Specular neutron reflection was used to investigate the density profile of polystyrene-poly-(ethylene oxide) (PS-PEO) block copolymers adsorbed from d-toluene onto quartz. The neutron beam passed through the quartz substrate and was reflected from the quartz/d-toluene interface. The PEO block, which comprises a small fraction of the total polymer molecular weight, strongly adsorbs onto the quartz substrate, while the PS block remains in solution. Thus, the chains form a terminally attached polymer "brush". The reflectivity profiles are well described by a parabolic or error function polymer density profile normal to the interface, but the data cannot be fitted to exponential or power law decay profiles. The layer thickness values are in good agreement with the results of interlayer force measurements for the same polymersolvent system adsorbing onto mica. The molecular weight dependence of the layer thickness and adsorbance obtained from the data obey scaling laws in accord with the theory of semidilute polymer brushes.

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The line-dipole approximation for the evaluation of the exciton transfer integral, J, between conjugated polymer chains is rigorously justified. Using this approximation, as well as the planewave approximation for the exciton center-of-mass wavefunction, it is shown analytically that J ∼ L when the chain lengths are smaller than the separation between them, or J ∼ L −1 when the chain lengths are larger than their separation, where L is the polymer length. Scaling relations are also obtained numerically for the more realistic standing-wave approximation for the exciton center-ofmass wavefunction, where it is found that for chain lengths larger than their separation J ∼ L −1.8 or J ∼ L −2 , for parallel or collinear chains, respectively. These results have important implications for the photo-physics of conjugated polymers and self-assembled molecular systems, as the Davydov splitting in aggregates and the Förster transfer rate for exciton migration decreases with chain lengths larger than their separation. This latter result has obvious deleterious consequences for the performance of polymer photovoltaic devices.

Since the discovery of electroluminescence in the phenyl-based conjugated polymers in 1990, the field of polymer optoelectronics has matured to the extent that presently a wide class of devices have been commercialized. These range from both miniature and wide-area light emitting devices to hybrid photovoltaic devices. Similarly, our understanding of the fundamental processes that determine these optoelectronic properties has also progressed. In particular, owing to insights from both experimental and theoretical investigations, the role of the primary excited states, i.e., excitons, is now considerably clearer. This review discusses these primary excited states and explains how the three key roles of electron-electron interactions, electron-nuclear coupling, and disorder determine their properties. We show that the properties of an exciton are more readily understood by decomposing it into two effective particles. First, a relative particle that describes the size and binding energy of the electron-hole pair. Second, a center-of-mass particle that describes the extent of the delocalization of the electron-hole pair. Disorder and coupling to the normal modes localizes the center-of-mass particle and provides a quantitative definition of chromophores in conjugated polymers, paving the way for a first-principles theory of exciton diffusion in these systems.

The disordered Frenkel-Holstein model is introduced to investigate dynamical relaxation and localization of photoexcited states in conformationally disordered poly(p-phenylenevinylene). It is solved within the Ehrenfest approximation, in which the excited state is treated fully quantum mechanically, but the nuclear displacements are treated classically. The following are shown: (i) Lower energy local exciton ground states (LEGSs) adiabatically relax to vibrationally relaxed states (VRSs) in the time scale of one or two vibrational periods (ca. 40 fs). The relaxation of LEGSs is accompanied by localization and fluorescence depolarization, as the transition dipole moment reduces and rotates. The amount of dynamical localization increases as the torsional disorder decreases, causing an increase in the fluorescence depolarization. (ii) Higher energy quasi-extended exciton states (QEESs) interconvert to VRSs via three distinct episodes. A brief initial period of adiabatic relaxation is followed by the time-evolving eigenstate becoming a linear superposition of instantaneous eigenstates of the Frenkel-Holstein Hamiltonian. Typically, after a few hundred femtoseconds, one of the instantaneous eigenstates dominates the linear superposition, and the remaining dynamics is again adiabatic relaxation to a VRS. (iii) Very high energy QEESs, which are delocalized over many chromophores, sometimes exhibit a splitting of the wave function into more than one VRS. This self-localization onto more than one chromophore is assumed to be a failure of the Ehrenfest approximation, as this approximation neglects quantum mechanical coherences between the electronic and nuclear degrees of freedom. (iv) QEESs exhibit larger, but slower, fluorescence depolarization than LEGSs. Thus, ultrafast fluorescence depolarization is a function of excitation energy and conformational disorder.

The theory of optical transitions developed in Barford and Marcus ["Theory of optical transitions in conjugated polymers. I. Ideal systems," J. Chem. Phys. 141, 164101 (2014)] for linear, ordered polymer chains is extended in this paper to model conformationally disordered systems. Our key result is that in the Born-Oppenheimer regime the emission intensities are proportional to S(1)/⟨IPR⟩, where S(1) is the Huang-Rhys parameter for a monomer. ⟨IPR⟩ is the average inverse participation ratio for the emitting species, i.e., local exciton ground states (LEGSs). Since the spatial coherence of LEGSs determines the spatial extent of chromophores, the significance of this result is that it directly relates experimental observables to chromophore sizes (where ⟨IPR⟩ is half the mean chromophore size in monomer units). This result is independent of the chromophore shape, because of the Born-Oppenheimer factorization of the many body wavefunction. We verify this prediction by density matrix renormalization group (DMRG) calculations of the Frenkel-Holstein model in the adiabatic limit for both linear, disordered chains and for coiled, ordered chains. We also model optical spectra for poly(p-phenylene) and poly(p-phenylene-vinylene) oligomers and polymers. For oligomers, we solve the fully quantized Frenkel-Holstein model via the DMRG method. For polymers, we use the much simpler method of solving the one-particle Frenkel model and employ the Born-Oppenheimer expressions relating the effective Franck-Condon factor of a chromophore to its inverse participation ratio. We show that increased disorder decreases chromophore sizes and increases the inhomogeneous broadening, but has a non-monotonic effect on transition energies. We also show that as planarizing the polymer chain increases the exciton band width, it causes the chromophore sizes to increase, the transition energies to decrease, and the broadening to decrease. Finally, we show that the absorption spectra are more broadened than the emission spectra and that the broadening of the absorption spectra increases as the chains become more coiled. This is primarily because absorption occurs to both LEGSs and quasi-extended exciton states (QEESs), and QEES acquire increased intensity as chromophores bend, while emission only occurs from LEGSs.

Exciton delocalization in conjugated polymer systems is determined by polymer conformations and packing. Since exciton delocalization determines the photoluminescent vibronic progression, optical spectroscopy provides an indirect link to polymer multiscale structures. This perspective describes our current theoretical understanding of how exciton delocalization in π-conjugated polymers determines their optical spectroscopy and further shows how exciton delocalization is related to conformational and environmental disorder. If the multiscale structures in conjugated polymer systems are known, then using first-principles modeling of excitonic processes it is possible to predict a wide-range of spectroscopic observables. We propose a reverse-engineering protocol of using these experimental observables in combination with theoretical and computational modeling to determine the multiscale polymers structures, thus establishing quantitative structure-function predictions.