Modelling-aided development of a RheoDSC, an instrument Modelling-aided development of a RheoDSC, an instrument for simultaneous rheological and calorimetric measurements G. Van Assche, R. Verhelle , L. Van Lokeren, C. Block, Vrije Universiteit Brussel, Physical Chemistry & Polymer Science, Pleinlaan 2, 1050 Brussels, Belgium, [email protected] Vrije Universiteit Brussel, Physical Chemistry & Polymer Science, Pleinlaan 2, 1050 Brussels, Belgium, [email protected] Introduction Introduction Introduction Introduction Transformations in polymers, such as polymerisation, Transformations in polymers, such as polymerisation, melting/crystallization, and phase separation/remixing, are associated with changes in both rheological and thermal properties. To permit simultaneous calorimetric and properties. To permit simultaneous calorimetric and rheometric measurements, the RheoDSC was developed. The RheoDSC combines two commercial instruments, a TA The RheoDSC combines two commercial instruments, a TA Instruments Q2000 DSC and a TA Instruments AR-G2 dynamic rheometer. A rheological measurement is Fig Fig Fig Fig. 1: RheoDSC RheoDSC RheoDSC RheoDSC setup setup setup setup: (left) (left) (left) (left) rotor rotor rotor rotor assembly assembly assembly assembly with with with with connection connection connection connection towards towards towards towards the the the the rheometer rheometer rheometer rheometer permitting permitting permitting permitting rotor rotor rotor rotor alignment, alignment, alignment, alignment, (middle) (middle) (middle) (middle) DSC DSC DSC DSC cell cell cell cell and and and and rotor rotor rotor rotor assembly assembly assembly assembly showing showing showing showing the the the the off off off off-centered centered centered centered positioning positioning positioning positioning of of of of performed on a sample sitting on a sample plate that is on top of the DSC sensor platform. This plate is fixed using insulated screws on an aluminium insert that sits around the the the the the DSC DSC DSC DSC cell cell cell cell compared compared compared compared to to to to the the the the rotor, rotor, rotor, rotor, and and and and (right) (right) (right) (right) DSC DSC DSC DSC sensor sensor sensor sensor platform platform platform platform with with with with stator stator stator stator assembly, assembly, assembly, assembly, sample, sample, sample, sample, and and and and rotor rotor rotor rotor (right) (right) (right) (right). Fig Fig Fig Fig. 2: (left) (left) (left) (left) Meshed Meshed Meshed Meshed geometry geometry geometry geometry with with with with about about about about 36000 36000 36000 36000 elements, elements, elements, elements, (right) (right) (right) (right) Mesh Mesh Mesh Mesh quality quality quality quality depicted depicted depicted depicted for for for for the the the the 5 % worst worst worst worst elements elements elements elements. insulated screws on an aluminium insert that sits around the base of the DSC sensor. The setup shown in Fig. 1. Finite Element modelling Finite Element modelling Finite Element modelling Finite Element modelling Through heat transfer modelling with COMSOL we Through heat transfer modelling with COMSOL we successfully optimized the design and the material selection. All finite element simulations were performed using Comsol 0.5 No Rotor Multiphysics v4.2 using the Heat transfer module and the Chemical reaction engineering module. The transient simulations were conducted with a direct PARDISO solver -1 -0.5 0 R / K 8.0 mm tower simulations were conducted with a direct PARDISO solver and backward differentiation formula (BDF) on a Windows XP 64 bit computer with an Intel® Core™ 2 Quad Q9550 @ -1.5 0 K PAI PU-foam -2 -1.5 -1 Δ Δ Δ Δ T SR 2.83 GHz processor and 16 GB RAM memory. The total assembly has approximately 36000 elements (Fig.2). -4.5 -3 Δ Δ Δ Δ T SR / K PAI -2.5 0 1000 2000 3000 time/s no tower For the optimization of the instrument design, DSC Comsol Comsol Comsol Comsol-aided design optimization aided design optimization aided design optimization aided design optimization -6 -4.5 0 1000 2000 3000 Pyrex Fig Fig Fig Fig. 3 Reduction Reduction Reduction Reduction of of of of the the the the thermal thermal thermal thermal lag lag lag lag in in in in RheoDSC RheoDSC RheoDSC RheoDSC by by by by placing placing placing placing a cylinder cylinder cylinder cylinder in in in in PAI, PAI, PAI, PAI, the the the the rotor rotor rotor rotor material, material, material, material, on on on on the the the the reference reference reference reference side side side side to to to to equilibrate equilibrate equilibrate equilibrate the the the the unbalance unbalance unbalance unbalance. For the optimization of the instrument design, DSC experiments were simulated using Comsol. Simulations were made for reacting or crystallizing samples by including 0 1000 2000 3000 time/s 0.35 K PAI PU-foam (top) (top) (top) (top) Geometrical Geometrical Geometrical Geometrical model model model model depicting depicting depicting depicting PAI PAI PAI PAI towers towers towers towers of of of of different different different different heights heights heights heights on on on on the the the the reference reference reference reference sensor sensor sensor sensor. (bottom) (bottom) (bottom) (bottom) Temperature Temperature Temperature Temperature difference difference difference difference between between between between sample sample sample sample and and and and reference reference reference reference sensor, sensor, sensor, sensor, ΔT T T SR SR SR SR , for for for for the the the the cure cure cure cure of of of of a thermosetting thermosetting thermosetting thermosetting resin resin resin resin made for reacting or crystallizing samples by including suitable models for the transformation kinetics. In this way, the simulated ‘measured heat flux’ can be compared to the 0.15 0.25 T no_reaction /K Pyrex PAI Al 2 0 3 SR SR SR SR for for for for different different different different tower tower tower tower heights heights heights heights (no (no (no (no tower, tower, tower, tower, 0.4 mm, mm, mm, mm, 1 mm, mm, mm, mm, 2 mm, mm, mm, mm, 4 mm, mm, mm, mm, 6 mm mm mm mm and and and and 8 mm) mm) mm) mm) of of of of PAI PAI PAI PAI towers towers towers towers on on on on the the the the reference reference reference reference sensor sensor sensor sensor side side side side and and and and for for for for comparison comparison comparison comparison a setup setup setup setup with with with with no no no no rotor rotor rotor rotor on on on on the the the the sample sample sample sample (heating (heating (heating (heating from from from from 25 25 25 25 °C to to to to 250 250 250 250 °C at at at at 5 K min min min min -1 ). heat release in the sample to evaluate thermal lag and peak distortions. - Thermal lag simulations (Fig. 3): 0.05 0.15 T reaction - Δ Δ Δ Δ T Al sample sample (heating (heating from from 25 25 C to to 250 250 C at at 5 K min min ) . - Thermal lag simulations (Fig. 3): In a heat flux type DSC, the heat flow rate to the sample is obtained by multiplying the temperature difference between -0.05 0 1000 2000 3000 time/s Δ Δ Δ Δ the sample and reference sensors with a calibration factor. Thermal lag is observed when going from an isothermal to a heating segment. It is due to a different time constant for heat Fig Fig Fig Fig. 4 : Simulations Simulations Simulations Simulations for for for for selecting selecting selecting selecting the the the the rotor rotor rotor rotor material material material material (top) (top) (top) (top) Temperature Temperature Temperature Temperature distributions distributions distributions distributions in in in in the the the the RheoDSC RheoDSC RheoDSC RheoDSC setup setup setup setup for for for for different different different different rotor rotor rotor rotor materials materials materials materials for for for for an an an an isothermal isothermal isothermal isothermal at at at at 100 100 100 100 °C. heating segment. It is due to a different time constant for heat transfer on sample and reference side. The high heat capacity and low thermal conductivity of the rotor cause a (mid) (mid) (mid) (mid) Temperature Temperature Temperature Temperature difference difference difference difference between between between between sample sample sample sample and and and and reference reference reference reference sensor, sensor, sensor, sensor, ΔT T T SR SR SR SR , for for for for different different different different types types types types of of of of rotor rotor rotor rotor materials materials materials materials. Simulation Simulation Simulation Simulation of of of of non non non non-isothermal isothermal isothermal isothermal cure cure cure cure experiments experiments experiments experiments of of of of a thermosetting thermosetting thermosetting thermosetting epoxy epoxy epoxy epoxy amine amine amine amine (25 25 25 25 °C to to to to 250 250 250 250 °C at at at at 5 K min min min min -1 ). slow equilibration and a considerable baseline shift upon heating. Both can be reduced by balancing sample and reference side by placing a PAI tower on it. (below) (below) (below) (below) Contribution Contribution Contribution Contribution of of of of the the the the reaction reaction reaction reaction exotherm exotherm exotherm exotherm to to to to ΔT T T SR SR SR SR . -0.5 0 1 120 No Rotor reference side by placing a PAI tower on it. - Rotor material (Fig. 4) Different rotor materials were evaluated for isothermal and -1.5 -1 -0.5 ate / W.g -1 40 80 1.25 mm CROSS Different rotor materials were evaluated for isothermal and nonisothermal conditions. For more conductive materials, more heat will flow into the rotor, leading to an important baseline in nonisothermal experiments. Subtracting the -0.5 0 0.5 1.75 mm CROSS no rotor -3 -2.5 -2 eat flow ra -40 0 / °C 1.25 mm baseline in nonisothermal experiments. Subtracting the baseline shows that the reaction exotherm observed in ΔT SR is only slightly deformed for PAI. -1.5 -1 -0.5 Δ Δ Δ Δ T SR / K 0.75 mm 1.25 mm CROSS -3.5 -3 300 1300 2300 time/s He -80 T No Holes EXO DOWN is only slightly deformed for PAI. - Rotor design (Fig. 5) To further reduce the heat conduction from the sample to the -2.5 -2 -1.5 plain time/s -0.2 0 W.g -1 80 120 No Rotor rotor, small holes were drilled in the lower section of the rotor. For crossed holes of 1.75 mm, the baseline offset is strongly reduced, as less rotor material is heated up. -2.5 0 1000 2000 3000 time/s -0.4 -0.2 ow rate / W 0 40 No Holes 1.25 mm No Rotor CROSS reduced, as less rotor material is heated up. - Validation (Fig. 6) Experiments with the different rotor designs for the Fig Fig Fig Fig. 5: Simulations Simulations Simulations Simulations for for for for optimizing optimizing optimizing optimizing the the the the rotor rotor rotor rotor geometry geometry geometry geometry. (top) (top) (top) (top) Geometrical Geometrical Geometrical Geometrical representation representation representation representation of of of of modified modified modified modified PAI PAI PAI PAI rotors rotors rotors rotors. (mid) (mid) (mid) (mid) Simulated Simulated Simulated Simulated temperature temperature temperature temperature distributions distributions distributions distributions in in in in the the the the RheoDSC RheoDSC RheoDSC RheoDSC setup setup setup setup for for for for a PAI PAI PAI PAI rotor rotor rotor rotor with with with with two two two two perpendicular perpendicular perpendicular perpendicular holes holes holes holes with with with with a -0.6 -0.4 Heat flo -80 -40 T / °C 1.25 mm EXO DOWN crystallization of an ethylene-vinyl acetate copolymer confirm the strong reduction of the baseline offset using the crossed holes rotor as well as the limited differences in peak radius radius radius radius of of of of 0.75 75 75 75 mm, mm, mm, mm, 1.25 25 25 25 mm, mm, mm, mm, and and and and 1.75 75 75 75 mm, mm, mm, mm, and and and and a rotor rotor rotor rotor with with with with two two two two levels levels levels levels of of of of holes holes holes holes in in in in a cross cross cross cross pattern pattern pattern pattern (cross) (cross) (cross) (cross) indicated indicated indicated indicated with with with with the the the the pictogram, pictogram, pictogram, pictogram, simulated simulated simulated simulated for for for for an an an an isothermal isothermal isothermal isothermal at at at at 100 100 100 100 °C. (below) (below) (below) (below) Temperature Temperature Temperature Temperature difference difference difference difference ΔT T T SR SR SR SR for for for for the the the the different different different different rotor rotor rotor rotor 300 1300 2300 time/s Fig Fig Fig Fig. 6.: .: .: .: Heat Heat Heat Heat flow flow flow flow rate rate rate rate signal signal signal signal for for for for a cooling cooling cooling cooling experiment experiment experiment experiment of of of of semi semi semi semi holes rotor as well as the limited differences in peak distortion. SR SR SR SR designs designs designs designs. Simulation Simulation Simulation Simulation of of of of non non non non-isothermal isothermal isothermal isothermal cure cure cure cure experiments experiments experiments experiments of of of of a thermosetting thermosetting thermosetting thermosetting epoxy epoxy epoxy epoxy amine amine amine amine (25 25 25 25 °C to to to to 250 250 250 250 °C at at at at 5 K min min min min -1 ). crystalline crystalline crystalline crystalline polymer polymer polymer polymer (EVA (EVA (EVA (EVA 33 33 33 33) from from from from 100 100 100 100 °C at at at at 5 K.min min min min -1 towards towards towards towards -60 60 60 60 °C with with with with the the the the different different different different rotor rotor rotor rotor setups setups setups setups without without without without (top) (top) (top) (top) and and and and with with with with (bottom) (bottom) (bottom) (bottom) subtracting subtracting subtracting subtracting a baseline baseline baseline baseline. This project was in collaboration with Prof. P. Van Puyvelde (KULeuven) and was supported by TA Instruments, FWO (Vlaanderen) and IWT (Vlaanderen). Excerpt from the proceedings of the 2015 COMSOL Conference in Grenoble