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Doros N. Theodorou

PREDICTION OF POLYMER PHYSICAL PROPERTIES THROUGH NEW, CONNECTIVITY-ALTERING MONTE CARLO ALGORITHMS. Doros N. Theodorou

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Doros N. Theodorou

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  1. PREDICTION OF POLYMER PHYSICAL PROPERTIES THROUGH NEW, CONNECTIVITY-ALTERING MONTE CARLO ALGORITHMS Doros N. Theodorou Department of Chemical Engineering, University of Patras and ICE/HT-FORTH, GR-26500 Patras, Greece and Institute of Physical Chemistry, NRCPS “Demokritos”, GR-15310 Ag. Paraskevi, Athens, Greece. doros@sequoia.chemeng.upatras.gr dtheo@mistras.chem.demokritos.gr

  2. SOLUTION Develop “bold” Monte Carlo algorithms that can quickly sample distant regions in configuration space Use moves that modify connectivity among polymer segments PROBLEM Dense, long-chain polymer systems are very difficult to equilibrate with conventional simulation methods Longest relaxation time of polymer melt:s – s Longest time that can be simulated with atomistic MD: ~ 10 ns

  3. UNITED ATOM LINEAR POLYETHYLENE C1000, 24000 interacting sites, flat MW distribution (I=1.05) T=450 K, P = 1 atm Atomistic model: •Lennard-Jones interaction sites • Constant bond lengths (l=1.54Å) • Flexible bond angles • Torsional potential Mavrantzas, V.G. et al., Macromolecules32, 5072 (1999)

  4. CONCERTED ROTATION MONTE CARLO L. R. Dodd, T.D. Boone, DNT, 1993

  5. “driver” angle “driver” angle CONCERTED ROTATION MONTE CARLO L. R. Dodd, T.D. Boone, DNT, 1993

  6. “driver” angle “driver” angle CONCERTED ROTATION MONTE CARLO L. R. Dodd, T.D. Boone, DNT, 1993

  7. “driver” angle “driver” angle CONCERTED ROTATION MONTE CARLO L. R. Dodd, T.D. Boone, DNT, 1993

  8. END-BRIDGING MONTE CARLO P.V.K. Pant & DNT, 1994

  9. END-BRIDGING MONTE CARLO P.V.K. Pant & DNT, 1994

  10. END-BRIDGING MONTE CARLO Convenient Ensemble: Fixed N total number of chains n total number of mers P pressure T temperature k* relative chemical potentials for all k-mer species but two k=1,…,m, ki, j Chain length distribution controlled throughk*profile

  11. R rcm t0=CPU time for <[rcm(t)-rcm(0)]2> to reach <R2> EBMC PERFORMANCE AS A FUNCTION OF CHAIN LENGTH

  12. o o R EQUILIBRATION OF CHAIN CONFORMATIONS C500: Mavrantzas, V.G., Boone, T.D., Zervopoulou, E., DNT, Macromolecules32, 5072 (1999)

  13. END-BRIDGING MONTE CARLO OF cis-1,4 POLYISOPRENE MELTS

  14. END-BRIDGING MONTE CARLO OF cis-1,4 POLYISOPRENE MELTS

  15. END-BRIDGING MONTE CARLO OF cis-1,4 POLYISOPRENE MELTS

  16. T=413K:

  17. END-BRIDGING IN ATACTIC POLYPROPYLENE

  18. END-BRIDGING IN ATACTIC POLYPROPYLENE

  19. END-BRIDGING IN ATACTIC POLYPROPYLENE

  20. END-BRIDGING IN ATACTIC POLYPROPYLENE

  21. END-BRIDGING IN ATACTIC POLYPROPYLENE

  22. R atactic (aPP)rmr…(random) m r isotactic (iPP) mmm… syndiotactic (sPP) rrr… CHARACTERISTIC RATIOS OF PP n skeletal bonds, each of length l [1] Ballard et al., Polymer19, 379 (1978); Zirkel et al., Macromolecules 52, 6148 (1992) [2]Suter, U.W. and Flory, P.J. Macromolecules 8, 765 (1975) [3]Ryckaert, J.-P., in Binder and Ciccotti (Eds)

  23. ~ In quiescent, underformed melt, c = I ~ A/N(,T,c) R SAMPLING ORIENTED POLYMER MELTS Conformation tensor: average over all chains unperturbed Helmholtz energy function in flowing melt: with N=number of chains, =mass density Introduce thermodynamic “fields” (1,3) ~ MC simulations performed at given b, T, . Resulting c()dependence integrated to yield A/N as a function of  at given b, T.

  24. xx yy = -P zz = -P . maximal relaxation time xx  ( ) PE MELT UNDER UNIAXIAL EXTENSIONAL FLOW Helmholtz energy, energy, and entropy of oriented melt Mavrantzas, V.G. and DNT, Macromolecules, 31, 6310 (1998)

  25. xx yy = -P zz = -P PE MELT UNDER UNIAXIAL EXTENSIONAL FLOW Birefringence Cpredicted=(2.350.10)10-9 Pa-1(C200 melt) Cexperimental= 2.20 10-9 Pa-1(Janeschitz-Kriegl) Mavrantzas, V.G. and DNT, Comp.Theor.Polym.Sci., 10, 1 (2000)

  26. SOLUBILITY OF OLIGOMERS IN POLYMER MELTS [f1'Npn0PT*] statistical ensemble f1'  f1/exp[(s1+3)(n)/(kBT)] f1= oligomer fugacity (n)=(i- j)/(si-sj), polymer chemical potential per segment Np: total number of polymer chains. n0 : number of polymer segments if all oligomers were connected to chains.P: pressure. T : temperature. * : profile of relative chemical potentials controlling polymer chain length distribution. SCISSION polymer polymer s1-mer FUSION Zervopoulou, E., Mavrantzas, V.G., DNT J.Chem.Phys. 115, 2860 (2001)

  27. SOLUBILITY OF C10 and C20 IN PE (NERD force field) Method 1: Insertion-deletion moves in the f1NpnPT* ensemble Method 2: Fusion-scission moves in the f1'Npn0PT* ensemble

  28. SWELLING OF PE UPON SORPTION OF C10 T=458K T=458K Method 1: Insertion-deletion moves in the f1NpnPT* ensemble Method 2: Fusion-scission moves in the f1'Npn0PT* ensemble

  29. SIMULATION OF STRICTLY MONODISPERSE MELTS: DOUBLE BRIDGING MONTE CARLO jb jc “predator” mer iof ich attacks “prey” mer j of jch i ja trimer (ja, jb, jc) adjacent to j j is excised from jch Double Bridging (Karayiannis et al., 2001) N. Karayiannis, V.G. Mavrantzas, DNT, 2001

  30. SIMULATION OF STRICTLY MONODISPERSE MELTS: DOUBLE BRIDGING MONTE CARLO “predator” mer j2of jch attacks “prey” mer i2 of ich ia ib j2 i2 ic trimer (ia, ib, ic) adjacent to i2 is excised from ich Double Bridging (Karayiannis et al., 2001) i j N. Karayiannis, V.G. Mavrantzas, DNT, 2001

  31. SIMULATION OF STRICTLY MONODISPERSE MELTS: DOUBLE BRIDGING MONTE CARLO trimer (ia’,ib’,ic’) connects j2and i2 ib’ ic’ ia’ jb’ jc’ trimer (ja’,jb’,jc’) connects i and j ja’ Double Bridging (Karayiannis et al., 2001) j2 i2 i j N. Karayiannis, V.G. Mavrantzas, DNT, 2001

  32. SIMULATION OF STRICTLY MONODISPERSE MELTS: DOUBLE BRIDGING MONTE CARLO new chain jch’ is formed new chain ich’ is formed Double Bridging (Karayiannis et al., 2001) N. Karayiannis, V.G. Mavrantzas, DNT, 2001

  33. INTRAMOLECULAR DOUBLE REBRIDGING (N. Karayiannis, V.G. Mavrantzas, DNT, 2001)

  34. DB & IDR: MONODISPERSE LINEAR PE at 450K,1atm

  35. DB & IDR: MONODISPERSE LINEAR C1000 MELT 8000 atoms, T=450K, P=1atm

  36. SUMMARY Algorithms based on End-Bridging Monte Carlo (EBMC) equilibrate atomistic models of polymer melts of average molecular weight 104-105 g/mol at all length scales. Performance at low temperatures can be enhanced by combining EBMC with parallel tempering. Free energy and birefringence of oriented melts under steady-state processing flows can be obtained through EBMC in the presence of orienting fields. Variable connectivity MC schemes allow prediction of sorption isotherms of oligomers in polymer melts without the need to insert/delete or exchange molecules between phases. Double Bridging and Intramolecular Double Rebridging equilibrate monodisperse melt systems with precisely defined molecular architectures.

  37. ACKNOWLEDGMENTS Collaborators Dr. Vlasis Mavrantzas Dr. Manolis Doxastakis Dr. Vagelis Harmandaris Mr. Nikos Karayiannis Dr. Christina Samara Dr. Vanessa Zervopoulou Sponsors DG12 of the European Commission, Brite-EuRam and GROWTH programmes (projects MPFLOW, PERMOD, DEFSAM) DG12 of the European Commission, TMR programme (NEWRUP Research Network) Greek GSRT, PENED programme, contracts 218-95E, 95-99E SIMU Network

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