Gelation of PNIPAM colloids with TMAO as co-solvent

An interesting behaviour can be seen by examination of sample 3 (κ= 4×). Taking a look at the diffusion coefficient D₀ as for the previous samples, one can recognize, that for low TMAO concentrations the suspension actually seems to accelerate, as indicated by D₀ values above those of 0M TMAO (red line in figure 4.12). At the highest temperature of 42^◦C the suspension apparently slows down as higher amounts of TMAO are realized, as visualized by the D0 below the red line for that temperature. For the highest TMAO concentration of 2.0M the coefficient rises up again, however shows a strong hysteresis between measurements at increasing and decreasing temperatures.

Figure 4.12: Development of the diffusion coefficient D0 with temperature and TMAO con-centration at Φ_eff,20 = 0.27.

Concerning the g₂ functions, it is visible that the q-dependence in figure 4.1(b) is altered for higher temperatures, while it is preserved for figure 4.1(a). Figure 4.13(a) displays the g₂ functions at 20^◦C showing shorter relaxation times with increasing wave vector transfer q, while in 4.13(b) the intensity auto-correlation functions at 30^◦C, are shown to be bundled together instead. This expresses that relaxation times are very similar for all q values at higher temperatures. Moreover, one can notice that the fits of the functions do not perfectly match the data in this example, because the slope is less steep and stretched in time. This observation can be attributed to a diminishing Kohlrausch- or stretching exponent γ, which

(a) (b)

Figure 4.13: Intensity auto-correlation functions for Φ_eff,20 = 0.27 with 1.0M TMAO at (a) 20^◦C and (b) 30^◦C.

is responsible for a stretched (γ < 1) or compressed (γ > 1) exponential (see. Eq. 3.3). As

Figure 4.14: Kohlrausch exponent γ for Φ_eff,20 = 0.27 with 1.0M TMAO. Here the LCST is presented by a vertical red line.

can be examined from figure 4.14, at a temperature which coincides with the LCST of the observed mixture (see Fig. 4.8), the Kohlrausch exponent clearly differs from that of diffusive systems (γ = 1) and is located between 0.6 and 0.85 depending on the scattering angle and temperature. There are numerous possible explanations for this perception, which are all based on the same main idea that structures of different sizes are present in the suspension at the same time. Smaller compounds move quicker than larger ones, which leads to various outputs for g₂(q, τ) with smaller or greater relaxation times τ, depending on the size of the

24 Dynamical Properties

structures. The experiment then averages these functions into one stretched exponential, lowering the γ coefficient (Fig. 4.15). Here, the blue line represents larger and slower

com-Figure 4.15: Representation of g₂ functions during the coexistence of differently sized struc-tures in the solution.

plexes, while the red line portrays smaller, faster structures. The average of the g₂ functions will then lead to a stretched exponential (black) with γ <1.

One possible interpretation displays that some particles are already in the globule state, which is expected beyond the LCST, while other particles still remain in the expanded form-ation. This would obviously lead to differently sized structures in the solution, i.e. individual particles of distinct volumes.

Further, agglomerations of particles, which dominate in the investigated regime of small q values under high densities, might be perceived as larger and therefore slow particles by the photon detector, since the particles are capable of interpenetrating one another. The result is the aforementioned stretched appearance of the intensity auto-correlation function.

There is another possible origin based on previous observations also made in colloidal sus-pensions, which state that for higher packing fractions spatial structural orderings emerge due to dynamic heterogeneity. This means that fast (slow) moving particles cluster together in space with equally fast (slow) moving ones to form domains of different dynamics (Fig.

4.16). This is a typical behaviour for super-cooled liquids and glass formers. The red col-oured grains are displaced by more than their own diameter, while the dark blue colour signifies no movement of the particle at all. Intermediate colours correspond to intermediate displacements (Garrahan, 2011). The figure therefore very well illustrates the formation of

Figure 4.16: Simulation of the equilibrium dynamics of 10,000 particles of a super-cooled fluid mixture over a time comparatively short to the systems relaxation time (Garrahan, 2011).

domains of mobile and immobile particles, respectively. If these domains are detected in the experiment, then the resulting g₂ function would also look like what is suggested in figure 4.15.

The change of g₂(q, τ) thereby leads to equation 3.4 not being valid anymore, since a non-diffusive behaviour of the particles occurs. This can be portrayed by plotting the fit of Γ to q², which should give a linear relation for diffusion (Fig. 4.17), but instead displays a curved line for temperatures above 24^◦C, which is around the LCST for the given sample. This

Figure 4.17: Fit for Γ(q) at Φ_eff,20= 0.27 with 1.0M TMAO between 20^◦C and 30^◦C.

26 Dynamical Properties

indication of non-diffusion points towards the formation of a colloidal gel, which is known to happen for PNIPAm samples at sufficiently high volume fractions once a gelation temperature T_gel is reached. To further investigate this hypothesis, a measurement on the sample with volume fraction Φ_eff,20 = 0.27 and 1.0M TMAO was performed in the 3D DLS mode, to avoid multiple scattering effects, at the cost of a reduced speckle contrast β by a factor of 4 to 5. Here, temperature steps of 0.1^◦C have been used, while each measurement took a time of 100 seconds. Also the temperature range was scaled down to the region around the LCST between 20^◦C to 27^◦C. Interestingly, the contrast of the g₂ functions decreases when

Figure 4.18: Temperature evolution of g₂(q, τ) for Φ = 2x at 1.0M TMAO and q = 20.10 µm⁻¹ around the LCST.

approaching the LCST, until it vanishes completely above this critical temperature (Fig.

4.18). No observable contrast at all, i.e. β = 0, means that the dynamics of the system are either too slow or too fast to be observed in the experiment. However, in this sample system, the dynamics cannot suddenly become too fast, which means they must be very slow. Then, the 3D DLS mode prints out a static signal and the cross-correlation becomes zero, indicating a gelation process. Possibly, an even longer measurement time is necessary to observe the relaxation process of this sample. To verify this discovery, the speckle contrast β has been set up against the time of the measurement and been compared to the change in scattering intensity during the measurement. The LCST is reached after a time of approximately 110 minutes, which is portrayed by the red vertical line. As figure 4.19(a) demonstrates, the

(a) (b)

Figure 4.19: (a) Speckle contrast β and (b) Scattering intensity I(q) normalized to the laser intensity for Φ_eff,20 = 0.27 with 1.0M TMAO and q= 20.10 µm⁻¹ between 20^◦C and 27^◦C.

speckle contrast decreases with the time of the measurement, especially once the LCST is reached, signifying a strong slow down in dynamics. This is confirmed by the scattering intensity falling towards zero for increasing temperatures in exactly the same manner. The shown graph in figure 4.19(b) gives information about the ratio of the photons received by the detector to the power used by the laser. A reduction of this normalized intensity happens when the sample turns opaque, as more laser power is needed for the same amount of photons to penetrate the sample and scatter towards the detector, which is typical for a PNIPAm gel. Thus, to observe the slow dynamics at larger timescales, dynamic light scattering is not sufficient enough, as it is limited to the range of small scattering wave vectors and by its strong deficiency upon the occurrence of multiple scattering. For these investigations short-wavelength beams like X-rays are necessary to detect such prolonged dynamic behaviour as the one found for sample 3. Therefore, X-Ray Photon Correlation Spectroscopy (XPCS) might provide valuable insights in this field of research.

Summarizing, due to curious changes to the diffusion and the intensity auto-correlation function, a reduced Kohlrausch exponent was found for the densest volume fraction of Φ_eff,20= 0.27. It was shown how smaller values for γ influence g₂(q, τ) to become a stretched exponential, through the existence of different particle sizes, agglomerations or various dy-namic domains, which are common indicators for the transition into a colloidal gel phase.

28 Dynamical Properties

Furthermore, it was discovered that for this case the relaxation rate Γ is not related to the diffusion coefficient D₀ for the dense sample, due to multiple scattering effects. Here, the 3D DLS mode was applied in order to extract the single scattering information. Thereby, a rapid decrease of speckle contrast β beyond the LCST indicates very slow dynamics in com-parison to the samples with lower effective volume fractions. Additionally, the normalized scattering intensity decreased during the time of the measurement, which shows that more laser power is needed to traverse the sample, because the dispersion becomes opaque. Such opacity moreover is typical for a PNIPAm gel phase and leads to the conclusion of such a transition. To analyse this in a deeper and more accurate way, one would have to apply scattering techniques, which are less affected by multiple scattering such as XPCS.

Chapter 5