Core-Shell Superparticle: Structure & Applications

• Core-shell superparticles are composite nanomaterials with a distinct inner core and one or more outer shells that enable precise control over physical properties.
• Advanced characterization and simulations, including atomic electron tomography and kinetic Monte Carlo methods, reveal details of interfacial strain, growth morphology, and exchange interactions.
• Design strategies focus on optimizing shell thickness, lattice mismatch, and polymer grafting to enhance catalytic, magnetic, and optical functionalities across diverse applications.

A core-shell superparticle is a composite nanomaterial or molecule consisting of a distinct inner region (core) encapsulated by one or more outer layers (shells) with different composition or structure. This architectural motif is central to strain engineering, interface-driven functional tuning, and hybrid property design across nanoscience, catalysis, photonics, and magnetism. The following review synthesizes the current state of the field, drawing exclusively on atomic-level structural, magnetic, optical, and synthetic evidence from key experimental and theoretical studies.

1. Atomistic Structure and Strain in Core-Shell Superparticles

Full 3D atomic structures, as revealed by atomic electron tomography (AET) in systems such as Pd@Pt core–shell nanoparticles, provide exact spatial maps of core-shell interfaces, atomic displacements, and local strains (Jo et al., 2022). At each atomic site, the displacement field $u(\vec{r})$ is defined as the vector from the measured atomic position to the ideal lattice point: $$u(\vec{r}) = R_\text{atom}(\vec{r}) - R_\text{ideal}(\vec{r})$$. The local (small) strain tensor is computed as $$\epsilon_{ij}(\vec{r}) = \frac{1}{2}(\partial_i u_j + \partial_j u_i)$$, typically evaluated via Gaussian kernel averaging ($\sigma \sim 4-5$ Å) and finite differences.

The interfacial lattice mismatch is quantified through the misfit parameter $$\delta = \frac{a_\text{shell} - a_\text{core}}{a_\text{core}}$$. For Pd@Pt, core and shell lattice parameters are

$\begin{array}{c|c} \text{Region} & \langle a \rangle \, [\text{Å}] \ \hline \text{Pd core} & 3.92 \pm 0.06 \ \text{Pt shell} & 3.87 \pm 0.08 \ \end{array}$

yielding $\delta \simeq -1.3\%$ (shell compressed) and a corresponding tensile strain (+2.1%) in the core, compressive ($-0.4\%$) in the shell.

Strain mapping reveals strong radial–azimuthal coupling (Poisson effect), highly anisotropic distribution controlled by overall particle geometry (faceting, partial-core exposure), and robust transmission of interface strain to the outer surface, with a correlation coefficient $R=0.74$ and slope $\sim 0.87$ between interface and surface radial strain. Even at the local bond scale, cross-coupled head-to-head and tail-to-tail displacements manifest.

2. Growth Morphology and Kinetic Control

Morphological control of core-shell superparticles, particularly in noble metal systems, is addressed by kinetic Monte Carlo (kMC) simulations that model atom-by-atom shell deposition on faceted cores (Gorshkov et al., 2014). The fundamental processes include:

• Off-lattice diffusion of shell precursors.
• Exact registration of incorporated atoms to the underlying fcc (or other) lattice.
• Surface restructuring by kinetically allowed atomic hops, governed by coordination-number-dependent activation barriers ($p_0 = \exp(-\Delta E_\text{diff}/k_B T)$).
• Detachment and on-surface migration probabilities orchestrated by local bond energy gains ($E_\text{eps}$).

Two growth regimes are distinguished:

Regime	Kinetic Parameters	Morphology
Smooth, epitaxial shell	High $T$, low $F$	Layer-by-layer, low $R_q$
Clustered, rough shell	Low $T$, high $F$	Pillar/pyramid islands, high $R_q$

Here, $R_q$ denotes surface roughness, rising from $0.1\, a$ in smooth to $1-3\, a$ in clustered shells (with $a$ the lattice parameter).

The crossover between regimes is determined by a competition between surface-diffusion and deposition timescales; smooth shells require $\tau_\text{dep} \gg \tau_\text{surf}$. This framework enables predictive tuning of shell smoothness vs. nanocluster density by balancing atom supply, temperature, and surface-diffusion kinetics.

3. Magnetic Coupling, Exchange Bias, and Anisotropy in Magnetic Superparticles

Core-shell superparticles with magnetic character, e.g., Fe@Pt, Co/Co$_3$O$_4$, Fe$_3$O$_4$@CoFe$_2$O$_4$@MnFe$_2$O$_4$, exhibit highly nontrivial exchange coupling and tunable anisotropy (Gavrilov-Isaac et al., 2014, Pisane et al., 2015, De et al., 2016). In Fe@Pt (~3 nm) particles, superparamagnetic blocking is observed at $T_B = 13$ K, with large coercivity ($H_c = 750$ Oe at 2 K), enhanced by surface disorder and interparticle interactions ($\phi = 0.09$ via Vogel–Fulcher analysis; $K_a \sim 3.6 \times 10^6$ erg/cm$^3$).

In Co/Co$_3$O$_4$ particles (27 nm overall), maximal exchange bias ($H_E \sim 450$ Oe) and coercivity (3.2 kOe) are realized for an intermediate shell thickness ($d_\text{shell} \sim 9$ nm), coinciding with maximum interfacial strain and pinning of uncompensated shell spins. Atomistic Monte Carlo simulations reproduce the nonmonotonic $H_E$ and $H_C$ trends, directly linking core–shell lattice mismatch, interfacial domain structure, and magnetic reversal pathways.

In the trimagnetic system Fe$_3$O$_4$@CoFe$_2$O$_4$@MnFe$_2$O$_4$, the addition of a soft MnFe$_2$O$_4$ outer shell paradoxically enhances coercivity relative to the bimagnetic core–shell ($H_c$ increases by $\sim 1.9\times$) due to cooperative exchange pinning, contradicting naive volume-fraction arguments and necessitating explicit tuning of shell ordering, thickness, and interfacial exchange (Gavrilov-Isaac et al., 2014).

4. Optical Resonances and Hybridization in Core-Shell Photonic Superparticles

Core-shell geometry is foundational in tailoring electromagnetic resonances and optical response, especially in plasmonic and quantum-dot superparticles (Geints, 11 Nov 2025, Thiessen et al., 2015). Mie theory, recast in terms of hybridized surface modes, depicts each spherical core–shell superparticle as supporting coupled “bonding” and “antibonding” resonances between the core–shell and shell–medium interfaces. The resonance conditions are: $$\left[E_n^2(x_2)\right] \left[E_n^1(x_1)\right] - X_n^\text{cp1}(x_1)Z_n^2(x_2) = 0$$ where each term encodes Riccati–Bessel functions of the core, shell, and medium, and $n$ is the multipolar order.

In quantum-dot-based superparticles, self-assembly yields micron-scale spheres enveloped by silica shells, forming high-Q whispering-gallery mode (WGM) optical resonators. The SiO$_2$ shell (thickness $d \sim 0.6\mu$m on a $5\mu$m core) enhances internal pump intensity by up to $2\times$, sharpens field confinement at the core–shell interface, and increases the probability of WGM excitation. Emission exhibits strong directional bias, with the SiO$_2$ shell reducing backward asymmetry and broadening the emission lobe. High-Q modes ($Q_\text{abs} \sim 430-500$) are achieved at specific core diameters and shell thicknesses matched to phase-matching conditions (Geints, 11 Nov 2025).

5. Interface Structure, Wetting, and Soft Polymer Shells

Core-shell superparticles with soft, deformable shells display complex wetting and interfacial properties, exemplified by silica@PNIPAM particles at fluid–fluid interfaces (Vasudevan et al., 2018). The equilibrium position ($z_\text{eq}$), shell deformation (stretch factor $\beta$), and interfacial coverage are predicted using a free-energy model combining Flory–Huggins polymer mixing, elastic penalty, and surface-tension gain: $$F_\text{tot}(z) = F_w(z) + F_o(z) + F_{e,i}(z) + F_\gamma(z)$$ Experimentally, core–shell particles either rest with the hard core just contacting the interface (for thin shells, $t < t^*$), or become fully immersed, with shell alone spanning the interface (for $t > t^*$). The stretched interfacial radius $R_i$ depends only on geometry and deformation, not on contact angle. Viscous drag and Brownian diffusion at the interface scale as $D_i = k_B T/(6\pi\eta_\text{eff} R_i)$, with $\eta_\text{eff}$ fixed by interfacial, not bulk, dissipation.

6. Self-Assembly and Hybrid Architectures

Grafting of crystallizable polymers (e.g., poly(2-iso-propyl-2-oxazoline), PiPrOx) onto inorganic cores (e.g., SiO$_2$) enables programmable self-assembly of anisotropic superstructures via ligand crystallization (Nabiyan et al., 2023). Key parameters include core size (15–25 nm), shell thickness (4–11 nm), and grafting density ($\sigma = 0.11$–$0.70\,\text{chains nm}^{-2}$). Two-stage assembly is observed:

1. Above the polymer cloud point, gelation and amorphous aggregation occur through brush collapse and dipolar hydrogen bonding.
2. Prolonged annealing induces radial fiber growth via directional crystallization, with shell chains acting as linkers for crystalline ribbons.

Coarse-grained simulations confirm the role of directional dipolar interactions and polymer brush architecture in directing anisotropic superparticle assembly.

7. Atomically Precise Core-Shell Molecules: Electronic Structure and Multicenter Bonding

Icosahedral-to-icosidodecahedral core-shell clusters, e.g., Au$_{12}$@Au$_{30}$ (I$_h$ symmetry), provide a unique instance of superatomic core-shell structuring, with direct implications for catalysis and nanomedicine (Bai et al., 2021). Bond distances (core–core 2.854 Å, core–shell 2.855 Å, shell–shell 2.954–2.955 Å) and vibrational analysis confirm high structural stability up to ~450 K. Electronic structure analysis reveals strong Au 5d/6s hybridization at the Fermi level. The multicenter AdNDP orbitals include 20 six-center, two-electron $\sigma$-bonds (each linking core–shell interfaces), a single 12-center $\sigma$-bond for core integrity, and 210 one-center valence lone pairs (ideal for coordination chemistry). The presence of these multicenter motifs imparts both stability and chemical tunability unavailable to monolithic clusters.

8. Functional Implications and Design Guidelines

Key functional advantages and design levers of core-shell superparticles include:

• Catalytic optimization: Uniform compressive strain at catalytically active facets ({111} in Pt), achieved by misfit engineering ($\delta \sim -1.3\%$ in Pd@Pt), maximizes oxygen reduction reaction (ORR) activity. Thin shells ($<1$ nm) transmit interfacial strain to the surface, but shell thickness, core–shell geometry, and facet exposure must be co-optimized to prevent inhomogeneities or strain hot-spots (Jo et al., 2022).
• Magnetic enhancements: Multishell and exchange-coupled architectures (e.g., Fe$_3$O$_4$@CoFe$_2$O$_4$@MnFe$_2$O$_4$) surpass the anisotropy and coercivity limits of single-phase nanoparticles, with the effective anisotropy $K_\text{eff}$ tunable via shell order, thickness, and interfacial exchange constant $J_\text{ex}$ (Gavrilov-Isaac et al., 2014).
• Optical tuning: Selective control over mode hybridization, field localization, and emission directivity via shell index, thickness, and core size (Mie resonance, WGM conditions) enables multiplexed photonic or sensor design (Geints, 11 Nov 2025, Thiessen et al., 2015).
• Polymer-mediated assembly: Sequence, density, and crystallinity of grafted polymers control not only soft shell deformability but also emergent superparticle architectures (anisotropic, highly ordered fibers vs. isotropic gels) (Nabiyan et al., 2023).

Summary Table: Essential Parameters and Structure-Function Relations

Parameter/Property	Typical Values	Functional Consequence
Lattice mismatch $\delta$	$-1.3\%$ in Pd@Pt	Strain transmission, facet-specific catalytic control
Shell thickness $t$	$<1$ nm (atomic); $4$–$11$ nm (polymer)	Strain transmission, mode hybridization
Magnetic anisotropy $K_a$	$3.6 \times 10^6$ erg/cm$^3$ (Fe@Pt)	Enhanced coercivity, superparamagnetic transitions
Optical $Q$-factor	$Q \sim 430$–$500$ (CdS@SiO$_2$)	Whispering-gallery mode performance
Grafting density $\sigma$	$0.1$–$0.7$ chains/nm$^2$	Colloidal stability, structural order
Multicenter bonds	$20$ 6c–2e, $1$ 12c–2e (Au$_{12}$@Au$_{30}$)	Delocalized stability, chemical tunability

Outlook

The core-shell superparticle architecture provides a multidimensional parameter space for the rational control of structural, electronic, magnetic, and optical properties. The integration of atomic-resolution structural mapping, kinetic growth modeling, atomistic simulations, and spectroscopically validated theories yields a design platform for functional superparticles, spanning from catalysis and magnetism to photonics, sensing, and molecular assembly. The coupling between interface structure, strain, shell morphology, and functional response remains a central area for future investigation and tailoring, with advances in tomographic imaging, simulation, and scalable synthesis enabling increasingly sophisticated core-shell superparticle design.