Homoclinic Chaos in 2-DOF Robot Manipulators Driven by PD Controllers

The existence of Smale horseshoes in the dynamics of twodegrees of freedom (2-DOF) robot manipulators with viscous damping anddriven by classical proportional-derivative (PD) controllers is proved.The situation where an actuator failure occurs is also analyzed. Thecontrollers correspond to the classical PD and the PD with gravitycompensation. They are considered as non-Hamiltonian perturbations of anundriven 2-DOF robot; then a technique developed by Holmes and Marsden,which uses a combination of a reduction scheme and Melnikov's methodwith an energy balance argument, is applied.     

Buckling instability in liquid crystalline physical gels

In a nematic gel we observe a low-energy buckling deformation arising from soft and semisoft elastic modes. We prepare the self-assembled gel by dissolving a coil-side-group liquid-crystalline polymer-coil copolymer in a nematic liquid crystal. The gel has long network strands and a precisely tailored structure, making it ideal for studying nematic rubber elasticity. Under polarized optical microscopy we observe a striped texture that forms when gels uniformly aligned at 35 degrees C are cooled to room temperature. We model the instability using the molecular theory of nematic rubber elasticity, and the theory correctly captures the change in pitch length with sample thickness and polymer concentration. This buckling instability is a clear example of a low-energy deformation that arises in materials where polymer network strains are coupled to the director orientation.     

Conjugated block copolymers via functionalized initiators and click chemistry

Conjugated block copolymers are potentially useful for organic electronic applications and the study of interfacial charge and energy transfer processes; yet few synthetic methods are available to prepare polymers with well‐defined conjugated blocks. Here, we report the synthesis and thin film morphology of a series of conjugated poly(3‐hexylthiophene)‐block‐poly(9,9‐dioctylfluorene) (P3HT‐b‐PF) and poly(3‐dodecylthiophene)‐block‐poly(9,9‐dioctylfluorene) (P3DDT‐b‐PF) block copolymers prepared by functional external initiators and click chemistry. Functional group control is quantified by proton nuclear magnetic resonance spectroscopy, size‐exclusion chromatography, and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry. The thin film morphology of the resulting all‐conjugated block copolymers is analyzed by a combination of grazing‐incidence X‐ray scattering, atomic force microscopy, and transmission electron microscopy. Crystallization of the P3HT or P3DDT blocks is present in thin films for all materials studied, and P3DDT‐b‐PF films exhibit significant PF/P3DDT co‐crystallization. Processing conditions are found to impact thin film crystallinity and orientation of the π–π stacking direction of polymer crystallites. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 154–163     

Structural investigation of PAMAM dendrimers in aqueous solutions using small-angle neutron scattering: effect of generation

We investigate a series of poly(amidoamine) starburst dendrimers (PAMAM) of different generations in acidic, aqueous solutions using small-angle neutron scattering (SANS). While the overall molecular size is found to be practically unaffected by a pD change, a strong generational dependence of counterion association is revealed. Upon increasing the dendrimer generation, the effective charge obtained from our SANS experiments only shows a small increase in contrast to the nearly exponential increase predicted by a recent atomic simulation. We also find that with the same degree of molecular protonation the specific counterion association, which is defined as the ratio of bound chloride anions to positively charged amines in solutions, is larger for higher-generation PAMAM dendrimer. The associated counterion density also increases upon increasing generation number.     

Quantitative analysis of structure and bandgap changes in graphene oxide nanoribbons during thermal annealing

Graphene oxide nanoribbons (GONRs) are wide bandgap semiconductors that can be reduced to metallic graphene nanoribbons. The transformation of GONRs from their semiconductive to the metallic state by annealing has attracted significant interest due to its simplicity. However, the detailed process by which GONRs transform from wide-bandgap semiconductors to semimetals with a near zero bandgap is unclear. As a result, precise control of the bandgap between these two states is not currently achievable. Here, we quantitatively examine the removal of oxygen-containing groups and changes in the bandgap during thermal annealing of GONRs. X-ray photoelectron spectroscopy measurements show the progressive removal of oxygen-containing functional groups. Aberration-corrected scanning transmission electron microscopy reveals that initially small graphene regions in GONRs become large stacked graphitic layers during thermal annealing. These structural and chemical changes are correlated with progressive changes in the electrochemical bandgap, monitored by cyclic voltammetry. These results show that small changes in the thermal annealing temperature result in significant changes to the bandgap and chemical composition of GONRs and provide a straightforward method for tuning the bandgap in oxidized graphene structures.     

Control of all‐conjugated block copolymer crystallization via thermal and solvent annealing

Control of the crystallization of conjugated polymers is of critical importance to the performance of organic electronics, such as organic photovoltaic devices, due to the effect on charge separation and transport, particularly for all‐polymer devices. The block copolymer poly(3‐dodecylthiophene)‐block‐poly(9,9‐dioctylfluorene) (P3DDT‐b‐PF), which has matched crystallization temperatures for each block, is used to study the effects of processing history on resulting crystallization. For longer annealing times and rapid quenching to room temperature, P3DDT crystals are preferred whereas for shorter annealing times and slower quenching, PF crystals are preferred. Both crystal forms are evidenced for long annealing time and slow quenching. Additionally, for room temperature annealing in the presence of a chloroform vapor, PF crystals are found in the PF β phase with the predominant crystal peak oriented perpendicular to the thermally annealed case. These results will provide guidance for optimizing annealing strategies for future donor/acceptor block copolymer photovoltaic devices. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 900–906     

Small‐angle neutron scattering analysis of bottlebrush backbone and side chain flexibility

Bottlebrush polymers have densely tethered side chains grafted to a linear polymer backbone, resulting in stretching of both the side chains and backbone. Prior studies have reported that the side chains are only weakly stretched while the backbone is highly elongated. Here, scaling laws for the bottlebrush backbone and side chains are determined through small‐angle neutron scattering analysis of a systematic series of poly(lactic acid) bottlebrush polymers synthesized via a “grafting‐through” ring‐opening polymerization. Scattering profiles are modeled with the empirical Guinier–Porod, rigid cylinder, and flexible cylinder models. Side chains are found to be only weakly stretched, with an end‐to‐end distance proportional to N^0.55, while the overall bottlebrush increases in size proportional to N^0.77. These results demonstrate that the bottlebrush backbone is not fully extended and that both side chains and backbone have significant conformational flexibility in solution. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 104–111     

Control of the Planar Takens–Bogdanov Bifurcation with Applications

It is well-known that on a versal deformation of the Takens–Bogdanov bifurcation is possible to find dynamical systems that undergo saddle-node, Hopf, and homoclinic bifurcations. In this document a nonlinear control system in the plane is considered, whose nominal vector field has a double-zero eigenvalue, and then the idea is to find under which conditions there exists a scalar control law such that be possible establish a priori, that the closed-loop system undergoes any of the three bifurcations: saddle-node, Hopf or homoclinic. We will say then that such system undergoes the controllable Takens–Bogdanov bifurcation. Applications of this result to the averaged forced van der Pol oscillator, a population dynamics, and adaptive control systems are discussed.     

Design of bicontinuous donor/acceptor morphologies for use as organic solar cell active layers

In recent works, we demonstrated the achievement of bicontinuous donor/acceptor morphologies by the addition of conjugated block copolymers to a blend of conjugated homopolymer donors and fullerene acceptors. However, the domain sizes resulting in experiments were much larger than those of interest for high‐performance organic solar cells. Moreover, a significant concentration of fullerene acceptors was present in the donor domains. Here, we utilize simulations to study the bicontinuous donor/acceptor morphologies that result for different parametric conditions. Using such results, we provide guidelines for how to blend polymer materials to give rise to bicontinuous phases with the smaller and more compositionally pure domains that are desirable for organic photovoltaic applications. Our results can be generalized to treat a large range of donor and acceptor monomers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 884–895     

Well-defined liquid crystal gels from telechelic polymers

Well-defined liquid crystal networks with controlled molecular weight between cross-links and cross-link functionality were prepared by "click" cross-linking of telechelic polymers produced by ring-opening metathesis polymerization (ROMP). The networks readily swell in a small molecule liquid crystal, 5CB, to form LC gels with high swelling ratios. These gels exhibit fast, reversible, and low-threshold optic switching under applied electric fields when they are unconstrained between electrodes. For a given electric field, the LC gels prepared from shorter telechelic polymers showed a reduced degree of switching than their counterparts made from longer polymer strands. The reported approach provides control over important parameters for LC networks, such as the length of the network strands between cross-links, cross-linker functionality, and mesogen density. Therefore, it allows a detailed study of relationships between molecular structure and macroscopic properties of these scientifically and technologically interesting networks.