Effect of the modification of the polymer-rich phase composition on the formation of structural defects in radical suspension PVC Purmova, Jindra

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1 University o Groningen Eect o the odiication o the olyer-rich hase coosition on the oration o structural deects in radical susension PC Purova, Jindra IPORTANT NOTE: You are advised to consult the ublisher's version (ublisher's PF i you wish to cite ro it. Please chec the docuent version below. ocuent ersion Publisher's PF, also nown as ersion o record Publication date: 7 Lin to ublication in University o Groningen/UCG research database Citation or ublished version (APA: Purova, J. (7. Eect o the odiication o the olyer-rich hase coosition on the oration o structural deects in radical susension PC Groningen: s.n. Coyright Other than or strictly ersonal use, it is not eritted to download or to orward/distribute the tet or art o it without the consent o the author(s and/or coyright holder(s, unless the wor is under an oen content license (lie Creative Coons. Tae-down olicy I you believe that this docuent breaches coyright lease contact us roviding details, and we will reove access to the wor iediately and investigate your clai. ownloaded ro the University o Groningen/UCG research database (Pure: htt:// For technical reasons the nuber o authors shown on this cover age is liited to 1 aiu. ownload date:

2 APPENI I Calculation o the diusion controlled rate coeicients and reaction rates 49

3 APPENI I iusion controlled reaction rate coeicients Aarent rate coeicients o the reactions taing lace in heterogeneous edia are usually coosed ro the ters che (rate coeicient corresonding to cheically controlled reaction and di (diusion contribution, having the ollowing relationshi: 1 1 obs 1 che 1 + di (-1 The diusion contributions to the rate coeicients or the reactions taing lace in our syste were calculated using the odel develoed by eroo et al. The diusion contribution di can be calculated using the Soluchowsi odel. 3 π N (- di, 4 ( ry + rz ( y + z A ( y z r + r ( y + z N A distance between the two secies when reaction occurs utual diusion coeicient consisting o two contributions o the reacting secies y and z Avogadro constant ( y z r + r was taen as the Lennard-Jones diaeter o a onoer olecule σ The general eression was used or the calculation o the diusion contributions o the rate coeicients o the roagation and chain transer to olyer in the ollowing or: roagation transer to olyer 4πσ N di, A (-3 4πσ N di, A (-4 sel-diusion coeicient o onoer sel-diusion coeicient + reaction diusion coeicient o olyer Sel-diusion coeicients These coeicients are calculated using ree volue theory, 5 * * E j, e e (-5 RT FH /γ 5

4 Calculation o the diusion controlled rate coeicients and reaction rates, * j e FH /γ (-6 where * * ˆ j j (-7, re-eonential actor * E * j FH / γ ˆ* FH activation energy needed to ae a diusional ju ree volue contribution seciic volue a olecule needs to ae a diusional ju hole ree volue o the olyer onoer iture o the olyer rich hase available or diusion γ overla actor FH / γ ˆ w j / γ w + FH j (-8 ˆ FH seciic hole ree volue w j onoer or olyer weight raction in the olyer rich hase olecular ass o the onoer or acroradical juing unit ˆ FH ( T ( + α ( T T ˆ ˆ G / γ w H, + w γ γ ( T ( ( α α ( T T G H, c, (-9 α T g, G H, γ onoer; olyer theral eansion coeicient glass transition teerature o the ure onoer or olyer ractional hole ree volue o the ure coonent at T g hole ree volue overla actor 51

5 APPENI I ˆ ( T ( Tg, 1/ ρ (-1 1+ ( 1 T / 43 ρ / (-11 4 ( T 3 ρ 1 e (-1 ( ˆ seciic volue o the ure coonent at T g T g, ρ density o the onoer or olyer ˆ ln G ( T ( 1 1 H, α c, (-13 T ˆ ( α c, Close-aced crystalline state eansion coeicient 6 ˆ ( seciic volue o the ure coonent at K, Pre eonential actors onoer, is calculated ro the ullien equation: 7, 16 /3 *.141 c, RT γ ˆ / K11 e η ˆ K1 Tg, + T (-14 c, η ˆ K11 / γ K 1 onoer critical volue onoer olecular ass Pure onoer viscosity Pure onoer volue onoer ree volue araeters ( Tg α γ K γ ˆ 11 /, / (-15 K G 1 H, / α (-16 5

6 Calculation o the diusion controlled rate coeicients and reaction rates Proerty Units onoer Polyer ρ 1/ ˆ 9,17 [g l -1 ] η [N - s] T 5.71 T * ˆ ˆ ( 8 * * 8 j ( [ 3 g -1 ] [ 3 ol -1 ] G H, 5 [-].5.5 α [K -1 ] ,1 T, [K] g γ [-] E * [J ol -1 ] [g ol -1 ].65 - Polyer, is deterined by calculating the olyer diusion coeicient di at w 1, and setting this coeicient equal to the diusion coeicient derived ro the retation theory. 11,1 retation G ρ N RT 135 G N R (-17 cr ηcr G N Shear odulus o the rubbery lateau R ean-square end-to-end distance o the olyer chain with olecular ass ρ η cr cr Polyer density Zero shear elt viscosity at the cr Critical olecular ass o the olyer retation (-18, w 1 ; T 1.T g, w 1; T 1. Tg, (-19 53

7 APPENI I Proerty Units alue/eression G ρ RT / N cr 1 [N - ] R 1/ [] logη cr (1.T 8 [N - s] 3.89 cr 8 [g ol -1 ] 6.5 Activation energy E * is estiated ro the it o its grah 6,13 vs. log( E * ( δ δ.8988ln(log(( δ δ / (- olar volue o the ure onoer at a reerence teerature C δ Solubility araeters 1/ δ ( Ecoh / (-1 E coh H RT (- va Proerty Units onoer Polyer H va [J ol -1 ].4 - δ 8 [(J -3 1/ ] Free volue araeters * j are calculated as the size o the ju unit at K. 6 is the volue o the olecule itsel. * j The equation or the calculation o the or soe coon olyers. 6 * , j T g * was obtained by itting o the tabulated values j (-3 γ and γ were set to their highest theoretical value 1. Reaction diusion coeicient The so-called reaction diusion coeicient eresses the segental otion o the radical chain end due to the roagation 4. 54

8 Calculation o the diusion controlled rate coeicients and reaction rates [ ] 1 ( rd a 6, obs (-4, Aarent roagation rate coeicient obs [ ] olar concentration o the onoer in the olyer rich hase a Root- ean-square end-to-end distance er square root o the nuber o onoer units in a olyer chain ( istribution o the onoer and olyer during the susension olyerization o vinyl chloride The aounts o onoer and/or olyer in either onoer or olyer-rich hase were calculated using the odel develoed by ie et al. 14 w, (-5,,, aq, w, ass o olyer ored at, weight raction o olyer in olyer rich hase at conversion, ass o C initially charged g,, ass o C in gaseous hase at aq,, ass o C in aqueous hase at A very iortant araeter in the descrition o the distribution o the onoer is critical conversion. At this oint, the onoer as a searate hase is consued and the ressure in the reactor begins to dro. The in our syste was deterined to occur at 6%. 15 < The aount o the onoer in the gaseous and aqueous hase does not contribute to the olyerization at conversions <. The coosition o the olyer rich hase reains constant (w.66, because onoer is being relaced ro the ure liquid onoer hase. P RT ( 1 v + 1 P ( 1/ ρ 1/ ρ,,, < r, r (-6, /( RTρ K, aq, < w (-7 55

9 APPENI I > At conversion > the ure liquid onoer hase is deleted and the olyerization goes on in the ure olyer rich hase. The onoer necessary or the roagation is being taen ro gas and aqueous hase. P RT ( v + ( 1/ ρ 1/ ρ ( ( 1/ ρ 1/ ρ,, > 1 r, r +, 1 ρ / ρ K P P, aq, w /, (-8 > (-9 ρ (-3, P, /( RT g vr, w w, r r ( / ρ + / ρ ρ / ρ /( (1 ρ / ρ (-31 Proerty Units alue/eression P ressure in the reactor [bar] P, vaor ressure o onoer [bar] P, 17e( 411.7/ T R universal gas constant [bar l ol -1 K -1 ] T teerature [K] 33.5 onoer conversion [-] critical onoer conversion [-] K solubility constant 16 [-] volue o the reactor [l] 1.77 r w ass water charged [g] 349.9, ass onoer initially charged [g] 175 v r, ρ w initial degree o charging o the reactor vaor density at the vaor ressure o the onoer [-].563 [g l -1 ] ρ water density 17 [g l -1 ] ρ w t 1.3 t teerature [ C] Calculations o the ratios o the reaction rates [ P] [ ] tr inter ν tr inter/ ν (-3 ν tr intra/ ν tr intra [ ] (-33 56

10 Calculation o the diusion controlled rate coeicients and reaction rates ν rate o interolecular transer ν tr ν tr inter intra tr inter tr intra rate o intraolecular transer roagation rate rate coeicient o interolecular transer rate coeicient o interolecular transer [] [P] roagation rate coeicient olar concentration o onoer olar concentration o olyer olar concentrations o olyer and onoer in the olyer rich hase The solubility o PC in C is etreely low; alost all the olyer is thus located in the olyer rich hase at whole conversion range. [ P] [ ], o / (-34 olyerrich hase, olyer rich hase, / (-35 olyerrich hase olyerrich hase + (-36 < At conversion u to only a art o the onoer is contained in the olyer rich hase. The coosition o this hase is constant during this eriod., φ, (-37 [( 1,, >,aq, > ]/ρ +, /ρ ], olyer rich hase,, olyer rich hase, (-38 (1 φ,, olyer rich hase, ( φ,, /ρ ρ (-39 / ρ (-4.6 φ,

11 APPENI I >, φ, > (-41 [ ( 1,, >,aq, > ]/ρ +, /ρ ] hase, > (,, >,aq, olyer rich > /ρ, 1 (-4 / ρ, olyer rich hase,, olyer rich hase, (-43 / ρ (-44, φ, olyer rich hase, volue raction o olyer in the olyer rich hase at conversion volue o olyer in the olyer rich hase, volue o onoer in the olyer rich hase Reerences 1. See or eale: Haielec, A.E. In Science and Technology o Polyer Colloids; Poehlein, G.W., Ottweil, R.H., Goodwin, J.W.E., Eds.; artinus Nijho Publishers: The Hague, enar, 1983; 14.. e Roo, T.; Heynderic, G. J.; arin, G. B. acrool.sy. 4, 6, Soluchowsi,.Z. Phys. Che. 1918, 9, Clay, P. A.; Gilbert, R. G. acroolecules 1995, 8, Bueche, F. Physical Proerties o Polyers; Wiley- Interscience: New Yor, See or eale: rentas, J. S.; rentas, C.. Eur. Poly. J. 1998, 34, See or eale: Zielinsi, J.. acroolecules 1996, 9, ; ullien, A.L. AIChE J. 197, 18(1, an Krevelen,.W. Proerties o Polyers, 3rd ed.; Elsevier: Asterda, Perry, R.H; Green,.W. Perry s Cheical Engineers Handboo, 7th ed.; cgraw-hill: New Yor, Bandru, J.; Iergut, E.H. Handboo o Polyers, 3rd ed.;wiley: New Yor, asaro, L.; Zhu,.. Prog. Poly. Sci. 1999, 4, Graessley, W.W. J. Poly. Sci., Poly. Phys. Ed., 198, 18, Tonge,. P.; Gilbert, R. G. Polyer 1, 4, ie, T. Y.; Haielec, A. E.; Wood, P. E.; Woods,. R. J. Al. Poly. Sci. 1987, 34, Pauwels, K.F.. New asects o the susension olyerization o vinyl chloride in relation to the low theral stability o oly(vinyl chloride, issertation: Groningen University, 4. htt://dissertations.ub.rug.nl/aculties/science/4/..d.auwels/ 16. Weast, R.C. Handboo o Cheistry and hysics; The Cheical Rubber Co.: Ohio, ie, T. Y.; Haielec, A. E.; Wood, P. E.; Woods,. R. Polyer 1991, 3,