characterizing mechanical properties of polymeric material...

Characterizing Mechanical Properties ofPolymeric Material: A Bottom-Up Approach

Lik-ho Tam and Denvid Lau

Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Atomistic Modeling of Polymeric Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Atomistic Model of Polymeric Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Atomistic Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Physical Properties of Polymeric Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Coarse-Grained Modeling of Polymeric Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Coarse-Grained Model of Polymeric Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Coarse-Grained Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 Effect of Structural Voids on Polymeric Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

AbstractPolymeric materials have received tremendous attention in both industrial andscientific communities, and can be readily found in applications across a largerange of length scales, ranging from the nanoscale structures, such as the photoresistlithography in the micro-electro-mechanical systems, to the macroscale compo-nents, such as the adhesive bonding in the aerospace industry and civil infrastruc-tures. The durability of these applications is mainly determined by the mechanical

L.-h. TamDepartment of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong,China

D. Lau (*)Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong,China

Department of Civil and Environmental Engineering, Massachusetts Institute of Technology,Cambridge, MA, USAe-mail: [email protected]

# Springer Nature Singapore Pte Ltd. 2018C.-H. Hsueh et al. (eds.), Handbook of Mechanics of Materials,https://doi.org/10.1007/978-981-10-6855-3_5-1

1

http://crossmark.crossref.org/dialog/?doi=10.1007/978-981-10-6855-3_5-1&domain=pdf

mailto:[email protected]

https://doi.org/10.1007/978-981-10-6855-3_5-1

reliability of the constituent polymeric materials. In this chapter, a review of thebottom-up approach to investigate the mechanical properties of the polymericmaterials is provided. A dynamic algorithm is developed to achieve the cross-linking process of the atomistic network,which possesses themechanical propertiesin a good accordance with the experimental measurements. Meanwhile, the mois-ture effect on themechanical properties is studied based on the atomisticmodel, andit is found that themechanical properties of the solvatedmodels show no significantdeterioration. Furthermore, the predicted mechanical properties at the atomisticlevel are used to develop the cross-linked network at the mesoscale, which enablesthe investigation of the effect of the structural voids on the polymeric materials. Thesimulation results demonstrate the strong mechanical reliability of the syntheticpolymeric materials during the long-term service life. The multiscale methodsummarized in this chapter provides a versatile tool to link the nano-level mechan-ical properties of the polymeric materials to the macro-level material behaviors.

KeywordsMolecular dynamics · Polymeric material · Mechanical properties · Moisture ·Structural voids

1 Introduction

Polymeric materials possess the three-dimensional covalent networks formed by thepolymerization process, which generally exhibit remarkable physical properties, such asstrongmechanical reliability as well as high thermal and chemical resistance. In practice,these materials are frequently used in various engineering applications across a largerange of length scales, including micro-electro-mechanical systems (MEMS), aerospaceindustry, and civil infrastructures. The increasing usage of the polymeric materials is dueto the fact that they have the potential to yield cheaper fabrication and cheaper devices,andmore fundamentally, their remarkable physical properties can be put into good use ina variety of products. As the polymeric materials are the basis for various engineeringapplications, a fundamental understanding of the material structure and mechanicalproperties is essential for predicting the long-term performance of the polymer-basedengineering applications and devices, as well as enabling new technologies. After thequantitative property characterization of the polymeric materials, the mechanical reli-ability of the polymeric materials under the environmental exposures shall also bequantified. Among various environmental factors, the moisture is the most critical factor.As the polymeric materials are sensitive to the humid environment, the moisture can beabsorbed into the polymeric material structure and interact with the constituent materials[1]. The interactions are found to influence the mechanical properties of the constituentmaterials [2–7]. Such moisture-affected difference in the mechanical properties can be amajor concern for the durability of the engineering applications involving the polymericmaterials, as it can lead to the structural failure ahead of the expected service life.However, the origin of the moisture-affectedmechanical behaviors is not entirely clear atthis stage, which can be a limitation on the further application of the polymeric materials.

2 L.-h. Tam and D. Lau

Consequently, a fundamental knowledge of the dependence of the polymer performanceson the moisture condition is required. After determining the mechanical properties of thepolymeric materials and the dependence on the moisture condition, the relationshipbetween the structural voids and the polymer mechanical properties needs to be clarified,as the voids affect the moisture diffusion into the system, which may initiate the cracksthat lead to the structural failure. During the curing process, microscopic structural voids,such as the free volume, can be developed and trapped in the polymerized structure [8, 9].Meanwhile, during the long-term service life, the voids can also be formed in thepolymerized structure even for the initially void-free specimens, leading to the changesin the material structure [10]. Microscopic structural voids generally exist in the poly-merized network and have a detrimental influence on the mechanical properties, but therelationship remains elusive, which is hindered by the complex structure of the polymericmaterials. Therefore, the investigations of the microscopic structural voids can provide abasic understanding of the mechanical properties of the polymeric materials, and even-tually lead to amore comprehensive understanding on the durability of the entire system.

In recent years, molecular dynamics (MD) simulation has been demonstrated as afundamental and versatile tool that enables us to investigate the molecular structure andinteraction of the polymeric materials, which can be useful for understanding themechanical properties of the polymeric materials and the interaction with the ambientenvironment (i.e., the moisture in particular). The molecular-level understandings enableone to explore the mechanism of the macroscopic behaviors of the polymeric materials,such as the fiber-reinforced polymer bonded concrete system in the civil infrastructures,which are difficult to obtain through the experimental and theoretical approaches. TheMD simulations are first applied to the structural characterization of the polymericmaterials at the nanoscale, which have been reported since 1990s [11–28]. Whereasthese MD studies have made significant progress in the atomistic modeling and propertymeasurement of the polymeric materials, several key obstacles are still present includingthe low cross-linking degree [12, 13] and relatively low accuracy in the propertyprediction [15, 19]. Therefore, it can be favorable to develop a computational modelingalgorithmwith a significant improvement in terms of the time efficiency and the accuracy,as well as a high extensibility to other cross-linked networks. With the developments inthe computational simulation of the polymeric materials, the structural behaviors of thesynthetic polymer have been studied under the influence of the surrounding environment,particularly in the presence of the moisture [6, 29–44]. From the previous studies, it canbe seen that the effect of moisture may be beneficial or detrimental to the polymericmaterials, and MD simulations are useful in providing the molecular mechanics behindthe experimental observations. The earlier studies mainly focus on the property mea-surements of the polymericmaterials, with lesser consideration of the structural voids thatexist in the structure, and their effect on the mechanical properties of the polymericmaterials [45, 46]. The experimental studies have reported that the voids dimension in thepolymericmaterials is normally of several nanometers [8, 9]. It is noted that the polymericmaterials with a certain number of voids are generally at the submicron scale, whichrequires excessive computational power to model the cross-linking process of thestructure. To overcome the limitation of the length scale, the coarse-grained (CG) MDsimulations can be performed by using the mesoscale models [47, 48].

Characterizing Mechanical Properties of Polymeric Material: A Bottom-Up. . . 3

In this work, one representative polymeric material is chosen and investigated.Specifically, the epoxy-based materials are an important family of the polymericmaterials, which are widely used for bonding the reinforced materials to the buildingstructures in the structural applications, and have become favorable in the MEMSapplications. Typically, SU-8 is a favorable epoxy photoresist, which possesses thecommon structural characteristics of the epoxy-based materials. A number of prelim-inary studies have shown that the SU-8 epoxy has a high Young’s modulus [49–51],which is important for achieving a good mechanical stability of the final products. Inaddition, the SU-8 epoxy has reasonably good adhesion to the commonly usedinorganic substrates, which is very crucial to the functionality of the final products.By investigating the SU-8 epoxy, it is expected that the mechanical behavior of thepolymeric materials commonly seen in the engineering fields can be interpreted.

In this chapter, we present the characterization of the mechanical behaviors of thepolymeric materials at the microscale by using a bottom-up approach, with a focuson the structural characterizations and property measurements, so as to develop amechanically durable polymeric material for the broad engineering applications,including micro-electronics device fabrication, aerospace industry, and civil con-struction. MD simulation is used to construct the atomistic and CG polymerizednetworks, which are close to what we can observe from the experiment. Theconstructed models are used as the basis for studying the mechanical behavior of thepolymeric materials at the nano- and mesoscale. It is inferred that this work can yieldmuch significant scientific knowledge and quantitative information upon themechanical behavior of the polymeric materials, and provide a bottom-up approachfor the microscopic investigation of the polymeric material systems.

2 Atomistic Modeling of Polymeric Material

This section shows the atomistic MD investigation on the structure and mechanicalproperties of the polymeric material. A computational algorithm is developed toconstruct the cross-linked network, and the mechanical properties are determined bymeans of dynamic deformations, which are compared with the experimental mea-surements to validate the constructed model. Furthermore, the moisture effect on themechanical behaviors of the polymeric material is investigated.

2.1 Atomistic Model of Polymeric Material

SU-8 epoxy possesses the common structural characteristics of the polymeric mate-rials, and it is selected as the representative here. In the MD simulation, it is a greatchallenge to build up the atomistic model close to the real system. The knowledge ofthe chemical reaction in the material synthesis is required to model the atomisticstructure. The SU-8 epoxy is a homogeneous material formed by the cross-linkingreaction between the monomers, which does not require the external liquid curing


agent. The cross-linking reaction occured in the material preparation can be simu-lated by using the MD simulation.

The detailed atomistic interactions in the SU-8 molecular structure are describedby a force field. A force field is developed for the specific material, which can mimicthe nature of the interactions in a realistic or appropriate way. As the accuracy of theMD simulations highly depends on the selected force field [15, 18], the investigationsof the SU-8 epoxy are carried out by using three different force fields independently inorder to obtain a comprehensive picture, which include Consistent Valence ForceField (CVFF) [52, 53], Dreiding force field [54], and Polymer Consistent Force Field(PCFF) [55, 56]. These three force fields are chosen as they are well reported for thesimulations of the polymeric materials [13, 19–23]. In addition, the AMBER(Assisted Model Building with Energy Refinement) and COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) force fieldshave also been used in the MD simulations of the polymeric materials [15, 33, 39, 40,57]. As AMBER and CVFF belong to the same group of the classical force fields,while COMPASS and PCFF belong to the same group of the second-generation forcefields, they are not used in this work. The applicability and limitation of the simulationusing these force fields are summarized in Table 1.

Partial charges assignment method of the atoms varies among these three forcefields. In the simulations using CVFF and PCFF, the partial charges are estimated byusing a bond increment method [56, 58]. The bond increment δij is described as thepartial charge contributed from atom j to atom i. This method assigns δij with equalmagnitude and opposite sign to each pair of the bonded atoms i and j. For atom i, thecharge is calculated by the summation of δij as given in Eq. (1),

qi ¼Xj

δij, (1)

where j runs over all the atomswhich are bonded to atom i directly. In addition, the δij forany pair of the same atom type is zero.Meanwhile, partial charges inDreiding forcefieldare calculated by the charge equilibrium (QEq) method [59]. It is reported that thecharge distributions by QEq result in a good agreement with the experimental measure-ments and ab initio calculations. During the MD modeling and simulation, the van derWaals (vdW) and Coulombic interactions are calculated with a cutoff distance of 10 Å.

Atomistic modeling of the SU-8 epoxy is performed in Materials Studio softwarefrom Accelrys [60]. After constructing the cross-linked SU-8 network with a cleardefinition of the molecular structure and interaction between atoms, MD simulationsare performed in the open source code LAMMPS (Large-scale Atomic/MolecularMassively Parallel Simulator) [61]. The msi2lmp tool in LAMMPS is used togenerate the input data containing the structural information and force field param-eters. Periodic boundary conditions are applied to all three directions of the cross-linked network to get rid of the boundary effect.

The cross-linked SU-8 epoxy is polymerized from the monomers. The SU-8 mono-mer comprises four components of diglycidyl ether of bisphenol A (DGEBA) and thechemical structure of which is shown in Fig. 1a. With eight epoxide groups in each


monomer, SU-8 possesses the highest epoxide functionality among the commerciallyavailable photoresists, which enables SU-8 epoxy to grow into a highly cross-linkednetwork. The molecular model of the SU-8 monomer is shown in Fig. 1b.

Before the cross-linking process, a total of forty SU-8 monomers (7960 atoms) arepacked into a three-dimensional periodic simulation cell with a density of 1.07 g�cm�3,which is the typical value for SU-8. The initial uncross-linked structure of the SU-8 epoxy is constructed at the temperature of 300 K, which uses a Monte Carlo packingalgorithm according to the rotational isomeric states model [62]. The amorphous SU-8 structure is equilibrated for 10 ps in the canonical (NVT) ensemble at 300 K, followedby another 10 ps equilibration in the isothermal and isobaric (NPT) ensemble at 300 Kand 1 atm. The corresponding integration time step is 1 fs. During the entire equilibrationprocess, constant temperature and pressure are controlled by the Nosé–Hoover thermo-stat and the Andersen barostat, respectively [63]. The reason for choosing this short timespan (10 ps NVTþ 10 ps NPT) is based on the observation of the potential energy (PE),as shown in Fig. 2. The results are obtained from the initial equilibration at 300 Kbefore the cross-linking process. The results from the CVFF simulation are used here asan illustration. It can be seen from Fig. 2a that the PE oscillates at a narrow range duringthe equilibration run, with an average of 56,506 kcal�mol�1. Additionally, there is a0.5 ps energy minimization process before and after the equilibration run, which alsominimizes the energy considerably. In comparison, a longer simulation (50 psNVT þ 50 ps NPT) has been performed based on the same initial structure. The resultindicates that the oscillation of PE continues during the 100 ps simulation, as shown in

Table 1 The applicability and limitation of the simulation using the specific force field

Force field CVFF Dreiding PCFF

Materials CVFF is derived forsmall organic crystalsand gas phase structures,and further optimizedfor organic, polymeric,and biological materials.

Dreiding force field isdeveloped for thesimulation of biological,organic, and someinorganic molecules.

PCFF is developed forpolymers, organic andinorganicmaterials, includingabout 20 inorganicmetals, as well as forcarbohydrates, lipids,and nucleic acids.

Properties CVFF is intended forstudying structures andbinding energies, and itpredicts vibrationalfrequencies,conformational energies,and mechanicalproperties reasonablywell.

Dreiding force fieldpredicts bulk materialproperties with amoderate accuracy,including geometries,conformational energies,intermolecular bindingenergies, and crystalpacking.

PCFF is intended for thestudy of cohesiveenergies, mechanicalproperties,compressibilities, heatcapacities, and elasticconstants.

Limitations In the simulations using these force fields, the atomistic interactions arenonreactive, where no charge transfer and chemical reactions occur. Therefore,these force fields are not applicable to the simulations of electronic transitions,electron transport phenomena, and proton transfer, where ab initio calculations aregenerally used.


Fig. 2b, and the average is 56,451 kcal�mol�1. Based on the similar trend of the PE andthe small difference between the averages, the short time span of the simulation (10 psNVT þ 10 ps NPT) is used in this work. It is always good to simulate for a longer timespan for a better equilibration, while the current strategy is believed to be sufficient forobtaining the SU-8 structure with no severe geometric distortion. As the cross-linkingreaction of the SU-8 epoxy is usually carried out at an elevated temperature, the sameequilibration process is used to equilibrate the structure at the elevated temperature

Fig. 1 Monomer of the SU-8 epoxy: (a) chemicalstructure and (b) molecularmodel


before performing the cross-linking reaction. A temperature of 368 K (95 �C) iscommonly used for the fabrication process of the SU-8 sample, and it is chosen here.After the above equilibration processes, the SU-8model is polymerized by using a cross-linking algorithm. Figure 3 shows the flowchart describing the modeling procedure.

Before each cross-linking reaction, the distance between the available reactiveatoms has been calculated, and the potential reactive atoms located inside the currentreaction radius are recognized, as shown in Fig. 4a. The reaction radius during thecross-linking process is set to be 3 Å initially and with an increment of 0.5 Å. Themaximum reaction radius is set to be 10 Å, as the cross-linking process with areaction radius over 10 Å usually requires a long equilibration process for alleviatingthe geometric distortion in the model. After the determination of the reactive atoms,the epoxide groups comprising those recognized reactive atoms are open, as shownin Fig. 4b. The recognized reactive atoms are then connected by a new bond toform the cross-link (Fig. 4c). After the bond creation (cross-links being formed), theunreacted atoms at the open epoxide groups are saturated with hydrogen atoms (Fig.4d). It is noticed that the combination of the distance and energy criteria wouldrequire a lot of computational power for the iteration process. In addition, thecomputation using the distance criteria is more straightforward and also requireslesser computational power, as shown from the various force field definitions. Fromthis perspective, we decide to use the distance-based cross-linking approach, whichis also well adopted by various researchers [12, 15, 19]. After each cross-linkingreaction, the structural information is updated by introducing new bonds, angles,torsional angles, and improper angles into the cross-linked structure.

In order to relax the SU-8 structure after each cross-linking reaction, a combinedequilibration process consisting of four steps is employed: (1) a 0.5 ps geometryoptimization; (2) a 5 ps NVT ensemble equilibration; (3) a 5 ps NPT ensembleequilibration; and (4) a 0.5 ps geometry optimization. During such equilibrationprocess, the lengths of the newly created bonds are relaxed to the equilibrium value,which can alleviate the geometric distortion in the newly cross-linked structure.Within each reaction radius, the cross-linking reaction is performed at most threetimes or it stops if no reactive atoms are identified. The cross-linking process of the

Fig. 2 Evolution of the potential energy of the SU-8 epoxy during (a) a short and (b) a long initialequilibration run at 300 K


SU-8 model is finished when the maximum reaction radius (10 Å) is achieved or allavailable potential reactive atoms are reacted.

Once the cross-linking process is finished, a short equilibration process is used, wherethe temperature is gradually changed from elevated temperature to room temperature.Specifically, the SU-8model is first equilibrated in theNVTensemble for 10 ps, and thenin the NPT ensemble for another 10 ps. The equilibration process is performed at thetemperature of 368 K, 334 K and 300 K, respectively. Three SU-8 epoxy networks arebuilt by performing the cross-linking process under the chosen force fields separately.

Though the cross-linked structure is equilibrated during the cross-linking process,the relatively short time frames used in the above equilibration processes are notsufficient for the epoxy network to reach the fully equilibrated state. In order to obtaina fully relaxedmolecular structure, the cross-linked SU-8model is further equilibrated.Several groups have developed the equilibration scheme with a control of temperatureand pressure that can speed up the equilibration process and relieve the residual stressof the polymeric networks [25, 31, 64]. Here, the equilibration scheme containingMD

Fig. 3 Flowchart of thecross-linking algorithm usedin the construction of the SU-8 epoxy. Reproduced fromRef. [45] with permissionfrom the Royal Society ofChemistry


simulations at high pressures is used for equilibrating the cross-linked network, whichaccelerates the compression of the cross-linked structure by overcoming the largeenergy barriers effectively. The details of the equilibration scheme are shown in Table2, which consists of seven equilibration cycles in both NVT and NPT ensembles at300 K. During the equilibration process, the density of the SU-8 model is adjustedthrough the pressure control. The pressure applied in the NPT simulation is graduallyincreased from atmospheric pressure to 50,000 atm in the first three equilibrationcycles (as indicated in Table 2) with a longer time frame (50–150 ps each) that allowsan adequate relaxation of the structure. The SU-8 epoxy network is compressedefficiently with the large pressure applied on the cross-linked structure. After that,the pressure is steadily reduced to 1 atm in the last four cycles (as indicated in Table 2)with a shorter time frame (5–15 ps each) in order to control the large pressure jumps.Along with the decrease of the applied pressure, the cross-linked structure isdecompressed accordingly. These compression and decompression steps only add ashort period of simulation time to the equilibration process, but they greatly improvethe accuracy of the achieved densities [25, 64]. Finally, a 5 ns relaxation under aconstant temperature of 300K and a constant pressure of 1 atm is carried out such that a

Fig. 4 Procedures of the cross-linking process of the SU-8 epoxy: (a) the reactive atoms locatedinside the reaction radius are recognized (marked with filled circles); (b) the epoxide groups compris-ing the recognized reactive atoms are open by deleting bonds; (c) the recognized reactive atoms areconnected by a new bond to form the cross-link; (d) the unreacted atoms at the open epoxide groupsare saturatedwith hydrogen atoms. Atoms located between the two epoxide groups are denoted as “R”for better clarity. Reproduced from Ref. [45] with permission from the Royal Society of Chemistry


fully equilibrated state can be achieved. By examining the root-mean-square displace-ment (RMSD) of the atoms, which keeps at a constant level before the 5 ns NPTequilibration run is completed, as shown in Fig. 5a, it implies that the fully equilibratedstate has been obtained. Meanwhile, the potential energy of the cross-linked SU-8 epoxy networks as a function of the simulation time is shown in Fig. 5b–d. Theaveragepotential energy is28,480�198kcal�mol�1 (CVFF),23,516�387kcal�mol�1

(Dreiding), and 11,811 � 180 kcal�mol�1 (PCFF), respectively. The variation ofpotential energy in the cross-linked system is small along the simulation time, whichalso implies that the cross-linked structure is close to the equilibrium state. After theequilibration process, the SU-8 epoxy network is further relaxed for 200 ps in NVTensemble in the case of bulk modulus calculation. One representative model of thehighly cross-linked SU-8 epoxy network is shown in Fig. 6.

In the investigation of the moisture effect on the SU-8 mechanical properties, theatomistic model constructed by using the CVFF potential is chosen as the startingconfiguration. The equilibrium moisture concentration is found to be 3.3 wt % inSU-8 [65], and is less than 4 wt % of the DGEBA-based epoxy [1, 2, 66], whereDGEBA is the basic component of the SU-8 monomer. In this work, differentamount of water molecules are added to the cross-linked SU-8 epoxy network.The added water molecules are located at the lowest energy sites in the cross-linkedstructure, which vary from 1, 2, 3, 4 wt % of the model molar mass. The epoxynetwork solvated with 4 wt % moisture content is used to investigate the SU-8 mechanical properties at the ultimate wet scenario. Water molecules employ theparameters of the TIP3P model with a cutoff distance of 10 Å [67]. During the MDequilibration, the bond lengths and angles of the water molecules are kept constantby using the SHAKE algorithm [68]. The solvated SU-8 epoxy networks experiencethe same equilibration process as shown in Table 2.

Table 2 Equilibration scheme incorporating the high pressure control used in the equilibrationprocess of the SU-8 epoxy

Cycle Ensemble Conditions Time frame (ps)

1 NVT 300 K 100

NPT 300 K, 1000 atm 50

2 NVT 300 K 150

NPT 300 K, 30,000 atm 50

3 NVT 300 K 150

NPT 300 K, 50,000 atm 50

4 NVT 300 K 150

NPT 300 K, 25,000 atm 5

5 NVT 300 K 15

NPT 300 K, 5000 atm 5

6 NVT 300 K 15

NPT 300 K, 5000 atm 5

7 NVT 300 K 15

NPT 300 K, 1 atm 5000


Fig. 5 Evolution of (a) root-mean-square displacement (RMSD) and (b, c, and d) potential energyof the SU-8 epoxy during the last 5 ns NPT equilibration run under three different force fields

Fig. 6 Cross-linked structureof the SU-8 epoxy


2.2 Atomistic Simulations

After the equilibration process of the SU-8 epoxy models, the Young’s modulus (E)and bulk modulus (K ) of the equilibrated models under dry scenario are calculatedby the uniaxial tensile deformations and the volumetric deformations, respectively.The shear modulus (G) and Poisson’s ratio (υ) are computed by applying the linearelasticity theory [69]. Due to the timescale limitation of the MD simulations, thestrain rate used in the dynamic deformations [20, 21, 23] is much higher than thatused in the experiments. Previous MD studies show that the calculated Young’smodulus of the polymeric materials is not sensitive to the change of the strain rate,while the yield stress increases with the strain rate [21, 23]. In the tensile deforma-tion here, the simulation cell along the loading direction X is elongated continuouslywith a strain rate of 1 � 108 s�1, which is in a range typical for the MD simulations,and the atmospheric pressure is maintained in the two perpendicular directions. Thedeformation is carried out at 300 K. At each deformation step, the equilibratedmodels are deformed by 0.1% in strain followed by a 10 ps equilibration processbefore next deformation step. For all the deformation processes, the equilibratedmodels are deformed by 3.0% in total. The virial stress tensors are recorded duringthe entire deformation process, and they are calculated by using Eq. (2), where a andb denote the values X, Y, Z to represent the six components of the symmetric tensor.

Sab ¼ 1

Vð2Kab þWabÞ,

Kab ¼ 1

2

XNn¼1

miviavib,

Wab ¼ Wpairwiseab þWbond

ab þWtorsionab þWout�of�plane

ab

¼ 1

2

XNp

n¼1

ðr1aF1b þ r2aF2bÞ þ1

2

XNb

n¼1

ðr1aF1b þ r2aF2bÞ

þ 1

3

XNa

n¼1

ðr1aF1b þ r2aF2b þ r3aF3bÞ

þ 1

4

XNt

n¼1

ðr1aF1b þ r2aF2b þ r3aF3b þ r4aF4bÞ

þ 1

4

XNoop

n¼1

ðr1aF1b þ r2aF2b þ r3aF3b þ r4aF4bÞ, (2)

where Sab is the virial stress tensor, Kab is the kinetic energy tensor, and Wab is thevirial tensor, which is calculated by considering various potential components.Specifically, Wab

pairwise is a pairwise energy contribution consisting of vdW andCoulombic interactions, where r1a and r1b are the positions of the two atoms in thepairwise interaction, and F1a and F1b are the forces on the two atoms resulting from


the pairwise interaction. There are similar terms for theWabbond bond,Wab

angle angle,Wab

torsion torsion, and Wabout-of-plane out-of-plane interactions.

After the deformation, E of the model is determined, which is calculated byperforming a regression analysis on the relatively linear portion of the stress–straincurve (i.e., the initial slope of the stress-strain curve) and is illustrated in Eq. (3),

E ¼ σXXeXX

, (3)

where σXX and eXX are the stress and strain tensor components along the loadingdirection X, respectively.

Bulk modulus describes the material response under a uniform pressure. Here, itis determined by the volumetric deformation, in which equal axial strains are appliedin all three orthogonal directions simultaneously. The calculation of bulk modulus iscarried out at a constant temperature of 300 K. The dynamic deformations areapplied in the form of dilatation by keeping the strain rate as 1 � 108 s�1. Theoverall dilation of the model is determined by e = eXX + eYY + eZZ, where eXX, eYY,and eZZ are the infinitesimal strain tensor components with respect to the coordinatedirections X, Y, and Z, respectively. The overall stress of the model is calculated byσ = 1/3 (σXX + σYY + σZZ), where σXX, σYY, and σZZ are the volume-averaged virialstress tensor components calculated by using Eq. (2). K is then calculated as theinitial slope of the curve representing the overall stress σ against the volumetricdeformation e as shown in Eq. (4),

K ¼ σ

e¼ 1=3ðσXX þ σYY þ σZZÞ

eXX þ eYY þ eZZ: (4)

Assuming that the material is homogeneous and isotropic, with any two elasticconstants available from direct measurements it is considered to be sufficient for afull characterization of the mechanical properties. Therefore, G and υ are computedbased on the calculated E and K by applying the linear elasticity theory [69].Particularly, G is given in Eq. (5),

G ¼ 3KE

9K � E, (5)

and υ is determined by using Eq. (6),

υ ¼ 3K � E

6K: (6)

For the solvated models, E is determined and used as an indicator to illustrate themoisture effect on the mechanical properties of the SU-8 epoxy.


2.3 Physical Properties of Polymeric Material

The physical properties of the SU-8 epoxy obtained from the MD simulations underdry scenario are compared with the experimental data in Table 3.

The cross-linking degree achieved after the polymerization process is an impor-tant parameter for validating the constructed atomistic model. It is defined as theratio of the cross-linked reactive atoms divided by all the potential reactive atomsbefore the cross-linking process. The SU-8 atomistic model is obtained by carryingout the cross-linking algorithm without termination. The resulted cross-linkingdegree of the SU-8 epoxy networks created by using different force fields isshown in Fig. 7. Initially, there are abundant reactive atoms available for the cross-linking reaction, which is indicated by the strong dependence between the cross-linking degree and the reaction radius. As the reaction goes on with the increasingreaction radius, lesser reactive atoms are available for the cross-linking reaction, andthe curve becomes steady when the reaction radius is over 6 Å. The final cross-linking degree of all the constructed atomistic models is higher than 80%. Specifi-cally, the SU-8 epoxy network constructed under Dreiding force field shows themaximum cross-linking degree of 88.1%, followed by 82.5% under PCFF and81.9% under CVFF. The influence of the equilibration time span on the maximumcross-linking degree is investigated by alternating the equilibration scheme beforethe cross-linking reaction. In consideration of the similar evolution of the cross-linking degree, the final cross-linked structure from the CVFF simulation is chosenas an illustration. The cross-linked structure undergoes a 10 ns equilibration (5 nsNVT þ 5 ns NPT) before the cross-linking process at a larger reaction radius.Another set of the cross-linking process is carried out on the same structure byusing the original equilibration scheme (5 ps NVTþ 5 ps NPT). The maximumreaction radius is found to be 11 Å for both cases, and the final cross-linking degreeof the model after the 10 ns equilibration is 85%, while the original model is 84%, asshown in Fig. 8. It can be seen that at the extended reaction radius, the new cross-links are formed slowly for both cross-linking process. Meanwhile, it is noted that alonger equilibration run can enhance the formation of cross-links, but it demandsmore computational power than the proposed equilibration scheme. Considering thelarge computational consumption and a limited improvement in the cross-linkingdegree, current reaction radius range and equilibration process can be considered

Table 3 Simulated and experimental results for the SU-8 epoxy at 300 K. Reproduced from Ref.[45] with permission from the Royal Society of Chemistry

Force field CVFF Dreiding PCFF Expt.

Cross-linking degree (%) 81.9 88.1 82.5 � 80

ρ (g�cm�3) 1.04 � 0.002 1.05 � 0.001 1.05 � 0.002 1.07–1.20

E (GPa) 4.43 � 0.23 4.42 � 0.12 2.67 � 0.16 2.70–4.02

K (GPa) 4.35 � 0.18 3.72 � 0.15 2.88 � 0.10 3.20

G (GPa) 1.66 � 0.11 1.70 � 0.06 0.99 � 0.07 1.20

υ 0.33 � 0.02 0.30 � 0.01 0.35 � 0.02 0.33


reasonable. Overall, the cross-linking algorithm used in this work is capable ofconstructing the epoxy network with the cross-linking degree close to thoseepoxy-based materials through various experimental approaches [70, 71].

For the structural characterization of the SU-8 epoxy network, density (ρ) is anothercritical parameter which should be consistent with the experimental value. In the last5 ns equilibration run in the NPT ensemble, the SU-8 epoxy network is equilibrated toreach the minimum potential energy. The three orthogonal directions of the simulationcell are adjusted independently under the atmospheric pressure. The density of thecross-linked SU-8 structure is sampled every 10 ps during this 5 ns equilibrationprocess, as shown in Fig. 9. The density at the last 2 ns simulation is relatively stable inthe three cases, which indicates that the equilibrium state is reached in the threesystems. In order to minimize the statistical error, only the recorded density from the

Fig. 7 Cross-linking degreeof the SU-8 epoxy as afunction of the reaction radiusunder three force fields.Reproduced from Ref.[45]with permission from theRoyal Society of Chemistry

Fig. 8 Cross-linking degreeof the SU-8 epoxy as afunction of the reaction radiusunder CVFF potential: effectof the equilibration time span


final 2 ns equilibration run is accounted for the density calculation. The averagedensity of the SU-8 epoxy network is shown in Table 3, with respect to the chosenforce fields. In comparison to the available value in the range of1.07–1.20 g�cm�3, the slight underestimations of the density are observed from thethree equilibrated SU-8 epoxy networks, with the value of 1.04 � 0.002 g�cm�3

(CVFF), 1.05 � 0.001 g�cm�3 (Dreiding), and 1.05 � 0.002 g�cm�3 (PCFF), respec-tively. The small discrepancies of the SU-8 epoxy networks demonstrate that theequilibration process as shown in Table 2 is effective to improve the accuracy of thedensities achieved, and also indicate that the potential function of the chosen forcefields are able to provide good mathematical approximations for calculating thepotential energy of the cross-linked SU-8 structure. In view of the good agreementof ρ with the experimental measurement, the generated models of the cross-linked SU-8 epoxy are regarded as reasonable structures close to those found in the real systems.

The stress–strain curves of the cross-linked SU-8 epoxy network under theuniaxial tensile deformation are shown in Fig. 10. The stress along the loadingdirection shows a linear elastic response to the applied strain during the wholedeformation process. The E is determined by performing a regression analysis onthe stress–strain data from the 3% deformation. The computed E of the SU-8 epoxyunder the chosen force fields is shown in Table 3 with a comparison to the experi-mental data. The data reported is from a single run, and the standard deviation comesfrom the linear regression of the stress–strain curve obtained from that simulationrun. The E obtained under CVFF and Dreiding potentials are 4.43 � 0.23 GPa and4.42 � 0.12 GPa, respectively, while a smaller value of 2.67 � 0.16 GPa is yieldedunder PCFF potential. In view of the experimental tensile test results ranging from2.70–4.02 GPa [49–51, 72], the simulated E of the three SU-8 epoxy networksprovide excellent agreements. Four other strain rates are examined in the tensiledeformations under the chosen force fields independently, including 1 � 107 s�1,5 � 107 s�1, 5 � 108 s�1, and 1� 109 s�1, respectively. The relatively superpositionof the stress–strain curves with different strain rates confirms that the Young’smodulus is not sensitive towards the change of strain rate, which is consistent withthe existing simulation works from other similar epoxy systems [21, 23].

Fig. 9 Evolution of densityof the SU-8 epoxy at the last5 ns NPT equilibration rununder three different forcefields


The K of the SU-8 epoxy network obtained under dry scenario is 4.35� 0.18 GPa(CVFF), 3.72 � 0.15 GPa (Dreiding), and 2.88 � 0.10 GPa (PCFF), respectively.Using the reported E and G from the experimental measurement [50], K is computedto be 3.20 GPa by using the linear elasticity theory [69], which is the closest point forcomparison with our data. Close agreements are observed between the three simu-lated data and the reference value.

By applying the linear elasticity theory, G and υ of the SU-8 epoxy network iscomputed and compared with the experimental measurements at 300 K, as shown inTable 3. The G of the SU-8 epoxy network under CVFF and Dreiding is1.66 � 0.11 GPa and 1.70 � 0.06 GPa, respectively, which are greater than thereported data (1.20 GPa), while a smaller value of 0.99� 0.07 GPa is observed in thecase of PCFF. In the meantime, a good agreement is found between the computed υ(0.33 � 0.02) under CVFF and the experimental value (0.33), while the values forother two force fields are 0.30� 0.01 (Dreiding) and 0.35� 0.02 (PCFF), which arealso in a reasonable accordance.

By using the three force fields, the simulated cross-linking and physical propertiesof the constructed SU-8 epoxy network are in a good accordance with variousexperimental observables, including cross-linking degree, density, Young’s modu-lus, bulk modulus, shear modulus, and Poisson’s ratio, which demonstrates that thechosen force fields are able to characterize the atomistic interactions in the cross-linked structure in an appropriate way. Therefore, the three force fields can be used toinvestigate the cross-linking and physical properties of the epoxy-based materialswith reasonable accuracy.

To determine the effect of NPT equilibration time span on the physical propertiesof the cross-linked network, a longer equilibration run (8 ns) has been conducted, incomparison with the original 5 ns NPT simulation. Similarly, CVFF case is used asan example. The ρ and E of the SU-8 cross-linked structure are calculated forcomparison. The average ρ from the last 2 ns equilibration is shown in Table 4,together with the ρ obtained from the original 5 ns case. The computed ρ between thetwo separate simulations is identical and the E is relatively the same, which dem-onstrates that current time span of the 5 ns NPT simulation is sufficiently long for the

Fig. 10 Stress–strain curvesobtained from the tensiledeformation of the SU-8 epoxy under three forcefields. Reproduced from Ref.[45] with permission from theRoyal Society of Chemistry


equilibration process. With the current simulation run, it can be observed that theoriginal predicted properties (e.g., ρ and E) are very close to the results from thelonger simulation run, as well as from the experimental observations.

Furthermore, in order to investigate the size effect on the physical propertiesof the SU-8 epoxy, a larger system originated from 15,920 atoms (eighty monomers)is simulated and compared with the original smaller system (forty monomers). Thesimulation is performed by using CVFF potential as an example. The modeling andsimulation conditions are the same as described in previous section. The cross-linking degree of the two SU-8 epoxy networks is shown in Fig. 11. The trend ofthe two resulted curves is very similar, leading to a cross-linking degree of 78% forthe larger system, while the value of the smaller system is 82%. Meanwhile, thecomputed ρ and E of the larger cross-linked structure are compared with the resultsof the smaller system, as shown in Table 5. The densities of the two cross-linkedstructures are nearly the same, and the measured Young’s moduli are also very closebetween these two systems. In view of the computed cross-linking degree, ρ, and E,a good agreement is observed between the two models with different sizes. Thus, itindicates the size adopted in the original simulation is large enough for evaluatingthe mechanical properties of the cross-linked SU-8 epoxy.

After characterizing the mechanical properties of the SU-8 epoxy network, themoisture effect on the epoxy mechanical properties can now be quantified. The ρ ofthe SU-8 epoxy networks is calculated and shown in Table 6, with respect to the

Table 4 Density and Young’s modulus of the SU-8 epoxy at 300 K: effect of NPT equilibrationtime span [45]

CVFF

Expt.Equilibration (ns) 5 8

ρ (g�cm�3) 1.04 � 0.002 1.04 � 0.002 1.07–1.20

E (GPa) 4.43 � 0.23 4.44 � 0.10 2.70–4.02

Fig. 11 Cross-linking degreeof the original and larger SU-8 epoxy as a function of thereaction radius under CVFFpotential


moisture content ranging from 0 to 4 wt %. For the solvated SU-8 epoxy networks,the ρ shows a steady increase with the increasing moisture content, and reaches1.056 � 0.001 g�cm�3 at 4 wt % moisture content. For the SU-8 epoxy, no relatedexperimental data are available for a direct comparison with the moisture-affected ρ.It is believed that the monotonic increase of ρ is due to the weight gain from theadded water molecules. In view of the small variation of the ρ between dry and wetscenarios, it is inferred that the added water molecules does not make a significantdifference to the SU-8 structural properties. Further investigation on the moisture-affected SU-8 mechanical properties can consolidate this finding.

During the uniaxial tensile deformation, the stress–strain curves of the cross-linkedSU-8 epoxy network are recorded as shown in Fig. 12 with respect to the moisturecontent. It can be observed that the stress of all the SU-8 epoxy networks along theloading direction shows a linear response to the applied strain, which indicates that theSU-8 epoxy networks are elongated elastically within the 3% deformation. Based onthe obtained stress–strain curves, the E is calculated by performing a linear regressionanalysis on the stress–strain data ranging within the 3% deformation. The calculated Eis shown in Table 6, and the data reported is from a single run. Aside from that, twoindependent simulation runs are performed on each epoxy network. As the computedEshows no significant difference to the reported data, it is not accounted for the reportedvalue. For the solvated SU-8 epoxy networks, the E reaches the peak of5.03 � 0.15 GPa at 1 wt% moisture content, and then decreased steadily to4.18 � 0.23 GPa at moisture content of 3 wt %, with another small increase to4.37� 0.19 GPa at moisture content of 4 wt %. Our results show that at low moisturecontent, the absorbed moisture may have a beneficial effect on the SU-8 Young’smodulus, which has been reported in various polymeric materials [73–75]. Theexplanation of this phenomenon can be made from a viewpoint of the moistureantiplasticization effect. As the SU-8 epoxy network is highly cross-linked after thecross-linking process, the added water molecules start to fill in the free volume of theepoxy structure, and thus enhances the stiffness of the SU-8 epoxy. As the moistureabsorption in the SU-8 structure continues to increase during the long-term service life,

Table 5 Density and Young’s modulus of the SU-8 epoxy at 300 K: effect of model size [45]

CVFF

Expt.Monomers 40 80

ρ (g�cm�3) 1.04 � 0.002 1.05 � 0.001 1.07–1.20

E (GPa) 4.43 � 0.23 4.29 � 0.47 2.70–4.02

Table 6 Density and Young’s modulus of the SU-8 epoxy at 300 K: effect of moisture

Moisturecontent(wt %) 0 1 2 3 4

ρ (g�cm�3) 1.044 � 0.002 1.049 � 0.001 1.050 � 0.002 1.053 � 0.001 1.056 � 0.001

E (GPa) 4.43 � 0.23 5.03 � 0.15 4.46 � 0.09 4.18 � 0.23 4.37 � 0.19


the absorbed moisture decreases the modulus of epoxy and it becomes softened. Thismoisture effect is called the plasticization. However, our results indicate that even withlarge amount of the moisture addition, the largest decline of E is only 5.5% at 3 wt%moisture content. Independently, the SU-8 epoxy network solvated with larger mois-ture content (i.e., 5, 6 wt%) are simulated to see if any change of the modulus can beobserved with the moisture content beyond the limit of 4 wt%. The results show thatthe downturn in E is not obvious in these epoxy networks with larger moisture content.The discrepancy between the simulation results and the prediction based on plastici-zation is resulted from the hydrophobic nature of the SU-8 epoxy, as it is only slightlymoisture-permeable, and the equilibrium moisture content is reported to be less than4 wt % [1, 2, 65, 66]. It is noted that a high moisture absorption, e.g., 10 wt%, maycause obvious plasticization of the SU-8 epoxy, but such highmoisture absorptionmaynot occur in the SU-8 epoxy. Equippedwith the relationship between the SU-8Young’smodulus and the added moisture content, it can be concluded that the moisture has nosevere impact on the SU-8mechanical properties, which further demonstrates that SU-8 is able to provide a strong mechanical reliability for the practical application duringthe whole life-circle.

3 Coarse-Grained Modeling of Polymeric Material

This section presents the study on the mechanical behaviors of the polymeric mate-rial at the mesoscale by using CG MD simulation. The CG model of the polymer isdeveloped by reducing some of the atomistic degrees of freedom, where the poly-merized structure is represented by a collection of beads connected by springs, asshown in Fig. 13. The interactions between the beads are characterized by the forcefield, which describes the resistance to the tensile load, bending and intramolecularinteraction of the polymerized structure. Furthermore, the effect of the structural voidson the mechanical behaviors of the investigated material is determined.

Fig. 12 Stress–strain curvesobtained from the tensiledeformation of the SU-8 epoxy with respect to themoisture content


3.1 Coarse-Grained Model of Polymeric Material

In this section, a series of mechanical loading cases to determine the force fieldparameters for the CG epoxy model are described. These studies consist of thefollowing two loading cases: (i) the tensile loading to determine the Young’smodulus of the epoxy; and (ii) the adhesion test of an assembly of two epoxycross-linked molecules to determine their adhesion energy. The different loadingcases are shown in Fig. 14. All studies are carried out by using the SU-8 atomisticmodel, which is constructed based on the method as describe previously.

The atomistic simulations are performed by using the classical MD [76]. Thedetailed molecular interactions of the epoxy structure are described by a force field,

Fig. 13 Coarse-grainedrepresentation of the SU-8 epoxy: (a) atomistic, andcorresponding (b) mesoscalebead-spring model


which is the core of the classical MD methods. Here the PCFF potential is used todescribe the molecular interactions of the epoxy structure, which captures not onlythe pairwise interactions of the non-bonded atoms but also additional cross-couplingterms from the local geometric configuration of the neighboring atoms [55, 56]. ThePCFF potential has been reported to be reliable for the simulations of the polymericmaterials [13, 23, 45]. The time step is chosen to be 1 fs, and the vdW andCoulombic interactions are truncated at a cutoff distance of 13.5 Å. The MDsimulations are performed by using the open source code LAMMPS [61].

The computational uniaxial tensile deformation of the epoxy structure is carriedout by keeping one end of the structure fixed, while slowly stretching the other end inthe axial direction of the structure. The loading configuration is shown in Fig. 14a.Three different displacement loading rates are applied in the tensile deformation,including 10, 5, and 2.5 m�s�1. During the entire tensile deformation, the virial stresstensors are monitored and averaged over the structure volume. The stress tensorcomponent in the loading direction is used to extract the information about the stressas a function of the applied uniaxial strain. The measured stress–strain curve is usedto calculate the Young’s modulus of the epoxy network. For the small deformation,the results of all the applied loading rates are similar, indicating the convergence ofthe elastic properties. Young’s modulus is determined by performing a regressionanalysis on the stress–strain data, which is estimated to be 3.21 � 0.69 GPa [77],close to the experimental observation of 2.70–4.02 GPa [45].

In the epoxy three-dimensional covalent network, there are molecules that are notdirectly connected, where no direct covalent interactions exist between these epoxymolecules. The primary interaction between these epoxy molecules are the weakdispersive interaction. The adhesion energy of the epoxy molecules is calculated byusing the metadynamics method [7, 78–85]. The geometry of the two epoxymolecules is depicted schematically in Fig. 14b. The system is first equilibrated

Fig. 14 Mechanical loading cases of the SU-8 epoxy for deriving the force field parameters for thecoarse-grained (CG) model: (a) tensile loading and (b) adhesion test


without the application of any external mechanical loading. The equilibrated state ofthe system is affirmed by examining the RMSD of the epoxy atoms, which becomesstable at the end of the equilibration. After that, the metadynamics simulation isperformed by using the PLUMED package in LAMMPS [86, 61]. The free energy ismeasured as a function of the center-to-center distance between the two epoxymolecules. The metadynamics simulation converges after a 17 ns time span, permit-ting a full exploration of all the possible states [77]. The equilibrium distancebetween the two epoxy molecules is found to beΔD� 31.40 Å, which approximatesto the thickness h0 of the epoxy molecule. A relationship between ΔD and h0 thatdepends on the dimension of the epoxy molecules can be arrived,

ΔDh0

� 1: (7)

For the epoxy molecules with the same size, the equilibrium distance ΔD in theweak dispersive interactions can be approximated as equal to the thickness. The freeenergy difference between the attached state and the separated state is102.36 kcal�mol�1 [77]. With the surface area being 14.00 nm2, the normalizedadhesion energy Es of the two epoxy molecules equals 25.40 mJ�m�2.

From the atomistic simulation results, it can develop a better understanding of theinteraction and force during the deformation of the epoxy at the mesoscale. Theinformation is used to develop a CG model, in which the beads are connected bysprings to represent the epoxy covalent network, whereas all parameters arecompletely derived from the atomistic simulations. With the reducing degrees offreedom in the CG model, it can model the epoxy structure with the length on theorder of few tens of nanometers. Therefore, this approach enables one to study themicroscopic structural voids.

The goal here is to develop a CG model suitable to perform the large-scalesimulation of the mechanics of the epoxy-based materials, eventually leading to theunderstanding of the structural voids effect on the behavior of these materials. Thetotal energy of the system can be expressed as

E ¼ ET þ EB þ Eweak, (8)

where ET is the energy stored in chemical bonds due to the stretching along the axialdirection, EB is the total bending energy, and Eweak constitutes the weak, dispersiveinteractions between the molecules of the epoxy structure that are not directlyconnected. Similar techniques have been used effectively to model the behavior ofcarbon nanotubes, collagen molecules, wood cell walls, and silica nanocomposites[77, 87–92].

The energy of the axial strain and bending is expressed by the harmonic potentialof the form


ETðrÞ ¼Xbonds

1

2KTðr � r0Þ2, (9)

EBðθÞ ¼Xangles

1

2KBðθ � θ0Þ2, (10)

where r is the distance between the bonded beads, θ is the angle formed by threeconsecutive beads, and r0, θ0 refer to the equilibrium distance and angle, respec-tively. Meanwhile, the weak, dispersive interactions are modeled by a 12: 6 Lennard-Jones (LJ) potential of the form

Eweak rð Þ ¼Xpairs

4eσ

r

� �12

� σ

r

� �6� �

, (11)

with e as the energy at equilibrium and σ as the distance parameter for each pairwiseinteraction. It is assumed that a pairwise interaction between different particles issufficient and that there are no multi-body contributions [87, 88]. Based on theseassumptions, the interaction between different molecules is modeled by using a LJ12:6 potential.

The mass of each bead can be determined by assuming a homogeneous distribu-tion of the mass in the model, which is an excellent assumption for the homogeneousstructure of the epoxy-based materials. The beads are connected through springs toform a network model of a primitive cubic system, which is considered as arepresentative of the epoxy cross-linked structure. Such three-dimensional bead-spring network is analogous to the CG crystalline silica, in which one bead isconnected with six neighboring beads by springs [90]. In the epoxy network withstructural voids, the beads in the void locations can be removed to create thestructural voids. Previous studies have shown that the void volume is 87–111 Å3

for the DGEBA-based epoxy resin, and 97� 33 Å3 for the uncured epoxy [8, 9, 93].In this work, it is designated that one bead has the same mean volume of the voids, i.e., 97 Å3. The equilibrium distance r0 of two beads is calculated to be 4.60 Å. As SU-8 has a density of 1.20 g�cm�3, it is determined that the mass of one bead with avolume of 97 Å3 is around 70 amu. Therefore, each bead has a weight of 70 amu.

The LJ parameters are chosen to reproduce the adhesion energy determinedfrom the full atomistic simulations. The equilibrium bond distance is related to thedistance ΔD between the two epoxy molecules in contact by the weak, dispersiveinteractions, with

D ¼ ΔD, (12)

where ΔD can be approximated to the thickness h0 of the epoxy molecule, i.e.,ΔD � 4.60 Å. The distance parameter in the LJ potential is then given by


σ ¼ Dffiffiffi26

p � 4:10, (13)

where D is the equilibrium bond distance.The LJ potential minimum is at r = D and is given by �e. Given that per unit cell

of bonds in this setup, the energy per unit area is given by

ES ¼ 1

S0½ϕweakðDÞ þ ϕweakð ~DÞ þ . . ., (14)

where

ϕweak Dð Þ ¼ �e, (15)

and ϕ( ~D) þ . . . denote the interaction energy to the second nearest neighbors and soon.

The numerical value for the adhesion strength of two epoxy molecules is deter-mined fromMD simulation as ES= 25.40 mJ�m�2. The parameter e in the CG modelis chosen so that the atomistic and CG model feature the same adhesion energy perunit area. For the nearest neighbors only,

e ¼ E1S0: (16)

For more than one nearest neighbors in the case of the larger cutoff radius,

e ¼ ESS0½ð1þ πð2Þ þ πð3Þ þ . . .Þ�1, (17)

where π = ϕweak ( ~D)/ϕweak (D). The term (1 þ π(2) + π(3) þ ... þ π(N )) = β(N ) isdefined and it is found that β(6) � 1.0988, which leads to e� 0.70 kcal�mol�1, with acutoff distance at rcut = 30 Å.

The tensile spring constant is determined from previous tensile loading deforma-tion, where the tensile deformation is carried out in the regime of small loads andconsequently small displacements. The stress–strain response of the SU-8 epoxyobtained from the full atomistic calculations is used to develop the interaction of thebonded beads. The spring constant kT is then defined as

kT ¼ Ac

r0E, (18)

with Ac being the cross-sectional area of the SU-8 epoxy structure with a value of0.21 nm2, and r0 the equilibrium distance of the two beads. Based on the low-strainrate tensile testing data discussed in previous section, kT is found to be around2.12 kcal�mol�1�Å�2.

Using the concept of energy conservation between the atomistic and CG model,the bending stiffness parameter kB is expressed as


kB ¼ 3EI

2r0, (19)

with r0 denoting the equilibrium bead distance, and EI as the bending stiffness of theepoxy. The cross-sectional moment of inertia for the epoxy is calculated by assuminga square cross section with a length of r0 and using I= r0

4/12. Based on the Young’smodulus discussed in previous section, kB is calculated to be about5.58 kcal�mol�1�rad�2.

3.2 Coarse-Grained Simulations

The parameters used in the CG simulations of the epoxy are summarized in Table 7.A series of samples are modeled to study the mechanical properties of the polymericmaterial at the mesoscale. Two cases are investigated: (i) a simple validation tocompare the CG simulation results to the experimental data; and (ii) a study of thestructural voids effect on the epoxy structure.

The initial CGmodel is set up by distributing the 9216 (36� 16� 16) beads in the17 � 7 � 7 nm3 simulation box. These beads are equally separated by 0.46 nm, andconnected with springs to form a covalent network. A large time step of 10 fs can beused for the integration of the equations ofmotion, as each bead has a largemass of fewtens of atomic mass units [88]. Nonperiodic and shrink-wrapped boundary conditionsare used in all three dimensions during the simulations, where the position of thesimulation box edge is adjusted in order to include all the beads in that dimension, nomatter how far they move. During the simulation, the system is subjected to anequilibration scheme with a control of temperature that can speed up the equilibrationprocess and relieve the residual stress inside the structure. Specifically, the system isfirst relaxed at absolute zero temperature for 0.5 ns in the microcanonical (NVE)ensemble with constant number of particles, volume, and energy of the system.Subsequently, the system is equilibrated in the NVT ensemble with constant numberof particles, volume, and temperature, which is corresponded to the constant temper-ature experiments. The temperature imposed during theNVTequilibration is graduallyramped up from absolute zero to amaximumof 600Kwith an increment of 100K, andthen gradually stepped back down to 300K, so as to allow the adequate fluctuation andrelaxation of the structure. At each temperature, the equilibration runs for 0.5 ns.Finally, the two layers of beads in the outermost, left part of the structure are restrictedin motion to mimic the fixed boundary condition, and a 2.5 ns NVT equilibration iscarried out before the tensile deformation, as similar to the loading case shown in Fig.14a. The temperature is controlled by Nosé–Hoover thermostat [63]. The equilib-rium state of the simulated system is identified by examining theRMSDof the beads inthe system, which reaches a constant level at the end of the equilibration.

Based on the previous defined CG model, the structural voids are introduced toquantify the effect on the mechanical properties. It is reported that the mean numberof structural voids per mass unit is 0.65 nm�3 [9]. For the initial CG model, itsvolume is around 897 nm3, and thus the number of structural voids in the model is


583. In this work, it is designated that one bead has the same mean volume of onevoid. To create the structural voids, 583 beads are removed from the initial CGmodel, and the springs connected to the removed beads are deleted accordingly.These 583 beads for structural voids are selected randomly across the CG model. Todetermine the effect of the void locations, two independent models with structuralvoids have been constructed. Same as the original model, 583 beads are selectedrandomly and removed accordingly, but the distributions of the removed beads aredifferent from each other. The volume fraction of the voids in the CG model iscalculated as about 6.3%. The weight of the CG models is summarized in Table 8.The CG SU-8 model is equilibrated adequately using the equilibration conditionscorresponding to previous case, and then the computational tensile deformation iscarried out to investigate the mechanical response of the model with structural voids.

3.3 Effect of Structural Voids on Polymeric Material

In equilibrium state, the epoxy network is relaxed to the potential energy minimum.Due to the incorporation of the angle bending term in the force field, the epoxy modelcan maintain the primitive cubic system after the equilibration, as shown in Fig. 15a.The evolution of the potential energy is plotted in Fig. 15b, where the potential energykeeps at a stable value during the final 2.5 ns NVT equilibration at 300 K. For thevalidation of the developed CG model, the density (ρ) is a critical parameter whichshall be consistent with the experimental value. During the final 2.5 ns NVT equili-bration, the ρ of the epoxy network is sampled every 250 ps. The average ρ of the CGnetwork without the structural voids is shown in Fig. 15c. The error bars shown in thefigure are obtained from the standard derivations of the averages. A ρ of1.26 � 0.003 g�cm�3 is obtained for the epoxy network with no structural voids. Aslight overestimation is observed in comparison with the experimental value of1.07–1.20 g�cm�3. Meanwhile, the Young’s modulus (E) of the CG model is anotherimportant material parameter for validation. During the uniaxial tensile deformation,the stress versus strain as obtained by using the CG model is recorded and shown inFig. 16a. The stress along the loading direction shows a linear response to the appliedstrain, which indicates that CG epoxy network is elongated elastically within the smallstrain deformation. The E is calculated by performing a linear regression analysisbased on the obtained stress–strain curve, and the result is shown in Fig. 16b. The data

Table 7 Summary of the CG force field parameters derived from the atomistic simulation

Parameter Numerical value

Equilibrium bead distance r0 (Å) 4.60

Tensile stiffness parameter kT (kcal�mol�1�Å�2) 2.12

Equilibrium angle θ0 (o) 90, 180

Bending stiffness parameter kB (kcal�mol�1�rad�2) 5.58

Dispersive parameter e (kcal�mol�1) 0.70

Dispersive parameter σ (Å) 4.10


Table 8 Weight of the CG SU-8 model

Without voids With voids Loss of weight

Weight (amu) 645,120 604,310 6.3%

Fig. 15 Equilibration analysis: (a) snapshot of the equilibrium configuration, and (b) plot of thepotential energy evolution of the CG network without voids; (c) density of the equilibrated models;and (d) evolution of RMSD of the beads

Fig. 16 Tensile test of the CG network: (a) stress versus strain data from tensile test; (b) histogramsshowing the Young’s modulus


reported is from a single run. The E of the CG network is 5.99 � 0.01 GPa, which islarger than the experimental tensile test measurements in the range of 2.70–4.02 GPa[49–51]. Realistically, MD simulation probes the modulus in the athermal limit.Compared with the experiment, the strain rate in MD simulation is several orders ofmagnitude higher, and the contribution of the thermal motions to the mechanicalresponse of the material is smaller. Both factors can result in the higher moduli asobserved. Therefore, MD simulation result can be in a closer agreement with thatfrom the high-strain rate or low-temperature pulling experiment. Meanwhile, theoverestimation of ρ and E could be due to the fact that the constructed CG model isfree of structural voids, as they normally exist in the experimental samples.

With the quantitative mechanical characterization of the pristine epoxy network,the effect of structural voids on the epoxy can now be quantified. During theequilibration process, the ρ of the epoxy network with structural voids is measuredand compared with the model with no voids, as shown in Fig. 15c. The computed ρwith voids is 1.13 � 0.003 g�cm�3, which is slightly smaller than the model withoutvoids, and agrees very well with the experimental value of 1.07–1.20 g�cm�3.Meanwhile, the density ρ of the two independent models with different distributionsof structural voids is found to be in a good accordance with the reported value. Incomparison with the sample without voids, a relatively smaller density is because thatthe existence of structural voids in the epoxy network causes a loss of weight, andmore essentially, it weakens the covalent interactions in the cross-linked network,where the monomers near the structural voids can flow more freely, which can leadto the expansion of the network. The movement of the monomers in the epoxy cross-linked structure, i.e., the beads in the CG model, can be quantified by using theRMSD of the beads during the equilibration run. By comparing the RMSD as shownin Fig. 15d, it is observed that the RMSD of the beads in the model with structuralvoids keeps at a higher level than that of the model without voids, which demon-strates the larger movements of beads, i.e., the beads flow more freely in the modelwith voids. Further investigation on the effect of structural voids focuses on theanalysis of the Young’s modulus. The stress–strain data of the epoxy network withvoids is shown in Fig. 16a. The E is calculated to be 4.32� 0.04 GPa, which is closerto the experimental results of 2.70–4.02 GPa when compared to the model withoutvoids. In the meanwhile, the measured E of the two independent models is also closeto the reported value. In view of the computed ρ and E of the three models withstructural voids, no significant variation is observed from the models with differentdistributions of the void. Furthermore, our results show that with the existence ofstructural voids, the epoxy model possesses the properties, i.e., ρ and E closer toexperimental data, in comparison with the larger variation of the model withoutvoids. Therefore, the developed CG model of the epoxy with structural voids can beregarded as a reasonable structure close to those found in the real systems, which canbe used as a basis in the various investigations involving the cross-linked networkat the mesoscale. Equipped with the relationship between the epoxy properties andthe structural voids, it can be concluded that the structural voids are intrinsic to theepoxy-based materials, and a certain number of the voids with a volume of 97 Å3

have no severe impact on the epoxy elastic properties.


4 Conclusion

In this chapter, the atomistic and CG MD simulations have been applied to study themechanical properties of the polymeric material.The SU-8 epoxy is chosen as therepresentative polymeric material used in the engineering applications. An effectivedynamic cross-linking algorithm has been developed to construct the atomisticcross-linked network, with the cross-linking degree and density close to the exper-imental observations. Mechanical properties of the constructed epoxy network aremeasured by means of dynamic deformations, which are in a good accordance withvarious experimental observables, including Young’s modulus, bulk modulus, shearmodulus, and Poisson’s ratio. For the investigation of the moisture effect, theconstructed epoxy network is solvated with a successive amount of moisture contentfrom 0 to 4 wt% to mimic the different moisture conditions. The MD simulationresults show that the Young’s modulus of the epoxy model is not deteriorated evenunder excessive moisture absorption, which is close to the experimental observation,and thus it can be concluded that moisture has no severe impact on the SU-8 mechanical properties. Meanwhile, the CG model of the epoxy is developedbased on the results of atomistic simulation. After subjected to different mechanicalloadings, the elastic and adhesion properties of the epoxy are obtained, which areused to derive the force field parameters of the CG epoxy model. The developed CGepoxy model possesses the density and Young’s modulus larger than the experimen-tal measurements. Further investigations shed light on the property changes due tothe influence of the structural voids. The epoxy structure with structural voidspossesses mechanical properties closer to the experimental data than that with nostructure voids, which leads to a more realistic CG modeling of the epoxy-basedmaterial.

The present MD simulation work provides a bottom-up approach for the micro-scopic investigation of the polymeric materials. The developed models enable us tounderstand the structural and mechanical behavior of the polymeric materials morein-depth, which can be used to investigate the effect of the environment and thevoids in the structure. With the availability of the additive manufacturing, the modelscan also be useful for the design and development of the polymer-based compositesfor the enhanced mechanical properties. It is expected that this work can provide thefoundation for further investigation of the polymeric materials at different hierarchi-cal levels, which can enable us to understand the mechanics in a more systematicway.

References

1. Zhou J, Lucas JP. Hygrothermal effects of epoxy resin. Part I: the nature of water in epoxy.Polymer. 1999;40:5505.

2. Núñez L, Villanueva M, Fraga F, Núñez MR. Influence of water absorption on the mechanicalproperties of a DGEBA (n=0)/1,2 DCH epoxy system. J Appl Polym Sci. 1999;74:353.

3. Lyons JS, Ahmed MR. Factors affecting the bond between polymer composites and wood.J Reinf Plast Compos. 2005;24:405.


4. Custódio J, Broughton J, Cruz H. A review of factors influencing the durability of structuralbonded timber joints. Int J Adhes Adhes. 2009;29:173.

5. Lau D, Büyüköztürk O. Fracture characterization of concrete/epoxy interface affected bymoisture. Mech Mater. 2010;42:1031.

6. Büyüköztürk O, Buehler MJ, Lau D, Tuakta C. Structural solution using molecular dynamics:fundamentals and a case study of epoxy-silica interface. Int J Solids Struct. 2011;48:2131.

7. Gunes O, Lau D, Tuakta C, Büyüköztürk O. Ductility of FRP-concrete systems: investigationsat different length scales. Constr Build Mater. 2013;49:915.

8. Pethrick RA. Positron annihilation – a probe for nanoscale voids and free volume? Prog PolymSci. 1997;22:1.

9. Dlubek G, Hassan E, Krause-Rehberg R, Pionteck J. Free volume of an epoxy resin and itsrelation to structural relaxation: evidence from positron lifetime and pressure-volume-temper-ature experiments. Phys Rev E. 2006;73:031803.

10. Shibuya Y, Zoledziowski S, Calderwood JH. Void formation and electrical breakdown in epoxyresin. IEEE Trans Power Apparatus Syst. 1977;96:198.

11. Hamerton I, Heald CR, Howlin BJ. Molecular modelling of the physical and mechanicalproperties of two polycyanurate network polymers. J Mater Chem. 1996;6:311.

12. Doherty DC, Holmes BN, Leung P, Ross RB. Polymerization molecular dynamics simulations:I. Cross-linked atomistic models for poly(methacrylate) networks. Comput Theor Polym Sci.1998;8:169.

13. Yarovsky I, Evans E. Computer simulation of structure and properties of crosslinked polymers:application to epoxy resins. Polymer. 2002;43:963.

14. Heine DR, Grest GS, Lorenz CD, Tsige M, Stevens MJ. Atomistic simulations of end-linkedpoly(dimethylsiloxane) networks: structure and relaxation. Macromolecules. 2004;37:3857.

15. Wu C, Xu W. Atomistic molecular modelling of crosslinked epoxy resin. Polymer.2006;47:6004.

16. Komarov PV, Chiu Y-T, Chen S-M, Khalatur PG, Reineker P. Highly cross-linked epoxy resins:an atomistic molecular dynamics simulation combined with a mapping/reverse mapping pro-cedure. Macromolecules. 2007;40:8104.

17. Fan HB, Yuen MM. Material properties of the cross-linked epoxy resin compound predicted bymolecular dynamics simulation. Polymer. 2007;48:2174.

18. Tack JL, Ford DM. Thermodynamic and mechanical properties of epoxy resin DGEBFcrosslinked with DETDA by molecular dynamics. J Mol Graph Model. 2008;26:1269.

19. Varshney V, Patnaik SS, Roy AK, Farmer BL. A molecular dynamics study of epoxy-basednetworks: cross-linking procedure and prediction of molecular and material properties. Macro-molecules. 2008;41:6837.

20. Li C, Strachan A. Molecular simulations of crosslinking process of thermosetting polymers.Polymer. 2010;51:6058.

21. Li C, Strachan A. Molecular dynamics predictions of thermal and mechanical properties ofthermoset polymer EPON862/DETDA. Polymer. 2011;52:2920.

22. Nouri N, Ziaei-Rad S. A molecular dynamics investigation on mechanical properties of cross-linked polymer networks. Macromolecules. 2011;44:5481.

23. Yang S, Qu J. Computing thermomechanical properties of crosslinked epoxy by moleculardynamic simulations. Polymer. 2012;53:4806.

24. Bandyopadhyay A, Valavala PK, Clancy TC, Wise KE, Odegard GM. Molecular modeling ofcrosslinked epoxy polymers: the effect of crosslink density on thermomechanical properties.Polymer. 2011;52:2445.

25. Larsen GS, Lin P, Hart KE, Colina CM. Molecular simulations of PIM-1-like polymers ofintrinsic microporosity. Macromolecules. 2011;44:6944.

26. Shenogina NB, Tsige M, Patnaik SS, Mukhopadhyay SM. Molecular modeling approach toprediction of thermo-mechanical behavior of thermoset polymer networks. Macromolecules.2012;45:5307.


27. Bandyopadhyay A, Odegard GM. Molecular modeling of crosslink distribution in epoxy poly-mers. Model Simul Mater Sci Eng. 2012;20:045018.

28. Shenogina NB, Tsige M, Patnaik SS, Mukhopadhyay SM. Molecular modeling of elasticproperties of thermosetting polymers using a dynamic deformation approach. Polymer.2013;54:3370.

29. Khalatur P, Papulov YG, Pavlov A. The influence of solvent on the static properties of polymerchains in solution: a molecular dynamics simulation. Mol Phys. 1986;58:887.

30. Tasaki K. Poly(oxyethylene)-water interactions: a molecular dynamics study. J Am Chem Soc.1996;118:8459.

31. Hofmann D, Fritz L, Ulbrich J, Schepers C, Böhning M. Detailed-atomistic molecular modelingof small molecule diffusion and solution processes in polymeric membrane materials. Macro-mol Theory Simul. 2000;9:293.

32. Lefebvre D, Elliker P, Takahashi K, Raju V, Kaplan M. The critical humidity effect in theadhesion of epoxy to glass: role of hydrogen bonding. J Adhes Sci Technol. 2000;14:925.

33. Mijovic J, Zhang H. Local dynamics and molecular origin of polymer network-water interac-tions as studied by broadband dielectric relaxation spectroscopy, FTIR, and molecular simula-tions. Macromolecules. 2003;36:1279.

34. Goudeau S, Charlot M, Vergelati C, Müller-Plathe F. Atomistic simulation of the waterinfluence on the local structure of polyamide 6,6. Macromolecules. 2004;37:8072.

35. Mijovic J, Zhang H. Molecular dynamics simulation study of motions and interactions of waterin a polymer network. J Phys Chem B. 2004;108:2557.

36. Lin Y, Chen X. Moisture sorption–desorption–resorption characteristics and its effect on themechanical behavior of the epoxy system. Polymer. 2005;46:11994.

37. Lin Y, Chen X. Investigation of moisture diffusion in epoxy system: experiments and moleculardynamics simulations. Chem Phys Lett. 2005;412:322.

38. Fan HB, Chan EK, Wong CK, Yuen MM. Investigation of moisture diffusion in electronicpackages by molecular dynamics simulation. J Adhes Sci Technol. 2006;20:1937.

39. Wu C, Xu W. Atomistic simulation study of absorbed water influence on structure andproperties of crosslinked epoxy resin. Polymer. 2007;48:5440.

40. Clancy TC, Frankland S, Hinkley J, Gates T. Molecular modeling for calculation of mechanicalproperties of epoxies with moisture ingress. Polymer. 2009;50:2736.

41. Hörstermann H, Hentschke R, Amkreutz M, Hoffmann M, Wirts-Rütters M. Predicting watersorption and volume swelling in dense polymer systems via computer simulation. J Phys ChemB. 2010;114:17013.

42. Lee SG, Jang SS, Kim J, Kim G. Distribution and diffusion of water in model epoxy moldingcompound: molecular dynamics simulation approach. IEEE Trans Adv Packag. 2010;33:333.

43. Hölck O, Dermitzaki E, Wunderle B, Bauer J, Michel B. Basic thermo-mechanical propertyestimation of a 3D-crosslinked epoxy/SiO2 interface using molecular modelling. MicroelectronReliab. 2011;51:1027.

44. Deshmukh SA, Sankaranarayanan SK, Suthar K, Mancini DC. Role of solvation dynamics andlocal ordering of water in inducing conformational transitions in poly(N-isopropylacrylamide)oligomers through the LCST. J Phys Chem B. 2012;116:2651.

45. Tam L-h, Lau D. A molecular dynamics investigation on the cross-linking and physicalproperties of epoxy-based materials. RSC Adv. 2014;4:33074.

46. Yagyu H, Hirai Y, Uesugi A, Makino Y, Sugano K, Tsuchiya T, Tabata O. Simulation ofmechanical properties of epoxy-based chemically amplified resist by coarse-grained moleculardynamics. Polymer. 2012;53:4834.

47. Kremer K, Grest GS. Dynamics of entangled linear polymer melts: a molecular-dynamicssimulation. J Chem Phys. 1990;92:5057.

48. Palkovic SD, Brommer DB, Kupwade-Patil K, Masic A, Buehler MJ, Büyüköztürk O.Roadmap across the mesoscale for durable and sustainable cement paste-a bioinspiredapproach. Constr Build Mater. 2016;115:13.


49. Lorenz H, Despont M, Fahrni N, LaBianca N, Renaud P, Vettiger P. SU-8: a lowcost negativeresist for MEMS. J Micromech Microeng. 1997;7:121.

50. Feng R, Farris RJ. The characterization of thermal and elastic constants for an epoxy photoresistSU8 coating. J Mater Sci. 2002;37:4793.

51. Hammacher J, Fuelle A, Flaemig J, Saupe J, Loechel B, Grimm J. Stress engineering andmechanical properties of SU-8-layers for mechanical applications. Microsyst Technol.2008;14:1515.

52. Dauber-Osguthorpe P, Roberts VA, Osguthorpe DJ, Wolff J, Genest M, Hagler AT. Structureand energetics of ligand binding to proteins: escherichia coli dihydrofolate reductase-trimeth-oprim, a drug-receptor system. Proteins Struct Funct Bioinf. 1988;4:31.

53. Maple JR, Dinur U, Hagler AT. Derivation of force fields for molecular mechanics anddynamics from ab initio energy surfaces. Proc Natl Acad Sci. 1988;85:5350.

54. Mayo SL, Olafson BD, Goddard WA. DREIDING: a generic force field for molecular simula-tions. J Phys Chem. 1990;94:8897.

55. Sun H, Mumby SJ, Maple JR, Hagler AT. An ab initio CFF93 all-atom force field forpolycarbonates. J Am Chem Soc. 1994;116:2978.

56. Sun H. Ab initio calculations and force field development for computer simulation of poly-silanes. Macromolecules. 1995;28:701.

57. Lin P-H, Khare R. Molecular simulation of cross-linked epoxy and epoxy� POSS nano-composite. Macromolecules. 2009;42:4319.

58. Oie T, Maggiora GM, Christoffersen RE, Duchamp DJ. Development of a flexible intra- andintermolecular empirical potential function for large molecular systems. Int J Quantum Chem.1981;20:1.

59. Rappe AK, Goddard WA III. Charge equilibration for molecular dynamics simulations. J PhysChem. 1991;95:3358.

60. Materials Studio; 2009. (San Diego, CA: Accelrys Software Inc.)61. Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys.

1995;117:1.62. Theodorou DN, Suter UW. Detailed molecular structure of a vinyl polymer glass. Macromol-

ecules. 1985;18:1467.63. Shinoda W, Shiga M, Mikami M. Rapid estimation of elastic constants by molecular dynamics

simulation under constant stress. Phys Rev B. 2004;69:134103.64. Abbott LJ, Hart KE, Colina CM. Polymatic: a generalized simulated polymerization algorithm

for amorphous polymers. Theor Chem Accounts. 2013;132:1.65. Nijdam A, et al. Fluidic encapsulation in SU-8 μ-reservoirs with μ-fluidic through-chip chan-

nels. Sensors Actuators A Phys. 2005;120:172.66. Kim J-K, Hu C, Woo RS, Sham M-L. Moisture barrier characteristics of organoclay-epoxy

nanocomposites. Compos Sci Technol. 2005;65:805.67. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML. Comparison of simple

potential functions for simulating liquid water. J Chem Phys. 1983;79:926.68. Ryckaert J-P, Ciccotti G, Berendsen HJ. Numerical integration of the cartesian equations of

motion of a system with constraints: molecular dynamics of n-alkanes. J Comput Phys.1977;23:327.

69. Landau LD, Lifshitz E, Sykes J, Reid W, Dill EH. Theory of elasticity: vol. 7 of course oftheoretical physics. Phys Today. 2009;13:44.

70. Hirschl C, et al. Determining the degree of crosslinking of ethylene vinyl acetate photovoltaicmodule encapsulants—a comparative study. Sol Energy Mater Sol Cells. 2013;116:203.

71. Chernev BS, Hirschl C, Eder GC. Non-destructive determination of ethylene vinyl acetatecross-linking in photovoltaic (PV) modules by Raman spectroscopy. Appl Spectrosc.2013;67:1296.

72. Feng R, Farris RJ. Influence of processing conditions on the thermal and mechanical propertiesof SU8 negative photoresist coatings. J Micromech Microeng. 2003;13:80.


73. Lawrence SS, Willett JL, Carriere CJ. Effect of moisture on the tensile properties of poly(hydroxy ester ether). Polymer. 2001;42:5643.

74. Ishiyama C, Higo Y. Effects of humidity on Young’s modulus in poly(methyl methacrylate).J Polym Sci B Polym Phys. 2002;40:460.

75. Ito S, et al. Effects of resin hydrophilicity on water sorption and changes in modulus ofelasticity. Biomaterials. 2005;26:6449.

76. Allen MP, Tildesley DJ. Computer simulation of liquids. Oxford: Oxford University Press;1989.

77. Tam L-h, Lau D. Effect of structural voids on mesoscale mechanics of epoxy-based materials.Coupled Syst Mech. 2016;5:355.

78. Tam L-h, Lau D. Moisture effect on the mechanical and interfacial properties of epoxy-bondedmaterial system: an atomistic and experimental investigation. Polymer. 2015;57:132.

79. Laio A, Gervasio FL. Metadynamics: a method to simulate rare events and reconstruct the freeenergy in biophysics, chemistry and material science. Rep Prog Phys. 2008;71:126601.

80. Lau D, Büyüköztürk O, Buehler MJ. Characterization of the intrinsic strength between epoxyand silica using a multiscale approach. J Mater Res. 2012;27:1787.

81. Tam L-h, Lau D. Molecular mechanics of organic composite materials: a case study of cellulose-adhesive system. MRS Online Proc Library Archive. 2014;1662:mrsf13-1662-vv05-02.

82. Lau D, Broderick K, Buehler MJ, Büyüköztürk O. A robust nanoscale experimental quantifi-cation of fracture energy in a bilayer material system. Proc Natl Acad Sci. 2014;111:11990.

83. Zhou A, Tam L-h, Yu Z, Lau D. Effect of moisture on the mechanical properties of CFRP-woodcomposite: an experimental and atomistic investigation. Compos Part B. 2015;71:63.

84. Tam L-h, Lau D. Molecular simulation of adhesion property recovery in the cellulose/phenolicadhesive interface: the role of water molecules. MRS Online Proc Library Archive.2015;1793:59.

85. Yu Z, Lau D. Nano-and mesoscale modeling of cement matrix. Nanoscale Res Lett.2015;10:173.

86. Bonomi M, et al. PLUMED: a portable plugin for free-energy calculations with moleculardynamics. Comput Phys Commun. 2009;180:1961.

87. Buehler MJ. Mesoscale modeling of mechanics of carbon nanotubes: self-assembly, self-folding, and fracture. J Mater Res. 2006;21:2855.

88. Buehler MJ. Atomistic and continuum modeling of mechanical properties of collagen: elastic-ity, fracture and self-assembly. J Mater Res. 2006;21:1947.

89. Adler DC, Buehler MJ. Mesoscale mechanics of wood cell walls under axial strain. Soft Matter.2013;9:7138.

90. Sen D, Buehler MJ. Atomistically-informed mesoscale model of deformation and failure ofbioinspired hiearchical silica nanocomposites. Int J Appl Mech. 2010;2:699.

91. Tam L-h, Lau D. Micromechanics of wood cell wall. MRS Adv. 2016;1:3837.92. Tam L-h, Zhou A, Yu Z, Qiu Q, Lau D. Understanding the effect of temperature on the

interfacial behavior of CFRP-wood composite via molecular dynamics simulations. ComposPart B. 2017;109:227.

93. Jeffrey K, Pethrick RA. Influence of chemical structure on free volume in epoxy resins: apositron annihilation study. Eur Polym J. 1994;30:153.


characterizing mechanical properties of polymeric material...

Documents