Periodic Reporting for period 1 - Multimech (Solving the multi-scale problem in materials mechanics: a pathway to chemical design)
Reporting period: 2022-09-01 to 2025-02-28
Despite advances in computational resources, there is a vast timescale disparity, at least six orders of magnitude, at which mechanical properties can be probed in simulations compared to experiments. The theoretical approach mainly developed by solving the equation of motion for the nonaffine displacement of a tagged particle in a disordered environment, has been very promising in predicting the mechanics of amorphous solids at lower frequencies, thus, making it possible to reach closer to experimentally accessible timescales. Our theoretical framework relies on the vibrational density of states based on both real and imaginary (instantaneous normal modes) eigenfrequencies determined through the dynamical (Hessian) matrix of the system. Our objective, in this context, is to develop an atomic-scale predictive calculation of the mechanical response (elastic and viscoelastic moduli) of real materials at experimentally accessible frequencies, something that, so far, has not been possible to achieve without adjustable parameters.
Timescale bridging in the materials mechanics of polymer glasses: We have used large-scale computer simulations to model an epoxy system comprised of diglycidyl ether of bisphenol A (DGEBA) cross-linked by poly(oxypropylene) diamine. The viscoelastic response of the system below the glass transition temperature is predicted under the framework of NALD at different external deformation (oscillation) frequencies and also via atomistic molecular dynamics simulations for the oscillatory shear. In particular, we showed that the NALD calculations of elastic modulus at ultra-low frequencies (~ 1Hz) match closely with experimental data from dynamic mechanical analysis, thus, opening a new paradigm in the field of polymer viscoelasticity research to bridge the timescale gap between experiments and computational predictions. Furthermore, our analysis shows that the non-affine displacements at the atomic level account for nearly two orders of magnitude reduction in the low-frequency elastic modulus of the polymer glass, compared to affine elasticity estimates.
The NALD approach uses system-specific microscopic inputs, mainly the nature of the potential energy surface, to predict the frequency-dependent mechanical response of the system. At its core lies the fundamental concept of non-affine displacements. When an external deformation is applied onto a material sample, each atom tends to follow the applied strain. Then, one defines affine displacement as the atomic displacement from the original position of the atom in the undeformed sample to the position prescribed by the macroscopic strain. Since, in a disordered material, every atom is not a center of inversion symmetry, the sum of all forces acting on the atom in the affine position (due to its interactions with its neighbours, that are also moving) is not zero. This is different from the situation in a perfect centrosymmetric crystal at zero temperature where the resultant of all forces in the affine position would be identically zero thanks to centrosymmetry. Hence, in a disordered material, the net force acting on the atom in the affine position has to be re-equilibrated, to maintain mechanical equilibrium, through an additional displacement, on top of the affine displacement. It is precisely this additional displacement which constitutes the non-affine displacement. We have extended this framework to multi-mass atomic systems to deal with real-world materials and verified it in the context of cross-linked epoxy polymer glass. For the first time, we managed to achieve a quantitative agreement between the in-silico NALD predictions based on atomistic input and the experimental data from the literature for a cross-linked epoxy system of diglycidyl ether of bisphenol A (DGEBA) and poly(oxypropylene) diamine. In the comparison, there are no adjustable parameters, which sets our NALD method apart from other state-of-art methods currently used to bridge the time-scale in the prediction of mechanical properties, all of which contain adjustable parameters (e.g. coarse-grained methods).
Construction of the dynamical (Hessian) matrix using experimental data: The Hessian or dynamical matrix defined in terms of the second derivative of the potential energy of the system with respect to atomic displacements of two atoms at a time, is a very important quantity to understand the dynamical behaviour of the system at the level of potential energy surface. Such an approach has been mainly adopted either in theoretical framework or in simulation data. We have shown, using a specialised system of colloidal particles whose interaction is tunable in the presence of a magnetic field, that it is possible to computationally reconstruct the Hessian based on the knowledge of inter-particle interaction and using the experimental data (microscopy) about all positions of the particles in the system. Also, we have established the significance of such a Hessian constructed based on experimental inputs.
Identification of topological defects as mediators of plastic deformation: another key step to bridge the time-scale between in-silico and experimental data is related to the ability of identifying the mechanism of plastic deformation via isolated plastic events as precursors of the mechanical failure. This will enable the prediction of mechanical failure without having to simulate the whole process at the atomic scale. We made significant methodological progress in identifying mathematically well-defined topological defects in both the displacement field and in the eigenvector field of amorphous solids, which play a similar role as dislocations in crystalline solids in triggering the plastic deformation. In particular, we managed to develop a full 3D characterization of topological defects in 3D amorphous materials in terms of a mathematical construction known as hedgehog defects, previously used in the field of liquid crystals. We successfully demonstrated the applicability of hedgehog defects to glasses and also demonstrated, in preliminary results, their strong correlation with plastic events as precursors of the mechanical yielding.
The NALD approach uses system-specific microscopic inputs, mainly the nature of the potential energy surface, to predict the frequency-dependent mechanical response of the system. At its core lies the fundamental concept of non-affine displacements. When an external deformation is applied onto a material sample, each atom tends to follow the applied strain. Then, one defines affine displacement as the atomic displacement from the original position of the atom in the undeformed sample to the position prescribed by the macroscopic strain. Since, in a disordered material, every atom is not a center of inversion symmetry, the sum of all forces acting on the atom in the affine position (due to its interactions with its neighbours, that are also moving) is not zero. This is different from the situation in a perfect centrosymmetric crystal at zero temperature where the resultant of all forces in the affine position would be identically zero thanks to centrosymmetry. Hence, in a disordered material, the net force acting on the atom in the affine position has to be re-equilibrated, to maintain mechanical equilibrium, through an additional displacement, on top of the affine displacement. It is precisely this additional displacement which constitutes the non-affine displacement. We have extended this framework to multi-mass atomic systems to deal with real-world materials and verified it in the context of cross-linked epoxy polymer glass. For the first time, we managed to achieve a quantitative agreement between the in-silico NALD predictions based on atomistic input and the experimental data from the literature for a cross-linked epoxy system of diglycidyl ether of bisphenol A (DGEBA) and poly(oxypropylene) diamine. In the comparison, there are no adjustable parameters, which sets our NALD method apart from other state-of-art methods currently used to bridge the time-scale in the prediction of mechanical properties, all of which contain adjustable parameters (e.g. coarse-grained methods).
Construction of the dynamical (Hessian) matrix using experimental data: The Hessian or dynamical matrix defined in terms of the second derivative of the potential energy of the system with respect to atomic displacements of two atoms at a time, is a very important quantity to understand the dynamical behaviour of the system at the level of potential energy surface. Such an approach has been mainly adopted either in theoretical framework or in simulation data. We have shown, using a specialised system of colloidal particles whose interaction is tunable in the presence of a magnetic field, that it is possible to computationally reconstruct the Hessian based on the knowledge of inter-particle interaction and using the experimental data (microscopy) about all positions of the particles in the system. Also, we have established the significance of such a Hessian constructed based on experimental inputs.
Identification of topological defects as mediators of plastic deformation: another key step to bridge the time-scale between in-silico and experimental data is related to the ability of identifying the mechanism of plastic deformation via isolated plastic events as precursors of the mechanical failure. This will enable the prediction of mechanical failure without having to simulate the whole process at the atomic scale. We made significant methodological progress in identifying mathematically well-defined topological defects in both the displacement field and in the eigenvector field of amorphous solids, which play a similar role as dislocations in crystalline solids in triggering the plastic deformation. In particular, we managed to develop a full 3D characterization of topological defects in 3D amorphous materials in terms of a mathematical construction known as hedgehog defects, previously used in the field of liquid crystals. We successfully demonstrated the applicability of hedgehog defects to glasses and also demonstrated, in preliminary results, their strong correlation with plastic events as precursors of the mechanical yielding.
1. Time-scale bridging in atomistic simulations of epoxy polymer mechanics using non-affine deformation theory
2. Experimental identification of topological defects in 2D colloidal glass
3. Development of the identification protocol for topological defects in 3D glasses as mediators of plasticity
4. Established correlations between topological defects and plasticity in polymer glass
5. Proposed a mechanism for topological defects alignment as the trigger of shear bands in glasses
All the above stated achievements can be regarded as breakthroughs which advance the whole research field.
2. Experimental identification of topological defects in 2D colloidal glass
3. Development of the identification protocol for topological defects in 3D glasses as mediators of plasticity
4. Established correlations between topological defects and plasticity in polymer glass
5. Proposed a mechanism for topological defects alignment as the trigger of shear bands in glasses
All the above stated achievements can be regarded as breakthroughs which advance the whole research field.