Co-Micellization Behavior in Poloxamers: Dissipative Particle

Article pubs.acs.org/JPCB

Co-Micellization Behavior in Poloxamers: Dissipative Particle Dynamics Study Ammu Prhashanna, Saif A. Khan, and Shing Bor Chen* Department of Chemical and Biomolecular Engineering National University of Singapore, Singapore 117585 S Supporting Information *

ABSTRACT: Dissipative particle dynamics simulations are applied to investigate comicellization behavior for binary mixtures of Poloxamers in dilute aqueous solution. In view of block length similarity/dissimilarity, four representative mixture cases are considered: F127/P123, F127/P105, P123/P84, and F127/L64. With appropriate interaction parameters, the simulations enable us to examine the formation of micelles, their types, size, shape, and composition. In the investigated concentration range, we find that pure and mixed micelles, both ellipsoidal, always coexist for all cases. At similar concentrations, both species form pure micelles of their own together with mixed micelles. In the case of F127/L64, it is found that the L64 chains are involved in the mixed micelles, even when the L64 concentration is below its CMC. The fraction of L64 involved in the mixed micelles is lower as compared to the other systems studied. For all cases, the proportion of mixed micelles can be increased when the two polymer species have similar concentrations. Moreover, shorter chains may prefer to straddle the core and corona in the region of ellipsoidal interface that is closer to the center of mixed micelle.

1. INTRODUCTION The majority of pharmaceutical drugs are hydrophobic in nature1 and require a carrier for their transport inside the body. Polymeric micelles (PM) formed via the self-assembly of block copolymers have been explored for drug delivery purposes.2 They possess the advantage of meeting the basic properties required for a nano drug delivery system:2 (1) biocompatible and hydrophilic block of copolymer enveloping the drug-loaded core allows for prolonged circulation of water-insoluble drug in the blood until it reaches the target site; (2) PMs have suitable size with a narrow distribution preventing rapid renal excretion and thus allowing accumulation into tumor tissues via the enhanced permeation and retention (EPR) effect after intravenous injection. PMs comprising a single species of block copolymer have been extensively studied over the years. Recently, the focus has been shifted to PMs from two or more dissimilar block copolymers as a direct, convenient approach to improve physical stability and enhance drug loading capacities.3 Mixed micelles fabricated from chemically diverse amphiphilic block copolymers have been employed in various situations, rendering significant improvements in thermodynamic (by lowering CMC)4 and kinetic stability,5 and drug loading,6,7 as well as ease of incorporating multiple functionalities (e.g., for stimuli-responsive drug release and cellular targeting).8 PEG-based block copolymers are widely used for biomedicine applications because of the biocompatible and water loving properties of PEG. Among these polymers, Poloxamer (commonly known by trade name as Pluronic), a triblock copolymer of poly(ethylene oxide) and poly(propylene oxide), is commercially available and thus popular. A series of Pluronic © 2014 American Chemical Society

can be manufactured by varying the polymer block lengths. These Pluronic species are named conventionally by a letter followed by 2 or 3 digits. The letter indicates the physical form at room temperature (P = Paste; L = Liquid; or F = Flake). The last digit multiplied by 10 gives the percentage poly(ethylene oxide) content. The remaining digit(s) in the numerical designation, multiplied by 300, represents the approximate molar mass of poly(propylene oxide). PMs from mixtures of Pluronics have been reported in the literature to be more robust as compared to PMs comprising a single species.9−15 These exploratory works include the formation of PMs of binary mixture of Pluronics using a thin film evaporation method9,10,12,13 or a direct dissolution method.11,14,15 PMs were characterized using DLS,14 rheometry, and SAXS,15 and other techniques16,17 to investigate drug loading and carrier size distribution. For binary mixtures, a bimodal distribution may signal separate micellization into two families rather than comicellization into mixed micelles. However, this size-based method may not have sufficient resolution to discern similarsized pure micelles of individual species, thereby yielding a unimodal distribution instead. The same difficulty could arise for coexisting mixed and pure micelles. Borovinskii and Khokhlov18 developed a theory based on free energy calculations for micelle formation with two diblock copolymers with equal hydrophilic block length but different hydrophobic block lengths in dilute solution. In this study, only copolymers with the hydrophilic block much longer than the Received: September 12, 2014 Revised: December 2, 2014 Published: December 18, 2014 572

DOI: 10.1021/jp509237r J. Phys. Chem. B 2015, 119, 572−582

Article

The Journal of Physical Chemistry B

where Fi is the total force acting on particle i with mass mi and position vector ri. The interparticle force Fij exerted on particle i by particle j is a combination of conservative, dissipative, and random forces

hydrophobic block were considered. Their prediction found that the longer block copolymer formed micelles first, which could incorporate the shorter chains at concentrations even below their CMC. A wide region was identified in the phase diagram where mixed micelles coexist with pure micelles made of shorter copolymers. At high enough concentrations, only mixed micelles can form if the hydrophobic block lengths of the two species do not differ much. Honda et al.19 investigated co-micellization behavior by means of dynamic and static light scattering for binary mixtures of block copolymers with different block lengths. They observed the formation of both pure and mixed micelles in the temperature range just below the critical micelle temperature of the shorter block copolymer. Esselink et al.20 also demonstrated through the free energy calculations that mixed and pure micelles can coexist in dilute solutions of binary mixture of diblock copolymers, and validated it experimentally for diblock copolymers with varying core forming block length. Furthermore, their theoretical analysis found that all types of micelles, i.e., mixed micelles and pure micelles from both larger and smaller block copolymers can be present at equilibrium. However, they were not able to observe the same in their experiments. Conflicting observations are also reported in the literature. Recently, Bourov and Bhattacharya21 worked on the co-micellization of diblock surfactant molecules with varying hydrophilic blocks, while Hafezi and Sharif22 studied diblock copolymers with varying hydrophobic blocks using Brownian Dynamics (BD) simulations. Both studies observed only a single family of micelles (mixed micelles) within the investigated ranges. To proceed further in enhancing the properties of micelles by means of the co-micellization process, it is important to gain a better understanding of the self-assembly process. In this study, we focus on Pluronics for two reasons: (1) they are commercially available and commonly used in many applications; (2) they are triblock copolymers that are much less studied computationally than diblock copolymers. To investigate the micellization phenomenon in binary mixture of Pluronics at the microscopic level would not be as easy via experimental approaches due to their time and length scales. Mesoscopic simulations turn out to be a suitable, useful tool to provide valuable insights and hopefully clear discrepancies, because of their capability to handle a wide variety of length and time scales. Herein, dissipative particle dynamics (DPD) is used to investigate the co-micellization behavior of binary mixture of Pluronics and the properties of the formed micelles.

Fi =

with FCij = aijwc(rij) riĵ

(3)

FijD = −γijwD(rij)( rijV ̂ ) riĵ

(4)

FijR =

σijθij Δt

wR (rij) riĵ

(5)

where rij is the separation distance between particles i and j; wc, wD, and wR are distance dependent weight functions; aij, γij, and σij are the coefficients of conservative, dissipative, and random forces respectively; θij is the random variable with zero mean and unit variance; riĵ is the unit vector directed from particle j to particle i; V is the velocity of particle i relative to particle j; Δt is the time step. The particles termed also as beads can interact with their neighbors only within the cutoff distance rc. The weighing functions are normally related to one another as r wc(r ) = wD(r ) = [wR (r )]1/2 = 1 − rc (6) Applying the fluctuation−dissipation theorem to DPD, Espanol and Warren26 showed that the coefficients of dissipative and random forces are inter-related as σij = (2γijkBT)1/2 with kBT being the thermal energy. Furthermore, every two neighboring beads in a polymer chain are connected to each other with a harmonic bonds represented by Fsij = −Krij riĵ with K being the spring constant. The above set of equations are integrated in LAMMPS27 by adopting a NVT ensemble.

3. SIMULATION DETAILS The coarse-graining of the polymer required for the DPD simulations is done as described by van Vlimmeren et al.28 The relationship between the atomistic chains and Gaussian chains for Pluronics is given as X /x = 4.3

Y /y = 3.3

(7)

where X and Y refer to the numbers of EO and PO monomers, while x and y are the corresponding numbers of coarse-graining beads in topology. Based on the relationship, the coarse-grained topologies for F127, L64, P123, P84, and P105 are constructed as A 23 B 21 A 23 , A 3 B 9 A 3 , A 5 B 21 A 5 , A 5 B 13 A 5 , and A 9 B 18 A 9 , respectively, with A representing an EO bead and B representing a PO bead. The polymer concentration is described by the number ratio of polymer beads to total beads with φ denoting the total polymer concentration, and φi the concentration of each species (i = 64, 84, 105, 123, or 127). For each binary polymer mixture, φH and φL represent the concentrations of higher and lower molecular weight polymers, respectively. We set rC = 1 and KBT = 1 and implement the periodic boundary condition over the domain to replicate the bulk solution in the problem definition. To avoid the box-size effect on the micellar structure and the properties,29 we varied the box size and found that side length of 30 is sufficient and will be

d2ri dt 2

(2)

i≠j

2. SIMULATION METHODOLOGY The co-micellization of Pluronics is studied for four different binary mixtures: F127/P123 representing the case with similar PPO blocks, P123/P84 with similar PEO blocks, F127/L64 and F127/P105 with both dissimilar PEO and PPO blocks (the former with large dissimilarity, and the latter with small dissimilarity). DPD simulations, a particle based coarse-grained methodology23 with the advantage of conserving momentum, was first proposed by Hoogerbrooke and Koelman.24 In this study, the terminology mentioned by Groot and Warren25 is used. Similar to MD simulations, DPD simulations follows Newton’s second law of motion Fi = mi

∑ FCij + FijD + FijR

(1) 573


Article

The Journal of Physical Chemistry B used in this study (see Figure S1 in the Supporting Information). In each case, a prescribed amount of chains are added to the simulation box that is then filled with water beads to maintain the total bead number density of 3. For the random and spring forces, we take σij = 3.0 and K = 4.0 from the literature.30 The coefficient of conservative force can be obtained using Flory−Huggins theory31 with the adopted literature values shown in Table 1, from which the simulated critical micelle concentration (CMC) of L64 agrees acceptably with the experimental data as will be discussed later.

hydrophobic beads in a given micelle; ri and rcm are the position vector of each bead and the center of mass of the micelles, respectively. Another useful parameter that provides the shape information on micelles is asphericity (∝) defined as35

Table 1. Interaction Coefficient of Conservative Forces

where R1, R2, and R3 are the eigenvalues of the gyration tensor in decreasing order. The asphericity ranges from 0 indicating a perfect sphere to 1 representing a very long rod.

PEO PPO Water

PEO

PPO

Water

25 48.9 25.9

25 38.4

25

∝=1−3

Figure 1. Concentration of unimers as a function of L64 concentration for pure L64 and F127/L64 systems.

found to reach a plateau gradually with increase φ64. Similar behavior was observed in the work of Lin et al.36 for the cases of diblock copolymers. The CMC could then be defined as the concentration at the intersection between the ideal line with unit slope and the horizontal extension of the plateau; i.e., it equals the free polymer concentration that remains constant after the formation of micelles.36 As such, the CMC of L64 based on the given set of parameters in Table 1 is found to be φ64 = 0.017, at which about 45% of L64 already forms aggregates. However, it has been mentioned in the literature that this method always underpredicts the CMC.33 Another method for CMC determination is based on the onset concentration for the appearance of a peak/shoulder in the distribution curve of micelle aggregation number.37 Figure 2a plots the mass-weighted distribution of aggregation number at three values of φ64. One can observe that for φ64 ≥ 0.04 there appears a peak/shoulder, and thus CMC is considered to fall in between 0.03 and 0.04. In comparison with the experimental data of CMC = 0.04(w/v) at 301 K,38 there appears an acceptable agreement when assuming an equal density for water, EO and PO. As such, we can claim that the parameters

(8)

where Pq,i is the number of polymer chains of type q in cluster i, and the sum is run over all the equilibrium configurations. The number-average radius of gyration for micelles and for their cores are determined by34

⟨R gc⟩ =

1 N

i=1

∑ (ri − rcm)2 N

1 N1

i=1

∑ (ri − rcm)2 N1

E2 = R1R 2 + R1R3 + R 2R3

5. VALIDATION To determine the CMC of L64 from simulations, we calculated the concentration of unimers by varying the L64 concentration with the results shown in Figure 1. The unimer concentration is

∑i Pq2, i

⟨R gm⟩ =

(10) (11)

4. MICELLE ANALYSIS From the simulations, it is observed that the initially randomly dispersed free-chains self-assemble to form micelles during the course of the simulation. To distinguish between unimers and aggregates in the system, we use the following criterion.32 Two chains are considered to belong to the same cluster if any of their hydrophobic beads are within the cutoff distance, which is fixed at 1.0 from several testing runs of the particular systems. The aggregation number and its average are calculated after determining the number of clusters and their compositions at each time point. The weight-average aggregation number (Pq) is defined as33 ∑i Pq , i

⟨E12⟩

E1 = R1 + R 2 + R3

In the present study, all beads are assumed to have an identical mass m, which is assigned to be unity for nondimensionalization. Therefore, the time unit is [(mr2c )/ (KBT)]1/2 according to the theorem of equipartition of energy. The time step chosen for the simulations is Δt = 0.04 such that the normalized temperature does not exceed 1.03. Around 1.6 × 105 time units are required for the system to reach equilibrium, and the properties are calculated thereafter for 1.2 × 105 time units, while data are stored every 400 time units. For each case, three independent runs are conducted with different initial configurations for the determination of average properties and corresponding error bars that represent 99.7% confidence interval. All the simulations are performed on the HPC clusters of NUS.

Pq =

⟨E2⟩

(9)

respectively, where the angular brackets denote an ensemble average; N and N1 are the total number of beads and number of 574


Article


Figure 2. Mass-weighted distribution of aggregation number.

Figure 3. Fractions of lower molecular weight Pluronic involved in aggregation and co-micellization as a function of its concentration for various mixtures.

Pluronics involved in the aggregation as well as in comicellization processes are investigated. Here two cases are considered: one by keeping φ constant and the other by keeping φH constant. Figure 3 shows the fraction of lower molecular weight Pluronics participating in aggregation as a function of its concentration φL. For the sake of brevity, the results for F127/P123 and F127/L64 are presented here, while those for F127/P105 and P123/P84 can be seen in Supporting Information Figure S2. Each presented result is the average of 3 independent simulations under the same condition but with different initial configurations, and the error bar represents 99.7% confidence intervals of the mean. A representative snapshot for F127/P123 mixture is shown in Figure 4. At constant φ = 0.06, this fraction is almost constant and very close to unity for F127/P123 and F127/P105 systems. This is because the investigated concentrations are far higher than the CMCs of P123 and P105, noting that the CMCs of F127, P123, and P105 are all ≪0.0139−40 at 300 K. Under this condition, the concentration of Pluronics in unimer state remains as low as about CMC, and hence the aggregation

shown in Table 1 represent the system at around 300 K. It should be noted that a majority of the L64 micelles in the simulation are dimers and trimers. Apart from L64, we made a similar effort to calculate the CMC of P84, and find it between 0.01 and 0.02 as shown in Figure 2b. It compares favorably with the experimental data φ84 = 0.0298 (w/v) at 298 K,39 given that the CMC is expected to decrease with increasing temperature. As for other Pluronic species, their CMCs are not calculated in the present study because the experimental data have shown very small values (≪1% (w/v)), implying a much larger domain/box required for simulation.

6. RESULTS AND DISCUSSION 6.1. Co-Micellization Behavior. We classify the formed aggregates into two types: (A) pure micelles consisting of only one Pluronic species, and (B) mixed micelles containing two different species, resulting from co-micellization. In the simulation, some aggregates could be as small as dimers. To understand the co-micellization behavior in each mixture system, the average fractions of lower molecular weight 575


Article


Borovinskii and Khokhlov18 that shorter block copolymer can be incorporated into the micelles formed by the longer counterpart to form mixed micelles at the concentrations lower than its CMC. Now we discuss the results for the mixture cases with constant φH = 0.01. The aggregation fraction of lower molecular weight copolymer varies very weakly for F127/ P123 and F127/P105, whereas it increases considerably with increasing φL for P123/P84 and F127/64. The fraction involved in co-micellization decreases except for F127/L64 where the fraction is nearly constant. Despite the decreasing trend of the co-micellization fraction, the absolute amount of lower molecular weight copolymer participating in comicellization still increases with φL. To better understand the micellization behavior, we investigate the populations for the two types of micelles. Figure 5 shows the number fraction of mixed micelles as a function of φL for F127/P123 and F127/L64 (see Supporting Information Figure S3 for F127/P105 and P123/P84). For F127/P123, F127/P105, and P123/P84, it is found that at constant φ = 0.06, the number fraction of mixed micelles reaches the maximum when φL ≈ 0.02. Also, the mixed micelles outnumber the pure micelles for most cases. This behavior is qualitatively similar to the theoretical prediction for binary mixture of diblock copolymers based on free energy calculations.18 For F127/L64, in contrast, the fraction of mixed micelles decreases with increasing φ64 (or decreasing φ127), probably due to the formation of small L64 aggregates like dimers, trimers, and so forth, leading to a significant contribution to the number fraction of pure micelles. Figure 6 shows the number fraction of pure micelles of each species as a function of φL for F127/P123 and F127/L64 at φ = 0.06 (see Supporting Information Figure S4 for F127/P105and P123/ P84). Our results suggest that pure micelles of both polymer species could coexist with the mixed micelles for the cases with two species at similar concentrations, although the calculated fractions could become small with high uncertainty. For the cases at constant φH = 0.01, the number fraction of mixed micelles decreases with increasing φL for all cases. Esselink et al.20 conducted experimental and theoretical studies on the diblock copolymers with varying core forming block. They

Figure 4. Snapshot of simulation box containing F127/P123 system. Red and blue represent the PEO and PPO block of P123, while cyan and green indicate PEO and PPO block of F127.

fraction is nearly unity, showing weak variation. At the lowest φL, the fraction involved in co-micellization is nearly equal to the aggregation fraction, indicating the dominance of comicellization. Although the co-micellization fraction decreases with increasing φL, the absolute amount of lower molecular weight polymer involved in co-micellization still increases. For P123/P84 where the calculated CMC of P84 is around 0.01− 0.02 as pointed out earlier, similar behavior is still observed except for a lower aggregation fraction of P84 (∼0.9). For the case of F127/L64, to the contrary, the aggregation fraction of L64 increases from 0.65 to 0.7 when φ64 varies from 0.01 to 0.05, while this fraction changes from 0.25 to 0.64 for the pure L64 solution as determined from Figure 1. The comparison clearly shows that the presence of F127 increases the fraction of L64 participating in aggregation, and this promotion reduces with increasing φ64. It is noteworthy that for φ64 lower than the CMC of pure L64 solution, a considerable amount of L64 is involved in the mixed micelles. For example, at φ64 = 0.01, 55% of L64 forms mixed micelles, while 10% forms pure micelles. Our finding is in agreement with the theoretical prediction of

Figure 5. Number fraction of mixed micelles as a function of φL in F127/P123 and F127/L64 mixtures. 576


Article


Figure 6. Number fraction of pure micelles as a function of φL in various mixtures with φ = 0.06.

Figure 7. Average composition of mixed micelles as a function of φL.

in binary mixture of Pluronics, it is essential to understand its effect on the micelle properties. The bead distribution is analyzed to find the structure of the micelles. Figure 8 shows the density profiles for hydrophilic and hydrophobic beads with r measured from the center of mass of a micelle for the single species Pluronic solution. The results for mixtures are plotted in Figure 9, where only the density profiles at extreme ratios of polymer concentrations are shown because qualitatively similar behavior is found for other ratios. Segregation of hydrophilic and hydrophobic beads to a considerable extent to form a core−shell structure is evident. We also investigate the shape of mixed micelles by calculating the asphericity α.35 For all the systems studied, the average asphericity for overall micelles is found to range from 0.11 to 0.22, while the value for micellar cores is between 0.13 and 0.25. They are relatively higher for F127/L64, but lower for F127/P105. Also, the results of eigenvalues R1, R2, and R3 find that the micelles and their cores are both ellipsoidal. Sheng et al.35 applied DPD to study diblock copolymer AnB5 with 5 ≤ n ≤ 60. For A10B5 with A−B interaction parameter equal to 50, the reported α is about 0.03 (overall micelle) and 0.09 (micellar core). In terms of the bead number ratio of A to B, it is similar

reported that under equilibrium pure micelles of both block copolymers and mixed micelles can coexist. This finding was obtained based on their free energy calculations, but they were not able to observe it clearly in their experiments. To further analyze the behavior of mixed micelles, their average composition is computed as a function of φL. The composition is represented by the bead number fraction of the lower molecular weight Pluronics in the mixed micelles as shown in Figure 7 and Supporting Information Figure S4. It is found that this fraction increases with increasing φL. At constant φ, the composition variation is nearly linear, similar to the finding of Hafezi and Sharif for mixtures of diblock copolymer.22 In addition, the fraction is ∼0.5 for F127/P123, F127/P105, and P123/P84 when the two species are at equal concentration (i.e., 1% or 3%). For F127/L64, however, the fraction of L64 in the mixed micelles is significantly lower than in the other mixture cases. Along with Figures 3 and 5, it indicates that participation of L64 in the co-micellization with F127 is less pronounced than for other mixtures, probably due to the higher dissimilarity of their block lengths. 6.2. Properties of Mixed Micellar System. Micelle Structure. Having confirmed the co-micellization phenomenon 577


Article


to each other around the peak location of the hydrophilic beads for Pluronics with very short hydrophilic blocks, i.e., P123, P84, and L64. This is attributed to the formation of ellipsoidal crewcut micelles with a thin corona and the fact that the bead density profile is not isotropic. In general, the bead segregation at the micelle periphery is less pronounced than for diblock copolymers (A3B2, A4B4, A6B4, and A8B4) studied by Li and Dormidontova.33 For the mixture cases at φ = 0.06, we find from Figure 7 that the lower molecular weight polymer accounts for about 20% and 70% of polymer beads in the mixed micelles for φL = 0.01 and 0.05, respectively, except for F127/L64 with the L64 contribution dropping to 15% and 43%. These values can be used to determine the percentage of hydrophobic beads in the mixed micelles, which come from the lower molecular weight polymer. At φL = 0.01, the percentage is 35%, 29%, 29%, and 26% for F127/P123, F127/P105, F123/P84, and F127/L64, respectively, while it is 83%, 79%, 70%, and 61% for φL = 0.05. These values are very similar to those near the core center, which can be estimated graphically from Figure 9, except for F127/L64 where the percentage near the center is apparently lower. Since the hydrophobic block of F127 is much longer than that of L64, the hydrophobic beads of the latter would experience an increased difficulty to access the central region. It can however be circumvented by those L64 chains straddling the core and shell in the interfacial area sufficiently near the micelle center because the core is ellipsoidal. This is not the case for the rest of L64 chains. Therefore, the hydrophobic bead distribution of L64 becomes broader, and the peak of hydrophilic bead distribution shifts to larger r when compared to the pure L64 case. Micelle Size. The number-average radius of gyration of mixed micelles Rgm and the corresponding value of their cores Rgc are calculated, and the results are shown in Figure 10 and Supporting Information Figure S6. At φ = 0.06, the micelle size decreases with increasing φL as expected for all four mixtures. The size of the mixed micelles is always in between the sizes of the pure micelles formed from individual Pluronics species. In contrast, the radius of gyration of the core could have a subtle dependence on the concentration. For pure micelles, the core size of P123 is larger than that of F127 due to the much smaller hydrophilic block of the former, leading to a greater ease of packing hydrophobic blocks into the core. For P123/F127, with increase in the concentration of P123, the core size increases, reaches a weak maximum, and then decreases. For the F127 and P105 pure solutions, the core sizes of their micelles are almost equal, and therefore the core size of mixed micelles in their mixture is nearly independent of the mixture composition. For P123/P84 mixture at low P84 concentration, the Rgc contributed by P84 hydrophobic beads is smaller than the overall Rgc value, indicating that the shorter P84 prefers to straddle the core and corona at the interfacial area of the ellipsoidal core near the micelle center. Since pure micelles coexist with mixed micelles, we investigate the distribution of Rgm for all the micelles present in the system. Figure 11 plots the probability density of Rgm based on intensity (as in the case of light scattering techniques) for F127/P123 and F127/L64 mixtures at φ = 0.06, and for the corresponding pure samples as comparison. All mixtures show a single-peak distribution except for 1%F127 + 5%L64 revealing slightly bimodal behavior. The left weak peak is located at the same Rgm as the peak of the pure L64 system, indicating a considerable amount of L64 pure micelles in this F127/L64

Figure 8. Bead density profiles for cases of single Pluronics species at φ = 0.06.

to F127, for which our calculated α is 0.11 and 0.13. For A5B5 similar to P105, α is about 0.05 (overall micelle) and 0.15 (micellar core) as opposed to 0.11 and 0.13 for P105. This comparison shows that asphericity in general appears larger for triblock copolymer. For pure solutions, the number density of hydrophobic beads near the micelle center is very close to the global bead density specified (= 3) in our simulation. It suggests formation of a rather dense core with near absence of water or hydrophilic beads, thereby creating a hydrophobic microenvironment helpful for drug loading purposes. Despite strong fluctuation of bead density near the core center, we can observe slight differences for various species: the density is around 3.5 for L64 and P84, 3 for P123 and P105, and 2.7 for F127. For the shell, in contrast, a broad, weak peak for the hydrophilic beads is seen with the corresponding bead density no larger than 0.5. It indicates a comparatively loose hydrophilic corona, where a considerable amount of water also resides. It is interesting to note that the bead densities for both types could be comparable 578


Article


Figure 9. Bead density profiles for various binary Pluronics mixtures.

Figure 10. Dependence of radius of gyration of mixed micelles on φL for φ = 0.06.

observed for most of the cases. Observation of discernible peaks requires not only sufficiently distinct sizes of pure and mixed micelles, but also large enough proportion for each, in particular

sample. Although binary mixtures of Pluronics could form pure micelles along with the mixed micelles as discussed earlier, only a single characteristic peak of micelle size distribution is 579


Article


Figure 11. Intensity-weighted distribution plots of radius of gyration of micelles of various systems at φ = 0.06.

Figure 12. Dependence of aggregation number of each Pluronics species on the concentration.

for the smaller micelles. Pragatheeswaran and Chen41 have reported unimodal size distribution for the equal ratios of F127/L64 mixture using DLS experiments. This is consistent with the present simulation results as a unimodal distribution can be seen for the case of 3%F127 and 3% L64 mixture sample. Aggregation number is another important parameter to characterize the micelles. Here the aggregation number is defined as the mass-average number of chains of each species involved in a mixed micelle. The results are presented for φ = 0.06 in Figure 12 and Supporting Information Figure S7. It is observed that the aggregation number for each species increases with increase in its concentration. This is simply due to the availability of more Pluronics chain for aggregation process. Interestingly, when mixed with F127, the aggregation number of P123 or P105 at φL = 005 in the mixed micelles is larger than corresponding value for its pure sample at φ = 0.06. Wide ranges of aggregation numbers for Pluronic have been documented in the literature. The aggregation number of F127 was reported to be 15 at 30 °C42 and 3.2 at 35 °C43 in comparison to 7.8 at ∼27 °C from our simulation. For L64,

Almgren et al.44 calculated the aggregation number based on static light scattering, and found it to be 2, 4, 19, and 85 at 21.0, 25.9, 40.0, and 60.0 °C, respectively. The present study predicts 6.92 at ∼27 °C.

■

CONCLUSION DPD simulations have been conducted to study four binary mixtures of Pluronics in dilute aqueous solution. In the investigated concentration range, pure and mixed micelles always coexist for all cases. At similar concentrations, both species could form pure micelles of their own together with mixed micelles. This behavior is noteworthy in particular for F127/P123 with similar hydrophobic block lengths, which was thought previously to form only mixed micelles in some literature. In the case of F127/L64, we find that the L64 chains are involved in the mixed micelles even when the L64 concentration is below its CMC. Both pure and mixed micelles are ellipsoidal, inferred from three distinct eigenvalues of gyration tensor. The composition of the mixed micelles varies almost linearly with the 580


Article


(11) Kulthe, S. S.; Inamdar, N. N.; Choudhari, Y. M.; Shirolikar, S. M.; Borde, L. C.; Mourya, V. K. Mixed micelle formation with hydrophobic and hydrophilic Pluronic block copolymers: Implications for controlled and targeted drug delivery. Colloids Surf., B 2011, 88 (2), 691−696. (12) Zhang, W.; Shi, Y.; Chen, Y.; Yu, S.; Hao, J.; Luo, J.; Sha, X.; Fang, X. Enhanced antitumor efficacy by Paclitaxel-loaded Pluronic P123/F127 mixed micelles against non-small cell lung cancer based on passive tumor targeting and modulation of drug resistance. Eur. J. Pharm. Biopharm. 2010, 75 (3), 341−353. (13) Wei, Z.; Hao, J.; Yuan, S.; Li, Y.; Juan, W.; Sha, X.; Fang, X. Paclitaxel-loaded Pluronic P123/F127 mixed polymeric micelles: Formulation, optimization and in vitro characterization. Int. J. Pharm. 2009, 376 (1−2), 176−185. (14) Oh, K. T.; Bronich, T. K.; Kabanov, A. V. Micellar formulations for drug delivery based on mixtures of hydrophobic and hydrophilic Pluronic® block copolymers. J. Controlled Release 2004, 94 (2−3), 411−422. (15) Newby, G. E.; Hamley, I. W.; King, S. M.; Martin, C. M.; Terrill, N. J. Structure, rheology and shear alignment of Pluronic block copolymer mixtures. J. Colloid Interface Sci. 2009, 329 (1), 54−61. (16) Zhou, D.; Alexandridis, P.; Khan, A. Self-assembly in a mixture of two poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) copolymers in water. J. Colloid Interface Sci. 1996, 183 (2), 339−350. (17) Artzner, F.; Geiger, S.; Olivier, A.; Allais, C.; Finet, S.; Agnely, F. Interactions between poloxamers in aqueous solutions: micellization and gelation studied by differential scanning calorimetry, small angle xray scattering, and rheology. Langmuir 2007, 23 (9), 5085−5092. (18) Borovinskii, A. L.; Khokhlov, A. R. Micelle formation in the dilute solution mixtures of block-copolymers. Macromolecules 1998, 31 (22), 7636−7640. (19) Honda, C.; Yamamoto, K.; Nose, T. Comicellization of binary mixtures of block copolymers with different block lengths in a selective solvent. Polymer 1996, 37 (10), 1975−1984. (20) Esselink, F. J.; Dormidontova, E. E.; Hadziioannou, G. Redistribution of block copolymer chains between mixed micelles in solution. Macromolecules 1998, 31 (15), 4873−4878. (21) Bourov, G. K.; Bhattacharya, A. Brownian dynamics of mixed surfactant micelles. J. Chem. Phys. 2005, 123 (20), 204712. (22) Hafezi, M.-J.; Sharif, F. Brownian dynamics simulation of comicellization of amphiphilic block copolymers with different tail lengths. Langmuir 2012, 28 (47), 16243−16253. (23) Frenkel, D.; Smit, B. Understanding Molecular Simulation: from Algorithms to Applications; Academic Press: London, 2002. (24) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 1992, 19 (3), 155. (25) Groot, R. D.; Warren, P. B. Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 1997, 107 (11), 4423−4435. (26) Español, P.; Warren, P. Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 1995, 30 (4), 191. (27) Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117 (1), 1−19. (28) van Vlimmeren, B. A. C.; Maurits, N. M.; Zvelindovsky, A. V.; Sevink, G. J. A.; Fraaije, J. G. E. M. Simulation of 3D mesoscale structure formation in concentrated aqueous solution of the triblock polymer surfactants (ethylene oxide)13(propylene oxide)30(ethylene oxide)13 and (propylene oxide)19(ethylene oxide)33(propylene oxide)19. Application of dynamic mean-field density functional theory. Macromolecules 1999, 32 (3), 646−656. (29) Velázquez, M. E.; Gama-Goicochea, A.; González-Melchor, M.; Neria, M.; Alejandre, J. Finite-size effects in dissipative particle dynamics simulations. J. Chem. Phys. 2006, 124 (8), 084104. (30) Cao, X.; Xu, G.; Li, Y.; Zhang, Z. Aggregation of poly(ethylene oxide)−poly(propylene oxide) block copolymers in aqueous solution: DPD simulation study. J. Phys. Chem. A 2005, 109 (45), 10418− 10423.

concentrations of the Pluronics in the solution when the total polymer concentration is kept constant. This behavior is consistent with the trend for change of the average micelle size with the concentration. For the F127/L64 mixture, the fraction of L64 involved in the mixed micelles is found to be lower as compared to the other systems studied. This is because L64 has a higher CMC comparable to the investigated concentrations, and much shorter block lengths than those of F127, leading to decreased compatibility. For all cases, the proportion of mixed micelles can be enhanced when the two polymer species have similar concentrations. Furthermore, shorter chains may prefer to straddle the core and corona in the region of ellipsoidal interface that is closer to the micelle center.

■

ASSOCIATED CONTENT

S Supporting Information *

Supplementary figures. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This is work is financially supported by National University of Singapore through grant R279-000-352-112. REFERENCES

(1) Liu, R. Water-Insoluble Drug Formulation, 2nd ed.; CRC Press: Boca Raton, 2008. (2) Kazunori, K.; Glenn, S. Block copolymer micelles as vehicles for drug delivery. J. Controlled Release 1993, 24, 119−132. (3) Ebrahim Attia, A. B.; Ong, Z. Y.; Hedrick, J. L.; Lee, P. P.; Ee, P. L. R.; Hammond, P. T.; Yang, Y.-Y. Mixed micelles self-assembled from block copolymers for drug delivery. Curr. Opin. Colloid Interface Sci. 2011, 16 (3), 182−194. (4) Kim, S. H.; Tan, J. P. K.; Nederberg, F.; Fukushima, K.; Yang, Y. Y.; Waymouth, R. M.; Hedrick, J. L. Mixed micelle formation through stereocomplexation between enantiomeric poly(lactide) block copolymers. Macromolecules 2008, 42 (1), 25−29. (5) Lo, C.-L.; Lin, S.-J.; Tsai, H.-C.; Chan, W.-H.; Tsai, C.-H.; Cheng, C.-H. D.; Hsiue, G.-H. Mixed micelle systems formed from critical micelle concentration and temperature-sensitive diblock copolymers for doxorubicin delivery. Biomaterials 2009, 30 (23−24), 3961−3970. (6) Wang, Y.; Yu, L.; Han, L.; Sha, X.; Fang, X. Difunctional Pluronic copolymer micelles for paclitaxel delivery: Synergistic effect of folatemediated targeting and Pluronic-mediated overcoming multidrug resistance in tumor cell lines. Int. J. Pharm. 2007, 337 (1−2), 63−73. (7) Yang, L.; Wu, X.; Liu, F.; Duan, Y.; Li, S. Novel biodegradable polylactide/poly(ethylene glycol) micelles prepared by direct dissolution method for controlled delivery of anticancer drugs. Pharm. Res. 2009, 26 (10), 2332−2342. (8) Yoo, H. S.; Park, T. G. Folate receptor targeted biodegradable polymeric doxorubicin micelles. J. Controlled Release 2004, 96 (2), 273−283. (9) Zhang, W.; Shi, Y.; Chen, Y.; Ye, J.; Sha, X.; Fang, X. Multifunctional Pluronic P123/F127 mixed polymeric micelles loaded with paclitaxel for the treatment of multidrug resistant tumors. Biomaterials 2011, 32 (11), 2894−2906. (10) Chen, L.; Sha, X.; Jiang, X.; Chen, Y.; Ren, Q.; Fang, X. Pluronic P105/F127 mixed micelles for the delivery of docetaxel against Taxolresistant non-small cell lung cancer: optimization and in vitro, in vivo evaluation. Int. J. Nanomed. 2013, 8, 73−84. 581


Article

The Journal of Physical Chemistry B (31) Guo, S. L.; Hou, T. J.; Xu, X. J. Simulation of the phase behavior of the (EO)13(PO)30(EO)13(Pluronic L64)/water/p-xylene system using MesoDyn. J. Phys. Chem. B 2002, 106 (43), 11397−11403. (32) Marrink, S.; Tieleman, D.; Mark, A. Molecular dynamics simulation of the kinetics of spontaneous micelle formation. J. Phys. Chem. B 2000, 104 (51), 12165−12173. (33) Li, Z.; Dormidontova, E. E. Kinetics of diblock copolymer micellization by dissipative particle dynamics. Macromolecules 2010, 43 (7), 3521−3531. (34) Wang, Y.; Li, B.; Zhou, Y.; Lu, Z.; Yan, D. Dissipative particle dynamics simulation study on the mechanisms of self-assembly of large multimolecular micelles from amphiphilic dendritic multiarm copolymers. Soft Matter 2013, 9 (12), 3293−3304. (35) Sheng, Y.-J.; Wang, T.-Y.; Chen, W. M.; Tsao, H.-K. A−B diblock copolymer micelles: effects of soluble-block length and component compatibility. J. Phys. Chem. B 2007, 111 (37), 10938− 10945. (36) Lin, Y.-L.; Wu, M.-Z.; Sheng, Y.-J.; Tsao, H.-K. Effects of molecular architectures and solvophobic additives on the aggregative properties of polymeric surfactants. J. Chem. Phys. 2012, 136 (10), 104905. (37) Ruckenstein, E.; Nagarajan, R. Critical micelle concentration. A transition point for micellar size distribution. J. Phys. Chem. 1975, 79 (24), 2622−2626. (38) Mata, J. P.; Majhi, P. R.; Guo, C.; Liu, H. Z.; Bahadur, P. Concentration, temperature, and salt-induced micellization of a triblock copolymer Pluronic L64 in aqueous media. J. Colloid Interface Sci. 2005, 292 (2), 548−556. (39) Kozlov, M. Y.; Melik-Nubarov, N. S.; Batrakova, E. V.; Kabanov, A. V. Relationship between pluronic block copolymer structure, critical micellization concentration and partitioning coefficients of low molecular mass solutes. Macromolecules 2000, 33 (9), 3305−3313. (40) Lopes, J. R.; Loh, W. Investigation of self-assembly and micelle polarity for a wide range of ethylene oxide−propylene oxide−ethylene oxide block copolymers in water. Langmuir 1998, 14 (4), 750−756. (41) Pragatheeswaran, A. M.; Chen, S. B.; Chen, C.-F.; Chen, B.-H. Micellization and gelation of PEO-PPO-PEO binary mixture with nonidentical PPO block lengths in aqueous solution. Polymer 2014, DOI: 10.1016/j.polymer.2014.08.031. (42) Rassing, J.; Attwood, D. Ultrasonic velocity and light-scattering studies on the polyoxyethylenepolyoxypropylene copolymer Pluronic F127 in aqueous solution. Int. J. Pharm. 1982, 13 (1), 47−55. (43) Attwood, D.; Collett, J. H.; Tait, C. J. The micellar properties of the poly(oxyethylene) - poly(oxypropylene) copolymer Pluronic F127 in water and electrolyte solution. Int. J. Pharm. 1985, 26 (1−2), 25− 33. (44) Almgren, M.; Bahadur, P.; Jansson, M.; Li, P.; Brown, W.; Bahadur, A. Static and dynamic properties of a (PEO·PPO·PEO) block copolymer in aqueous solution. J. Colloid Interface Sci. 1992, 151 (1), 157−165.

582


Co-Micellization Behavior in Poloxamers: Dissipative Particle

Recommend Documents