Design and preparation of functional nanomaterials with specific properties requires precise control over their microscopic structure. A prototypical example is the self-assembly of diblock copolymers, which generate highly ordered structures controlled by three parameters: the chemical incompatibility between blocks, block size ratio and chain length. Recent advances in polymer synthesis have allowed for the preparation of gradient copolymers with controlled sequence chemistry, thus providing additional parameters to tailor their assembly. These are polydisperse monomer sequence, block size distribution and gradient strength. Here, we employ dissipative particle dynamics to describe the self-assembly of gradient copolymer melts with strong, intermediate, and weak gradient strength and compare their phase behavior to that of corresponding diblock copolymers. Gradient melts behave similarly when copolymers with a strong gradient are considered. Decreasing the gradient strength leads to the widening of the gyroid phase window, at the expense of cylindrical domains, and a remarkable extension of the lamellar phase. Finally, we show that weak gradient strength enhances chain packing in gyroid structures much more than in lamellar and cylindrical morphologies. Importantly, this work also provides a link between gradient copolymers morphology and parameters such as chemical incompatibility, chain length and monomer sequence as support for the rational design of these nanomaterials.

Department of Engineering and Architecture University of Trieste 34127 Trieste Italy

Department of Informatics Faculty of Science Jan Evangelista Purkyně University in Ústí nad Labem 40096 Ústí nad Labem Czech Republic

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Bates F.S., Fredrickson G.H. Block copolymers—Designer soft materials. Phys. Today. 1999;52:32–38. doi: 10.1063/1.882522. DOI

Feng H.B., Lu X.Y., Wang W.Y., Kang N.G., Mays J.W. Block Copolymers: Synthesis, Self-Assembly, and Applications. Polymers. 2017;9:494. doi: 10.3390/polym9100494. PubMed DOI PMC

Yin J., Chen Y., Zhang Z.H., Han X. Stimuli-Responsive Block Copolymer-Based Assemblies for Cargo Delivery and Theranostic Applications. Polymers. 2016;8:268. doi: 10.3390/polym8070268. PubMed DOI PMC

Eggers S., Eckert T., Abetz V. Double thermoresponsive block-random copolymers with adjustable phase transition temperatures: From block-like to gradient-like behavior. J. Polym. Sci. Pol. Chem. 2018;56:399–411. doi: 10.1002/pola.28906. DOI

Rabyk M., Destephen A., Lapp A., King S., Noirez L., Billon L., Hruby M., Borisov O., Stepanek P., Deniau E. Interplay of Thermosensitivity and pH Sensitivity of Amphiphilic Block-Gradient Copolymers of Dimethylaminoethyl Acrylate and Styrene. Macromolecules. 2018;51:5219–5233. doi: 10.1021/acs.macromol.8b00621. DOI

Cui J., Ma Z., Pan L., An C.H., Liu J., Zhou Y.F., Li Y.S. Self-healable gradient copolymers. Mater. Chem. Front. 2019;3:464–471. doi: 10.1039/C8QM00592C. DOI

Zhao R.B., Shea K.J. Gradient Methylidene-Ethylidene Copolymer via C1 Polymerization: An Ersatz Gradient Ethylene-Propylene Copolymer. Acs Macro Lett. 2015;4:584–587. doi: 10.1021/acsmacrolett.5b00218. PubMed DOI

Matyjaszewski K. Advanced Materials by Atom Transfer Radical Polymerization. Adv. Mater. 2018;30:1706441–1706462. doi: 10.1002/adma.201706441. PubMed DOI

Ogura Y., Takenaka M., Sawamoto M., Terashima T. Fluorous Gradient Copolymers via in-Situ Transesterification of a Perfluoromethacrylate in Tandem Living Radical Polymerization: Precision Synthesis and Physical Properties. Macromolecules. 2018;51:864–871. doi: 10.1021/acs.macromol.7b02512. DOI

Posel Z., Svoboda M., Limpouchova Z., Lisal M., Prochazka K. Adsorption of amphiphilic graft copolymers in solvents selective for the grafts on a lyophobic surface: A coarse-grained simulation study. Phys. Chem. Chem. Phys. 2018;20:6533–6547. PubMed

Wang W.Y., Lu W., Goodwin A., Wang H.Q., Yin P.C., Kang N.G., Hong K.L., Mays J.W. Recent advances in thermoplastic elastomers from living polymerizations: Macromolecular architectures and supramolecular chemistry. Prog. Polym. Sci. 2019;95:1–31. doi: 10.1016/j.progpolymsci.2019.04.002. DOI

Sigle J.L., Clough A., Zhou J., White J.L. Controlling Macroscopic Properties by Tailoring Nanoscopic Interfaces in Tapered Copolymers. Macromolecules. 2015;48:5714–5722. doi: 10.1021/acs.macromol.5b01215. DOI

Hodrokoukes P., Floudas G., Pispas S., Hadjichristidis N. Microphase separation in normal and inverse tapered block copolymers of polystyrene and polyisoprene. 1. Phase state. Macromolecules. 2001;34:650–657. doi: 10.1021/ma001479i. DOI

Alam M.M., Jack K.S., Hill D.J.T., Whittaker A.K., Peng H. Gradient copolymers—Preparation, properties and practice. Eur. Polym. J. 2019;116:394–414. doi: 10.1016/j.eurpolymj.2019.04.028. DOI

Kim J., Gray M.K., Zhou H.Y., Nguyen S.T., Torkelson J.M. Polymer blend compatibilization by gradient copolymer addition during melt processing: Stabilization of dispersed phase to static coarsening. Macromolecules. 2005;38:1037–1040. doi: 10.1021/ma047549t. DOI

Tao Y., Kim J., Torkelson J.M. Achievement of quasi-nano structured polymer blends by solid-state shear pulverization and compatibilization by gradient copolymer addition. Polymer. 2006;47:6773–6781. doi: 10.1016/j.polymer.2006.07.041. DOI

Mok M.M., Kim J., Torkelson J.M. Gradient copolymers with broad glass transition temperature regions: Design of purely interphase compositions for damping applications. J. Polym. Sci. Pol. Phys. 2008;46:48–58. doi: 10.1002/polb.21341. DOI

Aksimentiev A., Holyst R. Phase behavior of gradient copolymers. J. Chem. Phys. 1999;111:2329–2339. doi: 10.1063/1.479504. DOI

Lefebvre M.D., de la Cruz M.O., Shull K.R. Phase segregation in gradient copolymer melts. Macromolecules. 2004;37:1118–1123. doi: 10.1021/ma035141a. DOI

Jiang R., Jin Q.H., Li B.H., Ding D.T., Wickham R.A., Shi A.C. Phase behavior of gradient copolymers. Macromolecules. 2008;41:5457–5465. doi: 10.1021/ma8002517. DOI

Tito N.B., Milner S.T., Lipson J.E.G. Self-Assembly of Lamellar Microphases in Linear Gradient Copolymer Melts. Macromolecules. 2010;43:10612–10620. doi: 10.1021/ma102296r. DOI

Mok M.M., Pujari S., Burghardt W.R., Dettmer C.M., Nguyen S.T., Ellison C.J., Torkelson J.M. Microphase separation and shear alignment of gradient copolymers: Melt rheology and small-angle X-ray scattering analysis. Macromolecules. 2008;41:5818–5829. doi: 10.1021/ma8009454. DOI

Mok M.M., Kim J., Wong C.L.H., Marrou S.R., Woo D.J., Dettmer C.M., Nguyen S.T., Ellison C.J., Shull K.R., Torkelson J.M. Glass Transition Breadths and Composition Profiles of Weakly, Moderately, and Strongly Segregating Gradient Copolymers: Experimental Results and Calculations from Self-Consistent Mean-Field Theory. Macromolecules. 2009;42:7863–7876. doi: 10.1021/ma9009802. DOI

Ganesan V., Kumar N.A., Pryamitsyn V. Blockiness and Sequence Polydispersity Effects on the Phase Behavior and Interfacial Properties of Gradient Copolymers. Macromolecules. 2012;45:6281–6297. doi: 10.1021/ma301136y. DOI

Jiang R., Wang Z., Yin Y.H., Li B.H., Shi A.C. Effects of compositional polydispersity on gradient copolymer melts. J. Chem. Phys. 2013;138:074906. doi: 10.1063/1.4792200. PubMed DOI

Pandav G., Pryamitsyn V., Gallow K.C., Loo Y.L., Genzer J., Ganesan V. Phase behavior of gradient copolymer solutions: A Monte Carlo simulation study. Soft Matter. 2012;8:6471–6482. doi: 10.1039/c2sm25577d. DOI

Pakula T., Matyjaszewski K. Copolymers with controlled distribution of comonomers along the chain. 1. Structure, thermodynamics and dynamic properties of gradient copolymers. Computer simulation. Macromol. Theor. Simul. 1996;5:987–1006. doi: 10.1002/mats.1996.040050514. DOI

Sun D.C., Guo H.X. Monte Carlo Studies on the Interfacial Properties and Interfacial Structures of Ternary Symmetric Blends with Gradient Copolymers. J. Phys. Chem. B. 2012;116:9512–9522. doi: 10.1021/jp3020172. PubMed DOI

Sun D.C., Guo H.X. Influence of compositional gradient on the phase behavior of ternary symmetric homopolymer-copolymer blends: A Monte Carlo study. Polymer. 2011;52:5922–5932. doi: 10.1016/j.polymer.2011.10.039. DOI

Fredrickson G.H., Milner S.T., Leibler L. Multicritical Phenomena and Microphase Ordering in Random Block Copolymer Melts. Macromolecules. 1992;25:6341–6354. doi: 10.1021/ma00049a034. DOI

Skvor J., Posel Z. Simulation Aspects of Lamellar Morphology: Incommensurability Effect. Macromol. Theor. Simul. 2015;24:141–151. doi: 10.1002/mats.201400079. DOI

Posel Z., Rousseau B., Lisal M. Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts. Mol. Simulat. 2014;40:1274–1289. doi: 10.1080/08927022.2013.869803. DOI

Karatrantos A., Composto R.J., Winey K.I., Kroger M., Clarke N. Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review. Polymers. 2019;11:876. doi: 10.3390/polym11050876. PubMed DOI PMC

Posel Z., Posocco P. Tuning the Properties of Nanogel Surfaces by Grafting Charged Alkylamine Brushes. Nanomaterials. 2019;9:1514. doi: 10.3390/nano9111514. PubMed DOI PMC

Guskova O.A., Seidel C. Mesoscopic Simulations of Morphological Transitions of Stimuli-Responsive Diblock Copolymer Brushes. Macromolecules. 2011;44:671–682. doi: 10.1021/ma102349k. DOI

Posocco P., Hassan Y.M., Barandiaran I., Kortaberria G., Pricl S., Fermeglia M. Combined Mesoscale/Experimental Study of Selective Placement of Magnetic Nanoparticles in Diblock Copolymer Films via Solvent Vapor Annealing. J. Phys. Chem. C. 2016;120:7403–7411. doi: 10.1021/acs.jpcc.6b01050. DOI

Posel Z., Posocco P., Fermeglia M., Lisal M., Pricl S. Modeling hierarchically structured nanoparticle/diblock copolymer systems. Soft Matter. 2013;9:2936–2946. doi: 10.1039/c2sm27360h. DOI

Posocco P., Posel Z., Fermeglia M., Lisal M., Pricl S. A molecular simulation approach to the prediction of the morphology of self-assembled nanoparticles in diblock copolymers. J. Mater. Chem. 2010;20:10511–10520. doi: 10.1039/c0jm01561j. DOI

Posel Z., Posocco P., Lisal M., Fermeglia M., Pricl S. Highly grafted polystyrene/polyvinylpyridine polymer gold nanoparticles in a good solvent: Effects of chain length and composition. Soft Matter. 2016;12:3600–3611. doi: 10.1039/C5SM02867A. PubMed DOI

Karatrantos A., Clarke N., Kroger M. Modeling of Polymer Structure and Conformations in Polymer Nanocomposites from Atomistic to Mesoscale: A Review. Polym. Rev. 2016;56:385–428. doi: 10.1080/15583724.2015.1090450. DOI

Posel Z., Svoboda M., Colina C.M., Lisal M. Flow and aggregation of rod-like proteins in slit and cylindrical pores coated with polymer brushes: An insight from dissipative particle dynamics. Soft Matter. 2017;13:1634–1645. doi: 10.1039/C6SM02751B. PubMed DOI

Espanol P., Warren P.B. Perspective: Dissipative particle dynamics. J. Chem. Phys. 2017;146:150901. doi: 10.1063/1.4979514. PubMed DOI

Groot R.D., Madden T.J. Dynamic simulation of diblock copolymer microphase separation. J. Chem. Phys. 1998;108:8713–8724. doi: 10.1063/1.476300. DOI

Martinez-Veracoechea F.J., Escobedo F.A. Simulation of the gyroid phase in off-lattice models of pure diblock copolymer melts. J. Chem. Phys. 2006;125:104907. doi: 10.1063/1.2345652. PubMed DOI

Plimpton S. Fast Parallel Algorithms for Short-Range Molecular-Dynamics. J. Comput. Phys. 1995;117:1–19. doi: 10.1006/jcph.1995.1039. DOI

Nguyen T.D., Plimpton S.J. Accelerating dissipative particle dynamics simulations for soft matter systems. Comp. Mater. Sci. 2015;100:173–180. doi: 10.1016/j.commatsci.2014.10.068. DOI

Beranek P., Posel Z. Phase Behavior of Semiflexible-Flexible Diblock Copolymer Melt: Insight from Mesoscale Modeling. J. Nanosci. Nanotechno. 2016;16:7832–7835. doi: 10.1166/jnn.2016.12548. DOI

Gavrilov A.A., Kudryavtsev Y.V., Chertovich A.V. Phase diagrams of block copolymer melts by dissipative particle dynamics simulations. J. Chem. Phys. 2013;139:224901. doi: 10.1063/1.4837215. PubMed DOI

Brown J.R., Sides S.W., Hall L.M. Phase Behavior of Tapered Diblock Copolymers from Self-Consistent Field Theory. Acs Macro Lett. 2013;2:1105–1109. doi: 10.1021/mz400546h. PubMed DOI

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. doi: 10.1063/1.4943982. PubMed DOI

Brown J.R., Seo Y.M., Sides S.W., Hall L.M. Unique Phase Behavior of Inverse Tapered Block Copolymers: Self Consistent Field Theory and Molecular Dynamics Simulations. Macromolecules. 2017;50:5619–5626. doi: 10.1021/acs.macromol.7b00522. DOI

Phase Behavior of Polydisperse Y-Shaped Polymer Brushes under Good Solvent Conditions