Microgel in a Pore: Intraparticle Segregation or Snail-like Behavior

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Microgel in a Pore: Intraparticle Segregation or Snail-like Behavior Caused by Collapse and Swelling Ivan V. Portnov,†,‡ Martin Möller,‡,§ Walter Richtering,‡,∥ and Igor I. Potemkin*,†,‡,⊥ †

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

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ABSTRACT: We demonstrate that a microgel can enter and exit a narrow cylindrical pore under external stimuli leading to collapse and swelling of the microgel. Attractive interactions between the microgel and the pore surface stimulate the microgel entering upon its collapse. The entering is driven by a gain in the surface energy: the area of the microgel−pore contacts is maximized within the pore. Swelling of the microgel within the pore of a finite size is thermodynamically favorable if the pore thickness exceeds a certain threshold value. Otherwise, the swelling leads to the microgel exit. The physical reason for this is a gain in the elastic free energy of the subchains which are less stretched outside the pore. We systematically study swelling and collapse of the microgel within the pore. Both longitudinal size and radial concentration profiles are calculated for different strength of interactions of the beads with each other and the pore surface. We predict an intramicrogel “phase” coexistence leading to the formation of a dense adsorbed layer near the pore surface and highly swollen central part of the microgel. Furthermore, the permeation of nanoparticles, whose size is smaller than the mesh size of the microgels, was simulated under different swelling and adsorption degrees. It is demonstrated that the microgel can slow down and completely stop the permeation of nanoparticles through the pore.

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INTRODUCTION Polymer microgels (μGs) are polymer networks in the size range between tens of nanometers and a few micrometers swollen in a solvent. From the physical viewpoint, they have a duality in properties. Viscous, liquid-like (or polymer) behavior is characteristic at the length scales smaller than the mesh size, where the subchains do not feel connectivity inside the network.1 Solid-like (or soft particle) behavior is known at larger lengths scales where the microgels reveal an elastic response.1 The most remarkable property of some μGs is their ability to dramatically swell and collapse in response to a weak variation of external conditions (temperature, pH, etc.). Like in the case of macroscopic gels,2 the softness of the microgels and swelling degree can be controlled by cross-linking density and charged groups. In contrast to solid inorganic nanoparticles, whose colloidal stability is usually achieved via steric3−6 or electrostatic7−9 stabilization, the microgel nanoparticles can be stable under good solvent conditions. Combination of adaptive shape, size, and internal structure together with their colloidal stability and permeability for various guest molecules makes the microgels very attractive for a number of applications. They are very perspective as carriers for drug delivery,10−14 scavengers,15,16 in membrane technologies,17 and as other functional systems.18 Recently, it has © XXXX American Chemical Society

been shown that the microgels can be adsorbed at liquid interfaces19−24 lowering their interfacial tension and serve as a stimuli-responsive and permeable25−27 alternative of solid particles for emulsion stabilization. Adsorption of microgels on solid surfaces28−31 can significantly modify their properties. In particular, μGs can be responsible for antifouling and self-healing effects,32,33 thermo-switchable cell adhesion,34 polymer adsorption onto multilayers,35 antimicrobial properties,36 etc. Adsorption of the microgels on the surface is due to the favorable adsorption of monomer units37 which competes with the elasticity of the subchains. Similar to the liquid interfaces, microgels are flattened on solid surfaces.31,38−40 The shape is determined by the strength of adsorption (spreading parameter of the polymer41) and cross-linking density which is opposed to the microgel “spreading”: the lower the cross-linking density, the more oblate the microgel. The microgels on the surface can swell or collapse in response to the change of the solvent quality. However, the swelling/collapse character depends on the strength of adsorption. Strongly adsorbed (stuck) microReceived: July 23, 2018 Revised: August 29, 2018

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DOI: 10.1021/acs.macromol.8b01569 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Characteristic snapshots (cross sections through the cylinder axis) of a microgel within the pore of the radius R = 15σ with attractive walls. Upper and bottom rows correspond to the regime of a good (εbb = 0.01 kT) and poor (εbb = 0.9 kT) solvents, respectively. The snapshots are obtained at different values of the adsorption energy per bead, εbw: from weak (εbw = 0.2 kT) to strong (εbw = 1.0 kT) adsorption.

gels can have a fixed contact area and swell/collapse in normal direction only. On the contrary, relatively weakly adsorbed microgels can change both their shape and volume upon swelling/collapse via variation of the contact area (variation of different surface tension coefficients or spreading parameter).31 This provides microgel’s in-plane mobility and ability to change surface properties under external stimuli. In the current article, we use the Brownian molecular dynamics simulations to demonstrate new features of microgels adsorbed on a porous solid surface. It turns out that adsorption of the microgel from a good solvent on the surface (the microgel diameter in the solution is larger than the diameter of the pore) leads to localization of the microgel above the pore with inessential penetration of some of the subchains into the pore. However, worsening of the solvent quality leads to the collapse of the microgel which is accompanied by its penetration into the pore. The driving force for the penetration is the gain in the surface energy: the microgel in the collapsed state has more monomer−surface contacts in the pore than outside. It has to be mentioned that such a penetration mechanism is different from conventional microgel translocation through the pore caused by a pressure gradient.42,43 Swelling of the microgel within the pore can lead to its exit if the pore thickness is smaller than some threshold value. The exit is entropically favorable: the swollen microgel is less deformed outside the pore. Thus, variation of the solvent quality in a cyclic manner can lead to a reversible shuttling of the microgel between the pore and the free surface (snail-like behavior). Such behavior can be exploited for the design of surfaces with switchable hydrophobicity/hydrophilicity in cosmetics, membrane technologies, etc. Besides, we systematically study the effect of swelling and collapse of the microgel confined in a cylindrical pore, when this confinement is thermodynamically favorable. Both longitudinal size and polymer density profiles are analyzed vs solvent quality. We have predicted an analogue of phase coexistence inside the microgel: dense adsorbed layer near the pore surface and swollen region around the cylinder axis. In addition, we demonstrate that the permeability of the microgel in the pore for nanometer-sized particles can be controlled by the swelling degree (solvent quality).

linkers to form a modified diamond unit cell. Each subchain consists of identical beads (“monomer units”) equidistantly located from each other. Each bead (including cross-linkers) has the radius σ and mass m. The number of the beads in the subchain is equal to 10 (10 beads between two neighbor crosslinkers). This approximately corresponds to microgels with 5% of cross-links, 100%·1/(4·5 + 1) ≈ 5%, which are commonly used in experimental studies.45−47 The positions of crosslinkers in the constructed cell repeat the pattern of a diamond cubic crystal structure. 15 × 15 × 15 modified unit cells (a frame) have been used to generate a microgel. To get the spherical microgel, a sphere is inscribed into the frame. All the beads, which are outside the sphere, were cropped out. The total number of the beads in the microgel is around 27000. The LAMMPS package48 was used to perform the Brownian molecular dynamics simulations within a standard coarsegrained model with implicit solvent. Connectivity of the beads into the polymer network was realized via combining the finite extension nonlinear elastic (FENE)49 and repulsive LennardJones potentials. The latter describes repulsion between the beads. It is quantified by the interaction parameter ε. Parameters of the FENE potential, i.e., the maximum of the bond length, R0, and spring constant, K, are taken in a standard form,49 R0 = 1.5σ and K = 30ε/σ2. The interactions between any pair of the beads (solvent quality) were described through the truncated-shifted Lennard-Jones potential.50,51 The value of the dimensionless Lennard-Jones interaction parameter εbb, describing bead−bead interactions, is taken as 0.01ε for a good solvent and increases upon solvent worsening; rcut = 2.5σ. The simulations were performed using dimensionless units of the parameters, ε = σ = m = 1. The equations of motion were integrated with a time step Δt = 0.01τ, where τ is the standard time unit for a Lennard-Jones fluid. For each of the simulations, we performed 10 × 106 equilibration runs and obtained statistics from the next 6 × 106 runs in the NVT ensemble at temperature T = 1. First, the equilibrium characteristics of the microgel in solution have been found. For this, we placed the microgel into the cubic simulation box of the size L = Lx = Ly = Lz = 100σ with imposed periodic boundary conditions. The characteristic radii of the microgel in swollen (εbb = 0.01ε) and collapsed (εbb > 0.8ε) states were 23σ and 15σ, respectively. A solid porous surface (both planar and cylindrical walls) is modeled as an array of immobile beads of the radius σ, which form smooth, impermeable surface. Interactions of the microgel beads with the surface beads are described by the truncated-

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MODEL The microgel was designed in a similar way as reported in the literature.44−47 Fully stretched subchains of the same length were arranged and connected through tetrafunctional crossB


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Macromolecules shifted Lennard-Jones potential50,51 with variable interaction parameter εbw (strength of adsorption) and rcut = 2.5σ. The simulation box of the linear sizes Lx = Ly = 130σ and Lz = 250σ was structured as follows. Upper and bottom parts of the box (z-axis is vertical) correspond to the solvent. The middle part of the box is impermeable for the microgel except for the cylindrical pore whose axis is parallel to the z-axis (Figure 1). The radius of the pore was chosen in such a way to be smaller, R = 10σ, on the same order, R = 15σ, and larger, R = 23σ, than the radius of the collapsed microgel in solution. The length of the pore is l = 150σ. As a starting structure, we have considered a microgel of the radius 15σ collapsed at εbb = 1.0ε under unconstrained conditions and placed into the pore middle (pore radii R = 15σ and 23σ). In the case of the thinner pore, R = 10σ, the microgel collapse near the pore entrance is accompanied by its entering into the pore. This is driven by minimization of the surface energy within the pore (see below). As a result, the starting structure of the collapsed microgel placed in the pore middle is nearly cylindrical. For demonstration of the snail-like effect, the upper part of the cylindrical pore was modified to be tapered. Such shape accelerates the microgel motion. The simulation box was divided into two parts: implicit solvent in the upper part of the size 150σ and closed pore of the length 100σ in the bottom part (Figure 7). We considered two starting structures of the microgels: (i) a collapsed microgel inside the pore and (ii) a swollen microgel adsorbed on the free surface above the pore.

Figure 2. Longitudinal size (semilength) of the microgel in the cylindrical pore of the radius R = 15σ as a function of the solvent quality, εbb. The curves are plotted at different values of the adsorption energy (parameter εbw). Dashed line is a collapse curve of the microgel in a dilute solution.

the longitudinal size (z-component of the gyration radius) is plotted as a function of the solvent quality (parameter εbb) at different values of the adsorption energy. The maximum length of the microgel is observed in a good solvent (small values of εbb) which decreases upon solvent worsening. Dashed reference curve corresponds to the microgel in solution. We can see that under good solvent conditions the length of the microgel in the pore is larger than the diameter in the solution: the higher the adsorption strength, the longer the microgel. On the other hand, the length in the collapsed state practically does not depend on the adsorption energy. Indeed, all solid curves in Figure 2 converge at εbb > 0.7 kT. The length of the collapsed microgel in the pore is smaller than the diameter of collapsed microgel in solution whose diameter D is approximately equal to the pore diameter, D = 30σ. Such a difference is due to adsorption of the beads to the pore surface. Indeed, in the case of the flat meniscus (εbw = 0.6 kT in Figure 1), the microgel in the pore can be approximated by a cylinder of the length L whose volume V = πLD2/4 is approximately equal to the volume of the collapsed microgel in solution, V = πD3/6. Therefore, L = 2D/3. Figure 2 also demonstrates that the character of the microgel collapse depends essentially on the adsorption strength. A gradual variation of the size with εbb is observed for weakly adsorbed microgels (εbw = 0.2 kT). On the contrary, an abrupt collapse is revealed at high attraction of the beads to the surface (εbw = 1 kT). One of the features of discontinuous transitions in infinitely large (macroscopic) polymer systems is phase coexistence;52−54 the transitions are also known as phase transitions of the first order. To find an analogy with macroscopic systems, we plot the concentration of the microgel beads as a function of the radial coordinate (Figure 3). The concentration was calculated for the cylindrical part of the microgel excluding meniscus regions. The cylinder was divided into few “slices”. The radial profile was calculated for each slice, and Φ(r) was obtained via averaging the concentrations in the different slices. If the attraction of the microgel to the pore is relatively weak (εbw = 0.2 kT), one can

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RESULTS AND DISCUSSION Swelling and Collapse of the Microgel in a Cylindrical Pore. The typical snapshots of the microgel in the pore are presented in Figure 1. They correspond to a good (upper row) and bad (bottom row) solvent conditions, respectively. We consider a regime of attractive walls, so that contacts of the microgel monomer units with the surface of the pore are energetically favorable. For all considered pore radii (except for R = 10σ), location of the microgel in the pore is thermodynamically advantageable in both swollen and collapsed states. In other words, swelling and collapse of the microgel in the pore is not accompanied by its escape. The radial size of the microgel in the pore remains constant and equal to the pore diameter in both swollen and collapsed states (Figure 1), which is due to the favorable contacts of the beads with the pore surface. On the contrary, longitudinal dimension depends on the solvent quality and the attraction strength to the surface. In the swollen state, the increase of attraction (parameter εbw) leads to elongation of the microgel and to the increase of its volume. Such behavior is caused by favorable increase of the number of adsorbed beads with εbw, which is opposed by a stretching of the subchains of the microgel interior. On the other hand, the longitudinal dimension practically does not change in the collapsed state (Figure 1). The latter is characterized by a practically fixed volume of the microgel which ensures favorable contacts of the beads with each other (they avoid contacts with the solvent). Therefore, increase of εbw in the collapsed state leads to a weak increase of the number of adsorbed beads because of their redistribution from the interior to the surface under condition of a fixed volume. Such redistribution is accompanied by a change of the meniscus curvature from convex at weak adsorption (εbw = 0.2 kT) to concave otherwise (εbw = 1.0 kT). The meniscus can be flat at an intermediate regime (εbw = 0.6 kT). The visual picture of the microgel behavior is quantified in Figure 2. Here, C


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observe a homogeneous swelling of the microgel under good solvent condition (εbb = 0.01 kT) through the whole pore except for the region near the surface (Figure 3a). Here, the concentration is slightly higher due to formation of the adsorption layer. Increase of the parameter εbb (worsening of the solvent quality) leads to elevation of the concentration which becomes practically constant through the whole pore thickness (Figure 3a). This means that the concentration in the adsorption layer becomes comparable with the concentration of the inner region, and the presence of the surface does not disturb the concentration. On the contrary, strong adsorption of the microgel on the pore surface, εbw = 0.8 kT and 1 kT, leads to the formation of dense surface layer (peaks in Figure 3b,c), whose concentration can be a few times higher than the concentration of the inner part of the microgel in the pore under good solvent conditions (εbb = 0.01 kT in Figure 3b,c). Furthermore, the concentration of the adsorption layer can slightly exceed the inner concentration even in the collapsed state (εbb = 1.2 kT in Figure 3b,c). A peculiar behavior is observed upon switching the solvent quality. Instead of a monotonous increase of the concentration of the inner part with the solvent quality worsening, one can see an intramicrogel segregation. The central part becomes even less dense than that in a good solvent, and the concentration growth proceeds near the adsorbed layer (Figure 3b,c). The coexistence of highly swollen internal and dense peripheral parts of the microgel is clearly seen in snapshots of Figure 4. Such behavior is analogous to that of polyelectrolyte microgels in dilute solutions whose quasi-hollow structure is a consequence of a competition between electrostatic repulsion of charged groups leading to their concentration at the periphery and elasticity of the subchains opposing this redistribution.44 However, “phase” segregation of the microgel in the pore is because of two sorts of attractive interactions: (i) bead−bead and (ii) bead−surface. Adsorbed beads of the microgel act as nucleus upon solvent worsening: they attract other beads as long as attractive force dominates among them. However, strong adsorption means that the bead−surface contacts are more favorable than the bead−bead ones at least at relatively small values of εbb. Thus, the nucleation proceeds upon nearly fixed number of bead−surface contacts (length of the microgel) via radial redistribution of the beads which is accompanied by stretching of inner subchains (“phase” coexistence). Only when the attraction between the beads reaches some threshold value allowing to compete with the attraction to the surface, the microgel longitudinally collapses. Such conclusion can be extracted via comparison of data in Figures 2 and 3. The increase of the pore radius up to 23σ does not lead to partial desorption of the microgel from the pore wall at least at high enough attraction energy. Figure 5 demonstrates the corresponding concentration profiles. In contrast to the thinner pore (Figure 3), the polymer concentration in a good solvent near the pore axis is smaller than that in the thinner pore, whereas the concentration of the adsorbed layer is nearly the same. In other words, the adsorbed layer remains nearly the same upon increase of the pore thickness, whereas the density of the inner part decreases because of the stretching of the subchains (Figure 5). An analogue of phase coexistence upon solvent worsening becomes negligible: the difference between concentrations of inner part of the microgel at εbb = 0.01kT and εbb = 0.4kT practically vanishes. Further increase of the attraction between the beads (parameter εbb) leads to the

Figure 3. Dimensionless concentration of the beads (monomer units) of the microgel in the pore, Φ, as a function of radial coordinate r measured in units of parameter σ under different solvent quality (parameter εbb) and strength of attraction to the pore surface: εbw = 0.2 kT (a), 0.8 kT (b), and 1 kT (c). The pore radius R = 15σ. D


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Figure 4. Snapshots of the microgel (upper row) and corresponding concentration profiles (bottom row) differing in the solvent quality: εbb = 0.01 kT (a), 0.4 kT (b), and 0.9 kT (c). εbw = 0.8 kT and R = 15σ.

and swelling did not lead to an escape of the microgel from the pore. A different behavior is detected if the pore radius is decreased. Adsorption of the microgel on the pore of the radius R = 10σ from a good solvent leads to partial penetration of the beads into the pore (Figure 7). Complete entering is observed upon solvent worsening. However, reswelling of the microgel in the pore enforces microgel escape (Figure 7). Further cyclic variation of the solvent quality does not change the back and forth movement of the microgel which is similar to a snail behavior. Like for the case of the thicker pore, the driving force for the microgel entering is the gain in the surface energy. However, reswelling within the pore (confined geometry) is always accompanied by entropic losses: the narrower the pore, the higher the losses. Indeed, the unconfined swollen microgel has a spherical shape whereas it is squeezed in the pore. Therefore, escape of the microgel from the narrow pore is driven by a gain in conformational entropy of the subchains. Gate-like Behavior. The ability of the microgel to collapse inside the pore, escape, or become permeable under variation of external conditions can be exploited as a gate for nanoparticles and liquids. Figure 8 demonstrates passing of nanoparticles through the pore with the microgel under different regimes of the microgel adsorption and swelling. 50700 nanoparticles of the radius σ were placed into the bottom part of the simulation box of the height Lz = 175σ. The pore has the radius R = 15σ and the length l = 45σ. The number of the nanoparticles above the porous wall was counted as a function of the simulation steps (time). Figure 8

collapse of the microgel in the pore whose concentration becomes approximately constant (Figure 5). Snail-like Behavior. Adsorption of the microgel from a good solvent on a pore of the radius R = 15σ is accompanied by a larger number of bead−wall contacts than in the case of an adsorption on a flat surface (Figure 6). The excess number of contacts comes from partial penetration of the microgel into the pore. It means that the adsorption on the pore is energetically more favorable. Solvent worsening leads to an expectable decrease of the number of contacts with the surface due to the microgel compaction (Figure 6). However, the difference in the numbers becomes even more pronounced (2fold at εbb = 1 kT) which is driven by penetration of the microgel into the pore. Indeed, from geometrical consideration of the collapsed microgel having a fixed volume, less than half of the microgel’s “surface” beads can have contacts with a plane wall: The number of the contacts tends to 50% in the regime of “pancake” (high value of εbw), and it is much smaller otherwise (partial wetting). On the contrary, the microgel in the pore has more than half contacts of the “surface” beads with the wall as long as its length L exceeds the pore radius, R < L. This inequality is obtained under assumption of ideal cylindrical microgel’s shape (with flat meniscus). Reswelling of the microgel in the pore upon improving solvent quality does not lead to an escape of the microgel from the pore: it is just subjected to axial swelling (with escape of a negligible fraction of the beads). Such swelling also increases the number of favorable contacts with the wall, which is approximately the same like before entering, Figure 6. Further cycles of collapse E


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Figure 6. Number ofcontacts of the microgel beads with the wall as a function of the solvent quality (parameter εbb). The bottom line corresponds to adsorption on a plane substrate. Black and red lines depict adsorption on a pore of the radius R = 15σ and length l = 45σ from a good solvent and placement of the collapsed microgel into the pore, respectively. Adsorption energy εbw = 0.6 kT.

microgel collapse. The penetration is practically stopped at εbb = 1 kT. Thus, the microgel in the pore can efficiently control penetration of the nanoparticles or block them depending on the external conditions.

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CONCLUSION We have performed computer simulations of the swelling and collapse of a microgel placed in a narrow cylindrical pore. The pore diameter is smaller than the microgel diameter in a swollen state in dilute solution. The pore surface was considered to be attractive; i.e., the microgel adsorbs on the surface. It turns out that the microgel collapse near the pore stimulates its entering into the pore due to the gain in energy: the number of favorable microgel−surface contacts within the pore is larger than outside. On the contrary, the microgel behavior upon swelling within the pore depends on the pore thickness. The microgel exits the pore if the pore thickness is smaller than a threshold value. The reason is the gain in the elastic free energy of escaped microgel, which gets more conformational degrees of freedom than in the confined geometry. Thus, a periodic swelling and collapse of the microgel can cause its motion similar to a snail which hides its body in a shell or gets it out for crawling. However, if the thickness of the pore is large enough, the microgel swelling within the pore leads to its elongation rather than escape. The microgel structure in the swollen state and under merely poor solvent conditions resembles a phase coexistence: a dense periphery due to adsorption of the microgel beads and a highly swollen inner part of the microgel. A more homogeneous structure is observed in a bad solvent. Furthermore, we have demonstrated that the permeability of the pore, which is filled with microgels, for nanoparticles can be controlled by the swelling degree of the microgel. The predicted behavior of the microgels within and near the pore can experimentally be realized with thermo- or pHsensitive microgels which have strong affinity for a substrate. One of the possibilities is using of poly(N-isopropylacrylamide) (PNIPAM) microgels which can physically be

Figure 5. Dimensionless concentration of the beads (monomer units) of the microgel in the pore, Φ, as a function of radial coordinate r measured in units of parameter σ under different solvent quality (parameter εbb) and strength of attraction to the pore surface: εbw = 0.8 kT (a) and 1 kT (b). The pore radius R = 23σ.

depicts a fraction of passed nanoparticles. The dashed line demonstrates permeability of the bare (without the microgel) pore. Very fast penetration proceeds during first 2 × 105 simulation steps when ∼30% of nanoparticles pass through the pore. Then the penetration slows down approaching plateau value ∼0.5, which corresponds to equilibrium distribution of the nanoparticles (their concentrations above and below the wall are equal). The effect of weakly adsorbed microgels (εbw = 0.2 kT) at different swelling degrees is demonstrated by solid lines. Despite a collapsed state of the microgel, it cannot serve as a stopper because of the weak adsorption. The microgel is pushed out from the pore due to the osmotic pressure of the nanoparticles. Therefore, all these curves approach the plateau value. On the contrary, strongly adsorbed microgel (εbw = 0.6 kT) can withstand the pressure. The microgel is permeable for the nanoparticles under good solvent conditions (εbb = 0.01 kT). However, it essentially slows down penetration in comparison with the bare pore (dotted lines in Figure 8). Further slowing of the penetration can be achieved via the F


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Figure 7. Snapshots (cross section through the cylinder axis) of the microgel adsorbed on a pore of the radius R = 10σ (a), entering the pore in bad solvent at εbb = 0.8 kT after 16 × 106 simulation steps (b), escape from the pore upon reswelling at εbb = 0.01 kT after 1 × 106 simulation steps (c), and further entering at εbb = 0.8 kT after 5 × 106 simulation steps (d). Adsorption energy εbw = 0.8 kT.

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ACKNOWLEDGMENTS

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REFERENCES

The financial support of the Deutsche Forschungsgemeinschaft (DFG) within the SFB 985 “Functional Microgels and Microgel Systems”, the Russian Foundation for Basic Research and the Government of the Russian Federation within Act 211, Contract 02.A03.21.0011, is gratefully acknowledged. M.M. thanks the Russian Ministry of Education and Science, Grant of the Government of the Russian Federation No. 14.W03.31.0018 for the financial support. The research is performed using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University. The authors also gratefully acknowledge the computing time granted by the John von Neumann Institute for Computing (NIC) and provided on the supercomputer JURECA55 at the Jülich Supercomputing Centre (JSC).

(1) Panyukov, S. V.; Potemkin, I. I. Statics and Dynamics of the “Liquid-” and “Solidlike” Degrees of Freedom in Lightly Cross-Linked Polymer Networks. J. Phys. I 1997, 7, 273−289. (2) Khokhlov, A. R.; Starodubtzev, S. G.; Vasilevskaya, V. V. Conformational Transitions in Polymer Gels: Theory and Experiment. Adv. Polym. Sci. 1993, 109, 123−171. (3) Cao, P.-F.; Yan, Y.-H.; Mangadlao, J. D.; Rong, L.-H.; Advincula, R. Star-like Copolymer Stabilized Noble-Metal Nanoparticle Powders. Nanoscale 2016, 8, 7435−7442. (4) He, J.; Liu, Y.; Babu, T.; Wei, Z.; Nie, Z. Self-Assembly of Inorganic Nanoparticle Vesicles and Tubules Driven by Tethered Linear Block Copolymers. J. Am. Chem. Soc. 2012, 134, 11342− 11345. (5) Zhao, D.; Di Nicola, M.; Khani, M. M.; Jestin, J.; Benicewicz, B. C.; Kumar, S. K. Self-Assembly of Monodisperse versus Bidisperse Polymer-Grafted Nanoparticles. ACS Macro Lett. 2016, 5, 790−795. (6) Kravchenko, V. S.; Potemkin, I. I. Self-Assembly of Rarely Polymer-Grafted Nanoparticles in Dilute Solutions and on a Surface: From Non-Spherical Vesicles to Graphene-Like Sheets. Polymer 2018, 142, 23−32. (7) Overbeek, J. T. G. The Rule of Schulze and Hardy. Pure Appl. Chem. 1980, 52, 1151−1161. (8) Kalsin, A. M.; Fialkowski, M.; Paszewski, M.; Smoukov, S. K.; Bishop, K. J. M.; Grzybowski, B. A. Electrostatic Self-Assembly of Binary Nanoparticle Crystals with a Diamond-Like Lattice. Science 2006, 312, 420−424. (9) Reetz, M. T.; Helbig, W. Size-Selective Synthesis of Nanostructured Transition Metal Clusters. J. Am. Chem. Soc. 1994, 116, 7401−7402. (10) Wu, W.; Yao, W.; Wang, X.; Xie, C.; Zhang, J.; Jiang, X. Bioreducible Heparin-Based Nanogel Drug Delivery System. Biomaterials 2015, 39, 260−268. (11) Strozyk, M. S.; Carregal-Romero, S.; Henriksen-Lacey, M.; Brust, M.; Liz-Marzan, L. M. Biocompatible, Multiresponsive Nanogel Composites for Codelivery of Antiangiogenic and Chemotherapeutic Agents. Chem. Mater. 2017, 29, 2303−2313.

Figure 8. Fraction of nanoparticles above the porous wall (the relative number of penetrated nanoparticles) as a function of the number of simulation steps. Dashed, solid, and dotted lines correspond to the bare pore, weak (εbw = 0.2 kT), and strong (εbw = 0.6 kT) microgel adsorption, respectively. Snapshots depict different regimes of penetration. The pore radius R = 15σ.

adsorbed on a solid (SiO2)/water interface.40 Such adsorption on a plane surface leads to the microgel flattening,40 i.e., PNIPAM microgels have strong affinity for SiO2 surface. Thus, adsorption of such microgels on porous SiO2 surface in water environment can be manipulated with temperature which causes the microgel swelling or collapse.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01569.

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AUTHOR INFORMATION

Corresponding Author

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

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

The authors declare no competing financial interest. G


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Microgel in a Pore: Intraparticle Segregation or Snail-like Behavior

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