Star-like microgels vs star polymers: similarities and differences

TL;DR

This study demonstrates that star-like PNIPAM-EGDMA microgels behave as ultrasoft particles with Gaussian two-body potentials similar to star polymers, particularly when the core is only partially covered. Using monomer-resolved simulations and umbrella sampling, the authors show that star-like microgels reproduce the effective potential form of partially covered stars, and that their softness (as reflected in the bulk modulus) and the ratio $R_g/R_H$ across the VPT closely match star-polymer behavior. Experimental SLS/DLS measurements of $R_g$ and $R_H$ across temperature corroborate the simulations, validating star-like microgels as accurate, tunable soft-model colloids. The work establishes star-like microgels as a practical proxy for studying softness-controlled phenomena in dense suspensions, with potential implications for phase behavior and rheology in colloidal materials. All findings are connected through careful consideration of the variable choice (CORE vs COM) in defining effective interactions, and the results are reinforced by cross-method comparisons (surface mesh vs convex hull) for volume- and modulus-estimation.

Abstract

Star-like microgels have recently emerged as a promising class of thermoresponsive soft colloids, that have an internal architecture similar to that of star polymers. Here, we perform extensive monomer-resolved simulations to theoretically establish this analogy. First, we characterize the effective potential between star-like microgels, finding that it is Gaussian for an extended range of distances, in stark contrast to the Hertzian-like one of standard microgels, but almost identical to that of star polymers with a core partially covered by chains. Next, we investigate the ratio between gyration and hydrodynamic radii across the volume-phase transition, showing qualitative agreement with both star polymers and experimental data. Finally, we estimate the bulk modulus, finding star-like microgels significantly softer than standard microgels and comparable to star polymers. The present work thus demonstrates that star-like microgels behave as ultrasoft particles, akin to star polymers, paving the way for their exploration at high concentrations.

Figures (19)

• Figure 1: Effective potential $\beta V_{eff}$ between star polymers with (a) $f=18, N_f=50$ and (b) $f=80, N_f=200$ versus both core-core distance $r_{core}$ (full symbols) and COM-COM distances $r_{COM}$ (open symbols). Lines are guides to the eye. The snapshots illustrate a typical equilibrium configuration of the two systems. For the large star with $N_f=200$, the core is hardly visible.
• Figure 2: (a): effective potential $V_{eff}$ between star polymers with $f = 50$, $N_f = 50$ and $f = 80$, $N_f = 200$ with $r_{core}$ as the natural variable. The diameter of the first corona of monomers near the core, $2R_d$, is subtracted in order to read the divergence in the origin. The two continuous lines represent the Likos potential fit with a Yukawa tail, as in Eq. \ref{['eq:likos']}. The theoretical prefactor $5/18$ is treated as a parameter, reported as $a_0$ in Table \ref{['tab:fit_Likos']}, in order to test the adherence to the $f \to \infty$ limit. The inset additionally shows a fit with a Gaussian tail for $f=80$. (b): effective potential $V_{eff}$ between the same star polymers with $r_{COM}$ as the natural variable, normalized by $R_g$. The dashed lines are Gaussian fits with parameters reported in Table \ref{['tab:fit_gauss']}.
• Figure 3: Left panel: effective potential $V_{eff}$ between star-like microgels and standard microgels at a crosslinker concentration $c = 1\%$. Hertzian fits are shown for both systems; the tail is highlighted in the log-scale inset. Right panel: the same potentials are shown on a Gaussian scale, where Gaussian profiles appear as straight lines. The Gaussian fit for the star-like microgel is shown as a dashed line. Fit parameters are reported in Tab.\ref{['tab:fit_mgels']}.
• Figure 4: (a) Effective potential $\beta V_{eff}$ between $c=1\%$ star-like microgel, between star polymers with $f=80$, $N_f=200$, $R_c = 2.2\, \sigma$ and between partially covered stars with $f=46$,$N_f=200$, $R_c = 2.2 \, \sigma$, as a function of $r_{COM}$ rescaled by the respective gyration radii. The inset enlarges the short distance behavior; (b) Snapshots between two of each macromolecus at a distance $r_{COM}/R_g \sim 0.6$ to visually explain the differences observed in the effective potentials. The top row shows the full macromolecules, while the bottom one reports the corresponding slices. Note that the cores of the stars as well as the crosslinkers of the star-like microgels have a different color.
• Figure 5: (a) Density profiles $\rho(r_{COM})$ and (b) form factors $P(q)$ for the star polymer with $f = 80$, $N_f = 200$, for the star-like microgel with $c = 1 \%$, and for the partially covered star with $f = 46$, $N_f = 200$. Data in panel (a) are normalized to yield a volume integral equal to 1, while in (b) they are only scaled by the respective gyration radii. The inset shows a zoom-in of the peak profiles.