Amphiphilic Arborescent Copolymers and Microgels: From

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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 Rustam A. Gumerov,†,‡ Andrey A. Rudov,†,‡ Walter Richtering,§ Martin Möller,‡ and Igor I. Potemkin*,†,‡,∥ †

Physics Department, Lomonosov Moscow State University, Moscow 119991, Russian Federation DWI−Leibniz Institute for Interactive Materials, Aachen 52056, Germany § Institute of Physical Chemistry, RWTH Aachen University, Aachen 52056, Germany ∥ National Research South Ural State University, Chelyabinsk 454080, Russian Federation ‡

ABSTRACT: Amphiphilic arborescent block copolymers of two generations (G2 and G3) and polymer microgels, obtained via cross-linking of diblock copolymers, were studied in a selective solvent and at liquid interface via dissipative particle dynamics (DPD) simulations. Depending on the primary structure, single arborescent macromolecules in selective solvent can have both core−corona and multicore structures. Self-assembly of the G2, G3, and microgels in the selective solvent is compared with equivalent linear diblock copolymers. The latter self-assemble into spherical micelles of large enough aggregation number. On the contrary, stability of unimolecular micelles is a feature of the arborescent copolymers and microgels, whereas their ability to aggregate is very low. Adsorption of the single molecules at liquid (oil−water) interface leads to their flattening and segregation of the amphiphilic blocks: hydrophilic and hydrophobic blocks are exposed toward water and oil, respectively. Depending on the character of interactions between monomer units, which can be controlled by temperature or solvent(s) quality, Janus, patchy, and nanosegregated structures can be formed within the macromolecules. Their self-assembly at the interface can lead to the formation of both loose and dense monolayers, which can be homogeneous and nanostructured. The pretty fast adsorption kinetics of G2 macromolecules make them efficient stabilizers of emulsions. KEYWORDS: arborescent molecules, amphiphilic polymers, unimolecular micelles, emulsion stabilization, liquid interface, block copolymer microgels, dissipative particle dynamics to not aggregate and to form unimolecular micelles,16−18 can give rise to a number of contemporary applications of these multicomponent molecules like templates for the formation of metallic nanoparticles19,20 of predefined shape, microcapsules for efficient drug delivery, 15,18 or polymer processing additives.21 Another possible application of the arborescent polymers is emulsion stabilization. The surface behavior of branched polymers at solid substrates shows that these molecules can form a monomolecular film of uniform thickness without interpenetrating each other.22 On the other hand, amphiphilic structure in combination with suppressed aggregation ability in

1. INTRODUCTION Arborescent (dendrigraft) polymers are known to be the class of dendritic molecules of high molecular weight. In contrast to hyperbranched molecules and similarly to dendrimers, the arborescent polymers can be obtained with a well-defined molecular structure. Their initial building blocks are pretty monodisperse linear chains, which are successively “grafted onto” the polymeric substrate by generation-based scheme. The number of grafts and their chemical composition in each generation can be varied and thus the highly branched copolymers can be achieved.1 Since first being introduced in 1991 by Gauthier and Möller2 and independently by Tomalia et al.,3 the synthetic strategies of production of dendrigraft molecules have been extensively developing,4−15 allowing to obtain the multicomponent macromolecules based on regular polymers,4−7,9−11,13 polyelectrolytes,8,12 and even biopolymers.14,15 The solution properties of the arborescent copolymers, such as their ability © 2017 American Chemical Society

Special Issue: Block Copolymers for Nanotechnology Applications Received: January 16, 2017 Accepted: April 4, 2017 Published: April 10, 2017 31302

DOI: 10.1021/acsami.7b00772 ACS Appl. Mater. Interfaces 2017, 9, 31302−31316

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Figure 1. Sketch of the design of arborescent molecules of different generations: G0, G1, and G2.

Figure 2. Primary structures of G2 and G3 arborescent copolymers, block copolymer microgel, BC-μG, and linear diblock copolymer, DBC. The gray beads correspond to A (nominally hydrophilic) blocks and the green ones correspond to B (nominally hydrophobic) blocks.

In trying to interrelate the internal structure of the arborescent copolymers and their properties to those of “canonic” molecular objects, one may consider the them as homologues in the row of linear chains, brush (comblike) molecules, hyperbranched molecules, and polymer (nano)microgels. Indeed, the feature of arborescent molecules of low generation weakly differs from the linear block copolymers: they should adopt strongly fluctuating conformations in a good, nonselective solvent and aggregate into micelles in the selective solvent. On the contrary, the arborescent copolymers of high generations should possess well-defined shape both in selective and nonselective solvents. This effect is expected to be as a result of strong intramolecular interactions of monomer units due their high concentration, which increases with the generation of the molecule. Similar behavior is known for densely grafted comblike macromolecules,27,28 where strong repulsion of monomer units of the side chains provides locally cylindrical shape of the macromolecule and enhanced persistence length:29,30 macromolecules with pretty short backbone are cylindrical in the shape. Long chains behave as persistent ones, whose induced persistence length increases with the increase of both grafting density and the length of the side chains.29,30 However, the well-defined shape of the cylindrical brushes is very adaptive. For example, adsorption

solutions (unimolecular micelles) can attribute them to quickly adsorbing molecules, which enhance their efficiency as stabilizers.23 Indeed, unlike linear block copolymers forming micelles in selective solvents, whose adsorption at the surface or liquid interface is hindered by a presence of dense corona,23 kinetics of adsorption of the single arborescent molecules is expected to be faster. In addition to the enhanced binding to the surface, amphiphilicity can promote structuring within the molecules: atomic force microscopy studies demonstrated formation of nanodomains within the adsorbed arborescent copolymers.9 Besides, one should mention that other characteristics like chemical composition (relative fraction of different components) and branching functionality play important role. It was found that amphiphilic arborescent polystyrene-graf tpoly(ethylene oxide) copolymers can self-assemble into superstructures at air−water interface,24,25 whose morphology strongly depends on aforementioned parameters. A similar conclusion is valid for other dendritic molecules. In particular, it has been reported recently that the interfacial activity of PAMAM−PCL dendrimers at the toluene−water interface depends on the length of PCL blocks.26 In spite of this, the interfacial behavior of arborescent copolymers, as well as their potential application as emulsion stabilizers, has not been widely studied yet. 31303


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rather than polar and azimuthal. Despite 3D conformations of the macromolecules, the distribution of the branching points is two-dimensional in respect that the arborescent macromolecule can be placed on a plane without intersections of the chains at least up to the third generation (Figures 1 and 2). Thus, the arborescent copolymers should possess peculiarities in properties, which can differ from those of the microgels, brush molecules, and linear copolymers. The aim of the current paper is to perform comparative studies of the arborescent copolymers using computer simulations. We analyze the conformations of single arborescent macromolecules of different generations in a selective solvent and study their self-assembly versus equivalent diblock copolymers and microgels formed via cross-linking of diblock copolymers. Then we investigate the conformations of single arborescent molecules adsorbed on interface of two immiscible liquids and their in-plane self-assembly. Finally, we compare the stabilization ability of the arborescent copolymers with the linear diblock copolymers and block copolymer microgels of similar molecular weight.

of the cylindrical brushes on solid and liquid interfaces can be responsible for the spontaneous break of the local cylindrical symmetry: strong adsorption of the side chains leads to the flattening (spreading) of the molecules with simultaneous increase of the persistence length.31−33 As a result, spontaneous curvature of the adsorbed macromolecules,34−36 “rod−coil” phase transition upon compression of the monolayer,37 or adsorption-caused backbone scission because of strong repulsion of the 2D side chains38 have been observed. Looking at the next molecular object in the homologue row, i.e., microgel, one can say that connectivity of linear chains into three-dimensional network can also provide a well-defined shape. The microgels in a good solvent look and behave like dispersed spherical soft particles.39,40 They reveal duality in physical properties. Liquidlike behavior is characteristic at length scales smaller than the mesh size, where the subchains do not “feel” connectivity into the network.41 Solidlike (elastic) response is a feature at larger scales41 because of the entropic elasticity of the subchains: deviation of the end-to-end distance of the subchains (position of cross-links) from the equilibrium state causes elastic response restoring the initial spherical shape. However, similarly to the cylindrical brushes, the shape of the microgels is very adaptive to the external stimuli42 due to the softness which is controlled by the length of the subchains. For example, adsorption of the microgel on solid43 or liquid44 interface leads to its flattening (spreading), which is controlled by a balance between gain in the interfacial energy45 due to the adsorption of the monomer units (subchains) and penalty in the elastic free energy of stretched subchains due to the microgel deformation (spreading). The ultimate shape of the microgel at the interface is controlled by the surface energy and cross-linking density: it can vary from a weakly deformed sphere (low surface energy and/or high cross-linking density)46,47 to a “pancake” (vice versa).43 Such adsorbed microgels can serve as soft, penetrable, and stimuli-responsive alternative to solid particles widely used for stabilization of emulsions.48,49 For example, pH-responsive polyelectrolyte microgels are unique stabilizers for stimuli-sensitive emulsions that can be broken on demand by changing the pH value.50 Furthermore, the electrostatic interactions between the microgels play a different role to that in conventional Pickering emulsions.50 The adsorbed microgels can facilitate mixing of two immiscible liquids which permeate the microgel,46,47 so that they can promote chemical reactions of incompatible reactants. Further studies on core−shell microgel particles with a swollen shell indicate that the interfacial adsorption is significantly enhanced by the conformational freedom and cooperative binding of the polymer segments in the shell.51−53 Microgels of lower cross-linking density are shown to adsorb more quickly and decrease the interfacial tension faster.43 Comparing topology of the arborescent copolymers with others in the proposed homologue row, we can introduce distinctions on the basis of distribution of branching points. The microgels can be defined as molecular objects with a threedimensional distribution of the branching points (cross-links) having cycles formed by the subchains (3D percolation due to the network structure). Despite 3D conformations of the macromolecules, distribution of the branching points (grafts) in the cylindrical brushes is one-dimensional: the grafts follow the backbone, i.e., their position in the backbone is described by one variable (contour length). In contrast to the microgels, the arborescent copolymers do not have the cycles: the 3D percolation is only radial (through the central branching point)

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MODEL AND SIMULATION METHOD

To investigate the above-mentioned systems, we used dissipative particle dynamics (DPD) technique,54−56 a well-acclaimed coarse-

Table 1. DPD Interaction Parameters (in units of kBT/rc) Used in Simulations; Variable Parameters Are Shown by the Letter a with Different Indexes aij

A

B

W

O

A B W O

25 35 aAW 40

35 25 aBW aBO

aAW aBW 25 60

40 aBO 60 25

grained method which has been widely used to simulate properties of polymeric systems in films and brushes,57−60 solutions61,62 and at the interfaces.43,46,47,63,64 The advantage of this technique is that the solvent molecules, as well as the polymer segments, are explicitly included and represented in terms of the beads, whereas each bead usually comprises a group of atoms. The beads interact with each other by a pairwise additive force

Fi =

∑ (FCij + FijD + FijR + FijB) (1)

i≠j

FCij

is a conservative force responsible for the repulsion via soft where potential characterized by parameters aij:54 the bigger the value of aij, the stronger the repulsion between ith and jth beads; FDij and FRij are the dissipative and random forces, respectively, which serve as heat sink and source. They are specified by a friction coefficient λ and noise amplitude σ; FBij is a bond force that acts only between polymer beads and keeps them in the chains. The sum runs among all number of the beads in the system, N. The first three terms in eq 1 act only within the certain cutoff radius rc, which usually serves as the characteristic length scale unit and therefore taken as 1. The forces are given by the following expressions55,56 ⎧ ⎪ aij(1 − rij) rij̅ , rij < 1 FCij = ⎨ ⎪ 0, rij ≥ 1 ⎩

(2)

FijD = − λ[ω(rij)]2 (vij· rij̅ ) rij̅

(3)

FijR 31304

= σω(rij)ξijΔt

−1/2

rij̅

(4) DOI: 10.1021/acsami.7b00772 ACS Appl. Mater. Interfaces 2017, 9, 31302−31316

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Figure 3. Simulation snapshots of single arborescent copolymers (G2 and G3) with symmetric composition of diblock grafts, A5B5, and block copolymer microgel (BC-μG) in nonselective (a) good and (b) poor solvents. Cross-sections through the center of mass are also shown for the case of the poor solvent. The radial concentration profiles correspond to the case of the good solvent. Following the synthetic approach of refs 13 and 19, we have designed the coarse-grained models of arborescent molecules as follows. Three linear chains of the sort A are end-grafted to the fourth linear chain of the same sort (Figure 1). Such molecule is called as arborescent macromolecule of zero generation, G0. Considering G0 as a precursor, we end-graft another three linear chains per each of the three dangling chains and obtain arborescent polymer of the next generation, G1 (Figure 1). If we then consider the G1 molecule as a precursor, one can obtain G2 with the same grafting procedure. Higher generations are designed in a similar way. If we use amphiphilic AB diblock copolymers instead of linear homopolymer chains in the last generation, we can get arborescent copolymers. G2 and G3 primary structures of the arborescent copolymers are shown in Figure 2. The distribution of insoluble B blocks, which can be considered as placed “inside” the macromolecule, attributes the primary structure of the arborescent copolymers to core−shell−corona (CSC). Such choice of the molecular architecture was made in order to obtain unimolecular micelles whose probability of formation will be higher than for the opposite case of “outer” insoluble blocks13,19 However, real spatial distribution of the blocks depends on selectivity and quality of the solvent. The length of each grafting chain is equal to 10 beads except for the linear substrate (“central” chain) which has 11 beads to provide a kind of central symmetry. The total number of the beads in the G2 and G3 copolymers are 401 and 1211, respectively (Figure 2). For G2, the composition of the grafted diblocks is limited by a symmetric case, while for G3 it varies from 20 to 80%. The branching points are distributed equidistantly so that the length of the subchains between them is equal. The regularity of the distribution is a simplification, whereas in actual polymers with arborescent structure, the branches are rather randomly grafted.1 Self-assembly of the macromolecules in a selective solvent (W) is considered for the case of insoluble B blocks (aBW = 50) and soluble A blocks (aAW = 25), while the blocks themselves are chosen to be

where rij̅ = (ri − rj)/rij is the unit vector pointing from jth to ith bead, ω(rij) = (1 − rij) is a weight function which turns to zero when rij ≥ 1, vij = vi − vj is the relative velocity of beads i and j, ξij is a zero-mean normally distributed random variable, and Δt is a simulation time step. The bond force is described by a harmonic potential, E = 1/2K(r − r0)2, where K is the spring constant and r0 is the equilibrium bond length. In the classic DPD approach, an NVT ensemble is usually applied where the momentum for each pair of beads is preserved. A relation σ2 = 2kBTλ must be provided to satisfy the fluctuation− dissipation theorem,55 where the value of λ is set to 4.5 for the decent rate of equilibration of the temperature. The evolution of the system is described by equations of motion expressed through the second Newton’s law, mdvi/dt = Fi. All quantities in the equations of motion are measured in units of the mass of the bead, m, thermal energy, kBT (kB is Boltzmann constant), and the cutoff radius rc. For convenience, we fix them as m = kBT = rc = 1, so that the characteristic time scale is defined as τ = (mrc/kBT)1/2 and also is equal to 1. The total number density of the system ρ = N/V is set to 3. With such value selection, the interaction parameters aij (in units of kBT/rc) can be mapped onto the Flory−Huggins parameters χij by linear relation

aij = χij /C + aii

(5)

where a constant C is equal to 0.286 for solvent−solvent interactions and to 0.306 for the polymer−polymer and polymer−solvent interactions.56 For any two beads of the same type, we set the repulsion parameter aii as 25 which common for the most of DPD simulations.57−64 Thus, according to eq 5, the polymer will be insoluble in the solvent when the interaction parameter will be higher than 32 (the corresponding value of χij will be higher than 2)60 The other simulation parameters applied for all studies are chosen to be as follows: K = 10, r0 = 0.7, and the simulation time step Δt = 0.04τ. 31305


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Figure 4. Snapshots of single arborescent copolymers G2 and G3 with symmetric composition of diblock grafts, and single block copolymer microgel, BC-μG, in a selective solvent of variable selectivity. (a) Leftmost column corresponds to high solubility of green beads and insolubility of gray beads. (d) Rightmost column demonstrates the opposite case (solubility of gray and insolubility of green beads). (b, c)Two missle columns represent intermediate cases. Smaller (“superscript”) images are cross-sections through the center of mass of the corresponding bigger images (G3 and BC-μG). performed in the box of sizes Lx = Ly = 50, Lz = 30, where axes x and y correspond to the interface plane. Equilibration lasted during 2.5 × 105 steps. The adsorption kinetics of ensemble of different macromolecules is simulated in the box of the sizes LxLyLz = 50 × 50 × 70 containing water and oil phases of the volume ratio 5:2, respectively. The boundary conditions are imposed in x and y directions (in the plane of the interface). Before annealing, the molecules are randomly distributed within the water phase. The average volume fraction of the polymers is set to be about 2.6% which is equal to 24 G2 or 8 G3 arborescent molecules and 8 microgels, respectively, to allow the macromolecules to move freely to the interface. The driving force for the adsorption is the gain in the interfacial energy (reduction of the area of unfavorable contacts of water and oil) and amphiphilic character of the constituent blocks. To avoid the adsorption onto the additional oil−water interface in the top and bottom of the box, two impenetrable walls were implied at the boundaries. The adsorption process is studied via analysis of the snapshots of the systems at different moments of time and via construction of the density profiles for polymer components along the z-axis. The adsorption process was simulated during 2 × 106 steps for all types of macromolecules which is enough for the chosen box size.47,63 Finally, in-plane self-assembly of the adsorbed macromolecules into equilibrium structures was simulated in the box of linear sizes Lx = Ly = 70 and Lz = 40 to avoid the finite size effects via expanding the box size in the interfacial plane. The simulations lasted during 2 × 106 steps.

incompatible (aAB = 35). The behavior of G2 copolymers is compared with the behavior of equivalent diblock copolymers. Here (and below) equivalency means that the average chemical composition of both molecular objects and their average polymer concentrations are equal. Thus, each diblock of 15 beads has a composition A10B5 (Figure 2). Such asymmetric copolymers are known to form spherical micelles.65 The aggregation of the G3 molecules is compared with aggregation of equivalent microgels. The microgels are designed as described in refs.66,67 In brief, the diamond lattice of fully stretched subchains connected by tetrafunctional cross-links is constructed. Then a sphere is inscribed into the lattice. Those beads, which are outside the sphere, are “cut off”. Each subchain between cross-linkers is a diblock of 10 beads and the total number of beads in the microgels is 1238. The cross-linkers bind either only A or B blocks (Figure 2). The single macromolecules in the selective solvent (W) are modeled in the cubic simulation box with imposed boundary conditions and a constant volume V = LxLyLz = 403. The size of the box is measured in units of the diameter of the bead rc. The selectivity rate is tuned by the variation of interaction parameters aAW and aBW (see Table 1). Self-assembly of the molecules is simulated in a bigger cubic box of the linear size 60. The whole set of the interaction parameters is presented in Table 1. Initial (before annealing) structures of the solution were homogeneously dispersed macromolecules. For all systems, simulations lasted for 3.5 × 106 simulation steps. The formation of the liquid interface in the simulation box is a straightforward: repulsive interactions between two different types of the beads (W and O corresponding to nominal “water” and “oil”) filling the box control thickness of the interface and its energy. For all the simulations, the liquids are chosen to be highly immiscible (aWO = 60, Table 1). Simulations of conformations of the single molecules are

3. RESULTS AND DISCUSSION 3.1. Bulk Solution. Single Molecules. First, let us demonstrate the behavior of single macromolecules in a 31306


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Figure 5. Upper row (left to right): Simulation snapshots of 5% solutions of linear diblock copolymers (DBC), arborescent copolymers of different generations (G2 and G3) and block copolymer microgels (BC-μG). The selective solvent is poor for the B beads and good for the A beads (aAW = 25, aBW = 50). Bottom row: fraction of the aggregates as a function of the number of insoluble beads (bottom axis) and the corresponding number of the molecules (upper axis) in the aggregate.

the dangling chains are immersed into the core forming by the branching A chains and the loops of the B blocks form patches. On the contrary, self-assembly of B blocks in the microgel proceeds throughout the whole volume because of the presence of cross-links (Figure 3b). More diverse behavior of the single macromolecules can be detected in a selective solvent. Figure 4 depicts snapshots of the macromolecules under variation of the selectivity. Left images (Figure 4a) correspond to the case of soluble B blocks (minor component) and insoluble A blocks. Both side view and crosssection through the center of mass demonstrate that for all types of the molecules a spherical core−corona structure is formed. The homogeneous dense core of the A blocks is surrounded by more-or-less homogeneous corona of the B blocks. In the case of the microgels, such structure is formed only due to the small size of the object. In general case of bigger microgels, many soluble blocks will be trapped inside because of the cross-links, and soluble nanodomains will coexist with insoluble ones (intramolecular nanophase segregation). Inversion of the solvent selectivity proceeds from left to right, Figure 4: the A beads become more and more soluble and vice versa. Worsening of the solvent quality for the B beads leads to the loss of coronae continuity and they become more perforated (Figure 4b). When the green beads are less soluble (aAW = 30, aBW = 40, Figure 4c), they form the core. Such core−shell morphology correlates with experimental results reported in refs 9 and 19 for similar arborescent copolymers. Although for G2 and microgel the morphologies are similar (core−shell), the most interesting case goes for the G3, where the topology starts to play a key role. Because of the high branching, the green blocks cannot form a spherical core, which results in formation

nonselective solvent. Figure 3a shows that in case of good solvent (aAW = aBW = 25) all the molecules are appear to be highly swollen. Despite an incompatibility between A and B monomer units (aAB = 35), the spatial segregation of the blocks is absent because of small polymer concentration within the swollen macromolecules: the number of AB contacts is small due to the presence of the solvent. This is also seen in the concentration profiles: the radial distribution of the green (B) beads is very broad for all types of the macromolecules. Comparing the concentration profiles of A beads, we can see stronger concentration decay with the radius r for G2 macromolecules and weaker for G3 and BC-μG, respectively. Weaker decay means that the high generation in the arborescent copolymer increases concentration at the periphery and makes the concentration more homogeneous. Some concentration oscillations within the microgel are related to the choice of the center of mass of the finite size object: the concentration can have maximum or minimum in the center of mass if the latter coincides with the cross-link or with the center of the elementary cell (“empty space”), respectively.66 Despite an equal number of monomer units (beads) in G3 and BC-μG, the G3 swells better because of the absence of cross-links. Collapse of both A and B blocks in the bad solvent (aAW = aBW = 40) expels the solvent out of the macromolecules with formation of dense, weakly fluctuating and nearly spherical globules (Figure 3b). The collapse is accompanied by intramolecular segregation of A and B blocks to reduce the number of unfavorable contacts between them. In the case of G2 and G3, the green beads self-assemble into nanodomains mainly at the periphery rather than follow the core−shell− corona structure shown in Figure 2. It means that the A ends of 31307


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Figure 6. Snapshots of single arborescent copolymers and block copolymer microgel adsorbed at the interface of two immiscible liquids. (a) First column corresponds to the case when the upper (oil) and bottom (water) liquids act as good solvents for the green (B) and the gray (A) beads, respectively, and vice versa (aAW = aBO = 25, aAO = aBW = 40). (b) Second column shows the regime when water is a good solvent for the A beads, poor solvent for the B beads and oil is poor solvent for both polymeric beads (aAW = 25, aBO = 40). (c) The third column represents the swelling of minor (B) component in the oil (aBO = 25, aAW = 40). Finally, (d) the fourth column demonstrates deformation of the molecules insoluble in both liquids (aAW = aBO = 40).

or intramolecular nanodomains (aggregates). Distribution function of the aggregates is calculated as follows. First, the system is equilibrated during 2.5 × 106 simulation steps. Then we calculated the number of the insoluble beads in each aggregate every 25 × 103 simulation steps and averaged the number on the basis of 40 different snapshots. The diagram was plotted as a relative number of the aggregates as a function of insoluble beads in the aggregate. The relative number is defined as a number of aggregates of certain aggregation number divided by the total number of the aggregates. The diagrams together with the corresponding snapshots are shown in Figure 5. In the case of the asymmetric diblock copolymers, they aggregate into spherical micelles. Despite a pretty broad distribution function ranging from 65 to 285 beads per aggregate (micelle), it has several maxima at 85, 125, 145, 155, and 170 beads: their relative number is higher than 0.05. It means that aggregation number (the number of macromolecules forming one micelle) ranges from 13 to 57 and the biggest populations of the micelles contain 17, 25, 29, 31, or 34 chains per micelle. The distribution function of the diblock copolymer micelles crucially depends on the length of the

of the ringlike globule with the hydrophilic blocks around. In case of the solvent of higher selectivity (Figure 4d), connectivity of the green blocks from different branches in one core becomes entropically unfavorable and the ring core splits into three spherical parts (clusters) due to the symmetry of the G3 molecule. Despite a penalty in the surface energy of the disintegrated core, the entropic gain minimizes the total free energy of the molecule. Similar unimolecular multicore structure has been predicted earlier by Košovan et al.68 for comb-like copolymers and very recently by Wengenmayr et al.69 for dendritic linear copolymers. Interestingly, the mean cluster size of such cores appears to be equal to the size of the single core of the arborescent copolymers of lower generation (G2), for which the lack of branching does not allow the formation of multicores. As for the microgels, the reason for the existence of the single core is also related to the small size. Aggregation in a Selective Solvent. In this subsection, we compare aggregation behavior of 5% solutions of the considered copolymer molecules. The solvent is good for A beads and bad for the B beads (aAW = 25, aBW = 50). As a result, the B-blocks aggregate with each other forming either micelles 31308


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Figure 7. Dimensionless lateral and normal components of the gyration radius of the adsorbed copolymers as functions of aBO at aAW = 25 (green), aAW at aBO = 25 (gray) and aAW = aBO (black). For all cases, aAO = aBW = 40.

we assume that 27 is the happy aggregation number, flip-flop of one or two branches (each of 3 grafts) between the cores proceeds with high probability. Furthermore, such flip-flop is possible not only within one G3 molecule but also between them. Therefore, the branch can play a role of a bridge between G3 molecules at least for the considered concentration (5%). The corresponding snapshots demonstrate that G3 molecules are less dispersed than the G2 ones due to the intermolecular bridges (Figure 5). Visual comparison of snapshots for insoluble units of diblock copolymer micelles, G2 and G3 molecules leads to the conclusion that the average size of the aggregates are nearly the same, whereas the internal structure and properties of the solutions are different. The physical reason is related to the diblock structure of dangling chains. In contrast, the microgels with the diblock copolymer subchains reveal different properties. Like in the case of the single molecule, the insoluble blocks aggregate into single core structure and soluble shell completely protects the microgels against aggregation. The size of the core is larger than the corresponding size of other molecules (Figure 5). 3.2. Liquid Interface. Single Molecules. The physical reason for the adsorption of AB amphiphilic macromolecules on liquid interface of two immiscible liquids (like oil and water) is dual, if each of the liquids is a good solvent only for one component of the macromolecules (A or B). First, the adsorption leads to the decrease of the interfacial tension due to the shielding of unfavorable contacts between immiscible liquids. This effect is not related to the amphiphilicity of the molecules and valid for homopolymers (like microgels36). In our simulations, immiscibility of the liquids (and interfacial tension) is quantified by the parameter aOW = 60, which has the biggest value among the interaction parameters, Table 1, and adsorption of the macromolecules decreases the total free energy of the system. Second, the amphiphilic structure of the macromolecules promotes adsorption like in the case of low molecular weight surfactants: hydrophilic groups and hydrophobic tails are localized in water and oil, respectively. It also enhances stability of the macromolecules at the interface in comparison with homopolymers counterparts. The simulation

insoluble block, overall length of the chain, and segregation of the blocks. The longer the insoluble block, the higher the aggregation number.65,70 As a result, the absolute value of the free energy increases and the width (relative to the height) of the distribution function decreases with the length of the insoluble block. In the current computer simulations, the length of the B block is 5 beads, which is small enough and explains pretty broad distribution function. The obtained most probable (“happy”) aggregation numbers of the diblock copolymers can explain behavior of the arborescent copolymers (Figure 5). The distribution function of G2 has two distinct maxima at 135 and 270 beads in the aggregate. It means that the aggregates comprise 27 and 54 diblocks, respectively. The number of diblock grafts per G2 molecule is exactly equal to 27. Thus, more than 50% of the molecules do not aggregate, forming unimolecular micelles. Such behavior can be explained by the fact that 27 lies between 25 and 29, which are the “happy” aggregation numbers of the diblocks. Therefore, in majority of the G2 molecules all vacancies for the formation of optimum aggregate are satisfied by the “own” diblocks. The rest of the G2 molecules reveal pairwise coupling. The second peak in the distribution function means that the paired molecules form a single core of the aggregation number 54 (about 15% of the whole amount of aggregates). The remaining fraction of the molecules displays a case of more complex structures: the presence of the cascade of smaller peaks located between two major ones. Apparently, such situation can occur when the pair of the molecules does not form a single aggregate and splits onto two cores with strong disproportion of sizes. Similar to the behavior of the single G3 molecules in selective solvent, when insoluble blocks aggregate in a complex triplecore structure (Figure 4d), self-assembly of the G3 molecules is also driven by formation of “happy” aggregates. The distribution function is broader and less discrete in comparison with that of the G2. However, the peaks at 105, 120, 135, 150, and 165 beads per aggregate, which correspond to 21, 24, 27, 30, and 33 grafts, respectively, include overwhelming majority of the molecules. The distance between these peaks is exactly equal to the one branch with 3 copolymer grafts. Therefore, if 31309


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Figure 8. Time evolution of biphasic system during adsorption of various macromolecules from aqueous solution on oil−water interface. Leftmost and rightmost columns represent volume fractions of hydrophilic (gray) and hydrophobic (green) blocks, respectively, as functions of normal coordinate z at different time moments. The corresponding snapshots are shown by three columns. The bottom and upper walls of the simulation box have coordinates z = 0 and z = 70, respectively. The oil−water interface is located at z = 50.

snapshots of the arborescent molecules and the microgel are shown in Figure 6. The upper and bottom liquids play a role of oil and water, respectively. The first column in Figure 6 corresponds to the strongest adsorption of the macromolecules, when oil is a good solvent for the B beads and bad solvent for the A beads, whereas water reveals the opposite behavior. Thus, we observe a vertical segregation of A and B blocks for all molecular objects which is clear seen in the side view (Figure 6). Adsorption of the molecules in this regime is accompanied by strong flattening and lateral spreading of the molecules at the interface. The spreading is driven by increasing number of adsorbed beads, which reduce interfacial tension, and opposed by the entropic elasticity of the subchains. The dispersed distribution of the beads in the first column, Figure 6 is due to the repulsion of monomer units in good solvents: the A and B beads repel each other in oil and water, respectively. Like in a nonselective solvent of Figure 3, the adsorbed G3 molecule has

bigger size than the microgel in the plane of the interface, which is also related to more degrees of freedom of the arms in comparison with the subchains (the absence of the cross-links). If oil and water become equally bad solvents for the B beads (aBW = 40, aBO = 40) and water remains good solvent for the A ones (aAW = 25, aAO = 40), we can observe a 2D analog of intramolecular “microphase segregation” (2nd column in Figure 6): the green beads attract each other forming flatten nanodomains (patches) and reducing lateral size of the macromolecules. They cannot form a single domain (an analog of intramolecular “macrophase segregation”) because their fraction is approximately 1/3 which is not enough to compete with the repulsive gray beads. Despite an equivalency of oil and water for the B beads in this regime, the nanodomains are exposed toward oil phase. The physical reason for that is incompatibility of A and B units with each other (aAB = 35). In contrast to one-component selective solvent (3D case), where 31310


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Figure 9. Simulation snapshots of liquid interface covered by different macromolecules. The green blocks are soluble in oil (aAW = aBO = 25, aAO = aBW = 40). The middle and bottom rows correspond to the same state. In the bottom row, different macromolecules have different colors.

the green beads form either one (G2, BC-μG) or three (G3) cores (Figure 4), the number of nanodomains in the adsorbed macromolecules is larger. The physical reason for that is smaller degrees of freedom (less number of possible conformations) for the (sub)chains and grafts in the adsorbed macromolecules. Regime of solubility of the minor (B) component in oil (aBW = 40, aBO = 25) and insolubility of major (A) component in both liquids (aAW = 40, aAO = 40) is presented in the third column of Figure 6. Due to attraction between the gray beads and formation of the globular structure, the lateral size of the adsorbed macromolecules decreases. The green blocks form nearly homogeneous layer exposed toward oil phase for all molecular objects, and we can say about stability of Janus-like morphology. Finally, if both liquids are bad solvents for both components of the macromolecules (aAW = aAO = aBW = aBO = 40), they form nanostructured globules at the interface (4th column in Figure 6). In contrast to the 3D bad solvent, the shape of the globule at the interface deviates from the spherical one to minimize the interfacial tension: the higher the tension, the more oblated the globule. More quantitative information on dimensions of the adsorbed macromolecules can be extracted from Figure 7. Here we plotted the collapse curves in terms of the lateral, Rr, and normal, Rz, components of the gyration radius which were calculated as R r2 =

1 2n2

R z2 =

i,j

n

∑ ⟨(zi − zj)2 ⟩ i,j

(7)

where n is the total number of beads in the macromolecule. The components are normalized on the corresponding values in the swollen state in solution, R0r = R0z , and plotted as functions of the interaction parameters. The black curves in Figure 7 correspond to simultaneous variation of two parameters, aAW = aBO, at fixed values of the other parameters, aAO = aBW = 40 (so-called symmetric case). First, both A and B blocks are swollen in water and oil, respectively, at aAW = aBO = 25 and they are collapsed at aAW = aBO = 40. The green curve demonstrates variation of the solvent quality of oil for the B blocks, aBO, keeping water as a good solvent for the A blocks (aAW = 25, aAO = aBW = 40). Finally, the gray curves depict worsening of water solvent quality for A beads, aAW, keeping oil as a good solvent for the B beads (aBO = 25, aAO = aBW = 40, Figure 7). For all types of the macromolecules, the lateral size decreases with worsening of the solvent quality of both or one of the liquids. On the contrary, the normal size demonstrates nonmonotonous behavior. First, it decreases because of the decrease of the volume of collapsed blocks. Rz of the dense globule then increases because of minimization of the surface area with the liquid(s). Adsorption Kinetics. The time evolution of biphasic system during adsorption of various macromolecules from aqueous solution on oil−water interface is presented in Figure 8. Regime of solubility of A beads in water and B beads in oil was considered (aAW = aBO = 25, aAO = aBW = 40). To analyze the

n

∑ ⟨(xi − xj)2 + (yi − yj )2 ⟩

1 2n2

(6) 31311


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Figure 10. Simulation snapshots of liquid interface covered by different macromolecules. The green blocks are soluble in oil and the gray beads attract each other. The bottom row depicts conformations of the molecules in the layer. Numbers of the macromolecules in the simulation boxes are the same as in Figure 9.

G2. Indeed, they reveal the fastest adsorption rate among the considered macromolecules (Figure 8, second row). The physical reason is related to the (i) stability of single molecules in the selective solvent (less than half of them is paired, Figure 5) and to (ii) looser soluble shell in comparison with the diblock copolymer corona. Thus, the single molecules can easier (and faster) adsorb on the interface because translocation of the hydrophobic aggregate into the oil is accompanied by lower entropic barrier. G3 molecules and microgels have nearly equal efficiency as stabilizers and take an intermediate position between G2 and linear diblock copolymers (Figure 8, third and fourth rows). Despite a stability of the microgels toward aggregation, they are much bulky than G2 molecules and aggregation of the hydrophobic blocks into bigger domain (in comparison with G2, Figure 5) is accompanied by formation of dense enough soluble shell which slows down redistribution of the hydrophobic block from water to oil. In the case of G3 molecules, which form a disintegrated core, association of the molecules into finite size clusters (or even supramolecular networks at high concentrations) also delays their adsorption at the interface because of a decrease in degrees of freedom.

adsorption rates, we plot the density profiles both for hydrophilic (leftmost column in Figure 8) and hydrophobic (rightmost column in Figure 8) polymer components along the z-axis at different time moments: after 1 × 105, 5 × 105, and 1 × 106 simulation steps. The numbers of A and B beads were calculated in each layer of the simulation box for 0 < z < 70 (the interface is located at z = 50) and their fractions were plotted as functions of z. Then the obtained profiles were averaged on the basis of 5 independent runs for each sort of the macromolecules. The resulting profiles and the corresponding snapshots are shown in Figure 8. First, the slowest growth of polymer concentration at the interface (both hydrophobic and hydrophilic components) is observed for linear diblock copolymers. They aggregate into the spherical micelles in water and pretty dense soluble corona of the micelle serves as an entropic barrier for adsorption: the corona has to deform in order to make a contact of hydrophobic core with the oil phase.23 Therefore, if we want to accelerate adsorption of the amphiphilic chains on the interface, one needs to reduce or suppress their aggregation ability. This can be done via sequence design23 or considering branched molecules like 31312


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Figure 11. Simulation snapshots of liquid interfaces covered by arborescent G3 copolymers with strongly asymmetric composition of diblock grafts: A2B8 (left two columns) and A8B2 (right two columns). The first and the third columns demonstrate a regime of attraction between the A and repulsion between the B beads, respectively. The second and the fourth columns represent an inverse regime.

Figure 12. Simulation snapshots of liquid interfaces covered by block copolymer microgels with strongly asymmetric composition of diblock subchains: μG-53.6% (left two columns) and μG-15.3% (right two columns). The numbers represent the total fraction of green beads.

Equilibrium Structures at Interfaces. Figure 9 depicts the equilibrium structures of monolayers formed by different polymers in the regime of solubility of the hydrophobic (green) blocks in the oil phase. The average polymer concentration is approximately equal for all systems. It is

provided by 30 molecules of G2, 10 molecules of G3, and 10 microgels (the total surface coverage is ∼40−45%). More-orless homogeneous structure of the monolayers is a consequence of mutual repulsion of hydrophobic beads in oil and hydrophilic beads in water leading also to the repulsion between the 31313


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accompanied by 2D reshaping of the molecules (Figure 12, second column). The latter is unfavorable for the adsorbed microgels because of their higher elasticity in comparison with the arborescent molecules. The behavior of the μGs-15.3% is practically the same like of G3-A8B2 (Figures 11 and 12).

macromolecules. Coloring different macromolecules in different colors (bottom row in Figure 9) allows concluding that the arborescent macromolecules do not penetrate into each other. Otherwise, interpenetration would stretch the branches in the plane of the interfaces which is entropically unfavorable. The microgels repel each other even more due to the network structure which provides more loops at the periphery and enhances repulsion. The presence of a larger uncovered area in the case of the microgels is related to their higher elasticity (in comparison with G2 and G3), which better keeps their circular form. The G2 and G3 have better ability for 2D reshaping. If the hydrophilic component of the macromolecules is thermosensitive, we can control its solubility via temperature variation. Switching on attraction between the gray beads in water (for example via temperature increase) induces aggregation of both G2 and G3 arborescent macromolecules (the ratio of the gray and green units is 2:1), whereas the microgels collapse remaining dispersed (Figure 10). Similar aggregates were obtained experimentally for arborescent copolymers of different structure adsorbed at the air−water interface.24,25 The aggregation of the arborescent copolymers with each other is governed by minimization of the line tension (a 2D analog of the surface tension). The stability of the microgels toward aggregation is provided by hydrophobic (B) blocks located at the periphery (see bottom view in Figure 10) in combination with higher elasticity. Indeed, the arborescent copolymers also have excess of hydrophobic blocks at the periphery. However, because of their 2D softness and ability for reshaping, the aggregation is not accompanied by elastic stress, like it would be in the case of the microgels. Up to now, we considered symmetric diblock copolymer as grafts for the arborescent copolymers and equivalent systems of diblock copolymers and microgels. Effect of composition of the grafts on monolayer of G3 macromolecules is demonstrated in Figure 11. Two left and two right columns in Figure 11 demonstrate G3 with A2B8 and A8B2 grafts, respectively. The first and the third columns correspond to the regime of attraction between the A beads and repulsion between the B beads, aAW = 40, aBO = 25, aAO = aBW = 40. In case of majority of the soluble blocks, A2B8, attraction between the A blocks does not lead to aggregation of the G3 molecules (images in the first column). On the contrary, their minority, A8B2, is not enough to keep the stable monolayer of the adsorbed molecules: part of them desorb forming a nonspherical oblated droplet at the interface (images in the third column). The second and the fourth columns correspond to the regime of attraction between the green and repulsion between the gray beads, aAW = 25, aBO = 40, aAO = aBW = 40. A2B8 grafts stimulate attraction between the macromolecules and formation of the dense layer. With this, the insoluble green blocks form a nanodomain structure exposed toward the oil (images in the second columns). On the contrary, attraction between the B beads of the minor fraction, A8B2, practically does not disturb loose and homogeneous structure of the monolayer (images of the fourth column). To complete our current research, we also studied the molecules of the block copolymer microgels with corresponding fraction of B blocks. Compositional equivalency of the microgels to G3 with A2B8 grafts and to G3 with A8B2 grafts is achieved at 53.6% and 15.3% of hydrophobic beads, respectively. The results are presented in Figure 12. In contrast to the arborescent copolymers (Figure 11, second column), the μGs-53.6% do not form a dense layer, which would be

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CONCLUSIONS We have performed computer simulations of AB amphiphilic arborescent copolymers of various generations (G2 and G3), equivalent linear diblock copolymers and microgels comprising diblocks as subchains under different conditions. Equivalency means that the diblock copolymers and microgels have the same average fraction of A and B units as in arborescent macromolecules. We have studied in details structures of the single macromolecules in selective solvents and on liquid interfaces. Difference in self-assembly of the macromolecules in solutions and on the interfaces was revealed. In particular, we have shown that the arborescent copolymers can form disintegrated (multi) core and unimolecular micelles in selective solvents. Kinetics of adsorption on oil−water interface predicts efficiency of the arborescent copolymers as stabilizers of emulsions (G2). Conditions for the formation of dense, loose and nanostructured monolayers were found. In particular, it has been shown that competition between attraction of insoluble blocks of minor component and repulsion of the soluble blocks in the monolayer is responsible for nanostructure formation (microphase segregation). Herewith, the arborescent macromolecules and microgels in the monolayer do not interpenetrate because of the high density of monomer units.

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AUTHOR INFORMATION

Corresponding Author

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

Walter Richtering: 0000-0003-4592-8171 Martin Möller: 0000-0002-5955-4185 Igor I. Potemkin: 0000-0002-6687-7732 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support of the German Science Foundation (DFG) within the SFB 985 “Functional Microgels and Microgel Systems”, the Russian Foundation for Basic Research within the projects 16-33-00256 (R.A.G., A.A.R.) and 16-03-00266 (I.I.P.) is gratefully acknowledged. The work was supported by the Government of the Russian Federation within Act 211, contract # 02.A03.21.0011. The simulations were performed on multiteraflop supercomputers Lomonosov and Lomonosov-2 at Moscow State University.

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