As described above, **Am-Random-SQ-IL** had an amorphous structure and displayed IL nature. Its amorphous structure is probably one of the most important factors for such IL properties. Therefore, to investigate the correlation between the IL nature and the structures of the silsesquioxanes, we investigated the preparation of a POSS compound with crystalline structure using the same reagent and superacid catalyst. When the hydrolytic conden-

(1:19 v/v) instead of the aqueous solution as described above, a powdered POSS compound (**Am-Cage-SQ**) was prepared (**Scheme 1b**) [21]. A visual flow temperature of **Am-Cage-SQ** (~155°C) was much higher than that of **Am-Random-SQ-IL** because of the presence of higher *T*m (172°C), although pyrolysis temperature was notably high (*T*d5 = 420°C) (Run 2 in **Table 1**). Such high *T*ms and flow temperatures of these POSS compounds are probably derived from

**3. Preparation of imidazolium-type ionic liquids containing random-**

the imidazolium-group-containing organotrialkoxysilane using aqueous HNTf2

1-propanol, 2-propanol, chloroform, diethyl ether, toluene, and *n*-hexane.

gosilsesquioxane compound composed of imidazolium cations and NTf2

idity at ~40°C, i.e., it was not a room temperature IL (RT-IL). Generally, imidazolium-type ILs have relatively low *T*m [24]. Therefore, to prepare a RT-IL containing a randomly structured oligosilsesquioxane framework (**Im-Random-SQ-IL**), the hydrolytic condensation of

gated [25]. **Im-Random-SQ-IL** could be prepared from 1-methyl-3-[3-(triethoxysilyl)propyl] imidazolium chloride (MTICl) as a starting material by the same procedure for the preparation of **Am-Random-SQ-IL** as described above (**Scheme 2a**). **Im-Random-SQ-IL** was soluble in DMSO, DMF, methanol, acetone, THF, and ethyl acetate, but insoluble in water, ethanol,

The EDX pattern of **Im-Random-SQ-IL** also indicated the absence of Cl. In addition, the Si:S elemental ratio of **Im-Random-SQ-IL** was estimated to be 1:2.03, indicating that the

aforementioned quaternary ammonium salt-type IL (**Am-Random-SQ-IL**), this compound was also stable, although it had a relatively high proportion of the silanol groups. The *M*w of **Im-Random-SQ-IL** estimated by SLS data obtained in methanol was ca. 8.8 × 102

on these results, it was concluded that **Im-Random-SQ-IL** was a randomly structured oli-

The DSC analysis of **Im-Random-SQ-IL** was performed. The baseline shift assigned to *T*g was observed at −25°C (Run 3 in **Table 1**). Conversely, the endothermic peak due to *T*m was not detected. The amorphous structure of **Im-Random-SQ-IL** may give rise to poor packing of the ions. The flow temperature of **Im-Random-SQ-IL** was confirmed by the same procedure for **Am-Random-SQ-IL** as described above. Consequently, it showed obvious fluidity at

at 60°C exhibited two broad signals in the *T*2

(−64 to −70 ppm) regions with an integrated ratio of ca. 40:60. Similar to the

as a catalyst in water/methanol mixed solvent

Preparation of Ionic Liquids Containing Siloxane Frameworks

http://dx.doi.org/10.5772/65892

583

anions was ca. 1:1. The 29Si NMR spectrum of

anions.

of 15°C and exhibited flu-

was investi-

(−53 to −61

. Based

sation of TTACl was performed using HNTf2

their highly symmetrical and crystalline structures.

molar ratio of imidazolium cations to NTf2

~0°C, i.e., it is a RT-IL (Run 3 in **Table 1**).

**Im-Random-SQ-IL** in DMSO-*d*6

ppm) and *T*3

**structured and cage-like oligosilsesquioxanes**

As described in the previous section, **Am-Random-SQ-IL** had *T*g

The flow temperature of **Am-Random-SQ-IL** was visually confirmed by the following procedure: **Am-Random-SQ-IL** was kept horizontal at 100°C for 15 min in a glass vessel, and the sample in the vessel was cooled to room temperature in the horizontal state. Then, the vessel stood at various temperatures for 15 min with tilting. Accordingly, **Am-Random-SQ-IL** showed obvious fluidity over 40°C (Run 1 in **Table 1**).

The thermal stability of **Am-Random-SQ-IL** on pyrolysis was investigated by thermogravimetric analyses (TGA). The temperatures of 3% (*T*d3), 5% (*T*d5), and 10% (*T*d10) weight losses of **Am-Random-SQ-IL** (411, 417, and 425°C, respectively) (Run 1 in **Table 1**) were higher than those of *N,N,N*-trimethyl-*N*-propylammonium bis(trifluoromethanesulfonyl) imide ([TMPA][NTf2 ]) (392, 400, and 411°C, respectively), which is an IL compound with the structure of the side-chains of **Am-Random-SQ-IL**. These results indicate that the thermal stability of **Am-Random-SQ-IL** was enhanced by connection to the silsesquioxane framework.

a Determined by DSC.

b Determined by visual observation.

c Determined by TGA.

d Not detected.

**Table 1.** Properties of ILs containing siloxane frameworks.

As described above, **Am-Random-SQ-IL** had an amorphous structure and displayed IL nature. Its amorphous structure is probably one of the most important factors for such IL properties. Therefore, to investigate the correlation between the IL nature and the structures of the silsesquioxanes, we investigated the preparation of a POSS compound with crystalline structure using the same reagent and superacid catalyst. When the hydrolytic condensation of TTACl was performed using HNTf2 as a catalyst in water/methanol mixed solvent (1:19 v/v) instead of the aqueous solution as described above, a powdered POSS compound (**Am-Cage-SQ**) was prepared (**Scheme 1b**) [21]. A visual flow temperature of **Am-Cage-SQ** (~155°C) was much higher than that of **Am-Random-SQ-IL** because of the presence of higher *T*m (172°C), although pyrolysis temperature was notably high (*T*d5 = 420°C) (Run 2 in **Table 1**). Such high *T*ms and flow temperatures of these POSS compounds are probably derived from their highly symmetrical and crystalline structures.

When the differential scanning calorimetry (DSC) measurement of **Am-Random-SQ-IL** was

(Run 1 in **Table 1**). On the other hand, the endothermic peak due to *T*m could not be detected, indicating that **Am-Random-SQ-IL** is an amorphous compound. So far, ILs without *T*m have been reported, e.g., 1-butyl-3-methylimidazolium tetrafluoroborate [22] and 1-ethyl-3-methy-

The flow temperature of **Am-Random-SQ-IL** was visually confirmed by the following procedure: **Am-Random-SQ-IL** was kept horizontal at 100°C for 15 min in a glass vessel, and the sample in the vessel was cooled to room temperature in the horizontal state. Then, the vessel stood at various temperatures for 15 min with tilting. Accordingly, **Am-Random-SQ-IL**

The thermal stability of **Am-Random-SQ-IL** on pyrolysis was investigated by thermogravimetric analyses (TGA). The temperatures of 3% (*T*d3), 5% (*T*d5), and 10% (*T*d10) weight losses of **Am-Random-SQ-IL** (411, 417, and 425°C, respectively) (Run 1 in **Table 1**) were higher than those of *N,N,N*-trimethyl-*N*-propylammonium bis(trifluoromethanesulfonyl)

the structure of the side-chains of **Am-Random-SQ-IL**. These results indicate that the thermal stability of **Am-Random-SQ-IL** was enhanced by connection to the silsesquioxane

 **Am-Random-SQ-IL** 15 NDd ~40 417 **Am-Cage-SQ** NDd 172 ~155 420 **Im-Random-SQ-IL** −25 NDd ~0 437 **Im-Cage-SQ-IL** −21 106 ~100 436

 **Amim-Cage-SQ-IL** −8 NDd ~30 420 **MeIm-CyS-IL-NTf2** −43 NDd ~0 415 **MeIm-CyS-IL-OTf** −14 NDd ~20 391 **HIm-CyS-IL-NTf2** −38 NDd ~0 – **EtIm-CyS-IL-NTf2** −44 NDd ~0 – **PrIm-CyS-IL-NTf2** −44 NDd ~0 – **BuIm-CyS-IL-NTf2** −45 NDd ~0 –

]) (392, 400, and 411°C, respectively), which is an IL compound with

 **(°C)a** *T***m (°C)a Flow temp. (°C)b** *T***d5 (°C)c**

−7 164 ~120 420

) was observed at 15°C

performed, the baseline shift assigned to the glass-transition point (*T*g

limidazolium phosphonate derivatives [23].

582 Progress and Developments in Ionic Liquids

**Run IL** *T***g**

5 Mixture of **Am-Cage-SQ** and **Im-Cage-SQ-IL**

imide ([TMPA][NTf2

framework.

a

b

c

Determined by DSC.

 Determined by TGA. d Not detected.

Determined by visual observation.

**Table 1.** Properties of ILs containing siloxane frameworks.

showed obvious fluidity over 40°C (Run 1 in **Table 1**).

### **3. Preparation of imidazolium-type ionic liquids containing randomstructured and cage-like oligosilsesquioxanes**

As described in the previous section, **Am-Random-SQ-IL** had *T*g of 15°C and exhibited fluidity at ~40°C, i.e., it was not a room temperature IL (RT-IL). Generally, imidazolium-type ILs have relatively low *T*m [24]. Therefore, to prepare a RT-IL containing a randomly structured oligosilsesquioxane framework (**Im-Random-SQ-IL**), the hydrolytic condensation of the imidazolium-group-containing organotrialkoxysilane using aqueous HNTf2 was investigated [25]. **Im-Random-SQ-IL** could be prepared from 1-methyl-3-[3-(triethoxysilyl)propyl] imidazolium chloride (MTICl) as a starting material by the same procedure for the preparation of **Am-Random-SQ-IL** as described above (**Scheme 2a**). **Im-Random-SQ-IL** was soluble in DMSO, DMF, methanol, acetone, THF, and ethyl acetate, but insoluble in water, ethanol, 1-propanol, 2-propanol, chloroform, diethyl ether, toluene, and *n*-hexane.

The EDX pattern of **Im-Random-SQ-IL** also indicated the absence of Cl. In addition, the Si:S elemental ratio of **Im-Random-SQ-IL** was estimated to be 1:2.03, indicating that the molar ratio of imidazolium cations to NTf2 anions was ca. 1:1. The 29Si NMR spectrum of **Im-Random-SQ-IL** in DMSO-*d*6 at 60°C exhibited two broad signals in the *T*2 (−53 to −61 ppm) and *T*3 (−64 to −70 ppm) regions with an integrated ratio of ca. 40:60. Similar to the aforementioned quaternary ammonium salt-type IL (**Am-Random-SQ-IL**), this compound was also stable, although it had a relatively high proportion of the silanol groups. The *M*w of **Im-Random-SQ-IL** estimated by SLS data obtained in methanol was ca. 8.8 × 102 . Based on these results, it was concluded that **Im-Random-SQ-IL** was a randomly structured oligosilsesquioxane compound composed of imidazolium cations and NTf2 anions.

The DSC analysis of **Im-Random-SQ-IL** was performed. The baseline shift assigned to *T*g was observed at −25°C (Run 3 in **Table 1**). Conversely, the endothermic peak due to *T*m was not detected. The amorphous structure of **Im-Random-SQ-IL** may give rise to poor packing of the ions. The flow temperature of **Im-Random-SQ-IL** was confirmed by the same procedure for **Am-Random-SQ-IL** as described above. Consequently, it showed obvious fluidity at ~0°C, i.e., it is a RT-IL (Run 3 in **Table 1**).

The DSC curve for **Im-Cage-SQ-IL** indicated the baseline shift due to *T*g

RT-IL, in addition to the types of substituent groups in the silsesquioxanes.

imidazolium bis(trifluoromethylsulfonyl)imide ([C3mim][NTf2

pared by hydrolytic condensation of MTICl using superacid HNTf2

described above.

side-chains and NTf2

**imidazolium side-chain groups**

endothermic peak due to *T*m at 105°C (Run 4 in **Table 1**). In addition, **Im-Cage-SQ-IL** showed fluidity at ~100°C (Run 4 in **Table 1**), confirmed by the same procedure as described above for **Im-Random-SQ-IL**. This indicated that **Im-Cage-SQ-IL** was not a RT-IL. Because **Im-Cage-SQ-IL** is a crystalline compound, its flow temperature was near its *T*m (~100°C). On the other

results suggest that the amorphous structure of **Im-Random-SQ-IL** is essential for achieving

The thermal stabilities of **Im-Random-SQ-IL** and **Im-Cage-SQ-IL** upon pyrolysis were investigated by TGA. The *T*d3, *T*d5, and *T*d10 values for **Im-Random-SQ-IL** were 429, 437, and 447°C, respectively (Run 3 in **Table 1**), while those of **Im-Cage-SQ-IL** were 427, 436, and 446 °C, respectively (Run 4 in **Table 1**). These values were higher than those of 1-methyl-3-propyl-

tively). This compound is an IL with the structure of the side-chains of **Im-Random-SQ-IL** and **Im-Cage-SQ-IL**. These results indicated that the thermal stabilities of **Im-Random-SQ-IL** and **Im-Cage-SQ-IL** were increased by incorporation of the silsesquioxane frameworks. Such a tendency was also observed in a quaternary ammonium-type IL, **Am-Random-SQ-IL**, as

**4. Preparation of ionic liquids containing cage-like oligosilsesquioxane (POSS) with the random distribution of quaternary ammonium and**

As described in Section 3, a highly thermostable POSS IL containing imidazolium cationic

tion, a quaternary ammonium-type POSS (**Am-Cage-SQ**) could also be prepared from TTACl as a starting material using the same procedure, as described in Section 2. However, visual flow temperatures of these compounds were relatively high (~155°C for **Am-Cage-SQ** and ~100°C for **Im-Cage-SQ-IL**) because of their higher *T*ms (172°C for **Am-Cage-SQ** and 105°C for **Im-Cage-SQ-IL**) (Run 2, 4 in **Table 1**). Such high *T*ms and flow temperatures of these POSS compounds are probably derived from their highly symmetrical and crystalline structures.

The development of POSS RT-ILs with high thermal stabilities is expected for both academic and application reasons because RT-ILs are particularly useful for many applications of green solvents and electrolyte materials. Therefore, to prepare such POSS ILs, we focused on our previous studies on the preparation of low-crystalline POSS [11] and amorphous POSS-linking polymer [12]. Their synthesis was achieved by hydrolytic condensation of a mixture of two types of amino-group-containing organotrialkoxysilanes. The molecular symmetry of the resulting POSS derivatives was low because of the random distribution of the two types of sidechain groups. Consequently, their crystallization was suppressed. In this section, we describe the preparation of a thermally stable POSS RT-IL (**Amim-Cage-SQ-IL**), which contained a

anions as counter ions (**Im-Cage-SQ-IL**) could be successfully pre-

hand, **Im-Random-SQ-IL** with an amorphous structure exhibited fluidity above its *T*g

at −22°C and the

http://dx.doi.org/10.5772/65892

Preparation of Ionic Liquids Containing Siloxane Frameworks

]) (366, 380, and 399°C, respec-

as a catalyst. In addi-

. These

585

**Scheme 2.** Preparation of (a) **Im-Random-SQ-IL** and (b) **Im-Cage-SQ-IL**.

We assumed that such IL properties were probably attributed to the amorphous structure. Therefore, as well as the quaternary ammonium-type ILs as described in the previous section, a POSS compound with crystalline structure was prepared. A POSS compound (**Im-Cage-SQ-IL**) was prepared by the hydrolytic condensation of MTICl using HNTf2 as a catalyst in water/methanol (1:19, v/v) mixed solvent (**Scheme 2b**) [25]. **Im-Cage-SQ-IL** was soluble in DMSO, DMF, methanol, acetone, THF, and ethyl acetate, but insoluble in water, ethanol, 1-propanol, 2-propanol, chloroform, diethyl ether, toluene, and *n*-hexane. The 1 H NMR and EDX results for **Im-Cage-SQ-IL** were almost same as those for **Im-Random-SQ-IL**.

The 29Si NMR spectrum of **Im-Cage-SQ-IL** in DMSO-*d*6 at 40°C showed two signals assigned to the *T*3 structures at −66.5 ppm (a main signal) and at −68.7 ppm (a minor signal), indicating the absence of silanol groups. These signals were derived from cage-like octasilsesquioxane (*T*8 ) and cage-like decasilsesquioxane (*T*10), respectively. Because the integrated ratio of these signals was estimated to be 75:25, the molar ratio of *T*8 :*T*10 was calculated to be 79:21 (= 75/8:25/10). In addition, the MALDI-TOF MS results supported the formation of such POSS structures. Finally, the XRD pattern of **Im-Cage-SQ-IL** showed many sharp diffraction peaks, indicating the formation of a crystalline structure, unlike that of **Im-Random-SQ-IL**, which did not exhibit any diffraction peaks.

The DSC curve for **Im-Cage-SQ-IL** indicated the baseline shift due to *T*g at −22°C and the endothermic peak due to *T*m at 105°C (Run 4 in **Table 1**). In addition, **Im-Cage-SQ-IL** showed fluidity at ~100°C (Run 4 in **Table 1**), confirmed by the same procedure as described above for **Im-Random-SQ-IL**. This indicated that **Im-Cage-SQ-IL** was not a RT-IL. Because **Im-Cage-SQ-IL** is a crystalline compound, its flow temperature was near its *T*m (~100°C). On the other hand, **Im-Random-SQ-IL** with an amorphous structure exhibited fluidity above its *T*g . These results suggest that the amorphous structure of **Im-Random-SQ-IL** is essential for achieving RT-IL, in addition to the types of substituent groups in the silsesquioxanes.

The thermal stabilities of **Im-Random-SQ-IL** and **Im-Cage-SQ-IL** upon pyrolysis were investigated by TGA. The *T*d3, *T*d5, and *T*d10 values for **Im-Random-SQ-IL** were 429, 437, and 447°C, respectively (Run 3 in **Table 1**), while those of **Im-Cage-SQ-IL** were 427, 436, and 446 °C, respectively (Run 4 in **Table 1**). These values were higher than those of 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide ([C3mim][NTf2 ]) (366, 380, and 399°C, respectively). This compound is an IL with the structure of the side-chains of **Im-Random-SQ-IL** and **Im-Cage-SQ-IL**. These results indicated that the thermal stabilities of **Im-Random-SQ-IL** and **Im-Cage-SQ-IL** were increased by incorporation of the silsesquioxane frameworks. Such a tendency was also observed in a quaternary ammonium-type IL, **Am-Random-SQ-IL**, as described above.

### **4. Preparation of ionic liquids containing cage-like oligosilsesquioxane (POSS) with the random distribution of quaternary ammonium and imidazolium side-chain groups**

We assumed that such IL properties were probably attributed to the amorphous structure. Therefore, as well as the quaternary ammonium-type ILs as described in the previous section, a POSS compound with crystalline structure was prepared. A POSS compound (**Im-Cage-SQ-IL**) was prepared by the hydrolytic condensation of MTICl using HNTf2

a catalyst in water/methanol (1:19, v/v) mixed solvent (**Scheme 2b**) [25]. **Im-Cage-SQ-IL** was soluble in DMSO, DMF, methanol, acetone, THF, and ethyl acetate, but insoluble in water, ethanol, 1-propanol, 2-propanol, chloroform, diethyl ether, toluene, and *n*-hex-

ing the absence of silanol groups. These signals were derived from cage-like octasilsesqui-

79:21 (= 75/8:25/10). In addition, the MALDI-TOF MS results supported the formation of such POSS structures. Finally, the XRD pattern of **Im-Cage-SQ-IL** showed many sharp diffraction peaks, indicating the formation of a crystalline structure, unlike that of **Im-Random-SQ-IL**,

H NMR and EDX results for **Im-Cage-SQ-IL** were almost same as those for

structures at −66.5 ppm (a main signal) and at −68.7 ppm (a minor signal), indicat-

) and cage-like decasilsesquioxane (*T*10), respectively. Because the integrated ratio

ane. The 1

to the *T*3

oxane (*T*8

**Im-Random-SQ-IL**.

584 Progress and Developments in Ionic Liquids

The 29Si NMR spectrum of **Im-Cage-SQ-IL** in DMSO-*d*6

**Scheme 2.** Preparation of (a) **Im-Random-SQ-IL** and (b) **Im-Cage-SQ-IL**.

which did not exhibit any diffraction peaks.

of these signals was estimated to be 75:25, the molar ratio of *T*8

as

at 40°C showed two signals assigned

:*T*10 was calculated to be

As described in Section 3, a highly thermostable POSS IL containing imidazolium cationic side-chains and NTf2 anions as counter ions (**Im-Cage-SQ-IL**) could be successfully prepared by hydrolytic condensation of MTICl using superacid HNTf2 as a catalyst. In addition, a quaternary ammonium-type POSS (**Am-Cage-SQ**) could also be prepared from TTACl as a starting material using the same procedure, as described in Section 2. However, visual flow temperatures of these compounds were relatively high (~155°C for **Am-Cage-SQ** and ~100°C for **Im-Cage-SQ-IL**) because of their higher *T*ms (172°C for **Am-Cage-SQ** and 105°C for **Im-Cage-SQ-IL**) (Run 2, 4 in **Table 1**). Such high *T*ms and flow temperatures of these POSS compounds are probably derived from their highly symmetrical and crystalline structures.

The development of POSS RT-ILs with high thermal stabilities is expected for both academic and application reasons because RT-ILs are particularly useful for many applications of green solvents and electrolyte materials. Therefore, to prepare such POSS ILs, we focused on our previous studies on the preparation of low-crystalline POSS [11] and amorphous POSS-linking polymer [12]. Their synthesis was achieved by hydrolytic condensation of a mixture of two types of amino-group-containing organotrialkoxysilanes. The molecular symmetry of the resulting POSS derivatives was low because of the random distribution of the two types of sidechain groups. Consequently, their crystallization was suppressed. In this section, we describe the preparation of a thermally stable POSS RT-IL (**Amim-Cage-SQ-IL**), which contained a random distribution of the two types of side-chain groups, by the hydrolytic condensation of a mixture of TTACl and MTICl using HNTf2 as a catalyst in water/methanol mixed solvent [26].

The XRD patterns of **Am-Cage-SQ** and **Im-Cage-SQ-IL** supported that they were crystalline compounds. Therefore, **Am-Cage-SQ** and **Im-Cage-SQ-IL** showed relatively high flow temperatures (~155 and ~100°C, respectively) because of their high crystallinity (Run 2, 4 in **Table 1**). In addition, a mixture of **Am-Cage-SQ** and **Im-Cage-SQ-IL** also maintained crystalline structure, because the endothermic peak due to *T*m was observed at 164°C; it showed

Conversely, the DSC curve of **Amim-Cage-SQ-IL** showed a baseline shift at −8°C due to

The *T*d3, *T*d5, and *T*d10 values estimated by TGA of **Amim-Cage-SQ-IL** were 414°C, 420°C, and 428 °C, respectively (Run 6 in **Table 1**). These values were higher than those of ILs with the

In the previous sections, we described that ILs containing silsesquioxane frameworks, such as randomly structured silsesquioxanes and POSSs, were successfully prepared. In particular, **Am-Random-SQ-IL, Im-Random-SQ-IL**, and **Amim-Cage-SQ-IL** had both relatively low flow temperatures (<~40°C) and high thermal stabilities (*T*d5 > ~400°C). However, they also displayed high viscosities, probably because of the presence of silanol groups for randomly structured silsesquioxane ILs and relatively higher degrees of polymerization (DP) for all silsesquioxane ILs. It is assumed that siloxane-based ILs without silanol groups and with lower DP probably exhibit high thermal stability, low flow temperature, and low viscosity. In this section, therefore, we describe the preparation and properties of ILs containing cyclic

To achieve the preparation of such ILs containing cyclic oligosiloxanes, we referred to our previous study for the facile preparation of cationic cyclotetrasiloxane (this is not an IL) by the hydrolytic condensation of 3-aminopropylmethyltriethoxysilane using the superacid trifluoromethanesulfonic acid (HOTf) [20]. Therefore, when the hydrolytic condensation of 1-[3-(dimethoxymethylsilyl)propyl]-3-methylimidazolium chloride (DSMIC) was performed

Therefore, the phase transition from amorphous solid to fluid occurred above *T*g

**5. Preparation of ionic liquids containing cyclic oligosiloxanes**

these results, it was concluded that **Amim-Cage-SQ-IL** had *T*g

, whereas an endothermic peak due to *T*m was not detected (Run 6 in **Table 1**), indicating that **Amim-Cage-SQ-IL** is an amorphous compound. The XRD pattern of **Amim-Cage-SQ-IL** did not show any diffraction peaks, supporting the amorphous structure of this compound. **Amim-Cage-SQ-IL** exhibited obvious fluidity at ~30°C (Run 6 in **Table 1**). Because the molecular symmetry of the resulting POSS compound with a random distribution of the two types of side-chain groups was low, its crystallization was suppressed.

. Based on

of −8°C and showed fluidity

] (392, 400, and 411°C, respectively) and [C3mim]

Preparation of Ionic Liquids Containing Siloxane Frameworks

http://dx.doi.org/10.5772/65892

587

and HOTf, we found that imidazolium salt-type

and **MeIm-CyS-IL-OTf**)

fluidity at 120°C (Run 5 in **Table 1**).

at ~30°C, i.e., it is a RT-IL.

side-chain structures of this IL: [TMPA][NTf2

oligosiloxanes as the siloxane frameworks.

using superacid catalysts such as HNTf2

were successfully prepared [27].

ILs containing cyclic oligosiloxane frameworks (**MeIm-CyS-IL-NTf2**

] (366, 380, and 399°C, respectively).

*T*g

[NTf2

**Amim-Cage-SQ-IL** was prepared from a mixture of TTACl and MTICl (1:1 mol/mol) by same procedures for the preparation of **Im-Cage-SQ-IL** and **Am-Cage-SQ** as described above (**Scheme 3**). **Amim-Cage-SQ-IL** was soluble in DMSO, acetonitrile, DMF, methanol, acetone, THF, and ethyl acetate, but insoluble in water, ethanol, 1-propanol, 2-propanol, chloroform, diethyl ether, toluene, and *n*-hexane.

**Scheme 3.** Preparation of **Amim-Cage-SQ-IL**.

The 1 H NMR spectrum of **Amim-Cage-SQ-IL** in DMSO-*d*6 showed the signals attributable to the side-chain groups of both the *N,N,N*-trimethyl-*N*-propylammonium group and the 1-methyl-3-propylimidazolium group. The average compositional ratio of TTACl to MTICl components in the product was estimated to be ca. 1:1 from the 1 H NMR spectrum. The EDX pattern of **Amim-Cage-SQ-IL** did not indicate any peaks originating from Cl, and the Si:S elemental ratio was estimated to be 1.00:2.03, indicating that the molar ratio of cation species (imidazolium and ammonium) to NTf2 anions was ca. 1:1.

The 29Si NMR spectrum of **Amim-Cage-SQ-IL** in DMSO-*d*6 at 40°C only showed four sharp signals due to the *T*3 structure at −66.8, −67.3, −68.8, and −69.3 ppm, indicating the absence of silanol groups. These signals could be attributed to the MTICl and TTACl components of *T*8 and the MTICl and TTACl components of *T*10, respectively, because these chemical shifts were almost same as those of **Am-Cage-SQ** and **Im-Cage-SQ-IL** as described in the previous sections. Because the integrated ratio of *T*8 :*T*10 signals was estimated to be 77:23, the molar ratio of *T*8 :*T*10 was calculated to be 81:19 (= 77/8:23/10), indicating that *T*8 was the main product. The MALDI-TOF MS analysis of **Amim-Cage-SQ-IL** also supported the 29Si NMR results.

The DSC curves of **Am-Cage-SQ** and **Im-Cage-SQ-IL** (POSS compounds as described in Sections 2 and 3) indicated the endothermic peaks for *T*ms at 172 and 105°C, respectively (Run 2, 4 in **Table 1**), i.e., **Am-Cage-SQ** and **Im-Cage-SQ-IL** are crystalline compounds. The XRD patterns of **Am-Cage-SQ** and **Im-Cage-SQ-IL** supported that they were crystalline compounds. Therefore, **Am-Cage-SQ** and **Im-Cage-SQ-IL** showed relatively high flow temperatures (~155 and ~100°C, respectively) because of their high crystallinity (Run 2, 4 in **Table 1**). In addition, a mixture of **Am-Cage-SQ** and **Im-Cage-SQ-IL** also maintained crystalline structure, because the endothermic peak due to *T*m was observed at 164°C; it showed fluidity at 120°C (Run 5 in **Table 1**).

random distribution of the two types of side-chain groups, by the hydrolytic condensation of a

**Amim-Cage-SQ-IL** was prepared from a mixture of TTACl and MTICl (1:1 mol/mol) by same procedures for the preparation of **Im-Cage-SQ-IL** and **Am-Cage-SQ** as described above (**Scheme 3**). **Amim-Cage-SQ-IL** was soluble in DMSO, acetonitrile, DMF, methanol, acetone, THF, and ethyl acetate, but insoluble in water, ethanol, 1-propanol, 2-propanol, chloroform,

to the side-chain groups of both the *N,N,N*-trimethyl-*N*-propylammonium group and the 1-methyl-3-propylimidazolium group. The average compositional ratio of TTACl to MTICl

pattern of **Amim-Cage-SQ-IL** did not indicate any peaks originating from Cl, and the Si:S elemental ratio was estimated to be 1.00:2.03, indicating that the molar ratio of cation species

silanol groups. These signals could be attributed to the MTICl and TTACl components of *T*8 and the MTICl and TTACl components of *T*10, respectively, because these chemical shifts were almost same as those of **Am-Cage-SQ** and **Im-Cage-SQ-IL** as described in the previous sec-

The DSC curves of **Am-Cage-SQ** and **Im-Cage-SQ-IL** (POSS compounds as described in Sections 2 and 3) indicated the endothermic peaks for *T*ms at 172 and 105°C, respectively (Run 2, 4 in **Table 1**), i.e., **Am-Cage-SQ** and **Im-Cage-SQ-IL** are crystalline compounds.

MALDI-TOF MS analysis of **Amim-Cage-SQ-IL** also supported the 29Si NMR results.

anions was ca. 1:1.

structure at −66.8, −67.3, −68.8, and −69.3 ppm, indicating the absence of

:*T*10 signals was estimated to be 77:23, the molar ratio

as a catalyst in water/methanol mixed solvent [26].

showed the signals attributable

at 40°C only showed four sharp

was the main product. The

H NMR spectrum. The EDX

mixture of TTACl and MTICl using HNTf2

586 Progress and Developments in Ionic Liquids

diethyl ether, toluene, and *n*-hexane.

H NMR spectrum of **Amim-Cage-SQ-IL** in DMSO-*d*6

components in the product was estimated to be ca. 1:1 from the 1

The 29Si NMR spectrum of **Amim-Cage-SQ-IL** in DMSO-*d*6

:*T*10 was calculated to be 81:19 (= 77/8:23/10), indicating that *T*8

(imidazolium and ammonium) to NTf2

**Scheme 3.** Preparation of **Amim-Cage-SQ-IL**.

tions. Because the integrated ratio of *T*8

signals due to the *T*3

The 1

of *T*8

Conversely, the DSC curve of **Amim-Cage-SQ-IL** showed a baseline shift at −8°C due to *T*g , whereas an endothermic peak due to *T*m was not detected (Run 6 in **Table 1**), indicating that **Amim-Cage-SQ-IL** is an amorphous compound. The XRD pattern of **Amim-Cage-SQ-IL** did not show any diffraction peaks, supporting the amorphous structure of this compound. **Amim-Cage-SQ-IL** exhibited obvious fluidity at ~30°C (Run 6 in **Table 1**). Because the molecular symmetry of the resulting POSS compound with a random distribution of the two types of side-chain groups was low, its crystallization was suppressed. Therefore, the phase transition from amorphous solid to fluid occurred above *T*g . Based on these results, it was concluded that **Amim-Cage-SQ-IL** had *T*g of −8°C and showed fluidity at ~30°C, i.e., it is a RT-IL.

The *T*d3, *T*d5, and *T*d10 values estimated by TGA of **Amim-Cage-SQ-IL** were 414°C, 420°C, and 428 °C, respectively (Run 6 in **Table 1**). These values were higher than those of ILs with the side-chain structures of this IL: [TMPA][NTf2 ] (392, 400, and 411°C, respectively) and [C3mim] [NTf2 ] (366, 380, and 399°C, respectively).

### **5. Preparation of ionic liquids containing cyclic oligosiloxanes**

In the previous sections, we described that ILs containing silsesquioxane frameworks, such as randomly structured silsesquioxanes and POSSs, were successfully prepared. In particular, **Am-Random-SQ-IL, Im-Random-SQ-IL**, and **Amim-Cage-SQ-IL** had both relatively low flow temperatures (<~40°C) and high thermal stabilities (*T*d5 > ~400°C). However, they also displayed high viscosities, probably because of the presence of silanol groups for randomly structured silsesquioxane ILs and relatively higher degrees of polymerization (DP) for all silsesquioxane ILs. It is assumed that siloxane-based ILs without silanol groups and with lower DP probably exhibit high thermal stability, low flow temperature, and low viscosity. In this section, therefore, we describe the preparation and properties of ILs containing cyclic oligosiloxanes as the siloxane frameworks.

To achieve the preparation of such ILs containing cyclic oligosiloxanes, we referred to our previous study for the facile preparation of cationic cyclotetrasiloxane (this is not an IL) by the hydrolytic condensation of 3-aminopropylmethyltriethoxysilane using the superacid trifluoromethanesulfonic acid (HOTf) [20]. Therefore, when the hydrolytic condensation of 1-[3-(dimethoxymethylsilyl)propyl]-3-methylimidazolium chloride (DSMIC) was performed using superacid catalysts such as HNTf2 and HOTf, we found that imidazolium salt-type ILs containing cyclic oligosiloxane frameworks (**MeIm-CyS-IL-NTf2** and **MeIm-CyS-IL-OTf**) were successfully prepared [27].

**MeIm-CyS-IL-NTf2** was prepared by the following procedure (**Scheme 4a**): DSMIC was stirred in a water/methanol (1:19, v/v) mixed solution of HNTf2 at room temperature. Then, the solvent was evaporated by heating at ~50°C in an open system. The resulting crude product was further heated at 100°C for 2 h, washed with water, and then dried at 150°C for ca. 5 h to obtain **MeIm-CyS-IL-NTf2** . On the other hand, **MeIm-CyS-IL-OTf** was prepared using almost same procedure as that of **MeIm-CyS-IL-NTf2** but using an aqueous HOTf as a catalyst (**Scheme 4b**). The EDX results of **MeIm-CyS-IL-NTf2** and **MeIm-CyS-IL-OTf** indicated the absence of Cl and the molar ratio of imidazolium cations to NTf2 or OTf anions were ca. 1:1.

and **MeIm-CyS-IL-OTf** were RT-ILs. The *T*d3, *T*d5, and *T*d10 values estimated by TGA were 407,

randomly structured oligosilsesquioxane framework, as described in Section 3. Both ILs have same side-chain groups and showed low flow temperatures (~0°C), yet the siloxane frameworks differed between the ILs. **Figure 1** shows the photographs of these two samples

**Im-Random-SQ-IL** did not show fluidity after 10 s. These results indicated that cyclic oligosiloxane frameworks were important factors for the lower viscosity of **MeIm-CyS-IL-NTf2**

For this chapter, we newly investigated the effects of the alkyl chain length in the imidazolium groups of ILs containing cyclic oligosiloxane frameworks. Therefore, imidazolium salt-type ILs containing cyclic oligosiloxane with various lengths of alkyl chains (R

of the corresponding imidazolium-group-containing dimethoxysilanes using the superacid

(R = CH2

mic peaks due to the *T*ms were not detected for all ILs. In addition, all ILs showed obvious fluidity at ~0°C (**Figure 2a–d** inset, Run 9–12 in **Table 1**). On the basis of these results, we concluded that the alkyl chain lengths in imidazolium groups of ILs containing cyclic oli-

gosiloxane frameworks had an insignificant effect on the IL natures, such as *T*g

uct) and cyclic pentasiloxanes (minor product), with some stereoisomers, respectively.

 in a water/methanol (1:19, v/v) mixed solvent (**Scheme 5**). Based on the results of the 29Si NMR and MALDI-TOF MS analyses, we determined that the resulting products [**HIm-**

CH3

Further detailed studies for viscosity determination are currently in progress.

(Run 7 in **Table 1**) and 380, 391, and 402°C for **MeIm-**

Preparation of Ionic Liquids Containing Siloxane Frameworks

was lower than that of **Im-Random-SQ-IL** containing

) were prepared by the hydrolytic condensation

(R = (CH2

(**Figure 2c**, Run 11 in **Table 1**),

)2 CH3 ),

s were observed

and flow

), **PrIm-CyS-IL-NTf2**

and (b) **Im-Random-SQ-IL** after 0 and 10 s with tilting at 14°C.

(**Figure 2a**, Run 9 in **Table 1**), −44°C for **EtIm-CyS-IL-NTf2**

(**Figure 2d**, Run 12 in **Table 1**). These values were almost

(−43°C) (Run 7 in **Table 1**). Conversely, the endother-

)] were mixtures of cyclic tetrasiloxanes (main prod-

obviously flowed after 10 s, while

http://dx.doi.org/10.5772/65892

.

589

415, and 427°C for **MeIm-CyS-IL-NTf2**

The viscosity of **MeIm-CyS-IL-NTf2**

after 0 and 10 s, with tilting at 14°C. **MeIm-CyS-IL-NTf2**

**CyS-IL-OTf** (Run 8 in **Table 1**).

= H, CH2

**CyS-IL-NTf2**

temperatures.

HNTf2

CH3

and **BuIm-CyS-IL-NTf2**

at −38°C for **HIm-CyS-IL-NTf2**

and −45°C for **BuIm-CyS-IL-NTf2**

same as that of **MeIm-CyS-IL-NTf2**

, (CH2 )2 CH3

**Figure 1.** Photographs of (a) **MeIm-CyS-IL-NTf2**

, and (CH2

(R = H), **EtIm-CyS-IL-NTf2**

(R = (CH2

(**Figure 2b**, Run 10 in **Table 1**), −44°C for **PrIm-CyS-IL-NTf2**

)3 CH3

)3 CH3

The DSC curves of the resulting ILs showed the baseline shifts assigned to *T*g

**Scheme 4.** Preparation of (a) **MeIm-CyS-IL-NTf2** and (b) **MeIm-CyS-IL-OTf**.

In the MALDI-TOF MS analysis of **MeIm-CyS-IL-NTf2** , several peaks assigned to cyclic siloxane tetramer (main peaks) and pentamer (minor peaks) were observed. Furthermore, the 1 H NMR spectrum exhibited multiplet signals due to methyl groups at 0.23 to −0.23 ppm. In addition, the 29Si NMR spectrum of **MeIm-CyS-IL-NTf2** in DMSO-*d*6 at 40°C also showed two multiplet signals due to the *D*2 structure (−19.2 to −19.6 ppm for cyclic tetrasiloxane (main signals) and −21.4 to −21.9 ppm for cyclic pentasiloxane (minor signals)). On the other hand, the MALDI-TOF MS results of **MeIm-CyS-IL-OTf** indicated the existence of a mixture of cyclic siloxane tetramer (main product), pentamer (main product), and hexamer (minor product). In addition, **MeIm-CyS-IL-OTf** had some stereoisomers, confirmed by the 1 H NMR spectrum with multiplet signals assigned to the methyl groups at 0.16–−0.23 ppm and the 29Si NMR spectrum with three multiplet signals due to the *D*2 structure (−19.1 to −19.7 ppm for cyclic tetrasiloxane (main signals), −21.3 to −21.9 ppm for cyclic pentasiloxane (main signals), and −22.2 to −22.5 ppm for cyclic hexasiloxane (minor signals)). These results indicated that **MeIm-CyS-IL-NTf2** was a mixture of cyclic tetrasiloxanes and cyclic pentasiloxanes, while **MeIm-CyS-IL-OTf** was a mixture of cyclic tetrasiloxanes, cyclic pentasiloxanes, and cyclic hexasiloxane, with some stereoisomers.

The DSC curves of the resulting products indicated the baseline shifts assigned to *T*g s at −43°C for **MeIm-CyS-IL-NTf2** (Run 7 in **Table 1**) and at −14°C for **MeIm-CyS-IL-OTf** (Run 8 in **Table 1**), respectively. These values were newly estimated using different DSC equipment from that in the original paper [27] and were slightly different from the values in the original paper. Conversely, the endothermic peaks due to *T*m were not detected. In addition, **MeIm-CyS-IL-NTf2** and **MeIm-CyS-IL-OTf** showed obvious fluidity at ~0 and ~20°C, respectively (Run 7, 8 in **Table 1**). On the basis of these results, it was concluded that **MeIm-CyS-IL-NTf2**

and **MeIm-CyS-IL-OTf** were RT-ILs. The *T*d3, *T*d5, and *T*d10 values estimated by TGA were 407, 415, and 427°C for **MeIm-CyS-IL-NTf2** (Run 7 in **Table 1**) and 380, 391, and 402°C for **MeIm-CyS-IL-OTf** (Run 8 in **Table 1**).

**MeIm-CyS-IL-NTf2**

h to obtain **MeIm-CyS-IL-NTf2**

588 Progress and Developments in Ionic Liquids

stirred in a water/methanol (1:19, v/v) mixed solution of HNTf2

absence of Cl and the molar ratio of imidazolium cations to NTf2

almost same procedure as that of **MeIm-CyS-IL-NTf2**

(**Scheme 4b**). The EDX results of **MeIm-CyS-IL-NTf2**

In the MALDI-TOF MS analysis of **MeIm-CyS-IL-NTf2**

addition, the 29Si NMR spectrum of **MeIm-CyS-IL-NTf2**

NMR spectrum with three multiplet signals due to the *D*2

multiplet signals due to the *D*2

**Scheme 4.** Preparation of (a) **MeIm-CyS-IL-NTf2**

**MeIm-CyS-IL-NTf2**

for **MeIm-CyS-IL-NTf2**

**CyS-IL-NTf2**

hexasiloxane, with some stereoisomers.

was prepared by the following procedure (**Scheme 4a**): DSMIC was

. On the other hand, **MeIm-CyS-IL-OTf** was prepared using

in DMSO-*d*6

structure (−19.2 to −19.6 ppm for cyclic tetrasiloxane (main sig-

was a mixture of cyclic tetrasiloxanes and cyclic pentasiloxanes, while

(Run 7 in **Table 1**) and at −14°C for **MeIm-CyS-IL-OTf** (Run 8 in

and **MeIm-CyS-IL-OTf** showed obvious fluidity at ~0 and ~20°C, respectively

the solvent was evaporated by heating at ~50°C in an open system. The resulting crude product was further heated at 100°C for 2 h, washed with water, and then dried at 150°C for ca. 5

ane tetramer (main peaks) and pentamer (minor peaks) were observed. Furthermore, the 1

NMR spectrum exhibited multiplet signals due to methyl groups at 0.23 to −0.23 ppm. In

and (b) **MeIm-CyS-IL-OTf**.

nals) and −21.4 to −21.9 ppm for cyclic pentasiloxane (minor signals)). On the other hand, the MALDI-TOF MS results of **MeIm-CyS-IL-OTf** indicated the existence of a mixture of cyclic siloxane tetramer (main product), pentamer (main product), and hexamer (minor product).

trum with multiplet signals assigned to the methyl groups at 0.16–−0.23 ppm and the 29Si

cyclic tetrasiloxane (main signals), −21.3 to −21.9 ppm for cyclic pentasiloxane (main signals), and −22.2 to −22.5 ppm for cyclic hexasiloxane (minor signals)). These results indicated that

**MeIm-CyS-IL-OTf** was a mixture of cyclic tetrasiloxanes, cyclic pentasiloxanes, and cyclic

**Table 1**), respectively. These values were newly estimated using different DSC equipment from that in the original paper [27] and were slightly different from the values in the original paper. Conversely, the endothermic peaks due to *T*m were not detected. In addition, **MeIm-**

(Run 7, 8 in **Table 1**). On the basis of these results, it was concluded that **MeIm-CyS-IL-NTf2**

The DSC curves of the resulting products indicated the baseline shifts assigned to *T*g

In addition, **MeIm-CyS-IL-OTf** had some stereoisomers, confirmed by the 1

at room temperature. Then,

but using an aqueous HOTf as a catalyst

and **MeIm-CyS-IL-OTf** indicated the

, several peaks assigned to cyclic silox-

structure (−19.1 to −19.7 ppm for

at 40°C also showed two

H NMR spec-

s at −43°C

H

or OTf anions were ca. 1:1.

The viscosity of **MeIm-CyS-IL-NTf2** was lower than that of **Im-Random-SQ-IL** containing randomly structured oligosilsesquioxane framework, as described in Section 3. Both ILs have same side-chain groups and showed low flow temperatures (~0°C), yet the siloxane frameworks differed between the ILs. **Figure 1** shows the photographs of these two samples after 0 and 10 s, with tilting at 14°C. **MeIm-CyS-IL-NTf2** obviously flowed after 10 s, while **Im-Random-SQ-IL** did not show fluidity after 10 s. These results indicated that cyclic oligosiloxane frameworks were important factors for the lower viscosity of **MeIm-CyS-IL-NTf2** . Further detailed studies for viscosity determination are currently in progress.

**Figure 1.** Photographs of (a) **MeIm-CyS-IL-NTf2** and (b) **Im-Random-SQ-IL** after 0 and 10 s with tilting at 14°C.

For this chapter, we newly investigated the effects of the alkyl chain length in the imidazolium groups of ILs containing cyclic oligosiloxane frameworks. Therefore, imidazolium salt-type ILs containing cyclic oligosiloxane with various lengths of alkyl chains (R = H, CH2 CH3 , (CH2 )2 CH3 , and (CH2 )3 CH3 ) were prepared by the hydrolytic condensation of the corresponding imidazolium-group-containing dimethoxysilanes using the superacid HNTf2 in a water/methanol (1:19, v/v) mixed solvent (**Scheme 5**). Based on the results of the 29Si NMR and MALDI-TOF MS analyses, we determined that the resulting products [**HIm-CyS-IL-NTf2** (R = H), **EtIm-CyS-IL-NTf2** (R = CH2 CH3 ), **PrIm-CyS-IL-NTf2** (R = (CH2 )2 CH3 ), and **BuIm-CyS-IL-NTf2** (R = (CH2 )3 CH3 )] were mixtures of cyclic tetrasiloxanes (main product) and cyclic pentasiloxanes (minor product), with some stereoisomers, respectively.

The DSC curves of the resulting ILs showed the baseline shifts assigned to *T*g s were observed at −38°C for **HIm-CyS-IL-NTf2** (**Figure 2a**, Run 9 in **Table 1**), −44°C for **EtIm-CyS-IL-NTf2** (**Figure 2b**, Run 10 in **Table 1**), −44°C for **PrIm-CyS-IL-NTf2** (**Figure 2c**, Run 11 in **Table 1**), and −45°C for **BuIm-CyS-IL-NTf2** (**Figure 2d**, Run 12 in **Table 1**). These values were almost same as that of **MeIm-CyS-IL-NTf2** (−43°C) (Run 7 in **Table 1**). Conversely, the endothermic peaks due to the *T*ms were not detected for all ILs. In addition, all ILs showed obvious fluidity at ~0°C (**Figure 2a–d** inset, Run 9–12 in **Table 1**). On the basis of these results, we concluded that the alkyl chain lengths in imidazolium groups of ILs containing cyclic oligosiloxane frameworks had an insignificant effect on the IL natures, such as *T*g and flow temperatures.

**6. Conclusions**

**Author details**

**References**

**NTf2**

oligosiloxanes (**MeIm-CyS-IL-NTf2**

of these siloxane-based ILs are found.

Challenging Exploratory Research) Number 15K13711.

Yoshiro Kaneko\*, Akiyuki Harada, Takuya Kubo and Takuhiro Ishii

\*Address all correspondence to<EMAIL_ADDRESS>
Rev. 1999;**99**:2071–2084. DOI: 10.1021/cr980032t

1998;1765–1766. DOI: 10.1039/A803999B

uid/supercritical CO2

6360. DOI: 10.1021/cm102263s

anie.200390070

nmat2448

sis. 2. Chem. Rev. 2011;**111**:3508–3576. DOI: 10.1021/cr1003248

, **PrIm-CyS-IL-NTf2**

In this chapter, we described the preparation and properties of thermally stable ILs containing siloxane frameworks, such as randomly structured oligosilsesquioxanes (**Am-Random-SQ-IL** and **Im-Random-SQ-IL**), POSSs (**Im-Cage-SQ-IL** and **Amim-Cage-SQ-IL**), and cyclic

The authors gratefully acknowledge Prof. J. Ohshita (Hiroshima University) and Dr. T. Mizumo (Samsung R & D Institute Japan) for their enthusiastic collaborations. The authors also gratefully give thanks for financial supports from JSPS KAKENHI (Grant-in-Aid for

Graduate School of Science and Engineering, Kagoshima University, Kagoshima, Japan

[1] Welton T. Room-temperature ionic liquids. Solvents for synthesis and catalysis. Chem.

[2] Hallett JP, Welton T. Room-temperature ionic liquids: solvents for synthesis and cataly-

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, and **BuIm-CyS-IL-NTf2**

, **MeIm-CyS-IL-OTf, HIm-CyS-IL-NTf2**

, **EtIm-CyS-IL-**

591

http://dx.doi.org/10.5772/65892

). We are expecting that new applications

Preparation of Ionic Liquids Containing Siloxane Frameworks

**Scheme 5.** Preparation of (a) **HIm-CyS-IL-NTf2** , (b) **EtIm-CyS-IL-NTf2** , (c) **PrIm-CyS-IL-NTf2** , and (d) **BuIm-CyS-IL-NTf2** .

**Figure 2.** DSC curves and photographs of (a) **HIm-CyS-IL-NTf2** , (b) **EtIm-CyS-IL-NTf2** , (c) **PrIm-CyS-IL-NTf2** , and (d) **BuIm-CyS-IL-NTf2** .

### **6. Conclusions**

In this chapter, we described the preparation and properties of thermally stable ILs containing siloxane frameworks, such as randomly structured oligosilsesquioxanes (**Am-Random-SQ-IL** and **Im-Random-SQ-IL**), POSSs (**Im-Cage-SQ-IL** and **Amim-Cage-SQ-IL**), and cyclic oligosiloxanes (**MeIm-CyS-IL-NTf2** , **MeIm-CyS-IL-OTf, HIm-CyS-IL-NTf2** , **EtIm-CyS-IL-NTf2** , **PrIm-CyS-IL-NTf2** , and **BuIm-CyS-IL-NTf2** ). We are expecting that new applications of these siloxane-based ILs are found.

The authors gratefully acknowledge Prof. J. Ohshita (Hiroshima University) and Dr. T. Mizumo (Samsung R & D Institute Japan) for their enthusiastic collaborations. The authors also gratefully give thanks for financial supports from JSPS KAKENHI (Grant-in-Aid for Challenging Exploratory Research) Number 15K13711.

### **Author details**

Yoshiro Kaneko\*, Akiyuki Harada, Takuya Kubo and Takuhiro Ishii

\*Address all correspondence to<EMAIL_ADDRESS>
Graduate School of Science and Engineering, Kagoshima University, Kagoshima, Japan

### **References**

**Figure 2.** DSC curves and photographs of (a) **HIm-CyS-IL-NTf2**

**BuIm-CyS-IL-NTf2**

.

**Scheme 5.** Preparation of (a) **HIm-CyS-IL-NTf2**

590 Progress and Developments in Ionic Liquids

, (b) **EtIm-CyS-IL-NTf2**

, (c) **PrIm-CyS-IL-NTf2**

, and (d) **BuIm-CyS-IL-NTf2**

.

, (b) **EtIm-CyS-IL-NTf2**

, (c) **PrIm-CyS-IL-NTf2**

, and (d)

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[18] Kaneko Y. Preparation of ionic silsesquioxanes with controlled structures and their functionalizations. Kobunshi Ronbunshu 2014;**71**:443–456. DOI: 10.1295/koron.71.443 [19] Kaneko Y, Toyodome H, Mizumo T, Shikinaka K, Iyi N. Preparation of a sulfo-groupcontaining rod-like polysilsesquioxane with a hexagonally stacked structure and its proton conductivity. Chem. Eur. J. 2014;**20**:9394–9399. DOI: 10.1002/chem.201402011

amino groups. Polymer 2005;**46**:1828–1833. DOI: 10.1016/j.polymer.2004.12.038

Polym. Adv. Technol. 2011;**22**:1223–1228. DOI: 10.1002/pat.1931

tion. Dalton Trans. 2013;**42**:4337–4339. DOI: 10.1039/C2DT32645K

Chem. 2012;**22**:14475–14478. DOI: 10.1039/C2JM32355A

Chem. C 2014;**2**:2496–2501. DOI: 10.1039/C3TC32292K

Chem. 2015;**6**:3039–3045. DOI: 10.1039/C5PY00192G

out using surfactants. Chem. Mater. 2004;**16**:3417–3423.

17651. DOI: 10.1021/ja105631j

592 Progress and Developments in Ionic Liquids

zkri.2<IP_ADDRESS>6

10.1155/2012/684278

polymer.2012.10.052

### *Edited by Scott Handy*

Ionic liquids, including the newer subcategory of deep eutectic solvents, continue to attract a great deal of research attention in an even increasing number of areas, including traditional areas such as synthesis (organic and materials), electrochemistry, and physical property studies and predictions, as well as less obvious areas such as lubrication and enzymatic transformations. In this volume, recent advances in a number of these different areas are reported and reviewed, thus granting some appreciation for the future that ionic liquid research holds and affording inspiration for those who have not previously considered the application of ionic liquids in their area of interest.

Progress and Developments in Ionic Liquids

Progress and Developments

in Ionic Liquids

*Edited by Scott Handy*

Photo by igorr1 / iStock


**Thermal Behaviour, Energy Efficiency in Buildings and Sustainable Construction**

Editor

**Paulo Santos**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editor* Paulo Santos Department of Civil Engineering, ISISE University of Coimbra Coimbra Portugal

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Energies* (ISSN 1996-1073) (available at: www.mdpi.com/journal/energies/special issues/Buildings and Sustainable Construction).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. *Journal Name* **Year**, *Volume Number*, Page Range.

**ISBN 978-3-0365-1175-7 (Hbk) ISBN 978-3-0365-1174-0 (PDF)**

© 2021 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.

### **Contents**

#### **Victor Lohmann and Paulo Santos**

**Paola Marrone, Francesco Asdrubali, Daniela Venanzi, Federico Orsini, Luca Evangelisti, Claudia Guattari, Roberto De Lieto Vollaro, Lucia Fontana, Gianluca Grazieschi, Paolo Matteucci and Marta Roncone**

On the Retrofit of Existing Buildings with Aerogel Panels: Energy, Environmental and Economic Issues

Reprinted from: *Energies* **2021**, *14*, 1276, doi:10.3390/en14051276 ................... **405**

### **About the Editor**

#### **Paulo Santos**

Paulo Santos [ORCID 0000-0002-0134-6762] is Assist. Prof. in Dep. of Civil Eng. of University of Coimbra, PT. He is a member of the ISISE (Institute for Sustainability and Innovation in Structural Engineering) research centre. His main current scientific research fields are Thermal Behaviour, Energy Efficiency in Buildings and Sustainable Construction. He is author of around 150 scientific publications and has been supervisor of around 50 Doctoral and master's theses. He participated in around 12 funded European and Portuguese research projects, now being the Principal Investigator of the Tyre4BuildIns: "Recycled tyre rubber resin-bonded for building insulation systems towards energy efficiency"research project. Furthermore, he is a member of iiSBE: International Initiative for a Sustainable Built Environment (2011,-) and Technical Committee TC14: Sustainability and Eco-efficiency of Steel Construction of the ECCS: European Convention for Constructional Steelwork (2008,-).

### **Preface to "Thermal Behaviour, Energy Efficiency in Buildings and Sustainable Construction"**

Nowadays, energy and sustainability are two of the major concerns of mankind. Given the relevant energy consumption share of the buildings sector, it is very important to search for innovative design solutions and for the optimal thermal performance of buildings to reduce energy bills and greenhouse gas emissions while maintaining the comfort levels of the occupants. Additionally, given the environmental burdens of the construction sector, seeking more environmentally responsible processes and a more efficient use of resources are currently attracting more attention.

This Special Issue (SI), published in the *Energies* journal, is dedicated to the analysis of recent advances in the following issues: (1) thermal behavior improvement of a building's elements (e.g., walls, floors, roofs, windows, doors, etc.), (2) energy efficiency in buildings, and (3) sustainable construction. The main goal is to compile scientific works within these topics, making use of different possible research approaches, such as experimental, theoretical, numerical, analytical, computational, case studies, and their combinations. This book compiles a set of original research works with academic excellence and scientific soundness.

The guest editor would like to express their sincere and deep gratitude for all of the scientific contributions from the authors among prestigious worldwide scientists as well as to the reviewers who significantly contributed to improving the quality of the manuscripts. Moreover, here, we express our acknowledgments to the research project Tyre4BuildIns—"Recycled tyre rubber resinbonded for building insulation systems towards energy efficiency", supported by FEDER funds through the Competitivity Factors Operational Programme—COMPETE and by national funds through FCT—Foundation for Science and Technology, within the scope of the project POCI-01-0145- FEDER-032061, which allowed the contribution of three scientific articles to this SI. Additionally, the guest editor also wants to thank the support provided by the following companies, partners of the research project Tyre4BuildIns: Pertecno, Gyptec Ib´eria, Volcalis, Sotinco, Kronospan, Hulkseflux, Hilti, and Metabo.

> **Paulo Santos** *Editor*

*Article*


**Po-Yen Chen 1, Wei-Chia Lee 1,\*, Hung-Jen Wang 1,2 and Yao-Chi Chuang 1,2**

Received: 20 December 2019; Accepted: 21 January 2020; Published: 23 January 2020

**Abstract:** Cystoscopic onabotulinumtoxinA (onaBoNTA) intradetrusor injection is an efficient and durable modality for treating sensory bladder disorders. However, the inconvenience of using the cystoscopic technique and anesthesia, and the adverse effects of direct needle injection (e.g., haematuria, pain, and infections) have motivated researchers and clinicians to develop diverse injection-free procedures to improve accessibility and prevent adverse effects. However, determining suitable approaches to transfer onaBoNTA, a large molecular and hydrophilic protein, through the impermeable urothelium to reach therapeutic efficacy remains an unmet medical need. Researchers have provided potential solutions in three categories: To disrupt the barrier of the urothelium (e.g., protamine sulfate), to increase the permeability of the urothelium (e.g., electromotive drug delivery and low-energy shock wave), and to create a carrier for transportation (e.g., liposomes, thermosensitive hydrogel, and hyaluronan-phosphatidylethanolamine). Thus far, most of these novel administration techniques have not been well established in their long-term efficacy; therefore, additional clinical trials are warranted to validate the therapeutic efficacy and durability of these techniques. Finally, researchers may make progress with new combinations or biomaterials to change clinical practices in the future.

**Keywords:** drug delivery; interstitial cystitis; onabotulinumtoxinA; overactive bladder; painful bladder syndrome

**Key Contribution:** This review examines the studies of injection-free onaBoNTA delivery for the treatment of sensory bladder disorders.


*3.1. Time Data*

As time is a very critical factor in the trends of electric energy consumption, we consider all variables that express time such as month, day, hour, day of the week, and holiday. Table 3 shows a list of the time factors we considered as input variables. Herein, month, day, and hour have a sequence form. It is difficult to reflect periodic information in machine learning algorithms when data are in a sequential format. Therefore, we enhanced the data to 2-dimensional data through the periodic function [36]. Table 4 summarizes some regression statistics of 1-dimensional, 2-dimensional, and 1-dimensional + 2-dimensional time factors. The table shows that 1-dimensional + 2-dimensional space data can represent the time factor most effectively. Therefore, we use both 1-dimensional data and continuous 2-dimensional data to represent time factor.

**Table 3.** Input variables of time factors.

**Table 4.** Regression statistics of time data representation.


**4.4 Analysis**

The next step in the data processing chain is then the analysis. There are two types of analysis: a scheduled analysis organized centrally and then the end-user, so-called chaotic analysis. Since processing of the end-user analysis jobs often brings some problems like a high memory consumption (see Figure 12) or unstable code, the scheduled analysis is organized in the form of so-called analysis trains (see [52]). The trains absorb up to 30 different analysis tasks running in succession with one data set read and with a very well controlled environment. This helps to consolidate the end-user analysis.

The computing model assumes that the scheduled analysis will be performed at Tier-1 sites, while the chaotic analysis and simulation jobs will be performed at Tier-2s. The experience gained during the numerous Data Challenges, the excellent network performance, the stable and mature Grid middleware deployed over all sites and the conditions at the time of the real data taking in 2010/2011 progressively replaced the original hierarchical scenario by a more "symmetric" model often referred to as the "cloud model".


2. Mechanism of the temperature distribution in logs during their freezing and subsequent defrosting

### 2.1 Mathematical model of the 2D temperature distribution in logs subjected to freezing

When the length of the logs, L, is larger than their diameter, D, by not more than 3–4 times, for the calculation of the change in the temperature in the logs' longitudinal sections (i.e., along the coordinates r and z of these sections) during their freezing in air medium the following 2D mathematical model can be used [24]:

$$\begin{split} \rho\_{\text{we-fr}} \cdot \rho\_{\text{w}} \frac{\partial T(r, z, \tau)}{\partial \tau} = \lambda\_{\text{wr}} \left[ \frac{\partial^2 T(r, z, \tau)}{\partial r^2} + \frac{1}{r} \frac{\partial T(r, z, \tau)}{\partial r} \right] + \frac{\partial \lambda\_{\text{wr}}}{\partial T} \left[ \frac{\partial T(r, z, \tau)}{\partial r} \right]^2 \\ + \lambda\_{\text{wp}} \frac{\partial^2 T(r, z, \tau)}{\partial z^2} + \frac{\partial \lambda\_{\text{wp}}}{\partial T} \left[ \frac{\partial T(r, z, \tau)}{\partial z} \right]^2 + q\_{\text{v}} \end{split} \tag{1}$$

Numerical Solution to Two-Dimensional Freezing and Subsequent Defrosting of Logs DOI: http://dx.doi.org/10.5772/intechopen.84706

with an initial condition

$$T(r, z, \mathbf{0}) = T\_{\mathbf{w}\mathbf{0}} \tag{2}$$

and boundary conditions for convective heat transfer:

• along the radial coordinate r on the logs' frontal surface during the freezing process (refer to Figure 3):

$$\frac{\partial T(r,\mathbf{0},\boldsymbol{\tau})}{\partial \boldsymbol{r}} = -\frac{a\_{\mathrm{wp-fr}}(r,\mathbf{0},\boldsymbol{\tau})}{\lambda\_{\mathrm{wp}}(r,\mathbf{0},\boldsymbol{\tau})} [T(r,\mathbf{0},\boldsymbol{\tau}) - T\_{\mathrm{m-fr}}(\boldsymbol{\tau})],\tag{3}$$

• along the longitudinal coordinate z on the logs' cylindrical surface during the freezing:

$$\frac{\partial T(\mathbf{0}, z, \tau)}{\partial \mathbf{z}} = -\frac{a\_{\text{wr-fr}}(\mathbf{0}, z, \tau)}{\lambda\_{\text{wr}}(\mathbf{0}, z, \tau)} [T(\mathbf{0}, z, \tau) - T\_{\text{m-fr}}(\tau)].\tag{4}$$

Eqs. (1)–(4) represent a common form of a mathematical model of the logs' freezing process, i.e., of the 2D temperature distribution in logs subjected to freezing.

### 2.2 Mathematical model of the 2D temperature distribution in logs subjected to defrosting

In cases when the length of the logs, L, is larger than their diameter, D, by not more than 3–4 times, for the calculation of the change in T in the longitudinal sections of the logs during their defrosting in air processing medium the following 2D mathematical model can be used [8, 9]:

$$\begin{split} c\_{\text{we-dfr}} \cdot \rho\_{\text{w}} \frac{\partial T(r, \mathbf{z}, \tau)}{\partial \tau} = \lambda\_{\text{wr}} \left[ \frac{\partial^2 T(r, \mathbf{z}, \tau)}{\partial r^2} + \frac{1}{r} \frac{\partial T(r, \mathbf{z}, \tau)}{\partial r} \right] + \frac{\partial \lambda\_{\text{wr}}}{\partial T} \left[ \frac{\partial T(r, \mathbf{z}, \tau)}{\partial r} \right]^2 \\ + \lambda\_{\text{wp}} \frac{\partial^2 T(r, \mathbf{z}, \tau)}{\partial \mathbf{z}^2} + \frac{\partial \lambda\_{\text{wp}}}{\partial T} \left[ \frac{\partial T(r, \mathbf{z}, \tau)}{\partial \mathbf{z}} \right]^2 \end{split} \tag{5}$$

with an initial condition

$$T(r, z, \mathbf{0}) = T(r, z, \tau\_{\text{fr}}) \tag{6}$$

and boundary conditions for convective heat transfer:

• along the radial coordinate r on the logs' frontal surface during the defrosting process:

$$\frac{\partial T(r,\mathbf{0},\boldsymbol{\tau})}{\partial r} = -\frac{a\_{\mathrm{wp-dfr}}(r,\mathbf{0},\boldsymbol{\tau})}{\lambda\_{\mathrm{wp}}(r,\mathbf{0},\boldsymbol{\tau})}[T(r,\mathbf{0},\boldsymbol{\tau}) - T\_{\mathrm{m-dfr}}(\boldsymbol{\tau})],\tag{7}$$

• along the longitudinal coordinate z on the logs' cylindrical surface during the defrosting process:

$$\frac{\partial T(\mathbf{0}, z, \tau)}{\partial \mathbf{z}} = -\frac{a\_{\text{wr-dfr}}(\mathbf{0}, z, \tau)}{\lambda\_{\text{wr}}(\mathbf{0}, z, \tau)} [T(\mathbf{0}, z, \tau) - T\_{\text{m-dfr}}(\tau)].\tag{8}$$

Eqs. (5)–(8) represent a mathematical model of the logs' defrosting process, i.e., of the 2D temperature distribution in logs subjected to defrosting immediately after their freezing.

### 2.3 Mathematical description of the thermo-physical characteristics of logs

On Figures 1 and 2 the temperature ranges are presented, at which the processes of the logs' freezing and subsequent defrosting respectively are carried out when u > ufsp.

There thermo-physical characteristics of the logs and of both the frozen free and bound water in them have also been shown. The information on these characteristics is very important for the solving of the mutually connected mathematical models given above.

During the first range of the logs' freezing process from Tw0 to Tfr˜fw only a cooling of the logs with fully liquid water in them occurs (Figure 1). During the second range from Tfr˜fw to Tfr˜bwm a further cooling of the logs occurs until reaching of the state needed for starting of the crystallization of the free water. During that range also the phase transition of this water into ice is carried out. The second range is absent when u is less than ufsp. During the third range from Tfr˜bwm to Tw˜fre˜avg a further cooling of the logs is carried out until reaching of the state needed for starting of the crystallization of the bound water. During this range also the phase transition of the bound water into ice is performed.

During the first range of the logs' defrosting process from Tw˜fre˜avg to Tdfr˜bwm a heating of the frozen logs is carried out until reaching of the state needed for starting and realization of the gradually melting of the frozen bound water in them

#### Figure 1.

Temperature ranges of the logs' freezing process at u > ufsp and thermo-physical characteristics of the wood and of the frozen free and bound water in it.

#### Figure 2.

Temperature ranges of the logs' defrosting process at u > ufsp and thermo-physical characteristics of the wood and of the frozen free and bound water in it.

Numerical Solution to Two-Dimensional Freezing and Subsequent Defrosting of Logs DOI: http://dx.doi.org/10.5772/intechopen.84706

(Figure 2). During the second range from Tdfr�bwm to Tdfr�fw a further heating of the logs occurs until reaching of the state needed for starting and realization of the melting of the frozen free water in them. During the third range from Tdfr�fw to Tw�dfre�avg a further heating of the logs with fully liquid water in them occurs.

The effective specific heat capacities of the logs during the pointed 3 ranges of the freezing process (see Figure 1) above the hygroscopic range, cwe‐fr, are equal to the below:

$$\text{I. range}: \mathcal{c}\_{\text{we-fr1}} = \mathcal{c}\_{\text{w-nfrv}} \tag{9}$$

$$\text{II. range}: c\_{\text{we-fr2}} = c\_{\text{w-nfr}} + c\_{\text{fw}} - c\_{\text{Lat-fw}} \tag{10}$$

$$\text{III. range}: \mathcal{c}\_{\text{we-fr}3} = \mathcal{c}\_{\text{w-fr}} + \mathcal{c}\_{\text{bwm}} - \mathcal{c}\_{\text{Lat-bwm}}.\tag{11}$$

The effective specific heat capacities of the logs during the pointed 3 ranges of the defrosting process (see Figure 2) above the hygroscopic range, cwe‐dfr, are equal to the below:

$$\text{I. range}: c\_{wc\text{-}df\text{r}1} = c\_{\text{w-fr}} + c\_{\text{bwm}}.\tag{12}$$

$$\text{III. range}: \mathcal{c}\_{\text{we-dfr2}} = \mathcal{c}\_{\text{w-nfr}} + \mathcal{c}\_{\text{fw}} \tag{13}$$

$$\text{III. Range } \colon \mathcal{c}\_{\text{we-dfr3}} = \mathcal{c}\_{\text{w-nfr}}.\tag{14}$$

Mathematical descriptions of the specific heat capacities cw�nfr, cw�fr, cfw, cbwm, and also of the thermal conductivities of non-frozen, λw‐nfr, and frozen wood, λw‐fr, have been suggested by the first co-author earlier [9, 10, 19] using the experimentally determined in the dissertations by Kanter [26] and Chudinov [2] data for their change as a function of t and u. These relations are used in both the European [5–10] and the American specialized literature [11–17] when calculating various processes of the wood thermal treatment.

Mathematical descriptions of the specific heat capacities, which are formed by the release of the latent heat of both the free and bound water during their crystallization in the wood, cLat�fw and cLat�bwm respectively (refer to Eqs. (10) and (11)) have been given by the authors in [23]. Mathematical descriptions of the internal heat sources separately for the free and bound water, qv‐fw and qv‐bw respectively, which participate in the right-hand part of Eq. (1), have been also given.

Our study has shown that for the calculation (in W�m�2 �K�1 ) of the radial and longitudinal transfer coefficients of the logs, which participate in the boundary conditions of the model the following equations are most suitable [27]:

• in the radial direction on the cylindrical surface of the horizontally situated logs:

$$a\_{\rm wr-fr} = 2.56[T(0, z, \tau) - T\_{\rm m-fr}(\tau)]^{E\_{\rm fr}},\tag{15}$$

$$a\_{\rm wr-dfr} = 2.56[T(\mathbf{0}, z, \tau) - T\_{\rm m-fr}(\tau)]^{E\_{\rm dfr}} \tag{16}$$

• in the longitudinal direction on the frontal surface of the logs:

$$a\_{\rm wp-fr} = \mathbf{1.123} [T(r, \mathbf{0}, \tau) - T\_{\rm m-fr}(\tau)]^{E\_{\rm fr}},\tag{17}$$

$$a\_{\rm wp-dfr} = \mathbf{1.123} [T(r, \mathbf{0}, \tau) - T\_{\rm m-fr}(\tau)]^{E\_{\rm dfr}},\tag{18}$$

where Еfr and Еdfr are exponents, whose values are determined during the solving and verification of the models through minimization of the root square mean error (RSME) between the calculated by the models and experimentally obtained results about the change of the temperature fields in subjected to freezing and subsequent defrosting logs.

#### 2.4 Transformation of the models to a form suitable for programming

Due to the correct cylindrical shape of the logs, for the solution of the above presented two mutually connected mathematical models an explicit form of the finite-difference method has been used. That form allows for the exclusion of any simplifications of the models and also of the necessity for any linearization of the mathematically described variables in them [8, 9, 18, 19].

The large calculation resources of the contemporary computers eliminate the inconvenience, which creates the limitation for the value of the step along the time coordinate Δτ by using the explicit form [9].

According to the idea of the finite-difference method, the temperature, which is a uninterrupted function of space and time, is presented using a grid vector, and the ∂T derivatives ∂T, and ∂T are approximated using the built computational mesh along ∂r ∂z ∂τ the spatial and time coordinates through their finite-difference (discrete) analogues.

#### 2.4.1 Transformation of the equations of thermo-conductivity in the models

The transformation of Eqs. (1) and (5) of the models in their suitable for programming discrete analogues has been realized using the presented on Figure 3 coordinate system. That system shows the positioning of the knots of the calculation mesh, in which the non-stationary distribution of the temperature in the longitudinal section of subjected to freezing and subsequent defrosting log has been calculated. The calculation mesh has been built on ¼ of the longitudinal section of the log due to the circumstance that this ¼ is mirror symmetrical towards the remaining 3/4 of the same section.

#### Figure 3.

Calculation mesh for the solution of the models (left) and positioning of the knots of 2D calculation mesh on 1/4 of longitudinal section of a log subjected to freezing and subsequent defrosting (right).

Numerical Solution to Two-Dimensional Freezing and Subsequent Defrosting of Logs DOI: http://dx.doi.org/10.5772/intechopen.84706

Taking into consideration the relationships [9, 19]

$$
\lambda\_{\rm w} = \lambda\_{\rm w0r,p} \cdot \boldsymbol{\gamma} \cdot [\mathbf{1} + \boldsymbol{\beta} \cdot (T - 27 \mathbf{3.15})],\tag{19}
$$

$$\lambda\_{\rm w0r} = K\_{\rm wr} \cdot v \cdot \left[ 0.165 + (1.39 + 3.8u) \cdot \left( 3.3 \cdot 10^{-7} \rho\_{\rm b}^2 + 1.015 \cdot 10^{-3} \rho\_{\rm b} \right) \right], \tag{20}$$

$$\lambda\_{\rm w0p} = K\_{\rm wp} \cdot v \cdot \left[ \mathbf{0.165} + (\mathbf{1.39} + \mathbf{3.8u}) \cdot \left( \mathbf{3.3 \cdot 10^{-7}} \rho\_{\rm b}^2 + \mathbf{1.015 \cdot 10^{-3}} \rho\_{\rm b} \right) \right], \tag{21}$$

and using the coefficient

$$K\_{\rm wp/wrr} = \frac{K\_{\rm wp}}{K\_{\rm wr}},\tag{22}$$

after applying the explicit form of the finite-differences method to Eq. (1), it is transformed into the following system of equations:

$$\begin{aligned} T\_{i,k}^{u+1} &= T\_{i,k}^{u} + \frac{\lambda\_{\text{wbr}} \cdot \chi \cdot \Delta \tau}{c\_{\text{we-fr1},2,3}^{u} \cdot \rho\_{\text{w}} \cdot \Delta r^{2}}, \\\\ \left\{ \left[ 1 + \beta \cdot \left( T\_{i,k}^{u} - 273.15 \right) \right] \cdot \begin{bmatrix} T\_{i-1,k}^{u} + T\_{i+1,k}^{u} + K\_{\text{p}/r} \left( T\_{i,k-1}^{u} + T\_{i,k+1}^{u} \right) - \\\\ - \left( 2 + 2K\_{\text{p}/r} \right) T\_{i,k}^{u} + \frac{1}{i-1} \left( T\_{i-1,k}^{u} - T\_{i,k}^{u} \right) \end{bmatrix} \right\}, \\\\ &+ \beta \cdot \left[ \left( T\_{i-1,k}^{u} - T\_{i,k}^{u} \right)^{2} + K\_{\text{wp}/\text{wr}} \left( T\_{i,k-1}^{u} - T\_{i,k}^{u} \right)^{2} \right] \end{aligned} \tag{23}$$

where λwor and λwop are the wood thermal conductivities at t = 0°C in radial and longitudinal direction respectively, W�m�1 �K�1 ; γ, β, and ν—coefficients for the determination of λw, λwor and λwop. Equation for calculation of γ, β, and ν for nonfrozen and frozen wood are given in [9, 19]; Kwr and Kwp —empirically determined coefficients, which take into account the influence of the radial and longitudinal anatomical directions on the wood thermal conductivity, -; Δτ—interval between time levels, i.e., step along the time coordinate, with which the model is solving, s; n—current number of the step Δτ along the time coordinate: n = 0, 1, 2, 3,… τfr/Δτ; τfr—duration of the freezing process of logs, s; Δr = Δz—step along the coordinates r and z, by which the model is being solved, m; i—current number of the knots of the calculation mesh along the coordinate r:1 ≤ i ≤ 1+(R/Δr); k—current number of the knots along the coordinate z:1 ≤ k ≤ 1 + [(L/2)/Δr]; R—log's radius, m; L—log's length, m.

The effective specific heat capacities of the log during the pointed above three ranges of its freezing process (see Figure 1), cwe‐fr1, cwe‐fr2, and cwe‐fr3, which are unitedly represented as cwe‐fr1,2, 3 in Eq. (23), are computed according to Eqs. (9)–(11) separately for each knot of the calculation mesh.

The density of the log's wood above the hygroscopic range, ρw, which participates in Eq. (23), is calculated (in kg�m�3 ) according to the following widely accepted in the literature equation [1–17, 28]:

$$
\rho\_{\mathbf{w}} = \rho\_{\mathbf{b}} \cdot (\mathbf{1} + \boldsymbol{\mu}),
\tag{24}
$$

where ρb is the basic density of the wood, based on dry mass divided to green volume, kg�m�3 ; u—wood moisture content, kg�kg�1 .

After applying the explicit form of the finite-differences method to Eq. (5), it is transformed into the following system of equations, which is similar to Eq. (23):

$$\begin{aligned} T\_{i,k}^{u+1} &= T\_{i,k}^{u} + \frac{\lambda\_{\text{w0r}} \cdot \boldsymbol{\chi} \cdot \Delta \boldsymbol{\pi}}{c\_{\text{we-diffr},2,3}^{u} \cdot \rho\_{\text{w}} \cdot \Delta \boldsymbol{\pi}^{2}}. \\\\ &\cdot \left\{ \left[ \mathbbm{1} + \boldsymbol{\beta} \cdot \left( T\_{i,k}^{u} - 273.15 \right) \right] \cdot \begin{bmatrix} T\_{i-1,k}^{u} + T\_{i+1,k}^{u} + K\_{\text{p}/r} \left( T\_{i,k-1}^{u} + T\_{i,k+1}^{u} \right) - \\ - \left( 2 + 2K\_{\text{p}/r} \right) T\_{i,k}^{u} + \frac{1}{i-1} \left( T\_{i-1,k}^{u} - T\_{i,k}^{u} \right) \end{bmatrix} \right\}, \\\ &\cdot \boldsymbol{\beta} \cdot \left[ \left( T\_{i-1,k}^{u} - T\_{i,k}^{u} \right)^{2} + K\_{\text{wp}/\text{wr}} \left( T\_{i,k-1}^{u} - T\_{i,k}^{u} \right)^{2} \right] \end{aligned} \tag{25}$$

where the effective specific heat capacities of the log during the pointed above three ranges of its defrosting process (see Figure 2), cwe‐dfr1, cwe‐dfr2, and cwe‐dfr3, which are unitedly represented as cwe‐dfr1, 2, 3in Eq. (25), are computed according to Eqs. (12)–(14) separately for each knot of the calculation mesh.

The current number of the step Δτ along the time coordinate, n, in Eq. (25) is equal to: n = τfr/Δτ, (τfr/Δτ) + 1, (τfr/Δτ) + 2, (τfr/Δτ) + 3, …., (τfr+τdfr)/Δτ, where τdfr is the duration of the log's defrosting process, s.

#### 2.4.2 Transformation of the equations of initial conditions in the models

The initial condition (2) of the model of logs' freezing process obtains the following discrete finite-difference form:

$$T\_{i,k}^{0} = T\_{\mathbf{w}0}.\tag{26}$$

The initial condition (6) of the model of logs' defrosting process obtains the following discrete finite-difference form:

$$T\_{i,k}^{0} = T\_{i,k}^{n=\mathbf{r}\_{\text{fr}}/\Delta \mathbf{r}}.\tag{27}$$

where τfr is the duration of the freezing process of logs, which precedes the beginning of their subsequent defrosting, s.

## 2.4.3 Transformation of the equations of boundary conditions in the models along the radial coordinate

The discrete finite difference analogue of the left-hand part of Eq. (3), which is suitable for programming in FORTRAN, has the following form [8, 9]:

$$\frac{\partial T(r, \mathbf{0}, \tau)}{\partial r} \approx \frac{T\_{i,1}^{n+1} - T\_{i,2}^{n}}{\Delta r}. \tag{28}$$

The discrete analogue of the right-hand part of Eq. (3) has the following form:

$$-\frac{a\_{\rm wp\,fr}(r,\mathbf{0},\tau)}{\lambda\_{\rm wp}(r,\mathbf{0},\tau)}[T(r,\mathbf{0},\tau)-T\_{\rm m\,fr}(\tau)] \approx -\frac{a\_{\rm wp\,-fr}^{\rm u}}{\lambda\_{\rm w0p}\cdot\chi\cdot\left[\mathbf{1}+\beta\cdot\left(T\_{i,1}^{\rm u}-273.15\right)\right]}\left(T\_{i,1}^{\rm u+1}-T\_{\rm m-fr}^{\rm u+1}\right),\tag{29}$$

Numerical Solution to Two-Dimensional Freezing and Subsequent Defrosting of Logs DOI: http://dx.doi.org/10.5772/intechopen.84706

where according to Eq. (17)

$$a\_{\rm wp-fr}^{\rm n} = \mathbf{1}.\mathbf{123} \left[ T\_{i,1}^{\rm n} - T\_{\rm m-fr}^{\rm n} \right]^{E\_{\rm fr}}.\tag{30}$$

After alignment of Eq. (28) with Eq. (29), it is obtained that

$$\frac{T\_{i,1}^{n+1} - T\_{i,2}^{n}}{\Delta r} \approx -\frac{a\_{\text{wp}-\text{fr}}^{n}}{\lambda\_{\text{w0p}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{i,1}^{n} - 273.15\right)\right]} \left(T\_{i,1}^{n+1} - T\_{\text{m-fr}}^{n+1}\right). \tag{31}$$

During the solving of the model it is needed to determine the temperature on the log's frontal surface, Tn i, þ 1 1 , for each next step n + 1 along the time coordinate. Using Eq. (31), Tn i, þ 1 1 is equal to

$$T\_{i,1}^{n+1} \approx T\_{i,2}^{n} - \frac{\Delta r \cdot d\_{\rm wp-fr}^{n} \cdot T\_{i,1}^{n+1}}{\lambda\_{\rm 0p} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{i,1}^{n} - 273.15\right)\right]} + \frac{\Delta r \cdot d\_{\rm wp-fr}^{n} \cdot T\_{\rm m-fr}^{n+1}}{\lambda\_{\rm w0p} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{i,1}^{n} - 273.15\right)\right]}.\tag{32}$$

After designation of

$$G\_{i, \text{1-fr}}^{\text{n}} = \frac{\Delta r \cdot a\_{\text{wp}-\text{fr}}^{\text{n}}}{\lambda\_{\text{w0p}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{i, \text{1}}^{\text{n}} - 273.15\right)\right]},\tag{33}$$

the boundary condition (3) of the logs' freezing process obtains the following final form, suitable for programming:

$$T\_{i,1}^{n+1} = \frac{T\_{i,2}^{n} + G\_{i,1-\text{fr}}^{n} \cdot T\_{\text{m-fr}}^{n+1}}{1 + G\_{i,1-\text{fr}}^{n}}.\tag{34}$$

Analogously, the boundary condition (7) of the logs' defrosting process obtains the following final form, suitable for programming:

$$T\_{i,1}^{n+1} = \frac{T\_{i,2}^n + G\_{i,1-\text{dfr}}^n \cdot T\_{m-\text{dfr}}^{n+1}}{1 + G\_{i,1-\text{dfr}}^n} . \tag{35}$$

The variable Gn i, 1�dfr in Eq. (35) is equal to

$$G\_{i,1-\text{dfr}}^{\text{n}} = \frac{\Delta r \cdot a\_{\text{wp}-\text{dfr}}^{\text{n}}}{\lambda\_{\text{w0p}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{i,1}^{\text{n}} - 273.15\right)\right]},\tag{36}$$

where according to Eq. (18)

$$a\_{\rm wp-dfr}^{\rm n} = \mathbf{1.123} \left[ T\_{i,1}^{\rm n} - T\_{\rm m-fr}^{\rm n} \right]^{E\_{\rm dfr}}.\tag{37}$$

#### 2.4.4 Transformation of the equations of boundary conditions in the models along the longitudinal coordinate

The discrete finite difference analogue of the left-hand part of Eq. (4) at Δz = Δr has the following suitable for programming form [8, 9]:

$$\frac{\partial T(0, z, \tau)}{\partial z} \approx \frac{T\_{1,k}^{n+1} - T\_{1,k}^{n}}{\Delta r}. \tag{38}$$

The discrete analogue of the right-hand part of Eq. (4) has the following form:

$$-\frac{a\_{\text{wr-fr}}(0,z,\tau)}{\lambda\_{\text{wr}}(0,z,\tau)}[T(0,z,\tau)-T\_{\text{m-fr}}(\tau)] \approx -\frac{a\_{\text{wr-fr}}^{\text{n}}}{\lambda\_{\text{wr0r}}\cdot\chi\cdot\left[1+\beta\cdot\left(T\_{1,k}^{\text{n}}-273.15\right)\right]}\left(T\_{1,k}^{\text{n+1}}-T\_{\text{m-fr}}^{\text{n+1}}\right). \tag{39}$$

where according to Eq. (15)

$$a\_{\rm wr-fr}^{\rm n} = 2.56 \left[ T\_{1,k}^{\rm u} - T\_{\rm m-fr}^{\rm u} \right]^{E\_{\rm fr}}.\tag{40}$$

After alignment of Eq. (38) with Eq. (35), it is obtained that

$$\frac{T\_{1,k}^{n+1} - T\_{2,k}^{n}}{\Delta r} \approx -\frac{a\_{\text{wr}-\text{fr}}^{n}}{\lambda\_{0\text{r}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{1,k}^{n} - 273.15\right)\right]} \left(T\_{1,k}^{n+1} - T\_{\text{m-fr}}^{n+1}\right). \tag{41}$$

Using Eq. (41), the temperature Tn 1, þ k 1 is equal to

$$T\_{1,k}^{n+1} \approx T\_{2,k}^{n} - \frac{\Delta r \cdot \alpha\_{\text{wr}-\text{fr}}^{n} \cdot T\_{1,k}^{n+1}}{\lambda\_{\text{w0r}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{1,k}^{n} - 273.15\right)\right]} + \frac{\Delta r \cdot \alpha\_{\text{wr}-\text{fr}}^{n} \cdot T\_{\text{m}-\text{fr}}^{n+1}}{\lambda\_{\text{w0r}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{1,k}^{n} - 273.15\right)\right]}.\tag{42}$$

After designation of

$$G\_{1,k-\text{fr}}^{\text{n}} = \frac{\Delta r \cdot a\_{\text{wr}-\text{fr}}^{\text{n}}}{\lambda\_{\text{w0r}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{1,k}^{\text{n}} - 273.15\right)\right]},\tag{43}$$

the boundary condition (4) of the logs' freezing process obtains the following final form, suitable for programming:

$$T\_{1,k}^{n+1} = \frac{T\_{2,k}^n + G\_{1,k-\text{fr}}^n \cdot T\_{m-\text{fr}}^{n+1}}{1 + G\_{1,k-\text{fr}}^n}.\tag{44}$$

Analogously, the boundary condition (8) of the logs' defrosting process obtains the following final form, suitable for programming in FORTRAN:

$$T\_{1,k}^{n+1} = \frac{T\_{2,k}^{n} + G\_{1,k-\text{dfr}}^{n} \cdot T\_{m-\text{fr}}^{n+1}}{1 + G\_{1,k-\text{dfr}}^{n}}.\tag{45}$$

The variable Gn 1,k�dfr in Eq. (45) is equal to

$$G\_{1,k-\text{dfr}}^{\text{n}} = \frac{\Delta r \cdot a\_{\text{wr}-\text{dfr}}^{\text{n}}}{\lambda\_{\text{w0r}} \cdot \chi \cdot \left[1 + \beta \cdot \left(T\_{1,k}^{\text{n}} - 273.15\right)\right]},\tag{46}$$

where according to Eq. (16)

$$a\_{\rm wr-dfr}^{\rm n} = 2.56 \left[ T\_{1,k}^{\rm n} - T\_{\rm m-dfr}^{\rm n} \right]^{E\_{\rm dfr}}.\tag{47}$$


**Meet the editor**

Ahmed Faheem Zobaa received the B.Sc.(Hons.), M.Sc., and Ph.D. degrees in electrical power and machines from Cairo University, Giza, Egypt, in 1992, 1997, and 2002, respectively. From 2007 to 2010, he was a Senior Lecturer in renewable energy with the University of Exeter, Cornwall, UK. He was also an Instructor from 1992 to 1997, a Teaching Assistant from 1997 to 2002, and an

Assistant Professor from 2003 to April 2008 with the Department of Electrical Power and Machines and the Faculty of Engineering, Cairo University, where he has also been an Associate Professor since April 2008. Currently, he is a Senior Lecturer in power systems with Brunel University, Uxbridge, UK. His main areas of expertise are power quality, photovoltaic energy, wind energy, marine renewable energy, grid integration, and energy management. Dr. Zobaa is Editor-in-Chief for the International Journal of Renewable Energy Technology. He is also an Editorial Board member, Editor, Associate Editor, and Editorial Advisory Board member for many international journals. He is a registered Chartered Engineer, European Engineer, and International Professional Engineer. He is also a registered member of the Engineering Council UK, Egypt Syndicate of Engineers, and the Egyptian Society of Engineers. He is a Fellow of the Institution of Engineering and Technology, the Energy Institute of UK, the Chartered Institution of Building Services Engineers and the Higher Education Academy of UK. He is a senior member of the Institute of Electrical and Electronics Engineers, and a member of the International Solar Energy Society, the European Society for Engineering Education, the European Power Electronics and Drives Association, and the IEEE Standards Association.

Contents

**Preface VII**

Chapter 1 **Power Quality Data Compression 1** Gabriel Găşpăresc

**Distribution Networks 21**

António Pina Martins

and Dario Zaninelli

Belkacem Mahdad

**in Industrial Facilities 105**

Chapter 7 **Harmonic Effects of Power System Loads: An**

**Experimental Study 175**

Chapter 2 **Electric Power Quality Recognition and Classification in**

Chapter 3 **Power Quality Enhancement Through Robust Symmetrical Components Estimation in Weak Grids 67**

Chapter 4 **Monitoring Power Quality in Small Scale Renewable Energy Sources Supplying Distribution Systems 93**

Chapter 5 **Active Power Conditioners to Mitigate Power Quality Problems**

João L. Afonso, J. G. Pinto and Henrique Gonçalves

Chapter 6 **Power Quality Management Based Security OPF Considering FACTS Using Metaheuristic Optimization Methods 139**

Bedri Kekezoğlu, Altuğ Bozkurt and C. Fadıl Kumru

Soliman Abdel-Hady Soliman and Rashid Abdel-Kader Alammari

Nicolae Golovanov, George Cristian Lazaroiu, Mariacristina Roscia

Celal Kocatepe, Recep Yumurtacı, Oktay Arıkan, Mustafa Baysal,