**4. Climate migration and social changes**

The suffering and hardship of the climate migrants is a never-ending challenge. They faced natural hardships and hazards at their point of origin, and these hardships do not end when they arrive at their urban destination. Here they experience multiple aspects of deprivation, which restrict their efforts to attain a decent standard of living. For example, more than 65% of residents in the urban slums of Khulna do not have any sanitation facilities, 45% of slum dwellers do not have any fixed place to dispose of their garbage, and 35% are outside the garbage collection system [22]. This increased influx of migrants, driven by extreme climate events, poses new burden for the existing urban services.

Concerning climate migration and social challenges, it was found that the migration destination offered them little or no improvement in their housing, as they could not afford the cost of formal housing. Few migrant households could gain access to established urban slums. However, a big number of the migrant communities have no alternatives but to established themselves as squatters in urban fringe areas, on marginal agricultural land, along rail corridors, next to the highway, or even in the natural drainage network, as well as in low-lying flood-prone areas and on river banks, using very informal construction materials. These various forms of informal settlements provided immediate shelter for some of those migrants but failed to ensure social security and justice for them in an urban setup. **Figure 3** shows the different land uses occupied by migrants in Khulna City, offering them some kind of shelter.

About half of the total respondents in Khulna located themselves in urban fringe areas. This urban fringe land has been preserved for further urban expansion or to support landless or homeless communities. **Figure 4** portrays the informal settlements/housing of those migrants in urban fringe.

This research demonstrated that climate actions not only forced migrants to find a new place of residence, but also forced them to accept any kind of low-paid occupation to survive in the urban areas. Migrant communities were forced to become involved with different and often new economic activities to support themselves. Since they often have no experience beyond farming or fishing, the city does not offer them many options. For example, most of the jobs available in urban areas are basic daily service jobs. Migrants lack job security and are particularly vulnerable as they might not get work every day. Migrants also often needed to work longer hours to meet the cost of living in the city.

*Climate Change and Agriculture*

to migrate.

surges [19].

climate migrants.

quent salinity problems.

and vulnerable to extreme climate events. The impacts of changing temperatures, level of precipitation, more extreme weather events and rising sea level are already felt in Bangladesh and will continue to intensify [16, 17]. For example, hundreds of thousands of lives have been lost in Bangladesh due to recent catastrophic cyclones,

In their search for alternative livelihoods, displaced communities generally opt for nearby urban destinations where they have opportunities to earn and livelihoods are perceived to be available. Hence, they can be labelled as climate migrants and

It is estimated that each year between 300,000 and 400,000 people migrate to the country's capital to improve their economic prospects [18]. The poor internal migrants usually end up in the urban slums. The proportion of internal migration within urban slum areas varies, ranging from 53% in Dhaka (the capital) to 70% in Khulna and Rajshahi districts. The proportion of migrants is higher in the coastal belt districts because of extreme climate events including cyclones and frequent

**Figure 1** shows the number of natural disasters that have hit Bangladesh since 1993 and the total number of affected people. Concurrent natural disasters at high intensity have forced many victims to consider migration as their only viable adap-

Since 1993, almost every year the country gets affected with different natural disasters including flood, storms and cyclone. With high population density each disaster affects a huge number of population and that act as a natural push for displacement. **Figure 2** shows the migration trend and the underlying reasons for migration, based on results of a field survey of 100 heads of households who were identified as

Based on primary data, the largest numbers of migrants identified themselves as driven out by Cyclone Aila in May 2009, both by the cyclone itself and by subse-

notably Cyclone Sidr in November 2007, which caused almost 4000 deaths. Moreover, the frequency of cyclones in Bangladesh has increased more than five times over the last three decades [16]. Following Sidr, Cyclone Aila hit the coast on 25 May 2009 and about half a million people lost their land, homestead and livelihoods and had no option but to sail for a new life to an unknown place. Large areas of productive farmland were rendered useless as a result of inundation and subsequent salinity and in other cases were permanently flooded, forcing residents

are really a sub-category of internally displaced persons.

tive response (data adapted from EM-DAT [20]).

*Number of people affected by different natural disasters in Bangladesh since 1993.*

**172**

**Figure 1.**

**Figure 3.** *Location of climate migrants in urban areas [21].*

Table 1, showing the migrants' occupation at their origin and their current occupation in the city since they migrated. Following table, clearly indicates they have little-option but to accept whatever work they can find in the city to survive, and in most cases, those are labor-intensive occupations, even for the women.

**Table 1** indicates that almost half of the respondents working as a day labourer in the city were involved in different occupations at their place of origin. For example, they had been farmers, seasonal workers and small businessmen, but now forced to be a day labourer. Many of them have no experience about city life, earning and living style and standard in a complex urban system. That put them at the edge of vulnerability, when they are already displaced from their origin and vulnerable. Approximately 24 respondents were rickshaw pullers, and almost none of them had any previous experience in such labour-intensive jobs. Even the women who were housewives before migrating now forced to work as day labourers and domestic helpers to support their families to survive in the city. This change

**175**

of life of the residents.

The typical size of a slum house is 14 m2

musclemen, if they fail to pay the required tolls.

*Climate Change and Uncharted Social Challenge in Existing Urban Setup in Bangladesh*

in economic status also affects social relations and self-esteem. The following case demonstrates how climate migration and occupational change can affect the social

*Occupation of migrant household heads in urban areas compared to their previous occupation at their place of*

*Mariam is a 32-year-old woman who migrated with her husband and two boys from Kyora to Khulna due to Cyclone Aila. Mariam's family decided to migrate as they had lost everything, including their home and agricultural land at their place of origin. Her husband was working as a day labourer, her 8-year-old son worked in a shop and her 4-year-old son stayed at home with her. Her husband's and son's incomes were not enough to pay rent and buy food in the city, as they did not get work every day. Therefore, her husband forced her to try to earn extra income, but she failed, as she had never been to the city and was not skilled enough to fit into the urban job market. As she failed to support her family, her husband divorced her. Now Mariam is living on the urban fringe with her 4-year-old son and is serving as a housemaid. Forced migration has made her earn an income but has taken away her family.*

The lack of job security and opportunity or regular income for climate migrants

for a family of four. The average size of

,

The housing conditions of migrant are proportionate to their income and their access to urban facilities. They do not have access to established urban slums and minimum standard of life, like fresh water supply, sanitation and waste management. Therefore, they try to build their own place which is very informal in nature, mostly made of mud, hard plastic, cardboard, dry leaves and bamboo. None of these materials are formally used as construction materials. Houses or structures in the existing slums are constructed with similar materials and provide shelter for the urban poor and migrants but have very limited facilities such as access to clean water and toilets. **Figure 5** shows the typical condition of informal settlements of the migrants, which completely fail to meet the minimum standard

an individual squatter dwelling on urban public land and in fringe areas is 10 m2

and occupants are always under threat of eviction either by the government or local

in the informal sector has direct impacts on their household income.

*DOI: http://dx.doi.org/10.5772/intechopen.83409*

and family structures of migrant households.

**Table 1.**

*origin [21].*

**Figure 4.** *Typical informal settlements of migrant communities in urban fringe of Khulna [21].*

*Climate Change and Uncharted Social Challenge in Existing Urban Setup in Bangladesh DOI: http://dx.doi.org/10.5772/intechopen.83409*

#### **Table 1.**

*Climate Change and Agriculture*

**174**

**Figure 4.**

**Figure 3.**

*Location of climate migrants in urban areas [21].*

*Typical informal settlements of migrant communities in urban fringe of Khulna [21].*

Table 1, showing the migrants' occupation at their origin and their current occupation in the city since they migrated. Following table, clearly indicates they have little-option but to accept whatever work they can find in the city to survive, and in most cases, those are labor-intensive occupations, even for the women.

**Table 1** indicates that almost half of the respondents working as a day labourer

in the city were involved in different occupations at their place of origin. For example, they had been farmers, seasonal workers and small businessmen, but now forced to be a day labourer. Many of them have no experience about city life, earning and living style and standard in a complex urban system. That put them at the edge of vulnerability, when they are already displaced from their origin and vulnerable. Approximately 24 respondents were rickshaw pullers, and almost none of them had any previous experience in such labour-intensive jobs. Even the women who were housewives before migrating now forced to work as day labourers and domestic helpers to support their families to survive in the city. This change

*Occupation of migrant household heads in urban areas compared to their previous occupation at their place of origin [21].*

in economic status also affects social relations and self-esteem. The following case demonstrates how climate migration and occupational change can affect the social and family structures of migrant households.

*Mariam is a 32-year-old woman who migrated with her husband and two boys from Kyora to Khulna due to Cyclone Aila. Mariam's family decided to migrate as they had lost everything, including their home and agricultural land at their place of origin. Her husband was working as a day labourer, her 8-year-old son worked in a shop and her 4-year-old son stayed at home with her. Her husband's and son's incomes were not enough to pay rent and buy food in the city, as they did not get work every day. Therefore, her husband forced her to try to earn extra income, but she failed, as she had never been to the city and was not skilled enough to fit into the urban job market. As she failed to support her family, her husband divorced her. Now Mariam is living on the urban fringe with her 4-year-old son and is serving as a housemaid. Forced migration has made her earn an income but has taken away her family.*

The lack of job security and opportunity or regular income for climate migrants in the informal sector has direct impacts on their household income.

The housing conditions of migrant are proportionate to their income and their access to urban facilities. They do not have access to established urban slums and minimum standard of life, like fresh water supply, sanitation and waste management. Therefore, they try to build their own place which is very informal in nature, mostly made of mud, hard plastic, cardboard, dry leaves and bamboo. None of these materials are formally used as construction materials. Houses or structures in the existing slums are constructed with similar materials and provide shelter for the urban poor and migrants but have very limited facilities such as access to clean water and toilets. **Figure 5** shows the typical condition of informal settlements of the migrants, which completely fail to meet the minimum standard of life of the residents.

The typical size of a slum house is 14 m2 for a family of four. The average size of an individual squatter dwelling on urban public land and in fringe areas is 10 m2 , and occupants are always under threat of eviction either by the government or local musclemen, if they fail to pay the required tolls.

**Figure 5.** *Living standard and quality of life of the migrants [21].*

In Khulna, climate migrants clustered on the urban fringe are highly exposed and remain vulnerable to floods and waterlogged soil. At the same time, complex urban governance systems have no options or policy strategies to recognise and support them with basic service facilities beyond their service jurisdiction. Therefore, migrants who are living in urban fringe and city coasts are deprived of access to these facilities and consequently are exposed to risks of an unhygienic and unhealthy life.

According to The Daily Star [23], Khulna WASA (Water Supply and Sewerage Authority) provided 90 million litres of water daily to meet the demand of 240 million litres per day – a daily shortage of about 150 million litres. The existing services are limited even to city residents, are uncommon in existing slum areas and are nonexistent in the fringe areas. Tube wells are the main source of fresh water supply for migrants. Some migrants also use surface water, such as water from ponds, for everyday use, and obtain their drinking water from tube wells. **Figure 6** presents the various sources of water supply used for both drinking and domestic use by respondents.

More than 85 respondents obtained their drinking water from tube wells. For domestic use, most of the respondents used natural sources such as ponds, rivers and lakes. Those who were far from service facilities and could not afford a tube well had no choice but to drink from the natural sources such as ponds.

Climate migrants are considered an isolated community; they are not only deprived economically but also socially. They lose their dignity and cannot achieve a minimum standard of living at the migration destination. A ranking model has

**177**

*Climate Change and Uncharted Social Challenge in Existing Urban Setup in Bangladesh*

been used to understand the key challenges faced by the climate migrants in urban societies. In Khulna, a total of 46 respondents identified five different problems they faced as migrants and a 5-degree ranking model identified the challenges faced

> \_\_\_ Ro

here, V = value under the 5-degree scale; Ro = number of respondents; Rt = total

**Figure 7** presents the outcomes of the ranking model. According to the model, 'eviction threat' was one of the main problems faced by the migrant communities,

Most of the migrants are always afraid of eviction from their home, since they were occupying land without any land right or tenure ship. Though they were paying toll or protection money to the local leaders and muscleman, but that is not a formal land right. They know government could evict them without any notice and

Respondents also ranked housing quality as and living standard another key problem. Water supply, employment and sanitation facilities were ranked third, fourth and fifth, respectively, based on the respondents' opinions under the 5-degree scale, as shown in **Figure 5**. In view of such clear-cut evidence of precarious living conditions, it is important to develop and design innovative and effective

rights-based domestic solutions to climate displacement in Bangladesh.

addressed as a negative impact of livelihood in NAPA 2005 [25].

**5. Limitation to understand climate migration in urban governance**

The Bangladesh Government introduced the first National Adaptation Programme of Action (NAPA) in 2005 to address climate change and a possible adaptation approach. However, NAPA treated migration as an undesirable outcome of climate change. Under the Programme of Action, Project No. 11 states: "Affected community would not migrate to cities for job and livelihood" [24] (p. 36), and "Social consequences of mass scale migration to cities would to some extent be halted" [24] (p. 36). Furthermore, internal migration due to climate change is

Rt) × Di}. (1)

*DOI: http://dx.doi.org/10.5772/intechopen.83409*

by the migrants in this new social context.

*Social challenges prioritised by the climate migrants in urban areas [21].*

**Figure 7.**

V = {(

hence, it is ranked 4.4 under the 5-degree scale.

they would be on the road again.

number of respondents; and Di = 5, a value of common scale.

*Climate Change and Uncharted Social Challenge in Existing Urban Setup in Bangladesh DOI: http://dx.doi.org/10.5772/intechopen.83409*

**Figure 7.** *Social challenges prioritised by the climate migrants in urban areas [21].*

been used to understand the key challenges faced by the climate migrants in urban societies. In Khulna, a total of 46 respondents identified five different problems they faced as migrants and a 5-degree ranking model identified the challenges faced by the migrants in this new social context.

$$\mathbf{V} = \left\{ \left( \frac{\mathrm{Ro}}{\mathrm{Rt}} \right) \times \mathrm{Di} \right\}. \tag{1}$$

here, V = value under the 5-degree scale; Ro = number of respondents; Rt = total number of respondents; and Di = 5, a value of common scale.

**Figure 7** presents the outcomes of the ranking model. According to the model, 'eviction threat' was one of the main problems faced by the migrant communities, hence, it is ranked 4.4 under the 5-degree scale.

Most of the migrants are always afraid of eviction from their home, since they were occupying land without any land right or tenure ship. Though they were paying toll or protection money to the local leaders and muscleman, but that is not a formal land right. They know government could evict them without any notice and they would be on the road again.

Respondents also ranked housing quality as and living standard another key problem. Water supply, employment and sanitation facilities were ranked third, fourth and fifth, respectively, based on the respondents' opinions under the 5-degree scale, as shown in **Figure 5**. In view of such clear-cut evidence of precarious living conditions, it is important to develop and design innovative and effective rights-based domestic solutions to climate displacement in Bangladesh.

#### **5. Limitation to understand climate migration in urban governance**

The Bangladesh Government introduced the first National Adaptation Programme of Action (NAPA) in 2005 to address climate change and a possible adaptation approach. However, NAPA treated migration as an undesirable outcome of climate change. Under the Programme of Action, Project No. 11 states: "Affected community would not migrate to cities for job and livelihood" [24] (p. 36), and "Social consequences of mass scale migration to cities would to some extent be halted" [24] (p. 36). Furthermore, internal migration due to climate change is addressed as a negative impact of livelihood in NAPA 2005 [25].

*Climate Change and Agriculture*

*Living standard and quality of life of the migrants [21].*

and unhealthy life.

**Figure 5.**

**176**

**Figure 6.**

*Water supply facilities for respondents for drinking and domestic use [21].*

In Khulna, climate migrants clustered on the urban fringe are highly exposed and remain vulnerable to floods and waterlogged soil. At the same time, complex urban governance systems have no options or policy strategies to recognise and support them with basic service facilities beyond their service jurisdiction. Therefore, migrants who are living in urban fringe and city coasts are deprived of access to these facilities and consequently are exposed to risks of an unhygienic

According to The Daily Star [23], Khulna WASA (Water Supply and Sewerage Authority) provided 90 million litres of water daily to meet the demand of 240 million litres per day – a daily shortage of about 150 million litres. The existing services are limited even to city residents, are uncommon in existing slum areas and are nonexistent in the fringe areas. Tube wells are the main source of fresh water supply for migrants. Some migrants also use surface water, such as water from ponds, for everyday use, and obtain their drinking water from tube wells. **Figure 6** presents the various sources of water supply used for both drinking and domestic use by respondents. More than 85 respondents obtained their drinking water from tube wells. For domestic use, most of the respondents used natural sources such as ponds, rivers and lakes. Those who were far from service facilities and could not afford a tube

well had no choice but to drink from the natural sources such as ponds.

Climate migrants are considered an isolated community; they are not only deprived economically but also socially. They lose their dignity and cannot achieve a minimum standard of living at the migration destination. A ranking model has

In 2008, the Bangladesh Climate Change Strategy and Action Plan (BCCSAP) was prepared to focus on long- and mid-term goals of NAPA. The revised BCCSAP 2009 documents predict that "hundreds of thousands of people" will be forced to migrate, especially from coastal zones, because of decreasing livelihood opportunities and lowering agricultural productivity. It estimates that globally 6–8 million people could be displaced by 2050 just because of climate change [25]. The slums in big cities have been referred to as a highly possible destination for those who migrate. Considering the fast and unplanned ongoing urbanisation in Bangladesh, this poses an impending problem [26]. Despite the acknowledgement of significant migration due to climate change, clear policy guidelines for migrants have not been addressed, neither in NAPA nor in BCCSAP. Also, there are no guidelines for the national and local government to face such long-term social consequences of climate change. It could be argued that the limitation of understanding about cumulative impacts of climate change on social and institutional systems and the lack of capacity to respond to cumulative impacts climate change (migration, change of social structure) are the main barriers to incorporating climate change adaptation within the mainstream development process.

According to the Climate Investment Fund [27], adaptation policies that can address all the different impact levels should have three major components: (i) a coordination between local and national levels in order to understand impacts and vulnerabilities, (ii) a participatory approach where a broad range of stakeholders are involved rather than a single line ministry from the national level, and finally, (iii) an ongoing implementation of the adaptation process. Climate migrants have limited options to be noticed by the policy makers. At the same time the policy makers have limited understanding to differentiate the climate migrants from the traditional economic migrants. Stakeholder participation where victims such as climate migrants can also be incorporated, as well as NGOs who can be the voice of the vulnerable communities, is important as it can help to explain how the adaptation process should be implemented case-by-case or at policy level.

The policy gap and lack of understanding of climate migration and its urban impacts is the key limitation of the government to address this emerging social challenge.

### **6. Conclusions**

The Australia and Switzerland based International Organisation called Displacement Solutions [28] indicates "climate displacement in Bangladesh will only worsen as climate change increases the frequency of extreme natural hazards that are already leading to displacement across Bangladesh". This research provides clear evidences in support of this statement. Climate events in Bangladesh induce forced migration from coastal areas towards urban areas. This research confirms that too little is being done in Bangladesh to address the negative socio-cultural and economic changes of such migration in urban areas. Furthermore, lack of active urban governance very limited initiatives has yet been taken by to ensure quality of life and social justice for those vulnerable communities. Those migrants suffer deprivation of basic rights—not because of some nasty state action, but following from adverse natural conditions, brought about by human actions [3]. TO address this proliferation social challenges and changes it is important to have a details climate risks reduction plan to cover such slow-onset impact of climate change and the rights of climate migrants. Climate migration is not an impossible problem to address, but it needs to be seen as more than increasing numbers of urban poor.

**179**

**Author details**

Reazul Ahsan

provided the original work is properly cited.

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. 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,

Ujigawa Open Laboratory, Research Center for Fluvial and Coastal Disaster, Disaster Prevention Research Institute (DPRI), Kyoto University, Japan

*Climate Change and Uncharted Social Challenge in Existing Urban Setup in Bangladesh*

is support it would be hard to complete the field survey. Thank you.

 A special gratitude I give to Mr. Mukto Quazi Chief Executive of Pothikkrreith, who organised the audio-visual presentation in urban slums in Khulna to identify my target respondents for this research. Without

*DOI: http://dx.doi.org/10.5772/intechopen.83409*

**Acknowledgements**

*Climate Change and Uncharted Social Challenge in Existing Urban Setup in Bangladesh DOI: http://dx.doi.org/10.5772/intechopen.83409*


**3. Results and discussions**

#### **3.1 Derivation of the original current expression for various types of electrode mechanisms**

#### *3.1.1 Simple reversible electron transfer reaction (Erev or Er)*

A theoretical current (i) as a function of the applied potential (E), under semiinfinite linear diffusion, is expressed by the following relationship for a simple reversible electron-transfer process [1, 38]

$$\text{O} + \text{ne}^- \rightarrow \text{R (Nernstein)}\tag{1}$$

$$\text{id}(\mathbf{E}) = \text{id}\left[\mathbf{1}/(\mathbf{1} + \mathbf{e})\right] \tag{2}$$

where

*Advances in Derivative Voltammetry - A Search for Diagnostic Criteria of Several… DOI: http://dx.doi.org/10.5772/intechopen.96409*

**2.2 Peak currents, peak potentials, and peak widths and the ratios**

*Analytical Chemistry - Advancement, Perspectives and Applications*

Theoretical expressions for the first- second- and third- derivatives of currentpotential curves were analytically derived from successive differentiations of the original current expression (i.e., zeroth order derivative) obtained; then the derivatives as function of potential were computed and plotted. The raw and derived parameters (**Figure 1**) for the simple reversible process (Erev), calculated from the theoretical equations (Eq. 1–21; refer to Section 3.1.1) for lower order derivatives and those values given in the last column of **Table 1**; this analytical approach requires only a pencil and papers. However, for third derivatives for Erev and all derivatives for other types (Eiir, CEr, and ErC), it is difficult to derive analytical solutions (equations) to calculate values of the parameter. Thus, numerical

approaches had to be employed; namely, the values of a parameter as a function of an independent variable (such as a rate constant, k) had to be plotted on a graphs first, then a possible value or ranges of values were read from the graphs, and an equation for the relationships to calculate the parameters had to be found from such graphs, and this numerical approach requires much of computations, graph papers

graphically are summarized (refer to the results sections for details) in **Table 2** for

Theoretical equations for first, second and third derivatives for irreversible (and quasi reversible) processes are obtained with successive differentiations of analytical expressions of the current [15]. The derivatives of the CE type of mechanism are obtained with successive differentiations in a similar fashion [12, 13, 42]. Whenever possible, analytical solutions are sought after first because it is computationally less expensive. Numeral differentiations had to be adopted when analytical solution cannot be found. Thus, the analytical solutions of current expression and it's first derivative for the EC type of mechanisms are so complicated that analytical differentiations for the second and third derivatives were practically impossible [11, 14], numerical differentiations had to be adopted [14]. A value of ΔE = 1.0 mV was used for a finer resolution for all curves. The differentiation methods are summarized in **Table 3**.

**3.1 Derivation of the original current expression for various types of electrode**

A theoretical current (i) as a function of the applied potential (E), under semiinfinite linear diffusion, is expressed by the following relationship for a simple

> O þ ne� ! R Nernstian ð Þ (1) i Eð Þ¼ id 1½ � *=*ð Þ 1 þ e (2)

*3.1.1 Simple reversible electron transfer reaction (Erev or Er)*

reversible electron-transfer process [1, 38]

and a ruler. Those values of parameters, found analytically or numerically/

**2.3 Obtaining theoretical derivatives for various types of electrode mechanisms - analytical method vs. numerical (digital) method**

four types of the mechanisms for comparisons.

**3. Results and discussions**

**mechanisms**

where

**8**

*Notes: (a) Calculated for n=1and T=298o K for the reversible e*� *transfer rection (Third Column).*

*(b) All values for the irreversible case were calculated for ko =1.0x10*�*5 cm/s and αn=0.50;*

*For the case with αn* 6¼ *0.50, these values are not restricted to the ranges given above. those values the parentheses are calculated with ks=1.0x10*�*5 cm/s*

*(c) Values for quasi-reversible processes, calculated for αn=0.5, lie in between those for reversible processes and those for irreversible processes, hence the column for quasi-reversible cases is omitted.*

#### **Table 2.**

*Comparisons of values independent variable and derived parameters for various mechanisms.*

$$\mathbf{i}\_d = \mathbf{n} \mathbf{F} \mathbf{A} \mathbf{D}\_o^{-1/2} \mathbf{C}\_o / (\pi \mathbf{t})^{1/2} \text{ (the diffusion-controlled current)} \tag{3}$$

$$\mathbf{e} = \exp\left(\mathbf{nFE/RT}\right) \tag{4}$$

*<IP_ADDRESS> For the first derivatives*

*DOI: http://dx.doi.org/10.5772/intechopen.96409*

Wq

*<IP_ADDRESS> For the second derivatives*

1. Peak Potentials

2. Peak Currents

3. Peak Widths

**11**

W1/2

a ¼ Wq

Wq a *=*Wq i 0

*Advances in Derivative Voltammetry - A Search for Diagnostic Criteria of Several…*

**Figure 1B**) and their ratios. For a reversible process it was found [14].

One can examine the second derivative (i"), Eq. (6), to find

ated with the peaks. The two peak heights for the anodic, ip

2a � Ep

∣Ep 2a*=*Ep

ip

∣ip 2a*=*ip

2a ¼ �ip

Following relationships are found for Er type.

Ep

peaks are defined at two peak potentials, Ep

W1*=*2

2a ¼ W1*=*2

W1*=*2

2a*=*W1*=*2

The peak-potentials in Eq. 15 can be found by solving i'"(E) = 0 (Eq. 7) for E.

Thus, the second derivative (**Figure 1C**, solid line) *has the same symmetry as the*

2c which are the peak-widths for the anodic (positive) and cathodic (negative) peaks in the second derivative. It should be pointed out that the adjectives "anodic" and "cathodic" in this context are *not* related to the actual redox processes associ-

2a and Ep

*current with respect to its inflection point*. One can define shape parameters W1/2

negative (cathodic) parts to define two semi-peak widths (Wq

ð Þ¼ �E i 0

This means that the *first derivative is symmetrical with respect to an axis E = 0* (**Figure 1B**, solid line). The value of the peak-width at a half-height for the reversible process proved to be 90.5/n mV at 298 K [18]. A shape parameter from the first derivative can be defined; the peak widths are divided into positive (anodic) and

ð Þ E (10)

W1*=*2 ¼ 90*:*5mV (11)

c ¼ 1 at any temperature (13)

2c ¼ 68*=*n mV at 298 K ð Þ (15)

2c∣ ¼ 1*:*00 (16)

2c∣ ¼ l*:*00 (18)

2c ¼ 1*:*00 (20)

2c ¼ 62*:*5*=*n mV at 298 K ð Þ or (19)

2c (17)

c ¼ ð Þ 1*=*2 W1*=*2 ¼ 45*:*3*=*n mV at 298 K (12)

i}ð Þ¼� �E i}ð Þ E and i}ð Þ¼ 0 0 (14)

a and Wq

c ,

2a and

2c,

2a, and the cathodic, ip

2c, respectively (**Figure 1C**).

Eq. 5 shows

and E is an applied potential with respect to the reversible polarographic halfwave-potential, E1/2 (rev) or Eh. Other parameters and variables have their usual meanings. Eq. 2 is derived assuming DO = DR. Successive differentiations of Eq. 2 with respect to E yields [15].

$$\mathbf{i}'(\mathbf{E}) = -\mathbf{i}\_d(\mathbf{nF}/\mathbf{RT}) \left[ \mathbf{e}/(\mathbf{1} + \mathbf{e})^2 \right] \tag{5}$$

$$\mathbf{i}''(\mathbf{E}) = -\mathrm{id}(\mathbf{nF}/\mathbf{RT})^2 \left[ \mathbf{e} (\mathbf{e} - \mathbf{1})/(\mathbf{1} + \mathbf{e})^3 \right] \tag{6}$$

$$\mathbf{i}\text{ "}\text{ (E) = }-\text{id}(\text{nF/RT})^3 \left[ \mathbf{e} \left( \mathbf{e}^2 - 4\mathbf{e} + \mathbf{1} \right) / \left( \mathbf{1} + \mathbf{e} \right)^4 \right] \tag{7}$$

Examination of Eq. 2 reveals that

$$\dot{\mathbf{i}}(-\mathbf{E}) = \dot{\mathbf{i}}\_d - \dot{\mathbf{i}}(\mathbf{E}) \tag{8}$$

$$\mathbf{i}(\mathbf{0}) = \mathbf{i}\_{\mathbf{d}}/2 \tag{9}$$

This implies that *the i-E curve (solid line, Figure 1A) is symmetrical with respect to its inflection point (0, id/2)*.

**Table 3.**

*Methods of differentiation for various electrode mechanisms. Derivatives are obtained from the analytical solutions of currents for each cases, except for i", i"' with the post kinetics system (ErC).*

*Advances in Derivative Voltammetry - A Search for Diagnostic Criteria of Several… DOI: http://dx.doi.org/10.5772/intechopen.96409*

#### *<IP_ADDRESS> For the first derivatives*

Eq. 5 shows

$$\dot{\mathbf{i}}'(-\mathbf{E}) = \dot{\mathbf{i}}'(\mathbf{E}) \tag{10}$$

This means that the *first derivative is symmetrical with respect to an axis E = 0* (**Figure 1B**, solid line). The value of the peak-width at a half-height for the reversible process proved to be 90.5/n mV at 298 K [18]. A shape parameter from the first derivative can be defined; the peak widths are divided into positive (anodic) and negative (cathodic) parts to define two semi-peak widths (Wq a and Wq c , **Figure 1B**) and their ratios. For a reversible process it was found [14].

$$\mathbf{W}\_{1/2} = \mathbf{90.5mV} \tag{11}$$

$$\mathbf{W\_q^a} = \mathbf{W\_q^c} = (\mathbf{1}/2)\mathbf{W\_{1/2}} = \mathbf{45.3/n}\text{ mV at 298 K} \tag{12}$$

$$\mathbf{W\_q \triangleq / W\_q}^\* = \mathbf{1} \text{ at any temperature} \tag{13}$$

#### *<IP_ADDRESS> For the second derivatives*

id ¼ nFADo

W½

*Notes: (a) Calculated for n=1and T=298o*

*calculated with ks=1.0x10*�*5*

**Table 2.**

**Rw**

**Rw**

**Rw**

*(b) All values for the irreversible case were calculated for ko*

*cm/s*

i}0

Examination of Eq. 2 reveals that

**Types of Mechanisms Current**

with respect to E yields [15].

*its inflection point (0, id/2)*.

**Table 3.**

**10**

1*=*2

*for irreversible processes, hence the column for quasi-reversible cases is omitted.*

*Analytical Chemistry - Advancement, Perspectives and Applications*

i 0

i}ð Þ¼� E id nF ð Þ *=*RT 2

**i**

ErC(Post Chemical) i di'/dE *Δi"/ΔE*

*solutions of currents for each cases, except for i", i"' with the post kinetics system (ErC).*

Co*=*ð Þ πt 1*=*2 ð Þ the diffusion‐controlled current (3) e ¼ exp nFE ð Þ *=*RT (4)

2 h i

e eð Þ � 1 *=*ð Þ 1 þ e 3 h i

4 h i

ið Þ¼ �E id � i Eð Þ (8) i 0ð Þ¼ id*=*2 (9)

> **2nd Der. i"**

di'/dE di"/dE di"'/dE

*(numerical)*

(5)

(6)

(7)

**3rd Der. i"'**

*Δi"'/ΔE (numerical)*

and E is an applied potential with respect to the reversible polarographic halfwave-potential, E1/2 (rev) or Eh. Other parameters and variables have their usual meanings. Eq. 2 is derived assuming DO = DR. Successive differentiations of Eq. 2

**Parameters Definitions Er Eirr ErC CEr**

3c (mV) 54 >54 (63) >32, <42 >50, <54

**3 W½3a/W½3c 1.00 >1.00 (1.62) >1.0, <1.7 >1.00,<1.19**

**3a W½3a/W½3m 1.32 >1.32 (1.60) >1.3, <1.6 >1.19,<1.32**

**3c W½3c/W½3m 1.32 <1.32 (0.98) >1.0, <1.3 >1.32, <1.43**

*K for the reversible e*� *transfer rection (Third Column).*

*cm/s and αn=0.50;*

*=1.0x10*�*5*

*For the case with αn* 6¼ *0.50, these values are not restricted to the ranges given above. those values the parentheses are*

*(c) Values for quasi-reversible processes, calculated for αn=0.5, lie in between those for reversible processes and those*

*Comparisons of values independent variable and derived parameters for various mechanisms.*

ð Þ¼� E idð Þ nF*=*RT e*=*ð Þ 1 þ e

ð Þ¼� E id nF ð Þ *=*RT 3 e e2 � 4e þ 1 � �*=*ð Þ 1 þ e

This implies that *the i-E curve (solid line, Figure 1A) is symmetrical with respect to*

**1sit Der. i'**

Er(rev) i di'/dE di"/dE di"'/dE Eirr(irreversible) i di'/dE di"/dE di"'/dE CEr (Prior Chemical) i di'/dE di"/dE di"'/dE

*Methods of differentiation for various electrode mechanisms. Derivatives are obtained from the analytical*

One can examine the second derivative (i"), Eq. (6), to find

$$\mathbf{i}\,\mathbf{i}''(-\mathbf{E}) = -\mathbf{i}\,\mathbf{i}''(\mathbf{E}) \text{ and } \mathbf{i}\,\mathbf{i}''(\mathbf{0}) = \mathbf{0} \tag{14}$$

Thus, the second derivative (**Figure 1C**, solid line) *has the same symmetry as the current with respect to its inflection point*. One can define shape parameters W1/2 2a and W1/2 2c which are the peak-widths for the anodic (positive) and cathodic (negative) peaks in the second derivative. It should be pointed out that the adjectives "anodic" and "cathodic" in this context are *not* related to the actual redox processes associated with the peaks. The two peak heights for the anodic, ip 2a, and the cathodic, ip 2c, peaks are defined at two peak potentials, Ep 2a and Ep 2c, respectively (**Figure 1C**).

Following relationships are found for Er type.

1. Peak Potentials

$$\mathbf{E\_p}^{\text{2a}} - \mathbf{E\_p}^{\text{2c}} = \mathbf{68} / \mathbf{n} \text{ mV (at 298 K)}\tag{15}$$

$$|\mathbf{E\_p}^{\text{2a}}/\mathbf{E\_p}^{\text{2c}}| = \mathbf{1.00} \tag{16}$$

2. Peak Currents

$$\mathbf{i\_p}^{\text{2a}} = -\mathbf{i\_p}^{\text{2c}} \tag{17}$$

$$|\mathbf{i\_p}^{\text{2a}}/\mathbf{i\_p}^{\text{2c}}| = \text{l.00} \tag{18}$$

3. Peak Widths

$$\left| \mathbf{W\_{1/2}}^{\text{2a}} = \mathbf{W\_{1/2}}^{\text{2c}} = \mathbf{62.5/n} \text{ mV (at 298 K) or} \right. \tag{19}$$

$$\mathbf{W\_{1/2}}^{\text{Ta}} / \mathbf{W\_{1/2}}^{\text{2c}} = \mathbf{1.00} \tag{20}$$

The peak-potentials in Eq. 15 can be found by solving i'"(E) = 0 (Eq. 7) for E.

$$-\text{id}(\mathbf{nF}/\mathbf{RT})^3 \left[ \mathbf{e} \left( \mathbf{e}^2 - 4\mathbf{e} + \mathbf{1} \right) / \left( \mathbf{1} + \mathbf{e} \right)^4 \right] = \mathbf{0} \tag{21}$$

with respect to the diffusion coefficient (D): an electron transfer reaction is considered reversible if e� transfer is much faster the diffusion (i.e., ko > > (D/t)1/2), and irreversible if e� transfer is much slower the diffusion (ko < < (D/t)1/2) and quasi-

In the following sections, other types of processes than the simple reversible

*3.1.2 Theoretical expression for and the derivatives for Equasirev and Eirr types of electron*

Currents (i) as a function of the applied potential (E) for non-Nernstian (i.e., irreversible and quasi-reversible) system with a slower electron transfer, have been previously derived and given in several references [44, 54–56, 72, 73], and has final

All symbols have their usual meanings and may be refer to the reference for

E1*=*2 ¼ Eo þ ð Þ RT*=*nF ln Dð Þ R*=*DO

F Qt1*=*2 � � ¼ exp Q2

surface area, mostly is dependent on the heterogeneous rate constants (ko

current with respect to potential (E) yields the first derivative,

transfer coefficient (α) and n, and the curve found to exhibit an asymmetry [15]. Successive differentiations of the current yield the following expressions for the

first-, second- and third- derivatives respectively [15]. Taking derivative of the

in ¼ ð Þ πt*=*D 1*=*2

normalizing the current, Eq. (22), to the diffusion current, Eq. (3), yields

kf exp Q2

This normalized current, which is independent of the concentration and electrode

kf ð Þ �nF*=*RT F Qt1*=*2 � � þ 2Q' QtF Qt1*=*2 � � � ð Þ t*=*π

h h i (29)

, by adopting typical values of D (=5x10�5 cm2

*cm/s,*

t � �erfc Qt½ � � � � (22)

Q ¼ ð Þ kf þ kb *=*D½ (23)

t � �erfc Qt½ � � � � (27)

t � �erfc Qt½ � � (28)

½ ¼ Eo (26)

), the

1*=*2 Þ

kf ¼ ko exp �αnF E � Eo f g ð Þ*=*RT (24)

kb ¼ ko exp 1ð Þ � α nF E � Eo f g ð Þ*=*RT (25)

/s) and t

reversible if those competing rates are comparable (ko � (D/t)1/2).

*Advances in Derivative Voltammetry - A Search for Diagnostic Criteria of Several…*

*cm/s.*

I ¼ nFACokf exp Q2

In terms of values of ko

process will be treated.

assumed DR = DO = D.

*transfer*

details, where,

where,

i' ¼ ð Þ πt*=*D 1*=*2

**13**

*reversible for ko > 0.020 cm/s,*

*DOI: http://dx.doi.org/10.5772/intechopen.96409*

*irreversible for ko < 5x10*�*5*

*quasi-reversible for 0.020 cm/s > ko > 5x10*�*5*

forms of the following equations for a planar diffusion:

(=1.000 s).

As given in the value of the unity (1.0) for those symmetry parameters (i.e. anodic to cathodic peak-current ratios, anodic to cathodic half-peak-width ratios, and anodic to cathodic peak potential ratios) for first or second derivatives, the derivative curves are symmetrical.

#### *<IP_ADDRESS> For the third derivatives*

It's symmetry is the same as that of the first derivative, *being symmetrical with respect to E = 0*. One can find the ranges of parameter values in similar fashion for the third derivatives. Details of the work can be found elsewhere [15]: the key findings on the peak potentials, peak current and half peak widths and the various ratio for symmetry are given in **Tables 1** and **2**. It should be noted that all those values for the anodic to cathodic symmetry parameters (those ratios Rs) are unity, the same as in lower order derivatives.

As shown above, the values of parameters above for Er process are derived analytically from the equations which are much simpler than others. However, for an irreversible electron process (Eirr, or Equasirev) and chemically coupled electron transfer reactions such as ErC and CEr, the expressions for the current and their derivatives are so complicated that it is practically impossible to derive the values of those parameters analytically by solving algebraic equation (Refer to later section). Therefore, a numerical approach had to be adopted. Namely, (a) about 10 curves for derivatives vs. potentials at various values of independent variables (the heterogeneous rate constant ko and αn for simple electron transfer; the homogeneous constant Keq, kf, kb and k for chemically coupled electron transfer) had to be calculated, (b) then, all those curves are plotted out, and (c) those plots are analyzed graphically by examining the curves carefully in order to obtain values or equations (relationships) for those parameters.


**1. Introduction**

Novel methods of printing circuit boards and sensing devices are currently being developed [1–4]. Compared with traditional lithographic approaches, printing circuit boards is cost-effective and allows the production of large quantities of circuit boards with less waste. In the printing of electronic circuit boards, a conductive or semiconductive wiring ink is printed onto an insulating substrate, and the ink is then subjected to heat treatment for sintering. However, thermal treatment is problematic in that it heats not only the ink but also the substrate, which can damage the final circuit board. Therefore, alternative postprocessing methods are needed.

As alternatives to heat sintering, the application of microwaves [5], infrared light [6], and laser light [7,8] have been examined. In particular, the use of intense pulsed light (IPL) irradiation has been intensely researched [9–15]. In IPL sintering, a short pulse of light generated by a high-power xenon flash is applied to the ink and substrate; the light generated by the xenon lamp is absorbed by the ink and converted to thermal energy, which spreads throughout the circuit by thermal diffusion and causes the ink to undergo a chemical reaction. The total time required for IPL sintering is less than 1 min; therefore, IPL sintering allows printed circuit boards to be processed at high speed.

Kim's group is actively researching the use of IPL irradiation for the sintering of copper nanoparticles [9], silver nanoparticles [16], mixed silver and copper particles [17], and mixed copper particles of different sizes [18]. In their work using silver nanoparticles, they examined the temperature profile of a printed circuit pattern subjected to IPL irradiation and reported that the temperature of the ink was briefly increased to over 120 ◦C (the temperature needed for sintering of silver nanoparticles) without damaging the polyethylene terephthalate substrate (glass transition temperature = 62 ◦C). One reason why the substrate was protected from thermal damage during IPL sintering was that the ink was selectively heated because the ink and the substrate were colored and transparent, respectively. The temperature of the ink only was selectively increased for only a short time. Thus, in this respect, a suitable ink for IPL sintering is one that readily absorbs visible light.

Because of their cost-effectiveness and anti-ion-migration properties compared to silver, copper and copper-containing compounds such as copper oxide, copper salts, and organic copper complexes are useful materials for producing conductive patterns [19–22]. Although copper nanoparticles are potentially useful, they easily oxidize, and harsh thermal or reduction treatments are needed to remove the oxide layer because copper(II) oxide is chemically stable. As a novel material with which to produce a wiring ink, copper nitride (Cu3N) may be useful because of its oxidation resistance [23] and low decomposition temperature [24]. Copper nitride has an anti-rhenium oxide structure with lattice parameters of *a* = *b* = *c* = 0.3807 nm and α = β = γ = 90◦ [25], and it decomposes to copper and nitrogen at around 400 ◦C [26]. Importantly, copper nitride is red-purple, which means that it absorbs visible light [27].

Here, we examined the suitability of using copper nitride for producing wiring inks sintered by using IPL irradiation. Dispersions containing copper nitride were prepared, and their light absorption and thermal decomposition properties were compared with those of inks containing copper nitride (Cu3N), copper(I) oxide (Cu2O), copper(II) oxide (CuO), and copper (Cu). Furthermore, two types of ink were examined: a low-viscosity liquid ink to examine the properties conferred to the ink by the copper compound, and a high-viscosity paste ink to examine a more real-world application of our ink formulations. The copper conversion ratio and sheet resistance of the inks were also determined.


*5.2.1. Propagation dependence of the soft mode in STO18*

STO18 undergoes the structural phase transition from cubic to tetragonal at about *T*0 =108 K, which is slightly higher than *T*0 =105 K of STO16. On further cooling at *Tc* =24 K, however, STO18 transforms to the ferroelectric phase with orthorhombic structure (C2v). [25] Ferroelec‐ tric properties of highly substituted STO18 (higher than 33%) were confirmed by the enormous increase of the dielectric constant and the appearance of the hysteresis curve.

All the samples used in many laboratories were provided from Itoh's laboratory. The samples are thin plates of size 0.3 x 2 (or 3) x 7 mm3 with the widest plane [110]c, and the longest and the shortest edges are parallel to [001]c and [110]c, respectively. In the early stage, most samples used were not a single tetragonal domain but included many domains with different Zdirections. Thus, the reports measured with multi-domain samples were controversial and could not give consistent results. Fig.9

4

Figure 9 is the summary of the temperature dependence of the soft mode frequency in STO18 measured by various experiments. The data are from samples with a single tetragonal domain except for the neutron diffraction.

Fig.9 Temperature dependence of the ferroelectric soft mode of SrTiO3. *Tc* of STO18 are slightly different for various experiments but here it is assumed to be about 24K. Lines are guide for eyes. ○and □are neutron diffraction of STO18.[34] ×are hyper Raman of STO16 [35] and ▲(red) are hyper Raman of STO18 above *Tc* **Figure 9.** Temperature dependence of the ferroelectric soft mode of SrTiO3. *Tc* of STO18 is slightly different for various experiments but here it is assumed to be about 24 K. The solid lines are guide for eyes. ○ and □ are neutron diffraction of STO18 [34]. **×** are hyper Raman of STO16 [35] and ▲ are hyper Raman of STO18 above *Tc* measured under the elec‐ tric field [27]. ● are Raman scattering below *Tc* in STO18-99 [36]. Below *Tc*, only the Raman data clearly show the soft mode behavior in STO18.

measured under the electric field.[27] ● are Raman scattering below *Tc* in STO18-99.[36] Below *Tc* , Only the Raman data clearly show the soft mode behavior in STO18. Hyper Raman data under DC-electric field from STO18-96 show the softening similar to STO16 above *Tc*, but they do not give reliable data below *Tc*.[27] Neutron diffraction data hardly detect the influence of the phase transition [34]. Thus, the space group of STO18 below *Tc* has not yet been determined definitely. As we shall show later, it is probably because of the inhomogeneity of STO18 due to the existence of the paraelectric phase as a matrix of ferroelectric domains. Below *Tc*, only the Raman data succeeded in getting reliable soft mode frequencies [36]. Note that all these data show that the freezing of the soft mode (perfect softening) does *not* occur.

Later, highly substituted single-domain samples, STO18-99, became available. The results discussed below are the data obtained from such samples. For the correct assignment and interpretation, we found that the following features should be carefully taken into account [36]:

All the samples used in many laboratories were provided from Itoh's laboratory. The samples are thin plates of size 0.3 x 2 (or 3) x 7 mm3 with the widest plane [110]c, and the longest and the shortest edges are parallel to [001]c and [110]c, respectively. In the early stage, most samples used were not a single tetragonal domain but included many domains with different Zdirections. Thus, the reports measured with multi-domain samples were controversial and

4

Figure 9 is the summary of the temperature dependence of the soft mode frequency in STO18 measured by various experiments. The data are from samples with a single tetragonal domain

Fig.9 Temperature dependence of the ferroelectric soft mode of SrTiO3. *Tc* of STO18 are slightly different for various experiments but here it is assumed to be about 24K. Lines are guide for eyes. ○and □are neutron diffraction of STO18.[34] ×are hyper Raman of STO16 [35] and ▲(red) are hyper Raman of STO18 above *Tc* measured under the electric field.[27] ● are Raman scattering below *Tc* in STO18-99.[36] Below *Tc* , Only the Raman data clearly show the soft mode behavior in

**Figure 9.** Temperature dependence of the ferroelectric soft mode of SrTiO3. *Tc* of STO18 is slightly different for various experiments but here it is assumed to be about 24 K. The solid lines are guide for eyes. ○ and □ are neutron diffraction of STO18 [34]. **×** are hyper Raman of STO16 [35] and ▲ are hyper Raman of STO18 above *Tc* measured under the elec‐ tric field [27]. ● are Raman scattering below *Tc* in STO18-99 [36]. Below *Tc*, only the Raman data clearly show the soft

Hyper Raman data under DC-electric field from STO18-96 show the softening similar to STO16 above *Tc*, but they do not give reliable data below *Tc*.[27] Neutron diffraction data hardly detect the influence of the phase transition [34]. Thus, the space group of STO18 below *Tc* has not yet been determined definitely. As we shall show later, it is probably because of the inhomogeneity of STO18 due to the existence of the paraelectric phase as a matrix of ferroelectric domains. Below *Tc*, only the Raman data succeeded in getting reliable soft mode frequencies [36]. Note that all these data show that the freezing of the soft mode (perfect softening) does *not* occur.

could not give consistent results.

16 Ferroelectric Materials – Synthesis and Characterization

Fig.9

STO18.

mode behavior in STO18.

except for the neutron diffraction.

In the ferroelectric phase of STO18, five modes are observed in the low-frequency part below 50 cm-1 as one can see in Fig.10 and 11. Three of them are from the structural soft modes, as A1 (from A1g) at 44 cm-1 and A2 and B1 (from Eg) at 11 and 17.5 cm-1, respectively. Since these modes are nonpolar, the line width is narrow and does not depend on *K* → *p* (Fig.11(b) and (c)). In contrast, the behavior of the ferroelectric soft modes, TO(A1) and TO(B2), very broad and sensitive to *K* → *p* (Fig.11). It is also sensitive to the scattering geometries. For example, the polarization dependence of the spectra with *K* → *p* // X at a temperature well below *Tc* (at about 7K) is shown for three different geometries in Fig.10. Note that in the geometry (c) of Fig.10, the VV(Z, Z) spectrum is quite different from other geometries, since even for the same *K* → *p*, the selection rules are different for different geometries.

Spectra for *K* → *p* // Y (not shown in Fig.11) were found to be exactly the same as *K* → *p* // X, sug‐ gesting that there are two kinds of small domains with *P* → // X and *P* → // Y equally distributed in the sample, as we will discuss later.

In Fig. 11, the spectra for *K* → *p* // Z and *K* → *p* // X look similar except that there are two broad peaks in *K* → *p* // Z spectra while in *K* → *p* // X there is only one. Moreover, their temperature dependences are essentially different as we shall show in the next section.

It should be emphasized that the *K* → *p* // X + Y spectra (Fig.11(c)) are qualitatively different from other directions in the following two points: (1) The strong and broad peak at 20 cm-1 in the VV spectra of *K* → *p* // Z and *K* → *p* // X appears in *K* → *p* // X + Y at a lower frequency 17 cm-1. This means that the depolarization field in *K* → *p* // X + Y is weaker than that in *K* → *p* // Z or *K* → *p* // X, so that the mode at 17 cm-1 is not a pure TO(A1) mode. (2) In *K* → *p* // X + Y, there appear spurious modes (arrows in Fig. 11(c)) that are unable to assign to any mode in STO18. As we shall discuss later, these modes are originated from the matrix of the paraelectric phase.

Our final assignment of displacement and the symmetry of the ferroelectric soft modes are illustrated in Fig. 12(a) for temperature above *Tc* and in Fig. 12(b) for well below *Tc*. All the features of the observed spectra, including the subtle differences in the polarized spectra and the expected selection rules, were consistently explained *only* if the spontaneous polarization *P* → is either parallel to the tetragonal axes X or Y. *P* → cannot be along one of the cubic directions

**Figure 10.** Three different scattering geometries for the same propagation direction, *K* → *p* // X. Broad mode at 20 cm-1 is TO(A1) and the shoulder in HV and VH of (b) (shown by arrows) is TO(B2) [36] In the geometry (c), the VV(Z, Z) spec‐ trum is quite different from other geometries.

as one might expect for the Slater mode [26], since it is neither parallel to X ± Y (=[100]c or [010]c ) nor *Z* (=[001]c). If *P* → were parallel to one of the cubic axes, observed spectra never satisfy any selection rules. Reason for this unexpected result will be given later.

As one can see in Fig. 12(b), the doubly degenerate TO(Eu) splits into TO(A1) + TO(B2) when it propagates along Z, but when it propagates in the X-Y plane, TO(A1) changes to TO(B1) , of which displacement is perpendicular to *P* → . Since the displacement of TO(A1) is parallel to *P* → , it is reasonable that the frequency of TO(A1) (20 cm-1) is higher than TO(B1) (17.5 cm-1) and its intensity is stronger. Similar to the very strong external DC-field effect observed in STO16 (Fig. 8(c)), these differences are due to the effect of the depolarization field produced by *P* → .

### *5.2.2. Temperature dependence of soft mode in STO18*

Figure 13 is the temperature dependence of Raman spectra for different *K* → *p* directions.

In Fig. 13(a) only the broad and underdamped mode TO(A1) softens and becomes weaker on approaching *Tc* as it should be. In contrast, Fig. 13(b) shows that two modes, TO(A1) and

**Figure 11.** Polarized spectra at the lowest temperature for different propagation vector *K* → *p*. (a) *K* → *p* // Z, (b) *K* → *p* // X, and (c) *K* → *p* // X + Y. Assignment of the peaks are given in red letters. Arrows in (c) are the spurious modes due to the paraelectric structure existing below *Tc* as the matrix of ferroelectric domains.

TO(B2) clearly soften. It is clear that frequencies of the soft modes never go down to zero. Instead in the *K* → *p* // Z spectra, in addition to the soft modes, a quasi-elastic mode appears near *Tc* (arrows in Fig. 13(b)). It is observed not only below *Tc* but also above *Tc*. Moreover, it is observed only when *K* → *p* is out of the X-Y plane such as for *K* → *p* // Z and *K* → *p* // Z + Y [36, 37].

The absence of the quasi-elastic mode in *K* → *p* // X (Fig. 13(b)) implies that it is *not* an overdamped soft mode as in the KDP case (section 4.1) but is a relaxational mode originated from the large fluctuations of *P* → near *Tc* in the X-Y plane.

as one might expect for the Slater mode [26], since it is neither parallel to

TO(A1) and the shoulder in HV and VH of (b) (shown by arrows) is TO(B2) [36] In the geometry (c), the VV(Z, Z) spec‐

spectra never satisfy any selection rules. Reason for this unexpected result will be given later.

As one can see in Fig. 12(b), the doubly degenerate TO(Eu) splits into TO(A1) + TO(B2) when it propagates along Z, but when it propagates in the X-Y plane, TO(A1) changes to TO(B1) , of

it is reasonable that the frequency of TO(A1) (20 cm-1) is higher than TO(B1) (17.5 cm-1) and its intensity is stronger. Similar to the very strong external DC-field effect observed in STO16 (Fig.

In Fig. 13(a) only the broad and underdamped mode TO(A1) softens and becomes weaker on approaching *Tc* as it should be. In contrast, Fig. 13(b) shows that two modes, TO(A1) and

8(c)), these differences are due to the effect of the depolarization field produced by *P*

Figure 13 is the temperature dependence of Raman spectra for different *K*

**Figure 10.** Three different scattering geometries for the same propagation direction, *K*

→ were parallel to one of the cubic axes, observed

→

→ . Since the displacement of TO(A1) is parallel to *P*

→

→ ,

→ .

*p* directions.

*p* // X. Broad mode at 20 cm-1 is

X ± Y (=[100]c or [010]c ) nor *Z* (=[001]c). If *P*

trum is quite different from other geometries.

18 Ferroelectric Materials – Synthesis and Characterization

which displacement is perpendicular to *P*

*5.2.2. Temperature dependence of soft mode in STO18*

Another peculiar nature of the ferroelecticity of STO18 is the fact that even for a sample with 99% substitution, STO18 is *not* homogeneous contrary to the report by Taniguchi et al. [39], because the ferroelectric domains with *P* → //*X* and *P* → //*Y* coexist in the matrix of the paraelectric structure. The appearance of the spurious peaks in the *K* → *p* // X + Y spectra (Fig. 13(c)), which is FMR (Ferroelectric Micro-Domain) intrinsic to STO16, verifies the inhomogeneity of STO18.

The presence of the quasi-elastic mode in *K* → *p* // Z and its absence in *K* → *p* // X in STO18 were also reported by the independent two reports by Takesada et al. [17, 38] and Taniguchi et al. [39], respectively. As mentioned above, however, their conclusions are inconsistent with our results. Therefore, let us discuss briefly their results from our point of view.

**a.** Perfect softening of the Slater mode in STO18 was claimed in ref. [17] using a highresolution spectrometer. Their results, however, are based on *only* the spectra with *K* → *p* // Z. Above *Tc*, they assign a *very weak bump* below 5 cm-1 sitting on the strong quasielastic (our relaxational) mode as the underdamped soft mode TO(Eu). But below *Tc*, no such a narrow mode is observed and the strong quasi-elastic (our relaxational) mode is

**Figure 12.** Ferroelectric soft-mode frequency surfaces for various directions of phonon propagation vector *K* → *p*. X =[110] c and Y = 11 ¯0 c are the crystal axes of the tetragonal structure. (a) In the paraelectric phase near *Tc*. (b) In the ferroelectric phase well below *Tc*. Figure 12(b) is drawn for the case of *P* → // Y. Since in a sample of STO18, do‐ mains with *P* → // X and *P* → // Y coexist (in the matrix of paraelectric phase), observed spectra are the sum of the similar figure with the X and Y axes exchanged. Red arrows are the displacements in the X-Y plane and blue arrows are those out of the X-Y plane.

suddenly assigned as the overdamped soft modes TO(A1) and TO(B2) . (We note that the lowest mode is *not* A1 *but* B2 contrary to the assignment by Takesada et al. [17].) From the computer fitting of the overdamped spectra below *Tc*, they obtain the extremely steep dropping of the frequency of TO(B2) down to zero. However, as mentioned in the case of KDP, such analysis is very ambiguous and the sudden qualitative change of the soft mode at *Tc* is unnatural. From these results they concluded that STO18 is an ideal displacivetype ferroelectrics induced by the Slater-type soft mode. If such a perfect softening took place at *Tc* it would be much more clearly observed in the *K* → *p* // X spectra, since as shown

**Figure 13.** Temperature dependence of Raman spectra for different propagation directions: (a) *K* → *p* // X, (b) *K* → *p* //*Z*, (c) *K* → *p* // X + Y. The spectra for *K* → *p* // Y was identical to those for *K* → *p* // X. Note that in (b), a relaxational mode (blue lines) appears near *Tc* and in (c), a spurious mode (the arrows) is seen at about 5 cm-1 and no *pure* TO(A1) is observed.

suddenly assigned as the overdamped soft modes TO(A1) and TO(B2) . (We note that the lowest mode is *not* A1 *but* B2 contrary to the assignment by Takesada et al. [17].) From the computer fitting of the overdamped spectra below *Tc*, they obtain the extremely steep dropping of the frequency of TO(B2) down to zero. However, as mentioned in the case of KDP, such analysis is very ambiguous and the sudden qualitative change of the soft mode at *Tc* is unnatural. From these results they concluded that STO18 is an ideal displacivetype ferroelectrics induced by the Slater-type soft mode. If such a perfect softening took

¯0 c are the crystal axes of the tetragonal structure. (a) In the paraelectric phase near *Tc*. (b) In

→ // Y coexist (in the matrix of paraelectric phase), observed spectra are the sum of the similar

**Figure 12.** Ferroelectric soft-mode frequency surfaces for various directions of phonon propagation vector *K*

figure with the X and Y axes exchanged. Red arrows are the displacements in the X-Y plane and blue arrows are those

→

*p* // X spectra, since as shown

→ // Y. Since in a sample of STO18, do‐

→ *p*.

place at *Tc* it would be much more clearly observed in the *K*

the ferroelectric phase well below *Tc*. Figure 12(b) is drawn for the case of *P*

X =[110] c

mains with *P*

out of the X-Y plane.

and Y = 11

20 Ferroelectric Materials – Synthesis and Characterization

→ // X and *P*

in Fig. 13(a), in the *K* → *p* // X spectra no quasi-elastic mode appears near *Tc*. Furthermore, if the perfect softening were related to the Slater-type mode, the direction of *P* → should be parallel to cubic axis, which contradicts our results. Therefore, the essential difference between their interpretation and ours cannot be attributed to the difference of the resolution of the spectra.

**b.** Another essentially incorrect result was reported by Taniguchi et al. related to the homogeneity of STO18 [39]. They measured O18 concentration dependence of Raman spectra for SrTi(O18x O161-x)3. In this paper, they measured the spectra again *only* with a single *K* → *p*, not *K* → *p* // Z but *K* → *p* // X, in which the quasi-elastic mode is absent. Then it was concluded that the homogeneous ferroelectric phase changes into theferroelectricparaelectric phase coexistence state as thesystem approaches quantum critical point *x* =0.33 and that highly substituted STO18 undergoes the ideal soft-mode-type quantum phase transition. As the evidence of the criticality, they claim that the mode at 15 cm-1 which is the Eg mode intrinsic to the paraelectric phase appears only in the low substitution samples below *x* =0.33. However, as we have shown in the *K* → *p* // X + Y spectra (Fig. 13(c)), in addition to the FMR at 5 cm-1, the Eg mode at 15 cm-1 (in our case 14.5 cm-1) is certainly observed even in a very highly substituted sample with *x* =0.99. This is a clear evidence of the existence of the paraelectric phase as the matrix of the ferroelectric domains. In other words, the *inhomogeneity is the intrinsic property* of STO18. Therefore, the transition of STO18 with high x is *not* the ideal (homogeneous) soft-mode-type quantum phase transition. In this case, they should have measured the *K* → *p* dependence more carefully, especially the *K* → *p* // X + Y spectra, since they have noticed from our results [36] that *P* → is not along the cubic axes which suggests that the soft mode cannot be the Slater mode.


3.5.2. Polychromy Modifications

The cross-section analyses allowed us to identify the modification to the original polychromy. The loincloth was covered with gypsum (CaSO4·2H2O), identified by the two bands at 3528 cm−1 and 3398 cm−1 from the νO-H, and the band at 1095 cm−1 from the νS=O [50] identified in the μ-FTIR spectra (Figure 6f). Furthermore, the μ-Raman analysis suggested that a small amount of anhydrite is also present (Figure 7c). Additionally, the bands at 1651 cm−1 and 1544 cm−1 indicate the use of animal glue as a binder (inset of Figure 6f).

Regarding the flesh-tones, we identified two over paintings; the first composed of a double layer made of Pb-based pigments, mainly lead white, as suggested by the μ-Raman and SEM-EDX results (Table 2 and Figure S4). In these two layers, the SEM-EDX detected Cl, which can be associated with the presence of laurionite (PbCl2OH−) as a contaminant from the Pb ore deposits [58] or by the use of the Dutch method—developed mainly after the 16th century in the Netherlands—for the synthesis of lead white as suggested by Noun and colleagues [55,59].

We supposed that the second over painting of flesh-tones was performed using lithopone (ZnS, BaSO4, and traces of ZnO), as suggested by the presence of Zn, Ba, and S. To obtain the required hue, other pigments containing Fe and Cr were added. The presence of lithopone in this layer allowed us to date this modification to after 1874 [60].

#### **4. Discussion**

Before our study, some scholars, particularly Orozco [44], who was also involved in the construction of the current *Nuestra Señora de la Soledad* church, suggested that the sculpture was probably a substitution of the original because its characteristics, mainly the polychromy and the hair, were atypical for the 16th-century maize stem images.

The multianalytical analysis allowed us to understand the complex structure of the sculpture and confirm that it is the original (Figure 8). The artist considered the function of the sculpture during the Holy Friday and the need for reinforcement in the areas subjected to higher mechanical stress, such as the hands, feet, knees, arms, and the neck. In particular, the wooden elements used to reinforce the neck and the modification of the hair, and the upper part of the head may suggest that, originally, the head could move for the representation of Christ and that, probably, a wig and metallic crown were applied, as was usual for these kind of sculptures during the liturgical representations. However, a more detailed investigation is required to confirm this hypothesis.

In addition to understanding the sculptural technology, based on the formal and technical examination, we were able to associate the sculpture to the Cortés workshop, particularly to the production in the 1580s decade, and identify the changes it has suffered over time. Indeed, the hollowed structure obtained using a two-half mold is similar to the structure of other previously studied sculptures attributed the Cortés workshop and can be associated to artists with a stronger influence of the Eu-

ropean traditions (*papelón* or *cartapesta*) concentrated in the capital of the New Spain viceroyalty [2,10,12].

**Figure 8.** General scheme of the *Señor del Santo Entierro* sculpture.

The polychromy modifications can be associated with changes in preference and taste, particularly the flesh-tones. As the cross-section samples show, the profuse blooding represented in the original polychromy, which is a characteristic of the Christ images of the 16th and 17th centuries, was covered and substituted with more decorous polychromy for the tastes of the 19th century. Indeed, the Guadalajara cathedral, where the sculpture was placed for several years, suffered a complete renovation during the 19th century to adapt it to the neoclassical taste [61].

Finally, the presence in Guadalajara city of a sculpture made close to Mexico City despite the vicinity of the Michoacán region, suggests a particular link between the confraternity and the capital of New Spain. The acquisition of a statue produced in a specific region can be linked to a particular interest on certain workshops. Further studies are required to understand the trade routes of this typology of sculptures.


**4.1. A rotary desiccant cooling system using PVT collectors and PCMs**

Rotary desiccant cooling systems have been considered as one of the alternative approaches to replacing conventional vapour compression systems as such systems do not use chlorofluorocarbons and have the capability of independent temperature and humidity control [34, 35]. Compared to traditional vapour compression systems, rotary desiccant cooling systems are more energy efficient and environmentally friendly [34]. In a rotary desiccant cooling system, the cooling process is achieved by removing the moisture from the process air using a desiccant wheel and reducing the temperature of the process air using evaporative cooling and other cooling technologies.

**Figure 13** presents the schematic of a rotary desiccant cooling system integrated with a hybrid photovoltaic thermal-solar air heater (PVT-SAH) and a PCM TES unit. In this system, the hybrid PVT-SAH (see **Figure 14**), in which the PVT collector and the SAH were connected in Solar-Assisted HVAC Systems with Integrated Phase Change Materials http://dx.doi.org/10.5772/intechopen.72187 31

**Figure 13.** Schematic of the desiccant cooling system with integrated PVT-SAH and a PCM TES unit.

series, was used for both electricity and low-grade thermal energy generation. A glass cover and fins were used to improve the thermal efficiency of the device. The thermal energy collected from the PVT-SAH can be used to drive the desiccant wheel regeneration in cooling conditions or for space heating in heating conditions. The use of such a hybrid system is to achieve a relatively higher air temperature from the PVT-SAH while still maintaining the necessary electricity generation. An air-based PCM TES unit was used to regulate the discrepancy between the thermal energy generated from the PVT-SAH and the thermal energy demand for the desiccant wheel regeneration. A number of PCM arrays were arranged in parallel to create air channels and form the PCM TES unit. A desiccant wheel and an indirect evaporative cooler as well as a heat recovery unit were used to condition the process air.

This system can be used for both daytime and night-time cooling dependent on the building cooling demand. During the daytime, if there is a cooling demand, the heated air from the PVT-SAH will be directly used for the desiccant wheel regeneration. Otherwise, the heated air from the PVT-SAH will be used to charge the PCM TES unit. During the night-time, the heat stored in the PCM TES unit will be used for the desiccant wheel regeneration if there is a cooling demand of the building. It is worthwhile to note that the night-time radiative cooling of the PVT-SAH could be potentially used for space cooling directly. However, such scenario was not considered in this study. During the winter daytime, the heated air from the PVT-SAH can be directly used for space heating or to charge the PCM TES unit. The main potential operation modes of this proposed system are presented in **Table 1**.

**Figure 14.** Schematic of the hybrid PVT-SAH system.

An air conditioning system with integrated PVT collectors and a PCM TES unit (see **Figure 12**) was developed by Fiorentini et al. [32] for a Solar Decathlon house. A hybrid model predictive control strategy was also developed to optimise the operation of this system [33]. The experimental results showed that the control strategy developed was capable of effectively

**Figure 12.** Schematic of the solar-assisted HVAC system (where S/A—supply air, O/A—outside air, R/A—return air,

From the above-mentioned review, it can be seen that solar-assisted HVAC systems with integrated PCMs offered more flexibility to maximise the system operation through the rational utilisation of solar energy. However, the research in this area is far from sufficient, and more

In this section, two different HVAC systems with integrated PCMs and air-based PVT collec-

Rotary desiccant cooling systems have been considered as one of the alternative approaches to replacing conventional vapour compression systems as such systems do not use chlorofluorocarbons and have the capability of independent temperature and humidity control [34, 35]. Compared to traditional vapour compression systems, rotary desiccant cooling systems are more energy efficient and environmentally friendly [34]. In a rotary desiccant cooling system, the cooling process is achieved by removing the moisture from the process air using a desiccant wheel and reducing the temperature of the process air using evaporative cooling

**Figure 13** presents the schematic of a rotary desiccant cooling system integrated with a hybrid photovoltaic thermal-solar air heater (PVT-SAH) and a PCM TES unit. In this system, the hybrid PVT-SAH (see **Figure 14**), in which the PVT collector and the SAH were connected in

prototypes are needed to demonstrate the practical performance of such systems.

**4. Development of solar-assisted HVAC systems with integrated**

**4.1. A rotary desiccant cooling system using PVT collectors and PCMs**

managing and optimising the efficiency of this system.

E/A—exhaust air, F—fan and D—damper) [32].

30 Sustainable Air Conditioning Systems

**PCMs**

tors are presented.

and other cooling technologies.

**Table 1.** Operation models of the desiccant cooling system with the PVT-SAH and PCM TES unit.

The performance of this system was evaluated based on a simulation system developed using TRNSYS [36]. The building load was calculated based on a DesignBuilder [37] model reported in a previous study [38]. The details about the models used can be found in Ref. [39]. **Figure 15** illustrates the simulated performance of this system under five consecutive Brisbane (Australia) summer working days when the system was operated under the operation modes III and IV. In this test, it was assumed that, during the working days, the house was occupied from 17:00 to 8:00 next day, and the cooling was provided if needed. Under the operation mode III, the ambient air was heated by the PVT-SAH and then used for charging the PCM TES unit during the daytime, and the charging process was suspended if the outlet air temperature of the PVT-SAH was lower than the average surface temperature of the PCM bricks in the TES unit. Under the operation mode IV, the PCM TES unit was discharged using the preheated air from the heat recovery unit. The outlet air from the PCM TES unit was then used for the desiccant wheel regeneration, and the electric heater was used if the outlet air temperature was lower than the desiccant wheel regeneration temperature (i.e. 65°C) required. At the process air side, the return air from the indoor space was first mixed with the fresh air and then used as the process air in order to improve the system efficiency. The results from **Figure 15** showed that the supply air temperature and humidity ratio can be generally controlled below 20°C and 0.008 kg/kg dry air, respectively. During the majority of the test period, the heat from the PVT-PCM system satisfied the heat required for the desiccant wheel regeneration. The total contribution of the solar energy for the desiccant wheel regeneration during the whole test period was 96.5%.

a PVT fan, a PCM fan and an air source heat pump. The PVT collectors were used to generate electricity and low-grade thermal energy simultaneously. The two PCM layers with an air channel between them were integrated into the building ceiling to increase the local thermal mass and to serve as a centralised TES unit to temporarily store the thermal energy collected

**Figure 15.** Simulation results of the rotary desiccant cooling system using PVT collectors and PCMs. (a) Ambient air and supply air conditions of the desiccant cooling system. (b) Energy required for desiccant wheel regeneration and energy

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33

As shown in **Figure 17**, the system can operate under different modes depending on the weather conditions, the thermal energy stored in the PCM and the indoor heating demand through ON/OFF control of the dampers of D1-D8, the PVT fan, the PCM fan and the air source heat pump system. The details of the operation modes are summarised in **Table 2**. During the daytime, the heated hot air from the PVT collectors can be directed into the PCM TES unit for thermal energy charging by switching on the PVT fan and opening the dampers D2 and D3 or it can be exhausted directly by switching on the PVT fan and opening the damper D1. The thermal energy stored in the PCMs can be used to facilitate the space heating via preheating the return air for the indoor unit of the air source heat pump by switching on the PCM fan and opening the dampers D4, D6 and D8 or could directly be used for space heating by switching on the PCM fan and opening the dampers D4, D6 and D7. In the normal air conditioning mode, only the air source heat pump will be used to maintain the indoor

from the PVT collectors for later use to facilitate the indoor space heating in winter.

supplied by the PVT-PCM system.

#### **4.2. A heat pump system with integrated PVT collectors and PCMs**

The schematic of a heat pump system with integrated PVT collectors and PCMs laminated onto the building ceiling is shown in **Figure 16**. This system was mainly designed for winter space heating, as the main benefit of using the low-grade thermal energy derived from the PVT collectors is for space heating, although the night-time radiative cooling effect of PVT collectors in summer can also be used to improve the energy performance of the proposed system for indoor space cooling. The system consisted of the PVT collectors, two PCM layers,

The performance of this system was evaluated based on a simulation system developed using TRNSYS [36]. The building load was calculated based on a DesignBuilder [37] model reported in a previous study [38]. The details about the models used can be found in Ref. [39]. **Figure 15** illustrates the simulated performance of this system under five consecutive Brisbane (Australia) summer working days when the system was operated under the operation modes III and IV. In this test, it was assumed that, during the working days, the house was occupied from 17:00 to 8:00 next day, and the cooling was provided if needed. Under the operation mode III, the ambient air was heated by the PVT-SAH and then used for charging the PCM TES unit during the daytime, and the charging process was suspended if the outlet air temperature of the PVT-SAH was lower than the average surface temperature of the PCM bricks in the TES unit. Under the operation mode IV, the PCM TES unit was discharged using the preheated air from the heat recovery unit. The outlet air from the PCM TES unit was then used for the desiccant wheel regeneration, and the electric heater was used if the outlet air temperature was lower than the desiccant wheel regeneration temperature (i.e. 65°C) required. At the process air side, the return air from the indoor space was first mixed with the fresh air and then used as the process air in order to improve the system efficiency. The results from **Figure 15** showed that the supply air temperature and humidity ratio can be generally controlled below 20°C and 0.008 kg/kg dry air, respectively. During the majority of the test period, the heat from the PVT-PCM system satisfied the heat required for the desiccant wheel regeneration. The total contribution of the solar energy for the desiccant wheel regeneration during the whole test period was 96.5%.

reach the required setting

Mode III: TES charging The heated air from the PVT-SAH is used for charging the PCM TES unit if there is no demand during the daytime

cooling demand during night-time Mode V: space heating The heated air from the PVT-SAH is directly used for space heating or is

**Table 1.** Operation models of the desiccant cooling system with the PVT-SAH and PCM TES unit.

The heated air from the PVT-SAH will be directly used for desiccant wheel regeneration. The electric heater will be used if the air temperature does not

A fraction of the heated air from the PVT-SAH will be used for the desiccant

The PCM TES unit is discharged for desiccant wheel regeneration if there is a

directed into the TES unit (note: PCM with a different melting temperature should be used). The heat in the PCM can be used later for space heating

wheel regeneration, and the rest will be used for TES charging

**Operation mode Description**

Mode I: regeneration with PVT-

32 Sustainable Air Conditioning Systems

Mode IV: regeneration with TES

Mode II: regeneration with PVT-SAH direct supply and TES

SAH direct supply

charging

discharging

**4.2. A heat pump system with integrated PVT collectors and PCMs**

The schematic of a heat pump system with integrated PVT collectors and PCMs laminated onto the building ceiling is shown in **Figure 16**. This system was mainly designed for winter space heating, as the main benefit of using the low-grade thermal energy derived from the PVT collectors is for space heating, although the night-time radiative cooling effect of PVT collectors in summer can also be used to improve the energy performance of the proposed system for indoor space cooling. The system consisted of the PVT collectors, two PCM layers,

**Figure 15.** Simulation results of the rotary desiccant cooling system using PVT collectors and PCMs. (a) Ambient air and supply air conditions of the desiccant cooling system. (b) Energy required for desiccant wheel regeneration and energy supplied by the PVT-PCM system.

a PVT fan, a PCM fan and an air source heat pump. The PVT collectors were used to generate electricity and low-grade thermal energy simultaneously. The two PCM layers with an air channel between them were integrated into the building ceiling to increase the local thermal mass and to serve as a centralised TES unit to temporarily store the thermal energy collected from the PVT collectors for later use to facilitate the indoor space heating in winter.

As shown in **Figure 17**, the system can operate under different modes depending on the weather conditions, the thermal energy stored in the PCM and the indoor heating demand through ON/OFF control of the dampers of D1-D8, the PVT fan, the PCM fan and the air source heat pump system. The details of the operation modes are summarised in **Table 2**. During the daytime, the heated hot air from the PVT collectors can be directed into the PCM TES unit for thermal energy charging by switching on the PVT fan and opening the dampers D2 and D3 or it can be exhausted directly by switching on the PVT fan and opening the damper D1. The thermal energy stored in the PCMs can be used to facilitate the space heating via preheating the return air for the indoor unit of the air source heat pump by switching on the PCM fan and opening the dampers D4, D6 and D8 or could directly be used for space heating by switching on the PCM fan and opening the dampers D4, D6 and D7. In the normal air conditioning mode, only the air source heat pump will be used to maintain the indoor

**Figure 16.** Schematic of the heat pump system with integrated PVT collectors and PCMs.

thermal comfort through opening the dampers D5 and D8. It should be noted that the PVT direct heating mode may cause overheating during the daytime. However, under some cold weather conditions, the direct heating mode could be considered.

The performance of this system was evaluated through numerical simulation. The heating demand of the house was simulated using TRNSYS, and the indoor thermostat setting was specified according to NatHERS [40]. A two-layer PCM TES model (**Figure 18**) and a PVT model developed in a previous study [41] were used to facilitate the performance simulation of the proposed system. The governing equations for the energy balance of the PCM layers and the fluid air in the PCM TES unit are described in Eqs. (1) and (2), respectively. In the model of the PVT collector, six nodes were vertically discretised, including the glass cover, PV plate, absorber plate, fins, fluid air and the bottom plate. The governing equations for the glass cover and the fluid air are described in Eqs. (3) and (4), respectively, while the governing equations of the other nodes can be described in the same way.

$$
\rho\_{\rm PCM} \frac{\partial h\_{\rm PCM}}{\partial t} = \dot{k}\_{\rm PCM} \frac{\partial^2 T\_{\rm PCM}}{\partial y^2} \tag{1}
$$

∂ *T*\_\_\_\_*air*

*cp*,*g mg*

*cp*,*air ρair Aair δair*

PVT direct heating

Normal air conditioning

*cp*

∂*t* = *uair*

**Table 2.** Operation models of the heat pump system with PVT collectors and PCMs.

∂ *T*\_\_\_\_*g*,*i*

**Operation mode ON/OFF status of the dampers, fans and heat pump**

∂ *T*\_\_\_\_\_*air*,*i*

**Figure 18.** Schematic of the PCM TES model.

 Otherwise, the heat pump will be used, damper D8 is ON and damper D7 is OFF.

 Illustration of the system operating modes.

\*If the PCM discharging mode can maintain the required indoor thermal comfort, the heat pump is switched off, damper D8 is OFF and damper D7 is ON. Otherwise, the heat pump will be used, damper D8 is ON and damper D7 is OFF. \*\*The ON/OFF status is not related to the operation mode.

**Table 2.** Operation models of the heat pump system with PVT collectors and PCMs.

thermal comfort through opening the dampers D5 and D8. It should be noted that the PVT direct heating mode may cause overheating during the daytime. However, under some cold

The performance of this system was evaluated through numerical simulation. The heating demand of the house was simulated using TRNSYS, and the indoor thermostat setting was specified according to NatHERS [40]. A two-layer PCM TES model (**Figure 18**) and a PVT model developed in a previous study [41] were used to facilitate the performance simulation of the proposed system. The governing equations for the energy balance of the PCM layers and the fluid air in the PCM TES unit are described in Eqs. (1) and (2), respectively. In the model of the PVT collector, six nodes were vertically discretised, including the glass cover, PV plate, absorber plate, fins, fluid air and the bottom plate. The governing equations for the glass cover and the fluid air are described in Eqs. (3) and (4), respectively, while the governing

∂ *h* \_\_\_\_\_ *PCM*

∂*t* = *kPCM*

∂2 *T* \_\_\_\_\_\_ *PCM*

∂ *y*2 (1)

weather conditions, the direct heating mode could be considered.

**Figure 16.** Schematic of the heat pump system with integrated PVT collectors and PCMs.

equations of the other nodes can be described in the same way.

*ρPCM*

34 Sustainable Air Conditioning Systems

**Figure 17.** Illustration of the system operating modes.

$$\frac{\partial \ T\_{\dot{w}}}{\partial t} = \mu\_{\dot{w}} \frac{\partial \ T\_{\dot{w}}}{\partial \mathbf{x}} + \frac{1}{\rho\_{\dot{w}} \frac{c}{c\_{\rho \dot{w} \dot{r}}} \frac{\partial}{\partial r}} (q\_{\text{PCM-air}} - q\_{\text{abs-PCM}}) \tag{2}$$

$$\sigma\_{p,\emptyset} m\_{\emptyset} \frac{\partial T\_{yj}}{\partial t} = A\_{ai} (\alpha\_{\emptyset} I\_t + q\_{ncPV-yj} + q\_{ndPV-yj} - q\_{wind} - q\_{sky}) \tag{3}$$

$$\mathcal{L}\_{p, \text{air}} \rho\_{\text{air}} A\_{\text{air}} \delta\_{\text{air}} \frac{\partial T\_{\text{air}j}}{\partial t} = \mathcal{L}\_{p, \text{air}} M(T\_{\text{air}, \text{air}} - T\_{\text{air}, \text{at}, \text{l}}) + A\_{\text{ul}} (q\_{\text{conv, p-air}, \text{l}} + q\_{\text{conv, b-air}, \text{l}}) + 2 \, A\_{\text{fin}} q\_{\text{conv, fu-in}, \text{l}} \tag{4}$$

where *ρ* is the density, *h* is the specific enthalpy, *k* is the thermal conductivity, *u* is the velocity, *cp* is the specific heat capacity, *δ* is the thickness, *q* is the heat flux, *M* is the mass flow rate, *A* is the heat transfer area, *m* is the mass, the subscripts *PCM1* and *PCM2* represent the two PCM layers respectively, the subscripts *g*, *PV* and *b* represent the glass cover, the PV panel and

**Figure 18.** Schematic of the PCM TES model.

the bottom plate of the PVT collectors, and the subscripts *conv*, *rad*, *nc*, *wind* and *sky* indicate convective, radiative, natural convective, wind-driven and sky radiative, respectively. More details about the PVT model and the model validation can be found in Ref. [41].

The coefficient of performance (COP) of the heat pump system with the integrated PVT collectors and PCMs is determined by Eq. (5).

\*\*C.\*\*C.\*\* 2 uma 1 \*\*C.\*\* us is \*\*c.\*\* uma \*\*c.\*\*  $\text{buj. (c): }$

$$\text{COP = } \frac{Q\_{\text{today}}}{E\_{\text{tpp}} + E\_{\text{p7T}\text{fm}} + E\_{\text{pCM}\text{fm}}} . \tag{5}$$

**5. Conclusion**

Electricity (kWh)

can always operate at the optimal performance.

Solar-assisted HVAC system with integrated PCMs are a good alternative to conventional fossil fuel-driven vapour compression systems. Due to the intermittency of solar energy, the integration of PCM thermal energy storage units with solar-assisted HVAC systems provides a great opportunity to maximise the utilisation of solar energy and thus to increase the efficiency of HVAC systems. Two different HVAC systems with integrated PCMs and solar photovoltaic thermal collectors were presented, and their performance was investigated. The results showed that the solar thermal contribution for the desiccant wheel regeneration was 96.5% when using integrated PVT collectors and PCMs during the test period. The average COP of the heat pump system with integrated PVT collectors and PCMs for space heating was 5.21 during the test period, which was higher than the baseline case with a COP of 3.06. The results showed that the system performance can be improved through the integration of PCMs. For solar-assisted HVAC systems, control will be essential to ensure that the system

**Figure 21.** ON/OFF state of the heat pump under the PVT-PCM case and the *baseline* case.

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 -100

**Figure 20.** Accumulated electricity generation and consumption under the *PVT-PCM* case and the *baseline case*.

PVT-PCM case, Net electricity generation PVT-PCM case, Electricity generation PVT-PCM case, Total electricity consumption Baseline case, Total electricity consumption

Time (h)

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where *E* is the electrical energy consumed, and *Qheating* is the heating energy demand.

To evaluate the performance of this system, two cases were designed and simulated under winter weather conditions in Melbourne. In the *baseline* case, only an air source heat pump was used to condition an Australian house. In the *PVT-PCM* case, the air source heat pump integrated with PVT and PCMs was used for space heating. **Figure 19** presents the one-week winter weather conditions used for performance tests.

**Figure 20** compares the accumulated electricity generation and consumption during the test days and **Figure 21** illustrates the operation status of the heat pump unit under the two test cases. It is worthwhile to note that the PVT direct heating mode was not considered in this study. It can be seen that the accumulated electricity consumption under the PVT-PCM case was 42.3 kWh, which was much lower than the baseline case of 72.0 kWh. In comparison to the baseline case, the electricity saving was 41.1%, which was achieved through decreasing the operating time of the air source heat pump. The total electricity generation of the PV panels was 156.5 kWh under the *PVT-PCM* case. The average COP of the heat pump system with the integrated PCM layers in the building ceiling and PVT collectors for space heating during the selected week was 5.21, which was higher than that of the air source heat pump system in the *baseline* case (i.e. 3.06). The above-mentioned results indicated that this integrated heat pump system with PCMs and PVT collectors can substantially reduce the electricity consumption for winter space heating.

**Figure 19.** Weather data of a winter week.

**Figure 20.** Accumulated electricity generation and consumption under the *PVT-PCM* case and the *baseline case*.

**Figure 21.** ON/OFF state of the heat pump under the PVT-PCM case and the *baseline* case.


*5.3. Generation Greater Than Load (PG > PL)*

The Figure 10 shows that the available power generation is greater than load. When *PG* > *PL*, the available power is supplied to the consumers and excess power is stored in batterries. However, before storing energy in the batteries, the EMS checks the *SoC* of both the batteries. First, the priority load battery *SoC* will be checked and be based on the requirement in a particular interval. It will be charged, and next, the load-side battery *SoC* will be measured based on the level of *SoC*. When the *SoC* is minimized, the power is not delivered to the load; rather, it is stored in the batteries. In certain cases, the power will be extremely high and the load is quite low.Then, the battery is charged completely. There will be surplus power.Thus, the generation of power is cutoff.

*Appl. Sci.* **2018**, *8*, 585

**Table 2.** Simulated result values ("kW") of the DC microgrid with EMS.

**Figure 10.** Generation greater than load (*PG* > *PL*) (power vs. time).


**Abstract**

This chapter expresses the views of a teacher-researcher who advocates and argues for the use of humor in the classroom setting, especially in the mathematics classroom. While existing research based literature has shown the use of humor to be promising and encouraging effecting teaching and learning tool, very little instructional humor or classroom humor–an appropriate type of humor often related to the content materials being discussed–has been used in the classroom setting–especially in the mathematics classrooms. The chapter explores, surveys and highlights ways in which the existing-related literature about the effective and appropriate use of humor in the classroom setting can be implemented in practice, especially in the teaching and learning of mathematics, in this challenging era of the increasingly rapid technological advancements referred to as 21th century technological revolution or the re-engineering of industrial education 5.0 relative to STEM subjects study areas. The use of humor as teaching and learning tool in the classroom setting has been shown to have so many associated benefits ranging from but not limited to a conducive-relaxed learning environment, enhanced students' learning experience, motivating and inspiring the students to learn more and even the improvement of student-teacher classroom rapport, just to mention a few. Hence, the literature recommends that classroom teachers should make more use of humor as an effective teaching and learning tool, especially the contextualizedappropriate humor types that are related to the content materials being discussed.

**Keywords:** Classroom humor, mathematical humor, interest in mathematics, teaching and learning