Dependence of electrical performance on structural organization in polymer field effect transistors

Organic semiconductors (OSCs) are strong contenders for use in printed, flexible electronics. Although organic electronic materials have been studied for many years, the physics of charge transport is still under investigation. This is in part due to variability resulting from the large variety of molecules that can be synthesized and inconsistency in electrical characterization due to device and processing conditions. Molecular ordering in OSCs is known to alter the charge transport characteristics and attention to long range and short range ordering provides clues as to the nature of transport pathways. Here, we study ordered regioregular poly(3‐hexylthiophene‐2,5‐diyl) films carefully prepared to obtain a set of three samples with incrementally increasing order on identical transistor architectures. Ordering was characterized using a variety of short and long range techniques to probe the coherence and number of crystallites formed during processing, and the correlation between these different measures of order are quantified. We observe three changes in transistor behavior that show a shift from non‐ideal to more textbook‐like characteristics with increasing order: reduction of the contact resistance, shift to field‐independent mobility, and a shift from a diode‐like (S‐shaped) to linear response at low lateral fields. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1063–1074     

Entropy, independent sets and antichains: A new approach to Dedekind's problem

For -regular, -vertex bipartite graphs with bipartition , a precise bound is given for the sum over independent sets of the quantity . (In other language, this is bounding the partition function for certain instances of the hard-core model.) This result is then extended to graded partially ordered sets, which in particular provides a simple proof of a well-known bound for Dedekind's Problem given by Kleitman and Markowsky in 1975.

     

Broken symmetries and pattern formation in two-frequency forced faraday waves

We exploit the approximate (broken) symmetries of time translation, time reversal, and Hamiltonian structure to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Using explicit parameter symmetries we determine, for the case of two-frequency forcing, how the strength of observed three-wave interactions depends on the frequency ratio and on the relative phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.     

Synthetic gene network for entraining and amplifying cellular oscillations

We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to a periodic process that is intrinsic to the cell. We investigate the synchronization properties of the coupled system, and show how the oscillator can be constructed to yield a significant amplification of cellular oscillations. We reduce the driven oscillator equations to a normal form, and analytically determine the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels.