crystallization and melting process in vulcanized rubbers

8/22/2019 Crystallization and Melting Process in Vulcanized Rubbers

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Crystallization and Melting Processes in Vulcanized Stretched Natural

Rubber

S. Trabelsi, P.-A. Albouy, and J . Rault*

Laborat oi r e de P hysi que des Sol i des, U M R 8502, Uni versi t e de P ari s-S ud,B at . 510, 91405 Orsay, Fr ance

Received April 15, 2003

ABS TRACT: We ha ve studied, by simulta neous force and WAXS m easurements, crysta llization a ndmelting properties of stretched natural poly ci s-isop r ene , vu lcanize d a t d i ffer e nt r a t e s , in s t a t ic anddynamic deformations. The overall effects of increasing NC , the number of monomers between cross-linkbridges, is to slow the kinetics of crystallization and to decrease the melting temperature, crystallitessizes, crystallinity, and mechanical hysteresis. The origin of these properties is discussed. The morphologiesof v u lca n i z ed r u bb er s d u r in g s t a t i c a n d d y n a m ic d ef or m a t i on s a r e v er y s im i la r . Th e p r oce ss ofcrystallization (and melting) occurs during these tw o types of deformation by nucleat ion (and disappear-an ce) of crysta llites with consta nt sizes. The role of the a ffine deforma tion of th e cross-link netw ork onthe crystallites dimension is pointed out. During cyclic deformations, real t ime measurements duringst r e t ching a nd r e cove r y p e r mit one t o c onc lu d e t ha t me chanic al hy st e r esis is d u e only t o t he c hainscr y st a l l izat ion or mor e e xac t ly t o t he su p er cooling (d iffer e nce b et we e n me lt ing and cr y st a l l izat iontemperatures). During stress ha rdening, the form of the stress-strain curve 2 is explained following

the Flory idea. Each new crystallite formed during stretching is considered as a cross-link. The Florystress-induced crystallization model is discussed. In the Appendix, we describe the new effect calledinverse yielding observed in weakly cross-linked rubbers.

1. Introduction

St ress-induced cryst a llizat ion (SIC ) of polymers h a vebeen studied for more than half a century, by differentt echni ques: X -ray scat t eri ng,1-4 infrared spectros-copy,5,6 birefringence, 6-10 electron microscopy,11-17

dilatometry,18-22 and stress relaxation.18,23-25 In crys-ta llizable elastomers, it is r ecognized tha t this phenom-enon explains th e interesting properties of these ma te-r i a l s s u c h a s t e a r i n g r e s i s t a n c e a n d h i g h s t r e s s a tbreak.26-29 Despite th e great amount of work done onstretched polymers, in pa rt icular on dry vulcanizedrubbers, the morphology of the semicrystal l ine phaseappearing during melting and crystallization processesby changing temperature or deformation, has not beenst udied i n det ai ls . By sm al l-angl e X -ray scat t ering3

(SAXS) a nd tra nsmission electron micoscopy11-15 (TEM),aut hors ha ve described t he supracrysta l line organ iza-tion of th e semicrysta lline st ructure (spherulitic, fibril-lar) but the evolution of crystal l ini ty and crystal l i tesdimensions as a function of temperature, draw rat io,and cross-l inking densi t y has not b een s t udied i ndetai ls.

Over the past 6 decades, numerous theoretical studieshav e b een devot ed t o t he l ow and hi gh elongat i on

behavior of rubberlike networks. Most of th e constit utivemodels,30-33 proposed t o capture the large elongationbehavior, do not t a ke into account th e SIC phenomenonwh ich could appear in isota ctic polymers a bove th e glasstemperature. Only a few authors fol lowing the Florypioneer work ga ve thermodyna mic models of th e stress-induced crysta l lizat ion in polymers netw orks at equi-librium. 34-40 These t heori es predi ct ra t her w el l t heincrea se of melting temperatu re Tm w i t h t he draw rat i oand the stress relaxation during crystal l izat ion; how-e ve r, t h ey f a il i n q u a n t i t a t iv e r eg a r d s . Th es e S I Ctheories a ssume tha t t he system is a t equilibrium (fixed

extension), they a re not supposed to apply to ma teria lsduring stretching and cycl ic deformation at constantstrain rate for example. To our knowledge, there is nocom m on t heory , w hi ch cov ers b ot h t herm al ly , andstra in-induced crysta llizat ion in polymer netw orks, andwh ich predicts t he semicryst a lline morphology a nd th emechanical properties.

In comparison, the semicrystalline state of isotropicpolymers is well documented.41-43 In these materials thedependences of the crystalline lC , and amorphous size

domains la , with the supercooling, annealing tempera-ture, a nd molecular weight distribution a re very w ell-known.44-46

In vulcan ized rubber, the chains a re cross-linked andno individual chain can be defined; one w onders wha tis the physical process which limits the crystallinity andwha t is th e influence of t he cross-l inking densi ty a nddeformation on parameters (lC ,) of th e semicryst a llinest at e i n s t ret ched net w orks, com pared t o i sot ropi cpolymers.

During mechanical cycles, Toki et al . have been thepioneers in investigat ing the varia t ion of crysta l lini tyindex and chain orientation during slow cycle of stretch-ing using wide-angle X-rays scattering47-49 technique.

In their study, the morphology of the crystalline struc-t ure a t a nanoscal e has not b een m easured a nd c om -pared to t hat observed in sta t ic deforma tion.

The aim of this paper is to describe the semicrystal-l ine s t a t e of a cryst a l l iz ab l e elas t om er i n di fferentexperimenta l conditions: at fixed draw ra tio an d duringslow dynamic deformation. Natural rubber (poly(ci s-isoprene)) with three different cross-linking densitieshas b een s t udied b y s i mult aneous m echani cal and(WAXS) measurements.

The pa per is divided a s follow. I n section 2, the r ubbermat erials a nd the t echniques a re described. In section

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3, the morphology of the semicryst alline sta te (cryst a l-l ites sizes, crystal l ite orientat ion, crystal l ini ty) is de-termined during crysta llizat ion an d melting at constan tlength. The influence of cross-links density a nd defor-mation on crystallinity and crystallite sizes is described.Section 4 is devoted to cyclic deformat ion a t low st ra inrat e. Crysta l li te sizes and orientat ion a re compared t othose obtained at equilibrium. The new effect of inverse

yi el d appeari ng i n w eakl y v ulcani z ed rub ber i s de-scribed. The correlation between relaxation stress andcrystallinity is given and the origin of the critical drawrat ios a t w hich th e beginning of crystal l izat ion a nd th eend of melting occur is discussed. Fina lly, in section 5,one explains the effect of cross-linking degree on themechan ical hysteresis of na tura l rubber.

2. Experimental Section

2.1. Material. The materials (supplied by Michelin Co.)ha ve been obta ined by sulfur vulcanizat ion of nat ural rubber.The formulations are given in Table 1, all samples called hereaf t e r I , II , and II I ha ve the sa me concentra tion of ingredients(stearic a cid, zinc oxide, ant ioxidant ) and only the concentra -tions of sulfur a nd a ccelera tor (CBS ) are different. The cross-

link density, s, has been determined by swelling in tolueneand b y You ng mod u lus me asu r eme nt s . The se t wo me t hod sgive very simila r results. NC the nu mber of monomers betw eencross-links is deduced from s whe r e NC ) (F/M0s); M0 ) 68 isthe molecular weight of the monomer, and F ) 0.9 2 g /cm 3 ist he d e nsit y . The samp le s ( le ng t h 30 mm) have t he t y p ic aldumbbell form, the thickness, t ) 1. 5 mm, is c lose t o t heoptimum thickness for diffraction measurements using Cu K Rr ad iat ion.50 The e f fe ct ive d r a w r at io is d e t er mined b yme asu r ing t he d is t anc e b e t we e n ink mar ks on t he samp le sduring deformation.

2.2. Instruments and Procedures. (a) Static Measure-ments. A home mad e ove n wit h X-r ay s t r ansp ar e nt Kap t onwindows, va cuum insulation, and external force measurementis used for isothermal crystallizat ion. This oven is connectedt o t w o t h e r m os t a t e d b a t h s w h i ch p er m i t q u en ch i n g t h e

sam ple from +100 to -30 C in short t imes (typically 40 C/min). The sample in this experimental set up can be extendedu p t o t he d r aw r at io ) 8. This oven is mounted on an X-rayg ene r at or e q u ip pe d w it h homemad e p ar al le l opt ics and aconventional -2 goniometer (conventional generat or, xenon-filled proportional counter) or in front of a pa ra llel beam optics(rotating anode generator, detection by photostimulated imageplates) or by a n indirect illuminat ion CCD cam era (PrincetonInstrum ent). This experimenta l setup enables us t o measuresimulta neously tensile stress a nd WAXS spectra.

(b) Dynamic Measurements. A home mad e s t r e t c hingmachine with symmetric extension is used at room tempera-ture for deformation at strain rate from d/d t ) 0.033 min -1

( ) 1 mm /min ) to 20 min -1. High resolution is n ecessary forreal-t ime measurements of reflection profiles during cyclicd ef or m a t i on ; f or t h i s p ur p os e t h i s d r a w i n g m a c h in e w a s

mounted a t th e stat ion D 43 of the synchrotron LURE , coupledwit h t he a b ove -me nt ione d C C D came r a (se e F ig u r e 1 for ageneral view of the experimenta l setup). The dra win g ma chineis t it led t o obtain t he (002) reflection a s shown in th e figure.For the m easurements of th e Br agg-scat tered intensit ies (i.e.,cr y s t a l li n it y ), t h e s et u p i s m ou n t ed on a r ot a t i n g a n o degenerator, and the detection is performed with a homemadelinear counter. During st retching, the thickness and t hen theabsorption of the sa mple decrease. The measur ements of th eabsorption taken by the photodiode, located along the beamaxis b e hind t he samp le, a r e u se d t o nor malize t he scat t e r ed

intensit ies.(c) Data Corrections and Analysis. Absorption Meas-

urements. I t is known t hat d i ff r ac t ed int e nsit y d e p end s onthe sample thickness t, m at erial absorption coefficient a ndp r imar y b e am int e nsit y I0 b y a f a ct or I0t exp(-t) i f o n eneglects a ny a ngular dependence.51 During the cycle of defor-ma tion, it is necessary to correct t he continuous va riat ions ofthe sample thickness t a nd the incident beam fluctuat ions. Thesignal provided by the photodiode placed behind the sampleis proportional to I0 exp(-t). By measuring the primary beamintensity I0 at r e g u lar t ime int e r vals , i t is t hu s p ossib le t oevaluate simultaneously t an d t he corresponding a bsorptioncorrection, knowing the init ial sample thickness; variat ionsin due to the cha nges of ma ss density during crysta llizationare presently negligible.

Reflection Profiles. The crystal structure is orthorhom-

bi c52 (spa ce group Pbca). The (002) diffraction line origina tesfrom the beam r eflection on lat tice plan es perpendicular to th ec c hain a xis , t his me r id ian r e flec t ion is obse r ve d w he n t hesamp le is t i l t ed a s shown in F ig u r e 1. I t s wid t h is r e la t e d t ot he ave r ag e c r y st a l l i t e d ime nsion l002 , (of t e n c al le d in t heliterature the stem length lC , used to describe the crystallitesize when the chains are folded or extended in the crystallite).The a zimu t hal p r of i le is d ir ec t ly l inke d t o t he c r y st a l l i t eorientation function. The intense (200) and (120) reflectionscorrespond t o lat t ice planes par allel to th e chain direction. I tis well-known t ha t reflections of low indices and high in tensityare associated with denser planes and generally correspondt o nat u r al ly occ ur r ing c r yst a l logr ap hic su r fac es . F or t hisr e ason, in t he fol lowing , t he c r y st a l l i t e s g r owt h fac e s ar esupposed to be parallel to the (100), (120), and (001) planes.

The a morphous ba ckground is removed using the n oncrys-

ta llized sam ple signal a s reference; the instrum enta l resolutionfunction is obtained from line profiles given by a fine qua rtzpowder a nd its contribution to line broadening is subtra cted.From these corrected WAXS spectra, one calculates the meandimensions and orientation of the crystallites.

The peaks integra l is proportional t o the sa mple crysta llin-ity; a precise conversion int o absolute crysta llinity necessitat esl en g t h y a n d ca r e fu l p ro ce du r es t h a t w e r e n ot p r es en t l yemployed.53 I n t his wor k, t he c r y st a l l ini t y is determinedusing t he simplified m ethod of Mitchell.4 From the scatteredintensity of the amorphous phase (halo centered at s ) 13.5

nm -1), in semicrystalline material Ia/(s) a t e ach t e mpe r at u r e

and in completely amorphous material Ia (s) (just above Tm),

one d e d u ce s t he c ry st a l l ini t y ) (Ia - Ia/)/Ia 100. Similar

me t hod s ha ve b e en ap p lie d b y D u mb let on a nd B owles ,54 byL ee e t a l .55 a n d b y Tr a b el s i e t a l .56 for d e t er mining t h e

c ry st a l l ini t y ar ou nd a c rac k t ip in na t u r al r u b be r .In cyclic deformation, th is method can not be used directly;

t he r e for e , one has me asu r e d t he nor malize d int e nsit y I002.Knowing the relation between a nd I002 at e ach t e mp e rat u r ean d dra w ra tio in sta t ic deformat ion (see Figure 3a of ref 56),we determined (%) during stretching an d recovery at roomtemperature. For NC ) 335, 238 , 145 a t 23 C and for ma x )5-6, t he maximu m c r y st a l l ini t ie s ar e , r e sp e c t ive ly , as fol-lows: ma x ) 25, 15, 10%.

The crysta llite sizes lhk l in th e direction norma l to the (h k l)planes are deduced from the Scherrer formula:

Here 1/2 is the reflection angular half-width, t he r ad iat ion

Table 1

natural rubberwith different density

ingr edient sa mple I sample II sample II I

g of n a tu ra l r ubber (TS R 20) 100 100 100g of st ea ric a cid 2 2 2g of zinc oxide 5 5 5g of a nt ioxida nt (6P P D ) 1 1 1g of sulfur 0.8 1.2 2g of a ccelera t or (C B S ) 0.8 1.2 2

Young modulus E (MP a ) 1.084 1.41 2.4swelling s*102 mol/m 3 0.40 0.57 0.94Young modulus 0.41 0.62 0.97no. of monomers between tw o

cross-linked NC ) (F/M0s)monomers

NC ) 335 NC ) 238 NC ) 145

lh kl ) K/(1/2 cos ) (1)

M acromolecul es, Vol. 36, N o. 20, 2003 Vulcanized S tretched Natura l Rubber 7625


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wavelength (0.1542 nm), and the Bra gg angle; K is a constantthat depends on such factors as the crystallite shape or sizedistribution and w hich is usually close to unity.50,57 A value of0.78 was presently chosen in view of simulations of experi-mental profiles based on parallepipedic crystallites and log-normal size distributions.

The crystallite orientation along the draw axis is deducedfrom the a zimutha l profile of the reflection.58,59 Experimentalprofiles are well-adjusted by Gaussian functions and can befully characterized by their half-width at half-height 1/2; thep ar ame t e r cos 2 is used in other publicat ions.36,53

3. Morphology during Static Deformation

3.1. Crystallization.(a) Crystallites Sizes duringCrystallization. Figure 2a shows the varia t ion of thecrystallinity and the tensi le stress as a function ofthe crystallization time. Sample II (NC ) 238) ha s beend r a w n a t ) 3 at 80 C , t hen quenched t o TC ) -25 C, at t his tempera ture the a pplied stress is 0. At shorttimes t < t0, ) 0 and ) 0 is consta nt, t he process ofcrystal l izat ion begins after the incubation t ime t0, forlonger times a nd vary in an opposite manner. Atthe end of the process, the crysta llinity rea ches a va luema x ) 25% a n d t h e s t r e s s a v a l u e m 0/4. Theinflection points of the curves (t) a n d (t) define thesame ha lf t ime t1/2 of crysta lliza tion. Similar curves a reobtained for the others samples (NC ) 145, 335) dra wnbelow < 4. This correla tion betw een the cryst a llinity

and the stress relaxation has been described by Gentfor di fferent kind of rubbers, and the crysta l linity wa smeasured by di latometry.18,22,23

For sample II (-25 C , ) 3, NC ) 238) completecrysta llizat ion occurs in 30 h, a nd t his slow cryst a lliza-tion ena bles us t o measure with accuracy the crystallitessizes during isothermal crystallization process, in par-ticular a t th e beginning, near t he incubat ion time. Suchstudy on highly dra wn sa mples is not possible for > 5as the incubation t ime (an d the h al f t ime t1/2) becomesshort er t ha n t he t i m e necessary t o reac h t he t herm alequilibrium during quenching.

Figure 2b gives t he va lues of t he crysta l sizes a longthe three different directions (200), (120), (002) vs thecrysta llizat ion t ime. The most importa nt featur e, whichshould be remarked, is the fact that all these dimensionsd o n o t v a r y w i t h t i me m ea n w h i le t h e cr y st a l li ni t yincreases up to 25%. One concludes tha t t he crysta llitesdo not thicken and do not rearrange to form lamellaeor other t ype of a rra ngements during crysta llization; theincrease of crystal l ini ty is due to the increase of thenumber of crystal l ites ha ving consta nt sizes.

In vulcanized rubber crystallized at high supercooling(for the sa mple of th e figure, NC ) 238, T ) 50 C , TC) -25 C , Tm ) 25 C , ) 3) the dimension lC ) l002al ong t he draw n di rect i on i s a b out 50 , w hi ch i stypically the stem length of quenched homopolymer PE,P ET, etc, crysta llized a t high supercooling.42,60 In these

Figure1. Experimenta l setup for dynam ic mecha nical a nd WAXS mea surements a t t he Synchrotron source (Lure). The dra wingma chine is t it led by a n a ngle 10 to observe the 002 reflection. The CCD camera is on the left side. A photodiode after the samplemeasures t he absorption of the X-ray beam. In insert , (on the right side), a typical ima ge of the meridian 002 reflection of nat ura lrubber is displayed.

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un-cross-linked polymers it is well-known tha t duringisothermal crystallization the crystallites formed at thebeginning of the process agglomerate laterally to formcrystalline lamella of constant thickness. This processof rearrangement from globular to lamellar structure(small crystallites to large crystalline lamellae) has beenobserved by electron microscopy techniques on poly-olefins see for example the book of Strobl 43 and on non-cross-linked rubbers by Luch and Yeh.15 From the workof these last authors one concludes that the process ofcrystal l izat ion of un-cross-l inked rubber an d otherpolymers (polyolefine, polyamide, polyesther) are notdifferent. The small-angle X-ray scattering (SAXS) ofstretched samples (NC ) 145, 238, and 335) at roomt em perat ure show s no i nt erference peak, and t hi ssuggest s t hat t he m orphol ogy i s i rregul ar i n a l l t hedirections of the sample and that no lamellar periodicitycan be defined in t hese vulca nized sam ples. B y electronmicroscopy, more or less regular periodic lamellar a ndshish-kebab st ructures h a ve been observed only in un -cross-linked r ubber. 15,17 In conclusion th e cross-links invulcanized rubber must be considered as obstacles fort he m ol ecul ar rearrangem ent s w hi ch are necessaryduring a nd/or aft er crysta llizat ion, for tra nsforming the

disorder structur e (the so-called gra nula te st ructure ofSt robl) at t he beginning of the crysta llizat ion into a one-dimensional lamellar structure a fter complete crystal-lization (after annealing).

In F igure 2c the ha lf time of crysta llizat ion t1/2 a t -25C is reported as a function of draw rat io and numberNC of monomers between cross-links. It is found thatlog t1/2 decreases l inearly with draw rat io:

Gent 18,23 found a s im i lar l aw for t w o na t ural rub bers(NR) vulca nized with sulfur, NC ) 110 and 152, drawnbelow ) 3, in butadiene rubber 18a (B R), cross-linkedwith 0.15 and 3% D C P d r a w n a t -15 C, an d in t r a n s -polychloroprene18c (TP C) a t di fferent crystal l izat iontemperatures (in this last material the curves log t1/2()present a certain curvature). The slope Bt for t he NR,BR and TPC samples is constant 1.1 > Bt > 1 and doesnot seem t o vary with tempera ture. This behavior ha snot been discussed in detai l in t he l i terature. H ere wereport similar results but in a somewha t la rge domainof extension, < 4.5. The slope Bt is constant for thet hree v ul c ani z ed rub b ers and i s equal t o t he v al uereported by Gent for the di fferent rubbers. When thenumber of monomers NC between cross-links decreasesfrom 335 to 145 the curve log t1/2 is shifted towa rd highdraw rat i o , b y a fac t or on the order of 1-1.3. Thes a m e s h if t f a ct or w i ll b e r ep or t ed f or t h e m el t in gtemperature, when NC is changed. Final ly one has toremark tha t cross-l inks a re compara ble to the defectsor non-cryst a llizable comonomers (or solvent) along t hechains, which decrease t he melt ing tempera ture of thepolymer and consequently slow-down the kinetics ofcrysta llizat ion (at fixed t emperat ure). The effect of th ecross-link density on th e crysta llite sizes is an a lyzed inthe fol lowing part .

(b) Crystallite Sizes after Complete Crystalliza-

tion. P a r t s a -c of Figure 3 give th e crysta llites dimen-sions a s a funct i on of draw rat i o and num b er NC ofisoprene monomers between cross-links; see Table 1 toknow t he correspondence between NC and t he m ass ofsuphur per 100 g of rubber. The samples (NC ) 145, 238,and 335) have been draw n a t high tempera ture (80 C )and t hen quenched at -25 C. All the measurementsha ve been done at equilibrium at -25 C a fter completecrystallization, that is to say when the WAXS intensityand the relaxation force level off. From this figure oneconcludes that

(a) The dimensions l200 a nd l120 decrease by a factorof 2 when increases from 3-5 and then levels off. Bytransmission electron microscopy, Shimizu 17 observedi n non-v ulcani z ed nat ura l rub ber (under t he sam econdi t ions) a decrease of t he av erage l engt h of t helamellae perpendicular to the str etching direction withincreasing str ain.

(b) The dimension l002 p a r a l le l t o t h e d r a w r a t i oincreases w ith .

(c) All t he dimens ions l200, l120 a nd l002 decrease withthe cross-link density, this effect becomes more impor-tant for l200 a nd l120 when the dra w ra tio increa ses above ) 4.

I n Fi gure 3d t he v ol um e VC ) l200l120l002 which isproportional to the crystallite volume Vcrystal ) VC cosR, is plott ed vs the dra w ra tio. The an gle R between th edirections of the (020) and (120) planes is 70 . From thisf igure, one concl udes t ha t t he m ean v ol um e of t he

Figure 2. C r y st al l izat ion of d r awn N R samp le II (NC ) 238monomers) a t ) 3 a n d TC ) -25 C. (a, b) Variation of the

crystallinity, tensile stress and crystallites dimensions l200, l120,a nd l002. (c)H alf tim e of crysta llization t1/2 of vulcanized naturalrubbers as a function of draw ratio and number of monomers(NC ) 145, 238, and 335) between two cross-links.

log t1/2 ) A t(NC) - Bt; Bt ) 1.1; 1 < < 4 (2)



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crystallites formed at -25 C ( < 5) or during quench-ing ( g 5) is independent of , and decreases when thedensity of cross-links increases. When the number ofmonomers betw een cross-links decreases by a factor of2.3, the volume decreases by a factor of 3. For th e lessvulca nized rubber NC ) 335, a sma ll increase w ith ishowever noted. The effect of cross-links on three sizesis evident ; cross-l inks decreases the mobili ty of t hechains, impedes t he rear ra ngement of the crystal l i tes,

l imits the final extent of crystal l ini ty and crystal l i tessize, and therefore decreases the crystallite volume.

The f irs t quest i on w hi ch shoul d b e asked i s t hefol lowing: Is t he crystal l izat ion st i ll isotherma l in a l lt hese draw n and quenched sa m ples? G or i t z et a l .19

distinguish tw o kinds of cryst a llizat ion: stress-inducedcrystallization a nd temperature-induced crysta llizat ion,corresponding here respectively to nonisothermal andisotherma l crystal l izat ion.

For vulcanized rubber of similar composition (with2.25 g of sulfur) Mitchell and Meier,25 usi ng a hi gh-speed tester instrument at room temperature, foundthat for ) 5-6 crystallization occurs in about 60 ms.In our sa mples (NC ) 145, 238, a nd 335, draw n a bove ) 5), the incubation t ime t

0a n d t h e h a l f t i m e t

1/2of

crystal l izat ion cannot be determined by the WAXSmethod. The first WAXS measurement, 3 min a fterthermal stabi l izat ion, shows that the crystal l ini ty hadattained i ts equil ibrium value. Below ) 4.5, WAXSmeasurement shows tha t crysta llization occurs a fter thethermal equil ibrium. One recal ls here tha t t he therma ldiffusivity of polymers is a bout a ) 10-3 cm 2/s; t her efore,the quenched samples of thickness 1 mm studied herereaches the thermal equilibrium in a time on the orderof te ) e2/a 10 s. The r esults of Mitchell a nd Meier 25

and ours show t hat cryst a l l iz at i on i n t he quenchedsam pl es draw n ab ov e ) 5 is nonisothermal . Theappearance of the plateau above ) 5 in Figure 3a,bseems to correspond to t his chan ge of regime. It w ould

b e i n t er es t in g t o k n ow w h y i n t h is n ew r eg im e ofcrystal l izat ion the sizes l200 a nd l120 level off, whereasthe crystal l ite size l002 is st i l l increasing w ith .

I n F i g u r e 3 d , i t i s i m p o r t a n t t o r e m a r k t h a t t h echange of regimes of crystal l izat ion when increases

does not involve a ny conspicuous change in the crys-tal l i te volume observed at -2 5 C , w h a t e v e r i s t h edegree of cross-links. The new effect reported in thisfigure is to our opinion related to the affine deformationof the cha ins before crysta lliza tion or of the crysta lliteswhen nucleation occurs.

In Figure 4, the data of sample II (NC ) 238) a t -25 C a re fit ted with the affine deforma tion law s for g 3:

The extrapolated crystallite sizes lhk l0 for ) 1 a n d t h e

correlation factors Rhk l of the fits are given in Table 2.One has rema rked that below ) 3 the crysta llite sizes

Figure 3. Crystallites dimensions l200, l120 , a n d l002 (a, b, c) and crysta llites volume VC (d ) as a fu nct ion of d r aw r at io for thethree different cross-linked samples NR (NC ) 145, 238, and 335) crystallized at TC ) -25 C .

Figure 4. Variation of the crystallite sizes l200 , l120 , a n d l002wit h d r a w r a t io of samp le II (NC ) 238) a t -25 C . L ines a r ethe best fits with the affine deformation laws (relation 3a).

l200 ) l2000 , l120 ) l120

0 0.5 , l002 ) l0020 0.5 (3a)



6/16

remain consta nt . The change of beha vior a t t his dra wra tio seems to correspond to the tr a nsition from la mellarto fibrilla r morphologies observed by some a uth ors.14,17,18a

In the isotropic supercooled melt the unperturbeddimension 61 rC of a ci s-polyisoprene chain having NC

monomers is rC ) 0.8 MC 6 N

C (in ), with MC )NCM0, the molecular weight of a m onomer being M0 )64. The volume around a cross-link is then V (4/3)*(rC)3 860NC 1.5 (3) which deforms in a affine manner(V ) c onst ant ) . Fi gures 3 and 4 t el l us t hat , i n t hi sdeformed region, the crysta llites undergo th e sam e typeof deforma tion. The cryst a llites volume VC (Figure 3d)and the calculated values of V verify for 145 e NC e335 the following linear law:

This experimental law and the good correlation factor,R, observed lea d t o the following importa nt conclusion:

The crystall i tes and the mesh of the cross-links havet h e sa m e or d er of si zes a n d t h en d ef or m i n a f fi n e

manner. VC i s con st a n t a n d i s a b ou t t h e v ol u m e p er cross-link.

Obviously this law is not va lid at low an d high valuesof NC . Cryst a lliza tion is limited by the cross-link densityfor high value of NC an d by t he entan glements for lowv al ues of NC as w a s suggest ed i n un-cross-l inkedpolymers. 45

One w onders i f the increase of t he crysta l li te size lC) l002 w i t h i s a c onsequenc e of t he c hange of t hesupercooling a s it w ould be predicted by th e secondar ynucleation theories42,43 or by the model of crystal l i teannealing and thickening appearing during crystalliza-tion.46 In these models without going into detai ls, the

cryst a l li t e s iz e v ari es i nversely w i t h t he degree ofsupercooling, T ) Tm - TC ; the La urizten and Hoffmanl a w , lC 1/T(), is in fact observed only in a smalldomain of crystal l izat ion tempera ture below Tm . Thewidth of this domain where lC is constant depends ont h e n a t u r e of t h e ch a i n s; f or e xa m p le i n b r a n ch edpolyethylene a nd cross-linked cha ins th e var iat ion of lCwith temperature is weaker than in l inear polyethyl-ene.44 I t must be noted a lso tha t , for most polymers,60

lC is found to be constant when the supercooling isgreater tha n 20 C. In nat ura l rubbers Luch and Yeh15

reported very sma ll varia t ions of the t hickness l002 ofthe crystal l ine lamellae with the crystal l izat ion tem-perature, this is confirmed by ours WAXS data dis-cussed hereafter. For > 4, in vulcanized rubbers,crystallization is nonisothermal, therefore one cannotestimate T. For < 4, crysta l lizat ion at TC ) -25 Cis isothermal , th e crysta l li tes sizes l002 ) lC for ) 2an d 4 a re respectively 40 and 60 for NC ) 238 (seeFigure 3c). The corresponding melting tempera tur es a reTm ) 0 C a n d 6 0 C (see Figure 6a). As the crystal-lization temperature is TC ) -25 C, the correspondingsupercooling T ) Tm - TC is respectively 25 and 75 C. Therefore, one concludes th a t lC cannot be derivedfrom the Lauri tzen and Hoffman law lC 1/T().

3.2. Melting of Drawn Samples. (a) Crystallinityand Melting Temperature. Figure 5a gives the crys-ta l linity of sample II (NC ) 238) drawn at ) 6 a s afunction of temperature. The sample has been drawn

ab ov e t he m el t i ng t em perat ure ( 90 C ) t o erase t he

thermal history,34 t hen quenc hed at -2 5 C a n d a n -nealed at tha t t emperatur e to obtain complete crystal-l izat ion. The sample is heated by steps of 5 C up tothe complete melt ing. At each temperature when thetensi le stress sta bi lizes (at the equil ibrium sta te), t heWAXS intensity is recorded and then the crystallinityis determined. From this figure one concludes that themelting process is progressive; between -25 and +90C crystal l ini ty and s t ress vary l inearly with T, ina n opposite ma nner. The melting temperat ure Tm ) 90C is obtained by extra polat ing t he crystal l inity curve(see arrow in Figure 5a). During crystallization at -25 C, the stress a nd therefore the a morphous chains relaxpart ially. During heat ing the stress increases gradua lly,indica ting tha t th e amorphous cha ins become more andmore stretched. Tm must be considered as the meltingtempera ture of the la st crystal l ite in equil ibrium withthe dra wn amorphous chains. At this melt ing temper-at ure t he l ocal draw rat i o of t he a m orphous c hai nsbecomes equal to the macroscopic draw ratio. Between-25 C and Tm, the crystallites are still in equilibriumwith the stretched amorphous chains but t he local andmacroscopic draw ratios are different. In Figure 5b,c itis shown that during progressive melting the morphol-ogy (crystallite sizes and orientation) does not changeconspicuously. This beha vior is very a na logous to w ha tis observed during crystal l izat ion (see Figure 2a,b).From Figures 2 and 5, one concludes that melting andcrysta llizat ion proceed by format ion a nd disa ppea ra nce

Table 2

lhk l0 () l200

0) 335 l120

0) 112 l002

0) 20

Rhk l R200 ) 0.92 R120 ) 0.94 R002 ) 0.96

Figure5. Melting process for the dra wn sam ple II (NC ) 238monomers) at f ixed draw rat io ) 6, crysta llized a t TC ) -25C . C r y st a l l ini t y and t he t e nsile s t r e ss (a), crystallitesdimensions l200, l120 a nd l002 (b), and orientation 1/2 alongstr etching dir ection 001 (c). Hea ting ra te is 0.5 C/min.

VC 0.25 * V, R ) 0.999 (3b)



7/16

of cryst allites of consta nt dimensions. These results a refound for all the samples I , II , a n d II I (NC ) 145, 238,and 335) whatever is the draw rat io.

In Figure 6a t he melt ing curves (T) of the samplesII (NC ) 238) drawn at different ratios (1 < < 7) ar egiven. (T) can be approximated by the linear relation:

At T0 ) -25 C the maximum crystal l ini ty ma x is onth e order of 25% and does not va ry much with the dra wra tio, while below T0 ) -25 C, th e crystallinity is foundt o b e c o n s t a n t . I t i s i m p o r t a n t t o r e m a r k t h a t t h emelting behavior is the same for isothermally ( < 4.5)an d non isotherma lly ( > 4.5) crystallized samples, butt he m el t i ng t em perat ure Tm of t he l as t cryst a l l it esincreases w ith (see ar rows in F igure 6a). Ta ylor et a l.10

found t he sa me effect in polybuta diene; the cryst allinitya t -35 C varies from 20 to 26% w hen t he draw rat i oincreases from 2.2 to 7.7. Eq uat ion 4 a pplies also forthe other samples, where the maximum crystal l ini ty

ma x is function of NC .In Figure 6b, one compares t he melting curves of the

three vulcanized sa mples draw n a t ) 5. As expected,the crystal l inity a nd t he melt ing temperatures of thesematerials, crystal l ized in the same condit ions at -25 C , dec rease w i t h t he c ross- l i nk densi t y ( 1/NC).Alexa nder et a l .2 an d Ta ylor et a l .10 using, respectively,X-ra y scat tering a nd birefringence found simila r linearlaw for draw n polybuta diene. From this figure one findst hat t he m a xim um c ryst a l li nit y ma x obtained at -25 C a s a f un ct ion of NC , i s g i v en b y t he fol low i ngempirical law:

At higher tempera ture one finds similar relat ions, theslope d/dNC being a consta nt .

From Figure 6a,b one concludes that /ma x vs T/Tmis a master curve, independent of a nd NC .

I t would be interesting t o verify i f t hese relat ions 4a nd 5 a pplies for higher va lues of NC when NC is aboutthe number of monomers between entanglements (inparticular in un-cross-linked rubbers).

In F igure 6c the melt ing temperatur e Tm is reportedas a func t i on of a nd NC . The melt ing temperaturededuced from the (T) curves increases l inearly withd r a w r a t i o, t h is i s a w e ll -k n ow n r es u lt .18,20,22,23 I ngenera l , the melt ing tempera ture, found in the l i tera-t ure, i s deduced from t he s t ress curv es22 or f romdilatometry.19,21 The role of t he c ross-l ink densi t yreported here is new; Tm can be put in the linear form.

The consta nt Tm0 (NC) obtained by extrapolation ( ) 1)

decreases with NC and does not coi nci de w i t h t hemelting t emperat ure of t he isotropic NR. The slope BT) dT

m/d 32 C varies weakly with N

Cand is about

the value found by G ent et a l . (BT ) 48 C , see fig. 5 ofref.22), in the domain of deformation, > 2.5, for naturalan d syn thetic rubbers cross-linked w ith 1% DCP . Theseauthors observed that Tm is constant (-5 C) for 3

(6)

) ma x

(Tm - T

Tm - T0),T0 ) -25 C ; ma x ) 0.25 (4)

ma x (%) ) -4.8 + 0.13 NC ; 335 g NC g 145 (5)



8/16

factor on the order of 1-1.1. For the same samples(NC ) 145, 238, and 335), the curve log t1/2(), givingthe hal f t ime of crystal l izat ion vs , is shi fted by thesam e a m ount , 1-1.1 (Figure 2c). One concludesthat the dependences of log t1/2() and Tm() w it h dra w rat i o (and w i t h NC) have th e sa me origin. This can beexpl ai ned s i m pl y b y t he m odel of t herm al ac t i v at edmotions. The chains crysta llize at a ra te wh ich is givenby the Arrhenius law :

I f T is far from Tm an d a pproaches to the Tg value, oneshould w rite the WLF equa tion, but t his will not chan geour discussion. To our knowledge, the experimenta lrelat ionship between the act ivat ion energy E of t hecrysta l li tes growth rat e and t he draw rat io has not beenstudied. I f one assumes tha t E is weakly dependent on, relat ions 6 an d 7a lead to the observed linear relat ionlog t1/2 given in relation 2.

(b) Relationship between Melting Temperatureand Crystallite Size l002. I n Fi gure 6d t he m el t ingtemperature Tm is plotted as a function of the inverseof the crystallite size l002. Tm a nd l002 are m easured a t-25 C respectively fr om Figure 3c a nd 6c. As discussedhereaf t er during heat i ng ( up t o t he m elt i ng) a sm al lincrease of l002 is noted. In the domain 40 < l002 2 o f t h e

experimenta l curve Tm() of sa mple II (NC ) 238) wit hrelation 10a. The correlation factor is R ) 0.991 andthe fi t parameters are as fol lows: Hm ) 2700 J /mola nd NC ) 213 instead of Hm ) 4700 J /mol a nd NC )238. In t his part icular ca se, the second and t hird termsof () in relat ion 10c a re n egligible and relat ion 10abecomes

The above relation predicts that the slope d Tm/d 1/

NC should increases when NC decreases from 335 to145. As sh own by Figure 6c, this is not observed.

Final ly, one has fi t ted t he results of Figure 7a w iththe Flory relation (relation 10b), the fit parameter NCis found to be NC ) 64 which is lower than the valueNC ) 238 ob t ai ned b y sw ell ing m easurem ent s. Aspointed out by Kim and Mandelkern, 20 in most cases ofinterest, in pa rt icular in cases of Figure 7, relat ion 10bl eads t o ) K[1 - /0] w i t h K ) (/6NC)( - 1/2).Aga in the predictions of Flory a re in contr a diction w iththe experimental law, relat ion 9, where K is not de-pendent on draw rat io.

In conclusion, th e Flory model gives accepta ble values

for Hm a nd NC when the variat ions of Tm w i t h a reconsidered. However, this model does not predict theobserved r elationship (relation 9) betw een a nd a ndt he fac t t hat t he c ryst a l l i ni t y a t l ow t em perat ure i sindependent of draw ra t io. Again, h ere we emphasizetha t th is model does not give any informa tion about thev ari a t i ons of t he c ryst a l l i t e s i z es w i t h t em perat ure,dra w ra t io, a nd cross-l ink densi ty.

4. Morphology during Dynamic Deformation

Samples I , II , and II I (NC ) 335, 238, 145) have beendra wn at room temperature (23 C) up to ma x 6 andthen relaxed at the constant strain rate ) 1 m m/mi n.Figure 8 gives the stress and the crystal l ini ty vs a s

explained in (section 2.2.c). Figure 9 gives the corre-sponding cryst allite orientat ion 1/2 and size l002 alongthe stretching direction vs . One di scusses i n t hefollowing the deformation processes occurring duringstretching and recovery.

4.1. Stretching.When the draw ratio increases above ) 3, the stress str a in curve begins to deviat e from thecurve predicted by the rubber elast ici ty theory. 31 I nFigures 8 and 9 crystal l izat ion a ppears at point A, ) 4. In samples I a nd II (N

C) 335, 238), the tensile

stress seems to be constant up to point B , ) 5. Thestress r eleases pa rt ial ly with t ime (about 20%) i f thesample is kept at a f ixed draw between A a nd B . I nthis domain the crystal l ini ty increases l inearly withdra w ra tio. These effects observed in different sa mplesconfirm that the semicrystalline phase in this region isnot in equilibrium. The platea u of the stra in stress curvecan be due to two antagonist effects of similar ampli-tude: the relaxation of the a morphous chains duringcryst a l l iz at i on and t he form at i on of new cryst a l l it eswhich act as new cross-links and then tend to increasethe st ress. This last effect wa s pointed out by Flory34

in his early work in 1947.

Toki et al .47 on similar cross-linked rubbers, found

that crystal l izat ion starts at > 4 an d tha t relaxationoccurs (a decrease of 20% of the stress) if the sampledeforma tion is stopped. However t hey did n ot observedthe plat eau AB described here a nd th ey reported highervalues for . I t is found in our sa mple tha t w hen thesta in rat e increases by a factor of 90, this dra w r at io isshifted to ) 4.5. In our opinion, these tw o effects a redue to the higher stra in rat e used by these aut hors,47,48

) 50 mm/min, in st ead of 1 mm/min in our w ork. Asnoted above the effect of increasing the strain rate increases an d decreases the length of the pla teau AB.In conclusion from our work and others, the cri t icald r a w r a t i o for t he onset of t he c ryst a l l i z at i on i sfunction of strain rate a nd t em perat ure47 and not ofcross-link density.

Above ) 5 stress ha rdening occurs. The str ess canbe put on the qua dra tic form 2 and the crystallinity increa ses linearly with dr aw ra tio up to the ma ximumextension ma x ) 5.5-6.

It is important to remark tha t during stretching, thecrystal l i te orientat ion and the crystal size l002 remainconsta nt (Figure 9a ,b). These da ta should be compar edwith the results obtained in condition of fixed extensionat room t emperature. F igure 10a gives the size l002 oft hese sam pl es (I , II , II I) i n s t a t i c deform at i on, forsamples draw n at 90 C (4 1 (10a )

)0 -

0(6NC )

1/2

[ - ( 12)]-1

-

(10b)

() ) ( 6NC)1/2 -

2

2NC-

1NC

(10c)

1

Tm0

-1

Tm

R

Hm( 6NC)

1/2 11.36

HmNC;

Hm in J /mol (11)



10/16

this region acts as a cross-link. The density of cross-

links is then the sum of the density of sulfur bridges Sand the density of crystallites cryst ) /VC . The crystal-linity varying linearly with as sh own in Figure 8b andVC being constant, the cross-link density is then

Applying t he rubber elast ici ty theory,31 one obtainswhen t he densi ty of crystal l ites becomes grea ter t ha nthe density of sulfur cross-links:

This is th e trend observed in t he str ess-ha rdening r egionBC. In conclusion, stress hardening in vulcanized elas-tomers ca n be explained by the Flory ar gument w ithoutinvoking t he limitat ion of extensibility of the chains, a ndthe curvat ure in the () curve for > 4.5 is due t o theincrease in density of cryst a llites of consta nt morphology(same volume). Obviously the qual i tat ive agreementbetween relation 13 an d the experimenta l dat a does notpreclude that the Langevin elast ici ty theory must beapplied for large local deformation of the chains.

Final ly, one emphasizes the similari ty between theprocess of crystal l izat ion during stretching (

crystallization and melting process in vulcanized rubbers

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