Assembling Vertical Block Copolymer Nanopores via Solvent Vapor Annealing on Homopolymer-Functionalized Substrates.

Utilizing the self-assembly of block copolymers with large Flory-Huggins interaction parameters (χ) for nanofabrication is a formidable challenge due to the attendant large surface energy differences between the blocks. This work reports a robust protocol for the fabrication of thin films with highly ordered cylindrical nanopore arrays via the self-assembly of an asymmetric poly(styrene-block-4-vinylpyridine) (PS-b-P4VP) diblock copolymer blended with a P4VP homopolymer. The desired vertical domain orientation is achieved at the air-polymer interface by controlled solvent vapor annealing (SVA) using acetone, a solvent with weak selectivity for PS over P4VP, and at the substrate interface by functionalization using a hydroxy-terminated poly(2-vinylpyridine) (P2VP-OH) homopolymer brush. In contrast, the vertical cylinder orientation is unstable during acetone SVA on substrates functionalized using hydroxy-terminated poly(methyl methacrylate) (PMMA-OH). Although PMMA exhibits more balanced interfacial energies between PS and P4VP than P2VP in the dry state, it is also swollen more selectively by acetone. We hypothesize that the nearly balanced solvent swelling of the three polymers (P2VP, P4VP, and PS) stabilizes the vertical cylinder orientation, while unbalanced swelling (PMMA > P4VP and PS) does not. We further characterize pore formation by addition of a P4VP homopolymer and its postassembly extraction using ethanol, revealing a narrow window of pore size tunability. Notably, minimal differences in nanopore morphologies are observed for P4VP volume fractions as high as 0.1, regardless of the P4VP molar mass. However, further increasing the P4VP volume fraction results in domain reorientation or macrophase separation when its molar mass is less than or greater than the P4VP block molar mass, respectively. Using a P4VP homopolymer that is nearly equal in length to the P4VP block enables the fabrication of well-ordered arrays of vertical, through-film nanopores with high aspect ratios (>10), small periods (<23 nm), and diameters less than 10 nm.

Controlling the Self-Assembly of DNA Origami Octahedra via Manipulation of Inter-Vertex Interactions.

Recent studies have demonstrated novel strategies for the organization of nanomaterials into three-dimensional (3D) ordered arrays with prescribed lattice symmetries using DNA-based self-assembly strategies. In one approach, the nanomaterial is sequestered into DNA origami frames or "material voxels" and then coordinated into ordered arrays based on the voxel geometry and the corresponding directional interactions based on its valency. While the lattice symmetry is defined by the valency of the bonds, a larger-scale morphological development is affected by assembly processes and differences in energies of anisotropic bonds. To facilely model this assembly process, we investigate the self-assembly behavior of hard particles with six interacting vertices via theory and Monte Carlo simulations and exploration of corresponding experimental systems. We demonstrate that assemblies with different 3D crystalline morphologies but the same lattice symmetry can be formed depending on the relative strength of vertex-to-vertex interactions in orthogonal directions. We observed three distinct assembly morphologies for such systems: cube-like, sheet-like, and cylinder-like. A simple analytical theory inspired by well-established ideas in the areas of protein crystallization, based on calculating the second virial coefficient of patchy hard spheres, captures the simulation results and thus represents a straightforward means of modeling this self-assembly process. To complement the theory and simulations, experimental studies were performed to investigate the assembly of octahedral DNA origami frames with varying binding energies at their vertices. X-ray scattering confirms the robustness of the formed nanoscale lattices for different binding energies, while both optical and electron microscopy imaging validated the theoretical predictions on the dependence of the distinct morphologies of assembled state on the interaction strengths in the three orthogonal directions.

Ionic Conductivity and Mechanical Reinforcement of Well-Dispersed Polymer Nanocomposite Electrolytes.

Nanoparticles are commonly added to polymer electrolytes to enhance both their mechanical and ion transport properties. Previous work reports significant increases in the ionic conductivity and Li-ion transference in nanocomposite electrolytes with inert, ceramic fillers. The mechanistic understanding of this property enhancement, however, assumes nanoparticle dispersion states─namely, well-dispersed or percolating aggregates─that are seldom quantified using small-angle scattering. In this work, we carefully control the inter-silica nanoparticle structure (where each NP has a diameter D = 14 nm) in a model polymer electrolyte system (PEO:LiTFSI). We find that hydrophobically modified silica NPs are stabilized against aggregation in an organic solvent by inter-NP electrostatic repulsion. Favorable NP surface chemistry and a strongly negative zeta potential promote compatibility with PEO and the resulting electrolyte. Upon prolonged thermal annealing, the nanocomposite electrolytes display structure factors with characteristic interparticle spacings determined by particle volume fraction. Thermal annealing and particle structuring yield significant increases in the storage modulus, G', at 90 °C for the PEO/NP mixtures. We measure the dielectric spectra and blocking-electrode (κb) conductivities from -100 to 100 °C, and the Li+ current fraction (ρLi+) in symmetric Li-metal cells at 90 °C. We find that nanoparticles monotonically decrease the bulk ionic conductivity of PEO:LiTFSI at a rate faster than Maxwell's prediction for transport in composite media, while ρLi+ does not significantly change as a function of particle loading. Thus, when nanoparticle dispersion is controlled in polymer electrolytes, Li+ conductivity monotonically, i.e., (κbρLi+), decreases but favorable mechanical properties are realized. These results imply that percolating aggregates of ceramic surfaces, as opposed to physically separated particles, probably are required to achieve increases in bulk, ionic conductivity.

Enhanced efficiency of water desalination in nanostructured thin-film membranes with polymer grafted nanoparticles.

Polyamide composite (PA-TFC) membranes are the state-of-the-art ubiquitous platforms to desalinate water at scale. We have developed a novel, transformative platform where the performance of such membranes is significantly and controllably improved by depositing thin films of polymethylacrylate [PMA] grafted silica nanoparticles (PGNPs) through the venerable Langmuir-Blodgett method. Our key practically important finding is that these constructs can have unprecedented selectivity values (i.e., ∼250-3000 bar-1, >99.0% salt rejection) at reduced feed water pressure (i.e., reduced cost) while maintaining acceptable water permeance A (= 2-5 L m-2 h-1 Bar-1) with as little as 5-7 PGNP layers. We also observe that the transport of solvent and solute are governed by different mechanisms, unlike gas transport, leading to independent control of A and selectivity. Since these membranes can be formulated using simple and low cost self-assembly methods, our work opens a new direction towards development of affordable, scalable water desalination methods.

Directional polymer crystallisation with a fast-moving sink.

It has previously been shown that non-isothermal directional polymer crystallisation driven by local melting (Zone Annealing), has a close analogy with an equivalent isothermal crystallisation protocol. This surprising analogy is due to the low thermal conductivity of polymers-because they are poor thermal conductors, crystallisation occurs over a relatively narrow spatial domain while the thermal gradient spans a much wider scale. This separation of scales, which occurs in the limit of small sink velocity, allows replacing the crystallinity profile with a step and the temperature at the step acts as an effective isothermal crystallisation temperature. In this paper, we study directional polymer crystallisation under faster moving sinks using both numerical simulations and analytical theory. While, only partial crystallisation occurs, regardless, a steady state exists. At large velocity, the sink quickly moves ahead of a region that is still crystallizing; since polymers are poor thermal conductors, the latent heat dissipation to the sink becomes inefficient, eventually resulting in the temperature increasing back to the melting point thereby resulting in incomplete crystallization. This transition occurs when the two length scales measuring the sink-interface distance and the width of the crystallizing interface become comparable. For steady state and in the limit of large sink velocity, regular perturbation solutions of the differential equations governing heat transport and crystallization in the region between the heat sink and the solid-melt interface are in good agreement with numerical results.

Dynamic crosslinking compatibilizes immiscible mixed plastics.

The global plastics problem is a trifecta, greatly affecting environment, energy and climate1-4. Many innovative closed/open-loop plastics recycling or upcycling strategies have been proposed or developed5-16, addressing various aspects of the issues underpinning the achievement of a circular economy17-19. In this context, reusing mixed-plastics waste presents a particular challenge with no current effective closed-loop solution20. This is because such mixed plastics, especially polar/apolar polymer mixtures, are typically incompatible and phase separate, leading to materials with substantially inferior properties. To address this key barrier, here we introduce a new compatibilization strategy that installs dynamic crosslinkers into several classes of binary, ternary and postconsumer immiscible polymer mixtures in situ. Our combined experimental and modelling studies show that specifically designed classes of dynamic crosslinker can reactivate mixed-plastics chains, represented here by apolar polyolefins and polar polyesters, by compatibilizing them via dynamic formation of graft multiblock copolymers. The resulting in-situ-generated dynamic thermosets exhibit intrinsic reprocessability and enhanced tensile strength and creep resistance relative to virgin plastics. This approach avoids the need for de/reconstruction and thus potentially provides an alternative, facile route towards the recovery of the endowed energy and materials value of individual plastics.

Microscale mobile surface double layer in a glassy polymer.

This study examines the origin of the widely different length scales, ht-nanometers to micrometers-that have been observed for the propagation of the near-surface enhanced mobility in glassy polymers. Mechanical relaxations of polystyrene films with thicknesses, h, from 5 nm to 186 µm have been studied. For h < ~1 µm, the films relaxed faster than the bulk and the relaxation time decreased with decreasing h below ~100 nm, consistent with the enhanced dynamics originating from a near-surface nanolayer. For h > ~1 µm, a bulk-like relaxation mode emerged, while the fast mode changed to one that extended over ~1 µm from the free surface. These findings evidence that the mobile surface region is inhomogeneous, comprising a nanoscale outer layer and a slower microscale sublayer that relax by different mechanisms. Consequently, measurements probing the enhanced mobility of different mechanisms may find vastly different ht's as shown by the literature.

Melt State Reinforcement of Polyisoprene by Silica Nanoparticles Grafted with Polyisoprene.

We systematically vary the nanoparticle (NP) dispersion state in composites formed by mixing polyisoprene homopolymers with polyisoprene grafted silica particles, and demonstrate how creep measurements allow us to overcome the limitations of small amplitude oscillatory shear (SAOS) experiments. This allows us to access nearly 13 orders in time in the mechanical response of the resulting composites. We find that a specific NP morphology, a percolating particle network achieved at intermediate graft densities, significantly reinforces the system and has a lower NP percolation loading threshold relative to other morphologies. These important effects of morphology only become apparent when we combine creep measurements with SAOS re-emphasizing the role of synergistically combining methods to access the mechanical properties of polymer nanocomposites over broad frequency ranges.

Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies.

We rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes. While gas permeabilities depend specifically on the chemistry of the polymers considered, we focus here on permeabilities relative to the corresponding pure polymer which show interesting, "universal" behavior. For a given NP radius, Rc, and for large enough areal grafting densities, σ, to be in the dense brush regime we find that gas permeability enhancements display a maximum as a function of the graft chain molecular weight, Mn. Based on a recently proposed theory for the structure of a spherical brush in a melt of GNPs, we conjecture that this peak permeability occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The corresponding brush thickness is predicted to be h max = 3 R c , independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕNP, ϕNP,max = [Rc/(Rc + hmax)]3 ≈ 0.049. Motivated by this conclusion, we measured CO-2 and CH4 permeability enhancements across a variety of Rc, Mn and σ, and find that they behave in a similar manner when considered as a function of ϕNP, with a peak in the near vicinity of the predicted ϕNP,max. Thus, the chain length dependent extension free energy appears to be the critical variable in determining the gas permeability for these hybrid materials. The emerging picture is that these curved polymer brushes, at high enough σ behave akin to a two-layer transport medium - the region in the near vicinity of the NP surface is comprised of extended polymer chains which speed-up gas transport relative to the unperturbed melt. The chain extension free energy increases with increasing chain length, up to a maximum, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that is akin to an unperturbed melt with slow gas transport. The permeability maximum and decreasing permeability with increasing chain length then follow naturally.

Physics of Directional Polymer Crystallization.

It has been proposed that the nonisothermal directional crystallization of a polymer driven by a moving sink has an exact analogy to an equivalent isothermal crystallization protocol. We show that this is substantially true because polymers are poor thermal conductors; thus, polymer crystallization occurs over a relatively narrow spatial regime, while the thermal gradients created by this freezing occur over a much broader scale. This separation of scales allows us to replace the crystallization process, which is spatially distributed, with an equivalent step. The temperature at this step, which corresponds to the desired equivalent isothermal crystallization temperature, scales linearly with sink velocity. However, a few metrics, such as the Avrami exponent characterizing the kinetics of crystallization are very different in the two cases. These findings provide new insights into the physics of these spatially varying crystallization protocols and should inspire new experiments to probe the underlying equivalences more deeply.

Microbial nanocellulose biotextiles for a circular materials economy.

The synthesis and bottom-up assembly of nanocellulose by microbes offers unique advantages to tune and meet key design criteria-rapid renewability, low toxicity, scalability, performance, and degradability-for multi-functional, circular economy textiles. However, development of green processing methods that meet these criteria remains a major research challenge. Here, we harness microbial biofabrication of nanocellulose and draw inspiration from ancient textile techniques to engineer sustainable biotextiles with a circular life cycle. The unique molecular self-organization of microbial nanocellulose (MC) combined with bio-phosphorylation with a lecithin treatment yields a compostable material with superior mechanical and flame-retardant properties. Specifically, treatment of MC with a lecithin-phosphocholine emulsion makes sites available to modulate cellulose cross-linking through hydroxyl, phosphate and methylene groups, increasing the interaction between cellulose chains. The resultant bioleather exhibits enhanced tensile strength and high ductility. Bio-phosphorylation with lecithin also redirects the combustion pathway from levoglucosan production towards the formation of foaming char as an insulating oxygen barrier, for outstanding flame retardance. Controlled color modulation is demonstrated with natural dyes. Life cycle impact assessment reveals that MC bioleather has up to an order of magnitude lower carbon footprint than conventional textiles, and a thousandfold reduction in the carcinogenic impact of leather production. Eliminating the use of hazardous substances, these high performance materials disrupt linear production models and strategically eliminate its toxicity and negative climate impacts, with widespread application in fashion, interiors and construction. Importantly, the biotextile approach developed in this study demonstrates the potential of biofabrication coupled with green chemistry for a circular materials economy.

Local Structure of Polymer-Grafted Nanoparticle Melts.

Polymer-grafted nanoparticle (GNP) membranes show unexpected gas transport enhancements relative to the neat polymer, with a maximum as a function of graft molecular weight (MWg ≈ 100 kDa) for sufficiently high grafting densities. The structural origins of this behavior are unclear. Simulations suggest that polymer segments are stretched near the nanoparticle (NP) surface and form a dry layer, while more distal chain fragments are in their undeformed Gaussian states and interpenetrate with segments from neighboring NPs. This theoretical basis is derived by considering the behavior of two adjacent NPs; how this behavior is modified by multi-NP effects relevant to gas separation membranes is unexplored. Here, we measure and interpret SAXS data for poly(methyl acrylate)-grafted silica NPs and find that for very low MWgs, contact between GNPs obeys the two-NP theory─namely that the NPs act like hard spheres, with radii that are linear combinations of the NP core sizes and the dry zone dimensions; thus, the interpenetration zones relax into the interstitial spaces. For chains with MWg > 100 kDa, the interpenetration zones are in the contact regions between two NPs. These results suggest that for MWgs below the transition, gas primarily moves through a series of dry zones with favorable transport, with the interpenetration zone with less favorable transport properties in parallel. For higher MWgs, the dry and interpenetration zones are in series, resulting in a decrease in transport enhancement. The MWg at the transport maximum then corresponds to the chain length with the largest, unfavorable stretching free energy.

In Situ Atomic Force Microscopy Tracking of Nanoparticle Migration in Semicrystalline Polymers.

We present in situ tracking of silica nanoparticle (NP) migration from a poly(ethylene oxide) (PEO) melt into interlamellar region using in situ atomic force microscopy (AFM). Our results confirm the previous hypothesis that NPs migrate into the interlamellar regions at crystallization growth rates smaller than a critical value under isothermal conditions. Under these slow crystallization conditions, bare silica NPs are rejected as defects by the growing crystal of PEO, and the in situ imaging on the large (50 nm) NPs helps track the migration into the amorphous zones. We extend this AFM technique to estimate lamellar growth rates that correlate with spherulite growth rates determined by polarized light optical microscopy (PLOM) but at smaller undercoolings than are typical for PLOM.

Organizing Nanoparticles in Semicrystalline Polymers by Modifying Particle Diffusivity.

We have previously shown that semicrystalline polymers can be reinforced by adding nanoparticles (NPs) and then ordering them into specific motifs using the crystallization process. A key result we have found is that when the spherulite growth rate is slowed below a critical value, then, NPs can order into the amorphous interlamellar regions of the semicrystalline structure. The effects of spherulite growth rate in this context have previously been examined, and here we focus on the role of NP diffusivity. We achieve this goal by changing the poly(ethylene oxide) (PEO) molecular weight as a route to altering the matrix viscosity. In particular, four molecular weights of PEO were employed ranging from 5.4-46 kDa. Each sample was loaded with 10 vol % of bare 14 nm diameter silica NPs. After initially studying spherulite growth rates, experiments were designed to fix the spherulite growth rate across sample molecular weights to study particle ordering, induced by polymer crystallization. We find that, at the fastest growth rate studied (12 µm/s), the lowest molecular weight sample showed the highest order, presumably due to enhanced particle mobility. However, as the spherulite growth rate is slowed, the maximum ordering behavior is observed at intermediate molecular weights. The trend observed at slow growth rates is explained by the large-scale segregation of NPs (presumably into the grain boundaries, i.e., the interspherulitic regions); evidence for this is the observed transition of spherulite growth to diffusion-control at slow growth rates in the lowest molecular weight PEO sample studied.

Unusual High-Frequency Mechanical Properties of Polymer-Grafted Nanoparticle Melts.

Brillouin light spectroscopy is used to measure the elastic moduli of spherical polymer-grafted nanoparticle (GNP) melts as a function of chain length at fixed grafting density (0.47 chains/nm^{2}) and nanoparticle radius (8 nm). While the moduli follow a rule of mixtures (Wood's law) for long chains, they display enhanced elasticity and anomalous dissipation for graft chains <100 kDa. GNP melts with long polymers at high σ have a dry zone near the GNP core, surrounded by a region where the grafts can interpenetrate with chain fragments from adjacent GNPs. We propose that the departures from Wood's law for short chains are due to the effectively larger silica volume fraction in the region where sound propagates-this is caused by the short, interpenetrated chain fragments being pushed out of the way. We thus conclude that transport mechanisms (of gas, ions, sound, thermal phonons) in GNP melts are radically different if interpenetrated chain segments can be "pushed out of the way" or not. This provides a facile new means for manipulating the properties of these materials.

Controlling toughness of polymer-grafted nanoparticle composites for impact mitigation.

Toughness in an entangled polymer network is typically controlled by the number of load-bearing topological constraints per unit volume. In this work, we demonstrate a new paradigm for controlling toughness at high deformation rates in a polymer-grafted nanoparticle composite system where the entanglement density increases with the molecular mass of the graft. An unexpected peak in the toughness is observed right before the system reaches full entanglement that cannot be described through the entanglement concept alone. Quasi-elastic neutron scattering reveals enhanced segmental fluctuations of the grafts on the picosecond time scale, which propagate out to nanoparticle fluctuations on the time scale 100s of seconds as evidenced by X-ray photon correlation spectroscopy. This surprising multi-scale dissipation process suggests a nanoparticle jamming-unjamming transition. The realization that segmental dynamics can be coupled with the entanglement concept for enhanced toughness at high rates of deformation is a novel insight with relevance to the design of composite materials.

Universal Polymeric-to-Colloidal Transition in Melts of Hairy Nanoparticles.

Two different classes of hairy self-suspended nanoparticles in the melt state, polymer-grafted nanoparticles (GNPs) and star polymers, are shown to display universal dynamic behavior across a broad range of parameter space. Linear viscoelastic measurements on well-characterized silica-poly(methyl acrylate) GNPs with a fixed core radius (Rcore) and grafting density (or number of arms f) but varying arm degree of polymerization (Narm) show two distinctly different regimes of response. The colloidal Regime I with a small Narm (large core volume fraction) is characterized by predominant low-frequency solidlike colloidal plateau and ultraslow relaxation, while the polymeric Regime II with a large Narm (small core volume fractions) has a response dominated by the starlike relaxation of partially interpenetrated arms. The transition between the two regimes is marked by a crossover where both polymeric and colloidal modes are discerned albeit without a distinct colloidal plateau. Similarly, polybutadiene multiarm stars also exhibit the colloidal response of Regime I at very large f and small Narm. The star arm retraction model and a simple scaling model of nanoparticle escape from the cage of neighbors by overcoming a hopping potential barrier due to their elastic deformation quantitatively describe the linear response of the polymeric and colloidal regimes, respectively, in all these cases. The dynamic behavior of hairy nanoparticles of different chemistry and molecular characteristics, investigated here and reported in the literature, can be mapped onto a universal dynamic diagram of f/[Rcore3/ν0)1/4] as a function of (Narmν0f)/(Rcore3), where ν0 is the monomeric volume. In this diagram, the two regimes are separated by a line where the hopping potential ΔUhop is equal to the thermal energy, kBT. ΔUhop can be expressed as a function of the overcrowding parameter x (i.e., the ratio of f to the maximum number of unperturbed chains with Narm that can fill the volume occupied by the polymeric corona); hence, this crossing is shown to occur when x = 1. For x > 1, we have colloidal Regime I with an overcrowded volume, stretched arms, and ΔUhop > kBT, while polymeric Regime II is linked to x < 1. This single-material parameter x can provide the needed design principle to tailor the dynamics of this class of soft materials across a wide range of applications from membranes for gas separation to energy storage.

Detecting bound polymer layers in attractive polymer-nanoparticle hybrids.

When polymer-nanoparticle (NP) attractions are sufficiently strong, a bound polymer layer with a distinct dynamic signature spontaneously forms at the NP interface. A similar phenomenon occurs near a fixed attractive substrate for thin polymer films. While our previous simulations fixed the NPs to examine the dilute limit, here, we allow the NP to move. Our goal is to investigate how NP mobility affects the signature of the bound layer. For small NPs that are relatively mobile, the bound layer is slaved to the motion of the NP, and the signature of the bound layer relaxation in the intermediate scattering function essentially disappears. The slow relaxation of the bound layer can be recovered when the scattering function is measured in the NP reference frame, but this process would be challenging to implement in experimental systems with multiple NPs. Instead, we use the counterintuitive result that the NP mass affects its mobility in the nanoscale limit, along with the more expected result that the bound layer increases the effective NP mass, to suggest that the signature of the bound polymer manifests as a change in NP diffusivity. These findings allow us to rationalize and quantitatively understand the results of recent experiments focused on measuring NP diffusivity with either physically adsorbed or chemically end-grafted chains.

Boundary layer description of directional polymer crystallisation.

Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger-Gryte ansatz.

Quantifying Nanoparticle Ordering Induced by Polymer Crystallization.

It has recently been established that polymer crystallization can preferentially place nanoparticles (NPs) into the amorphous domains of a lamellar semicrystalline morphology. The phenomenology of this process is clear: when the time for NP diffusion is shorter than the crystal growth time, then the NPs are rejected by the growing crystals and placed in the amorphous domains. However, since there is no quantitative characterization of this ordered NP state, we develop a correlation function analysis for small-angle X-ray scattering data, inspired by classical methods used for enunciating the local morphology of lamellar semicrystalline polymers. We show that when the spherulitic growth rate is slower than NP diffusion, then all the NPs are expelled from the crystals. As we increase the crystallization temperature, Tc, the long period characterizing the periodically repeating crystal-amorphous polymer structure, rcc, increases. This results in a smaller number of amorphous domains per unit volume-the number of NPs per amorphous domain thus increases. While the scattering contrast between the pure silica and the polymer is constant, these arguments predict that the apparent contrast between the NP-rich and the polymer-rich domains scale linearly with rcc, as we confirm from our experiments. These facts allow us to posit that the NPs become more efficiently packed in the interlamellar zone with increasing Tc until they form a fully filled monolayer. Above this temperature, NP multilayers form within each of the NP-rich domains. Our analysis approach, therefore, describes NP ordering that is achieved when driven by polymer crystallization.