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Colloids and Surfaces A: Physicochem. Eng. Aspects 334 (2009) 124–130

Contents lists available at ScienceDirect

Colloids and Surfaces A: Physicochemical andEngineering Aspects

journa l homepage: www.e lsev ier .com/ locate /co lsur fa

ggregation behavior of Pluronic copolymer in the presence of surfactant:esoscopic simulation

iming Lia,b, Guiying Xua,∗, Yanyan Zhua, Yajing Wanga, Houjian Gonga

Key Laboratory of Colloid and Interface Chemistry, Shandong University, Ministry of Education, Jinan 250100, PR ChinaKey Laboratory of Marine Chemistry Theory and Technology, Ocean University of China, Ministry of Education, Qingdao 266100, PR China

r t i c l e i n f o

rticle history:eceived 2 June 2008eceived in revised form4 September 2008ccepted 9 October 2008vailable online 30 October 2008

eywords:luronic copolymer64

a b s t r a c t

The mesoscopic dynamic (MesoDyn) simulation method was used to simulate the aggregation behaviorof Pluronic copolymer EO13PO30EO13 (L64) and EO26PO40EO26 (P85) solutions in the presence of SDS. Witha simple copolymer model, the morphology and kinetic formation process of copolymer aggregate wereobtained. Some factors influencing the aggregation behavior of the copolymer were discussed, such asconcentration, temperature and EO/PO ratio. Simulation results show that the presence of SDS induces theL64 spherical micelles formed at much lower L64 concentration comparing with the system without SDS.At the same L64 concentration, an increase in SDS concentration results in an increase in the size of L64micelles and decrease in the number of micelles. The morphology of L64 aggregates undergoes transitionsfrom spherical micelles → rod-like micelles → bicontinuous phases with L64 concentration increasing.

DSesoscopic simulation

ggregation

The kinetic process of micelles formation can be divided into three stages and the first diffusion stage willdisappear when L64 concentration is above 30%. Temperature investigation indicates that the formationof aggregates is an exothermic process, and it becomes more difficult and the formation rate decreaseswith temperature increasing. The size of micelles formed by P85 with higher EO/PO ratio value is largerthan that formed by L64 micelles. Further more, P85 is more difficult to form micelles comparing withL64. This is caused by the more hydrophilic EO groups in P85, leading to the fact that there are more water

icelle

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ttivci

molecules amongst P85 m

. Introduction

Amphiphilic poly(ethylene oxide)–poly(propylene oxide)–oly(ethylene oxide) (PEO–PPO–PEO) triblock copolymers, knowns Pluronics, are commercially available in a variety of molecu-ar weights and EO/PO ratios. In aqueous solution, these blockopolymers can build a wide variety of aggregates such as micellar,icontinuous, hexagonal and lamellar phases above a certainritical concentration or critical temperature as a consequence ofheir amphiphilic character [1–3]. As a result, Pluronic copolymersave been found widespread applications in emulsification, sol-bilization, controlled release and product formulation rangingrom agriculture to pharmaceuticals [4,5].

In the studies on the aggregation behavior of Pluronic copoly-

er, spherical micelles are typical at concentrations higher than

ritical micelle concentration (cmc), in which hydrophobic coreonsists of PPO blocks and the corona consists of the hydrated PEOlocks. A variety of experimental techniques, such as small-angle

∗ Corresponding author. Tel.: +86 531 88365436; fax: +86 531 88564750.E-mail address: xuguiying@sdu.edu.cn (G.Y. Xu).

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927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.colsurfa.2008.10.029

s.© 2008 Elsevier B.V. All rights reserved.

eutron scattering, dynamic light scattering, differential scanningalorimetry, surface tension, etc. have been used to investigate thetructural and dynamical properties of Pluronic copolymer [6,7].hough experimental results have obviously improved the under-tanding for the aggregation behavior of this system, its intrinsicggregation information is still ambiguous, and the theoretical sim-lation research on the system is rarely reported.

It is known that Pluronic copolymers can interact with surfac-ants in aqueous solution. By adding a third component surfactanto the Pluronic/water mixture, an additional degree of freedomn tuning nano-aggregate systems for specific applications is pro-ided. Their aqueous mixtures can be employed to design andreate new functional aggregates, which can be applied in manyndustries. So understanding the modality of Pluronic copolymer’sggregation behavior in the presence of surfactant is a fundamentaltep to achieve this objective.

During the last years, physicochemical studies were carried out

n aqueous Pluronic/surfactant mixtures [8–10]. Structural andhermodynamic investigations were performed by changing theironcentrations [11–15]. Some recent efforts were addressed to aass action model, which successfully fitted the experimental data

16,17]. Although there were a lot of experimental reports about

sicoch

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bp[sgltaooawPss

ittdawnftTp

2

dtocdtTiFtrin“

apdcwattisGtocbaoMfwabl

ibiiicImTrp

�

wov

aaacaTavalues between various beads are given in Table 1.

For all simulations, the dimensionless parameters in MesoDynsimulation were chosen as follows: the bond length was set to1.1543 to ensure isotropy of all grid-restricted operators [36]; to

Table 1Interaction parameters between various beads used in simulationa.

A B h t w

A 0 7.3 2.9 5.3 3.3B 7.3 0 7.6 2.8 4.1

Y. Li et al. / Colloids and Surfaces A: Phy

he aggregation behavior of Pluronic copolymer in the presencef surfactant [18,19], computer simulation based on mathematicalodels may provide a deeper understanding on their aggrega-

ion behavior and the structures formed at equilibrium, especiallyor their time development, which are difficultly observed fromxperiments [20,21]. The mesoscale structures are formed in a fewilliseconds, so it is very difficult to determine their growth mech-

nism experimentally. In the past decade, computer simulationethods have been proven to be a valuable tool to study the aggre-

ation behavior of polymer/surfactant system [22,23]. Mesoscopicynamic (MesoDyn) models receive increasing attention in recentears as they form a bridge between fast molecular kinetics andlow thermodynamic relaxation of macroscale properties. Meso-yn method is based on dynamic mean-field density functional

heory and the phase separation dynamic for polymer diffusions described by Langevin equations. One important advantage ofhis method is that there is no a priori assumption on the studiedhases, and the kinetics of phase formation, which is very difficulto observe experimentally, can be studied [24].

MesoDyn method has been used to simulate the aggregationehavior of Pluronic copolymer in aqueous solutions to obtain theirhase diagram, structure factors, as well as their time development25]. Zhao et al. used MesoDyn method to simulate the microphaseeparation of the binary mixture of P123 and water. Various aggre-ate structures of P123 in water including micellar, hexagonal, andamellar phases are produced [26]. Zhang et al. [27] simulatedhe microphase separation dynamics of triblock copolymer P65 inqueous solution by MesoDyn method in the absence and presencef shear. While these studies have achieved important results, theynly focus on the Pluronic/water binary systems. But this is notlways the practical situation. Pluronic copolymer often coexistsith surfactant in aqueous solution. The aggregation behavior of

luronic copolymer in the presence of ionic surfactants has shownome interesting alterations [28]. These features have prompted thetudies on them.

In this paper, the aggregation behavior of Pluronic copolymern the presence of surfactant was studied using MesoDyn simula-ion. The present study was an effort to extend our knowledge onhe changes of the Pluronic copolymer’s aggregation behavior pro-uced by varying the surfactant concentration, temperature, as wells the EO/PO ratio of the copolymer. The morphology formationas also simulated by an instantaneous quench from homoge-eous density distribution. To this aim, the aggregation behaviors

or the family of EO13PO30EO13 (L64) and EO26PO40EO26 (P85) inhe presence of sodium dodecyl sulfate (SDS) were investigated.he examination of the effect of EO/PO ratio of the copolymer waserformed by comparing these two different copolymers.

. Computational methods

The MesoDyn simulation is based on the dynamic mean-fieldensity functional theory (DDFT). The basic idea of this method ishat if the free energy F of an inhomogeneous liquid is a functionf the local density function �, then all thermodynamic functionsan be derived. The detailed theory in MesoDyn has been intro-uced in a previous paper [29]. To specify the chemical nature ofhe system, there are two sets of parameters need to be defined.hey are Gaussian chain architecture of the copolymer and thenteraction energies between different components, respectively.or the purpose of evaluating the density functions, we can replace

he real molecular chain with a Gaussian chain that has the sameesponse functions as the “real” molecular chain and specify thenteraction between each species. Each bead is of a certain compo-ent type representing covalently bonded groups of atoms. In thisspring and beads” model, springs mimic the stretching behavior of

htw

w

em. Eng. Aspects 334 (2009) 124–130 125

chain fragment and different beads correspond to different com-onents in the block copolymer. The Gaussian chain architectureepends on the coarsening degree of the original system. In thease of PEO–PPO–PEO triblock copolymer, this single bond lengthill represent a certain number of monomers of EO group anddifferent number of PO. Different procedures for determining

he bond length of the Pluronic system using atomistic simula-ions have been described in some papers [24]. They typicallynvolve methods to generate ensembles of chains, and an analy-is such as structure factors for the Gaussian chain fitting. Lam andoldbeck-Wood [30] used Monte Carlo method to obtain a statis-

ical sample of atomistic chains for some block polymers, and thenbtained the relationship between atomistic chains and Gaussianhains. According to Lam’s results, L64 and P85 are representedy Gaussian chains A7B16A7 and A7B12A7, respectively, where And B represent PEO and PPO beads. To define the Gaussian chainf the SDS molecule, a simulation was carried out using the RISetropolis Monte Carlo (RMMC) method in the Cerius2 software

rom Accelrys. It is, hence, a good approximation to represent SDSith two beads, one representing surfactant hydrophilic group (h)

nd another representing hydrophobic group (t). Moreover, oneead is used to represent water molecule (w) in MesoDyn simu-

ations.The interaction parameters (εIJ) of the various types of segments

n MesoDyn represent the pairwise interactions between differenteads. εIJ can be considered as the nonideal interactions that are

ncluded via a mean-field approach, and the strength of repulsionnteraction between different components is characterized by εIJ > 0n units of kiloJoules per mole. This parameter can be related to theonventional Flory–Huggins parameter (�) among different beads.t can be derived either from the atomistic simulation, empirical

ethods, or from experimental data such as vapor pressure [31,32].he simplest approach is based on regular solution theory andelates � to the component solubility parameter. The Flory–Hugginsarameter for solvent–polymer interaction is estimated as

sp = (ıs − ıp)2Vs

RT(1)

here ıs and ıp are Scatchard–Hildebrand solubility parametersf the solvent and the polymer, respectively [33], Vs is the molarolume of the solvent molecule.

In our study, the interaction parameters concerning PEO, PPOnd water in self-consistent-field calculations are not calculatedccording to Eq. (1). They were directly selected as the same as thosedopted in previous successful simulations for aqueous Pluronicopolymer [27,34]. The interaction parameters between PEO, PPOnd SDS were calculated using the Group Contribution Method [35].he interaction parameters between h, t and water were chosenccording to their solubility in water. All the interaction parameter

3.5 7.6 0 8.0 3.14.0 2.8 8.0 0 12.13.3 4.1 3.1 12.1 0

a A, B, h, t and w represent EO, PO, SDS hydrophilic group, hydrophobic group andater, respectively.

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3

3

epwwt

tmio(tarrsabe

asapawa

3

eomtiFoissmliimaonisa

ebo

Flt

26 Y. Li et al. / Colloids and Surfaces A: Phy

nsure a stable numerical algorithm, as an approximation, all beadiffusion coefficients of types h, t, w, A, B were 1.0 × 10−7cm2 s−1;he time step was 50 ns; the noise-scaling parameter was 100, andhe compressibility parameter was fixed at 10.0; the total simu-ation time was 5000 time steps [37]. All the simulations were in

cubic grid with 32 × 32 × 32 cells of mesh size and carried outith MesoDyn module in a commercial software package Cerius2,

ersion 4.6, from Accelrys, Inc.It is necessary to illustrate that all the simulation concentration

sed in this paper is the volume fraction of various molecules in theube. All beads have the same volume in MesoDyn simulation andherefore, beads of different types should contain similar volumef material. And therefore a water bead represents a lot of waterolecules. So the mass concentration of copolymer or surfactantolecules in aqueous solution is always lower though its volume

raction is higher.

. Results and discussion

.1. Aggregation behavior of L64 aqueous solution

It is well-known that L64 aqueous solution can form differ-nt structures in different concentration regions. In experimentalhase diagram of L64/water, isotropic micellar phase (10–45%,/w), hexagonal phase (48–58%, w/w), lamellar phase (65–82%,/w) and reverse micelle phase (>85%, w/w) can be formed, respec-

ively [38].Fig. 1 shows the dependence of simulated L64 mesoscale struc-

ures on its concentration. It is clearly seen that micelle, rod-likeicelle, bicontinuous and lamellar structure are gradually formed

n aqueous solution. At the concentration 12%, a few premicelles arebserved; then spherical micelles (12–35%) and rod-like micelles35–45%) are formed in aqueous solution. After the micelle struc-ure, the bicontinuous (45–60%) and lamellar phases (above 60%)re subsequently formed respectively by parallelly arranging longod-like micelles or the stacked bilayers. Comparing simulation

esults with the corresponding experimental phase diagram [38],imulation results can reproduce most phase regions, except for thebsence of reverse micelle phase at high concentrations. This cane attributed to the different phase mapping situations betweenxperiments and simulation [26]. Usually, chain model and inter-

hs2eg

ig. 1. Simulated phase diagram of L64 solution with concentration at 298 K. PM, M, RM, Bamellar phase, respectively. Green represents PPO isosurface. (For interpretation of the rhe article.)

em. Eng. Aspects 334 (2009) 124–130

ction parameters are responsible for the discrepancies betweenimulation and experiment. What is more hydrodynamic inter-ction may also be a possible reason, but as for our symmetricolymer, the effect is rather little. The experimental L64/waterggregation behaviors are mostly reproduced in our simulation,hich indicates that the selection of simulation method and inter-

ction parameters is effective and reasonable.

.2. Aggregation behavior of L64 in the presence of SDS

The morphologies of aggregates formed by 20% L64 in the pres-nce of various concentrations of SDS are shown in Fig. 2. Additionf 20% SDS induces the size or aggregation number of L64 sphericalicelles decreasing comparing with L64 single system. It shows

hat the presence of SDS in aqueous solution decreases the crit-cal micelle concentration (cmc) of L64 copolymer. According toig. 2, the development of L64 micellar structure in the presencef SDS may be divided into two stages with SDS concentration, ones formation stage and the other is growth stage. In the formationtage (SDS concentration <50%), L64 micelles are formed and theize of micelle is almost invariable; in the growth stage (>50%), theicelles starts to grow, manifested by a shift in average size towards

arger radii and a wider size distribution with SDS concentrationncreasing. A reason or atleast a contributing factor to this behav-or is that with an increase in SDS concentration, the core of L64

icelle experiences the poor solvent effects and tends to aggregates much as in a lower SDS concentration solution. The presencef SDS also can suppress the micellization of copolymer, so theumber of micelles in the cube decreases with SDS concentration

ncreasing. The micellar growth observed over SDS concentrationhows that the micelles can grow both individually by chain transfers well as by coalescence.

In order to interpret the aggregation process of L64 at differ-nt SDS concentrations, the order parameter changes of differenteads during the formation of aggregates are analyzed. Here, therder parameter is defined by the mean-squared deviation from

omogeneity in the system, which captures the effects of phaseeparation. Fig. 3 shows the order parameter of different beads for0% L64 + 25% SDS system as a function of simulation time. The timevolution of order parameters indicates that the process of aggre-ate formation can be divided into three stages. In the first stage, the

and L denote regions for premicellar, micellar, rod-like micellar, bicontinuous andeferences to color in this figure legend, the reader is referred to the web version of

Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 334 (2009) 124–130 127

F SDS coo

onatssiswTtmst

3

tw

Ft

iwotstfiSaTifamtp

ig. 2. PO isosurface representations for L64 micelles of various sizes formed withf L64 is 20%.

rder parameters keep invariable, indicating that micelles are stillot formed and this is a diffusion stage, which lasts 500 time stepspproximately. It shows an initial period of very little phase separa-ion (0–500 time steps) and this resembles a nucleation stage wheremall aggregates are not energetically stable to grow. In the secondtage (500–1500 time steps), the order parameters increase rapidly,ndicating that the micelles are forming and this is a formationtage. This stage is faster. The above observation is found over thehole micellar phase range of concentrations for this copolymer.

he last stage is the equilibrium stage. After about 1500 time steps,he order parameter increases very slowly, which indicates that the

icellar size and position remain constant on the whole. The finaltage is time-consuming stage, at which the system changes slowlyo overcome the defects formed in the previous stage.

.3. Effect of L64 concentration

A set of simulations were performed at fixed SDS concentra-ion (20%), while L64 concentration was varied. All simulationsere initiated from homogeneous concentration distributions with

ig. 3. Order parameter plot with increasing time steps for 20% L64 + 25% SDS sys-em.

mLh

cscottbilarabitnsaiv

ncentration (a) 0: (b) 20%, (c) 30%, (d) 50%, (e) 60%, and (f) 70%. The concentration

nstantaneous quench. Results of simulations are shown in Fig. 4,here different final morphologies are presented. From this figure,

ne can trace the mesoscale structures as a function of L64 concen-ration. Below about 15% L64, most micelles formed are sphericaltructure as the PO isosurface pictures show. As L64 concentra-ion is increased further, the structure of micelles becomes rod-likerstly and bicontinuous phase structure finally. The presence ofDS induces the various aggregate structures of L64 forming inlower concentration range comparing with L64 single system.

he size of micelles is sensitive to the amount of water presentn the system as it affects the interaction energies between dif-erent components. When L64 concentration is increased, there isn accompanying decrease in amount of water around the poly-er, hence their chains will not collapse easily and the core of

he micelles increases. The interaction between SDS and L64 alsorovides a hydrophobic environment around polymer, which pro-otes the formation of micellar core. So the various aggregates of

64 are formed in lower L64 concentrations. Another reason is theard-sphere interaction between the formed aggregates [7].

The order parameters of systems with 20% SDS and differentoncentrations of L64 are shown in Fig. 5. It is found that theseystems go through a similar process as shown in Fig. 3. For thease with 20% L64, three stages of aggregate formation can bebserved clearly. But when L64 concentration is further increased,he first stage disappears gradually. This indicates that the forma-ion of micelles at higher concentration needs less time steps andecomes much faster. Furthermore, the time steps used for form-

ng micelles (the time steps of the second stage) become obviouslyess with L64 concentration increasing. The rate of forming micellesppears faster. The concentration of L64 affects not only the occur-ence of different aggregate structure but also the formation rate ofggregate. Usually, the formation rate is difficult to observe directlyy experiment. It is known that order parameter with larger valuendicates the stronger phase separation. The more the L64 concen-ration is, the stronger the degree of phase separation is. This is

ot surprising because the thermodynamic driving forces for phaseeparation in higher concentration are larger. For 20% SDS/60% L64queous solution, the order parameter value is >0.1, indicating themmiscible nature of the blend; whereas for the order parameteralue <0.1, indicating the blend miscibility [24].

128 Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 334 (2009) 124–130

F oncenS

3

tdlpLaoiee(

aA

Ff

toTT[Ptb

3

gtvalues of EO/PO ratio for L64 and P85 are 0.43 and 0.58, respec-

ig. 4. PO isosurface representations for L64 micelles formed with increasing L64 cDS is 20%.

.4. Effect of temperature

It is now well established that aggregation of Pluronic copolymerakes place in a co-operative manner leading to aggregate formationriven by hydrophobic interaction [39]. An increase in temperature

eads to more compact micelles due to increased dehydration. Torobe the influence of temperature on the aggregation behavior of64 in the presence of SDS, 20% L64/25% SDS system was simulatedt different temperatures. Fig. 6 shows the effect of temperaturen the time evolution of PPO bead’s order parameter. Temperaturenfluences the rate of aggregate formation strongly. The van’t Hoffquation (Eq. (2)) is an expression for the slope of a plot of thequilibrium constant (specifically, ln K) as a function of temperatureT) [40]. �rH˚ is the standard enthalpy of chemical reaction.

d ln K �rH˚

dT=

RT2(2)

Eq. (2) shows that d ln K/dT < 0 (and therefore that dK/dT <0) forreaction that is exothermic under standard conditions (�rH˚ < 0).negative slope means that ln K, and therefore K itself, decreases as

ig. 5. Time evolution of the order parameter (PPO bead) for L64 system with dif-erent concentrations. The SDS concentration is 20%.

teit

Fs

tration: (a) 15%, (b) 25%, (c) 30%, (d) 40%, (e) 50%, and (f) 60%. The concentration of

he temperature rises. With temperature increasing, the formationf L64 micelles becomes more difficult and its rate becomes slower.his implies that the process of aggregate formation is exothermic.he result is consistent with the phenomena observed by Schwuger41], who reported that C18H37NMe3Cl can form aggregates withEG at 298 K and with the increase of temperature the interac-ion between them became weaker, and there was no interactionetween them at 333 K.

.5. Effect of EO/PO ratio

In order to investigate the effect of EO/PO ratio on the aggre-ation behavior of Pluronic copolymer, P85 aqueous solution inhe presence of SDS under the same conditions is simulated. The

ively. Comparing the two copolymers can help us to understand theffect of EO/PO ratio on their aggregation behavior. Earlier exper-mental works demonstrated that the energy increment for theransfer of a PO group from the aqueous to the micellar state is

ig. 6. Time evolution of the order parameter (PPO bead) for 20% L64/25% SDSystem at different temperatures.

Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 334 (2009) 124–130 129

Fig. 7. PO isosurface representations for L64 and P85 micelles in the presence

Fr

aao

ttibrbP

(iPtftif

4

uaIiiL

crTttdacttSccimiiiu

aci

A

N

R

ig. 8. Time evolution of the order parameters (PPO bead) for P85 and L64 systems,espectively.

bout (0.25 ± 0.05) kT. This micellization process is associated withlarge endothermic heat which is linearly dependent on the sizef the PO block [7].

Fig. 7 shows the aggregate morphology of L64 and P85 system inhe presence of SDS under the same conditions. Comparing thesewo systems, a difference is found to be that the size of P85 micelless a little larger than that of L64 micelles. Correspondingly, the num-er of micelles in P85 aqueous solution is less than that in L64. Theeason for the larger size is more hydrophilic EO groups in P85 com-ined with the fact that there are more water molecules amongst85 micelles.

From the dimensionless order parameters of two systemsFig. 8), it is found that, with the higher EO/PO ratio value, P85s more difficult to form micelles. This is because the decrease ofO block content is accompanied correspondingly by a decrease ofhe hydrophobic counterpart and hence the enhanced difficulty toorm the hydrophobic core and the phase separation. It is obvioushat the order parameters from simulation can supply a much eas-er and more intuitionistic way to understand the effect of variousactors on Pluronic’s aggregation behavior.

. Conclusions

The MesoDyn simulation method was successfully used to sim-late the aggregation behavior of Pluronic/surfactant mixtures. The

ggregate morphology and kinetic formation process are described.n the absence of surfactant, there are four morphologies formedn L64 aqueous solution. The presence of SDS induces L64 form-ng spherical micelles at a lower concentration comparing with64 single system. The size of L64 micelles is enhanced with SDS

of SDS, (a) 20% L64 + 25% SDS system and (b) 20% P85 + 25% SDS system.

oncentration increasing and rod-like micelles are formed. Cor-espondingly, the number of micelles in the cube is decreased.his indicates that the growth of micelles is caused both by chainransfer and by coalescence between micelles. Order parame-er plot shows that the kinetic process of forming micelles isivided into three stages: monomer diffusion, micelle formationnd equilibrium stage. The results of simulations on different L64oncentrations in the presence of SDS indicate that SDS induceshe bicontinuous phase formed in a much lower L64 concentra-ion compared with that in the absence of SDS. This is becauseDS in the solution provides a more hydrophobic environment foropolymer. The formation of L64 aggregates becomes more diffi-ult with temperature increasing, which indicates that this processs an exothermic process. The influence of EO/PO ratio value on the

orphology and size of copolymer micelles in the presence of SDSs also discussed. The size of P85 micelles with higher EO/PO ratios larger than that of L64 micelles. Such a substantial size increases caused by the more hydrophilic EO groups in P85. The time stepssed for forming P85 micelles is longer than that for L64.

In conclusion, mesoscopic simulation can be considered as andjunct method to describe the aggregation behavior of Pluronicopolymer in the presence of surfactant, and gives us an insightnto the important kinetic process of aggregate formation.

cknowledgment

We gratefully acknowledge financial support from the Nationalatural Science Foundation of China (20573067 and 20803069).

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