显式溶剂模型模拟嵌段共聚物在纳米微滴中的图案化结构

伍绍贵 孙 婷 周 萍 周 俊

(四川师范大学化学与材料科学学院,成都610068)

显式溶剂模型模拟嵌段共聚物在纳米微滴中的图案化结构

伍绍贵*孙 婷 周 萍 周 俊

(四川师范大学化学与材料科学学院,成都610068)

采用耗散粒子动力学(DPD)方法研究了嵌段共聚物在纳米微滴中的相分离行为.模拟是将共聚物纳米微滴置于溶剂环境中进行自发相分离,从而形成一些图案化结构.由于是受限体系,所形成的结构和在溶液或熔融体中形成的相分离结构有所差异,这些结构的形成与亲/疏溶剂嵌段比例(RH/T)有关系.随着亲/疏溶剂嵌段比例的增加,依次形成了枣糕球体、排球状相、多层囊泡(洋葱相)、笼状相、纳米杆状相和分散胶束等结构.我们对洋葱相的形成过程进行了详细的描述.溶剂粒子的集群属性有助于更加深入地了解洋葱相的结构衍化.采用密度曲线分析了洋葱相的结构.在较高的亲/疏溶剂嵌段的比例条件下,嵌段共聚物主要表现为亲溶剂性,通过吸收大量的溶剂溶胀形成疏松结构或瓦解形成分散的胶束悬浮在溶剂中.本文模拟结果与理论或实验结果基本吻合.

耗散粒子动力学;洋葱相;微相分离

1 Introduction

Block copolymers,composed of blocks of chemically distinct repeat units,can assemble into a variety of ordered structures in bulk or in solution,such as lamellae,hexagonally ordered cylinders,body-centered cubic arrays of spheres and other more complex structures.1-3These structures are of great in-terest in nanotechnological applications,including targeted drug-release capsules,micro-reactors and templates for heterogeneous catalysts,etc.4,5The main challenge of all these applications lies in the preparation of these nanostructures in a controllable way.Large amount of work has been done to address the problem of tailoring a desired nanostructure using block copolymers both experimentally and theoretically.6-9Groot and coworkers10studied the microphase separation of block copolymer melts after a temperature quench,and found the equilibrium structures to be lamellar,perforated lamellar,hexagonal rods,and micelles.This is in agreement with the results from experiments and mean-field theory qualitatively.However,as the result of using periodic boundary conditions,configurations fused with their periodic images forming across periodic structures11and made it hard to conceive the actual structures in space.Moreover,the phase separation in solvent condition was not covered in their work.Sevink and coworkers12investigated the self-assembly of amphiphilic polymers in solution using self-consistent field theory.A rich variety of complex vesicles were observed and the nanostructures could be tailored by both kinetic and thermodynamic factors.Restricted by the simplicity of the model,the simulation results cannot fully reproduce the real self-assembly process of amphiphilic polymers. Fraaije and coworkers13examined the microphase separation of dispersed droplets using a self-consistent-field simulation and discovered patterned structures formed in nanodroplets.However,since solvent has not been incorporated explicitly,the simulation results are inadequate to reveal the real microphase separation behaviors.

Dissipative particle dynamics(DPD)is a mesoscopic simulation technique primarily proposed to study the hydrodynamic behavior of complex fluids.With coarse-grained models and employment of soft potentials,DPD can perform efficient simulation of large systems for long period of time,as compared to atomistic molecular dynamics simulations.Furthermore,due to explicit solvent evolved,DPD can truly reproduce the hydrodynamic behavior of complex fluids.It has been successfully used to investigate the phase morphology and the dynamics of soft matter systems,such as lipids,14block copolymers,7surfactants.15In this study,DPD simulation technique is applied to elucidate the microphase separation in block copolymer nanodroplets,and the results are compared to experimental or theoretical results.

2 Experimental

2.1 DPD simulation

DPD is a mesoscopic simulation technique originally developed by Hoogerbrugge and Koelman.16Position r and velocity v of particles are governed by Newton′s second law of motion. Particles interact(fi)with each other via conservative force FC, dissipative force FD,random force FRand spring force FS.

The first three forces are applied for all inter-particle pairs, which are truncated by the cutoff radius rc.FSis used to refrain the relative distance of adjacent beads.The conservative force FCis a soft repulsion taking the form

where rijis the distance between particles i and j,and nijis the unit vector pointing from particle j to particle i.The dissipative force FDis given by

where γ is friction parameterand vijis the relative velocity between particles i and j.The random force FRis defined as

where ξijis a Gaussian-distributed random element.Dissipative and random forces serve as thermostat that ensures the evolution of system towards a Boltzmann-distributed equilibrium state.Amphiphile chain is modeled by tying particles together using Hookean springs with harmonic force FS,17

where i,i+1 represent adjacent beads in molecular chain;k2is spring constant and l0is unstretched bond length.

2.2 DPD model for block copolymer

Our simulation system contains diblock copolymers and solvent.There are a variety of block copolymers,in which the molecular structure and the volume ratio of solvophilic/solvophobic blocks(RH/T)are varied.Since the microphase separation structure mainly depends on the volume ratio of two blocks,18we adopt linear diblock copolymer model HMTN-Mto elucidate their microphase separation behaviors in nanodroplets,where M and N-M are the numbers of H and T particles,H and T denote solvophilic particles and solvophobic particles,respectively.The diblock copolymer model is built by tying soft spherical particles together using Hookean springs and each particle represents a group of atoms.It should be noted that all connections between adjacent particles are fully flexible in these models.Thus,many complex processes can be reproduced on relatively smaller time and length scales.19,20Each copolymer chain contains N=10 beads.And by changing the numbers of H and T particles we obtain diblock copolymers with different values of RH/T.A parameter is defined as f=M/N,denoting the overall volume fraction of the H component.In addition,solvent is modeled by S particle which represents several solvent molecules.The interaction parameters for the conservative force between DPD particles have been described previously.21The repulsion parameters are set at aij=25kBT for the solvophilic interaction(H-S)and 75kBT for the solvophobic interaction(H-T and S-T).The value of parameter aij=75kBT is a value high enough to induce strong phase segregation of a binary mixture system.The value of repulsion parameters between particles of the same type(H-H,T-T,and S-S)is set at aij=25kBT.22The unstretched bond length l0is chosen at 0.7r0,and spring constant is set at k2=100kBT/r02.

2.3 Simulation condition

All physical quantities in this paper are presented in reduced units.The units for mass,length,energy are m0,r0,kBT,respectively.23For simplicity,all particles are assumed to have the same mass m0and size r0.24All the simulations are carried out in the NVT ensemble with constant particle number N,simulation box volume V,and temperature kBT=1.In this work,we quenched a dispersed nanodroplet of block copolymer in a solvent bath and then relaxed the structure by a dissipative particle dynamics simulation method to obtain patterned inner structures.Nanodroplets are generally formed in solvent with random irregular shapes.We have proved that the initial shape of nanodroplet does not affect the final morphology.For solvophobic copolymers,their nanodroplet would minimize its contact with solvent so as to evolve into a sphere.For solvophilic copolymers,their nanodroplet would be swelled by solvent into irregular shapes independent of the initial shape.However, nanodroplets with spherical shapes may accelerate the evolution process.The initial configuration is built as follows:first, a cubic simulation box(76.59r0×76.59r0×76.59r0)is filled up with block copolymers to the density of ρ=3r0-3.After the filling,the total particle number reaches the value of 1387840 (~138784 HMT10-Mmolecules).Then the system is dispersed sufficiently to create a homogenous melt,as shown in Fig.1(A). Subsequently,all the copolymer particles beyond a certain diameter are replaced by solvent particles.Therefore,a spherical copolymer nanodroplet is cut from the original cubic melt as shown in Fig.1(B).These replaced particles turn into the solvent environment surrounding the block copolymer nanodroplet.The thickness of solvent layer should be large enough to circumvent the influence of periodic boundary conditions.

3 Results and discussion

The nanodroplet of diblock copolymer in solvent is a confined system,which allows the self-assembly process to occur only inside the sphere.The final configurations depend on f, which is similar to self-assembly of block copolymer melts. For copolymers with f<0.5,the nanodroplet maintains nearsphere shape during the whole simulation time.Extreme asymmetric polymer——H1T9exhibits strong solvophobicity.Its nanodroplet tries to minimize the surface and evolves into an energetically favorable regular sphere(Fig.2(A)).Since insufficient to aggregate into large domains,these H particles gather into a number of small inverted micelles randomly distributed in the nanodroplet resembling the“Plum Pudding Model”. Thus,in this case,there is no obvious patterned internal structure formed in the nanodroplet.This is in full agreement with the prediction of self-consistent field simulation.

Fig.1 Setup of initial configuration

Fig.2 Obtained morphologies for(A)H1T9,(B)H2T8, (C)H3T7,(D)H4T6

For the case of asymmetric copolymer H2T8,H particles gather into many solvophilic domains and T particles form the continuous phase.As shown in Fig.2(B),the resulted morphology is best described as a mixture of long wormlike and short inverted micelles.In melt systems,the mean-filed theory predicts a perfectly hexagonal array of micelles,while the DPD simulation expects a disordered peanut-shaped micellar phase.10Under current simulation conditions,influenced by the curved shape of the nanodroplet,these inverted micelles are aligned in concentric rings.For clear observation,a half of the ring is peeled off from the nanodroplet as shown in Fig.3.It is interesting to find that the original“long wormlike and short”inverted micelles are all long wormlike inverted micelles actually.The cluster analysis shows that the inverted micelles interconnect with each other forming a continuous phase with its appearance resembling volleyball.One ring is corresponding to a perforated shell structure in three-dimension.

Fig.3 Volleyball-like morphology for H2T8

As for H3T7(f=0.3)and H4T6(f=0.4),well-ordered structures composed of alternating H and T layers(the so-called onion phase)are formed.Solvent particles are encapsulated in the solvophilic H-rich layers.Onion phase is a particular structure composed of multiple lamellar layers.The gaps between any two solvophobic rings provide a space to encapsulate solvent and other solvophilic contents.This structure attracts great interest for its application in pharmaceutical formulations.The multiple lamellar layers not only protect the encapsulated contents,but also enable the sustained and controlled release of them.The obtained morphology for H4T6is a near-spherical onion with the size of 72.6r0,as shown in Fig.2(D).The onion includes four complete solvophobic rings and a micelle nucleus in the center,containing 19532,11488,5528,1710,and 123 copolymer molecules,respectively.The solvophilic H-rich regions form containers filled with a certain amount of solvent, which is introduced during the initial stage of onion formation. A total amount of 46549 S particles are encapsulated in the nanodroplet while the solvent content makes 12.1%.Each gap (including the central cavity)contains 33169,10060,2885,and 435 S particles,respectively.As for H3T7,affected by the central oblong vesicle,the obtained onion takes the shape of an ellipsoid,as shown in Fig.2(C).

Fig.4 Density profiles for the obtained morphologies (A)H1T9,(B)H2T8,(C)H3T7,(D)H4T6

In order to characterize the obtained structures,density profiles are evaluated among these morphologies and the results are summarized in Fig.4.For the extreme asymmetric case of H1T9,though no obvious internal structure is observed in Fig.2(A)as mentioned earlier,the existence of peaks in density curves(Fig.4(A))suggests otherwise:the morphology may have a certain orderly internal structure.As shown in Fig.4(A), there are four discernible H peaks(where H clusters gather) and three T peaks(where T clusters gather)and they appear to be staggered.With the increasing value of the radial distance, the intensity of these H and T peaks grows higher.This implies that the H clusters are arranged more in an incomplete ring when it comes closer to the surface of the nanodroplet and more random when closer to the center.As mentioned earlier, the microphase separation is confined inside the nanodroplet. The effect of the shape of the nanodroplet on the process peaks in the near-surface region,which probably causes the ring-like arrangement of the H clusters in this case.When moving away from the surface,this effect diminishes and results in randomly distributed H clusters.When it comes to the asymmetric model of H2T8(Fig.4(B)),six obvious H peaks emerge in the density curve and are arranged regularly.This shows that H clusters are arranged in incomplete rings in the nanodroplet,which is in agreement with Fig.2(B).Obviously,the outer rings are more regular than the inner ones in the nanodroplet.

For the systems of H3T7and H4T6(Fig.4(C)and 4(D)),although both form onions,their density curves are slightly different.The peaks for H3T7onion are arranged less regularly than those for H4T6onion,which is caused by the irregularity of the spherical shape of H3T7onion.The intensity of T peaks in Fig.4(D)is almost at the same height——slightly above 3, suggesting that H4T6onion is in the shape of regular sphere and its solvophobic particles are closely packed.The space between two solvophobic layers is a solvophilic layer filled with H and S particles.Thus H and S peaks emerge between two T peaks when illustrated in the density curves as shown in Fig.4 (D).Moreover,when being closer the surface,the intensity of S peaks increases while that of H peaks decreases.This indicates that the amount of solvent contents in outer solvophilic layers is greater than that in inner ones.In addition,on both sides of each T peak,there are two H peaks,which confirm the existence of bilayer structure of each shell25,26(It is similar to a lipid bilayer membrane).Finally,the narrow H peak at r≈32.5r0corresponds to the single layer of H particles coating the onion′s surface.

Fig.5 Kinetic pathway of onion formation(H4T6)Solvent particles are not displayed,but a slice illustration including solvent particles is depicted at t=8000t0.

Fig.5 shows a series of snapshots illustrating the evolution pathway of onion from a nanodroplet.At initial stage(t=0t0), phase segregation takes place quickly between H and T particles,forming a lot of small solvophilic and solvophobic domains,which will merge into large ones later.The feature of the structure formed after 50t0can be described as a collection of associated bilayers.Since the shell is not yet sealed,many solvent pores are remained on the surface,providing temporary channels for solvent transmission.This allows the S particles to diffuse into the nanodroplet then to enter the solvophilic domains of H particles.These pores can stay open as long as 6500t0before being fully sealed.The inner space of the droplet is filled with highly folded bilayers,which connect to each other or to the shell.The conjunctions play an important role during the structure transition towards an onion.They enable the bilayers to exchange copolymers to adjust the amount in each bilayer.When a bilayer has sufficient copolymers,all the conjunctions connecting to it begin to break up.Then the bilayer becomes an independent ring.In our simulation,it is found that onion formation is promoted when outer rings are formed earlier than inner ones.This is due to the fact that it is hard for the outer rings to seal with limited number of available copolymers if the inner rings are formed earlier.Therefore,the outer three rings take shape during the time t=(1500-2000)t0.The remaining copolymers are concentrated in the central region and form an unsealed ring with a superfluous part.By the time of t= 7000t0,it is closed and the superfluous part breaks away from it to generate a small spherical micelle nucleus.This marks the formation of the final onion.Sometimes,the superfluous part is very large and forms an oblate bilayer,which would result in an oval onion.

Fig.6 Particle cluster property

Fig.7 Obtained morphologies of diblock copolymer nanodroplets(A)H5T5,cage-like structure,(B)H6T4,nanorods,(C)H7T3and(D)H8T2,discrete micelles.H and S particles are not drawn for clear observation.

Another way to understand onion structure evolution is to investigate the change of particle cluster property.Given that particle i is already inside a cluster,the distance between particle j and i(rij)can be used to determine whether particle j is in a cluster:if rij

Fig.8 Cluster size(chain number)distributions for H7T3,H8T2and H9T1

The obtained morphologies of diblock copolymer nanodroplets(f≥0.5)are summarized in Fig.7.For the symmetric H5T5(f=0.5),Groot et al.10predict a lamellar phase in the situation of a pure melt.Under current simulation conditions,a lot of solvent diffuses into the nanodroplet,which makes the morphology swell into a loose cage-like structure,as shown in Fig.7(A).Due to the strong solvophobic interaction between T and S particles,the loose structure still maintains the integrity. The solvophobic regions are interconnected and the structure is actually like a perforated onion.For H6T4(f=0.6),since the number of solvophilic particles is higher than that of solvophobic particles,the diblock copolymer exhibits certain solvophilicity in whole.Therefore,more solvent molecules are attracted into the inner space of the nanodroplet.As a result,the nanodroplet can not keep integrity any more,and turns into a swarm of long worm-like micelles,as shown in Fig.7(B).For H7T3(f=0.7)and other diblock copolymers of f>0.7,due to the large ratio of solvophilic particles,the initial nanodroplets are disintegrated completely into a lot of small micelles,which are homogenously suspended in the solution,as shown in Fig.7(C) and Fig.7(D),respectively.The distribution of cluster sizes for each system is determined and is shown in Fig.8.Cluster sizes of the highest probability are 1,38 and 58 molecules for H9T1, H8T2and H7T3,respectively.With the increasing value of f,the sizes of micelles become smaller.H9T1molecules are almost soluble in the solvent,thus most exist in the free form.

4 Conclusions

In this study,DPD simulation is used to investigate the microphase separation behavior of block copolymer nanodroplets and the results are compared to the experimental or theoretical ones.It is found that block copolymer nanodroplets in solvent form many microphase separated structures,depending on the ratio of the solvophilic to the solvophobic blocks(RH/T).As RH/Tincreases,the formed morphologies are plum pudding microsphere,volleyball-like structure,onion,cage-like structure, nanorods,and discrete micelles in succession.At low value of RH/T,block copolymers exhibit mainly solvophobicity.To minimize the contact with the solvent,microspheres with patterned internal structures are formed.For highly asymmetric copolymer——H1T9,an almost regular sphere with disordered inverted micelles is formed.For H2T8system,H particles aggregate into long inverted micelles,which interconnect with each other and form a continuous phase resembling volleyball.Onion phases are obtained in H3T7and H4T6systems.The pathway of onion formation is described in detail for H4T6system.Density analysis denotes that the rings in onion have a bilayer structure like lipid membrane.Additionally,cluster particle number determination helps to get more intuition about the dynamics of the onion evolution.For symmetric molecule H5T5,different than the lamellar phase formed in melt,a cage-like structure is observed at the existence of solvent.At high value of RH/T, block copolymers exhibit mainly solvophilicity and the formed morphologies are mostly swelled loose structures.The morphology of small micelles suspending in solvent is formed when f>0.7.And the sizes of micelles reduce with the increasing value of f.The microphase separation structures of block copolymer nanodroplets in current simulation are qualitatively consistent with the self-consistent filed theory or the experimental results.Furthermore,with the inclusion of explicit solvent,this DPD technique reveals more actual dynamics of morphology evolution for these structures and represents the situation closer to the reality.

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Simulating Patterned Structures in Block Copolymer Nanodroplets Using Explicit Solvent Model

WU Shao-Gui*SUN Ting ZHOU Ping ZHOU Jun
(College of Chemistry and Materials Sciences,Sichuan Normal University,Chengdu 610068,P.R.China)

Dissipative particle dynamics(DPD)simulation technique is used to elucidate the microphase separation behavior of block copolymers in nanodroplets.The simulation is performed by relaxing disordered copolymer nanodroplets in a solvent bath.Microphase separation is then carried out inside the nanodroplet,which allows block copolymers self-assemble into many new morphologies differing from those formed in pure melts or in solution.These patterned structures depend on the volume ratio of solvophilic/solvophobic blocks(RH/T).As the value of RH/Tincreases,the following structures are formed: plum-pudding microsphere,volleyball-like structure,multilamellar vesicle,cage-like structure,nanorods, and discrete micelles.Density analysis is performed to characterize the onion′s structure.At high RH/Tvalues,block copolymers exhibit mainly solvophilicity and form swollen loose structures or small micelles suspended in the solvent.The simulation results are in good agreement with experimental and theoretical results.

Dissipative particle dynamics;Onion phase;Microphase separation

10.3866/PKU.WHXB201202142

O648

∗Corresponding author.Email:wsgchem@foxmail.com.

The project was supported by the Science and Technology Plan of Sichuan Province,China(2010JY0122),Science Research Fund of Sichuan Normal University,China(10MSL02),and 251 Key Talent Program of Sichuan Normal University,China.

四川省应用基础项目(2010JY0122),四川师范大学校级面上项目(10MSL02)和“251重点人才培养工程”资助