High enthalpy storage thermoset network with giant stress and energy output in rubbery state

Low output in stress and energy in rubbery state has been a bottleneck for wide-spread applications of thermoset shape memory polymers (SMPs). Traditionally, stress or energy storage in thermoset network is through entropy reduction by mechanical deformation or programming. We here report another mechanism for energy storage, which stores energy primarily through enthalpy increase by stretched bonds during programming. As compared to entropy-driven counterparts, which usually have a stable recovery stress from tenths to several MPa and energy output of several tenths MJ/m3, our rubbery network achieved a recovery stress of 17.0 MPa and energy output of 2.12 MJ/m3 in bulk form. The giant stress and energy release in the rubbery state will enhance applications of thermoset SMPs in engineering structures and devices.

. Therefore, bond rotation or dihedral angle change is the only mechanism for the deformation. The peaks begin to shift towards lower frequency direction for the sample with 20% programming strain, which falls on the TZ in Fig. 1C, meaning that the bond length begins to be stretched. Therefore, bond enthalpy starts to increase. Larger shift occurs for samples programmed by 30%, 40%, and 45% pre-strains, indicating that the bond length is stretched more and more in LZ2 in Fig. 1C.
Supplementary Figure 18. The bond length change by X-ray spectroscopy.
Bond length change was confirmed by Near Edge X-ray Absorption Fine Structure Spectroscopy.
The first peak located at the 285.4 eV is identified as the C 1s→ C=C* (ring) resonance, which is calibrated by polystyrene. The second and the third peaks located at 287.4 eV and 289.0 eV are peaks associated with the C-H bond in the ring. The area used in the study is the wide peak located in the energy higher than 291eV. The carbon associated single bonds are the resonance for peaks such as C-C, C-O or C-N bond. It is seen that there is no shift between the 10% programmed sample and the control sample without programming. Therefore, the bond length of the carbon associated single bond does not change. With the increase in programming pre-strain, the peaks begin to shift towards lower energy direction, which proves that the bonds are stretched. Larger programming strain leads to larger shift in peaks, suggesting higher bond stretch, which is similar to the result by Raman Spectroscopy.
Supplementary Figure 19. The relationship between force constant of anharmonic oscillation.  PCL-2T-MA**** N/A 1.5 N/A 400% *The real energy output is calculated by the area of the enclosed by the recovery stress-recovery strain curve for polymers. For metals, it is calculated by the elastic part of the area of stress-strain curve.
** The over-estimated energy output is calculated by the area of the right triangle determined by the fully constrained recovery stress and free shape recovery strain as the two vertexes of the right triangle.
Supplementary Although not synthesized, we believe that the system has a certain synthetic flexibility. We think that diamines with rigid cyclic structure which provides the large steric hindrance, such as methyl groups, are potential molecules. They are possible to help the formed thermoset network to store the energy as enthalpy during programming. This catalog of potential molecules is listed in the Supplementary Fig. 2A. Moreover, the poly-cyclic and heterocyclic diamines with the groups that can provide steric hindrance are also considered as potential candidates as shown in Supplementary Fig. 2B as the second catalog. Other than cyclic, poly-cyclic or heterocyclic structure serving as the rigid structural center, caged structures, such as carbon black, carbon nanotube (CNT) or polyhedral oligomeric silsesquioxanes (POSS), with amino groups, are also possible candidates, once the rigid structural center is surrounded by groups that can provide enough steric hindrance (such as the type I structure shown in Supplementary Fig. 2C). We can also graft the IPD onto the surface of acidized carbon black or CNT (such as the type II shown in Supplementary Fig. 2C). These structures can be considered as the catalog three. In summary, if the amines have a rigid center, such as cyclic or caged structure, and grafting by these groups may provide steric hindrance, which are the possible chemical structures for the enthalpy storage.
Grafting EPON epoxy onto the surface of rigid center such as carbon black, CNT or some nanoparticles, may be another way of synthesizing this type of SMPs.

Differential scanning calorimetry test
The differential scanning calorimetry (DSC) test was performed by DSC 4000 (PerkinElmer) for the investigation of the thermal behavior of the synthesized polymer network and the enthalpy release for the programed sample. The glass transition range and glass transition temperature were determined by the second heating branch. The temperature scan was conducted as following steps: equilibrate at 30° for three minutes, heat to 170°C, equilibrate at 170°C for three minutes, cool down to 30°, and equilibrate at 30° for three minutes. Then the heating and cooling cycle is repeated from second step to fifth step. All heating and cooling rates were Next, the baseline for the first order transition (enthalpy), i.e., the first heating cycle for the compression programmed specimen, was determined. We considered the natural physical process occurred during the first heating cycle of the programed sample. We assumed that the inverse peak shown in the first heating cycle in Supplementary Fig. 4 was a result of two competing physical processes. The first process was the normal glass transition, which absorbed heat, and the second process was the enthalpic energy release, which gave off heat. We also assumed that the evolution of the heat flow due to the glass transition alone was almost the same between the first and second heating cycles (Normally, there is a little difference between the first and second heating cycles due to the processing history.). We further assumed that the actual baseline of the first heating cycle for the programmed sample was separated into two parts. The first part was the glass transition and the trend of the baseline was the same as the second heating cycle glass transition baseline shown in Supplementary Fig. 4. The heat flow due to the enthalpy energy release can cause the glass transition baseline shift to lower value. This shifting baseline curve shown in the Supplementary Fig. 4 was used as the correction for the glass transition baseline. In this study, we assumed that the shifting baseline curve was a straight line connecting the two end points in the glass transition region. The combination of the shifting baseline curve and the glass transition baseline was the real baseline for calculating the energy release. Based on this real baseline, the heat release between 140 °C and 150°C was calculated to be 2.85 J/g by integrating the heat flow curve. Based on the density of the EPON-IPD, the enthalpy release was found to be 3.25 MJ/m 3 .

Dynamic mechanical analysis
The thermomechanical property of the synthesized polymer network was analyzed by a TA Instruments Q800 Dynamic Mechanical Analyzer (DMA). Using the multi-frequency mode, the three-point bending test was carried out with fixed displacement. The temperature was scanned at a rate of 10°C/min. The storage modulus, loss modulus and tanδ were recorded against temperature as shown in Supplementary Fig. 5.
The thermal expansion behavior was also measured by the DMA under the controlled force mode. The fixture was changed to the tensile clamps. The cyclic temperature was scanned from -25°C to 180°C. The obtained data are shown in Supplementary Fig. 6. From the calculation based on the data presented in Supplementary Fig. 6, the coefficient of thermal expansion is 1.25×10 -4 °C -1 for the EPON-IPD network.

Sample preparation and compression programming
A perfect alignment is a significant factor for the uniaxial compression test. Hence, the cured bulky polymer network was cut and then carefully milled into a cuboid. The tolerance for each pair of parallel surfaces was less than ten micrometers. The obtained cuboid samples are shown in Supplementary Fig.7A. All edges of the cuboid samples are between 6.5 mm and 7.5 mm.
Uniaxial compression programming was then conducted. Before this process, the oven, specimen and fixture have already been heated at 170°C for over an hour, to avoid the effect of thermal expansion. The compression process is shown in Supplementary Fig. 8.
Step one represents the relationship between the stress and strain during the compressive deformation up to 45% strain at 170 o C. After this, stress relaxation occurred in step two (Note: in the literatures, step 1 and step 2 are usually treated as one step. For clarity of presentation, we divided them into two steps). The step three shows the relationship between stress and temperature during the cooling process, while holding the strain constant. The air cooling process was performed by opening the door of the oven only. It is interesting to note that the unloading step, which is needed for a typical programming, is coupled with the cooling step. The load becomes zero at about 80 o C, due to thermal contraction of the specimen. The compression programming was completed when the temperature drops to room temperature.
In order to understand the shape fixity capabilities of the SMP, we have tested the shape fixity ratio of the polymer at different programming strains, which are listed in Supplementary   Table 1. Both the mean and standard deviation are given. Each shape fixity ratio in the table is the average of the test results of three compression programming with the same programming strain.
The compression programming was conducted at 170 o C.
From the test results, the shape fixity ratio is quite stable for different programming prestrains. These shape fixity ratios are regarded as very good values for such a stiff shape memory polymer. Lower programming pre-strain leads to a slightly higher deviation. This is a reasonable outcome due to the inherent instrument errors or resolutions.

Sample preparation and tension programming
During tensile programming, the specimen with a dimension of 50 mm × 14.5 mm × 5 mm was mounted onto one end of the grips of the mechanical test machine before the oven was equilibrated at 170°C for an hour. Then, the specimen was fixed by tightening the other end of the grips and tensile programming was executed. The specimen was stretched to 10% strain at 170 o C.
After holding for 10 minutes, the pre-stretched specimen was cooled down quickly to room temperature by spraying water onto the specimen while holding the programming strain constant.
The load was then removed to fix the programed shape.

Supplementary Discussion
Free shape recovery test Free shape recovery, as an important feature of shape memory polymers, is influenced by the deformation manner during the programming process. The polymer network in this study was an entirely continuous network. Permanent deformation rarely happens except for breaking the chemical bonds. Consequently, without defect and damage of the network, the free recovery should reproduce the permanent shape. To test this property, the sample, prepared in Supplementary Methods, was compressed by the Mechanical Testing System (MTS) QTEST 150 machine for 40% of strain at 170°C as shown in the digital photos in Supplementary Fig. 7B and 7C. After the sample was cooled down to room temperature and unloading, it was placed back into the oven and was heated up to 170°C to trigger the free shape recovery. The photo of the recovered sample is presented in Supplementary Fig. 7D. The free shape recovery ratio is 99.9%.

Fully constrained stress recovery test
The fully constrained recovery stress of a shape memory polymer indicates the potential as a mechanical actuator for future structural applications. Recovery stress is obtained by heating the network to above the glass transition temperature (in rubbery state), but without allowing any recovery strain. In order to obtain the stabilized recovery stress, the specimen was held at the recovery temperature for hours. To investigate this property, the fully constrained recovery stress test was conducted on specimens programmed by 45% compressive strain. The test was conducted by the MTS QTEST 150 machine for 8 hours, as shown in Fig. 1A in the main text. Before placing the programmed sample into the oven, the inside environment of the oven has been stabilized at 170°C for one hour.
For tension programmed specimens, the recovery stress evolution with time was determined following the same procedure as compression programmed specimens; as shown in Supplementary Fig. 9. From Supplementary Fig. 9, one can see that the specimen with 10% tensile pre-strain can produce 5.1 MPa stable recovery stress in the rubbery state. As shown in Supplementary Fig. 14, the tensile programming stress with 10% strain is about 7.0 MPa. We would say that with 7.0 MPa stress input, 5.1 MPa stress output (recovery stress) is reasonably high. However, because the tensile fracture strain of the polymer at 170 o C is about 12%, we did not do tensile programming higher than 10%.
To consider the effect of programming temperature on the recovery stress, two types of additional compression programming were conducted. In one type, a compression programming at the glass transition region (150 o C) has been conducted. The pre-strain is 45%, and the fixed strain is 41.8%, which is almost the same as the fixed strain by programming at rubbery state (170 o C) with the same pre-strain 45%. The similar fixed strain makes the comparison meaningful.
In the second type of programming, three specimens were programed into the same fixed compressive strain which was 32% at different temperatures (20 o C (glassy state), 150 o C (glass transition zone), and 170 o C (rubbery state)). All the programmed specimens, then, were recovered at 170°C under the fully constrained conditions.
From Supplementary Fig. 10, the peak recovery stress is about 15MPa and the stable recovery stress is about 14 MPa. Both the peak value and the stable value are lower than 17MPa, which is the stable recovery stress produced by the specimen programed in the rubbery state. This is an unusual phenomenon for shape memory polymers (SMPs). For entropy driven SMPs, the recovery stress is usually higher when the programming temperature lowers, i.e., glassy state programming has higher recovery stress than programming at glass transition zone, and the least is programming in the rubbery state. This can be understood due to the temperature memory effect, i.e., the recovery temperature is lower if the programming temperature is lower. At lower recovery temperature, the stiffness of the SMPs is higher, leading to higher fully constrained recovery stress.
For the enthalpy driven shape memory EPON-IPON network, it stores energy primarily through the enthalpy increase due to the change in bond length. Therefore, how much enthalpy is stored or how many bonds are stretched during programming determine the recovery stress produced in the rubbery state. As discussed in the main body of the paper, the bonds can be changed only when they are rotated to a very high energy level. Therefore, if some regions (segments) are not soft enough to rotate, most bonds located in the segments are not stretchable.
This means that the ability for enthalpy storage is not fully taking effect. At higher temperatures, bond rotation is more likely, and thus enthalpy can be increased through bond stretch. In conclusion, for this enthalpy driven SMP, programming in rubbery state leads to higher recovery stress than that in glass transition zone, which can be further validated by Supplementary Fig. 11.
From Supplementary Fig. 11, it is clear that the higher programming temperature can produce higher recovery stress. This is a proof of the argument that, for this enthalpy driven SMP, higher programming temperature leads to higher recovery stress. It is interesting to note that, for this SMP, temperature memory effect still exists. The specimen programmed at lower temperature recovers at slightly lower temperature. As mentioned previously, for entropy driven SMPs, this may lead to higher recovery stress for specimens programmed at lower temperature. For this enthalpy driven SMP, although this effect still exists, programming at lower temperature still leads to lower recovery stress. This is an evidence of the enthalpic dominance in this SMP system.

Relationship between recovery stress and recovery strain
A significant advantage for shape memory polymers, as compared to shape memory alloys (SMAs) or ceramics, is their large recovery strain. While SMAs have a very high fully constrained recovery stress, may be in hundreds of MPa, their free recovery strain is very small, may be less than 10%. Eventually, SMPs may output comparable energy against SMAs (1). For shape memory materials, fully constrained recovery stress and free shape recovery strain are the two extreme cases of measuring their memory capability. If recovery strain is allowed, the recovery stress will be reduced. In many applications, stress recovery must be accompanied by strain recovery, such as using shape memory effect for closing wide-opened cracks in self-healing applications or as actuators. Therefore, it is highly desired that SMPs have high recovery stress with considerable recovery strain. Actually, the area generated by the recovery stress -recovery strain curve is a direct measurement of the energy output. To obtain the relationship between recovery stressrecovery strain, the recovery stress at different recovery strains is tested as follows. A fully constrained recovery stress test for samples programmed by 45% strain was used to obtain one boundary point in the recovery stress -recovery strain curve, here zero recovery strain. The value of the recovery stress was measured after the stress was stabilized for 1.5 h at 170 o C. Another boundary point is the free shape recovery test, here zero recovery stress. The samples were allowed to recovery free of constraint in the oven at 170 o C for half an hour. For other points in the recovery stress -recovery strain curve, the clamp of the MTS machine was positioned to allow 2.5%, 7.5%, 12.5%, 17.5%, 22.5%, and 32.5% recovery strains, respectively. All the tests were conducted at 170 o C for 30 -40 minutes to obtain stabilized recovery stress. The exact recovery time was determined by the variation of the stress. When the change of the recovery stress was less than 0.01MPa in 10 minutes, the value was taken and the test was stopped. The whole process was repeated for three different samples, and the averaged recovery stress with one standard deviation at different recovery strains is plotted in Fig 1B in

Stress relaxation behavior at different temperature zones
At room temperature, the polymer network, which is in glassy and non-equilibrium state, will also relax to the equilibrium state although it will take a very long time. This circumstance is referred to as physical aging. At a high temperature, especially when it is close to the glass transition zone, the relaxation is accelerated significantly. Thus, to analyze the compression behavior during programming, the relaxation performance is needed. The stress relaxation test was conducted at four different temperatures, which were 120°C, 155°C, 170°C and 175°C. All samples were compressed to 40% strain, and then the deformation was maintained to let the stress relaxation occur. All relaxation data were normalized by the peak stress, σ0, obtained at the end of compression; see Supplementary Fig. 12. Although the higher temperature softens the thermoset network more, the intense steric hindrance helps the electrons pack more tightly. Consequently, the network is stable at even higher temperatures and this is one of the reasons for the giant stress recovery at rubbery state.

Strain rate effect on stress storage
Due to the time-dependent behavior of the polymer network, loading rate should have an effect on the relaxation behavior. We have conducted the stepwise stress relaxation test with three strain rates: 0.1mm/mm/min, 0.25mm/mm/min, and 0.5mm/mm/min; see Supplementary Fig. 13 A, B, and C. As expected, the stress increases as the strain rate increases; and the relaxed stress, or stored stress, see Supplementary Fig. 13D, also increases. This is understandable because higher strain rate means shorter time for stress to relax. It is noted that, regardless of the strain rate, the three zones exist; see Supplementary Fig. 13D. This suggests that the stress is stored by both entropy and enthalpy. However, we do see that higher strain rates lead to higher residual stress or stored stress, suggesting higher recovery stress and energy output.

Mechanical behavior at room temperature
Most applications of SMPs require that they work at ambient temperature. Hence, the mechanical property at room temperature is important. SMP samples were compressed until fracture at room temperature by the MTS QTST 150 machine. The strain rate was 1mm/min. The test results are shown in Supplementary Fig. 14.

Tensile behavior at rubbery state
The tensile stress-strain behavior of the SMP was also investigated at rubbery state. The specimens were fabricated into a rectangular shape with a dimension 50 mm × 14.5 mm × 5mm.
The strain is calculated by the gauge length of 15mm of the specimen, which is the length between the two marks as shown in Supplementary Fig. 15. The test temperature was 170 o C, and the strain rate was 0.03mm/mm/min. One can see that the polymer can only be stretched by about 12% strain before it fractures at 170 o C. The peak stress or tensile strength of the SMP is about 7.1 MPa.
Therefore, when we tested the tensile recovery stress of the SMP, we selected 10% strain as the tensile programming pre-strain at 170°C.
Temperature, as a critical parameter affecting the mechanical properties of polymers, can be separated into different regions around the glass transition. When the temperature is lower than the glass transition zone, sufficient energy input is needed to render the coordinated segmental rotation to occur. Within the glass transition zone or at even higher temperatures, the bond rotation can happen at any strain because the thermal energy has already overcome the energy barrier for segmental bond rotation. Therefore, the deformation applied is an energy source to compel the polymer network into a non-equilibrium and locally high energy state. The relaxation will happen to stabilize the total energy towards a locally low energy state simultaneously. Thus, the characteristics of the relaxation is associated with the conformational and structural evolution during deformation. However, the relaxation reflected on the testing machine is always delayed because the relaxation is time dependent. Hence, to uncover the conformational and structural variation hidden during the deformation, a stepwise iso-strain compression-relaxation test was performed as follows. The sample was equilibrated in rubbery state, which was 175°C, before compression. In each step, two percent compressive strain was applied, and then relaxation was allowed for four minutes. The sample was compressed for a total of forty-four percent of strain.
This test was conducted by the MTS QTEST 150 machine with an assembled oven controlled by a Eurotherm Controller (Thermodynamic Engineering Inc. Camarillo, CA). The stress against applied strain and temperature are plotted in the Supplementary Fig. 16.

Raman spectroscopy
Raman Spectroscopy, as a characterization method for the vibrational energy of chemical bond, is a very useful tool for revealing the variation of the bond length (8,9). In this study, bond length is a significant parameter for enthalpy storage. After programming (rubbery state compression, cooling and unloading), a temporary configuration is fixed in the network. Whether or not the bond length has been changed can be observed by Raman Spectroscopy at room temperature. The measurements for the samples programmed by different strains were performed by LABRAM integrated Raman spectroscopy system manufactured by Johin Yvon Horiba. The 1mW He-Ne Laser was used as the excitation probe and the wavelength was 632.81 nm. Both focusing and collecting the backscattered light were carried out by a 10× objective lens. The Raman shift was scanned from 800 cm -1 to 1300 cm -1 . The shifting of peaks is labeled with the type of bond as shown in Supplementary Fig. 17. Both qualitative and semi-quantitative result can be obtained.

X-ray spectroscopy
To further confirm the change of bond length, the Near Edge X-ray Absorption Fine Structure (NEXAFS) Spectroscopy technique was also used. NEXAFS as a specific element related technique can resolve the electronic structure of molecule or molecular fragments (10,11).
Carbon is the main element in the synthesized polymer network. Therefore, the C 1s K-edge spectrum was collected and used for the analysis of carbon involved bonds as shown in Supplementary Fig. 18. The first peak was identified as the C 1s→ π* (C=C) peak at 285.4 eV by polystyrene. The spectrum collection was carried out by the GEOL 7900 X-ray absorption spectrometer associated with the low energy beamline from the synchrotron located at the Center for Advanced Microstructures and Devices (CAMD), Baton Rouge. The grounded polymer powder was mounted on the copper tape as the testing sample. Subsequently, the sample was anisotropic and the shifting of the peak in the spectrum was due to the variation of the bond length only. The compressed polymer network by different strains was milled by sandpaper gently in a -20°C environment to reduce the heat produced by friction.

Enthalpy storage
The chemically cross-linked network in the rubbery state can be treated as a supramolecule.
When the deformed subject is treated as an elastic body in rubbery state, the energy stored is described by the Mooney's equation (12)(13)(14): where and are constants, , and are stretches in three-dimensional coordinate. For example, / where is the length after deformation in x direction and is the original length along the x axis. If the volume is assumed to be a constant, 1. As a simplified case, let , 1/ / , the retractive stress , given by , is: If is the stretch ratio in uniaxial test by a mechanical testing machine, the retractive stress can be used as the prediction of the deformation stress applied by loading. When is greater than 1, the sample is under tensile test. On the other hand, if the sample is compressed, the value of is less than one. In this case, the value of is negative, which represents that the retractive stress turns to compression.
The first term in the right-hand side of Supplementary Equation 2 is actually related to the change of conformational entropy. The change of the conformational entropy per volume (∆ ) is described by the following equation: where is density, is the gas constant, and is the molecular weight between closest crosslinking points or chain entanglements. The associated retractive or expansive stress ( ) is derived by ∆ / as the following equation: possibly dominant more than the first term because the value of α is less than 1 in compression programming. The 1/α 3 term is greater than 1/α 2 . Therefore, the second term is likely related to enthalpy increase, or bond stretch.
From the analysis in the main body of the paper, the energy storage is still entropy dominant when the programming strain is less than 20%, which can be confirmed by Supplementary

Recovery Stress
The energy storage mechanisms in the shape memory network can be further explained by the recovery stress. Let's first assume that the energy is stored by entropy only. The recovery stress at the maximum programming strain can be estimated by the following empirical equation for the change of entropy (15) where ∆ is the stored entropy, is the maximum programming strain and the is the associated recovery stress, is the ratio of loss modulus to storage modulus, and is the cross-link density which equals to / as defined in equation Supplementary

ln Supplementary Equation 7
By using the same parameters applied to the section of enthalpy storage in the Supplementary Discussions and the value of being 0.77 (from the data in Supplementary Fig.   5), is calculated for the 45% programed sample, which is equal to 7.0 MPa. This value is much lower than the measured recovery stress shown in Fig. 1A and 1B in the main text. Therefore, entropy reduction alone fails to predict the test result. Enthalpy increase can explain the difference between the measured recovery stress (about 17 MPa) and the entropic recovery stress (7 MPa).

Stress needed to change the bond length
From the section of enthalpy storage in the Supplementary Discussions, energy storage mechanism other than entropy reduction must be considered to explain the difference between test results and model predictions. The vibrational energy associated with the chemical bond is an effective indicator for the change of the bond length such as carbon-carbon single bond. Raman spectroscopy, as the characterization technique analyzing the vibrational energy corresponding to the chemical bonds, is a powerful tool to determine the change of the bond length qualitatively.
The semi-quantitative approximation can also be done by using the proportionality constant, between the change of chemical bond shift and the stress needed to cause the bond shift. The detailed theoretical explanation is as follows.
The potential energy of chemical bond during the deformation is approximated by the Morse function (16) for anharmonic oscillation: 1 Supplementary Equation 8 where is the potential energy, is the dissociation energy which is the energy needed to break the bond. Here b is a constant that equals to /2 , where is the force constant at the minimum point of this function. The term ( is the change of interatomic distance.
The second derivative of Supplementary Equation 8 provides the force constant of the oscillation as following:

Supplementary Equation 9
According to Tashiro (17), the chemical shift or frequency ( ) is proportional to √ . From Supplementary Equation 9, in a small range around x0, k decreases monotonically as shown in Supplementary Fig. 19. Therefore, when ∆ is positive, ∆ is negative and the chemical bond is under stretching. To the opposite, when ∆ is negative, the force constant increases, causing the frequency shift to higher values.
Based on Rretzlaff and Wool (18), the variation of frequency (∆ ) is proportional to the applied stress. In our case, the change of the chemical bond shift in the Raman spectroscopy is observed without external loading, thus it is caused by the internal stress. This internal stress is also proportional to ∆ .
The standard method to characterize the correlation between the Raman peak shift and the internal stress is the in-situ testing. The variation of the Raman shift should be observed during the deformation. The relationship between the peak shift and the external loading can be assumed as a linear fashion. During Raman test, the deformation is stepwise or very slow. Therefore, the internal stress is assumed the same as the external loading. Curve fitting may also be needed to estimate the precise coefficient. Based on this discussion, the EPON-IPD network also needs the coefficient for all the types of bonds. Without the in-situ Raman spectrometer associated with the mechanical deformation accessories, as a rough estimation, we turn to the equation proposed by Wei et al. (19), which links the internal stress, Raman shift, and modulus of elasticity of the materials:

∆ Supplementary Equation 10
where σ is the residual stress, E is the Young's modulus, ν is the Poisson's ratio, ∆ω is the variation of the Raman shift, and ω0 is the reference Raman peak (original peak where internal is the stored internal stress due to programming. N stands for the number of bonds and the subscript of N means the type of bond in a representative molecular unit (repeating unit).
The subscript total is the sum of the number of bonds for all types of bonds within the repeating unit, i.e., .
Next, let us count the numbers for each type of bonds in the repeating structure. This percentage is the same for the whole network when we neglect the defects and end groups. Plug in all the parameters in Supplementary Equation 11, we find that internal = 43.8 MPa.
Combining the entropic stress of 20.5 MPa, the total internal stress due to programming is 64.3 MPa, which is close to the programming stress of 60 MPa. It has been known from polymer physics that both entropy and enthalpy, along with other factors, contribute to energy storage (20). Again, this very rough estimation confirms that, for this thermoset SMP, both entropy and enthalpy contribute to energy storage; however, with higher programming strain, enthalpy storage predominates.

Steric hindrance
To prove the argument of the steric effect, we take four steps.
Step 1, based on the knowledge of organic chemistry and the chemical networks that have already been investigated, we assume that a certain group or groups provide the significant steric effect to the EPON-IPD network.
Step 2, we find a diamine molecule with the exact or very similar structure but without the groups which are assumed to supply the steric hindrance.
Step 3, we react the diamine with the EPON826 and obtain a thermoset network.
Step 4, we test the thermal property, recovery stress and the energy storage mechanism to check if our argument of the steric effect is correct or not.
The first three steps are illustrated as the Supplementary Fig. 22. We assume that the groups providing the significant steric hindrance are the methyl groups in the IPD molecule including position one and position three (the ones with scissor). The ideal diamine is the molecule without these three methyl groups as shown in Supplementary Fig. 22. By searching the available and commercialized molecules, the 1,3-Bis (aminomethyl)cyclohexane (BACH) is chosen as the model diamine because it is a very similar molecule with the ideal structure but without the high steric hindrance (methyl groups); see Supplementary Fig. 22. To keep stoichiometry, the molar ratio of EPON and BACH is two to one.
In step 4, the thermal property of the synthesized EPON-BACH network is tested by DSC and the result is shown in Supplementary Fig. 23. The range of the glass transition is between 140°C and 150°C, which is a comparatively high glass transition range. This means that the EPON-EPON-IPD network, the thermoset polymer is compression programmed into 45% pre-strain as illustrated in Supplementary Fig. 24A. The recovery stress is also investigated and the result is shown in Supplementary Fig. 24B. The only difference here is the temperature for the programming and recovery which is 160°C, other than 170°C for the EPON-IPD network. The 160°C is 10 °C higher than the end-set point for the glass transition region for the EPON-BACH, which ensures that the programming and the recovery occur at the rubbery state for this thermoset polymer.
From Supplementary Fig. 24A, one can see that the maximum compressive stress (about 38 MPa) corresponding to the 45% pre-strain is lower than the EPON-IPD network, which is about 60 MPa, suggesting that the EPON-IPD network is stiffer. From Supplementary Fig. 24B, the recovery stress for the EPON-BACH is only about 8.5MPa which is much lower than the EPON-IPD network (17 MPa). This is a clear evidence that, the polymer network without the methyl groups cannot provide the steric hindrance and thus the recovery stress is much lower.
To verify the mechanism for the energy storage, the programmed EPON-BACH sample with the 45% pre-strain is characterized by DSC and the result is shown in Supplementary Fig. 25.
Different from the EPON-IPD network, no inverse peak appears during the first heating cycle. It is proved that there is no enthalpy release during the free shape recovery process. Combining with the result of the recovery stress, it is concluded that the very similar thermoset network EPON-BACH, without the methyl groups attached on the cyclohexane structure in the diamine, cannot store energy in the form of enthalpy during the programming and the recovery stress is much lower than the EPON-IPD network, which consists of the methyl groups to provide the steric hindrance.
Therefore, the argument on steric hindrance due to the methyl groups is valid.

Detailed explanation of the multiple energy well model
The concept of energy well against change of conformation is not a creation out of nothing.
The potential energy changes by the rotational dihedral angle for butane and conformation for cyclohexane have been estimated for decades as the illustration shown in Supplementary Fig. 26.
The butane can be treated as the smallest polyethylene which is a dimer. During the rotation of σ bond in the middle, the potential energy of the molecule fluctuates in a well-shape. When the methyl groups, which are electron rich groups in a butane, are closest to each other, the electronrepelling leads to the highest potential energy. The spatial position between chemical bonds is the electron acceptable space (we can call it electron acceptor or electron hole). When the electron rich group is stabilized in the space lacking electrons, the total potential energy of the molecule is reduced. Once electron rich groups find the most comfortable positions as shown in Supplementary   Fig. 26A-a and j, the potential energy touches the ground state. On the other hand, the stable positions that can still be found are local lowest potential energy states which are called metastable states as shown in Supplementary Fig. 26A-c and e. It is obvious that the potential energy of the metastable state is higher than the ground state, and more polymer repeat units form more metastable states. For example, the metastable state in butane is 3.8 kJ/mol higher than that of the ground state. The energy evolution by free rotation of chemical bonds was studied by Flory (21) and Tylor in 1940s (22). The multiple energy well model is based on this established knowledge.
Nevertheless, some differences need to be pointed out. Firstly, the metastable position of bonds is not only affected by the intramolecular interaction like butane, but is also affected by the intermolecular interaction. In other words, the circumstance of the rotatable segments in a polymer network also affects the variation of the energy states. All interactions in molecular level can be generalized by electron repelling (peak of energy well) or electron stabilization (bottom of energy well) by electron acceptable space (electron acceptor) or electron vacancy space (electron hole).
During the rotation of the chemical bonds, the local metastable position can be reached. The process of searching then staying at a metastable position can be imaged as the CSBs fall into an energy well. Secondly, both tension and compression cannot rotate the torsional angle to exceed the limit, which is 180 degrees. Therefore, during the programming of the polymer network, the pattern of potential energy is not symmetry as butane. Only half of the pattern can be revealed and it is kept ramping up.

Free shape recovery versus exothermic chemical reaction
The free shape recovery, as a spontaneous process associated with Gibbs free energy variation, has a lot of analogies compared with an exothermic chemical reaction as shown in Supplementary Fig. 27. The classical interpretation of a chemical reaction is described as follow.
Although the free energy of reactants is higher than the product, the reaction will not occur without the activation energy. Before the spontaneous process happens, the reactants need to be excited into a high energetical level by heat, light, microwave or others. The total free energy will be stabilized by the variation of the molecular structure or degree of freedom. The Gibbs free energy of reactants is higher than the products and the free energy can be separated into enthalpy part and entropy part. The enthalpic part is due to the type of chemical bonding that is changed. In shape memory effect, although the free energy of the fixed polymer network is higher than the original shape, it will not recover spontaneously without energy input. After the excitation by heating, the spontaneous transition will happen. The total energy is stabilized by the conformational and structural variation in the network during the recovering. The total free energy of the polymer network can also be separated into the enthalpic part and entropic part. The difference between these two phenomena is that the chemical bonds, regardless of reactants or products, exist naturally. The conformation or structure of the polymer network located at high energy state needs programming.

Recovery rate
The recovery rate of SMPs during free shape recovery is a significant property for all shape memory polymers. In this multiple energy well model, it corresponds to the time for the CSBs to roll down to the ground state. The free recovery process can be divided into two regions. The driving force for the high-energy region is the combination of entropy and enthalpy. In this region, the CSBs will be pulled back to low energy well by the stretched bonds. Subsequently, the CSBs located at the peak of an energy well is not in an equilibrium state. In this case, the driving force from the stretched bonds is the dominant factor for controlling shape recovering rate. In the lowenergy region, the driving force that helps the CSBs fall back into low energy well is entropy only.
If the chance of falling into an old or new energy well is equal, the frequency of CSBs vibrating in one energy well will determine the recovery rate. These characteristics is affected by the intrinsic property of the network, the environment of rotatable bond, and the temperature.

Recovery ratio
Although the multiple energy well model assumes that the polymer network contains no defect and no permanent deformation happens during the programming process, this model is capable of explaining the shape memory effect (SME) with plastic deformation by slight modification as shown in Supplementary Fig. 28A. Even for a perfect polymer network, permanent deformation can happen such as breaking chemical bonds due to over-programming. It happens much more easily for physically crosslinked SMPs because the network is constructed by chain entanglements or intermolecular interaction. The shape is hardly recovered when permanent deformation occurs. In this case, the term named shape recovery ratio is employed to define the recovered shape or strain quantitatively.
As shown in Supplementary Fig. 28B, energetic wells will break into discontinuous pieces if the permanent deformation happens. The energy absorbed when the SME is triggered will be consumed by the completed recovering part. If the rest of the energy is not able to overcome the energy gap formed by permanent deformation, the shape recovering will not happen for the residual shape (strain).