Shape memory polymers are gaining significant interest as one of the major constituent materials for the emerging field of 4D printing. While 3D-printed metamaterials with shape memory polymers show unique thermomechanical behaviors, their thermal transport properties have received relatively little attention. Here, we show that thermal transport in 3D-printed shape memory polymers strongly depends on the shape, solid volume fraction, and temperature and that thermal radiation plays a critical role. Our infrared thermography measurements reveal thermal transport mechanisms of shape memory polymers in varying shapes from bulk to octet-truss and Kelvin-foam microlattices with volume fractions of 4%–7% and over a temperature range of 30–130 °C. The thermal conductivity of bulk shape memory polymers increases from 0.24 to 0.31 W m−1 K−1 around the glass transition temperature, in which the primary mechanism is the phase-dependent change in thermal conduction. On the contrary, thermal radiation dominates heat transfer in microlattices and its contribution to the Kelvin-foam structure ranges from 68% to 83% and to the octet-truss structure ranges from 59% to 76% over the same temperature range. We attribute this significant role of thermal radiation to the unique combination of a high infrared emissivity and a high surface-to-volume ratio in the shape memory polymer microlattices. Our work also presents an effective medium approach to explain the experimental results and model thermal transport properties with varying shapes, volume fractions, and temperatures. These findings provide new insights into understanding thermal transport mechanisms in 4D-printed shape memory polymers and exploring the design space of thermomechanical metamaterials.

Metamaterials are artificial materials with engineered architecture designed to have physical properties determined by micro-structural geometry rather than the chemical composition.1–4 The hierarchical topologies in metamaterials have led to unique properties such as ultra-high stiffness,5 ultra-low density,6 and ultrahigh surface-to-volume ratios that introduce a significant radiation contribution7 in the thermal transport phenomenon. The physical properties of these metamaterials arise from the geometry and spatial arrangement of microstructural elements. As a result, the incorporation of shape-shifting materials, such as shape memory polymers (SMPs), in 3D material architecture has opened up new possibilities toward the creation of novel multifunctional material systems.2 

Shape memory polymers (SMP) are highly deformable materials that can be mechanically reconfigured and recover their original shape when subjected to external stimuli such as electric potential,8 light,9 sound,10 humidity,11 and heat.12 This smart shape-shifting material has especially received interest in recent years due to its industrial viability, versatile morphology, and synthetic flexibility.13 In thermomechanical programming, stimuli-responsive SMPs can be deformed into arbitrary temporary shapes in its rubbery state and maintain their configuration during a glass transition or a crystallization process.14 At temperatures above glass transition temperature (Tg), the material is highly elastic, whereas at temperatures below Tg, the flexibility of chains forming the segment of the material in question is limited. The material is highly rigid when exposed to temperatures lower than Tg, which allows fixating a deformed shape. Upon reheating to above Tg, these SMPs can recover their original “memorized” shape. The possibility to use this temperature change to control the shape programming and recovery process of SMPs has led to their widespread application, including heat-shrink tubing and films for electrical insulation in electrical wire connections,15 smart textiles,16 and biomedical implants.17 However, the relatively simple shape of the current SMP applications impedes the full utilization of the unique advantages of SMPs. In particular, it is fairly challenging to achieve complex individualized structures—struts of a microlattice—with a high resolution using conventional manufacturing techniques, such as cutting, molding, and lithography. On the other hand, 3D printing has seen remarkable advances in the past decade, enabling facile production of otherwise unrealizable design concepts. Furthermore, 3D printing with shape-shifting materials, or 4D printing, offers unprecedented capability for the creation of dynamic and adaptive materials architectures.18,19

Incorporating SMP into metamaterials design results in 3D printed metamaterials with inherently reversible deformation20 and programmable mechanical properties2,21 that have an unmatched potential for creating unprecedented adaptive and tunable material systems. Examples of 3D printed SMP-based metamaterials include active composites of SMP fibers in an elastomeric matrix to realize complex three-dimensional configurations,22,23 programmable layered SMP composites for smart folding structures,24 chiral-lattice SMP metamaterials for adjustable Poisson’s ratio,25 and multi-material SMP architectures for programmable mechanical grippers.26 Although the mechanical properties of these SMP metamaterials have been comprehensively investigated in previous studies,25,27 their thermal properties have received little attention.

Here, we present thermal transport mechanisms in 3D printed SMP metamaterials. Stimuli-responsive deformation of SMP structures is governed by the thermo-mechanical property of the SMP, which is determined by the crosslinking network structure. It has been studied that the crosslinking network can be readily modified by varying the type or ratio of monomer/crosslinker.26,28,29 In this work, we prepared a photocurable SMP precursor solution comprised of acrylic acid (AA) as a monomer and bisphenol A ethoxylate dimethacrylate (BPA, Mn 1700) as a crosslinker.2 Upon the ultraviolet (UV) light illumination, vinyl functional groups in AA and BPA are activated by free radicals decomposited from photo-initiators and bonded with other surrounding activated monomers/crosslinkers. With the bonding reaction propagating in the resin, a polymeric network forms with BPA serving as the nodes to link AA chains. Since AA and BPA have their own Tg of 130 and −40 °C, respectively,6,30 the thermo-mechanical property of the resulting SMP, such as Tg, and storage/loss moduli can be tailored by using different mixing ratios of the monomer and crosslinker. Material preparation is described in detail in the supplementary material.

To fabricate the SMP metamaterials, a custom-built additive manufacturing platform based on the high-precision Projection micro-Stereolithography (PμSL) was used. PμSL is capable of swiftly printing complex micro-structures through a layer-by-layer projection of digital dynamic photomasks.31–33 A schematic of the PμSL process is presented in Fig. 1(a). Cross-sectional 2D images sliced from the 3D computer-aided design (CAD) model are sequentially displayed as dynamic masks on a digital micromirror device (DMD). The ultraviolet (UV) light stemmed from a light emitting diode (LED) is reflected off the dynamic mask and projects the corresponding image on the surface of the photocurable precursor solution through a projection lens to photo-polymerize the corresponding layer. Then, the linear stage moves the sample holder down at a specific distance and the next image is projected to form the next layer on the preceding one. This process repeats for all layers to build the 3D structure. In this study, an exposure time of 5 s was given to cure each layer having a thickness of 50 µm.

FIG. 1.

Fabrication setup and shape memory behavior of SMP microlattices. (a) 3D printing of SMP microlattices using the PµSL technique. (b) 3D printed SMP KF (left) and OT (right) samples with corresponding volume fractions of 4%, 5%, and 7%. The scale bar represents 2 mm. Detailed geometrical configurations for all structures can be found in Table S2 of the supplementary material. (c) We characterize the thermal properties of SMP microlattices and the contribution of both conduction and radiation heat transfer modes using the IR thermography methodology.

FIG. 1.

Fabrication setup and shape memory behavior of SMP microlattices. (a) 3D printing of SMP microlattices using the PµSL technique. (b) 3D printed SMP KF (left) and OT (right) samples with corresponding volume fractions of 4%, 5%, and 7%. The scale bar represents 2 mm. Detailed geometrical configurations for all structures can be found in Table S2 of the supplementary material. (c) We characterize the thermal properties of SMP microlattices and the contribution of both conduction and radiation heat transfer modes using the IR thermography methodology.

Close modal

Two microlattices were fabricated with PμSL in this study: Kelvin foam (KF) and octet truss (OT) microlattices. Figure 1(b) shows the unit cells for KF and OT microlattice, respectively, and their dimensional parameters. Specifically, = 45°, lKF = 1380 µm, and dKF ranging from 303 to 428 µm were used for KF samples, while lOT = 1380 µm and dOT ranging from 93 to 131 µm were used for OT samples (supplementary material, Table S2). By varying the diameter of struts, samples with volume fractions of 4%, 5%, and 7% for KF and OT were fabricated.

For thermal characterization of SMP microlattices, IR thermography7 was used in conjunction with a vacuum level below 10−4 Torr. Figure 1(c) demonstrates the experimental setup for measuring the thermal conductivity of the SMP microlattices. The samples were located in-between a compressible heat source and an anchored heat sink. Two reference quartz blocks with a known thermal conductivity of 1.38 W m−1 K−1 were utilized for calibrating the heat flux entering and leaving the microlattice control volume. The heat flux entering the system is a combination of conduction (qcond and radiation (qrad contributions (qin=qcond+qrad. Knowing that the exiting heat flux can only capture the conduction contribution (qout = qcond), the difference between the measured heat flux in the top and bottom reference quartz blocks is correlated with the radiation losses in the system. Therefore, the radiation heat flux can be calculated as qrad = qinqout. The emissivity calibration of the SMP microlattices in an isothermal boundary condition resulted in mid-IR emissivity values of 0.94 ± 0.01 and 0.94 ± 0.03 before and after glass transition, respectively. These values are in agreement with the mid-IR emissivity values reported for SMP materials in the literature.34 The calibrated emissivity values were used for temperature measurements of each corresponding sample. Therefore, by using the calibrated heat flux and the resultant temperature gradient in the SMP microlattices, the effective thermal conductivity was calculated using Fourier’s law (κeff = qinHT), where ∆T is the temperature gradient across the sample and H is the height of the sample as demonstrated in Fig. 1(c).

The effective thermal conductivity of the SMP microlattices is a combination of conduction (κcond) and radiation (κrad) heat transfer contributions, i.e., κeff = κcond + κrad. Thermal convection becomes insignificant with small unit cells below 10 mm due to limited surface areas and spaces allowed for bulk movements, even in the case of low thermal conductivity polymer foams.35 Additionally, by providing a vacuum environment, the convection contribution was eliminated in all thermal measurements. The conduction contribution, κcond, can be expressed as a product of the intrinsic thermal conductivity of SMP (κsolid), volume fraction (ν), and a geometrical factor (A) confirmed by finite element analysis (FEA)36 (supplementary material, Sec. 2.1). κrad can be calculated based on the approach proposed by Ashby36 by calculating the radiation heat flux, which is a function of the view factors, radiosity, calibrated emissivity, volume fraction, and temperature (supplementary material, Sec. 2.2). Details of the view factor derivation can be found in the supplementary material, Sec. 3. The radiation heat flux comprises the contribution of emission [qradY,emission] plus the reflection from the struts and the surrounding void surfaces [qradY,reflection]. Therefore, the effective thermal conductivity of the SMP microlattices can be expressed as below:
κeff=κcond+κrad=Aνκsolid+qradY,emission+qradY,reflectionH/ΔT.
(1)
Dynamic mechanical analysis (DMA) with the bulk SMP specimens (see the supplementary material for details) showed that the SMP with an AA/BPA ratio of 55:45 has a Tg of 71 °C. The glass transition temperature is indicated by tan δ (the ratio of loss to storage modulus) in Fig. 2(a). The temperature dependent storage modulus [E(T)] of the bulk SMP obtained from DMA (see the supplementary material for details) was also used to identify the fraction of “frozen bond” to “active bond” that coexist in the polymer. The frozen bonds represent the fraction of the C–C bonds with no conformational motion, while the active bonds are correlated with the C–C bonds that undergo free localized conformational motion.37,38 Therefore, at the glassy state, the frozen bonds are predominant. We used the approach proposed by Liu et al.39 and identified the volume fraction of frozen bonds as a function of temperature [Fig. 2(a)] using the following equation:
ET=1ϕfEi+1ϕf3NkT,
(2)
where ϕf is the fraction of frozen bonds, Ei is the modulus of internal energetic deformation, N is the cross-link density, k is Boltzmann’s constant (k = 1.38 × 10−23 N m/K), and T is the temperature. κsolid of the SMP increases from 0.235 W m−1 K−1 at 41 °C to 0.312 W m−1 K−1 at 106 °C due to glass transition of the SMP around its Tg of 71 °C. Applying the measured thermal conductivity data at glassy and rubbery states in conjunction with the Maxwell effective medium theory,40 we could explain the transition behavior in the intrinsic thermal conductivity of the bulk SMP sample [Fig. 2(b)].
FIG. 2.

(a) (Top) Storage modulus and the derived volume fraction of the frozen bonds as a function of temperature and (bottom) tan δ of the bulk SMP as a function of temperature. (b) Measured thermal conductivity of the bulk SMP and the applied Maxwell effective medium theory model for explaining the transition behavior in the thermal conductivity of the bulk SMP material. In both (a) and (b), the red-colored dashed line represents the glass transition temperature Tg.

FIG. 2.

(a) (Top) Storage modulus and the derived volume fraction of the frozen bonds as a function of temperature and (bottom) tan δ of the bulk SMP as a function of temperature. (b) Measured thermal conductivity of the bulk SMP and the applied Maxwell effective medium theory model for explaining the transition behavior in the thermal conductivity of the bulk SMP material. In both (a) and (b), the red-colored dashed line represents the glass transition temperature Tg.

Close modal

The high surface-to-volume ratio of the SMP microlattices (32–45 mm−1), in addition to their high IR emissivity (0.94), results in a significant contribution of radiative heat transfer, even near room temperatures. The emissivity of 0.94 was calculated by first applying a constant temperature to a reference object with known emissivity in a vacuum environment to induce a steady-state heat flow rate and measuring the temperature of the object with infrared thermography. Then, the bulk SMP was placed in the same environmental conditions with the temperature measured in the exact same location as the reference material. Finally, utilizing infrared thermography, the emissivity was calibrated until the measured temperature matched that of the reference object.

Figure 3(a) illustrates two primary heat transfer modes: the conduction contribution of solid struts and radiation heat transfer among individual struts and their surrounding non-participating media. We used Eq. (1) for predicting the effective thermal conductivity of KF and OT structures as a function of temperature. Due to the insulating nature of these low density architected materials, we used the temperature gradient data of the first row of unit cells in each corresponding lattice structure for thermal conductivity measurements. The temperature gradient across each sample was derived from the IR images as shown in Fig. 3(b). Figures 3(c) and 3(d) illustrate the effective thermal conductivity of KF and OT structures, respectively. The solid lines represent the effective thermal conductivity predicted by analytical modeling. The linear slope is derived by the surface emissivity and the surface-to-volume ratio of the lattice structures. For both structures, the thermal radiation contribution to overall heat transfer is significantly larger over a temperature range of 30–130 °C, while the conduction contribution remains small. Radiation contribution ranges from 68% to 83% across KF structures and from 59% to 76% across OT structures. The slight increase in conduction contribution as a function of temperature is due to the glass transition of the intrinsic SMP. A more apparent increase in the radiation contribution with temperature is because of the fact that both emission and reflection are highly dependent on temperature due to the Stefan–Boltzmann law (qradT4). Due to the dominant contribution of radiation heat transfer in low-density microlattices, the overall effective thermal conductivity of both OT and KF, therefore, increases significantly with temperature despite the steady thermal conductivity of the constituent SMP material.

FIG. 3.

(a) The primary heat transfer modes—conduction and radiation—in OT and KF SMP microlattices. (b) IR images of the KF (left) and OT (right) samples. The IR images contain information on the temperature gradient of each unit cell for calculating the thermal properties of SMP microlattices. (c) Measured and modeled effective thermal conductivity of OT samples and (d) KF samples with 4%–7% volume fraction ratios. (e) The conduction and radiation contributions as a percentage of the effective thermal conductivity in OT samples and (f) KT samples at 4% volume fraction. The conduction contribution makes up a greater percentage of the effective thermal conductivity over all measured temperatures for the OT samples compared to the KF samples, due to the higher geometrical factor in OT than KF. The radiation contribution as a percentage of the effective thermal conductivity increases with temperature due to the fourth-order relationship between radiative heat transfer and temperature.

FIG. 3.

(a) The primary heat transfer modes—conduction and radiation—in OT and KF SMP microlattices. (b) IR images of the KF (left) and OT (right) samples. The IR images contain information on the temperature gradient of each unit cell for calculating the thermal properties of SMP microlattices. (c) Measured and modeled effective thermal conductivity of OT samples and (d) KF samples with 4%–7% volume fraction ratios. (e) The conduction and radiation contributions as a percentage of the effective thermal conductivity in OT samples and (f) KT samples at 4% volume fraction. The conduction contribution makes up a greater percentage of the effective thermal conductivity over all measured temperatures for the OT samples compared to the KF samples, due to the higher geometrical factor in OT than KF. The radiation contribution as a percentage of the effective thermal conductivity increases with temperature due to the fourth-order relationship between radiative heat transfer and temperature.

Close modal

In comparison to KF counterparts with identical volume fractions, the OT structures show a higher effective thermal conductivity on average across the measured temperature range. This is attributed to the higher geometrical factor in OT (0.35) than KF (0.24) found in the conduction contribution to the effective thermal conductivity. The geometrical factors are based on the contribution of the struts parallel to the heat transfer direction from finite element modeling (FEM) analysis (supplementary material, Sec. 2.1).

The analytical modeling was utilized for creating a contour plot of the effective thermal conductivity as a function of volume fraction and temperature for both OT [Fig. 4(a)] and KF [Fig. 4(b)] lattice designs. The contour plots represent a design space for the effective thermal conductivity of OT and KF structures, where the dashed lines illustrate the constant effective thermal conductivity values. As shown, the slope of the constant thermal conductivity lines changes after transition for both lattice structures due to glass transition in the SMP material. For a given lattice structure (at a constant volume fraction), the effective thermal conductivity increases with temperature due to an increased radiation contribution. However, at a given constant temperature, the contribution of radiation heat transfer significantly decreases as the volume fraction of the structure increases, and conduction takes over as the primary heat transfer mode. At the volume fraction value of 1, the thermal conductivity of both designs converges to the intrinsic thermal conductivity of the bulk SMP, and the radiation contribution reaches zero.

FIG. 4.

(a) Contour plot of the effective thermal conductivity as a function of volume fraction and temperature for (a) OT and (b) KF samples. The dashed lines represent the constant thermal conductivity values, while the shaded regions are all thermal conductivity values in-between the dashed lines. When moving from the position of the yellow star to the green star, the temperature and effective thermal conductivity increase while the volume fraction remains constant. When moving from the position of the yellow star to the green star, the volume fraction and effective thermal conductivity increase while the temperature remains constant.

FIG. 4.

(a) Contour plot of the effective thermal conductivity as a function of volume fraction and temperature for (a) OT and (b) KF samples. The dashed lines represent the constant thermal conductivity values, while the shaded regions are all thermal conductivity values in-between the dashed lines. When moving from the position of the yellow star to the green star, the temperature and effective thermal conductivity increase while the volume fraction remains constant. When moving from the position of the yellow star to the green star, the volume fraction and effective thermal conductivity increase while the temperature remains constant.

Close modal

By increasing the volume fraction in Figs. 4(a) and 4(b), the OT lattice design demonstrates a higher effective thermal conductivity compared to the KF lattice due to a higher geometrical factor. For instance, for the OT sample at 50 °C and a volume fraction of 0.4 [represented by the yellow star in Fig. 4(a)], the thermal conductivity is ∼0.07 W m−1 K−1, and on an isothermal line, this value increases to 0.1 W m−1 K−1 at a volume fraction of ∼0.55 [represented by the blue star in Fig. 4(a)]. Conversely, its counterpart KF design demonstrates a thermal conductivity of ∼0.08 W m−1 K−1 at 50 °C and 0.8 volume fraction [represented by the yellow star in Fig. 4(b)], and its thermal conductivity increases up to 0.1 W m−1 K−1 while moving on an isothermal line to a volume fraction of ∼0.925 [represented by the blue star in Fig. 4(b)]. Figure 4 illustrates the significance of the geometrical factor in determining thermal transport within lattices of the same volume fraction. The results inform how future lattice design can optimize thermal transport by maximizing the fraction of struts in a lattice that lies parallel to the heat flow direction.

We investigated thermal transport in 3D printed shape memory polymers and identified the thermal conduction and radiation contributions. Our work showed that 60% or more of thermal transport in the KF and OT microlattices can be driven by thermal radiation even at relatively low temperatures due to the unique combination of the low intrinsic thermal conductivity, the high surface emissivity, and the high surface-to-volume ratio.

With lower material densities or higher porosities, thermal radiation becomes more important, and the architecture may play a more significant role in determining the thermal properties. This suggests that architectural design, as well as material selection, can lead to an effective means of controlling the thermal properties of 3D printed metamaterials. Furthermore, mechanical deformations and shape changes are expected to result in a significant change in thermal transport, and this suggests future opportunities to develop programmable thermal devices with 4D printing. Our findings provide a new understanding of thermal transport mechanisms in 3D printed shape memory polymers, and we believe that this can guide designs of future 4D printed metamaterials, shape-programmable architected materials, dynamic and adaptive thermal control devices, and building blocks of thermal information processing systems.

See the supplementary material for the complete information on the sample preparation and details of the analytical model.

H.L. acknowledges financial support from the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 1711154190) through the Institute of Advanced Machines and Design at the Seoul National University (SNU) and SNU Creative-Pioneering Researchers Program through the Institute of Engineering Research at SNU. Y.W. acknowledges the partial financial support from Rutgers University Busch Biomedical Grant Program. J.L. acknowledges financial support from the Civil, Mechanical, and Manufacturing Innovation (CMMI) Division of the National Science Foundation (NSF) (No. 1935371 and 1902685).

The authors have no conflicts to disclose.

Shiva Farzinazar: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (equal); Writing – review & editing (equal). Yueping Wang: Investigation (supporting); Validation (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Charles Abdol-Hamid Owens: Investigation (supporting); Validation (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Chen Yang: Investigation (supporting); Validation (supporting); Visualization (supporting); Howon Lee: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Jaeho Lee: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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Supplementary Material