Here, it is shown how carrier recombination through charge transfer excitons between conjugated polymers and fullerene molecules is mainly controlled by the intrachain conformation of the polymer, and to a limited extent by the mesoscopic morphology of the blend. This experimental result is obtained by combining near‐infrared photoluminescence spectroscopy and transmission electron microscopy, which are sensitive to charge transfer exciton emission and morphology, respectively. The photoluminescence intensity of the charge transfer exciton is correlated to the degree of intrachain order of the polymer, highlighting an important aspect for understanding and limiting carrier recombination in organic photovoltaics.
Key words Constructive reverse mathematics, unique existence, Brouwer's fan theorem.
MSC (2000) 03F60, 54E45Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum.It was proved in [6] that the lesser limited principle of omniscience LLPO :for each binary sequence {a n } ∞ n=0 with at most one term equal to 1, either a 2n = 0 for all n or a 2n+1 = 0 for all n is equivalent within Bishop's constructive mathematics 1) to each of the following statements:1. The Cantor intersection theorem 2) :
CIT :Each decreasing sequence of inhabited, closed, and located subsets of a compact metric space X has inhabited intersection. Where a subset A of a metric space X is located if d(x, A) = inf{d(x, a) | a ∈ A} exists for each x ∈ X.2. The minimum principle:
MIN :Each uniformly continuous function f from a compact metric space X to R has a minimum point.3. Weak König's lemma:
WKL :Each infinite tree has an infinite branch.A subset T of the set of all finite binary sequences is detachable ifA set T is a tree if it is detachable and closed under restrictions. The elements of T are called branches. A tree is infinite if it has arbitrarily long branches. We say that an infinite binary sequence α is an infinite branch if for each n we have αn ∈ T . 3) We define αn = (α 0 , . . . , α n−1 ) and call this the restriction of α to the first n components.
The existence and uniqueness of a maximum point for a continuous real–valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.
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