Minhwan
Lee
a,
Min Young
Ha
a,
Mooho
Lee
b,
Ju Hyun
Kim
b,
Sung Dug
Kim
b,
In
Kim
*b and
Won Bo
Lee
*a
aSchool of Chemical and Biological Engineering, Seoul National University, Seoul 08826, Republic of Korea. E-mail: wblee@snu.ac.kr
bMaterial Research Center, Samsung Advanced Institute of Technology, Samsung Electronics Co., Ltd, Gyeonggi-do 16678, Republic of Korea. E-mail: in1.kim@samsung.com
First published on 2nd March 2022
The epoxy-based crosslinked polymer with the mesogenic group has been studied as a candidate resin material with high thermal conductivity due to the ordered structure of the mesogenic groups. In this study, we conducted all atomic molecular dynamics simulations with iterative crosslinking procedures on various epoxy resins with mesogenic motifs to investigate the effect of molecular alignment on thermal conductivity. The stacked structure of aromatic groups in the crosslinked polymer was analyzed based on the angle-dependent radial distribution function (ARDF), where the resins were categorized into three groups depending on their monomer shapes. The thermal conductivities of resins were higher than those of conventional polymers due to the alignment of aromatic groups, but no distinct correlation with the ARDF was found. Therefore, we conducted a further study about two structural factors that affect the alignment and the TC by comparing the resins within the same groups: the monomer with an alkyl spacer and functional groups in hardeners. The alkyl chains introduced in the epoxy monomers induced more stable stacking of aromatic groups, but thermal conductivity was lowered as they inhibited phonon transfer on the microscopic scale. In the other case, the functional groups in the hardener lowered the TC when the polar interaction with other polar groups in the monomer was strong enough to compete with the pi–pi interaction. These results represent how various chemical motifs in mesogenic groups affect their alignment on the atomistic scale, and also how they have effects on the TC consequently.
To facilitate the intelligent design of mesogenic epoxy polymers with high thermal conductivity, it is crucial to develop a microscopic understanding of the correlation between molecular alignment and the transport of thermal energy. Molecular dynamics (MD) simulation can be a very advantageous tool to analyze the epoxy-based crosslinked polymers because it yields the atomistic details in the crosslinked structure and the macroscopic properties of the materials. A major obstacle in epoxy MD simulation is the proper construction of the crosslinked polymer network in a periodic simulation box: one-shot polymerization of randomly mixed monomers and hardener molecules might result in an unrealistic structure. In this regard, several reports suggested simulation procedures to construct stable atomistic configurations of resins where we utilized the method described by Varshney et al.15–17 They proposed numerical procedures to obtain stable crosslinked EPON-862/DETDA resin from iterative runs of MD simulations to gradually equilibrate the system. Furthermore, they showed the correlation between the TC and the structure in the other papers.16,18 Li et al. performed MD simulation with a similar procedure to study the thermal conductivities of ordered epoxy resin according to external strain.19 In respect of a variety of chemistry, simulation results from various epoxy resins have been reported, especially with more attention to the high-TC epoxy resin-based nanocomposites augmented with fillers such as graphene and boron nitrate.20–22
However, there are few computational studies focusing on the thermal conductivity of the epoxy resins generated from mesogenic monomers. Skačej et al. conducted Monte-Carlo simulation studies with the coarse-grained model to investigate the structure of a liquid crystal elastomer but did not deal with its thermal conductivity.23,24 Koda et al. compared experimental TC data of epoxy resin and intentionally ordered structures of liquid-crystalline epoxy monomers from MD simulation.25 However, their study lacks an explanation about how the MD configuration represents the microscopic structure of the material from which the TC results were measured. Especially, as Varshney et al. showed, generating structures by iterative crosslinking procedures is crucial for the accurate evaluation of thermal conductivities but the process was omitted in the previous reports.18 To the best of the authors' knowledge, there is no systematic study correlating the mesogenic structures and the resultant thermal conductivities in crosslinked polymer resins.
In this paper, we studied various kinds of cross-linked polymers using all-atomic MD simulation to reveal the effect of their molecular architectures on the TC. We performed iterative annealing and crosslinking simulations to generate realistic network structures. Then, we investigated the aligned structure of cross-linked polymers by calculating the angle-dependent radial distribution function (ARDF) among aromatic groups and measuring the thermal conductivities using the Green–Kubo relation. As aligning behavior showed distinct characteristics according to chemical motifs, we classified the studied epoxy resins into three different groups. Meanwhile, the TCs of resins were higher than that of conventional polymer materials as expected from the aligned structure noticed in the ARDF but no quantitative correlation was found between them. Therefore, two additional structural factors were studied by comparing resins within the same group; the first is a flexible alkyl chain that is introduced into monomers as a spacer and the second is the functional groups in hardeners whose polarity affects interaction with monomers. The results indicated that the aligning behavior of epoxy monomers and the TC of resins were both affected by those geometric factors complicatedly. Consequently, the detailed atomistic investigation by MD simulation gives a direction to enhance the thermal conductivities by exploiting the relationship between the chemical structure of molecules, the resultant aligned structure, and the thermal conductivity.
To generate epoxy crosslinking from an equilibrated EH mixture, all pairs of epoxy and amine functional groups were scanned, and the pairs closer than a prescribed cut-off distance were converted to crosslink bonds. The cut-off distance for the reaction was initially set to 4 Å but if no functional group pair was found the cut-off was increased by 1 Å. In addition, to prevent the formation of unphysically long bonds with extreme forces, the cut-off distance was not increased beyond the maximum cut-off of 6 Å. The positions and interaction parameters of atoms in the selected functional groups were modified to make a crosslinked bond structure mimicking the real ring-opening reaction of epoxy and amine groups as depicted in Fig. 1(b). The equilibrating MD procedures were then conducted again to stabilize the modified configuration. The MD simulation and crosslink formation with adaptive cut-off were iterated until the target crosslink ratio (ptarget) was reached, where the crosslink ratio p was defined by the ratio of the number of the reacted epoxy groups, ncross, to the entire initial number of the epoxy groups, nepoxy(1).
(1) |
For all the EH pairs studied in this work, the ptarget was set as 0.6 to compromise computational cost and also to be above the percolation threshold, pc = 0.577, of the epoxy resins made from diamine and diepoxide assuming a random reaction.27 As expected, the TC was affected by the crosslink ratio as represented in Fig. S4† and it is noteworthy that the TC went up rapidly after p = 0.7. It also corresponds with the previous study by Vasilev et al. about TC of crosslinked polyisoprene and polybutadiene.28 However highly cross-linked polymers are considered to have unstable structures from the unphysically connected topology as most reaction sites are exhausted in the later stages of crosslinking iterations. Therefore, it is reasonable to set the ptarget to be just above the pc to prevent numerical artifacts in calculating TC. The supplementary simulation results for choosing parameters other than the crosslink ratio can be found in the ESI.†
During the crosslinking iterations, a similar series of simulations were conducted to equilibrate the mixture containing newly formed crosslinking bonds. After searching for the epoxy–amine pairs and generating the crosslink bonds, the energy minimization was conducted with the steepest descent, conjugate gradient, and fire algorithms, consecutively.29 Then five steps of NVT simulations were followed: the system was equilibrated at 300 K, 400 K, and 500 K, where the temperature was linearly ramped between the equilibration runs, where each equilibration and ramping stage was 10 ps long. Finally, we conducted two rounds of NPT simulations at 1 atm, each 20 ps long, with the thermostat temperature set to 500 K and 300 K.
Starting from the equilibrated network structure, the TC of the crosslinked polymer was calculated using the Green–Kubo equilibrium simulation. The network was initially equilibrated for 200 ps in the NPT ensemble, and the production NVE simulation was conducted for 1 ns. The heat flux was computed and saved at every step to calculate the thermal conductivity from its time correlation function. The heat current autocorrelation function (HCACF) was obtained from 10 repeated independent runs with different initial velocities to get proper statistics.
The TC of the crosslinked polymer, κ, could be calculated by integrating the HCACF over the lag time t according to the Green–Kubo relationship where the heat flux J was from the history of energy flow (2).
(2) |
All simulations were conducted using LAMMPS software.30 The timestep of integration was set to 1 fs in the crosslinking step and 2 fs in the TC calculation step. All bonds associated with hydrogen atoms were constrained by the SHAKE algorithm.31 The OPLS-AA forcefield with 1.14*CM1A partial atomic charges was used to describe interactions among the atoms as obtained from the LigParGen server.32–34 Moltemplate software was used to tabulate interaction parameters from LigParGen and the initial system topology file.35 The interaction parameters for the crosslinked structure were from the topology files of monomer, hardener, dimer (one epoxy monomer + one hardener), and trimer (two epoxy monomers + one hardener) molecules where the original monomer and hardener parameters were replaced with the crosslinked structure. We assumed that the reaction changes only the interaction parameters related to crosslinking bond groups; therefore, only the products from one amine reaction site, which are a dimer with a secondary amine and an alcohol, and a trimer with a tertiary amine and two alcohol groups, were considered. The Nose–Hoover thermostat and MTK barostat were used to maintain the system temperature and pressure at the desired value.36–40
The peaks near r = 4–7 Å and θ = 0–40° were observed commonly throughout different resins, implying that there exist aligned structures in constructed crosslinked polymer MD configurations where the representative snapshot of the aligned aromatic group is inserted in Fig. S5.† The specific structure of the r − θ distributions differed among the choices of monomers and hardeners, which can be attributed to the chemical environment of the aromatic groups in each molecule. Merging the information of Fig. 3(a) and chemical features of the monomers and hardeners, the EH pairs in Table 1 were classified into three groups for explanation based on the connection group between two aromatic groups in monomers: first, monomers with biphenyl groups (EH1, EH2); second, monomers with imine groups (EH3, EH4, EH5); third, monomers whose aromatic groups are separated by ester groups (EH6, EH7, EH8). On the other hand, the hardeners have similar structures connected with two or three bonds which have fewer effects on the ARDF results compared to the monomers.
First, EH1 and EH2 resins with biphenyl groups in the monomer exhibited a single peak as shown in Fig. 3(a) near r = 4 Å, whereas all other resins showed a separation of the peak, which also featured a broad-angle peak in the narrow distance area. The narrow distance peak distribution is attributed to the similar inter-distance of two aromatic groups of the biphenyl group and hardener. Whereas the angular distribution can be explained by the structural mismatch of the straightly connected biphenyl groups and the two aromatic rings connected by two bent bonds in the hardener, where one pair of aromatic rings in the hardener and monomer should be stacked obliquely when the other pair is stacked in parallel.
EH3, EH4, and EH5 showed two vividly split peaks along the distance axis in r − θ distribution which is attributed to the imine group among the three aromatic groups in the monomer where it is also non-rotatable but the distance between two aromatic groups is farther than the biphenyl group. This difference in the inter-distance between aromatic groups also affects angle distribution; if one pair of aromatic groups of a monomer and a hardener are staked, the other aromatic group in the hardener should be located at a farther distance from another aromatic group of the monomer obliquely. Therefore, the former pair is comparatively stable due to less competition with the latter pair which results in contributing to the first narrow peak in the θ axis, while the second peak comes from the latter pair with broad-angle distribution due to their mismatch of the connected bond angle between the monomer and hardener like EH1 and EH2.
Finally, the aromatic groups in EH6, EH7, and EH8 monomers are separated by ester groups which have similar structures to imine groups resulting in double peaks in the distance axis in the same manner as in EH3, EH4, and EH5. A distinct characteristic of this third group was the intense peak near r = 4 Å which is attributed to rotatable bonds in ester groups, unlike biphenyl or imine groups. Without planar restriction, the aromatic groups could be stacked easily in parallel by changing configurations.
In summary, it was presented from the ARDF results the aligning behavior of aromatic groups in crosslinked polymers and how it was affected by the molecular structure. As a next step, we tried to correlate the microscopic stacked structure of aromatic groups with the TC results as shown in Fig. 3(b). The thermal conductivities of the resins were from 0.62 to 0.85 W m−1 K−1 and were higher than those of commonly used polymer materials which can be expected from the alignment peaks in Fig. 3(a). It is also in accord with well-known physics that crystalline likelystacked aromatic groups contribute to faster phonon transport than those stacked through the bond of polymers.41 However, any aligning parameter that quantitatively correlates the TC and the ARDF was not found and quite large deviations in the TC were noticed even in the same group. This is because different molecular structures other than the connecting parts of aromatic groups in epoxy monomers also affect the crosslinked polymer complicatedly. Therefore, we conducted further comparative analysis for several cases affected only by each factor which resulted in finding two structural factors affecting TC; one is flexible chains included in the epoxy monomer as spacers and the other one is the functional groups of hardeners connecting two aromatic groups. In the following sections, it is described how the molecular motifs affect TC considering their chemical properties from further analysis.
Fig. 4 Comparative representation to show the effect of the spacer in the epoxy monomer on aligning behavior. Radial distribution functions, g(r,θ = 0), of aromatic group pairs when the angle between normal vectors is zero are represented for EH1/EH2 (a) and EH6/EH7 (b). The ARDF density maps of Fig. 3 for EH1/EH2 and EH6/EH7 cases are zoomed in to show the peak level increment in EH2 and EH7 (c). |
In the same manner, the ester groups of the hardener in EH3 and the EH8 were also expected to have polar interaction with the imine group and the ester group in epoxy. In the case of EH3, the g(r,θ = 0) at r ≅ 5.5 Å which is the location of the peak in EH5 derived by the polar interaction was even higher than the peak value though there was no distinct peak as presented in Fig. 5(a). Also, from Fig. 5(b), it was observed that carbon atoms in the hardener also coordinated to nitrogen atoms in the epoxy. However, as the TC of EH3 was not as low asthat of EH5, it can be inferred that the polar interaction between the ester and the imine groups is not enough to affect heat transport. Furthermore, the ester–ester interaction which is included in EH8 had more subtle effects on the crosslinked polymer; a lower value at the first peak in g(r,θ = 0) and slightly higher value of the g(r)center between the carbons in ester group are noticed as presented in Fig. 5(b) and (d). As the small disadvantage of the polar interaction is offset by the structural similarity between the epoxy and hardener, the TC of EH8 was a little higher than that of EH7. Conclusively, it was noticed that the chemical structure of the hardener also has effects on the aligning behavior of mesogenic groups but is less important than other factors except for the EH5 case where there is strong polar interaction. This result suggests that it is important to take into account the characteristics of chemical motifs in monomers and hardeners carefully since they affect the alignment and TC of the crosslinked polymer complicatedly.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1na00896j |
This journal is © The Royal Society of Chemistry 2022 |