M ETHODS

Several methods were used in this thesis to characterize the particles (shape, size, size distribution, and microstructure), the assemblies (symmetry, and density), and the thermal properties (specific heat capacity, and thermal diffusivity). The most frequently used techniques are summarized in Figure 3.13.

Figure 3.13. Overview of the most frequently used characterization methods in this work.

In the following, the different methods will be introduced shortly. For more detailed information, the cited literature is recommended.

3.2.1 Particle Characterization

The particles were characterized by scanning and transmission electron microscopy (SEM, TEM), small-angle X-ray scattering (SAXS), and nitrogen sorption measurements.

SEM¹⁰⁶ is a type of electron microscope which creates images of a sample by scanning the surface with a focused electron beam. By the interaction of the electrons with the sample, various scattering events occur, which give information about the surface topography and the composition. In this work, the SEM was used as a tool to analyze the shape, size, and size distribution of the polystyrene particles and the polystyrene-silica core-shell particles. For the imaging of the hollow silica spheres, the TEM^107-108, another type of electron microscope, was used. It produces images of a sample by an electron beam transmitting the specimen. The interaction of the electrons within the sample creates an image. Due to the transmission of the electrons, information about the size and the shell thickness of silica hollow spheres are received. The shell thickness is given by the dark shaded ring surrounding the hollow core (Figure 3.13). Furthermore, the porosity of the shell is imaged. However, at large shell thicknesses, the contrast between the inner core and the silica shell becomes too weak. In that case, the SAXS¹⁰⁹ technique is the preferred method to determine the shell thickness. Small-angle X-ray scattering clarifies the structure of particles in terms of averaged particle sizes or shapes.

Thereby, a sample is illuminated by X-rays, and the scattered intensity is measured by a detector as a function of the scattering angle. The measurements are typically made at very small angles (~0.1 – 5°). Thus, with decreasing scattering angle, increasingly larger structural features on the length scale of nanometers (~1 – 100 nm) can be resolved. This clearly covers the range of the silica shell thicknesses of the hollow spheres. For finer geometric information about the microporosity of the shell and the overall surface area, Nitrogen sorption

measurements^110-111 were performed. The isotherms were recorded at 77 K between 0 and 100 kPa which corresponds to the full range of p/p0 (p0 is the saturation pressure). During the measurement, nitrogen is passed over the sample at 77 K, and the adsorbed quantity is determined (adsorption). Subsequent pressure reduction within the apparatus releases some of the nitrogen molecules from the surface. The result is an adsorption-desorption isotherm. In a certain pressure range (p/p0 = 0.05 – 0.3), the quantity of the adsorbed or released gas is proportional to the surface, the so-called BET surface area. The pore volumes and the pore sizes are usually determined by the non-local density functional theory (NLDFT) based on statistical methods.¹¹⁰

3.2.2 Assembly Characterization

The colloidal assemblies were characterized by scanning electron microscopy (SEM), optical microscopy, and density measurements.

SEM¹⁰⁶ is briefly described in the section before. It was used for the particle and the assembly characterization. However, for the latter one, the colloidal arrays were mounted in a particular specimen holder to enable the imaging of the side-view images. Hence, the packing symmetry could be determined. However, for an extensive impression of the symmetry, the use of the optical microscopy¹¹² is useful. Thereby, the sample is placed under the bright-field optical microscope to obtain side-view images of the colloidal assembly. For a close-packing of particles in the size range of the light, distinct Bragg reflections are detected.

Whereas for random close-packed structures, only a diffusive scattering is observed.

Moreover, the densities of the colloidal assemblies were determined. This is of peculiar interest for the thermal transport properties, because of the necessity to know this parameter to calculate the thermal conductivity (Chapter 3.2.3). The density was most frequently resolved by measuring the weight and the volume of the colloidal assembly. For the volume determination, a 3D non-contact surface profiler was used. It captures the volume by scanning the surface.

3.2.3 Thermal Characterization

The thermal conductivity can be calculated by multiplying the thermal diffusivity by the density and by the specific heat capacity. The latter one was measured with the help of the differential scanning calorimetry (DSC), and the thermal diffusivity was measured by using xenon flash analysis (XFA).

The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. It was measured in this work by DSC¹¹³ using a sapphire standard calibration. Thereby, the measured heat flow can be converted into the specific heat capacity [Jg^-1K^-1].

The most important method, used in this thesis, was the XFA. It is described in the following in more detail. With the xenon flash analysis, the thermal diffusivity α [cm²s^-1] was measured. This thermophysical property describes how fast temperature diffuses through a material. The XFA setup and a typical measurement signal, fitted with an appropriate fit model, are depicted in Figure 3.14.

Figure 3.14. Setup of the xenon flash analysis (XFA), and a typical measurement signal of a hollow silica sphere colloidal crystal, fitted by the radiation fit model. Reprinted from Ruckdeschel et al.¹⁰⁵ with permission from Wiley VCH.

Before the measurements, the 3D colloidal assemblies were coated with a thin graphitic layer (high emissivity) on both sides to ensure a proper absorption of the applied energy. Then, the specimen was subjected to a temperature increase at the bottom of the sample by a short xenon light flash. As a result, heat is conducted through the sample due to the temperature gradient. At the rear surface, an infrared (IR) detector measures the time-dependent temperature increase. By fitting the measurement signal with an appropriate model, the effective thermal diffusivity of the measured sample is received. For most cases, the radiation fit model is suitable. This model represents an extension to the finite-pulse and heat loss corrections given by the Combined fit model from Dusza¹¹⁴. In contrast, it allows for an amount of the xenon flash to be directly transmitted to the rear sample surface, leading to an instantaneous temperature jump analogous to Blumm et al.¹¹⁵.