Dilute and Concentrated Microgel Suspensions 




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While in the absence of dextrans, g1(t) is characterized by a single exponential decay, at higher dextran concentrations, g1(t) is characterized by two decays. In order to estimate the relaxation frequency associated to the microgel diffusion, we fit g1(t) to a triple exponential form:


 \( g_1(t)=A'_{slow}e^{-\Gamma_{slow}t}+A'_{fast}e^{- \Gamma_{fast}t}+A_{mgel}e^{- \Gamma_{mgel}t}\)




where the first two modes correspond to the dextran solution, and the third mode corresponds to the microgel suspension. In the fit, we fix the relaxation frequencies of the dextran at a given concentration, while leaving the amplitudes and the relaxation frequency of the microgel suspensions as free parameters. Our model correctly describes the experimental result, as shown in Figure 3b. From the fitted mgel, we calculate the diffusion coefficient and thus the particle radius.


 a) Dynamic structure factor obtained in cross-correlation for a highly dense microgel suspension (25.8% by weight); b) Blow-up of the initial decay.

Figure 4. a) Dynamic structure factor obtained in cross-correlation for a highly dense microgel suspension (25.8% by weight); b) Blow-up of the initial decay.

By determining a as a function of osmotic pressure, which corresponds to certain dextran concentration, we can estimate the particle bulk modulus [19]. We emphasize that this is only done in situation where Amgel >> A’slow, where we are certain that the slow decay is essentially dominated by the diffusion of the microgel particle. Using these microgels, we have recently started to explore the suspension dynamics at extremely high packings, which we can achieve due the ultrasoft character of these particles. In these experiments, we use cross-correlation in order to extract simple scattering from these multiply scattering samples. Interestingly, we find that despite the very high concentration used, these suspensions still are able to relax, as confirmed by the final relaxation of g1(t) shown in Figure 4a, which corresponds to a system at a concentration of 25.8% by weight. A closer look to the initial stages shows that there is also a faster relaxation, as shown in Figure 4b. By combining single-particle and suspension measurements, we hope to increase our current understanding of the behavior of dense microgel suspensions. In this case, it suffices to perform autocorrelation experiments, as there is also negligible multiple scattering; this, however, restricts the lowest accessible time scales to those above the times associated to detector afterpulsing. The influence of the dextrans to the field correlation function of the microgel suspension is evident.




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