Mechanical Properties of Polymer Nanocomposites via Atomistic simulation: From Glassy to the Liquide State

Mechanical Properties of Polymer Nanocomposites via Atomistic simulation: From Glassy to the Liquide State

1. Mechanical Properties of Polymer Nanocomposites via Atomistic simulation: From Glassy to the Liquide State Hilal Reda Vangelis Harmandaris SimEA Group CaSToRC / CyI 10.04.2024

2. 2 Polymer nanocomposites have been widely used in many applications, including among other the automotive and packaging industries, as well in energy generation and storage Optimizing material performance in engineering applications requires understanding how temperature and strain rate affect mechanical properties and viscoelasticity The major challenge in the study of PNMs lies in understanding and controlling their macroscopic behaviour, starting from their microscopic structure (chemistry) in order to obtain materials with advanced properties and high performance for tailored applications Introduction

3. 3 Accurate experimental investigation of parameters related to physical mechanisms on the atomic scale and consideration of temperature effects are generally challenging, time-consuming, and cost-intensive Experimental and simulation studies of mechanical properties consider the effect of temperature on the global (average) mechanical properties without dealing with the role of temperature on their (spatial) heterogeneous mechanical response. Challenges

4. 4 Influence of temperature on the local mechanical properties of the subdomains, mainly the interphase and matrix regions, during the increasing tensile test. Elucidate the mechanism(s) of the effect of temperature on the mechanical behavior of heterogeneous polymer-based hybrid materials. Objectives

5. 5 First, detailed atomistic molecular dynamics simulations will be performed on (relatively small) prototypical PNC systems . Applying uniaxial tensile stress on the atomistic configurations to obtain the overall macroscopic mechanical properties of the PNC . Compute the distribution of stress and strain fields in atomistic PNC configurations . Investigate the mechanical properties, across a broad range of temperatures from the glassy to the rubbery regime, focusing on the variation of the spatial distribution of stress and strain fields at the polymer/nanofiller interphase and matrix regions Methodology

6. 6 Atomistic Model Polymer matrix consists of 48 unentangled PEO chains of 50 monomers each (the molecular weight is about 2.2kDa), terminated with methyl groups, while a silica nanoparticle, with an almost spherical shape, of radius ≈ 2.0 nm, was dispersed in the PEO matrix A series of runs was conducted at temperatures T = 220, 250, 270, 300, 330, 350, 370, and 400 K. The size of the simulation box changes from 59 ̊A at 400 K to 57 ̊A at 220 K; this leads to a small decrease in volume percentage

7. 7 Several independent (uncorrelated) configurations of well-equilibrated atomistic PNCs, at high T (413 K) Atomistic model systems are cooled well below Tg , with a cooling rate of 10 K/ns down to 200 K (Effect of cooling rate). The experimental Tg of PEO is around 270K Uniaxially deformed with a constant strain rate of Assume a well dispersed NP scenario, in which silica NPs are in a simple cubic like arrangement within the polymer matrix, i.e there is no any aggregation of the NPs The overall applied deformation is up to 0.6, but we will focus more on the linear regime. Atomistic Molecular Simulations

8. 8 Distribution of density profile at equilibration Characterization of Polymer/Nanoparticle Interphase Density of the interfacial region, seems to be less sensitive with a decrease of temperature compared to that of the matrix region The average mass polymer density of the interphase, is found to be lower than that of the matrix at all temperatures investigated.

9. 9 Overall properties of the PNC Mechanical Properties of Atomistic PNCs mode coupling theory (MCT) Vogel- Fulcher- Tammann (VFT)

10. 10 Local properties of the Polymer Nanocomposite Derivation of elastic constitutive law within a defines subdomain Ω Analyze the deformed configurations to compute the stress distribution in the model systems by calculating the stress per atom; Analyze the deformed configurations to compute the strain distribution in the model systems by calculating the strain per atom; For a specific domain decomposition scheme, compute the average stress and strain within subdomains;

11. Mechanical Properties of Atomistic PNCs 11 Local stress computation Distribution of stress within the model nanostructured systems can be calculated through the atomic Virial formalism as Stress due to the interaction of two particles is equally distributed between the regions where the particles reside ( Harasima’s definition )  

12. Mechanical Properties of Atomistic PNCs 12 Applied incremental strain on the cubic box Uniaxially deformed the unit box with a constant strain rate of The uniaxial deformation of the box, as implemented in LAMMPS, respects the boundary condition along the axis of deformation In the deformation process, an affine strain field is produced in the bulk sample. However, in PNCs, the presence of highly stiff NPs leads to a non-affine strain field in the sample NPs practically do not experience any strain, but their presence alters the local strain within the polymer in the vicinity of the NP

13. Mechanical Properties of Atomistic PNCs 13 Atom m is located at the position X m  in the reference configuration Ω  and position  x m  in the current configuration Ω The deformation gradient F m of atom m is related to its neighboring atoms F m  of atom m cannot generally be determined by a single atom n F m can be determined through the squares error minimization function   W m  shown in the following equation : When the minimization function W m  reaches the minimum, the parameters F m   are the optimal components of the optimal deformation gradient matrix The Lagrangian Green strain tensor ε   within the interphase  

14. Mechanical Properties of Atomistic PNCs 14 Probability Density Function of Local Strain and Stress as a Function of Temperature a) T=220K, b) T=330K and c) T=400K PDF in NP exhibits a clear peak around zero due to its higher rigidity. In the interphase region, pdf is much broader, reflecting the high heterogeneity of the strain PDF for both regions (interphase and matrix) exhibits a wide distribution around the global applied strain PDF of local stress is quite broad for all regions, due to the part of the non-bonded interaction of the atomic Virial expression of stress (partly related to Lennard-Jones interactions)

15. Mechanical Properties of Atomistic PNCs 15 Local strain field in the interphase and matrix region at different temperatures as a function of the global applied engineering strain, focusing in the liner regime The interphase is less deformed and exhibits a reduced mobility during deformation compared to the matrix, for all but very high temperatures

16. Mechanical Properties of Atomistic PNCs 16 Local Stress-strain field at the interphase and matrix regions at different tempera- tures linear region starts to disappear as the temperature increases, reflecting the increase of the nonlinear stress-strain dependence in the melt state

17. Mechanical Properties of Atomistic PNCs 17 Temperature dependence of the Young’s modulus for the interphase, and matrix regions Young’s modulus of the matrix region drops from 1.9 GPa at 220 K to 0.51 at 400 K. The interphase region shows a similar drop from 2.62 GPa at 220 K to 0.56 GPa at 400 K. The interphase and matrix regions show an increase in Young’s modulus with respect to the bulk value when T is higher than Tg of the pure bulk PEO system (around 150 K), while it remains constant at T < Tg .

18. Coupling between Atomistic and Continuum scale via Homogenization Approaches 18 Linking MD simulations to strain gradient homogenized Anthony Chazirakis ( UoC , FORTH, Greece) Ioannis Tannis (Post Doc, CastorC ) “SimEA” Group (lead Prof. V. Harmandaris ) Acknowledgments Funding Horizon 2020, Marie Skłodowska -Curie grant agreement No. 101030430 . Computational time from the Greek Research & Technology Network (GRNET) in the National HPC facility ARIS. CyI High Performance Computing Facility (HPCF) under a project named NANOMEC

19. Coupling between Atomistic and Continuum scale via Homogenization Approaches 19 Linking MD simulations to strain gradient homogenized Publication Reda, H. , Chazirakis , A., Power, A. J. and Harmandaris , V. Mechanical Behavior of Polymer Nanocomposites via Atomistic Simulations: Conformational Heterogeneity and the Role of Strain Rate, the Journal of Physical Chemistry B    2022, 126, 38, 7429–7444 Reda , H., Chazirakis , A., Behbahani , A., Savva, N., and Harmandaris , V. Mechanical properties of glassy polymer nanocomposites via atomistic and continuum models: The role of interphases Computer Methods in Applied Mechanics and Engineering , 395, 114905, 2022 Reda, H., Chazirakis , A., Savva, N., Ganghoffer , JF., and Harmandaris , V. Gradient of Mechanical Properties in Polymer Nanocomposites: From Atomistic Scale to the Strain Gradient Effective Continuum, International journal of solid and structure , 256 ,  2022 , 111977 . Reda , H., Chazirakis , A., Power, A., Harmandaris , V. A methodology for determining the local mechanical properties of model atomistic glassy polymeric nanostructured materials, MethodX , 9, 101931. Reda, H., Chazirakis , A., Behbahani , A., Savva, N., and Harmandaris , V. Revealing the Role of Chain Conformations on the Origin of the Mechanical Reinforcement in Glassy Polymer Nanocomposites, Nano Lett .  2024, 24, 1, 148–155 M.Barakat , Reda , H., Chazirakis , A ., and Harmandaris , V. Investigating the mechanical performance of graphene reinforced polymer nanocomposites via atomistic and continuum simulation approaches, Polymer , 286 ,  2023 , 126379

20. Coupling between Atomistic and Continuum scale via Homogenization Approaches 20 Linking MD simulations to strain gradient homogenized Thank you for your attention [email protected]