Effect of Bidispersity on Polymer-Bound Layers of Carbon Black Primary Particles: Combining Large-Scale Simulations and Experiments

Caputo, Stefano; Hristov, Velichko; Munaò, Gianmarco; Herbst, Harald; Pizzirusso, Antonio; Donati, Greta; De Nicola, Antonio; Albunia, Alexandra Romina; Milano, Giuseppe

doi:10.1021/acs.macromol.3c01817

Cited by 4 publications

(5 citation statements)

References 76 publications

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“…For additional information regarding the spatiotemporal discretization of eq and the convergence of the self-consistent field the reader is referred to Section 2.4 of ref . The parameters of the calculations are reported in Table .…”

Section: Methodsmentioning

confidence: 99%

“…D ( p , p i ) indicates the great circle distance between points p and p i . For more details, the readers are referred to section 2.6.2 of ref .…”

Section: Methodsmentioning

confidence: 99%

“…In conjunction with the algorithm developed in ref , we have imposed an additional constraint; we have set a minimum distance r min between two grafting points, so that the maximum local grafting density does not exceed a threshold value σ g,max = 1.2 nm –2 , which is hard to achieve experimentally; assuming hexagonal close packing locally for grafting points, we get r min 2 = 2 3 1 σ normalg , max ≈ 1 0.25em nm 2 . In this manner, we also eliminate discrepancies in the resulting PMF in case two grafting points come too close to each other during the generation process (see Section S5 of the Supporting Information).…”

Section: Methodsmentioning

confidence: 99%

“…We introduce an important aspect missing from the literature, namely, the determination of the free energy of systems with two or multiple nanoparticles of arbitrary particle geometry, relative orientation, and grafting point distribution. Having an accurate model that can take into account all possible molecular degrees of freedom of such complicated systems could serve as a basis for the development of coarse-grained orientation-dependent potentials for particle and particle-field simulations − capable of addressing mesoscopic-microscopic regimes; hence, reducing the number (and cost) of experiments needed for molecular design without any a priori knowledge of equilibrium phase behavior and morphology.…”

mentioning

confidence: 99%

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Tailoring Nanoparticle Orientation in Polymer Matrices via Nonuniform Grafting: Implications for Nanoparticle Dispersions and Self-Assembled Nanocomposite Morphologies

Revelas,

Sgouros,

Lakkas

et al. 2024

ACS Appl. Nano Mater.

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We propose a three-dimensional model implementing a self-consistent field (SCF) mathematical formulation to predict the equilibrium orientation and morphology of grafted nanoparticles (NPs) in a polymer, based on two-and multibody interactions developed among them. First, we investigate the potential of mean force (PMF) between two spherical polystyrenegrafted silica NPs in a polystyrene melt as a function of the matrixto-grafted chain length ratio and, more importantly, of the distribution of grafting points on their surfaces. While the most common assumption when performing such calculations is an equidistant distribution of grafting points on the surfaces of the NPs, we demonstrate here that the pattern of grafting plays an essential role in the equilibrium orientation and shape assumed by the particles inside the polymer matrix. In equidistant grafting, the role of grafting density is dominant, but, when grafting the chains irregularly, the same number of grafted chains distributed differently can significantly affect the self-assembly tendencies of the particles and the thermodynamic behavior of the composite system. Next, we calculate the free energy of a system of multiple equidistantly grafted nanoparticles exposed to a melt when they are arranged in a simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) lattice as a function of their spatial density. We minimize the free energy with respect to nanoparticle density to impose the condition of thermodynamic equilibrium. Among the three arrangements, the FCC/SC is the most/least stable configuration. The three-dimensional SCF methodology proposed herein addresses all possible degrees of freedom for the molecular-level design of both stable dispersions and self-assembled nanocomposite morphologies with tailor-made properties. It offers a cost-effective approach to creating high-value nanocomposite materials such as polymer-matrix nanocomposites in the rubber industry as well as "particle-solids," the latter combining toughness with good optical properties.

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Section: Methodsmentioning

confidence: 99%

“…D ( p , p i ) indicates the great circle distance between points p and p i . For more details, the readers are referred to section 2.6.2 of ref .…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Tailoring Nanoparticle Orientation in Polymer Matrices via Nonuniform Grafting: Implications for Nanoparticle Dispersions and Self-Assembled Nanocomposite Morphologies

Revelas,

Sgouros,

Lakkas

et al. 2024

ACS Appl. Nano Mater.

View full text Add to dashboard Cite

show abstract

“…A variety of mesoscopic simulation approaches have been developed, including particle-based models [Brownian dynamics (BD), coarse-grained molecular dynamics (CGMD), and dissipative particle dynamics (DPD) − ], field-based models [density functional theory (DFT), , self-consistent field theory (SCFT − ), dynamic SCFT, and lattice Boltzmann methods , ], and hybrid particle-field models [smooth particle hydrodynamics (SPH), smooth dissipative particle dynamics (SDPD), , many-body dissipative particle dynamics (MDPD), − , hybrid molecular dynamics/self-consistent field schemes (MD-SCF), − and hybrid Brownian dynamics/kinetic Monte Carlo (BD/kMC) schemes , accounting for chain reptation − ].…”

Section: Introductionmentioning

confidence: 99%

Development of a Meshless Kernel-Based Scheme for Particle-Field Brownian Dynamics Simulations

Sgouros,

Theodorou

2024

J. Phys. Chem. B

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We develop a meshless discretization scheme for particle-field Brownian dynamics simulations. The density is assigned on the particle level using a weighting kernel with finite support. The system's free energy density is derived from an equation of state (EoS) and includes a square gradient term. The numerical stability of the scheme is evaluated in terms of reproducing the thermodynamics (equilibrium density and compressibility) and dynamics (diffusion coefficient) of homogeneous samples. Using a reduced description to simplify our analysis, we find that numerical stability depends strictly on reduced reference compressibility, kernel range, time step in relation to the friction factor, and reduced external pressure, the latter being relevant under isobaric conditions. Appropriate parametrization yields precise thermodynamics, further improved through a simple renormalization protocol. The dynamics can be restored exactly through a trivial manipulation of the time step and friction coefficient. A semiempirical formula for the upper bound on the time step is derived, which takes into account variations in compressibility, friction factor, and kernel range. We test the scheme on realistic mesoscopic models of fluids, involving both simple (Helfand) and more sophisticated (Sanchez−Lacombe) equations of state.

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Modeling the Interface Between Phases in Dense Polymer‐Carbon Black Nanoparticle Composites by Dielectric Spectroscopy: Where Are We Now and What are the Opportunities?

Brosseau

2024

Macro Theory & Simulations

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The macroscopic properties of polymer nanocomposites (PNC) rely largely on the interphase between the polymer chains and the filler particles. One significant difficulty to solve this issue is to quantitatively model the structure‐property correlations due to the interfacial region in these complex materials. While dielectric spectroscopy (DS) measurements are routinely used to characterize the effective permittivity of filled polymers, fitting standard effective medium models and mixing equations to these data remains notoriously difficult to interpret. This is due to the absence of explicit reference to internal length scales characterizing the interfaces in the PNC. As an illustrative example, a two‐level homogenization framework is proposed which enables the extraction of useful information on the impact of a thin interphase confined on a nanometer length scale based on broadband DS data. This model leads to new ways of tuning the interphase so as to optimize the material's response to electric field, a situation relevant for electromagnetic shielding. This approach provides guidance on how to observe directly and experimentally the actual properties of the interface between the phases (as opposed to model‐based inference). Aside from its secure physical foundation in the theory of effective medium, a significant advantage of this approach is that a genetic algorithm (GA) technique applied to this physics‐based model enables the uniqueness of the fit parameters to be considered, as the GA method is robust in terms of finding globally optimum solutions, therefore placing confidence in non‐universal values of the percolation exponents. Recent work in physics‐informed machine learning indicates that the effective dielectric properties of PNC with many degrees of freedom due to their complex morphology can be described by considering only a few degrees of freedom describing the interface features between the phases in these composites.

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Effect of Bidispersity on Polymer-Bound Layers of Carbon Black Primary Particles: Combining Large-Scale Simulations and Experiments

Cited by 4 publications

References 76 publications

Tailoring Nanoparticle Orientation in Polymer Matrices via Nonuniform Grafting: Implications for Nanoparticle Dispersions and Self-Assembled Nanocomposite Morphologies

Tailoring Nanoparticle Orientation in Polymer Matrices via Nonuniform Grafting: Implications for Nanoparticle Dispersions and Self-Assembled Nanocomposite Morphologies

Development of a Meshless Kernel-Based Scheme for Particle-Field Brownian Dynamics Simulations

Modeling the Interface Between Phases in Dense Polymer‐Carbon Black Nanoparticle Composites by Dielectric Spectroscopy: Where Are We Now and What are the Opportunities?

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