Phase behavior study of paclitaxel loaded amphiphilic copolymer in two solvents by dissipative particle dynamics simulations

Chemical Physics Letters 473 (2009) 336–342

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Phase behavior study of paclitaxel loaded amphiphilic copolymer in two solvents by dissipative particle dynamics simulations Xin Dong Guo a,b, Jeremy Pang Kern Tan b, Li Juan Zhang a, Majad Khan b, Shao Qiong Liu c, Yi Yan Yang b,*, Yu Qian a,* a

School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, PR China Institute of Bioengineering and Nanotechnology, 31 Biopolis Way, The Nanos, #04-10, 138669 Singapore, Singapore c Department of Chemical and Biomolecular Engineering, National University of Singapore, 119077 Singapore, Singapore b

a r t i c l e

i n f o

Article history: Received 17 February 2009 In final form 7 April 2009 Available online 9 April 2009

a b s t r a c t DPD simulations were employed to study the phase behavior of paclitaxel loaded PEO11-b-PLLA9 in water and N,N-Dimethylformamide. Different ordered structures were observed in water-rich solvents. All the structures were greatly affected by solvents compositions. By varying the fractions of each component, a phase diagram of paclitaxel loaded PEO11-b-PLLA9 in water and DMF was mapped. For all ordered structures, bicontinuous, lamella, rod, and spherical structures with different sizes could be easily observed for their wide distribution in the phase diagram. While the HPL, dumbbell, and spherical structures with uniform size were difficult to be obtained, due to their narrow distribution. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Amphiphilic block copolymers have been observed to selfassemble into various well-ordered structures [1,2], such as spherical micelles, tubules, rods, lamellas, vesicles, hexagonally packed layers, large compound micelles, etc. [3–13]. These ordered structures have attracted significant interest over the past decade due to many potential applications such as the cosmetic industry and encapsulation technologies [14]. Another special attractive application of some of the ordered structures is drug delivery system, due to the fact that they can not only stabilize hydrophobic molecules with otherwise limited water solubility but also decrease their eventual high toxicity to health cells [13,15–17]. These structures comprise of a hydrophobic core and hydrophilic shell. They are good vehicles for delivering hydrophobic drugs which are protected from possible degradation by enzymes [18,19]. A number of experimental studies have been carried out to investigate the various ordered structures self-assembled from amphiphilic block copolymers over the past decades [3–13,18– 21]. However, the theoretical work on the various ordered structures is relatively scarce [14,22]. To date, a few theoretical approaches, including molecular dynamics simulation [23–25], Monte Carlo simulation [26,27], Brownian dynamic simulations [28,29], and self-consistent field theory (SCFT) [14,30–32], have

* Corresponding authors. Fax: +65 6478 9080 (Y.Y. Yang); +86 20 22236337 (Y. Qian). E-mail addresses: [email protected] (Y.Y. Yang), [email protected] (Y. Qian). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.04.009

provided an important way to investigate the formation of ordered structures self-assembled from amphiphilic polymers. Recently, a novel approach, dissipative particle dynamics (DPD) simulation, has also attracted significant interests in this investigation [33]. DPD simulation approach, proposed by Hoogerbrugge and Koelˇ ol and Warren [35], is effecman [34] in 1992 and revised by Espan tive and precise to simulate soft spherical particles interacting through a simple, pair-wise potential that preserves the hydrodynamic modes of the fluid [36]. By establishing a relationship between a simple function form of the conservative repulsion in DPD and the Flory–Huggins parameter theory [37], DPD method has been widely applied in the study of mesoscale structures of complex systems [38–48]. The phase separation of diblock copolymers containing some energetically neutral nanoparticles was studied by He et al., and a phase diagram in terms of the nanoparticle volume fraction, size, and surface interaction strength was obtained [42]. The transition of different kinds of structures formed by amphiphilic block copolymer was studied and found thermoreversible [45]. The phase behavior of an amphiphilic molecule in the presence of two solvents was also studied by DPD simulations and found that the immiscibility parameter between two solvents can greatly affect the structures [48]. Though these studies demonstrated that the DPD simulation method is an appropriate technique to study the phase behavior of amphiphilic molecules in the presence of one or two solvents, it is still a challenge to extend to the drug deliver systems which are more complex than the prior studies. In this work, we explored the phase behavior of paclitaxel loaded amphiphilic copolymers in two solvents from a mesoscopic

X.D. Guo et al. / Chemical Physics Letters 473 (2009) 336–342

point of view by DPD simulations. We made a detailed study on how composition affects the phase behavior of paclitaxel loaded system. In particular, the effects of the solvents ratio and the volume fraction of paclitaxel and copolymer were investigated. Moreover, a phase diagram was finally obtained which provided a more complete qualitatively understanding of the phase behavior of paclitaxel loaded amphiphilic copolymer in water and DMF. 2. The simulation method

mi

dv i ¼ fi dt

ð1Þ

where ri, vi, mi, and fi denote the position vector, velocity, mass, and total force on the particle i, respectively. For simplicity, the masses of all particles are set to 1 DPD unit [49]. The force exerted on each particle by other particles in DPD is a sum of a conservative force (FCij ), a dissipative force (FDij ), and a random force (FRij ) [35]:

fi ¼

X C ðFij þ FDij þ FRij Þ

ð2Þ

j–i

where the sum runs over all particles within a certain cutoff radius, rc, whose value is set to be 1 unit of length in simulations. The conservation force is a soft repulsion and given by

( FCij

¼

aij ð1  r ij Þ^rij 0

ðr ij < 1Þ ðr ij  1Þ

ð3Þ

where aij denotes the maximum repulsion between particle i and j, rij = ri  rj, rij = |rij|, ^rij ¼ rij =jrij j. The dissipative force and the random force are both responsible for the conservation of the total momentum in the system. They are given by the following expressions:

FDij ¼ 

r2 ðxðrij ÞÞ2

2kT rxðrij Þ^rij f R pffiffiffiffi Fij ¼ dt

ðv ij  ^rij Þ^rij

ð4Þ ð5Þ

where vij = vi  vj, r is the noise amplitude, f denotes a randomly fluctuating variable with zero mean and unit variance, dt is time step of simulation, the r-dependent weight function x(r) = (1  r) for r < 1 and x(r) = 0 for r > 1. In order to calculate conservation force, Groot and Warren [37,49] made a link between the repulsive parameter aii and the Flory–Huggins parameters (vij) in Flory–Huggins-type models. To have the compressibility of water at room temperature, it is found that the repulsion parameter in Eq. (3) has to be chosen according to:

aii q ¼ 75kB T

ð6Þ

where kB is the Boltzmann constant and T is the system temperature. The particle density q = 3 has been used in this simulation, and kBT = 1 has been used. The values of repulsion parameters between different types of particles are linearly related with the Flory–Huggins parameters (vij) according to

aij ¼ aii þ 3:27vij

vij ¼ Eijmix =RT

ð8Þ

Eijmix

where is the mixing energy of two particles i and j. In addition, to describe the constraint between the bonded particles in one molecule, an extra spring force (FSi ) is introduced. By means of this spring, the particles can be interconnected to highly complex topologies. A simple harmonic force law is used for this force on particle i:

X

Crij

ð9Þ

j

In the dissipative particle dynamics (DPD) method, introduced by Hoogerbrugge and Koelman [34,36], a set of soft interacting particles is used to simulate a fluid system. Each particle represents a group of atoms or a volume of fluid. It aims to provide analysis in large length and time scales in comparison with the molecular dynamics simulation [34]. Newton’s second law is used in this approach to govern the dynamics evolution of particles, as given in Eq. (1):

dri ¼ vi ; dt

where the value of vij can be obtained from Eq. (8),

FSi ¼

2.1. DPD theory

337

ð7Þ

where C is the spring constant, and the sum runs over all particles to which particle i is connected. In this study, the default value C = 4 has been used, resulting in a slightly smaller distance for bonded particles than for non-bonded ones [37]. 2.2. Models and interaction parameters The system simulated in this work composes of paclitaxel, poly(ethylene oxide)-b-poly(L-lactide) (PEO-b-PLLA), water, and N,N-Dimethylformamide (DMF). The coarse-grained models of components used in this study are shown in Fig. 1. The molecules of water and N,N-Dimethylformamide were represented as particle W and DMF (Fig. 1a and b). The paclitaxel molecules were represented by three types of particles named PTX1, PTX2, PTX3, respectively (Fig. 1c). The PEO-b-PLLA block copolymer was coarse grained by two types of particles, EO and LLA, which were connected together by harmonic springs (Fig. 1d). The copolymer PEO11-b-PLLA9 was chosen to investigate the phase behavior of paclitaxel loaded systems in water and DMF solvents. In the Blends model of the Materials Studio software (Accelrys Inc.), one fragment of W, DMF, PTX1, PTX2, PTX3, EO, and LLA were chosen as seven units to calculate the Emix at 283.15 K, in which several interactions were considered, such as electronic, van der waals force, hydrogen bond interactions, and so on. The calculated interaction parameters used in this work are given in Table 1. 2.3. Simulation parameters A cubic simulation box with periodic boundary condition was applied in all three directions. It is necessary to test whether the simulation box is large enough to avoid the finite box size effects and the integration time step is short enough to achieve thermodynamic equilibrium. In this work we focus on the phase behavior of paclitaxel loaded PEO-b-PLA. Consequently, the size and number of the simulated aggregates are direct and important criteria to value the effects of simulation box size and integration time step. DPD simulations were performed in 10  10  10, 15  15  15, 20  20  20, 40  40  40 and 60  60  60 cubic box with 20 000 time steps, respectively, and the results are presented in Fig. S1 (Supporting information). From the number average diameter and total numbers of the simulated aggregates (sphere, rod and lamella) in different box sizes (Fig. S2, Supporting information), it can be found that the average diameter of simulated aggregates increases with the box size increasing when smaller box was adopted. However, the aggregate sizes are almost the same in 20, 40 and 60 boxes, whereas the number of aggregates increases, indicating that a box of 20  20  20 is sufficient to avoid the finite size effects. In addition, the number average diameter and total numbers of the simulated aggregates (sphere, rod and lamella) from different integration time step of 0.01, 0.02, 0.03, 0.04 and 0.05 is shown in Figs. S3 and S4 (Supporting information). The number average diameter and total numbers of the simulated aggregates remains unchanged, indicating that the integration

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Fig. 1. Schematic representation of the coarse-grained models of (a) water, (b) N,N-Dimethylformamide, (c) paclitaxel, and (d) PEO-b-PLLA.

Table 1 The interaction parameters used in DPD simulations (unit: kT). aij

W

DMF

PTX1

PTX2

PTX3

LLA

EO

W DMF PTX1 PTX2 PTX3 LLA EO

25 28.04 107.03 94.73 52.90 71.37 36.92

25 31.10 29.40 26.80 28.01 23.4

25 49.18 83.16 30.29 38.49

25 26.05 27.02 41.73

25 29.01 35.6

25 33.24

25

time step of 0.05 is small enough for our system to get thermodynamic equilibrium. Considering the simulation quality and computation efficiency, the integration time step of 0.05 was taken. In this work, the chosen particles have an average volume of 190 Å. Because the particle density is 3, a cube of r3c contains three particles and therefore corresponding to a volume of 570 Å. Then we can find the physical size of the interaction radius, rc = 8.29 Å. Thus, the box size in our work was characterized by effective dimensions of 165.8 Å  165.8 Å  165.8 Å, which can be used to calculate the length of the simulated structures. All the simulations were performed using DPD program incorporated in the Materials Studio 4.0 software (Accelrys). 3. Results and discussion 3.1. Ordered microphases of paclitaxel loaded PEO11-b-PLLA9 in water and DMF In the present study, the volume fractions of water, DMF, PEO11b-PLLA9, and paclitaxel are defined as Cw, Cd, Cpoly, and Cptx, respectively. In this section, the ratios of Cw to Cd and Cpoly to Cptx are fixed at 19 and 1.56. The formation of different ordered structures as the total fraction of PEO11-b-PLLA9 and paclitaxel, Cpoly + Cptx, was first studied. The dependence of the ordered structures formed in this section on different solvents ratios will be further investigated next. All the simulations started from a random disordered state, where all components are in homogeneous phase. With the evolu-

tion of simulations, the microphase separations were observed and finally formed different ordered structures at different compositions, as clearly shown in Fig. 2. The total fraction of PEO11-b-PLLA9 and paclitaxel, Cpoly + Cptx, was scanned from 0.05 to 0.5 with the step of 0.05, and then a phase diagram was plotted in the figure. The shape of the paclitaxel loaded system varies with the total volume fraction of paclitaxel and PEO11-b-PLLA9. When Cpoly + Cptx is from 0 to 0.07, the paclitaxel loaded system forms microspheres with small and uniform size, as shown in Fig. 2a. The hydrophobic PLLA segments and paclitaxel molecules distribute homogeneously in the core of microspheres based on the hydrophobic interactions. The hydrophilic PEG segments distribute on the surface of microspheres, making the microspheres stable. When the value of Cpoly + Cptx is between 0.07 and 0.16, the microspheres with different sizes can be observed in Fig. 2b. This is because some microspheres aggregate together as the fraction of PEO11-b-PLLA9 and paclitaxel increases. Microspheres with large and uniform size are observed in the Cpoly + Cptx region from 0.16 to 0.228, as shown in Fig. 2c. With the further increase of Cpoly + Cptx, spherical aggregates disappear, while rodlike structures form, as shown in Fig. 2d. It is found that the diameter of rodlike structures increased with Cpoly + Cptx. However, with the continuous increase of Cpoly + Cptx, the spaces among the rodlike structures decrease. Thus, the interactions among rodlike structures increase, resulting in the formation of more complicated structures which was named as hexagonal perforated layers structures, as shown in Fig. 2e. When Cpoly + Cptx exceeded 0.353, ordered microphases with lamellar interfaces formed, shown in Fig. 2f. In the all cases, the microphases obtained do not change with prolonged simulation time, which likely indicates that these micro-structures are the least in local free energy minima. The transformation from one structure to another is prevented by a free energy barrier. As shown in Fig. 2, three primary regions respecting nearly spherical, rodlike, and lamellar structures are indicated. Besides, in this system, the ratio of water and DMF may also be very important causes of different microphases. In order to get a better understanding on the phase behaviors of paclitaxel loaded PEO11b-PLLA9 in the presence of two solvents, the various phase transition of spherical, rodlike and lamellar structures on the ratio of water and DMF will be further discussed in the following sections.

X.D. Guo et al. / Chemical Physics Letters 473 (2009) 336–342

339

Fig. 2. Representation of ordered microphases of paclitaxel loaded PEO11-b-PLLA9 in water and DMF as the total fraction of PEO11-b-PLLA9 and paclitaxel (Cpoly + Cptx): (a) 0.05, (b) 0.1, (c) 0.2, (d) 0.31, (e) 0.34, and (f) 0.39. The values of Cw:Cd and Cpoly:Cptx are fixed at 19 and 1.56, respectively. Green and red regions represent PEG and PLLA segments, respectively. For clarity, the paclitaxel molecule, including three particles, is represented by blue color. Water and DMF are omitted. PEG segments are shown by surface density profiles and the bead model can be found in Fig. S5 (Supporting information). The same symbols are used in the following figures. Meanwhile, the snapshots are created with the simulation box replicated two times in each direction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

3.2. Effect of solvents compositions on the spherical structures The ordered spherical structures of paclitaxel loaded system altered with the ratio variation of water and DMF. In order to investigate the effects of the ratio of water and DMF on the spherical structure, Cpoly and Cptx are fixed at 0.11 and 0.07, respectively. Fig. 3 illustrates the phase variation of paclitaxel loaded systems with the increase of Cw/(Cw + Cd). As can be seen in Fig. 3, several phase structures can be observed before spherical structures at different water fractions, including homogeneous disordered phase, ordered bicontinuous, lamella, rod, and dumbbell structures. To further investigate the effect of solvents on the spherical struc-

tures, the value of Cw/(Cw + Cd) was scanned from 0 to 1 with the step of 0.05, and then a phase diagram was plotted, as shown in Fig. 3. When Cw/(Cw + Cd) is very low, between 0 and 0.175, it exhibits a homogeneous disordered structure as shown in Fig. 3a. This is because the major solvent is DMF, which is strongly miscible to each particle in this system. Although the strong repulsion between water and hydrophobic particles (paclitaxel and PLA segments), the scarce water can not lead to phase separation. When the value of Cw/(Cw + Cd) is between 0.175 and 0.3, the paclitaxel molecules and PLA segments trend to aggregate together because of the hydrophobic interaction of paclitaxel and PLA, allowing then the formation of hydrophilic PEG segments curve interfaces facing

Fig. 3. Representation of microphases of paclitaxel loaded PEO11-b-PLLA9 in water and DMF as the ratio of water and DMF by DPD simulations, the values of Cpoly and Cptx are fixed at 0.11 and 0.07, respectively. For the value of Cw/(Cw + Cd), (a) 0.1, (b) 0.25, (c) 0.5, (d) 0.6, (e) 0.88, and (f) 0.9. The bead model can be found in Fig. S6 (Supporting information).

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Fig. 4. Representation of microphases of paclitaxel loaded PEO11-b-PLLA9 in water and DMF as the ratio of water and DMF by DPD simulations, the values of Cpoly and Cptx are fixed at 0.14 and 0.09, respectively. For the value of Cw/(Cw + Cd), (a) 0.1, (b) 0.3, (c) 0.4, (d) 0.7, and (e) 0.9. The bead model can be found in Fig. S7 (Supporting information).

water (Fig. 3b). The lamella structures were observed at the Cw/ (Cw + Cd) interval between 0.3 and 0.57 (Fig. 3c). With the increase of water fraction, Cw/(Cw + Cd) is from 0.57 to 0.775, rod structures can be observed, as shown in Fig. 3d. This transition of lamella to rod structures is not surprising since increasing the water fraction in the two miscible solvents may resemble an enhance repulsion between water and hydrophobic particles, resulting in the formation of less planar interfaces of lamella structures. Interestingly, another observation is dumbbell structures in the Cw/(Cw + Cd) region from 0.775 to 0.885 (Fig. 3e). In this study, the tendency of rod to dumbbell structures depends on the increasing volume fraction of water. The hydrophobic particles are further repulsed by larger amount of water molecules, which makes the formation of more curved interfaces of rod structures, indicating the formation of dumbbell structures. The interface curvature effect is more pronounced as the increasing of Cw/(Cw + Cd). When Cw/(Cw + Cd) exceeds 0.885, spherical structures can be observed, as shown in Fig. 3f. The spherical structures exist only in a narrow range of Cw/(Cw + Cd) value, from 0.885 to 1. Consequently, the spherical structures can be greatly affected by solvents composition. Water, which is strongly immiscible with hydrophobic components, is the crucial component in phase separation. With the increase of water fraction, the addition of water can steadily repulse paclitaxel and PLLA segments into the hydrophobic domains as the miscible DMF is a minority component in the system. As a result, a sequence of microphase transition of disordered, bicontinuous, lamella, rod, dumbbell, and spherical structures occurs. 3.3. Effect of solvents compositions on the rod structures Rod structures can be observed when the value of Cpoly + Cptx is between 0.228 and 0.328, and the ratio of Cw to Cd is fixed at 19. From the discussion in Section 3.2, water plays a key role leading to phase separation. To further investigate the effect of solvents composition on the rod structures, we increase the water fraction continuously during the simulations, thus detect and control intermediate microstructures. In the simulation, Cpoly and Cptx are fixed at 0.14 and 0.09, respectively. By varying the ratio of water and DMF, various phase transition behaviors were observed and shown in Fig. 4. There are homogeneous disordered (Fig. 4a), bicontinuous

(Fig. 4b), lamella (Fig. 4c), hexagonal perforated layers (HPL) (Fig. 4d), and rod structures (Fig. 4e), respectively. In order to quantitatively investigate the microphases change with the increase of water fraction, we scanned the Cw/(Cw + Cd) interval from 0 to 1 with increments of 0.05 and a phase diagram was obtained. Ordered phases can not be observed at low Cw/(Cw + Cd) values (i.e. below 0.18). With the increase of Cw/(Cw + Cd), bicontinuous phase can be formed in the Cw/(Cw + Cd) region from 0.18 to 0.38 (Fig. 4b). As the value of Cw/(Cw + Cd) increasing, further phase separation occurred until reaching a lamella phase (Fig. 4c). For the transition from homogeneous to lamella phase upon raising the fraction of water, it can be explained as Section 3.2. When the Cw/(Cw + Cd) region is from 0.65 to 0.78, the HPL structure can be obtained as shown in Fig. 4d. Compared with Fig. 3, this structure can not be observed at low (Cpoly + Cptx) values. At lower hydrophobic fractions, the thickness of lamellas and the diameter of rods are both smaller. The lamella structures with smaller thickness can easily be repulsed into rod structures, resulting in an absence of HPL structures. The lamella structures with larger thickness, formed at high hydrophobic fractions, can not easily be repulsed into rod structures, leading to a formation of HPL structures. When the value of Cw/(Cw + Cd) exceeds 0.78, a further phase separation occurs and rod structures with paclitaxel molecules and PLLA segments in the core and hydrophilic PEG segments on the surface can be observed, as shown in Fig. 4e. Compared with the phase transition at low hydrophobic fractions, the dumbbell and spherical structures can not be observed. As can be seen from Fig. 4, the Cw/(Cw + Cd) region where rod structures formed is narrow. Hence, the rod structures can also be greatly affected by solvents composition. When Cpoly and Cptx are fixed at 0.14 and 0.09, respectively, a sequence of microphase transition of disordered, bicontinuous, lamella, HPL, and rod structures can be obtained by varying the water fractions. 3.4. Effect of solvents compositions on the lamella structures The spherical and rod structures are greatly affected by solvents compositions. A series of microstructures were obtained by varying the fraction of water. All the simulation results showed that the microstructures of paclitaxel loaded PEO11-b-PLLA9 in water and

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Fig. 5. Representation of microphases of paclitaxel loaded PEO11-b-PLLA9 in water and DMF as the ratio of water and DMF by DPD simulations, the values of Cpoly and Cptx are fixed at 0.24 and 0.15, respectively. For the value of Cw/(Cw + Cd), (a) 0.1, (b) 0.5, and (c) 0.6. The bead model can be found in Fig. S8 (Supporting information).

DMF significantly depended on the solvents compositions. To further investigate the effect of solvents compositions on the lamella structure, Cpoly and Cptx are fixed at 0.24 and 0.15, respectively. By varying the ratio of water and DMF, only homogeneous disordered, bicontinuous, and lamella structures were observed, as shown in Fig. 5. We also scanned the Cw/(Cw + Cd) interval from 0 to 1 with increments of 0.05, and then a phase diagram was proposed, as shown in Fig. 5. At low Cw/(Cw + Cd), from 0 to 0.19, it exhibits a homogeneous disordered structure as shown in Fig. 5a. With further increase of Cw/(Cw + Cd), only bicontinuous ordered and lamella structures were obtained at the regions of 0.19–0.55 and 0.55–1, respectively (Fig. 4b and c,). For the value of Cw/(Cw + Cd), from 0.55 to 1, only lamella structures can be observed but the thickness of lamella structure decreased, from 10.8 grids at 0.55–7.8 grids at 1, with the increase of Cw/(Cw + Cd), as shown in Fig. 6. This is because the solvent DMF is strongly miscible to each particle in this system. Although lamella structures form at the strong repulsion between water and hydrophobic particles, DMF molecules can still distribute in water and lamella structures, resulting in a thicker lamella at low water fractions. With the increase of water fraction, the polar of the solvents increases, leading to a stronger repulsion between solvents and hydrophobic particles and the formation of thinner lamellas. Hence, bicontinuous and lamella structures with different thickness can be obtained by varying the solvent compositions. The phase behavior of paclitaxel loaded PEO11-b-PLLA9 in water and DMF was greatly affected by the hydrophobic fractions and the solvents composition. In order to qualitatively clarify the phase

behavior, we also studied the phase transformations at different Cpoly + Cptx and solvents compositions. The phase transition points can be confirmed by DPD simulations. By the connection of the phase transition points, the phase diagram of paclitaxel loaded PEO11-b-PLLA9 in water and DMF for the ratio Cpoly/Cptx is 1.56 has been obtained, as shown in Fig. 7. Nine distinct phases can be observed with different phase structures. These phase structures include the following: (I) homogeneous disordered; (II) bicontinuous; (III) lamella; (IV) HPL; (V) rod; (VI) dumbbell; (VII) spherical structures with large and uniform size; (VIII) spherical structures with different size; and (IX) spherical structures with small and uniform size. For the ordered structures, bicontinuous, lamella, rod, and spherical structures with different size distributed in wide portions, indicating that these ordered structures can easily be observed. In contrast, the HPL; dumbbell; spherical structures with uniform size distributed in narrow portions, resulting in a difficult observation of these structures. For the spherical structures, they can only be obtained at low Cpoly + Cptx and high water fractions. For the bicontinuous structures, they can only be observed at high Cpoly + Cptx and low water fractions. The lamella structures are the easiest to be observed for their wide distribution. The HPL structures can be considered as the intergradations of lamella and rod structures. They can only be observed at high Cpoly + Cptx values (i.e. over 0.2). Dumbbell structures, the most difficult to be observed, can be considered as the intergradations of rod and spherical structures. 0.5

0.4 11

Cpoly+Cptx

Thickness (DPD Units)

0.3 10

9

I

II IV

III 0.2

VI VII

V 0.1

VIII IX

0.0

8

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Cw/(Cw+Cd) 7 0.5

0.6

0.7

0.8

0.9

1.0

Cw/(Cw+Cd ) Fig. 6. Thickness of lamella structures at different Cw/(Cw + Cd) values. The values of Cpoly and Cptx are fixed at 0.24 and 0.15, respectively.

Fig. 7. Phase diagram as a function of Cw/(Cw + Cd) and Cpoly + Cptx for the ratio Cpoly/ Cptx = 1.56. Different phase structures are observed in the portion of the phase diagram with nine distinct phases: (I) homogeneous disordered; (II) bicontinuous; (III) lamella; (IV) HPL; (V) rod; (VI) dumbbell; (VII) spherical structures with large and uniform size; (VIII) spherical structures with different size; and (IX) spherical structures with small and uniform size.

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X.D. Guo et al. / Chemical Physics Letters 473 (2009) 336–342

For all structures, the hydrophobic PLLA segments and paclitaxel molecules distribute homogeneously inside the structures based on the hydrophobic interactions, and the hydrophilic PEG segments distribute on the surface. The surface of all structures is rough at low water fractions and much smooth at high water fractions, which can be observed from Figs. 3–5. As discussed above, water is the key component leading to phase separation. With the increase of water fraction, more thorough phase separation occurs, resulting in a transformation of rough to smooth surface. 4. Conclusions The phase behavior of paclitaxel loaded PEO11-b-PLLA9 in the mesoscopic region has been successfully studied using dissipative particle dynamic (DPD) method. By varying the sum fraction of paclitaxel and PEO11-b-PLLA9, a display of rich variety of ordered structures was observed in water-rich solvents, including spherical, rod, hexagonal perforated layers (HPL), and lamella structures. The spherical, rod and lamella structures are the primary structures, all of which are greatly affected by solvents compositions. At low Cpoly + Cptx (i.e. 0.18), a transformation from homogeneous, bicontinuous, lamella, rod, dumbbell, to spherical structures can be observed. The dumbbell and spherical structures disappeared as increasing the Cpoly + Cptx to 0.23. Only homogeneous, bicontinuous, and lamella structures can be obtained at higher Cpoly + Cptx value (i.e. 0.39). By studying the phase transformations at different Cpoly + Cptx and solvents compositions, a phase diagram of paclitaxel loaded PEO11-b-PLLA9 in water and DMF for the ratio Cpoly/Cptx is 1.56 has been mapped. In the ordered structures, bicontinuous, lamella, rod, and spherical structures with different size can easily be observed for their wide distribution in the phase diagram. However, the HPL, dumbbell, spherical structures with uniform size are difficult to be obtained due to their narrow distribution. For the surface of all structures, a transformation from rough to smooth can be observed with the increase of water fraction. Acknowledgements This work was financially supported by National Natural Science Foundation of China (Nos. 20536020 and 20776049) and Institute of Bioengineering and Nanotechnology, Agency for Science, Technology and Research, Singapore. The first author also appreciates the China Scholarship Council’s support for his visiting study at IBN. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2009.04.009.

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