ABSTRACT
In this work, we use density functional theory to investigate the electronic structure of poly(3,4-ethylenedioxythiophene) (PEDOT) oligomers with co-located AlCl4- anions, a promising combination for energy storage. The 1980s bipolaron model remains the dominant interpretation of the electronic structure of PEDOT despite recent theoretical progress that has provided new definitions of bipolarons and polarons. By considering the influence of oligomer length, oxidation or anion concentration and spin state, we find no evidence for many of the assertions of the 1980s bipolaron model and so further contribute to a new understanding. No self-localisation of positive charges in PEDOT is found, as predicted by the bipolaron model at the hybrid functional level. Instead, our results show distortions that exhibit a single or a double peak in bond length alternations and charge density. Either can occur at different oxidation or anion concentrations. Rather than representing bipolarons or polaron pairs in the original model, these are electron distributions driven by a range of factors. Distortions can span an arbitrary number of nearby anions. We also contribute a novel conductivity hypothesis. Conductivity in conducting polymers has been observed to reduce at anion concentrations above 0.5. We show that at high anion concentrations, the energy of the localised, non-bonding anionic orbitals approaches that of the system HOMO due to Coulombic repulsion between anions. We hypothesize that with nucleic motion in the macropolymer, these orbitals will interfere with the hopping of charge carriers between sites of similar energy, lowering conductivity.
ABSTRACT
OBJECTIVES: Discrete choice experiments (DCEs) are increasingly used to elicit preferences for health and healthcare. Although many applications assume preferences are homogenous, there is a growing portfolio of methods to understand both explained (because of observed factors) and unexplained (latent) heterogeneity. Nevertheless, the selection of analytical methods can be challenging and little guidance is available. This study aimed to determine the state of practice in accounting for preference heterogeneity in the analysis of health-related DCEs, including the views and experiences of health preference researchers and an overview of the tools that are commonly used to elicit preferences. METHODS: An online survey was developed and distributed among health preference researchers and nonhealth method experts, and a systematic review of the DCE literature in health was undertaken to explore the analytical methods used and summarize trends. RESULTS: Most respondents (n = 59 of 70, 84%) agreed that accounting for preference heterogeneity provides a richer understanding of the data. Nevertheless, there was disagreement on how to account for heterogeneity; most (n = 60, 85%) stated that more guidance was needed. Notably, the majority (n = 41, 58%) raised concern about the increasing complexity of analytical methods. Of the 342 studies included in the review, half (n = 175, 51%) used a mixed logit with continuous distributions for the parameters, and a third (n = 110, 32%) used a latent class model. CONCLUSIONS: Although there is agreement about the importance of accounting for preference heterogeneity, there are noticeable disagreements and concerns about best practices, resulting in a clear need for further analytical guidance.
