Normalization of Compression Isotherms to the Size of Microgels

It was described in chapter 6 that the compression isotherms of different amounts of microgels at the interface overlap after normalization of the area to the mass of microgels that was placed at the interface. However, the size of the core (KG09) and the core-shell (KG15) microgels in bulk varies with the pH. The compression isotherms from Figure 21 and Figure 24 can thus be normalized to the microgel size at the interface which is independent from the pH.^[9] First, the area was normalized to the particle size by calculating the area per particle and the area covered by one microgel.

In a similar way, the area fraction φ covered by microgels can be calculated.

( 24 )

( 25 )

LANGMUIR TROUGH EXPERIMENTS

The area per particle is calculated from the area measured in the compression isotherm and the number of microgels at the interface (#particles). The number of particles at the interface was calculated from a formula proposed by Destribats et al..^[10] It was slightly modified by assuming that a microgel contains 50 wt% of bound water at 50°C.^[11] From the polymer content of the dispersion (c_polymer), the hydrodynamic diameter of the microgel in the collapsed state (d_50°C) and the density of polymer (ρpolymer) and water (ρwater ) the number of particles per milliliter (cparticles) can be calculated. The number of particles at the interface then depends on the volume of applied microgel dispersion.

( 26 )

The core microgels as well as the core-shell microgel show a core-corona structure at the interface (compare chapter 5) that has to be considered for the normalization of the isotherms to the microgel size.^[9] It is assumed that it is possible for the coronas to interpenetrate during compression, meaning that the size changes. For this reason, the particle size d_i,c of the core at the interface was used to normalize the isotherms to the particle size as the core size is assumed to be relatively constant. The microgel size was extracted from FreSCa cryo-SEM images (chapter 5).

Table 9. Parameters for the calculation of the number of particles placed at the interface in the Langmuir trough following equation (26). d50°C is the diameter of the microgel in the completely collapsed state. ρpolymer was calculated from the density of a microgel dispersion of 1 wt% and the density of water (ρH2O = 0.998 g/mL).

KG09 KG15

pH 3 pH 9 pH 3 pH 9

cparticles [mL^-1] 1.1175·10¹³ 1.0627·10¹³ 4.2015·10¹² 4.0808·10¹²

Mw [g/mol] 4.45·10⁸ 4.49·10⁸ 1.21·10⁹ 1.22·10⁹

di,c [nm] 358 352 436 438

cpolymer [mg/mL] 8.26 7.93 8.47 8.25

d50°C [nm] 138 193

ρpolymer [g/mL] 1.1632 1.1876 1.1558 1.1629

After normalization, the isotherms of both microgels in the uncharged state superimpose and collapse down to one master curve (Figure 72). This shows that they indeed show the same behavior under compression and that the trend of the isotherm does not depend on the microgel morphology or the size of the particle, as it was in detail discussed in chapter 6.^[12] The effect of charges is clearly visible in this plot because the isotherm of the charged core is situated at smaller areas compared to the uncharged one. The charged core-shell microgel is situated between the completely charged core and the uncharged one. This leads to the conclusion that the charges in the core of the core-shell microgel are not completely shielded from the outside and still influence the behavior under

LANGMUIR TROUGH EXPERIMENTS

compression. The charge effect is less pronounced than in the case of the core microgel where the charges are completely exposed.

The changing particle density during compression can be expressed with the area fraction φ. In chapter 7 it was shown that the transition from random to hexagonal packing during compression takes place before the first plateau is formed. The first rise in the compression isotherms takes place at area fractions between 0.5 and 1 (Figure 72b). That roughly corresponds to the values of φ for which development of local hexagonal order starts to emerge, as seen from the data in Figure 35 that was extracted from AFM images.

This correlation confirms that the increase in the surface pressure happens when the microgels start interacting at the interface and form a hexagonal array. Furthermore, the normalized compression isotherms show that the microgels indeed change their size during compression as area fractions above 1 represent compression of the microgels.

0,1 1 10 charged and the uncharged state. a) normalized to the area of one microgel; b) normalized to the covered area fraction. The inset in b) shows the isotherms on a logarithmic scale.

Additionally, all microgels reach the same surface pressure of approximately 35 mN/m at high compression. The measurement of the interfacial tension (IFT) of a 1 wt% microgel dispersion and n-decane gave quasi-equilibrium IFT values around 18.5 mN/m for both core and core-shell microgel in the charged and uncharged state (Table 10). This corresponds to a surface pressure of π = 34.7 mN/m (with π = γ0 – γi and γ0 = IFT n-decane/water = 53.2 mN/m^[1]) and represents the onset of the second plateau of the compression isotherms. It can thus be assumed that the arrangement of microgel particles at the interface of a pendant drop in quasi-equilibrium is similar to the one of a microgel layer at high compression. This implies that the microgels adosorb to the interface of the pendant drop in the compressed state.

LANGMUIR TROUGH EXPERIMENTS

Table 10. Interfacial tension of 1 wt% aqueous microgel dispersions of the core and the core-shell microgel at pH 3 and pH 9 versus n-decane after 60 s and after 8000 s in quasi-equilibrium.

1 wt% aq. dispersion versus n-decane after 60 s after 8000 s

core microgel uncharged (pH 3) 20.0 18.7

charged (pH 9) 23.8 19.2

core-shell microgel

uncharged (pH 3) 19.7 18.0

charged (pH 9) 21.2 18.2

Despite the conclusive results presented above, one has to keep in mind that the normalization is based on several parameters that are potentially inaccurate. First, the particle number was calculated from the concentration of the microgel dispersion instead of using the molecular weight determined with static light scattering. However, static light scattering also gives a value for the molecular weight that contains a significant error. Second, the assumption that the core size of the microgels at the interface does not change during compression may be inaccurate, but still serves the purposes in this chapter. Thus, the data presented in Figure 72 may contain an error in the normalized area that cannot be estimated correctly.