**Modification of Surface Energy and Wetting of Textile Fibers**

Franco Ferrero and Monica Periolatto

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60812

#### **Abstract**

The modification of the surface energy of textile fibers to improve functional prop‐ erties such as the wettability was reviewed. This modification can be achieved by physical or chemical methods or by the combination of both. Applications of plas‐ ma treatment to improve the wettability of natural and synthetic fibers were consid‐ ered and some methods of wettability measurement were mentioned. Subsequently the methods aimed to confer water and oil repellency were discussed and the treat‐ ment by UV curing of fluorochemicals was explained in detail. Finally the sol-gel techniques useful to modify the surface properties of textiles were introduced and the results of water and oil repellency achievable by sol-gel were presented.

**Keywords:** Surface energy, Wetting, Textile fibers, Plasma, Contact angle, Water re‐ pellency, Oil repellency, Fluorochemicals, UV-curing, Sol-gel

#### **1. Introduction**

The modification of the surface energy of textile fibers is pursued with the aim of improving their own hydrophilicity, wettability, and dyeability or of conferring functional properties such as hydro and oil repellency, soil release, adhesion improvement, and antistatic perform‐ ances. If the modification is confined to a thin surface layer of the fibers, the bulk properties of a textile material, such as mechanical strength, flexibility, breathability, and softness, should not be compromised.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The wettability of a surface depends on the surface tension of the liquid that goes into contact with the same. Water has a very high surface tension (72.8 mN/m), so it tends to wet only surfaces bearing highly polar groups; otherwise, it forms spherical drops with contact angles higher than 90°. Instead, apolar liquids of lower surface tension get drops flatter than those of water. Hydrophobic or oleophobic surfaces are difficult to wet by water or apolar liquids, respective‐ ly, and are called low-energy surfaces. Wetting, in reality, is much more complex than as described by classical laws. This primarily comes from the non-ideality of solid substrates that are both rough and chemically heterogeneous [1]. Such a situation commonly occurs in the case of textile materials and can be evidenced by the hysteresis of the contact angle [2].

The surface modification of textile fibers can be achieved by physical or chemical methods or by the combination of both. Plasma treatments and exposure to radiations are mainly represen‐ tative of physical methods, although their effects are often accomplished in the presence of reactive gases or after impregnation with suitable chemicals. However, chemical treatments can generally be carried out with oxidants or other finishing agents, followed by thermal treatment. Among the latter methods, sol–gel techniques are the more promising for surface modification.

Among the textile fibers, there are many differences regarding wettability and surface struc‐ ture. Natural fibers have cellular structures that are more complex than those of man-made fibers obtained by chemical spinning. Wool and fine animal fibers are mainly composed of keratin, but show the structure of composite material formed by an assembly of cuticle cells in the form of scales and cortical cells surrounded by a keratin cell membrane and held together by an intercellular cement. The cell membrane consists of a chemically resistant protein layer and a lipidic layer that constitutes a hydrophobic barrier to the transfer of water and dye molecules from an aqueous solution [3]. Therefore, a wettability improvement of these fibers can be obtained by the removal of the hydrophobic lipidic layer and by the introduction of polar groups on the surface, both performed by chemical and/or physical means. A chemical treatment is usually made by chlorination, which modifies the scale edges of wool and increases the critical surface tension of the fibers. In such a manner, the chlorinated fibers are made more wettable and dyeable and can be coated with polymers, conferring the shrink-resist effect. However, many research works are carried out to find alternative processes that avoid chlorination in order to remove the problem of the formation of absorbable organohalogen compounds in wastewaters [4]. To this aim, plasma treatments have extensively been studied, but even other cheaper eco-friendly processes have been experimented, in particular for dyeability improve‐ ment, such as treatment with enzymes or ultraviolet (UV) irradiation. A list of selected references is reported in Table 1.

Cotton and cellulose fibers are more homogeneous than wool and are richer in hydroxyl groups ththat confer higher hydrophilicity; hence, their surface modifications are mainly directed to confer hydro and oil repellency. This topic will be treated in paragraphs 3 and 4. Moreover, the exhaust dyeing of cotton with anionic dyes, i.e., direct and reactive, request a high concentration of electrolytes in dyebath to reduce negative charges on the fiber surface and to promote the exhaustion of dyes. This requirement creates environmental issues due to the removal of high concentrations of salts and dyes from wastewaters. To overcome such

**Table 1.** Processes of wool surface modifications.

The wettability of a surface depends on the surface tension of the liquid that goes into contact with the same. Water has a very high surface tension (72.8 mN/m), so it tends to wet only surfaces bearing highly polar groups; otherwise, it forms spherical drops with contact angles higher than 90°. Instead, apolar liquids of lower surface tension get drops flatter than those of water. Hydrophobic or oleophobic surfaces are difficult to wet by water or apolar liquids, respective‐ ly, and are called low-energy surfaces. Wetting, in reality, is much more complex than as described by classical laws. This primarily comes from the non-ideality of solid substrates that are both rough and chemically heterogeneous [1]. Such a situation commonly occurs in the case

The surface modification of textile fibers can be achieved by physical or chemical methods or by the combination of both. Plasma treatments and exposure to radiations are mainly represen‐ tative of physical methods, although their effects are often accomplished in the presence of reactive gases or after impregnation with suitable chemicals. However, chemical treatments can generally be carried out with oxidants or other finishing agents, followed by thermal treatment. Among the latter methods, sol–gel techniques are the more promising for surface

Among the textile fibers, there are many differences regarding wettability and surface struc‐ ture. Natural fibers have cellular structures that are more complex than those of man-made fibers obtained by chemical spinning. Wool and fine animal fibers are mainly composed of keratin, but show the structure of composite material formed by an assembly of cuticle cells in the form of scales and cortical cells surrounded by a keratin cell membrane and held together by an intercellular cement. The cell membrane consists of a chemically resistant protein layer and a lipidic layer that constitutes a hydrophobic barrier to the transfer of water and dye molecules from an aqueous solution [3]. Therefore, a wettability improvement of these fibers can be obtained by the removal of the hydrophobic lipidic layer and by the introduction of polar groups on the surface, both performed by chemical and/or physical means. A chemical treatment is usually made by chlorination, which modifies the scale edges of wool and increases the critical surface tension of the fibers. In such a manner, the chlorinated fibers are made more wettable and dyeable and can be coated with polymers, conferring the shrink-resist effect. However, many research works are carried out to find alternative processes that avoid chlorination in order to remove the problem of the formation of absorbable organohalogen compounds in wastewaters [4]. To this aim, plasma treatments have extensively been studied, but even other cheaper eco-friendly processes have been experimented, in particular for dyeability improve‐ ment, such as treatment with enzymes or ultraviolet (UV) irradiation. A list of selected references

Cotton and cellulose fibers are more homogeneous than wool and are richer in hydroxyl groups ththat confer higher hydrophilicity; hence, their surface modifications are mainly directed to confer hydro and oil repellency. This topic will be treated in paragraphs 3 and 4. Moreover, the exhaust dyeing of cotton with anionic dyes, i.e., direct and reactive, request a high concentration of electrolytes in dyebath to reduce negative charges on the fiber surface and to promote the exhaustion of dyes. This requirement creates environmental issues due to the removal of high concentrations of salts and dyes from wastewaters. To overcome such

of textile materials and can be evidenced by the hysteresis of the contact angle [2].

modification.

140 Wetting and Wettability

is reported in Table 1.

problems, many treatments with plasma, chemicals, and polymers were experimented to impart a cationic character to the cotton fiber surface [27]. Chitosan, 2-amino-2-deoxy-(1 → 4) β-D-glucopyranan, derived from the deacetylation of the chitin component of the shells of crustaceans, is undoubtedly one of the more promising multifunctional polymers for surface modification of textiles [28]. It is a biopolymer with unique properties such as biodegradability, nontoxicity, and antimicrobial activity; hence, it was mainly applied to textiles as an antimi‐ crobial finishing agent. Moreover, cotton treated with chitosan shows improved absorption of anionic dyes due to electrostatic attraction arising from the cationized amino groups of chitosan in an acidic medium. However, chitosan should stably be bonded to the fiber surface to ensure the fastness of treatment to washing. To this aim, crosslinking agents such as dialdehydes are used, although these are toxic chemicals. On the contrary, an eco-friendly grafting of chitosan onto cotton can be carried out by radical UV curing in the presence of a low concentration of a photoinitiator [29, 30].

A list of selected references on the surface modification of cotton and cellulose fibers is reported in Table 2, whereas a recent review was published by Kalia et al. [31].

**Table 2.** Processes of surface modifications of cotton and cellulose fibers.

Synthetic fibers such as polyamide and polyester have a compact structure with a low content of polar groups, whereas polypropylene is lacking of them; these are substantially hydropho‐ bic and can be subjected to surface etching by plasma and oxidation to increase porosity and wettability, but the latter purpose is often pursued by grafting of polar monomers or applica‐ tion of hydrophilic coating.

In a similar manner, hydrophobicity and oleophobicity can be increased with a suitable coating obtained by plasma. A selection of articles published in the last 15 years is reported in Table 3.

APP: Atmospheric pressure plasma; LPP: low-pressure plasma; PA: polyamide; PET: polyethylene terephtalate; PP: polypropylene.

**Table 3.** Selected articles on the surface modification of synthetic fibers by plasma treatment.

#### **2. Wettability by plasma treatments**

chitosan in an acidic medium. However, chitosan should stably be bonded to the fiber surface to ensure the fastness of treatment to washing. To this aim, crosslinking agents such as dialdehydes are used, although these are toxic chemicals. On the contrary, an eco-friendly grafting of chitosan onto cotton can be carried out by radical UV curing in the presence of a

A list of selected references on the surface modification of cotton and cellulose fibers is reported

in Table 2, whereas a recent review was published by Kalia et al. [31].

**Process type Topic Reference** LPP, APP Penetration into textile structures Poll 2001 [32]

LPP Dyeability of fabrics Ozdogan 2002 [33]

LPP Repellent coating Allan 2002 [34]

APP Hydrophobic coating Kim 2006 [37]

LPP Dyeability of Tencel Mak 2006 [40]

APP Dyeability of fabrics by acid dyes Karahan 2008 [38]

LPP Hydrophilicity improvement Pandiyaraj 2008 [39]

Chitosan Crosslinking for antimicrobial cotton El-tahlawy 2005 [41]

Chitosan Crosslinking on UV-irradiated fibers Alonso 2009 [42] Chitosan UV curing for antimicrobial textiles Ferrero 2012 [29]

Chitosan UV curing for antimicrobial textiles Periolatto 2012 [30]

Chitosan UV curing for antimicrobial cotton Ferrero 2013 [43]

Synthetic fibers such as polyamide and polyester have a compact structure with a low content of polar groups, whereas polypropylene is lacking of them; these are substantially hydropho‐ bic and can be subjected to surface etching by plasma and oxidation to increase porosity and wettability, but the latter purpose is often pursued by grafting of polar monomers or applica‐

In a similar manner, hydrophobicity and oleophobicity can be increased with a suitable coating obtained by plasma. A selection of articles published in the last 15 years is reported in Table 3.

APP: atmospheric pressure plasma; LPP: low-pressure plasma.

tion of hydrophilic coating.

**Table 2.** Processes of surface modifications of cotton and cellulose fibers.

LPP Fluorination McCord 2003 [35]

APP Bleaching and dyeing Prabaharan 2005 [36]

low concentration of a photoinitiator [29, 30].

142 Wetting and Wettability

Plasma is commonly defined as an ionized gas in a neutral state with an equal density of positive and negative charges. It is often referred to as the "fourth state of matter," which can be reached in a wide range of temperatures and pressures. From a chemical point of view, plasma mostly consists of a mix of activated gaseous particles comprising free electrons, radicals, ions, UV radiations, and various highly excited neutral and charged species. It is considered to be a very interesting medium for material processing technologies, with particular regard to surface engineering. In fact, a large variety of treatments aimed at surface modification of different substrates can be carried out, including etching, cleaning, activation, and coating, as detailed below:

**•** *Etching*: the removal of the bulk substrate material, occurs when the interaction between the solid surface and plasma generates gaseous byproducts, including atoms or molecules, carried away from the surface substrate, removing minimal fractions of bulk material.

Plasmas can be classified by taking into account the employed generation technology (power supply and pressure range) into two major categories: thermal plasmas (very high tempera‐ ture, not suitable for heat-sensitive materials) and non-thermal plasmas (close to room temperature and suitable for treating textiles). Non-thermal plasmas are also known as lowtemperature plasmas and can be subdivided into many different technologies considering the electrical power supply, the operating pressure (low or atmospheric), and the geometrical arrangements.

The laws of plasma physics would make it easier to generate large-volume plasmas at reduced pressure rather than at atmospheric pressure. Moreover, in a closed system under low pressure, it is easier to control the characteristics and composition of the gas atmosphere from which the plasma is generated and, hence, the process chemistry rather than in a system at atmospheric pressure open to ambient air. Nevertheless, a closed system is not easily adaptable to a continuous process of fabric treatment. Therefore, although most of the plasma applica‐ tions on polymeric materials, including textiles, have been studied using low-pressure plasma (LPP), the atmospheric pressure plasma (APP) technique has demonstrated to be the most interesting tool for large-scale applications on textiles.

Plasma treatments are able to modify the fiber surface, leaving the bulk properties unaffected, and this characteristic is very important for the modification of textile fibers that should not lose their mechanical and chemical properties after treatment. Moreover, the finishing of textile fabrics by plasma technologies can advantageously replace some wet chemical applications as environmental friendly processes, since they do not require water and a high amount of chemicals. By controlling the plasma variables, such as the nature of gas, discharge power, pressure, and exposure time, a great variety of surface properties can be improved, mainly cleaning, wettability, hydrophobic and oleophobic properties, soil release, adhesion of coatings, dyeability, printability, and flame resistance.

An exhaustive book on the applications of plasma technologies to textiles was published by Shishoo [62], whereas the surface modifications by plasma treatments were reviewed by Radu et al. [63] and Morent et al. [64]. Reviews on atmospheric plasma treatments were published by Kale et al. [65] and, more recently, by Wolf [66]. In particular, the plasma pre-treatments to improve dyeability were considered by Deshmukh and Bhat [67], whereas Hossain and Hegemann studied the deposition of thin coatings on synthetic fibers to confer a substrate independent dyeability [68].

The modification induced by plasma treatment on a polymeric surface as a film is easily measured by contact angle determination with the sessile drop method. In the case of textile materials, instead, the measure is strongly affected by the heterogeneous surface structure; therefore, the porosity of the fabrics can often determine a suction effect on the water drop, preventing the contact angle determination. Another technique consists of weight variation measurement by a Wilhelmy balance during capillary wicking. The variety of techniques commonly used to measure contact angles has recently been highlighted by Yuan et al. [69].

Moreover, the hydrophilicity of plasma-treated fabrics can be tested according to the BS 4554:1970 method, known as the drop test, in which a drop of 100.0 µL of deionized water is placed on the surface of the specimen. The time required for the droplet to completely penetrate the fabric was measured by means of a stopwatch.

Poll et al. [32] measured the hydrophilization effect induced by plasma through the suction test.  The liquid is absorbed by the fabric to form a colored circle. The diameter of the circle formed after an exposure time of 20 s is a measure of the hydrophilization effect.

Another wettability test can be performed on a fabric strip that is kept vertical, with the lower end immersed in water–dye liquor. A spontaneous wicking occurs due to capillary forces. The absorption height *h* is recorded as a function of time, and the absorption rate is calculated (capillary rise method, as shown in Figure 1; reprinted with the kind permission of the author in [70]).

**Figure 1.** Capillary rise method.

**•** *Cleaning*: the removal of contamination in the form of etching, but with very high selectivity. Only the unwanted surface contaminant is volatilized and removed, whereas the substrate

**•** *Activation*: the enhancement of the substrate energy, which generates chemically reactive

**•** *Coating*: the deposition of a functional thin film, occurs if the plasma–solid surface interac‐ tion creates a solid-phase material. This process is sometimes called plasma enhanced

Plasmas can be classified by taking into account the employed generation technology (power supply and pressure range) into two major categories: thermal plasmas (very high tempera‐ ture, not suitable for heat-sensitive materials) and non-thermal plasmas (close to room temperature and suitable for treating textiles). Non-thermal plasmas are also known as lowtemperature plasmas and can be subdivided into many different technologies considering the electrical power supply, the operating pressure (low or atmospheric), and the geometrical

The laws of plasma physics would make it easier to generate large-volume plasmas at reduced pressure rather than at atmospheric pressure. Moreover, in a closed system under low pressure, it is easier to control the characteristics and composition of the gas atmosphere from which the plasma is generated and, hence, the process chemistry rather than in a system at atmospheric pressure open to ambient air. Nevertheless, a closed system is not easily adaptable to a continuous process of fabric treatment. Therefore, although most of the plasma applica‐ tions on polymeric materials, including textiles, have been studied using low-pressure plasma (LPP), the atmospheric pressure plasma (APP) technique has demonstrated to be the most

Plasma treatments are able to modify the fiber surface, leaving the bulk properties unaffected, and this characteristic is very important for the modification of textile fibers that should not lose their mechanical and chemical properties after treatment. Moreover, the finishing of textile fabrics by plasma technologies can advantageously replace some wet chemical applications as environmental friendly processes, since they do not require water and a high amount of chemicals. By controlling the plasma variables, such as the nature of gas, discharge power, pressure, and exposure time, a great variety of surface properties can be improved, mainly cleaning, wettability, hydrophobic and oleophobic properties, soil release, adhesion of

An exhaustive book on the applications of plasma technologies to textiles was published by Shishoo [62], whereas the surface modifications by plasma treatments were reviewed by Radu et al. [63] and Morent et al. [64]. Reviews on atmospheric plasma treatments were published by Kale et al. [65] and, more recently, by Wolf [66]. In particular, the plasma pre-treatments to improve dyeability were considered by Deshmukh and Bhat [67], whereas Hossain and Hegemann studied the deposition of thin coatings on synthetic fibers to confer a substrate

remains unaffected by the process.

arrangements.

144 Wetting and Wettability

sites on a previously nonreactive surface.

chemical vapor deposition or plasma polymerization.

interesting tool for large-scale applications on textiles.

coatings, dyeability, printability, and flame resistance.

independent dyeability [68].

Ferrero [58] applied this method to the wettability measurements on plasma-treated synthetic fabrics (polyester and acrylic). The processing of capillary rise data proposed in this work allowed the assessment of wettability improvement by plasma treatment carried out in different gases (nitrogen, air, and oxygen). Wettability is strongly enhanced by plasma treatment, and after some time, the height reaches an equilibrium value *heq*, as shown, for example, in Figure 2, where the wicking curves of untreated and plasma-treated PETs are compared. It is evident that wettability is strongly improved by a mild nitrogen plasma treatment (25 W, 30 s, 65-Pa pressure in a Plasmod apparatus).

**Figure 2.** Comparison between the wicking curves of untreated and plasma-treated PET fabrics.

The maximum equilibrium height *h*eq can be related to the equilibrium static contact angle *θeq*, generally smaller than the dynamic one, by equation (1):

$$h\_{eq} = \frac{2\gamma\cos\theta\_{eq}}{\rho g R\_s} \tag{1}$$

where *γ* and *ρ* are the surface tension and density of the liquid, respectively, *RS* is the mean static radius of pores, and *g* is the gravity acceleration. In the early stages of the process, the hydrostatic pressure in equation (1) can be neglected; hence, *h* can be related to *θ*, advancing contact angle of the liquid on the solid, by Washburn's equation (2):

$$h^2 = \frac{r\chi\cos\theta}{2\eta}t\tag{2}$$

where *r* in fiber networks means an equivalent radius of the capillary porous structure, and *η* is the viscosity of the liquid.

Hence, *h2* values plotted against time show a straight line according to equation (3):

$$h^2 = D \cdot t \tag{3}$$

where the slope *D* is a capillary diffusion coefficient related to the size of the capillaries *r* and to the physicochemical characteristics of the liquid. Therefore, a surface treatment of a fabric that modifies *r* and the contact angle, such as plasma treatment, causes variation of this diffusion coefficient. It was observed that *D* is affected by the nature of the gas plasma, power, exposure time, and aging. On polyester fabric, nitrogen plasma induces higher wettability than air and oxygen, probably mainly due to surface etching, whereas the wettability of acrylic fabric slightly increases in air plasma with respect to nitrogen.

### **3. Water and oil repellency by UV curing**

different gases (nitrogen, air, and oxygen). Wettability is strongly enhanced by plasma treatment, and after some time, the height reaches an equilibrium value *heq*, as shown, for example, in Figure 2, where the wicking curves of untreated and plasma-treated PETs are compared. It is evident that wettability is strongly improved by a mild nitrogen plasma

treatment (25 W, 30 s, 65-Pa pressure in a Plasmod apparatus).

**Figure 2.** Comparison between the wicking curves of untreated and plasma-treated PET fabrics.

*eq*

*h*

contact angle of the liquid on the solid, by Washburn's equation (2):

fabric slightly increases in air plasma with respect to nitrogen.

generally smaller than the dynamic one, by equation (1):

is the viscosity of the liquid.

Hence, *h2*

146 Wetting and Wettability

The maximum equilibrium height *h*eq can be related to the equilibrium static contact angle *θeq*,

2 cos *eq*

*gR* g q

r

<sup>2</sup> cos 2 *<sup>r</sup> h t* g q

h

where *r* in fiber networks means an equivalent radius of the capillary porous structure, and *η*

values plotted against time show a straight line according to equation (3):

where the slope *D* is a capillary diffusion coefficient related to the size of the capillaries *r* and to the physicochemical characteristics of the liquid. Therefore, a surface treatment of a fabric that modifies *r* and the contact angle, such as plasma treatment, causes variation of this diffusion coefficient. It was observed that *D* is affected by the nature of the gas plasma, power, exposure time, and aging. On polyester fabric, nitrogen plasma induces higher wettability than air and oxygen, probably mainly due to surface etching, whereas the wettability of acrylic

*S*

where *γ* and *ρ* are the surface tension and density of the liquid, respectively, *RS* is the mean static radius of pores, and *g* is the gravity acceleration. In the early stages of the process, the hydrostatic pressure in equation (1) can be neglected; hence, *h* can be related to *θ*, advancing

<sup>=</sup> (1)

<sup>=</sup> (2)

<sup>2</sup> *h Dt* = × (3)

Cotton has always been the principal fiber for clothing fabrics due to its attractive character‐ istics such as softness, comfort, warmness, biodegradability, and low cost. However, the high concentration of hydroxyl groups on the cotton surface makes the fabric water absorbent and easily stained by liquids. Therefore, additional finishes are required to impart hydrophobicity and self-cleaning properties to cotton fabrics. The same finishes are applied to other fabrics, although based on less hydrophilic fibers such as wool, silk, polyamides, and polyester.

In general, water repellency of a fabric can be defined as the fabric's ability to withstand wetting or penetration by water under test conditions. It is important to distinguish between the terms "water repellent" and "waterproof". A fabric is made water repellent by the surface modifi‐ cation or deposition of hydrophobic material on the fibers. Water repellent fabrics have open pores and are permeable to air and water vapor. They are resistant to wetting by rain drops, water spreading, and wicking. Waterproofing involves filling the pores in the fabric with a material that is impermeable to water and, usually, to air as well. Water-repellent, but not waterproof, fabrics allow passage of water once the hydrostatic pressure is sufficiently high. Waterproof and water-repellent finishes are required, in particular, for cotton fabrics.

Polysiloxanes are widely used for textile finishing to impart desirable properties such as softness, crease resistance, and water repellency. However, the specific properties conferred by siloxanes depend on the nature of organic functional groups that are incorporated in the polymer structure [71]. Moreover, water and oil repellency is required for protective clothes and is currently achieved by thermal polymerization of fluorinated monomers, which enable a strong increase of water and oil contact angles on the treated fabrics [72]. However, the application of a polymeric coating to a cotton fabric in the form of a thin film ensures good homogeneity of the conferred properties, but the fabric could lose comfort characteristics, such as handling and breathability. Therefore, an alternative method that allows the uniform adsorption of monomers onto each fiber and the formation of polymer chains inside the fibers should be preferred, since the interpenetration of components and uniform distribution of monomers, even at a low concentration, contribute to obtaining textile materials with modified surface properties without a high add-on of polymer. This result can be achieved by a radiation curing method.

Radiation processes have several commercial applications for the coating of metals, plastics, and glass in printing, wood finishing, film and plastic crosslinking, and in adhesives and electrical insulations. The advantages of this technology are well known: energy savings (lowtemperature process), low environmental impact (no solvent emissions), simple, cheap, small equipment, and high treatment speed. Despite these advantages, there have been few appli‐ cations of radiation curing in the textile industry, such as nonwoven fabric bonding, fabric coating, pigment printing, silk grafting, and surface modification of cotton and synthetic fibers [73, 74]. In fact, in textile finishing processes, the conventional thermal curing technique is still used, regardless of energy consumption and cost. Among the textile finishing processes by radiation curing, pigment printing of fabrics has received much attention [75], whereas coatings for shrink-resistant wool, flame-retardant fabrics, and durable press finishes have also been investigated. Recently, studies on the effects of radiations on textile dyeing have been reviewed by Bhatti et al. [76], whereas the application of ultraviolet irradiation to wool dyeing processes has been experimented [24–26].

Water-repellent fabrics have been obtained by γ-radiation grafting of poly(vinyl methyl siloxane) or methyl hydrogen silicone on hydrophilic substrates. In industrial applications, UV light from a mercury vapor lamp is preferred for thin coatings because of its high efficiency of energy absorption and low equipment cost. In UV curing, radical or cationic species are generated by the interaction of UV light with a suitable photoinitiator, which quickly induces the curing reaction of reactive monomers and oligomers at low temperature, with lower environmental impact and lower process cost than the thermal process. If a monomer and photoinitiator mixture is adsorbed onto the fibers and subsequently UV cured, the polymeric chains can form inside the textile structure, which can be also involved in the formation of graft bonds, making the treatment solid and water resistant.

Ferrero et al. [77] proposed the water-repellent finishing of cotton fabrics by radical UV curing of silicone and urethane-acrylates with different formulations. The results of contact angle, wettability, and moisture adsorption showed that water repellency is already significant at a low resin add-on, whereas the treated fabric maintains its own breathability. SEM analysis confirmed that UV curing yields a coating layer onto each single fiber than a film on the fabric surface.

Polyester and nylon fabrics were made superhydrophobic by the UV curing of a polydime‐ thylsiloxane-containing polyurethane oligomer that was synthesized on purpose. The UVcurable system helps the super hydro-repellent polydimethylsiloxane moiety to anchor onto textile surface, improving the washing stability of the treatment [78].

Moreover, photografting as a surface modification method to provide permanent wettability and wicking performance to deep-groove polypropylene fibers was proposed by Zhu and Hirt [79]. In this case, polyacrylamide and polyacrylic acid were grafted on the fibers by UV irradiation; then, the advancing water contact angle on single fibers decreased from 100° to 55°, and spontaneous wicking of water was observed after surface modification.

On the other hand, a number of research papers have been published on the production and application of different types of fluorochemicals for textile finishing. Fluorochemicals are organic compounds consisting of perfluorinated carbon chains with more fluorine than hydrogens attached to carbon, having thermal and chemical stability. These chains, evenly distributed on the fiber with proper orientation, present an essentially fluorinated surface, which imparts water and oil repellency. In fact, the critical surface tension for fluorocarbon surfaces is in the range of 6 mN/m (-CF3) to 28 mN/m, whereas for bleached cotton, it is 44 mN/ m. One of the most successful ways of obtaining this condition is the incorporation of the fluorinated groups into polymer molecules in which perfluoro groups constitute the side chains [80]. The fluorochemicals used nowadays are based on C6 carbon chains, which have substituted the C8 fluorocarbons that release perfluorooctanesulfonate and perfluorooctanoic acid, higly hazardous and toxic substances. Selected articles regarding the surface modification of fibers achieved by fluorination are listed in Table 4.

**Table 4.** Selected articles on the surface modification of textile fibers by fluorination.

been investigated. Recently, studies on the effects of radiations on textile dyeing have been reviewed by Bhatti et al. [76], whereas the application of ultraviolet irradiation to wool dyeing

Water-repellent fabrics have been obtained by γ-radiation grafting of poly(vinyl methyl siloxane) or methyl hydrogen silicone on hydrophilic substrates. In industrial applications, UV light from a mercury vapor lamp is preferred for thin coatings because of its high efficiency of energy absorption and low equipment cost. In UV curing, radical or cationic species are generated by the interaction of UV light with a suitable photoinitiator, which quickly induces the curing reaction of reactive monomers and oligomers at low temperature, with lower environmental impact and lower process cost than the thermal process. If a monomer and photoinitiator mixture is adsorbed onto the fibers and subsequently UV cured, the polymeric chains can form inside the textile structure, which can be also involved in the formation of

Ferrero et al. [77] proposed the water-repellent finishing of cotton fabrics by radical UV curing of silicone and urethane-acrylates with different formulations. The results of contact angle, wettability, and moisture adsorption showed that water repellency is already significant at a low resin add-on, whereas the treated fabric maintains its own breathability. SEM analysis confirmed that UV curing yields a coating layer onto each single fiber than a film on the fabric

Polyester and nylon fabrics were made superhydrophobic by the UV curing of a polydime‐ thylsiloxane-containing polyurethane oligomer that was synthesized on purpose. The UVcurable system helps the super hydro-repellent polydimethylsiloxane moiety to anchor onto

Moreover, photografting as a surface modification method to provide permanent wettability and wicking performance to deep-groove polypropylene fibers was proposed by Zhu and Hirt [79]. In this case, polyacrylamide and polyacrylic acid were grafted on the fibers by UV irradiation; then, the advancing water contact angle on single fibers decreased from 100° to

On the other hand, a number of research papers have been published on the production and application of different types of fluorochemicals for textile finishing. Fluorochemicals are organic compounds consisting of perfluorinated carbon chains with more fluorine than hydrogens attached to carbon, having thermal and chemical stability. These chains, evenly distributed on the fiber with proper orientation, present an essentially fluorinated surface, which imparts water and oil repellency. In fact, the critical surface tension for fluorocarbon surfaces is in the range of 6 mN/m (-CF3) to 28 mN/m, whereas for bleached cotton, it is 44 mN/ m. One of the most successful ways of obtaining this condition is the incorporation of the fluorinated groups into polymer molecules in which perfluoro groups constitute the side chains [80]. The fluorochemicals used nowadays are based on C6 carbon chains, which have substituted the C8 fluorocarbons that release perfluorooctanesulfonate and perfluorooctanoic acid, higly hazardous and toxic substances. Selected articles regarding the surface modification

55°, and spontaneous wicking of water was observed after surface modification.

processes has been experimented [24–26].

surface.

148 Wetting and Wettability

graft bonds, making the treatment solid and water resistant.

textile surface, improving the washing stability of the treatment [78].

of fibers achieved by fluorination are listed in Table 4.

Fluorochemical finishings are commercially available as water emulsions and are applied to fabrics by the pad–dry–cure method, i.e., bath impregnation followed by squeezing, drying in air at 80–100 °C, and final curing at 150–175 °C in hot flue for some minutes. Fluorochemicals give water-repellent and soil-release finishes in conjunction with other water repellents, called extenders, which are able to yield fiber coatings with good resistance to washing. Castelvetro et al. [81] studied the performance of fluoropolymer latexes applied by padding to wool, cotton, and polyester fabrics. They evaluated the performances of the fabrics by means of technological standard test methods whose results correlated well with static and dynamic contact angle measurements.

Alternative fluorination methods have been proposed. Maity et al. [90] experimented the direct fluorination of cotton using elemental fluorine and admicellar polymerization, with a surfac‐ tant and fluoromonomer system. Selli et al. [91] used a SF6 plasma to confer water and oil repellency to cotton and PET, whereas plasma sputtering was used by Wi et al. to obtain a water-repellent PTFE coating on cotton fibers [92].

On the other hand, Ferrero et al. [88] extended the study of the UV-curing method to the use of perfluoro-alkyl-polyacrylate resins that are able to impart water as well as oil repellency to cotton fabrics, and the results obtained by UV curing were compared with those obtained by conventional thermal polymerization. This study was focused on the use of commercial finishes for thermal application, Repellan EPF and NFC, by Pulcra Chemicals, and Oleophobol CP-C, by Huntsman, supplied in water emulsions (about 17% solid content, dispersible in cold water in all ratios). Darocur 1173 (2-hydroxy-2-methyl-1-phenylpropan-1-one supplied by Ciba Specialty Chemicals) as a radical photoinitiator was added in an amount of 2% weight on the resin, enough to obtain a film by UV curing with each formulation considered. Water was added as a diluent to the mixtures, continuously stirred until complete homogeneity, in order to enable uniform spread of the liquids on cotton. The formulations were applied by dipping onto strips of fabric that were subsequently dried in an oven. The amount of resin put on the fabrics was adjusted according to the desired final weight add-on and the emulsion concentration. Weight percentages of 3% and 5% on the weight fiber were usually applied in order to obtain the desired properties without loss of fabric handling.

The surface-coated fabrics were exposed to UV radiation using a medium-pressure mercury lamp with a light irradiance on the fabric of about 20 mW/cm2 , in a small box equipped with a quartz window under nitrogen atmosphere, since oxygen interferes with the formation of radicals. The required radiation dose was obtained by adjusting the distance of the textile from the lamp and the exposure time, which was assessed between 40 and 60 s. Instead, thermal curing was carried out in 2–3 min at 140 °C or 150 °C according to the indications of the producer.

Resin emulsion is adsorbed by the fibers, so the polymerized product does not form films onto the fabric surface, but penetrate inside. To test if UV curing was effective even inside the fabric compared with the thermal treatment, the polymerization yield was evaluated by the deter‐ mination of the unpolymerized resin extracted by chloroform at room temperature from the cured fabrics. Repellan EPF shows the highest yields after UV curing and is about similar to those reached with the thermal treatment (93–96%), whereas Repellan NFC shows lower, although acceptable, yields in UV curing (80–81%) than in the thermal one (98%). With these finishes, the yields remained unaffected by exposure time and resin add-on. Oleophobol CP-C gives lower yields either in thermal or UV curing, with a marked dependence on add-on and exposure time; hence, 60 s is needed to obtain a good yield for a 3% add-on (91%).

The surface properties of coated and uncoated textiles were tested with optical measurements of static and dynamic contact angles of water and oil drops on the textile. The measuring liquids were HPLC grade water (72.8 mN/m at 25 °C) and olive oil (32.0 mN/m). The contact angle values should be higher, as the hydrophobic or oil repellency behavior of the textile is greater. On cotton samples finished with both curing methods, water and oil repellency fastness to domestic washing was evaluated after five washings according to UNI-EN ISO 105-C01.

In Figure 3, the results of dynamic contact angle measurements of water on cotton finished by Repellans before and after washing are compared. In this evaluation, the analysis of advancing and receding contact angles and the resulting difference, i.e. the hysteresis, can give informa‐ tion on the influence of surface roughness and chemical heterogeneity on fabric wettability [81]. A Δθ>0 is typical of most real surfaces, as confirmed by all the results obtained. With both resins, the advancing contact angles were slightly reduced after five washing cycles, and this proved the good wash fastness of water repellency, regardless of the curing type and polymer add-on. The hysteresis values generally decreased, indicating a lower surface heterogeneity, probably due to the washing effect. Oleophobol gave slightly lower contact angles but was practically unaffected by repeated washings.

water in all ratios). Darocur 1173 (2-hydroxy-2-methyl-1-phenylpropan-1-one supplied by Ciba Specialty Chemicals) as a radical photoinitiator was added in an amount of 2% weight on the resin, enough to obtain a film by UV curing with each formulation considered. Water was added as a diluent to the mixtures, continuously stirred until complete homogeneity, in order to enable uniform spread of the liquids on cotton. The formulations were applied by dipping onto strips of fabric that were subsequently dried in an oven. The amount of resin put on the fabrics was adjusted according to the desired final weight add-on and the emulsion concentration. Weight percentages of 3% and 5% on the weight fiber were usually applied in

The surface-coated fabrics were exposed to UV radiation using a medium-pressure mercury

a quartz window under nitrogen atmosphere, since oxygen interferes with the formation of radicals. The required radiation dose was obtained by adjusting the distance of the textile from the lamp and the exposure time, which was assessed between 40 and 60 s. Instead, thermal curing was carried out in 2–3 min at 140 °C or 150 °C according to the indications of the

Resin emulsion is adsorbed by the fibers, so the polymerized product does not form films onto the fabric surface, but penetrate inside. To test if UV curing was effective even inside the fabric compared with the thermal treatment, the polymerization yield was evaluated by the deter‐ mination of the unpolymerized resin extracted by chloroform at room temperature from the cured fabrics. Repellan EPF shows the highest yields after UV curing and is about similar to those reached with the thermal treatment (93–96%), whereas Repellan NFC shows lower, although acceptable, yields in UV curing (80–81%) than in the thermal one (98%). With these finishes, the yields remained unaffected by exposure time and resin add-on. Oleophobol CP-C gives lower yields either in thermal or UV curing, with a marked dependence on add-on and exposure time; hence, 60 s is needed to obtain a good yield for a 3% add-on (91%).

The surface properties of coated and uncoated textiles were tested with optical measurements of static and dynamic contact angles of water and oil drops on the textile. The measuring liquids were HPLC grade water (72.8 mN/m at 25 °C) and olive oil (32.0 mN/m). The contact angle values should be higher, as the hydrophobic or oil repellency behavior of the textile is greater. On cotton samples finished with both curing methods, water and oil repellency fastness to domestic washing was evaluated after five washings according to UNI-EN ISO 105-C01.

In Figure 3, the results of dynamic contact angle measurements of water on cotton finished by Repellans before and after washing are compared. In this evaluation, the analysis of advancing and receding contact angles and the resulting difference, i.e. the hysteresis, can give informa‐ tion on the influence of surface roughness and chemical heterogeneity on fabric wettability [81]. A Δθ>0 is typical of most real surfaces, as confirmed by all the results obtained. With both resins, the advancing contact angles were slightly reduced after five washing cycles, and this proved the good wash fastness of water repellency, regardless of the curing type and polymer add-on. The hysteresis values generally decreased, indicating a lower surface heterogeneity, probably due to the washing effect. Oleophobol gave slightly lower contact angles but was

, in a small box equipped with

order to obtain the desired properties without loss of fabric handling.

lamp with a light irradiance on the fabric of about 20 mW/cm2

practically unaffected by repeated washings.

producer.

150 Wetting and Wettability

**Figure 3.** Dynamic contact angles of water before and after washing on cotton fabrics finished with Repellan EPF and NFC (adv: advancing; rec: receding) [with kind permission from Springer Science+Business Media: Ferrero F., Periolat‐ to M., Udrescu C. Water- and oil-repellent coatings of perfluoro-polyacrylate resins on cotton fibers: UV curing in com‐ parison with thermal polymerization. Fibers and Polymers 2012; 13 (2), 191–198, p. 195, Fig. 1].

Static contact angles of oil before and after washing are compared in Figure 4, and the results confirmed the satisfactory wash fastness of oil repellency, in particular with Repellan NFC, without differences between the thermal and UV curing methods.

**Figure 4.** Static contact angles of oil before and after washing on cotton fabrics finished with Repellan EPF and NFC. [with kind permission from Springer Science+Business Media: Ferrero F., Periolatto M., Udrescu C. Water and oil-re‐ pellent coatings of perfluoro-polyacrylate resins on cotton fibers: UV curing in comparison with thermal polymeriza‐ tion. Fibers and Polymers 2012; 13(2), 191–198, p. 195, Fig. 2].

The contact angle value on untreated cotton, both with water and oil, was 0° due to the immediate absorption of the drops. It is evident of the high water and oil repellency conferred by the treatment. Measurements on 10 different points of the same sample surface are in good agreement (average values estimated with a confidence interval of ±2° at a 95% confidence level), showing a good uniformity of the coating. The results of thermal and UV curing are very close and poorly affected by weight gain and UV curing time, suggesting that a low polymer add-on is enough to modify the fiber surface.

With each finishing type, water contact angles are higher than with oil, in agreement with the results reported in the literature with other finishes on cotton [84, 94], although the values are lower than 150°, which is considered the lower limit for super hydrophobic surfaces showing the so-called Lotus effect. However, the UV-cured resins yielded oil contact angles mostly higher than 120°, denoting super oil-repellent surfaces.

X-ray photoelectron spectroscopy (XPS) analysis gives the chemical composition of the fabric surface and provides useful information on the fiber coating. Table 5 shows the relative peak intensities of C1s, O1s, F1s, and Cl2p in XPS measurements of untreated and finished cotton fabrics. For the untreated cotton, only two peaks corresponding to C and O are observed. F1s intensity was found to be about the same for samples that were thermally or UV cured, whereas Repellan NFC showed the lowest values.

**Table 5.** Relative intensities in the XPS spectra of untreated and resin-treated cotton fabrics (3% polymer add-on and 60-s UV curing time).

Information on how fluorine binds to the polymer surface can be obtained from the highresolution C1s signals. According to Selli et al. [91], the C1s spectrum was resolved into six components corresponding to the groups reported in Table 6 with the relative peak areas. For each resin, small differences arise from the comparison between thermal and UV curing, whereas higher differences can be observed between coatings of the different fluorocarbons. With Oleophobol CP-C, the coatings yielded the lowest percentage of the –CF2- groups and, conversely, the highest for the –CO- groups, although these differences did not affect water and oil repellency. However, in any case, a much lower concentration of the –CF3 groups was found. Such considerations suggest that the lower content of fluorine groups yielded by Repellan NFC coating is enough to confer the requested surface properties to cotton.

In conclusion, UV curing of cotton with commercial perfluoro-alkyl-polyacrylates applied in water emulsion yielded water- and oil-repellent cotton fabrics like the thermal process. The polymerization yields as well as the contact angles with water and oil were of the same order of those obtained with thermal curing, even at low-resin add-ons. Moreover, the UV-cured resins yielded mostly super oil-repellent surfaces, whereas water and oil repellency was adequately maintained after washing.

**Table 6.** High-resolution C1s spectra for resin-treated cotton fabrics (3% polymer add-on and 60-s UV curing time).

XPS analyses showed small differences between thermal and UV-cured coatings with each resin, whereas lower percentages of fluorine groups were observed in the case of Repellan NFC coatings without worsening of water and oil repellency, suggesting that such properties can be obtained with a low polymer add-on (3%) and with the lowest fluorine content.

Therefore, UV curing can be indicated as a valid alternative and environment-friendly method to confer water-resistant hydro and oil repellency to cotton fabrics. A comparison with plasma polymerization on cotton of the same perfluoro-alkyl-polyacrylates [93] confirmed that UV curing yields similar results, but with a simpler apparatus that can easily be introduced in the production lines of continuous fabric finishing.

#### **4. Water and oil repellency by sol–gel techniques**

very close and poorly affected by weight gain and UV curing time, suggesting that a low

With each finishing type, water contact angles are higher than with oil, in agreement with the results reported in the literature with other finishes on cotton [84, 94], although the values are lower than 150°, which is considered the lower limit for super hydrophobic surfaces showing the so-called Lotus effect. However, the UV-cured resins yielded oil contact angles mostly

X-ray photoelectron spectroscopy (XPS) analysis gives the chemical composition of the fabric surface and provides useful information on the fiber coating. Table 5 shows the relative peak intensities of C1s, O1s, F1s, and Cl2p in XPS measurements of untreated and finished cotton fabrics. For the untreated cotton, only two peaks corresponding to C and O are observed. F1s intensity was found to be about the same for samples that were thermally or UV cured, whereas

**Resin Curing C1s (%) O1s (%) F1s (%) Cl2p (%)**

UV 43.1 5.7 51.1 –

UV 46.0 8.7 43.5 1.7

UV 48.0 9.2 41.9 0.9

Untreated cotton – 60.6 39.4 – – Repellan EPF thermal 42.0 6.1 51.8 –

Repellan NFC thermal 44.7 10.7 43.3 1.3

Oleophobol CP-C thermal 46.4 7.7 44.7 1.3

**Table 5.** Relative intensities in the XPS spectra of untreated and resin-treated cotton fabrics (3% polymer add-on and

Information on how fluorine binds to the polymer surface can be obtained from the highresolution C1s signals. According to Selli et al. [91], the C1s spectrum was resolved into six components corresponding to the groups reported in Table 6 with the relative peak areas. For each resin, small differences arise from the comparison between thermal and UV curing, whereas higher differences can be observed between coatings of the different fluorocarbons. With Oleophobol CP-C, the coatings yielded the lowest percentage of the –CF2- groups and, conversely, the highest for the –CO- groups, although these differences did not affect water and oil repellency. However, in any case, a much lower concentration of the –CF3 groups was found. Such considerations suggest that the lower content of fluorine groups yielded by

Repellan NFC coating is enough to confer the requested surface properties to cotton.

In conclusion, UV curing of cotton with commercial perfluoro-alkyl-polyacrylates applied in water emulsion yielded water- and oil-repellent cotton fabrics like the thermal process. The polymerization yields as well as the contact angles with water and oil were of the same order of those obtained with thermal curing, even at low-resin add-ons. Moreover, the UV-cured resins yielded mostly super oil-repellent surfaces, whereas water and oil repellency was

polymer add-on is enough to modify the fiber surface.

higher than 120°, denoting super oil-repellent surfaces.

Repellan NFC showed the lowest values.

adequately maintained after washing.

60-s UV curing time).

152 Wetting and Wettability

There have been many articles in the literature on the improvement of hydrophobic properties of several kinds of fabrics using nanostructures achieved by nanotechnology. It was demon‐ strated that superhydrophobicity depends not only on surface chemistry but also on surface topology. Two theoretical models (Wenzel and Cassie–Baxter) have inspired how to engineer superhydrophobic surfaces by either roughening the same through microstructures or nanostructures or lowering the surface-free energy due to waxy materials applied on top of the rough structures, or both. An example is a microprocessing technique for producing rough surface and subsequent chemical treatment with silane- or fluorine-containing polymers to reduce the surface-free energy.

Roughened surfaces have commonly been obtained by the introduction of nano-size particles onto the pristine surface, and the sol–gel technique has been reported as a promising tool for the preparation of water-repellent coatings that is especially versatile for applications on glass, paper, and textile [95–100]. An exhaustive review on the application of sol–gel techniques to textiles has been published by Mahltig and Textor [101], and a series of selected articles is reported in Table 7.

**Table 7.** Selected articles on the surface modification of fabrics by sol–gel techniques.

In many research works, sol–gel formulations of fluoroalkylsilanes in combination with other silanes to obtain co-condensates are used. The solvents are mostly alcohols, but some waterbased systems have been described. In these nanocomposites, the organic and the inorganic networks are covalently bound and homogeneously intermingled at the nanometer scale so that the resulting coatings show enhanced mechanical stability [96].

These materials have a pronounced gradient structure, with a high concentration of fluoroalkyl groups at the coating–air interface so that only a small amount (1.7 mol%) of fluoroalkyl silane is necessary to obtain an effective repellency. Moreover, it accounts for an excellent adhesion of the coatings on various substrates such as glass, metals, and polymers. The gradient is due to the accumulation of surface-active fluorosilanol molecules and condensates at the interface.

Employing organically modified alkoxysilanes containing long-chained aliphatic or highly fluorinated groups, sol–gel offers far-reaching possibilities to prepare water- as well as oilrepellent textiles. A low required add-on is of great interest for textile applications; in fact, it keeps the typical hand and breathability of fabrics uncompromised. Furthermore, most fluorinated materials are very expensive and may often cause serious risks to the human health in case of skin contact and for the environment. Therefore, it is necessary to minimize the use of such substances.

**Fiber Topic Reference**

154 Wetting and Wettability

**Table 7.** Selected articles on the surface modification of fabrics by sol–gel techniques.

that the resulting coatings show enhanced mechanical stability [96].

In many research works, sol–gel formulations of fluoroalkylsilanes in combination with other silanes to obtain co-condensates are used. The solvents are mostly alcohols, but some waterbased systems have been described. In these nanocomposites, the organic and the inorganic networks are covalently bound and homogeneously intermingled at the nanometer scale so

These materials have a pronounced gradient structure, with a high concentration of fluoroalkyl groups at the coating–air interface so that only a small amount (1.7 mol%) of fluoroalkyl silane is necessary to obtain an effective repellency. Moreover, it accounts for an excellent adhesion of the coatings on various substrates such as glass, metals, and polymers. The gradient is due to the accumulation of surface-active fluorosilanol molecules and condensates at the interface.

Employing organically modified alkoxysilanes containing long-chained aliphatic or highly fluorinated groups, sol–gel offers far-reaching possibilities to prepare water- as well as oilrepellent textiles. A low required add-on is of great interest for textile applications; in fact, it keeps the typical hand and breathability of fabrics uncompromised. Furthermore, most

Nylon, PET/cotton Hydrorepellency Mahltig 2003 [102] Nylon Finishing of carpeting Satoh 2004 [103] Cotton Superhydrophobicity Daoud 2004 [104] Cotton Superhydrophobicity Yu 2007 [105] Wool, cotton, PET Superhydrophobicity Wang 2008 [106] Cotton Antimicrobial and repellency Tomšič 2008 [107] Cotton Superhydrophobicity Bae 2009 [108] Cotton Superhydrophobicity Erasmus 2009 [109] Cotton Durable hydrophobic finishing Roe 2009 [110] Cotton, PET Hydrorepellency Gao 2009 [111] PET, PET/cotton Hydrorepellency and antistaticity Textor 2010 [112] Cotton Superhydrophobicity Liu 2011 [113] Cotton Water and oil repellency, antimicrobial Simončič 2012 [114] Cotton Superhydrophobicity Shi 2012 [115] Cotton Superhydrophobicity and UV blocking Pan 2012 [116] Cotton Super hydro-oleophobicity, self-cleaning Vasiljević 2013 [117] Cotton Hydrorepellency Periolatto 2013 [118] Cotton Hydrorepellency and oil repellency Ferrero 2013 [119] Cotton, PET Hydrorepellency improved by plasma Montarsolo 2013 [120]

Periolatto et al. [118] obtained highly hydrophobic and oil-repellent cotton fabrics by a onestep deposition of a modified silica-based coatings by sol–gel prepared by co-hydrolysis and condensation in weakly acid medium of TEOS-based sols with low amounts of hydrophobic additives such as hexadecyltrimethoxysilane or fluorooctyltriethoxysilane. This work was further developed [119] with the aim of comparing the effect of the laboratory-grade fluori‐ nated reagent 1H,1H,2H,2H-Fluorooctyltriethoxy-silane (FOS) with that of a commercial product (Fluorolink S10). During the acid-catalyzed hydrolysis of TEOS or fluorinated alkoxysilanes, labile silanol groups are formed, which can first promote the silane adsorption onto the OH-rich cellulose structure of cotton fibers through hydrogen bonding. Successively, during the thermal curing step (120° for 1 h), the condensation reactions reported in Figure 5 can occur.

**Figure 5.** Grafting reactions of fluoromonomers on cotton [reprinted with permission from Elsevier: Ferrero F., Periolat‐ to M. Application of fluorinated compounds to cotton fabrics via sol–gel. Applied Surface Science 2013; 275, 201–207]

The procedure of preparation of the nanosols is illustrated in Figure 6.

The cotton samples were subjected to contact angle measurements by a Krüss DSA20E "Easydrop standard" drop shape analysis tensiometer using the sessile drop method for fitting. Measuring liquid drops were deposited from a glass syringe on the fabric's surface by means of software-controlled dosing. The contact angles were the average of at least five measurements for each sample, with a standard deviation of about 2–3%. The contact angles on untreated cotton were 0°C, whereas the drops are immediately absorbed. Moreover, the time necessary for the total absorption of both water and oil drops was measured. The results are summarized in Figure 7.

On samples finished with an impregnation time of 24 h, higher values of contact angles were measured (169°), denoting the importance of a deep penetration of the finishing agent inside the fibers.

A better behavior of Fluorolink-treated samples, with respect to the FOS-treated ones, was found: contact angles higher than 150 °C were measured, typical of super hydro- and oilrepellent surfaces. Absorption times higher than 2 h were measured with both water and oil drops, whereas on FOS-treated samples, the oil drop is absorbed in about 15 min, a good result but worse than Fluorolink's performance. This can be due to the molecular structure of Fluorolink, which is longer and more complex than FOS. The presence of TEOS seems to be ineffective.

**Figure 6.** Procedure of sol–gel preparation and its application to cotton fabrics to confer hydro and oil repellency.

The same measurements were made after five repeated washing cycles (at 40 °C for 30 min using 5-g/l ECE detergent according to ISO 105 C01 standard) to assess the durability of the treatments to laundering. The results are summarized in Figure 8.

fitting. Measuring liquid drops were deposited from a glass syringe on the fabric's surface by means of software-controlled dosing. The contact angles were the average of at least five measurements for each sample, with a standard deviation of about 2–3%. The contact angles on untreated cotton were 0°C, whereas the drops are immediately absorbed. Moreover, the time necessary for the total absorption of both water and oil drops was measured. The results

On samples finished with an impregnation time of 24 h, higher values of contact angles were measured (169°), denoting the importance of a deep penetration of the finishing agent inside

A better behavior of Fluorolink-treated samples, with respect to the FOS-treated ones, was found: contact angles higher than 150 °C were measured, typical of super hydro- and oilrepellent surfaces. Absorption times higher than 2 h were measured with both water and oil drops, whereas on FOS-treated samples, the oil drop is absorbed in about 15 min, a good result but worse than Fluorolink's performance. This can be due to the molecular structure of Fluorolink, which is longer and more complex than FOS. The presence of TEOS seems to be

**Fluorolink S10**

**NANOSOL**

15 mL Ethanol 1 ml HCl (0,01 N)

**Magnetic stirring for 24 h**

**Weight on: 5-10%**

**Drying and curing 1h at 120°C**

**Figure 6.** Procedure of sol–gel preparation and its application to cotton fabrics to confer hydro and oil repellency.

The same measurements were made after five repeated washing cycles (at 40 °C for 30 min using 5-g/l ECE detergent according to ISO 105 C01 standard) to assess the durability of the

1 mL HCl (0,01 N) 9 mL Fluorolink S10

treatments to laundering. The results are summarized in Figure 8.

**Fluorolink S10+ T EOS**

3,7 mL TEOS 2,5 mL Fluorolink S10 15 mL Ethanol 1 mL HCl (0,01 N)

> **Dipping in S10 or S10 + T EOS nanosol followed by 24 h impregnation**

are summarized in Figure 7.

**FOS**

9 mL FOS 15 mL Ethanol

**Dipping in FOS nanosol followed by impregnation:**

•**1 min** •**2 h**  •**24 h**

the fibers.

156 Wetting and Wettability

ineffective.

**Figure 7.** Results of contact angle measurements and drop absorption time on cotton fabrics treated with sol–gel finish‐ es. From left to right; for FOS-finished samples add-on and impregnation time: 5% 1 min, 10% 1 min, 5% 2 h, 10% 2h, 5% 24 h, and 10% 24 h; for the other finishes: 5% 24 h and 10% 24 h.

**OIL (paraffin oil: 31.5 mN/ m surf. tension)**

**Figure 8.** Contact angle and drop absorption time measurements after five washing cycles (description of samples as shown in Figure 7).

On FOS samples after washing, a decrease in contact angles was observed, but the behavior was better with 24 h of impregnation, showing that a longer contact time enables better interpenetration of the finishing agent inside the cotton fibers. Instead, the samples finished by Fluorolink S10 showed the best performance, without the influence of TEOS. After washing, the drop absorption times of water strongly decreased, whereas the oil drop absorption time of 2 h was maintained by samples finished with Fluorolink S10.

The strong loss of hydrophobicity after washing can be due to a rearrangement of the fluori‐ nated chains with an orientation toward the internal part of the fibers. In fact, it is well known that fluorine-containing polymers are usually quite susceptible to rapid rearrangement when the polymer surface is contacted with water, in particular with short perfluorinated-side chains to minimize the interfacial free-energy response to the environmental media. This was confirmed by the increase in contact angle and water drop absorption time of the washed samples after ironing.

The results of XPS analysis confirmed the presence of finishing agents on the surface as evidenced by the content of F and Si. CF3 groups are present in the structure of FOS, whereas CF2 groups are present in FOS as well as in Fluorolink. In fact, the F content was higher on the FOS-treated samples (58.3% on the cotton finished with 10% FOS) than that finished with 10% Fluorolink (38.9%). These values were significantly reduced after washing (53.2% and 28.3%, respectively).

In conclusion, the application of a fluorinated alkoxysilane to cotton textiles by sol–gel is a promising textile finishing process to confer durable hydro and oil repellency. In fact, high contact angles and drop absorption time values were measured on treated cotton with both water and oil. Low add-ons (5%) are enough to confer the properties, unaffecting the fabric's characteristics. A prolonged impregnation time (24 h) significantly improves repellency and fastness to washing, whereas ironing of the washed samples can partially restore the hydro and oil repellency lost after washing.

The best performances were obtained with a commercial product (Fluorolink S10). This can allow the application of the treatment at the industrial level, taking into account that the sol– gel process can immediately be implemented on existing production lines of fabric finishing.

#### **5. Conclusions**

The modification of surface energy and wettability of textile fibers can be achieved by several techniques, such as plasma treatments, thermal or UV curing of suitable monomers and oligomers, and, finally, nanotechnology based on sol–gel processes.

LPPs are versatile, enabling various treatment types: etching, grafting of groups onto the surface, coating with polymers produced *in situ* from gaseous monomers or liquid oligomers previously impregnated, sputtering, and so on. Despite this flexibility, the apparatus is complex, cumbersome, expensive, and unsuitable for continuous fabric finishing. APP processes are preferable to this aim, but are limited with regard to utilizable gases and plasma polymerization. In any case, the major drawback of plasma activation aimed at improving the following processes is because most of the free radicals remaining on the treated fiber surface is extinguished when exposed to air oxygen; therefore, the time lapse between the plasma treatment and the exploitation of the effects should be as short as possible.

UV curing of suitable monomers or oligomers can be a valid alternative to traditional thermal curing for fabric water and oil repellency and other surface properties. It is a low-cost and environment-friendly process that can easily be introduced in the finishing processes.

Finally, sol–gel processes applied to fabric finishings allow for obtaining engineered surfaces with a great variety of applications arising from the properties of the nanostructures. If lowcost precursors will be found and the need for organic solvents will be reduced to a minimum amount, these techniques will show a significant development in the next years.

#### **Author details**

The strong loss of hydrophobicity after washing can be due to a rearrangement of the fluori‐ nated chains with an orientation toward the internal part of the fibers. In fact, it is well known that fluorine-containing polymers are usually quite susceptible to rapid rearrangement when the polymer surface is contacted with water, in particular with short perfluorinated-side chains to minimize the interfacial free-energy response to the environmental media. This was confirmed by the increase in contact angle and water drop absorption time of the washed

The results of XPS analysis confirmed the presence of finishing agents on the surface as evidenced by the content of F and Si. CF3 groups are present in the structure of FOS, whereas CF2 groups are present in FOS as well as in Fluorolink. In fact, the F content was higher on the FOS-treated samples (58.3% on the cotton finished with 10% FOS) than that finished with 10% Fluorolink (38.9%). These values were significantly reduced after washing (53.2% and 28.3%,

In conclusion, the application of a fluorinated alkoxysilane to cotton textiles by sol–gel is a promising textile finishing process to confer durable hydro and oil repellency. In fact, high contact angles and drop absorption time values were measured on treated cotton with both water and oil. Low add-ons (5%) are enough to confer the properties, unaffecting the fabric's characteristics. A prolonged impregnation time (24 h) significantly improves repellency and fastness to washing, whereas ironing of the washed samples can partially restore the hydro

The best performances were obtained with a commercial product (Fluorolink S10). This can allow the application of the treatment at the industrial level, taking into account that the sol– gel process can immediately be implemented on existing production lines of fabric finishing.

The modification of surface energy and wettability of textile fibers can be achieved by several techniques, such as plasma treatments, thermal or UV curing of suitable monomers and

LPPs are versatile, enabling various treatment types: etching, grafting of groups onto the surface, coating with polymers produced *in situ* from gaseous monomers or liquid oligomers previously impregnated, sputtering, and so on. Despite this flexibility, the apparatus is complex, cumbersome, expensive, and unsuitable for continuous fabric finishing. APP processes are preferable to this aim, but are limited with regard to utilizable gases and plasma polymerization. In any case, the major drawback of plasma activation aimed at improving the following processes is because most of the free radicals remaining on the treated fiber surface is extinguished when exposed to air oxygen; therefore, the time lapse between the plasma

UV curing of suitable monomers or oligomers can be a valid alternative to traditional thermal curing for fabric water and oil repellency and other surface properties. It is a low-cost and environment-friendly process that can easily be introduced in the finishing processes.

oligomers, and, finally, nanotechnology based on sol–gel processes.

treatment and the exploitation of the effects should be as short as possible.

samples after ironing.

158 Wetting and Wettability

and oil repellency lost after washing.

respectively).

**5. Conclusions**

Franco Ferrero\* and Monica Periolatto

\*Address all correspondence to<EMAIL_ADDRESS>
Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy

#### **References**

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## **Surface Energy and Wetting in Island Films**

Sergei Dukarov, Aleksandr Kryshtal and Vladimir Sukhov

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60900

#### **Abstract**

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168 Wetting and Wettability

364.

The chapter describes the fundamental aspects of the effects of scale on surface phenomena in condensed films. Experimental and theoretical data for the size and temperature dependencies of the surface energy (including the solid phase); wetting of solid surfaces and free thin films by small metal particles are discussed. Several modern methods of contact angle measurement in small-sized systems based on the optical and electron microscopy methods are described.

**Keywords:** surface energy, small particles, thin films, wetting, size effects

#### **1. Introduction**

Surface energy is one of the most important characteristics of condensed matter. While methods available for the liquid phase enable to determine reliably not only the value but also the temperature dependence of surface energy [1–3], for the solid phase the accuracy of existing methods, as a rule, does not allow to trace its temperature dependence [4, 5]. Therefore, the following approach is justified: what information can be obtained about surface energy of the condensed matters on studies of various properties and processes in small size samples [6–9]. This article considers mainly the investigations of temperature and size dependence of surface energy of condensed matter based on the analysis of surface phenomena and phase transitions in nano-sized systems.

Wetting of solid surfaces with a liquid as well as spreading of a liquid over solid surfaces as a manifestation of interaction between the solid and liquid phases is one of the universal

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

phenomena and covers a wide variety of both fundamental and technological processes. Despite their crucial importance, these processes are still unclear [1, 2, 10]. Therefore, this paper focuses on effects of wetting in nanodispersed systems and considers various physical and chemical factors affecting it. Such statement of the problems seems actual since these details are important to describe a wide range of processes and phenomena, whereas the available data are disembodies and often ambiguous or even lacking.

#### **2. The surface energy of nanoparticles**

#### **2.1. The size dependence of the surface energy of nanoparticles**

In the framework of the Gibbs thermodynamics of heterophase systems, the size dependence of surface energy is due to the curvature of the phase interface. The Gibbs method applied to interfaces with a small curvature radius was first developed by Tolman [11], who derived the equation relating the surface energy σ of a spherical particle with its radius *R*

$$\frac{1}{\sigma} \frac{d\sigma}{dR} = \frac{\left(2\,\delta/R^2\right)\left(1+\delta/R+\delta^2/3R^2\right)}{1+\left(2\,\delta/R\right)\left(1+\delta/R+\delta^2/3R^2\right)}\tag{1}$$

where δ is the difference between the radii of equimolecular surface and surface of tension. Since the function δ = δ(*R*) is unknown, at δ << *R* the variable δ can be considered constant and equal to the value for plane interface, that is, δ ≈ δ∞. Under this assumption approximate solution to equation (1) was obtained in [11] known in literature as the Tolman formula:

$$
\sigma/\sigma\_{\circ} = 1/\left(1 + 2\delta\_{\circ}/R\right),
$$

For particles with *R* >> δ∞ the first term of the expansion will be sufficient

$$
\sigma = \sigma\_{\circ} \left( 1 - \alpha / \mathbb{R} \right). \tag{2}
$$

In this approach the parameter α = 2δ∞ has a definite physical meaning as a width of the respective phase interface for any condensed phases. Character of the dependence σ(*R*) is determined by the sign of the parameter δ∞. In the case when δ∞ > 0, surface energy of micro‐ particles will decrease, and at δ∞ < 0, conversely, increase of σ with decrease of *R*. Since the sign and value of parameter δ∞ cannot be obtained based on thermodynamic prerequisites, determination of the type of the dependence σ(*R*) calls for the use of the model of the structure of the transition layer for real systems or experimental results. In [3] this problem is solved for a simple idealized fluid using correlation function methods and it is shown that in this system the transition layer has a layered structure corresponding to some orderliness of particles therein. This is essential for many phenomena in surface physics.

Calculations of δ∞ for plane liquid–vapor interfaces made by statistical methods [12] has shown that the quantity δ∞ > 0 and has a value of approximately a few tenth of nanometer (e.g., according to [12] for argon at 90 K δ∞ = 0.36 nm). Further research with use of a computer simulation [13–17], electron theory of surface energy of metals [18, 19], the thermodynamic perturbation theory [20, 21] is consistent with the results in terms of the type of the dependence σ(*R*).

phenomena and covers a wide variety of both fundamental and technological processes. Despite their crucial importance, these processes are still unclear [1, 2, 10]. Therefore, this paper focuses on effects of wetting in nanodispersed systems and considers various physical and chemical factors affecting it. Such statement of the problems seems actual since these details are important to describe a wide range of processes and phenomena, whereas the available

In the framework of the Gibbs thermodynamics of heterophase systems, the size dependence of surface energy is due to the curvature of the phase interface. The Gibbs method applied to interfaces with a small curvature radius was first developed by Tolman [11], who derived the

> ( )( ) ( )( )

 dd

where δ is the difference between the radii of equimolecular surface and surface of tension. Since the function δ = δ(*R*) is unknown, at δ << *R* the variable δ can be considered constant and equal to the value for plane interface, that is, δ ≈ δ∞. Under this assumption approximate solution to equation (1) was obtained in [11] known in literature as the Tolman formula:

> a

In this approach the parameter α = 2δ∞ has a definite physical meaning as a width of the respective phase interface for any condensed phases. Character of the dependence σ(*R*) is determined by the sign of the parameter δ∞. In the case when δ∞ > 0, surface energy of micro‐ particles will decrease, and at δ∞ < 0, conversely, increase of σ with decrease of *R*. Since the sign and value of parameter δ∞ cannot be obtained based on thermodynamic prerequisites, determination of the type of the dependence σ(*R*) calls for the use of the model of the structure of the transition layer for real systems or experimental results. In [3] this problem is solved for a simple idealized fluid using correlation function methods and it is shown that in this system the transition layer has a layered structure corresponding to some orderliness of particles

 dd

12 1 3 *d R RR dR R RR*

2 2 2

 d¥ ¥ = + 11 2 ( ) *R*

2 2

= - ¥ ( ) 1 . *R* (2)

(1)

data are disembodies and often ambiguous or even lacking.

**2.1. The size dependence of the surface energy of nanoparticles**

equation relating the surface energy σ of a spherical particle with its radius *R*

d

ss

For particles with *R* >> δ∞ the first term of the expansion will be sufficient

ss

therein. This is essential for many phenomena in surface physics.

d

s

s

21 3 1

+ + <sup>=</sup> + ++

**2. The surface energy of nanoparticles**

170 Wetting and Wettability

Qualitatively, the decrease in the surface energy of small particles can be explained as follows. For the condensed phase being in equilibrium with its own vapor, the interface surface energy at first approximation is proportional to the difference between the number of atoms (mole‐ cules) per unit volume of the condensed and vapor phases. With decreasing particle size of the condensed phase vapor pressure increases, and, consequently, its density increases, which causes decrease of the surface energy of the particle – saturated vapor interface approximately in inverse proportion to the particle radius.

In this way, theoretical studies suggest the existence of the size dependence of surface energy in the nanodispersed systems. According to estimates made using different methods, depend‐ encies of σ on size for particles and films are manifested as a monotone decrease with de‐ creasing size starting from a radius of less than 20 nm for particles and a thickness of < 5 nm for films.

#### **2.2. Experimental foundations for the determination of surface energy of nanoparticles**

Experimental determination of surface energy of solid bodies is a challenging task. Experi‐ mental methods available to scientists today offer the measurement of values of surface energy of liquid-phase matters with a reasonable degree of accuracy and in a broad temperature band, which is not the case for the crystalline phase. Known experimental methods for the determi‐ nation of the surface energy for the crystalline phase are limited, and, as a rule, have a very narrow range of pre-melting temperatures and provide precision of not more than 10–20% [4]. This is largely due to the fact that surface energy is not a directly measurable value, but in most cases it is estimated as an adjustable parameter in various processes such as, for example, wetting, spreading, melting, crystallization, dissolution, analysis of high-temperature creep, electronic work function, etc. Among the best-known methods are the following: the crystal cleavage method, the dispersed powder dissolution method, the "neutral" droplet method, the multiphase equilibrium method, the growth and evaporation steps method, the "healing" scratch method, and, finally, the zero creep method [4]. Surface energy may also be evaluated by the measurement of electronic work function [18, 19]. However, the analysis of these methods shows that they are not applicable to the measurement of surface energies of small particles.

#### *2.2.1. Kinetics of evaporation of small particles and surface energy*

Surface energy of small particles can be determined by kinetics of evaporation in vacuum at a constant temperature [6]. The method is based on the concepts of the molecular-kinetic theory that supposes that the rate of evaporation from a unit of free surface in vacuum is defined by the expression

$$\frac{dM}{dt} = \left(\frac{m}{2\pi kT}\right)^{\sharp 2} P(T)\_r$$

where *m* is mass of atom (molecule), *k* is Boltzmann constant, *Р* is pressure of saturated vapor at temperature *Т*. For the particle with the radius *R* saturated vapor pressure is linked to the vapor pressure over a flat surface *P*∞(*Т*) with the Kelvin equation

$$P\left(T,R\right) = P\_{\text{av}}\left(T\right)\exp\left(\frac{2\text{v}\_{\text{a}}}{kT}\frac{\sigma}{R}\right). \tag{3}$$

(va is atomic volume). The evaporation rate will be equal to

$$\frac{dM}{dt} = \left(\frac{m}{2\pi kT}\right)^{1/2} P\_\circ \left(T\right) \exp\left(\frac{2\mathbf{v}\_s}{kT}\frac{\sigma}{R}\right). \tag{4}$$

For an array of particles on the substrate it is more practicable to measure not the evaporation rate *dM/dt*, but the dependence of the particle radius on its evaporation time *t* at a constant temperature. From the relation of *R* to *t* one can determine the variation of the particle radius *dR/dt* at different *R* and, consequently, find σ. Indeed, as it follows from (4)

$$\left|\frac{d\mathcal{R}}{dt}\right| = \frac{1}{\rho}\frac{dM}{dt} = \frac{1}{\rho}\left(\frac{m}{2\pi kT}\right)^{1/2}P\_o\exp\left(\frac{2\mathbf{v}\_s}{kT}\frac{\sigma}{R}\right)\text{or}\ln\left|\frac{d\mathcal{R}}{dt}\right| = \ln A + \frac{B\sigma}{R}\tag{5}$$

where

$$A = \frac{1}{\rho} \left(\frac{m}{2\pi kT}\right)^{1/2} P\_{\text{o}}\left(T\right) \text{ and } B = \frac{2\text{v}\_{\text{o}}}{kT}.\tag{6}$$

According to (5) and (6), knowing the temperature, particle size reduction rate *dR/dt*, and *Р*∞(*Т*), one can determine the value of σ. These expressions adequately describe evaporation kinetics of liquid Pb particles and crystalline Ag particles [6] at values of σ close to handbook ones.

Electron microscope investigation of the kinetics of particle evaporation was later used to register the melting temperature of small crystalline Au particles by breaks in dependencies *R*(*t*) [7]. This effect is due to the difference in evaporation rates for crystalline and liquid states. The melting temperature lowering data obtained for small Au particles from their evaporation kinetics [7] correlate well with similar results established later using electron diffraction analysis [22]. Investigating the kinetics of evaporation of silver particles on carbon substrates has shown that the observed sublimation temperature generally decreased with decreasing particle size [23], in agreement with the predictions from the Kelvin equation. However, sublimation of smaller nanoparticles was often observed to occur in discrete steps, which led to faceting of the nanoparticles.

This method was used to determine the surface energy of small particles in Bi, Pb, and Au island films [8, 9]. The sample film was heated in the electron microscope by electron beam up to the onset temperatures of evaporation. The temperature and, hence, evaporation rate was controlled with beam density. The particles radius variation rate ∆*R*/∆*t* during evaporation was established by the analysis of a series of successive electron micrographs taken at fixed time intervals. These data allowed to establish the temperature of particles heated by the electron beam. For this purpose, expression (6) at *R* → ∞ should be represented in the form

$$\mathbf{1g}\,P\_{\ll}\begin{pmatrix}T\\ \end{pmatrix}=\mathbf{1g}\,\mathbf{C}+\mathbf{1}\not\mathbf{1}\prime\prime\prime\tag{7}$$

Where *<sup>C</sup>* <sup>=</sup>*ρ*( <sup>2</sup>*π<sup>k</sup> <sup>m</sup>* ) 1/2 (*dR* / *dt*) <sup>R</sup>→*<sup>∞</sup>*.

that supposes that the rate of evaporation from a unit of free surface in vacuum is defined by

æ ö <sup>=</sup> ç ÷ è ø

where *m* is mass of atom (molecule), *k* is Boltzmann constant, *Р* is pressure of saturated vapor at temperature *Т*. For the particle with the radius *R* saturated vapor pressure is linked to the

æ ö = ç ÷

( ) () <sup>a</sup> 2v *P T,R P T* exp . *kT R*

( ) 1 2

æ ö æ ö <sup>=</sup> ç ÷ ç ÷ è ø è ø

*<sup>a</sup> dM m P T dt kT kT R*

p¥

*dR/dt* at different *R* and, consequently, find σ. Indeed, as it follows from (4)

1 2

¥

2

è ø

r p

r

where

 rp exp . <sup>2</sup>

For an array of particles on the substrate it is more practicable to measure not the evaporation rate *dM/dt*, but the dependence of the particle radius on its evaporation time *t* at a constant temperature. From the relation of *R* to *t* one can determine the variation of the particle radius

> 1 1 2v exp or ln ln , <sup>2</sup> *<sup>a</sup> dR dM m dR B P A dt dt kT kT R dt R*

> > ( )

*kT kT* ¥

According to (5) and (6), knowing the temperature, particle size reduction rate *dR/dt*, and *Р*∞(*Т*), one can determine the value of σ. These expressions adequately describe evaporation kinetics of liquid Pb particles and crystalline Ag particles [6] at values of σ close to handbook ones.

Electron microscope investigation of the kinetics of particle evaporation was later used to register the melting temperature of small crystalline Au particles by breaks in dependencies *R*(*t*) [7]. This effect is due to the difference in evaporation rates for crystalline and liquid states.

<sup>1</sup> 2v and .

*<sup>m</sup> <sup>a</sup> <sup>A</sup> PT B*

æ ö = = ç ÷

1/2

æ ö æ ö = = ç ÷ ç ÷ = + è ø è ø

s

¥

vapor pressure over a flat surface *P*∞(*Т*) with the Kelvin equation

(va is atomic volume). The evaporation rate will be equal to

1 2 , <sup>2</sup> *dM m P(T) dt kT* p

> s

2v

s

è ø (3)

 s (4)

(5)

(6)

the expression

172 Wetting and Wettability

Tabular data are available for the function *Р*∞(*T*), while the value (*dR/dt*)*<sup>R</sup>*→∞ is to be determined experimentally from the results of change of the radius of the particles during their evaporation represented in accordance with (5) and (6) in the coordinates "ln |∆*R*/∆*t*| — 1/*R*." Equation (7) can be solved graphically for *Т* and, thus, the temperature of the observed object can be found.

Figure 1а presents an example of a series of successive micrographs of Bi island films ob‐ tained in the process of their evaporation with the time interval of 15 s, and Figure 1b, c present the results of analysis of evaporation of Au island films. These data were used to find values of ∆*R* for different-sized particles at fixed time intervals ∆*t*. Resulting dependencies for the ensemble of particles in Au island films (the size range of 10–50 nm) are presented in Figure 1c in the coordinates "ln |∆*R*/∆*t*|— 1/*R*." Since these dependencies are linear, according to (5) and (6) they allow us to establish σ and values of (*dR*/*dt*)*R*→∞. The range of particle sizes in experi‐ ments [8, 9] made 10–150 nm. For Pb and Bi temperatures of particle evaporation were higher than melting temperatures, whereas for Au island films data on evaporation rates both in liquid and crystalline state were obtained.

Values of surface energies σ for Au, Pb, and Bi found as a result of the preceding experiments are presented in Table 1, which also presents available literature data for σ at similar temper‐ atures. Comparison of values of σ obtained by kinetics of evaporation of small particles with available data for bulk samples shows their satisfactory fit.

*Figure 1. Electron micrographs of successive stages of evaporation of Bi island films on amorphous Si films (а); change of particle size in the process of evaporation (temperatures are*  **Figure 1.** Electron micrographs of successive stages of evaporation of Bi island films on amorphous Si films (а); change of particle size in the process of evaporation (temperatures are given in the charts) (b), and relations of evaporation rate to reciprocal size of particles for gold island films on carbon substrates (c)

740 452 730 439 [7] **Table 1.** Comparison of surface energy values for Au, Pb, and Bi [8]

Bi 650 386 509–518 501 [5]

*1.2.2. Dependence of surface energy on particle size*

770 447

750 450 748 436 [7]

Table 1. Comparison of surface energy values for Au, Pb, and Bi [8]

regarding the sign of the size dependence of the surface energy of small particles.

Available experimental data, for example, [8, 9, 24, 25], offer contradictory conclusions

The preceding paragraph demonstrates that the surface energy of small particles can be

directly determined using the kinetics of their evaporation in vacuum. Table 1 presents the

6

Ме

Au

Pb

2 2

1

#### *2.2.2. Dependence of surface energy on particle size* 3 5 0.36 нм 0.36 nm

=

Proof Corrections Form

PROOF CORRECTIONS FORM

No. Delete Replace with

2 2

σ≈σ <sup>∞</sup> δ− <sup>∞</sup> <sup>∞</sup> RR +δ+ ( <sup>R</sup>) <sup>∞</sup> <sup>∞</sup> <sup>σ</sup> <sup>σ</sup> <sup>=</sup> <sup>11</sup> <sup>+</sup> <sup>2</sup><sup>δ</sup>

2 3

Author(s) Name(s): Sergei Dukarov, Aleksandr Kryshtal and 4 Vladimir Sukhov

( )( )

+ +

12 1 3

Chapter Title: Surface Energy and Wetting in Island Films

1 21 3

σ δ δδ

σ δ δδ

d R RR

Some characters are not recognized on the figure! Could you please replace it with a higher quality

8 35 = 0.24 nm α = 0.24 nm

9 18 ν – creep data – creep data

9 19 ο – data for Fe – data for Fe

12 2 energy σl energy σ<sup>l</sup>

9 16 Could you please replace fig 4 with a higher quality

dR R RR

+ ++

<sup>2</sup>Eq(1) ( )( )

=

<sup>2</sup>17 ( <sup>21</sup> (<sup>2</sup> ) ...) <sup>2</sup>

Available experimental data, for example, [8, 9, 24, 25], offer contradictory conclusions regarding the sign of the size dependence of the surface energy of small particles. 3 17 decencies dependencies

( )( )

+ +

12 1 3

1 21 3

σ δ δδ

σ δ δδ

d R RR

dR R RR

+ ++

( )( )

2 2 2

The preceding paragraph demonstrates that the surface energy of small particles can be directly determined using the kinetics of their evaporation in vacuum. Table 1 presents the results of such experiments for nanoparticles over 20 nm in size. At the same time, the kinetics of evaporation of Pb and Au nanoparticles with the size below 20 nm both in liquid and crystalline state was investigated in works [6, 7]. The authors of these studies used these results to test the applicability of the Kelvin equation (3) and to estimate values of σ at temperatures at which the evaporation of particles is observed. However, the authors [6, 7] did not analyze the dependence of particle evaporation rates on particle size. Such analysis was offered by the authors in [8, 9], where they demonstrate that for particles with a size of less than 10 nm their surface energy decreases. Figure 2а presents an example of the plot of *R*(*t*) for Pb particles at different temperatures, and Figure 2b presents particle size reduction rate in the coordinates "ln|Δ*R* /Δ*t* | −1 / *R*" plotted using these data. 4 13 Р<sup>∞</sup> Р∞(Т), 5 26 Figure Figure 1c

7 23 equation equation (2) **Figure 2.** Change of the radius of Pb particles in the process of evaporation (a) and the plot of their evaporation rate against size on the coordinate "ln│*∆*R/*∆*t│ — 1/R" (b) (calculated using data [7]). Curves 1, 2 correspond to particles of different initial size at Т = 720 K

1/3 α = 0.916v<sup>a</sup> 1/3 It is evident that at sizes of particles less than 10 nm significant deviation of the preced‐ ing relationship from linear is observed, which in accordance to (5) is an evidence of decreasing σ. Values of σ calculated using expression (5) are presented in Figure 3 (Curve 5), which also shows calculation data of the relation σ(*R*) for Pb microparticles using the Tolman equation (2) with the parameter α = 0.29 nm, which value is determined from the empirical relation α = 0.916v*<sup>a</sup>* 1/3 [26] (Curve 4). The same figure presents the results of calculation of values of gold and lead nanoparticles surface energy at different tempera‐ tures (Curves 2, 3, 5) obtained from the data of analysis of particle evaporation kinetics given in [6, 7].

8 33 Could you please replace fig 3 with a higher quality Comparison of these dependencies produces qualitatively the same result, that is, the surface energy of small particles decreases with decrease of their size, but nanoparticles evaporation experiments suggest a stronger relationship σ(*R*).

6

*Figure 1. Electron micrographs of successive stages of evaporation of Bi island films on*

**Figure 1.** Electron micrographs of successive stages of evaporation of Bi island films on amorphous Si films (а); change of particle size in the process of evaporation (temperatures are given in the charts) (b), and relations of evaporation

*amorphous Si films (а); change of particle size in the process of evaporation (temperatures are*

*given in the charts) (b), and relations of evaporation rate to reciprocal size of particles for gold*

figure?

139080 [5]

*island films on carbon substrates (c)*

174 Wetting and Wettability

Page No.

Line

1510 1160

770 447

Evaporation kinetics [8, 9] Literature data

rate to reciprocal size of particles for gold island films on carbon substrates (c)

7 16

1260 1430 1176–

1510 1160

770 447

*Т*, K , mJ/m2 *Т*, K , mJ/m2

**Evaporation kinetics [8, 9] Literature data**

4 14 (Т),

5 27 1c

1245<PHONE_NUMBER> 1410 [5]

1310 1320100 1297 1137 [6]

7 24 (2)

7 24 α =

1350 1230100 1348 1135 [6]

670 385 557–589 560 [5]

720 484 735 438 [7]

Bi 650 386 509–518 501 [5]

7 25 0.916v<sup>a</sup>

740 452 730 439 [7]

750 450 748 436 [7]

8 34 α

Table 1. Comparison of surface energy values for Au, Pb, and Bi [8]

regarding the sign of the size dependence of the surface energy of small particles.

Available experimental data, for example, [8, 9, 24, 25], offer contradictory conclusions

image?

image?

The preceding paragraph demonstrates that the surface energy of small particles can be

directly determined using the kinetics of their evaporation in vacuum. Table 1 presents the

Bi 650 386 509–518 501 [5]

**Table 1.** Comparison of surface energy values for Au, Pb, and Bi [8]

*1.2.2. Dependence of surface energy on particle size*

1306

 385 557–589 560 [5] 484 735 438 [7] 452 730 439 [7] 450 748 436 [7]

*Т*, K σ, mJ/m<sup>2</sup> *Т*, K σ, mJ/m<sup>2</sup>

 1410±20 1240 1410 [5] 1430 1176–1306 1390±80 [5] 1320±100 1297 1137 [6] 1230±100 1348 1135 [6]

Ме

Ме

Au

Pb

Au

Pb

8

(ρl/ρS)

Figure 3. The plot of surface energy against microparticles size: a – Au (1 – calculation using the Tolman equation at α = 0.24 nm, 2 and 3 – using microparticles evaporation data at **Figure 3.** The plot of surface energy against microparticles size: a – Au (1 – calculation using the Tolman equation at *α* = 0.24 nm, 2 and 3 – using microparticles evaporation data at Т = 1348 K and Т = 1316 K); b – Pb (4 – calcula‐ tion using the Tolman equation at *α* =0.29 nm, 5 – particle evaporation data at Т = 735 K)

#### *2.2.3. Decrease in small particles melting temperature and surface energy* Т = 1348 K and Т = 1316 K); b – Pb (4 – calculation using the Tolman equation at α =0.29 nm,

S RS It is common knowledge that melting temperature of small particles, thin metal, and alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of thermodynamics, there exist several models to describe the size dependence of melting temperature of small particles [27]; however, as the quantitative analysis of experimental data shows, the triple point model proves to be the most feasible. Within the framework of this model the problem of the melting temperature of the small particle was first solved by Pavlov [37], who obtained expression for the size dependence of melting temperature 5 – particle evaporation data at Т = 735 K) Comparison of these dependencies produces qualitatively the same result, that is, the surface energy of small particles decreases with decrease of their size, but nanoparticles evaporation experiments suggest a stronger relationship σ(R).

$$\frac{T\_s - T\_\text{R}}{T\_\text{S}} = \frac{3}{\lambda R} \left( \sigma\_\text{s} - \sigma\_\text{s} \left( \bigvee\_s \rho\_\text{s} \right)^{\text{Q3}} \right) \tag{8}$$

where *ТS* and *Т<sup>R</sup>* are the melting temperatures of a bulk sample and a particle with the radius *R*, λ is melting heat, σ and *ρ* are surface energies and densities of crystalline (*s*) and liquid (*l*) phases, respectively. As it is seen from (8) using experimental data *ТR*(*R*), one can establish the difference of surface energies of solid and liquid phases, that is, ∆Ω=σ*S*–σ*<sup>l</sup>* (*ρ<sup>l</sup>* /*ρS*) 1/3, and given known values of σ*<sup>l</sup>* find σ*S*. The possibility of determining surface energy in solid phase and its temperature dependence using experimental data *ТR*(*R*) are detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but changes in accordance to variation of σ*S* and σ*<sup>l</sup>* . Considering this, the expression for the melting temperature of small particles can be represented in the following form alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of thermodynamics, there exist several models to describe the size dependence of melting temperature of small particles [27]; however, as the quantitative analysis of experimental data shows, the triple point model proves to be the most feasible. Within the framework of this model the problem of the melting temperature of the small particle was first solved by Pavlov [37], who obtained expression for the size dependence of melting temperature

where ТS and ТR are the melting temperatures of a bulk sample and a particle with the radius

R, λ is melting heat, σ and ρ are surface energies and densities of crystalline (s) and liquid

(l) phases, respectively. As it is seen from (8) using experimental data ТR(R), one can

establish the difference of surface energies of solid and liquid phases, that is, ∆Ω=σS−σ<sup>l</sup>

energy in solid phase and its temperature dependence using experimental data ТR(R) are

detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but

1/3, and given known values of σ<sup>l</sup> find σS. The possibility of determining surface

$$\frac{T\_s - T\_r}{T\_s} = \frac{3\Delta\Omega\_0}{\lambda \left(R - \Delta R\right)^{\prime}}\tag{9}$$

where ∆Ω0 = *σ<sup>s</sup>* <sup>0</sup> <sup>−</sup>*σ<sup>l</sup>* 0 (1 + *δ<sup>V</sup>* / 3) is the variation of surface energy during melting at temperature *Ts*; ∆*R* = 3*Ts*[γ*<sup>l</sup>* (1 + δ*V*/3) – γ*s*]/λ*ρs*, γ*<sup>l</sup>* = ∂σ*<sup>l</sup>* /∂*T* is the temperature coefficient of liquid phase surface energy; γ*s* = ∂σ*s*/∂*T* is the temperature coefficient of solid phase surface energy, σ<sup>0</sup> is surface energy of relevant phase at bulk sample melting temperature *Тs*, δ*<sup>V</sup>* is relative variation of volume during melting.

It follows from (9) that using the experimental relation *ТR*(*R*) one can calculate ∆Ω at different temperatures and, provided known type of temperature dependence of liquid phase surface energy σ*<sup>l</sup>* (*Т*) below *Тs*, find dependence σ*s*(*Т*). This approach allowed to evaluate relations ∆Ω(*Т*) and σ*s*(*Т*) over a broad temperature interval using experimental data of *ТR*(*R*) for Sn and In [31, 32]. The validity of linear extrapolation of values of liquid phase surface energy σ*<sup>l</sup>* to the region of significant supercooling was substantiated in works [9, 38].

Considering the preceding, we calculated values of surface energies for a number of metals (In, Sn, Bi, Pb, Al, Au) in crystalline state over the temperature interval of (0.6–1)*Тs*. The obtained results are presented in Figure 4. These values agree well with available literature data on σ*s* for bulk samples obtained by other methods. the coordinates "ln(∆σ/σ) – 1/T" the paper also estimated the vacancy formation energy E<sup>V</sup> that yielded the following values: In – 0.5 eV, Sn – 0.62 eV and Pb – 0.6 eV. Close values of the values of EV support vacancy mechanism of nonlinear temperature dependence of

solid phase surface energy in the premelting temperature band.

*2.2.3. Decrease in small particles melting temperature and surface energy*

tion using the Tolman equation at *α* =0.29 nm, 5 – particle evaporation data at Т = 735 K)

the size dependence of melting temperature

5 – particle evaporation data at Т = 735 K)

176 Wetting and Wettability

known values of σ*<sup>l</sup>*

be represented in the following form

S RS

of σ*S* and σ*<sup>l</sup>*

8

(ρl/ρS)

*T T*

evaporation experiments suggest a stronger relationship σ(R).

*T R*

l

difference of surface energies of solid and liquid phases, that is, ∆Ω=σ*S*–σ*<sup>l</sup>*

*s T T T*

S

<sup>ρ</sup> σ−σ <sup>λ</sup> <sup>=</sup> <sup>−</sup> <sup>31</sup> <sup>3</sup>

<sup>l</sup> RT

It is common knowledge that melting temperature of small particles, thin metal, and alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of thermodynamics, there exist several models to describe the size dependence of melting temperature of small particles [27]; however, as the quantitative analysis of experimental data shows, the triple point model proves to be the most feasible. Within the framework of this model the problem of the melting temperature of the small particle was first solved by Pavlov [37], who obtained expression for

surface energy of small particles decreases with decrease of their size, but nanoparticles

Figure 3. The plot of surface energy against microparticles size: a – Au (1 – calculation using

**Figure 3.** The plot of surface energy against microparticles size: a – Au (1 – calculation using the Tolman equation at *α* = 0.24 nm, 2 and 3 – using microparticles evaporation data at Т = 1348 K and Т = 1316 K); b – Pb (4 – calcula‐

the Tolman equation at α = 0.24 nm, 2 and 3 – using microparticles evaporation data at

Т = 1348 K and Т = 1316 K); b – Pb (4 – calculation using the Tolman equation at α =0.29 nm,

<sup>3</sup> , *<sup>l</sup>*

where *ТS* and *Т<sup>R</sup>* are the melting temperatures of a bulk sample and a particle with the radius *R*, λ is melting heat, σ and *ρ* are surface energies and densities of crystalline (*s*) and liquid (*l*) phases, respectively. As it is seen from (8) using experimental data *ТR*(*R*), one can establish the

alloy films is a function of size [6, 7, 22, 27–36]. When considered in terms of

thermodynamics, there exist several models to describe the size dependence of melting

temperature of small particles [27]; however, as the quantitative analysis of experimental

data shows, the triple point model proves to be the most feasible. Within the framework of

this model the problem of the melting temperature of the small particle was first solved by

 ρ

where ТS and ТR are the melting temperatures of a bulk sample and a particle with the radius

R, λ is melting heat, σ and ρ are surface energies and densities of crystalline (s) and liquid

(l) phases, respectively. As it is seen from (8) using experimental data ТR(R), one can

establish the difference of surface energies of solid and liquid phases, that is, ∆Ω=σS−σ<sup>l</sup>

energy in solid phase and its temperature dependence using experimental data ТR(R) are

detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but

1/3, and given known values of σ<sup>l</sup> find σS. The possibility of determining surface

s l

its temperature dependence using experimental data *ТR*(*R*) are detailed in work [9]. It is possible since the difference ∆Ω is not a constant value, but changes in accordance to variation

( ) <sup>0</sup> <sup>3</sup> , *s r*

l*R R*

Pavlov [37], who obtained expression for the size dependence of melting temperature

è ø è ø

r

It is common knowledge that melting temperature of small particles, thin metal, and

Comparison of these dependencies produces qualitatively the same result, that is, the

r

*S R <sup>l</sup> <sup>S</sup> <sup>s</sup> <sup>S</sup>*

1.2.3. Decrease in small particles melting temperature and surface energy

s s

1 3

find σ*S*. The possibility of determining surface energy in solid phase and

. Considering this, the expression for the melting temperature of small particles can

TT , (8)

(8)

10

1/3, and given

 (*ρ<sup>l</sup>* /*ρS*)

data [6, 7, 22, 31–36] (the dotted lines are extrapolation of dependencies σl(T) to the area of supercooling state) – creep data [5], ⊕ – small particles evaporation data [7], – data for **Figure 4.** Surface energy temperature dependence for different metals according to the TR(R) data [6, 7, 22, 31–36] (the dotted lines are extrapolation of dependencies *σ*<sup>l</sup> (T) to the area of supercooling state) ■ – creep data [5], ⊕ – small par‐ ticles evaporation data [7], □ – data for Fe [39]

Figure 4. Surface energy temperature dependence for different metals according to the TR(R)

Fe [39] 2. Wetting in condensed films Information on values of surface energy and interfacial energy of contacting phases can be obtained when studying wetting in solid–liquid systems. Analysis of known methods for It is evident that there is a common tendency observed for all of the preceding metals mani‐ fested in the fact that the values of σ*<sup>s</sup>* have nonlinear temperature dependence. With relative temperatures below *T/Ts* ≤ (0.85–0.9) the temperature coefficient for these metals becomes approximately constant and makes module (0.3–0.4) mJ/m2 K (Figure 4). Nonlinear decrease in σ*s* at *Т* → *Т<sup>s</sup>* is probably common for metals. The result of work [39] supports this assumption. In this work, surface energy of macroscopic iron samples is determined using the method of wetted solid surface deformation over the range of temperatures (1580–1790) K (Figure 4).

the determination of the wetting contact angles θ shows that the use of traditional methods

[1, 40] for studying wetting in ultradispersed systems is quite limited. In view of these, new

methods [41, 42] were developed that allowed to investigate wetting in ultradispersed

systems with different types of contact interaction (i.e., applicable both at θ < 90°, and for

method on solid substrates, which, as a rule, were prepared using vacuum condensation as

well [9, 42–44]. The substance substrate was deposited on the NaCl (or KCl) cleavages in a vacuum of 10-7–10-9 mm Hg. After that the investigated metal was condensed at a substrate

temperature that ensured condensation of the metal into liquid phase. The obtained films

were cooled in vacuum to room temperature and the crystallized particles were further

analyzed using the methods of optical, scanning, and transmission electron microscopy.

According to the estimates and data of experimental research [42–44] (Figure 5) contact

Test samples were island films of various metals condensed in vacuum by vapor–liquid

θ > 90°), with typical phase size changing over a broad range.

The nonlinear increment effect │∂σ*S*/∂*Τ*│at *Т* → *Т<sup>S</sup>* was considered for In and Sn and supported by case study calculations of σ*S*, made for Bi, Pb, Al, Au in work [9]. A detailed analysis of nonlinear relation of the temperature coefficient ∂σ*S*/∂*Τ* in premelting temperature band showed its vacancy nature [9]. Based on the analysis of data on σ*S*(*T*) in the coordinates "ln(∆σ/σ) – 1/*T*" the paper also estimated the vacancy formation energy *EV* that yielded the following values: In – 0.5 eV, Sn – 0.62 eV and Pb – 0.6 eV. Close values of the values of *EV* support vacancy mechanism of nonlinear temperature dependence of solid phase surface energy in the premelting temperature band.

### **3. Wetting in condensed films**

Information on values of surface energy and interfacial energy of contacting phases can be obtained when studying wetting in solid–liquid systems. Analysis of known methods for the determination of the wetting contact angles θ shows that the use of traditional methods [1, 40] for studying wetting in ultradispersed systems is quite limited. In view of these, new methods [41, 42] were developed that allowed to investigate wetting in ultradispersed systems with different types of contact interaction (i.e., applicable both at θ < 90°, and for θ > 90°), with typical phase size changing over a broad range.

Test samples were island films of various metals condensed in vacuum by vapor–liquid method on solid substrates, which, as a rule, were prepared using vacuum condensation as well [9, 42–44]. The substance substrate was deposited on the NaCl (or KCl) cleavages in a vacuum of 10-7–10-9 mm Hg. After that the investigated metal was condensed at a substrate temperature that ensured condensation of the metal into liquid phase. The obtained films were cooled in vacuum to room temperature and the crystallized particles were further analyzed using the methods of optical, scanning, and transmission electron microscopy. According to the estimates and data of experimental research [42–44] (Figure 5) contact angle measurement error due to changing droplet volume during its solidification on the substrate is not more than 2°. In this way one can discard the variation of the angle during crystallization of liquid droplets and relate the values of θ found for crystallized particles to values of the contact angles of liquid droplets at the temperature of their formation.

**Figure 5.** Electron microscope images of crystalline (a) and liquid (b) lead particles on a carbon substrate and a sche‐ matic representation of a liquid droplet on a solid substrate (c)

In the case when the gravity effect can be disregarded, the shape of small droplets is a segment of a sphere (estimations show that this is knowingly true for metals with particle size below 105 nm). To find the angle θ it is sufficient to measure any two of the three quantities that define droplets on the substrate: the radius of droplet surface curvature *R*, the diameter of its base *d* (*d =* 2*r*), and the height *H* (Figure 5c).

The methods suggested in [41, 42] differ in approaches to measure geometric parameters of droplets. The most frequently used cleavage and convolution methods are based on measure‐ ment of the said parameters during direct observation of droplet profiles with an optical or electron microscope [41, 42]. In this case, the contact angle is determined from the relations

$$\theta = 2 \operatorname{arctg} \frac{2H}{d} = \arccos \left( 1 - \frac{H}{R} \right) = \begin{cases} \arcsin \frac{d}{2R}, & \theta < 90^{\circ}, \\ 180^{\circ} - \arcsin \frac{d}{2R}, & \theta > 90^{\circ}. \end{cases}$$

The developed complex of methods [41, 42] makes it possible to investigate the wetting of surfaces with small droplets, with the size of the latter ranging within 3–105 nm.

#### **3.1. Size effect in wetting**