Structural interactions in polymer-stabilized magnetic nanocomposites.

Superparamagnetic iron oxide nanoparticles (SPIONs) have attracted significant attention because of their nanoscale magnetic properties. SPION aggregates may afford emergent properties, resulting from dipole-dipole interactions between neighbors. Such aggregates can display internal order, with high packing fractions (>20%), and can be stabilized with block co-polymers (BCPs), permitting design of tunable composites for potential nanomedicine, data storage, and electronic sensing applications. Despite the routine use of magnetic fields for aggregate actuation, the impact of those fields on polymer structure, SPION ordering, and magnetic properties is not fully understood. Here, we report that external magnetic fields can induce ordering in SPION aggregates that affect their structure, inter-SPION distance, magnetic properties, and composite Tg. SPION aggregates were synthesized in the presence or absence of magnetic fields or exposed to magnetic fields post-synthesis. They were characterized using transmission electron microscopy (TEM), small angle X-ray scattering (SAXS), superconducting quantum interference device (SQUID) analysis, and differential scanning calorimetry (DSC). SPION aggregate properties depended on the timing of field application. Magnetic field application during synthesis encouraged preservation of SPION chain aggregates stabilized by polymer coatings even after removal of the field, whereas post synthesis application triggered subtle internal reordering, as indicated by increased blocking temperature (TB), that was not observed via SAXS or TEM. These results suggest that magnetic fields are a simple, yet powerful tool to tailor the structure, ordering, and magnetic properties of polymer-stabilized SPION nanocomposites.

Numerical modeling and in situ small angle X-ray scattering characterization of ultra-small SPION magnetophoresis in a high field and gradient separator.

Magnetic nanoparticles (MNPs) have recently gained significant attention in various fields, including chemical and biomedical applications, due to their exceptional properties. However, separating MNPs from solution via magnetophoresis is challenging when MNPs are smaller than 50 nm as Brownian forces become on the order of the magnetic forces. In this study, we successfully separated small MNPs (5-30 nm) by utilizing high magnetic fields and gradients generated by economical permanent magnets. In situ small angle X-ray scattering (SAXS) was used to investigate the time-dependent concentration changes in the ferrofluid, and the results validated that only the 30 nm particles experienced particle aggregation or agglomeration, indicating that dipole-dipole interactions did not play a discernable role in the separation process for particles smaller than ∼15 nm. However, numerical simulations have provided further validation that in the absence of particle-particle interactions, even MNPs with diameters less than 15 nm exhibited magnetophoresis that effectively counteracted the effects of Brownian motion.

The effects of methanol clustering on methanol-water nucleation.

The formation of subcritical methanol clusters in the vapor phase is known to complicate the analysis of nucleation measurements. Here, we investigate how this process affects the onset of binary nucleation as dilute water-methanol mixtures in nitrogen carrier gas expand in a supersonic nozzle. These are the first reported data for water-methanol nucleation in an expansion device. We start by extending an older monomer-dimer-tetramer equilibrium model to include larger clusters, relying on Helmholtz free energy differences derived from Monte Carlo simulations. The model is validated against the pressure/temperature measurements of Laksmono et al. [Phys. Chem. Chem. Phys. 13, 5855 (2011)] for dilute methanol-nitrogen mixtures expanding in a supersonic flow prior to the appearance of liquid droplets. These data are well fit when the maximum cluster size imax is 6-12. The extended equilibrium model is then used to analyze the current data. On the addition of small amounts of water, heat release prior to particle formation is essentially unchanged from that for pure methanol, but liquid formation proceeds at much higher temperatures. Once water comprises more than ∼24 mol % of the condensable vapor, droplet formation begins at temperatures too high for heat release from subcritical cluster formation to perturb the flow. Comparing the experimental results to binary nucleation theory is challenged by the need to extrapolate data to the subcooled region and by the inapplicability of explicit cluster models that require a minimum of 12 molecules in the critical cluster.

Freezing of Dilute Aqueous-Alcohol Nanodroplets: The Effect of Molecular Structure.

We investigate vapor-liquid nucleation and subsequent freezing of aqueous-alcohol nanodroplets containing 1-pentanol, 1-hexanol, and their 3-isomers. The aerosols are produced in a supersonic nozzle, where condensation and freezing are characterized by static pressure and Fourier transform Infrared (FTIR) spectroscopy measurements. At fixed water concentrations, the presence of alcohol enables particle formation at higher temperatures since both the equilibrium vapor pressure above the critical clusters and the cluster interfacial free energy are decreased relative to the pure water case. The disappearance of a small free OH peak, observed for pure water droplets, when alcohols are added and shifts in the CH peaks as a function of alcohol chain length reveal varying surface partitioning preferences of the alcohols. Changes in the FTIR spectra during freezing, as well as changes in the ice component derived from self-modeling curve resolution analysis, show that 1-hexanol and 1-pentanol perturb freezing less than their branched isomers do. This behavior may reflect the molecular footprints of the alcohols, the available surface area of the droplets, and not only alcohol solubility. The presence of alcohols also lowers the freezing temperature relative to that of pure water, but when there is clear evidence for the formation of ice, the ice nucleation rates change by less than a factor of ∼2-3 for all cases studied.

New Particle Formation from the Vapor Phase: From Barrier-Controlled Nucleation to the Collisional Limit.

Studies of vapor phase nucleation have largely been restricted to one of two limiting cases-nucleation controlled by a substantial free energy barrier or the collisional limit where the barrier is negligible. For weakly bound systems, exploring the transition between these regimes has been an experimental challenge, and how nucleation evolves in this transition remains an open question. We overcome these limitations by combining complementary Laval expansion experiments, providing new particle formation data for carbon dioxide over a uniquely broad range of conditions. Our experimental data together with a kinetic model using rate constants from high-level quantum chemical calculations provide a comprehensive picture of new particle formation as nucleation transitions from a barrier-dominated process to the collisional limit.

The freezing behavior of aqueous n-alcohol nanodroplets.

We generate water-rich aerosols containing 1-propanol and 1-pentanol in a supersonic nozzle to study the effects of these solutes on the freezing behavior of water. Condensation and freezing are characterized by two complementary techniques, pressure trace measurements and Fourier Transform Infrared spectroscopy. When 1-pentanol and 1-propanol are present, condensation occurs at higher temperatures because particle formation from the vapor phase is enhanced by the decrease in interfacial free energy of mixed aqueous-alcohol critical clusters relative to those of pure water. FTIR results suggest that when ∼6 nm radius droplets freeze, the tetrahedral structure of the ice is well preserved up to an overall alcohol mole fraction of 0.031 for 1-propanol and 0.043 for 1-pentanol. In this concentration range, the ice nucleation temperature decreases continuously with increasing 1-propanol concentration, whereas the onset of freezing is not significantly perturbed by 1-pentanol up to a mole fraction of 0.03. Furthermore, once freezing starts the ice nucleation rates in the aqueous-alcohol droplets are very close to those for pure water. In contrast, at the highest mole fractions of either alcohol it is not clear whether droplets freeze to form crystalline ice since the final state of the particles cannot be adequately characterized with the available experimental techniques.

Homogeneous nucleation of carbon dioxide in supersonic nozzles II: molecular dynamics simulations and properties of nucleating clusters.

Large scale molecular dynamics simulations of the homogeneous nucleation of carbon dioxide in an argon atmosphere were carried out at temperatures between 75 and 105 K. Extensive analyses of the nucleating clusters' structural and energetic properties were performed to quantify these details for the supersonic nozzle experiments described in the first part of this series [Dingilian et al., Phys. Chem. Chem. Phys., 2020, 22, 19282-19298]. We studied ten different combinations of temperature and vapour pressure, leading to nucleation rates of 1023-1025 cm-3 s-1. Nucleating clusters possess significant excess energy from monomer capture, and the observed cluster temperatures during nucleation - on both sides of the critical cluster size - are higher than that of the carrier gas. Despite strong undercooling with respect to the triple point, most clusters are clearly liquid-like during the nucleation stage. Only at the lowest simulation temperatures and vapour densities, clusters containing over 100 molecules are able to undergo a second phase transition to a crystalline solid. The formation free energies retrieved from the molecular dynamics simulations were used to improve the classical nucleation theory by introducing a Tolman-like term into the classical liquid-drop model expression for the formation free energy. This simulation-based theory predicts the simulated nucleation rates perfectly, and improves the prediction of the experimental rates compared to self-consistent classical nucleation theory.

Synthesis of polymer nanoparticles via electrohydrodynamic emulsification-mediated self-assembly.

HYPOTHESIS: Electrospray can rapidly produce fine, organic solvent-in-water emulsions in the absence of surfactant via electrohydrodynamic emulsification (EE), a reverse configuration of traditional electrospray. This paper investigates whether EE can produce high-quality nanocomposites comprised of block co-polymers and organic nanoparticles (NPs) via the interfacial instability (IS) self-assembly method. Surfactant-free approaches may increase encapsulation efficiency and product uniformity, process speed, and ease of downstream product purification. EXPERIMENTS: All particles were produced using EE-mediated self-assembly (SA) (EE-SA). Particles were produced using poly(lactic-co-glycolic acid) (PLGA) polymers as proof of concept. Then, block copolymer (BCP) micelles were synthesized from polystyrene-block-poly(ethylene oxide) (PS-b-PEO) (PS 9.5 kDa:PEO 18.0 kDa) in the presence and absence of superparamagnetic iron oxide nanoparticles (SPIONs) or quantum dots (QDs). Encapsulant concentration was varied, and the effect of encapsulant NP ligands on final particle size was investigated. FINDINGS: EE-SA generated both pure polymer NPs and nanocomposites containing SPIONs and QDs. PLGA particles spanned from sub- to super-micron sizes. PS-b-PEO NPs and nanocomposites were highly monodisperse, and more highly loaded than those made via a conventional, surfactant-rich IS process. Free ligands decreased the size of pure BCP particles. Increasing encapsulant levels led to a morphological transition from spherical to worm-like to densely loaded structures.

Mechanism of surface freezing of alkanes.

Using molecular dynamics simulation of octane (C8) and nonadecane (C19), we probe the mechanism of n-alkane surface freezing, the appearance of a crystalline monolayer above the liquid at a temperature Tsf above the bulk freezing point Tf. Formation of a crystalline monolayer occurs robustly in these systems. When Tf > Tsf, the surface frozen phase is metastable with respect to the solid but persists for long periods for study in simulations. Surface freezing of both C8 and C19 is driven by significant energy-lowering when alkane chains become ordered along the surface normal, and we elucidate the origins of this phenomenon. The degree of configurational disorder in the surface frozen layer relative to the solid is much larger for C8 compared to C19. From the Gibbsian viewpoint, we extract the excess energy and entropy of the liquid and surface frozen phases. We also consider the surface frozen layer as an intervening third phase, the viewpoint taken in previous theoretical analyses. Here, we find significantly increased entropy of the surface frozen phase of C8 associated with configurational disorder, while the energy and entropy of the surface frozen phase of C19 are marginally different from the bulk solid. Finally, by combining our previously determined solid-vapor surface free energies of C8 and C19 with liquid-vapor surface tensions from this work, we eliminate wetting as a possible mechanism for C8 surface freezing, but it remains a possibility for C19. We analyze the molecular structure of the liquid, surface frozen, and solid surfaces and discuss its relevance to thermodynamic properties.

Homogeneous nucleation of carbon dioxide in supersonic nozzles I: experiments and classical theories.

We studied the homogeneous nucleation of carbon dioxide in the carrier gas argon for concentrations of CO2 ranging from 2 to 39 mole percent using three experimental methods. Position-resolved pressure trace measurements (PTM) determined that the onset of nucleation occurred at temperatures between 75 and 92 K with corresponding CO2 partial pressures of 39 to 793 Pa. Small angle X-ray scattering (SAXS) measurements provided particle size distributions and aerosol number densities. Number densities of approximately 1012 cm-3, and characteristic times ranging from 6 to 13 µs, resulted in measured nucleation rates on the order of 5 × 1017 cm-3 s-1, values that are consistent with other nucleation rate measurements in supersonic nozzles. Finally, we used Fourier transform infrared (FTIR) spectroscopy to identify that the condensed CO2 particles were crystalline cubic solids with either sharp or rounded corners. Molecular dynamics simulations, however, suggest that CO2 forms liquid-like critical clusters before transitioning to the solid phase. Furthermore, the critical clusters are not in thermal equilibrium with the carrier gas. Comparisons with nucleation theories were therefore made assuming liquid-like critical clusters and incorporating non-isothermal correction factors.

Vapor-phase nucleation of n-pentane, n-hexane, and n-heptane: Critical cluster properties.

The first and second nucleation theorems provide a way to determine the molecular content and excess internal energies of critical clusters, which rely solely on experimental nucleation rates measured at constant temperatures and supersaturations, respectively. Here, we report the size n* and excess internal energy Ex(n*) of n-pentane, n-hexane, and n-heptane critical clusters when particles form under the highly supersaturated conditions present in supersonic expansions. In summary, critical clusters contain from ∼2 to ∼11 molecules and exhibit the expected increase in the critical cluster size with increasing temperature and decreasing supersaturation. Surprisingly, the n* values for all three alkanes appear to lie along a single line when plotted as a function of supersaturation. Within the framework of the capillarity approximation, the excess internal energies determined for the n-heptane critical clusters formed under the low temperature (∼150 K) conditions in our supersonic nozzle are reasonably consistent with those determined under higher temperature (∼250 K) conditions in the thermal diffusion cloud chamber by Rudek et al. [J. Chem. Phys. 105, 4707 (1996)].

CO2 condensation onto alkanes: unconventional cases of heterogeneous nucleation.

The classical picture invoked for heterogeneous nucleation is frequently that of a liquid condensing onto an immiscible solid particle. Here, we examine heterogeneous nucleation of CO2 onto particles comprised of n-pentane or n-hexane under conditions where CO2 should be a solid and the seed particles may be liquid or solid. Although CO2 condensed under all but one of the six conditions investigated, these experiments do not easily fit into the framework of standard heterogeneous nucleation experiments. Rather they explore unconventional regimes of heterogeneous nucleation in which the state of the seed particle may both affect whether deposition can proceed, and, in turn, be influenced by the presence of the condensing species. The work complements the earlier work of Tanimura et al. [RSC Adv., 2015, 5, 105537-105550] that investigated CO2 condensation onto ice nanoparticles, by using seed particles comprised of non-polar compounds that form and freeze under conditions where CO2 is already supersaturated with respect to the solid ice. In some cases, the conditions for seed formation approach the limit of homogeneous CO2 nucleation. Vibrational spectroscopy measurements help pinpoint where CO2 starts to condense. Furthermore, these IR measurements suggest that the n-alkanes never freeze in the presence of CO2, even if the temperatures are well below those required for them to freeze when CO2 is absent. Over the temperature range 65 < T/K < 140, the conditions corresponding to the onset of CO2 heterogeneous nucleation on pre-existing seed particle almost all lie very close to the extrapolated vapor-liquid equilibrium line of CO2 for a broad range of seed materials.

Vapor phase nucleation of the short-chain n-alkanes (n-pentane, n-hexane and n-heptane): Experiments and Monte Carlo simulations.

We measured the nucleation rates of n-pentane through n-heptane in a supersonic nozzle at temperatures ranging from ca. 109 K to 168 K. For n-pentane and n-hexane, these are the first nucleation rate measurements that have been made, and the trends in the current data agree well with those in the earlier work of Ghosh et al. [J. Chem. Phys. 132, 024307 (2010)] for longer chain alkanes. Complementary Monte Carlo simulations, using the transferable potentials for phase equilibria-united atom potentials, suggest that despite the high degree of supercooling, the critical clusters remain liquid like under experimental conditions for n-pentane through n-heptane, but adopt more ordered structures for n-octane and n-nonane. For all three alkanes, the experimental and simulated nucleation rates are offset by ∼3 orders of magnitude when plotted as a function of ln S/(Tc/T - 1)1.5. Explicitly accounting for the surface tension difference between the real and model substances, or alternatively using the Hale [Phys. Rev. A 33, 4156 (1986); Metall. Mater. Trans. A 23, 1863 (1992)] scaling parameter, Ω, consistent with the model potential, increases the offset to ∼6 orders of magnitude.

Nanoparticle packing within block copolymer micelles prepared by the interfacial instability method.

The interfacial instability method has emerged as a viable approach for encapsulating high concentrations of nanoparticles (NPs) within morphologically diverse micelles. In this method, transient interfacial instabilities at the surface of an emulsion droplet guide self-assembly of block co-polymers and NP encapsulants. Although used by many groups, there are no systematic investigations exploring the relationship between NP properties and micelle morphology. Here, the effect of quantum dot (QD) and superparamagnetic iron oxide NP (SPION) concentration on the shape, size, and surface deformation of initially spherical poly(styrene-b-ethylene oxide) (PS-b-PEO) micelles was examined. Multi-NP encapsulation and uniform dispersion within micelles was obtained even at low NP concentrations. Increasing NP concentration initially resulted in larger numbers of elongated micelles and cylinders with tightly-controlled diameters smaller than those of spherical micelles. Beyond a critical NP concentration, micelle formation was suppressed; the dominant morphology became densely-loaded NP structures that were coated with polymer and exhibited increased polydispersity. Transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) revealed that NPs in densely-loaded structures can be well-ordered, with packing volume fractions of up to 24%. These effects were enhanced in magnetic composites, possibly by dipole interactions. Mechanisms governing phase transitions triggered by NP loading in the interfacial instability process were proposed. The current study helps establish and elucidate the active role played by NPs in directing block copolymer assembly in the interfacial instability process, and provides important guiding principles for the use of this approach in generating NP-loaded block copolymer composites.

Ice nucleation rates near ∼225 K.

We have measured the ice nucleation rates, Jice, in supercooled nano-droplets with radii ranging from 6.6 nm to 10 nm and droplet temperatures, Td, ranging from 225 K to 204 K. The initial temperature of the 10 nm water droplets is ∼250 K, i.e., well above the homogeneous nucleation temperature for micron sized water droplets, TH ∼235 K. The nucleation rates increase systematically from ∼1021 cm-3 s-1 to ∼1022 cm-3 s-1 in this temperature range, overlap with the nucleation rates of Manka et al. [Phys. Chem. Chem. Phys. 14, 4505 (2012)], and suggest that experiments with larger droplets would extrapolate smoothly the rates of Hagen et al. [J. Atmos. Sci. 38, 1236 (1981)]. The sharp corner in the rate data as temperature drops is, however, difficult to match with available theory even if we correct classical nucleation theory and the physical properties of water for the high internal pressure of the nanodroplets.

Micelle-templated, poly(lactic-co-glycolic acid) nanoparticles for hydrophobic drug delivery.

PURPOSE: Poly(lactic-co-glycolic acid) (PLGA) is widely used for drug delivery because of its biocompatibility, ability to solubilize a wide variety of drugs, and tunable degradation. However, achieving sub-100 nm nanoparticles (NPs), as might be desired for delivery via the enhanced permeability and retention effect, is extremely difficult via typical top-down emulsion approaches. METHODS: Here, we present a bottom-up synthesis method yielding PLGA/block copolymer hybrids (ie, "PolyDots"), consisting of hydrophobic PLGA chains entrapped within self-assembling poly(styrene-b-ethylene oxide) (PS-b-PEO) micelles. RESULTS: PolyDots exhibit average diameters <50 nm and lower polydispersity than conventional PLGA NPs. Drug encapsulation efficiencies of PolyDots match conventional PLGA NPs (ie, ~30%) and are greater than those obtained from PS-b-PEO micelles (ie, ~7%). Increasing the PLGA:PS-b-PEO weight ratio alters the drug release mechanism from chain relaxation to erosion controlled. PolyDots are taken up by model glioma cells via endocytotic mechanisms within 24 hours, providing a potential means for delivery to cytoplasm. PolyDots can be lyophilized with minimal change in morphology and encapsulant functionality, and can be produced at scale using electrospray. CONCLUSION: Encapsulation of PLGA within micelles provides a bottom-up route for the synthesis of sub-100 nm PLGA-based nanocarriers with enhanced stability and drug-loading capacity, and tunable drug release, suitable for potential clinical applications.

Morphology of block copolymer micelles formed via electrospray enabled interfacial instability.

HYPOTHESIS: Elongated micelles may be preferred over spherical because of their increased loading capacity, differential mass transport and biodistribution. Although morphological transitions of block co-polymer (BCP) micelles have been extensively investigated in batch systems, research on continuous or semi-continuous scalable approaches such as flash nanoprecipitation and coaxial electrospray-enabled interfacial instability (Aero-IS) have primarily focused on producing spherical micelles. This paper investigates whether process changes intended to increase micelle production via Aero-IS also induce morphological transitions. EXPERIMENTS: BCP micelles were synthesized from carboxylated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) (PS 9.5 kDa:PEO 18.0 kDa) using Aero-IS. Volumetric flowrates, polymer concentrations, and emulsion temperature were varied to investigate their effect on the micelle production rate and resulting micelle structure, including transitions to worm-like micelles. FINDINGS: These findings report the first worm-like micelles formed via a scalable, interfacial instability approach. The morphological transitions obtained by increasing polymer concentration occurred at lower nominal values than in corresponding batch processes. Optimizing operating conditions also led to a 12-fold increase in micelle production rates over prior electrospray reports (Duong, 2014). Thus, the Aero-IS approach holds promise for scalable nanomanufacturing of worm-like micelles, potentially enabling applications in drug delivery, imaging, diagnostics, and separations.

Freezing of supercooled n-decane nanodroplets: from surface driven to frustrated crystallization.

Whether crystallization starts at the liquid-vapor interface or randomly throughout the bulk has been the subject of intense debate. In our earlier work, we investigated the freezing of supercooled nanodroplets of short chain (C8, C9) n-alkanes formed by homogeneous condensation in a supersonic nozzle. The rate at which the solid appeared suggested freezing starts at the droplet surface well before the rest of the droplet freezes. Experiments were, however, limited to a single condition for each compound and it was not clear whether freezing of n-alkanes always occurs in this two step manner. Here, we expand our work to include freezing of a third n-alkane, n-decane, and, furthermore, we vary the temperatures at which droplets are formed and freeze. The phase transitions are again characterized using three experimental techniques - pressure trace measurements (PTM), Fourier Transform Infrared Spectroscopy (FTIR), and Small Angle X-ray Scattering (SAXS). We also use Wide Angle X-ray Scattering (WAXS) to confirm, for the first time, the crystalline nature of our frozen n-alkane nanodroplets. As the temperature at which the droplets form and freeze decreases, the kinetics of the phase transition changes. At higher temperatures, the phase transition occurs in two steps characterized by different rates, whereas at lower temperatures we observe only a single step. Finally, in the lowest temperature experiment, where droplets start to form and freeze ∼50 K below the bulk melting temperature, we found that the particles develop a fractal structure and appear locked in a "frustrated" crystalline state.

How Cubic Can Ice Be?

Using an X-ray laser, we investigated the crystal structure of ice formed by homogeneous ice nucleation in deeply supercooled water nanodrops (r ≈ 10 nm) at ∼225 K. The nanodrops were formed by condensation of vapor in a supersonic nozzle, and the ice was probed within 100 µs of freezing using femtosecond wide-angle X-ray scattering at the Linac Coherent Light Source free-electron X-ray laser. The X-ray diffraction spectra indicate that this ice has a metastable, predominantly cubic structure; the shape of the first ice diffraction peak suggests stacking-disordered ice with a cubicity value, χ, in the range of 0.78 ± 0.05. The cubicity value determined here is higher than those determined in experiments with micron-sized drops but comparable to those found in molecular dynamics simulations. The high cubicity is most likely caused by the extremely low freezing temperatures and by the rapid freezing, which occurs on a ∼1 µs time scale in single nanodroplets.

Encapsulation of Nanoparticles During Polymer Micelle Formation: A Dissipative Particle Dynamics Study.

The formation of block copolymer micelles with and without hydrophobic nanoparticles is simulated using dissipative particle dynamics. We use the model developed by Spaeth et al. [ Spaeth , J. R. , Kevrekidis , I. G. , and Panagiotopoulos , A. Z. J. Chem. Phys. 2011 , 134 ( (16) ) 164902 ], and drive micelle formation by adjusting the interaction parameters linearly over time to represent a rapid change from organic solvent to water. For different concentrations of added nanoparticles, we determine characteristic times for micelle formation and coagulation, and characterize micelles with respect to size, polydispersity, and nanoparticle loading. Four block copolymers with different numbers of hydrophobic and hydrophilic polymer beads, are examined. We find that increasing the number of hydrophobic beads on the polymer decreases the micelle formation time and lowers polydispersity in the final micelle distribution. Adding more nanoparticles to the simulation has a negligible effect on micelle formation and coagulation times, and monotonically increases the polydispersity of the micelles for a given polymer system. The presence of relatively stable free polymer in one system decreases the amount of polymer encapsulating the nanoparticles, and results in an increase in polydispersity and the number of nanoparticles per micelle for that system, especially at high nanoparticle concentration. Longer polymers lead to micelles with a more uniform nanoparticle loading.