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    See discussions, stats, and author profiles for this publication at:https://www.researchgate.net/publication/229642168

    Production of Controlled-Rheology Polypropylene Resins by Peroxide PromotedDegradation During Extrusion

    Article in Polymer Engineering and Science · February 1988

    Impact Factor : 1.52 · DOI: 10.1002/pen.760280308

    CITATIONS

    109READS

    48

    3 authors , including:

    Costas Tzoganakis

    University of Waterloo

    139 PUBLICATIONS 1,459 CITATIONS

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    John Vlachopoulos

    McMaster University

    156 PUBLICATIONS 2,086 CITATIONS

    SEE PROFILE

    All in-text references underlined in blue are linked to publications on ResearchGate,letting you access and read them immediately.

    Available from: John VlachopoulosRetrieved on: 04 May 2016

    https://www.researchgate.net/profile/Costas_Tzoganakis?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Costas_Tzoganakis?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_4https://www.researchgate.net/profile/John_Vlachopoulos?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_1https://www.researchgate.net/profile/John_Vlachopoulos?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_7https://www.researchgate.net/institution/McMaster_University?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_6https://www.researchgate.net/profile/John_Vlachopoulos?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_5https://www.researchgate.net/profile/John_Vlachopoulos?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_4https://www.researchgate.net/profile/Costas_Tzoganakis?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_7https://www.researchgate.net/institution/University_of_Waterloo?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_6https://www.researchgate.net/profile/Costas_Tzoganakis?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_5https://www.researchgate.net/profile/Costas_Tzoganakis?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_1https://www.researchgate.net/publication/229642168_Production_of_Controlled-Rheology_Polypropylene_Resins_by_Peroxide_Promoted_Degradation_During_Extrusion?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_3https://www.researchgate.net/publication/229642168_Production_of_Controlled-Rheology_Polypropylene_Resins_by_Peroxide_Promoted_Degradation_During_Extrusion?enrichId=rgreq-d4f408be-efc8-464c-8b52-b218ab11a5c0&enrichSource=Y292ZXJQYWdlOzIyOTY0MjE2ODtBUzoyOTY3ODM0OTk1NDY2MzFAMTQ0Nzc3MDEwODk2Mw%3D%3D&el=1_x_2

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    Production of Controlled-Rheology Polypropylene Resins

    by Peroxide Promoted Degradation During Extrusion

    C. TZOGANAKIS, J . VLACHOPOULOS, and A. E. HAMIELEC

    Department of Chemical EngineeringMcMaster University

    Hamilton, Ontario, Canada

    Resu lts of experimen tal an d modeling studies of theperoxide promoted degr ada tion of polypropylene (PP] arepresented. Ex periments were carried out in glass ampoulesand in a plasticating extruder. The initiator, 2.5-dimethyl-2,5-bis(tert-butylperoxy)hexane as used as a radical gen-erator. The extruder used had a 38 mm diameter and 24: 1L/D single-screw. In these experiments, the effect of per-oxide concentration and screw speed on the molecularweight distr ibutio n (MWD) of th e polypropylene re sin wa sstudied. Samples collected from the experimental runswere ana lyzed fo r melt flow index (MFI), low curve, extr u-date swell, and MWD. The measured data are presentedand correlations among various parameters are consid-ered . Generally, it ca n be concluded t ha t controlled-rheol-ogy (CR) resins with lower molecular weight, narrowerMWD, and reduced viscosity and elasticity, can be pro-duced. A kinetic model for t he peroxide initiated degrada-tion of PP is proposed. Simulations based o n thi s modelar e compared with experimental data for the productionof CR resins. The experimental data were obtained fromthree sources: (i) industr y, (ii) litera ture, an d (iii) prese ntexperimental work. The c omparison was done in ter ms ofaver age molecular weig hts of t he res in. Agreement be-tween model predictions an d experimental results is quitesatisfactory suggesting th at t his model should find use incommercial prac tice.

    INTRODUCTIONolypropylene is a typical thermoplastic with

    Pnumber of desirable properties tha t make

    it a versatile material. Commercial PP resins,produced w ith t he conventional polymerizationprocess using Ziegler-Natta catalyst systems,have a weight average molecular weight (a,) nthe range 3 X lo5-7 x lo5. The MWD of theseresins is primarily a function of the catalysttype an d th e polydispersity @,/an) s normallyin t he range of 5 to 20 for heterogeneous and 2to 4 for homogeneous catalys ts (1.2). The broadMWD is generally believed to be due to t he broaddistribut ion of active sit es on th e heterogeneouscatalyst ( 3 , 4). Since th e MWD determine s th e

    flow properties an d the perfo rmance of th e poly-mer melt in processing, resins with differentMWD ar e used in t he gre at variety of e nd-useapp licat ions of PP. MWD is a difficult paramete rto control, especially when heterogeneous Zieg-ler-Natta catalysts a re being used.

    In order to modify t he MWD an d improve th eprocessabil ity of PP, various degradation pro-cesses in the presence of solvents have beendeveloped. However, the se processes a re unsat -isfactory from a technical point of view, as crit-icized by Babba, et al. (5). The peroxide initiat eddegradation is a relatively new flexible post-reactor method used for the production of con-trolled-rheology resins with tailor-made prop-erties (6). These resins have high MFI values,tend to relax more rapidly, and permit morerapid processing. In this method, th e narrowingof the MWD is a resu lt of t he action of thehighly reactive peroxide radicals on the PPchains. The cleavage of the polymer chains is

    primarily accomplished by radicals createdby the decomposition of a suitable peroxide(7-9) and is essentially of random nature.These radicals preferentially abstract the ter-tiary hydrogen atoms of the main chain andcause chain scission.

    170 POLYMER ENGINEERING AND SC IENCE, MID-FEBRUA RY,1988 Vol. 28, NO. 3

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    Production of Control led-Rheology Polypropylene Res ins

    REACTION KINETICS

    Although th e num ber of s tudie s on th e ther-mal and ultrasonic degradation of PP is enor-mous, th e num ber of publications on t he per-oxide initia ted degradation of PP seem to bequite limited. Even in most of th es e stud ies (10-14) he emphasis is on the degradation of PP in

    solutions rathe r th an in the melt.In one of the relevant publications (5) . pro-

    duction of crystalline PP resins by means ofperoxide degradation is described. The degra-dation w as carried out in a 65 mm single-screwextruder in th e temperature range of 210 to230°C using peroxide concentrations in therange of 100 to 2000 ppm. The produced resin sexhibited lower degree of stif fne ss, higher im-pact resistance, an d lower brittleness tempera-ture. Using these CR resin s, films with practi-cally no irregularities and very stron g and easilyspinnable fibers were produced. Hudec, et al.(7) presented a simple relation for the changesof the weight average aw)nd nu mber averageM,) molecular weights and th ey proposed th at

    the efficiency of t he initiator decompositionchanges with th e peroxide concentration .

    A s far as the modeling studie s of degradationreactions is concerned, Simha, et al. (15) pro-posed a free radical mechanism with initiation,propagation, transfer, and termination stepsand they solved the resulting equations for spe-cial cases under the assumption tha t the actualrate constants were independent of chain

    length.Boyd and Lin (16, 17) were the fir st to developa practical method for calculating th e degrada-tion behavior of a polymer of arbitrary initialMWD. They transformed th e rate equations de-scribing the kinetics into a se t of coupled equa-tions describing the ra te of change of t he mo-me nts of the MWD. By introducing approximatecorrelations between the first three and thehigher moments they decoupled th e rate e qua-tions an d solved the resu lting system of differ-ential equations using a Runge-Kutta method.David, et al. 18) summarized the statistical

    theories of chain scission an d crosslinking inthe degradation of polymers an d proposed amodel. Their model predicts th e changes of t heMWD with degradation and they conclude thatM , is ind epe ndent of th e initial MWD whenmain chain scissions only are involved. Veryrecently (19) a kinetic model for the peroxideinitiated degradation of PP was proposed andsome preliminary sim ulations were carried out.The model was ab le to predict satisfacto rily a,and if data obtained from experiments in a nextruder. N o data an d predictions for Hz eregiven. Also recently, a process control conceptfor peroxide-initiated degradation of PP in atwin-screw extruder was presented withoutconsideration of t he reaction modeling (9).

    In the res t of th is section, a plausible reactionmechanism for the free radical degradation ofPP is proposed and a model based on thi s mech-

    anism is developed. The proposed reactionscheme is th e following:

    Initiation:

    2R

    Cha in Scission:

    (21klPn + R + , + P ,_, + R

    Transfer:

    ( 3 )k

    Pn + P; + P: + Pn-sThermal Degradation:

    (4)k3P - ; + P ,_,

    Termination:

    (5)

    kP::

    + P: +P ,

    Based on the above mechanism , the followingmodel was developed for th e ch ange of the con-cent ration of t he various species with time:

    Model Equations:

    = -kd[I]d t

    CC

    ~-d[R l - 2fkd[r] - kl[R ] c ( n - l ) [Pn] ( 7 )d t n=2

    [Pi] - ( n - l)[P,]d t i = n + l

    - C[PPI. C [PY)i=1 J = n + l

    CC

    - -d[P'l 2kl[Ro] I Pi]i=n+lt

    CC m

    - k2 ~p::lc~Pil b I c lPl1) (9)( i=2 i = l j = n + lm CC

    + 2k3 C [Pi] - k4[PO,lC[PP]i=n+ 1 i= 1

    The above equations constitute a system ofdifferential equatio ns of very large dimensions.If the change of th e MWD with time is required,then the above system has to be solved. Forsuch problems it is essential to reduce the di-mension of t he system . This ca n be done not by

    a brute force lumping but by mea ns of consid-eration of t he physical system itself as sug-gested by Ederer, et al. (20). On the other hand,if only th e chan ges of t he average molecularweights are of interest, the moment equationsof t he above system can be solved instead.

    POLYMER ENGINEERING A ND SCIENCE, MID-FEBRUA RY,7988, VOI.28, NO. 3 171

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    C. Tzoganakis. J . Vlachopoulos, and A E . Hamielec

    Let us define the it moment (21 ) of th e poly-mer and the polymer radicals distribution as

    oc

    Qi = C ri[PrI (10)

    y i = 1 r ' [ ~ ; ] ( 1 1 )

    r=2

    oc

    r= 1

    If we now introduce these q uantities into E q s7-9 and take th e moment (up to the second one)equations, we end up with the following sys-tem s of equations:

    Equations 16 and 19 include a higher ordermoment (Q3). n order to solve the moment equa-tions a closure method is needed. The m ethodused is t ha t of Hulburt and Katz (22) accordingto which

    After solving the moment equations, t he aver-age molecular weights of the distribution canbe calculated by the formulae:

    a mogl/Qo (21)MUJ = mo92/91 (22)

    Mz m /g2 (23)EXPERIMENTAL

    Materials

    Polypropylene powder (Shell K Y 6 100): MFI(2.16 kg/230°C) = 2.5 g / l O O min., weight aver-age molecular weight = 330000. The flow curveof the resin for three different temperatures isgiven in F i g . 1.

    Peroxide (Akzo Chemie, Trigonox 101): 2,5-dimethyl-2.5-di-tert-butylperoxy exane (seeTable 1).

    5.0I N S T R O N C A P l L L A R l RHEOnLILR

    4 . 0 [I) 190 c0 210 c

    0 . 0 I . o 2 . 0 3 . 0 4 . 0

    L O G ( SHEAR R A T E 1

    F i g . 1 . Flow curve of initial resin used in experiments,as measured in the Instron 321 1 capillary rheometerusing a d ie wi th L I D = 40 .

    Table 1. Characteristics of Trigonox-101 23) .

    Molecular weightPeroxide contentOxygen contentFormulationAppearanceDensityViscosity (20°C)Melting PointFlash point (COC)Vapor pressure (4OOC)

    0.290 kglmole9211 02technically pureclear liquid870 kg/m36.4 mPa.s3 4 ° C56°C3.42 kPa

    Half-life datatw = 35 x 10-14 exp (14947 / r )t,[=lsT [=] K

    172 POLYMER ENGINEERING AN D SCIENCE, MID-FEBRUARY,1988 Yo/. 28, NO. 3

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    Production o Controlled-Rheology Polypropylene Resins

    Polypropylene was mixed with the peroxideand a master batch 5 percent) was prepared.This batch was used for the preparatio n of PP-peroxide mixtures of different concentrationsin peroxide which were used in the experi-ments.

    Degradation Experiments

    Experiments were carried out in ampoules0.3 m long with a n ID 0.005 m a nd OD 0.007

    m) and in a single-screw extrude r. The ampouleexperiments were don e in the presence and ab-sence of oxygen. Th e ampou les were placed ina n oil bath containing a Dow Corning 20 0 fluidand t he reaction was studied at two temperaturelevels (200 and 230°C) and two peroxide con-centration s (20 0 an d 40 0 ppm) for varying re-action time. T he melt flow index and th e MWDof t he sam ples were measured. In the extruderruns, a Killion 38 mm single-screw extruder

    with a rod die was used. More information onthe specifications of t he ex truder an d th e diecan be found elsewhere (24). Experiments weredone at three different screw speeds (20. 40 .6 0rpm) an d three peroxide concentrations (200,300, 400 ppm). The pressure w as continuouslymonitored at the die and before the breakerplate. For each set of experimen tal cond itionsthe following variables were measured: massflow rate , melt temperature, MFI, viscosity, ex-trud ate swell, an d MWD of th e produced resin.

    MFI and Viscosity MeasurementsThe MFI of th e collected samp les was meas-

    ured in a Monsanto capillary rheometer accord-ing to ASTM D1238-65T. T he flow curv e of t hesamples was measured in an Instron 3 2 1 1 cap-illary rheometer at three different temperatures

    190, 210, 230°C). The die used had an L/D =40. The da ta obtained were corrected accordingto th e Rabinowitch-Mooney equation (25):

    d In k p pTw = 4 j3-t d In rw

    MWD MeasurementsThe MWD of t he produced CR res ins w as

    measured by size exclusion chromatography(SEC) at the researc h laboratories of U S S Chem-icals.

    Extrudate Swell Measurements

    Several methods ca n be used for the ex trudateswell measurement as reviewed by Vlachopou-10s (26). In th e pr esent study two methods wereemployed. In the first one, the extrudate emerg-ing from the extruder wa s quenched in air and

    its diameter was determined by means of amicrometer. Care was tak en to minimize gravi-tational effects. In the second method, a proce-dure similar to tha t used by Utracki, et al 27)was followed. The polymer was extruded froma n Instron 3 21 1 capillary rheom eter into a ther-

    mosta ting silicone oil (see Table 2) contained inPyrex test tub es which were kept in a n oil bath.The temperature was kept constant at 170°C.The extruded strands were allowed to reach ast at e of complete elastic recovery. They werethe n allowed to solidify an d their diameter wasmeasured with a micrometer. Thermal contrac-tion due to the tempera ture difference betweenmelt and oil temperature was accounted forusing the appropriate thermal expansion coef-ficient (28).

    EXPERIMENTAL RESULTS ANDDISCUSSION

    Experiments were first carried out in glassampou les. Peroxide init iated deg radation of PPwas done in sealed ampoules with and withoutoxygen being presen t. A s can be se en from Fig.2, the MFI of t he resin in creases with time an d

    it ten ds to level off afte r a certain reaction time.Th is fina l value of th e MFI depends on thetemperature an d it seems (compare Figs. 2 and3) to increase with it. When the reaction iscarried out in the presence of oxygen th e MFI ofthe resin changes dramatically as is shown inFig. 4. This change is obviously due to a n in-creased reaction rate which is probably causedby the formatio n of highly reactive peroxy rad-icals resulting from the reaction between oxy-gen and primary peroxide radicals. Althoughoxygen incr ease s very much the MFI of theproduct its interference with the reaction m ustbe eliminated because it affects unfavorably t hecolor of th e product. In Figs. 5 and 6 the awand a f the samples from the ampoule exper-

    Table 2. Experimental Conditions in Ext rudate SwellMeasurements.

    Capillary:

    Thermostating liquid temperature 17OOCSilicone oil; Dow Corning 200 Fluid

    L = 0.0510 mD = 0.0013 rn

    Viscosity at 25OC 0.0046 Pa.sDensity at 25OC 920 kg/m3Flash point 135OC

    8.0 I 1

    I0 5. 10. 15. 20 .

    TIME , rnin )Fig. 2 . Change of melt index wi th time in ampoule exper-iments at a temperature of 200 C, using 200 and 400 ppmperoxide. (Reaction under vacuum.)

    POLYMER ENGINEERING AND SCIENC E, MID-FEBRUA RY,1988, Vol. 28 NO. 3 173

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    C . Tzoganakis, J . Vlachopoulos, and A . E . Hamielec

    C.E

    6.0=.0

    - 4.0XP

    I5

    2.0

    Wx T = 230 C

    a 400 p p mrn 2 0 0 p p m

    0.0 I I0. 5. 10. 15. 2 0

    TIME , min )

    F i g . 3 . Change of melt index wit h time in ampoule exper-iments at a temperature of 23 O T using 200 and 400 ppmperoxide. (Reaction under vacuum. )

    30.05.0 ~

    T 0.0E- 15.0=.- 10.0GI

    5.0

    0

    0.0 I0. 5 10. 15. 2 0 . 2 5 .

    Time (mln)

    F i g . 4. Change o melt index wi th time in ampoule exper-iments at a temperature o 200°C, using 200 and 400 p p mperoxide. (Reaction in the p resence of oxygen.)

    4.0 I3.6

    3.2

    : 2.8-

    2.4

    A q A

    2 . 0 L0. 5. 10. 15.

    M E LT INDEX , ( gr / lOmin )

    F i g . 5. Correlation bet wee n melt index and weight ave r-age molecular weight (A ampoule experiments , 0 extruderruns , U S SChemicals).)

    iments are presented along with th e experimen-tal data provided by USS Chemicals. The solidline represen ts a non-linear regression f i t to theU S S Chemicals data and it seems that our re-sults a re in good agreement with it.

    In extruder ru ns carried out without peroxide,no changes of t he MWD due to therm al or me-chanical degradation were observed. Some ofthe data obtained from o ur laboratory extruderrun s are summarized in Table 3. One can seethat for a given screw speed while the mass

    1.3

    1.1

    : 0.9z 0.7

    I Ir4

    0.5

    L o\

    I

    0. 5. 10. 15.

    MELT INDEX , gr/lOrnin )Fig. 6 Correlation betw een melt index and z-aver agemolecular weight 0 mpoule experiments, 0 extruderruns (USS Chemicals).)

    flow rate increases almost linearly (Fig. 7) , hepressure at the die and the extrudate swell de-

    crease with increasing peroxide concentration(Figs. 8 and 9 ) . The extruda te swell values re-ported in Fig. 9 were obtained by measuring theextrudate diameter after the extrud ate from theextruder die was cooled down and solidified inair. Extensive measurements of the extrudateswell of th e samples were carried out in theInstron rheometer and i t was found thatquenching of the extruda tes can introduce largeerrors. In Fig. 10, th e extrudate swell of th estarting PP resin is plotted us. shear stress.From thisfigure i t can be seen that the swellvalues obtained in a n oil bath differ a lot fromthe values obtained from quenched sam ples inagreement with previous swelling behaviorstudies (29). The effects of peroxide concentra-tion and shear stress on extrudate swell areshown in Fig. 1 1 where th e swell of thr ee sam -ples (see Tuble 3) s compared with t he swell ofthe s tartin g resin. Swell decreases with increas-ing peroxide concentration an d th is can be ex-plained very easily in term s of decreasing az(see Table 3 ) . This was expected since due tothe action of peroxide radica ls t he long polymerchains break into smaller ones and as a resultthe melt becomes less viscoelastic. The effectof peroxide concentration can be seen moreclearly in Fig. 12. Next, the extrudate swellvalues obtained in these measurements wereanalysed in ter ms of Tann er' s elastic recoverytheory (30). According to this theory the extru-da te swell may be expressed as

    -D_ -

    If it is assumed (31, 32) that:

    N = AT*2 T 2

    NiG = -

    1 6

    + 0.12 25)

    174 POLYM ER ENGINEERING AND SCIENCE, MID-FEBRUARY,1988, Vol. 28, NO. 3

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    Production of Controlled-Rheology Polypropylene R esi ns

    Table 3. Results from Extruder Runs.

    Peroxide Mass Flow EstimatedConcentration Screw Speed Rate reaction Die Pressure

    (lo- kg/s) time (min) (MPa) M w l M n M w x lo- Mz x lo-ample (PPm) (rpm)InitialPP - - - 7.60 330 1180

    200 20 1.07 3.85 2.14 6.14 226 5302 200 40 1.95 2.1 2.34 5.88 21 51 03 200 60 2.86 1.44 2.69 5.06 21 4 4984 300 20 1.13 3.64 1.72 5.50 191 4365 300 40 2.02 2.03 2 00 5.1 5 197 448

    7 400 20 1.17 3.52 1.48 5.08 178 418 400 40 2.06 1.99 1.72 4.57 180 3989 400 60 2.91 1.41 2.03 4.61 180 407

    6 300 60 2.88 1.43 2.28 4.49 195 444

    9 4.0IU

    ; .0vv

    .0

    wn

    14.0 I I

    -

    -

    -

    wI-

    6.0

    2.0 I0. 100. 200. 300. 400. 500.

    PEROXIDE , p p m )F i g . 7 . Effect of peroxide concentration on the m as sf lo wrate in the extruder or three different screw speeds.

    5 . 0

    'A

    0

    b

    1.0 I I0. 100. 200. 300. 400. 500.

    PEROXIDE , p p m )F i g . 8 . Effect of peroxide concentration on th e melt p res-sure at the die of the extrude r.

    1.8 -_I-1w

    1.6 -wI-

    3lxIX

    d 1.4 -

    I4 1.2 .

    A 20 rpm40 rpm

    1 .o-. 100. 200. 300. 400. 500.PEROXIDE , (ppm)

    Fig . 9. Effect of peroxide concentration on diameter ofthe extrudate as it emerges r om the extruder.

    I

    3.2 --3 2 6 --

    Q

    : .0 -0

    0U

    1.4 -c

    w

    0 . 8 L I0. 50. 100. 150. 200.

    Shear s t r e s s (kPa)

    Fig . 10. Effec t of annealing on th e ext ruda te swell of theinitial PP resin. Temperatures on th e graph represent dietemperatures in the Instron rheometer. Annealing wascarried out at 170°C in an oil b ath.

    3.8 r I

    2.6 1Q I2.0

    .4U

    W

    0 . 8 10. 50. 100. 150. 200.

    Shear s t r e s s kPo)

    Fig . 1 1 . Extrudate swell us . shear stress fo r the initialresin and some samples obtained ro m the extruder runs.Die temperature on the Instron w as 190°C. Annealingwas carried out at 170°C in an oil bath.

    Equation 25 may be trans formed to th e follow-ing equation for the prediction of extrudateswell from a circular cross-section die:

    Equution 27 wa s fitted to our dat a using non-

    linear regression and the parameters A and bare listed in Table 4 . This curve-fitting is illus-trated in F i g s . 13- 16. Considerations of thesevalues along with molecular weight data showsthat as the MWD becomes narrower, A de-creases while increases.

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    1.8

    /I 1/V. 2.0-\ 1.6

    5 1.4

    0 1.2

    0

    -t

    2 1.0

    c00

    X

    P> 1.6w

    -Tanner s equat ion

    , , ,:,0.8 0. 25. 50. 75. 100. 125. 150.Shea r stress k P a )

    Fig. 15. Extrudate swell correlation for sample 5 . Sym-bols represent experimental dat a. Line represents Eq 27.

    Sample 7Sample

    8Sample 9I - AI

    0.8 1 8 10. 2 5 . 50. 75. 100. 125. 150.

    F i g . 12. Extrudate swell us shear s t res s or three sam-ple s obtained r om the extruder runs. Die temperature inthe Instron rheometer w as 190°C. Annealing w as carriedout at 170°C in an oil bath.

    S h e a r stress k P o )

    1.8able 4. Values of the Parameters in Eq. 27.

    Material A b 1.6Initial PPSampleSample 2Sample 3Sample 4Sample 5Sample 6Sample 7Sample 8Sample 9

    0.01808

    0.01 0750.02410.16050

    0.061 90.25270

    0.031 9

    0.03866

    0.11280

    0.1 3880

    2.6722.1 a32.498

    1.8832.241

    1.9462.0361.808

    2.1571 .a27

    - Ta n n e r s equat ion

    A - 0 0 6 1 8 9b 2.036

    0

    t:2 1.0

    0.8

    0. 25. 50. 75. 100. 125. 150.S h e a r stress k P a )

    Fig. 16. Extrudate swell correlation for sample 6 . Sym-bols represent experimental dat a. Line represents E q 27.

    3.8

    3.2

    2 2.6P

    -al

    z 2.0

    2 1.4

    D

    0P

    c

    w0 8

    ,

    -- Tonner s e q u a t l o nA - 0.01808

    In Fig. 17 , th e chang e of th e resin flow curvewith peroxide concentration is given. It is ob-vious that increasing the peroxide concentra-tion decreases the melt viscosity at all shearrates . Th e effect of screw speed on t he viscosityis presented in Fig. 18. N o large differences forthe speeds used a re noticed. Finally, the changeof t he MFI with peroxide concentrat ion is shownin Fig. 1 9 and i t can be seen tha t the melt indexincreases linearly with peroxide concentration.

    All the forementioned changes in extrudateswell, viscosity, MFI, and flow rate, reflectchan ges of th e MWD of the PP resin. Dependingon the severity of the processing conditions(screw speed, peroxide concentratio n, an d tem-perature), resin s with narrow MWD can be pro-duced. The effect of the peroxide concen trationon the MWD of th e final product is shown inFigs. 20-21 for two different screw speeds andit can be seen how the high MW tail of thedistribution changes with peroxide content.

    0. 50. 100. 150. 2 0 0

    S h e a r stress k P a )

    Fig . 13. Extrudate swell correlation fo r initial P P. Sym-bols represent experimental dat a. Line represe nts E q 27.

    1 . 8 -

    > 1 .6 -5 1 . 4 -t0 1 . 2 -

    z 1.0 -

    n

    w

    -

    c

    00

    c

    w

    SIMULATION RESULTS

    The system of eq uations, Eq s 12-19, was

    solved for the simulation of some experimentaldata from industry that were available to us33). n Fig. 22, we have a schematic represen-

    tation of the experimental set-up tha t was used.Liquid peroxide was injected in the mixer/pel-letizer system for abou t 10 min and the change

    0 Sample-Tanner s equot icnTanner s equot icn

    0 A - 0 1 6 0 5; I0.8 I

    0 . 2 5 . 5 0 . 75. 100. 125. 150.S h e a r stress k P o )

    F i g . 14. Extrudate swell correlation for sample 4 . Sym-bols represent experimental dat a. Line repr esents E q 27.

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    P r o d u c t i o n of C o n t r o l le d - R h e o l o g y P o l y p r o p y l e n e R e s i n s

    > 7 . 0I-

    v)

    U

    -z 2.0>

    El

    5.0 , 1

    -

    -

    0.0 .o 2.0 3.0 4.0

    LOG ( S H E A R R AT EFig, 17. Variation offrow curve wit h peroxi de concentra-tion at screw speed 40 rpm. Viscosity measured at theInstron rheometer at 21 0°C.

    5 0

    PEROXIDE CONCENTRATION : 3W ppm

    4.0

    \.

    1: 190 T

    .

    1: 190 T

    1.0 I

    0.0 I o 2.0 3.0 4 .O

    LOG ( S H E A RRATE1Fig. 18 Variation offr ow curve w ith screw speed fo rperoxide concentration 300 pprn. Visc osity measured a tthe Instron rheometer at 190°C.

    of the M F I wa s monitored with the process rhe-ometer. The variation of the M F I for a typicalperoxide concentration is given in Fig . 23.

    In these simulations onlythe

    contributionsfrom reactions (1) and (2) were taken into ac-count and the steady state hypothesis for theperoxide radicals w as used. After thes e assu mp-tions were introduced in to E q s 12-19, th e fol-lowing syst em of equa tion s was solved:

    = - k d [ I ]d t

    (291

    1 1- 9 3 + 3 91 - 2Q0

    (31)- - 0Q2d t 8 1 - 90

    25

    0

    15

    10

    X

    4 s.-f

    g o0 100 200 300 400 500

    Peroxide , ppm)Fig. 19. Effect of peroxi de concentration on the melt in-dex of the resin produced.

    l o s o

    .0

    6 . 03bp

    4.0

    2.0

    0 0

    SCREW SPEED - 7.0 rpm1 Initial PP2 7.00 ppm

    2. 3. 4. 5 6 . 7.

    Fig. 20. Effect of peroxide concentration on the M W D ofthe resin (screw speed = 20 rpm).

    LOG ( M )

    where

    0 = 2fkd[l] (32)

    kd = ko exp(-A’/T) 33)

    (34)

    For th e decomposition of th e peroxide (23)

    ko = 1 .98 X 10” S-’

    A ‘ = 14947 K

    In these simulations, the temperature was200°C and the initiator efficiency was variedfrom 0.6 to 1. Model prediction and experimen-tal results a re compared in F i g . 24 and Table 5an d it can be seen th at agreement is good.

    The s ame model was used for the simulation

    of th e results obtained from our experimen ts inthe extruder. An average temperature of 207°Cwas used based on the barrel t emperature pro-file, and the initiator efficiency was 0.6 a s sug-gested by Suwanda, et al (19). The model pre-dictions are given in Table 6 along with the

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    I0.0

    6.03

    K4.0

    2.0

    0.0

    2. 3. 4. 5 . 6. 7.LOG ( M )

    F i g . 21. Effect of peroxide concentration on the M W D ofthe resin (screw speed = 60 rpm).

    P e r o x i d e

    I-+- Drive - - - -IIII

    Polypropylene Process

    Mixer / PelletizerSys tem

    F i g . 22. Schematic representation of the experimentalset-u p used by U S S .

    10

    XW

    znI - l

    10

    t_IWI

    loo 0. 2. 4 . 6. 8 . 10. 12. 1 4 . 16. 18.TI M , ( M I N I

    F i g . 23. Change of M F I with time f o r a peroxide concen-tration of 200 ppm. (Experimental da ta provided by U S SChemicals.)

    0.0

    100. 200. 300. 400. 5 0 0

    P e r o x i d e c o n c e n t r a t i o n (ppm)

    F i g . 24. Comparison between model predictions andexperimental data by USS in terms o molecularweight averages. Symbols represent experimental resultsEnd li nes re pres ent mod-el pre dict ion . (Initial resin :M , = 74400, M , = 35600 , = 1 17600, Efficiency o theinitiator was = 1 . )

    experimental results. It can be seen that thepredictions of th e model ar e quite satisfactoryfor a, and Mu, ut not for az. his can beattributed to th e plug flow assumption an d alsoto experimental errors involved in the measure-ment of th e high molecular weight tail of th eMWD Branching and crosslinking reactionsca n occur under ch ain degradation conditions.Th e presence of long bran ches and crosslinkscan significantly in crease a=. ur initial obser-vations indicate that branches and crosslinksare not pre sent, however th is possibility is beingfurther examined. Finally, the experimentaldata of Suw anda , et al. (19 ) were simulated andthe resu lts are given in Table 7. It can be seenthat the present model gives good predictionsprobably due to the fa ct tha t for small extrudersthe plug flow assumption is not unreasonable.

    The reaction time used in the simu lations wasestimated as follows. For the simulation of theda ta provided by USS a n average residence timewas estimated from Fig. 23 (2.8 min). The av-erage residence time in our extruder runs ( Ta -ble 3 ) was calculated by dividing the channelvolume by the volumetric flow rate at each setof experimenta l conditions. Finally, the reac-tion time used in the simulation of the dataprovided by Suwanda, et al. 19) was the onecalculated from their experimental measure-ment of the residence time distribution in theextruder.

    Simulations of t he d ata obtained in th e am-poule experiments were carried out as well. The

    Table 5. Experimental Results and Model Predictions (Data from USS Chemicals).~~ ~

    ~ ~ v 0 - 3~w*10-3-

    Mn*10-3

    Model Model ModelPeroxide ~ _ _ _ - - ~

    (PPm) Exper. f = 1.0 f = 0.6 Exper. f = 1.0 f = 0.6 Exper. f = 1.0 f = 0.60 74.4 74.4 74.4 356 356 356 1176 1176 1176

    100 69 70 72 274 277 304 790 960 1072200 64 67 70 244 227 265 61 0 643 807300 60 64 66 21 2 170 21 2 565 550 71 7

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    Production of Control led-Rheology Polypropylene Resin s

    model predictions were consisten tly lower th anthe experimental values [e.g. 30 percent lowervalues of Mu). he higher experimental valuescan be explained in term s of nonhomogeneousmelting and reaction in t he ampoules. The poly-mer powder closer to the ampoule wall meltsand reacts faste r than the polymer in the cen-ter. Th e inhomogeneities a re difficult to accountfor and we decided not to pursue a detailedsimulation of t he ampoule experimen ts.

    Although, the plug flow assumption wa s usedin the extruder simulations, back-flow mixingand temperature variation must be accountedfor in more elaborate modeling studies. Such amodel which includes combined considerationof fluid mechanics a nd reaction kinetics in theextruder channel is currently being developed.

    CONCLUDING REMARKS

    The degradation of polypropylene i n the pres-ence of a peroxide radical initiator has beenstudied experimentally in glass ampoules andin a single-screw extruder. In the ampoule ex-periments, it was found t ha t the melt flow indexof the resin increased with reaction time andthat it reached a steady value in approximatelyten minutes. The presence of oxygen increasedsignificantly this final melt index value. In theextruder run s th e effect of peroxide concentra-tion w as found to be the most domina nt variablewith the screw speed influence being less im-portant. The ma ss flow rate through th e extru-

    der increased and t he e xtrudate swell decreasedwith increasing peroxide concentration. Also,th e melt flow index increased linearly with per-oxide concentration a nd t he flow curve of th e

    Table 6. Experimental Results and Mod el Predictio ns(Extruder Runs).

    Screw Per- M n * w M w * ~ o - ~ Mz 10-3~-Speed oxide

    (rpm) (ppm) Exper. Model Exper. Model Exper. Model

    20 200 36.8 42 226 230 530 837300 34.7 41.3 191 206 436 743

    400 35.4 40 178 187 411 668

    40 200 36.2 42.8 211 230.5 510 838300 38.2 41 4 197 206.5 448 744400 39.3 40.5 180 187.5 398 669

    60 200 42.2 42 214 231.5 498 840300 43.6 41.4 195 207 444 745400 39.0 41 180 188 407 671

    resin was shifted to lower viscosities as theconcentration of the peroxide increased. For agiven conce ntration level, increas ing the screwspeed resulted in reduction of t he viscosity ofthe resin but the reduction was rather small.The extru date swell of t he r esin s produced wasextensively studied and the results were ana-lyzed in ter ms of Ta nn er 's theory. Finally, theMWD of t he res ins produced were narrowerth an th at of th e initial resin as it shifted tolower molecular weights.

    A kinetic model for the peroxide initiated deg-radation of PP ha s also been developed and itwas successfully used to sim ulate experimentaldata obtained with an industrial extruder, lit-erature data , and present laboratory data. Thismodel can be used to follow the changes of theMWD during the course of the degradation re-action.

    ACKNOWLEDGMENTSFinancial assistance from the Natural Sci-

    ences and Engineering Research Council ofCanada is gratefully acknowledged. Also, theauthors would like to thank Shell Canada forproviding the polypropylene resin , Akzo Chemiefor providing the peroxide, U S S Chemica ls (nowcalled Aristech Chemical Corporation) for pro-viding commercial degradation d at a, an d Dr. AE. Kostyo for th e MWD measurements .

    NOMENCLATURE

    = Parameter in E q 27.= Activation energy, K .= Parameter in E q 27.= Die diameter, m.= Extrudate diame ter, m.= Efficiency of th e peroxide decomposition.= Elastic modulus.= Peroxide initiator.= Peroxide co ncen tratio n, moles/m'.= Peroxide decomposition rate constant,

    = Collision f actor , s- .= Chain scission rate c onsta nt, m'/mole-s.= Chain trans fer r ate co nsta nt, m3/mole-s.= Thermal degradation rate constant,

    m3/moles-s.= Termination rate cons tant, m3/moles-s.= Die length, m.= Monomer molecular weight, kg/mole.= Number average molecular weight,

    S-' .

    kg/mole.

    Table 7. Simulation Results of Experimental Data Given by Suwanda, et a/. (19).

    Mw* 1 Mz*10-6Peroxide Present

    (PPm) Exper. Model f Present Model Exper. Mod elt Present Model Model

    100 81.5 78.8 79.0 3.87 3.50 3.35 1.180200 73.3 76.2 76.7 2.98 3.1 5 2.88 0.999400 69.8 71.8 72.0 2.66 2.69 2.27 0.763

    t Model by Suwanda, eta/. 19).** Fined to the experimental data.

    POLYMER ENGINEERING A ND SCIENC E, MID-FEBRUA RY,1988, VOI.28, NO. 3 179

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    17

    7 w

    7

    1.

    2.

    3.

    4 .5 .

    6.

    7.

    8 .

    Mw = Weight average molecular weight,

    M z = z-average molecular weight, kg/mole.N1 = First normal str ess difference.Pi = Polymer molecule of chain length iPp = Polymer radical of cha in leng th i.[Pi] Concent ration of polymer molecules with

    [Pp] = Concentration of polymer radicals with

    Q i = ith moment of t he polymer distri butio n,

    Ro = Peroxide radicals.[R“] = Concentration of peroxide radicals,

    t = Time, s.tt)LT = Temperature, K.Y i

    bution, mole/m3.

    Greek letters’? = Shear rate, s-’.

    app = Apparent shea r rate, s-’. It is equal to 32

    kg/mole.

    chai n length i , moles/m3.

    chai n length i moles/m3.

    mole/m3.

    mole/m3.

    = Half-life time of peroxide, s.

    = ith moment of the polymer radical distri-

    x (volumetric flow rate )/(= o3).= Viscosity, Pas.= Shear stress, Pa.= Shear stress a t the wall, Pa.

    REFERENCES

    J . Bloor, Jr .. “Ziegler-Natta cata lysts an d polymeriza-tion,” Academic Pr ess , New York (1979).

    G. Odian, “Principles of Polymerization,” John Wileyand Sons, New York (1981).N. G. Gaylord an d H. F. Mark, “Linear an d Stereoregular Addition Polymers,” Interscience Pub lishe rs, New York [1959). G. Natta, J. Polym . Sci., 34, 21 (1959).K. Babba, T. Shiota, K. Murakami. and K. Ono, Japa -nese patent 7379. 851 (1973), Sumitomo Chem. Co.,C.A., 80 (1974).T. S . Dziemianowicz and W. W. Cox, SPE Annual T ech .Papers. 31, 40 (1985).P. Hudec an d L. Obdrzalek, Agn ew. Makromol . Chem. .89.41 (1980).M. Dorn, Adu. Polyrn. Technol . , 5 , 87 (1985).

    9. H. G. Fritz, “A utomation an d Optimization of a PolymerCompounding Process for the Controlled Peroxide Deg-radatio n of Polypropylene,” 2nd A nnua l Meeting of th ePolymer Processing Society, Montreal, Ca nad a (1 986).

    10. E. Niki, C. Decker, and F. R Mayo. J. Polym. Sci..Polym. Chern. Ed., 11, 2813 (1973).

    11. A. V. Tobolsky, P. M. Norling, N. H. Frick. and H. Yu.J . Am. Chem. SOC. ,86,3 925 (1964).

    12. D. E. Van Sick le, J. Polym. Sci. . A-1 , 10, 355 (1972).13. Y. L. Shanina, V. A. Roginskii. and V. B. Miller. Polym.

    Sci. USSR, 18, 334 (1976).14. J. C. W . Chien and D. S. T. Wang, Macromolecules, 8,

    920 (1 975).15. R. Simha, L. A. Wall, and P. J . Blatz, J. Polym . Sci., 5 ,

    615 (1950).16. R H. Boyd an d T. Lin, J. Chern. Phys., 45, 773 (1966).17. R . H . Boyd and T . Lin, J. Chem. Phys . , 45 ,778 ( 1966).18. C. David and D. Baeyens-Volant, Eur. Polym. J. 14,

    29 (1978).19. D. Suwanda, R Lew, and S . T. Balke, “The Reactive

    Extrusion of Polypropylene,” 36th CSChE Conference,Sarn ia, Canada ( 1986).

    20. H. J . Ederer, A. M. Basedow, and K. H. Eb ert , “Modellingof Polymer Degrad ation Re action s,” in Modelling oC h e m ic a l R e a c ti o n S y s t e m s , Springer series in Chem-ical Ph ysics , Vol. 18, K. H. Ebert, P. Deufhard, and W.Jager. Eds. Heidelberg (1980).

    21. S. Liu and N. R. Amundson, C h e m . E n g. Sci., 17. 797(1962).

    22. H. M. Hulb ur t an dS . Katz, C h e m . Eng. Sci.. 19, 555( 1964).

    23. Akzo Chemie, Noury Initiators, Netherlands, personalcommunication (1985).

    24. E. E. Agur and J . Vlachopoulos, Polym. Eng. Sci., 22.1084 (1 982) nd E. E. Agur, “Numerical Simulation ofa Single-screw Plasticating Extruder,” Dept. of Chem.Eng., McMaster University, Hamilton, Ontario, Canada(1 982).

    25. C. D. Han, “Rheology n Polymer Processing”, Academic Press, New York (1 976).

    26. J . Vlachopoulos, Rev. Deform. Beh. Mat. , 3, 219(1981).27. L. A. Utracki, 2 Bakerdjian, and M. R Kamal, J. Appl .

    Polyrn. Sci.. 19, 81 (1975).28. J . Brandru p and E. H. Immergut, Eds., “Polymer Hand-

    book ,” Inters cience . New York (1966).29. A. P. Metzger and J . D. Matlack, Polym. Eng. Sci.. 8 ,

    l lO(1968) .30. R I. Tanner, J . Polyrn. Sci.. A 2 , , 2067 11970).31. J . L. White, Trans. Soc. Rheol. , 19, 71 (1975).32. D. C. Huangand J . L. White, Polym. Eng. Sci., 19, 09

    (1979).33. J . J . Godfrey, U S S Chemicals, Technical Center, Mon-

    roeville, PA, personal communication (1 985).

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