ia l ly la rger than in random ionomers due toreduced ster ic hindrance, t he ionic aggregates in tele-chel ics should be more read i ly de tec ted by e lec t ronmicroscopy techniques. Indeed , it has recen t ly beenreported t ha t m ultiplets in telechelics have been observeddirectly by S T EM methods.63 However, it should be bornein mind t ha t multiplet formation in samples cast fromsolution may be significantly less extensive tha n t ha t incompression-molded samples, as discussed in section 3.1.3.4. Plasticization Effects. Many studies have been

performed on the effects of both polar and nonpolarp last ic izers on the propert ies of random io n o m e r~ . '~ . ~ ~nthis section, some of th e observed effects are discussed inrelation to th e current model.3.4.1. Nonpolar Plasticizer s. Nonpolar p lasticizershave been widely reported as being able to plasticize boththe unclustered and clustered regions leading to a marked,and sometimes parallel, decrease in the cluster Tg nd theTgof the more mobile reg i0 11s . l~ ~~ ~ne explanation forthe decrease in the Tg f the cluster component on additionof no np ol ar p l a ~ t i c i z e r ~ ~as been th e so-called "therm al-stress" effect, according to which t he Tg f the dispersed" h a r d " p h a se i s a s su med t o d ec r ease b ecau se o f i t sproximity to a "soft" phase in a fashion similar to thatencountered in some block copolymers.M Another possible

Multiplet-Cluster Model for Random Ionom ers 4105explanation may be the incorporation of the nonpolarplasticizer into the clusters. However, most previousmodels are inconsistent with this explanation because thenonpolar diluent would not be expected to diffuse intoregions of high polarity. Th e curre nt model successfullyaccounts for the reduct ion in c luster Tgon nonpolarplasticization, w ithout recourse to th e therm al-stress effector plasticizatio n of the ionic doma ins. Clearly the non-polar dilue nt is able to plasticize the regions of restri ctedmobility between the multiplets in the cluster just aseasilyas the nonpo lar ma terial in th e regions of higher mobility.Ther e is no reason for the plasticizer to c oncentrate morein one component than in the other . Because the Tg fthe clusters is determined by the polymer chains betweenthe multiplets and no t the mu ltiplets themselves, it is notsurpr ising tha t th e Tgsof the clustered and unclusteredregions often decrease in parallel on addition of nonpo-lar plasticizer.3.4.2. Polar Pla sticiz ers. Polar plasticizers selectivelycause a reduction in the Tg f the clusters in randomi ~ n o m e r s . ' ~ + j " ~ ~his is completely consistent with thecurrent model in that polar plasticizers are expected tobe incorporated into the multiplet, shield t he electrostaticinteractions between the ion pairs, and intro duce more freevolume, thus reducing the firmness with which the ion pairsin the multiplet a re anchored. Thi s results in increasedmobility of the hydrocarbon chains attached to the ionp a ir s an d th u s a decrease in the Tg f the regions ofrestricted mobility.In a study of the dyn amic mechanical properties of poly-(styrene-eo-sodiummethacrylate) plasticized with glycerol,i t was observed th at the t an 6 peak associated with theu n c l u s t e re d m a t e r i a l i n c r e a s e d i n m a g n i t u d e w i t hincreasing g lycero l con ten t .71 This occurs becauseplasticization effectively increases the mob ility of th e ch ainsattached to the multiplets and thus reduces the volumeof the restricted mobility region surrounding each mul-t i p l e t . Hen ce , so me of t h e ma te r i a l i n t h e c lu s t e r seffectively becomes pa rt of th e unclustered region, therebyincreasing the volume fraction of the unclustered regionsand reducing the volume fraction of the clusters. Althoughthe tan 6 data for the clusters were not obtained in theplasticization study, the magnitude of the tan 6 peak isexpected to decrease with increasing amo unts of a polardiluent.Sufficient am ount s of a polar plasticizer may completelyobliterate the mechanical characteristics usually associatedwith two-phase b e h a v i ~ r . ' ~ * ~ ~ ? ~ ~his occurs because theplasticizer may reduce the firmness with which the ion pairsare anchored to such as extent, th at t he effective thicknessof the regions of restricted m obility within t he cluster isreduced to t he p oint wh ere overlap no longer occurs, hencedestroying the mechanical features associated with t hecluster.4. Predictions

T h e p r o p o s e d m o d e l r e c o n c i l es a w i d e r a n g e o fphenomena observed in random ionomers, notably in termsof relating molecular paramete rs t o two-phase behavior.Insofar as these have been verified experimentally, theyhave been discussed in section 3. Several, however, havenot yet been treated experim entally, and these are listedas predictions in this section. T he accuracy of thesepredictions will provide a n excellent test of th e validityand generality of the model.Usually, the cluster tan 6 peak and the "ionic" SAXSpeak are either both present or both a bsent in random ion-omers, provided th at sufficient con trast exists between the


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4106 Eisenberg et al.multiplets and the bulk polymer to observe a scatteringpeak. However, according to the curren t model, it maybe poss ible to observe only the SAXS peak in somesystems. Nonpolar plasticization of random ionomersintroduces additio nal free volume to the system and henceeffectively increases the mobility of the polymer chains.Consequently, this reduces th e thickness of the region ofrestricted mobility surround ing each multiplet. If sufficientplasticizer is add ed , these regions may be reduced inthickness to the po int where they no longer overlap. Insuch an instance th e mechan ical properties associated withthe clusters would no longer be evident. However, theSAXS peak should still persist.Very high levels of polar plasticizer may result in sol-vation of the ion pairs within the multiplets , therebyreducing the electrostatic interactions between t he ion pairsto th e point where the entropic and elastic forces opposingmultiplet formation are able to overcome the electrostaticattractions and even pull the multiplet apart. In this event,not only the mechanical features associated with th eclusters but also the SAXS peak should disappear.Another prediction of this model is that telechelicsd e r i v e d f r o m p o l y m e r s w i t h v e r y s t i ff c h a i n s ( t h epersistence length is greater than or equal to the half ofthe contour length of the chain) should exhibi t verydifferent mechanica l behavior from telechelics derived frommore flexible chains in that the entire sample should berestricted in mobility and therefore behave as if it wereclustered. Th is phenomenon should only be observed ifthe m orphologies of the two telechelic ionome rs are similar.Analogous behavior is expected in ABA blocks in whichthe len gth of the middle nonionic segment is less than orequal to twice the persistance length.Final ly , it i s p r e d ic t e d t h a t it may be poss ible todetermine the persistence length along the contour pathbetween ionic groups from dynamic m echanical and SAXSdata for materials that contain rigid multiplets and exhibittwo-phase behavior. As the ion conte nt is increased in suchmaterials, a point is reached a t which the cluster tan 6 peakbecomes dominant. The dgw measured at this ion contentshou ld give a reaso nable indication of twice the persistencelength of the polymer plus the diamete r of a multiplet ifthe ionic groups are at t ach ed direct ly to the polymerbackbone. T he diameter of a multiplet may be estimatedto within a few angstrom s, thus allowing a fairly preciseapprox imation of the persistence length. A great deal ofexper imenta l work on ionomers would be needed to verifythis hypothesis.5. Conclusions

Despite extensive studies on random ionomers, the exactstructure s of the ionic aggregates responsible for the u niquephysical properties of these m aterials have not yet beenfully elucidated. A number of models have been proposed,none of which satisfactorily account for all of the observedexper imental phenomena. Recent evidence of phaseinversion a t relatively low ion contents, coupled with SAXSresults th at suggest a continuity of morphology betweent e l e c h e l ic s a n d r a n d o m i o n o m e r s , h a s l e d t o t h edevelopment of a new model, which successfully acco untsfor a wide range of experim ental observations. T he modelis i n c o m p l e t e a g r e e m e n t w i t h t h e S A X S d a t a a sinterpreted by previous hard-sphere models.The model is based on the formation of multiplets .However, in co ntras t with previous cluster models, it isnot necessary to invoke electrostatic interactions betweenmultip lets in order t o explain the e xistence of clusters. Animportant feature of the model is a proposed region in

Macromolecules, Vol. 23 , No. 18 , 1990w h i c h t h e h y d r o c a r b o n p o l y m e r c h a i n s e g m e n t ssu r round ing each m ul t ip le t exper ience apprec iab lerestriction s in mobility. T he thicknes s of thi s region ispostulated to approximate the persistence length of thehost polymer. An individual multip let raises the T g f themateria l by effectively acting as a large cross-link, but th erestricted region surrounding such an individual multi-plet is not large enough to ex hibit its own Tg. nly whena num ber of these regions overlap to form a relatively largecontiguous region of restricted mobility with its own T gis the region considered to constitute a cluster. Th eclustered regions, which are likely to be highly irregularin shape, have no upper lim it on the num ber of ions pairsor multiplets tha t they may contain. T he clusters behaveas if they were ph ase-separa ted from th e regions of moremobile segmental motion in that they exhibit their ownT,, which is significantly higher than the Tg f the un-clustered comp onent. In these regions also, one wouldexpect a most prevalent intermultip let spacing. Thisspacing accounts for th e characteristic ionic peak in theSAXS profiles of these materials above a certain ioncontent.A w i d e r a n g e o f o t h e r e x p e r i m e n t a l l y o b s e r v e dphenom ena are also accounted for by the model. Theseinclude the weak dependence of the Bragg distance on theion content, pha se inversion a t relatively low ion contents ,the inabi l i ty to see clus ters by electron microscopytechniques, the absence of two-phase behavior in stiff-chain ionomers, and the effects of bo th polar and non-polar plasticizers.Th e model also leads to several predictions, includingthe possible observance of a SAXS peak in the absenceof a tan 6 peak in som e systems, complete disruption ofthe multiplets a t very high levels of polar plasticizers, adifference in m echanical propertie s of flexible-chain ands t i f f - c h a i n h a l a t o t e l e c h e l i c s , a n d t h e p o s s i b l ede te rm in a t ion o f pe r si s t ence l eng ths f rom dyna m icmechanical and SAXS data.

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A New Multiplet-Cluster Model for the Morphology of Random

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