1：Experimental Design and Method Selection:

The study involves the use of circularly polarized optical traps to assemble metal nanoparticles into arrays. The optical torque on these arrays is measured as a function of the number, separation, and configuration of the nanoparticles.

2：Sample Selection and Data Sources:

Silver nanoparticles with diameters of 151 ± 13 nm are used, coated by negatively charged polyvinylpyrrolidone. The experiments are performed in a liquid sample cell illuminated by a circularly polarized laser beam.

3：List of Experimental Equipment and Materials:

Optical trapping system built with an inverted Olympus IX73 microscope and CW Tunable Ti:Sapphire Laser operating at 800 nm, Ag NPs purchased from NanoComposix (NanoXact?), and a CMOS camera (Point-Grey Grasshopper 3) for recording.

4：Experimental Procedures and Operational Workflow:

The laser beam is expanded and collimated, then focused to the back aperture of a 60X objective to confine the NPs. The polarization state is controlled by a quarter-wave plate. Trapped Ag NPs are visualized by darkfield microscopy and recorded.

5：Data Analysis Methods:

Particle positions in each frame are determined and linked in different frames using TrackMate in ImageJ. Optical torques are calculated based on the rotation directions of the arrays.