Dynamic Structure Factor of Core–Shell Microgels: A Neutron

Article pubs.acs.org/Macromolecules

Dynamic Structure Factor of Core−Shell Microgels: A Neutron Scattering and Mesoscale Hydrodynamic Simulation Study Simona Maccarrone,†,∥ Ali Ghavami,‡ Olaf Holderer,† Christine Scherzinger,∥ Peter Lindner,⊥ Walter Richtering,∥ Dieter Richter,†,§ and Roland G. Winkler*,‡ †

Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), Forschungszentrum Jülich GmbH, Lichtenbergstr. 1, 85748 Garching, Germany ‡ Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation, and §Institute of Complex Systems, Forschungszentrum Jülich GmbH and JARA, 52425 Jülich, Germany ∥ Institute of Physical Chemistry, RWTH Aachen University and JARA - Soft Matter Science, Landoltweg 2, 52056 Aachen, Germany ⊥ Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, 38042 Grenoble, Cedex 9, France ABSTRACT: Polymeric microgels with core−shell morphology provide promising properties for many applications such as controlled uptake and release of guest nanoparticles. In this work we investigated how the structure and dynamics of the core and the shell in the microgel are coupled using both experimental and computer simulation approaches. The studied core−shell model systems which consist of a collapsed core and a swollen shell (CCSS) and a swollen core and collapsed shell (SCCS) show a different behavior in both structure and dynamics. The intermediate scattering profiles obtained from neutron spin echo (NSE) spectroscopy of CCSS microgels show an initial fast decay similar to that of bare swollen microgels followed by a slow decay similar to that of a purely collapsed microgel. This is also reflected in mesoscale hydrodynamic simulations using the multiparticle collision dynamics method. In the case of CCSS microgels, the decay rate of the intermediate scattering functions shows a crossover from collective diffusive dynamics at low wavenumbers to a Zimm-type dynamics at larger wavenumbers. This is similar to the behavior of a purely swollen microgels. In the case of SCCS microgels, the intermediate scattering profiles from experiment and simulations show a slow dynamics at small as well as large wavenumbers. Studying the dynamics of the individual compartments in the simulated structures suggests that the slower dynamics in SCCS microgels can be attributed to the collective motion of collapsed and aggregated shell parts which form in the periphery of the microgel. Additionally, in both CCSS and SCCS microgels, a slowdown of the dynamics is observed in the swollen compartment compared to the bare swollen microgel, which is a result of the interplay between core and shell compartments.

1. INTRODUCTION

with a molar methanol fraction of xMeOD = 0.2, PNIPAM is in a collapsed state at room temperature.11 Increasing the methanol fraction above 0.4, PNIPAM swells due to methanol excess.12 Interestingly, not all thermosensitve polymers display cononsolvency. Poly(N,N-diethylacrylamide) (PDEAAM) goes through a phase transition at temperatures above 26 °C in water, but it does not show a co-nonsolvency effect in mixtures of methanol and water.13−15 PDEAAM differs from PNIPAM only in the amide function (no proton). The different hydrogen-bonding patterns of secondary and tertiary amides seem to be relevant for the co-nonsolvency effect.16−18 In previous experiments,15,19,20 partially collapsed PNIPAM and swollen PDEAAM microgels under co-nonsolvency conditions of a molar fraction of 0.2 MeOD in D2O at 10 °C were structurally and dynamically characterized by means of small-angle neutron scattering (SANS) and neutron spin echo

Microgels are soft colloidal particles consisting of cross-linked polymers, which are able to undergo reversal volume changes upon external stimuli. Hence, microgels are unique and versatile materials,1,2 with possible applications ranging from drug delivery,3,4 sensing,5 photonic crystals,6 template-based synthesis of inorganic nanoparticles,7 to separation and purification technologies.8 Their sponge-like structure determines the characteristic properties of the microgel such as optical, mechanical, and swelling behavior. One of the most studied thermally sensitive microgels is poly(N-isopropylacrylamide) (PNIPAM). Below 32 °C, PNIPAM polymers are solvated in water, and the microgel is therefore in a swollen state. When temperature is increased above 32 °C, PNIPAM becomes insoluble and the microgel undergoes a phase transition, associated with a reduction of its volume. PNIPAM is sensitive not only to temperature but also to the composition of the solvent.9 This phenomenon is called co-nonsolvency10,11 and can already be triggered with a small methanol content. For example, in a methanol/water mixture © 2016 American Chemical Society

Received: February 1, 2016 Revised: April 18, 2016 Published: April 28, 2016 3608

DOI: 10.1021/acs.macromol.6b00232 Macromolecules 2016, 49, 3608−3618

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oxide (D2O), and methnaol-d4 (MeOD) were procured from Deutero, Germany. For synthesis and purification of the microgel products twice distilled Milli-Q water was used exclusively (twice distilled MilliQ water will be denoted as “water” in the following). 2.2. Microgels Core Synthesis. Microgels were produced according to an earlier described precipitation polymerization method.54 A three-necked round-bottom 500 mL flask, equipped with a septum for gas inlet, overhead stirrer, and reflux condenser, was filled with 125 mL of water; the water was purged with nitrogen for 30 min. Then, 24.4 mmol of monomer (NIPAM or DEAAM), 1.14 mmol (0.176 g) of BIS, and 0.44 mmol (0.176 g) of SDS were added under stirring. After another 30 min of degassing, the mixture was heated to 80 °C oil bath temperature under stirring at 350 rpm. The reaction was started subsequent by addition of 0.23 mmol of KPS dissolved in 5 mL of water under constant nitrogen flow and stirring. A milky tarnish appeared after 5 min and indicated the start of particle formation. The reaction was continued for 5 h and stopped afterward by cooling to room temperature. The obtained microgel particles were cleaned by three cycles of centrifugation (Sorvall Discovery 90SE with T-865 rotor at 20 °C and 35 000 rpm) and subsequent redispersion. Finally, the products were freeze-dried. 2.3. Shell Synthesis. The PDEAAM shell was applied onto the PNIPAM core by a simple two-step batch synthesis as described before.54 The PNIPAM shell on the PDEAAM core was prepared according to the work of Lyon and co-workers using the so-called seed and feed method.55,56 Batch. 400 mg of dried PNIPAM microgel was dispersed in 40 mL of water (in a three-necked round-bottom flask with reflux condenser, overhead stirrer, and septum for gas inlet); the mixture was degassed for 30 min with nitrogen. A small amount of SDS (16 mg) was added under stirring. Then 436 mg (3.43 mmol) of DEAMM and 27 mg (0.173 mmol) of BIS were added to the core mixture under stirring and nitrogen flow, followed by 10 min of further degassing. The reaction mixture was then heated to 70 °C oil bath temperature and started with 9 mg (0.0318 mmol) of KPS. After that, the reaction was continued like described for the core microgels. Seed and Feed. 350 mg of dried PDEAAM microgel was dispersed in 50 mL of water. The mixture was degassed for 30 min with nitrogen (in a three-necked round-bottom flask with reflux condenser, overhead stirrer, and septum for gas inlet). A small amount of SDS (30 mg) was added under stirring. In the meantime, an aqueous solution of 1.05 g (9.3 mmol) of NIPAM and 72 mg (0.46 mmol) of BIS was prepared in a second flask, and a solution of 26.5 mg of KPS in water was prepared in a third flask. The core mixture was heated to 70 °C oil bath temperature under stirring and constant nitrogen flow. After the reaction temperature was reached, about 20% of each separately prepared solution was added to the core mixture. The reaction mixture was stirred for 15 min, and then the rest of the monomer and the starter solution were added stepwise over a time span of 45 min to the reaction mixture. The reaction was continued as described before. 2.4. Small-Angle Neutron Scattering (SANS). Dispersions of 0.2 wt % PNIPAM-core−PDEAAM-shell (CCSS) and PDEAMMcore−PNIPAM-shell (SCCS) microgel were prepared in MeOD and D2O, respectively. The measured samples in the solvent mixture with xMeOD = 0.2 were prepared from these dispersions just before the experiment in order to avoid evaporation of methanol-d4 from the mixture. Experiments were performed at the D11 instrument at ILL in Grenoble, France. The incident wavelength of neutrons was set to 6 Å. Intensities were measured at detector distances of 1.2, 8, 20, and 39 m covering a total q-range of 0.001−0.5 Å−1. Standard Hellma quartz cells of 1 mm were used. Data were corrected for background scattering and calibrated on absolute scale by incoherent water scattering according to the standard procedure at the ILL.57 2.5. Neutron Spin Echo (NSE). To achieve maximum contrast and minimum incoherent background resulting from protonated material, we used deuterated solvents D2O and MeOD. The measured samples with xMeOD = 0.2 were mixed from 1 wt % parent dispersions just before the experiment in order to avoid evaporation of MeOD. Measurements on PNIPAM-core−PDEAAM-shell (CCSS) and PDEAMM-core−PNIPAM-shell (SCCS) microgel solutions in the q-

(NSE). Besides structural parameters such as mesh size and microgel radius, polymer density profiles were calculated and related to the polymer dynamics. Both swollen PDEAMM and partially collapsed PNIPAM are generally well described by a reduced mode spectrum of Zimm segmental dynamics. Only for the partially collapsed microgel at low q values, we could detect a crossover from single polymer (Zimm) to collective dynamics.20 While theoretical approaches to study the dynamics of polymer networks are typically limited to bulk gels,21−24 computer simulations provide a viable approach to unravel the polymer dynamics of finite-size cross-linked networks in solution. Recently, coarse-grained simulations with implicit solvent have been successfully employed to investigate the equilibrium properties of neutral and charged microgel systems,25,26,27 but little is known about the internal polymer dynamics of microgels. The porous structure of microgels, which allows for a free penetration and exchange of solvent molecules, requires a proper treatment of hydrodynamics interactions (HI) to suitably unravel the internal polymer dynamics. There are various mesoscale simulation approaches, which adequately capture hydrodynamic interactions and can be combined with embedded objects. Prominent examples are the lattice Boltzmann (LB) method,28−30 dissipative particle dynamics (DPD),31,32 and the multiparticle collision dynamics (MPC) approach.33−35 Here, we adopt the MPC approach, a particle-based simulation technique, which incorporates thermal fluctuations, provides hydrodynamic correlations and is easily coupled with molecular dynamics simulations for the microgels. It has successfully been applied to study equilibrium and nonequilibrium dynamical properties of colloids34−46 and polymers.34,35,47−53 In this article, we present experimental and simulation results of the dynamics of complex microgels composed of compartments (core and shell) with a different degree of swelling. Experimentally, we performed SANS and NSE studies of PNIPAM-core−PDEAAM-shell (CCSS) and PDEAMM-core− PNIPAM-shell (SCCS) microgels. Theoretically, the dynamics of similar model core−shell microgels has been investigated by mesoscale hydrodynamic simulations, exploiting the MPC approach. The major advantage of computer simulations in this context is the ability to distinguish the individual contributions of every compartment within the same core− shell microgel to the dynamics structure factor. Although the complexity of the experimental structures may not be quantitatively captured in the simulations, the results allow us to qualitatively unravel the complex interplay between swollen and collapsed compartments in core−shell microgels and to understand the influence of the core−shell coupling on the overall dynamics of the microgel. The rest of the paper is organized as follows. Section 2 describes the experimental methods and the simulation approach. The experimental and simulation results regarding the structure and dynamics of the core−shell microgels are presented in section 3, and section 4 includes the discussion and conclusions.

2. EXPERIMENTS: MATERIAL AND TECHNIQUES 2.1. Materials. N-Isopropylacrylamide (NIPAM), methylenebis(acrylamide) (BIS), potassium peroxodisulfate (KPS), and the surfactant sodium dodecyl sulfate (SDS) were purchased from VWR, Germany. Diethylacrylamide (DEAAM) and Rhodamine B were bought at Polysciences, Germany. Deuterated solvents, dideuterium 3609


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Figure 1. Absolute SANS intensities of CCSS (left) and SCCS (right) microgels in comparison with the corresponding bare cores (adapted with permission from ref 20) in xMeOD = 0.2 at 10 °C. The solid lines are fitted curves of the model proposed in ref 54. range between 0.02 and 0.15 Å−1 were performed at the J-NSE spectrometer58 at the FRM II research reactor in Garching (Germany) at a wavelength of 8 Å probing Fourier times up to 40 ns. The samples were mounted in a thermostat-controlled sample environment at 10 °C. Scattering from corresponding quartz cells containing the deuterated solvent mixture has been subtracted as background from the NSE data. 2.6. Computer Simulation. A hybrid simulation approach is adopted, combining multiparticle collision dynamics simulations (MPC) for the solvent and molecular dynamics simulations for the polymers.34,35,47,53,59 Solvent. In MPC, the solvent is composed of N pointlike particles of mass m, distributed in a cubic box of length L with periodic boundary conditions. The dynamics of the particles proceeds in a streaming step followed by a collision step. During streaming, the particles move ballistically for the time interval h according to

ri(t + h) = ri(t ) + h vi(t )

distance is set to rc = 21/6σ, whereas for poor solvent conditions rc = 2.5σ. The dynamics of the monomers is treated by molecular dynamics simulations (MD). The coupling to the MPC solvent is achieved by the inclusion of the monomers in the collision step.34,35,53,61 Core−Shell Microgels. A core−shell microgel is constructed by labeling monomers of polymers at a fully stretched configuration with at least one of their monomers closer than a certain radius rcore to the microgel center as core and the rest of the monomers as shell. For a CCSS microgel, the cutoff distances of the Lennard-Jones potential for core and shell particles are set to rc,core = 2.5σ and rc,shell = 21/6σ, respectively, and for a SCCS microgel, rc,core = 21/6σ and rc,shell = 2.5σ. The cutoff distance for interaction between core and shell monomers is set to rc,core−shell = 21/6σ in all cases. Parameters. The microgel systems studied in this work are composed of polymers with Nm = 20 monomers and Nc = 729 cross-links with 64 dangling ends at the outer surface of the microgel. l, kBT, and m were chosen as units of length, energy, and mass; the unit of time is τ = (ml2/kBT)0.5. In addition, we set ε/kBT = 1, σ = 0.8l, a = l, M = 10m, α̅ = 130°, and K = 103kBT/l2 and perform 20 MD simulation steps between MPC collisions. After equilibrating the structures, we perform at least 5 × 106 MPC steps in order to achieve a reasonable statistical accuracy.

(1)

where ri and vi are position and velocity of particle i, i = 1, ..., N. In the collision step, the particles are sorted in cubic collision cells of length a.34,35 Then, for each collision cell, the relative velocities of the particles, with respect to the center-of-mass velocity vcm of all particles in that cell, are rotated by a fixed angle α̅ around a randomly orientated axis. Hence, the velocities of the particles are updated according to vi(t + h) = vcm(t ) + R(α̅ )(vi(t ) − vcm(t ))

3. RESULTS AND DISCUSSION 3.1. Structure. 3.1.1. Experiment. Figure 1 displays scattering intensity curves of core−shell microgel particles together with the corresponding bare cores. The used fitting model (solid lines in Figure 1) is explained in detail in ref 54. As expected, the form factor minimum for both core−shell particles are shifted to lower q values compared to that of the bare particles. Thus, the radii of the core−shell microgels are larger than that of the bare microgels. Regarding the PNIPAMcore−PDEAAM-shell microgel, the form factor minimum is also less pronounced that that of the bare PNIPAM. Hence, we deduce that the surface of the PNIPAM-core−PDEAAM-shell microgel is fuzzier than the surface of the PNIPAM core. On the other hand, the PNIPAM-shell−PDEAAM-core form factor minimum appears more compact (less porous surface) than the PDEAAM microgel. From the fitting parameters, summarized in Table 1, we calculated the monomer density profiles as shown in Figure 2. The collapsed PNIPAM core in CCSS microgels appears slightly larger than that of the bare PNIPAM microgel.20 Most likely the swollen PDEAMM shell pulls the polymers of the core outward. The overlap region of the two compartments is rather narrow and only about 4 nm thick. In the case of SCCS, we observe a reduced core size compared to the bare microgel

(2)

where R(α̅ ) is the rotation matrix. To guarantee Galilean invariance, a random shift of the entire collision grid is applied for each collision step.60 Microgel. Microgels are modeled as a network of tetrafunctionally cross-linked polymers each of length Nm. The monomers are treated as point particles of mass M, which interact with their bound neighbors by the harmonic potential

Uib, i + 1 =

K (|ri + 1 − ri| − l)2 2

(3)

where l is the bond length and K is the spring constant. Nonbonded interactions are described by the truncated Lennard-Jones (LJ) potential

⎧ ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ ⎪ ⎢⎜ σ ⎟ σ ⎥ ⎪ 4ε ⎜ ⎟ − ⎜⎜ ⎟⎟ ⎥ − C , rij < rc ULJ = ⎨ ⎢⎣⎝ rij ⎠ ⎝ rij ⎠ ⎦ ⎪ ⎪ 0, rij > rc ⎩

(4)

where ε is the strength of the interaction, rij = |ri − rj|, σ indicates the diameter of the monomer, rc is the cutoff distance, and C = 4ε[(σ/rc)12 − (σ/rc)6]. In order to simulate good solvent conditions, the cutoff 3610


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distribution appears in the case of core−shell microgels. The distribution function for the collapsed microgel exhibits a rather sharp surface, while P(r) of the swollen microgel indicates a significantly fuzzier surface. The distribution function of the CCSS microgel suggest an even fuzzier outer surface comprising essentially the whole shell. However, the core− shell interface is rather sharp. The monomer distribution function of the SCCS microgel is flat up to half of the radius of gyration Rg of the microgel. For larger radii, the distribution function gradually increases, reaches a maximum at r/Rg ≈ 1.0, and decrease again with increasing r. Here, the interface between the core and shell is rather broad. The contributions from core and shell compartments to the overall monomer distribution functions are shown in the inset of Figure 4. The results suggest a minimal core−shell overlap in the case a CCSS microgel, while for a SCCS microgel the density distribution of the core polymers is outspread to the outer surface of the microgel. Hence, the core−shell interface properties are rather similar in experiments and simulations (cf. Figure 2). Furthermore, the gyration radii of polymers in the core and the shell compartments are calculated according to Rpg = [∑Ni=1m⟨(ri − rcm)2⟩/Nm]1/2, where rcm is the position of the center of mass of the polymer. The average polymer gyration radius R̅ pg of the swollen shell of the CCSS microgel is 2.52l, which is fairly similar to that of the swollen microgel R̅ pg, while the R̅ pg of the swollen core of the SCCS microgel is 2.45l due to the compression effect of the shell. The R̅ pg of the collapsed core of the CCSS and the bare collapsed microgels is 1.86l, and 1.88l, respectively, and R̅ pg of the collapsed shell of the SCCS microgel is 1.97l, which is slightly larger than that of the bare collapsed microgel. The structure of the microgels is further analyzed in terms of the spherically averaged static structure factor

Table 1. Structural Parameters of Two Core−Shell Microgels in the Solvent Mixture xMeOD = 0.2 at 10 °C Obtained by Fitting the SANS Data with the Model of Ref 54a microgel PNIPAM-core/ PDEAAM-shell (CCSS) PDEAAM-core/ PNIPAM-shell (SCCS)

comp

R [nm]

2σsurf [nm]

RSANS [nm]

ϕpoly [%]

core shell

38.5 63.8

3.7 20

83.8

36 15

0.0004

core shell

44 72.3

13 12

84.3

32.9 28.7

0.0015

constback

R is the radius of the microgel particle, σsurf denotes the width of the smeared particle surface, RSANS is the overall size of the particle obtained by SANS, σpoly describes relative particle size polydispersity, and constback accounts for residual incoherent scattering. a

particle. Now the swollen PDEAAM core is constrained by a collapsed PNIPAM shell. Here, the overlapping region is rather large and about 20 nm thick. The huge difference in the overlap region is intuitively understandable, when realizing the forces on the polymers at the interface. In the case of CCSS microgels, the collapsed core is compact in its interior, while the swollen shell pulls outward. The situation is reversed for SCCS microgels, where the core pushes radially outward and the collapsed shell exerts an inward pressure. The increased density in the core can be attributed to the penetration of “shell monomers” into the core region. Similar results were already obtained on previously investigated core−shell microgel with collapsed core.62 3.1.2. Simulation. In the simulations, we choose collapsedcore−swollen-shell microgels (CCSS) with Ncore/N = 0.61 and swollen-core−collapsed-shell microgels (SCCS) with Ncore/N = 0.34 as well as bare swollen and collapsed microgels. It should be noted that in both CCSS and SCCS microgels the swollen parts comprise approximately the same number of monomers. Simulation snapshots of the various gels are displayed in Figure 3. The equilibrium structure of the simulated microgels is characterized by the radial monomer distribution function P(r) with respect to the center-of-mass position of a microgel. The 2 distribution function is normalized such that ∫ ∞ 0 4πr P(r) dr = 1. Figure 4 shows the obtained radial distribution functions for the various microgels. For swollen and collapsed microgels, the monomer distribution is more or less flat while a biphasic

S(q) =

1 N

N

∑ i,j=1

sin(qrij) qrij

(5)

where q is the magnitude of the scattering vector. Respective results for the various microgels are presented in Figure 5. The initial sharp drop of S(q) in the regime ql ≲ 2 is determined by the radius of gyration of a microgel (Guinier regime). Consistent with direct calculations, the radius of gyration of the collapsed microgel is smallest, that of the swollen is largest, and the other two are in-between (cf. Figure 4). Thereby, the

Figure 2. Density profiles calculated from SANS intensities of SCCS (left) and CCSS (right) microgels in comparison with the corresponding bare cores in xMeOD = 0.2 at 10 °C (adapted with permission from ref 20). 3611


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Figure 3. Snapshots taken from simulations of swollen, collapsed, CCSS, and SCCS microgels. The red beads represent the cross-links. For the CCSS and SCCS microgels, the blue part represents the core and the cyan part the shell.

approximation for systems with sharp boundaries. The scattering profiles for core−shell microgels exhibit a somewhat different behavior. In the low-q regime, core−shell microgels show characteristics of a collapsed microgel, while for large q values, the slope of the scattering functions is closer to that of the swollen microgel. However, we cannot identify a clear power-law regime any longer, which we partly attribute to the shortness of the polymers. 3.2. Internal Dynamics. 3.2.1. Experiment. The internal microgel dynamics is characterized by the intermediate scattering function S(q,t). As shown in Figure 6, the ratio S(q,t)/S(q,0) measured by NSE shows the same trend for both CCSS and SCCS microgels for the two smallest scattering vectors q = 0.05 and 0.08 Å−1. In fact, the dynamics is rather similar to that of (partially) collapsed microgels. The scattering signal of both core−shell microgels basically overlaps with that of bare PNIPAM microgels. The intermediate scattering functions for the large q values (q = 0.11 and 0.15 Å−1) are rather different. As displayed in Figure 7 for the CCSS microgels and in Figure 8 for SCCS microgels, S(q,t)/S(q,0) exhibits an initial fast decay followed by a slower one for longer times. In the case of CCSS microgels, the later decay is slower, in-between that of the swollen and collapsed bare microgels. In the case of SCCS microgels, the long-time decay overlaps with the decay for the partially collapsed bare PNIPAM. 3.2.2. Simulation. In the simulations, the intermediate scattering function is determined according to

Figure 4. Radial monomer distribution function for swollen, collapsed, CCSS, and SCCS microgels. The inset figures show the distribution functions for CCSS (top) and SCCS (botton) microgels with contributions from core (orange) and shell (violet) compartments separately. The absolute radii of gyration for swollen, collapsed, CCSS, and SCCS microgels are Rg/l = 30.5, 13.51, 16.3, and, 19.4, respectively.

S (q , t ) = Figure 5. Static structure factor profiles of swollen, collapsed, and core−shell microgels. The upper dashed line, corresponding to ∼ql1/0.63, is obtained by fitting the S(q) curve of the bare swollen microgel in the interval 0.8 ≲ ql ≲ 2.0, and the lower dashed line, corresponding to ∼ql1/0.53, is obtained by fitting S(q) of the bare collapsed microgel in the interval 0.8 ≲ ql ≲ 1.5.

1 N

N

∑ ⟨exp[iq·(rj(t ) − ri(0))]⟩ (6)

i,j=1

This function follows the universal scaling relation S(q , t ) = S(q , 0)f (qγ t )

(7)

for suitable wavenumbers and time scales for polymers under Theta and good solvent conditions.63,64 The analytical calculation for a flexible Gaussian polymer and scaling considerations for a polymer with excluded volume interactions in solution (Zimm model) yields an exponential function for f(x), with x ∼ (qγt)2/γ and γ = 3.64−66 Polymer stiffness changes the exponent to γ = 8/3 for semiflexible polymers.64 The structure factor (Figure 5) and the monomer mean-square displacement in the center-of-mass reference frame (cf. inset of Figure 9) suggest a universal regime for 1.0 < ql < 2.0 and

Rg of the CCSS microgel is rather close to that of the collapsed one. Again, this is in agreement with the experimental findings. In the q range 0.8 < ql < 3.0, S(q) of the swollen microgels exhibits approximately the power-law dependence S(q) ∼ q−1/ν, with ν = 0.62. The scaling exponent ν is slightly larger than the theoretical prediction for a polymer in good solvent63 ν = 0.59, which is partially attributed to shortness of the polymers.47 The structure factor of a collapsed microgel is proportional to q−4 in the range 0.3 ≲ ql ≲ 1.0, in close agreement with Porod’s

20 < t / ma 2 /kBT < 100. As displayed by Figure 9, the intermediate scattering curve follows the scaling relation of eq 7 3612


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Figure 6. Intermediate scattering functions of SCCS (left) and CCSS (right) microgels in comparison with the partially collapsed PNIPAM and swollen PDEAAM micrgels (adapted with permission from ref 20) in the solvent mixture with xMeOD = 0.2 at 10 °C and for q = 0.08 Å−1.

Figure 7. Intermediate scattering functions of CCSS, partially collapsed PNIPAM, and swollen PDEAAM microgels (adapted with permission from ref 20) in the solvent mixture with xMeOD = 0.2 at 10 °C for q = 0.11 Å−1 (left) and q = 0.15 Å−1 (right). The solid lines (black) are fitted curves obtained as sum of two exponentials, and it serves as guide for the eye.

Figure 8. Intermediate scattering functions of SCCS, partially collapsed PNIPAM, and swollen PDEAAM (adapted with permission from ref 20) in the solvent mixture with xMeOD = 0.2 at 10 °C for q = 0.11 Å−1 (left) and q = 0.15 Å−1 (right).

rather well with γ ≈ 3. Therefore, the polymer dynamics in the cross-linked network of the microgel under good solvent conditions is governed by hydrodynamic interactions. The intermediate scattering functions of CCSS and SCCS microgels are presented in Figures 10 and 11, respectively, for ql = 0.5, 1.0, and 1.5. For a detailed understanding of the contributions of the various compartments, in addition,

scattering functions of the individual core and shell compartments as well as S(q,t) of swollen and collapsed microgels are presented. The intermediate scattering function of CCSS microgels reveals a fast initial decay on short time scales, similar to that of a swollen microgel, followed by a slow decay in longer times in analogy to that of a collapsed microgel. Looking at the 3613


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dynamics are not due to geometrical effects. Comparing the scaling results of the shell compartment of the CCSS microgel and the shell compartment of the (homogeneously) swollen microgel, we find only a small difference in the slopes of the two sets of curves, which might by due to a coupling of the core and shell dynamics. However, the results are not accurate enough for a definite statement. Yet, the analysis of the swollen core of SCCS microgels and the core compartment of bare swollen microgels shows a slower dynamics, which we attribute to the coupling of polymers in the core and shell compartments. Interestingly, each set of curves exhibits a reasonable good scaling behavior with a nearly exponential decay and an exponent of α = 3, which indicates the relevance of hydrodynamic interactions on the polymer dynamics. Additionally, the initial decay rate of S(q,t)/S(q,0) is determined for various q values by fitting the stretched exponential function S(q,t)/S(q,0) = exp[−(Γqt)β] to the simulation data. The obtained decay rates Γq for CCSS and SCCS microgels as well as bare swollen and collapsed microgels are displayed in Figure 13. At low q values, all decay rates exhibit approximately a q2 increase with increasing wavevector, which is attributed to a collective diffusion-like motion of the polymers inside the microgel network.20 For larger wavenumbers, Γq shows power-law-like regimes, with exponents between α = 3 and 4, depending on the extent of the microgel collapse. Swollen and CCSS microgels exhibit a dependence close to q3, which indicates that the polymer dynamics inside the swollen microgel is governed by HI interactions. In the SCCS microgels, the collapsed shell induces a certain shrinkage of the swollen core, such that the polymer scaling behavior does no longer correspond to good solvent conditions, but the critical exponent is somewhat smaller than 0.6. This is even more pronounced for the fully collapsed microgel. As shown in Figure 5, the scaling exponent in the relevant q-range is approximately ν = 0.53 in this case. Assuming additionally a (certain) screening of hydrodynamic interactions, which is certainly the case for the collapsed microgel, we expect to obtain the exponent α = 4, corresponding to the Rouse model,63 which explains the result of Figure 13. Regarding the exponent β, we find approximately β = 3/4 for swollen microgels and β ≈ 1/2 for collapsed gels. Hence, the decay of S(q,t) is strongly nonexponential. The polymer dynamics in the microgel network is further analyzed by calculating the polymer end-to-end vector Ree correlation function according to

Figure 9. Simulation results for the normalized intermediate scattering function of microgels in a good solvent. The results are plotted for 1.0 < ql < 2.0 and time the interval 10 < t / ma2 /kBT < 120 . The inset shows the mean-square displacement of monomers in the center-ofmass reference frame of the respective polymer.

intermediate scattering functions of core and shell compartments separately suggests that the dynamics of core and shell monomers is slightly slower than that of the bare collapsed and swollen microgels. However, this dynamical slowdown is more pronounced for SCCS microgel, as shown in Figure 11. The origin behind the slower dynamics of SCCS microgels compared to that of CCSS microgels can be explained by studying the individual contributions of core and shell compartments to the intermediate scattering function. As it is shown in Figure 11, the shell compartment of the SCCS microgel exhibits a much slower dynamics compared to that of the bare collapsed gel, in both the low and high q regime. This slow dynamics can be explained by the collective motion of individual clusters formed in the periphery of the core−shell particles (cf. Figure 3). The motion of these collapsed clusters is presumably governed by their interaction with the swollen polymers of the embedding core. In order to elucidate how the coupling between core and shell compartments affects their monomer dynamics, the universal scaling behavior is examined for core−shell microgels. Since the wavenumber and time interval of the scaling regime is very short for the collapsed parts, we only focus on the swollen compartments in both of the simulated core−shell microgels. The scaling curves for CCSS and SCCS microgels are presented in Figure 12 and are compared with those obtained from intermediate scattering functions of the equivalent shell and core compartment of a bare swollen microgel. The comparison helps to ensure that possible changes in the

Figure 10. Normalized intermediate scattering function S(q,t)/S(q,0) (green) as a function of time of CCSS microgels for the scattering vectors ql = 0.5, 1.0, and 1.5. The scattering profiles of bare swollen (black) and collapsed (red) microgels as well as contributions from core (blue) and shell (light blue) compartments are also included. 3614


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Figure 11. Normalized intermediate scattering function S(q,t)/S(q,0) (green) as a function of time of SCCS microgels for the scattering vectors ql = 0.5, 1.0, and 1.5. The scattering profiles of bare swollen (black) and collapsed (red) microgels as well as contributions from core (blue) and shell (light blue) compartments are also included.

Figure 12. Intermediate scattering functions as a function of the scaled time for the shell compartment of CCSS microgels (red), the corresponding shell compartment of a swollen microgel (black), the core compartment of SCCS microgels (green), and corresponding core compartment of a swollen microgel (blue). Results are presented

Figure 14. Semilogarithmic representation of end-to-end vector correlation functions of polymers in swollen, collapsed, and core− shell microgels. The correlation functions of the core−shell microgels for the respective core and shell are presented additionally. The effective relaxation time is calculated as τ = aΓ(1/b)/b, where a and b are obtained by fitting a stretched exponential function C(t) = exp[−(t/a)b] to the relaxation curves and the Γ(x) is the gamma function.67

for 1.0 < ql < 2.0 and the time interval 20 < t / ma2 /kBT < 100 . Note that the red and black curves are shifted vertically for better visibility.

Consistent with the intermediate scattering functions, the decay of C(t) in the shell compartment of CCSS microgels is slightly slower than that of the swollen microgel, and the slower relaxation of C(t) in the core compartment in SCCS microgels is even more noticeable (τswollen = 3235, τCCSS,shell = 4060, and τSCCS,core= 5803 (ml2/kBT)0.5). This significant slower dynamics of the polymers in the swollen compartment of the core−shell microgel compared to that of the bare swollen microgel is another confirmation that the coupling between the core and shell significantly affects the polymer dynamics of the swollen compartment in core−shell microgels. However, the end-toend vector relaxation of the polymers in the collapsed compartments in core−shell microgels is similar to that of the purely collapsed microgel. Hence, the dynamics of the individual polymers in the compact compartments of CCSS and SCCS microgels is similar to the bare collapsed microgels. This supports the idea that the slow decay of the intermediate scattering functions of polymers in the collapsed compartments of core−shell microgels stems from some sort of collective motion in these collapsed bundles. The synergic insights of neutron scattering and computer simulations in our study clearly demonstrates that the degree of swelling of one compartment affects not only the structure of the other compartment but also the dynamics.

Figure 13. Initial decay rates Γq of swollen, collapsed, and core−shell microgels obtained by fitting an stretched exponential function S(q,t)/ S(q,0) = exp[(Γqt)β] to the intermediate scattering functions in the time interval 0 < t / ma 2 /kBT < 300. Note that the data are shifted vertically for better visibility.

C(t ) =

⟨R ee(t ) ·R ee(0)⟩ ⟨R ee(0) ·R ee(0)⟩

(8)

Figure 14 shows end-to-end vector correlation functions averaged over all polymers in the core and shell compartments, respectively, of CCSS and SCCS microgels as well as that of purely swollen and collapsed microgels. Evidently, the correlation functions decay in a nonexponential manner. 3615


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(α ≈ 4), which we attribute to (partial) screening of hydrodynamic interactions and the (partial) shrinkage of polymers. Hence, for the collapsed microgel, the dynamics is more Rouse-like63 over the considered q range. In conclusion, the essential structural and dynamic microgel properties measured with neutron scattering experiments are confirmed and explained in detail by the simulation results. The long time behavior of the collapsed-core−swollen-shell microgel lies in-between the dynamics of the swollen and collapsed pure microgel. This is seen in experiment (Figure 6, left) as well as in the simulation (Figure 10, q = 1.5). On the other hand, the collapsed-shell−swollen-core particle shows in experiment and simulation the same long time behavior at large q, close to the response of the pure collapsed microgel. Hence, the experimental and simulation studies provide a consistent picture of the polymer dynamics in core−shell microgels. In addition, the simulation results yield insight into the dynamical coupling between the core and shell polymers. These findings are surely important not only for fundamental polymer physics but also regarding the potential application of these systems. As mentioned in the Introduction, microgels with nanoregions of different environmentally responsive polymers are regarded as promising carriers for encapsulated molecules. Furthermore, for collapsed-shell−swollen-core microgels, we find patches of collapsed polymers on the surface of the swollen core (cf. Figure 3). The extent of such patches can be controlled by the thickness of the shell and the degree of collapse. Thus, the synthesis of such core−shell microgels provides a route to create also patchy functional colloids.

4. SUMMARY AND CONCLUSIONS We have investigated the structural and dynamical properties of core−shell microgels by experimental and numerical approaches. Experimentally, we have performed SANS and NSE studies of PNIPAM-core−PDEAAM-shell (CCSS) and PDEAMM-core−PNIPAM-shell (SCCS) microgels. In simulations, we exploited a hybrid mesoscale hydrodynamics simulation approach, combining multiparticle collision dynamics simulations for the fluid with molecular dynamics simulations for microgels. Both experiments and simulations show that in CCSS microgels the core and shell compartments are clearly separated from each other with a minimum overlap. This is different for SCCS microgels, where in simulations polymers at the shell form stable but separated compact clusters which are floating above the swollen core of the microgel and core polymers can stretch out to the surface of the microgel. This stronger overlap between core and shell polymers is consistent with and explains the observed density profiles for SCCS microgels in SANS measurements. In simulations, the static structure factor shows a polymer scaling regime with S(q) ≈ q1/0.62 in the interval 0.8 < ql < 3.0 for the pure swollen microgel, where the lower bounds increase to ql ≈ 1.5 for the CCSS and SCCS core−shell microgels. The scattering profile for a bare collapsed microgel shows a ∼q−4 dependency at low q, reflecting its well-defined interface. The scaling analysis on the simulation results for intermediate scattering profiles shows that the internal polymer dynamics of the bare swollen microgel is mainly driven by hydrodynamics interactions. This Zimm-type scaling behavior is observed at short times (i.e., 20 < t / ma 2 /kBT < 100), where the mean-square displacement of the monomers in the center-of-mass reference frame of a polymer show a t2/3 dependency. At larger time intervals, the Zimm scaling breaks down due to the cross-links of the polymer network. The computed intermediate scattering functions for CCSS microgels show an initial fast decay similar to that of a swollen microgel, which is followed by a slow decay regime. This behavior is observed at low as well as high q values and is in agreement with experimental observations. However, the polymers in SCCS microgels show a different behavior, and the decay of the intermediate scattering functions is much slower than that of a bare collapsed microgel. Since this slow dynamics is not observed in the end-to-end vector correlation functions, a possible explanation for this slow decay could be the collective motion of collapsed clusters which form at the periphery of SCCS microgels. Our scaling analysis on the swollen compartments of the core−shell microgels reveals a Zimm-type behavior, but with a slower dynamics compared to the equivalent analysis of the pure swollen microgel. This is also confirmed by the end-to-end vector correlation function of the polymers belonging to the swollen compartments of core−shell microgels and clearly reflects the effect of the interplay between core and shell compartments on the overall polymer dynamics. The intermediate scattering functions can be best fitted by a stretched exponential function in the time interval 0 < t / ma 2 /kBT < 300. The decay rate Γq shows a collective diffusive-like motion of polymers, which is characterized by ∼q2 dependence, in the low q regime for all considered microgels. At larger q values, the decay rate exhibits a qα dependence, with α = 3, for swollen and CCSS microgels. The exponent α increases for SCCS (α ≈ 3.6) and a purely collapsed microgel

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph +49 (0)2461 61 4220 (R.G.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich (SFB 985) “Functional Microgels and Microgel Systems” is gratefully acknowledged. A.G. and R.G.W. gratefully acknowledge the computing time granted on the supercomputers JUROPA and JUQUEEN at Jülich Supercomputing Centre (JSC).

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REFERENCES

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