Article pubs.acs.org/Langmuir
Formation and Degradation of Multicomponent Multicore Micelles: Insights from Dissipative Particle Dynamics Simulations Houyang Chen* and Eli Ruckenstein* Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, New York 14260-4200, United States S Supporting Information *
ABSTRACT: Dissipative particle dynamics (DPD) simulation is employed to examine (i) the multicomponent multicore micelle (MMM) formation from two kinds of star-shaped copolymers: A2B4B4 and C2B4B4 where A, B, and C are the segments of the copolymers and (ii) the degradation of multicomponent multicore micelles. Regarding the micelle formation, single-core micelles with the core composed of two components (SCII), multicomponent multicore micelles with each core composed of two components (MMII), multicomponent multicore micelles with each of the cores composed of one component (MMI), and multicomponent multicore rod micelles (MMRI) are considered. By changing the ratio between the number of segments of one of the polymers and the total number of segments of the two copolymers, the number of cores generated and their composition can be controlled. Considering that only C2B4B4 is degraded to 2C1 + 2B4, it was found that SCII, MMII, and MMI micelles degraded to a single irregular network core, to multicores with cores formed of loose aggregates, and to multicore micelles, respectively. The dynamics of micelle formation has several stages (small aggregates (nuclei) → growth of aggregates → micellization) whereas the dynamics of degradation involves the diffusion of the degraded components inside and outside micelles and the rearrangement of the cores of the micelles into new cores. recently reported.13 By preparing micelles from blends of two kinds of block copolymers, one can better control the degradation process and the drug-delivery process. For instance, one can degrade only one of the block copolymers of the micelle, and thus the micelle is partially degraded or disassembled. Wang et al.14 prepared spherical aggregates by combining a double-hydrophilic block copolymer with an enzyme-responsive molecule. The aggregates disassemble as a result of the enzymatic hydrolysis of the enzyme-responsive molecule. Although multicore micelles have been identified by the above research groups, the formation mechanism and degradation mechanism of multicomponent multicore micelles still constitute a challenging topic. In this Article, we examine the formation and degradation of multicomponent multicore micelles and suggest possible mechanisms.
1. INTRODUCTION Micelles are important structures because of their broad applications in drug delivery,1−3 as drag-reducing agents,4 in pharmaceutical applications,5 and in gene delivery.6,7 Recently, a new kind of micellemulticore micelleswas reported.8−12 A multicore micelle is a micelle containing several cores, and a multicomponent multicore micelle (MMM) is a multicore micelle with each core composed of several components. Duxin et al.8 prepared multicore micelles from the triblock poly(ethylene oxide)-b-polystyrene-b-poly(acrylic acid). Iatridi and Tsitsilianis,9 using multiarm star-shaped terpolymer-containing nine polystyrene arms and nine poly(2-vinyl-pyridine)-bpoly(acrylic acid) arms, identified various multicore micelles when the pH was changed. Ueda et al.10 reported the formation of multicore micelles from sodium maleate and dodecyl vinyl ether copolymers and investigated the unicore−multicore micelle transition. Using self-consistent field theory, Wang and Lin11 examined the multicore micelle formation from the linear ABC terpolymers containing a solvophilic midblock and two mutually incompatible solvophobic headgroups. By employing dissipative particle dynamics simulations, our group12 examined the multicore micelle formation from a star-shaped copolymer by changing the latter and the solvent. In addition, the mechanisms of multicore micelle formation were suggested.12 Micelle degradation is important in the release of therapeutic drugs. A review regarding the block copolymer degradation was © 2013 American Chemical Society
2. SIMULATION METHOD AND MODEL In the dissipative particle dynamics15,16 method, the force f i acting on a DPD particle i is the sum of the conservative force FCij , the dissipative force FDij , the random force FRij , and the spring force FSi,β, Received: January 4, 2013 Revised: April 9, 2013 Published: April 11, 2013 5428
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Figure 1. Phase diagram of self-assembled aggregates formed from a blend of two star copolymers (two three-arms A2B4B4 and C2B4B4(φ = 0.5)) as a function of interaction parameters εAC and εAB. The other interaction parameters are fixed and listed in section 2 of the paper. (Circles) Single -core micelles with a core composed of A and C segments (SCII); (squares) multicomponent multicore micelles with cores formed of either A or C segments (MMI); (triangles) multicomponent multicore micelles with the cores formed of A and C segments (MMII); (stars) multicomponent multicore rod micelles with cores formed of either A or C segments (MMRI). The morphologies of micelles, MMII (a1, a2), SCII (b), MMRI (c), and MMI (d1, d2), are also presented. a1 and d1 present both the shell and the core of the micelles, whereas a2 and d2 present only the cores of the micelles. For the morphologies, green (white in the black/white version): A segments; red (gray in the black/white version): B segments; blue (black in the black/white version): C segments.
fi =
∑ (FCij + FijD + FijR ) + ∑ FSi ,β j≠i
between the solvophobic A and C segments on the formation and degradation of multicomponent multicore micelle, the repulsive interaction parameters εAB and εAC were varied between 30 and 90. For the other repulsive interaction parameters εij, the following values were selected: εAA = εBB = εCC = εSS = 25, εAS = εCS = 60 (because the A and C segments are solvophobic), εBS = 30 (because the B segment is solvophilic), and εBC = 90 (because the B segment is solvophilic and the C segment is solvophobic). For ρ = 3, a relationship between the Flory−Huggins parameter and the repulsion parameter was proposed by Groot.17 It has the form εij ≈ εii + 3.27χij, where εii = εjj. The simulations were performed using a (24rc)3 simulation box. The simulation has two stages: micelle formation and micelle degradation. In the former, two kinds of polymers, namely, A2B4B4 and C2B4B4, are assembled in a solvent and subjected to 106 DPD time steps; in the latter, copolymer C2B4B4 is degraded into two C1segments and two B4 blocks, whereas A2B4B4 remains unchanged. The initial configuration of the micelle degradation process is provided by the final time step of the micelle formation process; an additional 2 × 106 DPD time steps were employed to follow the micelle degradation process. To verify the reproducibility of our simulations, we selected three initial configurations for each micelle formation, and similar final configurations were obtained. One case is presented in Figure S2 in the Supporting Information.
(1)
with ⎧ rij < rc ⎪ εij(1 − rij / rc)riĵ FCij = ⎨ ⎪ rij ≥ rc 0 ⎩
(2)
FijD = −γωD(rij)(riĵ ·vij)riĵ
(3)
FijR = σωR (rij)ζijΔt −1/2 riĵ
(4)
where εij, rij, r̂ij, rc, and vij are the maximum repulsive interaction between the i and j DPD particles, the distance between two particles, the unit vector of the distance between two particles, the cutoff radius, and the relative velocity, respectively. In addition, γ is a friction coefficient, σ is the noise amplitude, Δt is the time step provided by Δt = 0.04τ (τ = (mrc2/kBT)1/2 where kB is the Boltzmann constant, T is the absolute temperature, m is the DPD particle mass), ζij is a random number of zero mean and unit variances, and ωD and ωR are weight functions, which can be found in ref 15. Following ref 15, we have taken σ = 3 and γ = (4.5)/(kBT). In addition, two neighboring segments of the polymer chain are connected through the bonding force FSi,β = −αri,β15 with α = 4. A modified velocity-Verlet algorithm with λ = 0.65 was employed in the integration of the equations of motion.15 All simulations were performed with a DPD simulation code that was developed inhouse. In the present simulation, a blend containing two three-arm star-shaped polymers A2B4B4 and C2B4B4 (Figure S1 in Supporting Information) as well as a solvent are considered. The A and C segments are solvophobic, whereas the B segment is solvophilic. The fraction of polymer segments (the ratio between the number of polymer segments and the number of polymer segments plus solvent (S)) was selected to be 0.1. In the polymer blend, the ratio between the number of segments in A2B4B4 over the total number of segments in both A2B4B4 and C2B4B4 is denoted as φ. The total number density of all DPD particles is 3 per rc3. The cutoff rc radius, the bead (DPD particle) mass m as well as the energy kBT are taken as the units. In order to examine the effects of the interactions between the solvophobic A and solvophilic B segments and
3. RESULTS AND DISCUSSIONS 3.1. Multicomponent Multicore Micelle Formation and Their Formation Mechanisms. Figure 1 presents the phase diagram of the self-assembled aggregates of the two star copolymers as a function of interaction parameters εAC and εAB for fixed values of the other interaction parameters listed in section 2. Four kinds of micelles are generated: single core with the core composed of A and C segments (SCII), multicomponent multicore with the cores composed of either A or C segments(MMI), multicomponent multicore with cores composed of A and C segments (MMII), and multicomponent multicore rod micelles with cores formed of either A or C segments (MMRI). This figure shows that (i) SCII micelles are formed when the repulsion between A and B segments is weak, regardless of whether the repulsion between A and C is weak or 5429
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Figure 2. Pathways for MMI generation in a solvent from A2B4B4 and C2B4B4 for (a) εAB = 80, εAC = 90, and φ = 0.5 (φ is the ratio between the number of segments of A2B4B4 and the sum of the number of segments of A2B4B4 and C2B4B4); (b) εAB = 50, εAC = 40, and φ = 0.5. t* = 104 DPD time steps. Green (white in the black/white version): A segments; red (gray in the black/white version): B segments; blue (black in the black/white version): C segments.
MMII micelles are generated. For strong repulsion εAC and weak repulsion εAB, the A and C segments tend to separate because of strong repulsion εAC; however, the weak repulsion εAB and the chain connectivity between A and B segments result in a weak separation between A and B domains. The weak separation between A and B domains causes the C domains to be surrounded by A domains (C domains are always surrounded by B domains) and generates a network-like single core micelle. Here, we emphasize that the single core micelles generated at strong εAC are not a normal compact single core micelles. From the phase diagram of Figure 1, one can conclude that a morphology transition from single-core to multicore micelles occurs by increasing the repulsion εAB. The number of micelles remains the same when this transition occurs, indicating that the number of solvophobic segments in each core becomes smaller. The results regarding both the morphology transition and the size of the cores are in agreement with experimental results.10 Figure 2 presents two dynamic processes of MMI formation. In all cases presented in the micelle formation section, the initial configuration was a homogeneously distributed polymer blend in the simulation box. In the first, because of the solvophobicity of the A and C segments, small aggregates are formed after about 0.05t* (with t* = 104 DPD time steps) (Figure 2a1). Later, the small aggregates grow into larger MMI micelles possessing solvophobic patches (Figure 2a2,a2′) . Finally, stable MMI micelles are generated (Figure 2a3,a4). The second one undergoes the following stages: small aggregates (Figure 2b1), small MMM and single Janus core micelles (Figure 2b2), and finally MMI (Figure 2b3,b4). The single Janus core micelle of Figure 2b2 is formed because the interaction εAC is moderate. A sufficiently strong repulsion will separate the A and C segments completely, and a weak one will stimulate their mixing. It should be emphasized that the number of DPD steps 100t* employed in our simulations is large enough to achieve equilibrium for micelle formation. In Figure 3, the number of aggregates of the polymer blends Nagg (an aggregate of polymer blends contains at least two polymer chains), their size Sagg (the average number of segments in the aggregates), the number of aggregates of the solvophobic segments Ncore (an aggregates of solvophobic segments contains at least two solvophobic blocks), and their
strong; (ii) MMII micelles involve a weak repulsion between A and C segments and a moderate repulsion between A and B segments; and (iii) the MMI micelles require a strong repulsion between A and B segments and a strong repulsion between A and C segments. For MMI micelles, the total number of cores is between 8 and 11 for εAB = 40 and between 6 and 8 for εAB between 50 and 90. The numbers of A and C cores in MMI micelles can be controlled by varying φ. The number of A cores increases from 1 at φ = 0.1 to 5 (or 6 in some cases) at φ = 0.9, whereas the number of C cores decreases from 5 (6 in some cases) at φ = 0.1 to 1 at φ = 0.9. The morphologies of the micelles are also listed around the phase diagram. Figure 1a presents an MMII micelle that possesses six cores composed of both A and C segments. In some cores, the A and C segments are well-separated and exhibit Janus structures. Figure 1b (SCII micelles) shows that A and C segments generate the core of SCII micelles, whereas the B segments build their shell. In some cases, in the cores of SCII micelles, A and C segments are mixed at random, but in other cases, the cores possess A-rich and/or C-rich domains. Such structures have been identified before.18−22 Figure 1c presents an MMRI micelle possessing one A and six C cores. In Figure 1d1,d2, there are also six cores, three containing A segments and the other three containing C segments. Figure 1d2 shows that the six cores possess an octahedral structure. To examine the structures of multicomponent multicore micelles in more detail, the density profiles of the above morphologies are plotted in Figure S3 in the Supporting Information. The three peaks of the C segments in Figure S3d reflect the three C cores of the micelle (Figure 1d) that are located in the d direction, whereas the one peak of the A segment reflects the single A core of the micelle because the three A cores are located normal to the d direction. A similar situation arises with the MMRI micelles (Figure S3c). The above micelles are formed because of the solvophobicity of the A and C segments and the solvophilicity of B segments as well as the chain connectivity between A and B. For weak repulsions εAC and εAB, cores containing both A and C segments are formed and thus SCII micelles are generated. For sufficiently strong repulsions εAC and εAB, A and C aggregates are formed separately inside the micelles and cores containing either A or C are formed, thus generating MMI and MMRI micelles. For weak repulsion εAC and strong repulsion εAB, 5430
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Figure 5 presents two pathways for SCII micelle generation. The first one starts from small aggregates of the copolymer
Figure 3. Number of aggregates of the polymer blends (Nagg), their size (Sagg), number of aggregates of the solvophobic segments (Ncore), and their size (Score) as functions of the DPD time steps (tDPD) for εAB = 80, εAC = 90, and φ = 0.5.
size Score (the average number of solvophobic segments in the aggregates) are plotted as functions of DPD time steps, tDPD, for εAB = 80, εAC = 90, and φ = 0.5. As the number of DPD time steps increases, Nagg and Ncore decrease but Sagg and Score increase. For a sufficiently large number of DPD time steps, almost all polymer segments aggregate into a single aggregate and the solvophobic segments generate several solvophobic aggregates. Combining Figures 2 and 3, one can conclude that a multicomponent multicore micelle is generated. Figure 4 presents two pathways for MMII formation in a solvent from the two copolymer blends. In the first one, the
Figure 5. Pathways for SCII generation in a solvent from A2B4B4 and C2B4B4 for (a) εAB = 30, εAC = 30, and φ = 0.1 and (b) εAB = 30, εAC = 40, and φ = 0.3. t* = 104 DPD time steps. Green (white in the black/ white version): A segments; red (gray in the black/white version): B segments; blue (black in the black/white version): C segments.
blend (Figure 5a1), which grow into small single-core micelles that form large aggregates (Figure 5a2,a3), and they finally generate stable SCII (Figure 5a4). The second one starts from small aggregates (Figure 5b1), followed by single-core and multicore micelles (Figure 5b2) and finally by a stable SCII micelle (Figure 5b3). In the case of SCII micelles, there are Arich and C-rich domains. Although no stable single Janus core micelle was identified in our simulation, it is likely that a moderate repulsion εAC can provide a Janus core micelle. Using scaling theory, Janus core micelles generated from a threemiktoarm ABC copolymer were predicted by Zhulina and Borisov.23 Figure S6 in Supporting Information provides the number of aggregates of the polymer blends (Nagg) and their size (Sagg) as functions of DPD time steps (tDPD) for the cases presented in Figure 5. The data from Figure S6 provides quantitative information regarding the SCII micelle generation. 3.2. Degradation Mechanisms of Multicomponent, Multicore Micelles. The degrading of micelles constitutes an important step in the release of stored drugs. The micelle degradation is examined in a particular case, namely, when only C2B4B4 is degraded into two C1 segments and two B4 polymers. In Wang’s research,14 which involves an enzyme-responsive molecule, the aggregates generated from two polymers disassemble under the action of an enzyme. In the present study, the aggregates (formed also from two copolymers) are degraded by degrading only one of the copolymers. This process may provide useful information regarding the drug release from multidrug-loading micelles. Figure 6 presents the phase diagram of the nanostructures resulting from degrading the nanostructures of Figure 1. Three kinds of micelles are formed: a single irregular network core micelle (SIN), a multicore micelle (MM), and a multicore micelle with cores composed of loose aggregates (MML). Comparing Figure 6 with Figure 1, one can conclude that SCII micelles are degraded to SIN micelles and MMI and MMII micelles are degraded into multicore micelles and MML, respectively. The morphologies of the above three kinds of micelles are presented in Figure 6. Figure 6a presents MML
Figure 4. Pathways for MMII generation in a solvent from A2B4B4 and C2B4B4 for (a) εAB = 50, εAC = 30, and φ = 0.5 and (b) εAB = 90, εAC = 30, and φ = 0.5. t* = 104 DPD time steps. Green (white in the black/ white version): A segments; red (gray in the black/white version): B segments; blue (black in the black/white version): C segments.
stages are small aggregates (Figure 4a1), small MMM and single Janus core micelles (Figure 4a2), and finally stable MMII (Figure 4a3). In the other one, the stages are small aggregates (Figure 4b1), MMII with solvophobic patches (Figure 4b2,b3), and finally stable MMII (Figure 4b4). It should be mentioned that, compared to MMI micelles, the repulsion εAC that provides MMII micelles is weaker than that for MMI. Figure S5 from Supporting Information plots the number of aggregates of the polymer blends (Nagg), their size (Sagg), the number of aggregates of the solvophobic segments (Ncore), and their size (Score) as functions of DPD time steps (tDPD) for the cases presented in Figure 4. The results from Figure S5 confirm the conclusions from Figure 4. The time dependence provides detailed information regarding the micelles and multicores generated. However, they could not distinguish MMI and MMII. 5431
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Figure 6. Phase diagram of the nanostructures degraded from the nanostructures of Figure 1. (Circle) A single irregular network core micelle (SIN); (square) multicore micelles (MM); (triangle) multicore micelles with cores composed of loose aggregates (MML). The morphologies of MML (a1, a2), SIN (b1, b2), and MM (c) are also presented. a1 and b1 present both the shell and the core of the micelles, whereas a2 and b2 present only the cores of the micelles. For the morphologies, green (white in the black/white version): A segments; red (gray in the black/white version): B segments.
Figure 7. Pathways of multicomponent multicore micelles MMI degraded into multicore micelles. (a) εAB = 50, εAC = 60, and φ = 0.5; (b) εAB = 70, εAC = 60, and φ = 0.5; and (c) εAB = 90, εAC = 70, and φ = 0.5. t* = 104 DPD time steps. Green (white in the black/white version): A segments; red (gray in the black/white version): B segments; blue (black in the black/white version): C segments.
micelles, and the core (or cores) inside the MML micelles possesses a loose structure. Figure 6b presents an SIN micelle possessing some B segments located inside a network-shaped core. In addition, the degrading of C cores generates C segments that are distributed randomly inside the micelle and in the solvent. Figure 6c presents multicore micelles with cores composed of one component. To examine these structures in a more quantitative way, Figure S4 in the Supporting Information plots the density profiles of multicomponent multicore micelles after degrading. The profiles with a peak in the B segment shown in Figures S4a−c represent the shells of MML micelles (Figure S4a), of SIN micelles (Figure S4b), and of multicore micelles (Figure S4c), respectively. In Figure S4b, the broad, low peaks of the A segment are due to the irregular network core inside the SIN micelles, whereas the low peaks of the A segments in Figure S4a,c are due to the cores inside the multicore micelles.
Figure 7 shows three pathways for MMI degradation into regular multicore micelles. Generally, the segments resulting from the degraded cores diffuse inside the micelles and later into the solvent. The nondegraded cores remain unchanged or change the number of cores (increasing or decreasing their number). During the first pathway, the degrading process starts from a stable MMI possessing three cores composed of A segments and three cores containing C segments (Figure 7a1). The C segments resulting from the C core (the degradable cores) diffuse into the micelles (Figure 7a2) and later into the solvent (Figure 7a3); after about 4t*, a fourth A core is generated (Figure 7a4,a4′), and the system achieves equilibrium in about 15t* (Figure 7a5). The second pathway starts from a stable MMI possessing three A segment cores and three C segment cores (Figure 7b1). The C segments resulted from the degraded cores diffusing into the micelles (Figure 7b2) and later into the solvent (Figure 7b3), and finally a stable multicore 5432
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kinds of multicomponent multicore micelles, SCII, MMII, MMI, and MMRI, are identified. SCII micelles are formed when the repulsion between the A and B segments is weak, regardless of whether the repulsion between A and C is weak or strong, whereas MMII micelles involve a weak repulsion between A and C segments and a moderate repulsion between A and B segments. The MMI micelles are generated when the repulsive interactions between A and B segments and between A and C segments are sufficiently strong. The number of cores composed of different components can be controlled by varying the ratio of polymers in the polymer blend. During the degradation of micelles, it was found that the SCII micelles degraded to SIN micelles, MMII micelles degraded to MML micelles, and MMI micelles degraded to regular multicore micelles. The formation and degradation mechanisms are examined in some detail. The mechanism for micelle formation contains the stages small aggregates → growth → micellization whereas the mechanism of degradation contains the stages of formation of segments and their diffusion, followed by the rearrangement of the cores.
micelle with three A cores is generated (Figure 7b4). During this pathway, the number of cores composed of A segments (nondegradable cores) remains the same. The third pathway undergoes the following stages: an initial stable MMI possessing three A segment cores and three C segment cores (Figure 7c1), diffusion of the segments resulting from the degraded cores into the micelles (Figure 7c2) and later into the solvent (Figure 7c3), and at about 2t*, the decrease in the number of surviving cores from three to two (Figure 7c4). The dynamic process regarding the change in the number of A cores and the number of polymer blends in Figure 7 is presented in Figures S7 and S8 of the Supporting Information. The fluctuations of Sagg occur (Figure S8) because the degraded C segments aggregate, generating small unstable aggregates. Figure 8 shows the pathway of degradation of SCII micelles into single-core micelles (SIN). The pathway starts from a
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ASSOCIATED CONTENT
S Supporting Information *
A schematic of two star-shaped copolymers, a figure for a reproducible test, density profiles of multicomponent multicore micelles, density profiles of multicore micelles degraded from multicomponent multicore micelles, number of aggregates of the polymer blends and their size as functions of DPD time steps, number of aggregates of the solvophobic segments and their size as functions of the DPD time steps, and number of aggregates for A solvophobic segments and their size as functions of DPD time steps. This material is available free of charge via the Internet at http://pubs.acs.org.
Figure 8. Pathways of SCII micelles degraded into SIN micelles for εAB = 30, εAC = 60, and φ = 0.5. t* = 104 DPD time steps. Green (white in the black/white version): A segments; red (gray in the black/white version): B segments; blue (black in the black/white version): C segments.
stable SCII micelle (Figure 8a1). The segments resulted from degradation diffuse in the micelle (Figure 8a2) and later in the solvent (Figure 8a3). After 1t*, the system achieves equilibrium and the C segments are distributed randomly in both the solvent and micelles (Figure 8a4). Figure S9 in the Supporting Information provides more detailed quantitative results than Figure 8. Figure 9 presents the stages of MML formation. The pathway starts from a stable MMII micelle. The segments resulted from degradation diffuse in the micelles (Figure 9a2) and later in the solvent (Figure 9a3), and the A core rearranges whereas the C core degrades and diffuses (Figure 9a4,a4′). Finally, a stable MML micelle is generated (Figure 9a5). Figure S10 in the Supporting Information provides more detailed quantitative information than Figure 9
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AUTHOR INFORMATION
Corresponding Author
*Tel: +1 716 645 1179. Fax: +1 716 645 3822. E-mail: hchen23@buffalo.edu (H.C.); feaeliru@buffalo.edu (E.R.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the Center for Computational Research at the State University of New York at Buffalo for the computer time provided. We are grateful for financial support from the State University of New York at Buffalo. H.C. is also grateful for financial support from the National Natural Science Foundation of China (no. 21206049).
4. CONCLUSIONS By employing dissipative particle dynamics simulations, the formation and degradation of multicomponent multicore micelles are examined, and their dynamics follow. Several
Figure 9. Pathways of MMII micelles degraded into MML micelles for εAB = 60, εAC = 30, and φ = 0.5. t* = 104 DPD time steps. Green (white in the black/white version): A segments; red (gray in the black/white version): B segments; blue (black in the black/white version): C segments. 5433
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dx.doi.org/10.1021/la400033s | Langmuir 2013, 29, 5428−5434
