![Introduction
Applications
Objective
What is a Janus particle?
1
• two symmetric hemispheres
characterized by different surface properties
• form a variety of clusters
such as micelles, vesicles or layers
analyze the process of cluster forming under shear flow
• design of future nano-materials
[1] Soft Matter, 2015.11, 3767-3771
[1]
• drug delivery
• emulsion stabilizers
[2] https://www.google.co.jp/search?q=cell+targeting
[2]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Dynamics and Structure of Janus Particles
- 1. Dynamics and Structure of Janus Particles B4 Okura Tatsuya Department of Chemical Engineering Transport Phenomena Lab.
- 2. Introduction Applications Objective What is a Janus particle? 1 • two symmetric hemispheres characterized by different surface properties • form a variety of clusters such as micelles, vesicles or layers analyze the process of cluster forming under shear flow • design of future nano-materials [1] Soft Matter, 2015.11, 3767-3771 [1] • drug delivery • emulsion stabilizers [2] https://www.google.co.jp/search?q=cell+targeting [2]
- 3. Janus Potential Model 2 jiijjanusijrepulsionjiij UrUU q,q,rq,q,r ˆˆ)(ˆˆ ijijijrΦj,i,ijU janus rqqqqr ˆˆˆˆ n ijr 1 2 n ijr 1 2 0 2 4 ε n ijr σ n ijr σ ε rU ijrepulsion 2 exp ijr σijrλCσ ijrΦ C : interaction strength : range of the anisotropic interaction iqˆ ijr jqˆtail head jiij rrr : diameter Potential Energy Repulsion Potential Janus Potential Truncated LJ potential LJU repulsionU
- 4. Multi-particle Simulation Previous Research [1] Soft Matter, 2015.11, 3767-3771 3 <M> E /N : Average cluster size : Shear rate : Energy per particle High Low breakup and reform unstable clusters destroy clusters: : rij iqˆ jqˆ Binary Simulation
- 5. Simulation Method ii VR other i H iiiM FFV H iii NΩI 0 fu pfftf fp )( σIuu Smoothed Profile Method a : Particle radius : Interface width : Interface function Fundamental Equations Particles Host fluid 4 R. Yamamoto et al., Phys. Rev. E, 71, 036707 (2005) Newton – Euler equations Navier – Stokes equation
- 6. 5 Results 1 • Phase diagram of pair stability connected separated C C : : : : D4 2 5 10-2 10-2 3 )2/,2/( Lu connected separated C 1 3 5 7 òòòò òò 10-4 10-3 10-2 10-1 Pe 0.05 0.5 5 50 òòòò òò kBT =13 Tk D B D uL Pe
- 7. 6 Results 2 C / kBT = 50C / kBT = 5 f = 0.01 = 0.01 high temperature low temperature
- 8. 7 N = 13 icosahedron Structure • Narrow peak of N=13 • Various cluster size between N=6 and N=12 [1] Soft Matter, 2015.11, 3767-3771 when conditions C / kBT = 0.1 Pe = 50 f = 0.01
- 9. Numerical analysis of the Structure 8 • Radial distribution function Rosenthal , Gubbins , and K lapp JCP, 136, 174901 (2012) g r( )= V 4pr2 N2 d r -rij( ) j¹i å i å gp r( )= V 4pr2 N2 d r -rij( ) ˆqi × ˆqj j¹i å i å ga r( )= V 4pr2 N2 d r -rij( ) ˆqi × ˆrij j¹i å i å rg rijiqˆ jqˆ rij iqˆ jqˆ gp r( )> 0 gp r( )< 0 ga r( )> 0 ga r( )< 0 peak peak peak peak g r( )®1 r ®¥ tail-to-tail head-to-head rgparallel rg elantiparall
- 10. 9 gp r( )= V 4pr2 N2 d r-rij( ) ˆqi × ˆqj j¹i å i å ga r( )= V 4pr2 N2 d r-rij( ) ˆqi × ˆrij j¹i å i å 0rga 0rga peak peak 0rgp 0rgp peak peak /r/r Numerical analysis of the Structure g r( )= V 4pr2 N2 d r -rij( ) j¹i å i å /r N = 13icosahedron ga(r) gp(r) g(r)
- 11. 10 Results 4 f = 0.2 = 5C γ= 0.01
- 12. 11 Results 5 Pe = 0 0 02.0 gyro layers f = 0.3 Pe =10 02.00
- 13. 12 rijiqˆ jqˆ Numerical analysis of Structure i ij ijiija rr Nr V rg rq ˆˆ 4 22 /r i ij jiijp rr Nr V rg qq ˆˆ 4 22 /r tetra-layers ga(r) gp(r) 0rgp 0rgp peak peak 0rga 0rga peak peak
- 14. 13 Rheology gyro tetra-layers ≃ 0.3f 0 : viscosity 02.001.0
- 15. 14 gyro tetra-layers ≃ 0.3f 0 02.001.0 ≃ 0.01f micelles (icosahedrons) elongated micelles ≃ 0.2f Conclusions
- 16. Thank you for your attention 15
- 17. Appendix 16
- 18. 17 LJU repulsionU Potential Model jiijjanusijrepulsionjiij UrUU q,q,rq,q,r )( ijijijrΦj,i,ijU janus rqqqqr ˆˆˆˆ 2 exp ijr σijrλCσ ijrΦ
- 19. 18 gp r( )= V 4pr2 N2 d r-rij( ) ˆqi × ˆqj j¹i å i å ga r( )= V 4pr2 N2 d r-rij( ) ˆqi × ˆrij j¹i å i å 0rga 0rga peak peak 0rgp 0rgp peak peak /r/r Numerical analysis of the Structure g r( )= V 4pr2 N2 d r -rij( ) j¹i å i å /r ga(r) gp(r) g(r) gyro ≃ 0.3f 0
- 20. 19 rijiqˆ jqˆ Numerical analysis of Structure i ij ijiija rr Nr V rg rq ˆˆ 4 22 /r i ij jiijp rr Nr V rg qq ˆˆ 4 22 /r tetra-layers ga(r) gp(r) 0rgp 0rgp peak peak 0rga 0rga peak peak g(r) g r( )= V 4pr2 N2 d r -rij( ) j¹i å i å ≃ 0.3f 02.0
- 21. 20 Appendix • Compare zigzag with Lees Edwards • Add terms of potential energy to the Janus potential model x y zigzag Lees Edwards x y artificial • Cluster size analysis with algorithm Rosenthal , Gubbins , and K lapp JCP, 136, 174901 (2012)
- 22. 21N = 13icosahedron Pe=50 ,Φ=0.01 , C=5 (a) i ij ijrr Nr V rg 22000 4 Ste /r rg000 Numerical analysis of the Structure time E/N
- 23. 22 Simulation Conditions 1 box size : 64×64×64 x y zigzag time step : 100×300 2Re uD ),1,1( u initial orientation : tail to tail Binary simulation : 10-4 ~ 10-2 : 6 : 1 TkB Re : 0.036 ~ 0.36 3 ijij ijr σijrλCσ jiijjanusU rqqq,q,r ˆˆ 2 exp ˆˆ where C : interaction strength : range of the anisotropic interaction : diameter
- 24. 23 Simulation Conditions 2 box size : 128×128×128 : 0.01 : 6 : 0.1 ~1 3 TkB ijij ijr σijrλCσ jiijjanusU rqqq,q,r ˆˆ 2 exp ˆˆ where time step : 300×500 2Re uD ),1,1( u Re : 0.036 ~ 0.36 Multi-particle simulation Initial distribution: uniform random Lees Edwards x y C : interaction strength : range of the anisotropic interaction : diameter
- 25. 24 2 Re uD ),1,1( u ijrjqiqjq,iq,ijr ˆˆ 2 exp ˆˆ ijr σijrλCσ janusU 0 0 0 )skrew( xy xz yz ΩΩ ΩΩ ΩΩ Ω Appendix
- 26. 25
- 27. 26 /r g110 r( ) g101 r( ) /r rg000 /r
Editor's Notes
- Thank you for coming to my presentation. Today, I will talk about Dynamical properties and Structure of Janus Particles dispersions.
- To begin with, I’m going to give you a feeling of what a Janus particle looks like. As you can see in this figure, a Janus particle has two symmetric hemispheres, characterized by different surface properties. According to the surface characteristics, these particles can form a variety of clusters such as micelles, vesicles, or layers. Such a system can be useful for the design of nano-materials which have potential applications as drug delivery systems or emulsion stabilizers. In this research, I focus on the process of cluster forming under shear flow.
- First, I’m going to explain how the model is constructed. This is one of the simplest Janus particle models. It’s a sphere where one half is covered with an attractive patch and the other one( is covered with) a repulsive patch. I call the blue part the tail and orange one the head. The Potential Energy is described as a sum of Urepulsion and Ujanus. r is the distance between particles, and normalized vector q denotes the orientation of the particle. Urepulsion includes an isotropic contribution. I adopted a truncated LJ potential to avoid overlapping of the particles. On the other hand, UJanus includes an anisotropic contribution, which depends not only on the distance but also on the orientation. where σ is the diameter and the parameters C and λ denote the interaction strength and range, respectively. The upper figure shows the Janus pair potential model for four distinct configurations. In this model, tail to tail is the most stable configuration.
- Previous research has studied what happens to these Janus particles under shear. (a) consider two particles which are in a tail-to-tail configuration. (b) If add the shear, it makes a particle move and rotate. (c) At one point, when the shear is strong enough, the pairs are not stable. So why shear flow? why is it important to apply shear? Multi-particle simulations suggest that at low shear rate, shear can help to breakup and reform aggregates which have energetically unfavorable configurations. Furthermore, shear flow increases the mobility of the dispersed particles and this improves the probability of merging free particles and unstable aggregates. However, this process cannot be sustained indefinitely, and clusters rapidly decay when shear rate is increased further.
- In order to investigate the behavior of Janus particles, I applied direct numerical simulations to spherical particles immersed in a host fluid, using the smoothed profile method. The motion of the particles is calculated by the Newton-Euler equations. The dynamic of the fluid is described by the Navier-Stokes equation.
- (From now, I am going to show you some simulation results.) At first, I conducted some simulations with two particles. This phase diagram shows the stability of a pair as a function of interaction strength and shear rate. I put two particles with tail to tail configuration at the center of the system. Then I added the shear. Here, I will show you two movies at different states. Two particles are moving and rotating, but they’re still stable. when hydrodynamic force affects two particles more than Janus attraction , they cannot keep the tail to tail configuration.
- Next, I conducted multi-particle simulations. Let me show you the comparison among two temperatures at low volume fraction. At high temperature you can see a lot of free particles and a few clusters because of the fluctuation of the particles. On the other hand, at low temperature, you can see more stable aggregates. We can also say that the lower temperature has a big influence on the process of making up the stable clusters.
- When I look at the detail of the structure, I observed micelles such as icosahedrons composed of 13 particles, including a single particle as the cluster center, at low volume fraction and low temperature. This behavior has been already reported in the literature.
- In order to identify the structure, I employed radial distribution function, defined here. g(r) counts the number of neighboring particles in a shell with distance r from a center particle. But just standard g of r is not enough because Janus particles have the orientation. So, I introduced extra g of r to get more detailed information. They can help me to distinguish the configuration. Gparallel , if positive, will give me parallel orientations. Gantiparallel, if positive, will give me antiparallel orientations. Specifically, positive values indicate tail to tail configuration.
- I calculated three g of r. Then, I got three peak positions almost corresponding to an ideal icosahedron, described as dotted line. In this sense, my data confirms the icosahedral structure indicated by the snapshot.
- More interestingly, at higher volume fraction (φ = 0.2), I observed larger micelles than icosahedrons even at high temperature. Then they become linked to one another in the direction of the shear flow and finally merge into huge , elongated micelles. They look like columns.
- When φ = 0.3, in the absence of shear (γ ̇ = 0), I did not find any well-regulated structure. But they look like gyroidal structure. As the shear rate is increased up to γ ̇ = 0.02, the structure has changed and eventually turned into clear layers.
- From the numerical analysis, I confirm that there are a lot of side by side configurations and tail to tail configurations, looking at the different g(r) Obviously, they are not icosahedrons anymore. They seem to be like tetra-layers.
- Finally, I’m going to show you the rheological results. This graph shows that at low volume fraction viscosity is constant regardless of shear rate. However, at high volume fraction, preliminary results represent shear-thickening. I found this behavior at the end of my research, so I don’t fully understand the mechanism yet. But, I expect that there is a correlation between their viscosity and large scale structure because the structure is different. (I think this is because shear rate becomes considerably large so that the interaction between particles can be neglected. At low shear rate, I could not find the steady state because the simulations take time much longer. So I’m not quite sure these values are safe. )
- In conclusions, I have analyzed the structure as a function of shear rate, temperature, volume fraction and interaction strength, and observed different types of aggregation depending on these factors. However, I did not find any clear bilayers or vesicles. I suspect that this is because of the lack of any attractive interaction for side-by-side configurations. In future work, I will consider this matter in detail. Thank you for your attention.
- I calculated three g of r. Then, I got three peak positions almost corresponding to an ideal icosahedron, described as dotted line. In this sense, my data confirms the icosahedral structure indicated by the snapshot. (I can also say that there is no head-to-head configuration with distance σ from every particles.)
- From the numerical analysis, I confirm that there are a lot of side by side configurations and tail to tail configurations, looking at the different g(r) Obviously, they are not icosahedrons anymore. They seem to be like tetra-layers.
- 「この挙動は、zigzagの不自然な部分が引き起こすものかどうかをチェッックするため、Lees_Edwards のシステムと比較してみました。」 先ほどの、動径分布関数は測定したターゲットの全情報を足し合わせた平均的な情報であるため、これだけでは、詳細なクラスターサイズはわかりません。 なので、右上のようなクラスター判定のアルゴリズムを考えて、 横軸がクラスターサイズ、縦軸が出現確率を示す、グラフを作成しようと思っています。 今までのシミュレーションはすべてzigzagシステムで行いました。 このシステムは上下L/4の場所でx方向に剪断が最大にかかっていて、その部分では定常剪断が不連続になってしまい、不自然です。 そのため、Lees_Edwrds と比べたいと思います。 最後にもし時間があれば、Janus potential の式にside by side の相互作用の項を加えて、どのようなクラスターが得られるのかを見たいと思っています。 以上で終わります。
- I tried to find a steady state from the time change of the total energy per particle. I extracted the data after the steady state (time= 8700) and calculated three radial distribution functions. I got three peak positions almost corresponding to an ideal icosahedron, described as dotted line. In this sense, my microscopic data confirms the icosahedral structure indicated by the snapshot.
- Next, I conducted multi-particle simulations to observe the effect of temperature on the structure. Here are the simulation conditions.