kinetics and mechanisms for thermal imidization

7/22/2019 Kinetics and Mechanisms for Thermal Imidization

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1174 Ma c romole c u le s 1989,22, 1174-1183coil, i.e., C* ;= M-4/5 w h e r e M i s the mole c u la r w e igh t o ft h e m a c r o m o le c u le s ) . 20 But the f o r m a t i o n o f i n t e r n a lcross-links in a polymer coil means the existence of loops.2oTheoretica121,22tudies have shown that i n a g o o d s o l v e n twhere e x c l u d ed - v o l u m e e f f e c t s p r e d o m i n a t e , the proba-bility that two given polymer s i t e s on the same chain comeinto close contact decreases s h a r p l y with t h e i r d i s t a n c e o nthe chain. In a p o l y h y d r o x y compound-borate s y s t e mwhere a n y p o l y m e r s i t e is able t o f o r m a c o m p l e x , i n t r a -c h a i n complexes would then i m p l y the existence of smallloops whose size should be g o v e r n e d b y the local structureof the cha in ( i .e . , r ig id i ty) . In t h i s small loop picture,the concentration of complexes is independent of thepolymer molecularweight as ar as he chain is longer thana possible minimal loop l e n g t h ) . S t i l l the number of in-trachain complexes per macromolecule i nc re a se s with themolecular w e igh t . As a c o n s e q u e n c e , f o r p o l y h y d r o x ycompound solutions we m a y expect that intrachain boratec o m p l e x f o r m a t i o n is more e a s y for flexible polymers suchas poly(viny1 a lcohol) or po ly(g lyc e ry1 m e tha c ry l a t e ) thanfor r i g id polysaccharides ( e .g . , g a l a c toma nna ns) a l t houghthe c o m p l e x a t i o n mechanism is v e r y similar.

1,2-Propanediol, 57-55-6; borax, 1303-96-4;poly(glycery1 methacrylate), 28474-30-8; poly(viny1 alcohol),9002-89-5; galactomann an, 11078-30-1.References and Notes

Registry No.

(1) Tsuchida, E.; Nishide, H. Adv . Polym. Sci. 1977, 24, 1.(2) Menjivar, J. In Water Soluble Polymers; Glass, L., Ed.; Am-

erican Chemical Society: Washington, DC, 1986, p 809.Allain, C.; Salome, L. M acromolecules 1987, 20, 11,2957.Pezron, E.; Liebler, L.; Ricard A.; Audebert, R. M acromole-cules 1988, 21, 1126.Ochiai, H.; Kurita, Y.; Murakami, I. Makromol. Chen. 1984,185, 167.Ochiai, H.; Shimizu, S.; Tadokoro, Y.; Murakami, I. Polym.Commun. 1981,22, 1456.Tsuchida, E.; Nishikawa, H. J . Phys. Chem. 1975, 79, 2072.Leibler, L.; Pezron, E.; Pincus, P. Polymer 1988, 29, 1105.Peeron. E.: Leibler. L.: Lafum a, F. Macromolecules. submitted.. . .Roy, G. L.; La Ferriere, A. L.;Edwards,J. D. J . Inorg. Nucl.Chem. 1957, 4 , 106.Henderson, W. G.; How, M. J.; Kennedy, G. R.; Money, E. F.Carbohydr. Res. 1973, 28, 1.Van Duin, M.; Peters, J. A.; Kieboom, A. P. G.; Van Bekkum,H. Tetrahedraon 1985,41, 3411; 1984, 15, 2901.Sinton, S. W. Macromolecules 1987,20, 2430.Shibayama, M.; Sato, M.; Kimu ra, Y.; Fujiwara, H.; Nomura,S. Polymer 1988,29, 336.Gey, G.; Noble, 0.;Perez, S.; Taravel, F. R. Carbohydr. Res.1987.Pezron, E.; Ricard, A.; Lafuma, F.; Audebert, R . Macromole-cules 1988, 21, 1121.Refojo, M. F. J . A p p l . Polym. Sci. 1965, 9, 3161.Macret, M.; Hild, G. Polymer 1982, 23, 81.Morawetz, H. J . Polym. Sci. 1957, 23, 247.de G ennes, P.-G. Scaling Concept in Polymer Physics; CornellUniversity Press: Ithaca, New York, 1979.Des Cloizeaux, J. J . Phys. (Paris) 1980, 401, 223.Cates, M. E.; Witten, T. A. Macromolecules 1986, 19, 732.

Kinetics and Mechanisms for Thermal Imidization of a PolyamicAcid Stud ied by Ultraviolet-Visible Spectrosc opyEumi Pyun, Richard J. Mathisen, and Chong Sook Paik Sung*In s t i t u t e of Mate r ia ls Sc ience , Departm ent of Chemistry, 97 Nor th Eaglevi l le Road,University of Connecticut, Storrs, Connecticut 06268. Received April 20, 1988;Revised Manuscript Received August 22, 1988

AB STR AC T Th e kinetics and th e mechanisms of thermal imidization of polyamic acid made from a conjugateddiamine @ ,p-diaminoazobenzene) an d a nonconjugated dianh ydride (6F-DA) were investigated both in dilutesolution and in solid s tate in th e tempera ture range 150-190 C. UV-vis absorption spectroscopy was themain tool used even though IR spectroscopy was also used for comparison with the results from W-vis studies.UV-vis spe ctra l changes as a function of imidiza tion time were analyzed on th e basis of th e previously reportedmodel comp ound stud ies in order to obtain th e composition of various imidization species (Macromolecules1987,20, 1414). In 1 N-methylpyrrolidone solution, dissociation and the first imide ring closure proceedfaster than the second imide ring closure of polyamic acid/imide a t all three temperatures studied (150,170,and 190 C). Th is trend is attrib uted to the reduced basicity of the amide group in polyamic acid/imide incomparison to t he analogous group in polyamic acid. Activation energies for the fast process and th e secondring closure were 11a nd 18kcal/m ol, respectively. Durin g the early stages of imidization in dilut e solution,IR s pectr a suggest some dissociation of polyamic acid as well as imidization. On th e basis of these findings,th e mechanism of imidization for dilut e solution has been proposed. In solid-state imidization, th e appare ntimidization r ate was initially faster tha n in dilut e solution du e to th e catalytic effect of the neighboring am icacid group bu t levels off probably due to vitrification. Therefore, the mechanism of solid-state imidizationmu st take into account th e catalytic effect of the neighboring amic acid groups and the decreasing mobilityeffect as a function of cure time. Modeling studies t o predict sp ectral changes as a function of th e ratio ofthe two imidization rate constants are consistent with the observed results in dilute solutions. Th e resultsare adequ ately modeled by assuming a first-order, two-step imidization reaction, assuming a small extentof dissociation. O n th e other hand , solid filmresults seem to be reasonably simulated by assuming a second-orderreaction for the first step , followed by a first-order reaction for the second ste p to account for th e decreasein th e concen tration of the con formationally favorable catalytic amic acid group. Finally, ther e is a goodcorrelation between UV-vis results and IR results, in regard to the overall extent of reaction i n solid films.Introduction

P o l y i m i d e s are an i m p o r t a n t c la s s o f h i g h - p er f o r m a n c ep o l y m e rs . E x c e l l e n t m e c h a n i c a l and electrical propertiesas well as h i g h - t e m p e r a t u r e s t a b i li t y make these p o l y m e r s0024-9297/89/2222-1174$01.50/0

s u i t a b l e f o r a p p l i c at i o n s i n the a e r o s p ac e i n d u s t r y ash i g h - p e r f o r m a n c e c o m p o s i t e s and i n the e l e c t ron ic s i n -d u s t r y as h i g h - t e m p e r a t u r e c o a t i n g s . D i f f i c u lt y in pro-c e ss ing , how e v e r , has s low e d the w i d e s p r e a d use of these989 A me r i c a n Che mic a l Soc ie ty


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Macromolecules, Vol. 22, No. 3, 1989 Imid ization of a Polyamic Acid 1175Scheme ISimplified Two-Stage Reaction Scheme for the PolyimideSynthesis

s o l u t i o nHz-R-NHz + 0 co+HN-R-NH-OC - CO+

h igh temperatures-o l i d stateHOOC COOH

po lyam ic ac id

-?@oc\Noc co +po ly im ide ; R = a roma t i c group

polymers by making them expensive and limiting theirapplicability. Facto rs responsible for this problem includepoor solubility and th e evolution of volatiles during he attreatment. Th e presence of voids in thick films is commonbecause of residual solvent and byproduct volatilizationthroughou t processing. Another reason for processingproblems is the lack of information about the imidizationmechanism s and kinetics; previous studies of these pro-cesses, especially solution studies, have often been con-tradictory and incomplete.2 In industry, complex, em-pirically established, and costly multistage processing isoften employed to reduce these problems.In order to shed light on the kinetic param eters and th emechanism s involved in thermal imidization, we exploredelectronic spectroscopy as a characterization tool. Byutilizing UV-vis abso rption sp ect ra, we were recently ableto distinguish several imidization products as demon-strated with the model compounds and to quantify theirformat ion and d i~a ppe aran ce .~uch a distinction ha s notyet been possible by othe r spectroscopic techniques suchas IR or NMR.Before elaborating on this technique, it is importan t toreview the c hem istry of polyimides and th e results of theimidization studies by other spectroscopic characterizationtechniques. In th e following section, we also propose a newreaction scheme (Scheme 11), including a tw o-step imidi-zation process applicable in some cases.Polyimide Synthesis: Reaction Schemes. Linearpolyimides are ma de by th e im idization of polyamic acids,which are formed by the reaction of dianhydride withdiamine. While polyamic acid formation proceeds quicklya t low temperatures, imidization requires much highertempe ratures. The se two stages are usually consideredseparately as illustrated in Sc heme I. Polyimides can beclassified into four groups, depending on w hether th e di-amin e or the dian hydride is conjugated or not. Each ofthese groups ha s differen t final properties a s well as dif-ferent processing requirements.lb Th e reason for this tren dcan be understood in view of the n ature of the reactionsinvolved.The formation of polyamic acids from diamines anddianhydrides procee ds via nucleophilic substitution on th eanhydride carbonyl atom with the amine acting as a nu-cleophile. It has been shown tha t the reaction rate isdepen dent on th e basicity of th e am ine, the electrophilicityof the anhy dride carbonyl, an d the basicity of the solvent.&It is well-known that the formation of polyamic acids isa reversible reaction where the factors des cribed above playimpo rtant roles in determining the rate c onstants and theequilibrium constants.4b Th is reversible degradatio n ofpolyamic acids into amines, acids, or anhydrides consti-tutes a serious competing reaction with the imidization

Scheme I1Polyimide Reaction SchemeNHz-R-NH:, + 2 C d

PAA HOOCP A 1

coP I 1

R = con juga ted a roma t i c g roupstep, as illustrated in S cheme II.lasbTh e therm al imidization of polyamic acids involves cy-clization through the nucleophilic attack on the acid car-bonyl carbon by the free electron pair of the am ide ni-trogen. As is the case in the form ation of polyamic acids,imidization kinetics are complicated by m any factors in-cluding the properties of the solvent and the precursorpolyamic acids. Rea ction rates have been found to increasewith decreasing solvent basicity in both solid films5aandsolutions.2cLavrov and co-workers showed tha t the cyclization rateis accelerated by an increase in the electron den sity on theamide nitrogen, which is directly related to the basicityof the initial amine.2b They also suggested that the re-activity would further increase with the electrophilicity ofthe acid carbonyl. In addition to the reversible hydrolysisof the am ide group from polyamic acids (PAA), anotherhydrolytic reaction can occur from polyamic acidlim ide(PAI) to a reacted species (PMI) containing imide andamine as illustrated in Scheme 11. Nonconjugated di-amines or dianh ydrides have spacer groups such as car-bonyl, oxygen, or sulfur between aroma tic rings. Thesegroups inherently influence the basicity of the amines orthe electrophilicity of the anhydrid e carbonyl mainly byinductive effects, so th at their reaction rates are differentfrom those of conjugated systems. However, the reactivityof amine, anhydride, or amic acid at the para position inthe conjugated system is expected to be strong ly influencedby the sub sti tuent at th e para posit ion. This is becausea strong electron acceptor such as an imide group para tothe amide nitrogen is found to increase the exte nt of hy-drolysis dramatically.6For example, in the case of the conjugated diamine, thehydrolysis step characterized by the equilibrium constantk5 is probably more important than the hydrolysis stepfrom PAA characterized by k2. In Schem e 11, we also choseto w rite the cyclic imidization by a two-step process ( k4and k6 ) . This scheme proposes the formation of an al-terna ting amide-imide backbone prior to complete imi-dization. Th is idea is justified in the case of the co njuga teddiam ine since the reactiv ity of the am ide nitrogen in PA1in comparison to PA A is expected to be lower due to th eelectron-withdrawing imide group in PA I. Indeed , Lavrov


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1176 Pyun et al.et al. confirmed th at the electron-accepting or -withdraw-ing nature of the substi tuent para to the amide nitrogenis the single largest factor in determ ining the imidizationrate of model mono amic acids.2b To the best of ourknowledge, such a two-step imidization process has neverbeen experimentally observed. This is due to the fact thatIR spectroscop y, which is most often used t o follow thekinetics of imidization, cannot distinguish between the twomajor imide species (PA1 and P II) .

Imidization kinetics are also influenced by factors suchas solvent content and t he physical state of the polyamicacid. Brekner and Feger reported that the hydrogen-bonded complex formed between the solvent N-methyl-pyrrolidone ( N M P) and polyamic acids can prevent thereactive groups of the amic acid from getting into theconformation required for imidization to occur.' Theynoted t ha t this effect is less pronounced in solution tha nin the solid state because the constant solvent exchangein solution increases the conform ational mobility of thereactive groups. Ginsburg and Susko dem onstrated th atthe rate of reaction in solid films increases with filmthickness due to solvent reten tions Polyamic acids havegenerally lower Tgs ha n polyimides. Therefo re, duringthe solid-state reaction of polyamic acids, vitrification canoccur due to the so lven t loss as well as the im id i~ at io n . ~It is speculated tha t the evaporation of solvent and water(an imidiza tion byproduct) as well as the imidization itselfis controlled by vitrification.

All the factors discussed above such as the types ofmonom ers and residual solvents, th e com peting reactions,and t he physical sta te of th e reaction strongly influencethe imidization characteristics of polyamic acids. T helimited solubility of polyimides further adds t o the diffi-culty of their characterization, and consequently moststudies of them have been limited to solid-state reactionstudies by IR spectroscopy.*J In solutions such as Nmethylpyrrolidone, solvent interference in IR spectrausually renders quantitative analyses difficult at best.Some researchers have tried t o minimize this by precipi-tating polyimides in water before IR analysis, but thisprocess could introduce errors due to the competing hy-drolysis of the unreacted amide groups.lob

Review of IR and NMR Studies. As mentionedabove, the most widely used technique for monitoringpolyimide formation is infrared spectroscopy. Absorptionban ds c haracte ristic of th e imide ring occur a t 1770-1800cm-' due to the symme tric imide carbonyl stretch, at1370-1380 cm-' from the imide carbon-nitrogen str etc h,and near 721 cm-l due to the imide ring bending. Th elatter two abs orptions can be used for quantita tive studies,but the carbonyl absorption may deviate from the Beer-Lambert law due to hydrogen bonding.2a The extent ofimidization by IR spectroscopy is usually estim ated by aratio of the im ide peak with a reference aromatic vibration.T he comm on trend observed in such plots of imidizationextent versus time in the solid films is a rapid initial ratefollowed by a more gradual conversion.Several ideas have been proposed to account for theapp aren t two-step cyclization, including the nonequiva lentkinetic states of the amic acid groups,ll vitrification asdefined before, or the decomposition of polyamic acidsback to the anhydride and amine groups. However, i t isnot possible to decide which if a ny of these idea(s ) is re-sponsible for the kinetic behavior since the IR method onlyprovides overall imide ring concentration and thus cannotdifferentiate between different reacted such as PII , PAI,and P M I in Schem e 11. Very recently, nitrogen-15 NMRusing dipolar decoupling, cross polarization, and magic

Macromolecules, Vol. 22, No. 3, 1989Scheme I11Chemical Structures of the Diamine and Dianhydride Usedin This Studym

d i ami noaz obenz ene D AA)cF3

/CO@ fmob?CO cF3 co'6F- DAangle spinning has been explored to characterize the re-action to polyimides.12 W eber and Mu rphy were able toidentify imide, amide, and am ine peaks in enriched N-15NM R spectra.15 However, qua ntitat ive analyses are notyet available since the detailed know ledge of th e relaxationparameters for each type of nitrogen is needed and it hasnot yet been demonstrated w hether N-15 NMR can dis-tinguish between different reacted species such as PA1 andPII .Design of the Experiments. In order to thoroughlyunders tand an d optimize the imidization process both insolution an d in the solid state, we needed a technique todifferentiate between th e various reacted species shownin Scheme 11, one which would not be influenced by thepresence of the solvent. For these req uirements, we choseUV-visible absorption spe ctroscopy because a solvent suchas N M P does not interfere with the polymer absorptionin mo st of the UV-visible range. If the various reactedspecies show sensitive changes in fluorescence, th at canalsobe used. Unfortunately, the cyclization species studiedin this work did not exhibit much fluorescence. As for thepolyimide system, we chose a conjugated diamine a nd anonconjugated dianh ydride in order to reduce thecharge-transfer complex formation known to occur whenboth monomers are conjugated.13J4 T he ch arge-transfercomplexes are usually intensely colored and could interferein the UV-vis spectra. In this study, diaminoazobenzene(DAA) is used as a conjugated diamine, while a fluorinateddianhydride is used as a nonconjugated dianhydride (seeSchem e I11 for their chemical structure s.) Recently, wehave used DAA to study the cure reactions and speciesw ith d i e p 0 ~ i d e . l ~n epoxy system s, we took advantage ofthe magnif ied spectral shif ts when the two amino sub-stituen ts are at th e oppos ite para positions. As the diaminogroups are chemically transform ed to the secondary andthe tertiary amines, the bathoch romic spectral shifts andthe large enhancem ent of the fluorescence intensity wereobserved in UV-vis absorption spectra and fluorescencespect ra, respectively. By analyzing these spectral chang es,we were able to m onitor composition, the kinetic param-eters, activation energy, and extent of reaction.In polyimides, UV-vis spectral shifts as well as thechanges in th e e xtinction coefficients are also observed,depending on the reacted specie^.^ Th is is observed whenusing DAA as he diam ine because of the u nique electronicsta tes associated with each cure species. As we recentlydem onstrated , the diamic acid derivative of DAA showsa blue shif t of 20 nm from th at of DAA. This shift is dueto the weaker electron-do nating capacity of the am ide bondas compared to the am ine toward the conjugated azo bond.When one of the am ic acids is cyclized, a red-shift of abo ut20 nm results from the greater resonance induced by thepush-pull effect of th e amide-im ide com binatio n. Imi-dization a t both sides of diamic acids destroys this effectand greatly reduces the electron density near the azo


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Macromolecules, Vol. 22, No. 3, 1989 Imidiza t ion of a Polyamic Acid 1177T a b l e IA bsorpt ion Ma x ima , Spe c t ra l Sh i f t s , a nd E x t inc t ionCoeff ic ients of Various Imidiza t ion Pr odu cts ofDiaminoazobenzene (DAA)

A AA,O 6 X lo ',cnmnniind nm nm L/mol.cmr_...H,NPhN=NPhNH,DAA

OCHNPhN=NPhNHCO

a C O O H noocdiamic acid

OCHNPhN=NP( co

amic acid-imide

diimide

~415393

413

343

417

0-22

+20

-68

+4

4.53.9

2.0

3.0

3.1

amine-imideThis is the successive spectral shift. For diimide and amine-imide, the spectral shift is measured from amic acid-imide, as il-lustrated in the sequence of reactions in Scheme 11.linkage. Thus, a la rge blue shift is observed fo r the d i imidederivative of DAA. For amine-imide, which can be a hy-d ro ly s i s product from a mic a c id - imide , the a b s o r p t i o nm a x i m u m appears at 417 nm, due to the push-pull effect.Since the amine is more d o n a t i n g than the amide, theabsorptionmaximum occursat a slightly longer wavelengththan that of the amide- imide species. Table I summarizesthe absorption maxima, spectral shifts, and extinctionc oe f f i c i e n t s of various DAA de r iva t ive s e xpe c t e d from theimidization process. Scheme IV shows the reaction routesused for t he s y n t h e s e s of various model reacted specie^.^Experimental Section

Materials. Diaminoazobenzene (DAA) was purcha sed fromEas tma n Kodak and recrystallized from methanol. Electronicgrade d ianhydride , 6F-DA, 5,5'-[2,2,2-trifluoro-l-(trifluoro-methy1)ethylidenelbis(l,3-isobenzofurandione), as a gift withAmerican H oechst and used without fu rthe r purification. N -methylpyrrolidone ( NM P) was purchased from A ldrich, dried overmolecular sieve type 4A, an d distilled twice at reduced pressures.Freshly disti l led NM P was used for imidization studies.Imi diza t i on S tudie s. NM P complicates imidiza tion studiesin solid films due to its complex formation w ith polyamic acid'an d its high boiling point, which mak es it difficult to remove; sowe used acetone as the casting solvent. All glassware used forpolyamic acid and polyimide synthe sis was oven dried a t 100 Cfor 1 h. Eq ual moles of DAA (0.0808 g) and 6F -DA (0.1962 g)were each dissolved in 1.5 mL of acetone a nd cooled to 0 C. T h edianhydride solution was slowly added to th e diamine solutionand the well-mixed solution was kept at 0 C for 30 min to m akepolyamic acids. A thin po lyamic acid f i l mwas cast on a large Petridish and vacuum dried for 2 days to remove the acetone. Afterremoving the acetone, we obtained films of polyamic acids whichare about 1mil in thickness. IR sp ectra of these films confirmedthe presence of amic acid struct ure by characteristic absorp tionsa t 3280 (N H), 3100 (OH), 1669 (C=O), 1598 (C=O), and 1537(NH) wavenumbers. Only trace amounts of unreacted anhydridewere detected in the IR spec t ra . T he UV-vis spec t ra in NM Psolution showed the main absorption peak a t 393 nm, corre-sponding to the diamic acid absorption. In addition, significantabsorption a t 415 nm due to th e presence of im ide am ide specieswas also observed. IR spectra confirmed the presence of some

S c h e m e I VRe a c tion Sc he m e fo r t he Syn the s i s of Model ImidizationProd ucts of Diaminoazobenzene

diamic acid

diimide

aminelimide

HOOCamic acidlimide

imide peaks. Therefore, the polyamic acid films we used forimidization studies were not 100 polyamic acid, but ratherpartially imidized or dissociated polyamic acids. Atte mp ts tosynthesize 100% pure polyamic acids were not successful.Th e thermal imidization of these partially imidized or disso-ciated polyamic acid s was followed by th e shifts n the UV-visspectra at various temperature s and concentrations. Sroog andco-workers noted the poor hydrolytic stability of polyimidesderived from conjugated diamines a6 Since our system employsa conjugated diamine, particular care was taken t o facili tate theremoval of water formed during imidization. Th e requirementof cons tant conce ntration com plicates th e removal of water be-cause of possible solvent loss. In order to overcome these prob-lems, the reaction appar atus using a three-necked flask was setup where a Dean S tark tube was used in th e center neck insteadof a condenser so th at water vapor could exit the reaction flaskwithou t loss of solvent. A cons tant flow of dried argon as purgegas was maintained so tha t water vapors were carried out of th ereaction a t a constant rate. Films were dissolved in freshly distilledN M P to the desired concentration and well-stirred solutions were

purged with dried argon before immersion in the preheatedconstant-tem perature bath. Samp les of 5 p L n volume were takenou t of the reaction flask through t he rubb er septum by using amicrosyringe. Sam ples were diluted to a constan t concen tration(1.33 x g/L) in f reshly d ist i lled NM P before spec t ra weretaken.As with solution studies, the reaction conditions in solid filmimidizations are most important. We used a modified, round-botto me d flask with a long, taper ed side arm. Sm all pieces ofth e polyamic acid film were placed into the lower bulb an d thereaction appa ratu s was purged w ith dried argon before beingimmersed in the preheated, constant-temperature bath. Sampleswere taken out with a long spatula at se t t ime in terva ls anddissolved in NM P for spectral analysis. Th e purge gas inlet tubewas extended well into th e oil bath before i t entered th e reactionflask, allowing the gas to be heated before enterin g the reac tion


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1178 Pyun et al.chamber and the water vapor formed during imidization to bepushed out. The flow rate of purge gas was kept constant. Sincethe weights of the film pieces were not always the same, thepolymer concentrationafter dissolving in NMP was not constantfor solid film studies.Spectroscopic Characterization. Infrared spectra wererecorded on a Nicolet 60SX FT-IR spectrophotometer. UV-visspectra were recorded on a Perkin-Elmer Lamda Array spectro-photometer (Model 3840 with a 7600 Data Station).Results and Discussion

Modeling Spectral Changes Based on ImidizationKinetics. Before we qua ntitat ively analyzed UV-visspectral chan ges in terms of imidization kinetics, we carriedout some modeling studies to predict how the kinetic pa-rameters could influence the spectral changes. It is im-porta nt to realize th at we always observed red shifts inepoxy curing as th e DAA label was converted to th e sec-ondary and tertiary amines. However, in imidization, thefirst imide ring closure (PA1 in Sch eme 11) results in amoderate red shift ( - 2 0 nm ) while the second imide ringclosure (PI1 in Scheme 11) is followed by a g reater blue shift-70 nm). In this case, the m agnitude of the ratio of th etwo imidization ra te constants, k , and k2 as defined below,is found to determine th e overall spe ctral changes.From Schem e 11, we can w rite the following three kineticdifferential equations for the two main im idization reac-tions by neglecting othe r competing reactions.

Macromolecules, Vol. 22, No. 3, 1989

ki k2PAA- A1- I1X Y 2- d x /d t = 2kix (1)

(2)d z / d t = k g (3)

-dy /d t = -2klx + k gwhere x , y, and z are the fraction of PAA, PAI, and P II,respectively, and their sum is equal to unity.Equations 2 and 3 can be solved in terms of x assumingtha t r is equal to k 2 / 2 k l as shown in eq 4 an d 5. On the

(4)(5)

basis of eq 4 an d 5, one can calculate y an d z values fora series of x values given the ratio r. Figure 1 llustratesplots of x,y, an d z values for two different r values as afunction of the extent of overall imidization, ti,which isdefined by eq 6.t = Y 2 2 ) / 2 (6)

As expected, Figure 1 shows that the formation of di-imide species ( z ) occurs sooner when k2 is the same as k ,( r = 0.5) as compared to the case when k2 is much smallerthan k , ( r = 0.05).Now, the nex t step is to generate UV-vis absorptionspectra for a wide range of r values by digital additioncorresponding to se ts of x, , and z values from the storedspec tra of each species. Exa mina tion of a series of th espectra thus generated shows that the overall spectralresponse can be divided into two trends depending on themagnitude of r . When R is greater than 0.3 no red shif tis predicted before blue shifts occur, as illustrated in thetop spectrum of Figure 2 for the case of r being equal t o0.5. When r is less than 0.3, some red shift is first pre-dicted, followed by th e blue shifts. However, when r is lessthan 0.001, a maximum red shift of 24 nm , from 345 to 415nm , is predicted as shown in the lower spe ctra of Figure2 for th e ca se of r = 0.0001. This am ount is the maximumpossible value since A of PA1 is at 415 nm. For the r

y = - x / ( l ^ + x r / ( l r )z = 1 + ( r / ( l r ) ) ( x / r x

1.o0.8C0 0.6

0a 0.4

I

* 0.20

Extent of Reaction

\21 ,/I----0 2 0 4 0 6 0 8 1.0

Extent of ReactionFigure 1. Theoretical prediction of the composition of the im-idization species as a function of overall extent of reaction E )according to eq 4-6 for two different reactivity ratios [(a)for r= 0.5; (b) for r = 0.051.values between 0.001 and 0.3, the am ount of the initial redshift predicted initially is smaller than th e maximum. Infact, it is a strong f unction of r as illustrated in Figure 3,varying from zero to 24 nm.Th e trends predicted by this type of modeling are usefulin understanding the actual experimental data, whendissociation can be assumed to occur to a small extent.Imidization Studies in NMP Solution. 1 % Po-lyamic Acid in NMP Solution. The isothermal imidi-zation of polyamic acids in 1 by weight) N M P solutionwas followed by UV-vis spectroscopy a t three tem pera-tures (150, 170, an d 190 C). Samp les were taken ou t ofthe reaction f lask a t various t imes and diluted to a setconcentration before spec tra were taken. Figure 4 showsa series of UV-vis sp ec tra as a function of reaction tim eat 150 C.Figure 4 is distinguished by two stages. At th eearly reaction times (Figure 4a), the absorption peaks arefirst red-shifted to longer wavelengths, due to either th eformation of amic acid/im ide species (PA1 in Schem e 11)an d/o r th e dissociation products (DAA or PAN in Scheme11). At 150 C, it takes only abo ut 40 min for the red sh iftsto be completed. After that, th e spectra is hardly shifteduntil the cure time of abo ut 180 min, bu t there is a decreasein absorbance. During this time interval, the diimideformation is a t best very small as judged by th e smallabsorbance at 343 nm. In th e longer reaction times (Figure4b) , the diimide (PI1species in Scheme 11) is formed asindicated by the growing peak at 343 nm and the de-creasing peak at 413 nm. Th e 170 and 190 C eactionexhibited spectral features very similar to th e 150 C e-action. T he presence of th e isosbestic point in th e secondstage of th e reaction indicates t ha t only two reaction in-termediates, PA1 and PI1 species, are present.T he abs ence of th e isosbestic point in th e first stage ofthe experimental data (Figure 4a) seems to suppo rt tha t


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Macromolecules, Vol. 22, No. 3, 1989I1 r . 0 5

= iOOCc 68% 61%. 55%, 41%

0.6

Imidization of a P olyam ic Acid 1179

r I O 001= 5 . 25 . 50qo

t

wavelength (nm)

\ = 99%. 80%. 6 5 0 0 .5 0 40.6

>---. , , ,1 '..400 500

o l e < ' 1300

wavelength (nm)Figure 2. Theoretically generated UV-vis spectra for differentreactivity ratios as a function of overall extent of reaction [(top)for F = 0.5; (bottom two spec tra) for r = 0.00011,the conversion of polyamic acid/imide (PAI) is not th e onlyreaction in the first stage and th at there are probably somedissociation products being formed by competing sidereactions. Two possible side reactions are shown inScheme 11: th e hydrolysis of PAA to PA N (polyamicacid/amine) and the hydrolysis of PA1 t o PMI (poly-amine/imide). Preliminary FTIR studies confirm tha timidization indeed occurs in 1% NMF' solution of polyamicacids, but no t as fast as UV-vis studies indicate when nodissociation is assume d. However, th e exten t of imidiza-tion by IR measured at 721 cm-' is greater than t he resultsby UV-vis studies when com plete dissociation is assum edin the first stage. Together w ith the appearance of freeamine absorption bands in IR spectra, the IR results, incomparison to UV-vis results, can be interpre ted as sug-gesting some dissociation as well as th e formation of theamic acid/imide species durin g the first stage. Unfortu-

reectlv i ty rat lo, rFigure 3. Extent of the in itial red sh ift predicted as a functionof the reactivity ratio, r .

(a)

pL2M d /;47 R eac tion T ime ( m i dA0 -s .0R -

051020f ?%\\ \ \\\

C

300 350 400 450 500WAVELEYCTH NMO(b)

rsx:l,iaac Reaction Time (minl320,420,600,800,1320,1560,1800,2820

300 . _: 400 4 5 0 500iI \ 'EL E\( ;TH I \M IFigure 4. UV-vis spectra following imidization of polyamic acidbased on 1 DAA and 6F-DA in N M P solution at 150 C (a)for early stages of reaction; (b) for later stages of reaction].nately, it is difficult to q uant ify how m uch dissociationoccurs. There fore, we propose Schem e V as a represent-ative reaction pathway occurring in 1% solution reaction.


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1180 Pyun et al.Scheme VProposed Reaction Pathways for Imidization of 1%Polyamic Acid in NMP Solution

f i r s t s tage :K iPAA - A 1i

P A Nsecond s t a g e .

K2P A 1 - I1

3, 1989

100 -8 -60 -40 -20 -C l

1 0 1 0 0 1 0 0 0 1 0 0 0 0r eac t i on t ime m in )

Figure 5. Experimental composition of imidization species asa function of reaction time at 150 C for 1 polyamic acid inN M P solution. (The maximum deconvolution error is &8 )Now we can attem pt to obtain more quantitative da tato characterize the rate c onstants involved in th e reactionpathways shown in Scheme V. Qua ntitative analyses re-quire the deconvolution of the spectra to obtain t he com-position of th e species. In the second stag e of imidization ,we are justified in assuming only two species, PA1 and PII.Th e first stage and th e intermediate period during whichthe sp ectra only show changes in intensity are more dif-ficult to tre at in a q uantitati ve way. Therefore, we analyzethe first few dat a points in the first stage by assuming thatonly PAA and PA1 are involved and t ha t dissociation oc-curs only to a sm all extent.Figure 5 illustrates an example of the composition of thethree m ain reacted species at 150 C by the deconvolutionof the UV-vis spectra based on the above assumptions.T he PA1 is formed quickly with subseq uent decrease ofPAA. Since there is some dissociation going on during thefirst stage, the concentration of PA 1 represents the max-imum possible value. Between 40 minutes to 180 minutes,we speculate some conversion of PM I to P AI, as deducedfrom the decrease in spectral intensity. Therefore, it isdifficult to e stimate the concentration of PA 1 in this time

period, even though it is certain th at th ere is no significantconcentration of the diimide (PII)species present. After180 min of imidization, the spe ctra can be easily decon-voluted with only two cure species, PA1 and PII. As shownin Figure 5, PI1 is slowly form ed following decrease of PA I.After 2820 min, the PI1 fraction is about 78 while thePA1 fraction is 2 2 %. Thi s corresponds to the overall im-idization exte nt of 89%. Th e maxim um deconvolutionerror in the composition of the reacted species could be=k2 to *7% as shown in Figure 5. A t 170 an d 190 C,the general features of th e reacted composition are exactlythe same as n Figure 5 , except that t he reactions are fasterand reach higher conversion.In order to obtain more quantitative rate constants andr values from th e exp erime ntal da ta , we use the following

Macromolecules, Vol. 22, No.(a)

0 1 0 20

time mln)Figure 6. First-order kinetic plot of In z or In y versus reactiontime for imidization at 150 C of 1 mic acid in NMP solution[ a ) for In x versus time plot; (b) for In y versus time plot].

Table I1Imidization Rate Constants, k t nd k2 nd the ActivationEnergies for Reaction of 1% Polyamic Acid in NMPE , = 11 E , = 182k , , kcal/mol; In 103k2, kcal/mol; InT "C min-' A = 11min-' min-' A = 13 min-' 10%

150 0.145 0.62 4.28170 0.171 1.40 8.19190 0.465 3.80 8.17solutions for the kinetic equations for the proposed reac-tion pathway (Scheme V).

In x = -2k, t + constant 7 )In y = -k,t + constant (8)

where x an d y are the fraction of PAA an d PAI , respec-tively. Equation 7 is an approx imate solution for the initialstage of the im idization reaction where the dissociation isconsidered to be small. Figure 6a and (b ) illustrates theplots of In x or In y as a function of time a t 150 C cure.It is noted in Figure 6a that k1 s based on only four dat apoints while kz s based on many more dat a points. Similaranalyses were carr ied out for the d ata a t 170 C and 190C. Pa rts a an d b of Figure 7 show Arrhenius plots for kland k2 espectively. Table I1 summarizes the values of

kl z , and r as well as the activation energy for each step.As seen from the last column of Table 11,r is less tha n 0.01a t all three imidization tempe ratures, indicating a muchfaster rate of th e first process. Th e activation energy forthe first process is abo ut 11kcal/mol while the analogousenergy for the second imide ring closure is about 18kcal/mol. Th e preexponential factors for the two processesare similar as shown in Table 11. The activation energyvalues observed in this stud y compare favorably with thevalue observed for the initial stage imidization of pyro-mellitic dianhydrid e with aniline in dilute solution (16) aswell as that of imidization of a polyamic acid. A widerange of the preexponential factors had also been reported,


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Macromolecules, Vol. 22, No. 3, 1989 Imid izatio n of a Poly amic Acid 11811 4 100 1 1a

-2 80.0021 0 . 0 0 2 2 0 , 0 0 2 3 0 . 0 0 2 41iT

NXC-

-8 Iu 3 0 2 1 0 0 0 2 2 3 0 0 2 3 0 0 0 2 4T

Figure 7. Arrhenius plot of In k , or In k2versus 1 / T [(a) or Ink ,; (b) for In k z ] .Cure Time b i n );GO 480,210,90,30.10.5,~

H I M B 882300 350 400 450 500W A V E L E X T H ( >I)

Figure 8. UV-vis spectra following imidization of polyamic acidfilm based on DAA and 6F-DA at 150 O C n solid state.depending on the chemical structures and t he state of thesamples.16J7Imidization Studies in Solid State. Th e isothermalimidization of partially imidized, polyamic acid films wasmonitored by UV-visible spectroscopy at three temp era-tures (150,170, and 190 C). It is known tha t the basicityof t he solvent affects the imidization processesk?& nd alsoth a t N M P forms complexes with polyamic acids.' Fu r-thermore, t he decomplexation kinetics is known to be quitetemperature and time dependent. In order to avoid thesepotential com plications, we chose acetone as a solvent and,prior to t he imidization studies, we removed it completely.Figure 8 shows a series of UV-visible spectra as afunction of reaction time at 150 Cwhere blue shifts areobserved. Also, a t other tempe rature s (170 and 190 C),only blue shiftsoccur, but w ith much fas ter rates of change.In view of the m odeling studies to predict spectral changesas described in the preceding section, blue shifts without

Sol ld state react ion at 150C

8-I- -

1 0 1 0 0 1 0 0 0 1 0 0 0 0

reaction time (min)Figure 9. Experim ental composition of imidization species asa function of reaction time at 150 C in the solid state. (Themaximum deconvolution error is f 10% .)the initial red shifts are predicted when r is greater tha n0.3 if we assume the same first-order kinetics. Th is cor-responds to a kl ess than 1.6 times kz whereas in dilutesolution, k1 s observed to be much faster compared to kz.Th is trend was explained due to the electron-withdrawingeffect of th e imid e group para to the amic acid in poly(amicacid-imide). As a result, the reactivity of th e amic acidin polyamic acid is predicted to be larger th an t ha t of th eamic acidfimide. This is believed only to be true in dilutesolutions since the add ition of carboxylic acids is knownto catalyze the imidization.2c In fact, up to a certainconcentration of acids, a linear relationship between therate constants and the acid concentration has been ob-served. When th e concentration of the solution begins toincrease to th e extent th at t he chains of polyamic acidsoverlap, then the amic acid groups in the neighboring chaincan catalyze the im idization intermolecularly. In fact, ourexperiments seem to suppo rt this argument. When westudied imidization in a 7.5 w t % solution, we observeda red shift, followed by a blue shift. However, the mag-nitud e of the red shift was only abo ut 16 nm. Accordingto Figure 3, such a magnitude is predicted when the r valueis about six times greater than that in a dilute (1w t % )solution, meaning tha t the values of kl nd kz ave becomecloser to each other. If th e catalysis of the neighboringamic acids are effective in 7.5% solution, it is likely tochange the values of kl nd kz n such a way that the valueof r is no longer the same as w hen there is only an elec-tronic effect. In solid films, th e catalytic effect may com-pletely overshadow the electronic effect, at least before thefilm is vitrified, thus ieading to an r value greater than 0.3.This possibility would be consistent w ith th e experimen-tally observed trends in the value of r .Th e deconvolution of th e UV-visible spectra with threespecies (PAA, PAI, PII) was carried out to obtain thecompo sition of each spec ies as a function of reaction time.The maximum deconvolution error in the composition ofthe reacted species in the solid film could be *lo % . Figure9 illustrates the results obtained at 150 C. In contrastto F igure 5, which corresponds to th e reacted compositionof solut ion imidiz ation, we observe a much faster increasein the concentration of th e diimide species 2 ) in Figure9, but it levels off a t abou t 53% after 500 min of reaction.Th e concentration of amic acid/ imide decreases while thediimide is increasing, but it also levels off at 20 after only100 min. Th e concentration of diamic acids x ) a t 5-minreaction tim e is 60 but becomes about 20 after 500 minof reaction. In Figure la , corresponding to the k = k2 ase,the experimental data show [AI] decreases much faster


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1182 Pyun et al. Macromolecules, Vol. 22, No. 3 1989

0.0 0 . 2 0 . 4 0.6 0 . 8 1 . 0Extent of React ionFigure 10. Theoretical prediction of the composition of theimidization species as a function of overall extent of reaction ( t )according to eq 9-11 for r = 1.r = 1.0

300 400 5WAVELENGTH nm)

Figure 11. Theo retically generated UV-vis spectra accordingt o eq 9-11 for r = 1.than [AA]. However, with only first-order kinetics thetheoretical plots, even with larger r values, do not quitesimulate curves like th e experimental plot. In addition,predicted s pect ra show much wider band widths in com-parison t o the actual spe ctra show shown Figure 8. Ourfirst approach was to try to take into account the de-creasing catalytic effect as the reaction was occurring.In order to simulate the catalytic effect, we used thefollowing set of kinetic equations:

- d x /d t = -2k1x2 (9)(10)

- d z /d t = - k ~ (11)- d y /d t = -2k1x2 + kD

As a first approximation, we used second order for thefirst step, followed by a first-order reaction for the secondstep to account for the decrease in the concentration ofthe catalytic amic acid group. A reduced mobility due tothe rising glass transition of the m atrix film would alsodecrease the changes for the catalytic group to be in afavorable conformation in the second step. Among severalr values tried, th e predicted value seems to simulate theresults reasonably well when r was approximately 1 Figure10). Th e predicted spectra from these kinetic expressionsan d r values are shown in Figure 11. Th e band widthsbecome narrower than in Figure 2a. However, it is stillbroader than actual experimental spectra, meaning t ha tth e above approach does not exactly simulate the kineticfeatures.For the 170 aIld 190 C solid-state reaction, we do nothave enough d ata points to obtain reliable values of k l and

' RFigure 12. Plot of the extent of reaction ([) by UV-vis analysesversus extent of reaction ([) by IR analysis for the solid-statereaction at 150 O C .k2 before the leveling off since the reaction is much faster.For the 150 C solid-state reaction, we were not able todetermine k 1 an d k2 ccurately because the error in thedeconvolution was sufficiently large as t o render dete r-mination of the r ate constants inaccurate.IR Studies and Comparison with UV-Vis Studies.In order to compare the e xten t of reaction m easured byUV-vis studies with other techniqu es, we carried ou t IRstudies with solid films at 150 C . In IR studies, theabsorption ratio of A721cm-~ue to a n imide ring dividedby an aromatic internal standard peak at 1015 cm-' hasbeen used t o represent a relative imide ring concentration.Th en we needed t o use this value to calculate the overallextent of reaction. In the past, othe r researchers assumedth at imidization would be complete after a certain reactioncondition (e.g., 300 C for 1h) was achieved and calibratedth e extent of reaction based on the absorbance ratio afterthe sample was subjected to that condition. We found thisprocedure to be unsatisfactory because the absorbanceratio would change upon additional reaction time even athigh temperatures. Similar trend s have been found byYoung.lS Th erefore , we used d at a from one of our UV-visstudies to calibrate the ex tent of reaction for IR data . Forexample, the UV-vis dat a after 1410 min at 150 C is quiteeasy to deconvolute. Its exten t of reaction, (ti)wyiSs 66 .We assume tha t value to be equal to under the samereaction condition an d scale the IR absorbance ratios ac-cordingly. Figure 12 shows the plot of the ex ten t of overallreaction, ([Jw- as meas ured by UV-vis studie s accordingto eq 6 versus the ex tent of overall reaction (tilIReasuredby IR studies. Within experimental errors, the d ata pointsin general indicate that the two values are similar,as shownby the closeness of the data points to the straight linewhich corresponds to the ( )uv-vis = ( )IR case.Summary

Th e objective of this paper is to characterize t he kineticparameters and th e mechanisms of the imidization processoccurring both in solution and in the solid state. Beforeelaborating on the main tool used in thi s study , namely,UV-vis spec trosc opy, we reviewe d th e chem istry of poly-imides and t he results of imidization s tudie s by otherspectroscopic techniques in order to illustrate th e problemsassociated with the imidization process and its charac-terization . In this review, we propose a reaction schem e(Scheme 11) for the polyimide synthesis showing variouscompeting reactions and a two-step im idization process as


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Macromolecules, Vol.22 No. 3 1989being representative of cases involving conjugated di-amines. We also show that previously used techniquessuch as IR and N MR failed to differentiate between severalimidization species proposed in S cheme 11.In order to accomplish such a differentiation, UV-visspectroscopy was chosen since various cure species showsensitive changes in the spectral shifts and extinctioncoefficients, due t o th e electronic effects of differen t sub-stituents. For the polyimide system to be used, a conju-gated diamine @ , p -diaminoazobenzene) and a nonconju-gated dianhydride were chosen to reduce the charge-transfer complex whose intense color could interefere withthe UV-vis spectra.First m odeling studies were carried out to predict howthe kinetic parameters could influence the spectralchanges, assuming two main imidization reactions andneglecting other competing reactions. Th is is necessarybecause th e first imide ring closure results in a red shiftwhile the second im ide ring closure results in a blue shift.Therefore, t he overall spectral changes are expected t o bea function of the ratio of the two imidization rate con-stants. Th e main result of the modeling studies is th at twotrends are observed depending on the magnitude of thereactivity ratio r ) . When r is greater tha n 0.3, only a blueshifts is predicted. When r is less than 0.3, a red s hift isinitially predicted followed by a blue shift. However, whenr is less than 0.001, a maximum red shift of 24 nm ispredicted p rior to a blue shift.During th e early stages of im idization in dilute solution,IR analysis suggests some dissociation of polyamic acid aswell as midization. In 1% N-methylpyrrolidone solution,the dissociation an d th e first imide ring closure proceedfaster than the second imide ring closure of polyamicacid/imide a t all three temperatures studied (150,170, and190 C). Th is trend is attr ibu ted to the reduced basicityof the amide group in polyamic acidlimide in comparisonto the analogous group in polyamic acid. Activation en-ergies for the first process an d t he second ring closure wereobtained to be 11 and 18 kcal/mol, respectively. Basedon these findings, a mechanism of imidization for dilutesolution has been proposed. Th is two-step imidization isalso expected to occur in dilute solution with other con-juga ted diamin es. In fact, we observed similar behaviorwhen 1,5-naphthylenediamine is used for 6F-DA.I9 In a7.5 wt % solution of NMP, the two rates are not as farapa rt as in a 1% solution , because of th e combination ofthe electronic and catalytic effects of th e neighboring amicacid groups. In solid-state imidization, the app arent im-idization rate was initially faster tha n in dilute solutiondue to t he catalytic effect but levels off probably d ue tovitrification. Modeling studies to predict spectral changesas a function of the ratio of the two imidization rat e con-stants are consistent with the observed results in dilutesolution. Th e results are adequately modeled by assuminga first-order, two-step imidization reaction. On the otherhand , solid film results seem to be reasonably simu latedby assuming a second-order reaction for the first step,

Imidization of a Polyam ic Acid 1183followed by a first-order reaction for the second step inorder to account for the decrease in th e concentration ofthe conformationally favorable catalytic am ic acid group.Finally, there is a good correlation between UV-vis resultsand IR results in regards to the overall exten t of reactionin solid film.

Acknowledgment. We acknowledge the financialsup port of this work by the National Science Foun dation,Materials Processing Initiative (Gran t DM R 8703908), andth e Army Research Office (Contract DAA 29-85-K-0055).E.P. is grateful for the Connecticut High TechnologyFellowship support. Preliminary FTI R studies were car-ried out by P. Dickinson. We also extend our gratitudeto Drs. T. St. Clair and P. Young of NASA Langley forhelpful discussions on the idd iza tio n processes and to Dr.Pa ul Frayer of Dartco an d Dr. Claudius Feger of IBM fortheir careful reading and constructive criticism of themanuscript.

RegistryNo. (DAA)(GF-DA) (copolymer), 108057-57-4; PAA,117827-87-9.References and Notes

(a) Mittal, K. L. Polyimides Syntheses Characterization andApplications: Plenum: Ne w York, 1984; Vols. I and 11. (b)Bessonov, M. I.; Koton, M. M.; Kudryavtsev, V . V.; Laius, L.A.; translated by Wright, W. W. Polyimides Thermally StablePolymers; Consultants Bureau; New York, 1987.(a) Kreuz, J. A.; Endrey, A. L.; Gay, F. P.; Sroog, C. E. J .Polym. Sci. Part A-1 1966,2607 . (b) Lavrov,S. V.; Kardash,I. E.; Pravednikov, A. N. Polym. Sei. U.S.S.R. 1977,19,2727.(c) Lavrov, S. V.; Ardashnikov, A. Y.; Kardash, I. E.; Praved-nikov, A. N . Polym. Sci. U.S.S.R. 977, 19, 1212.Mathisen, R. J.; Yoo, J. K.; Sung, C. S. P . Macromolecules1987,20 , 1414.(a) Koto n, M. M.; Kudriavtsev, V. V.; Svetlichny, V. M., ref.la , Vol. 1, p 171. (b) Kaas, R. L.J.Polym. Sci. Polym. Chem.Ed. 1981, 19, 2255.(a) Kardash, I. E.; Ardashnikov, A. Y.; Yukushin, F . S.;Pra-vednikov, A. N. Polym. Sci. U.S.S.R. 1975, A17 598. (b) Gay,F. P .; Berr, C. E. J . Polym. Sei. Part A-1 1968, 6 1935.Sroog, C. E.; Endrey, A. L .; Abramo, S. V.; Berr, C. E.; Ed-wards, W. M .; Olivier, K. L. J . Polym. Sci., A1 1965 ,3, 1373.Brekner, M. J.; Feger, C. J.Polym. Sci. Polym. Chem. Ed.1987.25 . 2479.Ginsburg, R.; Susko, J. R., ref l a , Vol. 1, p 237.Palmese,G. R.: Gillham.J. K. ACS PMSE Proc. 1986.55,390..Baise, A. I. J . Appl . Polym. Sei. 1986, 32, 4043.Laius, L. A.; Tsapovetsky, M. I., ref la , Vol. 1, p 295.Weber, W. D.; Murphy, P. D. ACS PMSE Proc. 1987,57,341.(a) Dine-Hart, R. A,; Wright, W. W. Makromol. Chem. 1971,143 189. (b) Gordina, T. A.; Kotov, B. V .; Kolnivov,0 .V.;Pravednikow, A. N. Vysokomol. Soed. 1973, B15 378.Kotov , B. V.; Gordina, T. A.; Voischchev, V . S.; Kolninov, 0.V.; Pravednikow, A. N . Vysokomol. Soed. 1977, A19 614.Sung, C. S.P.;Pyun, E.; Sun, H.-L. Macromolecules 1986,19,2922.Bublik, L. S.;Motseev, V. D.; Chernova, A. G.; Pilyaeva, V. P.;Nekrasova, L. P. Plast. Massy 1974, No. 3 10.Kamzolkina, E. V.; Necha ev, P . P.; Markin, V. S.;Vygodskii,Y. S.; Grigoreva, T. V.; Zaikov, G. E . Dokl. Akad. Nauk SSSR1974,219, 650.Young, P. Private communications, 1987.Dickinson, P.; Sung, C. S. P . ACS Polym. Prepr. 1988, 29-1,530.

kinetics and mechanisms for thermal imidization

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