## 2 Materials and Methods  
### J-Aggregate  
TPPS has three states with different absorption peaks: free-base \"F\" monomers, diacid \"D\" monomers, and J-aggregates. The state of TPPS changes depending on the pH and solute concentration. When the pH value is lowered and the proton concentration is raised, its state changes from F monomersto D monomers and from D- to J-aggregates [38; 39]. For the F monomer state, TPPS absorbs the near far-red region and blue region, called the Q band and B band, respectively. This band structure can be explained by [PERSON]'s four-orbital model and originates from HOMO-LUMO (Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital) splitting due to asymmetry of the molecular electronic structure [49; 50]. The TPPS monomer exists as an F monomer whose absorption peaks at 414 nm in poor solvent of protons. When protons are contained in the solution at a sufficiently high concentration, they coordinate to nitrogen atoms in porphyrin rings, and the TPPS molecules change into the D monomers, whose absorption peaks at 433 nm, 19-nm redshifted from the F monomers. The D monomers form stable J-aggregates with the Coulomb interaction, which is enhanced by proton coordination to nitrogen atoms in porphyrins [51]. When porphyrins form J-aggregates, the molecules align straight in the microscale, and the absorption peak redshifts to 490 nm and narrows due to the Coulomb interaction between the molecules' transition dipole moments, forming a so-called \"Frenkel exciton\" (Figure 1). The energy level is redshifted by the exciton formation described by the following Equations (1) and (2):  
\[E_{k}=E_{0}+2J\cos\!\left(\frac{k\pi}{N+1}\right), \tag{1}\]  
\[J=\frac{M^{2}}{4\pi\varepsilon r^{3}}\!\left(1-3\cos^{2}\theta_{0}\right), \tag{2}\]  
where \(M\) is the transition dipole moment, \(r\) is the distance between molecules, \(\theta_{0}\) is the aggregation angle, \(\varepsilon\) is the permittivity of the solvent, and \(k\) is the state number of the Frenkel exciton.  
A one dimensional aggregated state is termed a micro-aggregate or coherent aggregate, and its exciton wave function stays coherent. Then, micro-aggregates form a higher-order structure called \"macro-aggregates\", e.g., with a sheet or tube structure [52; 53]. Figure 1 shows the absorption spectra of TPPS samples in water in a 1-mm-thick quartz cell that were measured with a spectrophotometer (Shimadzu, UV-3150). When the monomer state was dominant in the sample solution, the F monomer absorption peak at 414 nm and the D monomer absorption peak at 433 nm appeared, forming the B band. However, when the J-aggregate was dominant, the J-aggregate absorption peak at 490 nm became prominent. During the change from monomers to aggregates, the absorption peak in the Q band was also redshifted.  
Figure 1: The electronic absorption spectra of 4-[10,15,20-tris(4-sulfophenyl)-21,24-dihydropypropyl-5-yl]benzenesulfonic acid (TPPS) in water, at room temperature in a 1-mm-thick quartz cell, measured with a spectrophotometer (Shimadzu, UV-3150). The TPPS concentration is 82 \(\upmu\)mol/L for monomer sample (black line), and J-aggregate sample (red line) obtained by adding 100 \(\upmu\)L of 1M, HCl aq. to 3.6 mL of 82 \(\upmu\)mol/L monomer sample.