Effect of Architecture on Micelle Formation and Liquid-Crystalline

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Effect of Architecture on Micelle Formation and Liquid-Crystalline Ordering in Solutions of Block Copolymers Comprising Flexible and Rigid Blocks: Rod-Coil vs Y-Shaped vs Comblike Copolymers Kirill E. Polovnikov, and Igor I. Potemkin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b09127 • Publication Date (Web): 06 Oct 2017 Downloaded from http://pubs.acs.org on October 7, 2017

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The Journal of Physical Chemistry

Effect of Architecture on Micelle Formation and Liquid-Crystalline Ordering in Solutions of Block Copolymers Comprising Flexible and Rigid Blocks: RodCoil vs Y-Shaped vs Comblike Copolymers Kirill E. Polovnikov#,§ and Igor I. Potemkin*,#, #

Physics Department, Lomonosov Moscow State University, Moscow 119991, Russian

Federation §

The Skolkovo Institute of Science and Technology, Skolkovo 143026, Russian Federation

DWI − Leibniz Institute for Interactive Materials, Aachen 52056, Germany

*E-mail: [email protected] (I.I.P.).

Abstract. Micelle formation of amphiphilic block copolymers of various architectures comprising both flexible and rodlike blocks were studied in a selective solvent via dissipative particle dynamics (DPD) simulations. Peculiarities of self-assembly of Y-shaped (insoluble rigid block and two flexible soluble arms) and comblike (soluble flexible backbone with insoluble rigid side chains) copolymers are compared with those of equivalent rod-coil diblock copolymer. We have shown that aggregation of the rigid blocks into dense core of the micelles is accompanied by their nematic ordering. However, the orientation order parameter and aggregation number of the micelles are strongly dependent on macromolecular architecture. Relatively small micelles of pretty high nematic order parameter, S2 »0.5-0.8, are the features of the Y-shaped and rod-coil copolymer micelles. They are characterized by different response to the solvent quality worsening. Aggregation number of the rod-coil diblock copolymer micelles increases and of Y-shaped copolymer micelles decreases at the solvent quality worsening. However, the order parameter grows in both cases achieving a maximum value for the Y-shaped copolymer micelles. Herewith, the core elongates. On the contrary, comblike copolymers selfassemble into bigger spherical micelles whose core possesses lower nematic order of the rods, S2 » 0.3-0.4. The aggregation number is shown to depend on the length of the combs (on the number of repeating elements in the architecture). Possible physical reasons for such behavior of the systems are discussed.

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Introduction

Self-assembly of block copolymers into micelles of various morphologies in selective solvents represents a reliable way for the design of many functional systems including carriers for drug delivery,1-5 templates for the formation of metallic nanoparticles of predefined shape and their ordering on substrate,6,7 for catalysis8-11 and many others. The “simplest” and most studied macromolecular objects capable of the formation of the micelles are diblock copolymers. Insoluble blocks aggregate into a dense core and the soluble blocks form swollen corona of the micelles which provides their colloidal stability.12-14 The shape of the micelles is primarily controlled by the chemical composition of the copolymer. Spherical micelles are stable in a wide range of compositions: the longer the insoluble block, the bigger the micelles. Formation of worm-like micelles and vesicles is possible in the so-called crew-cut regime, when the soluble blocks are shorter than the insoluble ones.15-18 Diversity in the self-assembly process and ultimate structure of the micelles can be introduced via proper design of the sequence of monomer units19-25 and architecture26-28 of the macromolecules as well as using polyelectrolyte copolymers29-34 or mixtures of different macromolecules.35-37 For example, “living” or weak micelles capable of the size transformation upon weak variation of external conditions (like “reel-in” effect38-40) can be formed by gradient copolymers24 or polypeptide diblock copolymers.19 Unimolecular micelles, sometimes with multiple core, are known for amphiphilic arborescent macromolecules.28,41-43 If the self-assembly of the linear chains in selective solvents is pretty well understood, the effect of the architecture remains a challenging task. In particular, micelle formation by amphiphilic comb-like macromolecules and effect of rigidity of the side chains on internal micellar structure is not studied yet. Up to now, comb-like macromolecules were studied as good candidates for the design of liquidcrystalline systems. Densely grafted macromolecules possess enhanced (induced) persistence length due to the strong interactions between the side chains: the persistence length increases with the increase of both the length of the side chains and their grafting density.44-49 Also, flexibility of the side chains influences the induced persistence length.50-53 Therefore, if the persistence length exceeds certain threshold value dependent on the macromolecular thickness, both solutions of the comblike macromolecules and their thin layers can be subjected to the liquid-crystalline ordering. The comblike structure in combination with the induced persistence length allows creating super-soft elastic materials54,55 and diverse nanostructures in monolayers of adsorbed macromolecules.56-64 Self-assembly of molten comb-copolymers, containing ACS Paragon Plus Environment

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immiscible backbone and/or side chains of different chemical structures, can result in microphase segregation.65-69

Solutions of amphiphilic comblike copolymers reveal peculiarity in self-assembly due to their architecture.

In particular, possible structures of single macromolecules with solvophobic

backbone and solvophilic side chains in dilute solutions were studied using a scaling approach.70 It has been demonstrated that depending on the grafting density of the side chains, the backbone collapse led to the formation of spherical, cylindrical or necklace-type structures. Similar behavior was observed by molecular dynamics71 and Monte-Carlo72 simulations. The aggregation of such macromolecules upon increase of polymer concentration was studied using dissipative particle dynamics (DPD) modelling73, where the authors revealed the stability of onion-like multilayer vesicles and demonstrated merging of several vesicles into the large one. Moreover, DFT approach was used to demonstrate formation of various nanostructures of comblike macromolecules bearing solvophobic side groups and solvophillic backbone in a 10% solution. They included spherical, cylindrical and toroidal micelles, vesicles and sphere-invesicle structures.74 The authors showed, that worsening the solvent for the side groups leads to the transitions from the spheres to the cylinders and then back to spheres. In the subsequent paper, they demonstrated an improved aggregation as the linear chains of the same chemical structure are added to the system.75

Using rigid (mesogenic) side groups in the comblike architecture may provide liquid-crystalline ordering in the resulting self-assembled structures, and, as a consequence, new properties of the materials. Up to now, the effect of the mesogenic groups was mainly studied in molten polymer systems. In particular, two-scale ordering in the melt of diblock copolymers with liquid crystalline side groups attached to one of the blocks76-82 were observed. In such systems, a competition of liquid crystalline (usually smectic) ordering of the mesogenic side groups and microphase segregation of the blocks is responsible for the morphology of the materials in which the liquid crystalline domains have the length scale in the range of 0.5-5 nm whereas amorphous domains can reach the size of 100 nm. The order-disorder transition83,84 as well as strong segregation regime85 in such systems were studied in details.

It has been shown also that the liquid

crystalline groups can be efficient to stabilize perpendicular orientation of the amorphous domains (cylinders and lamellae) in thin films.77,86-91

In aqueous solutions, hydrophobic mesogenic side groups should aggregate forming dense core ACS Paragon Plus Environment


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whereas soluble backbone can provide colloidal stability of the micelles forming their corona. Such aggregation is accompanied by liquid crystalline ordering like in melts.83-85 However, connectivity of the mesoges can influence their ordering in the core depending on their grafting density and the length. One can expect that the structure of the obtained micelles will be different as compared to rod-coil diblock copolymers.92,93 In this paper, using dissipative particle dynamics (DPD) method, we study the self-assembly in the solutions of comblike macromolecules with solvophobic rodlike side chains and solvophilic flexible backbone. We investigate the influence of the solvent quality and the number of the side rods on liquidcrystalline ordering in the micellar cores. To demonstrate the effect of the macromolecular topology, we compare the micelles with those formed by equivalent linear rod-coil diblock copolymers.

Model and Simulation Method The DPD method was introduced by Hoogerbrugge and Koelman in 1992 and suggests the means for mesoscale coarse-grained simulation that allows for hydrodynamics description of the system up to the microsecond range.94 In this method, each particle of mass mi represents a cluster of atoms that interact with each other via soft potential. The positions and velocities of the particles are renewed at each time step according to the instant pairwise net forces in the framework of the Newton's equation of motion: = ,

=

= ( + + )

where denotes a full force acting on the ith particle and , , stand for the conservative, dissipative and random forces, respectively. The summation concerns only the particles within a certain cutoff distance , beyond which all the forces vanish. The dissipative force responds for the energy loss due to the friction between the adjacent particles, while the random force describes the mesoscale “Brownian” influence of the other particles, incorporating causality to the particles motion and heating up the system. These two forces are implemented through a so-called “DPD thermostat” in the certain coupled fashion, so ACS Paragon Plus Environment

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that the fluctuation-dissipation theorem is satisfied:95

= −

and

= where = − is relative velocity between the pair of the ith and jth particles, and are the weight functions chosen as: () = { ()} = (1 − ) , < Also, γ and σ are the amplitudes of the forces with the certain relationship in the thermostat: = 2$% & Usually, the conservative force is represented by a soft repulsion between the particles within the cutoff distance: ' = ( ( ) where the conservative weight function () = 1 −

, <

and interaction parameters ( set the maximum values of the repulsion between the ith and jth particles.

One of structures of the comblike macromolecule with stiff side chains and flexible backbone is depicted in Figure 1, left. The solvent is selective for different parts of the macromolecules: side chains (B) are insoluble, while the backbone (A) is soluble. We consider here only the case of symmetric composition, setting the lengths of the side chains and the flexible spacers equal to 10 beads. We consider three different structures of the macromolecules having 14, 5 and 1 side chains, Figure 2. Self-assembly for the comblike macromolecules is compared with that of ACS Paragon Plus Environment


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equivalent symmetric rod-coil diblocks, Figure 1, right. Equivalency means that the lengths of the stiff and flexible blocks are equal to the lengths of the side chain and the spacer, respectively. Also, the polymer concentrations are equal in both cases.

Figure 1. Schematic representation of a comblike macromolecule with five side chains (left) and a symmetric rod-coil copolymer (right). Rod-like side chains (B) consist of insoluble beads and flexible backbone (A) is soluble.

Figure 2. Different comblike architectures containing 14 and 5 rod-like side chains (left and middle). Y-shaped molecule with two flexible arms (right).

We deal with a three-component system, which can be described with six interaction parameters: ()) , (%% , (** , ()% , ()* , (%* , where the subscripts A and B refer to A- and B-beads of the backbone and side chains and S denotes the solvent. The relationship between the interaction parameters ( and the Flory-Huggins parameters + has been established by Groot and Warren:96 ACS Paragon Plus Environment

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( = ( + 3.497+ for the density of the system ρ = 3. For the sake of convenience, dimensionless = $% & =

= 1 are introduced. Consequently, the time unit cannot be chosen independently: 1 = 2 /$% & , which is of the order of a picosecond. It turns out that, as a bonus of coarsegraining and soft potential implementation, the DPD method allows for a larger time step during the simulation in comparison with molecular dynamics method. It was shown96 that increasing of the time step up to 4 = 0.061 does not sufficiently alter the equilibrium temperature of the

system, which presents the optimal choice for a DPD simulation. The ( parameters set the self-incompatibility of the species and can be reconstructed from thermal incompressibility of a pure substance. In modelling, where no precise agreement with experiments is expected, for the sake of definiteness, it seems convenient to choose the incompressibility of water. As a result, the parameters ( = 75$% &/8 for the chosen density in the system should equal96 ()) = (%% = (** = 25.

It can be inferred, that fairly compatible species should be equipped with the interaction parameter near ( = 25 and ( increases with worsening of the compatibility. In our study, the

hydrophilic block A has the parameter ()* = 26, and the incompatibility between the blocks is

pretty weak, ()% = 28, and the strength of hydrophobicity of the B block is varied within the range (%* = 35 ÷ 70.

Connectivity of the beads into the certain polymer architecture is obtained via setting springs between the adjacent beads: * ' = ; − <

It’s known that precise values of the springs’ rigidity and their equilibrium lengths are not of tremendous impact on the qualitative effects in DPD system. In this study, we adopt the same springs for all the bead species: ; = 10 and < = 0.7. In order to simulate the stiffness of the side chains, let us introduce the force exerted on the angle between three sequential beads, ≅ >, in every side group: ACS Paragon Plus Environment


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? @ () = A (1 + cos()) We have found out that the stiffness of side chains at K = 50 ensures negligible deviations from the rod-like conformation of the side chains. Besides that, the calculated persistent length of the side chains was about several hundreds of the bead size that is well enough for the length of the side groups chosen.

In our simulations, the cubic box of the linear size 80 measured in units of the bead diameter with imposed periodic boundary conditions was used. The total number of the beads was 1536000. In all starts, we studied 1% polymer solution with initially random distribution of the molecules. Thus, the total number of the rod-coil molecules in the box was 768, while the total number of the combs depended on the degree of polymerization. It turned out, that 106 steps were enough for equilibration of the systems.

Liquid-crystalline ordering in the micellar core was evaluated quantitatively via calculation of the eigenvalues of the following quadratic tensor of orientations: 1 G EFG = H3〈JF J 〉 − 1L 2 where averaging is performed over all the rods in the micelle. Then the orientation order parameter of an aggregate can be defined as its maximum eigenvalue, M = max Q , and the corresponding eigenvector gives the mean direction of the nematic ordering, i.e. the director. Finally, the average order parameter of the micelles in the solution is calculated via averaging of M for all the micelles in the box. This order parameter equals 1 for the parallel alignment of the rods and it is decreasing to 0 as soon as the orientation of the rods inside the micelle is getting isotropic.


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Figure 3. Snapshots of micelles obtained in the solutions of Y-shaped macromolecules (upper row) and rod-coil macromolecules (bottom row) at two different values of the interaction parameter which quantifies solvent quality for the rod-like blocks, aRS =40, 70. Aquamarine and grey beads depict rod-like and flexible blocks, respectively.

Results and discussion 1. Solutions of rod-coil vs Y-shaped copolymers

First, let us compare aggregation of the simplest “comblike” macromolecules, i.e., flexible chains having one grafted rod-like block (Y-shaped copolymer), Figure 2, right, with aggregation of the rod-coil diblock, Figure 1, right. The difference between these two structures is that Yshaped molecule has an additional flexible arm of 10 beads in comparison with the diblock. Aggregation of the rod-like blocks into the core of nearly spherical micelles is accompanied by their nematic ordering. The typical micellar structures are shown in Figure 3. The upper and bottom rows correspond to the Y-shaped and rod-coil macromolecules, respectively. Left and right columns in Figure 3 distinguish solvent selectivity: moderately ((%* = 40) and very

((%* = 70) poor solvent for the rod-like blocks. The most apparent effect, which can be seen in ACS Paragon Plus Environment


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the snapshots, is that the solvent quality worsening for the rods promotes their liquid crystalline ordering. This effect has a clear physical reason. The rods tend to decrease the area of unfavorable contacts with the solvent upon worsening its quality. In contrast to the case of flexible blocks, which can densely pack without any orientations keeping the spherical shape of the core, the rod-like blocks have to get the parallel orientation and pack into the cylinder to minimize the solvent content in the core. Quantitative information about the orientation order parameter is presented in Figure 4. We can see that for both systems S2 increases with aBS. However, the nematic ordering in the core of micelles formed by Y-shaped copolymers is more pronounced. At the first glance, this effect is counterintuitive because corona-forming blocks, whose interactions with each other tend to make the core more isotropic and corona more homogeneous, are twice bulky in the case of the Y-shaped copolymers. Therefore, one can expect more stronger disorienting effect from the flexible blocks of the Y-shaped copolymers than the rod-coil ones. However, the bulkier corona is known to be responsible for the decrease of the aggregation number of the micelles in Y-shaped copolymers with flexible blocks.97 The aggregation number of the micelles, P, formed by Y-shaped and rod-coil diblocks as a function of the solvent quality (parameter aBS) is shown in Figure 5. A drastic difference can be detected. If the aggregation number of the rod-coil diblock copolymers increases with worsening solvent quality (like in the case of flexible diblock copolymers24), the micelles on the basis of Y-shaped copolymers reveal opposite behavior. They become smaller upon worsening solvent quality. Such behavior is dictated by a presence of the branching point in the Y-shaped macromolecule. If the solvent is moderately poor for the rods, aBS=40, they form more-or-less spherical core (Figure 3, upper row) for which the branching points pack with a minimum penalty in conformation entropy of the flexible blocks (they have enough space in the spherical geometry). Worsening of the solvent quality leads to the nematic ordering of the rods in the core (Figure 3, upper row) which is driven by their dense packing and core transformation into the cylinder. Such ordering has to accompany by polarization of the corona: maximum of concentration of the flexible blocks is achieved at the ends of the cylindrical core. Furthermore, the higher the nematic ordering, the denser the corona in the cylinder ends which is unfavorable. Therefore, if the aggregation number of the micelles would grow or remain the same with aBS, the nematic ordering would provide very unfavorable polarized coronae of high density in the ends of thick cylindrical or discoid core. Instead, decrease of the aggregation number with aBS leads to the formation of thin enough cylindrical core, for which the flexible chains have enough space. They can adopt a star-like structure near each of the ends of the thin cylinder instead of a brush-like structure near the core of high aggregation number.


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Figure 4. Nematic order parameter S2 as a function of the solvent quality for the rod-like blocks, aBS: Y-shaped (squares) and rod-coil diblock (circles) copolymers.



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Figure 5. Aggregation number P of the micelles as a function of the solvent quality for the rodlike blocks, aBS: Y-shaped (squares) and rod-coil diblock (circles) copolymers. It worth to be mentioned that the decrease of the aggregation number with aBS, which is proportional to the Flory-Huggins parameter +%* (see section Model and Simulation Methods), is related to unfavorable increase of the surface energy of the core, for which the surface tension coefficient ∼ 2+%* .98 However, the volume energy of the core has stronger dependence on +%* , ?UVW ∼ +%* , thus the gain in the volume energy due to the packing of the rods in the core

overcomes the penalty in the surface energy. All the aforementioned qualitative analysis is supported by calculations of linear sizes of the core. The maximum and minimum gyration radii of the core (square root of the corresponding moments of inertia, Ji1/2) are presented in Figure 6. The difference in the maximum and minimum gyration radii is a measure of asymmetry: the higher the difference, the more the shape asymmetry of the core. We can see that the rod-coil diblock copolymers form micelles of nearly spherical core at aBS=40 and practically spherical at aBS=70. On the contrary, asymmetry of the core formed by Y-shaped copolymers increases with aBS. The core becomes longer and narrower than that of the diblock copolymer, Figure 6. The core formed by Y-shaped molecules has bigger size than the core of the diblock copolymer micelles at aBS=40, Figure 6. Keeping in mind that the aggregation numbers of both micelles are nearly equal at

aBS=40,

Figure 5, we can conclude that the average polymer density of the core formed by Y-shaped molecules is lower. This effect is related to the presence of two soluble tails which make the corona denser in comparison with the case of the diblocks. Therefore, the increase of the core size is driven by the decrease of the corona’s density.


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Figure 6. Maximum (solid) and minimum (dashed) gyration radii of the cores of the micelles, Ji1/2, as functions of the solvent quality for the rod-like blocks, aBS: Y-shaped (squares) and rodcoil diblock (circles) copolymers.

2. Solutions of comblike macromolecules

In this section, we investigate solutions of comblike macromolecules having equal grafting density of the side chains and different backbone lengths (number of the side chains), Figure 2.



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Figure 7. Snapshots of micelles formed by comblike macromolecules differing in the number n of the side chains: n=5 (upper row), 14 (bottom row). Left and right columns correspond to moderately ((RS = 40) and very ((RS = 70) poor solvent for the rods, respectively.


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Figure 8. The nematic order parameter S2 in the micellar core formed by comblike macromolecules as a function of the solvent quality aBS. Circles and squares correspond to the macromolecules with 14 and 5 grafted rods, respectively.

The typical snapshots of the micelles are shown in Figure 7. In contrast to the rod-coil and Yshaped copolymer micelles, Figure 3, the comblike copolymer micelles exhibit more spherical shape of the core where the rods are less ordered. Also, the comblike copolymer micelles are bigger. The nematic order parameter as a function of the parameter (RS is shown in Figure 8. For both comblike copolymers, S2 grows with (RS . However, the values of S2 are approximately two

times smaller than in the case of the rod-coil and Y-shaped copolymers. This effect is related to connectivity of the rods by the soluble backbone. In contrast to the Y-shaped copolymers, polarization of the corona upon worsening the solvent quality and nematic ordering of the rods is impossible in the case of the comblike macromolecules. Therefore, the backbone hinders nematic ordering of the rods in the core. Indeed, if we consider packing of two different Y-shaped molecules in fully ordered nematic core (S2=1), their antiparallel orientation allows creating such structure with minimum possible stretching of the flexible blocks. Two neighbor rods of the comblike macromolecule cannot form the antiparallel structure in the core, whereas their parallel packing (with shifting of the rods) costs additional penalty in the entropy of the backbone. Thus, highly oriented rods in micelles of the combs is less favorable structure than the weakly oriented ACS Paragon Plus Environment


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ones. The aggregation number of the micelles (the number of comblike macromolecules per micelle) strongly depends on the length of the macromolecule. The micelles formed by the longer molecules can have 3 to 5 times smaller aggregation number, Figure 9. However, the overall number of the constituent blocks does not have significant difference. For example, the cores of the micelles formed by long and short combs at (RS = 70 contain 4·14=56 and 16·5=80 rods, respectively, Figure 8. The aggregation number of the micelles formed by longer combs reveals a non-monotonous behavior. First it grows with (RS from 4 to 6 and then drops up to 4 again. The initial growth is typical for many flexible block copolymers and driven by the surface energy of the core. Further decay is due to the slight nematic ordering of the rods which is accompanied by the decrease of the size of the core with more favorable packing of the coronaforming spacers (like in the case of Y-shaped molecules).

Figure 9. The average aggregation number P of micelles formed by comblike macromolecules with 14 (circles) and 5 (squares) grafted rods vs solvent quality parameter aBS.


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Figure 10. Maximum (solid) and minimum (dashed) gyration radii of the cores of the micelles, Ji1/2, as functions of the solvent quality for the rod-like blocks, aBS: Combs with 5 (squares) and 14 (circles) grafted chains.

The non-monotonous behavior of the core size of the micelles formed by longer combs is demonstrated in Figure 10. The fact that the shorter combs form bigger micelles is also related to ratio of soluble/insoluble blocks. For the combs of 5 and 14 side chains, this ratio is 6/5 and 15/14, respectively. Therefore, if the different copolymers would form micelles of equal sizes, the density of corona would be higher for the short combs. To reduce this density, the micelles have to be bigger.

Conclusion In this paper, we have studied micelle formation in solutions of amphiphilic macromolecules bearing both flexible and rod-like blocks using dissipative particle dynamics. Different architectures were compared: rod-coil diblock copolymers, Y-shaped and comblike copolymers of different lengths, Figures 1 and 2. We have considered a selective solvent which was good for the flexible blocks and poor for the rigid ones. Therefore, aggregation of the rigid blocks into the ACS Paragon Plus Environment


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core of the micelles is accompanied by their nematic ordering. We have demonstrated that the architecture essentially influences the self-assembled structures. In particular, bulky comblike macromolecules with flexible backbone and rodlike side chains form nearly spherical micelles if the length of the spacer between neighbor side chains is equal to the length of the rod. The nematic ordering of the rods in the core is pretty weak even under condition of very high solvent selectivity. The physical reason for that is connectivity of the rods by the backbone for which the liquid-crystalline ordering is accompanied by a penalty in the free energy due to the dense packing of the loops in corona. On the contrary, more compact rod-coil diblocks and Y-shaped macromolecules form smaller micelles whose core possesses better nematic ordering of the rigid blocks. This effect is due to the ability of the rod-like blocks to form “antiparallel” structures (the flexible blocks are located at different sides) in which flexible blocks have enough space and are not subjected to a high penalty in the free energy even under high ordering of the rods. Also, we have detected a drastic difference in the behavior of rod-coil and Y-shaped macromolecules. Worsening of the solvent quality for the rodlike blocks is responsible for the growth of the aggregation number of diblock copolymer micelles, whereas the micelles on the basis of Yshaped copolymer decrease the aggregation number. The latter is accompanied by very high nematic ordering. Pretty abrupt variation of order parameter and aggregation number of the Yshaped copolymer micelles caused by variation of the solvent quality (temperature), Figures 4, 5, might be exploited in a range of sensor applications. At the same time, interestingly to mention that a comblike architecture is responsible for the formation of the spherical micelles with weakly ordered nematic core that are very stable under variation of the external conditions (e.g. temperature) leading to the change of the solvent quality. This fact might be useful in many applications, where the stable liquid-crystal ordering is of much importance.

Acknowledgment The authors acknowledge financial support from the Russian Science Foundation, project # 1513-00124. The simulations were performed on multiteraflop supercomputer Lomonosov at Moscow State University.

References

(1) Adams, M. L.; Lavasanifar, A.; Kwon, G. S. Amphiphilic Block Copolymers for Drug Delivery. J. Pharm. Sci. 2003, 92, 1343-1355.


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(2) Xu, H.; Yang, P.; Ma, H.; Yin, W.; Wu, X.; Wang, H.; Xu, D.; Zhang, X. Amphiphilic Block Copolymers-Based Mixed Micelles for Noninvasive Drug Delivery. Drug Deliv. 2016, 23, 3063–3071. (3) Kataoka, K.; Harada, A.; Nagasaki, Y. Block Copolymer Micelles for Drug Delivery: Design, Characterization and Biological Significance. Adv. Drug Delivery Rev. 2001, 47, 113−131. (4) Schmaljohann, D. Thermo- and pH-Responsive Polymers in Drug Delivery. Adv. Drug Delivery Rev. 2006, 58, 1655−1670. (5) Ahmad, Z.; Shah, A.; Siddiq, M.; Kraatz, H.-B. Polymeric Micelles as Drug Delivery Vehicles. RSC Adv. 2014, 4, 17028−17038. (6) Spatz, J. P.; Mössmer, S.; Möller, M.; Herzog, T.; Boyen, H. G.; Ziemann, P.; Kabius, B. Ordered Deposition of Inorganic Clusters from Micellar Block Copolymer Films. Langmuir 2000, 16, 407-415. (7) Haupt, M.; Miller, S.; Glass, R. Arnold, M.; Sauer, R.; Thonke, K.; Möller, M.; Spatz, J. P. Nanoporous Gold Films Created Using Templates Formed from Self-Assembled Structures of Inorganic Block Copolymer Micelles. Adv. Mater. 2003, 15, 829-831. (8) Beletskaya, I. P.; Kashin, A. N.; Litvinov, A. E.; Tyurin, V. S.; Valetsky, P. M.; van Koten G. Palladium Colloid Stabilized by Block Copolymer Micelles as an Efficient Catalyst for Reactions of C-C and C-Heteroatom Bond Formation. Organometallics 2006, 25, 154-158. (9) Bukhryakov, K. V.; Desyatkin, V. G.; O’Shea, J.-P.; Almahdali, S. R.; Solovyeva, V.; Rodionov, V. O. Cooperative Catalysis with Block Copolymer Micelles: A Combinatorial Approach. ACS Comb. Sci. 2015, 17, 76-80. (10) Rathman, J. F. Micellar Catalysis. Curr. Opin. Colloid Interface Sci. 1996, 1, 514−518. (11) La Sorella, G.; Strukul, G.; Scarso, A. Recent Advances in Catalysis in Micellar Media. Green Chem. 2015, 17, 644−683. (12) Zhulina, E. B.; Birshtein, T. M. Conformations of Block-Copolymer Molecules in Selective Solvents (Micellar Structures). Polym. Sci. U.S.S.R. 1985, 27, 570−578.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 39

(13) Birshtein, T. M.; Zhulina, E. B. Scaling Theory of Supermolecular Structures in Block Copolymer-Solvent Systems: 1. Model of Micellar Structures. Polymer 1989, 30, 170−177. (14) Halperin, A. Polymeric Micelles: a Star Model. Macromolecules 1987, 20, 2943−2946. (15) Shen, H.; Eisenberg, A. Morphological Phase Diagram for a Ternary System of Block Copolymer PS310-b-PAA52/Dioxane/H2O. J. Phys. Chem. B 1999, 103, 9473-9487. (16) Jain, S.; Bates, F. S. On the Origins of Morphological Complexity in Block Copolymer Surfactants. Science 2003, 300, 460−464. (17) Bang, J.; Jain, S.; Li, Z.; Lodge, T. P.; Pedersen, J. S.; Kesselman, E.; Talmon, Y. Sphere, Cylinder, and Vesicle Nanoaggregates in Poly(styrene-b-isoprene) Diblock Copolymer Solutions. Macromolecules 2006, 39, 1199−1208. (18) Zhulina, E. B.; Adam, M.; LaRue, I.; Sheiko, S. S.; Rubinstein, M. Diblock Copolymer Micelles in a Dilute Solution. Macromolecules 2005, 38, 5330−5351. (19) Hassouneh, W.; Zhulina, E. B.; Chilkoti, A.; Rubinstein, M. Elastin-like Polypeptide Diblock Copolymers Self-Assemble into Weak Micelles. Macromolecules 2015, 48, 4183−4195. (20) Borisova, O.; Billon, L.; Zaremski, M.; Grassl, B.; Bakaeva, Z.; Lapp, A.; Stepanek, P.; Borisov, O. Synthesis and pH- and Salinity-Controlled Self-Assembly of Novel Amphiphilic Block-Gradient Copolymers of Styrene and Acrylic Acid. Soft Matter 2012, 8, 7649−7659. (21) Lee, S. B.; Russell, A. J.; Matyjaszewski, K. ATRP Synthesis of Amphiphilic Random, Gradient, and Block Copolymers of 2-(Dimethylamino)ethyl Methacrylate and n-Butyl Methacrylate in Aqueous Media. Biomacromolecules 2003, 4, 1386−1393. (22) Seno, K. I.; Tsujimoto, I.; Kanaoka, S.; Aoshima, S. Synthesis of Various StimuliResponsive Gradient Copolymers by Living Cationic Polymerization and their Thermally or Solvent Induced Association Behavior. J. Polym. Sci., Part A: Polym. Chem. 2008, 46, 6444−6454. (23) Filippov, S. K.; Verbraeken, B.; Konarev, P. V.; Svergun, D. I.; Angelov, B.; Vishnevetskaya, N. S.; Papadakis, C. M.; Rogers, S.; Radulescu, A.; Courtin, T. et al. Block and Gradient Copoly(2-oxazoline) Micelles: Strikingly different on the Inside, J. Phys. Chem. Lett. 2017, 8, 3800−3804.


Page 21 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(24) Kravchenko, V. S.; Potemkin, I. I. Micelles of Gradient vs Diblock Copolymers: Difference in the Internal Structure and Properties. J. Phys. Chem. B 2016, 120, 12211−12217. (25) Perelstein, O. E.; Ivanov, V. A.; Möller, M.; Potemkin, I. I. Designed AB Copolymers as Efficient Stabilizers of Colloidal Particles. Macromolecules 2010, 43, 5442−5449. (26) Alsehli, M.; Gauthier, M. Arborescent Polypeptides for Sustained Drug Delivery. MRS Online Proc. Libr. 2016, 1819, DOI: 10.1557/opl.2016.70. (27) Njikang, G. N.; Gauthier, M.; Li, J. Sustained Release Properties of Arborescent Polystyrene-graft-poly(2-vinylpyridine) Copolymers. Polymer 2008, 49, 5474−5481. (28) Gumerov, R. A.; Rudov, A. A.; Richtering, W.; Möller, M.; Potemkin, I. I. Amphiphilic Arborescent Copolymers and Microgels: From Unimolecular Micelles in a Selective Solvent to the Stable Monolayers of Variable Density and Nanostructure at a Liquid Interface. ACS Appl. Mater. Interfaces 2017, 9, 31302−31316. (29) Kroeger, A.; Deimede, V.; Belack, J.; Lieberwirth, I.; Fytas, G.; Wegner, G. Equilibrium Length and Shape of Rodlike Polyelectrolyte Micelles in Dilute Aqueous Solutions. Macromolecules 2007, 40, 105–115. (30) Zhulina, E. B.; Borisov, O. V. Theory of Block Polymer Micelles: Recent Advances and Current Challenges. Macromolecules 2012, 45, 4429–4440. (31) Erel-Unal, I.; Zhu, Zh.; Sukhishvili, S.; Patyukova, E.; Potemkin, I.; Kramarenko, E. Two Types of Block Copolymer Micelles with Ion-Containing Cores, Macromol. Rapid Commun. 2010, 31, 490-495. (32) Bodrova, A. S.; Kramarenko, E. Yu.; Potemkin, I. I. Microphase Separation Induced by Complexation of Ionic-non-Ionic Diblock Copolymers with Oppositely Charged Linear Chains. Macromolecules 2010, 43, 2622–2629. (33) Venev, S. V.; Reineker, P.; Potemkin, I. I. Direct and Inverse Micelles of Diblock Copolymers with a Polyelectrolyte Block: Effect of Equilibrium Distribution of Counterions. Macromolecules 2010, 43, 10735–10742. (34) Kalogirou, A.; Gergidis, L. N.; Miliou, K.; Vlahos, C. Complexation of Polyelectrolyte Micelles with Oppositely Charged Linear Chains. J. Phys. Chem. B 2017, 121, 1982–1991.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 39

(35) Borovinskii, A. L.; Khokhlov, A. R. Micelle Formation in the Dilute Solution Mixtures of Block-Copolymers. Macromolecules 1998, 31, 7636-7640. (36) Liu, T.; Qian, Y.; Hu, X.; Ge, Zh.; Liu, S. Mixed Polymeric Micelles as Multifunctional Scaffold for Combined Magnetic Resonance Imaging Contrast Enhancement and Targeted Chemotherapeutic Drug Delivery. J. Mater. Chem. 2012, 22, 5020–5030. (37) Palyulin, V. V.; Potemkin, I. I. Mixed versus Ordinary Micelles in the Dilute Solution of AB and BC Diblock Copolymers. Macromolecules 2008, 41, 4459−4463. (38) Okabe, S.; Seno, K.; Kanaoka, S.; Aoshima, S.; Shibayama, M. Micellization Study on Block and Gradient Copolymer Aqueous Solutions by DLS and SANS. Macromolecules 2006, 39, 1592−1597. (39) Okabe, S.; Seno, K.; Kanaoka, S.; Aoshima, S.; Shibayama, M. Small-Angle Neutron Scattering Study on Block and Gradient Copolymer Aqueous Solutions. Polymer 2006, 47, 7572−7579. (40) Okabe, S.; Fuse, C.; Sugihara, S.; Aoshima, S.; Shibayama, M. Structural Transition in Block and Gradient Copolymer Aqueous Solutions. Phys. B 2006, 385−386, 756−758. (41) Wengenmayr, P.; Dockhorn, R.; Sommer, J.-U. Multicore Unimolecular Structure Formation in Single Dendritic−Linear Copolymers under Selective Solvent Conditions. Macromolecules 2016, 49, 9215−9227. (42) Gauthier, M.; Li, J.; Dockendorff, J. Arborescent Polystyrene-graft-poly(2-vinylpyridine) Copolymers as Unimolecular Micelles. Synthesis from Acetylated Substrates. Macromolecules 2003, 36, 2642−2648. (43) Njikang, G.; Gauthier, M.; Li, J. Arborescent Polystyrene-graft-poly(2-vinylpyridine) Copolymers as Unimolecular Micelles: Solubilization Studies. Polymer 2008, 49, 1276−1284. (44) Birshtein, T. M.; Borisov, O. V.; Zhulina, Y. B.; Khokhlov, A. R.; Yurasova, T. A. Conformations of Comb-like Macromolecules. Polym. Sci. USSR. 1987, 29, 1293-1300. (45) Fredrickson, G. H. Surfactant-Induced Lyotropic Behavior of Flexible Polymer Solutions. Macromolecules 1993, 26, 2825-2831.


Page 23 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(46) Rouault, Y.; Borisov, O. V. Comb-Branched Polymers: Monte Carlo Simulation and Scaling. Macromolecules 1996, 29, 2605-2611. (47) Benoit, H.; Hadziioannou, G. Scattering Theory and Properties of Block Copolymers with Various Architectures in the Homogeneous Bulk State. Macromolecules 1988, 21, 1449-1464. (48) Potemkin, I. I. Persistence Length of Comblike Polymers Strongly Adsorbed on a Flat Surface, Macromolecules 2006, 39, 7178-7180. (49) Potemkin, I. I.; Popov, K. I. Effect of Grafting Density of the Side Chains on Spontaneous Curvature and Persistence Length of 2D Comb-like Macromolecules. J. Chem. Phys. 2008, 129, 124901. (50) Saariaho, M.; Subbotin, A.; Szleifer, I.; Ikkala, O.; ten Brinke, G. Effect of Side Chain Rigidity on the Elasticity of Comb Copolymer Cylindrical Brushes: A Monte Carlo Simulation Study. Macromolecules 1999, 32, 4439–4443. (51) Saariaho, M.; Subbotin, A.; Ikkala, O.; ten Brinke, G. Comb Copolymer Cylindrical Brushes Containing Semiflexible Side Chains: a Monte Carlo Study. Macromol. Rapid Commun. 2000, 21, 110-115. (52) Subbotin, A.; Saariaho, M.; Stepanyan, R.; Ikkala, O.; ten Brinke, G. Cylindrical Brushes of Comb Copolymer Molecules Containing Rigid Side Chains. Macromolecules 2000, 33, 6168– 6173. (53) Stepanyan, R.; Subbotin, A.; ten Brinke, G. Strongly Adsorbed Comb Copolymers with Rigid Side Chains. Phys. Rev. E 2001, 63, 061805. (54) Daniel, W. F. M.; Burdyńska, J.; Vatankhah-Varnoosfaderani, M.; Matyjaszewski, K.; Paturej, J.; Rubinstein, M.; Dobrynin, A. V.; Sheiko, S. S. Solvent-free, Supersoft and Superelastic Bottlebrush Melts and Networks. Nat. Mater. 2016, 15, 183-189. (55) Cao, Z.; Daniel, W. F. M.; Vatankhah-Varnosfaderani, M.; Sheiko, S. S.; Dobrynin, A. V. Dynamics of Bottlebrush Networks. Macromolecules 2016, 49, 8009–8017. (56) Matyjaszewski, K.; Xia, J. Atom Transfer Radical Polymerization. Chem. Rev. 2001, 101, 2921−2990.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 39

(57) Potemkin, I. I.; Palyulin, V. V. Comblike Macromolecules. Polym. Sci., Ser. A 2009, 51, 123−149. (58) Potemkin, I. I.; Khokhlov, A. R.; Reineker, P. Stiffness and Conformations of Molecular Bottle-brushes Strongly Adsorbed on a Flat Surface. Eur. Phys. J. E: Soft Matter Biol. Phys. 2001, 4, 93−101. (59) Potemkin, I. I. Elasticity Driven Spontaneous Curvature of a 2D Comb-like Polymer with Repulsive Interactions in the Side Chains. Eur. Phys. J. E: Soft Matter Biol. Phys. 2003, 12, 207−210. (60) Potemkin, I. I.; Khokhlov, A. R.; Prokhorova, S. A.; Sheiko, S. S.; Möller, M.; Beers, K. L.; Matyjaszewski, K. Spontaneous Curvature of Comb-Like Polymers at a Flat Interface. Macromolecules 2004, 37, 3918−3923. (61) Potemkin, I. I. Snaky Conformations of Strongly Adsorbed (2D) Comb-like Macromolecules. Macromolecules 2007, 40, 1238−1242. (62) Sheiko, S. S.; Prokhorova, S. A.; Beers, K. L.; Matyjaszewski, K.; Potemkin, I. I.; Khokhlov, A. R.; Möller, M. Single Molecule Rod−Globule Phase Transition for Brush Molecules at a Flat Interface. Macromolecules 2001, 34, 8354−8360. (63) Sheiko, S. S.; Sun, F. C.; Randall, A.; Shirvanyants, D.; Rubinstein, M.; Lee, H.; Matyjaszewski, K. Adsorption-induced Scission of Carbon-Carbon Bonds. Nature 2006, 440, 191−194. (64) Lee, H.; Pietrasik, J.; Sheiko, S. S.; Matyjaszewski, K. Stimuli-Responsive Molecular Brushes. Prog. Polym. Sci. 2010, 35, 24–44. (65) Shinozaki, A.; Jasnow, D.; Balazs, A. C. Microphase Separation in Comb Copolymers. Macromolecules 1994, 27, 2496-2502. (66) Foster, D. P.; Jasnow, D.; Balazs, A. C. Macrophase and Microphase Separation in Random Comb Copolymers. Macromolecules 1995, 28, 3450-3462. (67) Dobrynin, A. V.; Erukhimovich, I. Ya. Computer-aided Comparative Investigation of Architecture Influence on Block Copolymer Phase Diagrams. Macromolecules 1993, 26, 276281.


Page 25 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(68) Palyulin, V. V.; Potemkin, I. I. Microphase Separation in Melts of Double Comb Copolymers. Polym. Sci., Ser. A 2007, 49, 473-481. (69) Palyulin, V. V.; Potemkin, I. I. Microphase Separation of Double-Grafted Copolymers (Centipedes) with Gradient, Random, and Regular Sequence of the Branch Points. J. Chem. Phys. 2007, 127, 124903. (70) Borisov, O. V.; Zhulina, E. B. Amphiphilic Graft Copolymer in a Selective Solvent: Intramolecular Structures and Conformational Transitions. Macromolecules 2005, 38, 25062514. (71) Košovan, P.; Kuldová, J.; Limpouchová, Z.; Procházka, K.; Zhulina, E. B.; Borisov, O. V. Amphiphilic Graft Copolymers in Selective Solvents: Molecular Dynamics Simulations and Scaling Theory. Macromolecules 2009, 42, 6748-6760. (72) Kramarenko, E. Yu.; Pevnaya, O. S.; Khokhlov, A. R. Stoichiometric Polyelectrolyte Complexes as Comb Copolymers. J. Chem. Phys. 2005, 122, 084902. (73) Wang, H.; Liu, Y. T.; Qian, H. J.; Lu, Z. Y. Dissipative Particle Dynamics Simulation Study on

Complex

Structure

Transitions

of

Vesicles

Formed

by

Comb-like

Block

Copolymers. Polymer 2011, 52, 2094-2101. (74) Qi, H.; Zhong, C. Density Functional Theory Studies on the Microphase Separation of Amphiphilic Comb Copolymers in a Selective Solvent. J. Phys. Chem. B 2008, 112, 1084110847. (75) Qi, H; Liu, D.; Zhong, C. Cooperative Aggregation of Amphiphilic Comblike Copolymer/Linear Homopolymer Blends in Selective Solvents: A Density Functional Theory Study. J. Phys. Chem. B 2008, 112, 16409-16414. (76) Mao, G.; Wang, J.; Clingman, S. R.; Ober, C. K.; Chen, J. T.; Thomas, E. L. Molecular Design, Synthesis, and Characterization of Liquid Crystal−Coil Diblock Copolymers with Azobenzene Side Groups. Macromolecules 1997, 30, 2556-2567. (77) Hamley, I. W.; Castelletto, V.; Lu, Z. B.; Imrie, C. T.; Itoh, T.; Al-Hussein, M. Interplay between Smectic Ordering and Microphase Separation in a Series of Side-Group Liquid-Crystal Block Copolymers. Macromolecules 2004, 37, 4798-4807.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 39

(78) Anthamatten, M.; Hammond, P. T. A SAXS Study of Microstructure Ordering Transitions in Liquid Crystalline Side-Chain Diblock Copolymers. Macromolecules 1999, 32, 8066-8076. (79) Osuji, C. O.; Chen, J. T.; Mao, G.; Ober, C. K.; Thomas, E. L. Understanding and Controlling the Morphology of Styrene–Isoprene Side-Group Liquid Crystalline Diblock Copolymers. Polymer 2000, 41, 8897-8907. (80) Muthukumar, M.; Ober, C. K.; Thomas, E. L. Competing Interactions and Levels of Ordering in Self-Organizing Polymeric Materials. Science 1997, 277, 1225-1232. (81) de Jeu, W. H.; Serero, Y.; Al-Hussein, M. Liquid Crystallinity in Block Copolymer Films for Controlling Polymeric Nanopatterns. Adv. Polym. Sci. 2006, 200, 71-90. (82) Albrecht, K.; Mourran, A.; Zhu, X.; Markkula, T.; Groll, J.; Beginn, U.; de Jeu, W. H.; Möller, M. Thin Film Morphologies of Block Copolymers Complexed with Wedge-Shaped Liquid Crystalline Amphiphilic Molecules. Macromolecules 2008, 41, 1728-1738. (83) Anthamatten, M.; Hammond, P. T. Free-Energy Model of Asymmetry in Side-Chain Liquid-Crystalline Diblock Copolymers. J. Polym. Sci., Part B 2001, 39, 2671-2691. (84) Shah, M.; Pryamitsyn, V.; Ganesan, V. A Model for Self-Assembly in Side Chain Liquid Crystalline Block Copolymers. Macromolecules 2008, 41, 218-229. (85) Potemkin, I. I.; Bodrova, A. S. A Theory of Microphase Separation in the Melt of Diblock Copolymers with Smectic Liquid Crystalline Side Groups. Macromolecules 2009, 42, 28172825. (86) Verploegen, E.; McAfee, L. C.; Tian, L. T.; Verploegen, D.; Hammond, P. T. Observation of Transverse Cylinder Morphology in Side Chain Liquid Crystalline Block Copolymers. Macromolecules 2007, 40, 777-780. (87) Al-Hussein, M.; Serero, Y.; Konovalov, O.; Mourran, A.; Möller, M.; de Jeu, W. H. Nanoordering of Fluorinated Side-Chain Liquid Crystalline/Amorphous Diblock Copolymers. Macromolecules 2005, 38, 9610-9616. (88) Wong, G. C. L.; Commandeur, J.; Fischer, H.; de Jeu, W. H. Orientational Wetting in Hybrid Liquid Crystalline Block Copolymers. Phys. Rev. Lett. 1996, 77, 5221-5224.


Page 27 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(89) Ansari, I. A.; Castelletto, V.; Mykhaylyk, T.; Hamley, I. W.; Lu, Z. B.; Itoh, T.; Imrie, C. T. Hierarchical Order in a Side-Group Liquid Crystalline Block Copolymer. Macromolecules 2003, 36, 8898-8901. (90) Figueiredo, P.; Geppert, S.; Brandsch, R.; Bar, G.; Thomann, R.; Spontak, R. J.; Gronski, W.; Samlenski, R.; Müller-Buschbaum, P. Ordering of Cylindrical Microdomains in Thin Films of Hybrid Isotropic/Liquid Crystalline Triblock Copolymers. Macromolecules 2001, 34, 171180. (91) Verploegen, E.; Zhang, T.; Jung, Y. S.; Ross, C.; Hammond, P. T. Controlling the Morphology of Side Chain Liquid Crystalline Block Copolymer Thin Films through Variations in Liquid Crystalline Content. Nano Lett. 2008, 8, 3434-3440. (92) Halperin, A. Rod-Coil Copolymers: Their Aggregation Behavior. Macromolecules 1990, 23, 2724-2731. (93) Williams, D. R. M.; Fredrickson, G. H. Cylindrical Micelles in Rigid-Flexible Diblock Copolymers. Macromolecules 1992, 25, 3561-3568. (94) Hoogerbrugge, P. J.; Koelman, J. Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics. Europhys. Lett. 1992, 19, 155-160. (95) Espanol, P.; Warren, P. Statistical Mechanics of Dissipative Particle Dynamics. Europhys. Lett. 1995, 30, 191-196. (96) Groot, R.D.; Warren P.B. Dissipative Particle Dynamics: Bridging the Gap between Atomistic and Mesoscopic Simulation. J. Chem. Phys. 1997, 107, 4423-4435. (97) Pispas, S.; Hadjichristidis, N.; Potemkin, I.; Khokhlov, A. Effect of Architecture on the Micellization Properties of Block Copolymers: A2B Miktoarm Stars vs AB Diblocks, Macromolecules 2000, 33, 1741-1746. (98) Semenov, A. N.; Vasilenko, S. V. Theory of the Nematic-Smectic-A Transition in a Melt of Macromolecules Consisting of a Rigid and a Flexible Block. Zh. Eksp. Teor. Fiz. 1986, 90, 124140.



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Figure 1 164x85mm (220 x 220 DPI)



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Effect of Architecture on Micelle Formation and Liquid-Crystalline

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