Abstract
AbstractWe discuss a phenomenological, coarse‐grained simulation scheme, single‐chain‐in‐mean‐field (SCMF) simulation, for investigating the kinetics of phase separation in dense polymer blends and mixtures of polymers and solvents. In the spirit of self‐consistent‐field calculations, we approximate the interacting multichain problem by that of a single chain in an external field, which, in turn, depends on the local densities of the components. To study the time evolution of the mixture, we perform an explicit Monte Carlo (MC) simulation of an ensemble of independent chains in the external field and periodically calculate the average densities and update the external field. Unlike dynamic self‐consistent‐field theory, these SCMF simulations do not assume that the chain conformations relax much more quickly than the density and incorporate the single‐chain dynamics explicitly rather than via an Onsager coefficient. This allows us to study systems with large spatial inhomogeneities and dynamic asymmetries. To assess the accuracy and limitations of the simulation scheme, we compare the results of SCMF simulations using a discretized Edwards Hamiltonian with computer simulations of the corresponding multichain system for (1) the early stages of spinodal decomposition of a symmetric binary polymer blend in response to a quench from χN = 0.314 to χN = 5 (where χ is the Flory–Huggins parameter and N is the number of segments), for which the growth rate of composition fluctuations is compared with MC simulations of the bond fluctuation model and alternative dynamic self‐consistent‐field calculations, and (2) the evaporation of a solvent from a low‐molecular‐weight thin polymer film, for which a comparison is made with molecular dynamics (MD) simulations of a bead‐necklace model with a monomeric solvent. In the latter case, the polymer conformations are extracted from MD simulations and modeled in the SCMF simulations by a discretized Edwards Hamiltonian augmented by a chain‐bending potential. From the MD simulations of thin polymer films in equilibrium with its vapor, phase coexistence has been determined, and the second‐ and third‐order virial coefficients in the SCMF simulations have been adjusted accordingly. Finally, MD simulations of bulk solutions of a polymer and a solvent over a range of compositions, as well as the pure solvent at various densities, have been performed to determine self‐diffusion coefficients that enter the SCMF simulations in the form of density‐dependent segmental mobilities. A comparison of the polymer and solvent profiles in a thin film as a function of time and the fraction of the solvent evaporating from a solvent‐swollen film, as obtained from MD simulations and parameterized SCMF simulations, shows satisfactory agreement for this simple mapping procedure. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 934–958, 2005
Bibliography
Müller, M., & Smith, G. D. (2005). Phase separation in binary mixtures containing polymers: A quantitative comparison of singleâchainâinâmeanâfield simulations and computer simulations of the corresponding multichain systems. Journal of Polymer Science Part B: Polymer Physics, 43(8), 934â958. Portico.
References
102
Referenced
152
10.1021/ma60075a033
10.1016/B978-0-12-546802-2.50012-9
{'volume-title': 'Polymer Blends and Alloys', 'year': '1993', 'author': 'Folbes M. J.', 'key': 'e_1_2_9_3_3'}
/ Polymer Blends and Alloys by Folbes M. J. (1993)10.1146/annurev.fluid.34.082301.144051
10.1088/0957-4484/14/10/201
10.1103/PhysRevA.20.595
10.1103/PhysRevA.31.1103
{'key': 'e_1_2_9_6_2', 'series-title': 'In Encyclopedia of Physical Chemistry and Chemical Physics', 'first-page': '2087', 'author': 'Müller M.', 'year': '2001'}
/ In Encyclopedia of Physical Chemistry and Chemical Physics by Müller M. (2001)10.1002/1439-7641(20020916)3:9<754::AID-CPHC754>3.0.CO;2-U
10.1557/mrs2001.43
{'key': 'e_1_2_9_6_5', 'first-page': '407', 'volume-title': 'Coarse‐Graining Techniques in Simulation Methods for Polymers', 'author': 'Binder K.', 'year': '2004'}
/ Coarse‐Graining Techniques in Simulation Methods for Polymers by Binder K. (2004)10.1002/polb.10456
10.1063/1.1516591
10.1063/1.1497636
10.1063/1.465536
10.1063/1.473129
10.1063/1.474313
10.1103/PhysRevE.56.3240
10.1021/ma981648n
10.1021/ma961618p
10.1021/ma010346
10.1103/PhysRevE.64.041804
10.1063/1.1565105
10.1103/RevModPhys.49.435
10.1063/1.439809
10.1063/1.442226
10.1063/1.445747
10.1016/0378-4371(87)90158-0
10.1103/PhysRevE.49.3199
10.1021/ma951102q
10.1021/ma951071z
10.1063/1.1557052
10.1063/1.1677735
10.1063/1.430517
10.1021/ma50004a051
10.1103/PhysRevLett.72.2660
10.1021/ma011515t
- An accurate description of liquid–vapor interfaces in polymeric systems requires an accurate equation of state and a nonlocal interaction free‐energy functional that duly separates short‐range repulsions and weaker longer‐range attractions.27
10.1063/1.1535893
10.1088/0953-8984/15/19/201
10.1021/ma991796t
10.1063/1.1776555
10.1063/1.1505025
10.1021/ma960411t
10.1063/1.1597454
10.1063/1.1601214
10.1088/0953-8984/13/21/303
- If we are only interested in the equilibrium value more efficient schemes to update the fields can be used that speed up the convergence of the procedure.
10.1016/0032-3950(65)90209-1
10.1063/1.431268
{'volume-title': 'The Theory of Polymer Dynamics', 'year': '1986', 'author': 'Doi M.', 'key': 'e_1_2_9_37_2'}
/ The Theory of Polymer Dynamics by Doi M. (1986)10.1140/epje/i2002-10122-1
10.1063/1.1744102
10.1063/1.1730447
10.1016/0001-6160(70)90144-6
10.1007/BFb0017984
10.1002/(SICI)1521-3919(19990701)8:4<343::AID-MATS343>3.0.CO;2-F
10.1103/PhysRevE.59.728
10.1063/1.1750930
10.1063/1.1750971
10.1021/ma00187a030
10.1063/1.459901
10.1021/ma00110a016
10.1021/ma00181a028
10.1051/jp2:1991138
10.1021/ma001500f
10.1209/epl/i2000-00452-6
10.1063/1.1699180
{'volume-title': 'The Theory of Polymer Dynamics', 'year': '1994', 'author': 'Doi M.', 'key': 'e_1_2_9_48_3'}
/ The Theory of Polymer Dynamics by Doi M. (1994)10.1088/0370-1328/85/4/301
10.1021/ma001440d
10.1021/ma981311l
10.1140/epje/e2004-00014-7
10.1021/ma971349i
10.1021/ma9714070
10.1021/ma9910639
10.1021/ma011889m
10.1002/adma.200304906
10.1209/epl/i2002-00206-0
10.1016/j.polymer.2004.01.082
10.1016/j.polymer.2004.04.044
10.1063/1.1397333
- Lucretius: A Molecular Simulation Package.http://www.che.utah.edu/∼gdsmith/mdcode/main.html.
10.1006/jcph.1993.1045
10.1063/1.1765103
10.1016/S0010-4655(02)00309-0
10.1080/00268979600100761
10.1103/PhysRevE.65.030802
- The coexistence densities in the SCMF simulations only agree with the equilibrium SCF values in the limit of an infinitely large ensemble of single chains. If the ensemble consists only of a small number of independent chains the fluctuations of the densities and fields will give rise to corrections and will also impart a dependence of the results on the spatial discretization.
10.1063/1.343754
10.1007/s10189-002-8214-1
10.1021/ma049509v
10.1002/1521-4095(20020805)14:15<1041::AID-ADMA1041>3.0.CO;2-A
10.1021/ma011672s
10.1021/ma010854j
10.1021/ma001291z
10.1021/ma9902100
10.1016/j.cossms.2004.01.002
10.1002/polb.20055
10.1063/1.1511512
10.1063/1.1511513
10.1063/1.1463056
Dates
Type | When |
---|---|
Created | 20 years, 5 months ago (March 8, 2005, 4:46 p.m.) |
Deposited | 1 year, 11 months ago (Sept. 11, 2023, 8:59 a.m.) |
Indexed | 2 months ago (June 24, 2025, 9:25 a.m.) |
Issued | 20 years, 5 months ago (March 8, 2005) |
Published | 20 years, 5 months ago (March 8, 2005) |
Published Online | 20 years, 5 months ago (March 8, 2005) |
Published Print | 20 years, 4 months ago (April 15, 2005) |
Funders
3
Deutsche Forschungsgemeinschaft
10.13039/501100001659
Region: Europe
gov (National government)
Labels
3
- German Research Association
- German Research Foundation
- DFG
Awards
2
- Mu1674/3
- Mu1674/1
Alexander von Humboldt Foundation
10.13039/100005156
Alexander von Humboldt-StiftungRegion: Europe
pri (Trusts, charities, foundations (both public and private))
Labels
5
- Humboldt-Stiftung
- Humboldt Foundation
- Alexander von Humboldt Foundation
- Humboldt Stiftung
- AvH
National Science Foundation for their support through the CRC project “Multiply Bound Polymer Chains”
@article{M_ller_2005, title={Phase separation in binary mixtures containing polymers: A quantitative comparison of single‐chain‐in‐mean‐field simulations and computer simulations of the corresponding multichain systems}, volume={43}, ISSN={1099-0488}, url={http://dx.doi.org/10.1002/polb.20385}, DOI={10.1002/polb.20385}, number={8}, journal={Journal of Polymer Science Part B: Polymer Physics}, publisher={Wiley}, author={Müller, Marcus and Smith, Grant D.}, year={2005}, month=mar, pages={934–958} }