Pair Potentials between Polymer-Coated Mesoscopic Particles

Wijmans, Christopher M.; Leermakers, F.A.M.; Fleer, G.J.

doi:10.1021/la00024a021

Cited by 44 publications

(49 citation statements)

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“…10 Their use of a cylindrical coordinate system made it impossible to graft the chains a uniform distance, ε, from the spherical particles. Therefore, they grafted the chain ends in a narrow band above the particles with an appropriate weighting for each lattice site in order to achieve a reasonably uniform grafting density.…”

Section: Discussionmentioning

confidence: 99%

“…10,20 For particle one, the mesh has a regular spacing of ∆θ ) 0.0025π for θ ) 0 to π and a spacing of ∆r ) 0.01aN 1/2 for r ) R to R + R max . The value of R max is always chosen sufficiently large that φ 1 (r) < 10 -9 on the outer boundary.…”

Section: Theorymentioning

confidence: 99%

“…by performing a change of variable from θ to l. Although eq 24 already represents a relatively easy calculation, the standard Derjaguin approach goes a step further by taking the limit of large R, in which case the expression reduces to 10,24 …”

Section: Derjaguin Approximationmentioning

confidence: 99%

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Interaction between Polymer-Grafted Particles

Kim

Matsen

2008

Macromolecules

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Previous self-consistent field theory (SCFT) calculations have predicted that the steric interaction between two polymer-grafted particles in good solvent can become attractive, but this conclusion has since been questioned. Here we reexamine the problem with a new numerical scheme using multiple coordinate systems, and find that the interaction remains repulsive regardless of the particle size, brush thickness, or particle separation. The erroneous attraction in the earlier calculations can be attributed to numerical inaccuracy and a subtle issue with how the chains were grafted to the particles. Using our corrected SCFT solution, we also investigate the accuracy of a previous calculation based on strong-stretching theory (SST) and the applicability of the Derjaguin approximation, where the interaction between large particles is estimated from the one-dimensional uniform compression of polymer brushes.

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Section: Discussionmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

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Interaction between Polymer-Grafted Particles

Kim

Matsen

2008

Macromolecules

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“…Wijmans et al 25 used a two-dimensional lattice SCF to calculate the interaction between two polymer-coated particles whose radii of curvature are of the same order of magnitude as the polymer layer thickness. They found the repulsive interactions to be far less than those predicted by the Derjaguin approximation.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Interaction Forces between Nanoparticles: End-Grafted Polymer Modifiers

Marla

Meredith

2006

J. Chem. Theory Comput.

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Abstract:The interaction forces between nanoscale colloidal particles coated with end-grafted Lennard-Jones homopolymers are calculated using off-lattice Monte Carlo simulations in the NVT ensemble. The focus of this work is on grafted polymers that are of approximately the same size as the nanoparticle, a regime intermediate to the star-polymer and Derjaguin limits. The effects of chain length (N), nanoparticle diameter (σ c ), grafting density (F a ), and colloidpolymer and polymer-polymer interaction energies ( cp and pp ) on the polymer-induced force between the nanoparticles are explored. The inclusion of attractive dispersion interactions between the particle and polymeric modifier results in either long-ranged attraction and shortranged repulsion or pure repulsion, depending on the molecular parameters. The polymerinduced attraction occurs even under good solvent conditions below a threshold grafting density (F a ) and chain length (N) and could be attributed to both bridging (colloid-polymer) and intersegmental (polymer-polymer) attraction. Above the threshold F a and N values, chain entropy and excluded volume effects begin to dominate and lead eventually to polymer-induced repulsion and, consequently, nanoparticle stabilization. These results point to the importance of considering dispersion attractions between grafted segments and the nanoparticle surface in modeling these high-curvature colloid interactions.

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“…[5][6][7][8][9][10] Star polymers and polymer grafted nanoparticles (PGNPs) constitute an important class of such soft nanocolloidal particles, for which some work has emerged recently where the structure and dynamics of either the pristine colloids or their binary mixtures have been investigated. 3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18] Extensive research on star polymers over the last decade has led to the emergence of a reasonably good understanding of the microscopic origins of their observed phase behavior, including prediction and verification of an effective interaction potential between these entities. 5,[19][20][21] Unfortunately, the same cannot be said for PGNPs, a) Electronic mail: basu@physics.iisc.ernet.in despite the fact that they are also widely accepted as a prototypical additive in polymer matrices to create novel functional polymer nanocomposites (PNCs).…”

Section: Introductionmentioning

confidence: 99%

Suspensions of polymer-grafted nanoparticles with added polymers—Structure and effective pair-interactions

Chandran

Saw

Kandar

et al. 2015

The Journal of Chemical Physics

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We present the results of combined experimental and theoretical (molecular dynamics simulations and integral equation theory) studies of the structure and effective interactions of suspensions of polymer grafted nanoparticles (PGNPs) in the presence of linear polymers. Due to the absence of systematic experimental and theoretical studies of PGNPs, it is widely believed that the structure and effective interactions in such binary mixtures would be very similar to those of an analogous soft colloidal material-star polymers. In our study, polystyrene-grafted gold nanoparticles with functionality f = 70 were mixed with linear polystyrene (PS) of two different molecular weights for obtaining two PGNP:PS size ratios, ξ = 0.14 and 2.76 (where, ξ = Mg/Mm, Mg and Mm being the molecular weights of grafting and matrix polymers, respectively). The experimental structure factor of PGNPs could be modeled with an effective potential (Model-X), which has been found to be widely applicable for star polymers. Similarly, the structure factor of the blends with ξ = 0.14 could be modeled reasonably well, while the structure of blends with ξ = 2.76 could not be captured, especially for high density of added polymers. A model (Model-Y) for effective interactions between PGNPs in a melt of matrix polymers also failed to provide good agreement with the experimental data for samples with ξ = 2.76 and high density of added polymers. We tentatively attribute this anomaly in modeling the structure factor of blends with ξ = 2.76 to the questionable assumption of Model-X in describing the added polymers as star polymers with functionality 2, which gets manifested in both polymer-polymer and polymer-PGNP interactions especially at higher fractions of added polymers. The failure of Model-Y may be due to the neglect of possible many-body interactions among PGNPs mediated by matrix polymers when the fraction of added polymers is high. These observations point to the need for a new framework to understand not only the structural behavior of PGNPs but also possibly their dynamics and thermo-mechanical properties as well.

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Pair Potentials between Polymer-Coated Mesoscopic Particles

Cited by 44 publications

References 1 publication

Interaction between Polymer-Grafted Particles

Interaction between Polymer-Grafted Particles

Simulation of Interaction Forces between Nanoparticles: End-Grafted Polymer Modifiers

Suspensions of polymer-grafted nanoparticles with added polymers—Structure and effective pair-interactions

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