Formation mechanism of fractal structures on wax surfaces with reference to their super water-repellency

Abstract

Alkylketene dimer (AKD: a kind of wax) spontaneously forms a fractal structure and its surfaces show super water-repellency (the contact angle = 174°). However, the formation mechanism of the fractal surfaces of AKD is still unclear. In this work, surface structures, wettability and phase behaviors of various waxes have been investigated in order to understand the mechanism for spontaneous formation of super water-repellent fractal surfaces. We have found an empirical general rule without any exceptions at least for the wax samples tested. First, the wax must form a meta-stable crystalline phase when solidified from its melt. Then, the super water-repellent fractal surfaces form spontaneously during the phase transition from a meta-stable to a stable crystalline form. The tempering method also supported the above rule for the waxes showing the fractal structure formation on their surfaces.

---

1. Introduction

Alkylketene dimer (AKD: a kind of wax) spontaneously forms a fractal structure and its surfaces show super water-repellency.^1,2 The AKD fractal surface was found to give a contact angle of 174° for water.^1,2 Since then, the super water-repellent rough surfaces have attracted much attention and have been extensively studied.^3–22 However, the formation mechanism of the fractal surfaces of AKD is still unclear. The mechanism for the spontaneous formation of fractal surfaces of triglyceride waxes has been recently studied by the present authors' group, and it has been made clear that the fractal structure on the wax surfaces is formed during the phase transition from the meta-stable α-form to the stable β-crystalline form.²³ The triglyceride waxes form the α-form first when crystalized from their melt, and then transform to the thermodynamically most stable β-crystal. Super water-repellent fractal surfaces of the wax were formed during this phase transition process.²³ This is an extension of the previous work of above.

This paper deals with the surface structures, super water-repellency and the phase transition behaviors of various wax samples in order to generalize the mechanism for triglycerides mentioned above. Furthermore a tempering technique is applied to some wax samples which give the super water-repellent fractal surfaces. This is a technique to make the triglycerides transform directly to the stable β-crystal from their melts.

2. Experimental section

2.1 Materials

The wax samples used in this work and their chemical structure and melting point are listed in Table 1. Pure AKD was purchased from Dojindo Laboratories, Japan and used without further purification. They synthesized and purified the AKD according to our recipe.² A mixed AKD wax was kindly presented by Arakawa Chemical Industries, Ltd., Japan. It was synthesized from a mixture of n-hexadecanoic (30–40 mol%) and n-octadecanonic acid (70–60 mol%) chlorides utilizing essentially the same procedures as those for pure AKD. The mixed AKD sample was purified by recrystallization from n-hexane. Other wax samples were used without further purification. Water used was ultrapure water treated with a membrane system (Milli-Q, Millipore Corporation).

Table 1 List of waxes used in this work

Wax	Chemical structure		Supplier	M.p./°C
a Obtained from DSC curves. b Data taken from the catalogue of Wako Pure Chemicals Ind., Ltd. c Data taken from Siyaku.Com (URL: http//www.siyaku.com/). d Data taken from the catalogue of Tokyo Chemicals Ind. Co. Ltd.
Mixed AKD		R1, R2 = n-C14, n-C16; n-C14 : n-C16 = 30–40% : 60–70%	Arakawa Chemical Ind., Ltd.	48^a
Pure AKD		R1, R2 = n-C16	Dojindo Laboratories	61^a
Lauric acid	CH3(CH2)10COOH		Wako Pure Chemicals Ind. Ltd.	43–46^b
Stearic acid	CH3(CH2)16COOH		Wako Pure Chemicals Ind. Ltd.	68–71^b
Behenic acid	CH3(CH2)20COOH		Wako Pure Chemicals Ind., Ltd.	81–82^c
Erucic acid	CH3(CH2)7CH=CH(CH2)11COOH		Wako Pure Chemicals Ind. Ltd.	33.5^c
Cetyl alcohol	CH3(CH2)15OH		Wako Pure Chemicals Ind. Ltd.	49–53^b
Stearyl alcohol	CH3(CH2)17OH		Wako Pure Chemicals Ind., Ltd.	57–60^b
Heneicosane	CH3(CH2)19CH3		Wako Pure Chemicals Ind. Ltd.	40.5^c
Dotriacontane	CH3(CH2)30CH3		Wako Pure Chemicals Ind. Ltd.	68–72^b
Hexatriacontane	CH3(CH2)34CH3		Tokyo Chemicals Ind. Co., Ltd.	76^d
Palmityl palmitate	CH3(CH2)14COO(CH2)15CH3		Wako Pure Chemicals Ind. Ltd.	54^c
Stearyl stearate	CH3(CH2)16COO(CH2)17CH3		Wako Pure Chemicals Ind. Ltd.	52–58^c
Monostearin	CH3(CH2)16COO(CH2)(CH)(OH)(CH2)OH		Wako Pure Chemicals Ind. Ltd.	68–73^b
Distearin	(CH3(CH2)16COO)2(CH2CH)(CH2)OH		Wako Pure Chemicals Ind. Ltd.	58^a
Tristearin	(CH3(CH2)16COO)3(CH2CHCH2)		Wako Pure Chemicals Ind. Ltd.	73.5^c
Tripalmitin	(CH3(CH2)14COO)3(CH2CHCH2)		Wako Pure Chemicals Ind. Ltd.	65.5^c

---

2.2 Preparation of sample surfaces

A small amount (∼200 mg) of each wax sample was put on a glass slide, and heated up to its melting point on a hot-plate. The molten wax was spread on the glass slide, and cooled down slowly on the hot-plate to room temperature to solidify. The solidified sample was annealed just below its melting temperature for several hours.

2.3 Measurements

The surface structures of the wax samples were observed by a scanning electron microscope (SEM, Hitachi FE-SEM S-5200) after a week from surface preparation. In order to set the sample on an aluminium SEM stage a thin wax sample was pasted on the stage with a conductive carbon tape. An Au–Pd alloy was sputtered for 90 s onto the sample surface with an ion-sputter (Hitachi type E-1030) before SEM observation.

Contact angle measurements were carried out with an optical contact angle meter (DropMaster 300, Kyowa Interface Science Co. Ltd.) at room temperature. A water droplet having a diameter of 1–2 mm was used. Five droplets were put on different places of a wax surface and the 5 sets of data were averaged to give the contact angle.

Differential scanning calorimetry (DSC) was performed with a DSC apparatus (Rigaku Thermo Plus 2 DSC-8230). A wax sample of 5–7 mg was put in an aluminium pan and the pan was sealed. The heating or cooling rate was 2 °C min⁻¹.

Fractal analysis for the cross-sections of the wax samples was made by the box-counting method. A wax sample was cut to be a square of about 5 mm × 5 mm, and pasted perpendicularly on an SEM stage. The surface of a cross-sectional image was traced at some different magnifications, and the trace curve was analyzed by the box-counting method. The fractal dimension of the cross-section, D_cross, was calculated from eqn (1).

N(r) ∝r^−D_cross (1)

where r, N(r) and D_cross are the size of box, the number of boxes occupied by the trace curve and the fractal dimension, respectively. The fractal dimension of the surface, D, can be approximately written as D = D_cross + 1.

2.4 Tempering procedures

Pure and mixed AKD and tripalmitin samples were chosen for tempering operations. Tempering is a technique to let the waxes crystallize at the temperature in between the melting points of meta-stable and stable form of crystals. In this process the wax samples crystallize above the melting point of the meta-stable form, and transform directly to the stable crystalline phase from their melts.

About 10 g of each wax sample was put in a 200 mL beaker and heated up to its melting point. After the sample was melted completely, it was cooled down to and kept at just below the melting point of the stable crystalline form and stirred vigorously. The AKD samples were solidified at 48 °C (mixed AKD) and at 59 °C (pure AKD) for about 10 min, and then left standing at the same temperature for 1–2 h. Special care was taken for the tripalmitin samples. The molten tripalmitin wax was stirred vigorously at 58 °C, and a piece of the stable form was put in the sample as a seed crystal. After the sample was solidified, it was cooled down very slowly, i.e., kept for 5 days at each temperature of 58, 55, 51, 49 and 48 °C.

3. Results

3.1 Surface structures and contact angles of various waxes

Fig. 1 shows some examples of the surface structure (SEM image) of wax samples and a photograph of a water droplet placed on them. As can be seen clearly, three wax samples (mixed AKD, distearin and tristearin) give rough surfaces and exhibit super water-repellency (contact angle > 150°). The other two samples (lauric acid and dotriacontane) form a smooth surface and show normal wettability. The contact angles and the surface structures for all samples tested are summarized in Table 2.

Fig. 1 SEM images (left) of mixed AKD (a), distearin (b), tristearin (c), lauric acid (d) and dotriacontane (e) and photos of a water droplet on their surfaces (right). The bars in the SEM images represent 30 μm.

Table 2 Contact angle, surface structure and the existence of meta-stable crystalline form of wax samples

Wax	Contact angle	Surface structure	Meta-stable crystal
Mixed AKD	151°± 2°	fractal structure	Yes
Lauric acid	86°± 5°	flat and smooth	No
Stearic acid	89°± 5°	flat and smooth	No
Behenic acid	113°± 6°	flat and smooth	No
Erucic acid	83°± 2°	flat and smooth	No
Cetyl alcohol	61°± 4°	flat and smooth	No
Stearyl alcohol	93°± 2°	flat and smooth	No
Heneicosane	109°± 3°	flat and smooth	No
Dotriacontane	108°± 3°	flat and smooth	No
Hexatriacontane	105°± 1°	flat and smooth	No
Palmityl palmitate	107°± 1°	flat and smooth	No
Stearyl stearate	106°± 2°	flat and smooth	No
Monostearin	81°± 1°	flat and smooth	No
Distearin	153°± 2°	fractal structure	Yes
Tristearin	154°± 2°	fractal structure	Yes

---

Two (AKD and tristearin) of the three samples which show the super water-repellency are known to form fractal surfaces.^1,2,23,24 Fractal analysis was then made for one more wax sample (distearin), and the wax was confirmed to have a fractal surface with the fractal dimension of 2.3. The upper and lower size limits of self-similarity were 34 μm and 0.2 μm, respectively. Consequently, three waxes having the fractal surface show the super water-repellency among all the samples tested.

3.2 DSC thermograms and phase behaviors

In order to understand the common property in the phase behaviors of the three wax samples showing the super water-repellency, DSC thermograms were observed for all the wax samples. Fig. 2 shows two typical examples of the DSC thermogram for lauric acid and tristearin. The endothermic (exothermic) peak in the heating (cooling) process is assigned to the melting (crystallization) of the wax samples. In the first run of DSC measurement, the wax sample as received from the supplier, i.e., stored for long time, was used. This sample can be assumed to be in the thermodynamically stable crystalline phase. The second run of the DSC was performed just after the cooling process finished in the first run.

Fig. 2 DSC curves of lauric acid (a) and tristearin (b).

The two thermograms from the first and the second run of lauric acid are the same. However, the two thermograms of tristearin are completely different from each other in the first and the second run. In the second run of tristearin, an endothermic peak newly appears at lower temperature than its melting point. In addition, an exothermic peak also appears just after the new endothermic peak. The new endothermic peak in the second run is due to melting of the meta-stable α-crystal, and the following exothermic one is originated from crystallization to the stable β-form.²³ Similar endothermic and/or exothermic peaks were observed also in the second DSC run of mixed AKD and distearin, although the peaks were not so clear as those of tristearin. The existence or nonexistence of the meta-stable crystalline phase for all the wax samples is also summarized in Table 2.

The phase transition process from the meta-stable to the stable crystal was monitored elsewhere in detail by X-ray diffraction (XRD) techniques for triglycerides²³ and AKD.²⁴ The XRD results obtained also supported strongly the above phase transformation.

3.3 Effect of tempering on the surface structure and wetting

Fig. 3 shows the SEM images of the surfaces of mixed AKD, pure AKD and tripalmitin after the tempering operation. One can see the dramatic change of the surface roughness of the mixed AKD sample, comparing the SEM image in Fig. 1(a). The fractal rough structure disappears completely after the tempering operation. Although the fractal surface structures of pure AKD^1,2 and tripalmitin²³ are not shown here in this paper, they are quite similar to those of mixed AKD and tristearin. The photographs of the water droplets on the tempered AKD and tripalmitin surface are shown in Fig. 4. The contact angles are quite normal, and the AKD and tripalmitin waxes do not show at all super water-repellency.

Fig. 3 SEM images of surfaces of mixed AKD (a), pure AKD (b) and tripalmitin (c) after the tempering operation. The bars represent 30 μm.

Fig. 4 Photos of water droplets on mixed AKD (a), pure AKD (b) and tripalmitin (c) after the tempering operation. Contact angles are 110°± 0°, 109°± 2° and 109°± 4° for (a), (b) and (c), respectively.

The DSC thermograms for mixed AKD, pure AKD and tripalmitin are shown in Fig. 5. They do not have endothermic peak at lower temperature, but show only the melting peak. These experimental results strongly indicate that the tempering operation works quite well and the 3 wax samples transform directly to the stable crystalline form from their melt.

Fig. 5 DSC curves in first run of mixed AKD (a), pure AKD (b) and tripalmitin (c) after tempering operation.

4. Discussion

As reported previously, triglycerides form super water-repellent fractal surfaces during the phase transition from the meta-stable α-cryatalline form to stable β-form.²³ This empirical rule has been extended to various waxes without any exceptions in this work. The wax samples of AKD, diglyceride and triglyceride have a meta-stable form of crystal and give super water-repellent fractal surfaces. All of the other waxes have no meta-stable crystalline phase and do not form fractal surfaces. The empirical rule mentioned above may be a general one at least for the waxes tested here.

The effect of tempering on the fractal surface formation in AKD and tripalmitin is a strong support for the above empirical rule. After the tempering operation, super water-repellent fractal surfaces of AKD and triglyceride become ordinary flat surfaces. This result means that the spontaneous phase transition from the meta-stable to stable crystalline form is the essential process for the waxes to form fractal surface structures. But why are the structures fractal? A theoretical study is now in progress on the origin of the fractal structures.

The spontaneous formation of fractal surfaces in triglycerides has been known for a long time as the “blooming phenomenon” in chocolate industries, although it has not been known that the surface structure is fractal. The “blooming phenomenon” is a troublesome matter that the chocolate surface becomes rough and white when stored for long time. The tempering technique has been invented to avoid the “blooming phenomenon” in the industries. This technique also works well to make clear the formation mechanism for the super water-repellent fractal surfaces.

Conclusions

The surface structure, wettability and phase behaviors of various waxes have been investigated in order to understand the mechanism for spontaneous formation of super water-repellent fractal surfaces. We have found an empirical general rule without any exceptions at least for the wax samples tested. First, the wax must form a meta-stable crystalline phase when solidified from its melt. Then, the super water-repellent fractal surfaces form spontaneously during the phase transition from a meta-stable to a stable crystalline form.

References

1. T. Onda, S. Shibuichi, N. Satoh and K. Tsujii, Langmuir, 1996, 12, 2125.
2. S. Shibuichi, T. Onda, N. Satoh and K. Tsujii, J. Phys. Chem., 1996, 100, 19512.
3. S. Shibuichi, T. Yamamoto, T. Onda and K. Tsujii, J. Colloid Interface Sci., 1998, 208, 287.
4. K. Tadanaga, N. Katata and T. Minami, J. Am. Ceram. Soc., 1997, 80, 1040.
5. K. Tadanaga, N. Katata and T. Minami, J. Am. Ceram. Soc., 1997, 80, 3213.
6. A. Nakajima, A. Fujishima, K. Hashimoto and T. Watanabe, Adv. Mater., 1999, 11, 1365.
7. J. Bico, C. Marzolin and D. Quéré, Europhys. Lett., 1999, 47, 220.
8. D. Öner and T. J. McCarthy, Langmuir, 2000, 16, 7777.
9. H. Li, X. Wang, Y. Song, Y. Liu, Q. Li, L. Jiang and D. Zhu, Angew. Chem., Int. Ed., 2001, 40, 1743.
10. L. Feng, S. Li, H. Li, J. Zhai, Y. Song, L. Jiang and D. Zhu, Angew. Chem., Int. Ed., 2002, 41, 1221.
11. L. Feng, S. Li, Y. Li, H. Li, L. Zhang, J. Zhai, Y. Song, B. Liu, L. Jiang and D. Zhu, Adv. Mater., 2002, 14, 1857.
12. L. Feng, Z. Zhang, Z. Mai, Y. Ma, B. Liu, L. Jiang and D. Zhu, Angew. Chem., Int. Ed., 2004, 43, 2012.
13. T. Sun, G. Wang, L. Feng, B. Liu, Y. Ma, L. Jiang and D. Zhu, Angew. Chem., Int. Ed., 2004, 43, 357.
14. R. Mohammadi, J. Wassink and A. Amirfazli, Langmuir, 2004, 20, 9657.
15. H. Yabu, M. Takebayashi, M. Tanaka and M. Shimomura, Langmuir, 2005, 21, 3235.
16. M. Hikita, K. Tanaka, T. Nakamura, T. Kajiyama and A. Takahara, Langmuir, 2005, 21, 7299.
17. E. Hosono, S. Fujihara, I. Honma and H. Zhou, J. Am. Chem. Soc., 2005, 127, 13458.
18. M. Callies and D. Quéré, Soft Matter, 2005, 1, 55.
19. H. Yan, K. Kurogi, H. Mayama and K. Tsujii, Angew. Chem., Int. Ed., 2005, 44, 3453.
20. K. Kurogi, H. Yan, H. Mayama and K. Tsujii, J. Colloid Interface Sci., 2007, 312, 156.
21. H. Yan, K. Kurogi and K. Tsujii, Colloids Surf., A, 2007, 292, 27.
22. X. Feng and L. Jiang, Adv. Mater., 2006, 18, 3063 (a review article).
23. W. Fang, H. Mayama and K. Tsujii, J. Phys. Chem. B, 2007, 111, 564.
24. W. Fang, H. Mayama and K. Tsujii, Colloids Surf., A, 2007 DOI:10.1016/j.colsurfa.2007.09.010.

---