**1. Introduction**

Amphiphilic compounds have a well-defined structure; two parts clearly differentiated that will determine the behavior in aqueous systems [1] and is the key factor to their relationship with the internal and the external interfaces in aqueous systems [1]. One part of the amphiphilic compound is hydrophilic and the other part is hydrophobic [1, 2] and both are linked by a covalent bond [2].

In aqueous systems, the most important application of surfactants (in volume and economic impact terms), generally a long-chain hydrocarbon group is used as the hydrophobic group (although i) fluorinated, ii) oxygenated hydrocarbon or iii) siloxane chains can also be used) and an ionic or highly polar group as a head or hydrophilic group [3]. The different types of amphiphilic molecules can be differentiated according to the bonds between their two parts, hydrophilic and hydrophobic [2]. For example i) a hydrophilic head can be covalently bound to hydrophobic alkyl chain, whether single, double, or triple, also, ii) an amphiphilic bolaform is formed by two hydrophilic heads covalently linked with a hydrophobic alkyl chain and iii) a Gemini amphiphile is two surfactants covalently linked by their charged heads [2]. These compounds can be also classified based on the chemical nature of their hydrophilic group with subgroups according to the tail, so that, four basic categories can be defined: i) anionic, ii) cationic, iii) nonionic and iv) amphoteric (and zwitterionic) [3].

#### *Deep Learning Applications*

The property of amphiphiles to self-assemble in aqueous solution to design well-defined structures makes them become interesting molecules that can be applied in different fields [2] such as:


As previously said, these kinds of molecules can form different types of aggregates. These structures are formed when a certain concentration, called critical micelle concentration (cmc), is reached. This parameter can be defined as the specific concentration for a particular surfactant at which determinate solution properties change strongly [3]. According to Myers [3], different authors showed that the aggregated structure type depends on what is known as critical packing parameter. This parameter (CPP = v/aolc) establishes the relationship between the volume of the hydrophobic part of the molecule (v), the optimal area of the head group (ao) and the critical length of the hydrophobic tail (lc), and it controls the packing in aggregate structures [3]. The structures that can be formed are i) spherical micelles (when the value of CPP is less than 1/3), ii) cylindrical micelles (1/3 < CPP < 1/2), iii) bilayer vesicles (1/2 < CPP < 1), iv) lamellar phases (CPP ≈ 1) and, finally, v) inverted micelles (CPP > 1) [11]. Some of these structures are shown in **Figure 1**.

According to Gómez-Diaz et al. [1, 12], different physical properties have been used to characterize the aggregation processes by means of measured different experimental values. These authors have been demonstrate that density and kinematic viscosity do not alter when the micellization point is reached so that they are not utilized to determine knowledge about the behavior of the colloidal aggregate [1, 12]. On the other hand, the variation of the rest of the measured properties, speed of sound and surface tension, can be used to determine the cmc value. The property variation can give rise to the existence of two trend lines which intersection can be used to determine the cmc [1, 12]. As claimed by Gómez-Díaz et al. [1, 12], the cmc value, using the surface tension and the speed of sound was similar. Nevertheless, the cmc value using the surface tension was, for the hexyl, octyl and

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different areas such as:

*Modeling the Behavior of Amphiphilic Aqueous Solutions*

decyl trimethyl ammonium bromide, a bit lower than when the speed of sound is used [1, 12] (which can be attributed to the effect of small impurities amounts upon

*Critical packing parameter (where: v is the lipophilic chain volume; ao is the hydrophilic core cross-section area and lc is the lipophilic chain length), molecular shape and self-assembly entity formed by each different* 

study about this possibility were carried out by Astray & Mejuto [13].

The study of solutions behavior to know its properties, and to be able to calculate the cmc, required a lot of work, time-consuming and material cost. Due to these facts, modeling the physical properties of these solutions could help to reduce material and time costs. Thus, the study of methodologies such as artificial neural networks (ANN) and response surface (RS) are interesting and due to this in our research group, a

On the one hand, and regarding response surface methodology, it was firstly described by Box and Wilson in 1951 [13, 14]. The RSM is used as a tool for optimization tasks by relating the variables of the process and its response [15, 16]. The experimental data could be fit to a polynomial equation which must describe the data behavior to achieve statistical previsions [17], therefore, this methodology is based on the development of empirical mathematical models to describe the system under study [18]. These models can be used when the response, or responses, are influenced by different variables [17]. An RSM model can work with a reduced amount of experimental trials and can be used to develop, improve and optimize different process [19]. The RSM can use a set of mathematical and statistical tools to fit the experimental data to an Equation [17], usually, linear or square polynomial functions [17, 18]. Different experimental designs could be used which randomizes the experimental error and equals the experimental points distribution, for de independent variables, in the range investigated [20]. RSM models can be applied in

*DOI: http://dx.doi.org/10.5772/intechopen.95613*

the surface tension value) [1].

*amphiphile. Redraw from the original figure of Wang et al. [11].*

**Figure 1.**

*Modeling the Behavior of Amphiphilic Aqueous Solutions DOI: http://dx.doi.org/10.5772/intechopen.95613*

**Figure 1.**

*Deep Learning Applications*

detergency,

amphiphiles [8], or

among others.

applied in different fields [2] such as:

The property of amphiphiles to self-assemble in aqueous solution to design well-defined structures makes them become interesting molecules that can be

i.Pharmaceutical to overcome: i) the important manufacturing costs, ii) the poor pharmacokinetic characteristics and iii) the low bacteriological efficiency of the natural cationic antimicrobial peptides (AMPs), using novel and diverse cationic amphiphiles that can mimic the AMPs amphiphilic topology [4], or even as anti-cancer drug delivery vehicles using block copolymer micelles (poly(ethylene oxide) and poly(L-amino acid)) [5],

ii.in the cleaning sector, where they were used to clean oily deposits from solid surfaces using mixed solutions of fatty acid sulfonated methyl esters and using as cosurfactant dodecyldimethylamine oxide [6]. Yavrukova et al. [6] study the cleaning process of porcelain and stainless steel and concluded that the SME mixtures can be a hopeful system for formulations in household

iii.in Chemistry, where this kind of molecules are studied as a developer of

iv.in Medical Science to accelerate wound healing using antioxidant shape

v.in Food Chemistry using amphiphiles to modulate organoleptic properties in foods post harvested technology or for potential food applications [9, 10],

As previously said, these kinds of molecules can form different types of aggregates. These structures are formed when a certain concentration, called critical micelle concentration (cmc), is reached. This parameter can be defined as the specific concentration for a particular surfactant at which determinate solution properties change strongly [3]. According to Myers [3], different authors showed that the aggregated structure type depends on what is known as critical packing parameter. This parameter (CPP = v/aolc) establishes the relationship between the volume of the hydrophobic part of the molecule (v), the optimal area of the head group (ao) and the critical length of the hydrophobic tail (lc), and it controls the packing in aggregate structures [3]. The structures that can be formed are i) spherical micelles (when the value of CPP is less than 1/3), ii) cylindrical micelles (1/3 < CPP < 1/2), iii) bilayer vesicles (1/2 < CPP < 1), iv) lamellar phases (CPP ≈ 1) and, finally, v) inverted micelles (CPP > 1) [11]. Some of these structures are shown in **Figure 1**. According to Gómez-Diaz et al. [1, 12], different physical properties have been used to characterize the aggregation processes by means of measured different experimental values. These authors have been demonstrate that density and kinematic viscosity do not alter when the micellization point is reached so that they are not utilized to determine knowledge about the behavior of the colloidal aggregate [1, 12]. On the other hand, the variation of the rest of the measured properties, speed of sound and surface tension, can be used to determine the cmc value. The property variation can give rise to the existence of two trend lines which intersection can be used to determine the cmc [1, 12]. As claimed by Gómez-Díaz et al. [1, 12], the cmc value, using the surface tension and the speed of sound was similar. Nevertheless, the cmc value using the surface tension was, for the hexyl, octyl and

supramolecular nanotubes architectures [7],

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*Critical packing parameter (where: v is the lipophilic chain volume; ao is the hydrophilic core cross-section area and lc is the lipophilic chain length), molecular shape and self-assembly entity formed by each different amphiphile. Redraw from the original figure of Wang et al. [11].*

decyl trimethyl ammonium bromide, a bit lower than when the speed of sound is used [1, 12] (which can be attributed to the effect of small impurities amounts upon the surface tension value) [1].

The study of solutions behavior to know its properties, and to be able to calculate the cmc, required a lot of work, time-consuming and material cost. Due to these facts, modeling the physical properties of these solutions could help to reduce material and time costs. Thus, the study of methodologies such as artificial neural networks (ANN) and response surface (RS) are interesting and due to this in our research group, a study about this possibility were carried out by Astray & Mejuto [13].

On the one hand, and regarding response surface methodology, it was firstly described by Box and Wilson in 1951 [13, 14]. The RSM is used as a tool for optimization tasks by relating the variables of the process and its response [15, 16]. The experimental data could be fit to a polynomial equation which must describe the data behavior to achieve statistical previsions [17], therefore, this methodology is based on the development of empirical mathematical models to describe the system under study [18]. These models can be used when the response, or responses, are influenced by different variables [17]. An RSM model can work with a reduced amount of experimental trials and can be used to develop, improve and optimize different process [19]. The RSM can use a set of mathematical and statistical tools to fit the experimental data to an Equation [17], usually, linear or square polynomial functions [17, 18]. Different experimental designs could be used which randomizes the experimental error and equals the experimental points distribution, for de independent variables, in the range investigated [20]. RSM models can be applied in different areas such as:


On the other hand, artificial neural networks are computational modeling tool that consists of a set of simple processing elements (neurons), massively interconnected capable to process data [20]. This kind of models can try to simulate the path in which the human brain process the information, that it is, ANN are inspired in the biological system [25]. ANN is made up of different neurons layers: an input layer to receive the information, one or more intermediate (or hidden) layers where the information is processed, and an output layer, with one or more neurons, where the predicted value is generated (**Figure 2**). Each neural network is characterized by a specific topology or architecture. To facilitate your identification each neural model implemented can be named such as i-h-o, using the number of neurons presented in the input (i), hidden (h) and output (o) layer [13].

These models present different advantages such as: are non-linearity systems that allow better data fit, are non-sensitivity to noise (uncertain data and measurement errors), present high parallelism (fast processing and failure-tolerance), among others [26]. According to Baş and Boyaci [20], ANNs represent non-linearities better than RS, although ANNs cannot produce a similar model equation to RS models. This kind of approach can be used in a multitude of fields such as:


This book chapter summary the quadratic regression and neural models developed in our research group [13] to predict, for amphiphilic aqueous solutions, the i) density (*ρ* in g·cm−3), ii) speed of sound (*u* in m·s−1), iii) kinematic viscosity (*ν* in mm2 ·s−1), and iv) surface tension (*σ* in mN·m−1) taking into account i) concentration (*C*), ii) carbons number (*n °C*) and iii) molecular weight (*M*w).

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*Modeling the Behavior of Amphiphilic Aqueous Solutions*

*DOI: http://dx.doi.org/10.5772/intechopen.95613*

**2. Material and methods**

**Figure 2.**

**2.1 Artificial neural networks as an approximation approach**

predict density, dynamic viscosity, and surface tension, among others.

Artificial Intelligence models based on artificial neural networks have been widely used in the area of chemistry to model and predict processes related to physical properties. This type of model has shown great reliability to model and

*Representation of a typical neural network with 3 neurons in the input layer, 5 neurons in one hidden layer and one neuron in the output layer (topology 3–5-1). Redraw from the original figure of Astray & Mejuto [13].*

A good example of the use of artificial neural networks to determine properties of interest in micellar systems is the research carried out by Katritzky et al. [34] who developed a model to predict the critical micellar concentration of non-ionic surfactants based on different parameters related to its molecular structure. According to the authors, the models developed could be used for prediction or analysis of new non-ionic surfactants similar to those used in this research. On the other hand, Fatemi et al. [35] developed a model based on artificial neural networks to predict the critical micellar concentration of different anionic and cationic compounds. The selected input variables included the Balaban index, the heat of formation, among others. The results obtained were compared with the predictions of a multiple linear regression model and it was shown that the neural network is superior to multiple linear regression model to predict the log CMC of anionic and cationic surfactants. Along the same line, Kardanpour et al. [36] reported a wavelet neural network (WNN) to predict the critical micellar concentration of Gemini surfactants. The developed model used twelve different descriptors from the molecular structure. According to the authors, the results reveal the ability of the model to determine CMC and demonstrate, in comparison with MLR models, that the models based on neural networks are superior to the MLR approach (due to the ability of the WNN model to work with nonlinearities between the input variables and the CMC).

The researchs listed above demonstrate the ability of artificial neural networks to predict the critical micellar concentration of different surfactants. But to predict the value of this CMC, it is necessary to carry out different experimental studies to determine any particular property that allows determining the CMC value as a function of some abrupt variation of that property. Two of these properties are surface tension and speed of sound whose experimental work requires a great deal of work time and expense in labour and reagents. The different experiments carried out for each variable would determine the CMC as a function of the intersection

*Modeling the Behavior of Amphiphilic Aqueous Solutions DOI: http://dx.doi.org/10.5772/intechopen.95613*

#### **Figure 2.**

*Deep Learning Applications*

ratio [23] or in

inter alia.

temperature and calcining time) [21],

develop a bioremediation method [22],

i.Chemical Engineering to extract alumina from coal fly ash optimizing different variables involved in the process (K2S2O7/Al2O3 molar ratio, calcining

ii.in Environmental Science to study the biodegradation of the strobilurin fungicide Pyraclostrobin using bacteria from orange cultivation plots to

iii.in Biomedical applications to extract anthocyanins from blueberry optimizing the ultrasonic time, ultrasonic temperature, freezing time and liquid–solid

iv.in Biotechnology to optimize the culture media and reduce the production cost of urease bacteria to achieve an eco-friendly process controlling different parameters (yeast extract, whey and heating temperature) [24],

On the other hand, artificial neural networks are computational modeling tool that consists of a set of simple processing elements (neurons), massively interconnected capable to process data [20]. This kind of models can try to simulate the path in which the human brain process the information, that it is, ANN are inspired in the biological system [25]. ANN is made up of different neurons layers: an input layer to receive the information, one or more intermediate (or hidden) layers where the information is processed, and an output layer, with one or more neurons, where the predicted value is generated (**Figure 2**). Each neural network is characterized by a specific topology or architecture. To facilitate your identification each neural model implemented can be named such as i-h-o, using the number of neurons

These models present different advantages such as: are non-linearity systems that allow better data fit, are non-sensitivity to noise (uncertain data and measurement errors), present high parallelism (fast processing and failure-tolerance), among others [26]. According to Baş and Boyaci [20], ANNs represent non-linearities better than RS, although ANNs cannot produce a similar model equation to RS

i.Engineering to diagnose and classify of bearing faults [27] or to model hot

ii.in Food Technology to determine the botanical origin of honey using different parameters (ashes content, electrical conductivity, among others) [29] or food

iii.in Renewable Energy to predict three components of solar irradiation in

iv.or in diverse fields (also carried out in our laboratory) such as Palynology

This book chapter summary the quadratic regression and neural models developed in our research group [13] to predict, for amphiphilic aqueous solutions, the i) density (*ρ* in g·cm−3), ii) speed of sound (*u* in m·s−1), iii) kinematic viscosity (*ν* in

·s−1), and iv) surface tension (*σ* in mN·m−1) taking into account i) concentra-

tion (*C*), ii) carbons number (*n °C*) and iii) molecular weight (*M*w).

models. This kind of approach can be used in a multitude of fields such as:

presented in the input (i), hidden (h) and output (o) layer [13].

authenticity [30] (carried out in our laboratory),

deformation in titanium alloys [28],

[32] or Hydrology [33], among others.

Odeillo (France) [31], or

**86**

mm2

*Representation of a typical neural network with 3 neurons in the input layer, 5 neurons in one hidden layer and one neuron in the output layer (topology 3–5-1). Redraw from the original figure of Astray & Mejuto [13].*
