Solvent Controls Nanoparticle Size during Nanoprecipitation by Limiting Block Copolymer Assembly.

Control of the properties of nanoparticles (NPs), including size, is critical for their application in biomedicine and engineering. Polymeric NPs are commonly produced by nanoprecipitation, where a solvent containing a block copolymer is mixed rapidly with a nonsolvent, such as water. Empirical evidence suggests that the choice of solvent influences NP size; yet, the specific mechanism remains unclear. Here, we show that solvent controls NP size by limiting block copolymer assembly. In the initial stages of mixing, polymers assemble into dynamic aggregates that grow via polymer exchange. At later stages of mixing, further growth is prevented beyond a solvent-specific water fraction. Thus, the solvent sets NP size by controlling the extent of dynamic growth up to growth arrest. An a priori model based on spinodal decomposition corroborates our proposed mechanism, explaining how size scales with the solvent-dependent critical water fraction of growth arrest and enabling more efficient NP engineering.

Introduction

Polymeric nanoparticles (NPs) are increasingly applied as colloidal drug delivery systems and building blocks in advanced (bio)material design.[1−6] Efficient translation of NPs and NP-based materials into clinical and industrial products requires strict control over the physicochemical properties of the engineered colloids, including NP size.[7−11] Nanoprecipitation is a robust method to produce NPs from amphiphilic block copolymers.[12−14] In a typical nanoprecipitation, a solution containing a water-miscible organic solvent and a block copolymer is mixed with a nonsolvent (water). Mixing induces a rapid change in solvent composition causing dynamic block copolymer aggregation as the solubility of the hydrophobic block decreases. The aggregates grow and mature into kinetically trapped (frozen) NPs with a hydrophobic core and a hydrophilic corona. The NPs become frozen as the low solubility of individual block copolymer chains (unimers) in the final mixture prevents further growth by unimer exchange and the hydrophilic corona inhibits NP fusion.[15] Thus, nanoprecipitation is a kinetic process, and NP size can be controlled by the mixing time scale, τmix.[16] The physicochemical properties of the formed NPs can be further influenced by the block constituents, block molecular weights, polymer concentrations, and the choice of solvent.[17−20]

Experimental evidence has highlighted that the solvent in which the precursor materials are dissolved affect NP size following nanoprecipitation.[20,21] Yet, there is no physical explanation for the specific role of the solvent.[15] Solvent composition was shown to regulate the shape and dynamics of aggregating block copolymers.[22−24] During nanoprecipitation of monolithic hydrophobic polymers, NP size correlated to the Hansen solubility parameter (HSP) distance, or solvent–water affinity, of the selected solvent.[25,26] Solvents with high water affinity and low viscosity improved solvent diffusion into the aqueous phase, forming smaller NPs based on the rapid rate of change in solvent quality, χ. For solid lipid NPs, size increased with solvent viscosity.[27,28] However, for the nanoprecipitation of amphiphilic block copolymers NP size does not scale with solvent–water affinity or solvent viscosity.[21] Despite the importance of the solvent in block copolymer nanoprecipitation, a physical relation between solvent properties and NP size is lacking.

The effect of the mixing kinetics on block copolymer nanoprecipitation has been described.[29] Pioneering work by Prud’homme and co-workers demonstrated that the mixing time scale, τmix, and polymer composition influence NP size, dispersity, and corona density.[16,30−33] In these studies, flow-based mixing devices controlled τmix.[34] The assembly and growth of block copolymers into NPs was modeled via Smoluchowski diffusion-limited growth kinetics. Unimer exchange and aggregate fusion enabled growth until a sufficient corona density was formed and the NPs became kinetically trapped (frozen). τmix influenced NP size as the rate of change in the solvent composition controlled the amount of time for aggregate growth prior to NP freezing.[16,30,35,36] Evidence suggests that under intermediate solvent quality conditions self-assembly of block copolymers is preceded by liquid–liquid phase separation, and the dimensions of the initial polymer-rich liquid droplets influence the final aggregate size.[37−39] Drese and colleagues developed a computational model of nanoprecipitation to predict NP size based on τmix and a theoretical solvent with time-varying quality, χ(t).[40,41] In their computational model, an initial change in χ, upon mixing, induced spinodal decomposition and unimer aggregation. These aggregates grew via Ostwald ripening until they became kinetically trapped (frozen) at a critical solvent quality, χc. Here, χc was defined as a freezing point that prevented further unimer exchange or aggregate fusion. Thus, NP size was controlled by the rate of change in χ, governed by τmix, up to a critical set point, χc. These studies suggest a combined effect of mixing kinetics and solvent properties on NP size, but a relation to a measurable parameter of the selected solvent has not been shown.

Here, we investigate the specific role of the solvent on NP size during nanoprecipiation of block copolymers. Experimentally, we observed a significant influence of the choice of solvent on NP size. To explain this, we hypothesized that the solvent defines a measurable critical water fraction of growth arrest, ϕc, that is analogous to χc, beyond which further NP growth is prevented. Turbidity measurements confirmed that the block copolymer aggregates formed frozen NPs at ϕc for all solvents tested. NP size correlated to the measured ϕc and did not correlate with the HSP distance or solvent viscosity. In addition, the block copolymer assemblies were macroscopically dynamic below ϕc, enabling aggregation and growth up to this critical point. Thus, NP size was defined by the solvent choice and the mixing kinetics as the extent of growth was controlled by the time needed to reach the solvent-dependent ϕc. We observed a scaling behavior for NP size as a function of mixing kinetics, when NP size was scaled by the solvent-dependent ϕc. An a priori scaling model described the specific role of the solvent based on spinodal decomposition, growth by unimer exchange, and freezing of the NPs at the solvent-dependent point of growth arrest. In this model, the solvent controls NP size by setting ϕc, and the mixing kinetics dictate the rate at which the system reaches this freezing point. Our study offers fundamental insight into the role of the solvent on NP size during nanoprecipitation, and this understanding will enable more efficient engineering of this important class of materials.

Materials and Methods

Materials

Chemical reagents and solvent were purchased from Sigma-Aldrich or VWR and used as received unless otherwise noted.

Poly(ethylene glycol)5kDa-block-poly(dl-lactide)20kDa (PEG-b-PLA), PEG5kDa-b-poly(lactide-co-glycolide)20kDa (PEG-b-PLGA), and PEG5kDa-b-polycaprolactone20kDa (PEG-b-PCL) were purchased from Akina PolySciTech (USA). Deionized water was generated with a Millipore Milli-Q system and Biopak filter. All microfluidic components were purchased from BGB Analytics unless stated otherwise.

Dynamic Light Scattering

The hydrodynamic diameter, Dh, and dispersity, Đ, of the nanoparticles were measured via dynamic light scattering (DLS; Malvern ZetaSizer Nano ZS). DLS measurements were collected in a polystyrene semi-microcuvette (path length ∼10 mm) at a scattering angle of 173° and at a temperature of 25 °C. Dh and Đ were taken as the respective z-average and the dispersity index of the NP intensity distribution. Unless stated otherwise, the NP size reported corresponds to Dh and Đ which were calculated from the average of three DLS measurements per sample.

Transmission Electron Microscopy (TEM)

TEM pictures were taken of a FEI Morgagni 268 (Thermo Fisher) instrument at an acceleration of 100 kV. Samples were prepared on a 200-mesh Formvar and carbon-coated copper grids (Quantifoil Micro Tools GmbH) which were glow-discharged with negative polarity for 30 s (EMITECH K100X; Quorum Technologies). The treated grids were placed upside down for 2 min onto 50 μL of nanoparticle suspension to promote particle adsorption on the grids. The residual liquid was subsequently blotted away with filter paper, and the grid was negatively stained for 15 s with 2% w/v uranyl acetate aqueous solution by adopting the same blotting procedure. The residual moisture present on the grid was dried in air prior to imaging.

Batch Nanoprecipitation

Block copolymer solutions were prepared by dissolving polymer (2.5–10 mg mL–1; PEG-b-PLA, PEG-b-PLGA, or PEG-b-PCL) in a water-miscible organic solvent (DMF, acetone, acetonitrile, THF, or DMSO). Batch nanoprecipitation was performed by adding the block copolymer solution dropwise (∼25 μL per drop) to deionized water (10 mL) in a 20 mL scintillation vial under vigorous stirring (650 rpm; Heidolph MR Hei-Tec; 15 mm Teflon-coated stir bar). The solvent–water ratio, R, was defined as . The batch nanoprecipitations were performed with R = 0.005. The NP size (Dh) and dispersity (Đ) were measured via DLS. All experiments were performed in triplicate.

Turbidity Measurements

The block copolymers were dissolved in each of the water-miscible organic solvents (4 or 10 mg mL–1). The measurements were directly performed in disposable Brand Micro Cuvettes. Deionized water was titrated sequentially to increase the water fraction in the solution (volumetric fraction of water; v/v) and pipetted for ∼3 s prior to starting the turbidity measurement. The turbidity was measured on a PerkinElmer Lambda 35 UV–vis spectrophotometer (λabs = 500 nm). Rayleigh scattering of the polymer aggregates should have occurred when the objects were larger than λ/20 (∼25 nm).[42] The water fraction was increased in 0.02 steps from 0.0 to 0.5 or until further changes in turbidity upon water addition were negligible.

To investigate the reversibility of block copolymer assembly, an analogous procedure was used to reduce the water fraction. The water fraction was decreased in 0.02 steps by sequentially adding a solution of block copolymer dissolved in the related organic solvent (4 or 10 mg mL–1). The measurement was performed as described above where after each addition the suspension was mixed for ∼3 s and solution turbidity was measured. The addition of polymer solution was stopped when further changes in suspension turbidity were negligible.

During dynamic turbidity measurements, the suspension turbidity was monitored over time. Water or block copolymer solution was titrated as mentioned above. Upon each stepwise change of water fraction the suspension turbidity was monitored every second over 10–60 min until stabilization occurred.

Experimental Determination of ϕc

The critical water fraction of growth arrest, ϕc, was determined for each solvent–block copolymer pair from the respective turbidity measurements. ϕc represented the water fraction at which the turbidity plateaued after the turbidity maximum. The value of ϕc was defined as the lowest concentration of water at which the turbidity was ±20% of the final plateau (last four points). DMSO did not have a turbidity maximum; therefore, the threshold of deviation from the plateau was set to ±10%.

Coaxial Jet Mixer Nanprecipitation

The coaxial jet mixer CJM was developed based on studies published previously by our group.[14] The device consisted of two coaxial tubes, through which the polymer solution (inner fused silica tube) and water (outer PTFE tube) flowed. Flow was controlled with two CETONI NeMESYS syringe pumps and the related software Qmix elements (CETONI GmbH). The polymer solutions and water were injected with SETonic gastight syringes with volumes ranging from 0.5 to 50 mL. Syringe outlets were connected to PTFE tubes [outer diameter, OD: 1587 μm; inner diameter, ID: 793 μm; Cole-Parmer, USA]. The tube connected to the polymer solution syringe was further attached to a fused silica capillary (OD: 363 μm, ID: 100 μm, length (L): 7 cm) through a PEEK union body. The water tube lead to a PEEK Tee body that connected to the main PTFE main channel (OD: 1587 μm, ID: 793 μm, L: 15 cm; Cole-Parmer, USA). This main channel was manually aligned coaxial to the fused silica capillary. As described in our previous work, the capillary alignment was the most delicate step.[14] In the main channel the two fluids were mixed and the formed NP suspension was collected in glass vials. The Reynolds number, Re, was calculated by estimating the velocities and characteristic lengths based on the inner cross section of the outer PTFE tube.

For the nanoprecipitation experiments, 10 mg of polymer (PEG-b-PCL, PEG-b-PLA, or PEG-b-PLGA) was dissolved in 1 mL of solvent (DMF, acetone, acetonitrile, THF, or DMSO; Cpoly = 10 mg mL–1). Water volumetric flow rates, Qwater, and the polymer solution volumetric flow rates, Qpolymer solution, ranged from 16 to 35 mL min–1 and from 80 to 174 μL min–1, respectively. All flow-based experiments were performed with an R = 0.005, which was calculated as follows: . The flow rates corresponded to Re ranging from 428 to 937. The NP size and size distribution were measured via DLS. Every condition was performed at least in triplicate and NP size was given as mean ± standard error of the mean (SEM).

Results and Discussion

Solvent Choice Influences NP Size

In a typical nanoprecipitation, an amphiphilic block copolymer—composed of a hydrophobic core-forming block, e.g., poly(dl-lactide) (PLA), poly(lactide-co-glycolide) (PLGA), or polycaprolactone (PCL), and a hydrophilic corona-forming block, e.g., poly(ethylene glycol) (PEG)—is dissolved in a solvent, such as acetonitrile. The block copolymer solution is mixed rapidly with water, a poor solvent for the core-forming block (Figure a). The transition from a favorable solvent to the nonfavorable solvent–water blend is described by a change in solvent quality, χ, for the hydrophobic block (Figure b).[43] This change in χ induces block copolymer assembly into nanoscale objects that become kinetically trapped (frozen) at a critical solvent quality, χc. Prior to χc the nanoscale objects can grow by unimer exchange and aggregate fusion.[17,40] The rate of change in χ depends on the time scale of mixing, τmix, and controls the extent of growth.[16] In this manner, nanoprecipitation transforms block copolymer solutions into stable, core–shell NPs with kinetically controlled size.[30,40]

Figure 1

Solvent choice controls NP size. (a) During batch nanoprecipitation, a NP precursor solution containing a block copolymer dissolved in a water-miscible organic solvent is added dropwise to water under vigorous stirring. Rapid mixing of the block copolymer solution with water triggers polymer assembly and, ultimately, the formation of kinetically trapped (frozen) NPs. (b) The polymer assembly process proceeds in three steps: (1) Block copolymers are dissolved in a favorable solvent. (2) Solvent mixing with water alters the local solvent quality, χ. The change in χ triggers block copolymer assembly into dynamic aggregates, which can grow via unimer exchange or aggregate fusion. (3) A rise in water fraction increases the energy barrier for unimer exchange and fusion. Growth arrest occurs at a critical solvent quality, χc, forming kinetically trapped core–shell NPs. (c) The size of PEG-b-PLA NPs following nanoprecipitation with common solvents varied with the choice of solvent (5 mg mL–1 PEG-b-PLA; R = 0.005). NP size did not correlate with solvent viscosity (solvents are plotted in order of increasing viscosity) or the Hansen solubility parameter (HSP) distance, Ra (gray triangles), calculated between the solvent and water (Supporting Information Section S2). Data are plotted as mean (black line) ± SD (colored box) for three independent experiments (black circles).

To investigate the specific influence of the selected solvent on NP size, solutions of poly(ethylene glycol)-block-polylactide (PEG-b-PLA) were prepared in different water-miscible solvents. Core–shell NPs were produced from each block copolymer solution via nanoprecipitation. We prepared dilute solutions (Cpoly ≤ 10 mg mL–1) to limit the effect of polymer–polymer interactions in the organic phase. At the end of nanoprecipitation ϕ > 0.99, therefore, we assumed that the residual solvent fraction inside the NPs was negligible (Supporting Information Section S1). Batch nanoprecipitation of PEG-b-PLA formed spherical NPs with low dispersity in all solvents. Critically, the size of the formed NPs varied with the selected solvent, Dh = 65–101 nm (Đ ≈ 0.1) (Figure c). Nanoprecipitation with dimethylformamide (DMF) produced the smallest NPs, followed by acetone, acetonitrile, tetrahydrofuran (THF), and dimethyl sulfoxide (DMSO). NP size did not correlate with the HSP distance, Ra, or solvent viscosity (Supporting Information Section S2). This suggested that another physical parameter may explain the influence of solvent on NP size.

Critical Water Fraction of Growth Arrest Dictates NP Size

We hypothesized that the choice of solvent defines a critical solvent–water composition at which the NPs became kinetically trapped (frozen). By setting a solvent-dependent freezing point, the solvent would influence NP size by allowing for differential extents of growth for the same mixing conditions.[40] To investigate whether a freezing point existed for the different solvents, we systematically increased the water fraction in the block copolymer solutions while monitoring polymer assembly. Block copolymer assembly was characterized by quantifying Rayleigh scattering (turbidity) of the solution as a function of the water fraction (Figure a).[22,44]

Figure 2

NP size scales with the solvent-dependent critical water fraction of growth arrest, ϕc. (a) The turbidity of a PEG-b-PLA solution in acetonitrile was measured for 0.01 Δϕ increments in water volume fraction, ϕ. The suspension turbidity was negligible until ϕ ≈ 0.19, which marked the start of observable nanoassembly formation. Past ϕ ≈ 0.19, the turbidity varied with changes in ϕ, suggesting macroscopic nanoassembly dynamics. At a specific point, the turbidity did not change with further increases in ϕ. We defined this point as the critical water fraction of growth arrest, ϕc. (b) Turbidity curves for 10 mg mL–1 PEG-b-PLA solutions in different solvents (0.02 Δϕ increments in water fraction) were used to calculate ϕc for each of the solvents tested: ϕc,DMF ≈ ϕc,acetone < ϕc,acetonitrile < ϕc,THF < ϕc,DMSO. (c) NP size following nanoprecipitation from 2.5, 5, and 10 mg mL–1 PEG-b-PLA for each of the solvents tested. Size increased with the measured ϕc for the different solvents. Data plotted as mean (black line) ± SD (colored boxes) for three independent experiments (symbols: 2.5 mg mL–1, open circles; 5 mg mL–1, gray circles; 10 mg mL–1, solid circles). (d) NP size following nanoprecipitation from 5 mg mL–1 solutions of PEG-b-PLA (circles) in DMF, acetone, acetonitrile, THF, and DMSO correlated to the measured ϕc. Similar trends were observed for NPs formed from 10 mg mL–1 solutions of PEG-b-PLGA (triangles) and PEG-b-PCL (squares) in acetone, DMF, and acetonitrile. Data plotted as mean ± SD for three independent experiments. The x-error bars indicate the error in the ϕc measurements (±0.02).

In a typical nanoprecipitation, the water fraction goes from 0.0 to beyond 0.9 on the milliseconds time scale, and the specific solvent–water composition at which the NPs become frozen is difficult to determine. To simulate block copolymer assembly during the early stages of mixing, we investigated small rates of change in water fraction (Δϕ = 0.01–0.02 min–1) from 0.0 to 0.5. For PEG-b-PLA in acetonitrile, the solution exhibited negligible turbidity until ϕ ≈ 0.19. Further increasing the water fraction induced a sharp rise in turbidity followed by a sharp decrease and a plateau at ϕ ≈ 0.29, beyond which no further changes in turbidity and NP properties were observed. We defined this value as the critical water fraction of growth arrest ϕc. Negligible turbidity below ϕ ≈ 0.19 suggested that the block copolymer chains existed as unimers or aggregates below the critical dimension for Rayleigh scattering (∼25 nm).[42] Increasing the water fraction beyond the ϕ ≈ 0.19 induced assembly into structures that induced Rayleigh scattering.[22,23] The sharp increase and decrease in turbidity was attributed to the formation of dynamic assemblies (Supporting Information Section S3). The labile structures formed below ϕc could not be characterized reliably via DLS or TEM. Similar behavior has been reported for other block copolymers, such as PEG-b-PCL in acetonitrile and poly(N-isopropylacrylamide-co-dimethylacrylamide)-block-poly(dl-lactide) in N,N-dimethylacetamide, and were described as unstable and swollen nanostructures.[23,45] Beyond ϕc, these assemblies formed frozen core–shell NPs. NPs collected at different solvent–water compositions beyond ϕc were colloidally stable.

All of the water-miscible solvents exhibited similar behavior with a dynamic region and a solvent-dependent ϕc (Figure b). ϕc increased sequentially: ϕc,DMF ≈ ϕc,acetone < ϕc,acetonitrile < ϕc,THF < ϕc,DMSO. In the case of DMSO, we did not observe a decrease in turbidity prior to ϕc; however, the turbidity reached a plateau at ϕc ≈ 0.5, and the NPs were colloidally stable beyond this point. Solutions of PEG-b-PLA (Cpoly = 2.5, 5, and 10 mg mL–1) in DMF, acetone, acetonitrile, THF, and DMSO were used to form NPs via batch nanoprecipitation. Interestingly, NP size correlated to the measured ϕc of the solvents (Figure c). In addition, NP size correlated to ϕc for solutions of PEG-b-PCL and PEG-b-PLGA (Figure d; Supporting Information Section S4). The data with different block copolymers indicated that the measured ϕc is a feature of the block copolymer and solvent pair. Overall, these experiments demonstrated that a solvent-dependent water composition, ϕc, exists beyond which the polymer assemblies become kinetically trapped (frozen).

Block Copolymer Aggregates Exhibit Slow Dynamics below ϕc

To explain how ϕc influenced NP size, we further investigated the dynamics of block copolymer assembly below the freezing point. The observed turbidity behavior was similar for increasing or decreasing ϕ (Figure a). This indicated that the dynamic region and ϕc were defined by the specific solvent and polymer pair and did not depend on the direction of ϕ evolution.[22,46] We then characterized the time scale of the dynamics, τdyn, in response to discrete changes in ϕ in the dynamic region using time-resolved turbidity measurements. The turbidity evolved over the course of seconds to hours, indicating slow rearrangement processes in the dynamic region (τdyn > 1 s; Figure b; Supporting Information Section S5).[47,48] In addition, dynamic assemblies were unstable and prone to aggregation, whereas the nanoassemblies were colloidally stable beyond ϕc (Supporting Information Section S6). Depending on the storage conditions, frozen NPs remained stable over the course of weeks to months.

Figure 3

Dynamic turbidity measurements indicate dynamic assembly below ϕc. (a) The observed turbidity behavior as a function of ϕ was similar for increasing and decreasing Δϕ increments in water fraction. This indicated that below ϕc nanoassembly properties depended on the specific water content and not on the direction of ϕ evolution. (b) Time-resolved turbidity of a 4 mg mL–1 PEG-b-PLA acetonitrile solution upon a step change in ϕ from 0.20 to 0.22 exhibited assembly dynamics on the time scale of seconds (ϕc ≈ 0.28; Supporting Information Section S5). The time scale of polymer rearrangement dynamics τdyn was quantified by fitting the curve to an empirical model. The model fit the turbidity change, ΔT, as a function of time, t, with a single-exponential function of the form .[47,49] Similar results were observed for other discrete changes in ϕ within the dynamic region (ϕ < ϕc). (c) In our proposed framework, dynamic polymer assemblies rearrange and grow through unimer exchange in the dynamic region. At ϕc, further growth is arrested and the NPs become kinetically trapped, as the solvent–water composition prevents further unimer exchange for ϕ > ϕc. Therefore, our hypothesis is that the extent of NP growth is controlled by the amount of time the system spends in the dynamic region, as dynamic rearrangement is slow relative to mixing (τdyn ≫ τmix). This time is controlled by the solvent-dependent point of growth arrest, ϕc, and the mixing kinetics, rate of change in ϕ. These considerations are discussed further in the context of our a priori model.

Dynamic rearrangement of the formed aggregates below ϕc suggested a kinetic mechanism for the solvent-dependent NP size.[40] As the assembly dynamics were slow relative to the mixing kinetics (τdyn ≫ τmix), we hypothesized that the amount of time the system spends in this dynamic region prior to reaching ϕc controlled the extent of aggregate growth or ripening (Figure c). This time depends on the rate of change in ϕ during nanoprecipitation, which is governed by the mixing kinetics and the boundary for growth arrest—the solvent-dependent ϕc. These considerations are further discussed in our a priori model based on spinodal decomposition and growth.

NP Size Depends on the Critical Water Fraction of Growth Arrest and the Mixing Kinetics

To study the combined effects of mixing kinetics and ϕc on NP size, we used a coaxial jet mixer (CJM) to nanoprecipitate block copolymer solutions under flow.[14,50] In the CJM, a central stream containing the water-miscible solvent and block copolymer was mixed with an outer stream of water (Figure a). The flow conditions in the CJM were varied to tune Re, and thereby τmix in the mixing channel.[13,14,51]

Figure 4

NP size scales with the solvent-dependent ϕc and mixing kinetics. (a) The mixing kinetics during nanoprecipitation were tuned by using a coaxial jet mixer (CJM) and controlling the solvent and nonsolvent flow velocities (and Re). In the CJM a stream containing a water-miscible solvent and a block copolymer (red) was mixed with a surrounding annulus of water (blue). NPs were formed from 10 mg mL–1 PEG-b-PLA in different solvents (R = 0.005). (b) NP size following nanoprecipitation in the CJM with constant mixing kinetics (Re = 749) correlated to ϕc. Data plotted as mean (black line) ± SD (colored box) for at least three independent experiments (black dots). (c) NP size following nanoprecipitation plotted as a function of Re (Re = 400–1000) correlated to ϕc across all mixing conditions. These data suggested universal scaling behavior for NP size based on solvent and mixing kinetics. Data plotted as mean ± SEM for at least three independent experiments. (d) NP size scaled by ϕc6/11 as a function of mixing conditions (Re) collapsed onto a single curve. The scaled data agreed with the scaling model (solid line) based on spinodal decomposition and dynamic growth. The shaded region shows the influence of the uncertainty in ϕc (±0.02) on the model.

PEG-b-PLA was nanoprecipitated in the CJM for the different solvents by using the same flow conditions (Re = 749; Figure b). The NP size correlated to ϕc, supporting the central hypothesis that NP size depends on ϕc for a given τmix. To further investigate the influence of mixing kinetics on NP size, PEG-b-PLA solutions were nanoprecipitated in the CJM under varying flow conditions (Re ≈ 400–1000; Figure c). NP size decreased with increasing Re and NP size correlated to the measured ϕc for each solvent throughout the flow regime. We observed self-similar behavior for NP size as a function of Re across the different solvents, suggesting a scaling relation for NP size as a function of ϕc and Re.

Physical Model of Solvent Effects in Block Copolymer Nanoprecipitation

To explain the observed scaling behavior for NP size based on solvent and mixing kinetics, we developed a physical model of block copolymer assembly based on spinodal decomposition and growth up to the solvent-dependent freezing point, ϕc. A complete description of the physical model is included in the Supporting Information (Section S7). In the CJM, convective processes break up the polymer stream, and mixing between the polymer solution and water occurs within the smallest fluid element in which kinetic energy is dissipated, the Kolmogorov length scale, which was estimated to be ∼0.1–1 μm.[13,52] Following the work of Drese and colleagues, the main assumptions were that the initial stage of nanoprecipitation was governed by spinodal decomposition and that solvent controlled the extent of aggregate growth.[40,53] The system was described as block copolymers interacting in a solvent with time-varying χ. The initial state was taken as block copolymer unimers in pure solvent. The assembly of block copolymers into dynamic aggregates upon mixing with water was modeled via spinodal decomposition. Growth was allowed via unimer exchange up to ϕc. The time-dependent assembly process was modeled by using the Cahn–Hilliard equation[54]where p is the local aggregation number of block copolymers (Supporting Information, Section S8), M(p) is the species mobility, f is the free energy per unit volume, and ξ and λ are constants. On the basis of the work of de Gennes, M(p) for the initial phase of unimer aggregation scaled with p.[55,56] Following the work of Nose and Iyama, we estimated the free energy aswhere γe is the effective interfacial energy between the hydrophobic core and the surroundings and N1 is the degree of polymerization of the core forming block.[57] We combined eqs and 2 to describe the evolution of the local aggregation number, p, as a function of timewhere C is a constant that depends on the physical parameters of the system.

The surface energy, γe, was related directly to the time-varying water fraction, ϕ(t).[58−61] As a first approximation, we assumed a linear increase in ϕ(t) up to ϕc.[58,59] The predicted NP size was calculated by using the dimension of the corona: NP size = LNP ∝ N23/5p1/5, where N2 is the degree of polymerization of the corona forming block. Solving eq , with the above assumptions, from the initial condition to the freezing point, ϕc, we related NP size to ϕc and τmix or Re (using τmix ∝ Re–11/8).[13,52]This model, based on spinodal decomposition and growth via unimer exchange up to ϕc, predicted that NP size scales with the mixing kinetics (τmix or Re) and the solvent-dependent critical water fraction of growth arrest (ϕc).

On the basis of the developed relationship, we scaled the experimental NP size by the measured ϕc6/11. The scaled NP size collapsed onto the predicted curve as a function of Re for all solvents (Figure d). In the tested regime, the scaling behavior supports the proposed physical model—dynamic aggregates grow in a similar process for all solvents, and growth is limited by the solvent-dependent ϕc (growth arrest). In this manner, the NP size was controlled by how fast the system reaches growth arrest. This can be tuned with τmix by varying the flow conditions of mixingor with ϕc by changing the solvent. The scaling law suggested how solvent controls NP size and provides useful guidelines to tailor the size of block copolymer NPs. It remains to be seen if these observed effects are limited to nonequilibrium (kinetically trapped systems), and further studies should explore other block copolymer–solvent systems as well as the role of solvent in equilibration nanoprecipitation.[62,63]

Conclusion

In this work, we explained how solvent affects NP size during block copolymer nanoprecipitation. Our proposed model suggests that dynamic polymer aggregates grow from the onset of assembly to growth arrest and that the water fraction for growth arrest is determined by the solvent. Turbidity measurements indicated dynamics below a critical water fraction and that kinetically trapped NPs were formed beyond this point. We defined this point as the critical water fraction of growth arrest, ϕc, which was measured for each solvent. The NP size correlated to the experimental ϕc for all solvents, block copolymers, and mixing kinetics tested in this work. We developed an a priori model, based on spinodal decomposition and growth via unimer exchange up to growth arrest, that described how NP size scales with ϕc and mixing kinetics. The experimental data for NP size collapsed onto the predicted curve from the model when scaled by ϕc. This supported the hypothesis that growth arrest ϕc controls NP size during nanoprecipitation. Overall, our study provides fundamental insight into the role of the solvent during the commonly used nanoprecipitation method and provides insight into another control variable in the design and engineering of block copolymer NPs.