Unraveling the Influence of Excluded Volume on Orientational Relaxation Dynamics in Dendrimers

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 \( P_2^{(i)}(t) \) 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 \( P_2^{(i)}(t) \) at varying excluded volume parameters, \( v_\theta \) and \( v_\psi \), shows trends consistent with experimental observations under different temperatures.~\cite{yimer2012static} The spectral density, \( J(\omega) \), obtained via the Fourier cosine transform of \( P_2^{(i)}(t) \), is significantly influenced by excluded volume interactions. In the high-frequency regime, \( J(\omega) \) 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 \( v_\theta \) and \( v_\psi \) 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 \( v_\theta = 0.24 \) and \( v_\psi = 2.12 \) aligns precisely with experimental data,~\cite{yimer2012static} validating the theoretical model. The spin-spin relaxation rate, \( \left[ \frac{1}{T_{2H}} \right] \), 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 \( \left[ \frac{1}{T_{1H}} \right] \) at lower correlation times due to enhanced low-frequency contributions. However, for generation \( G=5 \), \( \left[ \frac{1}{T_{2H}} \right] \) follows a similar trend to \( \left[ \frac{1}{T_{1H}} \right] \) and aligns well with experimental observations.~\cite{yimer2012static}