Thermal Analysis of Directional Freezing Based Graphene Aerogel Three-Dimensional Printing Process

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Guanglei Zhao Department of Industrial and Systems Engineering, Thermal Analysis of Directional University at Buffalo, State University of New York, Buffalo, NY 14260 Freezing Based Graphene e-mail: [email protected] Aerogel Three-Dimensional Dong Lin Department of Industrial and Manufacturing Systems Engineering, Printing Process

Kansas State University, Downloaded from http://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/5/1/011006/5949597/jmnm_005_01_011006.pdf by guest on 29 September 2021 Manhattan, KS 66506 A novel directional freezing based three-dimensional (3D) printing technique is applied e-mail: [email protected] to fabricate graphene aerogel (GA). Thermal property of the graphene ink is one of the key impacts on the material morphology and process efficiency/reliability. We develop a Chi Zhou1 heat transfer model to predict temperature evolution of the printed materials and then Mem. ASME estimate layer waiting time based on it. The proposed technique can not only improve the Department of Industrial and process efficiency and reliability but also serve as a flexible tool to predict and control Systems Engineering, the microstructure of the printed graphene aerogels. Both the simulation and experiment University at Buffalo, results demonstrate the efficiency and effectiveness of the proposed approach. State University of New York, [DOI: 10.1115/1.4035392] Buffalo, NY 14260 e-mail: [email protected]

Introduction potential to fabricate multiscale and multifunctional 3D graphene architectures. Similar technology has been utilized to develop Graphene, an emerging two-dimensional (2D) nanomaterial rapid freezing prototyping (RFP) 3D-printing process, which that offers extraordinary mechanical, electrical, thermal, and builds 3D ice structure by depositing and rapidly freezing water acoustic properties [1–5], possesses the great potential to assemble droplet layer-by-layer. Extensive work has been done based on multiscale, multifunctional three-dimensional (3D) monolith this process [19–22], however, the application of this technology structures with widespread applications in flexible electronics, is limited to visualization and molding purpose. In this research, catalysis, energy storage, biomedical tissues and scaffolds, and we integrate directional freezing based 3D-printing with freeze thermal/acoustic insulation [6–16]. However, in order to fully drying technique to form a seamlessly integrated novel process unlock its exotic physicochemical properties and explore its multi- for printing multiscale multifunctional 3D graphene architectures. functional performance, it is highly desirable to design and fabri- As one type of crystalline material, the aqueous graphene sus- cate engineered 3D graphene structure, such as graphene aerogel, pension experiences phase changing during the solidification pro- in a controllable manner. Three-dimensional printing or additive cess. Therefore, the excessive latent heat must be released before manufacturing (AM) is an emerging technology that can fabricate the solidified material further decreases its temperature toward the physical objects directly from a computer-aided design (CAD) environmental temperature. The buildup latent heat not only pre- model without part-specific tooling and fixture, such unique prop- vents proper freezing of the new material which consequently erty opens up great opportunities to spatially manipulate graphene results in printing failure, it also affects the structure integrity and nanomaterial and form them into desired engineering structures the material morphology due to the nonuniform temperature gra- [16]. However, due to the complex graphene morphology and dient. In order to effectively release the latent heat and super heat nontrivial material forming mechanism, it is until very recently for ice printing, Leu’s group investigated the heat transfer mecha- two research groups have investigated 3D-printing graphene aero- nism during the printing process with customized simulation gel through micro-extrusion technique. The key concept of these model. The optimal waiting time was studied by using thermal techniques is to develop printable graphene ink by increasing the finite element analysis (FEA) technique [20,23,24]. However, all viscosity and form it as shearing thin non-Newtonian material the works focused on rather simple models (vertical column and [7,17,18]. Though the 3D structures are successfully printed, these vertical wall) with fixed waiting time for all the layers. The actual approaches suffer from several drawbacks including the necessity models for 3D printing are usually quite complicated with differ- of fillers, possible poor bonding and limited structure complexity. ent cross-sectional shapes for different layers. In order to further In order to fundamentally address these challenges, we introduced improve the 3D-printing efficiency, it is natural to extend the con- a new 3D-printing technique to fabricate 3D graphene structures stant waiting time to adaptive waiting time to accommodate the with pure graphene material, better material bonding, higher struc- shape changes between the layers. Furthermore, in order to funda- ture integrity, and complex architecture printing capability. This mentally understand the microstructure formation process which technique is based on inkjet printing and directional freezing, is primarily governed by temperature gradient, it is very desirable where the ejected aqueous nanomaterials are frozen, and then, the to develop a framework based on analytic and/or numeric thermal growing ice crystals squeeze the graphene sheets into 3D network. model to predict the solidification behavior (temperature and Since the macrostructure can be controlled by the 3D-printing pro- time) for each single droplet. Li and Leu developed FEA-based cess and the microstructure can be controlled by the freezing con- tool to simulate the heat transfer process, however, this work dition and material composition, such new technique has great highly relies on commercial FEA software which lacks the flexibility to explore rather complex 3D-printing process. Furthermore, 1Corresponding author. the inefficient data transfer mechanism as well as the generic algo- Contributed by the Manufacturing Engineering Division of ASME for publication rithm itself severely increase the computational cost, both time in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received September 27, 2016; final manuscript received November 26, 2016; published online and space. In our research work, we optimized the simulation pro- January 10, 2017. Editor: Jian Cao. cess and developed an efficient in-house tool by using MATLAB

Journal of Micro- and Nano-Manufacturing Copyright VC 2017 by ASME MARCH 2017, Vol. 5 / 011006-1 programming language. Some researchers modeled other 3D- the temperature of the material is constant and just above the printing processes based on FEA simulation technique. Costa melting point in order to keep reliable printing property. A two- utilized MATLAB to solve 3D filament based free form extrusion nozzle platform is setup to print graphene and supporting material process, which is also a temperature-reduction model with ele- (ice), as shown in Fig. 1(b). The whole system was placed in ment mutual effect [25,26]. Shen and Le formulated models to a freezer with inside temperature (20 C) well below the study the thermal behavior under the effect of powder sintering in material’s freezing point (0 C). electron beam AM [27,28]. However, these research works are For inkjet printing, the graphene nanomaterial is hydrophobic quite different from ours in that all these simulation models are and thus segregates in water even at very low concentration unless formulated for heating-up process, where the raw material has no surfactants added for their surfaces are functionalized. The segre- fixed solidification point. In our freezing-based model, the raw gation of graphene leads to the nozzle clogging and thus severely material experiences phase-changing process, which makes the affects the printability. Due to the presence of hydrophilic func- model more complicated than other techniques. In order to tional groups, graphene oxide (GO) is hydrophilic and can be eas- address these research challenges, we propose a thermal model ily dispersed in water at relatively high concentrations. Although based FEA approach to investigate the relationship between the GO is not electrically conductive, it can be thermally, chemically, Downloaded from http://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/5/1/011006/5949597/jmnm_005_01_011006.pdf by guest on 29 September 2021 temperature history and fabrication process and ultimately suggest and photothermally reduced to graphene. Based on the excellent optimal settings to control and assure the process reliability, part properties stated above, GO is suitable to serve as raw material. quality, and structure integrity. Low concentration (10 mg/ml) aqueous GO ink was selectively The remainder of the paper is organized as follows: We will ejected onto an aluminum platform with a certain amount of flow first introduce the system setup of the directional freezing based rate and moved following a predefined path. The ink is then frozen 3D-printing process and overview the mechanism of this new through the heat conduction with the platform and heat convection technique. Second, we will discuss problem description and model with the ambient. During the frozen process, the phase changing formulation, and a detailed algorithm framework will also be and separation can force the nonfreezable solid nanomaterials introduced. Third, based on the analytic model and the predication (GO) to accumulate between the growing ice crystals. The nano- framework, several test cases will be studied to demonstrate the materials trapped by the ice crystals form bridges between the temperature revolution and optimized waiting time, and heat crystals. If the loading of nanomaterial is enough, the entrapped transfer behavior will be analyzed based on the simulation results. nanomaterials will form a continuous 3D network molded by crys- Finally, we conclude and discuss the future work. tals. The 3D-printed “green” part will then be freeze dried and the water will be removed to achieve the final graphene aerogel (GA) with porous structures. Figures 1(c)–1(e) show multiple 3D- System Setup and Motivation printed GA structures. The interested readers are referred to our System Setup. The experimental setup used in this project is previous work for detailed explanation of the 3D-printing GA shown in Fig. 1(a). A personal computer controls the whole sys- process [29]. tem, including the three-axis motion driving system, material jetting system, and temperature and pressure control system. Besides, the computer also stores the software that can import 3D Motivation of the Proposed Work. The aqueous GO ink in digital model and convert them into machine commands for the the aforementioned 3D-printing process is a low-viscosity Newto- motion trajectory, material extrusion, and other process parame- nian fluid, allowing it to be printed in a drop-on-demand (DOD) ters. The material jetting system consists of a pressure regulator, mode, where the material is jetted drop-by-drop only if needed. multiple material reservoirs, and piezo-based jetting devices. A These discrete droplets serve as the basic elements in jetting- temperature control system is applied to the print head such that based printing process. The discrete ejection mode differs our technique from other continuous 3D GA printing approaches. The DOD-based technique can achieve much higher accuracy and flexibility. In this process, the layer bonding and structure forming are based on the freezing-induced solidification; therefore, the sta- bility of the ink solidification and the efficiency of the printing process are two crucial but contradictory criteria. The solidification of the newly deposited droplet is powered by the conduction with the previous solidified layers and the convection with the low-temperature environment. Because the phase- changing process takes non-negligible time due to the release of latent heat, the newly deposited droplet will not be properly solidified if the previous layer is not yet frozen. Therefore, certain amount of waiting time is desired to solidify the most recent layer of material, which otherwise will damage and even fail the printing process. Figure 2 shows a failure case where inadequate waiting time is applied. Theoretically, the longer waiting time is preferable to allow for the complete heat dissipation and assure the reliability of the solidification process, however, longer waiting time, on the other hand, prolongs the fabrication time. In addition, the aqueous GO ink is prone to dry or freeze at the tip of the printing nozzle and subsequently clogs the print head if the waiting time is too long. Thus, the optimal waiting time is expected to balance the process reliability, efficiency, and part quality. The thermal management, therefore, plays an important role in controlling the macroscopic structure of the 3D-printed part. The final product of the proposed 3D-printing process is graphene aerogel, which is obtained by freeze drying the 3D-printed Fig. 1 (a) and (b) Three-dimensional printing graphene aero- ice green part. According to the mechanism of the freeze drying gel, 3D-printed (c) truss structure and (d) 2.5D structure on calt- process, the integrity and morphology of the graphene aerogel are kin, and (e) graphene aerogel with various wall thicknesses [29] highly dependent on the temperature gradient. At low

011006-2 / Vol. 5, MARCH 2017 Transactions of the ASME 1 @T r2T ¼ (2) a @t

In Cartesian coordinate system, the Laplacian term r2T can also be expressed as ð@2T=@x2Þþð@2T=@y2Þþð@2T=@z2Þ, which rep- resents heat flux from three directions into the current unit volume. Shape simplification: Solidified part is built up by ink droplets, which are deposited drop-by-drop. When a droplet is deposited, it will spread and contact with the adjacent droplets. Since the spreading speed is much higher than the freezing speed [20], the droplet can be modeled as thin rectangular slab shape without loss of accuracy. Considering the small volume (<100 pL) of each Downloaded from http://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/5/1/011006/5949597/jmnm_005_01_011006.pdf by guest on 29 September 2021 droplet, we believe this shape simplification is valid and it can significantly improve the computational efficiency. “Thermally small” element: Even with the shape simplification, Fig. 2 A failed test case caused by inadequate waiting time calculating the temperature for every element (droplet) is still computationally challenging. In addition, solving Eqs. (1) and (2) is not trivial. Based on our observation, homogenizing the internal temperature, the nucleation rate of the ice is much higher than the temperature for each element can significantly reduce the compu- crystal growth rate, thus crystals do not have enough time and tational cost and increase the simulation efficiency. If the heat space to grow and a large number of small ice crystals form. At conduction inside the element body is significantly faster than its higher freezing temperatures, crystal growth dominates and larger surface heat exchange with outside environment, we can consider pores form after freeze drying [30,31]. Therefore, besides the the element to be thermally small. To verify this assumption, Biot important role in controlling the macroscopic structure, the ther- number is introduced in this work. Biot number is a dimensionless mal management is also critical to control the microscopic struc- number which indicates a ratio of heat transfer resistance inside a ture (pore size, density, and morphology) of the 3D-printed GA body and on the surface of the body. If a Biot number is much part. smaller than 1, heat transfer resistance inside the body is much smaller than heat transfer resistance on the surface, which also Problem Description and Approach Overview means heat transfers much faster inside the body than on the surface. Generally, if Biot number is smaller than 0.1, the body then Problem Description. As discussed in the previous section, can be considered “thermally simple” or “thermally small”. The “Motivation of the Proposed Work,” certain waiting time is Biot number is defined as the following equation [33]: expected between two adjacent layers in order to assure the printing quality and success rate. However, balance has to be made between hLc Bi ¼ (3) the process efficiency and reliability. Therefore, finding out the opti- kb mal waiting time for a specific print is the key research question. The major criterion of the waiting time is to assure that the previ- where h is the surface heat transfer coefficient. For frozen GO ink, ously deposited layer is completely solidified and/or reaches certain h is around 6–30 W=ðm2 KÞ. In this case, the contact heat trans- low-temperature level. In the jetting-based 3D-printing process, the fer is considered as one type of the film heat transfer, we approxi- 2 new droplet is ejected from the nozzle, lands on the ice surface, mately set it as a relatively large value, 50 W=ðm KÞ. Lc is the deforms, spreads, freezes, and bonds with previous layer through characteristic length, a typical value is 0.05 mm based on the real hydrogen bonding. The driving force of solidification is from the size of a droplet. kb is the thermal conductivity of the body. For low-temperature ambient through convection and the cold ice sur- liquid GO ink, thermal conductivity is around 0.6 W=ðmKÞ, thus face through conduction. The thermal behavior and thermal man- it follows that Bi ¼ 0.00416 0.1. For frozen GO ink, thermal agement are the keys to identify the optimal waiting time in this conductivity is around 2.0 W=ðmKÞ; therefore, the corresponding dynamic process. However, as the materials are deposited sequen- Bi ¼ 0.00125 0.1. Based on this calculation, one droplet, or tially and the layer geometry varies for typical parts, it is very chal- one element, can be reasonably considered to be thermally small. lenging if not impossible to solve this problem through analytic With the thermally small property, the internal conduction approach with closed-form formulation. Instead, numerical approach can be ignored without losing computational accuracy. such as FEA based modeling and simulation can effectively charac- Therefore,P ð@2T=@x2Þþð@2T=@y2Þþð@2T=@z2Þ can be replaced 00 terize and analyze the complex dynamic process, we will therefore by MkiAiqi , as they both represent heat flow into the element in investigate the thermal behavior of the directional freezing based the equivalent way. Equation (2) can be further simplified as 3D-printing process through FEA simulation based on the thermal modeling described in the following sections, “Process Modeling” X dT 00 and “Parameter Settings and Algorithm.” qcdV þ kiAiqi ¼ 0 (4) dt M

Process Modeling. The process modeling for thermal analysis where T is the temperature, t is the time, q is the density of the is based on the heat transfer theory, and the general governing ink, c is the specific heat of ink, dV is the volume of a liquid drop- 00 equation [32]is let, and ki, Ai, and qi are the boundary condition (BC) coefficient, working area, and heat transfer of the ith surface, respectively. 2 q_ 1 @T Equation (4) can be expanded into specific heat transfer equation r T þ ¼ (1) k a @t as follows: where T is the temperature, q_ is the internal heat generation rate, k dT X X qcdV þ k A h ðÞT T þ k A h ðÞT T is the material conductivity, and a ¼ k=qc is the thermal diffusiv- dt i i sur a j j n n ity of the material and related to material conductivity k, material XM1 M2 density q, and specific heat c. In this case, no internal heat is gen- þ kkAkhsðÞT Ts ¼ 0 (5) erated inside the elements, thus q_ ¼ 0 and Eq. (1) is simplified as M3

Journal of Micro- and Nano-Manufacturing MARCH 2017, Vol. 5 / 011006-3 where Ta is the ambient temperature, hsur is the surface heat trans- Table 1 Initial conditions of simulation fer coefficient, including several types of film heat transfer, such as convection, radiation, and evaporation, hn is the contact heat Droplet temperature ( C) 5 Ambient and substrate temperature (C) 20 transfer coefficient with the n th adjacent element, hs is the recip- rocal of thermal contact resistance between elements and substrate, Tn is the temperature of the nth element, and Ts is the temperature of substrate, which is identical with the ambient temperature in this simulation. Equation (5) can be further derived Table 2 Properties of materials into Density-ink (kg=m3) 1000 Density-frozen ink (kg=m3) 917 dT qcdV þ C T C ¼ 0 (6) Specific heat-ink (J=ðkg KÞ) 4197 dt 1 2 Specific heat-frozen ink (J=ðkg KÞ) 2030 Latent heat (J=kg) 334,000 Downloaded from http://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/5/1/011006/5949597/jmnm_005_01_011006.pdf by guest on 29 September 2021 where the constant numbers are denoted as C1 and C2 for the sake of simplicity. Solving Eq. (6), we obtain C2 C2 T ¼ T0 exp½C1ðÞt tc þ (7) C1 C1 Table 3 Process parameters of simulation where tc is the exact time at which the current droplet is deposited. Step time (s) 0.001 When calculating the temperature of an element, the temperatures Drop frequency (Hz) 100 of adjacent elements keep unchanged within one step. Based on Nozzle moving speed (mm=s) 15 this approximation, Eq. (7) can be further written as Heat transfer coefficient (W=m2 K) With substrate 200 With adjacent elements 100 C2 C2 Tiþ1 ¼ Ti exp½C1 Dt þ (8) With ambient 20 C1 C1 where Tiþ1 and Ti are the temperature in current and previous step, respectively, and Dt is the step size. Equation (8) is the final explicit analytic solution and can be directly utilized for temperature update during the iteration-based dynamic thermal evolution process.

Parameter Settings and Algorithm. During the printing process, a moving printing head continuously deposits GO droplet on a cold plate or previous cold layer. The newly deposited droplet can be modeled as a moving heat source in the simulation, and thus, the BCs have to be iteratively updated when a new droplet is deposited. Because of considerably small volume, each droplet being modeled as one element can still have a reasonable accuracy. The aforementioned shape simplification is shown as follows: the two-dimensional (2D) model of one element can be simplified as rectangular shape as shown in Fig. 3. With such simplification, it is more computationally efficient to define and update the BCs of the model. For all the elements, only three types of heat transfer modes need to be considered as shown Fig. 3: (1) heat transfer with substrate (Fig. 3(a)); (2) heat transfer with adjacent elements (Fig. 3(b)); and (3) heat transfer with ambient (Fig. 3(c)). As substrate has a considerably large conductivity compared with ink, the boundary condition for the bottom of first layer is set as constant temperature same as the ambient temperature. The initial conditions, material properties, and process parameters are listed in Tables 1–3, respectively. Based on the heat transfer model and parameter settings, an efficient thermal FEA-based algorithm is developed to study the heat transfer mechanism of the directional freezing 3D-printing process. The algorithm is illustrated in the following framework (Fig. 4). The algorithm takes the tool path data based on the input geometry and converts them into information for the FEA model. After setting the material properties, process parameters, and the initial conditions of

Fig. 3 Three types of heat transfer conditions Fig. 4 Framework of the thermal analysis algorithm

011006-4 / Vol. 5, MARCH 2017 Transactions of the ASME every element, substrate, and the ambient, the algorithm updates the temperature of each element (droplet) iteratively until the entire printing process is completed. At the beginning of each iteration, one droplet (element) will be deposited and the related BCs will be updated unless the layer- change condition is met. After that, the system will judge whether the current element is in its phase-changing process, if not, the temperature of every deposited element will be simply computed and updated. If the current element is under phase-changing process, the latent heat of the element will be updated and the next iteration starts. If the current layer is completed, i.e., the last droplet of the layer has been deposited, the waiting time will be reset and updated and the criterion of “whether it is ready to print next layer” will be evaluated. We set a target temperature for all the Downloaded from http://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/5/1/011006/5949597/jmnm_005_01_011006.pdf by guest on 29 September 2021 deposited elements especially the ones in the most recently deposited layer, when the temperature of all the deposited elements reaches the threshold, the system is ready for the next layer. If it is ready to print next layer, the waiting time register will be reset and a new layer will be ready for process. If not, the temperature of all the elements will be computed for another step time and the Fig. 7 Waiting until temperature of the deposited layers drops waiting time will be updated. The whole process will terminate down to 219 C when the preset step number is met, normally the whole simulation process consists of the whole material building process and a postcooling process. Note that the liquid ink and solid frozen ink Table 4 Waiting time before fabricating a new layer have different material properties, and their material properties Layer number Second Third Fourth

Drop down to 19 C 0.111 0.556 0.973

Fig. 5 A 4 3 4 square model

Fig. 8 Waiting time for the 40 3 4 model are temperature dependent, when the temperature of an element is updated, its material properties need to be updated if necessary.

Results and Discussion The aforementioned algorithm is implemented and tested in MATLAB environment, with parallel computing strategy applied to improve computation efﬁciency. Both 2D and 3D models with different geometries are tested. The effect of the waiting time is studied for various cases including no waiting time, constant waiting time, and adaptive waiting time. The detailed results are discussed in the following sections, “Two-Dimensional Model Study” and “Three-Dimensional Model Study.”

Two-Dimensional Model Study. Case 1: No waiting time study. A simple 4 4 square shape was ﬁrst used to study the heat transfer during the printing process and verify the predictive Fig. 6 A 4 3 4 temperature evolution for square model without model. The tool path is shown in Fig. 5. Four vertically aligned waiting time between layers elements (1, 8, 9, and 16) are selected to study the heat transfer

Journal of Micro- and Nano-Manufacturing MARCH 2017, Vol. 5 / 011006-5 quickly than elements above it, showing the influence from substrate to element 1 is more significant than elements above. Other interesting results can also be found in Fig. 6. When droplet 16 is deposited on top of droplet 9, because of the high temperature of the new droplet, temperature of droplet 9 starts to increase above 0 C during its phase-changing stage, indicating that droplet 9 starts to melt. This case is common in real fabricating process. Figure 2 shows a real melting case, several top layers melt during printing, resulting in a rough surface and inevitable imprecision. Case 2: Constant threshold temperature waiting time. To avoid melting during fabrication process, one straightforward way is to wait until the deposited materials are completely solidified and/or Fig. 9 A 20 3 20 square and 20 3 20 triangle models reach to a certain threshold temperature (lower than freezing point) before a new layer is deposited. Simulation is performed to Downloaded from http://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/5/1/011006/5949597/jmnm_005_01_011006.pdf by guest on 29 September 2021 test the effect of waiting time before depositing new layers using the same test case. Figure 7 shows the results of same test case with a threshold temperature of 19 C in Fig. 7. Clearly, no melting issues are observed as existed materials are more prepared for a new layer. Table 4 shows the waiting time for every layer. As can be seen from the table, to reach the same threshold temperature, it takes less and less waiting time as the layer number increases. The major reason is the effect of the heat conduction with the platform is attenuating as the part grows, and the thermal conductivity of the frozen ink is much lower than the metal platform. As waiting time is inevitable for every layer except for the first one, it becomes a critical factor for the fabrication efficiency of freezing-based 3D-printing process. In this work, waiting time is studied with the help of heat transfer simulation model. In order to better understand the property of waiting time, the previous 4 4 case is extended to 40 4 case. The simulation results of the waiting time are shown in Fig. 8. As can be seen from Fig. 8, the waiting time stays at an approximately constant value after the number of layers reaches a certain level. In this case, the waiting time stays as 4.5220 s after layer Fig. 10 Layer waiting time for models in Fig. 9 #35 is deposited. As the temperature of substrate is considered as a constant at relatively low value, the influence from substrate to temperature evolution of the first deposited layers is significant. and temperature evolutions. In this study, no waiting time is But as the layer number increases, this influence is attenuating, assigned between two consecutive layers. and after certain layers (#35 in this case) this influence disappears In Fig. 6, four curves are plotted to indicate the temperature and the waiting time for the following layers will keep unchanged. evolution of element 1, 8, 9, and 16 within 1 s. During this time We believe the waiting time is related to layer thickness, ambient period, only elements 1 and 8 completed phase-changing process. temperature [24], and the geometry and dimensions of the part. Latent heat releasing process has considerable impact on tempera- Case 3: Adaptive waiting time. Constant waiting time cannot ture evolution of adjacent elements. For instance, temperature of assure both the process reliability and efficiency. An adaptive element 1 keeps at around 16 C before element 8 released all waiting time is desirable to maximize the fabrication efficiency its latent heat during phase-changing stage. After element 8 without losing the reliability. A 20 20 square case, as displayed released all the latent heat, temperature of element 1 continues to in Fig. 9(a), is simulated and the waiting time is collected for drop to a lower value, which indicates the influence from element every layer. In this case, the threshold temperature of depositing a 8 on element 1. Besides, temperature of element 1 drops more new layer is still 19 C. Figure 10(a) shows the relationship

Fig. 11 Two similar geometries with different number of base layers

011006-6 / Vol. 5, MARCH 2017 Transactions of the ASME Downloaded from http://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/5/1/011006/5949597/jmnm_005_01_011006.pdf by guest on 29 September 2021

Fig. 13 Printing process of 3D cubic model

Fig. 12 Layer waiting time for models in Fig. 11 between the waiting time and layer number. This plot is evidently different from the first 20 layers plot line in Fig. 8, verifying our hypothesis that the part dimension affects the waiting time. Figure 10(b) shows the waiting time trend for the 20 20 right triangle in Fig. 9(b). Different from the square shape cases, the waiting time decreases after layer #15, which is mainly caused by the decrease of layer dimension. In conclusion, without geometry change, the waiting time will gradually reach a constant value with the attenuation of substrate effect. However, if there is geometry change, the waiting time will vary accordingly after certain number of layers. For other more complicated cases, the waiting time is expected to vary depending on layer location, ambient temperature, layer thickness, and the part geometry and dimension. From the above scenarios, we can conclude that for the first several layers, the impact of substrate is the most significant fac- Fig. 14 Waiting time for 3D cubic model tor, and the waiting time linearly increases with the layer number. After certain number of layers, the effect of substrate will gradually attenuate and eventually disappear. In order to further verify the impact of substrate, two models with same top half part (Fig. 11) are simulated. Figure 12(a) clearly shows the influence of the substrate for the case in Fig. 11(a). The waiting time continuously increases till layer #16 and then decreases because of the reduction of layer size. The part in Fig. 11(b) has 12 more layers duplicating the first layer compared with the part in Fig. 11(a), and the simulated result is shown in Fig. 12(b). As can be seen from Fig. 12(b), the first several layers are significantly influenced by the heat drainage of substrate, and the waiting time increases linearly with the number of layers. From layer #20, the waiting time suddenly decreases because of sudden reduction of layer size, and it then stays at approximately constant level because of constant layer size. Finally, the waiting time gradually decreases due to the decrease of the layer size. The comparison between these two test cases clearly demonstrated that the waiting time is Fig. 15 Printed part with designed waiting time between layer influenced by the part geometry and the cold substrate. fabrications

Three-Dimensional Model Study model. Similar to 2D model, the element shape is simplified as Model Formulation. The 2D model in the previous section, flat cube for 3D model. The droplet (element) will be deposited “Two-Dimensional Model Study,” is effective to investigate and one by one with the predefined printing parameters and tool path understand the thermal behavior of the freezing-based printing to build the large cubic part, as shown in Fig. 13. process. In practice, the real parts are printed in 3D space, and it The thermal evolution equations (6)–(8) are also applicable to is more likely that layers printed with different toolpath and print- 3D models. The major difference between 3D and 2D model is ing strategies have different optimal waiting times. However, it is the heat transfer conditions and boundary conditions, which is computationally more expensive to simulate the 3D model than updated according to toolpath strategy, speed, and waiting times. the 2D model. For the sake of computational simplicity, a typical In this model, as every layer is same in size and geometry, tool- cubic model is formulated to study the thermal behavior of the 3D path strategies for each layer will be identical.

Journal of Micro- and Nano-Manufacturing MARCH 2017, Vol. 5 / 011006-7 Simulation Results. Figure 14 shows the history of the waiting [7] Jakus, A. E., Secor, E. B., Rutz, A. L., Jordan, S. W., Hersam, M. C., and Shah, time for the 3D cubic model. It can be clearly seen that the wait- R. N., 2015, “Three-Dimensional Printing of High-Content Graphene Scaffolds for Electronic and Biomedical Applications,” ACS Nano, 9(4), pp. 4636–4648. ing time for 3D model shows the same trend of “increase-slow- [8] Leigh, S. J., Bradley, R. J., Purssell, C. P., Billson, D. R., and Hutchins, D. A., stable” as its counterpart 2D model and the substrate effect also 2012, “A Simple, Low-Cost Conductive Composite Material for 3D Printing of plays a crucial role in the solidification process of the first few Electronic Sensors,” PLoS One, 7(11), p. e49365. layers. It is expected that the waiting time is likely to vary with [9] Maiti, U. N., Lim, J., Lee, K. E., Lee, W. J., and Kim, S. 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Three-dimensional graphene aerogel has widespread applica- [13] Ye, S., Feng, J., and Wu, P., 2013, “Highly Elastic Graphene Oxide–Epoxy tions. We presented a novel 3D-printing technique based on direc- Composite Aerogels Via Simple Freeze-Drying and Subsequent Routine Curing,” tional freezing to fabricate complex graphene aerogel J. Mater. Chem. A, 1(10), pp. 3495–3502. [14] Vickery, J. L., Patil, A. J., and Mann, S., 2009, “Fabrication of architectures with multifunctional and multiscale properties. The Graphene–Polymer Nanocomposites With Higher-Order Three-Dimensional heat transfer is vital to the structural integrity and morphology of Architectures,” Adv. Mater., 21(21), pp. 2180–2184. the graphene structure, as well as the reliability and efficiency of [15] Estevez, L., Kelarakis, A., Gong, Q., Da’as, E. H., and Giannelis, E. P., 2011, the process. This paper studied the temperature evolution and “Multifunctional Graphene/Platinum/Nafion Hybrids Via Ice Templating,” J. Am. Chem. 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Both the simulation and experimental results [21] Ossino, A., Barnett, E., Angeles, J., Pasini, D., and Sijpkes, P., 2009, “Path demonstrated the effectiveness of the proposed technique. Future Planning for Robot-Assisted Rapid Prototyping of Ice Structures,” Trans. Can. work includes integrating the predictive model into tool path plan- Soc. Mech. Eng., 33(4), pp. 689–700. ning framework to further optimize the efficiency and reliability. [22] Zhao, X., Landers, R. G., and Leu, M. C., 2010, “Adaptive Extrusion Force Control of Freeze-Form Extrusion Fabrication Processes,” ASME J. Manuf. Sci. Eng., 132(6), p. 064504. [23] Sui, G., and Leu, M. C., 2003, “Thermal Analysis of Ice Walls Built by Rapid Acknowledgment Freeze Prototyping,” ASME J. Manuf. Sci. Eng., 125(4), pp. 824–834. [24] Liu, Q., and Leu, M. C., 2007, “Finite Element Analysis of Solidification in The authors acknowledge the seed funds support from the Sus- Rapid Freeze Prototyping,” ASME J. Manuf. Sci. 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