Mathematical Modeling of Chemical Reactions at Basque Center for Applied Mathematics. Simone Rusconi. December 11, 2015

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1 Mathematical Modeling of Chemical Reactions at Basque Center for Applied Mathematics Simone Rusconi December 11, 2015

2 Basque Center for Applied Mathematics (BCAM) BCAM - Basque Center for Applied Mathematics, a world class interdisciplinary research center on Applied Mathematics Started operation in September 2008 as a Basque Excellence Research Center (BERC) Located in Bilbao, Basque Country, Spain Currently includes more than 90 researchers and 8 staff members In 2014 BCAM has been accredited as one of the Severo Ochoa Excellence Centers

3 BCAM: Research Areas Computational Mathematics (CM) Reliable Finite Element Simulations CFD Modelling and Simulation CFD Computational Technology Mathematical Modelling with Multidisciplinary Applications (M3A) Modelling and Simulation in Life and Materials Sciences Mathematical Modelling in Biosciences Mathematical Physics (MP) Fluid Mechanics Statistical Physics Quantum Mechanics Singularity Theory and Algebraic Geometry Partial Differential Equations, Control and Numerics (DCN) PDEs, Control and Numerics Kinetic Equations Data Science (DS) Networks Applied Statistics Machine Learning

4 Modeling and Simulation in Life and Materials Sciences (MSLMS) group Researchers: 6 PhD, 5 PhD Students Group Leader: Elena Akhmatskaya, Ikerbasque Professor (70+ publications, 8 US-GB-EU patents, 13 years of industrial experience (Fujitsu Japan-UK)) Group Publications since 2010: 93 Grants since 2010: European (5), National (2), Industrial (Iberdrola 2014), PhD (5) In-house Software: 2 GPL parallel software packages, 7 open source software packages Collaborations: UPV-EHU (Bizkaia), POLYMAT (Donostia), BioGUNE (Bizkaia), EnergiGUNE (Alava), Universidad Carlos III de Madrid (Spain), Valladolid University (Spain), ITQB (Portugal), University of Cambridge (UK), Warwick University (UK), University of Sussex (UK), University of St Andrews (UK), Potsdam University (Germany), University of Amsterdam (Netherland), Utrecht University (Netherland), University of Savoie (France), CNR (Italy), University of Perugia (Italy), University of Udine (Italy), University of Maryland (USA), UC Santa Barbara (USA)

5 MSLMS: What we are doing Goal: Multiscale modeling and simulation of complex systems and processes with applications in Biology, Materials Sciences and Statistics

6 Scientific Topics Enhanced Sampling Methodologies for Simulating Complex Systems Mathematical Modeling of Chemical Reactions Numerical Bifurcation Analysis for Physiologically Structured Population Models Polymerization Reactions with Delays Dynamical Development of Particles Morphologies Understanding Chemical Reactivity at the Quantum Level

7 Polymerization Reactions with Delays Collaboration: S. Rusconi (BCAM), E. Akhmatskaya (BCAM), D. Sokolovski (UPV-EHU), J.M. Asua (POLYMAT), N. Ballard (POLYMAT), J.C. de la Cal (POLYMAT) Motivations: polymerization kinetics affects resulting materials properties classical kinetics models do not account for delaying processes experimental evidences contradict to the theoretical predictions based on classical analysis Objective: to propose mathematical models capable to explain experimental evidences and to correctly predict resulting materials properties

8 Polymerization Reactions with Delays: Results Monte Carlo algorithms for modeling Controlled Radical Polymerization: N. Ballard, S. Rusconi, E. Akhmatskaya, D. Sokolovski, J. de la Cal, J.M. Asua, Impact of Competitive Processes on Controlled Radical Polymerization, Macromolecules 47 (19), , 2014 Analytical representation of time probability density functions for modeling polymerization reactions with delaying events: D. Sokolovski, S. Rusconi, E. Akhmatskaya, J.M. Asua, Non-Markovian models of the growth of a polymer chain, Proc. R. Soc. A , 2015 Analytical alternatives to Monte Carlo algorithms for prediction of polymers properties in reactions with delaying events: S. Rusconi, E. Akhmatskaya, D. Sokolovski, N. Ballard, J.C. de la Cal, Relative Frequencies of Constrained Events in Stochastic Processes: an Analytical Approach, Phys. Rev. E 92 (4) , 2015

9 Polymerization Reactions with Delays: Results Computitonal Time (s) Analytical Solution for Experiment 1 Analytical Solution for Experiment 2 Monte Carlo for Experiment 1 Monte Carlo for Experiment 2 Branching Fraction (%) Data Experiment 1 Data Experiment 2 Monte Carlo Fitting Analytical Solution Fitting Optimization Routine Iterations The proposed analytical approach is up to 10 4 times faster than comparatively accurate Monte Carlo methods Control Agent Concentration (mol/l) Both analytical and Monte Carlo methods accurately predict experimental results

10 Dynamical Development of Particles Morphologies Collaboration: S. Rusconi (BCAM), E. Akhmatskaya (BCAM), D. Dutykh (Université de Savoie), S. Hamzehlou (POLYMAT), J.M. Asua (POLYMAT), D. Sokolovski (UPV-EHU) Motivation: multiphase polymer particles provide performance advantages over particles with uniform compositions Current status: synthesis of multiphase polymers is time and resources consuming and it largely relies on heuristic knowledge Objective: to develop a computationally feasible modeling approach for prediction of the multiphase particles morphology formation complex multivariate system slow (rare event) processes interest in full dynamics Jönsson et al. Macromolecules, 1991, 24, 126

11 Mathematical Modeling Individual-Based Approach: simulates a single composite polymer particle consisting of different phases Dynamics: Langevin Dynamics Interactions: Lennard-Jones potential Sampling Scheme: Generalized Shadow Hybrid Monte Carlo (GSHMC) In-house Enhanced Sampling Method: Akhmatskaya, Reich, , GB patent 2009, US patent 2011 Population-Based Approach: a coarse grained description of particles ensembles attempts for accurate predictions and on-the-fly recommendations in synthesis of multiphase polymers Model Derivation: Population Balance Equations (PBE) Deterministic Method: Generalized Method of Characteristics (GMOC) Stochastic Method: Stochastic Simulation Algorithm (SSA)

12 Individual-Based Approach: Results Predictions are in excellent agreement with experimental evidences Computationally very demanding (weeks of simulations) E. Akhmatskaya, J.M. Asua, Dynamic modeling of the morphology of multiphase waterborne polymer particles, Colloid and Polymer Science, Special issue on Morphologies and Functions of Polymeric Microspheres, 291 (1), 87 98, 2013 J.M. Asua, E. Akhmatskaya, Dynamical modelling of morphology development in multiphase latex particles, European Success Stories in Industrial Mathematics, Springer, 2011

13 Population-Based Approach: Results Derivation of Population Balance Equations (PBE) to model the Dynamical Development of Particles Morphologies: m(v, t) t (g(v, t)m(v, t)) + = m(v, t) k a(v, u, t) m(u, t) du v 0 k m m(v, t) + 1 v k a(v u, u, t) m(v u, t) m(u, t) du 2 0 Numerical methods: Generalized Method of Characteristics (GMOC) and Stochastic Simulation Algorithm (SSA) Future work: to reduce numerical instabilities of GMOC and to improve sampling efficiency of SSA

14 Understanding Chemical Reactivity at the Quantum Level Collaboration: D. Sokolovski (UPV-EHU), J.N.L Connor (Manchester), V. Aquilanti (Perugia), D. De Fazio (Rome) Motivation: three steps in modelling of a chemical reaction creating a potential surface (a job for a quantum chemist) solving the Schrödinger equation (state-of-the-art codes available) understanding the results (this is where we come in) Objective: to understand integral and differential cross sections (ICS-DCS), especially at low temperatures, where they are strongly influenced by scattering resonances Importance: cold chemistry, e.g. in the early Universe Method: Complex Angular Momentum (CAM) analysis of numerical scattering data Results: in-house packages PADE II: Padé reconstruction of the reactive S-matrix ICS Regge: CAM analysis of the integral cross sections Future work: development of computer code(s) for CAM analysis of the differential cross sections (DCS Regge)

15 Example: resonance structures in the ICS of the F + H 2 HF + H reaction At low energies, the probability for the reaction to occur is strongly affected by formation of various metastable tri-atomics. We have identified these complexes, and know now how much each process contributes to the ICS. Regge trajectories contributions The ICS and resonance from the Regge trajectories Results obtained by using ICS Regge package [PCCP, 17, 18577, 2015]

16 BCAM Severo Ochoa Accreditation SEV Grant SVP