Low-Grade Thermal Energy Harvesting: Advances in Materials, Devices, and Emerging Applications

Low-Grade Thermal Energy Harvesting: Advances in Thermoelectrics, Materials, and Emerging Applications provides readers with fundamental and key concepts surrounding low-grade thermal energy conversion while also reviewing the latest research directions. The book covers the most promising and emerging technologies for low-grade heat recovery, harvesting and conversion, including wearable thermoelectrics and organic thermoelectrics. Each chapter includes key materials, principles, design and fabrication strategies for low-grade heat recovery. Special attention on emerging materials such as organic composites, 2D materials and nanomaterials are also included. The book emphasizes materials and device structures that enable the powering of wearable electronics and consumer electronics.

The book is suitable for materials scientists and engineers in academia and R&D in manufacturing, industry, energy and electronics.

• Introduces key concepts and fundamental principles of low-grade thermal energy harvesting, storage and conversion
• Provides an overview on key materials, design principles and fabrication strategies for devices for low energy harvesting applications
• Focuses on materials and device designs that enable wearable thermoelectrics and flexible electronics applications

• Language: English
• Publisher: Elsevier Science
• Release date: Mar 22, 2022
• ISBN: 9780128236918

Book preview

Chapter 1

Principles of low-grade heat harvesting

Wei Lia, Shiren Wanga,b

aDepartment of Industrial and Systems Engineering, Texas A&M University, College Station, TX, United States bDepartment of Materials Science and Engineering, Texas A&M University, College Station, TX, United States

Abstract

Low-grade heat (below 100°C) is an abundant but often wasted source of energy. For example, 72% of the primary energy consumption in global industrial production is wasted as low-grade heat. Natural low-grade heat such as geothermal activity and solar spectrum even exceeds the annual energy consumption. Thus, harvesting such a tremendous amount of energy holds significant promise for a more sustainable society. To this end, various thermoelectric materials and concepts have been developed to convert a heat flux into an electrical current. The thermoelectric carriers can be categorized into electronic conductors, non-redox ions, and redox ions/molecules. Based on the basics of thermoelectric phenomena, three types of thermoelectric devices are among the state-of-the-art options, including thermoelectric generators, ionic thermoelectric supercapacitors/batteries, and thermogalvanic cells.

Keywords

Low-grade heat; Thermodiffusion effect; Thermoelectric material; Thermopower

1.1 Motivation

Low-grade heat (below 100°C) is an abundant but often wasted source of energy [1–3]. For example, 72% of the primary energy consumption in global industrial production is wasted as low-grade heat [1,4]. Natural low-grade heat such as geothermal activity and solar spectrum even exceeds the annual energy consumption [5–8]. Thus, harvesting such a tremendous amount of energy holds significant promise for a more sustainable society [9]. To this end, various thermoelectric materials and concepts have been developed to convert a heat flux into an electrical current. The thermoelectric carriers can be categorized into electronic conductors [10–12], nonredox ions [46], and redox ions/molecules [4,13–17]. Based on the basics of thermoelectric phenomena, three types of thermoelectric devices are among the state-of-the-art options, including thermoelectric generators [18], ionic thermoelectric supercapacitors/batteries [19], and thermogalvanic cells [20].

In this chapter, we present the general principles of thermoelectric materials. In the second section, we present the basic working principle of three thermoelectric devices. Then, we compare the performances of these thermoelectric devices in the third section [21].

1.2 Working principles of low-grade heat harvesting

1.2.1 Thermodiffusion effect

The thermodiffusion effect, also known as thermophoresis or the Soret effect, describes the mobile particle (uncharged) motion under a temperature gradient (∇T) [22]. Generally, mobile particles at the hot end move faster than those at the cold end. Therefore, hot particles have a larger mean free path and can spread farther than cold particles, resulting in a higher net particle density at the cold end, as shown in Fig. 1.1A. The particle current density (j) can be expressed as:

(1.1)

where c, D, and DT are particle concentration, diffusion coefficient, and thermodiffusion coefficient of a colloidal suspension, respectively. The two components of Eq. (1.1) respectively represent the movement of particles under a concentration gradient (∇c, kinetic diffusion) and a thermal gradient (∇T, thermal diffusion).

Fig. 1.1 (A) Schematic diagram of the thermodiffusion effects ( S T > 0) of particles; (B) Various thermoelectric effects based on different charge carriers, including electronic conductors, nonredox ions, and redox electrolytes [21].

According to the sign of DT, the particles will gather on the cold or the hot side. In a closed system, the steady-state means zero particle current (j = 0), resulting in a stationary concentration gradient:

(1.2)

where ST = DT/D is the Soret coefficient, which represents the ratio of DT to the ordinary diffusion coefficient D. The transport properties of mobile particles in liquids are strongly affected by molecular interactions, such as electrostatic and dispersion forces, as well as the hydrodynamic flows induced by moving particles [23].

If the particles under the thermal gradient are charged, the gathering of particles at the cold end will generate a repulsive electrostatic force and thus electric potential, pushing the charged particles back to the hot end. The electric potential difference (ΔV) induced by the temperature difference (ΔT) is called the Seebeck effect:

(1.3)

where S is the Seebeck coefficient, also known as thermopower. In the thermoelectric material with a ∆T, charge carriers move from the hot side (high entropy) to the cold side (low entropy), producing a steady-state voltage. The charge carriers include electrons, nonredox electrolytes, and redox electrolytes. Based on the types of the carriers, different working principles have been explored for thermoelectric conversion, as discussed in the following sections.

1.2.2 Seebeck effects

As for electronic thermoelectric materials, free electrons and holes are the charge carriers [24]. At the hot end of the thermoelectric material, there are more free charge carriers, so the entropy is larger than at the cold end. As a result, electrons and holes flow steadily to the cold end, where they recombine. From the perspective of thermodynamics, the thermoelectric effect is driven by the corresponding entropy flow from the hot to the cold end. In a closed geometry, the Seebeck coefficient is easily obtained from the case where thermodiffusion and thermoelectric current cancel each other out:

(1.4)

where σ and σT are the conductivity and thermodiffusion coefficients, respectively.

Similar to the Soret effect discussed in Section 1.2.1, the Seebeck coefficient is defined as:

(1.5)

where σ is always positive, and the sign of σT depends on whether electrons or holes dominate thermodiffusion.

In n-doped semiconductors, electrons are the main mobile charge carriers, thus a negative charge builds up at the cold end, creating a negative potential. Similarly, when holes are the main free carriers (p-type material), they will generate a positive potential at the cold end. By convention, the sign of the electronic Seebeck coefficient (S) is determined by the potential of the cold side relative to the hot side. In other words, with S < 0 for n-type semiconductors and S > 0 for p-type semiconductors. As shown in Fig. 1.2, the basic elements of an electronic thermoelectric device is a thermocouple composed of n-type and p-type TE materials, which are electrically connected in series and thermally in parallel. Dimensionless figure-of-merit, zT = σS²T/k, is used to evaluate the conversion efficiency of the electronic thermoelectric device. A detailed review of the electronic thermoelectric device is presented in Chapters 2 and 3.

Fig. 1.2 Schematic diagram of the electronic thermoelectric device relies on an p-type and a n-type material that drives electrons or holes from a heat source to sink [25].

1.2.3 Ionic Soret effects

Analogous to electrons, when the ions in the electrolyte are subjected to a thermal gradient (∇T), they thermally diffuse from the hot side to the cold side. This phenomenon leads to a concentration gradient ∇c/c = −ST∇T, which is the Soret effect, and an internal electric field E = −Si∇T, which is the Seebeck effect. These effects cause entropy flow through the nonequilibrium system [22]. Gradients of the Massieu−Planck entropy potentials −μ±/T provide the underlying thermodynamic forces on small ions, which comprise gradients of both temperature T(r) and concentration c±(r) quantities:

(1.6)

where the first term can drive thermodiffusion through the solvation enthalpy H±, and the second term can drive gradient diffusion. Considering the zero ion currents and Gauss’ law, the Soret coefficient of the salt solution and the Seebeck coefficient of the electrolyte are expressed as [26]:

(1.7)

(1.8)

Since the measured ionic enthalpies are generally negative (~kBT) [27], the Soret coefficient is usually positive. The Seebeck coefficient may take either sign with absolute value at the order of kB/e (~100 μV/K). Experimentally, the Si of the nonredox electrolyte sandwiched between two electrodes is measured from the ratio of the open-circuit potential (ΔV) to the ΔT between the hot and cold sides.

A typical thermionic capacitor is illustrated in Fig. 1.3. Although ions can be used as charge carriers to diffuse along the temperature gradient, they cannot pass through the metal electrodes to create an external current. Instead, ions will accumulate at the interface between the electrolyte and the metal electrodes. At this interface, the ions in the electrolyte and the electrons in the metal electrodes form an electric double layer (EDL), which generates a transient current when connected by an external circuit. The charge stored in EDL capacitors can be characterized by integrating the current [29,30]. Therefore, the ionic thermoelectric effect is not suitable for continuous operation. However, when high capacitance electrode materials such as porous carbon materials are used, the amount of accumulated charge can be greatly enhanced [31,32]. In a thermionic supercapacitor, thermal energy is first converted into stored electrical energy through the ionic thermoelectric effect and then consumed during discharging. A detailed review of nonredox electrolytes and ionic thermoelectric applications is presented in Chapters 4, 5, and 11.

Fig. 1.3 Schematic diagram of thermionic capacitors based on nonredox electrolyte [28]. (A) Thermal diffusion model of thermoelectric conversion. A tight bulk-liquid zone is close to the cold electrode, while a high ion mobility zone is close to the hot electrode. (B) The amounts of cations and anions are imbalanced at the cold and hot electrodes as the external connection is off in I-TE materials. (C) The imbalance of carriers induces electron flow in the circuits as the external connection is on, generating electricity.

1.2.4 Thermal electrochemical effects

When the redox-active electrolyte is subjected to the thermal gradient, it will undergo electrochemical reactions at the hot/cold electrodes:

(1.9)

During the electron transfer process, the free energy (ΔG) released or required by the reaction is expressed as the contributions of entropy (ΔS) and enthalpy (ΔH) [45]:

(1.10)

The temperature difference at the electrodes leads to a spatial change in fugacity, which in turn imposes a gradient of oxidant and reductant. In the stationary state, each ion species has zero current (Ji = 0). Thus, the potential difference between hot and cold electrodes can be denoted as ΔVredox = −Sredox ΔT, where the Seebeck coefficient is determined by the enthalpy of reaction:

(1.11)

As illustrated in Fig. 1.4, a typical thermocell (thermogalvanic cell) is composed of an electrolyte containing a redox couple and two electrodes at different temperatures. Since the redox electrolyte will transport the charge carrier through convection, diffusion, and migration between the two electrodes, constant power can be obtained by connecting two electrodes to the external load (RL) [34]. A detailed review of redox-active electrolytes in thermoelectric conversion is presented in Chapters 4, 6, 7, 8, and 9.

Fig. 1.4 Schematic diagram of thermocell based on redox-active electrolyte [33].

1.3 Performance characterization and comparison

1.3.1 Thermopower

Although the different working principles of the internal circuit, the three devices discussed in Section 1.2 can convert temperature difference input (∆T) into a device voltage output (∆VD) so that the electrons in the external circuit can do work [35]. Thermopower, also known as the Seebeck coefficient, is a numeric performance index of the energy conversion device used to evaluate the ∆VD/∆T ratio. Fig. 1.5 compares the electrical conductivity-dependent Seebeck coefficients of different thermoelectric materials. Unlike the electrical conductivity (σ) which is directly proportional to the charge carrier concentration (n) in the material, the Seebeck coefficient (S) generally decreases with the increase of the charge carrier concentration. High Seebeck coefficients (≥1 mV/K) are likely to be obtained in less conductive materials with large energy gaps [36]. However, the low electrical conductivity (below 10−12 S/cm) causes a large internal resistance, making practical applications challenging.

Fig. 1.5 Seebeck coefficient as a function of the electrical conductivity for electronic conductors, thermionic capacitors, and thermogalvanic cells [21].

Alternatively, the thermoelectric power factor (S²σ) is used to evaluate the heat-to-electricity conversion, which typically shows a maximum in semiconducting materials (10−5 S/cm < σ <10⁴ S/cm, and 50 μV/K < S < 500 μV/K). Therefore, research on electronic thermoelectric materials has mainly concentrated on semiconductors and semimetals. In addition, nonredox electrolytes (ionic capacitors) and redox electrolytes (thermocells) can produce larger Seebeck coefficients than electronic semiconductors, which make them promising for thermoelectric applications despite their low electrical conductivity [21].

However, some researchers have pointed out that it is misleading to equate or compare the measured value of ∆V/∆T ratio to the thermopower [35]. Thermopower originates in the Seebeck effect and is an intrinsic physical property of material described by a rank-2 tensor [20,37,38]. When ∆T is applied to the electronic conductor, charge carriers diffuse from the hot end to the cold end until the ∆V generated by the conductor counterbalances further diffusion. The thermopower of an electronic conductor is expressed as the material-specific ∆V/∆T ratio, in which the sign indicates the type of the majority carriers and the magnitude shows the average entropy per carrier charge [39]. Similarly, the ionic thermopower is used to describe the Soret effect of an ionic conductor [35]. In addition to this physically ΔT-induced V, chemical reactions can also contribute to the voltage difference. The ΔT-driven ∆V of the thermocell includes the thermodiffusive and thermogalvanic voltages [20]. The ∆VD/ΔT ratio of the thermocell can hardly reflect the thermopower of the constituent active materials [35]. Therefore, the ΔVD/ΔT ratio is distinct from the thermopower in concept and practice. It is faulty to compare the ΔVD/ΔT ratios of different thermoelectric devices at face value or reappropriate the formula of thermoelectric figure of merit of material to assess the performance of a device [35].

1.3.2 Power density

In addition to thermopower, power density is also an important indicator for evaluating the performance of thermoelectric devices [35]. The normalized maximum power density is denoted as PA−1ΔT−2, where P is the maximum power output and A is the cross-sectional area of the module perpendicular to the direction of heat flow. For thermionic capacitors and thermocells, the normalized maximum power density is at least one order of magnitude lower than that of the thermoelectric devices [40,41]. This difference is caused by the large internal resistance of thermoionic capacitors and thermocells. It is ineffective to shorten the distance between electrodes to reduce the internal resistance because it also reduces the driving force, ΔT. Compared with the eV-level driving force in conventional capacitors and batteries, a common ΔT = 20 K in low-grade heat harvesting energetically equals 1.72 meV. In addition, due to the weak driving forces, the power density and energy density of thermionic capacitors [42] are much lower than those of conventional capacitors and batteries [43].

1.3.3 Working mode

With the ΔT as the common driving force, the thermoelectric energy conversion devices’ working modes are determined by the specific mechanism of the ΔT-induced ΔV. Thermoelectricity is a single-fold process with a simple working principle, and the working media of its internal and external circuits are electrons. The heat-to-electricity conversion process of the thermionic capacitor is two-fold, and its ion diffusion is driven by ΔT and the interactions between the gathered ions and the electrodes [42]. The heat-to-electricity conversion process of the thermocell comprises the ΔT-induced ionic diffusion, the ionic concentration gradient caused by chemical reactions, the redox reactions at the electrodes, and the interactions between the electrolyte and the electrodes [20]. As a consequence, the electronic thermoelectric device and thermocell work in a continuous mode, and the main performance indicator is the power density. In contrast, the working mode of the thermionic capacitor is intermittent, and thus power density and energy density are the main performance indicators [35]. The high ΔVD/ΔT ratios (on the order of mV/K) have been achieved for thermionic capacitors [37,44] and thermocells [20], which are important to the application of wearable electronics and sensors [21].

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