Theory for the Dynamics of Polymer Grafted Nanoparticle in Solution

Abstract

We develop a theory for the dynamics of polymer grafted nanoparticles (PGNP) in a dilute solution. A formalism of multiscale generalized Gaussian structure (mGGS) is developed where the multiscale nature is described as a variable size of monomers connected to each other through harmonic springs with different spring constants. This formalism allows for the study of various dynamic properties of polymer chains or networks grafted nanoparticles at arbitrary positions. We analyze three dynamic properties of PGNP, viz. (i) the mean displacement of a specified monomer of the polymer chain and its time evolution under external (unit step) forces, (ii) loss and storage moduli, and (iii) intrinsic viscosity. The study highlights the unfolding dynamics of a polymer chain with different sizes of nanoparticles and shows that the chain dynamics depends on the position of applied step force in PGNP. Similarly, the elastic moduli and the intrinsic viscosity reflects the viscoelastic properties of PGNP. The storage and the loss moduli of PGNP show anomalous enhancement with temporal slow down in low and intermediate frequency regimes. The increase in the size and the number fraction of nanoparticles in the polymer chain suppresses the power-law exponent in the intermediate frequency regime. The transition frequency between solid-and liquidlike viscoelastic region decreases with an increase in the size and the number fraction of NPs in PGNP. The intrinsic viscosity and the radius of gyration increase with increasing the size of a nanoparticle grafted on the polymer chain. Finally, we conclude that the viscoelastic properties of PGNP are altered by tuning their molecular architectures.

Dynamic Mixing Behaviors of Ionically Tethered Polymer Canopy of Nanoscale Hybrid Materials in Fluids of Varying Physical and Chemical Properties

“…More specifically, the specific viscosity of the untethered HPE (η sp ∝ c 1.37±0.11 ) was observed to scale according to what was expected based on the Rouse theory , for good solvents, while the scaling of the specific viscosity of NOHM-I-HPE did not (η sp ∝ c 2.81 ± 0.08 ). The deviation of the viscosity behavior of NOHMs from the untethered polymer at higher concentrations likely results from a combination of the tethered polymer confinement ,, and increased strength of nanoparticle–nanoparticle interactions. ,, …”

Static Structure Factor and Viscoelastic Properties of Dendrimer Grafted Nanoparticles in Solution

“…The dynamics of heteropolymeric systems demand the incorporation of the multiscale polymeric structural components in the theory. Therefore, the bead–spring model of the generalized Gaussian structure with unequal bead size and spring constants can address such problems through the multiscale generalized Gaussian structure (mGGS) . A general multiscale generalized Gaussian structure (mGGS) consists of N number of different size of beads attached with harmonic springs having different spring constants.…”

“…The vectors and matrices are 3 N -dimensional. M is dimensionless diagonal mobility , N × N matrix which accounts the mobility of the individual bead. The mobility matrix accounts the hydrodynamic interactions for the homogeneous systems usually based on the preaveraged Oseen tensor, , M mn = δ mn + ζ r ⟨1/ R mn ⟩(1 – δ mn ), where the reduced monomer friction coefficient, ζ r = ζ/6 πη s b , is a measure of the effective monomer hydrodynamic radius in units of b and η s is the viscosity of the solvent.…”

“…K is the dimensionless spring connectivity stiffness in the N × N matrix, K mn , which accounts for the connectivity of beads and different entropic springs. The diagonal elements of spring connectivity stiffness, K mm , , accounts for all entropic springs attached to the m th bead ,and its off-diagonal term K mn (in units of K 0 ) accounts for the entropic spring between the m th and the n th bead. The product MK is a multiscale connectivity matrix which accounts for the multiscale nature in beads and springs through bead mobility, spring stiffness, and their connectivity.…”

“…The isolated branched structures in a solution impact the conformation and dynamical properties. − Blumen et al − studied the isolated copolymeric systems through the generalized Gaussian structure approach. − The main focus of this work is to explore the structural dynamics of dendrimer-grafted nanoparticles (see Figure ) within the framework of multiscale generalized Gaussian structure . This study evaluates the viscoelastic relaxation moduli, intrinsic viscosity, and static structure factors of dendrimer-grafted nanoparticles with different molecular architecture.…”