THE RHEOLOGY OF CONCENTRATED SLURRIES: EXPERIMENTAL EVALUATION AND THE EFFECTS ON POLYMER PROCESSING

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1 THE RHEOLOGY OF CONCENTRATED SLURRIES: EXPERIMENTAL EVALUATION AND THE EFFECTS ON POLYMER PROCESSING Mark D. Wetzel Florence, Oregon, Jon C. Howe, Micael T. Sterling DuPont, Wilmington, Delaware 1983 Gregory A. Campbell Castle Associates, Jonesport, Maine 4649 Abstract Higly illed polymer compounds can present processing callenges, including ig screw sat torque, energy consumption, die pressure and melt temperature rise. Previous teoretical development and experimental evaluations o igly illed polymer melts sowed tat te reology can be described wit a percolation model [1-4]. Tis paper re-evaluates a batc mixer caracterization metod used to measure te eects o iller concentration on melt processing. Te experimental results are compared wit capillary reometer measurements using several low-density polyetylene resins, calcium carbonate and titanium dioxide. Te teoretical treatment o te reology as a particulate percolating system wit power-law beavior is used to analyze reometer and batc mixer data. Te eects o resin molecular weigt, iller type and size on reology and melt processing are described. Introduction Campbell and Forgacs used percolation teory to model te viscosity o concentrated suspensions [4]. Oter researcers investigated te eects o particles on viscosity were a percolation tresold ranged rom 16 to 52 vol. %, depending on te luid caracteristics, particle type and size [1-3]. Batc mixers ave been used extensively to examine dispersive mixing o solid illers in polymer melts. Recently, a 15 cc conical twinscrew batc mixer was used to study te reological eects o illers in polymer compounding [1,3]. An axial orce measurement was made wit a cantilever mounting o te mixer barrel linked to a orce transducer. Te reactive orce o te tapered screws pumping te material into te recirculation loop was related to te viscosity o te blend during processing. For te work presented in tis paper, a 15cc conical twin screw batc mixer supplied by Xplore Instruments BV, Neterlands was used to evaluate te eects o melt viscosity o several polymers illed wit dierent particulate solids or a mixture o illers. Te axial barrel orce and a melt termocouple measurement were recorded to quantiy te process response to iller concentration and operating conditions. Titanium dioxide, TiO 2, and calcium carbonate, CaCO 3, powders were pre-dispersed in Low Density Polyetylene, LDPE, or Linear LDPE, LLDPE, wit dierent molecular weigt distributions using a compounding twin-screw extruder. Te masterbatces were letdown in te bat mixer to dierent iller concentrations. Te eects o te iller type, size and loading on melt viscosity and process response were analyzed wit resin reology constitutive equations and te percolation model. Material Systems and Masterbatces Table 1 lists te commercially available polyetylene (PE) resins and particulate solids used in te experiments. Te LDPE/TiO 2 system publised previously was used to re-evaluate te batc mixer caracterization metod [1]. Tree LLDPE polymers made wit te UNIPOL process (catalyst not speciied) wit melt index values o 16, 2 and.7 were used to explore CaCO 3 illed compounds. Te ~45µm 4-UL CaCO 3 grade ad no surace modiier applied, wile te ~5µm 5-FL material did ave a surace treatment. Publised particle size values are listed in te table. Table 1. Polymers and Fillers used. ρ (g/cc) Melt Index (g/1min) (19ºC, 2.16kg) Power Law Index (ig sear rates) Polymer T MP ( C) Equistar LDPE Petrotene NA ~ Dow LLDPE DNDA Dow LLDPE GRSN-982 NT Dow LLDPE GRSN-27 NT Filler ρ (g/cc) d 5 (µm) Surace Modiier Cemours Ti-Pure R-14 TiO Yes OMYACARB 4-UL CaCO No OMYACARB 5-FL CaCO Yes Masterbatces containing 65 vol. % o te illers listed in Table 2 were prepared on a Coperion ZSK- 18mm Mega-lab 1 barrel, 41 L/D, twin-screw extruder itted wit a conventional powder dispersive mixing screw. Polymer pellets were metered into te irst barrel using a loss-in-weigt eeder. Filler powder was ed into a twin-screw side stuer in barrel #5 wit a second lossin-weigt eeder. Te extruder screw speed was 25 RPM. Te trougput was set to 6.8 kg/r (15 lb/r), but was reduced to 4.55 kg/r (1 lb/r) or te ig viscosity LLDPE and te LDPE/TiO 2 system. Barrel temperatures were proiled rom 17 to 2ºC. For te SPE ANTEC Anaeim 217 / 1144

2 CaCO 3 system, masterbatces containing a 7/3 blend o 4-UL/5-FL were compounded in an attempt to determine te eects o particle size combinations on reducing te melt viscosity at ig iller loadings. Packing teory calculations and experiments suggested tat te maximum packing density could be increased wit mixed illers wit a particle diameter ratio o 7 or greater [5], wic could reduce te viscosity relative to te pure particle compositions wit a small particle component o 15 to 3% [6]. Table 2. ZSK-18mm Compounded Masterbatces. Master batc Polymer Filler Loading (vol. %) MB-1 LLDPE 182 MI 16 OMYA 4-UL (CaCO 3 ) 65% MB-2 LLDPE 182 MI 16 OMYA 5-FL (CaCO3) 65% MB-3 LLDPE 182 MI 16 4-UL/5-FL 7/3 Blend 65% MB-4 LLDPE 982 MI 2 OMYA 4-UL (CaCO 3 ) 65% MB-5 LLDPE 982 MI 2 OMYA 5-FL (CaCO3) 65% MB-6 LLDPE 982 MI 2 4-UL/5-FL 7/3 Blend 65% MB-7 LLDPE 27 MI.7 OMYA 4-UL (CaCO 3 ) 65% MB-8 LLDPE 27 MI.7 OMYA 5-FL (CaCO3) 65% MB-9 LLDPE 27 MI.7 4-UL/5-FL 7/3 Blend 65% MB-1 LDPE NA-26 MI 13.5 Ti-Pure R-14 TiO 2 65% Reology Measurements and Models Te melt viscosity o te LLDPE resins, te CaCO 3 masterbatces and batc mixer letdown samples were measured in accordance wit ASTM D 3835 using a Dynisco LCR 71 capillary reometer. Te diameter o te die was conirmed beore te start o eac test using a Meyer Gage Company Class X GO/NOGO gage wic as a tolerance o ± 3 in. Te barrel temperature was calibrated at least once a quarter ollowing te procedure in ASTM D 3835 using a calibrated Hart Scientiic model 152A termometer readout equipped wit a NIST-traceable SDI model A temperature probe. Te combined accuracy o te readout and probe is better tan.1 C. Te viscosity o eac LLDPE resin was tested at 17, 19 and 21 C and at sear rates rom 25 to 1 s -1 using a 1. mm diameter die wit L/D = 3 and a 18 degree inlet angle. Te melt time was 3 s. A 1.5 kn or a 1 kn load cell was used to measure te orce generated by pusing te molten polymer troug te die. Te KARS sotware implementation o te steady-state algoritm procedure in ASTM D 3835 was used to determine tat eac data point was taken at steady-state low conditions. Te test was perormed in duplicate at all temperatures wit a res sample loading or eac test. Te test-to-test repeatability, expressed in te terms o te repeatability coeicient o variation, was less tan 3% at all sear rates. To conirm te melt stability, as part o te sear rate sweep, te irst sear rate in te sweep was repeated. Te calibration o te LCR 71 was conirmed by testing te viscosity o a polypropylene standard at sear rates rom 25 to 1 s -1. Te repeatability coeicient o variation was less tan 2%. A Cross constitutive model was used to predict viscosity as a unction o sear rate or te LDPE and LLDPE resins: (!γ) = (1) 1n 1+ λ!γ were is te zero-sear viscosity, n is a power-law exponent and l is a relaxation time [7]. Assuming tat te time-temperature superposition principle eld, te WLF relationsip was used to model te eect o temperature wit a sit actor a T : ( ) ( ) = a =1 T T T re ( ) C 1 TT re C 2 + ( TT re ) were C 1 and C 2 are model parameters and T Re is te reerence temperature, 125 C (LDPE) or 19 C (LLDPE) [7]. Figure 1 sows LDPE capillary reometer viscosity data rom [8] as a unction o sear rate and temperature along wit model prediction curves. Equation 1 and 2 coeicients or all viscosity data were estimated using time-temperature superposition data sits to a Cross model master curve and a set o Generalized Reduced Gradient (GRG) nonlinear constrained minimizations wit te Microsot Excel Solver. For te LDPE/TiO 2 system analysis, viscosity estimates sown in te igure were extrapolated to te batc mixer experimental melt temperatures o 185 C to 195 C. Viscosity Cross Model Coeicients: = 8, Pa.s at T Re = 125ºC λ =.2911 sec n =.3883 WLF Temperature Coeicient: C 1 = 1., C 2 = C C Cross C C Cross 145 C 145 C Cross 185 C Cross DSM Cannel Est. 1 1 Figure 1. NA-26 LDPE viscosity data and model. Figure 2 troug Figure 4 plot te melt viscosity data and Cross model its or te 182 (16 MI), 982 (2 MI) and 27 (.7 MI) LLDPE resins. Te low molecular weigt 182 sear rates were limited to values above tose used or te batc mixer analysis. All resins, especially at iger sear rates, exibit power-law beavior. Te Cross model its te power-law and transition regions wit suicient accuracy or te analysis. Te viscosity models were used to extrapolate to te operating conditions o te mixer. (2) SPE ANTEC Anaeim 217 / 1145

3 Viscosity C 19 C Cross Cross Model Coeicients: 17 C 17 C Cross = 6 Pa.s at T Re = 19ºC 21 C λ = 5 sec 21 C Cross n = C Cross WLF Temperature Coeicient: DSM Cannel Est. C 1 = 1.43, C 2 = Figure LLDPE MI 16 viscosity data and model. Viscosity Cross Model Coeicients: = 2,25 Pa.s at T Re = 19ºC λ = sec n =.6787 WLF Temperature Coeicients: C 1 = 2.51, C 2 = C 19 C Cross 17 C 17 C Cross 21 C 21 C Cross 185 C Cross DSM Cannel Est. 1 Figure LLDPE MI 2 viscosity data and model. Viscosity C 19 C Cross Cross Model Coeicients: 17 C 17 C Cross = 2,62,651 Pa.s at T Re = 19ºC 21 C λ = 5,638 sec 21 C Cross n = C Cross WLF Temperature Coeicient: DSM Cannel Est. C 1 = 2.6, C 2 = Figure 4. LLDPE 27 MI.7 viscosity data and model. Capillary reometer measurements were made on te LLDPE/CaCO 3 masterbatc letdown samples processed wit te Xplore batc mixer. Figure 5 troug Figure 7 sow te melt viscosity data or masterbatc letdowns wit CaCO 3 concentrations at 1, 3 and 6 vol. %. For te 16 MI 182 LLDPE, bot CaCO 3 grades and te 7/3 blend increased te melt viscosity wit a signiicant jump at 6 vol. %. Te viscosities exibited power-law beavior over te sear rate range o interest and ad similar proiles, regardless o particle size or surace treatment. Te 2 MI 982 LDPE ad a similar trend wit iller loading. However, te ~5µm 5- FL surace treated CaCO 3 reduced te viscosity as compared wit te ~45µm 4-UL untreated grade. Te 7/3 blend did not decrease te viscosity as suggested by packing teory. For te.7 MI 27 LLDPE, te batc mixer reaced torque or orce limits and could not process 6 vol. % compositions. Trends in viscosity canges were similar to tose o te 2 MI LLDPE. Viscosity LLDPE 182 (16 MI) 182/4UL 3% 182/5FL 1% 182/5FL 3% 182/5FL 6% 182/4UL/5FL 1% 182/4UL/5FL 6% 1% Blend T = 19 o C 6% 5-FL 6% Blend 3% 4-UL 3% 5-FL 1% 4-UL LLDPE Figure 5. LLDPE 182 MI 16 / CaCO 3 melt viscosity. Viscosity T = 19 o C 6% Blend 6% 4-UL 6% 5-FL 3% Blend 3% 4-UL 3% 5-FL 982 (MI 2) 982/4UL 1% 982/4UL 3% 982/4UL 6% 982/5FL 1% 982/5FL 3% 982/5FL 6% 982/4UL/5FL 1% 982/4UL/5FL 3% 982/4UL/5FL 6% 6 vol. % 3 vol. % 1 vol. % LLDPE Figure 6. LLDPE 982 MI 2 / CaCO 3 melt viscosity. Viscosity T = 19 o C Xplore (DSM) limited to maximum o 3 vol. % CaCO (MI.7) 27/4UL 1% 27/4UL 3% 27/5FL 1% 27/5FL 3% 27/4UL/5FL 1% 27/4UL/5FL 3% 3 vol. % 1 vol. % LLDPE Figure 7. LLDPE 27 MI.7 / CaCO 3 melt viscosity. Figure 8 plots power law index n estimates at sear rates above s -1 or te masterbatc letdowns. For most states, n decreased wit increasing CaCO 3 SPE ANTEC Anaeim 217 / 1146

4 concentration, especially above te percolation tresold, c. Te cange in n was te lowest or te ig molecular weigt 27.7 MI LLDPE system. Power Law n (> s -1 ) MI 2 MI.5 MB-4 982/4-UL.7 MI MB-5 982/5-FL.4 MB-6 982/Blend MB-2 182/5-FL MB-3 182/Blend.3 MB-7 27/4-UL MB-8 27/5-FL MB-9 27/Blend.2 Figure 8. LLDPE / CaCO 3 letdown power law estimates. Te Campbell-Forgacs iller percolation model was used to it batc mixer letdown sample capillary reometer data and mixer orce measurement viscosity estimates [1,3,4]. Te percolation model as te orm = r æ - ö çm c ç ç - è m ø = a = e -1 (3) or c, were te is te iller volume concentration, c is te percolation tresold, m is te maximum iller packing and is te luid viscosity. Below c, a Batcelor relationsip was used K 2 r = = a = 1+ A + (4) were te A is te usually te Einstein coeicient, 2.5, and te deault value or K is 6.2. Applying te concentration sit actor, a, to te zero-sear viscosity, constitutive Eq. 1 becomes ( ) ( ) a T a φ (!γ,t,φ) = 1+ λ a T!γ 1n (5) To compare reometer data wit batc mixer viscosity estimates, te percolation model was it to viscosity values at 19ºC and 5 s -1. Bot c and m were itting parameters. Figure 9 troug Figure 11 plot LLDPE/CaCO 3 masterbatc letdown sample measurements and percolation model predictive curves were suicient data were available. Since sit actor Eqs. 3 and 4 ave dierent orms, tere is a discontinuity at c. Altoug samples were limited at ig iller concentrations, te MI and MI compounds sowed signiicant increases in viscosity consistent wit te percolation teory. Te eect o CaCO 3 concentration above c was muc more pronounced wit te low molecular weigt resin system wit r o 33 to 35 or te 16 MI LLDPE and r o 4 to 1 wit te 2 MI resin. Since te batc mixer could not process ig CaCO 3 loadings in 27.7 MI LLDPE, te model prediction is an extrapolation above c. However, since te batc mixer exceeded its torque or orce limits, te melt viscosity increase was likely to trend similar to oter systems above 3 vol. %. / MB-1 4-UL MB-2 5-FL MB-3 7/3 Blend MB-2 Model Batcelor (it) φm φ φ r = e 1 r = φ φ 2 T = 19 o C, 5 s -1 7/3 Blend φ C = φ m = FL: 5µm ( φ C ) Figure 9. LLDPE 182 MI 16 / CaCO 3 MB letdown percolation model at 5 s -1. / MB-4 4-UL MB-5 5-FL MB-6 7/3 Blend MB-4 Model Batcelor (it) φm φ φ r = e 1 r =1+1.33φ φ 2 T = 19 o C, 5 s -1 φ C =.21 φ m =.92 ( φ C ) /3 Blend 4-UL: 45µm Figure 1. LLDPE 982 MI 2 / CaCO 3 MB letdown percolation model at 5 s -1. / Figure 11. LLDPE 27 MI.7 / CaCO 3 MB letdown percolation model at 5 s FL: 5µm MB-7 4-UL MB-8 5-FL MB-9 7/3 Blend MB-7 Model φm φ φ r = e 1 Batcelor (it) r =1+1.58φ φ 2 T = 19 o C, 5 s -1 φ C =.24 φ m =.97 ( φ C ) 4-UL: 45µm Batc mixer limited to maximum o 3 vol. % CaCO 3. it lacks suicient data. SPE ANTEC Anaeim 217 / 1147

5 Batc Mixer Experiments Melt blending experiments were conducted on a 15 cc conical twin screw batc mixer supplied by Xplore Instruments BV, Neterlands to evaluate te reological eects o iller concentration in polyetylene. Te batc mixer was used to melt and mix PE masterbatces prepared on te ZSK-18mm extruder wit PE and to measure te process response as a unction o iller concentration and sear rate. Te ollowing test protocol was used: 1. Masterbatc letdowns rom 1 to 6 vol. % were made by diluting te 65 vol. % concentrates wit additional polymer pellets or granules. PE and te masterbatc were pre-weiged to maintain a ixed material volume o 12 cc. Ingredients were preblended and ed as pellet or granule mixtures. Eac polymer was processed in te batc mixer as well. 2. Barrel top, center and bottom zone temperatures were set to 19, 19 and 195 C respectively to maintain melt temperatures close te 19 C reometer reerence value. Te bottom zone was set to a iger value to compensate or increased eat loss wit te metal mass tat included te sample valve and recirculation low cannels. 3. Ater loading te pellets into te mixer at 6 RPM, te material was melted and melt-mixed or about 3 minutes to reac an equilibrium state wit suicient TiO 2 distribution to orm a omogenous blend. 4. Te mixer was ten run or 3 minutes at 6 RPM to obtain te steady state barrel orce and melt temperature measurements. 5. Te screw speed was increased to 12 RPM and te mixer was run or anoter 3 minutes. 6. Te screw speed was increased to 24 RPM and te mixer was run or te inal 3 minutes. 7. Barrel orce and te melt temperature were recorded at a requency o 1 sample/second. At eac screw speed, 9 seconds o data at steady-state conditions were used to calculate average values and standard deviations. 8. To minimize te experimental workload, only two replicate tests were run or eac composition. Te mean and standard deviations or orce and temperature measurements were calculated or eac replicate data set. At te end o eac test, extrudate samples were collected or viscosity measurements. Replicate batc mixer melt time istories or MI LLDPE are sown in Figure 12. Barrel orce and te melt temperature termocouple signals sow te material loading, polymer melting and equilibration transitions. Data or analysis were taken ater te melting or screw speed transitions were completed to determine te average orce and melt temperature wit approximately 9 samples at 6, 12 and 24 RPM. Te plots sow tat te LLDPE exibited a sligt termal degradation wit a negative slope and exponential-like decay in te orce as a unction o time. Increasing screw speed caused te orce and melt temperature to increase. Dierences in event times were corrected by time-siting replicates to te initial melting peak orce. Wile te material volume or eac run was constant, tere were measurable dierences in barrel orce levels. Barrel Figure 12. Batc mixer barrel orce and melt temperature or te unilled 982 LLDPE polymer. Figure 13 sows replicate tests o te 5 vol. % 4-UL CaCO 3 in 982 LLDPE letdown process proiles in te batc mixer. Wile barrel orce and melt temperature traces were reproducible, tere were sligt dierences in levels. Relative to te LDPE state, te viscosity o igly illed composition resulted in increased orce values and greater deviations in te melt temperature. Average values and standard deviations calculated or te orce and temperature measurements or all CaCO 3 concentrations are listed in Table 3. Barrel 3,5 3, 2,5 2, 1,5 1, LLDPE 982 1B LLDPE LLDPE 982 1B LLDPE 982 Material loading, barrel eat transer, melting Time (Sec) 6 6B 6 6B 6 rpm 6 rpm 1 LDPE 12 rpm 1B T Melt 1 T Melt 12 rpm Figure 13. MB LLDPE/5 vol. % 4-UL CaCO 3 letdown barrel orce and melt temperature. Average barrel orce values listed in 6 6 T Melt 6B T Melt 24 rpm 1B LDPE 24 rpm 6B Table 3 or MB-4 are plotted as a unction o sear rate and CaCO 3 loading in Figure 14. Error bars are ±1 standard deviation or two replicates per state. Barrel Time (Sec) Melt Temperature (ºC) Melt Temperature (ºC) SPE ANTEC Anaeim 217 / 1148

6 orce increased wit sear rate and nonlinearly wit iller loading. Average melt temperatures are plotted as a unction o sear rate and CaCO 3 loading in Figure 15. Temperature increased wit sear rate over te range o CaCO 3 concentrations; 155ºC at 21 s -1, 156ºC at 42 s -1 and 157ºC at 83 s -1. Te dissipated energy increased signiicantly wit iller concentration wit a temperature cange rom te LLDPE resin to 5 or 6 vol. %; 1.9ºC at 21 s -1, 3.6ºC at 42 s -1 and 7.6ºC at 83 s -1. Barrel Figure 14. MB-4 LLDPE 982 / 4-UL CaCO 3 letdown average barrel orce. Error bars are ± 1 s. Melt Temperature rpm (21 1/s) 12rpm (42 1/s) 24rpm (83 1/s) Xplore torque/power limits reaced or 6 vol. % CaCO 3 at 12 and 24 rpm. 6rpm (21 1/s) 12rpm (42 1/s) 24rpm (83 1/s) T = 194ºC, ΔT = 7.6ºC T = 188ºC, ΔT = 3.6ºC 186 T = 186ºC, ΔT = 1.9ºC 184 Figure 15. MB-4 LLDPE 982 / 4-UL CaCO 3 letdown melt temperature. Error bars are ± 1 s. For te purpose o analysis, batc mixer sear rates were estimated as a unction o screw speed by calculating an average cannel dept o te screws. Te average cannel sear rate can be approximated by D g! Can = p N = mcann( rpm) (6) were D is te screw tip diameter, N is te screw speed and is te cannel dept. Dimensions were measured at 13 locations down te tapered lengt o te screw. Te average values were used to estimate D and. A constant.1mm tip to barrel gap was assumed to calculate te clearance sear rates. Sear rate estimates as a unction o screw speed are sown in Figure 16. Te cannel sear rate expression as slope m Can =.346. Using te sear rate estimates, melt viscosities were calculated rom te barrel orce data using te approximation ( g ) k! g F F Barrel!» (7) Can were F Barrel is te orce measurement and k F is a mixer and material system speciic constant calculated to be 23.3 or LDPE/TiO 2, 9.7 or 982 LLDPE/CaCO 3, 7. or 128 LLDPE/CaCO 3 and 15.8 or 27 LLDPE/CaCO 3 to matc capillary reometer unilled viscosity values at te mixer melt temperature and 21 s -1. Te LDPE/TiO 2 k F value used in previous publications was 28.5 [1,3]. Average Cannel Cannel Clearance 2.8 SR c =.346*RPM SR clr = 6.823*RPM Screw Speed (RPM) Figure 16. Xplore 15cc batc mixer sear rate estimates. Figure 17 plots te melt viscosity estimates rom te barrel orce data as a unction o sear rate and iller concentration. Error bars are ±1 standard deviation or te two replicate viscosity estimates rom te orce values measured at eac state. Te dierence between viscosity estimates at te tree sear rates increased signiicantly wit iller loading. Tis was due, in part to te increase in melt temperature. However, te rectangular cannel sear approximation is likely to be incorrect or sel-wiping screws. Energy dissipation in te clearances was also likely to be signiicant increasing te eective sear rate. 5 Average Clearance SPE ANTEC Anaeim 217 / 1149

7 Viscosity rpm (21 1/s) 12rpm (42 1/s) 24rpm (83 1/s) ( γ ) k F F k! F = 9.7 γ! Barrel Figure 17. MB-4 letdown melt viscosity estimates rom barrel orce measurements. In Figure 18, te orce measurement viscosity estimates are plotted as a unction o sear rate and CaCO 3 loading along wit te percolation model curve itted at 21 s -1 using te Batcelor relationsip below c =.239 and wit a maximum packing m =.989, te upper constraint limit used or te Excel Solver minimization. / rpm (21 1/s) 12rpm (42 1/s) 24rpm (83 1/s) Batcelor (it) r =1+1.4φ + 5.4φ 2 φ C =.239 φ m = /s ( φ C ) φm φ φ r = e 1 Figure 18. MB MI LLDPE / 4-UL CaCO 3 mixer relative viscosity estimates and percolation model curve itted at 21 s -1. Viscosity Model r = = a φ φm φ φ = e 1 r =1+1.4φ + 5.4φ 2 φ C =.239 φ m =.989 6rpm (21 1/s) 12rpm (42 1/s) 24rpm (83 1/s) Viscosity rom Experiment Figure 19. MB-4 LLDPE 982 / 4-UL CaCO 3 batc mixer viscosity estimates vs. model predictions using 21 s -1 data. Te percolation model predictions are plotted against te orce measurement viscosity estimates in Figure 19 using te Batcelor model wit A = 1.4 and K = 5.4 below c. Te model, itted to 21 s -1 data, makes reasonable predictions o te viscosity cange as a unction o iller concentration or all sear rates. However, prediction errors increase at ig iller loadings at 42 and 83 s -1. Te ocus o te analysis was on ig loadings above te percolation tresold. Relative viscosity estimates are plotted in Figure 2 or te MI LLDPE letdowns wit ~45µm 4-UL, ~5µm 5-FL and te 7/3 iller blend letdowns as a unction o sear rate and CaCO 3 concentration. Te table inset lists te model parameter estimates wit c ranging rom.14 to.22 and m rom.78 and.8. Percolating beavior and te trends wit iller type and concentration are consistent wit capillary reometer measurements. Wile absolute values are dierent te relative viscosities at 6 vol. % are similar, wit te 4-UL mixer value o 5.59, reometer 8.35, te 5-FL mixer 3.47, reometer 4.13, and te iller blend mixer 6.18, reometer Like te reometer, te batc mixer estimates relect te dierences between te untreated 4µm and te surace modiied 5µm CaCO 3 grades. SPE ANTEC Anaeim 217 / 115

8 / MB-4 4-UL MB-5 5-FL MB-6 7/3 Blend MB-4 Model MB-5 Model MB-6 Model MB4 MB5 MB6 φ m φ c A K Capillary 19 C, 5 s -1 4-UL FL 4.13 Blend /3 Blend Figure 2. MB-4, 5 and 6 LLDPE 982 / CaCO 3 batc mixer viscosity estimates and model curves. Following te same approac, batc mixer experiments were run wit te low viscosity MI LLDPE as exempliied in Table 4. Figure 21 plots viscosity data and estimates or te MI LLDPE letdowns wit ~45µm 4-UL, ~5µm 5-FL and te 7/3 iller blend letdowns as a unction o sear rate and CaCO 3 concentration. / Figure 21. MB-1, 2 and 3 LLDPE 128 / CaCO 3 batc mixer viscosity estimates and model predictions. Te table inset lists te model parameter estimates wit c ranging rom.14 to.22 and m rom.78 and.8. For te low viscosity LLDPE, te treated 5-FL CaCO 3 increased te viscosity at ig loadings relative to te untreated 4-UL and te 7/3 blend. Te model its wit 21 s -1 batc mixer data captured te trends wit small dierences in c and m. Batc mixer estimates were lower tan reometer values MB-1 4-UL MB-2 5-FL MB-3 7/3 Blend MB-1 Model MB-2 Model MB-3 Model Capillary 19 C, 5 s -1 5-FL Blend MB1 MB2 MB3 φ m φ c A K UL: 45µm FL: 5µm 5-FL: 5µm determine i it is robust and accurate as a viscosity measurement tool. Figure 22 plots LDPE/TiO 2 data and te itted percolation model curve using rom te ANTEC 216 paper [1]. Te same system was run in te present work, but under dierent conditions. A 65 vol. % masterbatc was produced on te ZSK-18mm extruder. Letdowns o MB-1 were made on te batc mixer at te same conditions used or te LLDPE/CaCO 3 systems. Table 5 lists batc mixer orce data and viscosity estimates using a k value or Eq. 7 o 23.3 verses 28.5 in te previous work. Te orce values were approximately double in tis work. Tis could be due to te dispersion state o te masterbatces, were te 65 vol. % concentrate was diicult to make on te extruder wit submicron TiO 2 particles. Furtermore, new screws were used in te batc mixer, reducing leakage lows over te ligt tips, increasing te orce. / rpm (18 1/s) rpm (35 1/s) 2rpm (7 1/s) Model Batcelor 2 = 1+.5φ φ r T = 155 o C, 18 s -1 φ C =.36 φ m =.98 ( φ C ) φm φ φ r = e 1 TiO 2 Volume % Figure 22. ANTEC 216 NA-26 LDPE/ TiO 2 batc mixer viscosity estimates and model predictions [1]. In te present work, te TiO 2 letdown concentration was extended to 6 vol. %, but ewer compositions were run to minimize te experimental workload. Figure 23 plots te MB-1 batc mixer letdown orce viscosity estimates and te percolation model curve itted to te 21 s -1 data. Te viscosity estimates are about double tose o te previous experiment. A deinitive cause o te dierences between experiments cannot be identiied. Reproducibility requires tat te same materials be used on te same equipment, run under identical conditions and preerably wit te same operator or identical protocols. Metod and Analysis Limitations Te igly illed polymers used in te experiments exibited reological percolation and a rapid rise in viscosity wit increasing solids concentration above c. Te experiments, model orms and itting routines are very sensitive to iller concentration at ig loadings. Te batc mixer test metod was re-evaluated to SPE ANTEC Anaeim 217 / 1151

9 / rpm (21 1/s) 12rpm (42 1/s) 24rpm (84 1/s) Batcelor (it) r = φ +8.33φ 2 T = 186 o C, 21 s -1 φ C =.15 φ m = /s ( φ C ) φm φ φ r = e 1 TiO 2 Volume % Figure 23. MB-1 NA-26 LDPE/ TiO 2 batc mixer viscosity estimates and model predictions. In order to capture te curvature o te viscosity increase at ig iller concentrations, more compositions are required tat were used in te present experiments. Furtermore, additional replicates are needed to quantiy and account or te variability witin a compositional state. Also, te apparent sear rate was used in all calculations. Applying a Rabinowitsc correction reduced te LLDPE resin viscosity by 2 to 5%, so it was ignored. Since n decreased wit increasing iller concentration, a more compreensive analysis would require estimating n at eac illed composition and applying te correction. For te LLDPE/CaCO 3 systems, it was recognized tat te 4-UL grade ad no surace treatment wile te smaller particle 5-FL material ad a surace modiier applied. Tis canged te surace energy or dispersion. Furtermore, it is likely tat an excess o surace modiier may ave ad a plasticizing eect on te iger molecular weigt LLDPE resins, causing a measurable reduction in viscosity as illustrated in Figure 6 and Figure 2. It was assumed tat untreated ~45µm particles could be dispersed suiciently in PE primarily rom sear and elongational stresses in te compounding extruder. Te smaller ~5µm particles were selected to increase te maximum packing o te 7/3 iller blend; only a surace modiied version was commercially available. Dispersion analysis was not conducted in tis study. Te percolation model is capable o capturing te eects o iller loading wit te rapid increase o melt viscosity, especially at ig concentrations. However, te power law index n did cange and tended to reduce wit increasing iller content as sown in Figure 8. Te Cross equation and percolation model do not account or tis cange. Te original percolation teory development assumed te luid to be Newtonian [4]. Te LLDPE resins and illed compounds were non- Newtonian. Te percolation model and te parameter itting minimization employed are sensitive to ow many data points are available in order to determine te percolation tresold and maximum packing values. Model parameters and viscosity estimates are useul wen working witin one system, but quantitative comparison could be inaccurate. As described earlier, tere is a discontinuity between te Batcelor and percolation models due to teir orm, ow muc data are available above and below c. Also, parameter estimates or and m tended to be ig. From packing teory, nonsperical particles and non-monodisperse particle size distributions can enable iger packing densities. Furtermore, te model itting metods wit limited data at ig iller concentrations likely contributed to tese ig values. One cannot draw deinitive conclusions to wat te actual maximum packing would be or tese systems or quantiy te morpology rom te reology and batc mixer experiments. Conclusions Melt blending tests were conducted on a batc mixer using LLDPE and two dierent CaCO 3 powders to determine te eects o iller size and type, concentration and operating conditions on te process reological response. Te experiments, reology measurements and viscosity models sowed: 1. Te experimental metod developed using a batc mixer correlated wit capillary reometer measurements. Wile batc mixer viscosity estimates did not matc te measurement data, te metod was able to quantiy dierences in te process response wit polymer molecular weigt, iller size and surace treatment. 2. All resins and illed compositions sowed seartinning power-law like beavior, especially at sear rates near and above te average values estimated or te batc mixer cannel. Estimates or te power law exponent n tended to decrease wit increasing iller loading, especially at ig iller loadings. 3. LLDPE molecular weigt ad a signiicant eect on te sape o te increase in viscosity wit CaCO 3 loading or all combinations tested. Te 16 MI LLDPE exibited little sensitivity to CaCO 3 particle size or surace treatment, wile te 2 MI LLDPE sowed a reduced increase in viscosity or te ~5µm surace treated CaCO 3 relative to te untreated ~45µm material and a 7/3 blend o te illers. 4. Te percolation model was used to it capillary reometer measurements and batc mixer viscosity estimates or te LLDPE/CaCO 3 and LDPE/TiO 2 systems. Wit limitations, te model captured te sapes o te viscosity increases wit iller loading on a system-by-system basis. teory and te experimental metod employed are useul tools or gaining insigts into te beavior o igly illed polymer systems during melt processing operations. SPE ANTEC Anaeim 217 / 1152

10 Reerences 1. M. D. Wetzel, D. R. Pettitt, Jr., G. A. Campbell, Development o a Predictive Power Law Relationsip or Concentrated Slurries, Part 2: Experiment and Processing Implications, SPE ANTEC 216, Indianapolis, IN, May G. A. Campbell, M. E. Zak, J. S. Radakrisnan, M. D. Wetzel, Development o a Predictive Power Law Relationsip or Concentrated Slurries, Part 1: Teory, SPE ANTEC, Indianapolis, IN, May, G. A. Campbell, M. D. Wetzel, Caracterizing te Flow o Slurries using Teory Based Functions, Polym Eng Sci. doi:1.2/pen Sept. 13, G. A. Campbell, G. Forgacs, Pysical Review A Volume 41, Number 8, 15 April D. J. Cumberland, R. J. Craword, Handbook o Power Tecnology, Volume 6: Te Packing o Particles, Elsevier, Amsterdam, 1987, pp A. J. Poslinski, R. K. Gupta, et al., Journal o Reology, 32(B), (1988). 7. J. M. Dealy, K. F. Wissbrun, Melt Reology and its Role in Plastics Processing, Capman & Hall, New York, 1995, Niedenzu, P. M., Sedar, Jr., W. T., Wetzel, M. D., Hig Solids Viscosity or TiO 2 Masterbatc, SPE Color and Appearance Division RETEC, 211. Table 3. MB-4 LLDPE 982/4-UL CaCO 3 batc mixer barrel orce and melt temperature data and viscosity estimates. Te batc mixer could not be run at 12 and 24 RPM. Screw RPM: : φ # CaCO 3 (wt.%) CaCO 3 (vol %) 1 % % % 1% % 2% % 3% % 4% % 5% % 6% Avg: K orce : 9.7 Max: Min: Di: Table 4. MB-1 LLDPE 128/4-UL CaCO 3 batc mixer barrel orce and melt temperature data and viscosity estimates. Screw RPM: : φ # CaCO 3 (wt.%) CaCO 3 (vol %) 1 % % % 1% % 2% % 3% % 4% % 5% % 6% Avg: K orce : 7. Max: Min: Di: SPE ANTEC Anaeim 217 / 1153

11 Table 5. MB-1 LDPE/TiO 2 batc mixer barrel orce and melt temperature data and viscosity estimates. Screw RPM: : φ # TiO 2 (wt.%) TiO 2 (vol %) 1 % % % 1% % 2% % 3% % 4% % 5% % 6% Avg: K orce : Max: Min: Di: Te advice contained erein is based upon tests and inormation believed to be reliable, but users sould not rely upon it absolutely or speciic applications since perormance properties will vary wit processing conditions. It is given and accepted at user s risk and conirmation o its validity and suitability in particular cases sould be obtained independently. Te autors and teir ailiate entities make no guarantees o results and assume no obligation or liability in connection wit its advice. Tis publication is not to be taken as a license to operate under, or recommendation to inringe, any patents. SPE ANTEC Anaeim 217 / 1154