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Self-Assembly into Strands in Amphiphilic Polymer Brushes Daniil E. Larin, Alexei Alexandrovich Lazutin, Elena N Govorun, and Valentina V. Vasilevskaya Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01208 • Publication Date (Web): 06 Jun 2016 Downloaded from http://pubs.acs.org on June 8, 2016
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Self-Assembly into Strands in Amphiphilic Polymer Brushes Daniil E. Larin,† Alexei A. Lazutin,‡ Elena N. Govorun,†,* Valentina V. Vasilevskaya‡ †
Faculty of Physics, M. V. Lomonosov Moscow State University, Leninskie gory, Moscow, 119991
Russia ‡
A. N. Nesmeyanov Institute of Organoelement Compounds RAS, Vavilova str., 28, Moscow,
119991 Russia Self-assembly of amphiphilic macromolecules end-grafted to a plane surface is studied by meanfield theory and computer simulations. Chain backbones are built from hydrophobic groups, whereas side groups are hydrophilic. The brush is immersed in a solvent, which can be good or poor, but on the average is not far from θ conditions. It is demonstrated that the strong amphiphilicity of macromolecules at a monomer unit level leads to their self-assembly into a system of strands with 2D hexagonal order in a cross-section parallel to the grafting plane. The structure period is determined by the length of side groups. In theory, this effect is explained by the orientation of strongly amphiphilic monomer units at a strand/solvent boundary that leads to an effective negative contribution to the surface tension. Computer simulations with molecular dynamics are used for a detailed study of the local brush structure. The aggregation number of strands grows with increasing the grafting density and side group length.
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INTRODUCTION At present, layers of macromolecules end-grafted to different surfaces (polymer brushes) are extensively studied due to their promising properties for different applications.1-20 Polymer brushes reveal stimuli-responsive characteristics,1-5 absorbing or antifouling activity toward proteins and living cells.6-10 Micro- and nanopatterned polymer brushes are important in biotechnologies and electronics.11-15 Theoretical and computer simulation studies are focused on the detailed analysis of structured polymer brushes.16-25 Brush properties and their dependence on the external conditions can be sensitive to the selfassembly of macromolecules with complex structure. For example, the wetting and adhesion properties of amphiphilic comb-like copolymer brushes correlate with their spatial structure, in particular, with the segregation of side segments.4-5 Lateral structures in polymer brushes were found earlier for diblock copolymers in selective and non-selective solvents in theory, computer modeling and experiments.15,22-25 Depending on the relative lengths of blocks and the energies of their interactions with each other and solvent, the macromolecules in not densely grafted brushes can self-assemble into “onion-like” and “garlic-like” micelle structures with the cores of less soluble blocks surrounded by more soluble blocks,22 or into “flower-like” micelles with dense cores and loose “petals”.23,24 In densely grafted brushes, blocks of different types segregate into layers parallel to the grafting plane or such structures as hexagonally arranged micelles, inverse micelles and stripes consisting of outer blocks are formed on the layer of inner blocks in selective and non-selective solvents.15,24 Unusual structures, for example, “stalactites” and parallel “gullies” and “ridges”, were observed in computer simulations in nonselective solvents.25 In the experimental study of tethered films of polystyrene-block-poly(methyl methacrylate) copolymers,15 hemispherical aggregates were observed in the inner (PMMA) blockselective solvent and a textured structure with smaller aggregates was found in the outer blockselective solvent. The spatial scale of the lateral structures in diblock copolymer brushes is defined by sizes of blocks which are swollen or not depending on the solvent quality for them. Notice that the solvent selectivity can be related to the amphiphilicity of a diblock copolymer and therefore, all structures found in selective solvents are possibly observable for amphiphilic diblock copolymers. Brush properties can be controlled by incorporating amphiphilic surfactant molecules into the brush.14,16 It was predicted theoretically that non-symmetric interactions of the hydrophobic and polar parts of surfactant molecules with a polymer can lead to the self-assembly of macromolecules into strands perpendicular to the grafting plane.16 A considerable amount of surfactant molecules are incorporated into the strands and an interaction energy gain due to the perpendicular orientation of the surfactant molecules at a strand surface gives rise to the macromolecular aggregation. The
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strand radius is of the order of a surfactant molecule size and the aggregation number is proportional to the grafting density. It can be expected that for macromolecules with amphiphilic monomer units or amphiphilic comb-like copolymers, a similar aggregation is possible in polymer brushes without surfactants. Amphiphilic monomer units contain both hydrophobic and hydrophilic groups. In a mixture of oil and water type solvents, such monomers are concentrated at the interface rather than in the bulk revealing a surface activity. Monomers of synthetic polymers and amino acid residues were classified based on their interfacial and partitioning properties for hexane/water mixture.26,27 A simple model of a macromolecule with dumbbell monomer units consisting of hydrophobic and hydrophilic beads was suggested to analyze polymer conformations in computer simulations.28 Due to the surface activity, macromolecules with amphiphilic monomer units, which are many among synthetic polymers and biopolymers, have different structures depending on the solvent selectivity and stiffness of macromolecular backbones. It was found that necklace-like conformations, colloidally stable aggregates (mesoglobules), cylinders, vesicles, torus-like and disk-like structures can be formed in solution.28-38 End-grafted amphiphilic macromolecules in a solvent poor for side groups can form an ultra-thin almost flat micelles on the surface.21 The thickness of micelles is about the double size of a monomer unit or twice larger and their shapes change with increasing the grafting density as follows: circular micelles – prolonged micelles – inverse micelles – continuous bilayer. In the present investigation, we study densely grafted to a plane uncharged amphiphilic macromolecules in a selective solvent which is (opposite to the previous study21) good for side groups and poor for backbones. The conditions of self-assembling into strands are addressed. A mean-field theoretical approach describing the self-assembly in polymer brushes in the presence of surfactants16 is extended to the brushes of amphiphilic macromolecules, the negative interaction energy contribution to the surface tension due to the orientation of side parts of monomer units being taken into account. In the computer simulations, the molecular dynamics technique is used similarly to the modeling of grafted amphiphilic macromolecules with polar backbone and hydrophobic side groups.21 Additionally, a set of different side-bond lengths is considered in the present computer modeling, where the side-bond length is controlled by the parameters of the covalent bond potential.
THEORY AND COMPUTER SIMULATIONS 1.Theoretical approach We consider m macromolecules grafted to a plane of area S. The surface density of grafting is equal to ns=m/S (Σ=1/ns is the surface area per macromolecule). A macromolecule contains N 3 Environment ACS Paragon Plus
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amphiphilic monomer units of volume υp consisting of hydrophobic (H) and polar (P) parts at a distance l between their centers (Figure 1). Each H group represents a part of a purely hydrophobic chain of the length a equal to the Kuhn-segment length of such chain. H and P groups differ in the interactions with surrounding solvent, the averaged interaction energy of a whole monomer unit with the solvent is characterized by the Flory-Huggins parameter χ. The volume of a solvent molecule is equal to υs. We consider sufficiently large grafting densities (Σ 0), the length of bond between P and H-parts, l >> a. We consider the limiting case of strong amphiphilicity (εϕp >>1), when all dimer units at the surface are oriented so that their P-groups are surrounded by solvent molecules only. A steric interaction energy of the oriented dimer units is neglected, as in the previous considerations,16,31,35 which corresponds to a monomer unit model with the volume of H-part, υ1, to be much larger than the volume of P-part, υ2; i. e., υ1 >>υ2, υp≈υ1. The negative interaction energy contribution of P-groups at a plane surface of area S is equal to ∆EP=−Nsurfε kBTϕp, where Nsurf =ϕplS/υр is the number of oriented dimers in the surface layer. Then, the surface tension can be written in the form
σ~0 (ϕ p ) = σ 0 (ϕ p )
υp
l = ϕ p s0 − ε ϕ 2p , a a
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(5)
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where the first term describes the surface tension provided all P-groups are in the polymer containing phase, the second term is equal to ∆EPυр/(akBT). It is assumed that the second contribution prevails, s0 > 0, σ0 < 0. The surface tension of globules and aggregates of macromolecules with amphiphilic monomer units depends on the surface curvature. In the limit of high amphiphilicity, the surface tension has the form: 35
l a
σ~ = σ~0 (ϕ p ) − ϕ p
l 1l l2 ϕp 2 , 1.47 − εϕ p 2 + R 8a R
(
)
l Σ c ≈2.5, the strand radius is equal to the side bond length, R=l. Those strands are assumed to be hexagonally packed to provide a maximum surface area. The other parameters, such as the volume fraction of monomer units in strands, ϕp, brush height (equal to the strand length), H, and aggregation number, M, (Figure 5) were calculated using Eqs. (1)-(10). The polymer volume fraction in strands (Figure 4a), is slightly less than unity and it grows with increasing the grafting density and interaction energy, ε. The average polymer volume fraction in the brush, ϕ p , is proportional to the volume fraction ϕp with the coefficient approximately equal
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to 0.4 (see the theoretical model section): ϕ p ≈ 0.4ϕ p . The brush height and polymer volume fraction do not depend on the side bond length, l, polymerization degree, N, and surface tension term with s0 (in the absence of the amphiphilicity effect). The smooth curves are plotted under the assumption that the aggregation number can take any positive value. The stepwise curves are plotted (Figure 4, ε=2) for a discrete set of the aggregation number values. The value of the Flory-Huggins parameter, χ, is taken to relate the θsolvent conditions, χ=υp/(2υs)=0.5. However, the difference in the strand parameters for χ=0.05, for example, is not more than 1-2 %, and moderate values of the parameters χ and s0 (χ, s0
