High Thermal Conductivity of Bulk Epoxy Resin by Bottom-Up Parallel

Subscriber access provided by University of Massachusetts Amherst Libraries

C: Physical Processes in Nanomaterials and Nanostructures

High Thermal Conductivity of Bulk Epoxy Resin by BottomUp Parallel-Linking and Strain: A Molecular Dynamics Study Shouhang Li, Xiaoxiang Yu, Hua Bao, and Nuo Yang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02001 • Publication Date (Web): 30 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

High Thermal Conductivity of Bulk Epoxy Resin by Bottom-Up Parallel-Linking and Strain: A Molecular Dynamics Study Shouhang Li1,2,#, Xiaoxiang Yu2,3,#, Hua Bao1,* , Nuo Yang2,3,* 1

University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University,

Shanghai 200240, P. R. China 2

State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan

430074, P. R. China 3

Nano Interface Center for Energy (NICE), School of Energy and Power Engineering, Huazhong

University of Science and Technology, Wuhan 430074, P. R. China

Abstract The ultra-low thermal conductivity (~0.3 Wm-1K-1) of amorphous epoxy resins significantly limits their applications in electronics. Conventional top-down methods e.g. electrospinning usually result in the aligned structure for linear thermoplastic polymers thus satisfactory enhancement on thermal conductivity, but they are deficient for thermoset epoxy resin polymerized by monomers and curing agent due to completely different cross-linked network structure. Here, we proposed a bottom-up strategy, namely parallel-linking method, to increase the intrinsic thermal conductivity of bulk epoxy resin. Through equilibrium molecular dynamics simulations, we reported on a high thermal conductivity value of unstretched parallel-linked epoxy resin (PLER) as 0.80 Wm-1K-1, more than twofold higher than that of amorphous structure. Furthermore, by applying uniaxial tensile strains along the intra-chain direction, a further enhancement in thermal conductivity was obtained, reaching 6.45 Wm-1K-1. Interestingly, we also observed that the inter-chain thermal conductivities decrease with increasing strain. The single chain of epoxy resin was also investigated and, surprisingly, its thermal conductivity was boosted by 30 times through tensile strain, as high as 33.8 Wm-1K-1. Our study may provide a new insight on the design and fabrication of epoxy resins with high thermal conductivity.

#

S.L. and X.Y. contributed equal to this work.

*

To whom correspondence should be addressed. Email: [email protected] (HB); [email protected]

(NY)

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Introduction Epoxy resins are classical thermoset polymers widely used in coatings, adhesives and electronic packaging for their excellent thermal mechanical properties and high electrical resistance.1 However, most of epoxy resins have very low thermal conductivity on the order of 0.1 Wm-1K-1 2 owing to the existence of entanglement, voids etc.3 In some special situations, for example, aerospace and flexible electronics fields, heat dissipation is becoming a crucial issue and the epoxy resin with higher thermal conductivity is desirable.4 The general strategy to increase the thermal conductivity of polymers is doping materials with high thermal conductivities, such as ceramics,5-8 metals 9, carbon nanotubes10 and graphene11. Adding fillers increases the cost. More importantly, the fillers will degrade the original electrical and mechanical properties of polymers and affect the performance of the relevant products. Thus, it is necessary to enhance the intrinsic thermal conductivity of epoxy resin. The heat transport properties of cross-linked epoxy resin (CLER) are well revealed theoretically and experimentally. Varshney et al.12 calculated the thermal conductivity of CLER employing both equilibrium molecular dynamics method (EMD) and non-equilibrium molecular dynamics method (NEMD) and the thermal conductivity value is determined to be in the range of 0.30-0.31 Wm-1K-1 at 300 K. By using EMD method, Kumar et al.2 found the positive temperature dependence of thermal conductivity. Kline et al.13 measured the thermal conductivity of epoxy resin and found the thermal conductivity value goes from 0.23 Wm-1K-1 to 0.27 Wm-1K-1 when the temperature raises from 275 K to 375 K. The heat dissipation ability of epoxy resin is similar to other polymers and it cannot meet the stringent requirement in relevant fields. In the past decades, researchers found that polymers with highly ordered structures have appreciable thermal conductivities. Chen and Henry14-15 found that the thermal conductivity of polyethylene single chain can be even divergent which is several orders of magnitude larger than that of amorphous bulk PE. The amazing discovery reveals that the intrinsic thermal conductivities of polymers have not been fully excavated. Zhang16-19 and his cooperators found that polymer nanofibers with intrinsically ordered backbones, strong backbone bonds, and strong dihedral angles could be the high thermal conductivity candidates. The aligned polymers have very high thermal conductivities is also verified by experiments. Shen et al.3 found the thermal conductivity of ultra-drawn polyethylene nanofibers can be as high as ~104 Wm-1K-1 at 300K. Xu et al.20 found polyethylene film consists of nanofibers with crystalline and amorphous regions owns high thermal conductivity of 62 Wm-1K-1. Cao et al.21 investigated on the thermal conductivity of polyethylene nanowire arrays and they found the value of the nanowire array with the diameter of 100 nm can reaches 21.1 Wm-1K-1 at 80 ℃. Singh et al.22 measured the thermal conductivity of chain-oriented amorphous polythiophene and the value can be as high as ~4.4 Wm-1K-1 at room temperature. To attain ordered structure in epoxy resin, some arisen technology23 and materials24 based on top-down methods were adapted to enhance thermal conductivity. Akatsuka et al.25 measured the thermal conductivity of liquid-crystalline epoxy resin with macroscopic isotropic structure at 30°C and the value can be as high as 0.3 - 0.96 Wm-1K-1. The exact value depends on the type of monomer and curing agent. Correspondingly, Koda et al.26 calculated the thermal conductivity of liquid crystalline epoxy resins at 300K using molecular dynamics and they got the value of 0.37 2


Page 2 of 22

Page 3 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.96 Wm-1K-1, which is consistent with the experimental results. Zeng et al.27 measured the thermal conductivity of the epoxy resin fibers made by electrostatic spinning technology and they found the thermal conductivity of epoxy resin fibers increases from 0.14 to 0.30 Wm-1K-1, when the diameter decreases from 572 nm to 211 nm. However, it should be noted that the conventional epoxy resin is amorphous cross-linked network prepared by the polymerization of monomers and curing agents, which is different from those amorphous linear polymers consisting of many chains. The top-down methods mentioned above like electrospinning could be applied to straighten many unconnected chains and achieve the long-range alignment. Nevertheless, for epoxy resin, top-down methods could only construct short-range ordered structure, and also fail to avoid crosslinking and long-range disorder27, thus form network structure giving rise to strong intra-molecule phonon scatterings in heat transport contributed by covalent bonding. This is the dominant reason why top-down methods based on cross-linking does not work well in enhancement of thermal transport in epoxy resin. Therefore, how to carefully design the linking structure with long-range alignment and better understanding of heat transport mechanism in epoxy resin remains to be explored. In this work, to further enhance the intrinsic thermal conductivity, we propose a bottom-up linking strategy to construct parallel-linked epoxy resin (PLER). The procedure is similar to the bottom-up manufacture technology, molecular layer deposition (MLD), which can be used to make high quality polymer films28-29. At the same time, the effects of morphology on the thermal conductivity of epoxy resin are investigated. We first studied the relationship between the degree of crosslinking and thermal conductivity of amorphous cross-linked network. Then we calculated the thermal conductivities of bulk PLER and the strain effects are discussed. In addition, the intrinsic thermal conductivity of PLER single chain is presented.

Model and Simulation Details The commonly used monomer and curing agent of epoxy resin are EPON-862 (di-glycidyl ether of bisphenol F) and DETDA (diethylene toluene diamine), respectively. The corresponding chemical structures are shown in Fig. 1(a) and (b). These two materials are well investigated12, 30-32 and it is convenient to compare our results with others12. The reacted carbon atoms in epoxied groups of EPON-862 and nitrogen atoms in amine groups of DETDA generate C-N bonds in cross-linked epoxy resin structure as shown in Fig. 1(c). The degree of crosslinking is the ratio of reacted epoxy carbon atoms to the total epoxy carbon atoms in monomers32-33. Several methods have been proposed to construct crosslinking atomic model of epoxy resin network, for which the properties can be consistent with experiments30, 34-35. In this work, we employed the methods described in the Ref. 34. Firstly, we build an amorphous cell containing both monomers and curing agents randomly with the density of 1.2g/cm3. The reactive carbon atoms in EPON-862 and nitrogen atoms in DETDA are recorded. Then the initial cutoff distance for chemical reaction was set as 3.5 Å. The following steps are required for every recurrence: The distances between the reactive atoms are calculated and bonding is assumed if the distance is within the cutoff. Subsequently, the structure is relaxed by energy optimization and then dynamics simulations (NVT at 600K then NPT at 1 atm, 600K). The above procedure is executed with an increasing of cutoff by 0.5 Å every recurrence to get the cross-linked structures with different conversions. The maximum 3



Page 4 of 22

reaction cutoff was set as 10 Å. The curing reaction will be terminated when it reaches the maximum reaction cutoff or the target percent conversion is achieved. In our simulations, the cross-linked structure is generated through two reactions of primary amine. The primary amine reacts with the epoxy group and will generate secondary amine, which can then react with new epoxy resin group and the twice reaction occurs. For cross-linked epoxy resin, the number of atoms is 4736, including 64 monomers and 64 curing agents. The relaxed cross-linked network is shown as the Fig. 1(d). To build ordered epoxy resin structure, we changed the conventional crosslinking method and proposed a new parallel-linking method, which is like the principle of MLD. MLD is widely used to manufacture polymer films with high quality28-29. The polymer films are fabricated by stacking molecules on substrates layer by layer. The schematic of MLD is shown in Fig. 1(e). For parallel-linking model, the monomer and curing agent form different molecular layers. Then one monomer is bonded with one curing agent, i.e. epoxy carbon atom in monomer is bonded with primary amine nitrogen atom in curing agent and the C-N bonds are generated, and then we could get one parallel-linked segment, as shown in Fig. 1(c). For PLER structure, every segment contains one monomer and one curing agent. Several molecular layers replicate along the chain direction (z axis) and then we could get the paved semi-crystal structure, as shown in Fig. 1(f). In this study, there are 4 chains on x and y axes for bulk PLER, respectively. The molecular dynamics simulations are performed at the temperature of 300K using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package36. According to the former simulations2, 12, the consistent valence force field (CVFF)37-38 is accurate enough to characterize the thermal properties of epoxy resins and therefore it was employed to describe the interatomic interactions in this work. As Kumar et al.2 pointed out, the simulation results can be consistent with the experiments when the long-range interactions are included. Thus, both van der Waals (vdW) force and electrostatic force are included in our simulation. The exact formula of CVFF force field is:

Etotal = ∑ K b ( r − r0 ) + ∑ Kθ (θ − θ 0 ) + ∑ Kφ (1 + d cos ( nφ ) ) + 2

θ

b

 σ  4 ε ∑  rij i> j 

2

12

 σ  −    rij

φ

  

6

 1 N N qq + ∑ ∑ i j  2 i =1 j =1, j ≠i ε 0 rij 

.

(1)

The terms on right hand side of Eq. (1) stand for bond force, angle force, dihedral force, vdW force and Coulomb interaction, respectively. The Lennard-Jones (LJ) potential parameters across different types of atoms were calculated by using the Lorentz-Berthlot mixing rules (i.e., ߝ௜௝ = ‫ݐݎݍݏ‬൫ߝ௜ ߝ௝ ൯, ߪ௜௝ = ൫ߪ௜ + ߪ௝ ൯/2). The cutoff distance of the 12-6 LJ potential for all structures was set to 9 Å . All potential parameters are available in Ref. 37 and 38. The NEMD39 and EMD40 are two mainstream methods for thermal conductivity calculations using molecular dynamics. For NEMD, the finite system size and the external thermostat have impacts on thermal transport properties. Although the finite size effect can be conquered using extrapolation method, the computation cost would be high. Besides, the temperature gradient and heat flux density is very large in this method so that it is controversial whether linear response still 4


Page 5 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


holds.41 EMD method is also called Green-Kubo method. In EMD simulation, the system is at equilibrium state without external perturbation. The Green-Kubo formula relates the ensemble average of the heat current auto-correlation function to the thermal conductivity. There is no boundary scattering in EMD simulation and it can be applied to infinite system by employing periodic boundary condition. Therefore, we adopted EMD method in our work. The calculation of heat flux is a critical step in EMD method. The heat flux is defined as:

r r r r  r 1 r 1 J =  ∑ ei vi + ∑ f ij ⋅ ( vi + v j ) xij  , 2 i< j V  i 

(

)

(2)

where V is the volume of the simulation cell, i and j are the indexes of atoms, ei is the total energy of atom i,

vi and v j are atom velocities of atom i and j, fij is the force between atom i and j,

r xij is the

relative position of atom i and j. We can obtain the thermal conductivity by directly integrating heat current autocorrelation function (HCACF), namely

κ=

r τ0 r V J ( 0) ⋅ J (τ ) dτ , 2 ∫0 3kBT

(3)

where T is the system temperature, kB is the Boltzmann constant, τ0 is the integral upper limit of HCACF, which is also called correlation time. The angular bracket denotes an ensemble average. The velocity Verlet algorithm42 is employed to integrate equation of motion, and the time step is set as 0.25 fs. The initial structures are first minimized by standard conjugate-gradient energy-minimization methods in LAMMPS. After that, the system runs in the isothermal-isobaric ensemble (NPT) for 250 ps to relax the whole system at the given temperature and pressure. Then it runs another 250 ps in the canonical ensemble (NVT) at the given temperature 300 K. Later, it runs in the microcanonical ensemble (NVE) for 250 ps for further relaxation. Finally, it runs at least another 2.5 ns in NVE, during which the heat current is recorded at an interval of 2.5 fs. To achieve better ensemble average, we obtained the results on the average of at least 4 independent simulations with different initial conditions. All the aforementioned simulation parameters were carefully checked to ensure the results were converged [37]. Note that the thermal conductivities were averaged over three orthogonal directions for CLER to get better statistics as they were considered to be isotropic in nature for cross-linked network structure. For parallel-linked bulk and single chain structures, the thermal conductivity on the z axis is different from that on the other two axes due to anisotropy. For these anisotropic cases, we calculate the thermal conductivities on the three axes separately.

5



Fig. 1. (a-b) Chemical structures of monomer EPON-862 and curing agent DETDA. (c) One cross-linked segment of epoxy resin, consisting of carbon (blue), hydrogen (green), oxygen (red) and nitrogen (purple). (d) The relaxed cross-linked epoxy resin. (e) An illustration of MLD method. (f) An illustration of PLER structure.

6


Page 6 of 22

Page 7 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Results and Discussions We first calculated the thermal conductivity of CLER with 50% degree of crosslinking and the results are depicted in Fig. 2(a) as an illustration of the EMD method. HCACF fluctuates dramatically for 1 ps, which means the strong reflection of heat current, and then decays to zero rapidly within 3ps for the sake of strong phonon scatterings in CLER, thus giving rise to the quick convergence of integral, i.e., thermal conductivity value. In practical usage of CLER, degree of crosslinking raises with the increase of curing reaction time, so CLER could have different degrees of crosslinking33. Therefore, we further investigated the thermal conductivity of amorphous CLER with respect to degree of crosslinking. As Fig. 2(b) shows, the value is in the range of 0.32 - 0.35 Wm-1K-1. It is comparable to the previous simulation12 and experiment results43, which validates our calculations results about epoxy resins. We can see that degree of crosslinking has little impacts on thermal conductivity of CLER. It is quite different from polyethylene44 whose thermal conductivity increases with degree of crosslinking. This is attributed to the different contributions of heat transport in these two kinds of cross-linked polymers. Cross-linking bridges the separated molecules in polymers and thus paves the way for heat transport by covalent bonding interactions while it almost has no influences on heat transport by nonbonding interactions. For linear polymer chains, bonding interactions are main contributors44, so crosslinking further improves the heat transport. However, for epoxy resin, it has been verified that nonbonding interactions are the most predominant among different interactions contributions to thermal conductivity12. It is note worthy that the contribution to thermal transport by bonding interactions is determined by the molecular structure of polymer. Generally, for smooth, straight and strongly bonded polymer like polyethylene, heat can propagate well via bonded interactions16, 45 , while for branched, curly and weakly bonded polymer, like polynorbornene46, bottlebrush polymers47 and epoxy resin12 , there are strong phonon scatterings along backbone and nonbonding interactions become considerable.

Fig. 2. (a) Normalized heat current autocorrelation function (black line) and thermal conductivity (red line) of cross-linked epoxy resin with 50% degree of crosslinking. (b) Thermal conductivity of cross-linked network epoxy resin as a function of degree of crosslinking. To show the enhancement on thermal conductivity by bottom-up parallel linking, we performed further simulation on bulk PLER. Due to the well-known simulation size effects of 7



EMD, we performed convergence test with different simulation domain sizes. The thermal conductivity values of systems with 1, 2, 4, 8 segments along chain are calculated and the results are shown in Fig. 3 (a). It can be seen that the simulation domain size effect is not significant for bulk PLER. We use 8 segments as the length of simulation system in the subsequent simulations for bulk PLER. The converged thermal conductivity along intra-chain (z axis) direction (κz) at 300K is 0.80 Wm-1K-1, which is twofold higher than that of CLER. Our results are comparable with the thermal conductivity of highly ordered liquid-crystalline epoxy resins as Akatsuka et al.25 reported. Unlike common liquid epoxy resin, the relaxed PLER owns long-range ordered structure, as shown in the inset of Fig. 3(a). Besides, there is no bonding interactions between chains, which can further decrease the intra-chain scatterings. It is noteworthy that the thermal conductivity value can be even further enhanced if monomer and curing agent with stronger backbone are employed in PLER. The thermal conductivities along inter-chain (x and y axes) directions (κx and κy) are ~ 0.25 Wm-1K-1, which are close to that of CLER. This is to be expected because the nonbonding interactions are the main contributors for heat transport along x and y directions, while the bonding interactions dominate heat transport along z direction. PLER owns strong anisotropy due to semi-crystal structure (the inset of Fig. 3 (a)), which is much more ordered than amorphous bulk CLER in Fig. 1 (d). However, the thermal conductivity value of PLER is still much smaller than that of bulk aligned PE16, 45, 48-49. Previous studies suggested that the thermal conductivities of nanowires and nanoribbons can be decreased with the increasing number of kinks and folds50-52. There is also buckling in chains of the relaxed bulk PLER, which indicates that semi-crystalline structure still owns low degree of crystallinity and it can induce intra-chain phonon scatterings, which is also observed in other bulk aligned buckled polymers46.

Fig. 3. (a) Thermal conductivity of PLER as a function of number of segments in the chain 8


Page 8 of 22

Page 9 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


direction. The inset is a side-view of the relaxed bulk PLER (16 chains are allocated with different colors). (b) The thermal conductivities of stretched PLER with respect to different strains. (c) XRD patterns of different epoxy resin structures. (d) The radial distribution function g(r) as a function of radius r of PLER with different strains. For further improvement of thermal conductivity, we studied the thermal conductivities of bulk PLER with uniaxial tensile strains53-54. Figure 3(b) shows the strain dependence of thermal conductivity along different directions. κz increases dramatically with tensile strain. When the strain is smaller than 0.15, κz increases slowly with strain. Then it increases significantly for larger strain. The value of κz reaches 6.45 Wm-1K-1 with 0.50 strain, which is around 20 times larger than that of the bulk CLER and also much larger than the value of electrostatic spinning fiber27. However, κx and κy decrease from 0.25 Wm-1K-1 to 0.12 Wm-1K-1. Similarly, Zeng et al.55 found the thermal conductivity of fibrous epoxy on the through-plane decreases with the strain rising. We did not compute the cases with even larger strain for the confinement of computational ability for the well-known size effects of EMD method. In order to quantitatively describe the morphologies of CLER, pristine PLER and stretched PLER, we compared the X-ray diffraction (XRD) patterns of three different structures, as it can reflect the crystallinity of structure. The XRD intensity is calculated based on a mesh of reciprocal lattice nodes defined by entire simulation domain using a simulated radiation of wavelength lambda36, 47. As presented in Fig. 3(c), the XRD patterns show significant differences among these three structures. As we can see, stretched PLER shows several discrete peaks, and PLER without strain has fewer peaks. CLER shows many broad continuous peaks. The phenomenon indicates that the stretched PLER has a higher crystallinity of structure compared to the structure without strain, while the latter owns more ordered structure compared to the amorphous cross-linked network. There are less phonon scatterings in more ordered structures. That is why the stretched PLER has the highest thermal conductivity among the three structures. Besides, the XRD pattern of PLER with 0.15 strain is similar to that with 0.50 strain. It elucidates that the crystallinity of PLER with strain larger than 0.15 is higher than the ones with smaller strains which results in the saltation of κz at the strain 0.15. We analyzed the inter-chain radial distribution function (RDF) of stretched PLER to further understand the negative strain dependence of inter-chain thermal conductivity. The heat transfer along inter-chain directions is dominated by nonbonding interactions, which are related to the atom distribution around the reference atom. We choose all the atoms in an isolate chain as the reference atoms of RDF. The distance from a reference atom to the atom in other chains is defined as ܴ = ඥሺ‫ ݔ‬− ‫ݔ‬଴ ሻଶ + ሺ‫ ݕ‬− ‫ݕ‬଴ ሻଶ + ሺ‫ ݖ‬− ‫ݖ‬଴ ሻଶ . The RDF is recorded as ݃ሺ‫ݎ‬ሻ = ర య

௡ గሾሺ௥ାௗ௥ሻయ ି௥ య ሿ

,

where r is the distance between reference atoms and other atoms, and ݊ is the number of atoms with a distance of ܴሺ‫ ݎ < ܴ < ݎ‬+ ݀‫ݎ‬ሻ to the reference atoms16, ݀‫ ݎ‬is set to be 0.2 Å. The results are shown in Fig. 3 (d). It can be seen ݃(‫ )ݎ‬decreases with the increase of strain, which indicates that atomic density around the reference atoms is reduced. As a result, the inter-chain nonbonding interactions also decrease. Since nonbonding interactions are mainly responsible for inter-chain heat transfer, κx and κy decrease with tensile strains. The differences of ݃(‫ )ݎ‬are more significant when the strain is larger than 0.3. Correspondingly, κx and κy decrease dramatically in this range. Recently, He et al.56 also found the thermal conductivity of crystalline polyethylene in 9



the radial direction decreases with the increase of strain, owing to the decrease in inter-chain nonbonding interactions, which also proves our observation.

Fig. 4. (a) Epoxy resin single chains with 0.15 and 0.30 strain. (b) The thermal conductivities of single chain with respect to different number of segments. (c) The thermal conductivities of stretched single chain as a function of strains. To gain insights into how the inter-chain nonbonding interactions impact on the thermal conductivity of PLER, the single chain structure (Fig. 4 (a)) was investigated which can avoid such inter-chain phonon scatterings, and help us obtain the upper limit thermal conductivity of epoxy resin. In this study, a sufficiently large vacuum space was introduced artificially to ensure that the single chain is isolate and there are no other chains interacting with it. The relaxed chain length obtained from the bulk PLER is used for isolated single chain at the same temperature. We deformed the foregoing relaxed single chain and bulk structure with corresponding strains and we could get the stretched structures. The thermal conductivity of unstretched PLER single chain structure is shown in Fig. 4 (b). The converged value is ~ 1.13 Wm-1K-1 on z axis, which is about threefold higher than that of amorphous cross-linked network and larger than that of bulk PLER. The converged length of single chain structure is much larger than the bulk PLER, which can also verify that the absence of inter-chain interactions could reduce the phonon scatterings and facilitate the propagation of the long-wavelength phonons. We also calculated the thermal conductivity of stretched PLER single chain. The tensile strain increases from 0 to 0.80 and it can have strong effects on the morphology of the single chain and greatly affect κz of PLER single chain, as shown in Fig. 4 (a). The values increase by 30 times, from ~ 1.13 Wm-1K-1 to ~ 33.82 Wm-1K-1. The variation trend of thermal conductivity with strain is analogous to that of stretched bulk PLER: The thermal conductivity increases slowly with small strain and then increases linearly when the strain is higher than 0.15. As shown in Fig. 4(a), the morphology of single chain with 0.15 strain is straighter than that of unstretched structure and this phenomenon is more 10


Page 10 of 22

Page 11 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


significant in the structure with 0.30 strain. The thermal conductivity still keeps the increasing trend with strain raising. This implies the thermal conductivity of bulk PLER could be further enhanced through decreasing both intra-chain and inter-chain phonon scatterings.

Conclusions In summary, we performed equilibrium molecular dynamics simulations to investigate the thermal conductivities of cross-linked and parallel-linked epoxy resins as well as epoxy resin single chain. Our results show that the thermal conductivity of cross-linked epoxy resin is in the range of 0.32 - 0.35 Wm-1K-1 and the degree of crosslinking has little effects because the nonbonding interactions are the main contributors in heat transport. We proposed a bottom-up parallel-linking method, which is shown to be efficient and the along-chain thermal conductivity of bulk parallel-linked epoxy resin structure can be enhanced more than twofold compared to the cross-linked network structure due to the much more ordered morphology. The thermal conductivity can be boosted with the increasing strain, and reaches a value as high as 6.45 Wm-1K-1 with 0.50 strain. The thermal conductivity firstly increases slightly and then increases significantly with the strain raising. X-ray diffraction pattern shows that deformed parallel-linked epoxy resin owns perfect crystalline structure, which explains the surprising high thermal conductivity. The thermal conductivity on x and y axes would decrease with the increase of strain for degraded nonbonding interactions. For parallel-linked single chain, the thermal conductivity is about threefold higher than that of cross-linked network and the value can be enhanced greatly by 30 times, reaching as high as ~ 33.82 Wm-1K-1 when strain reaches 0.80. The stretched structures own higher thermal conductivities than that of unstreched one due to more ordered morphology and the suppression of both inter-chain and intra-chain phonon scatterings. Our method can be applied on other epoxy resin systems and polymers with similar parallel-linked structures to increase their thermal conductivities. In the end, we would like to discuss the implication of our findings in future experiments and industry applications. The previous research shows that the traditional top-down alignment method27 is invalid in increasing the thermal conductivity of epoxy resin. The thermal conductivity of stretched PLER proposed by us has absolute superiority compared to the top-down aligned electrospun nanofibers. Besides, the thermoset property of PLER makes it more practical compared to the traditional thermoplastic aligned polymers. The curing reaction between epoxy group and amino group makes PLER realistic by the experiment of MLD. Furthermore, quasi-2D films made by electrospun could achieve enhancement of thermal conductivity along stretching direction only55. This method is insufficient in heat dissipation perpendicular to thermal interfaces in electronic devices. Herein, by bottom-up manufacture, like MLD method, PLER forms films along the perpendicular direction and shows good thermal transport which meets the critical requirement, thus it indicates great advantages for practical applications.

11



Supporting Information Details of molecular dynamics simulations.

Acknowledgements We would like to thank Dr. Chao Chen and Prof. Zhigang Xue for valuable discussions. This work was supported by the National Natural Science Foundation of China No. 51676121 (HB), 51576076 (NY) and 51711540031 (NY), the Hubei Provincial Natural Science Foundation of China No. 2017CFA046 (NY) and the Fundamental Research Funds for the Central Universities No. 2016YXZD006 (NY). The authors thank HPC (π) from Shanghai Jiao Tong University, the National Supercomputing Center in Tianjin (NSCC-TJ) and China Scientific Computing Grid (ScGrid) for providing assistance in computations.

12


Page 12 of 22

Page 13 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


References 1.

Jin, F.-L.; Li, X.; Park, S.-J., Synthesis and Application of Epoxy Resins: A Review. Journal

of Industrial and Engineering Chemistry 2015, 29, 1-11. 2.

Kumar, A.; Sundararaghavan, V.; Browning, A., Study of Temperature Dependence of

Thermal Conductivity in Cross-Linked Epoxies Using Molecular Dynamics Simulations with Long Range Interactions. Modelling and Simulation in Materials Science and Engineering 2014, 22, 025013. 3.

Shen, S.; Henry, A.; Tong, J.; Zheng, R.; Chen, G., Polyethylene Nanofibres with Very High

Thermal Conductivities. Nature Nanotechnology 2010, 5, 251. 4.

Burger, N.; Laachachi, A.; Ferriol, M.; Lutz, M.; Toniazzo, V.; Ruch, D., Review of Thermal

Conductivity in Composites: Mechanisms, Parameters and Theory. Progress in Polymer Science 2016, 61, 1-28. 5.

Yu, S.; Yang, S.; Cho, M., Multiscale Modeling of Cross-Linked Epoxy Nanocomposites to

Characterize the Effect of Particle Size on Thermal Conductivity. Journal of Applied Physics 2011, 110, 124302. 6.

Fu, Y.-X.; He, Z.-X.; Mo, D.-C.; Lu, S.-S., Thermal Conductivity Enhancement with

Different Fillers for Epoxy Resin Adhesives. Applied Thermal Engineering 2014, 66, 493-498. 7.

Chen, C.; Tang, Y.; Ye, Y. S.; Xue, Z.; Xue, Y.; Xie, X.; Mai, Y.-W., High-Performance

Epoxy/Silica Coated Silver Nanowire Composites as Underfill Material for Electronic Packaging. Composites Science and Technology 2014, 105, 80-85. 8. Thermal

Chen, C.; Wang, H.; Xue, Y.; Xue, Z.; Liu, H.; Xie, X.; Mai, Y.-W., Structure, Rheological, Conductive

and

Electrical

Insulating

Properties

of

High-Performance

Hybrid

Epoxy/Nanosilica/Agnws Nanocomposites. Composites Science and Technology 2016, 128, 207-214. 9.

Zhou, W., Effect of Coupling Agents on the Thermal Conductivity of Aluminum

Particle/Epoxy Resin Composites. Journal of Materials Science 2011, 46, 3883-3889. 10. Gojny, F. H.; Wichmann, M. H.; Fiedler, B.; Kinloch, I. A.; Bauhofer, W.; Windle, A. H.; Schulte, K., Evaluation and Identification of Electrical and Thermal Conduction Mechanisms in Carbon Nanotube/Epoxy Composites. Polymer 2006, 47, 2036-2045. 11.

Song, S. H.; Park, K. H.; Kim, B. H.; Choi, Y. W.; Jun, G. H.; Lee, D. J.; Kong, B. S.; Paik,

K. W.; Jeon, S., Enhanced Thermal Conductivity of Epoxy–Graphene Composites by Using Non‐ Oxidized Graphene Flakes with Non‐Covalent Functionalization. Advanced Materials 2013, 25, 732-737. 12. Varshney, V.; Patnaik, S. S.; Roy, A. K.; Farmer, B. L., Heat Transport in Epoxy Networks: A Molecular Dynamics Study. Polymer 2009, 50, 3378-3385. 13. Kline, D. E., Thermal Conductivity Studies of Polymers. Journal of Polymer Science Part A: Polymer Chemistry 1961, 50, 441-450. 14. Henry, A.; Chen, G., Anomalous Heat Conduction in Polyethylene Chains: Theory and Molecular Dynamics Simulations. Physical Review B 2009, 79, 144305. 15. Henry, A.; Chen, G., High Thermal Conductivity of Single Polyethylene Chains Using Molecular Dynamics Simulations. Physical Review Letters 2008, 101, 235502. 16. Zhang, T.; Luo, T., Morphology-Influenced Thermal Conductivity of Polyethylene Single Chains and Crystalline Fibers. Journal of Applied Physics 2012, 112, 094304. 13



17. Zhang, T.; Luo, T., High-Contrast, Reversible Thermal Conductivity Regulation Utilizing the Phase Transition of Polyethylene Nanofibers. ACS Nano 2013, 7, 7592-7600. 18. Zhang, T.; Luo, T., Role of Chain Morphology and Stiffness in Thermal Conductivity of Amorphous Polymers. The Journal of Physical Chemistry B 2016, 120, 803-812. 19. Zhang, T.; Wu, X.; Luo, T., Polymer Nanofibers with Outstanding Thermal Conductivity and Thermal Stability: Fundamental Linkage between Molecular Characteristics and Macroscopic Thermal Properties. The Journal of Physical Chemistry C 2014, 118, 21148-21159. 20. Xu, Y.; Wang, X.; Zhou, J.; Song, B.; Jiang, Z.; Lee, E. M.; Huberman, S.; Gleason, K. K.; Chen, G., Molecular Engineered Conjugated Polymer with High Thermal Conductivity. Science Advances 2018, 4, eaar3031. 21. Cao, B.-Y.; Li, Y.-W.; Kong, J.; Chen, H.; Xu, Y.; Yung, K.-L.; Cai, A., High Thermal Conductivity of Polyethylene Nanowire Arrays Fabricated by an Improved Nanoporous Template Wetting Technique. Polymer 2011, 52, 1711-1715. 22. Singh, V.; Bougher, T. L.; Weathers, A.; Cai, Y.; Bi, K.; Pettes, M. T.; McMenamin, S. A.; Lv, W.; Resler, D. P.; Gattuso, T. R., High Thermal Conductivity of Chain-Oriented Amorphous Polythiophene. Nature Nanotechnology 2014, 9, 384-390. 23. Harada, M.; Ochi, M.; Tobita, M.; Kimura, T.; Ishigaki, T.; Shimoyama, N.; Aoki, H., Thermal‐Conductivity Properties of Liquid‐Crystalline Epoxy Resin Cured under a Magnetic Field. Journal of Polymer Science Part B: Polymer Physics 2003, 41, 1739-1743. 24. Huang, Z.-M.; Zhang, Y.-Z.; Kotaki, M.; Ramakrishna, S., A Review on Polymer Nanofibers by Electrospinning and Their Applications in Nanocomposites. Composites Science and Technology 2003, 63, 2223-2253. 25. Akatsuka, M.; Takezawa, Y., Study of High Thermal Conductive Epoxy Resins Containing Controlled High‐Order Structures. Journal of Applied Polymer Science 2003, 89, 2464-2467. 26. Koda, T.; Toyoshima, T.; Komatsu, T.; Takezawa, Y.; Nishioka, A.; Miyata, K., Ordering Simulation of High Thermal Conductivity Epoxy Resins. Polymer Journal 2013, 45, 444. 27. Zeng, X.; Xiong, Y.; Fu, Q.; Sun, R.; Xu, J.; Xu, D.; Wong, C.-P., Structure-Induced Variation of Thermal Conductivity in Epoxy Resin Fibers. Nanoscale 2017, 9, 10585-10589. 28. Zhou, H.; Bent, S. F., Fabrication of Organic Interfacial Layers by Molecular Layer Deposition: Present Status and Future Opportunities. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 2013, 31, 040801. 29. Yoshimura, T.; Tatsuura, S.; Sotoyama, W., Polymer Films Formed with Monolayer Growth Steps by Molecular Layer Deposition. Applied Physics Letters 1991, 59, 482-484. 30. Varshney, V.; Patnaik, S. S.; Roy, A. K.; Farmer, B. L., A Molecular Dynamics Study of Epoxy-Based Networks: Cross-Linking Procedure and Prediction of Molecular and Material Properties. Macromolecules 2008, 41, 6837-6842. 31. Nouri, N.; Ziaei-Rad, S., A Molecular Dynamics Investigation on Mechanical Properties of Cross-Linked Polymer Networks. Macromolecules 2011, 44, 5481-5489. 32. Demir, B.; Walsh, T. R., A Robust and Reproducible Procedure for Cross-Linking Thermoset Polymers Using Molecular Simulation. Soft Matter 2016, 12, 2453-2464. 33. Xin, D.; Han, Q., Study on Thermomechanical Properties of Cross-Linked Epoxy Resin. Molecular Simulation 2015, 41, 1081-1085. 14


Page 14 of 22

Page 15 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


34. Shenogina, N. B.; Tsige, M.; Patnaik, S. S.; Mukhopadhyay, S. M., Molecular Modeling Approach to Prediction of Thermo-Mechanical Behavior of Thermoset Polymer Networks. Macromolecules 2012, 45, 5307-5315. 35. Wu, C.; Xu, W., Atomistic Molecular Modelling of Crosslinked Epoxy Resin. Polymer 2006, 47, 6004-6009. 36. Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of computational physics 1995, 117, 1-19. 37. Dauber‐Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J.; Genest, M.; Hagler, A. T., Structure and Energetics of Ligand Binding to Proteins: Escherichia Coli Dihydrofolate Reductase‐ Trimethoprim, a Drug‐Receptor System. Proteins: Structure, Function, and Bioinformatics 1988, 4, 31-47. 38. Maple, J. R.; Dinur, U.; Hagler, A. T., Derivation of Force Fields for Molecular Mechanics and Dynamics from Ab Initio Energy Surfaces. Proceedings of the National Academy of Sciences 1988, 85, 5350-5354. 39. Müller-Plathe, F., A Simple Nonequilibrium Molecular Dynamics Method for Calculating the Thermal Conductivity. The Journal of chemical physics 1997, 106, 6082-6085. 40. McGaughey, A. J.; Kaviany, M., Phonon Transport in Molecular Dynamics Simulations: Formulation and Thermal Conductivity Prediction. Advances in Heat Transfer 2006, 39, 169-255. 41. Che, J.; Çağın, T.; Deng, W.; Goddard III, W. A., Thermal Conductivity of Diamond and Related Materials from Molecular Dynamics Simulations. The Journal of Chemical Physics 2000, 113, 6888-6900. 42. Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R., A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical Clusters of Molecules: Application to Small Water Clusters. The Journal of Chemical Physics 1982, 76, 637-649. 43. Ganguli, S.; Roy, A. K.; Anderson, D. P., Improved Thermal Conductivity for Chemically Functionalized Exfoliated Graphite/Epoxy Composites. Carbon 2008, 46, 806-817. 44. Kikugawa, G.; Desai, T. G.; Keblinski, P.; Ohara, T., Effect of Crosslink Formation on Heat Conduction in Amorphous Polymers. Journal of Applied Physics 2013, 114, 034302. 45. Liao, Q.; Liu, Z.; Liu, W.; Deng, C.; Yang, N., Extremely High Thermal Conductivity of Aligned Carbon Nanotube-Polyethylene Composites. Scientific Reports 2015, 5, 16543. 46. Robbins, A. B.; Minnich, A. J., Crystalline Polymers with Exceptionally Low Thermal Conductivity Studied Using Molecular Dynamics. Applied Physics Letters 2015, 107, 201908. 47. Ma, H.; Tian, Z., Effects of Polymer Topology and Morphology on Thermal Transport: A Molecular Dynamics Study of Bottlebrush Polymers. Applied Physics Letters 2017, 110, 091903. 48. Shulumba, N.; Hellman, O.; Minnich, A. J., Lattice Thermal Conductivity of Polyethylene Molecular Crystals from First-Principles Including Nuclear Quantum Effects. Physical Review Letters 2017, 119, 185901. 49. Yu, X.; Deng, C.; Huang, X.; Yang, N., Enhancing Thermal Conductivity of Bulk Polyethylene Along Two Directions by Paved Crosswise Laminate. arXiv preprint 2016 arXiv:1605.01540. 50. Yang, L.; Chen, J.; Yang, N.; Li, B., Significant Reduction of Graphene Thermal 15



Conductivity by Phononic Crystal Structure. International Journal of Heat and Mass Transfer 2015, 91, 428-432. 51. Jiang, J.-W.; Yang, N.; Wang, B.-S.; Rabczuk, T., Modulation of Thermal Conductivity in Kinked Silicon Nanowires: Phonon Interchanging and Pinching Effects. Nano Letters 2013, 13, 1670-1674. 52. Yang, N.; Ni, X.; Jiang, J.-W.; Li, B., How Does Folding Modulate Thermal Conductivity of Graphene? Applied Physics Letters 2012, 100, 093107. 53. Shao, C.; Yu, X.; Yang, N.; Yue, Y.; Bao, H., A Review of Thermal Transport in Low-Dimensional Materials under External Perturbation: Effect of Strain, Substrate, and Clustering. Nanoscale and Microscale Thermophysical Engineering 2017, 21, 201-236. 54. Xie, H.; Ouyang, T.; Germaneau, É.; Qin, G.; Hu, M.; Bao, H., Large Tunability of Lattice Thermal Conductivity of Monolayer Silicene Via Mechanical Strain. Physical Review B 2016, 93, 075404. 55. Zeng, X.; Ye, L.; Guo, K.; Sun, R.; Xu, J.; Wong, C. P., Fibrous Epoxy Substrate with High Thermal Conductivity and Low Dielectric Property for Flexible Electronics. Advanced Electronic Materials 2016, 2, 1500485. 56. He, J.; Kim, K.; Wang, Y.; Liu, J., Strain Effects on the Anisotropic Thermal Transport in Crystalline Polyethylene. Applied Physics Letters 2018, 112, 051907.

16


Page 16 of 22

Page 17 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic

17


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46


Page 18 of 22

Page 19 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

(a)


(b)


(a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

(c)


(b)

y x

z

PLER with 0.50 strain

(d)

PLER with 0.15 strain Parallel-linked epoxy resin Cross-linked epoxy resin


Page 20 of 22

Page 21 of 22


(a)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Unstretched 0.15 strain

y

x (b)

0.30 strain z (c)


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Page 22 of 22

Bottom-Up Parallel-Linking

Along chain

Radial


High Thermal Conductivity of Bulk Epoxy Resin by Bottom-Up Parallel

Recommend Documents