Surface tensiometry

The surface tension of test fluids was determined using the tensiometer K11 MK3 of Krüss GmbH (Hamburg, Germany). Since the surface tension is supposed to correlate to the energy required to create new internal surfaces within a PE-HD material (section 2.3.2, especially Eq. 19), it is considered to have a decisive influence on SCG. The creation of new internal surfaces is part of the craze-crack mechanism. Due to the attractive forces between molecules (cohesion), a characteristic energy is required to change the size of an interface or surface. The interfacial or surface tension is considered as the force that has to be spent to increase the interface or surface area by a specific amount. The term ‘surface tension’ is used for a liquid bordering to a gaseous phase. The term ‘interfacial tension’ refers to an interface between two liquids or a liquid and a solid.

The tensiometer determines the surface tension with a measuring probe which is suspended from a force sensor. This probe is a ring or a plate consisting of a material with optimum wetting properties and a high surface energy. Therefore, a platinum-iridium alloy is used for the ring and the plate is made of roughened platinum. During the measurement, the liquid is brought into contact with the probe by adjusting the height of a sample vessel. A force acts on the balance as soon as the probe touches the liquid surface. Using the value of wetted length of the probe, the measured force can be utilized to calculate the surface tension.

Ring method

The ring method (also described in ASTM D971 [133] for two liquids) was developed by Lecomte du Noüy [134]. The test liquid in the sample vessel is raised until contact with the ring surface is realized. The sample vessel is subsequently lowered, which stretches the liquid film lamella created beneath the ring (Fig. 15 a). When this lamella is stretched, a maximum force occurs which is

recorded (Fig. 15 b). At this maximum, the force vector is parallel to the direction of motion and the measured force correlates to the surface tension. The contact angle  is 0° for a material with optimum wetting properties such as platinum and iridium.

a) b)

Figure 15: Schematic depiction of the ring method (a) and schematic plot of force vs. distance of the ring to the liquid surface (b).

Practically, the distance between the ring and the liquid surface is increased until the region of maximum force has been covered (Fig. 15 b). Afterwards, the sample vessel is moved down, passing through the maximum of the force for a second time. The maximum force is then determined precisely considering the first as well as the return movement. Tearing of the lamella is avoided during the measurement. The surface tension is calculated according to (Eq. 34):

𝛾 =𝐹𝑚𝑎𝑥−𝐹𝑉

𝐿 cos 𝜃 (34)

with : surface tension, Fmax: maximum force measured, FV: weight force of raised volume of liquid,

L: wetted length, : contact angle. The contact angle  decreases with increasing strain of the liquid lamella and reaches a value of 0°, which results in cos  = 1.

Correction of ring method measurements

The results of the ring method are influenced by two effects: (1) The weight force of the liquid uplifted underneath the ring (FV) increases the value detected by the force sensor and has to be

subtracted. (2) The flexion of the lamella is higher on the inner than on the outer side of the ring. Hence, the force maximum (at  = 0°) is not reached at the same time on the inner and the outer side of the ring. Therefore, values obtained by the ring method were corrected according to a method introduced by Huh and Mason [135]. Permitting the highest range of validity, the Huh and Mason correction method provides an accuracy of measuring values of ± 0.19 %. The correction was performed automatically in the tensiometer software.

Plate method

According to the Wilhelmy plate method, the test liquid vessel moved upward at a constant speed to partly immerse the plate (Fig. 16) [136].

a) b)

Figure 16: Schematic image of Wilhelmy plate method; plate immersed in liquid during measurements, a) front view, b) side view.

The microbalance sensor measured the force applied to the moving plate. Using algorithms based on the Wilhelmy plate method, the force value and the advancing dynamic contact angle, the surface tension was calculated according to (Eq. 35):

𝛾 =_{𝐿 cos 𝜃}𝐹 (35)

with : surface tension, F: measured force, L: wetted length, : contact angle. The speed of the vessel platform was set to a constant value to maintain a steady motion during the experiment. When the plate moved upwards, the contact angle  reached 0°, which leads to cos  = 1. Then, the measured force and the plate length have to be considered only. Due to the plate method setup, no corrections of measured values are necessary.

In this study, surface tension of water, biodiesel, diesel, Arkopal, NB, NBA and NBL was obtained by using the ring and the plate method at 23°C and 50°C.

3.1.3. Gravimetry

To characterize the sorption and desorption behavior, the mass uptake of PE-HD was determined gravimetrically by immersion in diesel, biodiesel, Arkopal, NB, NBA and NBL at 60°C. Due to its high polarity and surface tension, water is expected not to be absorbed by PE-HD. Arkopal is an aqueous solution (2 wt% aq., section 4.2.1) and expected to be absorbed only slightly. Nevertheless, its sorption behavior was determined as well. Specimens applied for gravimetric analysis were round discs milled from sheets (section 4.1). They had a diameter of 80.0±3.0 mm, a thickness of 2.0±0.2 mm and a central hole with a diameter of 10.0±1.0 mm (Fig. 17 a, b). The central hole allowed for fixing the discs on a vertical glass shaft with glass spacers separating the specimens (Fig. 17 c).

a) b) c)

Figure 17: Specimens used for gravimetric analysis, a), b) schematic representations, c) depiction of 5 individual specimens attached to a glass shaft.

Such attached specimens (Fig. 17 c) were immersed in glass jars (height: approx. 20 cm, inner diameter: approx. 10 cm) filled with the test liquid and closed with a PTFE sealed glass lid. The jars were placed in temperature-controlled water baths at 60°C. A temperature of 60°C was selected to induce an accelerated diffusion (section 2.2.2) leading to a faster saturation of the specimens to test within practical timescales (in accordance with [53]). The final equilibrium concentration (saturation) obtained for biodiesel and diesel at 60°C is slightly higher compared to 50°C but sorption effects that depend on the fluids are equivalently evident (section 2.2.1) [53]. The size of specimens was selected to approximate plane sheet geometry but maintain mechanical stability. Considering plane sheet geometry, the polymer in which diffusion occurs is defined only by the two parallel opposing surface planes and fluxes through the edges can be neglected (section 2.2.2). Thus, diffusive transport can be considered as restricted to one dimension [48, 53].

Five identical discs were placed in each jar. To measure the mass uptake, specimens were removed from the jar, dried carefully by a tissue paper, weighed and re-immersed in the jar within less than five minutes. Such procedures were performed at preselected time intervals.

The concentrations C of penetrants are given as mass fractions w by (Eq. 36): 𝐶 = 𝑤 =𝑚−𝑚0

𝑚0 (36)

m0: initial mass of the specimen prior to immersion, m: current mass of specimen measured after

certain time intervals.

For the calculation of diffusion coefficients, equation 37 was used, which is derived from Fick’s second law and which is based on plane sheet geometry [48, 53]:

𝑀𝑡 𝑀∞= 1 − 8 𝜋2∑ 1 (2𝑖+1)𝑒𝑥𝑝 {− 𝐷(2𝑖+1)2𝜋2𝑡 𝑙2 } ∞ 𝑖=0 (37)

Mt: time-dependent mass uptake (𝑀𝑡 = 𝑚(𝑡) − 𝑚0), M∞: equilibrium mass uptake

(𝑀∞= 𝑚(𝑡 → ∞) − 𝑚0), D: diffusion coefficient, t: time, l: doubled specimen thickness h (l = 2ℎ)

because diffusion occurs from both sides of the specimen. Diffusion coefficients were obtained by nonlinear curve fitting (included module of Origin software, OriginLab Corporation, Northampton, MA, USA) the mass uptake curves using the first ten terms of the infinite sum in equation 37.

Desorption behavior was determined by measuring the mass loss of the specimens after they had reached their equilibrium mass uptake. Therefore, they were kept at a constant temperature of 60°C suspended freely in an oven with circulating air (UT 6200 of Heraeus Instruments, Heraeus Holding GmbH, Hanau, Germany).

Moreover, sorption procedure was applied for the preparation of saturated specimens for subsequent FNCT (section 3.2.2). Therefore, FNCT specimens were immersed in sorptive liquids diesel and biodiesel until they reached the equilibrium mass uptake. The mass uptake of these specimens was measured on a regular basis. When they reached the equilibrium mass uptake, they were immediately tested in FNCT.