Engineering entropy in soft matter: the bad, the ugly and the good.

The role of entropic interactions, often subtle and sometimes crucial, on the structure and properties of soft matter has a well-recognized place in the classic and modern scientific literature. However, the lessons learned from many of those studies do not always form part of the standard arsenal of strategies that are taught or used for de novo studies relevant to the engineering of new materials. Fortunately, a growing number of examples exist where entropic effects have been designed a priori to achieve a desired or new outcome. This tutorial review describes some recent such examples, selected to illustrate the potential benefits of a more pro-active approach to harnessing the often overlooked power of entropy.

[1]  R. Stewart,et al.  Cement Proteins of the Tube-building Polychaete Phragmatopoma californica* , 2005, Journal of Biological Chemistry.

[2]  Daan Frenkel,et al.  Why colloidal systems can be described by statistical mechanics: some not very original comments on the Gibbs paradox , 2013, 1312.0206.

[3]  Francisco J. Martinez-Veracoechea,et al.  Molecular dynamics simulation of the mesophase behaviour of a model bolaamphiphilic liquid crystal with a lateral flexible chain , 2008 .

[4]  A. Balazs,et al.  Predicting the Mesophases of Copolymer-Nanoparticle Composites , 2001, Science.

[5]  Qian Chen,et al.  Directed self-assembly of a colloidal kagome lattice , 2014 .

[6]  M. Dijkstra,et al.  Dense regular packings of irregular nonconvex particles. , 2011, Physical review letters.

[7]  S Torquato,et al.  Exact constructions of a family of dense periodic packings of tetrahedra. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  U. Wiesner,et al.  A bicontinuous double gyroid hybrid solar cell. , 2009, Nano letters.

[9]  J. Overbeek,et al.  Phase separation in polyelectrolyte solutions; theory of complex coacervation. , 1957, Journal of cellular physiology. Supplement.

[10]  Patrick B. Warren,et al.  COMBINATORIAL ENTROPY AND THE STATISTICAL MECHANICS OF POLYDISPERSITY , 1998 .

[11]  M. Dijkstra,et al.  Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: a comparison of simulation techniques. , 2010, The Journal of chemical physics.

[12]  E. M. Terentjev,et al.  Liquid Crystal Elastomers , 2003 .

[13]  Francisco J. Martinez-Veracoechea,et al.  Monte Carlo study of the stabilization of complex bicontinuous phases in diblock copolymer systems , 2007 .

[15]  Jian Zhang,et al.  DNA-nanoparticle superlattices formed from anisotropic building blocks. , 2010, Nature materials.

[16]  E. W. Edwards,et al.  Directed Assembly of Block Copolymer Blends into Nonregular Device-Oriented Structures , 2005, Science.

[17]  F. Escobedo Mapping coexistence lines via free-energy extrapolation: application to order-disorder phase transitions of hard-core mixtures. , 2014, The Journal of chemical physics.

[18]  C. Cohen,et al.  Toughness and fracture energy of PDMS bimodal and trimodal networks with widely separated precursor molar masses , 2010 .

[19]  T. Hashimoto,et al.  Microdomain structures with hyperbolic interfaces in block and graft copolymer systems , 1996 .

[20]  P. Damasceno,et al.  Predictive Self-Assembly of Polyhedra into Complex Structures , 2012, Science.

[21]  I. Coluzza,et al.  Telechelic star polymers as self-assembling units from the molecular to the macroscopic scale. , 2012, Physical review letters.

[22]  F. Sciortino,et al.  Two dimensional assembly of triblock Janus particles into crystal phases in the two bond per patch limit , 2011 .

[23]  Xiaoming Mao,et al.  Entropic effects in the self-assembly of open lattices from patchy particles. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Salvatore Torquato,et al.  Optimized monotonic convex pair potentials stabilize low-coordinated crystals , 2010, 1010.6293.

[25]  Design rule for colloidal crystals of DNA-functionalized particles. , 2011, Physical review letters.

[26]  D. Frenkel,et al.  The other entropy , 2013 .

[27]  C. Cohen,et al.  Sawtooth Tensile Response of Model Semiflexible and Block Copolymer Elastomers , 2014 .

[28]  S. Torquato,et al.  Dense packings of the Platonic and Archimedean solids , 2009, Nature.

[29]  T. Mason,et al.  Suppressing and enhancing depletion attractions between surfaces roughened by asperities. , 2008, Physical Review Letters.

[30]  Effect of quenched size polydispersity on the ordering transitions of hard polyhedral particles. , 2012, The Journal of chemical physics.

[31]  E. W. Meijer,et al.  Spatiotemporal control and superselectivity in supramolecular polymers using multivalency , 2013, Proceedings of the National Academy of Sciences.

[32]  Susan C. Roberts,et al.  Polyelectrolytes for cell encapsulation , 2005 .

[33]  Aaron S. Keys,et al.  Self-assembly of patchy particles into diamond structures through molecular mimicry. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[34]  I. Cohen,et al.  Entropy-driven crystal formation on highly strained substrates , 2013, Proceedings of the National Academy of Sciences.

[35]  Werner Krauth,et al.  Two-step melting in two dimensions: first-order liquid-hexatic transition. , 2011, Physical review letters.

[36]  Dissipative particle dynamics simulation of T- and X-shaped polyphilic molecules exhibiting honeycomb columnar phases , 2009 .

[37]  Daeha Seo,et al.  Polyhedral gold nanocrystals with O h symmetry: from octahedra to cubes. , 2006, Journal of the American Chemical Society.

[38]  David Pines,et al.  The Many-body Problem , 1971 .

[39]  Claudiu B. Bucur,et al.  Ideal mixing in polyelectrolyte complexes and multilayers: entropy driven assembly. , 2006, Journal of the American Chemical Society.

[40]  T. Hanrath Colloidal nanocrystal quantum dot assemblies as artificial solids , 2012 .

[41]  Francisco J. Martinez-Veracoechea,et al.  The Plumber’s Nightmare Phase in Diblock Copolymer/Homopolymer Blends. A Self-Consistent Field Theory Study. , 2009 .

[42]  S. Glotzer,et al.  Anisotropy of building blocks and their assembly into complex structures. , 2007, Nature materials.

[43]  M. Tirrell,et al.  Thermodynamic characterization of polypeptide complex coacervation. , 2012, Langmuir : the ACS journal of surfaces and colloids.

[44]  Sharon C Glotzer,et al.  Entropically patchy particles: engineering valence through shape entropy. , 2013, ACS nano.

[45]  K. Dill,et al.  Principles of maximum entropy and maximum caliber in statistical physics , 2013 .

[46]  Experiments and Simulations: Enhanced Mechanical Properties of End-Linked Bimodal Elastomers , 2008 .

[47]  F. Sciortino,et al.  Liquids more stable than crystals in particles with limited valence and flexible bonds , 2013, Nature Physics.

[48]  M. Engel,et al.  Phase diagram of hard tetrahedra. , 2011, The Journal of chemical physics.

[49]  C. Hall,et al.  Polymer-induced phase separations in nonaqueous colloidal suspensions , 1983 .

[50]  Salvatore Torquato,et al.  Communication: Designed diamond ground state via optimized isotropic monotonic pair potentials. , 2012, The Journal of chemical physics.

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

[52]  Fernando A Escobedo,et al.  Mesophase behaviour of polyhedral particles. , 2011, Nature materials.

[53]  Fernando A Escobedo,et al.  Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study. , 2005, The journal of physical chemistry. B.

[54]  Hanqiong Hu,et al.  Directed self-assembly of block copolymers: a tutorial review of strategies for enabling nanotechnology with soft matter. , 2014, Soft matter.

[55]  L. Archer,et al.  Surface‐Functionalized Nanoparticles with Liquid‐Like Behavior , 2005 .

[56]  C. Tschierske,et al.  Complex tiling patterns in liquid crystals , 2012, Interface Focus.

[57]  Umang Agarwal,et al.  Phase behavior of binary mixtures of hard convex polyehdra , 2013, 1309.2989.

[58]  S. Gruner,et al.  Mesophase Structure-Mechanical and Ionic Transport Correlations in Extended Amphiphilic Dendrons , 2004, Science.

[59]  C. Avendaño,et al.  Phase behavior of rounded hard-squares , 2012 .

[60]  Samanvaya Srivastava,et al.  Thermal jamming of a colloidal glass. , 2011, Physical review letters.

[61]  T. Mason,et al.  Directing colloidal self-assembly through roughness-controlled depletion attractions. , 2007, Physical review letters.

[62]  Fumio Oosawa,et al.  Interaction between particles suspended in solutions of macromolecules , 1958 .

[63]  M. Dijkstra,et al.  Phase diagram and structural diversity of a family of truncated cubes: degenerate close-packed structures and vacancy-rich states. , 2013, Physical review letters.

[64]  Frank S. Bates,et al.  Origins of Complex Self-Assembly in Block Copolymers , 1996 .

[65]  Jiwon Kim,et al.  Self-assembly: from crystals to cells , 2009 .

[66]  Costantino Creton,et al.  Toughening Elastomers with Sacrificial Bonds and Watching Them Break , 2014, Science.

[67]  L. Onsager THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES , 1949 .

[68]  D. Koch,et al.  Structure of solvent-free grafted nanoparticles: molecular dynamics and density-functional theory. , 2011, The Journal of chemical physics.

[69]  A. Hyman,et al.  Beyond Oil and Water—Phase Transitions in Cells , 2012, Science.

[70]  Peter G. Bolhuis,et al.  Tracing the phase boundaries of hard spherocylinders , 1997 .

[71]  Venkat Ganesan,et al.  Theory and simulation studies of effective interactions, phase behavior and morphology in polymer nanocomposites. , 2014, Soft matter.

[72]  D. Frenkel ENTROPY-DRIVEN PHASE TRANSITIONS , 1999 .

[73]  Alfons van Blaaderen,et al.  Self-assembly route for photonic crystals with a bandgap in the visible region. , 2007, Nature materials.

[74]  Arieh Ben-Naim,et al.  Entropy Demystified: The Second Law Reduced To Plain Common Sense , 2007 .

[75]  Ludwik Leibler,et al.  Silica-Like Malleable Materials from Permanent Organic Networks , 2011, Science.

[76]  E. Bianchi,et al.  Patchy colloids: state of the art and perspectives. , 2011, Physical chemistry chemical physics : PCCP.

[77]  Francisco J. Martinez-Veracoechea,et al.  Bicontinuous Phases in Diblock Copolymer/Homopolymer Blends : Simulation and Self-Consistent Field Theory , 2009 .

[78]  Thomas M. Truskett,et al.  Inverse design of simple pairwise interactions with low-coordinated 3D lattice ground states , 2013, 1303.1049.

[79]  F. Escobedo,et al.  Phase behavior of colloidal hard perfect tetragonal parallelepipeds. , 2008, The Journal of chemical physics.

[80]  Michael W. Deem,et al.  Entropy, disease, and new opportunities for chemical engineering research , 2005 .

[81]  Abraham D Stroock,et al.  Experimental investigation of selective colloidal interactions controlled by shape, surface roughness, and steric layers. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[82]  B. Alder,et al.  Phase Transition for a Hard Sphere System , 1957 .

[83]  Linda S. Schadler,et al.  Anisotropic self-assembly of spherical polymer-grafted nanoparticles. , 2009, Nature materials.

[84]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[85]  Sharon C. Glotzer,et al.  Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra , 2009, Nature.

[86]  Mario Viani,et al.  Molecular mechanistic origin of the toughness of natural adhesives, fibres and composites , 1999, Nature.

[87]  P. Damasceno,et al.  Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces. , 2011, ACS nano.

[88]  F. Escobedo,et al.  Exploration of Factors Affecting the Onset and Maturation Course of Follicular Lymphoma through Simulations of the Germinal Center , 2009, Bulletin of mathematical biology.

[89]  M. Tirrell,et al.  Complex coacervation of poly(ethylene-imine)/polypeptide aqueous solutions: thermodynamic and rheological characterization. , 2013, Journal of colloid and interface science.

[90]  K. Dill,et al.  The Protein-Folding Problem, 50 Years On , 2012, Science.

[91]  Qian Chen,et al.  Entropy favours open colloidal lattices. , 2013, Nature materials.

[92]  Daan Frenkel,et al.  Soft condensed matter , 2002 .

[93]  P. Bolhuis,et al.  Monte Carlo study of freezing of polydisperse hard spheres. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[94]  Mihir R Khadilkar,et al.  Self-assembly of binary space-tessellating compounds. , 2012, The Journal of chemical physics.

[95]  A D Wissner-Gross,et al.  Causal entropic forces. , 2013, Physical review letters.

[96]  D. Frenkel,et al.  Superselective Targeting Using Multivalent Polymers , 2014, Journal of the American Chemical Society.

[97]  J. Shapiro,et al.  How life changes itself: the Read-Write (RW) genome. , 2013, Physics of life reviews.

[98]  Robert H. Swendsen,et al.  Gibbs' Paradox and the Definition of Entropy , 2008, Entropy.

[99]  David J. Pine,et al.  Engineering shape: the novel geometries of colloidal self-assembly , 2013 .

[100]  Xiaoming Mao,et al.  Self-assembly of three-dimensional open structures using patchy colloidal particles. , 2014, Soft matter.

[101]  D. Frenkel,et al.  Designing super selectivity in multivalent nano-particle binding , 2011, Proceedings of the National Academy of Sciences.

[102]  A. Jayaraman,et al.  Polydisperse homopolymer grafts stabilize dispersions of nanoparticles in a chemically identical homopolymer matrix: an integrated theory and simulation study , 2013 .

[103]  D. Chandler Interfaces and the driving force of hydrophobic assembly , 2005, Nature.