Pathways and challenges towards a complete characterization of microgels.

Structure and morphology of densely packed microgel-based materials The colloidal phase behavior of microgels, and charged and neutral soft spheres in general, has been the subject of many studies 95 , 106 – 108 . For a sufficiently monodisperse pNIPAM microgel suspension that is slowly cooled below T LCST , we expect crystallization at an effective volume fraction ζ ≳ 0.5. For a polydispersity greater than δ R H / R H ~ 0.1 or for a rapid quench, crystallization is suppressed or slowed down, leading to an amorphous solid phase 108 . In an experiment, it is not always obvious which phase has been obtained. Typically, for smaller microgels, the crystal phase shows iridescence 109 , whereas, for larger, micron-sized, microgels, small-angle light scattering (SALS) can detect the presence or absence of sharp Bragg peaks 110 . In both cases, the particles eventually touch and, upon reaching higher values of ζ > 0.7, have to adapt their morphology. A number of things can happen. Microgels can deform like elastic spheres 2 , 8 , 106 , they can interpenetrate, or they can shrink 28 , 111 . Usually, all three processes may proceed at the same time, such that the total free energy reaches a local or global minimum. Recent SRFM experiments have been instrumental in identifying the various responses of microgels upon packing 110 . These experiments also highlighted the enormous potential of SRFM techniques applied to microgels and soft matter in general since they illustrated how qualitatively new information about bulk polymeric systems can be obtained. In the study reported in ref. 110 , submicron-sized, highly swollen pNIPAM microgels were synthesized with ≈5% BIS cross-linker. Dense suspensions were prepared above T LCST and then quenched to 22 °C, well below the LCST. Effective volume fractions from ζ = 0.7 to ζ ≃ 3 were investigated. We may note in passing that overpacking ( ζ > 1) cannot be reached using incompressible soft colloids, for example oil droplets in a dense emulsion 112 . The dSTORM experiments revealed that the packing progresses in different stages. In Fig. 6 a, we reproduce typical two-color dSTORM images for several packing fractions. Initially, the fuzzy corona is compressed onto the core, resulting in rather homogeneous soft spheres at ζ = 1. Next, the particles deform, facet, and weakly interpenetrate, thereby reducing spatial density fluctuations. Eventually, no further interpenetration takes place, prevented by the network topology. Once this stage is reached, the spatial polymer distribution is nearly homogeneous on length scales larger than the network correlation length ξ , as confirmed by the vanishingly low light-scattering contrast 110 , and the microgels shrink when increasing the concentration further. Fig. 6 Densely packed suspensions of neutral microgels: deformation, interpenetration, and compression. a Two-color 2D dSTORM of dye-labeled microgels embedded in a matrix of unlabeled microgel particles, indicated by dashed circles in the left upper panel. ζ is the effective volume fraction. SRFM imaging of specifically labeled microgel pairs reveals partial interpenetration, faceting, and finally isotropic compression, leading to a decreasing global size. Contour lines are shown for ζ = 1.89 to illustrate the overlap area Δ F relative to the total area F of a particle for the image section shown. Image adapted from ref. 110 . b Interpenetration mechanism at the particle–particle interface suggested in ref. 25 based on the dSTORM data. c Evidence that the dissipative behavior, expressed by the excess dissipation documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$tan {delta }_{text{exc}}={G}^{^{primeprime} }/{G}^{prime}-{left({G}^{^{primeprime} }/{G}^{prime}right)}_{{mathrm{min}}}$$end{document} tan δ exc = G ″ / G ′ − G ″ / G ′ min at ω ≃ 1 rad/s, scales with the overlap area 0.4 × Δ F / F . The solid blue line is a guide to the eye, and the red dash-dotted line denotes documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$1/{G}^{prime}$$end{document} 1 / G ′ . These results suggest that information from nanoscale SRFM imaging can be directly used to model viscoelastic properties. Panels ( b ) and ( c ) were adapted from ref. 25 . The neutral microgels studied in refs. 25 , 110 are of the most common pNIPAM based type, with a radius of R H ≃ 500 nm and ≃5% BIS, and therefore the results are representative for many microgel studies carried out in the past. However, a plethora of other types of microgels have been discussed as well, and the characteristics can vary substantially. Differences can arise due to different polymer chemistry, size, cross-link density, and charges. We expect SRFM to play an essential role in disentangling the packing behavior of dense microgel suspensions for a number of microgel types and under different conditions. Potentially, SRFM can also be applied under out-of-equilibrium conditions, such as macroscopic shear deformation. Still, we need to keep in mind that it takes minutes 25 , rather than seconds, to record a single dSTORM image. Recently, progress in localization microscopy has been reported pointing toward second-scale image acquisition in biological applications, but the performance of these approaches has not yet been tested on soft materials 113 . A fascinating open question, concerning dense microgel suspensions, is the spontaneous deswelling by counterion clouds 114 . Earlier work by Fernandez-Nieves et al. showed that microgels deswell when subject to a high external osmotic pressure, by adding dextran to the solution 84 . Scotti et al. suggested that the counterions released by the microgels themselves could lead to a reduction in particle size with increasing microgel concentration. From this, they conclude that in bimodal or polydisperse mixtures, larger particles selectively shrink. As a consequence, uniform shrinkage may suppress or delay the liquid-to-solid transition and facilitate crystallization 115 . If and under which conditions such deswelling may occur is not entirely clear and has been debated 25 , 92 , 116 . SRFM and scattering techniques will play a pivotal role in settling this question.

Rheology of microgel-based materials Microgels possess remarkable properties, such as a very low mass density, porosity, softness, and responsiveness to external stimuli. The nano- and microscale properties of microgels are widely exploited in bulk formulations where microgels act as viscosity modifiers and lubricants 2 , 14 . Microgels have also become popular model systems in experimental studies of soft and adaptive colloids in highly concentrated and jammed suspensions 3 , 106 , 117 – 121 . The rheology of microgels is especially interesting because it is susceptible to the particle morphology, swelling, and particle–particle interactions. Mattsson et al. reported that some microgel systems can be overpacked up to ninefold ( ζ ≈ 9), and exhibit viscous flow properties over the entire range 122 , while other systems, like the one discussed in Fig. 6 , jam at ζ ≈ 0.6 like elastic spheres and form fairly strong solids for ζ > 1 25 , 62 , 109 , 110 with elastic moduli exceeding 10 3 Pa. Clearly, the microscopic properties of the microgels must be responsible for this fundamentally different macroscopic behavior. Ikeda et al. discussed the interplay between the entropically driven glass transition and the buildup of deformation energy due to contact formation 108 . Quite generally, the size, the softness, and the architecture of microgels play an important role 97 . However, in many previous studies, the microgels under investigation have not been characterized in much detail. Modern SRFM techniques provide an opening here to make progress toward a complete characterization of individual microgels, dense microgel-based systems, and consequently reach a better understanding of their rheological properties. In the following section, we present an example of such an attempt to use the microscopic knowledge obtained from SRFM for the interpretation of rheological data. Oscillatory shear experiments on neutral, submicron-sized pNIPAM microgels, some dating back to the 1990s 109 , have reported a sharp onset of the low-frequency ( ω ~ 1 rad/s) elastic modulus documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${G}^{prime}$$end{document} G ′ at random close packing or “jamming,” followed by a more gradual linear increase for ζ > 1 25 , 107 . Some experiments suggest a critical behavior at ζ c ~ ζ J ~ 0.6, characteristic of a jamming transition 62 , 104 , 107 , 109 . To account for the increase in the elastic modulus documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${G}^{prime}left(zeta right)$$end{document} G ′ ζ , different elaborate models have been proposed 62 , 63 , 91 , 104 , 107 – 108 . A quantitative assessment of the microscopic packing behavior, a key ingredient for all modeling attempts, has been missing however. In particular, it was unknown to which extent microgel particles facet or interpenetrate, and if and when they may spontaneously shrink. We recently established such a relationship between the nanoscale structure and the rheological properties, using two-color dSTORM microscopy 25 . The packing evolution, shown in Fig. 6 a, suggests that for ζ < 1, pairwise interactions are dominated by the compression of the microgel corona. For ζ > 1, we observe the faceting and subtle interpenetration of fairly homogeneous soft spheres followed by the shrinkage or isotropic compression of the individual microgels. In tandem, for ζ > 1, the low-frequency elastic shear modulus documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${G}^{prime}$$end{document} G ′ increases linearly with ζ . From this, we conclude that for ζ > 1, the elastic modulus is set by the jamming and compression of homogeneous microgel spheres. At lower concentrations, the corona compression dominates that of the pairwise interactions between microgels, and therefore documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${G}^{prime}(zeta )$$end{document} G ′ ( ζ ) rises much more rapidly once particles are touching, for ζ ≳ 0.6. Similar results for documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${G}^{prime}(zeta )$$end{document} G ′ ( ζ ) have been reported recently by Pellet and Cloitre 107 . We also looked at losses under oscillatory shear. For weak corona compression ζ < 1, the loss modulus G ″ ( ω ) matches the trend expected for other soft spheres with lubrified interfaces, such as emulsion droplets. At higher densities however, the contribution of viscous losses increases substantially. The latter can be quantified by the ratio of the loss modulus and the storage modulus at low frequencies, documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$tan delta ={G}^{^{primeprime} }/{G}^{prime}$$end{document} tan δ = G ″ / G ′ . Interestingly, we find that the degree of overlap between adjacent microgels measured by dSTORM, Δ F / F , is directly proportional to the excess dissipation, as shown in Fig. 6 c.