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Methods for Structural and Chemical Characterization of Nanomaterials  149

          For measuring nanoparticle contact angle two different techniques are
        available. Nanoparticles may be deposited onto a surface to form a lawn
        of particles. Here the deposited nanoparticles form a surface onto which
        the contact angle with different liquids may be measured. This technique
        requires that the surface formed be smooth and even in order to get
        reproducible results and to minimize the influence of roughness on the
        measured contact angle. Furthermore, this technique gives an average
        contact angle as the surface energies of many particles are contribut-
        ing to the measurement. However, there is no limitation with regards
        to minimum particle size in using this technique, so the contact angle
        for very small nanoparticles may be measured. More precise informa-
        tion may be obtained using an AFM where the contact angle for a single
        nanoparticle with a liquid may be measured.
          Nanoparticle contact angle may be measured based on the equilib-
        rium position (i.e., zero net pressure) of a nanoparticle probe from
        AFM force curves [Yakubov et al., 2000]. The nano-probe is formed by
        attaching or gluing a single nanoparticle to the end of a tipless AFM
        cantilever. The receding contact angle is measured by placing an air
        bubble (diameter ~ 1–1.5 mm) on the bottom of a liquid cell. The
        nano-probe is then brought toward the air bubble. Once the nano-
        probe makes contact with the bubble, a three-phase interface is formed
        (air-liquid-solid) and the capillary force pulls the colloid into the air
        bubble. As the probe is extended further into the bubble, a point is
        reached where the net force acting on the nano-probe is equal to zero
        (Figure 4.28). This zero-force equilibrium position of the nanoparti-
        cle is characterized by a penetration depth D , which can be directly
                                                   b
        determined from the AFM force curve. Penetration depth is defined
        as the difference between the jump in point and the zero-force posi-
        tion. The receding contact angle may then be calculated according to
        the following relationship:

                                             D b
                                  cos u 5 12                          (29)
                                      r
                                              R
        where R is the nanoparticle radius. The procedure for determining the
        advancing contact angle is similar to that for the receding contact
        angle. For the advancing contact angle a drop of water (diameter ~
        1–1.5 mm) is placed on the AFM stage and the nano-probe is extended
        into it. From the penetration depth of the colloid into the zero-force posi-
        tion of the drop surface D the advancing contact angle may be calcu-
                                d
        lated according to:
                                            D d
                                  cos u 5                             (30)
                                      a
                                          R 2 1
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