Universal Polymeric-to-Colloidal Transition in Melts of Hairy Nanoparticles

Abstract

Two different classes of hairy self-suspended nanoparticles in the melt state, polymer-grafted nanoparticles (GNPs) and star polymers, are shown to display universal dynamic behavior across a broad range of parameter space. Linear viscoelastic measurements on well-characterized silica-poly­(methyl acrylate) GNPs with a fixed core radius (R core) and grafting density (or number of arms f) but varying arm degree of polymerization (N arm) show two distinctly different regimes of response. The colloidal Regime I with a small N arm (large core volume fraction) is characterized by predominant low-frequency solidlike colloidal plateau and ultraslow relaxation, while the polymeric Regime II with a large N arm (small core volume fractions) has a response dominated by the starlike relaxation of partially interpenetrated arms. The transition between the two regimes is marked by a crossover where both polymeric and colloidal modes are discerned albeit without a distinct colloidal plateau. Similarly, polybutadiene multiarm stars also exhibit the colloidal response of Regime I at very large f and small N arm. The star arm retraction model and a simple scaling model of nanoparticle escape from the cage of neighbors by overcoming a hopping potential barrier due to their elastic deformation quantitatively describe the linear response of the polymeric and colloidal regimes, respectively, in all these cases. The dynamic behavior of hairy nanoparticles of different chemistry and molecular characteristics, investigated here and reported in the literature, can be mapped onto a universal dynamic diagram of f/[R core 3/ν0)1/4] as a function of (N armν0 f)/(R core 3), where ν0 is the monomeric volume. In this diagram, the two regimes are separated by a line where the hopping potential ΔU hop is equal to the thermal energy, k B T. ΔU hop can be expressed as a function of the overcrowding parameter x (i.e., the ratio of f to the maximum number of unperturbed chains with N arm that can fill the volume occupied by the polymeric corona); hence, this crossing is shown to occur when x = 1. For x > 1, we have colloidal Regime I with an overcrowded volume, stretched arms, and ΔU hop > k B T, while polymeric Regime II is linked to x < 1. This single-material parameter x can provide the needed design principle to tailor the dynamics of this class of soft materials across a wide range of applications from membranes for gas separation to energy storage.

Structure of Polymer-Grafted Nanoparticle Melts

“…Indeed, independent experimental rheology measurements of similar GNPs revealed that these cage rearrangements occur on macroscopic time scales (up to several days in some cases). 55 In our simulations, we have achieved the first stage of equilibration, that is, local relaxation of the grafted chains, but the entire system has not reached equilibrium.…”

Colloidal Jamming in Multiarm Star Polymer Melts

“…2,5 At extreme functionalities ( f ≈ 900), they are less soft than at f = 128 and can be considered as approaching the hard sphere limit. 26 In such a case, particle scale excluded volume effects dramatically slow down their center-of-mass motion resulting in caging, and the stars jam over the time scales corresponding to the experimental frequency window, like microgel particles, emulsions, or foams. 2,27,28 This unexpected behavior arises from the extremely high branching functionality and the short arm length.…”

“…15 Moreover, recent data with polystyrene-grafted silica nanoparticle melts having constant grafting density and varying molar mass of polystyrene also comply with this picture. 26 Hence, the representation of Figure 4 should be generic. However, given that stars and grafted nanoparticles are different (particularly with respect to core size), we prefer to restrict our discussion to well-defined stars of the same chemistry, while pointing out the analogies with other systems.…”

“…A more general description shall be presented in the near future. 26 There is also an interesting analogy with microgel melts, the only other soft colloidal system that is chemically homogeneous. The limited available linear viscoelastic data on polystyrene microgels in the melt 44 have been compared against those of entangled linear chains in three regimes: (i) at high frequencies, the data reflect local dynamics and are indistinguishable for different systems; (ii) the intermediate plateau region has an amplitude similar to that of the entanglement network and its extent in frequency depends on the degree of cross-linking; and (iii) the terminal relaxation is slowed down as compared to linear polymers, and for high degrees of crosslinking, it is arrested in the accessible frequency range, which was proposed at the time as a proof for nonreptative polymer dynamics.…”

Transient dynamics of soft particle glasses in startup shear flow. Part II: Memory and aging

“…Soft particle glasses (SPGs) are amorphous materials made of deformable particles which are packed at large volume fractions above the jamming transition [1,2]. Important examples include concentrated emulsions [1], microgel suspensions [3], and concentrated dispersions of hairy particles such as star polymers [4,5] or grafted nanoparticles [6]. In SPGs, each particle is constrained in a cage by elastic repulsive forces and cannot move over long distances unless a mechanical action exceeding the yield point is applied.…”