One- and Two-Component Bottle-Brush Polymers: Simulations Compared to Theoretical Predictions

Scaling predictions for bottle-brush polymers with a rigid backbone and flexible side chains under good solvent conditions are discussed and their validity is assessed by a comparison with Monte Carlo simulations of a simple lattice model. It is shown that typically only a rather weak stretching of the side chains is realized, and then the scaling predictions are not applicable. Also two-component bottle brush polymers are considered, where two types (A,B) of side chains are grafted, assuming that monomers of different kind repel each other. In this case, variable solvent quality is allowed. Theories predict "Janus cylinder"-type phase separation along the backbone in this case. The Monte Carlo simulations, using the pruned-enriched Rosenbluth method (PERM) give evidence that the phase separation between an A-rich part of the cylindrical molecule and a B-rich part can only occur locally. The correlation length of this microphase separation can be controlled by the solvent quality. This lack of a phase transition is interpreted by an analogy with models for ferromagnets in one space dimension.

[1]  P. Gennes,et al.  Statistics of macromolecular solutions trapped in small pores , 1977 .

[2]  A. W. Rosenbluth,et al.  MONTE CARLO CALCULATION OF THE AVERAGE EXTENSION OF MOLECULAR CHAINS , 1955 .

[3]  S. Alexander,et al.  Adsorption of chain molecules with a polar head a scaling description , 1977 .

[4]  Pavel G. Khalatur,et al.  Conformational properties and dynamics of molecular bottle‐brushes: A cellular‐automaton‐based simulation , 2000 .

[5]  Gary S. Grest,et al.  Structure of a grafted polymer brush: a molecular dynamics simulation , 1989 .

[6]  K. Binder,et al.  How does the pattern of grafting points influence the structure of one-component and mixed polymer brushes? , 2005 .

[7]  G. Grest,et al.  Structure of grafted polymeric brushes in solvents of varying quality: a molecular dynamics study , 1993 .

[8]  H. Gausterer,et al.  Computational Methods in Field Theory , 1992 .

[9]  J. Pichard,et al.  Finite-size scaling approach to Anderson localisation. II. Quantitative analysis and new results , 1981 .

[10]  Martin Möller,et al.  Cylindrical molecular brushes under poor solvent conditions: microscopic observation and scaling analysis , 2004, The European physical journal. E, Soft matter.

[11]  P. Grassberger,et al.  Polymers confined between two parallel plane walls. , 2003, The Journal of chemical physics.

[12]  G. J. Fleer,et al.  Effect of Free Polymer on the Structure of a Polymer Brush and Interaction between Two Polymer Brushes , 1994 .

[13]  K. Fischer,et al.  New perspectives for the design of molecular actuators: thermally induced collapse of single macromolecules from cylindrical brushes to spheres. , 2004, Angewandte Chemie.

[14]  Stefano Elli,et al.  Size and persistence length of molecular bottle-brushes by Monte Carlo simulations. , 2004, The Journal of chemical physics.

[15]  M. Daoud,et al.  Star shaped polymers : a model for the conformation and its concentration dependence , 1982 .

[16]  O. Borisov,et al.  Structure of densely grafted polymeric monolayers , 1988 .

[17]  Scott T. Milner,et al.  Polymers grafted to a convex surface , 1991 .

[18]  G. Brinke,et al.  Comb copolymer brush with chemically different side chains , 2002 .

[19]  K. Binder Phase transitions in polymer blends and block copolymer melts: Some recent developments , 1994 .

[20]  R. Baxter Exactly solved models in statistical mechanics , 1982 .

[21]  I. Szleifer,et al.  Phase Behavior of Grafted Polymers in Poor Solvents , 1994 .

[22]  F. McCrackin,et al.  Monte Carlo Studies of Self-Interacting Polymer Chains with Excluded Volume. II. Shape of a Chain , 1973 .

[23]  Inwardly curved polymer brushes: concave is not like convex , 2001, cond-mat/0102092.

[24]  A. Khokhlov,et al.  Unusual conformation of molecular cylindrical brushes strongly adsorbed on a flat solid surface , 2000 .

[25]  Thomas A. Vilgis,et al.  Scaling theory of planar brushes formed by branched polymers , 1995 .

[26]  K. Binder,et al.  Glassy Materials and Disordered Solids: AN Introduction to Their Statistical Mechanics (revised Edition) , 2011 .

[27]  Krzysztof Matyjaszewski,et al.  On the shape of bottle-brush macromolecules: systematic variation of architectural parameters. , 2005, The Journal of chemical physics.

[28]  A. Halperin On Polymer Brushes and Blobology: an Introduction , 1994 .

[29]  T. Witten,et al.  Colloid stabilization by long grafted polymers , 1986 .

[30]  W. Burchard Static and dynamic light scattering from branched polymers and biopolymers , 1983 .

[31]  Peter Grassberger,et al.  Two-dimensional self-avoiding walks on a cylinder , 1999 .

[32]  R. Toral,et al.  Density profile of terminally anchored polymer chains: a Monte Carlo study , 1990 .

[33]  Matthew Tirrell,et al.  Polymers tethered to curves interfaces: a self-consistent-field analysis , 1992 .

[34]  Hsiao-Ping Hsu,et al.  Simulations of lattice animals and trees , 2004, cond-mat/0408061.

[35]  Manfred Schmidt,et al.  Shape Changes of Statistical Copolymacromonomers: From Wormlike Cylinders to Horseshoe- and Meanderlike Structures , 2002 .

[36]  M. Huggins Solutions of Long Chain Compounds , 1941 .

[37]  William J. Brittain,et al.  Polymer brushes : synthesis, characterization, applications , 2004 .

[38]  O. Borisov,et al.  Conformations of comb-like macromolecules☆ , 1987 .

[39]  K. Binder,et al.  Intramolecular phase separation of copolymer “bottle brushes”: No sharp phase transition but a tunable length scale , 2006, cond-mat/0607186.

[40]  E. Zhulina,et al.  Conformations of star-branched macromolecules , 1984 .

[41]  A. Balazs,et al.  Lateral instabilities in a grafted layer in a poor solvent , 1993 .

[42]  I. Potemkin Elasticity-driven spontaneous curvature of a 2D comb-like polymer with repulsive interactions in the side chains , 2003, The European physical journal. E, Soft matter.

[43]  Effective interactions between star polymers , 2003, cond-mat/0312194.

[44]  T. Witten,et al.  Polymers grafted to convex surfaces: a variational approach , 1994 .

[45]  Olli Ikkala,et al.  Effect of Side Chain Rigidity on the Elasticity of Comb Copolymer Cylindrical Brushes: A Monte Carlo Simulation Study , 1999 .

[46]  Edith M Sevick,et al.  Shear Swelling of Polymer Brushes Grafted onto Convex and Concave Surfaces , 1996 .

[47]  Scott T. Milner,et al.  Theory of the grafted polymer brush , 1988 .

[48]  Jt Johan Padding,et al.  Theory of polymer dynamics , 2007 .

[49]  Hsiao-Ping Hsu,et al.  Scaling of Star Polymers with one to 80 Arms , 2003, cond-mat/0310534.

[50]  G. Fredrickson The equilibrium theory of inhomogeneous polymers , 2005 .

[51]  Arun Yethiraj,et al.  A Monte Carlo simulation study of branched polymers. , 2006, The Journal of chemical physics.

[52]  K. Binder Finite size effects at phase transitions , 1992 .

[53]  E. Zhulina,et al.  Polymer brushes at curved surfaces. , 1993 .

[54]  Yannick Rouault,et al.  From Comb Polymers to Polysoaps: A Monte Carlo Attempt , 1998 .

[55]  M. Carignano,et al.  Tethered Polymer Layers , 1996 .

[56]  O. Borisov,et al.  Temperature-concentration diagram for a solution of star-branched macromolecules , 1986 .

[57]  Timothy P. Lodge,et al.  Tethered chains in polymer microstructures , 1992 .

[58]  Gary S. Grest,et al.  Polymers end-grafted onto a cylindrical surface , 1991 .

[59]  K. Ohno,et al.  Entropy of Polymer Brushes in Good Solvents: A Monte Carlo Study , 2007 .

[60]  P. Grassberger Pruned-enriched Rosenbluth method: Simulations of θ polymers of chain length up to 1 000 000 , 1997 .

[61]  K. Matyjaszewski,et al.  Spontaneous Curvature of Comblike Polymers at a Flat Interface , 2004 .

[62]  Polymer brushes in cylindrical pores: simulation versus scaling theory. , 2006, The Journal of chemical physics.

[63]  G. Grest Grafted polymer brushes: a constant surface pressure molecular dynamics simulation , 1994 .

[64]  Jean Zinn-Justin,et al.  Critical exponents from field theory , 1980 .

[65]  Glenn H. Fredrickson,et al.  Surfactant-induced lyotropic behavior of flexible polymer solutions , 1993 .

[66]  A. Ravve,et al.  Principles of Polymer Chemistry , 1995 .

[67]  N. Denesyuk,et al.  Conformational properties of bottle-brush polymers. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[68]  K. Binder,et al.  Structure and dynamics of polymer brushes near the Θ point: A Monte Carlo simulation , 1992 .

[69]  K. Binder,et al.  Chain desorption from a semidilute polymer brush: A Monte Carlo simulation , 1994 .

[70]  K. Binder,et al.  Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface , 1991 .

[71]  L. Leibler Theory of Microphase Separation in Block Copolymers , 1980 .

[72]  Jena,et al.  Relationship between topological and magnetic order in small metal clusters. , 1985, Physical review. B, Condensed matter.

[73]  K. Binder,et al.  Structure and dynamics of grafted polymer layers: A Monte Carlo simulation , 1991 .

[74]  Robijn Bruinsma,et al.  Soft order in physical systems , 1994 .

[75]  K. Matyjaszewski,et al.  Bottle-brush macromolecules in solution: Comparison between results obtained from scattering experiments and computer simulations , 2006 .

[76]  A. Burin,et al.  Glassy Materials and Disordered Solids , 2006 .

[77]  P. G. de Gennes,et al.  Conformations of Polymers Attached to an Interface , 1980 .

[78]  Structure of Polymer Brushes in Cylindrical Tubes: A Molecular Dynamics Simulation , 2006, cond-mat/0606637.

[79]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

[80]  P. Gennes Scaling Concepts in Polymer Physics , 1979 .

[81]  Marcus Müller,et al.  Phase diagram of a mixed polymer brush. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[82]  D. Theodorou,et al.  Simulation Methods for Polymers , 2007 .

[83]  G. Brinke,et al.  Conformational aspects and intramolecular phase separation of alternating copolymacromonomers: A computer simulation study , 2004 .

[84]  E. Zhulina,et al.  Self-consistent field theories for polymer brushes: lattice calculations and an asymptotic analytical description , 1992 .

[85]  Kurt Kremer,et al.  The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions , 1988 .

[86]  S. Bywater,et al.  Preparation and Characterization of Four-Branched Star Polystyrene , 1972 .

[87]  N. Denesyuk Bottle-brush polymers as an intermediate between star and cylindrical polymers. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[88]  Olli Ikkala,et al.  On lyotropic behavior of molecular bottle-brushes: A Monte Carlo computer simulation study , 1997 .

[89]  Samuel A. Safran,et al.  Size distribution for aggregates of associating polymers. II. Linear packing , 1988 .

[90]  Terence Cosgrove,et al.  Configuration of terminally attached chains at the solid/solvent interface: self-consistent field theory and a Monte Carlo model , 1987 .

[91]  F. L. McCrackin,et al.  Configuration properties of comb-branched polymers , 1981 .

[92]  O. Borisov,et al.  Curved polymer and polyelectrolyte brushes beyond the Daoud-Cotton model , 2006, The European physical journal. E, Soft matter.

[93]  O. Borisov,et al.  Coil-globule type transitions in polymers. 1. Collapse of layers of grafted polymer chains , 1991 .

[94]  K. Binder,et al.  Static properties of end-tethered polymers in good solution: a comparison between different models. , 2004, The Journal of chemical physics.

[95]  K. Binder,et al.  Diblock Copolymers at a Homopolymer−Homopolymer Interface: A Monte Carlo Simulation , 1996 .

[96]  Olli Ikkala,et al.  Extended conformations of isolated molecular bottle‐brushes: Influence of side‐chain topology , 1998 .

[97]  Netz,et al.  Polymer Brushes: From Self-Consistent Field Theory to Classical Theory. , 1998, Macromolecules.

[98]  O. Borisov,et al.  Comb-Branched Polymers: Monte Carlo Simulation and Scaling , 1996 .

[99]  Yuri A. Kuznetsov,et al.  Intrinsic and +topological stiffness in branched polymers , 2005 .

[100]  Ian W. Hamley,et al.  The physics of block copolymers , 1998 .

[101]  G. Fredrickson The theory of polymer dynamics , 1996 .

[102]  Olli Ikkala,et al.  Elasticity of Comb Copolymer Cylindrical Brushes , 2000 .

[103]  Katsunori Itoh,et al.  Simulations of the shape of a regularly branched polymer as a model of a polymacromonomer , 1999 .

[104]  Karl Fischer,et al.  Conformation of Cylindrical Brushes in Solution: Effect of Side Chain Length , 2006 .

[105]  K. Binder,et al.  A polymer chain trapped between two parallel repulsive walls: A Monte-Carlo test of scaling behavior , 1998 .

[106]  Pavel G. Khalatur,et al.  Microphase Separation within a Comb Copolymer with Attractive Side Chains: A Computer Simulation Study , 2001 .

[107]  Isidor Kirshenbaum,et al.  The Vapor Pressure and Heat of Vaporization of N15 , 1941 .

[108]  Kurt Kremer,et al.  Monte Carlo simulation of lattice models for macromolecules , 1988 .

[109]  Berend Smit,et al.  Novel scheme to study structural and thermal properties of continuously deformable molecules , 1992 .

[110]  Ludwik Leibler,et al.  Decoration of rough surfaces by chain grafting , 1990 .

[111]  K. Binder Monte Carlo and molecular dynamics simulations in polymer science , 1995 .