Unraveling the influence of excluded volume on orientational relaxation dynamics in dendrimers

Abstract

This study investigates the orientational relaxation dynamics of flexible dendrimers while incorporating excluded volume interactions among non-bonded monomers using the optimized Rouse–Zimm formalism. Excluded volume effects are modeled as an effective co-volume between adjacent non-bonded monomers through a delta function pseudopotential, while hydrodynamic interactions are accounted for using the preaveraged Oseen tensor. This work examines P⁽ⁱ⁾₂(t) as a function of dendrimer generation and the strength of excluded volume interactions between nearest non-bonded monomers. The theoretical framework builds upon the work of [Kumar and Biswas, Phys. Chem. Chem. Phys., 2013, 15, 20294], which analyzed orientational relaxation in semiflexible dendrimers but did not consider excluded volume interactions. The temporal decay of P⁽ⁱ⁾₂(t) at varying excluded volume parameters, v_θ and v_ψ, shows trends consistent with experimental observations under different temperatures, [Yimer and Tsige, J. Chem. Phys., 2012, 137, 204701.] The spectral density, J(ω), obtained via the Fourier cosine transform of P⁽ⁱ⁾₂(t), is significantly influenced by excluded volume interactions. In the high-frequency regime, J(ω) decreases with increasing frequency, exhibiting a crossover pattern as excluded volume interactions vary in the intermediate frequency range. The area under the spectral density curve increases as the excluded volume parameters v_θ and v_ψ decrease. The reduced spin–lattice relaxation rate, [1/T_1H], follows a power-law scaling in the intermediate frequency regime, with exponents dependent on dendrimer generation and the strength of excluded volume interactions. Notably, for generation G = 5, the calculated scaling exponent at v_θ = 0.24 and v_ψ = 2.12 aligns precisely with experimental data, validating the theoretical model. The spin–spin relaxation rate, exhibits a distinct trend influenced by excluded volume interactions. In the intermediate frequency regime, its scaling behavior is closely linked to structural constraints and segmental motion, deviating from at lower correlation times due to enhanced low-frequency contributions. However, for generation G = 5, follows a similar trend to and aligns well with experimental observations.