Modelling realistic microgels in an explicit solvent

Abstract

Thermoresponsive microgels are polymeric colloidal networks that can change their size in response to a temperature variation. This peculiar feature is driven by the nature of the solvent-polymer interactions, which triggers the so-called volume phase transition from a swollen to a collapsed state above a characteristic temperature. Recently, an advanced modelling protocol to assemble realistic, disordered microgels has been shown to reproduce experimental swelling behavior and form factors. In the original framework, the solvent was taken into account in an implicit way, condensing solvent-polymer interactions in an effective attraction between monomers. To go one step further, in this work we perform simulations of realistic microgels in an explicit solvent. We identify a suitable model which fully captures the main features of the implicit model and further provides information on the solvent uptake by the interior of the microgel network and on its role in the collapse kinetics. These results pave the way for addressing problems where solvent effects are dominant, such as the case of microgels at liquid-liquid interfaces.

Figure 1

Microgel swelling curves. Radius of gyration R_g across the VPT transition for (a) the implicit model, V_α; (b) the explicit LJ solvent with LJ monomer-solvent interactions at a solvent density ρ_s = 0.73; (c,d) explicit solvent with V_λ monomer-solvent interactions at ρ_s = 0.73 and ρ_s = 0.87, respectively; (e) DPD simulations where the microgel is modeled as a bead-spring polymer network. All curves report the gyration radius R_g as a function of the parameter controlling the solvophobic interactions in each model: (a) α, (b) ε_ms, (c,d) λ and (e) a_ms.

Figure 2

Effect of microgel topology and solvent arrangement. Swelling curves for the implicit- (full line) and explicit-solvent models that best reproduce the swelling behavior, namely MD simulations with V_λ at ρ = 0.87 (dashed lines) and DPD simulations (dotted lines) for (a) a loose microgel (Z = 25σ) and (b) a more compact microgel (Z = 15σ). Corresponding microgel snaphots are also shown. Symbols refer to state points in explicit solvent simulations (MD: circles, DPD: triangles) for which further analysis is provided in the next sections, whereas similar colors/shapes refer to similar swelling degrees between the two explicit solvent models. Panels (c.I-c.III) display a central slab of the simulation box for three different values of χ_eff, respectively corresponding to the swollen state (c.I), a state very close to the VPT (c.II) and the collapsed state (c.III). The arrangement of the solvent (blue spheres) within/around the polymer network (red spheres) depends on χ_eff. For the sake of visual clarity, only half of the solvent particles are shown.

Figure 3

Density profiles for a loose microgel configuration across the VPT. Monomer radial density profile ρ_m(r) for a Z = 25σ microgel as a function of the distance r from its center of mass. Full lines refer to the implicit-solvent model, while symbols are used for MD (circles) and DPD (triangles) simulations. Each sub-panel refers to a different swelling state as in Fig. 2(a).

Figure 4

Microgel form factors for a loose microgel across the VPT. P(q) as a function of qσ. Full lines refer to the implicit-solvent model, while symbols are used for MD (circles) and DPD (triangles). Each sub-panel refers to a different swelling state according to Fig. 2(a).

Figure 5

Solvent density profiles for a loose microgel configuration across the VPT. We show the solvent density profile ρ_s normalized by the bulk solvent density ρ_s,bulk, as a function of the distance r from the center of mass of the microgel. Circles and triangles refer to MD and DPD solvent, respectively. Each sub-panel refers to a different swelling state according to Fig. 2(a).

Figure 6

Microgel density profiles, solvent density profiles and form factors for a compact microgel across the VPT. (a–c) Microgel density profiles ρ_m as a function of the distance r from the center of mass of the microgel; (d–f) solvent density profiles ρ_s normalized with respect to the solvent bulk density ρ_s,bulk as a function of r; (g–i) microgel form factors as a function of the wavenumber. Data are reported for a swollen state (χ_eff = 0.1), a state close to the VPT (χ_eff = 0.6) and a compact state (χ_eff = 1.0). Full lines refer to the implicit solvent (V_α), while symbols are used for DPD (triangles) and MD (circles). The insets in panels g and h show an enlargement of the high wavevector region where solvent-monomer excluded volume interactions induce an excess of signal for the MD data.

Figure 7

Collapse kinetics. Radius of gyration R_g as a function of time for a loose microgel (Z = 25σ) for χ_eff = 1.1 (a.I) and 0.7 (a.II) for implicit (V_α, full line), DPD (dotted lines) and MD solvents (dashed lines); (b) cluster size distribution n(s) for R_g = 14.9 (indicated as III in a.I) for implicit and DPD solvents. In order to improve statistics data are averaged over six different microgels configurations. The inset reports the number of clusters (black circles) and their average size (red squares) as a function of the collapsing time; (c.I-III) simulation snapshots for state points I-III (circles in a.I). Clusters are highlighted by different colors according to their size N_c (as indicated in the color bar). Light grey monomers are either found in small clusters (N_c < 10) or belong to the main network (N_c > 100).