Simulating Polymers: From Particles to Fields (More Math)
This video describes how one can formulate fast, efficient and precise theoretic simulations, starting from a particle-based polymer model. Some of what I said is not super precise (this is a video overview, not a textbook) so for more details see chapter 4 of Ref. 3 below.
Alternative version (less math): • Simulating Polymers: From Particles to Fie...
MD simulations were conducted using LAMMPS, except the ubiquitin extension video – that was done using NAMD and the data were taken from an NAMD tutorial, linked below.
Correction: The integral that appears at 9:32 should integrate the entire thing over W, not just the term on the RHS.
Refs:
1. NAMD tutorial: http://www.ks.uiuc.edu/Training/Tutor...
2. D. E. Tanner (2012). https://www.semanticscholar.org/paper...
3. G. H. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers (International Series of Monographs on Physics), Oxford University Press, USA, 2006. http://dx.doi.org/10.1093/acprof:oso/...
See particularly chapter 4.
4. M. W. Matsen and M. Schick, Physical Review Letters (1994) 72, 2660 https://doi.org/10.1103/PhysRevLett.7...
5. Reviews on polymer field theories:
G. H. Fredrickson, V. Ganesan and F. Drolet, Macromolecules (2002) 35, 16-39 https://doi.org/10.1021/ma011515t
M. W. Matsen, The Journal of Chemical Physics (2020) 152 (11), 110901 https://doi.org/10.1063/1.5145098
6. References for images of block copolymer structure
K. Aissou, M. Kogelschatz and T. Baron, Nanotechnology (2009) 20, 9 http://dx.doi.org/10.1088/0957-4484/2...
N. Balsara, Current Opinion in Solid State and Materials Science (1999) 4, 553 https://doi.org/10.1016/S1359-0286(00...
N. Sota and T. Hashimoto, Polymer (2005) 46, 10392 https://doi.org/10.1016/j.polymer.200... Note: This image is actually for a triblock, not diblock copolymer, but the structure is basically the same.
7. Theory/Experiment phase diagram:
Experiment: A. K. Khandpur et al. Macromolecules (1995) 28, 26, 8796 https://doi.org/10.1021/ma00130a012
SCFT: M. W. Matsen and M. Schick, Physical Review Letters (1994) 72, 2660 https://doi.org/10.1103/PhysRevLett.7...
CL-FTS: K. T. Delaney and G. H. Fredrickson, The Journal of Physical Chemistry B (2016) 120, 31, 7615 https://doi.org/10.1021/acs.jpcb.6b05704
Timestamps:
0:00 Introduction
1:54 Molecular dynamics
4:39 Coarse-grained molecular dynamics
6:10 Deriving a polymer field theory
11:59 Polymer flexibility
13:15 Polymer behavior in fields
18:52 Field-theoretic simulations
22:39 Self-consistent field theory
24:23 Outro