Zhen-Gang Wang Publications List

  1. A. Li, Z.-G. Wang, P. Zhang, “Conformation and Energetics in Asymmetric Polyelectrolyte Complexation,” ACS Appl. Polym. Mater.  8, 15, 12695-12708 (2026)
  2. Z. Wang, Y. Lu, L. An, Z.-G. Wang, “Topological Friction: Insight from Dynamics of a Test Chain in a Fixed-Topology Polymer Network,” Phys. Rev. Lett. 136, 248101 (2026)
  3. S. Varner, P. J. Walker, A. Venkatachalam, B. Zhuang, Z.-G. Wang, “Stockmayer fluid with a shifted dipole. II. Interfacial behavior,” J. Chem. Phys. 164, 18, 184512 (2026)
  4. P. J. Walker, A. Venkatachalam, S. Varner, B. Zhuang, Z.-G. Wang, “Stockmayer fluid with a shifted dipole. I. Bulk behavior,” J. Chem. Phys. 164, 18, 184511 (2026)
  5. S. Varner, T. P. Lodge, and Z.-G. Wang, “Kinetic Pathways to Diblock Copolymer Micelles via Thin Film Dissolution and Cosolvent Variation,” Macromolecules 59, 9, 5122-5139 (2026).
  6. S. Chen, Z.-G. Wang, “Simulating highly entangled polymer melts using Gaussian soft-core potential,” J. Chem. Phys. 164, 15, 154902 (2026).
  7. D. Beyer, C. Holm, and Z.-G. Wang, “A Sequence-Specific Theory for Charge-Regulating IDPs,” The Journal of Physical Chemistry B 130, 16, 4325-4332 (2026).
  8. Y. Wang, P. Zhang, and Z.-G. Wang, “Interfacial Structure of Positively Charged Polypeptide Condensates,” Biomacromolecules 27, 5, 3267-3280 (2026).
  9. Z. Wu, Z.-G. Wang, and S. Chen, “Mixing protocols determine liquid–liquid phase separation dynamics in polyelectrolyte complex coacervation,” Nat. Commun. 17, 1580 (2026).
  10. Z. Wu, Z.-G. Wang, and S. Chen. “Mixing protocols determine liquid–liquid phase separation dynamics in polyelectrolyte complex coacervation,” Nat. Commun. 17, 1580 (2026). 
  11. H. Zhou, Z. Wu, L. Jiang, S. Chen, and Z.-G. Wang. “Sequence and length-scale dependent dynamics in biocondensates of highly charged disordered proteins,” Commun. Chem. 9, 98 (2026).
  12. S. Chen, and Z.-G. Wang, “Hydrodynamics in semidilute polyelectrolyte solutions and complex coacervates,” J. Chem. Phys. 163, 171101 (2025). 
  13. C.J. Stewart, A.J. Tsamopoulos, B.B. Ye, and Z.-G. Wang, “Chain dynamics and conductivity of polymerized ionic liquids: Effects of electrostatic correlation and chain length,” J. Chem. Phys. 163, 194904 (2025).
  14. P.J. Walker, and Z.-G. Wang, “Anomalous Phase Behavior of Polymer–Ionic Liquid Mixtures,” J. Phys. Chem. B 129, 12032–12041 (2025).
  15. D. Beyer, C. Holm, and Z.-G. Wang, “Charge regulation effects in weak polyelectrolyte complexation,” J. Phys. Chem. Lett. 16, 32, 8245–8251 (2025).
  16. A. Glisman, S. Mantha, D. Yu, E. P. Wasserman, S. Backer, L. Reyes, Z.-G. Wang, “Binding Modes and Water-Mediation of Polyelectrolyte Adsorption to a Neutral CaCO3 Surface”, Langmuir 40, 25931−25939 (2024).
  17. T. Zhou, D. Bruch, Z.-G. Wang, “Image charge effects under metal and dielectric boundary conditions”, Phys. Rev. E 110, 044129 (2024).
  18. Y. Dai, Z.-G. Wang, R. N. Zare, “Unlocking the electrochemical functions of biomolecular condensates”, Nat Chem Biol 20, 1420–1433 (2024).
  19. D. Bruch, Z.-G. Wang, “A model for zwitterionic polymers and their capacitance applications”, J. Chem. Phys. 161, 104901 (2024).
  20. Y. Basdogan, D. R. Pollard, T. Shastry, M. R. Carbone, S. K. Kumar, Z.-G. Wang, “Machine learning-guided discovery of polymer membranes for CO2 separation with genetic algorithm”, J. Membr. Sci. 712, 123169 (2024).
  21. S. Lee, P. J. Walker, S. J. Velling, A. Chen, Z. W. Taylor, C. J. B. M. Fiori, V. Gandhi, Z.-G. Wang, and J. R. Greer,  “Molecular control via dynamic bonding enables material responsiveness in additively manufactured metallo-polyelectrolytes”, Nat Commun 15, 6850 (2024).
  22. S. Varner, C. Balzer, and Z.-G. Wang, “A Jacobian-free pseudo-arclength continuation method for phase transitions in inhomogeneous thermodynamic systems”, J. Chem. Phys. 161, 064107 (2024).
  23. B. B. Ye, S. Chen, and Z.-G. Wang, “GCMe: Efficient Implementation of the Gaussian Core Model with Smeared Electrostatic Interactions for Molecular Dynamics Simulations of Soft Matter Systems”, J. Chem. Theory Comput. 20 (15), 6870-6880 (2024).
  24. P. J. Walker, A. Riedemann, and Z.-G. Wang, “GCIdentifier.jl: A Julia package for identifying molecular fragments from SMILES”, Journal of Open Source Software 9, 96: 6453 (2024).
  25. S. Mantha, A. Glisman, D. Yu, E. P. Wasserman, S. Backer, and Z.-G. Wang, “Adsorption isotherm and mechanism of Ca2+ binding to polyelectrolyte”, Langmuir 40, 6212-6219 (2024).
  26. Y. Ruan, Y. Lu, L. An, and Z.-G. Wang, “Multiple entanglements between two polymer chains: An analysis of primitive path based on Frenet trihedron”, Macromolecules 57, 2792-2800 (2024).
  27. A. J. Tsamopoulos and Z.-G. Wang, “Ion conductivity in salt-doped polymers: Combined effects of temperature and salt concentration”, ACS Macro Lett. 13, 322-327 (2024).
  28. A. Glisman, S. Mantha, D. Yu, E. P. Wasserman, S. Backer, and Z.-G. Wang, “Multivalent ion-mediated polyelectrolyte association and structure”, Macromolecules 57, 1941-1949 (2024).
  29. T. Shastry, Y. Basdogan, Z.-G. Wang, S. K. Kumar, and M. R. Carbone, “Machine learning-based discovery of molecular descriptors that control polymer gas permeation”, J. Membrane Sci. 697, 122563 (2024).
  30. S. Chen and Z.-G. Wang, “Charge asymmetry suppresses coarsening dynamics in polyelectrolyte complex coacervation”, Phys. Rev. Lett. 131, 218201 (2023) (Editor’s Suggestion).
  31. C. Balzer and Z.-G. Wang, “Electroresponse of weak polyelectrolyte brushes”, Eur. Phys. J. E 46, 82 (2023).
  32. R. Wang, V. V. Ginzburg, J. Jiang, and Z.-G. Wang, “Adsorption of a polyelectrolyte chain at dielectric surfaces: Effects of surface charge distribution and relative dielectric permittivity”, Macromolecules 56 (19), 7653-7662 (2023).
  33. S. Chen and Z.-G. Wang, “Using implicit-solvent potentials to extract water contributions to enthalpy–entropy compensation in biomolecular associations”, J. Phys. Chem. B 127, 6825-6832 (2023).
  34. K. D. Dorfman and Z.-G. Wang, “Liquid-like states in micelle-forming diblock copolymer melts”, ACS Macro Lett. 12, 980-985 (2023).
  35. S. Varner, C. Balzer, and Z.-G. Wang, “Entropic origin of ionic interactions in polar solvents”, J. Phys. Chem. B 127, 4328-4337 (2023).
  36. Z. Wang, Z.-G. Wang, A.-C. Shi, Y. Lu, and L. An, “Behaviors of a polymer chain in channels: From Zimm to Rouse dynamics”, Macromolecules 56, 2447-2453 (2023).
  37. P. Zhang, Z. Wang, and Z.-G. Wang, “Conformation transition of a homopolymer chain in binary mixed solvents”, Macromolecules 56, 153-165 (2023).
  38. S. Mantha, H. Chao, A. S. Ylitalo, T. C. Fitzgibbons, W. Zhou, V. V. Ginzburg, and Z.-G. Wang, “Surfactant in a polyol–CO2 mixture: Insights from a classical density functional theory study“, Langmuir 38, 16172-16182 (2022).
  39. S. Varner and Z.-G. Wang, “Effect of dilutions in ionic liquid supercapacitors“, Phys. Chem. Chem. Phys. 24, 27362-27374 (2022).
  40. A. Ghosh, Q. MacPherson, Z.-G. Wang, and A. J. Spakowitz, “Semiflexible polymer solutions. II. Fluctuations and Frank elastic constants“, J. Chem. Phys. 157, 154906 (2022).
  41. A. S. Ylitalo, H. Chao, P. J. Walker, J. Crosthwaite, T. C. Fitzgibbons, V. V. Ginzburg, W. Zhou, Z.-G. Wang, E. Di Maio, and J. Kornfield, “Competition between CO2-philicity and mixing entropy leads to CO2 solubility maximum in polyether polyols“, Ind. Eng. Chem. Res. 61, 12835-12844 (2022).
  42. S. Chen and Z.-G. Wang, “Driving force and pathway in polyelectrolyte complex coacervation“, Proc. Nat. Acad. Sci. 119, e2209975119 (2022).
  43. C. Balzer, P. Zhang, and Z.-G. Wang, “Wetting behavior of polyelectrolyte complex coacervates on solid surfaces“, Soft Matter 18, 6326-6339 (2022)
  44. P. Zhang and Z.-G. Wang, “Supernatant phase in polyelectrolyte complex coacervation: Cluster formation, binodal, and nucleation“, Macromolecules 55, 3910-3923 (2022).
  45. S. Chen, P. Zhang, and Z.-G. Wang, “Complexation between oppositely charged polyelectrolytes in dilute solution: Effects of charge asymmetry“, Macromolecules 55, 3898-3909 (2022).
  46. B. B. Ye and Z.-G. Wang, “A coarse-grained model of room-temperature ionic liquids between metal electrodes: A molecular dynamics study“, Phys. Chem. Chem. Phys. 24, 11573-11584 (2022).
  47. D. Bruch, C. Balzer, and Z.-G. Wang, “Thermodynamics of electrolyte solutions near charged surfaces: Constant surface charge vs constant surface potential“, J. Chem. Phys. 156, 174704 (2022).
  48. B. Mei, B. Zhuang, Y. Lu, L. An, and Z.-G. Wang, “Local-average free volume correlates with dynamics in glass formers“, J. Phys. Chem. Lett. 13, 3957-3964 (2022).
  49. Z. Wang, R. Wang, Y. Lu, L. An, A.-C. Shi, and Z.-G. Wang, “Mechanisms of flow-induced polymer translocation“, Macromolecules 55, 3602-3612 (2022).
  50. A. Ylitalo, C. Balzer, P. Zhang, and Z.-G. Wang, “Electrostatic correlations and temperature-dependent dielectric constant can model LCST in polyelectrolyte complex coacervation“, Macromolecules 54, 11326-11337 (2021).
  51. Y. Xu and Z.-G. Wang, “Coil-to-globule transition in polymeric solvents“, Macromolecules 54, 10984-10993 (2021).
  52. P. Zhang and Z.-G. Wang, “Interfacial structure and tension of polyelectrolyte complex coacervates“, Macromolecules 54, 10994-11007 (2021).
  53. Y. Ruan, Y. Lu, L. An, and Z.-G. Wang,”Shear banding in entangled polymers: Stress plateau, banding location, and lever rule“, ACS Macro Lett. 10, 1517-1523 (2021).
  54. C. Balzer, L. Qing, and Z.-G. Wang, “Preferential ion adsorption in blue energy applications“, ACS Sustainable Chem. Eng. 9, 9230-9239 (2021).
  55. Z. Lian, H. Chao, and Z.-G. Wang, “Effects of confinement and ion adsorption in ionic liquid supercapacitors with nanoporous electrodes“, ACS Nano 15, 11724-11733 (2021).
  56. C. Balzer, J. Jiang, R. L. Marson, V. V. Ginzburg, and Z.-G. Wang, “Nonelectrostatic adsorption of polyelectrolytes and mediated interactions between solid surfaces“, Langmuir 37, 5483–5493 (2021).
  57. C. Y. Son and Z.-G. Wang, “Image-charge effects on ion adsorption near aqueous interfaces“, Proc. Nat. Acad. Sci. 118, e2020615118 (2021).
  58. B. Zhuang, G. Ramanauskaite, Z. Y. Koa, and Z.-G. Wang. “Like dissolves like: A first-principles theory for predicting liquid miscibility and mixture dielectric constant“, Science Advances 7, eabe7275 (2021).
  59. L. Qing, S. Zhao, and Z.-G. Wang, “Surface charge density in electrical double layer capacitors with nanoscale cathode–anode separation“, J. Phys. Chem. B 125, 625-636 (2021).
  60. M. Li, B. Zhuang, Y. Lu, L. An, and Z.-G. Wang, “Salt-induced liquid-liquid phase separation: Combined experimental and theoretical investigation of water–acetonitrile–salt mixtures“, J. Am. Chem. Soc. 143, 773-784 (2021).
  61. P. Zhang, N. M. Alsaifi, and Z.-G. Wang, “Revisiting the Θ point“, Macromolecules 53, 10409-10420 (2020).
  62. C. Y. Son and Z.-G. Wang, “Ion transport in small-molecule and polymer electrolytes“, J. Chem. Phys. 153, 100903 (2020).
  63. H. Chao and Z.-G. Wang, “Effect of surface transition and adsorption on ionic liquid capacitors“, J. Phys. Chem. Lett. 11, 1767-1772 (2020).
  64. A. K. Omar, Z.-G. Wang, and J. F. Brady, “Microscopic origins of the swim pressure and the anomalous surface tension of active matter“, Phys Rev. E 101, 012604 (2020).
  65. J. Jiang, V. V. Ginzburg, and Z.-G. Wang, “On the origin of oscillatory interactions between surfaces mediated by polyelectrolyte solution“, J. Chem. Phys. 151, 214901 (2019).
  66. B. Mei, Y. Lu, L. An, and Z.-G. Wang, “Two-step relaxation and the breakdown of the Stokes-Einstein relation in glass-forming liquids“, Phys. Rev. E 100, 052607 (2019).
  67. A. P. Steinberg, Z.-G. Wang, and R. F. Ismagilov, “Food polyelectrolytes compress the colonic mucus hydrogel by a Donnan mechanism“, Biomacromolecules 20, 2675-2683 (2019).
  68. Y. Ruan, Y. Lu, L. An, and Z.-G. Wang, “Nonlinear rheological behaviors in polymer melts after step shear“, Macromolecules 52. 4103-4110 (2019).
  69. N. M. Alsaifi, M. Alkater, H. Binous, I. A. Aslani, Y. Alsunni, and Z.-G. Wang, “Nonphysical behavior in several statistical mechanically based equations of state“, Ind. Eng. Chem. Res. 58, 1382-1395 (2019).
  70. A. K. Omar, Y. Wu, Z.-G. Wang, and J. F. Brady, “Swimming to stability: Structural and dynamical control via active doping”, ACS Nano 13, 560-572 (2019).
  71. P. B. Rapp, A. K. Omar, B. R. Silverman, Z.-G. Wang, and D. A. Tirrell, “Mechanisms of diffusion in associative polymer networks: Evidence for chain hopping“, J. Am. Chem. Soc. 140, 14185-14194 (2018).
  72. B. Zhuang and Z.-G. Wang, “Statistical field theory for dipolar fluids“, J. Chem. Phys. 149, 124108 (2018).
  73. P.-F. Zhang, K. Shen, N. M. Alsaifi, and Z.-G. Wang, “Salt partitioning in complex coacervation of symmetric polyelectrolytes“, Macromolecules 51, 5586-5593 (2018).
  74. P.-F. Zhang, Nayef M. Alsaifi, J. Wu, and Z.-G. Wang, “Polyelectrolyte complex coacervation: Effects of concentration asymmetry“, J. Chem. Phys. 149, 163303 (2018).
  75. J. Jiang, V. V. Ginzburg, and Z.-G. Wang, “Density functional theory for charged fluids“, Soft Matter 14, 5878-5887 (2018).
  76. M. A. Webb, U. Yamamoto, B. M. Savoie, Z.-G. Wang, and T. F. Miller III, “Globally suppressed dynamics in ion-doped polymers“, ACS Macro Lett 7, 734-738 (2018).
  77. J. Jiang and Z.-G. Wang, “Improved local lattice Monte Carlo simulation for charged systems“, J. Chem. Phys. 148, 114105 (2018) (Editor’s choice as featured article).
  78. K. Shen and Z.-G. Wang, “Polyelectrolyte chain structure and solution phase behavior“, Macromolecules 51, 1706-1717 (2018).
  79. Z.-G. Wang, “Polymer conformation—A pedagogical review“, Macromolecules 50, 9073-9114 (2017) (Invited perspective for the 50th anniversary of Macromolecules).
  80. A. K. Omar and Z.-G. Wang, “Shear-induced heterogeneity in associating polymer gels: Role of network structure and dilatancy“, Phys. Rev. Lett. 119, 117801 (2017).
  81. P. P. Lin, J. N. Liu, Z. C. Zhao, Z.-G. Wang, and S.-Q. Wang” Origin of mechanical stress and rising internal energy during fast uniaxial extension of SBR melts“, Polymer 124, 68-77 (2017).
  82. M. Li, B. Zhuang, Y. Lu, Z.-G. Wang and L. An, “Accurate determination of ion polarizabilities in aqueous solutions“, J. Phys. Chem. B 121, 6416-6424 (2017).
  83. P. B. Rapp, A. K. Omar, J. J. Shen, M. E. Buck, Z.-G. Wang, and D. A. Tirrell, “Analysis and control of chain mobility in protein hydrogels“, J. Am. Chem. Soc. 139, 3796-3804 (2017).
  84. K. Shen and Z.-G. Wang, “Electrostatic correlations and the polyelectrolyte self-energy“, J. Chem. Phys. 146, 084901 (2017).
  85. T. F. Miller, Z.-G. Wang, G. W. Coates, and N. P. Balsara, “Designing polymer electrolytes for safe and high capacity rechargeable lithium batteries“, Acc. Chem. Res. 50, 590-593 (2017) (Invited article for the special issue on “Holy Grails in Chemistry”).
  86. N. M. Alsaifi, I. A. Aslani, H. Binous, and Z.-G. Wang, “A priori determination of the region of the three physical volume root loci in the Perturbed-Chain SAFT EOS“, Fluid Phase Equilib. 434, 152-166 (2017).
  87. P.-F. Zhang, Nayef M. Alsaifi, J. Wu, and Z.-G. Wang, “Salting-out and salting-in of polyelectrolyte solutions: A liquid-state theory study“, Macromolecules 49, 9720-9730 (2016).
  88. B. Zhuang and Z.-G. Wang, “Molecularly based theory for electron transfer in solvent mixtures“, J. Phys. Chem. B 120, 6373-6382 (2016).
  89. R. Wang and Z.-G. Wang, “Inhomogeneous screening near the dielectric interface“, J. Chem. Phys. 144, 134902 (2016).
  90. B. Zhuang and Z.-G. Wang, “A molecularly based theory for electron transfer reorganization energy“, J. Chem. Phys. 143, 224502 (2016).
  91. B. Li, Z.-Y. Sun, L.-J. An, and Z.-G. Wang, “The scaling behavior of the second virial coefficient of linear and ring polymers“, Science China Chemistry 59, 619-623 (2016).
  92. C.-L. Ren, I. Nakamura, and Z.-G. Wang, “Effects of ion-induced crosslinking on the phase behavior in salt-doped polymer blends“, Macromolecules 49, 425-431 (2016).
  93. B. Li, Z.-Y. Sun, L.-J. An, and Z.-G. Wang, “Influence of topology on the free energy and metric properties of an ideal ring polymer confined between a slit“, Macromolecules 48, 8675-8680 (2015).
  94. N. An, B. Zhuang, M. Li, Y. Lu and Z.-G. Wang, “Combined theoretical and experimental study of refractive indices of water–acetonitrile–salt systems“, J. Phys. Chem. B 119, 10701-10709 (2015).
  95. M. A. Webb, B. M. Savoie, Z.-G. Wang, and T. F. Miller III, “Chemically specific dynamic bond percolation model for ion transport in polymer electrolytes“, Macromolecules 48, 7346-7358 (2015).
  96. X. Xu, D. E. Cristancho, S. Costeaux, and Z.-G. Wang, “Density-functional theory for mixtures of AB random copolymer and CO2“, Macromolecules 48, 6035-6046 (2015).
  97. M. A. Webb, Y. Jung, D. M. Pesko, B. M. Savoie, U. Yamamoto, G. W. Coates, N. P. Balsara, Z.-G. Wang, and T. F. Miller III, “Systematic computational and experimental investigation of lithium-ion transport mechanisms in polyester-based polymer electrolytes“, ACS Cent. Sci. 1, 198-205 (2015).
  98. M. K. Sing, Z.-G. Wang, G. H. McKinley, B. D. Olsen, “Chain configuration and rate-dependent mechanical properties in transient networks“, Soft Matter 11, 2085-2096 (2015).
  99. R. Wang and Z.-G. Wang, “On the theoretical description of weakly charged surfaces“, J. Chem. Phys. 142, 104705 (2015).
  100. S. Medina, J.J. Zhou, Z.-G. Wang, and F. Schmid, “An efficient dissipative particle dynamics-based algorithm for simulating electrolyte solutions“, J. Chem. Phys. 142, 024103 (2015).
  101. X. Xu, D. E. Cristancho, S. Costeaux, and Z.-G. Wang, “Nanoparticle solvation in polymer–CO2 mixtures“, J. Phys. Chem. B 118, 8002-8007 (2014).
  102. X. Wang, J. L. Thielen, A. A. Teran, M. Chintapalli, I. Nakamura, Z.-G. Wang, M. C. Newstein, N. P. Balsara, and B. A. Garetz, “Evolution of grain structure during disorder-to-order transitions in a block copolymer/salt mixture studied by depolarized light scattering“, Macromolecules 47, 5784-5792 (2014).
  103. R. Wang and Z.-G. Wang, “Theory of polymer chains in poor solvent: Single-chain structure, solution thermodynamics, and Θ point“, Macromolecules 47, 4094-4012 (2014).
  104. I. Nakamura and Z.-G. Wang, “Thermodynamics of Salt-Doped Block Copolymers”, ACS Macro Lett. 3, 8: 708–711 (2014).
  105. J. L. Thelen, A. A. Teran, X. Wang, B. A. Garetz, I. Nakamura, Z.-G. Wang, and N. P. Balsara, “Phase behavior of a block copolymer/salt mixture through the order-to-disorder transition“, Macromolecules 47, 2666-2673 (2014).
  106. R. Wang and Z.-G. Wang, “Continuous self-energy of ions at the dielectric interface“, Phys. Rev. Lett. 112, 136101 (2014).
  107. X. Xu, C. L. Ting, I. Kusaka, and Z.-G. Wang, “Nucleation in polymers and soft matter“, Ann. Rev. Phys. Chem. 65, 449-475 (2014).
  108. R. Wang and Z.-G. Wang, “Effects of image charges on double layer structure and forces“, J. Chem. Phys. 139, 124702 (2013).
  109. X. Xu, D. E. Cristancho, S. Costeaux, and Z.-G. Wang, “Bubble nucleation in polymer–CO2 mixtures“, Soft Matter 9, 9675-9683 (2013).
  110. Y.-Y. Lu, L.-J. An, and Z.-G. Wang, “Intrinsic viscosity of polymers: General theory based on a partially permeable sphere model“, Macromolecules 46, 5731-5740 (2013).
  111. I. Nakamura, N. P. Balsara, and Z.-G. Wang, “First-order disordered-to-lamellar phase transition in lithium salt-doped block copolymers“, ACS Macro Lett. 2, 478-481 (2013).
  112. I. Nakamura and Z.-G. Wang, “Effects of dielectric inhomogeneity in polyelectrolyte solutions“, Soft Matter (Communication) 9, 5686-5690 (2013).
  113. X. Xu, D. E. Cristancho, S. Costeaux, and Z.-G. Wang, “Discontinuous bubble nucleation due to a metastable condensation transition in polymer–CO2 mixtures“, J. Phys. Chem. Lett. 4, 1639-1643 (2013).
  114. I. Nakamura, A.-C. Shi, and Z.-G. Wang, “Ion solvation in liquid mixtures: Effects of solvent reorganization“, Phys. Rev. Lett. 109, 257802 (2012).
  115. B. Zhuang and Z.-G. Wang, “Anomalous concentration effects on phase behavior and nematic order in mixtures of side-chain liquid crystal polymers and low-molecular-weight liquid crystals“, Macromolecules 45, 6220-6229 (2012).
  116. R. Wang and Z.-G. Wang, “Theory of polymers in poor solvent: Phase equilibrium and nucleation behavior“, Macromolecules 45, 6266-6271 (2012).
  117. C. L. Ting and Z.-G. Wang, “Minimum free energy paths for a nanoparticle crossing the lipid membrane“, Soft Matter 8, 12066-12071 (2012).
  118. I. Nakamura and Z.-G. Wang, “Salt-doped block copolymers: Ion distribution, domain spacing and effective χ parameter“, Soft Matter 8, 9356-9367 (2012).
  119. X. Xu, D. E. Cristancho, S. Costeaux, and Z.-G. Wang, “Density-functional theory for polymer–carbon dioxide mixtures: A perturbed-chain SAFT approach“, J. Chem. Phys. 137, 054902 (2012).
  120. X. Xu, D. E. Cristancho, S. Costeaux, and Z.-G. Wang, “Density-functional theory for polymer carbon dioxide mixture“, Ind. Eng. Chem. Res. 51, 3832-3840 (2012).
  121. Y.-Y. Lu, T.-F. Shi, L.-J. An, and Z.-G. Wang, “Intrinsic viscosity of polymers: From linear chains to dendrimers“, Europhys. Lett. 97, 64003 (2012).
  122. C. L. Ting, J. Wu, and Z.-G. Wang, “Thermodynamic basis for the genome to capsid charge relationship in viral encapsidation“, Proc. Nat. Acad. Sci. 108, 16986-16991 (2011).
  123. C. L. Ting, D. Appelö, and Z.-G. Wang, “Minimum energy path to membrane pore formation and rupture“, Phys. Rev. Lett. 106, 168101 (2011).
  124. C. L. Ting and Z.-G. Wang, “Interactions of a charged nanoparticle with a lipid membrane: Implications for gene delivery”, Biophys. J. 100, 1288-1297 (2011).
  125. I. Nakamura, N. P. Balsara, and Z.-G. Wang, “Thermodynamics of ion-containing polymer blends and block copolymers“, Phys. Rev. Lett. 107, 198301 (2011).
  126. R. Wang and Z.-G. Wang, “Theory of side-chain liquid crystal polymers: Bulk behavior and chain conformation“, Macromolecules 43, 10096-10106 (2011).
  127. R. Wang and Z.-G. Wang, “Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures“, J. Chem. Phys. 135, 014707 (2011).
  128. J.-Y. Guo, H.-J. Liang, and Z.-G. Wang, “Coil-to-globule transition by dissipative particle dynamics simulation“, J. Chem. Phys. 134, 244904 (2011).
  129. Y.-Y. Lu, T.-F. Shi, L.-J. An, L.-P. Jin, and Z.-G. Wang, “A simple model for the anomalous viscosity of dendrimers“, Soft Matter Communication 6, 2619-2622 (2010).
  130. N. S. Wanakule, J. M. Virgili, A. A. Teran, Z.-G. Wang, and N. P. Balsara, “Thermodynamic properties of block copolymer electrolytes containing imidazolium and lithium salts“, Macromolecules 43, 8282-8289 (2010).
  131. Z.-G. Wang, “Fluctuation in electrolyte solutions: The self energy“, Phys. Rev. E. 81, 021501 (2010).
  132. J.-F. Wang, K.-K. Guo, L.-J. An, M. Mueller, and Z.-G. Wang, “Micelles of coil–comb block copolymers in selective solvents: Competition of length scales“, Macromolecules 43, 2037-2041 (2010).
  133. Y.-B. Yang, Z.-Y. Sun, C.-L. Fu, L.-J. An, and Z.-G. Wang, “Monte Carlo simulation of a single ring among linear chains: Structural and dynamic heterogeneity“, J. Chem. Phys. 133, 064901 (2010).
  134. J. Wang, M. Mueller, and Z.-G. Wang, “Nucleation in A/B/AB blends: Interplay between microphase assembly and macrophase separation“, J. Chem. Phys. 130, 154902 (2009).
  135. T. Jiang, Z.-G. Wang, and J. Wu, “Electrostatic regulation of genome packaging in human hepatitis B virus“, Biophys. J. 96, 3065-3073 (2009).
  136. C. L. Ting, D. Makarov, and Z.-G. Wang, “A kinetic model for the enzymatic action of cellulase“, J. Phys. Chem. B. 113, 4970-4977 (2009).
  137. Z. Li, J. Wu, and Z.-G. Wang, “Osmotic pressure and packaging structure of caged DNA“, Biophys. J. 94, 737-746 (2008).
  138. Z.-Q. Li, Z.-Y. Sun, L.-J. An, and Z.-G. Wang, “Heterogeneity in structurally arrested hard spheres“, Euro. Phys. Lett. 84, 26005 (2008).
  139. Z.-G. Wang, “Effects of ion solvation on the miscibility of binary polymer blends“, J. Phys. Chem. B 112, 16205-16213 (2008).
  140. Z.-G. Wang, “Variational electrostatics for charge solvation“, J. Theor. Comp. Chem. 7, 397-419 (2008).
  141. C.-Z. Zhang and Z.-G. Wang, “Nucleation of membrane adhesions“, Phys. Rev. E. 77, art. 021906 (2008).
  142. C.-Z. Zhang and Z.-G. Wang, “Polymer-tethered ligand-receptor interaction between surfaces. II“, Langmuir 23, 13024-13039 (2007).
  143. S. B. Hutchens and Z.-G. Wang, “Metastable cluster intermediates in the condensation of charged macromolecule solutions“, J. Chem. Phys. 127, 084912 (2007).
  144. J. E. Witman and Z.-G. Wang, “A lattice model of vitrification and gelation“, J. Phys. Chem. B 110, 6312-6324 (2006).
  145. J. I. Martin, C.-Z. Zhang, and Z.-G. Wang, “Polymer tethered ligand-receptor interaction between surfaces“, J. Poly. Sci. B. – Poly. Phys. 44, 2621-2637 (2006).
  146. C. Z. Zhang and Z.-G. Wang, “Random isotropic structures and possible glass transitions in diblock copolymer melts“, Phys. Rev. E 73, 031804 (2006).
  147. J. Cho and Z.-G. Wang, “A simple field-theoretic simulation method for compressible block copolymer systems“, Macromolecules 39, 4576-4584 (2006).
  148. Z.-G. Wang, “Area expansion and adsorption isotherm in protein binding to mixed lipid membranes“, Ind. & Eng. Chem. Res. 45, 5538-5547 (2006).
  149. Z.-G. Wang, “Challenges and opportunities in polymer theory“, J. Poly. Sci. B – Poly. Phys. 44, 3445-3447 (2006) (Invited viewpoint article for the APS Special Issue).
  150. J. F. Wang, Z.-G. Wang, and Y. L. Yang, “Nature of disordered micelles in sphere-forming block copolymer melts“, Macromolecule 38, 1979-1988 (2005).
  151. J. S. Bois, S. Venkataraman, H. M. T. Choi, A. J. Spakowitz, Z.-G. Wang, and N. A. Pierce, “Topological constraints in nucleic acid hybridization kinetics“, Nucleic Acid Res. 33, 4090-4095 (2005).
  152. A. J. Spakowitz and Z.-G. Wang, “DNA packaging in bacteriophage: Is twist important?“, Biophys. J. 88, 3912-3923 (2005).
  153. A. J. Spakowitz and Z.-G. Wang, “End-to-end distance vector distribution with fixed end orientations for the wormlike chain model“, Phys. Rev. E. 72, 041802 (2005).
  154. A. J. Spakowitz and Z.-G. Wang, “Exact results for a semiflexible polymer chain in an aligning field“, Macromolecules 37, 5814-5823 (2004).
  155. J. B. Endelman, J. J. Silberg, Z.-G. Wang, and F. H. Arnold, “Site-directed protein recombination as a shortest-path problem“, Protein Eng., Design & Selection 17, 589-594 (2004).
  156. Y. Bohbot-Raviv, T. M. Snyder, and Z.-G. Wang, “Reversible association of telechelic molecules: An application of graph theory“, Langmuir 20, 7860-7870 (2004).
  157. J. Wang, Z.-G. Wang, and Y. Yang, “Nucleation in binary polymer blends: Effects of foreign mesoscopic spherical particles“, J. Chem. Phys. 121, 1105-1113 (2004).
  158. J. Wang, H. Zhang, F. Qiu, Z.-G. Wang, and Y. Yang, “Nucleation in binary polymer blends: Effects of adding diblock copolymers“, J. Chem. Phys. 118, 8997-9006 (2003).
  159. A. J. Spakowitz and Z.-G. Wang, “Semiflexible polymer solutions. I. Phase behavior and single-chain statistics“, J. Chem. Phys. 119, 13113-13128 (2003).
  160. A. J. Spakowitz and Z.-G. Wang, “Semiflexible polymer confined to a spherical surface“, Phys. Rev. Lett. 91, 166102 (2003).
  161. S. M. Bhattacharyya, Z.-G. Wang, and A. H. Zewail, “Dynamics of water near a protein surface“, J. Phys. Chem. B 107, 13218-13228 (2003).
  162. M. M. Meyer, J. J. Silberg, C. A. Voigt, J. B. Endelman, S. L. Mayo, Z.-G. Wang, and F. H. Arnold, “Library analysis of SCHEMA-guided protein recombination“, Protein Sci. 12, 1686-1693 (2003).
  163. R. A. Wickham, A.-C. Shi, and Z.-G. Wang, “Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt“, J. Chem. Phys. 118, 10293-10305 (2003).
  164. Z.-G. Wang, “Concentration fluctuation in binary polymer blends: Χ parameter, spinodal and Ginzburg criterion“, J. Chem. Phys. 117, 481-500 (2002).
  165. S. M. Wood and Z.-G. Wang, “Nucleation in binary polymer blends: A self-consistent field study“, J. Chem. Phys. 116, 2289-2300 (2002).
  166. C. A. Voigt, C. Martinez, Z.-G. Wang, S. L. Mayo, and F. H. Arnold, “Protein building blocks preserved by recombination“, Nature Struc. Biol. 9, 553-558 (2002).
  167. H. H. Lee, W. Y. Jeong, J. K. Kim, K. J. Ihn, J. A. Kornfield, Z.-G. Wang, and S. Qi, “Orientational proliferation and successive twinning from thermoreversible hexagonal-body-centered cubic transitions“, Macromolecules 35, 785-794 (2002).
  168. Z.-G. Wang, “Morphology, fluctuation, metastability, and kinetics in ordered block copolymer phases“, in Molecular Modeling and Theory in Chemical Engineering, edited by A. Chakraborty (Academic Press, San Diego, 2001), pp 439-463.
  169. P. Dimitrakopoulos, J. F. Brady, and Z.-G. Wang, “Short- and intermediate-time behavior of the linear stress relaxation in semiflexible polymers“, Phys. Rev. E (Rapid Communication) 64, 050803R (2001).
  170. I. Kusaka, D. W. Oxtoby, and Z.-G. Wang, “On the direct evaluation of the equilibrium distribution of clusters by simulation. II“, J. Chem. Phys. 115, 6898-6906 (2001).
  171. A. J. Spakowitz and Z.-G. Wang, “Free expansion of elastic filaments“, Phys. Rev. E. 64, 061802 (2001).
  172. C. A. Voigt, S. L. Mayo, F. H. Arnold, and Z.-G. Wang, “Computationally focusing the directed evolution of proteins“, J. Cell. Biochem. 84, S37, 58-63 (2001).
  173. C. A. Voigt, F. H. Arnold, S. Mayo, and Z.-G. Wang, “Computational method to reduce the search space for directed protein evolution“, Proc. Natl. Acad. Sci. 98, 3778-3783 (2001).
  174. C. A. Voigt, S. Kaufmann, and Z.-G. Wang, “Rational evolutionary design: The theory of in vitro protein evolution“, in Evolutionary Protein Design, edited by Frances H. Arnold (Academic Press, San Diego, 2001), pp. 79-82.
  175. Y. Bohbot-Raviv and Z.-G. Wang, “Discovering new ordered phases of block copolymers“, Phys. Rev. Lett. 85, 3428-3431 (2000).
  176. S. Qi and Z.-G. Wang, “Transient instability upon temperature quench in weakly ordered block copolymers”, J. Chem. Phys. 111, 10681-10688 (1999). https://doi.org/10.1063/1.480422.
  177. I. Kusaka, D. W. Oxtoby, Z.-G. Wang, “On the direct evaluation of the equilibrium distribution of clusters by simulation”, J. Chem. Phys. 111, 9958-9964 (1999). https://doi.org/10.1063/1.480349.
  178. I. Kusaka, Z.-G. Wang, J. H. Seinfeld, “Binary nucleation of sulfuric acid-water: Monte Carlo simulation”, J. Chem. Phys. 108, 6829-6848 (1998). https://doi.org/10.1063/1.476097.
  179. I. Kusaka, Z.-G. Wang, J. H. Seinfeld, “Direct evaluation of the equilibrium distribution of physical clusters by a grand canonical Monte Carlo simulation”, J. Chem. Phys. 108, 3416-3423 (1998). https://doi.org/10.1063/1.475741.
  180. Z.-G. Wang, “Kinetics and anisotropic fluctuations in weakly ordered block copolymers”, Curr. Opin. Colloid Interface Sci. 3, 4, 428-435 (1998). https://doi.org/10.1016/S1359-0294(98)80061-7.
  181. S. Qi and Z.-G. Wang, “Weakly segregated block copolymers: anisotropic fluctuations and kinetics of order-order and order-disorder transitions”, Polymer 39, 19, 4639-4648 (1998). https://doi.org/10.1016/S0032-3861(97)10139-2.
  182. S. P. Gido and Z.-G. Wang, “Interfacial curvature in graft and diblock copolymers and implications for long range order in cylindrical morphologies”, Macromolecules 30, 22, 6771-6782 (1997). https://doi.org/10.1021/ma9703564.
  183. S. Qi and Z.-G. Wang, “On the nature of perforated layer phase in undiluted diblock copolymers”, Macromolecules 30, 15, 4491-4497 (1997). https://doi.org/10.1021/ma970206t.
  184. S. Qi and Z.-G. Wang, “Kinetics of phase transitions in weakly segregated block copolymers: pseudostable and transient states”, Phys. Rev. E 55, 2, 1682-1697 (1997). https://doi.org/10.1103/PhysRevE.55.1682.
  185. J. I. Martin, Z.-G. Wang, D. Zuckermann, R. Bruinsma, and P. Pincus, “Forces between surfaces with weakly end-adsorbed polymers”, J. de Physique II 7, 8, 1111-1121 (1997). https://doi.org/10.1051/jp2:1997175.
  186. S. Qi and Z.-G. Wang, “Kinetic pathways of order-disorder and order-order transitions in weakly segregated microstructured systems”, Phys. Rev. Lett. 76, 10, 1679-1682 (1996). https://doi.org/10.1103/PhysRevLett.76.1679.
  187. R. D. Johnson, Z.-G. Wang, and F. H. Arnold, “Surface site heterogeneity and lateral interactions in multipoint protein adsorption”, J. Phys. Chem. 100, 12, 5134-5139 (1996). https://doi.org/10.1021/jp9523682.
  188. J. I. Martin, Z.-G. Wang, and M. Schick, “Effects of polymer brush self-assembly on spreading and thin-film stability”, Langmuir 12, 20, 4950-4959 (1996). https://doi.org/10.1021/la960305k.
  189. W. Zheng and Z.-G. Wang, “Morphology of ABC triblock copolymers”, Macromolecules 28, 21, 7215-7223 (1995). https://doi.org/10.1021/ma00125a026.
  190. I. Kusaka, Z.-G. Wang, J. H. Seinfeld, “Ion-induced nucleation. II. Polarizable multipolar molecules”, J. Chem. Phys. 103, 8993-9009 (1995). https://doi.org/10.1063/1.470089.
  191. I. Kusaka, Z.-G. Wang, J. H. Seinfeld, “Ion-induced nucleation: A density functional approach”, J. Chem. Phys. 102, 913-924 (1995). https://doi.org/10.1063/1.469158.
  192. J. I. Martin and Z.-G. Wang, “Polymer brushes: scaling, compression forces, interbrush penetration, and solvent size effects”, J. Phys. Chem. 99, 9, 2833-2844 (1995). https://doi.org/10.1021/j100009a045.
  193. Z.-G. Wang, “Chain dimensions in amorphous polymer melts”, Macromolecules 28, 2, 570-576 (1995). https://doi.org/10.1021/ma00106a022.
    L. Golubovic and Z.-G. Wang, “Kardar-Parisi-Zhang model and anomalous elasticity of two- and three-dimensional smectic-A liquid crystals”, Phys. Rev. E 49, 4, 2567-2578 (1994). https://doi.org/10.1103/PhysRevE.49.2567.
  194. X. Qiu and Z.-G. Wang, “Competing adsorption and micellization of diblock copolymers: effects of colloidal sizes”, J. Coll. and Interface Science 167, 2, 294-300 (1994). https://doi.org/10.1006/jcis.1994.1364.
  195. Z.-G. Wang, “Response and instabilities of the lamellar phase of diblock copolymers under uniaxial stress”, J. Chem. Phys. 100, 2298-2309 (1994). https://doi.org/10.1063/1.466528.
  196. J. V. Selinger, Z.-G. Wang and R. Bruinsma, “Chiral symmetry breaking and pattern formation in two-dimensional films”, Mat. Res. Soc. Symp. Proc. 292, 235-240 (1993). https://doi.org/10.1557/PROC-292-235.
  197. J. V. Selinger, Z.-G. Wang, R. Bruinsma and C. M. Knobler, “Chiral symmetry breaking in Langmuir monolayers and smectic films”, Phys. Rev. Lett. 70, 8, 1139-1142 (1993). https://doi.org/10.1103/PhysRevLett.70.1139.
  198. Z.-G. Wang, M. E. Costas, and W. M. Gelbart, “Flexible micelles and the n  0 vector spin model”, J. Phys. Chem. 97, 6, 1237-1242 (1993). https://doi.org/10.1021/j100108a021.
  199. Z.-G. Wang, “Spatially modulated phases in monolayers of mixed surfactants”, J. Chem. Phys. 99, 4191-4200 (1993). https://doi.org/10.1063/1.466116.
  200. Z.-G. Wang, “Curvature instability of diblock copolymer bilayers”, Macromolecules 25, 14, 3702-3705 (1992). https://doi.org/10.1021/ma00040a015.
  201. Z.-G. Wang, “Mean-field approximations and coupled maps for kinetic lattice models”, Phys. Rev. A 45, 2, 692-701 (1992). https://doi.org/10.1103/PhysRevA.45.692.
  202. M. E. Costas, Z.-G. Wang and W. M. Gelbart, “Spin Hamiltonian analyses of grafted rod transitions”, J. Chem. Phys. 96, 2228-2235 (1992). https://doi.org/10.1063/1.462073.
  203. L. Golubovic and Z.-G. Wang, “Anharmonic Elasticity of Smectics A and the Kardar-Parisi-Zhang Model”, Phys. Rev. Lett. 69, 17, 2535-2538 (1992). https://doi.org/10.1103/PhysRevLett.69.2535.
  204. D. C. Turner, Z.-G. Wang, S. M. Gruner, D. A. Mannock, and R. N. McElhaney, “Structural study of the inverted cubic phases of di-dodecyl alkyl--D-glucopyranosyl-rac-glycerol”, J. de Physique II 2, 2039-2063 (1992). https://doi.org/10.1051/jp2:1992250.
  205. R. B. Selinger, Z.-G. Wang, and W. M. Gelbart, “Effects of temperature and small-scale defects on the strength of solids”, J. Chem. Phys. 95, 9128-9141 (1992). https://doi.org/10.1063/1.461192.
  206. R. L. B. Selinger, Z.-G. Wang, W. M. Gelbart, and A. Ben-Shaul, “Statistical thermodynamic approach to fracture”, Phys. Rev. A 43, 85, 4396-4400 (1991). https://doi.org/10.1103/PhysRevA.43.4396.
  207. K. R. Myers, A. M. Nemirovsky, K. F. Freed and Z.-G. Wang, “Conformations of a polymer boxed into a corner: Role of excluded volume”, J. Chem. Phys. 95, 8, 6112-6123 (1991). https://doi.org/10.1063/1.461580.
  208. Z.-G. Wang, U. Landman, R. L. B. Selinger, and W. M. Gelbart, “Molecular-dynamics study of elasticity and failure in ideal solids”, Phys. Rev. B 44, 1, 378-381 (1991). https://doi.org/10.1103/PhysRevB.44.378.
  209. Z.-G. Wang and S. A. Safran, “Curvature elasticity of diblock copolymer monolayers”, J. Chem. Phys. 94, 1, 679-687 (1991). https://doi.org/10.1063/1.460334.
  210. S. Shin, Z.-G. Wang and S. A. Rice, “An interpretation of the multiple fluid-fluid transitions in liquid supported amphiphile monolayers”, J. Chem. Phys. 92, 2, 1427-1434 (1990). https://doi.org/10.1063/1.458101.
  211. Z.-G. Wang, “Aggregation (micellization) of associating polymers”, Langmuir 6, 5, 928-934 (1990). https://doi.org/10.1021/la00095a007.
  212. Z.-G. Wang, “A mean-field study of a model system of grafted rods”, J. de Physique 51, 13, 1431-1444 (1990). https://doi.org/10.1051/jphys:0199000510130143100.
  213. Z.-G. Wang, A. M. Nemirovsky, K. F. Freed, and K. R. Myers, “Effects of surface, wedge, corner, and mixed boundary conditions on the local critical behaviour”, J. Physics A: Math. Gen. 23, 12, 2575-2585 (1990). https://doi.org/10.1088/0305-4470/23/12/033.
  214. Z.-G. Wang and S. A. Safran, “Curvature elasticity of ordered bicontinuous structures”, Europhys. Lett. 11, 5, 425-430 (1990). https://doi.org/10.1209/0295-5075/11/5/007.
  215. Z.-G. Wang and S. A. Safran, “Curvature elasticity of block copolymers and the structure of emulsified polymer blends”, Mat. Res. Soc. Symp. Proc. 177, 15-20 (1990). https://doi.org/10.1557/PROC-177-15.
  216. Z.-G. Wang and S. A. Safran, “Equilibrium emulsification of polymer blends by diblock copolymers”, J. de Physique 51, 185-200 (1990). https://doi.org/10.1051/JPHYS%3A01990005102018500.
  217. S. T. Milner, Z.-G. Wang, and T. A. Witten, “End-confined polymers: corrections to the Newtonian limit”, Macromolecules 22, 1, 489-490 (1989). https://doi.org/10.1021/ma00191a093.
  218. T. A. Witten, S. T. Milner, and Z.-G. Wang, “Theory of stress distribution in block copolymer microdomains”, in Multiphase Macromolecular Systems, edited by Bill M. Culbertson (Plenum, New York, 1989) Vol. 6, pp 655-663.
  219. Z.-G. Wang and S. A. Safran, “Size distribution for aggregates of associating polymers. II. Linear packing”, J. Chem. Phys. 89, 8, 5323-5328 (1988). https://doi.org/10.1063/1.455623.
  220. Z.-G. Wang and S. A. Rice, “A lattice model of a liquid supported monolayer of amphiphile molecules: mean-field analysis”, J. Chem. Phys. 88, 2, 1290-1297 (1988). https://doi.org/10.1063/1.454199.
  221. Z.-G. Wang, “Effects of surface nonlinear interactions on the local critical behavior”, Z. Phys. B 68, 475-483 (1987). https://doi.org/10.1007/BF01471078.
  222. A. M. Nemirovsky, Z.-G. Wang, and K. F. Freed, “Crossover renormalization-group approach to semi-infinite inhomogeneous critical behavior”, Phys. Rev. B 36, 7, 3755-3762 (1987). https://doi.org/10.1103/PhysRevB.36.3755.
  223. Z.-G. Wang, A. M. Nemirovsky, and K. F. Freed, “Polymers with excluded volume in various geometries: renormalization group methods”, J. Chem. Phys. 86, 7, 4266-4279 (1987). https://doi.org/10.1063/1.451887.
  224. Z.-G. Wang, A. M. Nemirovsky, and K. F. Freed, “Interaction of a polymer chain with an asymmetric liquid-liquid interface”, J. Chem. Phys. 85, 5, 3068-3077 (1986). https://doi.org/10.1063/1.451014.
  225. A. M. Nemirovsky, Z.-G. Wang, and K. F. Freed, “Two coupled semi-infinite systems near criticality”, Phys. Rev. B 34, 11, 7886-7895 (1986). https://doi.org/10.1103/PhysRevB.34.7886.