**5. The lifetime dependency graph model**

In this section, we introduce the Lifetime Dependency (LD) Graph as a model for the maximum lifetime coverage problem defined in Section 3. This model is a key contribution of this dissertation since the heuristics and algorithms that follow in subsequent sections rely heavily on the LD Graph.

Recall from Section 3 that given a sensor network and a set of static targets, the maximum lifetime sensor scheduling problem is to select a subset of sensors that covers all targets and then periodically shuffle the members of this subset so as to maximize the total time for which the network can cover all targets.

Since these sensors are powered by batteries, energy is a key constraint for these networks. Once the battery has been exhausted, the sensor is considered to be dead. The lifetime of the network is defined as the amount of time that the network can satisfy its coverage objective, i.e., the amount of time that the network can cover its *area* or *targets* of interest. Having all the sensors remain "on" would ensure coverage but this would also significantly reduce the lifetime of the network as the nodes would discharge quickly. A standard approach taken to maximizing the lifetime is to make use of the overlap in the sensing regions of individual sensors caused by the high densit y of deployment. Hence, only a subset of all sensors need to be in the "on" or "sense" state, while the other sensors can enter a low power "sleep" or "off" state. The members of this active set, also known as a *cover* set, are then periodically updated so as to keep the network alive for longer duration. In using such a scheduling scheme, there are two problems that need to be addressed. First, we need to determine how long to use a given cover set and then we need to decide which set to use next. This problem has been shown to be NP-complete [1, 6].

A key problem here is that since a sensor can be a part of multiple covers, these covers have an impact on each other, as using one cover set reduces the lifetime of another set that has sensors common with it. By making greedy choices, the impact of this dependency is not being considered, since none of the heuristics in the literature study this reduction in the lifetime of other cover sets caused by using a sensor that is a member of several such sets. The earlier disjoint formulations mentioned in the previous section, entirely avoided this problem by preventing it.

We capture this dependency between covers by introducing the concept of a local Lifetime Dependency (LD) Graph. This consists of the cover sets as nodes with any two nodes connected if the corresponding covers intersect. The graph is an example of an intersection graph since it represents the sensors common to different cover sets. By looking at the graph locally (fixed 1-2 hop neighbors), we are able to construct all the local covers for the local targets and then model their dependencies. Based on these dependencies, a sensor can then prioritize its covers and negotiate these with its neighbors. We also present some simple heuristics based on the graph. The material presented in this section was published in [35].

**Figure 1.** A sensor network

8 Will-be-set-by-IN-TECH

lives. A target is defined as a *sink* if it is the shortest-life target for at least one sensor covering that target. Otherwise, it is a *hill*. To guard against leaving a target uncovered during a shuffle, each target is assigned an in-charge sensor. For each sink, its in-charge sensor is the one with the largest battery for which this is the shortest-life target. For a hill target, its in-charge is that neighboring sensor whose shortest-life target has the longest life. An in-charge sensor does not switch off unless its targets are covered by someone. Apart from this, the rules are identical as those in LBP protocol. DEEPS relies on two-hop information to make these decisions.

In this section, we introduce the Lifetime Dependency (LD) Graph as a model for the maximum lifetime coverage problem defined in Section 3. This model is a key contribution of this dissertation since the heuristics and algorithms that follow in subsequent sections rely

Recall from Section 3 that given a sensor network and a set of static targets, the maximum lifetime sensor scheduling problem is to select a subset of sensors that covers all targets and then periodically shuffle the members of this subset so as to maximize the total time for which

Since these sensors are powered by batteries, energy is a key constraint for these networks. Once the battery has been exhausted, the sensor is considered to be dead. The lifetime of the network is defined as the amount of time that the network can satisfy its coverage objective, i.e., the amount of time that the network can cover its *area* or *targets* of interest. Having all the sensors remain "on" would ensure coverage but this would also significantly reduce the lifetime of the network as the nodes would discharge quickly. A standard approach taken to maximizing the lifetime is to make use of the overlap in the sensing regions of individual sensors caused by the high densit y of deployment. Hence, only a subset of all sensors need to be in the "on" or "sense" state, while the other sensors can enter a low power "sleep" or "off" state. The members of this active set, also known as a *cover* set, are then periodically updated so as to keep the network alive for longer duration. In using such a scheduling scheme, there are two problems that need to be addressed. First, we need to determine how long to use a given cover set and then we need to decide which set to use next. This problem has been

A key problem here is that since a sensor can be a part of multiple covers, these covers have an impact on each other, as using one cover set reduces the lifetime of another set that has sensors common with it. By making greedy choices, the impact of this dependency is not being considered, since none of the heuristics in the literature study this reduction in the lifetime of other cover sets caused by using a sensor that is a member of several such sets. The earlier disjoint formulations mentioned in the previous section, entirely avoided this problem

We capture this dependency between covers by introducing the concept of a local Lifetime Dependency (LD) Graph. This consists of the cover sets as nodes with any two nodes connected if the corresponding covers intersect. The graph is an example of an intersection graph since it represents the sensors common to different cover sets. By looking at the graph locally (fixed 1-2 hop neighbors), we are able to construct all the local covers for the local targets and then model their dependencies. Based on these dependencies, a sensor can then

**5. The lifetime dependency graph model**

heavily on the LD Graph.

the network can cover all targets.

shown to be NP-complete [1, 6].

by preventing it.


**Abstract**

The development of surface engineering techniques to tune-up the composition, structure, and function of materials surfaces is a permanent challenge for the scientific community. In this chapter, the electrospinning process is proposed as a versatile technique for the development of highly hydrophobic or even superhydrophobic surfaces. Electrospinning makes possible the fabrication of nanostructured ultrathin fibers, denoted as electrospun nanofibers (ENFs), from a wide range of polymeric materials that can be deposited on any type of surface with arbitrary geometry. In addition, by tuning the deposition parameters (mostly applied voltage, flow rate, and distance between collector/needle) in combination with the chemical structure of the polymeric precursor (functional groups with hydrophobic behavior) and its resultant viscosity, it is possible to obtain nanofibers with highly porous surface. As a result, functionalized surfaces with water-repellent behavior can be implemented in a wide variety of industrial applications such as in corrosion resistance, high efficient water-oil separation, surgical meshes in biomedical applications, or even in energy systems for long-term efficiency of dye-sensitized solar cells, among others.

**Keywords:** electrospinning, superhydrophobicity, wettability properties, polymeric precursors, industrial applications

## **1. Introduction**

The measurement of the contact angle (CA) value is one of the most important parameters used for the determination and quantification of the wettability of solid surfaces. This CA is used to describe the behavior of a liquid droplet on a solid surface in air and is measured as the angle between the tangent at three phase points and the solid surface [1]. Accordingly, a surface is considered hydrophilic when the resultant solid surface shows a water contact angle (WCA) less than 90°, whereas a solid surface is considered hydrophobic when the WCA is higher than 90°. Nowadays, due to the development of the nanotechnology, bioinspired surfaces with special wettability properties are continuously emerging in the scientific research areas. Some representative examples are the design of novel surfaces with superhydrophilic (WCA < 10°) [2] or superhydrophobic (WCA > 150°) [3] behavior measured by water as well as surfaces with superoleophilic (CA < 10°) [4] or even superoleophobic (CA > 150°) [5] behavior measured by using oil droplets.

By convention, a superhydrophobic surface exhibits an extraordinary water contact angle value that is greater than 150° with a low sliding angle (typically less than 10°). The effect of the surface microstructure on the resultant water repellency can be explained by two distinct models depending on the degree of surface roughness such as the Wenzel model [6] and the Cassie-Baxter model [7]. According to the Wenzel model, the liquid is in contact with the entire exposed surface of the solid because the large interfacial energy at the water-solid interface induces the penetration of water into the surface cavities. However, in the Cassie-Baxter model, the liquid does not penetrate the hollows or cavities of the corrugated surface and the water droplets mostly contact air pockets that are formed between water and a rough solid surface. Consequently, in the Cassie-Baxter model, the superhydrophobic shows a lower sliding angle in comparison with the Wenzel state [8]. Till, the Cassie-Baxter state is preferred because of very small hysteresis and excellent rolling behavior even at till angles of a few degrees. In addition, it is known that some plants (i.e., lotus left), animal fur, or insect wings found in the nature can show this superhydrophobic behavior. According to this, in order to simulate this biological surface, the design of synthetic superhydrophobic surfaces is a continuous challenge in the scientific community [9].

The research is focused on the design of surfaces with a low surface energy combined with a hierarchical surface roughness on at least two different length scales (i.e., micrometric and nanometric morphology) [10]. Accordingly, multiple deposition techniques have been implemented for this specific purpose such as layer-by-layer assembly [11], sol-gel process [12], electrochemical deposition [13], chemical vapor deposition [14], lithography [15], physical vapor deposition [16], and chemical etching [17], among others. However, an interesting deposition technique is the electrospinning process because it is possible to induce the dual effect of low surface energy and the desired roughness with multiscale surface morphology, respectively [18]. In the electrospinning process, an electrostatic force is used to obtain electrically charged polymeric jet, which overcomes the surface tension of the polymeric solution. As a result, elongated fibers are accelerated from capillary tip and are then deposited onto collector with the corresponding evaporation of the solvent, thereby making possible the fabrication of fibers with a good control over their corresponding morphological, optical, and wetting properties [19]. In this sense, the fabrication of ultrathin or nanofibers can be obtained as a strict control of the several parameters such as applied voltage, flow rate, and viscosity of the polymeric precursor or distance to collector, among others [20, 21]. The surface modification to control the wettability of electrospun mats is possible due to the presence of fibers with micrometric and sub-micrometric diameter, thereby providing hierarchical surface with superhydrophobic behavior because of the small size of the resultant electrospun mats [22]. Finally, the number of scientific works based on the combination of electrospun fibers and superhydrophobic surfaces published in indexed journals has gradually increased. Potential applications can be found in areas as diverse as removal of oil from water, separation membranes, corrosion protection in metallic surfaces, or even in biomedical applications.

To sum up, this chapter is divided into the following subsections such as operational parameters in the electrospinning process, design of superhydrophobic surfaces composed of electrospun mats, and a summary table of the main applications derived from this work with their corresponding conclusions.

**191**

**Figure 1.**

*Electrospinning Technique as a Powerful Tool for the Design of Superhydrophobic Surfaces*

Electrospinning is a very versatile technique that can be implemented in a wide variety of polymeric precursors from biodegradable [23–24], copolymer [25–26], natural [27], or even synthetic nature [28–29]. The fundamentals of this deposition technique are based on the use of electrostatic forces with the aim to obtain polymeric electrospun fibers with the desired morphology (submicron or nanometric scale) as a function of the experimental parameters [30, 31]. The basic features of this deposition process are shown in **Figure 1** where a characteristic "Taylor cone" is formed during the projection of the fibers [32]. Under the action of the electric field, the droplets formed in the tip of needle are gradually elongated forming a characteristic conic shape. In addition, when the polymeric precursor has traveled through the air, the solvent is gradually evaporated during the flight of the fibers, and as a result, the fibers are finally deposited onto the

**Figure 2** shows the three main key factors that have to be controlled to obtain the electrospun fibers with the desired morphology. The first factor is related to the nature of the polymeric precursor, which is associated with its molecular weight, viscosity, molar concentration, surface tension, electrical conductivity, and solvent nature [35]. The second factor is inherent to the operation of the electrospinning setup such as applied high voltage, the flow rate, and tip-to-collector distance [36]. And the third factor is derived by the external environmental conditions such as the

*(a) The aspect of the fibers being electrospun from the needle that contains the polymeric precursor solution (poly acrylic acid, PAA). (b) Detail of the "Taylor cone" formed at the tip of the needle as a function of the*

*operational parameters. Reprinted with permission of Rivero et al. [32].*

**2. Operational parameters in electrospinning process**

*DOI: http://dx.doi.org/10.5772/intechopen.92688*

corresponding collector [33, 34].

relative humidity and temperature [37].

*Electrospinning Technique as a Powerful Tool for the Design of Superhydrophobic Surfaces DOI: http://dx.doi.org/10.5772/intechopen.92688*