Abstract
Density functional theory (DFT) is a powerful approach utilized successfully in both quantum and classical theoretical and computational physics. Since the 1970s, DFT has been applied to predict the phase behavior of simple fluids, including the liquid-to-crystal transition in hard-sphere and Lennard–Jones fluids. Beginning in the 1990s, it was recognized that DFT can be adapted to describe the equilibrium morphologies of polymer-based nanocomposites (PNC). Here, we review various examples where DFT is applied to PNCs, from polymer–clay and polymer-nanotube mixtures to one-component hairy nanoparticle assemblies. We also discuss hybrid approaches where DFT is combined with other coarse-grained field theories, in particular, the Self-Consistent Field/Density Functional Theory (SCF-DFT) method and its applications.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Q. Zeng, A. Yu, G. Lu, Prog. Polym. Sci. 33, 191 (2008)
L.-T. Yan, X.-M. Xie, Prog. Polym. Sci. 38, 369 (2013)
J. Yan, M. R. Bockstaller, K. Matyjaszewski, Progr. Polym. Sci., 101180 (2019)
G. Allegra, G. Raos, M. Vacatello, Prog. Polym. Sci. 33, 683 (2008)
V. V. Ginzburg, in Problems of Nonlinear Mechanics and Physics of Materials (Springer, 2019), p. 205.
A. C. Balazs, J. Bicerano, V. V. Ginzburg, in Polyolefin Composites (Wiley, 2007), p. 415.
A.C. Balazs, V.V. Ginzburg, Y. Lyatskaya, C. Singh, E. Zhulina, in Polymer-Clay Nanocomposites. ed. by T. Pinnavaia, G.W. Beall (Wiley, New York, 2000), p. 281
A. Karatrantos, N. Clarke, M. Kröger, Polym. Rev. 56, 385 (2016)
J.J. de Pablo, Annu Rev Phys Chem 62, 555 (2011)
J. Feng, H. Heinz, Adv. Polyolefin Nanocompos., 205 (2010)
N.J. Fernandes, H. Koerner, E.P. Giannelis, R.A. Vaia, MRS Commun. 3, 13 (2013)
V. Ganesan, A. Jayaraman, Soft Matter 10, 13 (2014)
S.C. Glotzer, M.J. Solomon, Nat. Mater. 6, 557 (2007)
H. Heinz, S.S. Patnaik, R.B. Pandey, B.L. Farmer, Modeli. Simul. Polym., 37 (2010).
S.K. Kumar, B.C. Benicewicz, R.A. Vaia, K.I. Winey, Macromolecules 50, 714 (2017)
S.K. Kumar, V. Ganesan, R.A. Riggleman, J. Chem. Phys. 147, 020901 (2017)
S.K. Kumar, N. Jouault, B. Benicewicz, T. Neely, Macromolecules 46, 3199 (2013)
R.L. Marson, T.D. Nguyen, S.C. Glotzer, MRS Commun. 5, 397 (2015)
W.-B. Zhang et al., Macromolecules 47, 1221 (2014)
Z.L. Zhang, M.A. Horsch, M.H. Lamm, S.C. Glotzer, Nano Lett 3, 1341 (2003)
A. Jayaraman, in Theory and Modeling of Polymer Nanocomposites, ed. by V. Ginzburg, L. Hall (Springer, 2020)
L.M. Hall, A. Jayaraman, K.S. Schweizer, Curr. Opin. Solid State Mater. Sci. 14, 38 (2010)
P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)
W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)
W. Kohn, Rev. Mod. Phys. 71, 1253 (1999)
T. Ramakrishnan, M. Yussouff, Phys. Rev. B 19, 2775 (1979)
P. Tarazona, Phys. Rev. A 31, 2672 (1985)
P. Tarazona, L. Vicente, Mol. Phys. 56, 557 (1985)
W. Curtin, N. Ashcroft, Phys. Rev. A 32, 2909 (1985)
A. Denton, N. Ashcroft, Phys. Rev. A 39, 4701 (1989)
R. Leidl, H. Wagner, J. Chem. Phys. 98, 4142 (1993)
J.F. Lutsko, M. Baus, Phys. Rev. A 41, 6647 (1990)
J.F. Lutsko, M. Baus, Phys. Rev. Lett. 64, 761 (1990)
Y. Rosenfeld, Phys. Rev. E 50, R3318 (1994)
Y. Rosenfeld, J. Phys.: Condens. Matter 8, 9289 (1996)
Y. Rosenfeld, M. Schmidt, H. Löwen, P. Tarazona, Phys. Rev. E 55, 4245 (1997)
Y. Rosenfeld, P. Tarazona, Mol. Phys. 95, 141 (1998)
Y. Rosenfeld, J. Phys.: Condens. Matter 14, 9141 (2002)
P. Tarazona, Phys. A 306, 243 (2002)
P. Tarazona, J.A. Cuesta, Y. MartĂnez-RatĂłn, in Theory and Simulation of Hard-Sphere Fluids and Related Systems (Springer, 2008), pp. 247.
M. Baus, J.F. Lutsko, Phys. A 176, 28 (1991)
A. Somoza, P. Tarazona, J. Chem. Phys. 91, 517 (1989)
A. Somoza, P. Tarazona, Phys. Rev. A 41, 965 (1990)
E. Velasco, A. Somoza, L. Mederos, J. Chem. Phys. 102, 8107 (1995)
E. Velasco, L. Mederos, J. Chem. Phys. 109, 2361 (1998)
E. Velasco, L. Mederos, D. Sullivan, Phys. Rev. E 62, 3708 (2000)
E. Velasco, L. Mederos, D. Sullivan, Phys. Rev. E 66, 021708 (2002)
G.J. Vroege, H.N. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992)
V.V. Ginzburg, M.A. Glaser, N.A. Clark, Liq. Cryst. 23, 227 (1997)
H. Graf, H. Löwen, J. Phys.: Condens. Matter 11, 1435 (1999)
A. Yethiraj, C.E. Woodward, J. Chem. Phys. 102, 5499 (1995)
A. Yethiraj, J. Chem. Phys. 109, 3269 (1998)
C.E. Woodward, J. Chem. Phys. 94, 3183 (1991)
C.E. Woodward, A. Yethiraj, J. Chem. Phys. 100, 3181 (1994)
D. Chandler, J.D. McCoy, S.J. Singer, J. Chem. Phys. 85, 5971 (1986)
D. Chandler, J.D. McCoy, S.J. Singer, J. Chem. Phys. 85, 5977 (1986)
E. Kierlik, M. Rosinberg, J. Chem. Phys. 97, 9222 (1992)
E. Kierlik, M. Rosinberg, J. Chem. Phys. 99, 3950 (1993)
S.K. Nath, P.F. Nealey, J.J. de Pablo, J. Chem. Phys. 110, 7483 (1999)
J.B. Hooper, J.D. McCoy, J.G. Curro, J. Chem. Phys. 112, 3090 (2000)
L. Frink, A. Salinger, M. Sears, J. Weinhold, A. Frischknecht, J. Phys.: Condens. Matter 14, 12167 (2002)
A.L. Frischknecht, J.D. Weinhold, A.G. Salinger, J.G. Curro, L.J. Douglas Frink, J.D. McCoy, J. Chem. Phys. 117, 10385 (2002).
J. Wu, AIChE J. 52, 1169 (2006)
C.P. Emborsky, Z. Feng, K.R. Cox, W.G. Chapman, Fluid Phase Equilib. 306, 15 (2011)
J.D. McCoy, K.G. Honnell, K.S. Schweizer, J.G. Curro, J. Chem. Phys. 95, 9348 (1991)
J.D. McCoy, K.G. Honnell, K.S. Schweizer, J.G. Curro, Chem. Phys. Lett. 179, 374 (1991)
N. Sushko, P. van der Schoot, M. Michels, J. Chem. Phys. 115, 7744 (2001)
T. Cherepanova, A. Stekolnikov, Chem. Phys. 154, 41 (1991)
J.B. Hooper, J.D. McCoy, J.G. Curro, F. van Swol, J. Chem. Phys. 113, 2021 (2000)
A. Yethiraj, Adv. Chem. Phys. 121, 89 (2002)
X. Xu, D. Cao, J. Wu, Soft Matter 6, 4631 (2010)
M. Wertheim, J. Stat. Phys. 35, 19 (1984)
M. Wertheim, J. Stat. Phys. 35, 35 (1984)
M. Schmidt, H. Löwen, J.M. Brader, R. Evans, Phys. Rev. Lett. 85, 1934 (2000)
J. Brader, R. Evans, M. Schmidt, H. Löwen, J. Phys.: Condens. Matter 14, L1 (2001)
R. Evans, J. Brader, R. Roth, M. Dijkstra, M. Schmidt, H. Löwen, Philos. Trans. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 359, 961 (2001)
J.M. Brader, R. Evans, M. Schmidt, Mol. Phys. 101, 3349 (2003)
S. Asakura, F. Oosawa, J. Chem. Phys. 22, 1255 (1954)
S. Asakura, F. Oosawa, J. Polym. Sci., A: Polym. Chem. 33, 183 (1958)
M. Rubinstein, R. H. Colby, Polymer Physics, vol. 23 (Oxford University Press, New York, 2003)
A. Gast, C. Hall, W. Russel, J. Colloid Interface Sci. 96, 251 (1983)
H.N. Lekkerkerker, W.-K. Poon, P.N. Pusey, A. Stroobants, P. Warren, EPL (Europhys. Lett.) 20, 559 (1992)
E. McGarrity, A. Frischknecht, M. Mackay, J. Chem. Phys. 128, 154904 (2008)
E. McGarrity, A. Frischknecht, L. Frink, M. Mackay, Phys. Rev. Lett. 99, 238302 (2007)
S. Tripathi, W.G. Chapman, J. Chem. Phys. 122, 094506 (2005)
S. Tripathi, W.G. Chapman, Phys. Rev. Lett. 94, 087801 (2005)
D. Cao, J. Wu, J. Chem. Phys. 126, 144912 (2007)
H.-Y. Yu, D.L. Koch, Langmuir 26, 16801 (2010)
A. Chremos, A.Z. Panagiotopoulos, H.-Y. Yu, D.L. Koch, J. Chem. Phys. 135, 114901 (2011)
H.-Y. Yu, D.L. Koch, Langmuir 29, 8197 (2013)
H.-Y. Yu, S. Srivastava, L.A. Archer, D.L. Koch, Soft Matter 10, 9120 (2014)
A.B. Bourlinos, R. Herrera, N. Chalkias, D.D. Jiang, Q. Zhang, L.A. Archer, E.P. Giannelis, Adv. Mater. 17, 234 (2005)
A.B. Bourlinos, S. Ray Chowdhury, R. Herrera, D.D. Jiang, Q. Zhang, L.A. Archer, E.P. Giannelis, Adv. Funct. Mater. 15, 1285 (2005).
S. Srivastava, P. Agarwal, L.A. Archer, Langmuir 28, 6276 (2012)
A.L. Frischknecht, M.J. Hore, J. Ford, R.J. Composto, Macromolecules 46, 2856 (2013)
A.L. Frischknecht, J. Chem. Phys. 128, 224902 (2008)
M.J.A. Hore, R.J. Composto, Macromolecules 47, 875 (2014)
A.C. Balazs, C. Singh, E. Zhulina, Macromolecules 31, 8370 (1998)
A.C. Balazs, C. Singh, E. Zhulina, Y. Lyatskaya, Accounts Chem. Res. 32, 651 (1999)
Y. Lyatskaya, A.C. Balazs, Macromolecules 31, 6676 (1998)
V.V. Ginzburg, A.C. Balazs, Macromolecules 32, 5681 (1999)
V. Ginzburg, A. Balazs, Adv. Mater. 12, 1805 (2000)
V.V. Ginzburg, C. Singh, A.C. Balazs, Macromolecules 33, 1089 (2000)
P.K. Jog, V.V. Ginzburg, R. Srivastava, J.D. Weinhold, S. Jain, W.G. Chapman, in Advances in Chemical Engineering (Elsevier, 2010), p. 131
S. Jain, V.V. Ginzburg, P. Jog, J. Weinhold, R. Srivastava, W.G. Chapman, J. Chem. Phys. 131, 044908 (2009)
R.B. Thompson, V.V. Ginzburg, M.W. Matsen, A.C. Balazs, Science 292, 2469 (2001)
R.B. Thompson, V.V. Ginzburg, M.W. Matsen, A.C. Balazs, Macromolecules 35, 1060 (2002)
G. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers (Oxford University Press, 2006)
M.W. Matsen, F.S. Bates, Macromolecules 29, 1091 (1996)
A.C. Shi, in Developments in Block Copolymer Science and Technology, ed. by I.W. Hamley (Wiley-VCH, Weinheim, 2004)
F. Schmid, J Phys-Condens Mat 10, 8105 (1998)
S.F. Edwards, Proc. Phys. Soc. 85, 613 (1965)
P.J. Flory, J. Chem. Phys. 9, 660 (1941)
M.L. Huggins, J. Chem. Phys. 9, 440 (1941)
N.F. Carnahan, K.E. Starling, J. Chem. Phys. 51, 635 (1969)
M.R. Bockstaller, Y. Lapetnikov, S. Margel, E.L. Thomas, J. Am. Chem. Soc. 125, 5276 (2003)
B.J. Kim, J.J. Chiu, L. Bang, C.J. Hawker, D.J. Pine, E.J. Kramer, Abstr. Pap. Am. Chem. S. 230, U1066 (2005)
B.J. Kim, J.J. Chiu, G.R. Yi, D.J. Pine, E.J. Kramer, Adv. Mater. 17, 2618 (2005)
B.J. Kim, G.H. Fredrickson, C.J. Hawker, E.J. Kramer, Langmuir 23, 7804 (2007)
B.J. Kim, G.H. Fredrickson, E.J. Kramer, Macromolecules 41, 436 (2008)
J.Y. Lee, R.B. Thompson, D. Jasnow, A.C. Balazs, Macromolecules 35, 4855 (2002)
J.-Y. Lee, R.B. Thompson, D. Jasnow, A.C. Balazs, Phys. Rev. Lett. 89, 155503 (2002)
R.B. Thompson, J.Y. Lee, D. Jasnow, A.C. Balazs, Phys. Rev. E 66, 031801 (2002)
G.A. Buxton, J.Y. Lee, A.C. Balazs, Macromolecules 36, 9631 (2003)
J. Y. Lee, Z. Shou, and A. C. Balazs, Phys. Rev. Lett. 91 (2003)
J.Y. Lee, Z.Y. Shou, A.C. Balazs, Macromolecules 36, 7730 (2003)
J.Y. Lee, A.C. Balazs, R.B. Thompson, R.M. Hill, Macromolecules 37, 3536 (2004)
S. Tyagi, J.Y. Lee, G.A. Buxton, A.C. Balazs, Macromolecules 37, 9160 (2004)
X. Yu et al., Proc. Natl. Acad. Sci. 110, 10078 (2013)
B. Ni, X.-H. Dong, Z. Chen, Z. Lin, Y. Li, M. Huang, Q. Fu, S.Z. Cheng, W.-B. Zhang, Polym. Chem. 5, 3588 (2014)
W. Zhang, Y. Liu, J. Huang, T. Liu, W. Xu, S. Cheng, X. Dong, Soft Matter 15, 7108 (2019)
T. Zhang, C. Fu, Y. Yang, F. Qiu, J. Chem. Phys. 146, 054902 (2017)
S.C. Glotzer, M.A. Horsch, C.R. Iacovella, Z. Zhang, E.R. Chan, X. Zhang, Curr. Opin. Colloid in 10, 287 (2005)
B. Zhang, X. Ye, B.J. Edwards, J. Chem. Phys. 139, 244909 (2013)
T. Zhang, C. Fu, Y. Yang, F. Qiu, Macromolecules 51, 1654 (2018)
Y. Wang, J. Cui, Y. Han, W. Jiang, Langmuir 35, 468 (2019)
M.G. Moffitt, J. Phys. Chem. Lett. 4, 3654 (2013)
P. Akcora et al., Nat. Mater. 8, 354 (2009)
I. Borukhov, L. Leibler, Macromolecules 35, 5171 (2002)
A. Jayaraman, J. Polym. Sci. B: Polym. Phys. 51, 524 (2013)
V. Ganesan, C.J. Ellison, V. Pryamitsyn, Soft Matter 6, 4010 (2010)
V. Pryamtisyn, V. Ganesan, A.Z. Panagiotopoulos, H. Liu, S.K. Kumar, J. Chem. Phys. 131, 221102 (2009)
V.V. Ginzburg, Macromolecules 46, 9798 (2013)
H. Koerner, L. Drummy, B. Benicewicz, L. Yu, R. Vaia, Acs Macro Lett. 2, 670 (2013)
J. Lee, Z. Wang, J. Zhang, J. Yan, T. Deng, Y. Zhao, K. Matyjaszewski, M.R. Bockstaller, Macromolecules (2020)
V.V. Ginzburg, Macromolecules 50, 9445 (2017)
V. Goel, J. Pietrasik, H.C. Dong, J. Sharma, K. Matyjaszewski, R. Krishnamoorti, Macromolecules 44, 8129 (2011)
K. Hong, J. Noolandi, Macromolecules 14, 1229 (1981)
K. Chen, H.-S. Li, B.-K. Zhang, J. Li, W.-D. Tian, Sci. Rep.-Uk 6, 20355 (2016)
G. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers, vol. 134 (Oxford University Press on Demand, 2006)
V. Ginzburg, J. Weinhold, P. Hustad, P. Trefonas, B. Kim, N. Laachi, and G. Fredrickson, in Directed Self-assembly of Block Co-polymers for Nano-manufacturing (Elsevier, 2015), p. 67
A. Arora, D.C. Morse, F.S. Bates, K.D. Dorfman, J. Chem. Phys. 146, 244902 (2017)
A. Arora, J. Qin, D.C. Morse, K.T. Delaney, G.H. Fredrickson, F.S. Bates, K.D. Dorfman, Macromolecules 49, 4675 (2016)
F.S. Bates, G.H. Fredrickson, Phys. Today 52, 32 (1999)
Acknowledgements
I am thankful to Dow for supporting this work and gratefully acknowledge Drs. Jeffrey Weinhold and Jian Yang for helpful discussions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ginzburg, V.V. (2021). Density Functional Theory-Based Modeling of Polymer Nanocomposites. In: Ginzburg, V.V., Hall, L.M. (eds) Theory and Modeling of Polymer Nanocomposites. Springer Series in Materials Science, vol 310. Springer, Cham. https://doi.org/10.1007/978-3-030-60443-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-60443-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-60442-4
Online ISBN: 978-3-030-60443-1
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)