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RSC Advances RSC Advances PAPER View Article Online View Journal | View Issue Dissipative particle dynamics simulation of multicompartment micelle nanoreactor with Cite this: RSC Adv.,2018,8, 37866 channel for reactants Seung Min Lee,a Nicholas Bond,a Connor Callaway,a Benjamin Clark,a Emily Farmer,a MacKensie Mallarda and Seung Soon Jang *abcd The structural variation of multicompartment micelles is investigated using a dissipative particle dynamics simulation method for nano-reactor application. It turns out that well-defined multicompartment micelles with channel structures can be generated through the self-assembly of triblock copolymers consisting of a hydrophilic (A), a lipophilic (B), and a fluorophobic (C) block arranged in a B–A–C sequence: The corona and core are formed by the hydrophilic A block and the fluorophilic C block, respectively while the channel between the aqueous phase and core is formed by the lipophilic B block and the core. By performing a set of simulations, it is confirmed that channel size can be controlled as Creative Commons Attribution-NonCommercial 3.0 Unported Licence. a function of the block length ratios between blocks A and B. Furthermore, it is also confirmed that the reactants pass through such channels to reach the micelle core by analyzing the pair correlation Received 22nd August 2018 functions. By monitoring the change of the number of reactants in the multicompartment micelle, it is Accepted 6th November 2018 revealed that the diffusion of reactants into the core is slowed down as the concentration gradient is DOI: 10.1039/c8ra07023g decreased. This work provides mesoscopic insight for the formation of multicompartment micelles and rsc.li/rsc-advances transport of reactants for use in the design of micelles as nanoreactors. 1. Introduction catalysts in the cores of MCMs.5 The outer corona of MCMs can This article is licensed under a be used to stabilize the hydrophobic core and immobilize Multicompartment micelles (MCMs) have attracted intensive a catalytic site, preventing the active center from precipitating attention recently in the colloidal science community since the in water.13,14 MCMs contain multiple well-dened spaces in a nanoscale An additional advantage of MCMs is that the internal Open Access Article. Published on 12 November 2018. Downloaded 9/25/2021 1:39:34 PM. structure, which has shown great potential for nanoreactor structure of a multicompartment micelle is precisely tunable by technology.1–10 Thanks to the successful progress in ne altering polymer block lengths and functional groups.15,16 synthesis in polymer chemistry, well-dened architecture in Previous studies by Weck et al. suggested that the shell cross- a multi-block copolymer chain can lead to highly controlled linked MCM could be used as nanoreactors for the hydrolysis congurations in their aggregates.7 kinetic resolution of epoxides.5 The outer shell of the MCM can In general, a simple micelle is comprised of a hydrophilic provide increased selectivity for catalysis by modifying the shell and a hydrophobic core. MCMs are comprised of hydro- polymers that make up the corona. philic shells and segregated hydrophobic cores.11 MCMs have Although many experimental studies have been conducted to been studied for their unique structures with distinct spaces study the behavior of micelles, it is not easy to experimentally which can potentially see use in applications of drug-delivery by obtain detailed information regarding the internal structures of selectively encapsulating drugs11 and by releasing the drugs the MCM with high resolution.17 In this context, the computer under changes in external conditions like temperature and simulation methods have become powerful tools for studying the pH.12 These ideas can be applied for nanoreactors by equipping structures and behaviors of micelles consisting of amphiphilic multiblock copolymers. Dissipative particle dynamics (DPD) has been effectively used in simulating amphiphilic copolymers at 18 aComputational NanoBio Technology Laboratory, School of Materials Science and the mesoscale by employing the Flory–Huggins parameter Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, Atlanta, GA theory.19 In our previous study, indeed, such DPD simulation has 30332-0245, USA. E-mail: [email protected] been used to study the feasibility of producing complex- b Institute for Electronics and Nanotechnology, Georgia Institute of Technology, structures of MCMs formed from multiblock copolymers.20–22 Atlanta, GA, USA Aer these previous works, our interest has been focused on cParker H. Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, GA, USA how to regulate the transport of reactant molecules into the 19 dStrategic Energy Institute, Georgia Institute of Technology, Atlanta, GA, 30332, USA MCM. Therefore, using DPD simulation method, rst, we 37866 | RSC Adv.,2018,8,37866–37871 This journal is © The Royal Society of Chemistry 2018 View Article Online Paper RSC Advances investigate how the channel structures can be designed on the the blocks B, A, and C are covalently bound. All DPD simula- corona of MCM built from B–A–C triblock copolymers, and tions were performed in a simulation box of size 30 Â 30 Â 30 ff 3 secondly, we characterize the e ects of such channel size on the rc with periodic boundary conditions with a reduced bead 3 transport of reactants. density r(rc /Vm) of 3, meaning that the number of DPD beads are the same 81 000 for all DPD simulation. The concentration 2. Models and simulation method of triblock copolymer is 5% of the total number of beads, and the remainder of the system (95%) is beads representing water. 2.1 DPD simulation method All the simulations were started from a random congura- In a dissipative particle dynamics simulation, we use bead- tion. The repulsive parameters used for our DPD simulations spring model, meaning that one bead represents a group of are summarized in Table 1. Although, this study was primarily multiple atoms. This approach is very benecial to simulate based on DPD simulations, the relevance of reactant transport mesoscale systems which is very hard to be described by full- to the physical scale can be made through assuming a bead has ˚3 atomistic methods.18 the volume of 5 water molecules, about 150 A , as demonstrated by Wang and coworker.17 Thus, the physical length scale from The motions of beads are described by integrating Newton's pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ˚ equations of motion the reduced length is rc ¼ 3 Â Vbead z 7:66 A, the average À1 dr dv mass is about 90 g mol . The reduced time step was 0.05 and, i ¼ v and m i ¼ f (1) dt i i dt i accordingly,pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the physical time scale from the reduced time scale is t ¼ r 2 m=K T z 4:61 ps. Since the friction coefficient (g) where r , v , and m denote the position, velocity, and mass of the c B i i i and noise amplitude (s) are calculated by the uctuation– i-th particle, respectively, and fi denotes the force acting on the i- pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 23 g ¼ : = s ¼ th particle. The force acting on a bead contains three parts: dissipation theorem, 4 5 mkBT rc and 25kBT/rc. The X harmonic spring constant for the bond between beads was set ¼ C þ D þ R fi Fij Fij Fij (2) to be 4. The equilibration of the system was con rmed by Creative Commons Attribution-NonCommercial 3.0 Unported Licence. jsi monitoring the pressure and temperature of the system. The 5 C simulations were run for 3.5 Â 10 reduced time steps until the Fij is the conservative repulsive force given by À Á À Á equilibrium states of micelle structures are obtained; the details 1 À ^ \ C ¼ aij À rij rÁc rij rij rc of the block lengths of triblock copolymers used in this study Fij (3) 0 r $ rc ij are summarized in Table 2. The blocks A is hydrophilic while where aij is the maximum repulsion force between bead i and the blocks B and C are hydrophobic and more hydrophobic, bead j and rij is the distance between two beads i and j. Groot respectively. The simulations were perform using DPD module and Warren proposed a relationship between the repulsive in Materials Studio.24 – This article is licensed under a parameter and the Flory Huggins interaction parameter cij expressed as:19 2.3 Association of reactants into micelle aij ¼ aij + 3.5cij (4) Aer the micelle structures were prepared in equilibrium state, Open Access Article. Published on 12 November 2018. Downloaded 9/25/2021 1:39:34 PM. 1% of the water beads were randomly replaced with reactant – where aij is equal to 25. The Flory Huggins interaction param- beads in order to simulate the association of reactants into the eter can be calculated using the newly developed method by our micelle. Although the simulations were run for 5 Â 104 time 22 group. steps, most reactants were associated into micelle within 1.0 Â D R 4 The dissipative force Fij and the random force Fij depend on 10 time steps. only on the position and velocity of the i-th particle. The posi- Aer the association of reactants into micelle, the gyration ¼ À ¼ À tion and velocity are given by rij ri rj and nij ni nj, tensors were calculated for the core of the micelle and the prin- respectively. The forms of these forces are expressed as: cipal moments were calculated. To determine whether or not the À ÁÀ Á D ¼ D b $! b core of the micelle is spherical, the asphericity was calculated for Fij gu rij rij n ij rij (5) each of the micelles. It is noted that the micelle is a perfect sphere À Á R ¼ R b if the asphericity is zero.
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