Calculation of photothermal conversion efficiency

Photothermal conversion efficiency was measured and calculated according to literature¹⁵. HSN or HSN₀ solution (2 mL, optical density at 1064 nm = 1) was placed in a 3.5-mL quartz cuvette (5.66 g, Sangon Biotech, Shanghai, China), followed by 1064 nm laser irradiation (1 W cm⁻²) for 30 min to reach the thermal equilibrium and subsequent natural cooling process in the absence of laser irradiation. During the measurement, solution temperature was monitored by a dual input J/K type thermometer (TM300, Extech Instruments, Waltham, MA). Calculation was briefly given as follows:

Energy input and dissipation in the measurement system could be expressed as:

where m_i and C_p,i are the mass and heat capacity of the component (e.g. water and quartz cuvette) in the measurement system, respectively. Q_NP stands for the input of energy from HSN or HSN₀; Q_sys is the energy input from the other components in the measurement system; and Q_diss represents the loss of energy from measurement system to surroundings. The laser-induced term Q_NP could be interpreted as:

where I is the power of 1064 nm laser; A_λ is the absorbance of HSN or HSN₀ at 1064 nm; η stands for photothermal conversion efficiency. On the other hand, Q_diss could be expressed as:

where h is heat transfer coefficient; S is surface area of the quartz cuvette exposed to laser; T_surr is the ambient temperature. When the measurement system reached a thermal equilibrium, temperature was recorded as T_max. At this time, the total energy input to the system is equal to the energy dissipation:

After removal of laser irradiation, the energy input drops to zero, and Eq. ¹ is expressed as:

After rearrangement followed by integration, Eq. ⁵ gives:

The time constant τ_s is expressed as:

A dimensionless factor θ is defined as:

Then Eq. ⁶ could be expressed as:

Therefore, τ_s could be calculated by linear regression of time versus negative lnθ. And hS could be obtained through Eq. ⁷. Q_sys could be measured by replacing nanoparticles with pure solvent:

At last, η could be calculated as: