# A new method for evaluating the most stable contact angle using tilting plate experiments

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Review by Bryan Hassell: AP 255 Fall 11

From: A new method for evaluating the most stable contact angle using tilting plate experiments F. J. Montes Ruiz-Cabello, M. A. Rodríguez-Valverde and M. Cabrerizo-Vílchez Soft Matter, 2011

## Introduction

Contact angle measurements are used in many applications where the study of the solid–liquid affinity is a matter of interest. Each solid–liquid–vapor system is characterized by a range of observable contact angles, usually referred to as the contact angle hysteresis range. This range is defined by the Advancing Contact Angle (ACA) and the Receding Contact Angle (RCA), which are further the most meaningful angles because they are related to the shear and tensile adhesion forces. The tilting plate method consists of the formation of a immobile drop on the solid surface that is subsequently inclined. The values of ACA and RCA are measured at the downhill and uphill points of the contact line respectively, during the incipient motion of the drop. Unfortunately, ACA and RCA provided by tilting plate experiments are very controversial because the drop placement on the horizontal surface determines the resulting motion of the contact line and so, the observed contact angle. Another measurable contact angle with important physical meaning is the most-stable contact angle (MSCA) which is defined as the configuration of the minimum free energy of the system. This contact angle is the only one with a theoretical support for a connection between contact angle measurements and calculation of the surface energy of solids but it difficult to measure. This work describes a novel methodology based on tilting plate experiments for measuring the MSCA. The MSCA values of different polymer surfaces obtained by tilting plate experiments were compared with those obtained by mechanical vibration experiments.

## Materials and Methods

Fig. 1 Schematic representation of two drops with ACA (a, right) and RCA (b, right) after the addition or removal of liquid, accordingly. If the surface is then tilted, the incipient motion of the contact line of the drop with ACA should be firstly observed at the downhill point (a, left). Instead, for the drop with RCA, the incipient motion should primarily occur at the uphill point (b, left).

Here 8 surfaces with different wetting properties were investigated: polypropylene (PP), polycarbonate (PC), polytetrafluoroethylene (PTFE), polyethylene terephthalate (PET), and unplasticized polyvinyl chloride (uPVC) and polydimethylsiloxane (PDMS)

#### Tilting Plate Experiment

For each tilting step (0.5$^o$), the system acquired an image. On each image, what was focused on was the two contact line points where the highest and lowest contact angles were observed, or the downhill and uphill points, respectively. As illustrated in Fig. 1, the contact line point that moved first depended on the previous history. If the initial drop configuration was closer to the advancing metastable configuration (as in Fig. 1a), once the surface was tilted, the downhill point began to move before the uphill one. Otherwise, if the contact angle of the initial drop was closer to the RCA value (see Fig. 1b), the uphill contact line point began to move before the downhill one. For these cases, the $^\alpha_1$ value was relatively small because the incipient motion of the drop occurred very rapidly. Each initial drop formed with the same volume but with different contact angles was characterized by a critical tilt angle $^\alpha_1$. Instead, the critical tilt angle $^\alpha_2$ was just related to the drop volume and the magnitude of contact angle hysteresis and it was expected to be constant for all the drops of the same volume, independent of their previous history. The mechanically most stable configuration corresponded to the initial drop for which the critical tilt angle $^\alpha_1$ reached a maximum value and the difference $^\alpha_{2}-\alpha_1$ a minimum value.

#### Mechanical vibration experiments

The MSCA values provided were validated with the methodology described above with the corresponding MSCA values obtained using vibrations. For measuring the MSCA with the mechanical vibration methodology, first drop were created as above but with different contact angles. In this case, the water drops were carefully formed (at 2 $\mu L s^-1$) using a micro injector controlled by a computer. Once the drop was formed and its initial contact angle $\theta_0$ measured by ADSA-P, the drop was vibrated using a stochastic (white noise) signal driven by a mechanical oscillator controlled by a computer. After 10 s, the vibration was stopped and the final contact angle $\theta_f$ was measured. We identified the MSCA configuration as the initial drop with the changeless contact angle: |$\theta_{f}-\theta_i$|~0.

## Results

Table 1 Advancing and receding contact angle values measured by low rate dynamic contact angle experiments, arithmetic mean of these values and the most stable contact angle measured with the tilting plate method and the mechanical vibration method, for all the polymers employed in this study. Mostly observed was good agreement between both methods

The table basically summarizes what was shown in many figures. It is noticeable that there is an excellent agreement in the MSCA values measured with both methods. This good agreement was mostly found for the rest of the polymer surfaces. It is emphasized the agreement between the arithmetic mean of the ACA and RCA values with the MSCA values, except for those surfaces (uPVC and PDMS-r) where there was a disagreement between the two methods. However for surfaces with very high hysteresis, such as the PDMS-r sample it was observed observed that the minimum point was clearer for identifying the MSCA from the tilting plate method rather than the mechanical vibration method. Unlike the PP–water system, the change in contact angle of the PDMS-r–water system, after the corresponding stimulus (tilting or vibration), was asymmetric regarding the initial contact angle. This explains the disagreement between the mean angle $\theta$ and the MSCA values.

## Conclusions

The main conclusions of this work are summarized as follows: 1. In this work, a novel methodology to identify the MSCA using tilting plate experiments was proposed from the operative definition of the most stable drop, i.e. the drop with the highest resistance to slide down. It was found that the most stable drop began to slide down globally at the maximum critical tilt angle. Further work should be addressed to understand this experimental finding. 2. The MSCA values provided by the tilting plate experiments were compared to those obtained with mechanical vibration, obtaining a good agreement for the polymer surfaces employed in this study. However, the tilting plate method became more appropriate than the mechanical vibration method when the system revealed a high contact angle hysteresis. 3. This methodology validates the mean contact angle computed from the ACA and RCA values as a rough estimate of the MSCA, except for those systems with asymmetric change in the contact angle regarding the initial contact angle, after the corresponding stimulus. 4. It was not observed any volume dependence in the MSCA values measured with the tilting plate method. This postulates the MSCA value as the contact angle that appears in the Wenzel or Cassie equation, accordingly. However, the MSCA configuration seems to be noticeably easier to identify with the tilting plate method when the drop volume is not so large (<100 ml), although enough to allow the sliding of the drop and to apply the Wenzel or Cassie equations.