Molecular simulations are performed to study the self-assembly of particles with discrete, attractive interaction sites − “patches” − at prescribed locations on the particle surface. Chains, sheets, rings, icosahedra, square pyramids, tetrahedra, and twisted and staircase structures are obtained through suitable design of the surface pattern of patches. Our simulations predict that the spontaneous formation of two-dimensional sheets and icosahedra occurs via a first-order transition while the formation of chains occurs via a continuous disorder-to-order transition as in equilibrium polymerization. Our results show how precise arrangements of patches combined with patch “recognition” or selectivity may be used to control the relative position of particles and the overall structure of particle assemblies. In this context, patchy particles represent a new class of building block for the fabrication of precise structures.

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Self-Assembly of Patchy Particles.

A review of current chemorheological techniques and measurement systems is presented for unfilled and filled thermoset resins. The specific measurement techniques for the kinetics, chemorheology, and modeling of these systems are presented, with particular emphasis on the chemorheological techniques and measuring systems. These techniques and measurement systems provide a greater understanding of traditionally complex thermoset processes, provide effective quality control measures for these processes, and will reduce design and operating costs in associated industries.

Chemorheology of thermosets—an overview

Polycyanate esters: Science and applications

Molecular modeling and simulations are invaluable tools for the polymer science and engineering community. These computational approaches enable predictions and provide explanations of experimentally observed macromolecular structure, dynamics, thermodynamics, and microscopic and macroscopic material properties. With recent advances in computing power, polymer simulations can synergistically inform, guide, and complement in vitro macromolecular materials design and discovery efforts. To ensure that this growing power of simulations is harnessed correctly, and meaningful results are achieved, care must be taken to ensure the validity and reproducibility of these simulations. With these considerations in mind, in this Perspective we discuss our philosophy for carefully developing or selecting appropriate models, performing, and analyzing polymer simulations. We highlight best practices, key challenges, and important advances in model development/selection, computational method choices, advanced sampling met...

Modeling and Simulations of Polymers: A Roadmap

The search for advanced, high performance, high temperature resistant polymers is on the rise in view of the growing demand for polymer matrix composites that are to meet stringent functional requirements for use in the rapidly evolving high-tech area of aerospace. Cyanate esters (CEs) form a family of new generation thermosetting resins whose performance characteristics make them attractive competitors to many current commercial polymer materials for such applications. The chemistry and technology of CEs are relatively new and continue to evolve and enthuse researchers. The CEs are gifted with many attractive physical, electrical, thermal, and processing properties required of an ideal matrix resin. These properties are further tunable through backbone structure and by blending with other polymer systems. The structure-property correlation is quite well established. Several new monomers have been reported while some are commercially available. The synthesis of new monomers has come to a stage of stagnation and the present attention is on evolving new formulations and processing techniques. The blends with epoxy and bismaleimide have attracted a lot of research attention and achieved commercial success. While the latter is now known to form an IPN, the reaction mechanism with epoxy is still intriguing. Extensive research in blending with conventional and high performance thermoplastics has led to the generation of key information on morphological features and toughening mechanisms, to the extent that even simulation of morphology and property has now become possible. Despite the fact that the resin and its technology are nearly two decades old, the fundamental aspects related to curing, cure kinetics, reaction modeling, etc. still evince immense research interest and new hypotheses continue to emerge.

Cyanate Ester Resins, Recent Developments

An efficient continuum model for simulating polymer blends and copolymers is presented. In this model, the interactions are short‐range and purely repulsive, thus allowing for excellent computational performances. The driving force for phase separation is a difference in the repulsive interaction strength between like and unlike mers. The model consists essentially of a molecular‐dynamics algorithm, supplemented by an appropriate Monte Carlo exchange process. To demonstrate the effectiveness of the model we study two systems, a symmetric binary blend of polymers and a symmetric diblock copolymer system. For the binary blend, we determine the phase diagram and find, as predicted by theory, that the critical interaction parameter scales with the inverse of the chain length of the polymers. For the diblock copolymer system, we study both the one‐phase region and the microphase separated lamellar region. For the latter, we show that constant‐pressure algorithms are more appropriate since, contrary to recent lattice simulations, the lamellar spacing can self‐adjust in such an ensemble.

Efficient continuum model for simulating polymer blends and copolymers

We present a self‐consistent‐field structure for the thermodynamic description of concentrated solutions of liquid‐crystal polymers. The polymers are assumed to be locally stiff but capable of curvature over large distances. The formulation of the chain geometry is that of a wormlike polymer, but the final analysis is simpler than the Kratky–Porod form. The phase behavior is analyzed for a cylindrically symmetric mean‐field nematic ordering interaction. As expected, in two dimensions the system undergoes a second‐order phase transition and in three dimensions the nematic transition is first‐order uniaxial. The three relevant physical parameters which describe the phase behavior of the polymers are the molecular mass of the polymers, a measure of the chain stiffness and strength of the nematic interaction. The formulation in this paper is for infinitely long polymers. If the chain stiffness is measured by the bending energy e, with u as the strength of the hardcore repulsion and U that of the soft interact...

Mean-field theory of phase transitions in liquid-crystalline polymers

Synthesis and characterization of tightly branched, rigid, network polymers based on the cyanate functional group are reported. Polymers based on the bifunctional compound 2,2-bis(4-cyariatophenyl)propane (BCP) were synthesized thermally in bulk without a catalyst. Molecular weight M n and molecular weight M w are reported as a function of cyanate group conversion. The gel conversion is found to be over 60%, significantly higher than the mean-field value of 50%. The source of this disagreement is discussed.

Characterization and modeling of rigid branched polycyanates

We have developed a new algorithm that simulates the structure buildup process during homopolymerization of Af monomers. The algorithm is an off lattice percolation solution on a cube with periodic boundary conditions. All monomers are treated as point particles. After choosing any two nodes at random, the probability of their reaction is computed and compared with a random number. We present results where the probability rule is a step function over the interunitary distance between the chosen pair. We reason that this simulates, in a simplistic but effective fashion, the importance of diffusion vs reaction times in the problem. Thus, the case where units react in immediate neighborhoods corresponds to a diffusion limited growth and where they react with equal probability with all other units to the mean field or kinetic limited growth. We present results for five step reactive potentials with careful analysis of finite size effects. We find that the gel conversion is delayed as a consequence of diffusio...

Monte Carlo description of Af homopolymerization: Diffusional effects

The chemistry and growth of polymer structures based on the cyanate linkage has been studied. The monofunctional model compound 2-(4-cyanatophenyl)-2-phenylpropane was used to study the reaction products. The synthesis was performed with four different transition metal catalysts and also without a catalyst. The quenched products were analyzed using Size Exclusion Chromatography(SEC) and 13C NMR. It was found that the reaction is relatively clean, with trimerization being the major product. A few side products were also detected, which included dimers and higher oligomeric species. Crosslinked polymers were synthesized without catalyst based on the bifunctional monomer 2, 2-bis(4-cyanatophenyl)propane. The structure was analyzed using 13C NMR. The conversion and number-average degree of polymerization based on 13C NMR is reported. Conversion at the gel point was found to be higher than 60%. On this basis it was concluded that polymerization based on cyanate linkages at the conditions studied is diffusion controlled and therefore not described by Flory's mean-field theory.

Anshu M. Gupta

Papers

Efficient continuum model for simulating polymer blends and copolymers

Mean-field theory of phase transitions in liquid-crystalline polymers

Characterization and modeling of rigid branched polycyanates

Monte Carlo description of Af homopolymerization: Diffusional effects

Synthesis and characterization of polymers based on the cyanate functional group