**8.2 Entry with bank angle modulation**

Aerodynamic efficiency can be varied implicitly without using AoA modulation opportunely changing the bank angle *μa*. Bank modulates the lift force into two components *Leff* ¼ *L* cos *μa* and *Lside* ¼ *L* sin *μa*. The lateral force, *Lside*, deviates the lift vector outside the plane of trajectory, thus allowing a cross-range performance in the lateral direction. Therefore, trajectory footprint can be decomposed into two components: the down-range Δ*xp* � *L D cos μa* and the cross-range Δ*yp* � *L D sin μa* . In **Figure 7** the effect bank modulation on vehicle trajectory is shown.

### **Figure 5.** *Entry analysis with no bank angle modulation.*

**Table 3.** *Total energy absorbed during entry.*

**Figure 6.**

*Trade-off effects of flight path angle for entry flight at ve = 3484 m/s, α = 30°, μa = 0°.*

**Figure 7.** *Entry trade-off analysis with bank angle modulation.*

*Lifting Entry Analysis for Manned Mars Exploration Missions DOI: http://dx.doi.org/10.5772/intechopen.101993*

**Table 4.**

*Total energy absorbed during re-entry.*

Increasing *μa* at constant AoA (i.e., constant *L=D*Þ the total range (cross-range and downrange) increases. The effective lift component *Leff* is reduced, and the vehicle attains a lower altitude at *M*∞ ¼ 2, *μa* ¼ 20° with respect to *μa* ¼ 40° as it is shown in **Figure 5c**. Therefore, control authority increases at expense of a higher terminal speed. Another effect of bank angle modulation can be observed in **Figure 7d**. The lower lift reduces the skip motion when the vehicle encounters the Martian atmosphere. Higher heat flux peaks over a shorter entry time are experienced. Therefore, at constant AoA, bank modulation improves the capability to reach the predefined landing spot.

Finally, in **Table 4** the total energy absorbed during the entry with bank modulation is computed.

From an energetic point of view, bank modulation toward higher *μa* favors lower total energy stored but shifts trajectory toward a ballistic-like behavior.


**1. Introduction**

Caatinga is a Brazilian biome with a semi-arid climate, vegetation with small leaves and adapted to dry periods, as well as great biodiversity. This biome is found in areas of northeastern Brazil, in the states of Maranhão, Piaui, Ceará, Rio Grande do Norte, Paraiba, Pernambuco, Alagoas, Sergipe, Bahia and part of Minas Gerais. This whole area covers about 844,000 km2 , or 11% of the Brazilian territory [1]. This ecosystem is very important from the biological point of view because it has unique fauna and flora, formed by vast biodiversity, rich in genetic resources and vegetation consisting of species, woody, herbaceous, cactus, and bromeliads. It has 932 species of plants, 148 mammals and 510 birds, for example, and many of these species occur only in the Caatinga.

The main characteristics of the Caatinga are: Strong presence of shrubs with twisted branches and deep roots; Presence of cacti and bromeliads; Shrubs usually lose their leaves almost completely in times of drought (property used to prevent evaporative water loss). The leaves of this vegetation type are small in size; Caatinga soil has low fertility and is stony. Caatinga biodiversity supports various economic

activities aimed at agroforestry and industrial purposes. Despite its importance, Caatinga vegetation is a type of vegetation adapted to the aridity of the soil and the scarcity of water in the region. They are classified depending on the natural conditions of the areas and different characteristics like strata: arboreal: with species ranging between 8 and 12 m in height; shrub: with species ranging between 2 and 5 m in height; herbaceous: with species below 2 m in height [2]. *Copernicia prunifera* (Miller) H. E. Moore (Arecaceae) family, a typical desert flora animal categories and exclusively located of areas through the Caatinga biome [3]. It is also known as "Tree of life", *carnauba*, *carandauba*, *carnaba*, *carnaubeira*, *caranaiba*, *carnaúva*, among others.

The carnauba is a palm tree very common in the northeast region whose main feature is its height, which can reach 15 m. The stem is straight and cylindrical, with a diameter that can vary from 10 to 20 cm and has thorns at the bottom. The tree provides fruits from November to March. They are greenish when young and turn purple when they mature. Its fruits are well used to feed farm animals. According to Brazilian specialized guidelines characterize the "pó de olho" and "pó de palha" wax powder as category A and B, respectively [4–6]. Meanwhile, the apical leaves have found lower chlorophyll content, type A wax has a pigmentation that shifts from white to light yellow and has a higher incentive than category B, which has a greenish-gray pigmentation.

Carnauba wax is derived besides the leaves regarding the *Copernicia prunifera* tree (**Figure 1**) and is made principally out of long-chain wax esters (80%), 20% contained fatty acids, fatty alcohols, and hydrocarbons [7–9]. Carnauba wax has the most maximum melting point conditions of all vegetable waxes and has been utilized in an assortment of items, including cosmetic and food products, nourishment items, and the paper area [9]. Additionally, this material is widely used in folk medicine, including the treatment of rheumatism and syphilis. However, carnauba

**75**

*DOI: http://dx.doi.org/10.5772/intechopen.90252*

biotechnological applications.

tography of 0.6 × 105 g mol−1

performances.

**2.2 Triterpenes**

**2.1 Pectin**

**2. Nutritional and chemical composition**

*The Phytochemical Composition of Medicinal Plants: Brazilian Semi-Arid Region (Caatinga)*

wax is utilized as a stabilizer to different waxes, for example, beeswax to improve the melting point, taking into account expanded utilization of these waxes [10]. Despite that, a great deal of research has been carried out into an attempt to extend the chances of potential outcomes of utilizations of this crude material. With this goal, analysis has been finished streamlining customary applications and examining advancements, for example, the utilization of wax for the microencapsulation of flavors and as a wellspring of molecules following up on the avoidance and treatment of, diabetes, dyslipidemia, and others. The wax is an item to show the level of local consumption with extraordinary potential for use all through the Brazilian food production chain. Along these lines, it is imperative to experts in the food area to more likely comprehend this crude material so as to misuse its maximum capacity. In this way, this review talks about the utilization of carnauba wax in food ranging from the nutritional, phytochemical evaluation, ethnobotanical and

Carnauba wax consists of complex mixture regarding long-chain fatty acids, free

alcohols, esters, aromatic acids, aliphatic acids, triterpene diols, cinnamic acids, proteins, and hydroxy acids and ω-hydroxycarboxylic free acids [10–14]. Recently, one triterpene carnaubadiol was also isolated and identified present in the leaves were reported. The inorganic compounds existing such as aluminum, copper, magnesium, zinc, manganese, calcium, iron, and sodium [15]. Recent studies continued to assess more genetic resource of carnauba wax while revealing a more extensive variety in the nutritional composition as described in the following sections.

Paim et al. [16] extracted the pectin from the aqueous pulp extracts (APE) of *Copernicia prunifera* analyzed by chromatographic and spectroscopic methods. From this study, the pectin substance acquired from the pulp of unripe fruits of *C. prunifera* demonstrated an estimation of 2.9%. Additionally, the pectin was observed by using the absorption spectra by demonstrating several carbonyl groups in the form of esterified and carboxylate compounds. Furthermore, the thin layer chromatography (TLC) technique identified galactose, galacturonic acid patterns, and arabinose compounds, respectively. By using, 13C NMR spectroscopy analysis method, various forms of polymers were recognized in the pectic polysaccharides chain compounds including D-galacturonic acid (major signs), D-galactose (lower signs) and the peak molar mass (*M*pk) was determined by gel permeation chroma-

higher molecular weight and a igher degree of esterification displaying improved

Almeida et al. [11], explored phytochemical investigation of hexane and ethanolic extracts carnauba wax (types 1 and 4) was analyzed and identified 16 dammaranetype triterpenes, with 13 newly categorized as (24R\*)-methyldammara-20,25-dien-3α-ol and a mixture of alkyl (24R\*)-methyldammar25-en-20-ol-3β-carboxylates, and 3 triterpenes such as carnaubadiol,(24R\*)-methyldammara-20,25-dien-3β-ol and (24R\*)-24-methyldammara-20,25-dien-3-one. Furthermore, fatty alcohols such as docosanol, eicosanol, and hexacosanol, tetracosanol as well as four sterols

. All these studies highlighted that pectin presence of

**Figure 1.** Copernicia prunífera *tree (from Fortaleza, Brazil).*

#### *DOI: http://dx.doi.org/10.5772/intechopen.90252 The Phytochemical Composition of Medicinal Plants: Brazilian Semi-Arid Region (Caatinga)*

wax is utilized as a stabilizer to different waxes, for example, beeswax to improve the melting point, taking into account expanded utilization of these waxes [10].

Despite that, a great deal of research has been carried out into an attempt to extend the chances of potential outcomes of utilizations of this crude material. With this goal, analysis has been finished streamlining customary applications and examining advancements, for example, the utilization of wax for the microencapsulation of flavors and as a wellspring of molecules following up on the avoidance and treatment of, diabetes, dyslipidemia, and others. The wax is an item to show the level of local consumption with extraordinary potential for use all through the Brazilian food production chain. Along these lines, it is imperative to experts in the food area to more likely comprehend this crude material so as to misuse its maximum capacity. In this way, this review talks about the utilization of carnauba wax in food ranging from the nutritional, phytochemical evaluation, ethnobotanical and biotechnological applications.


**5.7 Building the gas holder**

A wood or steel structure in form of umbrella is built, and then a mesh network is relayed on the umbrella structure (Figs. 14 and 15). The air supported double membrane cover, which includes the gas holder, is mounted over the structure. The flexible membrane of the gas collector, i.e. holder, moves up and down as a function of the gas pressure. On the other hand, the storage tank covers are numerous: (1) closed cover (concrete, plastic, and tent), (2) straw cover, (3) granulate (perlite), (4) swimming vinyl covering, and (5) open as open lagoons and open storage tanks.

Fig. 14. Wood structure and mesh network that supports the gas holder of digester in a commercial biogas plant (MT-ENERGIE GmbH & Co. KG)

A wood or steel structure in form of umbrella is built, and then a mesh network is relayed on the umbrella structure (Figs. 14 and 15). The air supported double membrane cover, which includes the gas holder, is mounted over the structure. The flexible membrane of the gas collector, i.e. holder, moves up and down as a function of the gas pressure. On the other hand, the storage tank covers are numerous: (1) closed cover (concrete, plastic, and tent), (2) straw cover, (3) granulate (perlite), (4) swimming vinyl covering, and (5) open as open

Fig. 14. Wood structure and mesh network that supports the gas holder of digester in a

commercial biogas plant (MT-ENERGIE GmbH & Co. KG)

Fig. 13. Integrating the heating tubes (BIOGAS NORD GmbH)

**5.7 Building the gas holder**

lagoons and open storage tanks.

Fig. 15. Mesh network that supports the gas holder of a household unit


*2.2. X-ray Fluorescence and X-ray Diffraction Characterisation*

Elemental analysis of the fabricated substrates was performed three times and averaged using a BRUKER TITAN S1 X-ray fluorescent (XRF) handheld analyser (Coventry, UK) to ensure that the bulk components in the manufactured substrates match the composition standards. This was done by placing the substrate on a working station then adjusting the lens of the XRF device vertically on the substrate before starting the measurements, which required 10 s to complete for each single measurement. Moreover, X-ray diffraction (XRD) analysis was performed using a 9 kW Rigaku SmartLab, Tokyo, Japan, XRD device that utilizes a CuKα X-ray source at a diffraction angle of 2θ and an incidence beam angle of 0.02◦. This was done in order to identify the Bragg's peaks of each element contained within the substrates and to define the phase of the stainless steel alloy used. The diffraction scanning angle ranged from 20◦ to 80◦, with a scanning rate of 2 ◦/min.


**Appendix A**

In order to simulate the pressing/compression molding process, the flow analysis in 3D TIMON is based on the standard equations of traditional fluid dynamics: the equation of continuity, the equation of motion, and the equation of energy. These governing equations for the filling phase are given in the general and special form of the balance equations as follows:

The mass **continuity equation** (mass balance):

$$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial \mathbf{x}} (\rho u\_\mathbf{x}) + \frac{\partial}{\partial y} (\rho u\_\mathbf{y}) + \frac{\partial}{\partial z} (\rho u\_\mathbf{z}) = 0,\tag{A1}$$

where ρ is the density, *t* is time and *ui* stands for the fluid velocity vector in direction x, y, and z, respectively. For incompressible flow ρ is constant and Equation (A1) can be reduced to a volume continuity equation:

$$
\frac{
\partial
\mathbf{u}\_\mathbf{x}
}{
\partial
\mathbf{x}
} + \frac{
\partial
\mathbf{u}\_\mathbf{y}
}{
\partial y
} + \frac{
\partial
\mathbf{u}\_\mathbf{z}
}{
\partial z
} = \mathbf{0}.\tag{A2}
$$

The **equation of motion** (momentum balance) in fluid flow in all three directions can be expressed in terms of deviatoric stress τ*ij* and this form of the equation is commonly called the Cauchy momentum equation:

$$
\rho \frac{\mathrm{D}u\_i}{\mathrm{D}t} = -\frac{\partial p}{\partial \mathbf{x}\_i} + \frac{\partial \tau\_{ji}}{\partial \mathbf{x}\_j} + \rho \mathbf{g}\_{i\nu} \tag{A3}
$$

which in the x-direction becomes:

$$\rho \left( \frac{\partial \mathbf{u\_{x}}}{\partial t} + \mathbf{u\_{x}} \frac{\partial \mathbf{u\_{x}}}{\partial \mathbf{x}} + \mathbf{u\_{y}} \frac{\partial \mathbf{u\_{x}}}{\partial y} + \mathbf{u\_{z}} \frac{\partial \mathbf{u\_{x}}}{\partial z} \right) = -\frac{\partial p}{\partial \mathbf{x}} + \left( \frac{\partial \tau\_{\mathbf{xx}}}{\partial \mathbf{x}} + \frac{\partial \tau\_{\mathbf{yx}}}{\partial y} + \frac{\partial \tau\_{\mathbf{xz}}}{\partial z} \right) + \rho \mathbf{g\_{x}} \tag{A4}$$

where *p*: pressure, *gi*: body force acting on the continuum, for example, gravity. In this force balance the mass is represented by the fluid density ρ and the following bracket represents the acceleration, meaning how the velocity of a particle changes with time. Therein, ∂*u*x ∂*t* stands for the change of velocity over time and the three following terms represent the speed and direction in which the fluid is moving. The right hand side of the equation shows all forces acting in the fluid, where −∂*p* ∂*x* stands for the internal pressure gradient of the fluid, the second term is representing the internal stress forces acting on the fluid (viscous e ffects are considered), and the last term represents all external forces acting on the fluid, such as gravity.

In fluid mechanics the deviatoric stress tensor τ*ij* is commonly defined as:

$$
\pi\_{i\bar{j}} = \mu \dot{\gamma}\_{i\bar{j}}.\tag{A5}
$$

.

with μ: viscosity and . γ*ij*: rate of deformation tensor reducing the Cauchy momentum equation to the Navier–Stokes equation for a simple Newtonian fluid with constant density ρ and viscosity μ:

$$
\rho \frac{\mathrm{D}u\_i}{\mathrm{D}t} = -\frac{\partial p}{\partial \mathbf{x}\_i} + \mu \frac{\partial^2 u\_i}{\partial \mathbf{x}\_j \partial \mathbf{x}\_j} + \rho g\_{i\nu} \tag{A6}
$$

which in the x-direction looks like:

$$
\rho \left( \frac{\partial \mathbf{u}\_{\mathbf{x}}}{\partial t} + \mathbf{u}\_{\mathbf{x}} \frac{\partial \mathbf{u}\_{\mathbf{x}}}{\partial \mathbf{x}} + \mathbf{u}\_{\mathbf{y}} \frac{\partial \mathbf{u}\_{\mathbf{x}}}{\partial \mathbf{y}} + \mathbf{u}\_{\mathbf{z}} \frac{\partial \mathbf{u}\_{\mathbf{x}}}{\partial \mathbf{z}} \right) = -\frac{\partial p}{\partial \mathbf{x}} + \mu \left( \frac{\partial^2 \mathbf{u}\_{\mathbf{x}}}{\partial \mathbf{x}^2} + \frac{\partial^2 \mathbf{u}\_{\mathbf{x}}}{\partial \mathbf{y}^2} + \frac{\partial^2 \mathbf{u}\_{\mathbf{x}}}{\partial \mathbf{z}^2} \right) + \rho \mathbf{g}\_{\mathbf{x}}.\tag{A7}
$$

The **equation of energy** (energy balance) for a Newtonian fluid with constant properties is given by:

$$
\rho c\_p \frac{\text{DT}}{\text{Dt}} = k \left( \frac{\partial^2 T}{\partial \mathbf{x}^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + \dot{Q}\_{\text{viscous heating}} + \dot{Q}\_{\text{\textquotedblleft}} \tag{A8}
$$

where ρ: density, *cp*: specific heat, *T*: temperature, *t*: time, *k*: thermal conductivity, *Q*viscous heating: viscous dissipation and . *Q*: arbitrary heat source (i.e., exothermic reaction).

The viscous heating for a Newtonian material is written as:

$$\dot{Q}\_{\text{viscous heating}} = \mu \dot{\nu}\_{i\dot{j}} ^2 = \mu \left( \frac{\partial u\_i}{\partial x\_{\dot{j}}} + \frac{\partial u\_{\dot{j}}}{\partial x\_{\dot{i}}} \right)^2. \tag{A9}$$

Inserting the viscous heating term into Equation (A8) gives the energy equation in Cartesian coordinates:

$$\begin{split} \rho c\_{p} \Big( \frac{\partial T}{\partial t} + \mu\_{\text{X}} \frac{\partial T}{\partial \mathbf{x}} + \mu\_{\text{Y}} \frac{\partial T}{\partial \mathbf{y}} + \mu\_{\text{Z}} \frac{\partial T}{\partial \mathbf{z}} \Big) \\ = \kappa \Big( \frac{\partial^{2}T}{\partial \mathbf{x}^{2}} + \frac{\partial^{2}T}{\partial y^{2}} + \frac{\partial^{2}T}{\partial z^{2}} \Big) + 2\mu \Big[ \left( \frac{\partial u\_{\text{x}}}{\partial \mathbf{x}} \right)^{2} + \left( \frac{\partial u\_{\text{y}}}{\partial y} \right)^{2} + \left( \frac{\partial u\_{\text{z}}}{\partial z} \right)^{2} \Big] \\ + \mu \Big[ \left( \frac{\partial u\_{\text{x}}}{\partial \mathbf{y}} + \frac{\partial u\_{\text{y}}}{\partial \mathbf{x}} \right)^{2} + \left( \frac{\partial u\_{\text{x}}}{\partial z} + \frac{\partial u\_{\text{z}}}{\partial \mathbf{x}} \right)^{2} + \left( \frac{\partial u\_{\text{y}}}{\partial z} + \frac{\partial u\_{\text{z}}}{\partial y} \right)^{2} \Big] + \overset{\cdot}{Q} .\end{split} \tag{A10}$$

With the convention to denominate the viscosity of Newtonian fluids with μ and the viscosity of non-Newtonian fluids as η Equation (A9) can be rewritten as:

$$
\dot{Q}\_{\text{viscous heating}} = \eta \dot{\eta}^2. \tag{A11}
$$

In the compression molding process the polymer melt can be considered as a viscous fluid. When the material is pressed through the cavity to fill the mold, the melt is assumed to behave as a generalized Newtonian fluid (GNF). Therefore, the non-isothermal 3D flow can be described by the following simplified variant of the energy equation:

$$\rho c\_p \left( \frac{\partial T}{\partial t} + u\_\mathbf{x} \frac{\partial T}{\partial \mathbf{x}} + u\_\mathbf{y} \frac{\partial T}{\partial \mathbf{y}} + u\_\mathbf{z} \frac{\partial T}{\partial \mathbf{z}} \right) = k \left( \frac{\partial^2 T}{\partial \mathbf{x}^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + \eta \dot{\chi}^2. \tag{A12}$$

During the exothermic curing reaction of thermosets, heat generates. This effect is considered with an additional energy source terms on the right hand side in Equation (A13), where the energy balance for thermosets in a mold is shown.

$$
\rho c\_p \left( \frac{\partial T}{\partial t} + u\_\mathbf{x} \frac{\partial T}{\partial \mathbf{x}} + u\_\mathbf{y} \frac{\partial T}{\partial \mathbf{y}} + u\_\mathbf{z} \frac{\partial T}{\partial \mathbf{z}} \right) = k \left( \frac{\partial^2 T}{\partial \mathbf{x}^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + \eta \dot{\eta}^2 + \frac{\mathbf{d}Q}{\mathbf{d}t}.\tag{A13}
$$

Therein, the left terms stands for the temperature change and the convective heat transfer (more precisely thermal advection), whereas the terms on the right hand side of the equation represent the thermal conduction, shear heat generation (viscous heating), and the heat generation due to an exothermic reaction. Equation (A14) shows the relation between the heat generation velocity d*Q*d*t* and the total amount of generated heat *Q*0 in the exothermic curing reaction affected by the curing reaction rate dαd*t*:

$$\frac{\mathrm{d}Q}{\mathrm{d}t} = Q\_0 \frac{\mathrm{d}a}{\mathrm{d}t}.\tag{A14}$$

With the viscosity standardly defined as:

$$
\mu = \frac{\pi}{\dot{\nu}} \text{ or } \eta = \frac{\pi}{\dot{\nu}'} \tag{A15}
$$

and substituting μ in Equation (A9) the viscous dissipation can also be written as:

$$Q\_{\text{viscous heating}} = \tau\_{ij} \dot{\gamma}\_{ij}.\tag{A16}$$

For generalized Newtonian fluids (incompressible viscous fluids), the deviatoric stress τ can be expressed by:

$$
\pi\_{i\bar{j}} = \eta \dot{\gamma}\_{\bar{i}\bar{j}} = \eta \Big(\nabla u + \left(\nabla u\right)^{\mathsf{T}}\Big),\tag{A17}
$$

where η is the non-Newtonian viscosity that depends both on temperature *T* and the rate of deformation tensor . γ*ij*, ∇*u* is the velocity gradient tensor and (∇*u*)T is the transposed velocity gradient tensor.

Since η is a scalar it must depend only on scalar invariants of .γ. Therefore, another notation for the symmetric rate of deformation tensor .γ*ij* in the Generalized Newtonian Fluid (GNF) model in Equation (A17) is the scalar strain rate .γ:

$$\left| \dot{\mathbf{y}} = \left| \dot{\mathbf{y}}\_{\dot{\boldsymbol{\eta}}} \right| = \sqrt{\frac{1}{2} (\dot{\boldsymbol{\gamma}}\_{\dot{\boldsymbol{\eta}}} : \dot{\boldsymbol{\gamma}}\_{\dot{\boldsymbol{\eta}}})} = \sqrt{\frac{1}{2} \Pi} = \sqrt{\frac{1}{2} \sum\_{i} \sum\_{j} \dot{\boldsymbol{\gamma}}\_{\dot{\boldsymbol{\eta}}} \dot{\boldsymbol{\gamma}}\_{\ddot{\boldsymbol{\eta}}}}} \text{ with } i, \; j = \text{x, y, z} \tag{A18}$$

where .γ is the magnitude of the rate of deformation tensor .γ*ij* and II is the second invariant of the rate of deformation tensor.

The rate of deformation tensor components in Equation (A18) are defined by:

$$
\dot{\gamma}\_{ij} = \frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i} \tag{A19}
$$

which yields:

$$\dot{\gamma} = \sqrt{2\left(\frac{\partial u\_{\mathbf{x}}}{\partial \mathbf{x}}\right)^{2} + 2\left(\frac{\partial u\_{\mathbf{y}}}{\partial \mathbf{y}}\right)^{2} + 2\left(\frac{\partial u\_{\mathbf{z}}}{\partial \mathbf{z}}\right)^{2} + \left(\frac{\partial u\_{\mathbf{x}}}{\partial \mathbf{y}} + \frac{\partial u\_{\mathbf{y}}}{\partial \mathbf{x}}\right)^{2} + \left(\frac{\partial u\_{\mathbf{y}}}{\partial \mathbf{z}} + \frac{\partial u\_{\mathbf{z}}}{\partial \mathbf{y}}\right)^{2} + \left(\frac{\partial u\_{\mathbf{z}}}{\partial \mathbf{x}} + \frac{\partial u\_{\mathbf{x}}}{\partial \mathbf{z}}\right)^{2}}\,,\tag{A20}$$

respecting the flow field in thickness direction.

The stress tensor components for GNFs in Cartesian coordinates are consequently given by:

$$\begin{aligned} \tau\_{\rm XY} &= 2\eta \frac{\partial u\_{\rm x}}{\partial x} & \tau\_{\rm XY} &= \tau\_{\rm Yx} = \eta \left(\frac{\partial u\_{\rm x}}{\partial y} + \frac{\partial u\_{\rm y}}{\partial x}\right) \\ \tau\_{\rm YY} &= 2\eta \frac{\partial u\_{\rm y}}{\partial y} & \tau\_{\rm Yz} &= \tau\_{\rm zy} = \eta \left(\frac{\partial u\_{\rm y}}{\partial z} + \frac{\partial u\_{\rm z}}{\partial y}\right) \\ \tau\_{\rm ZZ} &= 2\eta \frac{\partial u\_{\rm z}}{\partial z} & \tau\_{\rm xz} = \tau\_{\rm xz} = \eta \left(\frac{\partial u\_{\rm z}}{\partial x} + \frac{\partial u\_{\rm x}}{\partial z}\right) \end{aligned} \tag{A21}$$

$$
\tau\_{ij} = \begin{bmatrix}
\tau\_{\rm{xx}} & \tau\_{\rm{xy}} & \tau\_{\rm{xz}} \\
\tau\_{\rm{yx}} & \tau\_{\rm{yy}} & \tau\_{\rm{yz}} \\
\tau\_{\rm{xz}} & \tau\_{\rm{xy}} & \tau\_{\rm{zz}}
\end{bmatrix} = \eta \begin{bmatrix}
2\frac{\partial u\_{\rm{x}}}{\partial x} & \frac{\partial u\_{\rm{x}}}{\partial y} + \frac{\partial u\_{\rm{y}}}{\partial x} & \frac{\partial u\_{\rm{x}}}{\partial x} + \frac{\partial u\_{\rm{x}}}{\partial z} \\
\frac{\partial u\_{\rm{x}}}{\partial y} + \frac{\partial u\_{\rm{y}}}{\partial x} & 2\frac{\partial u\_{\rm{y}}}{\partial y} & \frac{\partial u\_{\rm{y}}}{\partial z} + \frac{\partial u\_{\rm{x}}}{\partial y} \\
\frac{\partial u\_{\rm{x}}}{\partial x} + \frac{\partial u\_{\rm{x}}}{\partial z} & \frac{\partial u\_{\rm{y}}}{\partial z} + \frac{\partial u\_{\rm{x}}}{\partial y} & 2\frac{\partial u\_{\rm{x}}}{\partial z}
\end{bmatrix}. \tag{A22}
$$

With Equation (A16) the stress tensor components are implemented into Equation (A10), which results in the energy equation for thermoset materials, written as:

$$\begin{split} \rho c\_{p} \Big( \frac{\partial T}{\partial t} + \boldsymbol{\mu}\_{\text{x}} \frac{\partial T}{\partial \mathbf{x}} + \boldsymbol{\mu}\_{\text{y}} \frac{\partial T}{\partial \boldsymbol{y}} + \boldsymbol{\mu}\_{\text{z}} \frac{\partial T}{\partial \boldsymbol{z}} \Big) \\ = & k \Big( \frac{\partial^{2}T}{\partial \mathbf{x}^{2}} + \frac{\partial^{2}T}{\partial y^{2}} + \frac{\partial^{2}T}{\partial z^{2}} \Big) + \tau\_{\text{xx}} \frac{\partial \boldsymbol{u}\_{\text{x}}}{\partial \mathbf{x}} + \tau\_{\text{yy}} \frac{\partial \boldsymbol{u}\_{\text{y}}}{\partial y} + \tau\_{\text{zz}} \frac{\partial \boldsymbol{u}\_{\text{z}}}{\partial z} \\ \quad + \tau\_{\text{xy}} \Big( \frac{\partial \boldsymbol{u}\_{\text{x}}}{\partial y} + \frac{\partial \boldsymbol{u}\_{\text{y}}}{\partial \mathbf{x}} \Big) + \tau\_{\text{yz}} \Big( \frac{\partial \boldsymbol{u}\_{\text{y}}}{\partial z} + \frac{\partial \boldsymbol{u}\_{\text{z}}}{\partial y} \Big) + \tau\_{\text{xz}} \Big( \frac{\partial \boldsymbol{u}\_{\text{z}}}{\partial \mathbf{x}} + \frac{\partial \boldsymbol{u}\_{\text{y}}}{\partial z} \Big) + \dot{Q}\_{\text{y}} \end{split} \tag{A23}$$

where *Q* denotes the heat generation due to the exothermic reaction in the thermoset curing process. In order to calculate the temperature distribution in the thermoset molding compound, 3D TIMON, however, assumes the heat conduction in thickness direction is dominant and therefore simplifies Equation (A23) to:

$$\rho c\_p \mathrm{d}\frac{\partial T}{\partial t} + u\_\mathrm{x} \frac{\partial T}{\partial \mathbf{x}} + u\_\mathrm{y} \frac{\partial T}{\partial y} + u\_\mathrm{z} \frac{\partial T}{\partial \mathbf{z}}\bigg) = k \frac{\partial^2 T}{\partial z^2} + \tau\_\mathrm{yz} \left(\frac{\partial u\_\mathrm{y}}{\partial z}\right) + \tau\_\mathrm{xc} \left(\frac{\partial u\_\mathrm{x}}{\partial z}\right) + Q\_0 \frac{\mathrm{d}\mathbf{z}}{\mathrm{d}t},\tag{A24}$$

where . *Q* is substituted with Equation (A14).

Using the simplification τyz = η∂*u*y ∂*z* and τzx = η ∂*u*x ∂*z* (assumption of simple shear flow) yields to the final energy equation applied in 3D TIMON's Light 3D Heat Transfer:

$$
\rho c\_p \left( \frac{\partial T}{\partial t} + \mu\_\mathbf{x} \frac{\partial T}{\partial \mathbf{x}} + \mu\_\mathbf{y} \frac{\partial T}{\partial \mathbf{y}} + \mu\_\mathbf{z} \frac{\partial T}{\partial z} \right) = k \frac{\partial^2 T}{\partial z^2} + \eta \left( \frac{\partial \mu\_\mathbf{y}}{\partial z} \right)^2 + \eta \left( \frac{\partial \mu\_\mathbf{x}}{\partial z} \right)^2 + Q \nu \frac{\mathbf{d}\alpha}{\mathbf{d}t}.\tag{A25}
$$


**7. Conclusions**

This paper presented a large-scale cognitive experiment for estimating the entropy rate for English. Using AMT, we conducted Shannon's experiment online and collected 172,954 character predictions in total across 683 subjects. It was by far the largest cognitive experiment conducted thus far, and the scale enabled us to analyze the factors that influence the estimation.

While Shannon implied that subjects' prediction performances improved with increasing context length, others disagreed with his implication. Our experiment showed that subjects' prediction performances improved consistently with increasing context length, at least up to 100 characters.

Further, we investigated the influence of the number of observations on the estimation via the bootstrap technique. One of the most important insights gained is that the number of prediction observations must be at least 1000 in order to produce an estimate with a reasonable margin of error. In the case of small samples, the value of *h* could be potentially underestimated. Hence, Shannon's original experiment and other previous experiments provided estimates that could have been underestimated. We believe that this present work reports a statistically reliable estimate with a reasonable margin of error.

Due to the online environment, the performances of the subjects varied, and the upper bound should be evaluated based on filtered results. With a sufficient number of well-performing samples, we obtained an upper bound of *h* ≈ 1.22 bpc, which is slightly smaller than Shannon's reported value of *h* = 1.3 bpc.

Future work could include finding a new experimental design, one in which the participants use longer contexts to predict the next character; thus, reducing the cognitive load. Such an experiment would contribute to the tighter evaluation of the upper bound of the entropy rate. It would be also interesting to examine the entropy rates of other languages and at the word level while still utilizing a cognitive experiment.

**Author Contributions:** Conceptualization, K.T.-I.; Data curation, G.R.; Funding acquisition, K.T.-I.; Investigation, G.R., K.T.-I. and S.T.; Methodology, G.R., K.T.-I. and S.T.; Project administration, K.T.-I.; Resources, K.T.-I.; Software, G.R. and S.T. ; Supervision, K.T.-I.; Validation, S.T. and K.T.-I.; Visualization, G.R., S.T. and K.T.-I.; Writing—original draft, S.T. and K.T.-I.; Writing—review & editing, K.T.-I. and S.T.

**Funding:** This research was funded by RISTEX-HITE<PHONE_NUMBER>14 of Japan Science Technology Agency, Japan.

**Conflicts of Interest:** The authors declare no conflict of interest.


**Acknowledgements**

The authors, DPN and SSP are highly indebted to Department of Science and Technology, Science and Engineering Research Board (DST-SERB), Government of India, for providing full financial assistance to carry out the present work under the major research project (File No. EEQ/2016/000275).


**5. Potentiometric response of membranes modified with undecylcalix[4] – resorcinarene derivatives towards of unprotonated diaminobenzene isomers**

According to presented mechanism of anionic potentiometric signal generation by membranes modified with nitrogen containing macromolecules as host molecules and stimulated with neutral form of phenol derivatives the crucial phenomenon is transfer of protons from the membrane surface to surface of water phase. From this point of view it was logical and interesting to check if generation of cationic potentiometric signal by membranes modified with macrocycles containing the phenolic group stimulated with unprotonated derivatives of aniline would be possible [25, 52]

There are summarization of systematic research results of the intermolecular recognition processes at the water/polymer membrane border between some derivatives of undecylca‐ lix[4]resorcinarene (Figure 2) and neutral (unprotonated) forms of aniline and its derivatives such as: aminoaniline, chloroaniline, hydroxyaniline, methylaniline, methoxyaniline and nitroaniline obtained with using potentiometry.

**Figure 2.** The structure of host molecules.

In the measuring condition (pH = 5.5), paracetamol molecules exists in undissociated form (pKa =9.5). The formation of the above mentioned complex, according to a combination of mesomeric and inductive effects, causes an increase of the acidity of the phenolic OH function from paracetamol molecule. As a consequence, this leads to a more facile dissociation of the

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

This event is responsible for the generation of an anionic response of the polymeric liquid membranes modified with metalloporphyrins after their stimulation with undissociated

The reaction of the metalloporphyrin complex with paracetamol was confirmed by spectro‐ scopic measurements at the border between water and the polymeric membrane. The UV-Vis absorption spectrum of a thin membrane film containing Mn(III)-porphyrin deposited onto glass slides conditioned in 0.01 M phosphate buffer solution (pH = 5.5) exhibited one main band at 470 nm and two weaker bands at 376 and 400 nm. After conditioning in phosphate buffer with an increasing concentration of paracetamol, the absorbance maximum decreased and shifted to shorter wavelength. This blue shift was expected due to the increase in electron density around the Mn(III) centers by the coordinated amide. These data confirm the creation

The electrochemically active Cu(II) dipyrromethene complex immobilized on the surface of gold electrodes previously modified with a dodecanethiol monolayer was successfully applied for voltammetric determination of paracetamol [23]. The interaction of paracetamol with Cu(II) redox centers was a base of analytical signal generation. The presence of human plasma in the measuring solution influence very little on the sensor performance. Its linear dynamic range ( 0.2-3.2 mM) was sufficient for controlling the toxic level of paracetamol in human plasma [23].

**5. Potentiometric response of membranes modified with undecylcalix[4] –**

According to presented mechanism of anionic potentiometric signal generation by membranes modified with nitrogen containing macromolecules as host molecules and stimulated with neutral form of phenol derivatives the crucial phenomenon is transfer of protons from the membrane surface to surface of water phase. From this point of view it was logical and interesting to check if generation of cationic potentiometric signal by membranes modified with macrocycles containing the phenolic group stimulated with unprotonated derivatives of

There are summarization of systematic research results of the intermolecular recognition processes at the water/polymer membrane border between some derivatives of undecylca‐ lix[4]resorcinarene (Figure 2) and neutral (unprotonated) forms of aniline and its derivatives

**resorcinarene derivatives towards of unprotonated diaminobenzene**

of a complex between the Mn(III)-porphyrin and paracetamol [22].

ejection from the interface to the aqueous layer adjacent to the

OH group and finally to H+

organic phase.

Applications

504

paracetamol.

**isomers**

aniline would be possible [25, 52]

In Table 4 the values of potentiometric response of PVC supported liquid membranes incor‐ porated with calixarene host generated in the presence of aniline derivatives are collected. The measurements for all membranes studied were done at pH 7. At this pH investigated aniline derivatives exist in water almost entirely as neutral (unprotonated) compounds (see Table 5).

**Analyte pK1 pK2**

**Table 5.** Percentage of protonated and neutral species at pH 7 [25]

possibility to form intramolecular hydrogen bonds.

the strongest acids between the investigated compounds.

isomer *ortho*, in another meta.

observed phenomena.

 *p*-nitroaniline 1.02 100.0 0.0 *o*-chloroaniline 2.66 100.0 0.0 *m*-chloroaniline 3.52 100.0 0.0 *p*-chloroaniline 3.98 99.9 0.1 *m*-anisidine 4.20 99.8 0.2 *o*-toluidine 4.45 99.7 0.3 *o*-anisidine 4.53 99.7 0.3 *o*-aminoaniline 4.61 1.81 99.6 0.4 *m*-toluidine 4.71 99.5 0.5 aniline 4.87 99.3 0.7 *m*-aminoaniline 5.01 2.56 99.0 1.0 *p*-toluidine 5.08 98.8 1.2 *p*-anisidine 5.36 97.8 2.2 *p*-hydroxyaniline 5.48 97.1 2.9 *p*-aminoaniline 6.22 2.99 85.8 14.2

Potentiometry for Study of Supramolecular Recognition Processes Between Uncharged Molecules

The comparison of the results we have got for all of guest molecules showing the following general tendency: with increase of analyte basicity the response increases. This is truth for all of modified membranes. In most of the cases the isomer *para* generate the highest response. For another isomers is difficult to estimate with one generate higher signal. In some cases it is

Explanation of weak response of membranes after stimulation with *ortho* isomers is the

The correlation between the partition coeffiction of guest (Table 4) and value of potentiometric response is very week. And this suggests that this parameter is rather less important for

The weakest response we have observed for nitro- and chloro- derivatives of aniline. They are

The main differences between the host molecules under study are structure of upper rim. Ligand 1 poses in their upper rim dihydroxybenzene substituents in which the OH groups are in position 1, 3 in relation to each other. Because of this distance the intramolecular hydrogen bounds are very week [43]. Additionally this ligand is substituted in position 2 with azonitro‐ benzene. The presence of this substituent, because of its inductive and rezonance effect causing

**pH 7.0 RNH2 (%) RNH3 + (%)**

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507

As it is seen from results introduced from Table 4, all types of membranes generate cationic response towards aniline derivatives

ΔE[mV] = E0 -Ei E0 – potential recorded in buffer solution, Ei – potential record in the presence of analyte at is final concentration

**Table 4.** Potentiometric response of PVC supported liquid membranes incorporated with host undodecylcalix[4] resorcinarene derivatives generated in the presence of aniline derivatives. Log Poct/water – logarithm of partition coefficient between n-octanol and water [36, 37] pKa – acidity constants [35, 36]

Potentiometry for Study of Supramolecular Recognition Processes Between Uncharged Molecules http://dx.doi.org/10.5772/52803 507

**Table 5.** Percentage of protonated and neutral species at pH 7 [25]

In Table 4 the values of potentiometric response of PVC supported liquid membranes incor‐ porated with calixarene host generated in the presence of aniline derivatives are collected. The measurements for all membranes studied were done at pH 7. At this pH investigated aniline derivatives exist in water almost entirely as neutral (unprotonated) compounds (see Table 5).

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

As it is seen from results introduced from Table 4, all types of membranes generate cationic

*p*-aminoaniline 6.22 -0.26 148.9 138.4 88,4 86.9 41.5

*p*-anisidine 5.36 1.15 118.6 68.9 53,9 59.4 37.4

*m*-anisidine 4.20 1.32 92.6 62.2 55,1 20.1 28.4

*o*-aminoaniline 4.61 0.37 66.8 57.2 64,2 31.0 31.5

*m-*aminoaniline 5.01 0.03 36.2 42.1 35,8 13.8 7.6

*p*-toluidine 5.08 1.43 92.3 36.2 44.1 27.0 30.2

*p*-chloroaniline 3.98 1.81 31.5 24.2 22,8 -0.6 6.2

*o*-anisidine 4.53 1.65 62.7 20.1 35,7 19.8 7.8

aniline 4.87 1.24 57.7 12.8 34,5 10.7 13.1

*m*-toluidine 4.71 1.59 84.2 9.7 32,9 14.9 22.0

*o*-toluidine 4.45 1.61 75.8 9.4 20,8 10.7 7.7

*p*-nitroaniline 1.02 1.19 4.7 3.0 - - 2.4

*m*-chloroaniline 3.52 1.88 19.8 0.7 2 - 9.2

*o*-chloroaniline 2.66 2.02 8.6 -4.5 1,2 - 1.9

**Table 4.** Potentiometric response of PVC supported liquid membranes incorporated with host undodecylcalix[4] resorcinarene derivatives generated in the presence of aniline derivatives. Log Poct/water – logarithm of partition

E0 – potential recorded in buffer solution, Ei

coefficient between n-octanol and water [36, 37] pKa – acidity constants [35, 36]

p-hydroxyaniline 5.48 -0.24 27.6 15.5 25,2 -2.1 2.4

**ΔE[mV] Lig 2**

**ΔE[mV] Lig 3**

**ΔE[mV] Lig 4**

– potential record in the presence of analyte at is final

**ΔE[mV] Lig 5**

**ΔE[mV] Lig 1**

response towards aniline derivatives

Applications

506

**Guests pK1 Log Po/w**

ΔE[mV] = E0 -Ei

concentration

The comparison of the results we have got for all of guest molecules showing the following general tendency: with increase of analyte basicity the response increases. This is truth for all of modified membranes. In most of the cases the isomer *para* generate the highest response. For another isomers is difficult to estimate with one generate higher signal. In some cases it is isomer *ortho*, in another meta.

Explanation of weak response of membranes after stimulation with *ortho* isomers is the possibility to form intramolecular hydrogen bonds.

The correlation between the partition coeffiction of guest (Table 4) and value of potentiometric response is very week. And this suggests that this parameter is rather less important for observed phenomena.

The weakest response we have observed for nitro- and chloro- derivatives of aniline. They are the strongest acids between the investigated compounds.

The main differences between the host molecules under study are structure of upper rim. Ligand 1 poses in their upper rim dihydroxybenzene substituents in which the OH groups are in position 1, 3 in relation to each other. Because of this distance the intramolecular hydrogen bounds are very week [43]. Additionally this ligand is substituted in position 2 with azonitro‐ benzene. The presence of this substituent, because of its inductive and rezonance effect causing

the increase of acidity of phenol groups from upper ring. Ligand 2 contains in its structure dihydroxybenzene with OH groups in positions 1 and 3.

Upon complexation of *para*–diaminobenzene, the absorbance decrease at 214 nm, characteristic for UDC[4]Rene was observed. The absorbance at 239 nm characteristic for *para*–diaminoben‐ zene also decrease and shifted towards red. Additionally, new peak was visible at 267 nm. These absorbance changes clearly indicated that a supramolecular complex UDC[4]Rene-

Potentiometry for Study of Supramolecular Recognition Processes Between Uncharged Molecules

http://dx.doi.org/10.5772/52803

509

Therefore, it might be concluded that the cationic potentiometric signals observed in the study presented were generated as a result of the supramolecular recognition phenomenon occurring

Based on obtained results and literature data we have proposed the following mechanism of cationic potential signal generation by membranes modified with derivatives of undecylca‐ lix[4]resorcinarene after stimulation with unprotonated derivatives of aminobenzene. In the first step, which is going during the membrane conditioning some of phenolic groups of derivatives of undecylcalix[4]resorcinarene located at the surface of polymeric membranes dissociated and membranes became minus charged. Such type of dissociation of OH groups of upper rim of undecylcalix[4]resorcinarene was described in [53, 54]. In next step, the network of hydrogen bonds between the derivatives of aminobenzene and phenolic groups is formed. In such situation the amino groups are donors of hydrogen atoms and polarity of them are correlated with acidity of phenol groups. The formation of such network is described in [49-51]. As a result of this, the supramolecular complex of undecylcalix[4]resorcinarene – aminobenzene derivatives located at the interface is formed. As a consequence of above complex formation the density of electrons on nitrogen of aminobenzene increases. The measurements were carried out at pH 7. In this condition all of investigated amines exist in solution mostly as unprotonated compounds (Table 5). The increase of the density of electrons at amine nitrogen atoms causing the increase of their basicity. Because of this, they became protonated in spite of pH condition in bulk solution. This protonation is done by means of transfer of proton from surface of water face to surface of organic one. The transfer of proton leading to the increase of plus charge of membrane and we can observe the generation of

The first one concerns dissociation of some phenolic groups from upper rim of investigated

+ H3O+

Next step consist of transfer of analyte from bulk solution to the interface and formation of

The consequence of this is the increase of basicity on nitrogen atom from supramolecular

interface + H2O

*para*-diaminobenzene is formed at the membrane surface.

at the organic/aqueous interface.

potentiometric cationic signal.

ligands.

**ii.** HostO-

**iii.** HostO-

complex and its protonation.

Proposed mechanism is based on the three steps:

supramolecular complex ligand –analyte through hydrogen bonds.

interface + NH2-AR ↔ HostO-

**i.** HostOHmembrane+ H2O↔ HostO-

Next host, number 3, in its upper rim contains the dihydroksybromobenzene. The OH groups are in position 2, 6 in relation to azabenzene substituent. This substituent, because of its inductive and mesomeric effect, increased the acidity of phenols in relation to previous one.

The upper rim of ligand 4 contains the bromo- 2, 5 hydroksybenzene. The close vicinity of OH groups creates the very good conditions for creation of intramolecular network of hydrogen bonds [43]. The last ligand (no 5) posses in upper rim trihydroksybenzene. Similarly as in previous one this system allows to create the intramolecular hydrogen bound network.

Comparison of value of potentiometric response we have got for each ligand showing the general tendency which is as follow:

Ligand 1 > ligand 2 > ligand 3, ligand 4 > ligand 5

This indicates that increase of the acidity of phenols groups in upper rim causing the increase of response value.

The strongest response we have observed for membrane modified with ligand 1 containing in its structure dihydroxybenzene substituted with azonitrobenzene. Acidity of these OH groups is the highest.

Next in this sequence is ligand 2 substituted with dihydroxybenzene. In this case the acidity of OH groups is lower in relation to the previous one, but the accessibility of them for guest is much easier. As consequence the creation of hydrogen bound (H…O…H…N) between host and guest is relatively easy. The next ligand in the discussed sequence, ligand 3 contained in its structure dihydroxybenzene substituted with azobenzene. This causing the increase the acidity of phenolic group in upper rim, but at the same time presence of rather large substituent makes the hindrance in accessibility of OH groups for guest molecules. The value of generated potentiometric signal is the consequence of these two opposite effects.

Membrane modified with host containing the bromo-derivatives of dihydrobenzene in its structure (no 4) is next in sequence of response value. In this case from one side the inductive effect bromine atom causing increase of acidity of phenolic group and from another one large atom of bromine constitute hindrance in accessibility of phenols groups for guest.

The lowest answer we have got for membrane modified with ligand 5, which poses in its structure trihydroksybenzene. In this ligand the network of intramolecular hydrogen bounds is the strongest. And because of this the formation of supramolecular complex with guest is the most difficult between the ligand under study.

The comparison of lipophilicity of investigated guest molecules showing that there is no direct relation between the lipophilicity of amines and values of signal generated by them.

In order to confirm the supramolecular complex formation between undecylcalix[4]resorci‐ narene and aniline derivatives at the border of organic/aqueous interface UV-Vis measure‐ ments were performed according to procedure reported [52].

Upon complexation of *para*–diaminobenzene, the absorbance decrease at 214 nm, characteristic for UDC[4]Rene was observed. The absorbance at 239 nm characteristic for *para*–diaminoben‐ zene also decrease and shifted towards red. Additionally, new peak was visible at 267 nm. These absorbance changes clearly indicated that a supramolecular complex UDC[4]Rene*para*-diaminobenzene is formed at the membrane surface.

Therefore, it might be concluded that the cationic potentiometric signals observed in the study presented were generated as a result of the supramolecular recognition phenomenon occurring at the organic/aqueous interface.

Based on obtained results and literature data we have proposed the following mechanism of cationic potential signal generation by membranes modified with derivatives of undecylca‐ lix[4]resorcinarene after stimulation with unprotonated derivatives of aminobenzene. In the first step, which is going during the membrane conditioning some of phenolic groups of derivatives of undecylcalix[4]resorcinarene located at the surface of polymeric membranes dissociated and membranes became minus charged. Such type of dissociation of OH groups of upper rim of undecylcalix[4]resorcinarene was described in [53, 54]. In next step, the network of hydrogen bonds between the derivatives of aminobenzene and phenolic groups is formed. In such situation the amino groups are donors of hydrogen atoms and polarity of them are correlated with acidity of phenol groups. The formation of such network is described in [49-51]. As a result of this, the supramolecular complex of undecylcalix[4]resorcinarene – aminobenzene derivatives located at the interface is formed. As a consequence of above complex formation the density of electrons on nitrogen of aminobenzene increases. The measurements were carried out at pH 7. In this condition all of investigated amines exist in solution mostly as unprotonated compounds (Table 5). The increase of the density of electrons at amine nitrogen atoms causing the increase of their basicity. Because of this, they became protonated in spite of pH condition in bulk solution. This protonation is done by means of transfer of proton from surface of water face to surface of organic one. The transfer of proton leading to the increase of plus charge of membrane and we can observe the generation of potentiometric cationic signal.

Proposed mechanism is based on the three steps:

the increase of acidity of phenol groups from upper ring. Ligand 2 contains in its structure

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

Next host, number 3, in its upper rim contains the dihydroksybromobenzene. The OH groups are in position 2, 6 in relation to azabenzene substituent. This substituent, because of its inductive and mesomeric effect, increased the acidity of phenols in relation to previous one.

The upper rim of ligand 4 contains the bromo- 2, 5 hydroksybenzene. The close vicinity of OH groups creates the very good conditions for creation of intramolecular network of hydrogen bonds [43]. The last ligand (no 5) posses in upper rim trihydroksybenzene. Similarly as in previous one this system allows to create the intramolecular hydrogen bound network.

Comparison of value of potentiometric response we have got for each ligand showing the

This indicates that increase of the acidity of phenols groups in upper rim causing the increase

The strongest response we have observed for membrane modified with ligand 1 containing in its structure dihydroxybenzene substituted with azonitrobenzene. Acidity of these OH groups

Next in this sequence is ligand 2 substituted with dihydroxybenzene. In this case the acidity of OH groups is lower in relation to the previous one, but the accessibility of them for guest is much easier. As consequence the creation of hydrogen bound (H…O…H…N) between host and guest is relatively easy. The next ligand in the discussed sequence, ligand 3 contained in its structure dihydroxybenzene substituted with azobenzene. This causing the increase the acidity of phenolic group in upper rim, but at the same time presence of rather large substituent makes the hindrance in accessibility of OH groups for guest molecules. The value of generated

Membrane modified with host containing the bromo-derivatives of dihydrobenzene in its structure (no 4) is next in sequence of response value. In this case from one side the inductive effect bromine atom causing increase of acidity of phenolic group and from another one large

The lowest answer we have got for membrane modified with ligand 5, which poses in its structure trihydroksybenzene. In this ligand the network of intramolecular hydrogen bounds is the strongest. And because of this the formation of supramolecular complex with guest is

The comparison of lipophilicity of investigated guest molecules showing that there is no direct

In order to confirm the supramolecular complex formation between undecylcalix[4]resorci‐ narene and aniline derivatives at the border of organic/aqueous interface UV-Vis measure‐

relation between the lipophilicity of amines and values of signal generated by them.

atom of bromine constitute hindrance in accessibility of phenols groups for guest.

potentiometric signal is the consequence of these two opposite effects.

dihydroxybenzene with OH groups in positions 1 and 3.

general tendency which is as follow:

of response value.

Applications

508

is the highest.

Ligand 1 > ligand 2 > ligand 3, ligand 4 > ligand 5

the most difficult between the ligand under study.

ments were performed according to procedure reported [52].

The first one concerns dissociation of some phenolic groups from upper rim of investigated ligands.

**i.** HostOHmembrane+ H2O↔ HostO- + H3O+

Next step consist of transfer of analyte from bulk solution to the interface and formation of supramolecular complex ligand –analyte through hydrogen bonds.

$$\begin{array}{cccc} \text{iii} & \text{HostO}^{\cdot}\_{\text{interface}} + & \text{NH}\_{2}\text{-}\text{AR} & \longleftrightarrow & \text{HostO}^{\cdot}\text{---}\text{H}\text{--}\text{NH-}\text{AR}\_{\text{interference}} \\\end{array}$$

The consequence of this is the increase of basicity on nitrogen atom from supramolecular complex and its protonation.

$$\text{iii.} \qquad \text{HostO} \cdot \text{---} \text{H-} \text{-NH-AR}\_{\text{interface}} \text{+H}\_{\text{3}} \text{O}^{\*} \leftarrow \text{HostO} \text{---} \text{H-} \text{-NH}\_{2} \text{-AR}^{\*} \text{}\_{\text{interface}} \text{+H}\_{2} \text{O}^{\*}$$

The formation of such complex at the border we confirmed by means of spectroscopic method. The conformation of first step is based on result we have got for membrane modified with ligand 1 in which the acidity of phenolic groups is the highest.

**•** The sensitivity and selectivity of these processes are governed by the acidity of the target molecules studied as well as the ability of host molecules for creation of hydrogen bonds.

Potentiometry for Study of Supramolecular Recognition Processes Between Uncharged Molecules

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511

The described phenomena open the totally new and very promising field of analytical

Institute of Animal Reproduction and Food Research of Polish Academy of Sciences, Olsz‐

[3] Umezawa Y., "Ion-Selective Electrodes" , in "Encyclopedia of Supramolecular Chem‐

[4] Ito, T., Radecka, H, Tohda, K., Odashima, K., Umezawa,Y. *J. Am. Chem. Soc.* 1998, 120,

[5] Odashima , K., Naganava, R., Radecka, H., Kataoka, M., Kiura, E., Koike, T., Tohda, K., Tange, M., Furta, H., Sessler, J. L.,. Yagi, K., Umezawa, Y. *Supramolecular Chemistry* 1994,

[6] Ito, T., Radecka, H., Umezawa, K., Kiura, T., Yashiro, A., Lin, X., Kataoka, M., Kiura,

[7] M. De Serio H. Mohapatra , R. Zenobi , V. Deckert , Chemical Physics Letters 417 (2006)

[9] Spichiger –Keller U.E., "Chemical Sensors and Biosensors for Medical and Biological

[11] L. Bulgariu, H. Radecka, M. Pietraszkiewicz, O. Pietraszkiewicz, Analytical Letters,

[10] Pretsch, E., Bühlmann, P., Bakker, E., *Chem Rev.,* 1997, 97, 3083; 1998 , 98, 1593.

E., Sessler, J.L., Yagi, K., Umezawa, Y. *Anal. Sciences*. 1998 14, 89.

The lipophilicity of analytes it the secondary parameter.

application of potentiometric method.

and Hanna Radecka

[1] Bakker, E., *Talanta*, 2004 , 63, 21.

\*Address all correspondence to<EMAIL_ADDRESS>
[2] Gale, P.A., *Coordination Chemistry Reviews* , 2003, 240, 191.

istry", 2004, Marcel Dekker, New York, p.747.

[8] Russell, E., Morris *Nature Chemistry* 2011, 3, 347–348.

Applications" , 1998, Wiley-VCH, Weinheim, Germany.

**Author details**

Jerzy Radecki\*

tyn, Poland

**References**

3049.

4,101.

452–456

2003, 36, 1325-1334.

The results we observed for bromo- and azobenzo- derivatives of investigated undecylca‐ lix[4]resorcinarene showing that the accessibility of phenols groups is very important param‐ eter for intermolecular recognition processes which are going between investigated ligands and analytes.

The weakest response we have observed in case of membranes modified with ligand which has in its structure trihydroxybenzene was explained by possibilities to form the network of intramolecular hydrogen bonds. This is a relatively strong energetic barrier for the described phenomenon.

The second step of proposed mechanism relays on transfer of protons from water phase to organic one. This is supported by fact that independently on the host structure, the strongest signal we have observed for the strongest base between guest compounds under study. The results we have got showed that lipophilicity of analytes it is not crucial parameter.