This letter presents an experimental study and the associated numerical modeling of fast-curing, thermosetting droplets spreading on a heated surface. The results show a significant morphological dependence of the spreading droplets of Ecoflex 0050 (a heat-sensitive, platinum-catalyzed silicone material) on thermal conditions. Differential scanning calorimetry and rheometry provide quantifiable data for modeling the cure kinetics and rheological properties of the material. This work demonstrates an approach to developing a phenomenological model suitable for predicting the morphological variation of fast-curing, thermosetting materials without prior knowledge of their chemical composition. The developed multiphysics models for cure kinetics and chemorheology can serve as a functional tool for predictions requiring accurate dimensional control of free-forming thermosetting materials, such as nozzle-based additive manufacturing, centrifugal coating and forming, fabrication of soft robots, and soft lithography.
|Original language||English (US)|
|Journal||Applied Physics Letters|
|State||Published - Dec 16 2019|
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- Physics and Astronomy (miscellaneous)
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Spreading of fast-curing, thermosetting silicones. / Xie, Jingjin; Randolph, Robert; Simmons, Gary et al.In: Applied Physics Letters, Vol. 115, No. 25, 253701, 16.12.2019.
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TY - JOUR
T1 - Spreading of fast-curing, thermosetting silicones
AU - Xie, Jingjin
AU - Randolph, Robert
AU - Simmons, Gary
AU - Vinciguerra, Michael
AU - Suri, Sahil
AU - Bonini, Nicholas
AU - Root, Anna
AU - Hull, Patrick V.
AU - Mazzeo, Aaron D.
N1 - Funding Information: https://orcid.org/0000-0002-2204-5862 Xie Jingjin 1 https://orcid.org/0000-0002-5580-3631 Randolph Robert 1 Simmons Gary 1 https://orcid.org/0000-0003-1612-4676 Vinciguerra Michael 1 https://orcid.org/0000-0003-1612-4676 Suri Sahil 1 Bonini Nicholas 1 https://orcid.org/0000-0002-0463-7514 Root Anna 1 Hull Patrick V. 2 https://orcid.org/0000-0002-1565-7481 Mazzeo Aaron D. 1 a) 1 Department of Mechanical and Aerospace Engineering, Rutgers University , Piscataway, New Jersey 08812, USA 2 NASA Marshall Space Flight Center , Huntsville, Alabama 35811, USA a) Author to whom correspondence should be addressed: firstname.lastname@example.org 16 12 2019 115 25 253701 30 05 2019 12 11 2019 18 12 2019 2019 Author(s) Published under license by AIP Publishing. 0003-6951/2019/115(25)/253701/5/ $30.00 This letter presents an experimental study and the associated numerical modeling of fast-curing, thermosetting droplets spreading on a heated surface. The results show a significant morphological dependence of the spreading droplets of Ecoflex 0050 (a heat-sensitive, platinum-catalyzed silicone material) on thermal conditions. Differential scanning calorimetry and rheometry provide quantifiable data for modeling the cure kinetics and rheological properties of the material. This work demonstrates an approach to developing a phenomenological model suitable for predicting the morphological variation of fast-curing, thermosetting materials without prior knowledge of their chemical composition. The developed multiphysics models for cure kinetics and chemorheology can serve as a functional tool for predictions requiring accurate dimensional control of free-forming thermosetting materials, such as nozzle-based additive manufacturing, centrifugal coating and forming, fabrication of soft robots, and soft lithography. National Science Foundation https://doi.org/10.13039/100000001 1610933 Marshall Space Flight Center https://doi.org/10.13039/100006197 NNX16AG17A-439573 Rutgers, The State University of New Jersey https://doi.org/10.13039/100011132 crossmark Comprehensive understanding of the solidification of free-forming, thermosetting materials is still an open challenge. Spreading of noncuring liquids (e.g., water, silicone oil, and liquid metal) and curing of thermosetting polymers [e.g., polyurethane, polydimethylsiloxane (PDMS), and epoxies] have established relationships and experiments describing their corresponding physics. 1–6 However, there are no available physical models that capture simultaneous spreading and fast curing of thermosetting polymers, which involve multiple couplings of physical phenomena (i.e., liquid wetting, thermal mechanics, and cure kinetics). Curing is a chemical reaction that converts a polymeric material from a liquid or quasisolid state to a solid state by cross-linking individual polymer chains and forming a network of covalent bonds. It is usually an exothermic process where the amount of heat released during cross-linking can vary by orders of magnitude, dependent upon the cross-linking mechanism, the involved chemical chains, and the bond energies. For example, the curing of silicones is usually a low exothermic reaction, while the curing of epoxies is usually a considerable exothermic reaction. The chemical composition of thermosets dictates whether curing will depend primarily on heat, radiation, pressure, moisture, or change in pH. 7 Fast-curing thermosets are ideal for fabricating devices; however, in nonideal conditions, such as low temperature, reduced power density of UV, or uneven absorption of moisture, the curing rate could be very low. Likewise, a slow-curing thermosetting system may have the potential to work with additive manufacturing (AM) in accelerated curing conditions (e.g., optimized thermal or UV conditions). Differential scanning calorimetry (DSC) is a well-developed experimental method to characterize the cure extent. 8 We quantified the cure extent by normalizing the incremental change in enthalpy to the total change in enthalpy during the exothermic cross-linking reaction, α = Δ H Δ H total , (1) where Δ H is the partial heat of reaction during the curing process and Δ H total is the total heat of reaction. The value of α is normalized to [0, 1] with 1 representing the fully cured state and 0 representing the “zero” cure extent. The intermediate cure extent α t at different time steps has the following representation: α t = 1 Δ H total ∫ 0 t d H d s d s . (2) The quantification and modeling of viscosity as a function of cure extent require further development. For noncuring liquids, parameters that dictate the shear rate ( γ ̇ ) and shear stress ( σ ) and thus dynamic viscosity ( η ) are η = σ γ ̇ . (3) Thus, a systematic way to express such a model becomes η = T , P , γ ̇ , t , F , (4) where T is the temperature, P the pressure, γ ̇ the shear rate, t the time, and F the filler properties. However, it is challenging to adopt such a mechanistic approach as it requires thorough and accurate characterizations of modeling parameters. Chemorheological modeling provides a tool to understanding the rheological properties of a thermosetting system. One possible model for the viscosity of a thermosetting material is the Castro-Macosko model, 9 η = η ∞ exp E η R T α gel α gel − α A + B α , (5) where η ∞ is the long-term viscosity, E η is the activation energy for viscosity, R is the ideal gas constant, α gel is the cure extent at the gel point of the material, and A and B are two temperature-dependent constants obtained by fitting the experimental data. This work aims to understand spreading behavior on a heated flat surface through experimentation, phenomenological modeling, and numerical simulations. We used Ecoflex 0050 (Smooth-On Inc., PA)—a fast-curing, platinum-catalyzing silicone—as our sample thermosetting material. We monitored its morphological changes at temperatures ranging from 40 to 160 °C on a goniometric platform and then performed DSC and rheological measurements to develop models describing the time-temperature-dependent curing reaction and rheological evolution. The numerical simulations consider the rheological characteristics and cure kinetics, along with inertial, viscous, capillary, and contact-line forces from incompressible Navier–Stokes theory. The experimental results on the curing and spreading of thermosetting droplets will facilitate further understanding of material processing in (1) additive manufacturing, which requires extruded beads and lines; 10 (2) coating of films on substrates with varying surface properties; 11 and (3) soft robotics, which primarily relies on three-dimensional (3D) components made of thermosetting polymers. 12–15 Potential applications for rapidly cured thermosetting resins include additive manufacturing (AM), 16 producing hybrid 3D printed structures to form structurally composite parts for microelectromechanical (MEMS) devices, 17–22 and fabricating silicone-based, stretchable sensors, 23 locomotors, 15 and actuators. 24 Figure 1(a) depicts the experimental setup for monitoring the curing droplet dispensed onto a temperature-controlled surface using a 22-gauge (0.64 mm) straight steel tip (Nordson EFD, RI). The substrate used in this study was a rigid, temperature-controlled piece of aluminum 6061 coated with a thin polyimide film. Supplementary material Fig. 1 shows the goniometric platform used for monitoring the evolution of curing droplets/beads. A high-precision dispensing controller (Performus II, Nordson EFD) and a two-component, in-line mixing and dispensing system (2K Equalizer, Nordson EFD) generated droplets with repeatable size. A dual cartridge contained equal volumes 25 of the base and crosslinker of Ecoflex 0050 separately. To ensure the homogeneity and the same low-curing state of the mixture, we attached a static mixer with 24 mixing elements directly to the dual cartridge. Prior to filling both the base and crosslinker of Ecoflex 0050 into the dispensing cartridge, we degassed the material in vacuum for 5 min to avoid the formation of bubbles. The dispensed fluids went through the mixing elements and then immediately formed droplets at the dispensing tip. The dispensing pressure of Ecoflex 0050 was 20 psi, and the dispensing time was 2 s, which resulted in an average droplet volume of 2.9 ul. In our experiments, the detachment of liquid occurred after the droplet reached the surface with minimal impact force and a negligible effect on the initial shape of the droplet. FIG. 1. (a) Diagram of the experimental setup for dispensing a droplet of Ecoflex 0050 onto a heatbed. (b) Images of droplets spreading at 40, 80, 120, and 160 °C. (c) Plotted change in the diameter of droplets as a function of time. (d) Plotted change in the height of droplets as a function of time. The error bars in (c) and (d) indicate one standard deviation of seven repeated measurements at each temperature. The droplets consistently showed axisymmetric profiles based on experimental visual observations. At increasing temperatures from 40 to 160 °C, the cure rate of the thermosetting droplet increases. Figure 1(b) and supplementary material Video 1 show the monitored morphological change of Ecoflex 0050 at varying temperatures. By using image processing techniques in MATLAB, we measured the diameter and height of spreading droplets as a function of time [ Figs. 1(c) and 1(d) ]. As expected, at higher temperatures, the diameter ceased to increase as Ecoflex 0050 cured quickly at the contact surface. To characterize the cure kinetics of Ecoflex 0050, we used DSC (Q2000, TA Instruments) for measuring the heat of reaction, which reflects the extent of cure of thermosetting materials; DSC also measured the heat capacity at constant pressure. During measurements, we first dispensed a drop with a measured mass ranging from 6 to 10 mg into an aluminum crucible (Tzero, TA Instruments). We placed both the sample crucible and reference crucible in the measurement chamber and then started isothermal measurements. Ecoflex 0050 takes approximately 8 h at room temperature (25 °C) but only minutes at an elevated temperature to cure fully. Therefore, rapid loading and unloading of samples became very important to avoid the loss of recorded heat of reaction during isothermal DSC measurements. In this work, we started from 40 °C and increased the temperature by increments of 5 °C up to 60 °C. For isothermal measurements above 60 °C, the loss of recorded heat of reaction became significant during loading and unloading samples, and curing profiles became inaccurate. Future efforts to characterize the cure kinetics above 60 °C might employ dynamic scanning calorimetry instead of isothermal characterization. We conducted rheological measurements (Kinexus Ultra+, Malvern Instruments) to monitor the change of viscosity at varying temperatures. We adopted the “parallel-plate method” with two 25-mm-diameter plates sandwiching Ecoflex 0050 samples. The oscillating frequency was 1 Hz, while the shear strain was 1% in all the isothermal measurements. In the dynamic measurements, which we used to obtain the activation energy for modeling the evolution of viscosity, the temperature increased from 25 to 150 °C with heating rates of 1, 2, 5, and 10 °C/min. In general, the DSC data of curing thermosetting systems with smooth transitions can fit well into basic models for cure kinetics; multiple models 26–29 exist describing cross-linking reactions, which typically account for the cure kinetics of epoxy-type thermosetting materials. However, fast-curing thermosets, such as Ecoflex 0050, present a different curing behavior; they start with a low reaction rate to ensure sufficient operation time and then proceed with a much higher reaction rate to the fully cured state. In this work, we proposed a model by superposing basic n-th order models and autocatalytic models to describe the curing behavior of Ecoflex 0050. These phenomenological methods profile the cure kinetics of the thermosetting resin and may be applicable to other systems as well. The proposed model has a form shown in the following equation: d α d t = k 1 + k 2 α l + k 3 α m 1 − α 2 n (6) and k i = A i exp − E a i R T , (7) where l, m, and n are temperature-dependent exponents; A i is a temperature-dependent, pre-exponent factor; and E a i is the activation energy fitted from the DSC results. This model accounts for the three regimes [i.e., the onset, the plateau, and the peak of cure rate visible in Fig. 2(b) ]. FIG. 2. (a) Measured heat flow as a function of time in a dynamic DSC scan. The temperature ranged from 25 to 150 °C; (b) plotted heat flow as a function of time from DSC measurements of Ecoflex 0050; (c) plotted cure extent as a function of time; (d) plotted cure rate as a function of α from isothermal DSC measurements of Ecoflex 0050. We performed nonlinear data fitting with the Levenberg-Marquardt iteration algorithm using Origin (V2018, OriginLab). This step yielded the temperature-dependent exponents ( l, m , and n ) and coefficients, k i . By taking the logarithm of both sides of Eq. (6) , we generated a series of Arrhenius plots of ln ( k i ) vs ln ( A i ) , and the slope of these straight lines yielded the activation energy, E a i . As introduced earlier, this model assumed a constant activation energy, and a dynamic scan from 25 to 150 °C provided the total heat of reaction ΔH = 1.16 J/g [see Fig. 2(a) ]. Table I lists the fitted parameters for the proposed model. Figure 3(a) shows the comparison between the modeled and measured cured extent as a function of time at varying temperatures. TABLE I. Parameters calibrated from isothermal measurements of DSC for Ecoflex 0050. Parameter Value Unit Note A 1 5.49 × 10 10 1/s Pre-exponential constant A 2 1.51 × 10 16 1/s Pre-exponential constant A 3 1.05 × 10 21 1/s Pre-exponential constant E a 1 83.80 kJ / mol Activation energy E a 2 112.21 kJ / mol Activation energy E a 3 130.65 kJ / mol Activation energy L 2 1 Exponent m ( T ) 6073.7/T (K) − 14.52 1 Temperature-dependent exponent n ( T ) −6837.6/T (K) + 23.78 1 Temperature-dependent exponent FIG. 3. Comparison of (a) measured and modeled cure extent as a function of time and (b) measured and modeled viscosity as a function of cure extent for Ecoflex 0050. Dynamic rheological measurements of Ecoflex 0050 show the evolution of viscosity and shear moduli when the temperature increased from 25 to 100 °C at heating rates of 1, 2, 5, and 10 °C/min. The overall results showed that Ecoflex 0050 had a maximum shear viscosity of 6300 Pa⋅s and a minimum shear viscosity of 5.09 Pa⋅s [see Fig. 4(a) ], a negligible increase compared with its initial viscosity of 5 Pa⋅s. For simplicity, we assume a monotonic increase in the viscosity of Ecoflex during the curing process. The measured viscoelastic properties also revealed the key properties of the curing Ecoflex. The gel point appears at different temperatures for varying heating rates, but the shear moduli were consistently 418 Pa. When fully cured, Ecoflex 0050 demonstrated a maximum storage modulus of 40 000 Pa and a maximum loss modulus of 2300 Pa. FIG. 4. Plotted results from dynamic rheological measurements of Ecoflex 0050: (a) complex viscosity and (b) storage modulus ( G′ ) and loss modulus ( G″ ) as a function of temperature. As described earlier, the Castro-Macosko model is primarily for modeling viscosity in mold-based fabrication of thermosetting materials. Nevertheless, this model only accounts for the cure extent up to the gel point, as the processability/flowability of the curing thermoset is the primary concern in mold-based manufacturing. Their model encounters a singular point when the cure extent approaches the gel point. For additive manufacturing, it is plausible to extend this model to the maximum cure extent (i.e., close to 1) to reflect the solidification of extruded materials. A modified chemorheological model has a form as follows: η = η ∞ exp E η R T C 1 − α A + B α , (8) where η ∞ is the long-term viscosity, E η is the activation energy of flow, C is the constant fitted from the experimental value, and A and B are two temperature-dependent constants obtained by fitting the experimental data. Table II lists the fitted parameters for Ecoflex 0050 based on Eq. (8) . Figure 3(b) shows the comparison between the measured and modeled viscosity as a function of cure extent. TABLE II. Fitted parameters for cure kinetics and the modified Castro-Macosko model. Parameter Value Unit Note η ∞ 1 Pa⋅s Pre-exponential constant E η 614.76 kJ/mol Activation energy of flow A ( T ) −24.65 + 0.118T (1/K) 1 Temperature-dependent exponent B ( T ) 22.7 − 0.105T (1/K) 1 Temperature-dependent exponent C 1 1 Constant We considered the uncured/curing thermoset precursor as an incompressible, Newtonian fluid and utilized COMSOL Multiphysics (V5.3, COMSOL, Inc.) to implement the numerical simulation and considered a 2D axisymmetric case in which the spreading of a droplet had a perfect axisymmetric profile (see the supplementary material Fig. 4 ). The governing equations include the Navier–Stokes (N–S) equation for an incompressible fluid, ρ ∂ u ∂ t + ρ u ⋅ ∇ u = ∇ ⋅ − p I + μ ∇ u + ∇ u T + F st + ρ g , (9) ρ ∇ ⋅ u = 0 , (10) where ρ is the density of fluid, u the velocity field, μ the dynamic viscosity of fluid, t the time, p the pressure of fluid, F st the surface tension, g the gravity, and I the identity matrix. As heat transfer in this work is primarily governed by conduction, we coupled a heat conduction equation with the N−S equation, ρ C p u ⋅ ∇ T + ∇ ⋅ − k ∇ T = ρ Δ H d α d t , (11) where C p is the heat capacity of the liquid, k is the thermal conductivity of the liquid, Δ H is the enthalpy involved in the curing process of the thermosetting resin, and d α d t is the curing rate. To predict the hydrodynamic behavior of the curing liquid, we used the phase field method to model the evolution of the air−liquid interface. Specifically, this method solved the Cahn–Hilliard equation to resolve a phase variable representing the transition from one phase to the other. The Cahn–Hilliard equations have the following form: ∂ ϕ ∂ t + ∇ ⋅ u ϕ = ∇ ⋅ γ ∇ G , (12) where ϕ is the phase field variable, γ is the interface thickness, λ is the mixing energy density, G is the chemical potential. Figures 5(a)–5(d) show the simulated spreading of the noncuring and curing droplets from t = 0 to t = 60 s. The developed model for cure kinetics only existed in the curing droplets, while the noncuring droplets used the constant viscosity of the base of Ecoflex in the simulations. It presents a series of phenomena that occurred in the experiments, including initial contact with the heatbed, initial spreading and pinching of the liquid, detachment from the nozzle, and the synergistic curing–spreading effect. The results simulated mostly agree with the experimental results as plotted in Fig. 5(e) . The simulation slightly overpredicted the results at low temperatures (i.e., 40 °C) and showed good agreement when the temperature reached 80 °C. When the temperature is above 80 °C, the simulation was difficult to converge because of the lack of accurate DSC data at elevated temperatures. The dynamic contact angle (DCA) model also assigned varying contact angles in the simulation at each time step, based on the calculated capillary number, Ca . In addition, after implementing the techniques for conserving the dimensionless field variable, ϕ , it maximally conserved the mass with a loss less than 0.1%. Supplementary material Video 2 shows the evolution of the cure extent for a droplet of Ecoflex 0050 spreading without a dynamic contact angle from 0 to 50 s on a surface set to 60 °C. FIG. 5. (a)–(d) Simulated morphological change of noncuring and curing Ecoflex 0050. (e) Plotted experimental and simulated diameters as a function of time. In this work, we have shown that models based on cure kinetics and chemorheology can provide essential predictions of curing and spreading of fast-curing silicones. A soft silicone (Ecoflex 0050) served as the test material to obtain models for cure kinetics and viscosity. The developed models align with isothermal and dynamic measurements made from DSC and rheology. The DSC monitored the change in the heat of reaction, which reflects the rate and degree of cure at different cross-linking stages. Rheological measurements quantified changes in complex viscosity, shear moduli, and yield stress. By combining DSC and rheological measurements, we profiled the cure kinetics and chemorheology without prior knowledge of chemical composition. With the developed models, we numerically simulated the evolving morphology of the droplets. The models developed in this work provide a technique to predict the spreading behavior of curing, thermosetting liquids in coating processes, or extrusion-based additive manufacturing in varying gravitational fields. See the supplementary material for the details concerning the experimental platform, thermogravimetric analysis of Ecoflex 0050, dynamic contact angle, change of contact angle vs curing, setup of the simulations, and videos for experimental and simulated spreading of droplets. The authors acknowledge support from NASA (No. NNX16AG17A-439573), the National Science Foundation (No. 1610933), the NASA Marshall Space Flight Center Faculty (MSFC) Fellows program, the NASA MSFC Summer Internship Program, and the Rutgers Honors College. Malvern Instruments provided the equipment for rheological measurements in Professor Richard Haber's lab, and the authors thank John Casola and Chuck Rohn at Malvern Instruments for the helpful suggestions concerning rheological measurements. The authors also thank Jason Waggoner and Alex Few at the NASA MSFC for their assistance in initiating the work, Niki Werkheiser also at the NASA MSFC for her helpful suggestions and conversations, Professor Eugene Speer from the Rutgers Department of Mathematics for discussing the fitted models in this work, Professor Mehdi Javanmard from the Rutgers Department of Electrical and Computer Engineering for access to a potentiostat, and Professor Alberto Cuitiño, Professor Assimina Pelegri, and Professor Howon Lee for participating on the Ph.D. thesis committee for J.X. 1. R. Chebbi , J. Colloid Interface Sci. 300 , 688 ( 2006 ). 10.1016/j.jcis.2006.04.018 2. A. Bernath , L. Kärger , and F. Henning , Polymers (Basel). 8 , 390 ( 2016 ). 10.3390/polym8110390 3. C. Feger , S. E. Molis , S. L. Hsu , and W. J. Macknight , Macromolecules 17 , 1830 ( 1984 ). 10.1021/ma00139a036 4. A. Y. Malkin and S. G. 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PY - 2019/12/16
Y1 - 2019/12/16
N2 - This letter presents an experimental study and the associated numerical modeling of fast-curing, thermosetting droplets spreading on a heated surface. The results show a significant morphological dependence of the spreading droplets of Ecoflex 0050 (a heat-sensitive, platinum-catalyzed silicone material) on thermal conditions. Differential scanning calorimetry and rheometry provide quantifiable data for modeling the cure kinetics and rheological properties of the material. This work demonstrates an approach to developing a phenomenological model suitable for predicting the morphological variation of fast-curing, thermosetting materials without prior knowledge of their chemical composition. The developed multiphysics models for cure kinetics and chemorheology can serve as a functional tool for predictions requiring accurate dimensional control of free-forming thermosetting materials, such as nozzle-based additive manufacturing, centrifugal coating and forming, fabrication of soft robots, and soft lithography.
AB - This letter presents an experimental study and the associated numerical modeling of fast-curing, thermosetting droplets spreading on a heated surface. The results show a significant morphological dependence of the spreading droplets of Ecoflex 0050 (a heat-sensitive, platinum-catalyzed silicone material) on thermal conditions. Differential scanning calorimetry and rheometry provide quantifiable data for modeling the cure kinetics and rheological properties of the material. This work demonstrates an approach to developing a phenomenological model suitable for predicting the morphological variation of fast-curing, thermosetting materials without prior knowledge of their chemical composition. The developed multiphysics models for cure kinetics and chemorheology can serve as a functional tool for predictions requiring accurate dimensional control of free-forming thermosetting materials, such as nozzle-based additive manufacturing, centrifugal coating and forming, fabrication of soft robots, and soft lithography.
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U2 - 10.1063/1.5106388
DO - 10.1063/1.5106388
M3 - Article
AN - SCOPUS:85076970353
SN - 0003-6951
VL - 115
JO - Applied Physics Letters
JF - Applied Physics Letters
IS - 25
M1 - 253701