Influence of the gradient distribution of VO₂ particles on the performance of thermochromic smart window films

Smart windows play an important role in regulating solar radiation and reducing building energy consumption. Thermochromic smart windows based on <i>V</i><i>O</i>₂ nanoparticles offer great potential for large-scale applications. However, non-uniform distributions of particle size and volume fraction along the film thickness direction are often present in <i>V</i><i>O</i>₂ films, which not only affect optical modulation but also induce uneven local phase transitions, further impacting thermal regulation and response efficiency. In this study, a multiscale coupled model was developed using the finite-difference time-domain (FDTD) method and the finite element method (FEM) to investigate how these non-uniformities influence the optical and thermal behavior of <i>V</i><i>O</i>₂ nanoparticle films. When the particle size gradient increased from 30-40-50 to 30-50-100 nm, <i>τ</i>_{<i>l</i><i>u</i><i>m</i>} dropped by 8.29% and <i>Δ</i><i>τ</i>_{<i>s</i><i>o</i><i>l</i>} by 7.43%, with similar trends observed across different film thicknesses. In 15 µm films, the peak temperature of the film with a uniform particle size distribution is 2.31°C higher than that of the non-uniform film, which promotes more complete and more synchronous phase transition. The influence of non-uniform volume fraction on optical performance was limited, but its effect on local temperature response was pronounced. In 5 µm films, a downward-<i>f</i>_<i>v</i> distribution increased the peak temperature by 0.75°C. When the particle size variation is within 10 nm, a uniform model remains effective; however, with larger gradients or thicker films, fine modeling is required to ensure predictive accuracy. Optimizing particle size and volume fraction distributions can improve the optical-thermal response of <i>V</i><i>O</i>₂ films and lower the required transition temperature.