exess olymer Letters Vol., o. (009) 84 96 Avilble online t www.expresspolymlett.om DOI: 10.144/expresspolymlett.009.1 Theoretil nd experimentl study of foming proess with hin extended reyled ET I. oorullo *, L. Di Mio, S. Montesno, L. Inrnto Deprtment of hemil nd Food Engineering, University of Slerno, vi onte don Melillo, I-84084 Fisino (Slerno), Itly eeived 1 Otober 008; epted in revised form 0 Deember 008 Abstrt. The theoretil nd experimentl study of thermoplsti polymer foming proess is presented. Industril srps of ET were used for the prodution of fomed sheets. The proess ws performed by mking use of hemil blowing gent (BA) in the extrusion proess. Due to the low intrinsi visosity of the reyled ET, hin extender ws lso used in order to inrese the moleulr weight of the polymer mtrix. yromelliti dinhydride (MDA) nd Hydroerol T 54 were hosen s hin extender nd BA, respetively. The retive extrusion nd foming were performed in two step proess. heologil hrteriztion ws rried out on ET smples previously treted with MDA, s well s the morphologil study ws performed to define the ellulr struture of the foms produed. Moreover, in order to predit the morphology of the fom, non isotherml model ws developed by tking into ount both mss trnsfer phenomenon nd visous fores effet. Model results were ompred with experimentl obtined nlyzing the fomed smples. The model ws vlied in reltion to working onditions, hemil blowing gent perentge nd initil rheologil properties of reyled polymer. A pretty good greement between experimentl nd lulted ws hieved. Keywords: proessing tehnologies, modeling nd simultions, reyling, industril pplitions 1. Introdution Sine their origin in the 190s, ellulr plstis or polymeri foms hve reeived wide suess in industril nd onsumer pplitions due to the low mteril osts, high strength-to-weight rtios, wide rnge of properties, nd ese of proessing. Moreover, these mterils re prtiulrly ttrtive sine they n be produed with verge ell sizes rnging from few mirons to hundreds of mirons. For ny given polymer, the use of different blowing gents nd proess onditions n yield new mterils with different densities, strutures, nd properties. Foming onsists of generting tiny gs bubbles in the polymer melt phse in order to produe lightweight mterils without srifiing mehnil nd physil properties of the polymer. Gs bubbles n be generted by mens of physil or hemil blowing gents. The finl fom produts usully possess better insultion properties, s well s higher degrees of impt resistne with respet to the strting mteril, thnks to the presene of the gs bubbles in the polymer melt [1]. There re mny types of polymer foming proesses, suh s fom extrusion, fom injetion molding, ompression molding, nd miro-foming [, ]. The finl fom density depends on the originl gs loding, the gs losses to the environment, nd the fom expnsion t quenhing. The ell size nd the ell size distribution depend on the intensity nd kinetis of nuletion, on the hrteristis of the bubble growth proesses following *orresponding uthor, e-mil: ioorullo@unis.it BME-T nd GTE 84
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 nuletion, nd on the degree of ell wll ollpsing, or ell olesene, during expnsion. Sine the performne of fomed polymer is strongly relted to mny spets of bubble growth, it is ruil to understnd nd ontrol the bubble growth during the melt proessing [1]. In the lst few yers the prodution of poly(ethylene terephthlte) (ET) fomed items, prtiulrly sheets for insulting pplitions, is enountering rising interest. Moreover, by the ontrst to the ommonly used thermoplsti resins, ttention ws d to reyled mterils [4, 5]. In order to inrese the polymer visosity nd to enhne the fombility of reyled ET, vrious tehniques hve been investigted, inluding hin extension by retive extrusion [4 10]. The results obtined with this tehnique re enourging sine it llows to perform in single step the rheologil upgrding of reyled polymer nd foming proess. However, in reent yers the qulity ontrol requirements for plsti fomed produts hve beome inresingly stringent. Therefore, reserhers hve ttempted to optimize the foming proesses in order to produe high qulity finl produts. One of the most used methods for the optimiztion of the mnufturing proess, s well s finl produt qulity is numeril modeling: lrge number of mthemtil models for bubble growth were presented in the literture [11 1]. Some models hve been written for bubble growth ssumed to be governed by mss trnsfer lone, while others ssumed momentum trnsfer lone. Using n integrl method, the ombintion of these phenomen ws presented by some uthors. Extensive reviews nd referenes n be found in monogrph edited by Lee nd mesh []. The gol of this work is twofold: strting from preliminry results obtined in previous work [7], the first gol of this work is to improve the proess of extrusion foming by hemil blowing gent (BA) in order to produe high density foms from ET industril srps with very low visosity; the seond gol of this work is to develop simple nd useful tool whih n help the ompnies in hoosing foming onditions without performing omplited lbortory tests. With this im, ording to literture inditions [11, 14, 16], the growth of spheril bubble in polymeri liquid hs been theoretilly studied by tking into ount both mss trnsfer phenomenon nd visous fores effet. Moreover, with the im of prediting the morphology of the finl fom, non isotherml model ws developed. Model results were ompred with experimentl obtined nlyzing fomed sheets produed in lbortory strting from industril srps of ET nd using hemil blowing gent. The model ws vlied in reltion to working onditions, hemil blowing gent perentge nd initil rheologil properties of reyled polymer.. Experimentl.1. Mterils ET industril srps of low intrinsi visosity, oming from the fibre prodution of ntionl ompny (Montefibre, Itly) were used. The hin extender used in this work is the yromelliti dinhydride (MDA) purhsed by Aldrih. The hemil modifition, in the proportion required for the im of extrusion foming, is hieved with very low ontent of MDA in ET; speifilly three levels of MDA ontents were nlyzed: 0.5, 0.50 nd 0.75 weight% whih proved to be the right ompromise to tilor the required rheologil modifition nd suitble foming proessbility of ET. As fr s the fom prodution is onerned, the hoie ws direted to hemil foming gent bsed proess. In prtiulr Hydroerol T 54, kindly supplied by lrint, ws used s hemil foming gent nd speifilly two levels of Hydroerol ontents were nlyzed: 0.0 nd 0.50 weight%. It ws provided in powder form, nd it is lssified s n endothermi foming gent, reommended for ET foming, bsed on mixture of both orgni nd inorgni foming substnes. The gs yielding during the proess is reported s non toxi, presumbly blend of, O nd O with very low level of wter... etive nd foming proesses The retive proessing of ET with the MDA nd the foming extrusion proess were both performed with Brbender single srew extruder (D 0 mm, L/D 0). The opertion ws omplished in two steps. 85
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 Tble 1. Operting onditions for hemil modifition nd foming proess etive extrusion proess Extruder temperture (hopper, brrel) [ ] 80, 80 Stti mixer temperture [ ] 90 Die temperture [ ] 70 Srew speed [revolution per minute] 040 Fom extrusion proess Extruder temperture (hopper, brrel) [ ] 70, 80 Die temperture [ ] 80 Extrusion die: slit die [mm ] 0 1 Srew speed [revolution per minute] 040 The min opertive onditions for hemil modifition nd foming proess re reported in Tble 1. The reyled ET ws tilored by the hin extension retion with the MDA. The modified polymers were then used for the fom prodution...1. etive proessing The retive proessing of ET with the MDA ws relized by mking use of the mentioned extruder equipped with stti mixer to llow the required residene time for the retion between ET nd MDA. The temperture profile used for the extrusion proess ws the following: extruder temperture ( zones) 80 ; mixer temperture 90 ; die temperture 70. In Tble 1, the working onditions for retive proess re reported. Modified ET ws hrterized in terms of rheologil properties (flow urves, melt strength nd breking strething rtio (BS)), mehnil properties (tensile nd flexurl properties) nd densities. heologil properties heologil behvior of the modified ET ws refully nlyzed in this work beuse this prmeter strongly ffets the fom morphology. The dynmi flow properties of the polymer mtrix produed by the hin extension proess were mesured with heometris Dynmi Spetrometer Mod. DS-II (heometris, In.) using prllel pltes geometry (plte rdius 5 mm; gp mm). Frequeny sweep tests (ω 0.1 100 rd/s were mde t 80 t onstnt strin mplitude (10% strin) under nitrogen gs purge in order to minimize thermo-oxiive degrion phenomen. heologil mesurement in sher flow were performed using llry Extrusion heometer (Bohlin Instruments) with die rdius of 1 mm nd 16:1 length/dimeter, equipped with twin bore for the Bgley orretion. Visosity mesurements were performed t 80 within sher rte rnge of 0 10 000 s 1. As the sher rte t the wll is greter for pseudoplsti thn for ewtonin fluids t given volumetri flow rte, the binowitsh orretions were pplied in ll ses. The llry Extrusion heometer is equipped with tensile module. The mesurements were performed using 1 mm dimeter llry die (L/D 0) with the tensile module situted bout 0 m from the extrusion die. An extrusion temperture of 80 nd wll sher rte of 15 s 1 were used. The tests llowed the determintion of the melt strength nd the breking strething rtio (BS). The smples for testing were dried t 10 in vuum oven for 1 h. Mehnil properties nd densities The tensile properties were nlyzed ording to the stndrd ASTM D-68, the flexurl ones were nlyzed ording to the stndrd ASTM D-790 nd the densities were mesured ording to the stndrd ASTM D-16.... Foming proess The seond step of proessing onsisted in the fom prodution by extruding the modified ET with the hemil blowing gent (BA). Dry blends of treted ET nd BA powder were fed to the previously desribed extruder pprtus, whih ws operted without the stti mixer. In Tble 1 the working onditions for the proesses of polymer foming re reported. Further detils on retive proess nd foming n be found elsewhere [7]. Fom produed ws hrterized in terms of rheologil properties (flow urves, melt strength nd BS), mehnil properties (tensile nd flexurl properties), densities nd finlly in terms of ell size nd ell size distribution by mens of snning eletroni mirosopy. 86
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 ell size nd ell distribution ell size nd ell distribution ws evluted by mens of eletroni snning mirosopy (SEM). In order to evlute ell size nd ell distribution from the SEM mirogrphs, softwre for imge nlysis ws developed nd implemented in Lbview (tionl Instruments). This softwre lotes, ounts, nd mesures objets in retngulr serh re. The softwre uses threshold on the xel intensities to segment the objets from their bkground. Optionl filters give the pbility to ignore the objets smller or lrger thn given sizes. Other options llow rejeting the objets touhing the borders of the serh re nd ignoring the holes tht the segmenttion proess my rete in the objets. The segmented objets re then loted nd mesured. The softwre n lso overly on the imge returned the position of the serh re, the enters nd bounding boxes of the objets deteted.. Experimentl results.1. hrteriztion of modified ET Modified ET ws hrterized in terms of rheologil properties (flow urves, melt strength nd BS), mehnil properties (tensile nd flexurl properties) nd densities. In Tble min experimentl results obtined nlyzing modified ET smples were reported..1.1. heologil properties heologil behvior of the modified ET ws refully nlyzed in this work beuse this prmeter strongly ffets the fom morphology. A signifint inrese in visosity due to the use of MDA s hin extender in ET srps (ET) is evident from the flow urves reported in Figure 1. These smples lso exhibit pronouned sher thinning behvior prtiulrly the blend ET+ MDA 0.75%. Figure 1. Flow urves for unmodified nd modified ET smples (T80 ) Vlues of zero sher visosity, obtined nlyzing rheologil, re reported in Tble for unmodified nd modified ET smples. Moreover, in order to verify if the modified ET possesses melt properties suitble for foming proess, melt strength mesurements were performed nd the results being reported in Tble. As it n be seen in Tble, shrp inrese in melt strength is enountered with inresing MDA ontent. Both the effets, the sher thinning behviour nd melt strength improvement, n be sribed to the struturl hnges ourring during the hin extension proess, i.e. the inrese in M w, the brodening of M w /M n nd brnhing phenomen omplished during the retive extrusion. Atully, too lrge vlues of the MS tend to inhibit the bubble growth during the foming proess. As reported lter, the prmeters so obtined llow in ll ses the prodution of foms, lthough with some differenes. However, the smple treted with 0.50% of MDA ppers s the best omplishment between the two prmeters. Sine the polymer mtrix ws produed by hin extension proess, we onsidered the visosity hnging with the hin extender ontent using polynomil fittings urve to interpolte the experimentl of η 0 vs. %MDA [11] using Eqution (1): Tble. Min properties of the modified ET smples ode %MDA η 0 [ s] Melt strength Density η (T80 ) [10 BS ] [kg/m ] [dl/g] ET 0 0108 not mes. not mes. 1410 0.49 ET_MDA05 0.5 054 0.005 080 1414 0.59 ET_MDA050 0.50 175 0.01 10 145 0.67 ET_MDA075 0.75 55 0.054 09 145 0.77 87
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 η 0 (%MDA) 6577 (%MDA) 74.64 (%MDA) + 160 (1) Visosity is relted to temperture by n Arrhenius expression [] nd its vrition with therml profile is given by Eqution (): η ln η 0T 0T r E g 1 1 T Tr () where E is n tivtion energy for visous flow (94 000 J/mol []), η 0 nd η 0Tr re the zero sher visosity orresponding to T nd T r, respetively. The effetiveness of the foming proess is strongly dependent on the visosity of the polymer mtrix nd, onsequently, on onentrtion of the hin extender. With n mount of MDA lower thn 0.5% no fom n be obtined. Figure. SEM mirogrph ET_MDA050_BA05.. hrteriztion of fom Fom produed ws hrterized in terms of rheologil properties (flow urves, melt strength nd BS), mehnil properties (tensile nd flexurl properties), densities nd finlly in terms of ell size nd ell size distribution by mens of snning eletroni mirosopy. In Tble min experimentl results obtined nlyzing fomed smples were reported. Dt reported in Tble show tht without signifintly srifie the mehnil nd physil properties (see results of tensile modulus nd strength) it is possible to produe lightweight mterils...1. ell size nd ell distribution The fomed strips obtined hve losed-ell struture (see SEM mirogrphs). losed-ell foms re most suitble for therml insultion nd re produed when the ell membrnes re suffiiently strong to withstnd rupture t the mximum fom rise. Figure. SEM mirogrph ET_MDA075_BA0 Figure 4. SEM mirogrph ET_MDA075_BA05 ell size nd ell distribution ws evluted by mens of eletroni snning mirosopy (SEM). SEM mirogrphs of the ross setion re reported in Figures 4 for the smples nlyzed in this work. Tble. Min properties of the fomed smples ode %MDA %BA Density Tensile modulus Tensile strength [kg/m ] [M] [M] ET 0 0 1410 1810 55.1 ET_MDA050_BA05 0.50 0.50 085 140.4 ET_MDA075_BA0 0.75 0.0 1165 165 9.5 ET_MDA075_BA05 0.75 0.50 0900 104.8 88
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 Tble 4. The ell size nd ell distribution for smples nlyzed in this work Smples bubble ell rdius [/mm ] [μm] ET_MDA050_BA05 ~110 44 ± 15 ET_MDA075_BA0 ~0 1 ± 10 ET_MDA075_BA05 ~90 7 ± 15 Bubble dimensions, s evluted by the imge nlysis softwre, re lmost onstnt in the smple, onfirming the ssumption tht temperture is onstnt long thikness diretion. The ell size nd ell distribution, reported in Tble 4, re strongly dependent, during the foming proess, on the onentrtion of the hin extender nd, onsequently, on the high visosity of the polymer mtrix. 4. Modeling 4.1. Bubble growth dynmis (Theoretil bkground) onsider polymer melt tht hs dissolved gs onentrtion 0 in equilibrium with the gs t some elevted pressure B0. With the relese of pressure t t 0, the solution beomes supersturted, nd nuletion nd bubble growth begin. As the bubble growth proeeds, the pressure inside the bubble nd the dissolved gs onentrtion t the bubble surfe derese. With time, gs diffuses into the bubble nd onentrtion grdient propgtes rdilly in the polymer melt. A shemti of the bubble growth is shown in Figure 5. The rdius nd the dissolved gs onentrtion re denoted by (t) nd (r,t). In nlyzing the bubbles growth proess, the following ssumptions n be mde: 1. The bubble is spherilly symmetri when it nuletes nd remins so for the entire period of growth.. The gs pressure in the bubble B (t) is relted to the dissolved gs onentrtion t the bubble surfe (,t) by the Henry lw: (,t)k H B (t).. There re no hemil retions during bubble growth. 4. Grvittionl effets nd ltent het of solution re negleted. 5. Inertil effets re negleted nd the fluid is ssumed to be inompressible nd ewtonin. 6. The surfe tension t the gs-liquid interfe hs onstnt vlue σ. 7. The effet of fom densities on therml ondutivity of gs-filled polymeri bubble system is negleted. The mteril properties suh s polymer struture, moleulr weight nd its distribution, rystllinity nd others re independent of the dissolved gs onentrtion nd re ignored. The neglet of inerti nd the ssumption of ewtonin behvior is imposed beuse the fluids re very visous nd the initil bubble growth rtes re very smll. evertheless, Amon nd Denson [1] studied het trnsfer nlysis in polymer-gs systems in gret detil. They found from relible emril orreltions tht the effetive therml ondutivity of gs-filled polymeri bubble system hnges by no more thn few perentge points over the whole rnge of fom densities. Moreover, s for thermoplsti fom extrusion, growth ours in the molten-to-solid trnsition stte. The polymer is ooled from 80 (die temperture) to 5 (mbient temperture) in reltively short time: sine in these irumstnes ll physil properties of the system undergo rd hnge, trnsient het trnsfer problem is onsidered here. 4.. Governing equtions for the bubble growth Figure 5. Shemti of single bubble growth In view of the bove restritions, the eqution of motion, integrl mss (gs) blne over the bubble nd differentil mss (dissolved gs) blne in the 89
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 surroundings mother phse tke the following forms [14]. Eqution of motion is given by Eqution (): d () The initil ondition for the bove eqution is: (0) i. Here i is the initil rdius of the bubble, the pressure in the ontinuous phse, σ surfe tension nd η melt visosity. Integrl mss (gs) blne over the bubble A differentil mss blne in binry system ssuming spheril symmetry, onstnt density nd diffusion oeffiient (D) is of the form of Eqution (4): + v t (4) where is the dissolved gs onentrtion in the melt nd D is the binry diffusion oeffiient. The boundry nd initil onditions for Eqution (4) re given by Eqution (5): (5) At distne fr from the bubble surfe, the solution is not ffeted by the growing bubble nd the dissolved gs onentrtion remins, the sme s before the onset of nuletion. The quntity is the dissolved gs onentrtion t the bubble surfe. It is relted to the gs pressure in the bubble through the solubility oeffiient K H. The quntity i (r) is the initil onentrtion profile in the melt. The mss blne on the bubble requires tht the rte of mss dded to the bubble equls the rte tht mss diffuses in through the bubble surfe. Thus, simple mss blne t the bubble surfe reltes the bubble pressure to the onentrtion grdient t the surfe (see Eqution (6)): r B (, t) (, t) 4η ( r,0) ( r) i σ η 1 D r r r r ( t) K d 4π D ZgT dr H ( t) d 4π B B r r (6) The initil ondition for the bove eqution is B (0) B0. Here B0 is the initil bubble pressure, Z the ompressibility ftor of the gs inside the bubble, T temperture nd g universl gs onstnt. 4..1. Dimensionless form of the governing equtions To filitte the subsequent nlysis, the following dimensionless vribles nd groups n be defined by Equtions (7) (15): r r t t t (7) (8) (9) (10) (11) (1) (1) (14) (15) In defining the bove dimensionless quntities, we ked the ritil bubble rdius (Eqution (16)): (16) nd the ritil momentum trnsfer time (Eqution (17)): t K H K B G e si k ηd K B0 B B0 H B σ B0 T 4η H T ( ( B 0 σ B0 16πσ B0, ) ) (17) s our hrteristi bubble rdius nd bubble growth time, respetively. 90
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 In terms of the dimensionless vribles, the equtions governing the bubble growth dynmis tkes the following forms (see Equtions (18) (0)): d B 1 (18) where A is defined by Eqution (8): 1 π A + 4 G 1 1 1 (8) d Z r si ( 1 B + B e r r (19) (0) The orresponding initil nd boundry onditions re given by Equtions (1) (5): (0) i (1) B (0) B i () (r,0) i (r ) () (,t ) B (4) (,t ) 1 (5) Sine the ritil luster represents n equilibrium stte, this speifition of the initil onditions will not produe bubble growth. To hieve the ltter, we must perturb one or more of these vribles from the equilibrium stte. The bubble growth is strong funtion of the vlue of the initil rdius, rbitrry hoie of it n led to onsiderble error [11]. 4... Initil onditions for bubble growth In order to lulte the initil onditions for bubble growth, the pproh used follows from Shfi et l. [11]. Following this proedure, we get the initil onditions for bubble growth (see Equtions (6) nd (7)): A(1+ A) (0) (1+ A) + A(1+ A)(1+ B (0) 1 si si e ) e r d 1 + r r r e r ) d r (6) (7) The methodology for hndling the trnsport proesses round single expnding bubble is vlid for bubble growing in n infinite expnse of liquid with no dissolved gs limittions. In tul foming, there is finite mount of dissolved gs tht is ontinuously depleted by the simultneous growth nd nuletion of bubbles. In order to extend the nlysis in finite mount of dissolved gs, in this work, the proedure presented by Shfi et l. [11] ws dopted (see Figure 5). Shfi et l. pplying the integrl method to the present problem introdue n undetermined funtion of time, V b. hysilly it represents the volume of the melt between the bubble surfe nd the rdil position where the dissolved gs onentrtion pprohes the initil dissolved gs onentrtion 0. Moreover, they define two new vribles: x, whih represents the melt volume between the bubble surfe nd rdil position r normlized to the volume of onentrtion boundry region V b nd lso new onentrtion vrible s in Equtions (9) nd (0): 4π r x (9) (0) Equtions (9) nd (0) trnsform moving boundry problem with vrible boundry onditions to fixed boundry problem with onstnt boundry onditions. is lwys 0 t the bubble surfe (x 0), nd is 1 t the fr end of the onentrtion boundry (x 1) nd it n be ssumed s funtion of x only. In view of Equtions (9) nd (0) nd defining dditionl dimensionless vribles nd groups s shown in Equtions (1) nd (): 0 K K 0 V b H H B B (1) 91
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 V b V 4π b () this se, the energy eqution ombined with Fourier's lw of het ondution, is given by Eqution (8): the equtions governing the bubble growth dynmis in terms of dimensionless quntities n be rewritten by Equtions () (5): d d V b e 9 siz ( (1 ) d + ( si V 1 b + (1 ) dx 1 (1+ ) (1 )dx 0 x 0 () (4) (5) With the initil onditions given by Equtions (6) nd (7): ) ) d T t ρ (8) where ρ, p, nd k p re density, speifi het nd therml ondutivity, respetively. The initil nd boundry onditions re then given by Eqution (9): T T k t t 0, 0 T 0, x 0 x T h ( T T x T p, x AI ), xδ (9) where δ is the hlf-thikness of the fom sheet, T 0 is the initil temperture of the polymer (die temperture), T AI is the mbient temperture nd h is the het trnsfer oeffiient. A(1+ A) (0) (1+ A) + A( A+ 1)(1+ (0) 1 si si e ) e (6) (7) 4.. Model formultion In order to lulte the evolution of the bubbles size in the fom sheet strting from mteril properties nd working onditions, the model bove desribed ws implemented in simultion ode developed in Lbview (tionl Instruments). With this im Equtions () (5) must be solved with the initil onditions given by Equtions (6) nd (7). Moreover, s for thermoplsti fom extrusion, growth ours in the molten-to-solid trnsition stte. The polymer is ooled from 80 (die temperture) to 5 (mbient temperture). heologil property vrition ertinly hnges the isotherml growth senrio nd hene, trnsient het trnsfer problem is onsidered here. The polymer is ooled by mens of two ooling fns, in Figure 6. Flow hrt desribing the sequene of the lultions in the model 9
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 A flow hrt desribing the sequene of the lultions is reported in Figure 6. In Tble 5, the min vribles involved in the model re reported. 4..1. Solution methodology The equtions governing the bubble growth dynmis re highly nonliner nd stiff. These equtions were solved using the Ger s method. The nonliner equtions re solved by Brown s method. The equtions were solved using finite differene sheme. It is worth mentioning tht in the model dopted in this work there re no involved djustble prmeters so tht the model strting from of mterils properties nd the opertive onditions is ble to predit bubble dimensions. 5. Model results Model developed in this work following the literture inditions llows to lulte the evolution of the temperture, of the bubble pressure nd rdius strting from the opertive onditions nd mteril properties (Tbles 1 nd 6). onsistently with experimentl, with n mount of hin extender lower tht 0.5% ording to the model the lusters re not suffiiently lrge ompred to the ritil luster in order to grow spontneously to mroso bubble nd no fom n be obtined. In Figure 7, the lulted evolution of temperture nd bubble rdius during the foming proess re reported for ET_MDA050_BA05 nd ET_MDA075_BA05. Figures show tht bubbles growth tkes bout one seond, fter this time temperture beome too low nd visosity too high. Tble 5. Min vribles involved in the model dopted in this work σ surfe tension D binry diffusion oeffiient η melt visosity Z ompressibility ftor of the gs K H solubility oeffiient g Universl gs onstnt B0 initil bubble pressure initil gs onentrtion i initil rdius of the bubble i(r) initil gs onentrtion profile (t) bubble rdius (r,t) dissolved gs onentrtion B(t) V b gs pressure in the bubble (,t) dissolved gs onentrtion t the bubble surfe ressure in the ontinuous phse volume of the melt between the bubble surfe nd the rdil position where the dissolved gs onentrtion pprohes the initil dissolved gs onentrtion 0 Tble 6. hysil properties [] nd opertive onditions used in the model hysil properties Opertive onditions ET speifi het p 110 J/(kg K) Therml ondutivity K 0.18 W/(m K) Ativtion energy for visous flow E 94 000 J/mol heologil referene temperture 55 K Surfe tension σ 0.0446 /m Diffusivity 10 1 m /s Die pressure 1.5 10 6 Ambient pressure 1.01 10 5 Die temperture T 0 54 K In Figure 8, the lulted evolution of bubble pressure nd rdius during the foming proess re reported for ET_MDA050_BA05 nd ET_MDA075_BA05. Figure 7. Temperture profile for the bubble growth simultion of extrusion. ET_MDA050_BA05; b ET_MDA075_BA05 9
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 Figure 8. ressure profile for the bubble growth simultion of extrusion foming, ET_MDA050_BA05; b ET_MDA075_BA05 Figure 9. Evolution of the bubble rdius for ET_MDA050_BA05 nd ET_MDA075_BA05 The bubble pressure strt from mximum nd dereses to vlue lose to the mbient pressure. The evolution of the bubble rdius for the smples nlyzed in this work ws ompred in Figure 9. As it n be seen from the figure, the rdius of the bubbles in the smple oded s ET_MDA050_BA05 is bigger thn the one of the bubbles in ET_MDA075_BA05. From figure the effet of the MDA ontent is evident, in ft, the bubble rdius inreses on deresing of the MDA ontent: this is minly due to the higher melt strength (shown by the ET_MDA075_BA05) whih limits the growth of the bubbles. The omprison between experimentl results nd model predition for the bubble rdius is reported in Figure 10. Beuse t the moment only few experimentl re vilble, literture [5, 6] re lso reported in figure. Moreover, the model desribed in this work ws dopted in order to lulte the evolution of the bubble rdius in literture experimentl onditions nd results were lso reported in figure. The stisftorily greement Figure 10. omprison between experimentl results nd model predition for the bubble rdius (literture re lso reported in figure) Tble 7. omprison between experimentl results nd model predition for the bubble rdius Smples Experimentl ell rdius [μm] lulted ell rdius [μm] ET_MDA050_BA05 44 ± 15 49 ET_MDA075_BA0 1 ± 10 ET_MDA075_BA05 7 ± 15 between literture experimentl nd model preditions is further vliion of the model dopted in this work. In order to underline results hieved in this work, the omprison between experimentl results nd model predition for the bubble rdius for ET_MDA050_BA05, ET_MDA075_BA0, ET_MDA075_BA05 is reported in Tble 7. omprison shows tht model seems to be ble to predit experimentl of bubble rdius, even if, t the moment only few experimentl re vilble. 94
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 The omprison between experimentl nd model predition shown in Figure 10 is stisftorily, however, better results of predition of the evolution of the bubble rdius during foming proess ould be hieved by mens of better rheologil desription, tht is dopting more omplex models whih better desribe visoelsti properties of the mteril. 5. onlusions In this work, the proess of extrusion foming by hemil blowing gent (BA) ws improved in order to produe high density foms from ET industril srps with very low visosity. Due to the low intrinsi visosity of the reyled ET (IV 0.48 dl/g), hin extender ws lso used in order to inrese the moleulr weight of the polymer mtrix. The retive proessing of ET nd the foming extrusion proess were both performed with Brbender single srew extruder. The opertion ws omplished in two steps. The hemil modifition, in the proportion required for the im of extrusion foming, is hieved with very low ontent of MDA in ET; speifilly three levels of MDA ontents were nlyzed: 0.5, 0.50 nd 0.75 weight% whih resulted to be the right ompromise to tilor the required rheologil modifition nd suitble foming proessbility of ET. As fr s the fom prodution is onerned, the hoie ws direted to hemil foming gent bsed proess. In prtiulr Hydroerol T 54 ws used s hemil foming gent nd speifilly two levels of Hydroerol ontents were nlyzed: 0.0 nd 0.50 weight%. Modified ET ws hrterized in terms of rheologil properties (flow urves, melt strength nd BS), mehnil properties (tensile nd flexurl properties) nd densities. Fom produed ws hrterized in terms of rheologil properties (flow urves, melt strength nd BS), mehnil properties (tensile nd flexurl properties), densities nd finlly in terms of ell size nd ell size distribution by mens of snning eletroni mirosopy. Finlly, the growth of spheril bubble in polymeri liquid hs been theoretilly studied by tking into ount both mss trnsfer phenomenon nd visous fores effet. Model results were ompred with experimentl obtined nlyzing fomed sheets produed in lbortory strting from industril srps of ET. As for thermoplsti fom extrusion, growth ours in the molten-to-solid trnsition stte. heologil property vrition ertinly hnges the isotherml growth senrio nd hene, trnsient het trnsfer problem is onsidered nd non isotherml model for bubble growth ws developed. The model ws vlied in reltion to working onditions, hemil blowing gent perentge nd initil rheologil properties of reyled polymer. A good greement between experimentl nd lulted ws hieved, even if, t the moment only preliminry experimentl re vilble. In order to hieve better understnding of the foming proess, future work will onsider n dditionl vliion by ompring model results with wider set of experimentl nd the nlysis of the bubble nuletion. eferenes [1] Lee. H., Lee K-J., Jeong H. G., Kim S. W.: Growth of gs bubbles in the fom extrusion proess. Advnes in olymer Tehnology, 19, 97 11 (000). DOI: 10.100/(SII)1098-9(000)19:<97:: AID-ADV>.0.O;-B [] Kumr V., Suh..: roess for mking miroellulr thermoplsti prts. olymer Engineering nd Siene, 0, 1 19 (1990). DOI: 10.100/pen.7600010 [] Bldwin D. F., Suh.., rk. B., h S. W.: Supermiroellulr fomed mterils, U.S. tent 5456, USA (1994). [4] Xnthos M., Dey S.: Fom extrusion of polyethylene terephthlte (ET). in Fom extrusion: riniples nd prtie (ed.: Lee S. T.) Tehnomi, Lnster, 07 6 (000). [5] Brnh G. L., Wrdle T.: Mnufture of fully reylble fomed polymer from reyled mteril. Interntionl tent T/US004/01545 (004). [6] Inrnto L., Srfto., Di Mio L., Aierno D.: Struture nd rheology of reyled ET modified by retive extrusion. olymer, 41, 685 681 (000). DOI: 10.1016/S00-861(00)000-X [7] Di Mio L., oorullo I., Montesno S., Inrnto L.: hin extension nd foming of reyled ET in extrusion equipment. Mromoleulr Symposi, 8, 185 00 (005). DOI: 10.100/msy.00551017 [8] Awj F., Dumitru.: Sttistil models for optimistion of properties of bottles produed using blends of retive extruded reyled ET nd virgin ET. Europen olymer Journl, 41, 097 106 (005). DOI: 10.1016/j.eurpolymj.005.04.010 95
oorullo et l. exess olymer Letters Vol., o. (009) 84 96 [9] Jpon S., Boogh L., Leterrier Y., Mnson J. A. E.: etive proessing of poly(ethylene terephthlte) modified with multifuntionl epoxy-bsed dditives. olymer, 41, 5809 5818 (000). DOI: 10.1016/S00-861(99)00768-5 [10] Awj F., vel D.: Injetion streth blow moulding proess of retive extruded reyled ET nd virgin ET blends. Europen olymer Journl, 41, 614 64 (005). DOI: 10.1016/j.eurpolymj.005.05.06 [11] Shfi M. A., Lee J. G., Flumerfelt. W.: redition of ellulr struture in free expnsion polymer fom proessing. olymer Engineering nd Siene, 6, 1950 1959 (1996). DOI: 10.100/pen.10591 [1] Venerus D..: Diffusion-indued bubble growth in visous liquids of finite nd infinite extent. olymer Engineering nd Siene, 41, 190 198 (001). DOI: 10.100/pen.1089 [1] Amon M., Denson. D.: A study of the dynmis of fom growth: Anlysis of the growth of losely sped spheril bubbles. olymer Engineering nd Siene, 4, 106 104 (1984). DOI: 10.100/pen.7604106 [14] Fvelukis M., Zhng Z., i V.: On the growth of non-idel gs bubble in solvent-polymer solution. olymer Engineering nd Siene, 40, 150 159 (000). DOI: 10.100/pen.1164 [15] mesh. S., smussen D. H., mpbell G. A.: The heterogeneous nuletion of miroellulr foms ssisted by the survivl of mirovoids in polymers ontining low glss trnsition prtiles. rt I: Mthemtil modeling nd numeril simultion. olymer Engineering nd Siene, 4, 1685 1697 (1994). DOI: 10.100/pen.760406 [16] tel. D.: Bubble growth in visous ewtonin liquid. hemil Engineering Siene, 5, 5 56 (1980). [17] Joshi K., Lee J. G., Shfi M. A., Flumerfelt. W.: redition of ellulr struture in free expnsion of visoelsti medi. Journl of Applied olymer Siene, 67, 15 168 (1998). DOI: 10.100/(SII)1097-468(19980)67: 8<15::AID-A>.0.O;-D [18] Yue., Feng J. J., Bertelo. A., Hu H. H.: An rbitrry Lgrngin-Eulerin method for simulting bubble growth in polymer foming. Journl of omputtionl hysis, 6, 9 49 (007). DOI: 10.1016/j.jp.007.07.007 [19] Otsuki Y., Kni T.: umeril simultion of bubble growth in visoelsti fluid with diffusion of dissolved foming gent. olymer Engineering nd Siene, 45, 177 187, (005). DOI: 10.100/pen.095 [0] Everitt S. L., Hrlen O. G., Wilson H. J.: ompetition nd intertion of polydisperse bubbles in polymer foms. Journl of on-ewtonin Fluid Mehnis, 17, 60 71 (006). DOI: 10.1016/j.jnnfm.006.0.005 [1] Fvelukis M.: Dynmis of fom growth: Bubble growth in limited mount of liquid. olymer Engineering nd Siene, 44, 1900 1906 (004). DOI: 10.100/pen.019 [] Lee J. G., mesh. S.: olymeri foms: Mehnisms nd mterils. ress, ew York (004). [] Vn Krevelen D. W.: roperties of polymers. Elsevier, ew York (1990). [4] Amon M., Denson. D.: A study of the dynmis of fom growth: Simplified nlysis nd experimentl results for bulk density in struturl fom molding. olymer Engineering nd Siene, 6, 55 67 (1986). DOI: 10.100/pen.7606011 [5] Hn. D., Yoo H. J.: Studies on struturl fom proessing. 4. Bubble growth during mold filling. olymer Engineering nd Siene, 1, 518 5 (1981). [6] Xu D., op-iliev., rk. B., Fenton. G., Jing H.: Fundmentl study of BA-blown bubble growth nd ollpse under tmospheri pressure. Journl of ellulr lstis, 41, 519 58 (005). DOI: 10.1177/001955X0505901 96