Multi-scale entropic depletion phenomena in polymer liquids (original) (raw)
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In this work, we have synthesized polystyrene particles that carry short end-grafted polyethylene glycol (PEG) chains. We then added dissolved 100 kDa PEG polymers and monitored potential flocculation by confocal microscopy. Qualitative predictions, based on previous theoretical developments in this field (Xie, F.; et al. Soft Matter 2016, 12, 658), suggest a nonmonotonic temperature response. These theories propose that the "free" (dissolved) polymers will mediate attractive depletion interactions at room temperature, with a concomitant clustering/ flocculation at a sufficiently high polymer concentration. At high temperatures, where the solvent is poorer, this is predicted to be replaced by attractive bridging interactions, again resulting in particle condensation. Interestingly enough, our theoretical framework, based on classical density functional theory, predicts an intermediate temperature regime where the polymer-mediated interactions are repulsive! This obviously implies a homogeneous dispersion in this regime. These qualitative predictions have been experimentally tested and confirmed in this work, where flocs of particles start to form at room temperature for a high enough polymer dosage. At temperatures near 45°C, the flocs redisperse, and we obtain a homogeneous sample. However, samples at about 75°C will again display clusters and eventually phase separation. Using results from these studies, we have been able to fine-tune parameters of our coarse-grained theoretical model, resulting in predictions of temperature-dependent stability that display semiquantitative accuracy. A crucial aspect is that under "intermediate" conditions, where the polymers neither adsorb nor desorb at the particle surfaces, the polymer-mediated equilibrium interaction is repulsive.
Nanoparticle Diffusion in Polymer Nanocomposites
Physical Review Letters, 2014
Large-scale molecular dynamics simulations show that nanoparticle (NP) diffusivity in weakly interacting mixtures of NPs and polymer melts has two very different classes of behavior depending on their size. NP relaxation times and their diffusivities are completely described by the local, Rouse dynamics of the polymer chains for NPs smaller than the polymer entanglement mesh size. The motion of larger NPs, which are comparable to the entanglement mesh size, is significantly slowed by chain entanglements, and is not describable by the Stokes-Einstein relationship. Our results are in essentially quantitative agreement with a force-level generalized Langevin equation theory for all the NP sizes and chain lengths explored, and imply that for these lightly entangled systems, activated NP hopping is not important.
Reentrant equilibrium disordering in nanoparticle–polymer mixtures
2017
A large body of experimental work has established that athermal colloid/polymer mixtures undergo a sequence of transitions from a disordered fluid state to a colloidal crystal to a second disordered phase with increasing polymer concentration. These transitions are driven by polymer-mediated interparticle attraction, which is a function of both the polymer density and size. It has been posited that the disordered state at high polymer density is a consequence of strong interparticle attractions that kinetically inhibit the formation of the colloidal crystal, i.e., the formation of a non-equilibrium gel phase interferes with crystallization. Here we use molecular dynamics simulations and density functional theory on polymers and nanoparticles (NPs) of comparable size and show that the crystal-disordered phase coexistence at high polymer density for sufficiently long chains corresponds to an equilibrium thermodynamic phase transition. While the crystal is, indeed, stabilized at intermediate polymer density by polymer-induced intercolloid attractions, it is destabilized at higher densities because long chains lose significant configurational entropy when they are forced to occupy all of the crystal voids. Our results are in quantitative agreement with existing experimental data and show that, at least in the nanoparticle limit of sufficiently small colloidal particles, the crystal phase only has a modest range of thermodynamic stability.
The Journal of Chemical Physics, 2013
In this work, we study the influence of polymer chain length (m), based on Lennard-Jones potential, and nanoparticle (NP)-polymer interaction strength (ɛnp) on aggregation and dispersion of soft repulsive spherically structured NPs in polymer melt using coarse-grain molecular dynamics simulations. A phase diagram is proposed where transitions between different structures in the NP-polymer system are shown to depend on m and ɛnp. At a very weak interaction strength ɛnp = 0.1, a transition from dispersed state to collapsed state of NPs is found with increasing m, due to the polymer's excluded volume effect. NPs are well dispersed at intermediate interaction strengths (0.5 ⩽ ɛnp ⩽ 2.0), independent of m. A transition from dispersion to agglomeration of NPs, at a moderately high NP-polymer interaction strength ɛnp = 5.0, for m = 1–30, is identified by a significant decrease in the second virial coefficient, excess entropy, and potential energy, and a sharp increase in the Kirkwood-B...
Do Attractive Polymer–Nanoparticle Interactions Retard Polymer Diffusion in Nanocomposites?
Macromolecules, 2013
Diffusion of deuterated poly(methyl methacrylate) (dPMMA) is slowed down in a PMMA matrix filled with hydroxyl-capped spherical silica nanoparticles, from 13 to 50 nm in diameter and at loadings up to 40 vol %. At constant T − T g = 75 K, the normalized diffusion coefficients (D/D 0 ) collapse onto a master curve, when plotted against the confinement parameter, ID/2R g , where ID is interparticle distance and 2R g is probe size. This result suggests that the confinement parameter captures the effect of nanoparticle size, size polydispersity, and volume fraction on polymer dynamics for the PMMA composite. For ID < 2R g , the master curve exhibits a strongly confined region where D/D 0 decreases by up to 80%, whereas for ID > 2R g , the curve falls in a weakly confined region where D/D 0 decreases only moderately by up to 15%. Surprisingly, D/D 0 is reduced even when ID is 8 times larger than 2R g . A comparison between the master curves for PMMA and polystyrene nanocomposites indicates that attractive interactions in the PMMA system do not significantly alter the centerof-mass diffusion of macromolecules in polymer nanocomposites.
Thermodynamic Behavior of Particle/Diblock Copolymer Mixtures: Simulation and Theory
Macromolecules, 2000
We investigate the influence of hard nanoparticles on the phase behavior of diblock copolymers. Using Monte Carlo simulations, we obtain phase diagrams as a function of the nanoparticle size and concentration. When the size of the nanoparticles becomes comparable to the radius of gyration of the minority (A) block, we observe the formation of new superstructures, where the particles selfassemble inside the copolymer micelles. We develop a theoretical model, based on the strong segregation limit approximation, and show that these self-assembled structures can be either stable or metastable, depending on the particle size and volume fraction. The formation of such phases is due to the interplay between the particle-particle excluded-volume interactions, preferential particle/block-A interactions, and the enthalpic and stretching interactions within the diblock.
Theory and Simulation of Attractive Nanoparticle Transport in Polymer Melts
Macromolecules, 2018
We theoretically study the diffusion of a single attractive nanoparticle (NP) in unentangled and entangled polymer melts based on combining microscopic "core−shell" and "vehicle" mechanisms in a dynamic bond percolation theory framework. A physical picture is constructed which addresses the role of chain length (N), degree of entanglement, nanoparticle size, and NP−polymer attraction strength. The nanoparticle diffusion constant is predicted to initially decrease with N due to the dominance of the core−shell mechanism, then to cross over to the vehicle diffusion regime with a weaker N dependence, and eventually plateau at large enough N. This behavior corresponds to decoupling of NP diffusivity from the macroscopic melt viscosity, which is reminiscent of repulsive NPs in entangled melts, but here it occurs for a distinct physical reason. Specifically, it reflects a crossover to a transport mechanism whereby nanoparticles adsorb on polymer chains and diffuse using them as "vehicles" over a characteristic desorption time scale. Repetition of random desorption events then leads to Fickian long time NP diffusion. Complementary simulations for a range of chain lengths and low to moderate NP−polymer attraction strengths are also performed. They allow testing of the proposed diffusion mechanisms and qualitatively support the theoretically predicted dynamic crossover behavior. When the desorption time is smaller than or comparable to the onset of entangled polymer dynamics, the NP diffusivity becomes almost chain length independent.
Molecular Physics, 2004
We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. MC simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer to colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces.
Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts
Molecular Simulation, 2014
We present a dissipative particle dynamics (DPD) study of scaling behaviour for three polymer models. The scaling behaviour is explored for the conformational and dynamic properties of unentangled polymer melts. DPD employs a beadspring model together with an aggressive coarse-graining to represent polymers at the mesoscale. The first model studied utilises a simple soft repulsion potential for the bead-bead interactions together with a harmonic spring potential to connect beads into a polymer chain. The second model differs from the first model by replacing the harmonic spring with a finitely extensible nonlinear elastic spring. The third model uses realistic coarse-grain potentials for the bead-bead, spring and bending interactions based on the iterative Boltzmann inversion procedure and it corresponds to a mesoscopic model of polyethylene. We systematically vary the chain length and spring constant (in the case of the first and second models), and simulate the conformational properties such as the end-to-end distance or radius of gyration, and dynamic properties such as the centre-of-mass self-diffusion coefficient or viscosity. The scaling of the conformational and dynamic properties with chain length (scaling laws) is compared with the Rouse theory, which is considered as a standard theory for unentangled polymer melts. The comparison shows that simulated scaling laws typically agree with the Rouse scaling laws for the DPD polymer models with more than 10 DPD beads. For the shorter DPD polymers, deviations from the Rouse theory exist and become significant for the dynamic properties, especially for the viscosity of the polymer melts.