High Charge Density Coacervate Assembly via Hybrid Monte Carlo Single Chain in Mean Field Theory

Macromolecules

Volumn 49, Issue 24, 2016, Pages 9693-9705

  Lytle, Tyler K ^a   Radhakrishna, Mithun ^b   Sing, Charles E ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY GANDHINAGAR   (India)

Author keywords

[No Author keywords available]

Indexed keywords

BIOPOLYMERS; CHAINS; FREE ENERGY; INTELLIGENT SYSTEMS; IONIC STRENGTH; MEAN FIELD THEORY; PHASE SEPARATION; POLYELECTROLYTES; POLYMERS; SELF ASSEMBLY; SOLUTIONS;

ASSOCIATIVE PHASE SEPARATIONS; COARSE-GRAINED DESCRIPTION; COMPLEX COACERVATION; FREE ENERGY LANDSCAPE; MEAN-FIELD CALCULATIONS; OPPOSITELY CHARGED POLYELECTROLYTES; POLY(STYRENE SULFONATE); THERMODYNAMIC INFORMATION;

MONTE CARLO METHODS;

EID: 85008313705     PISSN: 00249297     EISSN: 15205835     Source Type: Journal    
DOI: 10.1021/acs.macromol.6b02159     Document Type: Article

References (108)

1. Israelachvili, J. N. Intermolecular and Surface Forces, 3 rd ed.; Academic Press: Waltham, MA, 2011.
2. Bungenberg de Jong, H. B.; Kruyt, H. R. Coacervation (Partial Miscibility in Colloid Systems) Proc. Sect. Sci, Koninkijke Nederlandse Akademie van Wetenschappen 1929, 32, 849-856
3. Michaeli, I.; Overbeek, J. Th. G.; Voorn, M. J. Phase separation of polyelectrolyte solutions J. Polym. Sci. 1957, 23, 443-450 10.1002/pol.1957.1202310337
4. Spruijt, E.; Westphal, A. H.; Borst, J. W.; Cohen Stuart, M. A.; van der Gucht, J. Binodal Compositions of Polyelectrolyte Complexes Macromolecules 2010, 43, 6476-6484 10.1021/ma101031t
5. Sing, C. E. Development of the modern theory of polymeric complex coacervation Adv. Colloid Interface Sci. 2016, 10.1016/j.cis.2016.04.004
6. Srivastava, S.; Tirrell, M. V. Polyelectrolyte Complexation Adv. Chem. Phys. 2016, 161, 499-544 10.1002/9781119290971.ch7
7. Castelnovo, M.; Joanny, J.-F. Formation of Polyelectrolyte Multilayers Langmuir 2000, 16, 7524-7532 10.1021/la000211h
8. Hammond, P. T. Form and function in multilayer assembly: New applications at the nanoscale Adv. Mater. 2004, 16, 1271-1293 10.1002/adma.200400760
9. Sukhishvili, S. A.; Kharlampieva, E.; Izumrudov, V. Where Polyelectrolyte Multilayers and Polyelectrolyte Complexes Meet Macromolecules 2006, 39, 8873-8881 10.1021/ma061617p
10. Jeon, J.; Dobrynin, A. V. Molecular Dynamics Simulations of Polyampholyte-Polyelectrolyte Complexes in Solutions Macromolecules 2005, 38, 5300-5312 10.1021/ma050303j
11. Ou, Z.; Muthukumar, M. Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations J. Chem. Phys. 2006, 124, 154902 10.1063/1.2178803
12. de Vries, R.; Cohen Stuart, M. Theory and simulations of macroion complexation Curr. Opin. Colloid Interface Sci. 2006, 11, 295-301 10.1016/j.cocis.2006.09.004
13. Wang, Q.; Schlenoff, J. B. The Polyelectrolyte Complex/Coacervate Continuum Macromolecules 2014, 47, 3108-3116 10.1021/ma500500q
14. Hoffmann, K. Q.; Perry, S. L.; Leon, L.; Priftis, D.; Tirrell, M.; de Pablo, J. J. A molecular view of the role of chirality in charge-driven polypeptide complexation Soft Matter 2015, 11, 1525-1538 10.1039/C4SM02336F
15. Perry, S. L.; Leon, L.; Hoffmann, K. Q.; Kade, M. J.; Priftis, D.; Black, K. A.; Wong, D.; Klein, R. A.; Pierce, C. F.; Margossian, K. O.; Whitmer, J. K.; Qin, J.; de Pablo, J. J.; Tirrell, M. Chirality-selected phase behaviour in ionic polypeptide complexes Nat. Commun. 2015, 6, 6052 10.1038/ncomms7052
16. Weinbreck, F.; de Vries, R.; Schrooyen, P.; de Kruif, C. G. Complex Coacervation of Whey Proteins and Gum Arabic Biomacromolecules 2003, 4, 293-303 10.1021/bm025667n
17. Biesheuvel, P. M.; Cohen Stuart, M. A. Electrostatic Free Energy of Weakly Charged Macromolecules in Solution and Intermacromolecular Complexes Consisting of Oppositely Charged Polymers Langmuir 2004, 20, 2785-2791 10.1021/la036204l
18. de Kruif, C. G.; Weinbreck, F.; de Vries, R. Complex coacervation of proteins and anionic polysaccharides Curr. Opin. Colloid Interface Sci. 2004, 9, 340-349 10.1016/j.cocis.2004.09.006
19. van der Gucht, J.; Spruijt, E.; Lemmers, M.; Cohen Stuart, M. A. Polyelectrolyte complexes: bulk phases and colloidal systems J. Colloid Interface Sci. 2011, 361, 407-422 10.1016/j.jcis.2011.05.080
20. Priftis, D.; Laugel, N.; Tirrell, M. Thermodynamic characterization of polypeptide complex coacervation Langmuir 2012, 28, 15947-15957 10.1021/la302729r
21. Priftis, D.; Farina, R.; Tirrell, M. Interfacial energy of polypeptide complex coacervates measured via capillary adhesion Langmuir 2012, 28, 8721-9 10.1021/la300769d
22. Priftis, D.; Tirrell, M. Phase behaviour and complex coacervation of aqueous polypeptide solutions Soft Matter 2012, 8, 9396 10.1039/C2SM25604E
23. Shamoun, R. F.; Reisch, A.; Schlenoff, J. B. Extruded Saloplastic Polyelectrolyte Complexes Adv. Funct. Mater. 2012, 22, 1923-1931 10.1002/adfm.201102787
24. Chollakup, R.; Beck, J. B.; Dirnberger, K.; Tirrell, M.; Eisenbach, C. D. Polyelectrolyte molecular weight and salt effects on the phase behavior and coacervation of aqueous solutions of poly(acrylic acid) sodium salt and poly(allylamine) hydrochloride Macromolecules 2013, 46, 2376-2390 10.1021/ma202172q
25. Ghostine, R. A.; Shamoun, R. F.; Schlenoff, J. B. Doping and Diffusion in an Extruded Saloplastic Polyelectrolyte Complex Macromolecules 2013, 46, 4089-4094 10.1021/ma4004083
26. Perry, S. L.; Li, Y.; Priftis, D.; Leon, L.; Tirrell, M. The effect of salt on the complex coacervation of vinyl polyelectrolytes Polymers 2014, 6, 1756-1772 10.3390/polym6061756
27. Priftis, D.; Xia, X.; Margossian, K. O.; Perry, S. L.; Leon, L.; Qin, J.; De Pablo, J. J.; Tirrell, M. Ternary, tunable polyelectrolyte complex fluids driven by complex coacervation Macromolecules 2014, 47, 3076-3085 10.1021/ma500245j
28. Salehi, A.; Desai, P. S.; Li, J.; Steele, C. A.; Larson, R. G. Relationship between Polyelectrolyte Bulk Complexation and Kinetics of Their Layer-by-Layer Assembly Macromolecules 2015, 48, 400-409 10.1021/ma502273a
29. Fu, J.; Schlenoff, J. B. Driving Forces for Oppositely Charged Polyion Association in Aqueous Solutions: Enthalpic, Entropic, but Not Electrostatic J. Am. Chem. Soc. 2016, 138, 980-990 10.1021/jacs.5b11878
30. Obermeyer, A. C.; Mills, C. E.; Dong, X. H.; Flores, R. J.; Olsen, B. D. Complex coacervation of supercharged proteins with polyelectrolytes Soft Matter 2016, 12, 3570 10.1039/C6SM00002A
31. Bella, E. Y.; Firestone, W.; Langer, R.; Kohane, D. S. Complex coacervates for thermally sensitivity controlled release of flavor compounds J. Agric. Food Chem. 2005, 53, 7518-7525 10.1021/jf0507947
32. Turgeon, S. L.; Schmitt, C.; Sanchez, C. Protein-polysaccharide complexes and coacervates Curr. Opin. Colloid Interface Sci. 2007, 12, 166-178 10.1016/j.cocis.2007.07.007
33. Schmitt, C.; Turgeon, S. L. Protein/polysaccharide complexes and coacervates in food systems Adv. Colloid Interface Sci. 2011, 167, 63-70 10.1016/j.cis.2010.10.001
34. Black, K. A.; Priftis, D.; Perry, S. L.; Yip, J.; Byun, W. Y.; Tirrell, M. Protein Encapsulation via Polypeptide Complex Coacervation ACS Macro Lett. 2014, 3, 1088-1091 10.1021/mz500529v
35. Hwang, D. S.; Waite, J. H.; Tirrell, M. Promotion of osteoblast proliferation on complex coacervation-based hyaluronic acid-recombinant mussel adhesive protein coatings on titanium Biomaterials 2010, 31, 1080-1084 10.1016/j.biomaterials.2009.10.041
36. Stewart, R. J.; Wang, C. S.; Shao, H. Complex coacervates as a foundation for synthetic underwater adhesives Adv. Colloid Interface Sci. 2011, 167, 85-93 10.1016/j.cis.2010.10.009
37. Lim, S.; Moon, D.; Kim, H. J.; Seo, J. H.; Kang, I. S.; Cha, H. J. Interfacial tension of complex coacervated mussel adhesive protein according to the hofmeister series Langmuir 2014, 30, 1108-1115 10.1021/la403680z
38. Feldstein, M. M.; Dormidontova, E. E.; Khokhlov, A. R. Pressure sensitive adhesives based on interpolymer complexes Prog. Polym. Sci. 2015, 42, 79-153 10.1016/j.progpolymsci.2014.10.006
39. Hwang, D. S.; Zeng, H.; Srivastava, A.; Krogstad, D. V.; Tirrell, M.; Israelachvili, J. N.; Waite, J. H. Viscosity and interfacial properties in a mussel-inspired adhesive coacervate Soft Matter 2010, 6, 3232 10.1039/c002632h
40. Keating, C. D. Aqueous phase separation as a possible route to compartmentalization of biological molecules Acc. Chem. Res. 2012, 45, 2114-2124 10.1021/ar200294y
41. Brangwynne, C. P. Phase transitions and size scaling of membrane-less organelles J. Cell Biol. 2013, 203, 875-881 10.1083/jcb.201308087
42. Audus, D. J.; Gopez, J. D.; Krogstad, D. V.; Lynd, N. A.; Kramer, E. J.; Hawker, C. J.; Fredrickson, G. H. Phase behavior of electrostatically complexed polyelectrolyte gels using an embedded fluctuation model Soft Matter 2015, 11, 1214-1225 10.1039/C4SM02299H
43. Cohen Stuart, M. A.; Besseling, N. A. M.; Fokkink, R. G. Formation of Micelles with Complex Coacervate Cores Langmuir 1998, 14, 6846-6849 10.1021/la980778m
44. Fan, Y.; Tang, S.; Thomas, E. L.; Olsen, B. D. Responsive block copolymer photonics triggered by protein-polyelectrolyte coacervation ACS Nano 2014, 8, 11467-73 10.1021/nn504565r
45. Harada, A.; Kataoka, K. Formation of Polyion Complex Micelles in an Aqueous Milieu from a Pair of Oppositely-Charged Block Copolymers with Poly(ethylene glycol) Segments Macromolecules 1995, 28, 5294-5299 10.1021/ma00119a019
46. Harada, A.; Kataoka, K. Chain Length Recognition: Core-Shell Supramolecular Assembly from Oppositely Charged Block Copolymers Science 1999, 283, 65-67 10.1126/science.283.5398.65
47. Hunt, J. N.; Feldman, K. E.; Lynd, N. A.; Deek, J.; Campos, L. M.; Spruell, J. M.; Hernandez, B. M.; Kramer, E. J.; Hawker, C. J. Tunable, high modulus hydrogels driven by ionic coacervation Adv. Mater. 2011, 23, 2327-2331 10.1002/adma.201004230
48. Krogstad, D. V.; Lynd, N. A.; Choi, S.-H.; Spruell, J. M.; Hawker, C. J.; Kramer, E. J.; Tirrell, M. V. Effects of Polymer and Salt Concentration on the Structure and Properties of Triblock Copolymer Coacervate Hydrogels.pdf Macromolecules 2013, 46, 1512-1518 10.1021/ma302299r
49. Ortony, J. H.; Choi, S.-H.; Spruell, J. M.; Hunt, J. N.; Lynd, N. A.; Krogstad, D. V.; Urban, V. S.; Hawker, C. J.; Kramer, E. J.; Han, S. Fluidity and water in nanoscale domains define coacervate hydrogels Chem. Sci. 2014, 5, 58-67 10.1039/C3SC52368C
50. Pergushov, D. V.; Müller, A. H. E.; Schacher, F. H. Micellar Interpolyelectrolyte Complexes Chem. Soc. Rev. 2012, 41, 6888 10.1039/c2cs35135h
51. Van Der Kooij, H. M.; Spruijt, E.; Voets, I. K.; Fokkink, R.; Cohen Stuart, M. A.; Van Der Gucht, J. On the stability and morphology of complex coacervate core micelles: From spherical to wormlike micelles Langmuir 2012, 28, 14180-14191 10.1021/la303211b
52. Voets, I. K.; de Keizer, A.; Cohen Stuart, M. A. Complex coacervate core micelles Adv. Colloid Interface Sci. 2009, 147-148, 300-18 10.1016/j.cis.2008.09.012
53. Krogstad, D. V.; Choi, S.-H.; Lynd, N. A.; Audus, D. J.; Perry, S. L.; Gopez, J. D.; Hawker, C. J.; Kramer, E. J.; Tirrell, M. V. Small Angle Neutron Scattering Study of Complex Coacervate Micelles and Hydrogels Formed from Ionic Diblock and Triblock Copolymers J. Phys. Chem. B 2014, 118, 13011-13018 10.1021/jp509175a
54. Overbeek, J. T.; Voorn, M. J. Phase separation in polyelectrolyte solutions; theory of complex coacervation J. Cell. Comp. Physiol. 1957, 49, 7-22 10.1002/jcp.1030490404
55. Veis, A.; Aranyi, C. Phase separation in polyelectrolyte systems. I. Complex coacervates of gelatin J. Phys. Chem. 1960, 64, 1203-1210 10.1021/j100838a022
56. Tainaka, K.-I. Effect of counterions on complex coacervation Biopolymers 1980, 19, 1289-1298 10.1002/bip.1980.360190705
57. Castelnovo, M.; Joanny, J. F. Complexation between oppositely charged polyelectrolytes: Beyond the Random Phase Approximation Eur. Phys. J. E: Soft Matter Biol. Phys. 2001, 6, 377-386 10.1007/s10189-001-8051-7
58. Kudlay, A.; Ermoshkin, A. V.; Olvera de la Cruz, M. Complexation of oppositely charged polyelectrolytes: effect of ion pair formation Macromolecules 2004, 37, 9231-9241 10.1021/ma048519t
59. Kudlay, A.; Olvera de la Cruz, M. Precipitation of oppositely charged polyelectrolytes in salt solutions J. Chem. Phys. 2004, 120, 404-12 10.1063/1.1629271
60. Popov, Y. O.; Lee, J.; Fredrickson, G. H. Field-theoretic simulations of polyelectrolyte complexation J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 3223-3230 10.1002/polb.21334
61. Lee, J.; Popov, Y. O.; Fredrickson, G. H. Complex coacervation: A field theoretic simulation study of polyelectrolyte complexation J. Chem. Phys. 2008, 128, 224908 10.1063/1.2936834
62. Riggleman, R. A.; Kumar, R.; Fredrickson, G. H. Investigation of the interfacial tension of complex coacervates using field-theoretic simulations J. Chem. Phys. 2012, 136, 024903 10.1063/1.3674305
63. Qin, J.; Priftis, D.; Farina, R.; Perry, S. L.; Leon, L.; Whitmer, J.; Hoffmann, K.; Tirrell, M.; De Pablo, J. J. Interfacial tension of polyelectrolyte complex coacervate phases ACS Macro Lett. 2014, 3, 565-568 10.1021/mz500190w
64. Perry, S. L.; Sing, C. E. PRISM-Based Theory of Complex Coacervation: Excluded Volume versus Chain Correlation Macromolecules 2015, 48, 5040-5053 10.1021/acs.macromol.5b01027
65. Qin, J.; De Pablo, J. J. Criticality and connectivity in macromolecular charge complexation Macromolecules 2016, 49, 8789 10.1021/acs.macromol.6b02113
66. Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953.
67. McQuarrie, D. A. Statistical Mechanics; University Science Books: Sausalito, CA, 2000.
68. Borue, V. Y.; Erukhimovich, I. Y. A Statistical-Theory of Globular Polyelectrolyte Complexes Macromolecules 1990, 23, 3625-3632 10.1021/ma00217a015
69. Fredrickson, G. H.; Ganesan, V.; Drolet, F. Field-theoretic computer simulation methods for polymers and complex fluids Macromolecules 2002, 35, 16-39 10.1021/ma011515t
70. Fredrickson, G. H. The Equilibrium Theory of Inhomogeneous Polymers; Oxford University Press: Oxford, 2006.
71. Manning, G. S. Limiting laws and counterion condensation in polyelectroyte solutions. I. Colligative properties J. Chem. Phys. 1969, 51, 924-933 10.1063/1.1672157
72. Muthukumar, M. Theory of counter-ion condensation on flexible polyelectrolytes: Adsorption mechanism J. Chem. Phys. 2004, 120, 9343-9350 10.1063/1.1701839
73. Peng, B.; Muthukumar, M. Modeling competitive substitution in a polyelectrolyte complex J. Chem. Phys. 2015, 143, 243133 10.1063/1.4936256
74. Radhakrishna, M.; Sing, C. E. Charge Correlations for Precise, Coulombically Driven Self Assembly Macromol. Chem. Phys. 2016, 217, 126-136 10.1002/macp.201500278
75. Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Elsevier: Boston, MA, 2006.
76. Frenkel, D.; Smit, B. Understanding Molecular Simulation, 2 nd ed.; Academic Press: San Diego, CA, 2001.
77. Detcheverry, F. A.; Kang, H.; Daoulas, K. C.; Müller, M.; Nealey, P. F.; De Pablo, J. J. Monte Carlo Simulations of a Coarse Grain Model for Block Copolymers and Nanocomposites Macromolecules 2008, 41, 4989-5001 10.1021/ma702514v
78. Pike, D. Q.; Detcheverry, F. A.; Müller, M.; De Pablo, J. J. Theoretically informed coarse grain simulations of polymeric systems J. Chem. Phys. 2009, 131, 084903 10.1063/1.3187936
79. Daoulas, K. C.; Müller, M. Single chain in mean field simulations: Quasi-instantaneous field approximation and quantitative comparison with Monte Carlo simulations J. Chem. Phys. 2006, 125, 184904 10.1063/1.2364506
80. Detcheverry, F. A.; Pike, D. Q.; Nealey, P. F.; Müller, M.; de Pablo, J. J. Monte Carlo Simulation of Coarse Grain Polymeric Systems Phys. Rev. Lett. 2009, 102, 197801 10.1103/PhysRevLett.102.197801
81. Daoulas, K. C.; Müller, M.; De Pablo, J. J.; Nealey, P. F.; Smith, G. D. Morphology of multi-component polymer systems: single chain in mean field simulation studies Soft Matter 2006, 2, 573-583 10.1039/B602610A
82. Yakub, E.; Ronchi, C. An efficient method for computation of long-ranged Coulomb forces in computer simulation of ionic fluids J. Chem. Phys. 2003, 119, 11556 10.1063/1.1624364
83. Jha, P. K.; Sknepnek, R.; Guerrero-Garcia, G. I.; Olvera de la Cruz, M. A Graphics Processing Unit Implementation of Coulomb Interaction in Molecular Dynamics J. Chem. Theory Comput. 2010, 6, 3058-3065 10.1021/ct100365c
84. Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1989.
85. Kumar, S. K.; Szleifer, I.; Panagiotopoulos, A. Z. Determination of the chemical potentials of polymeric systems from monte carlo simulations Phys. Rev. Lett. 1991, 66, 2935-2938 10.1103/PhysRevLett.66.2935
86. Sheng, Y. J.; Panagiotopoulos, A. Z.; Kumar, S. K.; Szleifer, I. Monte Carlo Calculation of Phase Equilibria for a Bead-Spring Polymeric Model Macromolecules 1994, 27, 400-406 10.1021/ma00080a012
87. Towns, J.; Cockerill, T.; Dahan, M.; Foster, I.; Gaither, K.; Grimshaw, A.; Hazlewood, V.; Lathrop, S.; Lifka, D.; Peterson, G. D.; Roskies, R.; Scott, J. R.; Wilkens-Diehr, N. XSEDE: Accelerating Scientific Discovery Comput. Sci. Eng. 2014, 16, 62-74 10.1109/MCSE.2014.80
88. Panagiotopoulos, A. Z. Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble Mol. Phys. 1987, 61, 813-826 10.1080/00268978700101491
89. De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979.
90. Riggleman, R. A.; Fredrickson, G. H. Field-theoretic simulations in the Gibbs ensemble J. Chem. Phys. 2010, 132, 024104 10.1063/1.3292004
91. Krogstad, D. V.; Lynd, N. A.; Miyajima, D.; Gopez, J. D.; Hawker, C. J.; Kramer, E. J.; Tirrell, M. V. Structural Evolution of Polyelectrolyte Complex Core Micelles and Ordered-Phase Bulk Materials Macromolecules 2014, 47, 8026-8032 10.1021/ma5017852
92. Sanoja, G. E.; Popere, B. C.; Beckingham, B. S.; Evans, C. M.; Lynd, N. A.; Segalman, R. A. Structure-Conductivity Relationships of Block Copolymer Membranes Based on Hydrated Protic Polymerized Ionic Liquids: Effect of Domain Spacing Macromolecules 2016, 49, 2216-2223 10.1021/acs.macromol.5b02614
93. Evans, C. M.; Sanoja, G.; Popere, B. C.; Segalman, R. A. Anhydrous Proton Transport in Polyemrized Ionic Liquid Block Copolymers: Roles of Block Length, Ionic Content, and Confinement Macromolecules 2016, 49, 395-404 10.1021/acs.macromol.5b02202
94. Sing, C. E.; Zwanikken, J. W.; Olvera de la Cruz, M. Electrostatic control of block copolymer morphology Nat. Mater. 2014, 13, 694-698 10.1038/nmat4001
95. Sing, C. E.; Zwanikken, J. W.; de la Cruz, M. O. Theory of melt polyelectrolyte blends and block copolymers: Phase behavior, surface tension, and microphase periodicity J. Chem. Phys. 2015, 142, 034902 10.1063/1.4905830
96. Nakamura, I.; Wang, Z.-G. Salt-doped block copolymers: ion distribution, domain spacing and effective χ parameter Soft Matter 2012, 8, 9356 10.1039/c2sm25606a
97. Hamley, I. W.; Castelletto, V.; Lu, Z. B.; Imrie, C. T.; Itoh, T.; Al-Hussein, M. Interplay between Smectic Ordering and Microphase Separation in a Series of Side-Group Liquid-Crystal Block Copolymers Macromolecules 2004, 37, 4798-4807 10.1021/ma0498619
98. Majewski, P. W.; Gopinadhan, M.; Jang, W.-S.; Lutkenhaus, J. L.; Osuji, C. O. Anisotropic ionic conductivity in block copolymer membranes by magnetic field alignment J. Am. Chem. Soc. 2010, 132, 17516-17522 10.1021/ja107309p
99. Milner, S. T.; Witten, T. A.; Cates, M. E. Theory of the grafted polymer brush Macromolecules 1988, 21, 2610-2619 10.1021/ma00186a051
100. Brettmann, B. K.; Laugel, N.; Hoffmann, N.; Pincus, P.; Tirrell, M. V. Bridging contributions to polyelectrolyte brush collapse in multivalent salt solutions J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 284-291 10.1002/pola.27959
101. Sing, C. E.; Zwanikken, J. W.; de la Cruz, M. O. Interfacial Behavior in Polyelectrolyte Blends: Hybrid Liquid-State Integral Equation and Self-Consistent Field Theory Study Phys. Rev. Lett. 2013, 111, 168303 10.1103/PhysRevLett.111.168303
102. Sing, C. E.; Zwanikken, J. W.; Olvera De La Cruz, M. Ion correlation-induced phase separation in polyelectrolyte blends ACS Macro Lett. 2013, 2, 1042-1046 10.1021/mz400511r
103. Sing, C. E.; Olvera de la Cruz, M. Polyelectrolyte Blends and Nontrivial Behavior in Effective Flory-Huggins Parameters ACS Macro Lett. 2014, 3, 698-702 10.1021/mz500202n
104. Kwon, H.-K.; Zwanikken, J. W.; Shull, K. R.; Olvera de la Cruz, M. Theoretical Analysis of Multiple Phase Coexistence in Polyelectrolyte Blends Macromolecules 2015, 48, 6008-6015 10.1021/acs.macromol.5b00901
105. Nakamura, I.; Balsara, N. P.; Wang, Z.-G. Thermodynamics of Ion-Containing Polymer Blends and Block Copolymers Phys. Rev. Lett. 2011, 107, 1-5 10.1103/PhysRevLett.107.198301
106. Ren, C.-L.; Nakamura, I.; Wang, Z.-G. Effects of Ion-Induced Cross-Linking on the Phase Behavior in Salt-Doped Polymer Blends Macromolecules 2016, 49, 425-431 10.1021/acs.macromol.5b02229
107. Brown, J. R.; Seo, Y.; Maula, T. A. D.; Hall, L. M. Fluids density functional theory and initializing molecular dynamics simulations of block copolymers J. Chem. Phys. 2016, 144, 124904 10.1063/1.4943982
108. Seo, Y.; Brown, J. R.; Hall, L. M. Effect of tapering on morphology and interfacial behavior of diblock copolymers from molecular dynamics simulations Macromolecules 2015, 48, 4974-4982 10.1021/ma502309h