Systematic Coarse-Graining and Concurrent Multiresolution Simulation of Molecular Liquids

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1 Systematic Coarse-Graining and Concurrent Multiresolution Simulation of Molecular Liquids Cameron F. Abrams Department of Chemical and Biological Engineering Drexel University Philadelphia, PA USA 9 June 2005 IMA Workshop: Effective Theories for Materials and Macromolecules

2 The Short Version Systematic molecular coarse-graining: Bulk bisphenol-a polycarbonate (BPA-PC) Inhomogeneously resolved coarse-graining: BPA-PC at interfaces Concurrent multiresolution simulation of molecular liquids Dual resolution NVT ensemble

3 The Tension Between Specificity and Generality in Polymer Molecular Simulation Bead-Spring Chains: Bonded and nonbonded degrees of freedom: GENERIC; RELATIVELY EASY TO EQUILIBRATE Bisphenol-A Polycarbonate (BPA-PC): An atomically resolved system (~50K atoms); SPECIFIC; DIFFICULT TO EQUILIBRATE

4 The Compromise: Systematic Molecular Coarse-Graining Bisphenol-A Polycarbonate? Important considerations - mapping points - potentials

5 Generalized Coarse-Graining: Mapping r N Fine-scale degrees of freedom R M Coarse-grained ( CG, collective ) degrees of freedom: Mapping Points M mapping matrix Configuration r satisfies a mapping R if

6 Linking the Statistics at Different Scales: Boltzmann Inversion Probability of observing CG configuration R M is an ensemble average: Defines CG potential U CG (actually a restricted free energy) U CG (R M ) can be generated by Monte Carlo simulation on an ensemble spanned by fine-scale configurations r N [an evaluation of P(R M )]

7 Determining U CG : Reasonable Assumption #1 Bonded and nonbonded variables are uncorrelated Probability distribution factorizes Probability of observing molecule i in conformation X i Probability of observing molecule configuration of center-of-mass positions & molecular orientations

8 Determining U CG : Reasonable Assumption #2 Intramolecular bonded CG degrees of freedom X are not (strongly) correlated Intramolecular bonded coarse-grained probability distributions factorize Intramolecular CG potential has a useful additive form:

9 Determining U CG : Reasonable Assumption #3 Nonbonded correlations are constructed primarily of independent pairwise contributions An example: The Weeks- Chandler-Andersen Potential Nonbonded potential energy is pairwise additive

Practical Matters: Systematic Molecular Coarse Graining of Bisphenol-A Polycarbonate (BPA-PC) Atomically resolved intramolecular bonded degrees of freedom are backbone torsions, φ i Total potential:

10 Practical Matters: Systematic Molecular Coarse Graining of Bisphenol-A Polycarbonate (BPA-PC) Atomically resolved intramolecular bonded degrees of freedom are backbone torsions, φ i Total potential: Tasks: 1. Generate atomically resolved potential U(φ): ab initio calculations 2. Construct a mapping scheme 3. Generate intramolecular coarse-grained potential U(X) at T = 570 K using MC sampling and Boltzmann inversion 4. Nonbonded: Determine bead diameters (e.g., second virial coeff.)

11 Bisphenol-A Polycarbonate: Torsional Potentials HF/6-31G* SPE calculations ph-c ph-o c-o +nb Tschöp et al., Acta Polymer. 49:61 (1998)

12 Bisphenol-A Polycarbonate: 4:1 Boltzmann Inversion of Carbonate Angle Potential U P

13 MD of Coarse-Grained Bisphenol-A Polycarbonate: Prediction of atomically resolved structure factor CFA & K. Kremer, Macromolecules 36:260 (2003)

14 MD of Coarse-Grained Bisphenol-A Polycarbonate: Prediction of Entanglement Molecular Weight A topological representation of a bulk sample of BPA-PC; the primitive path method predicts N e ~ 5 repeat units Leon, Delle Site & Kremer (in prep)

15 Generality vs. Specificity: Modeling Polymer/Metal Interfaces Atomic-scale interactions: small-scale conformations Chain-like molecules: conformational freedom influenced by the surface Specific molecule-surface interactions: local interface structure and properties

16 Ab initio Car-Parrinello MD Investigations of Comonomer Analogs on Nickel (with L. Delle Site) but phenol interaction orientational carbonate & isopropylidene do not stick to nickel not accessible in our coarse-grained epresentation!

excluded volume (Bridging O) (CG phenoxy end) bond vector

17 Solution: Dual-Resolution CG BPA-PC Terminal CG carbonate atomically resolved carbonate C atom carries total carbonate excluded volume (Bridging O) (CG phenoxy end) bond vector C1-C4 Interaction of terminal phenoxy with Ni site is orientation dependent

18 Dual-Res MD of a Confined BPA-PC Melt N = 10 repeat units; N m = 240 chains Center of mass density profiles R g Three regimes: z < R g : both ends ads. R g < z < 2R g : single-end ads. z > 2R g : no ends ads.

19 Dual-Res MD of a Confined BPA-PC Melt: Stratified Chain Structure Gyration tensor zz-component vs COM distance from wall Three regimes: z < R g : chains flattened R g,zz < R g,xx,yy both ends ads. R g < z < 2R g : chains extended R g,zz < R g,xx,yy single-end ads. z > 2R g : bulk structure

20 Conclusions: The Liquid Polycarbonate/ Nickel Interface Ab initio (CPMD) calculations: A mechanism of PC/Ni adhesion: Phenoxy chain ends adsorb on nickel Internal chain segments do not stick Dual-resolution simulations: Specificity gives a new picture of interface structure Chain sequence apparent from liquid structure Adsorbing ends influence liquid structure out to 2R g Two-layer (compressed-stretched) structure in chain anisotropy Publications: L. Delle Site, C. F. Abrams, A. Alavi, and K. Kremer. Phys. Rev. Lett., 89(15): C. F. Abrams and K. Kremer, Macromolecules 36: (2003). C. F. Abrams, L. Delle Site, and K. Kremer, Phys. Rev. E 67: (2003). L. Delle Site, A. Alavi, and C. F. Abrams, Phys. Rev. B 67 (19): (2003).

21 Concurrent multiresolution simulation of molecular liquids Why? Conduct full-blown atomistic MD with realistic boundary conditions Enforce collective behavior to test hypotheses AKA: Concurrent Coupling of Length Scales

22 What is concurrent multiresolution simulation? MAAD Silicon Broughton et al. Phys. Rev. B. 60:2391 (1999)

23 What is concurrent multiresolution simulation? Continuum-particle hybrid coupling for liquids R. Delgado-Buscalioni and P. V. Coveney Phys. Rev. E. 67: (2003)

24 Concurrent multiresolution simulation of molecular liquids Why is it difficult? - Mass can cross resolution boundaries. - No fixed reference (e.g., crystal lattice) - Interaction potentials must be compatible across scales AND resolution interface. - system equation of state must (ideally) be independent of particle resolution - interface can dominate

25 Monte Carlo Simulations of Liquid Methane in the Dual-Resolution NVT ensemble N total molecules, cubic periodic box, two domains V 1 + V 2 = V n 1 explicit CH 4 molecules in V 1 resolution boundary N-n 1 superatom CH 4 in V 2 Goal:

26 The dual-resolution NVT ensemble bulk explicit bulk superatom resolution interface

27 The dual-resolution NVT basic idea given this find these such that

28 u 11 : 5-Center Lennard-Jones Pseudo-Methane

29 u 22 Option 1: Zero-Density Reversible Work (ZDWR) McCoy and Curro, Macromolecules 31:9362 (1998) r Averaged over angular orientations of 2 molecules i and j at fixed r. Density-independent

30 u 22 Option 2: Reverse Monte Carlo (RMC) Soper, Chem. Phys. 202:295 (1996); Reith and Pütz, J. Comput. Chem., 24:1624 (2003). - Iteratively refine u 22 beginning with a reasonable guess - Corrections to mimic correlations in bulk atomic fluid

31 Bulk phase chemical potentials: How good is u 22 for a single-resolution description? - chemical potential: - Interface complicates things: in its absence, - change in free energy upon insertion of explicit into bulk explicit phase SAME as insertion of superatom into bulk superatom phase u 22 should satisfy for V 1 = V/2 -For CH 4 at 179K, (spherical rotor)

32 Bulk phase chemical potentials: How good is u 22 for a single-resolution description? ZDRW looks great; both are pretty good.

33 Dual resolution NVT Monte Carlo What about mixed-resolution interactions, u 12? Assume explicit-superatom interaction identical to a superatom-superatom interaction: Conduct standard NVT Monte Carlo, except trial displacements include resolution changes if a boundary is crossed superatom explicit

34 Dual resolution NVT MC: ZDRW vs RMC for u 22 & u 12 Can we tweak the RMC u 22?

35 Tweaking u 22 from RMC: Ad hoc hardening Idea: Make repulsive branch of u 22 more repulsive. Should increase µ 22 and drive superatoms into the explicit subdomain.

36 Tweaking u 22 from RMC: Hardening, n = 2 A = 300, n = 2

37 Conclusions and outlook Successful demonstration of a systematic way to generate u 22 for dual-resolution liquid simulation. Particular to small molecules? Useful in non-equilibrium setting? Real surfaces? Polymers?

38 Acknowledgments - Luigi Delle Site, Kurt Kremer (MPIP) - BMBF (German Ministry of Education and Research) - US Office of Naval Research (award No. N )

Coarse-Grained Models!

Coarse-Grained Models! Large and complex molecules (e.g. long polymers) can not be simulated on the all-atom level! Requires coarse-graining of the model! Coarse-grained models are usually also particles