Thermal transport in binary colloidal glasses: Composition dependence and percolation assessment

The combination of various types of materials is often used to create superior composites that outperform the pure phase components. For any rational design, the thermal conductivity of the composite as a function of the volume fraction of the filler component needs to be known. When approaching the nanoscale, the homogeneous mixture of various components poses an additional challenge. Here, we investigate binary nanocomposite materials based on polymer latex beads and hollow silica nanoparticles. These form randomly mixed colloidal glasses on a sub-$\mu \mathrm{m}$ scale. We focus on the heat transport properties through such binary assembly structures. The thermal conductivity can be well described by the effective medium theory. However, film formation of the soft polymer component leads to phase segregation and a mismatch between existing mixing models. We confirm our experimental data by finite element modeling. This additionally allowed us to assess the onset of thermal transport percolation in such random particulate structures. Our study contributes to a better understanding of thermal transport through heterostructured particulate assemblies.

Figure 1

Relative effective thermal conductivities ${\kappa }_e$ for the series, the parallel, the Maxwell-Eucken (ME), and the effective medium theory (EMT) model and the corresponding equations. In the ME1 model, 1 is the continuous phase, whereas, in the ME2 model, 1 is the dispersed phase. Adapted with permission from Carson et al. [13].

Figure 2

Finite element modeling (FEM) of binary colloidal assemblies with hollow silica spheres. (a) Thermal conductivity data of the binary particle mixtures, the EMT, ME1, and ME2 models in comparison to simulated data obtained from FEM. (b) Thermal conductivity data from FEM of binary colloidal glasses consisting of hollow spheres and diamond particles and the corresponding EMT (black line), ME1 (dark blue line), and ME2 (light blue line) models. The gray lines show the EMT model for binary particle mixtures with a decreasing thermal conductivity ratio $({\kappa }_1$:${\kappa }_2)$ between the two types of particles. The black dashed line represents the fit by a percolation model [Eq. (2)]. (c) The geometry of the binary colloidal glass with a diamond particle volume fraction of 36.5% (blue particles) used for the FEM simulations and the corresponding heat flux streamlines for the different directions ($x, y$, and $z$).

Figure 3

(a) Transmission electron microscopy images of the hollow silica nanoparticles. (b) Scanning electron microscopy images of the P(MMA-$co$-nBA) particles.

Figure 4

Schematic setup of the vacuum filtration system. The parts were held together by a spring clamp and put on a filter flask.

Figure 5

Thermal conductivity data of the binary colloidal glasses measured in vacuum at $25{}^{\circ }\mathrm{C}$ (black squares) in comparison to different mixing models: effective medium theory (EMT), series model, parallel model, and Maxwell-Eucken (ME) model 1 and 2. The inset shows a side-view scanning electron microscopy (SEM) image of the colloidal assembly with a polymer particle volume fraction of 53% (53P). The hollow silica spheres are red-colored.

Figure 6

Scanning electron microscopy images of the colloidal assembly with a polymer particle volume fraction of 53% (53P) taken at different positions of the sample. The hollow silica spheres are red colored.

Figure 7

Scanning electron microscopy images of the binary colloidal glasses comprising polymer particle volume fractions between 100% and 0% before the heating process.

Figure 8

(a) The density of the different binary colloidal glasses. (b) Differential scanning calorimetry measurements of the particle mixtures.

Figure 9

(a) Temperature-dependent thermal conductivity of colloidal glasses in helium at 1000 mbar. (b) Thermal conductivity of the particle assemblies in vacuum before and after heating to $150{}^{\circ }\mathrm{C}$. The red dashed line represents the EMT model. (c) Density of the colloidal assemblies before and after heating to $150{}^{\circ }\mathrm{C}$. (d) Scanning electron microscopy images of the colloidal assemblies after heating to $150{}^{\circ }\mathrm{C}$.

Figure 10

Schematic setup of the xenon flash analysis and the corresponding measurement signal with radiation fit. This fit model represents an extension to the finite-pulse and heat loss corrections given by the combined fit model from Dusza [21]. Moreover, it takes into account that part of the xenon flash is transmitted to the rear sample surface, leading to an instantaneous temperature jump analogous to Blumm et al. [22].

Figure 11

The radial distribution function of a random close-packed particle assembly from molecular dynamics simulation (program lampps). The two red lines are at $\sqrt{3}$ and 2.