**3.1 Postulated healing mechanism**

212 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

contrast and topography images were highly dependent on storage time and temperature. This research group also observed the bee phase, a soft matrix phase surrounding the bee phase and a hard matrix dispersed on the soft phase, similar to findings reported by Jäger et al. (2004) and Masson et al. (2006). The authors also observed that the bee-shaped structure completely disappeared for samples at temperatures higher than 70°C and upon cooling to

Concurrently, the changing microstructure after aging of bitumen was studied using AFM by Wu et al. (2009). In these studies, both neat and SBS polymer modified bitumen was aged using a pressure aging vessel (PAV). Comparing the obtained images before and after aging, the authors reported that the bee-shaped structure significantly increased after aging. To support the observed phenomena, the researchers related this to the production of asphaltene micelle structures during the aging process. These findings are consistent with

Tarefder et al. (2010a, 2010b) studied nanoscale characterization of asphalt materials for moisture damage and the effect of polymer modification on adhesion force using AFM. They observed wet samples always showed higher adhesive force compared with dry one. The authors concluded that the adhesion behaviour of bitumen can vary with the chemistry

Recently, Pauli et al. (2009, 2011) reported that all of these interpretations, including their previous findings were at least partially wrong and came up with a new hypothesis in which they stated that the ''bees are mainly wax". To prove their hypothesis, they scanned different fractions of bitumen and found bee-shaped structures even in the maltenes which contain no asphaltenes, while the de-waxed bitumen fractions did not show any microstructures. The authors concluded that the interaction between the crystallizing paraffin waxes and the remaining bitumen are responsible for much of the microstructuring, including the well-known bee-shaped structures. They also reported sample variables such as film thickness, the solvent spin cast form, and the fact that solution concentration could

Even though different research groups concluded significantly different reasons for the structures to appear, the extensive atomic force microscopy (AFM) studies showed that bitumen has the tendency to phase separate under certain kinetic conditions and is highly dependent on its temperature history. Besides focusing on the reasons behind the microstructure growth, it is also important to relate these microstructures to the

From Atomic Force Microscopy (AFM) scans, it was found that bitumen is not a homogeneous bulk material as microstructures are observed in almost all the bitumen (Loeber et al., 1996, 1998; Pauli et al., 2001, 2009, 2011; Jäger et al., 2004; Masson et al., 2006). All the previous studies showed that bitumen appeared to have some form of 'phase separation' dependence on its temperature history, storage time and crude source. Changing the temperature of the bitumen showed a movement of the phases and sometimes resulted in an overall homogeneous material, where the clusters seem to have 'melted' back into the matrix structure. The ability of bitumen to phase separate and redistribute its phases

**3. Utilizing the AFM images as a basis for asphalt healing model** 

66°C they began nucleating.

the study by Zhang et al. (2011).

of the tip and functional groups on it.

performance of bitumen.

also strongly influence the corresponding AFM images.

From mechanical considerations, it is known that the interfaces between two materials with different stiffness properties serve as natural stress inducers. This means that when the material is exposed to mechanical and or environmental loading, these interfaces will attract high stresses and are prone to cracking. On this scale, this would result in a crazing pattern, which can be detected on a higher (macro) scale by a degradation of the mechanical properties of the material, such as the stiffness or fracture strength. If this process would continue, these micro-cracks (or crazes) would continue developing, start merging and finally form visible cracks.

A finite element simulation done by Kringos et al. (2012) demonstrated the concept of diminished response and the introduction of high stresses in an inhomogeneous material, as shown in Fig. 3, for a constant displacement imposed on a homogeneous and an inhomogeneous bitumen. The bituminous matrix is hereby simulated as a visco-elastic material and the inclusions as stiff elastic. From the deformation pattern it can be seen that the inhomogeneous material acts not only stiffer, but is no longer deforming in a smooth, uniform, manner and high stresses appear from the corners of the stiffer particles.

From the bitumen AFM scans it was shown that many bitumen sapmles, under certain circumstances, will form such inhomogeneities. If then, by changing the thermodynamic conditions of the material by inputting thermal or mechanical energy, these inclusions rearrange themselves or disappear; restoration of the mechanical properties would appear on a macro-scale. Since the phase-separation is occurring on the nano-to-micro scale, the interfaces between the clusters and the matrix could start crazing when exposed to (thermo) mechanical loading. A change of these clusters, either by rearranging themselves or by merging into the main matrix, would then lead to a memory loss of these micro-crazes and

Atomic Force Microscopy to Characterize the Healing Potential of Asphaltic Materials 215

important input parameters to the model and need to be determined for the individual bitumen samples. In Fig. 4 a comparison between AFM scans and the model is given for three different bitumen samples. More details about the analyses can be found in Kringos

Fig. 4. Comparison between AFM scans and computed phase configuration (Kringos et al.,

AAA-1 AAD-1 AAM-1

0 -10-5 -15 -20 -25 -30 -35 -40 -45 -50 -55

**Displacement (mm)**

The model can also be utilized in an 'upscaled' manner, in which the rearrangement of the phases, the appearance and thickness of the interfaces are linked to a healing function that becomes an intrinsic parameter that controls the evolution of dissipated energy. More details on the equations of this model and the parameters can be found from Kringos et.al.

Fig. 5. Simulation of healing versus no-healing asphalt beam (Kringos et al., 2012)

et.al. (2012).

2012)


0

no healing beam healing beam

1000 2000 3000

**Force (N)**

Fig. 3. Displacement and normal stress development in a homogeneous vs. inhomogeneous bitumen (Kringos et al., 2012)

the bitumen would show a restoration of its original properties, which may be referred to as physico-chemical "healing". The driving force for the rearrangement of the phases upon a changed thermodynamic state is explained in the following section.

#### **3.2 Governing equations**

To develop the governing equations for the phase-separation model, the general mass balance equation can be expressed as

$$
\rho \frac{\partial\_{\alpha} \mathbf{c}}{\partial \mathbf{t}} - \text{div} \left( \rho\_{\alpha} \mathbf{M} \cdot \nabla\_{\alpha} \mu \right) = 0 \tag{1}
$$

where **V** <sup>m</sup> is the density, is the chemical potential and <sup>M</sup> is the diffusional mobility tensor of phase in the material.

The chemical potential can be written as the functional derivative of the free energy :

$$
\mu\_a \mu = \frac{\delta\_a \mathbf{c}}{\delta\_a \mathbf{c}} \tag{2}
$$

The free energy is composed of three terms

$$
\Psi = \Psi\_0 + \Psi\_\chi + \Psi\_a \tag{3}
$$

where 0 is the configurational free energy, is the Cahn Hilliard surface free energy and is the strain energy.

Solving these equations, allows for the simulation of phase separation from various starting configurations. The free energy potentials and the mobility coefficient are hereby the

homogeneous

inhomogeneous

Fig. 3. Displacement and normal stress development in a homogeneous vs. inhomogeneous

the bitumen would show a restoration of its original properties, which may be referred to as physico-chemical "healing". The driving force for the rearrangement of the phases upon a

To develop the governing equations for the phase-separation model, the general mass

<sup>c</sup> div M 0

(1)

is the diffusional

(3)

(2)

The chemical potential can be written as the functional derivative of the free energy :

c 

 <sup>0</sup> 

where 0 is the configurational free energy, is the Cahn Hilliard surface free energy

Solving these equations, allows for the simulation of phase separation from various starting configurations. The free energy potentials and the mobility coefficient are hereby the

changed thermodynamic state is explained in the following section.

t

<sup>m</sup> is the density, is the chemical potential and <sup>M</sup>

bitumen (Kringos et al., 2012)

**3.2 Governing equations** 

**V**

and is the strain energy.

where

balance equation can be expressed as

mobility tensor of phase in the material.

The free energy is composed of three terms

important input parameters to the model and need to be determined for the individual bitumen samples. In Fig. 4 a comparison between AFM scans and the model is given for three different bitumen samples. More details about the analyses can be found in Kringos et.al. (2012).

Fig. 4. Comparison between AFM scans and computed phase configuration (Kringos et al., 2012)

Fig. 5. Simulation of healing versus no-healing asphalt beam (Kringos et al., 2012)

The model can also be utilized in an 'upscaled' manner, in which the rearrangement of the phases, the appearance and thickness of the interfaces are linked to a healing function that becomes an intrinsic parameter that controls the evolution of dissipated energy. More details on the equations of this model and the parameters can be found from Kringos et.al.

Atomic Force Microscopy to Characterize the Healing Potential of Asphaltic Materials 217

t0 t1 t2

t3 t4 t5

=0.014 =0.01 =0.006

=0.004 =0.002 =0.001

Fig. 7. Spinodal composition resulting in bee structure formation (Kringos et al., 2012)

Fig. 8. End configurations with varying Cahn Hilliard parameter (Kringos et al., 2012)

Defining the matrix, the distinct phases (the bees) and the interfaces (IF) as the three fractions in the end configuration, the normalized fractions are plotted as a function of the varying Cahn Hilliard parameter, Fig. 9. As can be seen from the graph, an increased Cahn Hilliard parameter causes an increased interface (IF) fraction. Since this parameter controls the gradient energy distribution this result seems certainly logical. Interestingly thought, it can also be seen that both the matrix and the bees seem reduced. Which means that with an increased gradient distribution coefficient fewer bees are formed with thicker interfaces.

Changing the configurational free energy function whereby normalizing the energy barrier

as shown in Fig. 10 (a) has the effect shown in Fig. 10 (b).

(2009b). The force versus displacement diagram is shown for a simulation of a fatigue test using this model. It can be seen from the graphs that in the case on the 'healing beam' the material has lost its memory of the previous loading cycle, whereas in the case of the 'nohealing beam' the material is considerably weaker after the first loading cycle.
