Formation of double helical and filamentous structures in models of physical and chemical gels

Finite size effects in critical fiber networks

Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.

Supramolecular Helical Systems: Helical Assemblies of Small Molecules, Foldamers, and Polymers with Chiral Amplification and Their Functions

In this review, we describe the recent advances in supramolecular helical assemblies formed from chiral and achiral small molecules, oligomers (foldamers), and helical and nonhelical polymers from the viewpoints of their formations with unique chiral phenomena, such as amplification of chirality during the dynamic helically assembled processes, properties, and specific functionalities, some of which have not been observed in or achieved by biological systems. In addition, a brief historical overview of the helical assemblies of small molecules and remarkable progress in the synthesis of single-stranded and multistranded helical foldamers and polymers, their properties, structures, and functions, mainly since 2009, will also be described.

Structure and cohesive energy of dipolar helices

This paper deals with the investigation of cohesive energy in dipolar helices made up of hard spheres. Such tubular helical structures are ubiquitous objects in biological systems. We observe a complex dependence of cohesive energy on surface packing fraction and dipole moment distribution. As far as single helices are concerned, the lowest cohesive energy is achieved at the highest surface packing fraction. Besides, a striking non-monotonic behavior is reported for the cohesive energy as a function of the surface packing fraction. For multiple helices, we discover a new phase, exhibiting markedly higher cohesive energy. This phase is referred to as ZZ tube consisting of stacked crown rings (reminiscent of a pile of zig-zag rings), resulting in a local triangular arrangement with densely packed filaments parallel to the tube axis.

A correlation study between hydrogen-bonded network and gelation ability of three galactose derivatives

The hydrogen bonding network in the crystals of the three saccharides was correlated with their gelling ability or inability, and unexpectedly, a 2D hydrogen-bonded system was found to show efficient gelation, whereas a 1D hydrogen bonding system was a nongelator.

Self-assembly of novel benzimidazole N-glycosylamines into nanofibers and nanospheres

Cu²⁺ ions induce the change in the morphology of self-assembled benzimidazole N-glycosylamines from nano-fibers to nano-spheres.

Using mesoscopic models to design strong and tough biomimetic polymer networks

Using computational modeling, we investigate the mechanical properties of polymeric materials composed of coiled chains, or "globules", which encompass a folded secondary structure and are cross-linked by labile bonds to form a macroscopic network. In the presence of an applied force, the globules can unfold into linear chains and thereby dissipate energy as the network is deformed; the latter attribute can contribute to the toughness of the material. Our goal is to determine how to tailor the labile intra- and intermolecular bonds within the network to produce material exhibiting both toughness and strength. Herein, we use the lattice spring model (LSM) to simulate the globules and the cross-linked network. We also utilize our modified Hierarchical Bell model (MHBM) to simulate the rupture and reforming of N parallel bonds. By applying a tensile deformation, we demonstrate that the mechanical properties of the system are sensitive to the values of N(in) and N(out), the respective values of N for the intra- and intermolecular bonds. We find that the strength of the material is mainly controlled by the value of N(out), with the higher value of N(out) providing a stronger material. We also find that, if N(in) is smaller than N(out), the globules can unfold under the tensile load before the sample fractures and, in this manner, can increase the ductility of the sample. Our results provide effective strategies for exploiting relatively weak, labile interactions (e.g., hydrogen bonding or the thiol/disulfide exchange reaction) in both the intra- and intermolecular bonds to tailor the macroscopic performance of the materials.

Fivefold symmetry as an inhibitor to hard-sphere crystallization

Through molecular simulations we investigate the dynamics of crystallization of hard spheres of uniform size from dense amorphous states and the role that hidden structures in an otherwise disordered medium might have on it. It is shown that short-range order in the form of sites with fivefold symmetry acts as a powerful inhibitor to crystal growth. Fivefold sites not only retard crystallization, but can self-assemble into organized structures that arrest crystallization at high densities or lead to the formation of defects in a crystal. The latter effect can be understood in terms of a random polyhedral model.

Unique organogel formation with macroporous materials constructed by the freeze-drying of aqueous cyclodextrin solutions

Macroporous cyclodextrin materials (MP-alpha-, beta-, and gamma-CDs) were easily fabricated by the freeze-drying of aqueous solutions of alpha-, beta-, and gamma-CDs. These MP-CDs showed the absorption ability toward various organic solvents and oils to give organogels at ambient temperature. The morphological changes of the MP-CD microstructures were observed through the absorption of organic solvents. In particular, the absorption of polar organic solvents with hydrogen-bond forming ability, including 1,4-dioxane and ethanol, by the MP-CDs caused remarkable morphological changes in the microstructures. The absorption of these polar solvents by MP-alpha- and gamma-CDs resulted in the formation of channel-type assemblies of alpha- and gamma-CDs, respectively.

Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

Effect of network topology on phase separation in two-dimensional Lennard-Jones networks

We generate two-dimensional Lennard-Jones networks with random topology by preparing a perfect four-functional network of identical harmonic springs and randomly cutting some of the springs. Using molecular-dynamics simulations we find that the fraction p of active springs affects both the temperature of phase separation and the type of structures observed below this temperature, from networklike high-density patterns at p>0.5 ("gel") to dropletlike structures at p<0.5 ("sol"). In the gel domain, these patterns are determined by the interplay between free energy and network topology, with the former dominant as p-->1 and the latter as p-->0.5 .

Coarse-grained single-particle dynamics in two-dimensional solids and liquids

We consider the dynamics of a single tagged particle in a two-dimensional system governed by Lennard-Jones interactions. Previous work based on the Mori-Zwanzig projection operator formalism has shown that the single-particles dynamics can be described via a generalized Langevin equation (GLE) which is exact within the harmonic approximation, that is, for a low-temperature solid [J. M. Deutch and R. Silbey, Phys. Rev. A 3, 2049 (1971)]. In the present work we explore to what an extent the GLE reproduces the effective dynamics under thermodynamic conditions where the harmonic approximation is no longer justified. To this end we compute characteristic time autocorrelation functions for the tagged particle in molecular dynamics simulations of the full system and compare these functions with those obtained from solving the GLE. At low temperatures we find excellent agreement between both data sets. Deviations emerge at higher temperatures which are, however, surprisingly small even in the high-temperature liquid phase.

Linear self-assembly under confinement

An exactly solvable model is used to obtain the response to confinement of the cluster distribution of linear aggregation. A direct relevance to simulation studies of linear self-assembly in discotic solutions and in peptide tape formation is proposed. The mapping predicts, for typical simulation procedures, that a finite reservoir of solute leads to a dramatic departure from isodesmic chemical equilibria for solute-solute interaction strengths higher than only a few k(B)T .