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. 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 SOLUTION Develop “bold” Monte Carlo algorithms that can quickly sample distant regions in configuration space Use moves that modify connectivity among polymer segments

3. UNITED ATOM LINEAR POLYETHYLENE C 1000, 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., Macromolecules 32, 5072 (1999)

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

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

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

7. CONCERTED ROTATION MONTE CARLO “driver” angle “driver” angle 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. 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 END-BRIDGING MONTE CARLO k=1,…,m, k  i, j Chain length distribution controlled through  k * profile

11. EBMC PERFORMANCE AS A FUNCTION OF CHAIN LENGTH r cm t 0 =CPU time for to reach R

12. EQUILIBRATION OF CHAIN CONFORMATIONS o o Mavrantzas, V.G., Boone, T.D., Zervopoulou, E., DNT, Macromolecules 32, 5072 (1999) R C 500 :

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

17. T=413K:

18. END-BRIDGING IN ATACTIC POLYPROPYLENE

23. CHARACTERISTIC RATIOS OF PP R n skeletal bonds, each of length l m isotactic (iPP) mmm… r syndiotactic (sPP) rrr… atactic (aPP) rmr… (random) [1] Ballard et al., Polymer 19, 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)

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

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

26.  xx  yy = -P  zz = -P PE MELT UNDER UNIAXIAL EXTENSIONAL FLOW Mavrantzas, V.G. and DNT, Comp.Theor.Polym.Sci., 10, 1 (2000) C predicted =(2.35  0.10)  10 -9 Pa -1 (C 200 melt) C experimental = 2.20  10 -9 Pa -1 (Janeschitz-Kriegl) Birefringence

27. SOLUBILITY OF OLIGOMERS IN POLYMER MELTS s 1 -mer polymer SCISSION FUSION [f 1 'N p n 0 PT  * ] statistical ensemble f 1 '  f 1 /exp[(s 1 +3)  (n) /(k B T)] f 1 = oligomer fugacity  (n) =(  i -  j )/(s i -s j ), polymer chemical potential per segment N p : total number of polymer chains. n 0 : 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. Zervopoulou, E., Mavrantzas, V.G., DNT J.Chem.Phys. 115, 2860 (2001)

28. SOLUBILITY OF C 10 and C 20 IN PE (NERD force field) Method 1: Insertion-deletion moves in the f 1 N p nPT  * ensemble Method 2: Fusion-scission moves in the f 1 'N p n 0 PT  * ensemble

29. SWELLING OF PE UPON SORPTION OF C 10 T=458K Method 1: Insertion-deletion moves in the f 1 N p nPT  * ensemble Method 2: Fusion-scission moves in the f 1 'N p n 0 PT  * ensemble T=458K

30. Double Bridging (Karayiannis et al., 2001) i “predator” mer i of ich j attacks “prey” mer j of jch trimer (j a, j b, j c ) adjacent to j jaja jbjb jcjc is excised from jch SIMULATION OF STRICTLY MONODISPERSE MELTS: DOUBLE BRIDGING MONTE CARLO N. Karayiannis, V.G. Mavrantzas, DNT, 2001

31. Double Bridging (Karayiannis et al., 2001) i j “predator” mer j 2 of jch j2j2 attacks “prey” mer i 2 of ich i2i2 trimer (i a, i b, i c ) adjacent to i 2 iaia ibib icic is excised from ich SIMULATION OF STRICTLY MONODISPERSE MELTS: DOUBLE BRIDGING MONTE CARLO N. Karayiannis, V.G. Mavrantzas, DNT, 2001

32. Double Bridging (Karayiannis et al., 2001) i j j2j2 i2i2 trimer (j a ’,j b ’,j c ’ ) connects i and j ja’ja’ jb’jb’ jc’jc’ ia’ia’ ib’ib’ ic’ic’ trimer (i a ’,i b ’,i c ’ ) connects j 2 and i 2 SIMULATION OF STRICTLY MONODISPERSE MELTS: DOUBLE BRIDGING MONTE CARLO N. Karayiannis, V.G. Mavrantzas, DNT, 2001

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

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

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

36. DB & IDR: MONODISPERSE LINEAR C 1000 MELT 8000 atoms, T=450K, P=1atm

37. SUMMARY Algorithms based on End-Bridging Monte Carlo (EBMC) equilibrate atomistic models of polymer melts of average molecular weight 10 4 -10 5 g/mol at all length scales. 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. Performance at low temperatures can be enhanced by combining EBMC with parallel tempering. Double Bridging and Intramolecular Double Rebridging equilibrate monodisperse melt systems with precisely defined molecular architectures.

38. 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