Effect of chain architecture on the compression behavior of nanoscale polyethylene particles
© Wu et al.; licensee Springer. 2013
Received: 14 May 2013
Accepted: 6 July 2013
Published: 15 July 2013
Polymeric particles with controlled internal molecular architectures play an important role as constituents in many composite materials for a number of emerging applications. In this study, classical molecular dynamics techniques are employed to predict the effect of chain architecture on the compression behavior of nanoscale polyethylene particles subjected to simulated flat-punch testing. Cross-linked, branched, and linear polyethylene chain architectures are each studied in the simulations. Results indicate that chain architecture has a significant influence on the mechanical properties of polyethylene nanoparticles, with the network configuration exhibiting higher compressive strengths than the branched and linear architectures. These findings are verified with simulations of bulk polyethylene. The compressive stress versus strain profiles of particles show four distinct regimes, differing with that of experimental micron-sized particles. The results of this study indicate that the mechanical response of polyethylene nanoparticles can be custom-tailored for specific applications by changing the molecular architecture.
KeywordsChain architecture Nanoscale particle Spherical hydrostatic compression Compression properties Flat-punch MD simulation
Polymers play an indispensable and ubiquitous role in daily life. One approach to produce high-performance or multifunctional polymer materials is to blend chemically different monomers, add advanced fillers, and synthesize specific molecular architectures. It is well known that varying molecular architecture through branching and networking strongly influences the mechanical, dielectric, and thermal properties of polymers. For example, cross-linked molecular architectures enhance the strength and modulus of polymers but generally reduce their fracture toughness [1–3]. However, it has been recently shown that polymer hydrogels that form ionically and covalently cross-linked networks and have fracture energies of 9,000 J/m2 can withstand stretches of over 20 . Thus, tuning the molecular architecture can provide opportunities to custom-tailor polymer material properties for specific applications.
On the other hand, polymers at nanoscale dimension are a novel class of materials that offer diverse properties, which can be distinguished from their bulk counterparts. Nanoscale polymeric particles have attracted extensive attention from both the scientific community and industry. Polymeric nanoparticles are featured prominently in a wide variety of applications such as toners, coatings, adhesives, instrument calibration standards, column packing materials for chromatography, biomedicine, and biochemical analysis [5–7]. An emerging application focuses on metal-coated conductive polymeric particles for anisotropic conductive adhesives used in liquid crystal displays and microsystems. The use of these particles could reduce package sizes and manufacturing costs and entirely eliminate the use of lead in these systems [8–11]. The continued expansion of polymeric nanoparticles to new applications has revealed unexpected behaviors and potential shortcomings. Therefore, a complete understanding of their properties is of great importance for their successful use.
Most of the previous research on nanoscale polymers have been focused on properties of thin polymer films due to their relatively easy preparation, characterization, and established applications. It has been explicitly shown that the glass transition temperature (Tg) of polymer thin films is reduced from that of the bulk due to the presence of a free interface, and Tg is found to be strongly dependent on the film thickness and chain architecture [12–15]. Several studies have been conducted on the thermal properties of polymeric particles and reached similar conclusions as with thin films [16–18]. However, few studies have been performed on the mechanical characterization of freestanding polymeric nanoparticles because of their small size and spherical geometry. Recently, a nanoindentation-based flat-punch experimental technique was developed to characterize the mechanical properties of isolated micron-sized polymeric particles [19, 20]. The mechanical response was shown to be highly dependent on the particle size and cross-link density [21, 22].
A limited number of computational studies have been carried out to investigate structure and properties of polymeric nanoparticles at the molecular level. Fukui et al.  developed a method based on molecular dynamics (MD) to generate polymeric nanoparticle models with linear chain architectures in a layer-by-layer manner. Their results indicated that structural and thermal properties are dependent on particle size. Hathorn et al.  investigated the dynamic collision of polyethylene (PE) nanoparticles containing linear molecular architectures. Very recently, our group has studied the effect of size on the mechanical properties of PE nanoparticles via coarse-grained MD simulation (Zhao JH, Nagao S, Odegard GM, Zhang ZL, Kristiansen H, He JY: Size-dependent mechanical behavior of nanoscale polymer particles through coarse-grained molecular dynamics simulation. submitted). Although these pioneering experimental and simulation works have provided insight into the macroscopic properties of polymeric particles, fundamental knowledge of molecular-level behavior is still missing, particularly for different chain architectures.
In this paper, a novel method to construct MD simulation models of ultrafine and stable PE nanoparticles with different molecular architecture is introduced. The MD models are used to examine the compressive flat-punch behavior of PE nanoparticles with linear, branched, and cross-linked chains. It is shown that the chain architecture has a significant effect on the compression behavior of freestanding individual PE nanoparticles.
Potential functions and parameters of united atom force field
r c (Å)
k b (kcal/(mol·Å 2 ))
r 0 (Å)
k θ (kcal/mol)
θ 0 (deg)
A 0 (kcal/mol)
A 1 (kcal/mol)
A 2 (kcal/mol)
A 3 (kcal/mol)
CH x … CH y
(x = 1, 2, 3; y = 2, 3) 
CH x -CH y
CH x -CH2-CH y
CH x -CH2-CH2-CH y
(x, y = 1, 2, 3) 
(x, y = 1, 2, 3) 
(x, y = 1, 2, 3) 
CH… CH 
CH x -CH-CH y
CH x -CH-CH2-CH y
(x, y = 2) 
(x, y = 2) 
where R and R0 are the instantaneous and initial radius of the spherical wall, respectively, S is a positive constant, and n has progressive values of positive integers corresponding to elapsed time of the simulation (i.e., n = 1, 2, 3, …). For the simulations described herein, S was 0.99 and n increased by a value of 1 for every 5 ps of simulation time. Prior to this dynamic relaxation, the confined PE models were first quasi-statically relaxed to a local minimum potential energy configuration using the conjugate gradient method. For each increment of the subsequent dynamic compression, the systems were simulated in the NVT ensemble at 1,000 K, and the density of the polymeric particle was monitored. When the density reached 1.0 g/cm3, the compression was terminated. The confined nanoparticle were annealed at 1,000 K for 200 ps to reach a favorable energy configuration and then cooled down to 50 K at a rate of 2.375 K/ps in the absence of the spherical wall. The isolated nanoparticle was heated to 600 K at a rate of 1.1 K/ps, followed by cooling down to 200 K at a rate of 2 K/ps. Finally, 200 ps NVT runs were performed for relaxing the system, and the ultrafine PE nanoparticles were complete.
Results and discussion
Tensile and compressive modulus of bulk and particle PE with different chain architectures
MD models of ultrafine monodisperse polymeric nanoparticles with networked, branched, and linear chain architectures were developed using simulated spherical hydrostatic compression of groups of coarse-grained PE molecules. The mechanical response of these nanoparticles subjected to a simulated flat-punch compression test was predicted and compared to that predicted from a 3D bulk simulation of PE. It was determined that the network configuration yielded stronger nanoparticles than those with branched or linear chain configurations. These findings were consistent with the predictions of the bulk PE models. It was also shown that the nanoparticles have a relatively uniform mass density and that individual chains have unique morphologies for high values of compression for the three different architecture types. The results of this study are important for the understanding of chain architecture on the behavior of polymeric nanoparticles that are used in a wide range of engineering applications. The mechanical properties of these particles can be tailored to specific levels simply by adjusting the chain architecture between network, branched, and linear systems. While it is evident that the network architecture yields nanoparticles with a stiffer response, the linear system results in nanoparticles with lower compressive loads for a given compressive strain.
This work is supported by the Research Council of Norway (RCN) under NANOMAT KMB (MS2MP) project no. 187269 and the U.S.-Norway Fulbright Foundation. The computational resources are provided by the Norwegian Metacenter for Computational Science (NOTUR).
- Donnellan TM, Roylance D: Relationships in a bismaleimide resin system. Part II: thermomechanical properties. Polym Eng Sci 1992, 32(6):415–420. 10.1002/pen.760320605View Article
- Lu J, Wool RP: Sheet molding compound resins from soybean oil: thickening behavior and mechanical properties. Polym Eng Sci 2007, 47(9):1469–1479. 10.1002/pen.20846View Article
- Thompson JI, Czernuszka JT: The effect of two types of cross-linking on some mechanical properties of collagen. Biomed Mater Eng 1995, 5(1):37–48.
- Sun JY, Zhao XH, IlleperumaW RK, Chaudhuri O, Oh KH, Mooney DJ, Vlassak JJ, Suo ZG: Highly stretchable and tough hydrogels. Nature 2012, 489: 133–136. 10.1038/nature11409View Article
- Lok KP, Ober CK: Particle size control in dispersion polymerization of polystyrene. Can J Chem 1985, 63(1):209–216. 10.1139/v85-033View Article
- Okuo M: Polymer Particles (Advances in Polymer Science). 1st edition. Berlin: Springer; 2005.
- Sugimoto T: Monodispersed Particles (Studies in Surface Science and Catalysis). 1st edition. Amsterdam: Elsevier Science; 2001.
- Conpart Technology http://www.conpart.no/
- Lai Z, Liu J: Anisotropically conductive adhesive flip-chip bonding on rigid and flexible printed circuit substrates. IEEE Transactions on Components, Packaging, and Manufacturing Technology. Part B. Advanced Packaging 1996, 19(3):644–660. 10.1109/96.533908View Article
- Kristiansen H, Liu J: Overview of conductive adhesive interconnection technologies for LCDs. IEEE Transactions on Components, Packaging, and Manufacturing Technology 1998, 21: 208–214. 10.1109/95.705466View Article
- Kristiansen H, Gronlund TO, Liu J: Characterisation of metal-coated polymer spheres and its use in anisotropic conductive adhesive. In Proceedings of 16th IEEE CPMT Conference on High Density Microsystem Design and Packaging and Component Failure Analysis: 30 June-3 July 2004; Shanghai. Piscataway: IEEE; 2004:259–263.
- Forrest JA, Dalnoki-Veress K, Stevens JR, Dutcher JR: Effect of free surfaces on the glass transition temperature of thin polymer films. Phys Rev Lett 1996, 77(10):2002–2005. 10.1103/PhysRevLett.77.2002View Article
- Prucker O, Christian S, Bock H, Rühe J, Frank CW, Knoll W: On the glass transition in ultrathin polymer films of different molecular architecture. Macromol Chem Phys 1998, 199(7):1435–1444. 10.1002/(SICI)1521-3935(19980701)199:7<1435::AID-MACP1435>3.0.CO;2-#View Article
- Kim C, Facchetti A, Marks TJ: Probing the surface glass transition temperature of polymer films via organic semiconductor growth mode, microstructure, and thin-film transistor response. J Am Chem Soc 2009, 131(25):9122–9132. 10.1021/ja902788zView Article
- Glynos E, Frieberg B, Oh H, Liu M, Gidley DW, Green PF: Role of molecular architecture on the vitrification of polymer thin films. Phys Rev Lett 2011, 106(12):128301–128304.View Article
- Zhang C, Guo YL, Priestley RD: Glass transition temperature of polymer nanoparticles under soft and hard confinement. Macromolecules 2011, 44(10):4001–4006. 10.1021/ma1026862View Article
- Sasaki T, Shimizu A, Mourey TH, Thurau CT, Ediger MD: Glass transition of small polystyrene spheres in aqueous suspensions. J Chem Phys 2003, 119(16):8730–8735. 10.1063/1.1613257View Article
- Zhang C, Guo YL, Priestley RD: Confined glassy properties of polymer nanoparticles. J Poly Sci Part B: Polyr Phys 2013, 51(7):574–586. 10.1002/polb.23268View Article
- He JY, Zhang ZL, Kristiansen H: Mechanical properties of nanostructured particles for anisotropic conductive adhesives. Int J Mater Res 2007, 98(5):389–392.View Article
- He JY, Zhang ZL, Kristiansen H: Nanomechanical characterization of single micron-sized polymer particle. J Appl Poly Sci 2009, 113(3):1398–1405. 10.1002/app.29913View Article
- He JY, Zhang ZL, Midttun M, Fonnum G, Modahl GI, Kristiansen H, Redford K: Size effect on mechanical properties of micron-sized PS–DVB polymer particles. Polymer 2008, 49(18):3993–3999. 10.1016/j.polymer.2008.07.015View Article
- He JY, Zhang ZL, Kristiansen H, Redford K, Fonnum G, Modahl GI: Crosslinking effect on the deformation and fracture of monodisperse polystyrene-co-divinylbenzene particles. eXPRESS Polym Lett 2013, 7(4):365–374. 10.3144/expresspolymlett.2013.33View Article
- Fukui K, Sumpter BG, Barnes MD, Noid DW: Molecular dynamics studies of the structure and properties of polymer nano-particles. Comput Theor Polym Sci 1999, 9(3–4):245–254.View Article
- Hathorn BC, Sumpter BG, Noid DW, Tuzun RE, Yang C: Computational simulation of polymer particle structures: vibrational normal modes using the time averaged normal coordinate analysis method. Polymer 2003, 44(13):3761–3767. 10.1016/S0032-3861(02)00436-6View Article
- Capaldi FM, Boyce MC, Rutledge GC: Molecular response of a glassy polymer to active deformation. Polymer 2004, 45(4):1391–1399. 10.1016/j.polymer.2003.07.011View Article
- Laso M, Perpete EA: Multiscale Modelling of Polymer Properties. Amsterdam: Elsevier; 2006. pp. 31–45 and 333–357 pp. 31–45 and 333–357
- Pant PVK, Han J, Smith GD, Boyd RH: A molecular dynamics simulation of polyethylene. J Chem Phys 1993, 99(1):597–604. 10.1063/1.465731View Article
- Abbarzadeh AJ, Atkinson JD, Tanner RI: Effect of molecular shape on rheological properties in molecular dynamics simulation of star, H, comb, and linear polymer melts. Macromolecules 2003, 36(13):5020–5031. 10.1021/ma025782qView Article
- Theodorou DN, Suter UW: Detailed molecular structure of a vinyl polymer glass. Macromolecules 1985, 18(7):1467–1478. 10.1021/ma00149a018View Article
- Hoover WG: Canonical dynamics: equilibrium phase-space distributions. Phys Rev A 1985, 31(3):1695–1697. 10.1103/PhysRevA.31.1695View Article
- Hoover WG: Constant-pressure equations of motion. Phys Rev A 1986, 34(3):2499–2500. 10.1103/PhysRevA.34.2499View Article
- Shinoda W, Shiga M, Mikami M: Rapid estimation of the elastic constants by molecular dynamics simulation under constant stress. Phys Rev B 2004, 69: 134103–134110.View Article
- Harmandaris VA, Daoulas KC, Mavrantzas VG: Molecular dynamics simulation of a polymer melt/solid interface: local dynamics and chain mobility in a thin film of polyethylene melt adsorbed on graphite. Macromolecules 2005, 38(13):5796–5809. 10.1021/ma050177jView Article
- Daoulas KC, Harmandaris VA, Mavrantzas VG: Detailed atomistic simulation of a polymer melt/solid interface: structure, density, and conformation of a thin film of polyethylene melt adsorbed on graphite. Macromolecules 2005, 38(13):5780–5795. 10.1021/ma050176rView Article
- Mansfield KF, Theodorou DN: Atomistic simulation of a glassy polymer surface. Macromolecules 1990, 23(20):4430–4445. 10.1021/ma00222a016View Article
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.