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Controlling and Predicting Nanoparticle Formation by Block-Copolymer Directed Rapid Precipitations Robert F Pagels, Jasmine Edelstein, Christina Tang, and Robert K Prud'homme Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04674 • Publication Date (Web): 03 Jan 2018 Downloaded from http://pubs.acs.org on January 3, 2018
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Nano Letters
Controlling and Predicting Nanoparticle Formation by Block-Copolymer Directed Rapid Precipitations Robert F. Pagels,† Jasmine Edelstein, † Christina Tang, †,‡ and Robert K. Prud’homme*,† †
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ
08544, USA. ‡
Department of Chemical and Life Science Engineering, Virginia Commonwealth University,
Richmond, VA 23284, USA.
ABSTRACT Nanoparticles have shown promise in several biomedical applications, including drug delivery; however, quantitative prediction of nanoparticle formation processes that scale from laboratory to commercial production has been lacking. Flash NanoPrecipitation (FNP) is a scalable technique to form highly-loaded, block-copolymer protected nanoparticles. Here, the FNP process is shown to strictly obey diffusion-limited aggregation assembly kinetics, and the parameters that control the nanoparticle size and the polymer brush density on the nanoparticle surface are shown. The particle size, ranging from 40 to 200 nm, is insensitive to the molecular weight and chemical composition of the hydrophobic encapsulated material, which is shown to be a consequence of the diffusion-limited growth kinetics. In a simple model derived from these kinetics, a single constant describes the 46 unique nanoparticle formulations produced here. The polymer brush densities on the nanoparticle surface are weakly dependent on the process parameters and are among the densest reported in the literature. Though modest differences in brush densities are observed, there is no measurable difference in the amount of protein adsorbed
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within this range. This work highlights the material independent and universal nature of the Flash NanoPrecipitation process, allowing for the rapid translation of formulations between different stabilizing polymers and therapeutic loads.
KEYWORDS Nanoparticle, drug delivery, flash nanoprecipitation, polymer brush, aggregation kinetics, block copolymer
TABLE OF CONTENTS GRAPHIC
TEXT For over a decade, nanoparticles have been heralded as the next-generation of vaccines, diagnostics, and targeted therapeutics.1, 2 However, the substantial research on polymeric nanoparticles for biomedical applications has resulted in few real-world successes. This limited success is in part because complex nanoparticles made in a laboratory cannot be adequately scaled to an industrial level while maintaining precise control over the physical characteristics of the final product.3
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Polymeric nanoparticles have been produced through several methods including molecular selfassembly, emulsion-stripping, lithographic techniques, and nanoprecipitation. For biomedical applications, the nanoparticle size must be carefully controlled.4 In self-assembly, the particle size is predominately determined by the molecular geometry of the amphiphilic material. In emulsion-stripping and lithographic techniques, the particle size is determined by a template (the oil droplet in the case of emulsions). Nanoprecipitation is a simple method to produce nanoparticles; however, the control over particle size is less intuitive and more difficult to predict a priori.5 In traditional nanoprecipitation, hydrophobic materials are dissolved in a watermiscible solvent which is then mixed with water to precipitate the material into nanoparticles. The material concentration, stabilizer [typically a poly(ethylene glycol) (PEG) containing blockcopolymer (BCP)], and mixing rate are just a few of the variables that can influence the particle size.5
Here we consider Flash NanoPrecipitation (FNP), a nanoprecipitation technique that employs extremely rapid mixing, thereby removing mixing speed as a variable in the complex particle assembly process.6 FNP is a scalable technique to form polymeric nanoparticles with control over size, composition, and surface characteristics.4, 7-9 FNP has been used to encapsulate hydrophobic core materials ranging from small molecule drugs and imaging contrast agents to polymers and inorganic colloids.10 Hydrophobic drugs are of particular interest for nanoparticle delivery because they suffer from poor bioavailability.11
The goal of this work was to determine, at a fundamental level, how material properties and FNP process parameters affect the size and PEG grafting density of the resulting nanoparticles, two important features for biomedical applications. This knowledge permitted the development of an
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easy to use model that allows us to predict the optimal FNP formulation for a given therapeutic load and application. This model is far superior to the guess-and-check methods that have been applied previously to optimize nanoprecipitation formulations and indicates that FNP is a true platform technology. The scalability of FNP means that the control over nanoparticle characteristics demonstrated here at a lab-bench scale will also apply to an industrial production scale.10
In the FNP process, hydrophobic core material and amphiphilic stabilizing material, typically a PEG containing BCP, are dissolved in a water-miscible solvent (Figure 1a). This solvent stream is rapidly mixed with an aqueous antisolvent stream using special geometries that achieve homogenous mixing on the order of 1.5-3 milliseconds,6, 12 and relative supersaturations as high as 1000.13 The supersaturated core material and hydrophobic block of the copolymer assemble by diffusion-limited aggregation. The high supersaturation eliminates nucleation barriers to assembly, and simulations suggest collisions are irreversible.14, 15 Growth is arrested when there is sufficient BCP density on the particle surface to stop further aggregation.16 Particles with low polydispersity are produced because the mixing time is faster than the particle formation time, which occurs on the order of 10 to 100 ms.17
Control over nanoparticle size in FNP is accomplished through two process variables: the percent core of the formulation and the total mass concentration of solids in the solvent stream (Figure 1a). Total mass concentration is the mass concentration of the core material and stabilizer together in the solvent stream. Percent core is the weight percent of the core material in the nanoparticle (hydrophobic homopolymer or vitamin E) and does not include the hydrophobic block of the stabilizer. The importance of these formulation parameters has been described
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previously to a limited extent; however, the ability to translate FNP formulations across diverse materials has not been demonstrated.13, 18, 19 Many proof of concept studies with FNP have used polystyrene (PS) based materials due to low costs and long-term storage stability. However, to be clinically relevant, these PS nanoparticles need to be translated to biocompatible materials such as poly(lactic acid) (PLA), an FDA “Generally Regarded as Safe” hydrophobic polymer.20
Figure 1. Size control of nanoparticles produced with Flash NanoPrecipitation. (a) Schematic illustrating the Flash NanoPrecipitation (FNP) process. (b) Effect of percent core on nanoparticle size at a total mass concentration of 20 mg/mL. Left: PS1.8 kDa or vitamin E core, and PS1.6 kDa-bPEG5 kDa BCP. Right: PLA11 kDa or vitamin E core, PLA4.3 kDa-b-PEG5 kDa BCP. (c) Effect of total mass concentration on the nanoparticle size. Left: PS1.8 kDa core and PS1.6 kDa-b-PEG5 kDa BCP. Right: PLA11 kDa core and PLA4.3 kDa-b-PEG5 kDa BCP. Sizes were measured by dynamic light scattering (DLS). For (b) and (c), error bars are reported as +/- the standard deviation of the intensity weighted average diameters across samples, with n ≥ 5 independently synthesized samples for each formulation. All concentration are given as those in the THF stream. PDIs and n-values for all formulations are given in the Supporting Information.
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Here-in, nanoparticles with homopolymer cores (PS1.8 kDa or PLA11 kDa) and diblock-copolymer stabilizers (PS1.6 kDa-b-PEG5 kDa or PLA4.3 kDa-b-PEG5 kDa) were made by FNP using the full practical operating space (see Supporting Information for full Materials and Methods). Vitamin E (430.7 Da) was employed as a model small molecule hydrophobic therapeutic. The first aim of this work was to determine the dependence of nanoparticle size on the FNP formulation variables. Increasing the percent core of the formulation increases the nanoparticle size (Figure 1b). This increase in size can be understood through geometric arguments: increasing the core mass (volume) relative to the BCP (surface area) will result in larger nanoparticles. However, this geometric argument assumes a constant block-copolymer surface coverage, which we will later show is not the case. Particle size also increases with increasing total mass concentration (Figure 1c). This has been attributed to an increase in the growth rate of the particle core relative to the nucleation rate.13 Through tuning the percent core and total mass concentration, nanoparticle size can be controlled from 40 to 200 nm, a range of interest for medical applications.21
When comparing the PS, PLA, and vitamin E results, it is surprising and significant that the size trends are independent of the composition of either the core or of the BCP (Figure 1b-c). This is especially notable considering the materials differ in molecular weight, chemical composition, and phase (vitamin E is a liquid). This behavior is explained by the universality of diffusionlimited growth kinetics. We present a detailed model that (1) provides insight into the lack of dependence on material characteristics and (2) captures the effects of formulation parameters on nanoparticle size.
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Previously, Smoluchowski diffusion-limited growth kinetics were used to understand the encapsulation of inorganic colloids into polymeric nanoparticles with FNP, and a single particle assembly time was estimated.22, 23 Here, we look to apply these growth kinetics to starting materials that are much smaller than the final nanoparticles, and we do not assume a single particle assembly time. Smoluchowski’s model of diffusion-limited growth gives the average aggregate radius, R, as a function of time, t, for aggregates much larger than the starting material (equation (1)):24
(1)
tk Tc R= πμρ
where T is the absolute temperature, µ is the solvent viscosity, ρ is the bulk density of the core, and ccore is the mass concentration of the core material during particle assembly (one-half of the concentration in the THF stream).
The model proposes that nanoparticle growth rate is independent of the molecular weight of the component that composes the core. To test this, nanoparticles were made with varying PS molecular weights and compared to the PLA and vitamin E formulations (Figure S8). Indeed, within experimental reproducibility, nanoparticle size is independent of molecular weight. However, a 1.5x103 kDa PS core did not form nanoparticles, but instead formed large aggregates. The molecular weight at which the PS chains overlap in solution, at the concentration tested, is ~2.5x102 kDa.25 Therefore, chain entanglements cause network formation rather than individual chain collapse. This provides an upper limit to the concentration allowable in the FNP process: any polymeric material should be below the overlap concentration in the solvent stream.
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The time, tf, required for each formulation to reach the final experimentally measured radius, R, was calculated from equation (1). The calculated times were on the order of tens of milliseconds, similar to a previously estimated value.22 To a first order approximation, through data analysis particle formation time was found to scale inversely with the BCP concentration (equation (2), Figure S9).
(2)
c Surface Area of Core t = K ∝ c Surface Area of BCP
The surface area that the BCP can protect is proportional to cBCP. The hydrophobic volume that requires steric protection is proportional to ccore, therefore the surface area that requires protection is proportional to ccore2/3 (see Supporting Information for more discussion). Particle growth is arrested by BCP coating the surface, so increasing the BCP concentration halts particle growth more quickly. Similarly, increasing the core concentration increases the surface area that needs to be protected. A single scaling constant value, K = 253 ms·g1/3·m-1, fits both the PLA-bPEG and PS-b-PEG stabilized formulations well because the PEG size, which dominates the BCP diffusion rate once the hydrophobic block has collapsed, is the same for both polymers. The K value will likely depend on stabilizer geometry and composition, but the rest of the scaling will still follow (see the Supporting Information for a more in depth discussion on the K value, and a full derivation of the Smoluchowski growth kinetics).
Equation (3) then provides a means for size and drug loading optimization of future formulations:
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(3)
R = 'K
( k Tc
πμρc
)
Impressively, this model allows us to collapse all the data onto a single line (Figure 2). The micelle size of the BCP is the lower bound for nanoparticle size. Because the BCP size is not included explicitly in the model, equation (3) does not hold for low core loadings (
