Long Wavelength Concentration Fluctuations and Cage Scale Ordering of Nanoparticles in Concentrated Polymer Solutions

Abstract

Ultrasmall-angle X-ray scattering is employed to probe the local and long wavelength collective structure of ternary mixtures of silica nanoparticles suspended in concentrated solutions of polyethyleneglycol in the good solvent ethanol. In the dilute polymer limit, these suspensions are stabilized via electrostatic repulsions, at intermediate polymer concentrations the nanoparticles aggregate, while in the polymer melt limit they again become homogeneous due to the formation of thermodynamically stable discrete adsorbed polymer layers on the nanoparticles. Solvent dilution of the polymer melt is found to modify the nanoparticle concentration fluctuations on all length scales in a manner that can be understood as a monotonic reduction of the favorable polymer-particle interfacial cohesive attraction. The measurements are quantitatively compared with predictions of the two-component Polymer Reference Interaction Site Model theory modified to account in an implicit manner for solvent addition via an effective contact strength of interfacial attraction, ε pc . Good agreement between theory and experiment is found without adjustable parameters based on the idea that ε pc linearly decreases with solvent volume fraction. The joint experimental-theoretical work suggests a new mechanism for restabilization of aggregated particle suspensions at high polymer concentration based on the thermodynamically controlled interface cohesion of weakly adsorbing polymers that contrasts with the classic kinetic repulsive barrier mechanism under nonadsorbing depletion attraction conditions.

Multiscale Structure, Interfacial Cohesion, Adsorbed Layers, and Thermodynamics in Dense Polymer-Nanoparticle Mixtures

“…Hence, we predict a direct connection between changes of polymer organization around nanoparticles and mixture microstructure with nanocomposite stiffness. Crucial to this rich behavior is that the total mixture volume fraction varies with c in a manner consistent with melt and concentrated solution experiments [16,18]. The striking prediction [25] that lowering " pc towards the depletion demixing boundary stiffens the nanocomposite while increasing the attraction strength away from it results in softening provides a new route to controlling the bulk modulus based on rational manipulation of polymer-particle interfacial cohesion and nanoparticle concentration.…”

“…Scattering patterns are compared with the standard polymer nanocomposite version of PRISM integral equation theory where the solvent enters implicitly, details of which are thoroughly documented in the literature and Supplemental Material [11][12][13][16][17][18][19]. All species interact via pair decomposable site-site hard-core repulsions.…”

Controlling effective interactions and spatial dispersion of nanoparticles in multiblock copolymer melts

“…First, the HNC closure has been used in many prior studies 35 and it has been well documented that for large enough nanoparticles (D/d 5) it results in predictions in good agreement with simulation and experiment. [8][9][10][11][12] Most importantly, it predicts the correct scaling of the PMF with D/d. In contrast, use of the PY closure for n-n direct correlations does not capture the correct PMF scaling, and can also lead to unphysical negative pair correlation functions for large particles.…”

“…34,35 This approach has been extensively applied to systems of hard spheres in homopolymer melts 8,[18][19][20][21] and its predictions for structure, effective interactions and miscibility compared favorably with simulations and experiments. [8][9][10][11][12] A key parameter is the effective monomer-particle attraction strength which determines, to zeroth order, the competition between entropy and enthalpy and the qualitative form of the polymer-mediated particle potential of mean force (PMF). When the polymer-particle attraction is very weak compared to the thermal energy, k B T, entropy favors the polymers to dewet the particle surface leading to depletion-induced contact aggregation.…”

Multi-scale entropic depletion phenomena in polymer liquids

“…The most elementary question is the potential of mean force (PMF) between two dilute hard spheres dissolved in a nonadsorbing polymer liquid. This defines the basic "entropic depletion" problem which has been the subject of many theoretical, [10][11][12][13][14][15][16][17][18][19][20][21][22] simulation, [23][24][25][26][27][28][29][30][31][32][33] and experimental [6][7][8][34][35][36][37][38][39][40][41] investigations in diverse parameter regimes. For physically distinct reasons, the depletion interaction can be net attractive which induces particle clustering and potentially macrophase separation and/or nonequilibrium physical gelation.…”