Dynamic modelling of morphology development in multiphase latex particle Elena Akhmatskaya (BCAM) and Jose M. Asua (POLYMAT) June 7 2012
Publications (background and output) J.M. Asua, E. Akhmatskaya Dynamic modelling of morphology development in multiphase latex particles Akhmatskaya E., Asua J.M., Dynamic modeling of the morphology of latex particles with in situ formation of graft copolymer, Journal of Polymer Science - A - Polymer Chemistry Edition, Vol. 50, 7, pp 1383-1393 (2012) Akhmatskaya E., Asua J.M., Dynamic modeling of the morphology of multiphase waterborne polymer particles, preprint 2012. Akhmatskaya E., Reich S., New Hybrid Monte Carlo Methods for Efficient Sampling: from Physics to Biology and Statistics, Progress in Nuclear Science and Technology, Vol. 2, pp. 447-462(2012). June 2012
Outline Motivation Challenges Novel model Size reduction Dynamics Effective sampling Mimicking the technological conditions Prediction of the dynamic development of the morphology for waterborne systems Model testing Multiphase waterborne polymer Graft copolymer Conclusions
Explanation of Terms Phase domain: Region of a material that is uniform in chemical composition and physical state. Multiphase polymer: polymer comprising phaseseparated domains. Morphology: Shape or form of phase domains observed, often by microscopy or scattering techniques in polymers, polymer blends, composites, and crystals. Multiphase Equilibrium Morphologies (clays: Laponite) Multiphase Non-equilibrium Morphologies Jönsson et al. Macromolecules,1991, 24, 126 Negrete-Herrera et al. Macromol. Rapid Commun. 2007, 28, 1567
Motivation Waterborne polymers applications: synthetic rubber, paints, adhesives, cosmetics, leather treatments, diagnostic tests, drug delivery Multiphase particles provide advantages over particles with uniform compositions Performance of multiphase particles depends on particle morphology Assembling multiphase particles is of great practical interest Current status: The synthesis of new morphologies is time and resources consuming: largely relies on heuristic knowledge Little known: theoretical work is mainly restricted to 2-phase systems number of morphologies of 3-phase polymers is unknown no general methodology predicting the dynamic development of morphologies for multiphase waterborne systems is available. Objective: to develop the first ever computationally feasible modeling approach for prediction of dynamics of the particle morphology development in the multiphase waterborne systems Sundberg- Sundberg, J Appl Polym Sci, 1993, 47, 1277
Challenges Simulation scale: atomistic / coarsegrained to reproduce the properties of interest Large size systems: Practice: 200 nm particle (1500 polymer chains) surrounded by water Simulation: up to µm Slow (rare event) processes : Practice: hours Simulation: up to few seconds Dynamics is important: Practice: non-equilibrium morphologies are governed by kinetics Simulation: major enhanced samplers do not reproduce dynamics (MCMC type) Mimicking technological process: Practice: the complex multivariate process Simulation:?
Technological Polymerization Process Production of Composite Latex Particles Seeded emulsion polymerization Monomer(s) 1 SEED (Polymer 2) Inorganic Initial Charge Water Composite particles Emulsifier Final Product http://wn.com/miniemulsion
Particle Morphology Development Phase I Monomer swollen particle Monomer converts to polymer Phase II Non-equilibrium morphology Equilibrium morphology process time Monomer + Polymer 1 process + Water time process time or Monomer + Polymer 1 + Inorganic + Water or More Phases process Monomer time Polymer 2 or N% Monomer Polymer 2 + (100% - N%) Monomer Copolymer 3 M% Polymer Copolymer 3 or More Phases
Simulation Model: Size Typical size of polymer particle: D = 200 nm Estimated minimal number of molecules:~ 10 7 not feasible Solution: particles instead of atoms Phase / inorganic particle: a polymer chain Water particle: water molecules packed into a particle of the diameter of the phase Number of particles for each species (phase / inorganic), N i : a number of polymer chains, ~ 1.5x10 3 Number of water particles, N waters : Water Polymer 1 N species N waters =! N i ~ N species " 1.5 " 10 3 Monomer i=1 Inorganic Simulation sphere: Wall Diameter = 2xD Surrounded by impenetrable structureless wall to keep phases & inorganic within polymer particle and to reproduce continuous aqueous phase out of the sphere
Simulation Model: Dynamics Langevin equation: Fluctuation-dissipation contributions (i) maintain temperature; (ii) mimic the impact of non- resolved finer details of an all-atom model on the coarse grained length and time scales. m d 2 r dr =!U "!m dt 2 dt + 2!k TmR( t ) B r is position, m is mass, γ is friction factor, k B is Boltzmann constant, T is temperature, U potential energy. t-time! controls the rate at which the phases move in the particle; increases with the internal viscosity of the particle:! =! 0 ( 0.5 +0.5 X ) 5! 0 = k T B mdf X is the conversion of monomer, Df is an effective diffusion coefficient that includes both Brownian and the interaction terms!c i = "# $ Df #C Material balance equation for polymerizing system!t i + R i suggests the way to mimic longer processes by choosing! ~ K!! exp,r i ~ K! R exp simulation _length i,k = real _ process _length C i is concentration and R i is rate of generation of phase i!r( t )" = 0;!R( t )R( t ' )" =!( t # t ' ).
Simulation Model: Sampler GSHMC: Generalized Shadow Hybrid Monte Carlo by Akmatskaya, Reich (2008-2012) UK patent (2009), US patent (2011) Thermodynamically consistent implementation of constant-temperature molecular dynamics (MD) m d 2 r Based on MD and Monte Carlo (MC) Numerically integrates Newton equations dt =!U 2 and accepts new trajectories according to modified Metropolis criterion Improves sampling efficiency and retains dynamical information due to use of Modified Hamiltonians - asymptotic expansions in powers of the discretization parameter Δt, that are conserved by symplectic integrators to higher accuracy than true Hamiltonians; Introducing partial momentum update the noise vector is normally i.i.d. distributed; 0< φ π/2; φ = (2 Δt) ½ rigorous implementation of stochastic Langevin dynamics GSHMC is applied in current study after full conversion of monomer / polymers to speed up development of equilibrium morphologies (a factor of 3 in the presented simulations)
Interactions Lennard Jones (LJ): similar phases P1-P1; P2-P2; I-I; G-G; M2-M2; W-W; P1-M2; P1-G; P2-M2; P2-G; G-M2; W-W; W-wall U water!wall ( r ij ) = U LJ ( R c! r ij ) for r ij > R c! 2.5! 0 for r ij " R c! 2.5! Repulsive generalized soft sphere: dissimilar phases P1-P2; P1-I; P1-W; P1-wall; P2-I; P2-W; P2-wall; I-W, I-wall; M2-W; M2-wall; G-I; G-W; G-wall )! U r ( r ij ) =! " # r ij " $ & % 6 U poly!wall ( r ij ) = + * + # % $ & % " " %! $ # R c! r ' ij & 6 for r ij > R c! 2 1/ 6 " + 0 for r ij ( R c! 2 1/ 6 ", ε ij is depth potential well, σ is distance at which LJ = 0; R c is distance from the centre of the simulation sphere to the wall; ε is estimated from surface and interfacial tensions P-polymer; M-monomer; surface _tension = a!! bk B T I-Inorganic; G-graft; W-water;
Mimicking the Technological Conditions (Algorithm) Specify: Composition of the synthetized polymer: N p - number of monomer particles to be converted to polymer and (G) N g - number of polymer particles to be converted to graft copolymer; Conversion rate: number P p (P g ) of stages of length tp i (tg i ), i=1, P p/g required for polymerization and (G) graft formation; M p and (G) M g numbers of convertible particles per polymerization, graft formation (G) stage Phase I: Forming the monomer swollen initial particle 1. Randomly distribute simulated particles 2. Minimize initial structure using Steepest descent method 3. Equilibrate the system using Langevin Dynamics (LD) simulation Phase II: Polymerization / graft formation (G) 1. Move the simulation walls towards the centre of the simulation sphere to imitate pressure increase, applied between two phases 2. Choose randomly M p monomer particles and (G) M g polymer particles 3. Run LD for tp/g i, gradually changing LJ interaction of each of M p/g particle to the characteristic values of the new polymer / copolymer 4. Repeat Step 3 for P p / P g (G) times 5. Continue simulation using GSHMC with fixed values of LJ parameters and! value corresponding to! if non-equilibrium morphologies are of interest. Use large values of otherwise.!,!! " 2
Parameters Parameters of the Model Composition of the particle Composition of the formed polymer Rate of conversion Friction coefficients Parameters of the potentials Current Status: heuristic parameters based on the experimental data or obtained from expensive simulation Future Work: parameter optimization using Particle Swarm Optimization based approaches(with Universidad de Oviedo, Spain) Parameters of the Sampler Order of Time-step, Δt Number of MD steps, N MD Angle, ϕ Current Status: prior tuning of parameters through short simulation runs Future Work: development of adaptive GSHMC schemes
Results: 2-phase polymer systems All calculations are performed in parallel on i2basque, the computing cluster comprising 29 computing elements composed by 2 Intel QuadCore Xeon processors (GROMACS / GSHMC codes) Tested the model on 2-phase polymer systems All possible equilibrium morphologies are accurately reproduced Core-shell Inverted core-shell Hemi-spheres Sandwich
Results: Dynamic Modelling of 3-phase polymer particles Simulated dynamics of the development of particle morphology of 3-phase polymer systems Investigated effect of potential parameters, friction coefficients, conversion rates, composition of the particle on the morphology development X=0 ; T = 0 X=30; T=6000 X=50; T=10000 X=70; T=14000 X=90; T=18000 X=100; T=20000
Results: Effect of Polymerization Rate and Friction Factors on Morphology Development Faster polymerization rate X=0.3; T=1800 X=0.5; T=3000 X=0.7; T=4800 X=0.9; T=5400 X=1; T=6000 aging; T=15000 Faster polymerization rate. Increasing friction factor No se puede mostrar la imagen. Puede que su equipo no tenga suficiente memoria para abrir la imagen o que ésta esté dañada. Reinicie el equipo y, a continuación, abra el archivo de nuevo. Si sigue apareciendo la x roja, puede que tenga que borrar la imagen e insertarla de nuevo. X=0.3; T=1800 X=0.5; T=3000 X=0.7; T=4800 X=0.9; T=5400 X=1; T=6000 aging; T=25000
Results: Effect of Polymerization Rate and Friction Factors on Morphology Development (II) Run1: fast polymerization rate Run2: slow polymerization rate Run3: fast polymerization rate with increasing friction constants Faster polymerization rate leads to faster convergence to equilibrium morphologies Large friction constants prevent development of equilibrium morphologies
Results: In Situ Formation of Graft Copolymer Simulated the dynamics of of the development of particle morphology of composite waterborne systems in which a graft copolymer is produced in situ during the process Investigated effect of potential parameters, friction coefficients, conversion rates, composition of the particle, composition of copolymer on the morphology development No se puede mostrar la imagen. Puede que su equipo no tenga suficiente memoria para abrir la imagen o que ésta esté dañada. Reinicie el equipo y, a continuación, abra el archivo de nuevo. Si sigue apareciendo la x roja, puede que tenga que borrar la imagen e insertarla de nuevo. X=0; T=0 X=0.3; T=1800 X=0.5; T=3000 X=0.9; T=5400 X=1; T=6000 X=1; T=50000
Conclusions A novel modeling approach for prediction of dynamics of the particle morphology development in the composite waterborne systems including the systems with in situ formation of graft copolymer is presented The proposed model is based on stochastic dynamics (SD) accounts for the effect of phase compatibility and internal viscosity of the particles for the first time, is able to predict the morphologies of interesting new materials, such as polymer-polymer, polymer-polymer-inorganic complex hybrids The future work will include developing the parameter optimization technique; improving sampling and increasing accuracy through more advanced force fields and water representation