This folder contains the analysis for the data shown in section 4.4 Colloidal interactions.
Run Fig24.m in folder Potential_analysis to obtain time evolution of the probability density distribution of the inter-particles distance r (t) obtained from 400 different trajectories after the optical traps are switched off at t = 0 ms for decreasing values of ΔT: (a) ΔT = 456 ± 2mK, (b) 200 ± 2mK, (c) 163 ± 2mK, and (d) 108 ± 2mK. The solid lines indicate representative individual trajectories while the coloured background represents the . The dashed horizontal line indicates the distance r corresponding to the diameter d of the colloids. Sometimes r (t) is smaller than d because a displacement of the colloids along the vertical z-axis causes their projections onto the xy-plane to overlap. This occurs more frequently in the presence of critical Casimir forces and particularly if the particles are stuck together. These cases, however, are rare compared to those in which the particles do not leave the xy-plane. (e-h) Equilibrium distribution Peq(r) of the inter-particle distance r (0) (i.e., when the optical tweezers are switched off) for two optically trapped colloids at temperatures (f) ΔT = 456 ± 2mK, (g) 200 ± 2mK, (h) 163 ± 2mK, and (i) 108 ± 2mK. Each histogram is obtained from 400 different experimental values. The solid black lines are the theoretical distribution of r (0), obtained via Monte Carlo integration (106 samples) of two optically trapped particles subjected to the theoretical total potential V (R1, R2)
Run Fig25.m in folder Diffusion_coefficients to obtain(a) Experimental values of the normalized parallel D∥/D0 (circles) and perpendicular D⊥/D0 (triangles) diffusion constants as functions of r/d. The parallel and perpendicular directions refer to the line connecting the centers of the two colloids, and D0 is the bulk diffusion constant (Eq. (35)) calculated from experimental data. The various colors refer to data taken at ΔT = 456 ± 2mK (blue), 273 ± 2mK (light blue), 200 ± 2mK (green), 163 ± 2mK (yellow), 127 ± 2mK (orange), and 108 ± 2mK (red). The solid lines represent the theoretical predictions accounting for the effect of the hydrodynamic interaction between the colloids. Error bars represent the standard deviation of the experimental values. The nature of the deviations observed in Dk at short and long distances is discussed in the main text.
Run Fig26.m in folder Drift_velocities to obtain Parallel v∥ (second row) and perpendicular v⊥ (third row), drift velocities, respectively, to the direction connecting the centers of the two colloids for (b, f) ΔT = 456 ± 2mK, (c, g) 200 ± 2mK, (d, h) 163 ± 2mK and (e, i) 108 ± 2mK. In the second and third row, the symbols with errorbars represent the experimental data, and the thick, coloured lines represent the corresponding simulation results. The shaded areas represent the error of the numerical estimates due to the uncertainties in the fit parameters.
This repository includes the analysis and plot codes for the the article Optical Tweezers: A comprehensive Tutorial from Calibration to Applications by Jan Gieseler, Juan Ruben Gomez-Solano, Alessandro Magazù, Isaac Pérez Castillo, Laura Pérez García, Martha Gironella-Torrent, Xavier Viader-Godoy, Felix Ritort, Giuseppe Pesce, Alejandro V. Arzola, Karen Volke-Sepulveda and Giovanni Volpe.