Self-assembly of polymer blends and nanoparticles through rapid

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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

Self-assembly of polymer blends and nanoparticles through rapid solvent exchange Nannan Li, Arash Nikoubashman, and Athanassios Z. Panagiotopoulos Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b04197 • Publication Date (Web): 13 Feb 2019 Downloaded from http://pubs.acs.org on February 14, 2019

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Self-assembly of polymer blends and nanoparticles through rapid solvent exchange Nannan Li,† Arash Nikoubashman,∗,‡ and Athanassios Z. Panagiotopoulos∗,† †Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA ‡Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany E-mail: [email protected]; [email protected]

Abstract Molecular dynamics simulations were performed to study the fabrication of polymeric colloids containing inorganic nanoparticles (NPs) via the Flash NanoPrecipitation (FNP) technique. During this process, a binary polymer blend, initially in a good solvent for the polymers, is rapidly mixed with NPs and a poor solvent for the polymers that is miscible with the good solvent. The simulations reveal that the polymers formed Janus particles with NPs distributed either on the surface of the aggregates, throughout their interior, or aligned at the interface between the two polymer domains, depending on the NP-polymer and NPsolvent interactions. The loading and surface density of NPs can be controlled by the polymer feed concentration, the NP feed concentration, and their ratio in the feed streams. Selective localization of NPs by incorporating electrostatic interactions between polymers and NPs has also been investigated, and shown to be an effective way to enhance NP loading and surface density compared to the case with only van der Waals attractions. This work demonstrates 1

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that the FNP process is promising for the production of structured and hybrid nanocolloids in a continuous and scalable way, with independent control over particle properties such as size, NP location, loading and surface density. Our results provide useful guidelines for experimental fabrication of such hybrid nanoparticles.

Introduction Hybrid nanomaterials which consist of metal, semiconducting or magnetic nanoparticles (NPs) dispersed in various polymeric matrices have potential applications in a broad range of areas, including optics, electronics, sensors, catalysis, imaging, and pharmaceuticals. 1–4 The selective localization of NPs in different domains of the aggregates, such as cores, surfaces, and interfaces between polymer domains, may critically affect the properties and applications of these materials. For example, encapsulation of quantum dots (QDs) in the core of polymer micelles improves their stability and reduces their toxicity in biological environments. 5 Such hybrid materials are also potentially useful in labeling and imaging applications. Further, Janus nanoparticles with one or both domains modified with metal NPs are excellent interfacial catalysts for reactions in biphasic systems with controlled phase selectivity. 6–8 Two primary methods have been widely employed for incorporation of NPs into polymeric aggregates. The first one involves in situ formation of metal NPs using chemical reactions, 9–11 and the second one is the co-assembly of polymers and NPs. 12–17 The second approach is suitable for a wider range of polymer and NP systems, and offers more precise control in NP size and position. In this work, we study a co-assembly technique named Flash NanoPrecipitation (FNP), where a polymer solution and NPs are rapidly mixed with an excess amount of a miscible non-solvent to induce supersaturation and aggregation. 18–20 FNP is a continuous and scalable process which has low energy consumption, and is able to produce narrowly distributed aggregates with tunable size, morphology, and NP loading. Previous efforts have focused on studying the incorporation of hydrophobic drugs, QDs,

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and metal NPs into either the core or the surface of block copolymer micelles using FNP. 21–25 Recently, it was demonstrated that, Janus nanocolloids with controlled surface decoration could also be obtained from the FNP process using commercially available homopolymer blends and gold NPs (AuNPs). 26 In addition to Janus structures, it has been shown in both experiments and simulations that FNP can also be used to generate core-shell and patchy structures with reliable control over size, composition, and morphology, 27–31 which greatly expands the number of accessible hybrid architectures if NPs are included in the feed streams. Given the extensive parameter space involved, such as polymer and solvent types, NP chemistry and size, polymer and NP feed concentrations, etc., simulations are a useful tool for guiding experiments and predicting assembly morphologies. Numerous theoretical and computational studies have been reported, mainly focusing on the self-assembly of block copolymers and NPs through solvent evaporation or gradual addition of a poor solvent to a solution of polymers and NPs. 32–40 For example, a study which combined experiments and self-consistent field theory calculations showed that the location of AuNPs in vesicle walls or spherical micelles depends on the size of NPs and is an entropically driven process. 33 In another study, molecular dynamics (MD) simulations were used to relate molecular design of block copolymers and NPs, such as the solvophobicity and composition of block copolymers, and NP size and concentration, to the location and quantity of NPs in the hybrid micell structures. 36 However, systems which involve binary hydrophobic polymer blends and NPs have not been studied before. In the present work, we are inspired by the wide range of structures that can be potentially obtained from binary polymer blends and NPs undergoing the FNP process, 26–30 and use MD simulations to explore the parameter space. Our previous computational studies on binary polymer blends undergoing FNP in the absence of NPs have explained how the morphology, size and composition of the polymeric aggregates can be controlled through the types of feed polymers, and processing parameters specific to the FNP technique, e.g., mixing rate and polymer feed concentration and ratio. 29,30,41 In the present study, we shift our

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focus to how NP localization, loading and surface density can be tuned in the precipitated hybrid structures. These factors will play significant roles in determining the properties and performance of the hybrid colloids. The remainder of this paper is structured as follows: we first introduce the MD simulation model and methods used in the present work. Next, we present our simulation results, and examine how the above-mentioned properties of the hybrid structures can be independently controlled by the interaction strengths between different species and the feed concentrations of polymers and NPs. Lastly, we summarize our results and comment on their implications.

Simulation model and methods Our previous MD model for binary polymer blends undergoing the FNP process serves as a foundation for our current study. 29 In this model, a polymer is described as a linear beadspring chain with N beads, each with unit diameter σ and unit mass m. Each bead represents a Kuhn segment of the polymer chain. We used N = 23 for all homopolymer chains in our simulations, which corresponds to, e.g., polystyrene (PS) chains with a molecular weight of 16.5 kg/mol. 26,27 The bonded interactions between polymer beads are modeled via the finitely extensible nonlinear elastic (FENE) potential 42 with the standard Kremer-Grest parameters to prevent unphysical bond crossing. 43 In addition to the bonded interactions, polymer beads also interact with one another via the standard Lennard-Jones (LJ) potential. Binary polymer blends (of type A and B) have been considered in the current work. We set the prefactor of the LJ potential, εLJ , for the intraspecies interaction of both polymer A and polymer B equal such that εAA = εBB = kB T , with Boltzmann constant kB and temperature T . The interspecies A-B interaction strength, εAB , was varied between 0.9εAA and 0.3εAA , to represent the chemical incompatibility of the two polymer types. The cutoff radius of the LJ potential was set to rcut = 3.0σ.

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Following Ref. 44, solvent particles are modeled explicitly as LJ particles with the same size and mass as the polymer beads. A reduced number density of ρS = 0.66 has been chosen, which leads to a dynamic solvent viscosity of η = 1.01. Similar to previous computational studies on FNP, 29,30,44–46 the transition from good to poor solvent conditions was mimicked by varying the non-bonded particle interactions. In our studies, we control the interaction between solvent particles and monomers by a dimensionless parameter λ: 47

UMS (r) = λUWCA (r) + (1 − λ)ULJ (r),

(1)

where UWCA (r) is the purely repulsive Weeks-Chandler-Anderson (WCA) potential. 48 As λ increases from 0 to 1, the solvent quality gradually degrades. In this work, we chose the values of λ for good and poor solvent conditions to be 0 and 0.5, respectively. In order to make meaningful comparisons between our simulations and experimental results, it is important to establish a connection between units of energy, length, and time in the two domains, which has been done in Ref. 44 for the homopolymer-solvent model. For our model, we found ε =4.11 × 10−21 J , σ =1.5 nm, and τ =0.28 ns for the characteristic energy, length, and time scales, respectively. NPs are modeled as spherical clusters of LJ beads of the same size and mass as chain monomers and solvent particles, forming spheres of diameter σNP . In experiments, the diameter of AuNPs is approximately 10 nm, 26 which corresponds to roughly 6 σ in simulation units. However, the typical radii of the polymeric aggregates, a, obtained in the simulations (assumed to be approximately 1.3 times the radius of gyration 44 ) are between 25 to 30 nm, which are significantly smaller than the values of 100 to 200 nm obtained in the experiments. We have thus chosen σNP = 2σ =3.0 nm in the simulations (2 times the diameter of a monomer or a solvent particle), so that σNP /a is approximately 0.1, which is close to the experimental values. The NP clusters are considered to be uniform spheres of unit reduced density, ρ∗ = ρNP σ 3 ,

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where ρNP is the number density of LJ beads within each NP, and set to σ −3 . The potential between NPs is determined by integrating over all LJ particles in the two interacting NPs and has the form: 49

UNP,NP (r) = UA (r) + UR (r).

(2)

The attractive component, UA (r), is 2 2 2 2 HNP,NP σNP σNP r − σNP + 2 + ln , UA (r) = − 2 6 2(r2 − σNP ) 2r r2

(3)

and the repulsive component, UR (r), is 2 2 2 /2 r2 + 7rσNP + 27σNP /2 2(r2 − 15σNP /2) HNP-NP σ 6 r2 − 7rσNP + 27σNP + − . UR (r) = 37800 r (r − σNP )7 (r + σNP )7 r7 (4) The cut-off radius of UNP,NP was set to 5.5σ. HNP-NP is the Hamaker constant and HNP-NP = 4π 2 εNP , where εNP is the prefactor of the LJ interaction between the constituent beads of the NPs. To determine the value of HNP-NP , we considered the equivalent Hamaker constant between polymeric aggregates in our simulations, which has a value of 4π 2 kB T , because polymeric aggregates consist of standard LJ beads with εAA = εBB = kB T . Since the experimentally measured Hamaker constant of Au is approximately 5 times that of PS, 50 we chose εNP = 5kB T , which led to HNP-NP = 20π 2 kB T . The potential between an NP and a polymer bead or a solvent particle is given by: 49 3 6 4 2 σNP σ 3 HNP-P/S (5σNP /64 + 45σNP r2 /16 + 63σNP r4 /4 + 15r6 )σ 6 1− , (5) UNP,P/S (r) = 2 36(σNP /4 − r2 )3 15(σNP /2 − r)6 (σNP /2 + r)6 where HNP-P/S = 24πεNP-P/S . The cutoff radius of UNP,P/S was set to 5.0σ. Experimentally, the surface of NPs can be modified by different chemical groups, which gives rise to either hydrophobic or hydrophilic NPs. 2 In our simulations, we varied εNP-P and εNP-S between 6


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0.025kB T and 5kB T to control the NP-polymer and NP-solvent affinities. When εNP-S = kB T and εNP-P = kB T , i.e., the LJ beads that formed the NPs interact with the solvent particles and monomers with an equal strength as the solvent particles and monomers interact with themselves, the NPs aggregate in the solvent and the polymer matrix. NP-solvent and NPpolymer miscibility occur at approximately εNP-S = 1.5kB T and εNP-P = 2.5kB T for the chosen HNP-NP of 20π 2 kB T . In addition to electroneutral NPs and polymers, we also considered charged NPs and polymers with charged end groups. In previous experiments, AuNPs stabilized by citrate groups were shown to electrostatically interact with amine-terminated PS polymer chains, so that the NPs were dispersed exclusively on the PS domain of the aggregates. 26 In our simulations, the end groups were modeled by the last bead of every polymer chain. The screened electrostatic interaction between the NPs and the charged end groups is given by: 51 UYukawa (r) = λB

ZEG eκσ/2 1 + κσ/2

ZNP eκσNP /2 e−κr , 1 + κσNP /2 r

(6)

where λB is the Bjerrum length, and κ is the inverse Debye screening length, λD . For water with pH = 7 at room temperature, we used λB = 0.7 nm, and λD = 0.15 µm. 44 The parameters ZEG and ZNP denote the charges of the end groups and the NPs, respectively. For amine end groups and citrate stabilized AuNPs studied in the experiments, ZEG = +e and ZNP = −3e. These values translate to 6.1 and -18.3 in our simulations, respectively, where the unit of charge is (4πE0 σε)1/2 , and E0 is the vacuum permittivity. The MD simulations were run using the HOOMD-blue simulation package. 52,53 A cubic box with an edge length of 80σ was adopted, containing a total of up to 2,048 polymers. An A:B ratio of 1:1 was chosen throughout this paper. The only exception was the simulation snapshot shown in Figure 5(c), where a ratio of 2:1 was chosen to facilitate a comparison with previous experiments also performed with a 2:1 ratio. 26 The number of NPs in the system varied between 100 to 2000 (the remaining volume of the box was filled with solvent

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particles to reach the desired density of ρS = 0.66). We have checked the influences of box size on simulation results at selected state points and did not find any appreciable finite size effects when the box edge length is above 80σ. It is noted that the total number of 1,024 polymers in our systems limits the maximum aggregate size to a ≈ 28nm, which is one order of magnitude smaller than those produced in the experiments. To realize in the simulations an aggregate with a radius of a = 100nm, approximately 105 polymers and 107 solvent particles are required, which is computationally infeasible. Despite this limitation, however, the employed model is useful for predicting morphologies and it is able to reproduce the most important trends observed in the experiments. 29,44 A Nos´e-Hoover thermostat was employed to maintain the temperature at T = 1.0 and the equations of motion were integrated at a timestep of 4t = 0.01 in the reduced units defined earlier. Measurement uncertainties of the results presented in the following section were determined from the standard error of the mean from three independent runs. In our previous MD simulations, 29,44 a negative surface potential was applied to all the aggregates to mimic the effect of charge stabilization on the precipitated aggregates. Since the effect of this surface potential on aggregate size has been elucidated in our previous studies and we are mainly concerned with understanding the equilibrium morphologies that can arise from the polymer-NP-solvent systems, such a negative surface potential is not included in the current work. In our simulations, the systems were allowed to evolve until one single polymeric aggregate remained, and this approach enabled us to access larger aggregates with a wider range of NP loading and surface density despite the limited system size accessible to our simulations. Typical simulations were run up to 107 timesteps until equilibrium structures were achieved, which corresponds to approximately 28 µs, using the time scales developed in Ref. 29 for the homopolymer-solvent model.

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Results and discussion We first present results on particle morphology as a function of affinities between the different constituents in the system. Affinities are represented by the values of the Hamaker constant, which can be calculated using the relationship H = 4π 2 ε as mentioned in the previous section, where ε is the prefactor of the LJ interaction between the constituent beads of the two interacting bodies. Considering the large parameter space, we first kept the A-B cross interaction and polymer-solvent interaction constant at HA-B = 1.5 × 10−19 J, and HA-S = HB-S = 8 × 10−20 J. Here, we chose polymers A and B to have equal affinities to the solvent (the effect of HP-S on the equilibrium morphologies will be discussed further below). Therefore, we use the notation HP-S to represent the identical Hamaker constants between both types of polymer beads and the solvent in the remainder of this paper, i.e., HA-S = HB-S = HP-S . This combination of interaction strengths gives rise to Janus aggregates in the absence of NPs. 29 In this work, we focus on the dispersion of NPs in Janus aggregates, because such particles have been produced in previous experiments using FNP, 26 and they have potential applications in catalysis. HNP-NP was set to 8.1 × 10−19 J as explained in the previous section. We varied systematically the NP-polymer and NP-solvent Hamaker constants, i.e., HNP-P , and HNP-S . The NPs are first chosen to be non-selective to either polymer A or B, as we are interested in controlling the radial distribution of NPs in the polymer matrix, i.e., surface, interior or A-B interface. The case when NPs are selectively localized on one polymer domain will be studied in a subsequent section. The initial configurations consisted of polymer chains and NPs homogeneously distributed in the solvent. After an equilibration period at good solvent conditions (λ = 0), λ was set to 0.5. Unlike our previous studies, 29,44 we changed the solvent conditions instantaneously, and did not consider the effect of mixing rate. We followed this procedure, because the mixing rate has been shown to affect only the final size of the aggregates for the FNP process. 29,41,44 In the current work, we are interested in the equilibrium morphologies of the hybrid aggregates, and have thus chosen the instantaneous mixing condition for simplicity. 9


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The morphology diagram obtained from varying NP-solvent affinity (HNP-S ) and NPpolymer affinity (HNP-P ) is presented in Figure 1. Each point in the morphology diagram corresponds to a simulation result. It can be seen that NPs are distributed either (1) on the surface, (2) in the interior of the polymeric aggregates, or (3) they remain dispersed in the solution. When the difference between HNP-S and HNP-P is small, NPs locate on the surface, as shown by regions (I) and (II). Within regions (I) and (II), the degree of dispersion can be controlled by the values of HNP-S and HNP-P . When both values are large, NPs are uniformly dispersed on the surface of the aggregates to maximize contact with both the polymers and the solvent. However, for small HNP-S and HNP-P , NPs aggregate on the surface of the polymeric aggregate. When either HNP-S or HNP-P is significantly higher than the other, NPs are distributed in the energetically more favorable domain, i.e., inside the polymer aggregate (III) or in the solvent (IV). To understand the morphology diagram in more detail, we consider the following structural properties of the aggregates: (1) Fraction of NP uptake from the solution, fNP = NNP /Nt , where NNP is the total number of NPs that are attached to the aggregate, and Nt is the total number of NPs in the simulation box. (2) Surface density of NPs on the aggregates, SNP = NNP,s /A, where NNP,s is the number of NPs on the surface of an aggregate, and A = 4πa2 is the surface area of the aggregate. The surface NPs were identified by counting the number of surrounding monomers. For our systems, we determined that NPs are located on the surface when they have 20 or fewer nearest neighbors. (3) Volume fraction of NPs at the A-B interface, fi = 8NNP,i /NM,i , where NNP,s , and NM,i are the numbers of NPs and monomers at the A-B interface region, respectively. The factor 8 arises from the volume ratio of a single NP and a single monomer in our simulations. The interface monomers were identified by taking all the monomers that have at least one bead of an opposite type in their immediate neighborhood. We divided NNP,s by NM,i to

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(III)

4

(I) 2

(IV)

(II)

0 0

2

4 HNP-S (10-19 J)

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Figure 1: Morphology diagram for different values of HNP-S and HNP-P . Other interaction parameters are kept constant at HNP-NP = 8.1 × 10−19 J, HA-A = HB-B = 1.6 × 10−19 J, HA-B = 1.5 × 10−19 J, and HP-S = 8 × 10−20 J. The triangles and the circles represent equilibrium morphologies with NPs dispersed and aggregated on the surface of the aggregates, respectively. The pentagons represent morphologies with NPs distributed in the interior, and the squares represent no aggregation between polymers and NPs. Approximate boundaries between the regions are indicated by dashed lines for visual clarity. Beads of polymers A and B are represented by the red and blue particles, respectively, while the AuNPs are shown as golden spheres. The same coloring scheme has been used for all other simulation snapshots as well. The snapshots show the cross sections of the equilibrium morphologies, and are produced using VMD. 54

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take into account the decreasing A-B interfacial area in the aggregates with decreasing A-B interaction strength. (4) Aspect ratio of the aggregates, α = L3 /L1 , where L3 and L1 are the largest and smallest eigenvalues of a particle’s radius of gyration tensor, respectively. A spherical aggregate has α = 1. In Figure 2, we plot the fraction of NP uptake, fNP , as a function of HNP-P for different HNP-S values. The results were obtained from initial configurations with a constant polymer feed concentration of 5.7 × 10−4 nm−3 , and NP concentration of 5.6 × 10−4 nm−3 , which leads to a pure polymeric aggregate to NP volume ratio of approximately 3. It can be seen that fNP increases monotonically with HNP-P , and lower HNP-S leads to more efficient NP uptake from the solution.

1.0 2.8E-19 J 3.2E-19 J 4.9E-19 J 0.8 6.5E-19 J fNP

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0.6 0.4 0.2 0.0 0

2

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6

8

Figure 2: Fraction of NP uptake from the solution, fNP , as a function of HNP-P for different HNP-S values, as indicated. Error bars are shown only when they are larger than symbol size. Next, we study the effects of HNP-S and HNP-P on the surface density of NPs, SNP . It can be seen in Figure 3 that a decrease in HNP-S leads to higher SNP , which is similar to the trend in fNP . However, the maximum NP surface density only occurs at a HNP-P value comparable to the corresponding HNP-S . Further increase in HNP-P results in an increasing number of NPs locating in the interior of the aggregates and a decrease in SNP as shown by 12


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the simulation snapshots.

2.8E-19 J 3.2E-19 J 4.9E-19 J 6.5E-19 J

0.050

SNP (nm-2)

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0.025

0.000 0

2

4 6 -19 HNP-P (10 J)

8

Figure 3: Number density of NPs on the surface of the aggregates, SNP , as a function of HNP-P for different HNP-S values, as indicated. The snapshots show the cross sections of the aggregates taken for HNP-S = 3.2 × 10−19 J. The maximum values of SNP occur at HNP-P = 3.2 × 10−10 J for HNP-S = 2.8 × 10−10 J, HNP-P = 4.9 × 10−10 J for HNP-S = 3.2 × 10−10 J, and HNP-P = 6.5 × 10−10 J for HNP-S = 4.9 × 10−10 J, respectively. In addition, higher HNP-P also gives rise to larger and more spherical aggregates as shown in Figure 4. When the NPs are dispersed on the surface of the aggregates, they lower the surface tension between polymers and solvent, and increase the area of contact between the aggregate and the solvent, which explains the higher α compared to polymeric aggregates without NP (indicated by the dotted line). However, as HNP-P increases, NPs locate increasingly at the interior of the aggregates, which gives rise to larger aggregates. The internal NPs, which show equally high affinities to both polymer types, improve the compatibility between the immiscible polymer blend and lead to more spherical aggregates. So far, we have kept the polymer-solvent interaction (HP-S ) and polymer cross interaction (HA-B ) constant. To study the effect of these two parameters, we varied them systematically for two sets of HNP-S and HNP-P values, i.e., HNP-S = HNP-P = 3.2 × 10−19 J, and HNP-S = 13


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1.2

1.0 0

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4 -19

HNP-P (10

6 J)

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Figure 4: Aspect ratio of the aggregates, α, as a function of HNP-P for HNP-S = 3.2 × 10−19 J. The dotted line indicates α of an aggregate with the same interactions in the absence of NPs. 3.2 × 10−19 J, HNP-P = 6.5 × 10−19 J, which correspond to the equilibrium morphologies in regions (I) and (III) shown in Figure 1. HP-S and HA-B were tuned by the dimensionless solvent parameter, λ, and the strength of the A-B cross interaction, εA-B , respectively. From Figure 5(a), it can be seen that increasing HP-S , i.e., decreasing hydrophobicity of the polymers, leads to a decrease in the density of NPs on the surface of the aggregates. In addition, a decrease in HA-B results in A-B interfacial regions more densely occupied by the NPs as shown in Figure 5(b). For the experimental system studied in Ref. 26, which consisted of electroneutral PS, polyisoprene (PI), and AuNPs, with water used as the non-solvent, typical values of Hamaker constants are HPS-PS = 8 × 10−20 J, HAu-PS = 1.7 × 10−19 J, HAu-Water = 1.4 × 10−19 J, and HPS-PI = 6 × 10−20 J. 50 Since HAu-PS and HAu-Water are similar, our simulations indicate that NPs is expected to be distributed on the surface of the polymeric aggregates (see Figure 1). In addition, HAu-PS is approximately 3 times larger than HPS-PI , indicating that a large fraction of NPs on the surface of the aggregates should be at the PS-PI interface. Indeed, it was observed in the experiments that such a PS-PI-Au system gave rise to Janus structures

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(a) -2

S NP (nm )

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0.4 0.2 0.0 0.4

0.8 1.2 -19 HA-B (10 J)

1.6

(c)

Figure 5: (a) Density of NPs on the surface of the aggregates, SNP , as a function of HP-S . (b) Volume fraction of NPs at polymer-polymer interface, fi , as a function of HA-B . The snapshots show the external views for HNP-S = HNP-P = 3.2 × 10−19 J, which corresponds to the structures with NPs dispersed on the surface of the aggregates.(c) SEM image of colloids obtained from an electroneutral PS/PI homopolymer blend and citrated-stabilized AuNPs undergoing FNP. 26 (Copyright 2017, American Chemical Society.) A snapshot from the MD simulations in this work is also included for comparison. The scale bar is 200 nm for the SEM image and 8 nm for the simulation snapshot. 15 ACS Paragon Plus Environment

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with NPs aligned on the PS-PI interface as shown by the scanning electron microscopy (SEM) image in Figure 5(c). In order to reproduce this structure, we performed additional simulations, where we used the same ratios between the Hamaker constants as in the experiments. (Note that the absolute values of H in the experiments and simulations differ by a factor of HPS-PS /HA-A ≈ 0.5.) Similar to the experiments, an A:B ratio of 2:1 was also adopted. It can be seen in Figure 5(c) that a structure in qualitative agreement with the experiments was obtained in the simulations. In this case, an increase in polymer-polymer cross interaction relative to the polymer-NP interaction will lead to more uniformly dispersed NPs over the entire surface of the aggregates. An increase in NP-polymer interaction and a decrease in NPwater interaction, e.g., by using AuNPs functionalized with a hydrophobic group, will lead to an increase in NP uptake from the solution and more NPs at the interior of the polymers. Having understood the range of morphologies that can arise from the polymer-NP-solvent system by varying the interactions between different constituents, we then studied how NP loading and surface density can be controlled by processing parameters such as polymer feed concentration (ΦP ), NP feed concentration (ΦNP ), and polymer to NP volume ratio in the feed streams. Here, we focus on the structures from regions (I) and (III) shown in Figure 1, i.e., NPs dispersed either exclusively on the surface or throughout the entire volume of the aggregate. For structures with NPs dispersed on the surface of the aggregates [region (I) in Figure 1], we chose HNP-S = 3.2 × 10−19 J, and HNP-P between 1.2 × 10−19 J and 3.2 × 10−19 J. Other interaction parameters were chosen to be consistent with those in Figure 1. Figure 6(a) shows the dependence of fNP on ΦNP . Here, we prepared initial configurations with a fixed number of polymer chains and varying number of NPs between 100 and 2000. Similarly, we kept the number of NPs constant at, Nt = 1000, and varied the number of polymer chains in the range of 288 and 2,048 to understand the dependence of fNP on ΦP [see Figure 6(b)]. In order to understand the results shown in Figure 6, we consider the adsorption of NPs

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on the surface of the polymeric aggregates: k+1

− * NP + SP − ) − − NP-SP,

(7)

k−1

where SP are the polymer beads on the surface of the aggregates, which are available for adsorption, and k+1 and k-1 are the rate constants of adsorption and desorption, respectively. The rate of adsorption, r+1 , can be represented as r+1 = k+1 (1 − fNP )ΦNP (ΦSP − BfNP ΦNP ), where (1 − fNP )ΦNP is the concentration of free NPs in the solution, and (ΦSP − BfNP ΦNP ) is the concentration of unoccupied polymer beads on the surface of the aggregates. The parameter B is a geometric constant which takes into account that a single NP binds to multiple polymer beads, since the NP diameter is twice the monomer diameter. The rate of desorption is r-1 = k-1 fNP ΦNP , where fNP ΦNP is the concentration of NPs which are adsorbed on the surface of the polymeric aggregate. At equilibrium, r+1 = r-1 , which leads to

k+1 (1 − fNP )(ΦSP − BfNP ΦNP ) = k-1 fNP .

(8)

Solving Eqn. (9) for fNP , and choosing the solution which is 0 for ΦSP = 0 gives rise to

fNP =

(ΦSP + BΦNP + k-1 /k+1 ) −

p (ΦSP + BΦNP + k-1 /k+1 )2 − 4BΦSP ΦNP . 2BΦNP

(9)

Having derived the dependence of fNP on ΦNP and ΦSP , we fitted the data in Figure 6(a) 2/3

and (b) according to this relationship. Here, we assumed ΦSP = CΦP , where C is also a fitted constant. It can be seen from Figure 6 that good agreement was obtained between the results from our MD simulations and Eqn. (9). We obtained B = 5.5 ± 0.5, which is 2 close to the ratio of the surface area of an NP to that of a monomer, σNP /σ 2 = 4. The 2/3

fitted constant C can be considered as NSP /(V 1/3 NP ), where V is the system volume; NSP and NP are the numbers of monomers on the surface of the aggregate, and in the entire 2/3

volume of the aggregate, respectively. We obtained NSP /NP

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= 6.2 ± 0.6 from fitting. This

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value is consistent with the number of surface monomers for aggregates obtained from our simulations. The fitted values of the constants in Eqn. (9) are summarized in Table 1. Table 1: Estimates for the parameters B, C, and k-1 /k+1 and fitted values obtained from fitting the data in Figure 6 according to Eqn. (9). The value of B was estimated from the ratio of the surface area of an NP to that of a monomer. C was estimated from counting the number of surface monomers for aggregates obtained from our simulations.

Constants

Fitted values

Estimated values

B

5.5 ± 0.5

4

C k-1/k+1

1/3

1/3

6/V

(6.2 ± 0.6)/V

0.0005 to 0.1, decreases with increasingH NP-P

< 1, decreases with increasingH NP-P

Results in Figure 6 show that an increase in the concentration of polymers in the feed stream leads to a more efficient uptake of NPs from the solution. However, increasing the NP concentration results in an increase in the absolute number of adsorbed NPs as shown by the snapshots in Figure 6(a), but a decrease in the relative fraction of uptake. This is because an increase in NP concentration at a constant polymer concentration leads to fewer monomers available for interactions with solvent and other monomers. In addition, the more saturated surface of the aggregate makes it increasingly difficult to take up additional NPs due to the repulsions between NPs. This also explains why the decrease in fNP is more pronounced at higher HNP-P , because the surface is more densely occupied by NPs. Therefore, the number of NPs adsorbed does not increase proportionally with the total number of NPs in the system, which gives rise to a decrease in fNP . Eqn. (9) also allows us to predict the dependence of SNP on ΦNP and ΦP , since SNP can be estimated to be proportional to fNP NNP /NSP . In addition, we also plot in Figure 7 the Gibbs free energy change of the adsorption per NP, ∆G, vs. the strength of NP-polymer interaction, HNP-P . ∆G was calculated using the relationship k-1 /k+1 = e∆G/kB T , and we obtained two sets of values of k-1 /k+1 from the two 18


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(a)

0.8 fNP

2.4E-19 J 2.8E-19 J 3.2E-19 J

1.2E-19 J 1.6E-19 J 2.0E-19 J

1.0

0.6 0.4 0.2 0.0 0.0000

0.0004

0.0008

0.0012

-3

Φ NP (nm )

(b)

1.0 0.8

1.2E-19 J 1.6E-19 J 2.0E-19 J

2.4E-19 J 2.8E-19 J 3.2E-19 J

0.6 fNP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.4 0.2 0.0 0.0000

0.0004

0.0008

0.0012

-3

Φ P (nm )

Figure 6: Fraction of NP uptake from the solution, fNP , as a function of (a) ΦNP for constant ΦP , and (b) ΦP for constant ΦNP for different values of HNP-P , as indicated. The solid lines are fits according to Eqn. (9). The snapshots in (a) are the external views of the aggregates obtained for HNP-P = 3.2 × 10−19 J and ΦNP = 0.0002 and 0.001 nm−3 .

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independent fitting procedures shown in Figure 6(a) and 6(b) using Eqn. (9). It can be seen that ∆G < 0, which indicates that adsorption is energetically more favorable than desorption for our system. The two sets of data show good agreement, and they can be fitted according to a linear relationship, ∆G = −0.09HNP-P as indicated by the dotted line in Figure 7. In addition, we obtained from the simulations that the enthalpy change of adsorption of one NP is approximately −HNP-P . Therefore, the adsorption process has a negative entropy change as expected.

-0.1

∆G (10-19 J)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Figure 6(a) Figure 6(b)

-0.2

-0.3

1.0

1.5

2.0 2.5 -19 HNP-P (10 J)

3.0

3.5

Figure 7: Gibbs free energy change of adsorption per NP, ∆G, obtained from fitting the two independent sets of data in Figure 6(a) and (b), respectively, as a function of HNP-P . The dotted line represents a linear fit to the data. The red data points were obtained from fitting the data shown in Figure 6(a), and the blue data points were obtained from fitting the data shown in Figure 6(b). When HNP-P increases further, the NPs aggregate simultaneously with the polymers, and equilibrium structures with NPs dispersed throughout the entire volume of the aggregates are obtained [region (III) in Figure 1]. To study the spatial distribution of NPs in this case, we chose the same value of HNP-S = 3.2 × 10−19 J, and HNP-P between 5.6 × 10−19 J and 8.1 × 10−19 J. We varied systematically the volume fraction of NPs in the final polymer aggregates by increasing the number of NPs while keeping the number of polymer chains constant in the initial configurations. 20


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In Figure 8(a), we plot the surface density of NPs on the surface of the aggregates, SNP , vs. the volume fraction of NPs in the aggregate, fv . We determined fv using the relationship fv =

8NNP , 8NNP +NM

where NM is the total number of monomers in the aggregate. The factor 8 that

appears in this relationship arises from the volume ratio of a single NP and a single monomer in our simulations. The dotted line indicates the prediction for SNP if the distribution of NPs is uniform throughout the entire volume of the aggregate with the assumption that the aggregate is spherical. This prediction was derived from the relationship between the number of NPs on the surface of the aggregate, NNP,s , and NNP , which is NNP,s = NNP Vss /Va . Here, Va is the volume of the aggregate, Va = 4/3πa3 , and Vss is the volume of a spherical shell on the surface of the aggregate with a thickness of an NP diameter, σNP . It can be seen that the results for HNP-P = 5.6 × 10−19 J follow the prediction for uniform distribution very well. For higher values of HNP-P , SNP is zero for nonzero fv , which means that for small fv , the NPs are distributed exclusively in the interior. The behavior can be explained by the competition between enthalpic and entropic effects. The larger HNP-P with respect to HNP-S leads to NPs which prefer the interior of the aggregates. However, as more NPs are incorporated to the interior of the aggregates, i.e., fv increases, it results in a larger conformation entropy loss of the polymer chains that distribute around the NPs. When this entropy loss outweighs the enthalpic gain due to the more favorable NP-polymer interactions, NPs are driven to the surface of the aggregates. In addition, for the same value of fv , stronger NP-polymer interactions lead to higher NP internal density, and a smaller number of NPs on the surface. This is because the stronger enthalpic attraction between NPs and polymers can afford a larger entropy loss and allow more NPs to be incorporated to the interior of the aggregates, i.e., a higher threshold fv before NPs start to emerge on the surface. When we plot in Figure 8(b) SNP vs. fv shifted by its value when SNP first becomes nonzero, results for different values of HNP-P collapse onto the dotted line, which means that the distribution of NPs is uniform when fv is above its corresponding threshold value, fv,0 .

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These findings provide guidelines for tuning the internal and surface density of NPs via fv , which can in turn be controlled by the ratio of NPs and polymers in the feed streams and the size of the NPs during the experiments.

S NP (nm-2)

(a)

0.15

5.6E-19 J 6.5E-19 J 8.1E-19 J

0.10

0.05

0.00 0.0

0.1

0.2

0.3

0.4

0.5

0.3

0.4

0.5

fv

(b)

S NP (nm-2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.15

5.6E-19 J 6.5E-19 J 8.1E-19 J

0.10

0.05

0.00 0.0

0.1

0.2 fv-fv,0

Figure 8: Surface density of NPs on the aggregates, SNP . vs. (a) volume fraction of NPs, fv, and (b) fv minus its value when SNP first becomes nonzero for different values of HNP-P . The dotted line represents prediction for SNP if NPs are uniformly distributed throughout the entire aggregate. We now move on to study how NP loading and localization are affected when NPs selectively interact with one polymer domain. With only van der Waals interactions between NPs and polymers, selective localization can be achieved by choosing different state points for NP-A and NP-B interactions in Figure 1. For example, by choosing a state point for 22


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NP-A interaction in region (I), and a state point for NP-B interaction in region (IV), NPs will be dispersed exclusively on the surface of polymer A domain [Figure 9(a)]. Similarly, a combination of state points in regions (III) and (IV) will lead to aggregates with NPs dispersed exclusively in the interior of the polymer A domain [Figure 9(b)].

(a)

(b)

HNP-A = 6.5×10-19 J HNP-B = 4.1×10-20 J HNP-S = 3.2×10-19 J

-19

HNP-A = 3.2×10 J -20 HNP-B = 4.1×10 J -19 HNP-S = 3.2×10 J

Figure 9: Cross sections of the precipitated aggregates, which demonstrate selective localization of NPs, by choosing (a) NP-A interaction in region (I), NP-B interaction in region (IV), and (b) NP-A interaction in region (III), NP-B interaction in region (IV). Other interaction parameters are kept constant at HNP-NP = 8 × 10−19 J, HA-A = HB-B = 1.6 × 10−19 J, HA-B = 1.5 × 10−19 J, and HP-S = 8 × 10−20 J, which are consistent with Figure 1. In addition to van der Waals interactions, other polymer-NP interactions have also been used experimentally to achieve selective localization, such as hydrogen bonding, electrostatic interactions, and ligand replacement. 3 Motivated by this procedure, we consider electrostatic interactions in addition to the van der Waals attraction between NPs and polymers. In the experiments, such electrostatic interaction was achieved by incorporating charged amine end groups to PS chains. 26 It can be seen from the snapshot in Figure 10(a) that the negatively charged NPs are selectively localized on the polymer A domain, where the positively charged end beads are incorporated into. The general trends in fNP and SNP remain the same as the case with uncharged polymers and NPs. However, the stronger electrostatic interactions between NPs and polymers increase NP uptake for small HNP-P . In addition, the charged end groups are distributed on the surface of the aggregates to minimize the electrostatic repulsion among themselves, resulting in an increased surface density of NPs compared to the electroneutral case. Therefore, our results show that incorporating electrostatic interactions between

23


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polymers and NPs can enhance NP loading and surface density in the polymeric aggregates.

Conclusions In this work, MD simulations were carried out to study the assembly of a binary polymer blend and NPs under a rapid solvent exchange, a process experimentally realizable as Flash Nanoprecipitation (FNP). We systematically varied the interaction strengths between the different constituents, i.e., NP-solvent, NP-polymer, polymer-solvent, and polymer-polymer cross interaction, and demonstrated how the morphologies and the selective localization of the NPs can be tuned in the final structures. From our simulation results, we observed that three types of hybrid structures can arise with NPs distributed (1) on the surface, (2) throughout the entire volume of the polymeric aggregates, or (3) aligned at the interface between the two polymer domains. The loading and surface density of the NPs in the polymeric aggregates for each of these three cases can also be reliably tuned by the polymer and NP feed concentrations, and their volume ratio in the feed streams. In addition, we have also demonstrated that electrostatic interactions between polymers and NPs can enhance NP loading and surface density. We have thus demonstrated FNP as a simple, continuous and scalable process to produce polymer-NP hybrid materials with nanoscale control over particle properties, i.e., size, morphology, NP loading, surface density and localization. Our results also provide guidelines for future design and preparation of polymer-NP hybrid materials with desired properties, and thus facilitate their applications in areas such as drug delivery, sensors and catalysis.

Acknowledgments Financial support for this work was provided by the Princeton Center for Complex Materials (PCCM), a U.S. National Science Foundation Materials Research Science and Engineering Center (Grant DMR-1420541). Furthermore, N.L. acknowledges funding from Agency 24


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(a)

1.0 Uncharged Charged

0.8

fNP

0.6 0.4 0.2 0.0 0

2

4 -19

HNP-P (10

(b) 0.04

6 J)

8

Uncharged Charged

0.03 -2

S NP (nm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.02 0.01 0.00 0

2

4 HNP-P (10

6 -19

8

J)

Figure 10: (a) Fraction of NP uptake, fNP , and (b) surface density of NPs, SNP . vs. HNP-P for HNP-S = 3.2 × 10−19 J and different values of HNP-P . Results for both the charged and uncharged cases were obtained from initial configurations with a constant polymer feed concentration of 5.7 × 10−4 nm−3 , and NP concentration is 2.2 × 10−4 nm−3 . An A:B ratio of 1:1 leads to a concentration for the charged end groups of 2.9 × 10−4 nm−3 . A simulation snapshot is included in (a) which shows the external view of the Janus hybrid aggregate obtained at HNP-P = 3.2 × 10−19 J for the charged case. The charged end beads of polymer A are represented by the green particles.

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for Science, Technology and Research (A*STAR), Singapore. A.N. acknowledges funding from the German Research Foundation (DFG) under project number NI 1487/2-1.

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(36) Ma, S.; Hu, Y.; Wang, R. Amphiphilic block copolymer aided design of hybrid assemblies of nanoparticles: nanowire, nanoring, and nanocluster. Macromolecules 2016, 49, 3535–3541. (37) Zhang, L.; Lin, J.; Lin, S. Self-Assembly Behavior of Amphiphilic Block Copolymer/Nanoparticle Mixture in Dilute Solution Studied by Self-Consistent-Field Theory/Density Functional Theory. Macromolecules 2017, 40, 5582–5592. (38) Yang, J.; Hu, Y.; Wang, R.; Xie, D. Nanoparticle encapsulation in vesicles formed by amphiphilic diblock copolymers. Soft Matter 2017, 13, 7840–7847. (39) Beltran-Villegas, D. J.; Jayaraman, A. Assembly of Amphiphilic Block Copolymers and Nanoparticles in Solution: Coarse-Grained Molecular Simulation Study. J. Chem. Eng. Data 2018, 63, 2351–2367. (40) Yang, J.; Wang, D., R.and Xie Precisely controlled incorporation of drug nanoparticles in polymer vesicles by amphiphilic copolymer tethers. Macromolecules 2018, 51, 6810– 6817. (41) Li, N.; Nikoubashman, A.; Panagiotopoulos, A. Z. Multi-scale Simulations of Polymeric Nanoparticle Aggregation During Rapid Solvent Exchange. J. Chem. Phys 2018, 149, 084904–08. (42) Bishop, M.; Kalos, M. H.; Frisch, H. L. Molecular Dynamics of Polymeric Systems. J. Chem. Phys. 1979, 70, 1299–1304. (43) Grest, G. S.; Kremer, K. Molecular Dynamics Simulation for Polymers in the Presence of a Heat Bath. Phys. Rev. A 1986, 33, 3628–3631. (44) Nikoubashman, A.; Lee, V. E.; Sosa, C.; Prud’homme, R. K.; Priestley, R. D.; Panagiotopoulos, A. Z. Directed Assembly of Soft Colloids through Rapid Solvent Exchange. ACS Nano 2016, 10, 1425–1433. 31


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(45) Chen, T.; Hynninen, A. P.; Prud’homme, R. K.; Kevrekidis, I. G.; Panagiotopoulos, A. Z. Coarse-Grained Simulations of Rapid Assembly Kinetics for Polystyrene-bpoly(ethylene oxide) Copolymers in Aqueous Solutions. J. Phys. Chem. B 2008, 112, 16357–16366. (46) Spaeth, J. R.; Kevrekidis, I. G.; Panagiotopoulos, A. Z. A Comparison of Implicit- and Explicit-Solvent Simulations of Self-assembly in Block Copolymer and Solute Systems. J. Chem. Phys. 2011, 134, 164902–164913. (47) Polson, J. M.; Moore, N. Simulation Study of the Coil-globule Transition of a Polymer in Solvent. J. Chem. Phys. 2005, 122, 024905. (48) Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids. J. Chem. Phys. 1971, 54, 5237–5247. (49) Everaers, R.; Ejtehadi, M. R. Interaction Potentials for Soft and Hard Ellipsoids. Phys. Rev. E 2003, 67, 041710. (50) Visser, J. On Hamaker constants: A comparison between Hamaker constants and Lifshitz-van der Waals constants. Adv. Colloid Interface Sci. 1972, 3, 331 – 363. (51) Yukawa, H. On the Interaction of Elementary Particles. Proc. Phys. Math. Soc. Japan. 1935, 17, 48–57. (52) http://codeblue.umich.edu/hoomd-blue. (53) Anderson, J. A.; Lorenz, C. D.; Travesset, A. General Purpose Molecular Dynamics Simulations Fully Implemented on Graphics Processing Units. J. Comput. Phys. 2008, 227, 5342–5359. (54) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graph. 1996, 14, 33 – 38.

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Page 32 of 44

Page 33 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Solvent

Non-solvent

Polymers Nanoparticles

33


Langmuir

HNP-P (10-19 J)

6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Page 34 of 44

(III)

4

(I) 2

(IV)

(II)

0 0

2

4 HNP-S (10-19 J)


6

Page 35 of 44

fNP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.0 2.8E-19 J 3.2E-19 J 4.9E-19 J 0.8 6.5E-19 J

Langmuir

0.6 0.4 0.2 0.0 0

2ACS Paragon 4Plus Environment 6 -19 HNP-P (10 J)

8

Langmuir

SNP (nm-2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Page 36 of 44

2.8E-19 J 3.2E-19 J 4.9E-19 J 6.5E-19 J

0.050

0.025

0.000 0


2

4 6 HNP-P (10-19 J)

8

Page 37 of 44

Langmuir

1.6

1.4

α

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.2

1.0 0

2 ACS Paragon 4 Plus Environment 6 -19 HNP-P (10 J)

8

(a)

Langmuir

0.10 -2

S NP (nm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Page 38 of 44

0.05

NPs on surface NPs at interior 0.00 0.0

0.5

1.0

HP-S (10

-19

J)

fi

(b) 0.8

NPs on surface NPs in interior

0.6 0.4 0.2 0.0 0.4

0.8 1.2 -19 HA-B (10 J)

(c)


1.6

Page 39 of 44

(a)

0.8 fNP

2.4E-19 J 2.8E-19 J 3.2E-19 J

1.2E-19 J 1.6E-19 J 2.0E-19 J

1.0

0.6 0.4 0.2 0.0 0.0000

0.0004

0.0008

0.0012

-3

Φ NP (nm )

(b)

1.0 0.8

1.2E-19 J 1.6E-19 J 2.0E-19 J

2.4E-19 J 2.8E-19 J 3.2E-19 J

0.6 fNP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

0.4 0.2 0.0 0.0000

0.0004


-3

0.0008

Φ P (nm )

0.0012

-0.1

∆G (10-19 J)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Langmuir

Figure 6(a) Figure 6(b)

Page 40 of 44

-0.2

-0.3

1.0

1.5 ACS Paragon 2.0 Plus Environment 2.5 3.0 -19 HNP-P (10 J)

3.5

(a) 0.15 Page 41 of 44 S NP (nm-2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

S NP (nm-2)

(b)

5.6E-19 J 6.5E-19 J 8.1E-19 J

Langmuir

0.10

0.05

0.00 0.0

0.1

0.2

0.3

0.4

0.5

0.4

0.5

fv 0.15

5.6E-19 J 6.5E-19 J 8.1E-19 J

0.10

0.05

0.00 0.0


0.1

0.2

0.3

fv-fv,0

(a) 1 2 3 4 5 6

Langmuir

(b)

Page 42 of 44

-19

-19 HNP-A = 3.2×10 ACS J Paragon Plus Environment HNP-A = 6.5×10 J -20 HNP-B = 4.1×10-20 J HNP-B = 4.1×10 J -19 HNP-S = 3.2×10-19 J HNP-S = 3.2×10 J

(a)

Page 431.0 of 44

Uncharged Charged

0.8 0.6

fNP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Langmuir

0.4 0.2 0.0 0

2

4

6 HNP-P (10-19 J)

Uncharged Charged

0.03

-2

S NP (nm )

(b) 0.04

8

0.02 0.01 0.00 0


2

4

HNP-P (10

-19

6

J)

8

Constants B

1 2 C 3 4 5 k-1/k+1 6 7

Fitted valuesLangmuir

Estimated values Page 44 of 44 4

5.5 ± 0.5 1/3

(6.2 ± 0.6)/V

1/3

6/V

Paragon Plus Environment < 1, decreases with 0.0005 toACS 0.1, decreases increasingH NP-P with increasingH NP-P

Self-assembly of polymer blends and nanoparticles through rapid

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