Analytical rheology of branched polymer melts: Identifying and resolving degenerate structures

Journal of Rheology

Volumn 55, Issue 1, 2011, Pages 177-194

  Shanbhag, Sachin ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Analytical rheology; Bayesian analysis; Degeneracy; Hierarchical tube model

Indexed keywords

ANALYTICAL RHEOLOGY; BAYESIAN ANALYSIS; BAYESIAN DATA ANALYSIS; BRANCHED POLYMER; COMPUTATIONAL ALGORITHM; DEGENERACY; DEGENERATE STRUCTURES; LINEAR RHEOLOGY; POLYMER FRACTIONS; POLYMER MIXTURE; PROOF OF CONCEPT; RHEOLOGICAL DATA; RHEOLOGICAL EXPERIMENT; TUBE MODEL;

ALGORITHMS; BAYESIAN NETWORKS; ELASTICITY; MIXTURES; POLYMER MELTS; VISCOSITY;

RHEOLOGY;

EID: 78650785778     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.3523627     Document Type: Article

References (36)

1. Anderssen, R. S. B., " Inverse problems: A pragmatist's approach to the recovery of information from indirect measurements.," ANZIAM J. 1445-8735 46, C588-C622 (2005).
2. Das, C., N. J. Inkson, D. J. Read, M. A. Kelmanson, and T. C. B. McLeish, " Computational linear rheology of general branch-on-branch polymers.," J. Rheol. 0148-6055 50, 207-234 (2006). 10.1122/1.2167487
3. Dealy, J. M., and R. G. Larson, Molecular Structure and Rheology of Molten Polymers, 1st ed. (Hanser, Cincinnati, OH, 2006).
4. Doerpinghaus, P. J., and D. G. Baird, " Separating the effects of sparse long-chain branching on rheology from those due to molecular weight in polyethylenes.," J. Rheol. 0148-6055 47, 717-736 (2003). 10.1122/1.1567751
5. Frenkel, D., and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed. (Academic, Orlando, FL, 2002).
6. Frischknecht, A. L., S. T. Milner, A. Pryke, R. N. Young, R. Hawkins, and T. C. B. McLeish, " Rheology of three-arm asymmetric star polymer melts.," Macromolecules 0024-9297 35, 4801-4820 (2002). 10.1021/ma0101411 (Pubitemid 34630569)
7. Green, P. J., " Reversible jump Markov chain Monte Carlo computation and Bayesian model determination.," Biometrika 0006-3444 82, 711-732 (1995). 10.1093/biomet/82.4.711
8. Green, P. J., and A. Mira, " Delayed rejection in reversible jump Metropolis-Hastings.," Biometrika 0006-3444 88, 1035-1053 (2001).
9. Janzen, J., and R. H. Colby, " Diagnosing long-chain branching in polyethylenes.," J. Mol. Struct. 0022-2860 485-486, 569-584 (1999). 10.1016/S0022-2860(99)00097-6 (Pubitemid 29406422)
10. Larson, R. G., " Combinatorial rheology of branched polymer melts.," Macromolecules 0024-9297 34, 4556-4571 (2001). 10.1021/ma000700o (Pubitemid 34217411)
11. Larson, R. G., T. Sridhar, L. G. Leal, G. H. McKinley, A. E. Likhtman, and T. C. B. McLeish, " Definitions of entanglement spacing and time constants in the tube model.," J. Rheol. 0148-6055 47, 809-818 (2003). 10.1122/1.1567750
12. Larson, R. G., Q. Zhou, S. Shanbhag, and S. J. Park, " Advances in modeling of polymer melt rheology.," AIChE J. 0001-1541 53, 542-548 (2007). 10.1002/aic.11064 (Pubitemid 46473306)
13. Lohse, D. J., S. T. Milner, L. J. Fetters, M. Xenidou, N. Hadjichristidis, R. A. Mendelson, C. A. Garcia-Franco, and M. K. Lyon, " Well-defined, model long chain branched polyethylene. 2. Melt rheological behavior.," Macromolecules 0024-9297 35, 3066-3075 (2002). 10.1021/ma0117559 (Pubitemid 34586534)
14. MacKay, C., " Bayesian methods for adaptive modeling.," Ph.D. thesis, California Institute of Technology, 1991.
15. McLeish, T. C. B., and R. G. Larson, " Molecular constitutive equations for a class of branched polymers: The pom-pom polymer.," J. Rheol. 0148-6055 42, 81-110 (1998). 10.1122/1.550933
16. Mead, D. W., " Determination of molecular-weight distributions of linear flexible polymers from linear viscoelastic material functions.," J. Rheol. 0148-6055 38, 1797-1827 (1994). 10.1122/1.550527
17. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, " Equation of state calculations by fast computing machines.," J. Chem. Phys. 0021-9606 21, 1087-1092 (1953). 10.1063/1.1699114
18. Mira, A., " On Metropolis-Hastings algorithms with delayed rejection.," Metron 0026-1424 59, 3-4 (2001).
19. Murray, I., and I. Ghahramani, " A note on the evidence and Bayesian Occam's razor.," Gatsby Unit Techical Report Nos. 1-4, 2005.
20. Park, S. J., S. Shanbhag, and R. G. Larson, " A hierarchical algorithm for predicting the linear viscoelastic properties of polymer melts with long-chain branching.," Rheol. Acta 0035-4511 44, 319-330 (2005). 10.1007/s00397-004-0415-2 (Pubitemid 40106517)
21. Shanbhag, S., " Analytical rheology of blends of linear and star polymers using a Bayesian formulation.," Rheol. Acta 0035-4511 49, 411-422 (2010). 10.1007/s00397-010-0443-z
22. Shanbhag, S., and R. G. Larson, " A slip link model of branch-point motion in entangled polymers.," Macromolecules 0024-9297 37 (21), 8160-8166 (2004). 10.1021/ma034532m
23. Shanbhag, S., S. J. Park, Q. Zhou, and R. G. Larson, " Implications of microscopic simulations of polymer melts for mean-field tube theories.," Mol. Phys. 0026-8976 105, 249-260 (2007). 10.1080/00268970601143333 (Pubitemid 46447519)
24. Shroff, R. N., and H. Mavridis, " Long-chain-branching index for essentially linear polyethylenes.," Macromolecules 0024-9297 32, 8454-8464 (1999). 10.1021/ma9909354 (Pubitemid 30545622)
25. Stark, H., and J. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Upper Saddle River, NJ, 1986).
26. Tarantola, A., Inverse Problem Theory and Methods for Model Parameter Estimation (Society for Industrial and Applied Mathematics, Philadelphia, 2005).
27. Tuminello, W. H., " Molecular-weight and molecular-weight distribution from dynamic measurements of polymer melts.," Polym. Eng. Sci. 0032-3888 26, 1339-1347 (1986). 10.1002/pen.760261909
28. van Ruymbeke, E., S. Coppola, L. Balacca, S. Righi, and D. Vlassopoulos, " Decoding the viscoelastic response of polydisperse star/linear polymer blends.," J. Rheol. 0148-6055 54, 507-538 (2010). 10.1122/1.3368729
29. van Ruymbeke, E., A. Kaivez, A. Hagenaars, D. Daoust, P. Godard, R. Keunings, and C. Bailly, " Characterization of sparsely long chain branched polycarbonate by a combination of solution, rheology and simulation methods.," J. Rheol. 0148-6055 50, 949-973 (2006). 10.1122/1.2357188 (Pubitemid 44724866)
30. van Ruymbeke, E., R. Keunings, and C. Bailly, " Prediction of linear viscoelastic properties for polydisperse mixtures of entangled star and linear polymers: Modified tube-based model and comparison with experimental results.," J. Non-Newtonian Fluid Mech. 128, 7-22 (2005a). 10.1016/j.jnnfm.2005.01.006 (Pubitemid 40936340)
31. van Ruymbeke, E., V. St́phenne, D. Daoust, P. Godard, R. Keunings, and C. Bailly, " A sensitive method to detect very low levels of long chain branching from the molar mass distribution and linear viscoelastic response.," J. Rheol. 0148-6055 49, 1503-1520 (2005b). 10.1122/1.2048743 (Pubitemid 44538290)
32. Vega, J., M. Aguilar, J. Peon, D. Pastor, and J. Martinez-Salazar, " Effect of long chain branching on linear-viscoelastic melt properties of polyolefins.," e-Polymers 1618-7229 46, 1-35 (2002).
33. Wasserman, S., " Calculating the molecular weight distribution from linear viscoelastic response of polymer melts.," J. Rheol. 0148-6055 39, 601-625 (1995). 10.1122/1.550723
34. Wood-Adams, P. M., and J. M. Dealy, " Using rheological data to determine the branching level in metallocene polyethylenes.," Macromolecules 0024-9297 33, 7481-7488 (2000). 10.1021/ma991534r
35. Wood-Adams, P. M., J. M. Dealy, A. W. deGroot, and O. D. Redwine, " Effect of molecular structure on the linear viscoelastic behavior of polyethylene.," Macromolecules 0024-9297 33, 7489-7499 (2000). 10.1021/ma991533z
36. Wu, S., " Polymer molecular-weight distribution from dynamic melt viscoelasticity.," Polym. Eng. Sci. 0032-3888 25, 122-128 (1985). 10.1002/pen.760250211