The photon initiators of BP and BPL present a carbonyl double bond and a lone pair of electrons, which can be excited by UV photons from the ground state
S0 to the first singlet state
S1(n,π*), to the second singlet state
S2(π,π*), to the first triplet state
T1(n,π*), and to the second triplet state
T2(π,π*) with the calculated excitation energies shown in
Figure 2. The spontaneous transition time of internal conversion
S2→
S1 is only about 10
−12 s, while the inter-system crossing (ISC) of
S1→
T1 needs 10
−10 s, which means that inter-system crossing through
S2/
S1/
T1 three-state intersection can occur with a high rate. After photon excitation, the free radicals on PE molecular chains can be generated by hydrogen abstraction from PE molecules to active carbonyl of photon-initiators in
T1 excited state [
37,
38]. Since the benzene-bridged carbonyl on BP is the functional group to initiate the hydrogen abstraction reaction, the photon excitation and hydrogen abstraction processes will be identically initiated by UV irradiation on BPL, which maintains this functional group. The BPL molecule with a larger molecular weight than that of BP possesses a long alkyl chain with high compatibility to polyethylene, leading to attenuated evaporation and higher initiation efficiency in the process of generating free radicals on PE molecules. Compared with BP, the energy levels of BPL in the
S1 and
T1 states are closer, which implies a higher ISC frequency of
S1→
T1. Therefore, a higher density of
T1 excited states can be produced by UV irradiation in BPL molecules than in BP, resulting in a higher reaction rate of hydrogen abstraction to achieve more free radicals on polyethylene molecules. In order to further explore the efficiency and performance mechanism of producing free radicals by photon initiators, the charge populations of BP and BPL in the ground state and excited states are analyzed by Mulliken atomic charges, as the calculated results listed in
Table 2. In comparison to the ground state
S0 and excited state
S1, the photon initiators in excited state
T1 provide double radicals on ketone carbonyl (C=O) as indicated by the significantly higher positive and lower negative Mulliken charges on C
7 and O
8 atoms (the labeled numbers for each atom are shown in
Figure 2) respectively, while the charges populated on other carbon atoms are almost unchanged. These photon-excited variations of charge population in BPL are more appreciable than in BP, which means that a higher reaction activity of C
7 and O
8 in BPL for causing the partial fracture of the ketone C=O double bond will engender the higher efficiency of producing free radicals and subsequent hydrogen abstraction by the oxygen atom. Eventually, in addition to the direct crosslinking by forming chemical bonds between free radicals on PE molecules, the radical PE molecules and the hydrogenated BPL with a free radical on C
7 will coordinately react with the auxiliary crosslinking agent such as STAIC to fulfill the indirect crosslinking of PE molecules through the partial fracture and hydrogenation of allyl double bonds on STAIC molecules.
The stationary energies and geometries of the reactants, transition states, and products of BPL photon-initiated free radical generations are optimized by minimizing the total energy based on the conjugated gradient algorithm. The fractured or formed lengths of carbon–hydrogen (C–H) and oxygen–hydrogen (O–H) bonds in hydrogen abstraction and hydrogenation processes, the broken/forming ratios of hydrogen bond length at transition states and their imaginary frequencies, and the energy barriers and Gibbs free energies of radical-generating reactions are calculated, as shown by the results listed in
Table 3. Each transition state has only one corresponding imaginary frequency of the broken or bonding vibration mode, while the harmonic oscillations of the reactants and products are all real frequencies. BPL in a
T1 excited state (BPL
T1) produces the PE molecules with a secondary carbon free radical (C
2-PE*) or tertiary carbon radical (C
3-PE*) by the hydrogen abstraction reaction, while the hydrogenated BPL with a free radical on the carbonyl carbon atom (BPL
*H) will cause the partial fracture and free radical of carbon double bonds on TAIC/STAIC molecules through donating hydrogen. In these hydrogen transfer reactions generating free radicals on PE and STAIC molecules, the elongation of the broken bond is smaller than that of forming a bond at the transition state, which means that the bonding pathway of O–H to BPL or C–H to an auxiliary crosslinking agent is longer than the breaking process of C–H from the PE molecule or OH from BPL
*H, as shown in
Table 3. Based on Hammond’s hypothesis, these radical-generating reactions being accompanied with hydrogen transfer, which engender C
2-PE*, C
3-PE*, TAIC* (as shown in
Figure 1), and STAIC with free radicals (STAIC*) for PE crosslinking, are expected to be exothermic. According to the height of the reaction energy barrier (
Eb), which indicates the difficulty of breaking the C–H or O–H bond, it can be predicted that the reaction path producing C
2-PE* is the main reaction channel of hydrogen abstraction due to its remarkably lower energy barrier than the C
3-PE* path. Negative values of reaction Gibbs free energy (Δ
G < 0) indicate that all four reactions can occur spontaneously, in which the BPL
*H + STAIC reaction represents the superiority in both thermodynamics and kinetics due to the lower
Eb and Δ
G than the BPL
*H + TAIC reaction. To this end, the BPL photo-initiation reactions of generating free radicals can be realized primarily by the BPL
T1 abstracting hydrogen atom on the non-branched-chain of PE molecules and then partially breaking the allyl double bond by hydrogenating the auxiliary crosslinking agents (STAIC is more preferable than TAIC).