# From Femtoseconds to Hours--Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays
## 4 Studies
### Towards Microsecond Real-Time XPCS at Storage-Ring Sources
#### 4.1.4 Phase Behaviour of Soft Colloids  
Despite their simple interaction, colloidal hard spheres show different phases depending on their volume fraction and size dispersity [127], covering liquid, crystal and glass. Soft colloids show an even more complex phase diagram [128; 129; 130], including, e.g., different crystalline phases as well as glasses and gels. The most frequently studied soft colloidal system is micro- or nanogels of poly(N-isopropylacrylamide) (PNIPAm) particles dispersed in water [131; 132]. These particles show a reversible volume transition at a lower critical solution temperature (LCST) around 306 K. Below the LCST, the particles are swollen with water, while they become hydrophobic above and reduce their volume. Different from hard spheres, these microgels can reach overpacked states, i.e., volume fractions well above the packing limit of spheres of 0.74.  
Several XPCS studies have recently studied the phase behaviour of PNIPAm-based colloidal suspension. [PERSON] et al. [133] used a core-shell systems of a silica core and PNIPAm shell. In a densely-packed system, the relaxation rate showed an anomalous \(q^{-3}\)-behaviour together with a compressed \(g_{2}\) function below the LCST that might be connected to the chain-dynamics of the polymer. Above the LCST, the dynamics slowed down by several orders of magnitude, and changed to a \(q^{-1}\)-dependence and \(\gamma>1.5\), indicating the formation of colloidal gel. This was later extended to effective volume fractions between about 0.01 and overpacked states above 1, revealing the temperature and concentration-dependence of the gelation via the structure and dynamics of the dispersion [134]. Furthermore, the influence of the co-solvent trimethylamine N-oxide (TMAO) on the gelation temperature has been investigated [135]. A reduction of the gelation temperature with increasing TMAO concentration was found, indicating a reduction of PNIPAm-water hydrogen bonds. This results in a stabilisation of the collapsed PNIPAm state and suppresses gelation of the nanogel dispersion.  
[PERSON] et al. performed combined DLS and XPCS studies on interpenetrating networks of PNIPAm and poly(acrylic acid) (PAAc) [136; 137]. By tuning the ratio of both constituents, a different particle softness was achieved and thus the system's fragility [138]. The experiment was focused on two temperatures below and above the LCST, studying the dynamics as function of volume fraction. In this way more than nine orders of magnitude in time were covered from us to more than 1000 s, see Figure 8a. At a critical volume fraction the behaviour of the relaxation time changes from a super-Arrhenius to a slower than Arrhenius behavior. At the same volume fraction, a minimum for the KWW exponent was found that coincides with a maximum of the exponent \(n\) reflecting the \(q\)-dependence of the relaxation time (see Figure 8). A similar behaviour was observed for other soft systems using light scattering, the origin of this behaviour is currently under discussion [139].