Fluctuation effects on the order-disorder transition in polydisperse copolymer melts.

Using single chain in mean field simulation approach, we examine the influence of fluctuation effects on the order-disorder transition (ODT) of polydisperse copolymer systems. We consider two model systems: (i) molecular weight polydisperse systems represented by AB diblock copolymer melts having monodisperse A blocks and polydisperse B blocks; and (ii) compositionally polydisperse symmetric diblock copolymer systems. In each case, we present results for the fluctuation-induced shift in the ODT from the corresponding mean-field predictions. In both models, an increase in polydispersity enhances the influence of fluctuations. Moreover, for compositionally polydisperse systems, we observe that the effects of fluctuations show similar trends in systems containing quenched and annealed representation of sequences.

[1]  M. Ouchi,et al.  Transition metal-catalyzed living radical polymerization: toward perfection in catalysis and precision polymer synthesis. , 2009, Chemical reviews.

[2]  David M. Trombly,et al.  Interfacial properties of statistical copolymer brushes in contact with homopolymer melts. , 2011, The Journal of chemical physics.

[3]  J. Noolandi,et al.  Theory of inhomogeneous multicomponent polymer systems , 1981 .

[4]  Marc A. Hillmyer,et al.  Polydisperse Block Copolymer Melts: Beyond the Schulz-Zimm Distribution , 2008 .

[5]  H. Kawai,et al.  Structure and Properties of Tapered Block Polymers of Styrene and Isoprene , 1980 .

[6]  Marc A. Hillmyer,et al.  Polydispersity and block copolymer self-assembly , 2008 .

[7]  Marcus Müller,et al.  Calculating the free energy of self-assembled structures by thermodynamic integration. , 2008, The Journal of chemical physics.

[8]  Juan J de Pablo,et al.  Directed copolymer assembly on chemical substrate patterns: a phenomenological and single-chain-in-mean-field simulations study of the influence of roughness in the substrate pattern. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[9]  Linda J. Broadbelt,et al.  Stochastic modelling of gradient copolymer chemical composition distribution and sequence length distribution , 2010 .

[10]  Benjamin D. Hamilton,et al.  The role of polydispersity in the lamellar mesophase of model diblock copolymers , 2007 .

[11]  M. Matsen,et al.  Fluctuation effects in block copolymer melts , 2003 .

[12]  V. Ganesan,et al.  Communication: Self-assembly of semiflexible-flexible block copolymers , 2012 .

[13]  Marcus Müller,et al.  Memory effects of diblock copolymer brushes and mixed brushes. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[14]  Zhen‐Gang Wang.  Concentration fluctuation in binary polymer blends: Χ parameter, spinodal and Ginzburg criterion , 2002 .

[15]  M. Schick,et al.  Self-assembly of block copolymers , 1996 .

[16]  Qiang Wang,et al.  Effects of interaction range and compressibility on the microphase separation of diblock copolymers: Mean-field analysis. , 2008, The Journal of chemical physics.

[17]  F. Bates,et al.  Order, disorder, and fluctuation effects in an asymmetric poly(ethylene‐propylene)‐poly(ethylethylene) diblock copolymer , 1992 .

[18]  Bumjoon J. Kim,et al.  Hybrid particle-field simulations of polymer nanocomposites. , 2006, Physical review letters.

[19]  V. Ganesan,et al.  Flow deformation of polymer blend droplets and the role of block copolymer compatibilizers , 2006 .

[20]  S. Sides,et al.  Continuous polydispersity in a self-consistent field theory for diblock copolymers. , 2004, The Journal of chemical physics.

[21]  D. Morse,et al.  Renormalized one-loop theory of correlations in disordered diblock copolymers. , 2011, The Journal of chemical physics.

[22]  S. Sides,et al.  Field-theoretic simulations of polymer solutions: finite-size and discretization effects. , 2005, The Journal of chemical physics.

[23]  D. Morse,et al.  Relationships among coarse-grained field theories of fluctuations in polymer liquids. , 2011, The Journal of chemical physics.

[24]  Marc A. Hillmyer,et al.  Effects of Polydispersity on the Order-Disorder Transition in Block Copolymer Melts , 2007 .

[25]  Andrew L. Schmitt,et al.  Polydispersity-driven shift in the lamellar mesophase composition window of PEO-PB-PEO triblock copolymers , 2012 .

[26]  G. Fredrickson,et al.  Field‐theoretic simulations of polyelectrolyte complexation , 2007, 0705.0718.

[27]  G. Fredrickson,et al.  Diblock Copolymer Thin Films: A Field-Theoretic Simulation Study , 2007 .

[28]  G. Fredrickson,et al.  Field-Theoretic Computer Simulation Methods for Polymers and Complex Fluids , 2002 .

[29]  L. Broadbelt,et al.  Factors Affecting the Formation of the Monomer Sequence along Styrene/Methyl Methacrylate Gradient Copolymer Chains , 2009 .

[30]  M. Matsen.  Polydispersity-induced macrophase separation in diblock copolymer melts. , 2007, Physical review letters.

[31]  Baohui Li,et al.  Quantitative Study of Fluctuation Effects by Fast Lattice Monte Carlo Simulations. 2. Homopolymer Brushes in an Implicit, Good Solvent , 2011 .

[32]  S. Whittington,et al.  The statistical mechanics of random copolymers , 2004 .

[33]  L. Leibler,et al.  Theory of Polydisperse Multiblock Copolymers , 1997 .

[34]  Marcus Müller,et al.  Microphase Separation of Diblock Copolymer Brushes in Selective Solvents: Single-Chain-in-Mean-Field Simulations and Integral Geometry Analysis , 2009 .

[35]  Thomas H. Epps,et al.  Design and Synthesis of Network-Forming Triblock Copolymers Using Tapered Block Interfaces. , 2012, ACS macro letters.

[36]  Andrew L. Schmitt,et al.  Unexpected consequences of block polydispersity on the self-assembly of ABA triblock copolymers. , 2012, Journal of the American Chemical Society.

[37]  E. Shakhnovich,et al.  STATISTICAL MECHANICS OF RANDOM HETEROPOLYMERS , 1997 .

[38]  G. Fredrickson,et al.  Field-theoretic simulations of confined polymer solutions , 2003 .

[39]  E. Harth,et al.  New polymer synthesis by nitroxide mediated living radical polymerizations. , 2001, Chemical reviews.

[40]  F. Schmid,et al.  Formation and structure of the microemulsion phase in two-dimensional ternary AB+A+B polymeric emulsions. , 2004, The Journal of chemical physics.

[41]  L. Broadbelt,et al.  Model‐Based Design for Preparing Styrene/Methyl Methacrylate Structural Gradient Copolymers , 2011 .

[42]  J. Genzer,et al.  Cloud point suppression in dilute solutions of model gradient copolymers with prespecified composition profiles , 2011 .

[43]  Thomas H. Epps,et al.  Manipulating ordering transitions in interfacially modified block copolymers , 2009 .

[44]  B. Cherayil,et al.  Semiflexible random A–B block copolymers under tension , 2003 .

[45]  Bates,et al.  Fluctuation-induced first-order transition of an isotropic system to a periodic state. , 1988, Physical review letters.

[46]  Linda J. Broadbelt,et al.  Explicit Sequence of Styrene/Methyl Methacrylate Gradient Copolymers Synthesized by Forced Gradient Copolymerization with Nitroxide-Mediated Controlled Radical Polymerization , 2009 .

[47]  Jiafang Wang,et al.  Microphase separation of mixed polymer brushes: dependence of the morphology on grafting density, composition, chain-length asymmetry, solvent quality, and selectivity. , 2009, The journal of physical chemistry. B.

[48]  F. Bates,et al.  Fluctuations, conformational asymmetry and block copolymer phase behaviour , 1994 .

[49]  Graeme Moad,et al.  Radical addition-fragmentation chemistry in polymer synthesis , 2008 .

[50]  Baohui Li,et al.  Quantitative study of fluctuation effects by fast lattice Monte Carlo simulations. I. Compressible homopolymer melts , 2011 .

[51]  D. Morse,et al.  Test of a scaling hypothesis for the structure factor of disordered diblock copolymer melts , 2012, 1207.1322.

[52]  P. Nealey,et al.  Theoretically informed coarse grain simulations of block copolymer melts: method and applications , 2009 .

[53]  H. Kawai,et al.  Structure and properties of tapered block polymers. 4. "Domain-boundary mixing" and "mixing-in-domain" effects on microdomain morphology and linear dynamic mechanical response , 1983 .

[54]  Sarah E. Mastroianni,et al.  Double-Gyroid Network Morphology in Tapered Diblock Copolymers. , 2011, Macromolecules.

[55]  U. Schubert,et al.  Amphiphilic gradient copolymers containing fluorinated 2‐phenyl‐2‐oxazolines: Microwave‐assisted one‐pot synthesis and self‐assembly in water , 2008 .

[56]  R. E. Cunningham,et al.  Preparation and stress–strain properties of ABA‐type block polymers of styrene and isoprene or butadiene , 1968 .

[57]  Marcus Müller,et al.  Monte Carlo Simulations of a Coarse Grain Model for Block Copolymers and Nanocomposites , 2008 .

[58]  David M. Trombly,et al.  Self-Assembly of Diblock Copolymer on Substrates Modified by Random Copolymer Brushes , 2011 .

[59]  David M. Trombly,et al.  Curvature effects upon interactions of polymer-grafted nanoparticles in chemically identical polymer matrices. , 2010, The Journal of chemical physics.

[60]  Glenn H. Fredrickson,et al.  Fluctuation effects in a symmetric diblock copolymer near the order–disorder transition , 1990 .

[61]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[62]  J. Genzer,et al.  Phase behavior of gradient copolymer solutions: a Monte Carlo simulation study , 2012 .

[63]  D. Morse,et al.  Fluctuations in symmetric diblock copolymers: testing theories old and new. , 2012, Physical review letters.

[64]  V. B. Golubev,et al.  Gradient copolymers: Synthesis, structure, and properties , 2009 .

[65]  I. Kuntz.  The copolymerization of 1,3‐butadiene with styrene by butyllithium initiation , 1961 .

[66]  David M. Trombly,et al.  Surface energies and self-assembly of block copolymers on grafted surfaces. , 2011, Physical review letters.

[67]  A. Shi,et al.  Effects of Polydispersity on Phase Behavior of Diblock Copolymers , 2006 .

[68]  Zhen‐Gang Wang,et al.  Fluctuation in electrolyte solutions: the self energy. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  D. Bedrov,et al.  Properties of Random Block Copolymer Morphologies: Molecular Dynamics and Single-Chain-in-Mean-Field Simulations , 2012 .

[70]  Marcus Müller,et al.  Single chain in mean field simulations: quasi-instantaneous field approximation and quantitative comparison with Monte Carlo simulations. , 2006, The Journal of chemical physics.

[71]  Bruno H. Zimm,et al.  Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyrene Solutions , 1948 .

[72]  M. Matsen,et al.  Effects of polydispersity on the order-disorder transition of diblock copolymer melts , 2008 .

[73]  Fluctuation Effects in Ternary AB + A + B Polymeric Emulsions , 2003, cond-mat/0303654.

[74]  Zhong-yuan Lu,et al.  The influence of one block polydispersity on phase separation of diblock copolymers: The molecular mechanism for domain spacing expansion , 2013 .

[75]  F. Bates.  Polymeric Bicontinuous Microemulsions , 2018 .

[76]  G. Fredrickson,et al.  Field-theoretic polymer simulations , 2001 .

[77]  E. Helfand,et al.  Fluctuation effects in the theory of microphase separation in block copolymers , 1987 .

[78]  D. Morse,et al.  Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[79]  Marc A. Hillmyer,et al.  Influence of Polydispersity on the Self-Assembly of Diblock Copolymers , 2005 .

[80]  Grant D. Smith,et al.  Phase separation in binary mixtures containing polymers: A quantitative comparison of single‐chain‐in‐mean‐field simulations and computer simulations of the corresponding multichain systems , 2005 .

[81]  J. Genzer,et al.  Influence of gradient strength and composition profile on the onset of the cloud point transition in hydroxyethyl methacrylate/dimethylaminoethyl methacrylate gradient copolymers , 2012 .

[82]  K. Matyjaszewski,et al.  Atom transfer radical polymerization. , 2001, Chemical reviews.

[83]  M. Matsen,et al.  Monte Carlo Phase Diagram for a Polydisperse Diblock Copolymer Melt , 2011 .

[84]  V. Ganesan,et al.  Interfacial Phenomena in Polymer Blends: A Self-Consistent Brownian Dynamics Study , 2004 .