Quantitative analysis of reactive dye–cellulose affinity via molecular dynamics simulations verified by diffusion experiments

Quantifying affinity differences between various dyes and cellulose fibers is essential for optimizing low-water and low-salt pad dyeing processes for cotton fabrics. Molecular dynamics (MD) simulations were used to model interactions within the water–dye–cellulose system. The absolute binding free energy between the dye and cellulose was calculated to understand how their affinity influences dye diffusion and adsorption. The simulations examined the effects of system size, pore size, salt concentration, and dye structure on dye solvation free energy (ΔG A ) and dye-cellulose binding free energy (ΔG binding ). Results showed that ΔG A was independent of system size and solely dependent on dye structure. Dyes containing more sulfonic acid groups exhibited higher ΔG A values. NaCl reduced electrostatic repulsion between the dye and cellulose through a dispersion–aggregation–redispersion mechanism, which enhanced dye–cellulose binding. Increasing NaCl concentrations further enhanced ΔG binding . Larger pore sizes also resulted in higher ΔG binding . This affected dye diffusion paths by modulating hydrogen bonding strength between the dye–cellulose and dye–water, thereby affecting dye–cellulose interactions. Reactive dyes containing more aromatic rings, hydroxyl groups, and amino groups exhibited stronger interactions with cellulose, leading to higher ΔG binding values. Furthermore, experimental dye diffusion coefficients in cotton fibers were measured using confocal Raman spectroscopy. Among the dyes studied, B194 had the highest ΔG binding and the lowest experimental diffusion coefficient, while B19 exhibited the lowest ΔG binding and the highest diffusion coefficient. Higher ΔG binding was associated with stronger dye–cellulose affinity and lower diffusion coefficients, validating the reliability of the MD system for quantitative analysis of dye–cellulose interactions.