Scaling Perspective on Dynamics of Nanoparticles in Polymers: Length- and Time-Scale Dependent Nanoparticle–Polymer Coupling

Abstract

The motion of nanoparticles in a polymer matrix is dictated by the intricate coupling of the nanoparticles and surrounding polymers. Various length- and time-scale dependent features of nanoparticle–polymer coupling in a polymer matrix have been delineated in the past decade by combining scaling theory and molecular simulations. Representative scenarios of nanoparticle dynamics in polymers, which embody the roles of polymer matrix topology, the polymers grafted to nanoparticle surface, the anisotropic shape of nanoparticles, and an external driving force, are reviewed. The systems examined demonstrate both the richness of the physics in the nanoparticle–polymer coupling and the capability of the scaling-level description in providing unique insights into the size- and time-dependence of nanoparticle mobility. Following a review of recent work, more scenarios of nanoparticles in polymer matrices, which reflect new pieces of physics in the nanoparticle–polymer coupling, are discussed. Together with the advances in the chemical synthesis of nanoparticles and polymers as well as in the techniques of tracking nanoparticle motion and measuring nanoparticle diffusivity, the microscopic picture of nanoparticle–polymer coupling revealed theoretically and computationally is anticipated to aid in the manipulation of nanoparticles in complex polymeric environments and thus benefit many technological applications.

Activity-Triggered Rheological Strengthening and Toughening of Nanoparticle-Doped Supramolecular Gels

“…Due to the entropic depletion effect, which reduces the interference of NPs with the conformation of NBSCs, passive NPs are partially aggregated in the matrix network . Moreover, the thermal motion-driven diffusion of passive NPs is coupled to the structural relaxation of entangled NBSCs. − Thus, each passive NP is under the confinement of the surrounding NBSCs whenever the relaxed mesh size is smaller than the NP diameter. − If the self-propelling force applied to active NPs is sufficiently strong to displace surrounding strands of NBSCs, the dynamics of active NPs becomes dynamically decoupled from the structural relaxation of NBSC strands . In this case, the attractive depletion force induced by NBSCs is negligible when compared to the self-propelling force of active NPs.…”

Structure and Dynamics of Hybrid Colloid–Polyelectrolyte Coacervates: Insights from Molecular Simulations

“…The latter is the Rouse viscosity of the PE chain fragments with a size comparable to the particle radius, R . ,− This results in the following scaling law for small, unentangled colloids D normalp , normalI unent 0.25em ≃ 0.25em k normalB T η normals ϕ normalI 2 R 3 0.25em ≃ 0.25em D 0 u − 6 / 5 f − 8 / 5 Q − 4 / 5 R − 3 where η s is the solvent viscosity and D 0 is the diffusion coefficient of a single disjointed monomer (statistical segment). In the opposite scenario, when the particle size exceeds the tube diameter, the diffusion of the colloids is constrained by topological entanglements. ,, Their diffusion coefficient is inversely proportional to the viscosity of the entangled semidilute solution of PEs, η rep I ≃ η s ϕ I 14/3 N 3 / N e 2 , and reads D normalp , normalI ent 0.25em ≃ 0.25em k normalB T η rep R 0.25em ≃ 0.25em D 0 u − 14 / 5 f − 56 /…”

“…Their dynamics are also Rouse-like, and the diffusion coefficient D p unent is determined by the effective viscosity experienced by the particles . The latter is the Rouse viscosity of the PE chain fragments with a size comparable to the particle radius, R . ,− This results in the following scaling law for small, unentangled colloids where η s is the solvent viscosity and D 0 is the diffusion coefficient of a single disjointed monomer (statistical segment). In the opposite scenario, when the particle size exceeds the tube diameter, the diffusion of the colloids is constrained by topological entanglements. ,, Their diffusion coefficient is inversely proportional to the viscosity of the entangled semidilute solution of PEs, η rep I ≃ η s ϕ I 14/3 N 3 / N e 2 , and reads Here, N e is the entanglement strand length in the melt.…”

Universal scaling of the diffusivity of dendrimers in a semidilute solution of linear polymers

“…Several theories have been developed over the past few years to describe the dynamics of nanoparticles in semidilute polymer solutions. 24 Early theoretical studies of the diffusion of hard spheres in linear polymer solutions proposed a stretched exponential dependence of the reduced diffusion coefficient of the probe on the concentration of solution. 25–27 This was modified by Phillies et al 28 to include the effect of size of the probe and the molecular weight of the linear polymers to obtain the generalized scaling relation D / D 0 = exp(− bR u M x c y ), where D and D 0 are the diffusion coefficients of the probe in the polymer solution and in the pure solvent, R is the size of the probe, M is the molecular weight of the polymer, c is the solution concentration, with exponents u = 0 ± 0.2, x = 0.8 and y ranging from 0.5 to 1.0.…”