Dependence of the relative viscosity η r = η/η o on polymer concentration c at pH7 (circles) and pH8 (squares). The solid line is a fit to the Einstein-Batchelor relation: η r = 1 + 2.5(k·c) + B(k·c)2 giving k = (2.2 ± 0.2) × 102 and B = 4 ± 2. Dashed line is a fit to the Einstein equation. The inset shows the fluorescent particles deposited on a glass slide.
Number of ionized groups per particle q as function of pH, obtained from titration of three solutions at polymer concentrations c= 0.19% (diamonds), 0.56% (squares), 0.9% (triangles). The solid line is a fit to the equation and gives Q = 6.7 × 106 and pK a = 5. The inset shows the product of the total number of ions per unit volume and particle mass as function of polymer concentration c for samples at pH ≃ 7; the slope of the linear fit is Q = 7.8 × 106.
MSD curves for different wavevectors q(1/μm). q = 9 (squares), 13.2 (circles), 17 (triangles), 20.2 (reverse triangles), 22.9 (diamonds) as a function of lag-time τ for a sample at ζ ≃ 1.2. In the inset, the time average correlation function of the electric field is reported as function of lag-time. Symbols are the same of the main plot.
Scattered intensity (arbitrary units) as function of wavevector q for samples at volume fractions ζ = 0.15 (open circles) and ζ = 3.1 (solid circles). Solid line is the fitting of data-points of the dilute sample to the form factors of polydisperse inhomogeneous spheres (Eq. (9)) giving a radius R = 0.65 μm. Dashed line is the form factor of monodisperse inhomogeneous spheres of radius R = 0.48 μm.
Left: 2D superposition of 25 slices vertically separated by 0.3 μm obtained from a solution of microgels at c = 0.6% (ζ = 1.35). Right: Contours of the only particles measured by the software after image processing.
Prediction of the dependence of the swelling ratio α, normalized to its value at infinite dilution α∞, on the generalized volume fraction ζ, as obtained from Eq. (11) (dashed line), and from Eq. (17) (solid line).
Dependence of the microgel radius on generalized volume fraction. The radius measured from confocal images R conf is reported on the left axis for samples at pH7 (circles) and pH8 (stars). The radius measured from static light scattering R SLS (crosses) is reported on the right axis for samples at pH7. Vertical axes are scaled to collapse R conf and R SLS in dilute samples on the same horizontal line (dashed line). Solid line is a plot of the equation R∝ζ−1/3.
Left: Dependence of the MSD on lag-delay time τ for particle volume fractions ζ = 0.02 (squares); 0.5 (circles); 1.22 (triangles); 1.96 (diamonds); 2.77 (stars). Open symbols are from DLS and solid symbols from CM. The images on the right represent particle trajectories at ζ = 0.02 (top) and ζ = 1.96 (bottom) of duration 26 and 500 s respectively.
Left: displacement distributions for samples at ζ = 0.02 (top) and ζ = 1.96 (bottom). Lines are Gaussian fits to the data. For each sample, solid and empty symbols are for shorter and longer τ values respectively. Right: Non-Gaussian parameter α2 for samples at different ζ as function of lag-time. Symbols are the same as in Figure 8.
Structural relaxation time τ r for microgel solutions at pH7 (circles) and pH8 (diamonds) and relative zero-shear viscosity (squares) as function of ζ. Solid line is a fit of the data in the supercooled state (ζ > 1.1) to the VFT equation with A = 22.32 and ζ g = 6.87. The inset shows a log-log plot of ln (τ r ) as function of the normalized volume fraction ζ/ζ g . Solid line is the same as in the main figure and the dashed line describes the divergence of hard spheres according to with C = 0.0098 and ϕ g = 0.64 (Ref. 35).
Physical and chemical properties of the partially ionic microgel particles: polymer volume fraction in a particle φ0 at preparation conditions; Flory interaction parameter χ at 20 °C; particle volume at preparation conditions v 0; particle volume in the swollen state v; swelling ratio at infinite dilution α∞; particle polymer mass m p ; polymer charge Q per particle; effective number of chains N c ; counterion screening length ; Γ is the fraction of counterions that leave the microgel particle at infinite dilution.
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