Mathematical Modeling of Chemical Reactions at Basque ... · Mathematical Modeling of Chemical Reactions at Basque Center for Applied Mathematics ... at the Quantum Level.

Mathematical Modeling of Chemical Reactions atBasque Center for Applied Mathematics

Simone Rusconi

December 11, 2015

Basque Center for Applied Mathematics (BCAM)

I BCAM - Basque Center forApplied Mathematics, a worldclass interdisciplinary researchcenter on Applied Mathematics

I Started operation in September2008 as a Basque ExcellenceResearch Center (BERC)

I Located in Bilbao, Basque Country, SpainI Currently includes more than 90 researchers and 8 staff membersI In 2014 BCAM has been accredited as one of the Severo Ochoa

Excellence Centers

BCAM: Research Areas

I Computational Mathematics (CM)

X Reliable Finite Element SimulationsX CFD Modelling and SimulationX CFD Computational Technology

I Mathematical Modelling with Multidisciplinary Applications (M3A)

X Modelling and Simulation in Life and Materials SciencesX Mathematical Modelling in Biosciences

I Mathematical Physics (MP)

X Fluid MechanicsX Quantum Mechanics

I Partial Differential Equations, Control and Numerics (DCN)

X PDEs, Control and NumericsX Kinetic Equations

I Data Science (DS)

X NetworksX Applied StatisticsX Machine Learning

X Statistical PhysicsX Singularity Theory and Algebraic Geometry

Modeling and Simulation in Life and Materials Sciences (MSLMS) group

I Researchers: 6 PhD, 5 PhD Students

I Group Leader: Elena Akhmatskaya, Ikerbasque Professor (70+publications, 8 US-GB-EU patents, 13 years of industrial experience(Fujitsu Japan-UK))

I Group Publications since 2010: 93

I Grants since 2010: European (5), National (2), Industrial (Iberdrola2014), PhD (5)

I In-house Software: 2 GPL parallel software packages, 7 open sourcesoftware packages

I 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)

MSLMS: What we are doing

I Goal: Multiscale modeling and simulation of complex systems andprocesses with applications in Biology, Materials Sciences and Statistics

Scientific Topics

Enhanced SamplingMethodologies for

SimulatingComplex Systems

MathematicalModeling of

Chemical Reactions

Numerical BifurcationAnalysis for

PhysiologicallyStructured

Population Models

PolymerizationReactions

with Delays

DynamicalDevelopment of

Particles Morphologies

UnderstandingChemical Reactivity

at the Quantum Level

Polymerization Reactions with Delays

I Collaboration: S. Rusconi (BCAM), E. Akhmatskaya (BCAM), D.Sokolovski (UPV-EHU), J.M. Asua (POLYMAT), N. Ballard(POLYMAT), J.C. de la Cal (POLYMAT)

I Motivations:

X polymerization kinetics affectsresulting materials properties

X classical kinetics models do notaccount for delaying processes

X experimental evidences contradictto the theoretical predictionsbased on classical analysis

I Objective: to propose mathematical models capable to explainexperimental evidences and to correctly predict resulting materialsproperties

Polymerization Reactions with Delays: Results

I 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), 6580− 6590, 2014

I Analytical representation of time probability density functions formodeling polymerization reactions with delaying events:

D. Sokolovski, S. Rusconi, E. Akhmatskaya, J.M. Asua, Non-Markovian models ofthe growth of a polymer chain, Proc. R. Soc. A 471 20140899, 2015

I Analytical alternatives to Monte Carlo algorithms for prediction ofpolymers properties in reactions with delaying events:

S. Rusconi, E. Akhmatskaya, D. Sokolovski, N. Ballard, J.C. de la Cal, RelativeFrequencies of Constrained Events in Stochastic Processes: an Analytical Approach,Phys. Rev. E 92 (4) 043306, 2015

Polymerization Reactions with Delays: Results

Optimization Routine Iterations

Com

putito

nal T

ime (

s)

25 50 75 100 125 150 175 200

10

−2

10

−1

10

01

01

10

21

03

10

4

Analytical Solution for Experiment 1

Analytical Solution for Experiment 2

Monte Carlo for Experiment 1

Monte Carlo for Experiment 2

The proposed analytical approach is upto 104 times faster than comparativelyaccurate Monte Carlo methods

0.00 0.02 0.04 0.06 0.08 0.101

.52

.02

.53

.0

Control Agent Concentration (mol/L)

Bra

nchin

g F

raction (

%)

Data Experiment 1Data Experiment 2Monte Carlo FittingAnalytical Solution Fitting

Both analytical and Monte Carlo methodsaccurately predict experimental results

Dynamical Development of Particles Morphologies

I Collaboration: S. Rusconi (BCAM), E. Akhmatskaya (BCAM), D.Dutykh (Universite de Savoie), S. Hamzehlou (POLYMAT), J.M.Asua (POLYMAT), D. Sokolovski (UPV-EHU)

I Motivation: multiphase polymer particles provide performanceadvantages over particles with uniform compositions

I Current status: synthesis of multiphase polymers is time andresources consuming and it largely relies on heuristic knowledge

I Objective: to develop a computationally feasible modeling approachfor prediction of the multiphase particles morphology formation

X complex multivariate system

X slow (rare event) processes

X interest in full dynamicsJonsson et al. Macromolecules, 1991, 24, 126

Mathematical Modeling

I Individual-Based Approach: simulates a single composite polymerparticle consisting of different phases

X Dynamics: Langevin DynamicsX Interactions: Lennard-Jones potentialX Sampling Scheme: Generalized Shadow

Hybrid Monte Carlo (GSHMC)X In-house Enhanced Sampling Method:

Akhmatskaya, Reich, 2008-2014,GB patent 2009, US patent 2011

I Population-Based Approach: a coarse grained description ofparticles ensembles attempts for accurate predictions and on-the-flyrecommendations in synthesis of multiphase polymers

X Model Derivation: Population Balance Equations (PBE)X Deterministic Method: Generalized Method of Characteristics (GMOC)X Stochastic Method: Stochastic Simulation Algorithm (SSA)

Individual-Based Approach: Results

I Predictions are in excellent agreement with experimental evidencesI Computationally very demanding (weeks of simulations)

E. Akhmatskaya, J.M. Asua, Dynamic modeling of the morphology of multiphasewaterborne polymer particles, Colloid and Polymer Science, Special issue on “Morphologiesand Functions of Polymeric Microspheres”, 291 (1), 87− 98, 2013

J.M. Asua, E. Akhmatskaya, Dynamical modelling of morphology development in multiphaselatex particles, European Success Stories in Industrial Mathematics, Springer, 2011

Population-Based Approach: Results

I Derivation of Population Balance Equations (PBE) to model theDynamical Development of Particles Morphologies:

∂m(v , t)

∂t=−

∂ (g(v , t)m(v , t))

∂v−m(v , t)

∫ +∞

0ka(v , u, t)m(u, t) du

− km m(v , t) +1

2

∫ v

0ka(v − u, u, t)m(v − u, t)m(u, t) du

I Numerical methods: Generalized Method of Characteristics (GMOC)and Stochastic Simulation Algorithm (SSA)

I Future work: to reduce numerical instabilities of GMOC and toimprove sampling efficiency of SSA

Understanding Chemical Reactivity at the Quantum Level

I Collaboration: D. Sokolovski (UPV-EHU), J.N.L Connor (Manchester),V. Aquilanti (Perugia), D. De Fazio (Rome)

I Motivation: three steps in modelling of a chemical reaction

X creating a potential surface (a job for a quantum chemist)X solving the Schrodinger equation (state-of-the-art codes available)X understanding the results (this is where we come in)

I Objective: to understand integral and differential cross sections(ICS-DCS), especially at low temperatures, where they are stronglyinfluenced by scattering resonances

I Importance: cold chemistry, e.g. in the early UniverseI Method: Complex Angular Momentum (CAM) analysis of numerical

scattering dataI Results: in-house packages

X PADE II: Pade reconstruction of the reactive S-matrixX ICS Regge: CAM analysis of the integral cross sections

I Future work: development of computer code(s) for CAM analysis ofthe differential cross sections (DCS Regge)

Example: resonance structures in the ICS of the F + H2 → HF + H reaction

At low energies, the probability for the reaction to occur is strongly affected byformation 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 theRegge trajectories

Results obtained by using ICS Regge package [PCCP, 17, 18577, 2015]

BCAM Severo Ochoa Accreditation SEV-2013-0323Grant SVP-2014-068451