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2.4.4 Linear Relationship between Fluorescence Intensity and Amorphous Aggregate Size

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As the major existing form of AIEgens in experiments, the AIE mechanism of amorphous aggregate is rarely studied theoretically and is a great challenge because of their structural heterogeneity. Here, we proposed a theoretical protocol combining MD simulations and quantum mechanics/molecular mechanics calculations, and the TVCF spectrum and rate theory, to quantitatively investigate the AIE property in amorphous state and explore the relationship between molecular packing, optical spectra, and fluorescence quantum efficiency [70]. Take HPS [37] as an example; amorphous aggregates with five different sizes were set up in aqueous solution to demonstrate clearly the relationship between molecular packing, optical spectra, and ΦF, as well as their size effect. MD simulations indicate that HPS aggregates are generally near‐spherical and the packing density of aggregates is size‐independent and smaller than that of crystals (Figure 2.8a, b). Due to the structural heterogeneity of the aggregates, AIEgen in amorphous aggregate could not be represented by an aggregate of the solely fixed conformation. Thus, at each size, five embedded and one exposed QM/MM models were set up for all sizes of aggregates. As shown in Figure 2.8c, the absorption of amorphous aggregates is similar to that of crystals, while the emission is clearly red‐shifted from the crystalline one. This can be explained by the lower‐packing‐density‐induced larger reorganization energies in amorphous HPS aggregates than that in crystal. Strikingly, ΦF of the embedded HPS is size‐independent and about 1 or 2 orders of magnitude larger than those of the exposed ones (<7%), see Figure 2.8d. In addition, kr is insensitive to environments, kic is very sensitive to the environment, and kic of embedded HPS molecules are 2–4 orders of magnitude smaller than those of the exposed ones because of the restriction of the intramolecular low‐frequency rotational motions of embedded HPS molecules. More excitingly, the size‐independent ΦF predicts a linear relationship between the fluorescence intensity and aggregate size of the nanosized HPS aggregates. This indicates that the electron–vibration and vibration–vibration coupling are dependent on the compactness of molecular packing other than the size of the aggregate. In addition, the crystallization‐enhanced emission phenomenon in the experiment can be explained by the calculated blue‐shifted emission and enhanced fluorescence intensity of HPS from amorphous aggregate to the crystalline phase.

Table 2.6 Calculated room‐temperature kic (s−1) for nondeuterated (H‐all) and fully deuterated (D‐all) isotopomers of the AIEgens and nonAIEgens in both solution and solid phases.

Source: © 2016 Royal Society of Chemistry [64].

Solution Solid Solution Solid Solution Solid
HPS BtTPS HPDMCb
H‐all 2.44 × 1011 8.58 × 106 2.20 × 1011 2.73 × 107 1.31 × 1011 2.26 × 107
D‐all 2.22 × 1011 2.61 × 106 1.97 × 1011 6.89 × 106 1.27 × 1011 7.11 × 106
IE –9.0% –69.6% –10.5% –74.8% –3.1% –68.5%
TPBD DPTDTP BPS
H‐all 2.16 × 1010 4.21 × 106 1.79 × 109 6.76 × 105 1.13 × 1010 2.19 × 109
D‐all 1.96 × 1010 2.77 × 105 1.61 × 109 2.23 × 105 7.05 × 109 1.44 × 109
IE –9.3% –93.4% –10.1% –67.0% –37.6% –34.2%
Perylene DSB Anthracene
H‐all 1.19 × 103 0.61 × 103 3.84 × 103 5.51 × 103 0.81 × 103 5.25 × 103
D‐all 0.29 × 103 0.18 × 103 1.04 × 103 0.66 × 103 0.23 × 103 1.05 × 103
IE –75.6% –70.5% –72.9% –88.0% –71.6% –80.0%

Figure 2.8 (a) The average packing density of amorphous HPS aggregates. (b) The average RDFs as a function of the intermolecular Si–Si distance. The lattice constants of the HPS crystal and the intermolecular distance of two HPS molecules in the unit cell are shown by dashed lines for comparison. (c) The calculated absorption (left) and emission (right) spectra for five embedded and one exposed HPS for aggregates with size 60. (d) ΦF of five embedded and one exposed HPS molecule in amorphous aggregates with different sizes.

Source: Reproduced from Ref. [70]. Copyright 2016 The Royal Society of Chemistry.

Handbook of Aggregation-Induced Emission, Volume 1

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