**1. Introduction**

The use of electronic compact devices with batteries such as remote controls, watches, electric toys, and pocket lamps has become an integral part of our society. Furthermore, these batteries have a certain lifetime, and the increase in volume of spent batteries over the last few years requires an innovative recycling process. Findings from research into metal recovery in recent years indicate the importance of recycling spent batteries [1–8]. In Canada, Call2recycle collected more than 2.5 kt of batteries for recycling in 2017 and 2.7 kt in 2018, of which 78% consisted of alkaline and Zn–C batteries [9]. However, the collected quantity only represents approximately 20% of all batteries sold in the market [10]. Alkaline batteries consist of a negative zinc metal electrode and a positive manganese dioxide (MnO2) electrode with an alkaline potassium hydroxide electrolyte, instead of the acidic ammonium chloride electrolyte used in zinc–carbon batteries. After collection, batteries are separated by type and sent to appropriate processing plants. Alkaline and carbon zinc batteries are sent to Retriev (Trail, BC, Canada), Inmetco (Elwood City, PA, USA), Raw Materials Company (Port Colbone, ON, Canada), and Battery Solutions Recovery (Brighton, MI, USA), where the batteries

are treated by pyrometallurgical processes [10,11]. These processes separate metals by volatilization and melting, and, therefore, require high-energy consumption and, due to the release of toxic gases, require an additional collection/cleaning system. By contrast, hydrometallurgical processes usually have a lower energy consumption and lower environmental impacts than pyrometallurgical processes. Hydrometallurgical processes consist of metal leaching followed by the separation, purification, and recovery of valuable metals through various techniques including, among others, precipitation, solvent extraction, and electrowinning. Numerous studies have used leaching processes under various conditions for the leaching of Zn and Mn from battery powder (Table 1).

**Table 1.** Leaching yields of Zn and Mn from alkaline battery by acid leaching.

Notably, the respective reaction time, temperature, acid concentration, and solid/liquid (S/L) ratio should be compared, as these parameters vary across the different studies. Sulfuric acid is commonly used either singly or in combination with an auxiliary agent. For example, the addition of H2O2 (4% *v*/*v*) in a sulfuric acid solution was used to remove 100% of Zn and 95.7% of Mn from battery powder [12]. In another study, the combination of ascorbic acid with sulfuric acid led to the dissolving of 99.5% of Zn and 98.8% of Mn [13]. Although the use of an auxiliary agent is key to dissolving Mn in sulfuric acid, results from a study where no auxiliary agents were used indicate a 90% removal of Zn and less than 20% removal of Mn in a sulfuric acid medium [14]. Furlani et al. (2009) studied the use of carbohydrates, primarily lactose, as reducing agents for the leaching of manganese from the zinc alkaline battery powder [15]. The carbohydrates reduced Mn(IV) and Mn(III) oxides to acid-soluble Mn(II), and approximately twice the stoichiometric amount of lactose was used for complete leaching [15]. Gallegos et al. (2018) proposed a process using biogenerated sulfuric acid with 5 vol.% H2O2 or 1 wt.% Na2SO3 for the leaching of Zn and Mn in a single step [16]. In their study, 99% of Zn and 90–98% of Mn was extracted after 2 h of leaching at 30 ◦C and 0.04 g/mL [16]. Sodium metabisulfite (Na2S2O5) was also used as a reducing agent for the dissolution of metals from a mixture of spent batteries. In their research, Tanong et al. (2017) obtained 94 and 99% removal yields for Mn and Zn, respectively, by adding 0.45 g Na2S2O5/g to battery powder in H2SO4 1.34 M in a single leaching step, with an S/L ratio of 10.9% for 45 min at ambient temperature [6]. In other studies, a thermal pre-treatment was added to increase the efficacy of leaching. For example, Petranikova et al. (2018) investigated the effects of a thermal treatment at 300–950 ◦C of battery powder on the acid leaching (0.5 M H2SO4 at 25 ◦C for 60 min) [17]. In general, these studies indicate that sulfuric acid leaching allows for the complete dissolving of Zn and partial extraction of Mn (MnO, Mn2O3, and Mn3O4). The total dissolving of Mn (including MnO2) demands an auxiliary agent to reduce MnO2 to MnO, soluble in sulfuric acid. Therefore, the leaching process can dissolve Zn and Mn

simultaneously in a single step or via selective leaching in a two-step process. Selective leaching allows for the use of different techniques for recovery.

After leaching, the second challenge in the hydrometallurgical process is the efficient recovery of metals at high purities. The metals present in the leachate can be recovered by precipitation in the form of hydroxides, sulfides, or carbonates according to their respective pH and redox potential. Sobianowska-Turek et al. [18] used NH4HCO3 3 M and NH4OH 1 M to recover almost 100% of manganese, iron, cadmium, and chromium, as well as 98.0% of cobalt, 95.5% of zinc, and 85.0% of copper and nickel from the solution after reductive acidic leaching (H2SO4 + C2H2O4) [18]. Furthermore, Sayilgan et al. used KOH 2 M and NaOH 2 M for the selective precipitation of manganese and zinc, with complete precipitation obtained for Zn at pH 7–8 and Mn at pH 9–10 [19].

In industry, zinc is usually recovered in metallic form by electrowinning. In a study by Alfantazi and Dreisinger (2003), electrowinning experiments were conducted at an 80 min plating time, 500 A/m2 current density, and temperature of 38 ◦C with zinc-containing electrolyte zinc and H2SO4 concentrations of 62 and 170 g/L, respectively [20]. In this study, 90% of zinc was recovered by using an Al cathode and Pb anode. Similar results were recorded by Ivanov (2004) with an electrolyte containing 45–55 g Zn/L, 5–6 g Mn/L, and traces of other metals including, among others, Ni, Sb, and Ge [21].

In our study, in addition to developing an efficient battery recycling process, relevant economic factors were also considered. Economic factors generally include processing and operating costs, as well as transport and residue disposal costs. For example, Gasper et al. (2013) evaluated the economic viability for recycling alkaline batteries using mechanical separation [22]. Although the mechanical process developed in their study was cheaper than other reported processes (\$US529/ton), it was still not economically feasible, due to the low end-product value. The revenue of the end products was \$US 383/ton of batteries that consisted of brass, Zn/ZnO powder, mixed Mn oxides powder, and KOH powder. In our study, we developed and described a complete hydrometallurgical process including the recovery of Zn by electrowinning and Mn by precipitation from alkaline battery powder. The process included dismantling, magnetic separation, leaching, and metal recovery. Furthermore, an economic evaluation was carried out to assess the feasibility on a global scale, especially for applications in Quebec (Canada), where an alkaline battery recycling process is not yet available.

### **2. Materials and Methods**

## *2.1. Process Description*

Figure 1 represents a flow sheet of the entire process for the recovery of Zn and Mn from spent alkaline batteries for this study. The globally relevant process includes two steps, namely, a physical pre-treatment step and a chemical treatment step. After dismantling, a representative sample of batteries is subjected to the attrition process followed by filtration and rinsing to remove any metallic powder attached to the coarse fraction. In addition to the separation of battery products, the removal of alkaline-soluble salts during this process reduces acid consumption in the following step. The coarse fraction is then transferred to the magnetic separator, allowing the magnetic fraction to be recycled as ferrous material and the non-magnetic fraction containing nylon, carton, and plastic to be used as energy sources.

**Figure 1.** Detailed flow sheet of the hydrometallurgical route to treat the spent alkaline batteries.

The fine fraction containing manganese and zinc described as "metallic powder" is transferred to the chemical treatment, where zinc is dissolved during the first leaching step using sulfuric acid (Equation (1)). A portion of manganese, in the form of MnO, Mn2O3, and Mn3O4, is also dissolved according to Equations (2) to (4) as follows:

$$\text{ZnO} + \text{H}\_2\text{SO}\_4 \to \text{ZnSO}\_4 \tag{1}$$

$$\text{MnO} + \text{H}\_2\text{SO}\_4 \rightarrow \text{MnSO}\_4 + \text{H}\_2\text{O} \tag{2}$$

$$\rm Mn\_2O\_3 + H\_2SO\_4 \to MnSO\_4 + MnO\_2 + H\_2O \tag{3}$$

$$\text{Mn}\_3\text{O}\_4 + 2\text{H}\_2\text{SO}\_4 \to 2\text{MnSO}\_4 + \text{MnO}\_2 + 2\text{H}\_2\text{O} \tag{4}$$

As MnO2 is insoluble in sulfuric acid, sodium metabisulfite (Na2S2O5) is added during the second leaching step to reduce Mn(IV) to Mn(II) [6]. During this leaching step, MnO2 in metallic powder is transferred in the leachate solution according to Equation (5):

$$\rm Na\_2S\_2O\_5 + 2MnO\_2 + H\_2SO\_4 \to 2MnSO\_4 + Na\_2SO\_4 + H\_2O \tag{5}$$

After precipitation for the removal of iron, and cementation for the removal of trace metals such as Ni and Cu, the first pregnant leach solution (PLS-1) is treated using sodium persulfate (Na2S2O8) to oxidize manganese for MnO2 recovery. Then, zinc is reduced by electrodeposition, resulting in a high-purity zinc metal. Furthermore, the second pregnant leach solution (PLS-2) is treated for the removal of iron and zinc followed by the precipitation of manganese as MnCO3. While the water used during this process can be reused through a counter-current mode, the final carbon-rich residue can be used for the fabrication of new batteries.

#### *2.2. Physical Pre-Treatment*

#### 2.2.1. Sampling and Pre-Treatment

The sample of spent alkaline Zn-MnO2 and Zn-C batteries was obtained from Laurentide Re-Sources Inc. (Victoriaville, QC, Canada). This company receives used batteries from various collection centers located throughout the Province of Quebec (Canada). During physical pre-treatment, spent alkaline batteries were shredded to approximately 1 cm × 4 cm fractions using a mechanical grinder (Muffin Monster, model 30005, JWC Environmental®, Santa Ana, CA, USA).

#### 2.2.2. Attrition Process

The neutral attrition consisted of three 20 min steps with a solid/liquid (S/L) ratio fixed at 30% (*w*/*w*) and 700 rotations per minute (rpm). The high rotation speed accelerates the separation of fine powder from other parts of the battery including carton pieces, ferrous scraps, and plastic. This step is also useful in removing soluble potassium hydroxide from the battery powder. Attrition experiments were carried out using a 40 L stainless tank reactor equipped with three internal baffles. For each experiment, 3 kg of shredded battery material was combined with 10 L tap water for 20 min at ambient temperature. After each step, S/L separation was carried out using 1.7 mm sieves. The remaining coarser fraction was then rewashed until three attrition stages were complete. The metallic powder was removed from the liquid phase after 2 h of settling. The water used for the washing process was recycled via counter-current mode, the result will show the media after three cycles.

#### *2.3. Chemical Treatment*

#### 2.3.1. Leaching Process

After washing, the metal powder was collected and different conditions were used to leach a maximum amount of zinc and manganese from the metallic powder. The challenge within this process is to obtain a high leaching efficiency and a PLS zinc concentration ≥40 g/L. This is important for avoiding energy loss during the electrowinning process. The selective leaching process was carried out in two stages in a 40 L stainless steel reactor. The water was recycled three times (LC 1 to 3) as presented in Figure 2. During the first cycle (LC 1), leaching was conducted with 4 kg of metallic powder in 2 M H2SO4 and an S/L ratio fixed at 40% (*w*/*v*) for 45 min at ambient temperature. For the second and third cycles (LC 2 and 3, respectively), leaching was conducted with 2 kg of metallic powder, and an S/L ratio of 20% in 1 M H2SO4, using the recycled solution after electrowinning (approximately 35–40 g Zn/L).

**Figure 2.** Schematic representation of the counter-current leaching and recovery process including rinsing steps performed on metallic powder.

During the second leaching step, 0.45 g Na2S2O5 per gram of metallic powder was added to reduce Mn(IV) to Mn(II), soluble in 1.34 M H2SO4, with an S/L ratio of 14% for 45 min at ambient temperature. The PLS-2 obtained from the second leaching step contained a significant proportion of manganese. Following each leaching step, S/L separation was carried out by filtration.

#### 2.3.2. Purification

Both PLS-1 and PLS-2 were purified prior to zinc and manganese recovery. The iron removal from PLS-1 was carried out at pH 4.0–4.5 by the addition of sodium hydroxide (NaOH) and hydrogen peroxide (H2O2). The added H2O2 dose was 1.5 times that of the stoichiometric molar ratio (SMR) of the total iron concentration (approximately 2 mM for PLS-1 and 30 mM for PLS-2).

After iron removal, the solution was purified by cementation using Zn powder to remove metal traces, such as Ni, Cu, and Co via the following equation:

$$\text{Zn}\_{\text{(s)}} + \text{M}^{2+}\text{ (aq)} \rightarrow \text{Zn}^{2+}\text{ (aq)} + \text{M}\_{\text{(s)}}\tag{6}$$

where M represents metal traces such as Ni, Cu, and Co.

In our study, a quantity of Zn metal powder equal to 20 times the impurity of metals (around 200 mg/L) was added, and cementation was conducted at 80 ◦C at pH 4.0–4.5 for 30–120 min.

Using the same principle, iron was also removed from PLS-2. Thereafter, the Zn residual (about 0.1 mol/L) in the PLS-2 was precipitated out using sodium sulfide (Na2S) at pH 4.0–5.0. The SMR values of 1, 2, and 3 were used during these experiments. The ZnS precipitate was then returned to the first leaching step and the PLS-2 was transferred to the MnCO3 recovery step.

#### 2.3.3. Metal Recovery from PLS-1


In this section, we present our theoretical outcomes and deduce which of the dendrimer structures depicted above is more irregular than the remaining ones with respect to a specific irregularity index. Each dendrimer structure relies on a single variable *n*. We plot the graph with irregularity index of *D*1(*n*), *D*2(*n*), and *D*3(*n*) (on a single graph) as a dependent variable and *n* as an independent variable. We observe that all the irregularity indices behave in a particular way with the increase in the value of *n*. We provided the graphical appearances of these indices with respect to the change in the growth stage of the dendrimer structure. In this graphical examination, the blue colour shows the graphical functioning of the PETIM dendrimer structure, the red colour shows the graphical behaviour of the PETAA dendrimer structure, and the green colour shows the graphical response of the PAMAM dendrimer structure. We present the values of various irregularity indices for the dendrimer structures in Tables 1–3. With the help of these tables, the comparative behavior of these irregularity indices for dendrimer structures has been expressed in Figures 4–7. These figures show that the molecular structure of PAMAM dendrimer is highly irregular as compared to the other dendrimer structures

and the molecular structure of PETAA dendrimer is more irregular than the molecular structure of PETIM dendrimer.

**Figure 5.** *σ* irregularity index.

**Figure 6.** Total irregularity index.

**Figure 7.** Variance index.

#### **4. Conclusions**

A modern trend in QSAR/QSPR studies is the use of properties which can be secure from the molecular structure without any other input data. The basic reason for this is to forecast the chemical properties of such a huge collection of compounds and drugs takes a large number of chemical inspections, thereby these tasks increase the burden of work of the chemical and pharmaceutical researchers. Thus, the strategy of estimating the topological indices has offered the explanations of such medicinal behaviour of various compounds and drugs. Hence, the irregularity indices for the molecular graphs of dendrimers are demonstrated by a mathematical derivation method and we presented the comparison of the molecular structures by using the graph structures. Our outcomes could perform a significant role in estimating and comparing the properties of these molecular structures.

**Author Contributions:** The contribution of the authors is as follows: Conceptualization, Z.I. and M.K.J.; methodology, Z.I.; validation, R.I., A.F. and M.A.C.; investigation, Z.I.; M.K.J.; writing–original draft preparation, Z.I., A.F., R.I.; writing—review and editing, D.Z., M.I.

**Funding:** This research received no external funding.

**Acknowledgments:** All the authors are thankful to their respective institutes for providing the research facilities.

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

#### **References**

c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Numerical Simulations of Polymer Solution Droplet Impact on Surfaces of Di**ff**erent Wettabilities**†

#### **Moussa Tembely 1,\*, Damien Vadillo 2, Arthur Soucemarianadin 3 and Ali Dolatabadi 1,\***

Received: 30 August 2019; Accepted: 24 October 2019; Published: 2 November 2019

**Abstract:** This paper presents a physically based numerical model to simulate droplet impact, spreading, and eventually rebound of a viscoelastic droplet. The simulations were based on the volume of fluid (VOF) method in conjunction with a dynamic contact model accounting for the hysteresis between droplet and substrate. The non-Newtonian nature of the fluid was handled using FENE-CR constitutive equations which model a polymeric fluid based on its rheological properties. A comparative simulation was carried out between a Newtonian solvent and a viscoelastic dilute polymer solution droplet. Droplet impact analysis was performed on hydrophilic and superhydrophobic substrates, both exhibiting contact angle hysteresis. The effect of substrates' wettability on droplet impact dynamics was determined the evolution of the spreading diameter. While the kinematic phase of droplet spreading seemed to be independent of both the substrate and fluid rheology, the recoiling phase seemed highly influenced by those operating parameters. Furthermore, our results implied a critical polymer concentration in solution, between 0.25 and 2.5% of polystyrene (PS), above which droplet rebound from a superhydrophobic substrate could be curbed. The present model could be of particular interest for optimized 2D/3D printing of complex fluids.

**Keywords:** droplet impact; viscoelasticity; volume of fluid method

#### **1. Introduction**

The dynamics of the impact and spreading of liquid drops onto a solid substrate is a highly active subject of research for both academic and industrial purposes. Indeed, these phenomena are widely encountered in everyday life, such as raindrops impacting on a surface. From an industrial perspective, there is much interest in the physics of non-Newtonian drop–surface interactions because of their wide range of applications. As such, a detailed knowledge of droplet impingement onto solid materials is required for the overall process development and improvement of many engineering operations. The impact of fluid drops on solid surfaces leads to different outcomes, such as partial or total spreading, recoil, or splashing [1]. One essential condition for the accurate placement of drops—a stringent requirement for technological applications—is the ability to control the maximum spreading diameter through different means. Although the problem has been considered from several angles for over 50 years, it is only during the past 10 years that repeatable and consistent results have been reported both on well-characterized homogenous substrates and on purpose-designed media with either chemical or topological heterogeneities [2,3]. Very recently, Antonini et al. [4] performed

a comprehensive study of the impact of drops on hydrophobic and superhydrophobic surfaces so as to help select the appropriate substrate for a given application. Complex fluid droplet impact has gained attention recently due to the key role it plays in applications ranging from 3D printing, polymer light-emitting diode technology, and lab-on-chip technology, to biotechnology for protein engineering [5–10]. The liquids involved in these processes are likely to exhibit non-Newtonian properties, such as viscoelasticity, which results from adding flexible polymers to solvent liquids. In order to address these challenges, numerical tools are essential for the accurate modeling of droplet dynamics on surfaces exhibiting different wettabilities.

Numerical models to handle droplet impact have been investigated since the initial work by Fukai et al. [11] based on the volume of fluid (VOF) method first introduced by Hirt and Nichols [12]. Since then, a wide range of numerical techniques have been developed for computing multiphase flow with moving interfaces, including, for example, the level set method [13], the front tracking method [14], and the lattice–Boltzmann method [15,16]. Among those cited, the VOF method has enjoyed a rather special place in the simulation of drop spreading for many reasons. These include its inherent mass conservation property, its suitability for problems where large surface topology changes occur, the ease of its implementation, and its reduced computational costs. However, it may be less accurate in interface calculations than, for example, the level set method, which is particularly adapted for resolving intricate topological changes of interfaces. In spite of this limitation, it is still the most preferred method for computations of drop impact and spreading where quite strong interfacial effects occur both at the substrate level and at the free surface of the drop [17,18]. To be more complete on the issue of numerical simulations of drop impact, it should be mentioned that the lattice–Boltzmann and phase field methods have recently been used for characterizing drop impact behavior. Additionally, another approach using the coupled level set and volume of fluid (CLSVOF) formulation has been implemented, with the VOF method dealing with the interface motion and the level set technique handling surface tension effects. This approach also remedied the problem of mass conservation typically encountered with level set methods.

A fundamental understanding of the droplet dynamics of complex fluids is a key element for future breakthroughs in the growing domain of micro-fabrication and micro-fluidics [7,9]. Regarding droplet impact, the question of whether a droplet will be deposited on the substrate or will eventually rebound is of particular interest, and a full understanding of the entire droplet impact dynamic is required.

Although Newtonian droplet impact has been extensively studied in the literature, the non-Newtonian viscoelastic droplet impact—despite its plethora of useful applications—has been only loosely documented both experimentally and numerically, even though recent works, showing an increasing interest for these fluids, make them an active research area. A finite element method was pioneered in Reference [19] to model the die swell of an Oldroyd-B fluid through an ad-hoc iterative technique for the free surface, based on the kinematic condition. The split Lagrangian–Eulerian method was extended by [20] to study viscoelastic jet breakup. Recently, Reference [21] simulated free surface flow using both marker-and-cell (MAC) and finite difference (FD) techniques. In addition, a mesh-free method using the smoothed particle hydrodynamics (SPH) technique has been applied to model an Oldroyd-B drop impact in 2D while neglecting the surface tension [22]. These different techniques neglect both the surface tension and the dynamic contact angle during spreading, along with the presence of air. Additionally, it is worth noting the interface-capturing techniques used to model non-Newtonian free surface flow such as the level set method [23] or the phase field method [24]. Finally, a one-dimensional approach [25] to model free surface flow of non-Newtonian fluid using an arbitrary Lagrangian–Eulerian (ALE) method should be mentioned, as it has shown good results in modeling filament thinning using the FENE-CR model.

Although the low viscosity of dilute polymers are of particular interest in inkjet fluids [26,27], it is only recently that they have been experimentally investigated using a controlled stretching

rheometer [28]. The present work benefitted from the rheological characterization of these fluids to optimize the simulation.

Most numerical studies have considered polymeric internal flow, but few have considered droplet interaction with a solid substrate. Within the VOF framework, the present model (accounting for the substrate hysteresis) investigated viscoelastic droplets impact using a single mode FENE-CR model in an axisymmetric configuration. The numerical model enabled the effect of monodisperse polymer concentration in solution and the resulting liquid droplet dynamics on both hydrophilic and superhydrophobic surfaces to be investigated.

The paper is organized as follows. Section 2 details the equations governing the numerical model and the polymers solutions' rheological properties. After validation of the model in the Newtonian case, the main results regarding the polymer droplet impact on hydrophilic and superhydrophobic flat surfaces are discussed in Section 3. Section 4 concludes the paper.

#### **2. Methodology**

#### *2.1. Numerial Methods*

The equations governing the impact of a non-Newtonian droplet are based on the discretization of the mass and momentum equations within the VOF framework. In the present work, the focus was be on modeling the impact and spreading of a droplet of dilute polymer solution which displays a viscoelastic behavior. Therefore, the momentum conservation equation incorporated this effect through an additional stress tensor (τp), and the governing equations can be written as follows:

$$
\nabla \cdot \mathbf{V} = 0 \tag{1}
$$

$$\frac{\partial(\rho \mathbf{V})}{\partial t} + \nabla.(\rho \mathbf{V} \mathbf{V}) = -\nabla p + \rho \mathbf{g} + \nabla.(\eta\_{\mathbb{P}} \nabla \mathbf{V}) + \nabla.\mathbf{r}\_{\mathbb{P}} + \gamma \kappa \nabla a \tag{2}$$

where κ is the curvature of the free surface, γ is the surface tension, α is the phase fraction of the liquid phase, η*s* is the viscosity of the solvent, g is the gravity acceleration, *p* is the pressure, and *V* the velocity.

In Equation (2), the continuum surface force (CSF) method of Brackbill et al. [29] was used to model the surface tension as a body force acting only on interfacial numerical cells, and the mean curvature at the interface is given by

$$\kappa = -\nabla. \left( \frac{\nabla \alpha}{|\nabla \alpha|} \right) \tag{3}$$

The outcome of an impacting drop is affected by various factors including droplet properties and kinematic and surface characteristics. In the present paper, the impact of a droplet of diameter *D*0 impacting at an initial velocity of *V*0 was simulated. To analyze droplet impact dynamics, we used the spreading factor, defined as the ratio between the spreading diameter and droplet initial diameter (*D*0). In addition, the time was made dimensionless using the kinematic time scale *t*c = *D*0/*V*0.

In order to model the polymer solution rheology, we used the dumbbell approximation based on a finitely extensible nonlinear elastic fluid in Reference [30], known as FENE-CR. This choice of FENE-CR was motivated by its superior performance for modeling viscoelastic behavior, as we have previously shown in the context of filament thinning and stretching [25,31,32]. The equation relating the stress tensor to conformation tensor *A* was expressed as follows:

$$\kappa = -\nabla.\pi\_{\mathcal{P}} = Gf(\ R \ ) \ (A - I) \tag{4}$$

where the elastic modulus is denoted by G and *f*(*R*) the finite extensibility factor is given by

$$f(\mathbb{R}) = \frac{1}{1 - \mathbb{R}/L^2} \tag{5}$$

which relates the finite extensibility parameter *L*, which corresponds to the maximum possible extension of the dumbbell, to the parameter *R* = Tr(*A*).

The polymer impact on the flow behaviour can be expressed through the constitutive equations based the evolution of the conformation tensor:

$$\frac{dA}{dt} - \nabla V^T A - A \nabla v = -\frac{f(R)}{\lambda}(A - I) \tag{6}$$

where λ denotes the relaxation time and *I* the identity tensor.

Finally, the transport of the phase fraction equation was simulated through an interface compression method:

$$\frac{\partial \alpha}{\partial t} + \mathcal{V} \nabla \alpha + \nabla. [V\_t \alpha (1 - \alpha)] = 0 \tag{7}$$

The interface compression speed *V*c, describing the relative velocity at the free surface between the fluids, followed the equation below [33]:

$$\mathbf{V}\_c = \mathbf{n}\_f \min \left[ \mathbf{C}\_\alpha \frac{\phi\_f}{S\_f}, \max \left( \frac{\phi\_f}{S\_f} \right) \right] \tag{8}$$

where *Sf* and φ*f* represent cell surface area and mass flux, respectively, while the coefficient *C*α, set here to 1, defines the degree of compression at the interface. It is worth noting that the adoption of an interface compression scheme avoids the tedious geometrical reconstruction of the interface habitually done in implementation of the VOF method. In addition, the algebraic method used here can readily be extended to unstructured meshes. Further details of the numerical discretization schemes and techniques can be found in Reference [34].

Within the VOF framework, the different physical parameters in each cell of the domain were expressed through the liquid fraction as follows:

$$
\xi = \alpha \xi\_{liquid} + (1 - \alpha)\xi\_{\text{gas}} \tag{9}
$$

where ξ represents any physical properties, such as the density, velocity, or viscosity, for both the liquid and gas phases.

To handle the liquid–substrate interaction, a more physically-based dynamic contact angle model was used. Droplet impact dynamics are highly controlled by the manner in which its dynamic contact angle is modeled. In the present work, Kistler's dynamic contact angle model [34,35] was implemented:

$$\theta\_d = f\_{\rm H}[\mathbb{C}a + f\_{\rm H}^{-1}(\theta\_{\rm E})] \tag{10}$$

with the Hoffman function expressed as

$$f\_{H}(\mathbf{s}) = \arccos\left\{ 1 - 2 \tan \mathbf{h} \left[ 5.16 \left[ \frac{\mathbf{s}}{1 + 1.31 s^{0.99}} \right]^{0.706} \right] \right\} \tag{11}$$

where the capillary number *Ca* = μ*Ucl*/γ, in which *Ucl* corresponds to the contact line velocity, was numerically approximated by taking the velocity within the first cell above the substrate. The effect of the surface hysteresis was accounted for by replacing the equilibrium contact angle θ*E* in Equation (9) by either the receding contact angle θ*R* or the advancing contact angle θ*A* according to the direction of the triple line velocity. By adopting this approach, our model became sensitive to the substrate hysteresis, which plays a significant role in simulating droplet impacts on surfaces with varied wettabilities. It is worth noting that unlike in Reference [36], the presented model did not rely heavily on experimental measurements of the dynamic contact angle evolution in order to match a given experiment.

Finally, the governing Equations (1)–(11) were implemented in OpenFOAM/C++ using second order linear upwind-biased schemes. The simulations (in axisymmetric geometry) were performed in parallel using the domain decomposition method. The pressure implicit with splitting of operators (PISO) algorithm was used to calculate the pressure, while the evolution of the conformation tensor was solved using a preconditioned bi-conjugate gradient technique; further details on implementation and discretization can be found in our previous work in References [10,34,37]. The convergence criteria set for the pressure, velocity, and conformation tensor fields were of the order of 10−6.

#### *2.2. Polymer Solution and Substrates Properties*

In order to evaluate our numerical model, a viscoelastic liquid and its properties were measured based on a"Cambridge Trimaster" filament stretching and thinning experimental set-up [28]. This extensional rheometer proceeded by performing filament stretching at a constant velocity for a liquid initially placed between two pistons of initial diameter 1.2 mm. The two pistons, which operate on opposite sides of a belt, move away from each other at a prescribed distance, letting the mid-filament remain in a central position. The ensuing measurements of the filament mid-diameter allows accurate estimation the relaxation time of the liquid, which has been shown previously to be crucial in numerical modeling of filament thinning dynamics [25].

The numerical simulation investigated a Newtonian solvent—diethyl phthalate (DEP)—in addition to a polymer solution consisting of polystyrene (PS), 110,000 g/mol, dissolved into the DEP solvent. Table 1 presents the interfacial surface tension and viscosity values of the two liquids.

**Table 1.** Liquid physical properties. DEP: diethyl phthalate, PS: polystyrene.

Finally, the relaxation time measured from the polymer solution, DEP + 2.5 wt % PS, was λ = 1.19 ms, while the extensibility parameter *L*, accounting for the liquid physical properties, was taken as *L* = 15 [25].

Regarding fluid–substrate interaction, we considered two types of substrate in the numerical experiment, hydrophilic and superhydrophobic, the properties of which were similar to the aluminum and WX2100 properties for a water droplet, respectively [38]. Experimentally, it may be challenging to find a substrate exhibiting those chemical properties with respect the DEP and DEP + 2.5 wt. % PS, though the aim of this study was to highlight the relevant features in viscoelastic droplet dynamics, which have been poorly numerically documented in the literature, especially with the added effect of substrate hysteresis. The contact angles (CAs) consisting of the equilibrium contact angles, in addition to the hysteresis with the advancing and receding contact angles of these two substrates, are given in Table 2.

**Table 2.** Substrate contact angles (CAs).

#### **3. Results**

#### *3.1. Validation of Newtonian Droplet Impact Dynamics*

We first tested the model in a Newtonian case for validation. For this purpose, we have provided a comparison of the VOF method using our modified Kistler's model to tackle the challenging case of droplet impact on a surface with contact angle hysteresis (CAH). The comparison was performed with an experiment performed in Antonini et al. [39] for the impact of a 2.5 mm diameter droplet impacting at 1 m/s with receding and advancing contact angles of 108◦/169◦. The results are shown in Figures 1 and 2 for the transient profile and spreading diameter evolution, respectively. We observed a good agreement between the experiment and simulation of the droplet upon impact on a surface exhibiting a significant contact angle hysteresis, CAH = 61◦, highlighting the robustness and capability of our model and paving the way for an accurate assessment of the impact of non-Newtonian fluids.

**Figure 1.** Transient profiles of a Newtonian droplet impacting a superhydrophobic surface.

**Figure 2.**  VOF: volume of fluid.

#### *3.2. Impact of Polymer Solution Droplet*

#### 3.2.1.  The transient evolution of 1 mm diameter drop at a velocity of 1 m/s is shown in Figure 3. The left-hand side corresponds to the Newtonian liquid, while the polymer droplet is shown on the right hand-side. We plotted the dimensionless spreading diameter (*D*/*D*0) function of the dimensionless time (*tc* = *t V*0/*D*0). We observed that during the kinematic phase (*tc* < 1), droplet spreading seemed to be independent of the fluid model (Figure 4). However, at subsequent phases of the two droplets' spreading, we observed a much more marked difference between the two cases. Additionally, the viscoelastic liquid droplet displayed little oscillation while having a greater maximum spreading diameter, due to the dominance of the elastic normal stress over of the surface tension, which favored retraction. Interestingly, the liquid flowing out of the droplet center towards its periphery seemed to behave similarly to the filament thinning and stretching situation we reported in Reference [25].

**Figure 3.** A comparative simulation of a 1 mm diameter droplet impacting at 1 m/s on a hydrophilic substrate between (**right**) a Newtonian solvent DEP and (**left**) polymer solution, DEP + 2.5 wt. % PS.

**Figure 4.** Evolution of the dimensionless spreading diameter on the hydrophilic surface.

#### 3.2.2. Superhydrophobic Surface

We simulated the impact of a 1 mm droplet at 1 m/s on a superhydrophobic (SH) substrate comparing a Newtonian and polymer solution, which was modeled by a FENE-CR fluid. Comparative transient profiles between the two cases are depicted in Figure 5. The left-hand side corresponds to the Newtonian DEP solvent, while the right-hand side represents the polymer solution, which consisted of a dilution of polymer (PS) into the solvent. The addition of a minute quantity of polymer to a Newtonian liquid has been found to affect droplet dynamics, mainly during the recoiling stage for the impact conditions that were investigated in the present work. The kinetic energy of a impacting droplet is converted to the elastic and surface energy; that stored energy contributes to droplet retraction and rebound on superhydrophobic surface, after partial dissipation by viscous effect. As expected, the Newtonian (DEP) droplet rebounded and detached after impact on the superhydrophobic substrate; however, the rebound was suppressed with the dilute polymer solution (DEP + 2.5 wt. % PS), where the high elongational viscosity dissipated much of the drop kinetic energy during the spreading phase. As the Newtonian DEP droplet rebounded from the superhydrophobic surface, the dilute polymer settled at its equilibrium position during the wetting phase, as depicted in Figure 6.

Finally, the contrast between the Newtonian and the polymer solution behavior is quantified in Figure 7 by the dimensionless spreading diameter evolution. For superhydrophobic substrate, it is worth noting that the maximum spreading diameter in contact with substrate should not be confused with the maximum (deformation) diameter. The latter was higher for the viscoelastic fluid than the Newtonian one. In addition, we found that with a much lower concentration of polymer (DEP + 0.25 wt. % PS), the droplet bounced back again on the superhydrophobic substrate, which exhibited per se a higher retraction energy (Figure 7). Therefore, this implies the existence of a critical polymer concentration between 0.25 wt. % PS and 2.5 wt. % PS, above which droplet rebound can be suppressed on a superhydrophobic surface. The capability of our numerical model to retrieve such a feature is of particular interest for various processes, such as nutrients deposited as spray on plants and 2D/3D drop-on-demand printing.

**Figure 5.** Simulated comparison between (**right**) the Newtonian solvent DEP and (**left**) viscoelastic polymer solution, DEP + 2.5 wt. % PS, for the impact of a 1 mm diameter droplet at 1 m/s on the superhydrophobic substrate.

**Figure 6.** Impact of a 1 mm droplet of polymer solution, DEP + 2.5 wt. % PS, at 1 m/s on the superhydrophobic substrate.

**Figure 7.** Simulated spreading diameter of 1 mm droplets of a Newtonian (DEP) fluid and two polymer solutions, DEP + 0.25 wt. % and DEP + 2.5 wt. % PS, impacting at 1 m/s.

#### **4. Conclusions**

Numerical simulations of droplet impact on different substrates based the VOF method were performed for both Newtonian and polymer solutions. The liquid–substrate interaction was also accounted for with a more realistic dynamic contact angle, as opposed to solely relying on the equilibrium contact angle. The constitutive equations considered for the viscoelastic fluids came from the FENE-CR model. While no noticeable difference was found in the early stages of droplet impact (beyond the kinematic phase), we observed that the substrate and fluid viscoelasticity influence became much more dominant on droplet dynamics during the recoiling phase particularly. The results of the simulation indicated that the dilute polymer solution droplet had a higher spreading diameter compared to a Newtonian solvent on a hydrophilic substrate. This can be explained by the dominance of the elastic normal stress over both the kinetic energy dissipation and surface tension force, which tends to favor droplet retraction. In addition, the existence of a critical polymer concentration—at which a droplet may no longer detach, even on superhydrophobic substrates—was inferred. The present model, based on a single mode FENE-CR fluid, could be extended to multimode constitutive models, along with tailored experiments for a comprehensive description of polymer droplet impact.

**Author Contributions:** M.T., D.V., A.S. and A.D. designed the study. M.T. performed the study and wrote the paper. All the authors contributed to the paper.

**Funding:** M.T. and A.D. gratefully acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC).

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

#### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **On the Recovery of PLP-Molar Mass Distribution at High Laser Frequencies: A Simulation Study**

#### **Shaghayegh Hamzehlou 1, M. Ali Aboudzadeh 2 and Yuri Reyes 3,\***

Received: 13 May 2019; Accepted: 23 July 2019; Published: 2 August 2019

**Abstract:** Due to the inherent difficulties in determination of the degree of branching for polymers produced in pulsed laser polymerization (PLP) experiments, the behavior of the degree of branching and backbiting reaction in high laser frequency and relatively high reaction temperatures have not been well-established. Herein, through a simulation study, the validity of different explanations on the recovery of PLP-molar mass distribution at high laser frequencies is discussed. It is shown that the reduction of the backbiting reaction rate at high laser frequency, and consequent decrease in the degree of branching, is not a necessary condition for recovering the PLP-molar mass distribution. The findings of this work provide simulation support to a previous explanation about the possibility of using high laser frequency for reliable determination of the propagation rate coefficient for acrylic monomers.

**Keywords:** PLP-SEC; *n*-butyl acrylate; degree of branching

#### **1. Introduction**

Having accurate rate coefficients of polymerization reactions is crucial to obtaining basic knowledge about complex polymerization reactions, modeling and better controlling the industrial processes. Pulsed laser polymerization (PLP) has been used to measure the rate coefficients of polymerization reactions of different monomers [1–5]. In particular, PLP together with size exclusion chromatography (PLP-SEC), has been recommended by International Union of Pure and Applied Chemistry (IUPAC) and successfully applied to calculate the propagation rate coefficient of several academically and industrially relevant monomers. A PLP-SEC experiment can be carried out as a function of temperature, and hence it is possible to calculate Arrhenius' parameters, pre-exponential factor, and activation energy [6]. In a PLP-SEC experiment, a reacting mixture containing monomer (optionally a solvent) and a photoinitiator is initially irradiated with a laser pulse at *t*0, generating radicals, [R0], in the order of 10−5 moL L−1 [7]. These radicals initiate the polymer chains that grow altogether during the so called dark period, i.e., when the mixture is not irradiated by the laser and therefore, there is not any new radical. At a later time, *t*1, another laser pulse hits the reacting mixture and the new radicals terminate a large fraction of the growing chains (those who did not undergo termination during the dark period) or initiate new chains. In a posterior multiple of *t*1 − *t*0, i.e., *td*, another laser pulse hits the sample and this continues; *td* is controlled by the laser frequency or laser repetition rate. Obviously, some chains grow during more than one dark period. Once the polymerization finishes, either at a fixed time or after a number of laser pulses, the molar mass distribution (MMD) is measured by size

exclusion chromatography (SEC), and the MMD or the chain length distribution (CLD) should show distinctive peaks at defined chain lengths according to the following equation:

$$L\_n = nk\_p[M]t\_d \; n \ge 1 \tag{1}$$

where *Ln* is the chain length at which the CLD shows a critical point (calculated by the maximum of the first derivative), *n* is an integer number related to the number of dark periods that the chains were able to grow (i.e., L1 = 1L0, L2 = 2L0 and so forth); [*M*] is the monomer concentration; and *kp* is the propagation rate coefficient, as the unknown parameter. To provide reliable results in a PLP-SEC experiment, several consistency criteria must be fulfilled. First, at least two peaks should be present in the CLD, which are multiples of L0; second, it is desirable to reach conditions for the independence of *kp* on initiator concentration, laser power, laser frequency, and monomer concentration [1,8]. The PLP-SEC method has provided good results within a broad temperature range for some widely used monomers, such as styrene [2], methyl, and alkyl methacrylates [1,3], among others. Laser frequencies up to 100 Hz were used in most of the above-mentioned PLP-SEC experiments. Nevertheless, accurate estimation of *kp* from a PLP experiment is still a challenge [9].

However, the PLP-shape of the MMD (distributions with clearly defined critical points) was not obtained for acrylic monomers, specifically for *n*-butyl acrylate at temperatures ≥30 ◦C. Although it was found that by carrying out the PLP reaction at sufficient low temperatures the PLP-MMD was recovered, the origin of this phenomena was not known initially [10,11]. It is well known now that in addition to the common reactions of a free radical polymerization (initiation, propagation, and termination), acrylic monomers undergo significant intramolecular chain transfer to polymer or backbiting. Intermolecular chain transfer reaction is present as well, which is important at high polymer concentration. However, this is not the case in a standard PLP-SEC experiment due to the low monomer-to-polymer conversion. In the backbiting reaction, a growing chain-end radical wraps around itself to abstract a hydrogen atom from a monomer unit on its own backbone via the formation of a six-membered ring [4,12]. The stability of the resulting mid-chain radical (MCR) has a significant effect on the polymerization kinetic and the microstructure of the polymer chains, leading to a featureless MMD, which in turn invalidates the *kp* determination by PLP-SEC above c.a. 30 ◦C [13,14]. As the activation energy of backbiting is higher than the activation energy of the propagation of the chain-end radicals, the *kp* of *n*-butyl acrylate (BA) could be determined accurately between −65 ◦C and 20 ◦C using frequencies up to 100 Hz [4].

It is worth noting that simulation studies dealing with the polymerization of acrylic monomers have been very important for better understanding of this phenomenon and better estimation of the propagation rate coefficient [15], and even later used to estimate the rate coefficients of the secondary reactions in acrylic radical polymerization [16,17]. Using a simulation approach, it was demonstrated that the increment of the laser frequency in a PLP-SEC experiment could lead to a better determination of the *kp* of the chain-end radicals. For BA, at frequency around 300–500 Hz and temperature of 20 ◦C, the PLP-MMD is recovered and makes the average propagation coefficient (considering both MCR and chain-end radicals) independent from the laser frequency [14]. With the development of the laser technology, this simulation finding was experimentally confirmed. With a laser frequency of 500 Hz, it was possible to calculate the *kp* of BA up to 70 ◦C. This temperature was 50 ◦C higher than the previously reported experiments, meeting the consistency criteria, showing up to three inflection points in the derivative of the CLD, providing a very good agreement of Arrhenius' parameters between the two data sets [18]. It was logical to carry out the PLP-SEC experiment at such frequency and higher temperature than in previous experiments for other acrylic monomers: up to 80 ◦C for isobornyl acrylate, tert-butyl acrylate and 1-ethoxyethyl acrylate [19], and for methyl acrylate and 2-ehtylhexyl acrylate [20,21]. Nevertheless, as an MCR can undergo β-scission at high temperatures, the MMD can be even more complex to analyze.

As in a PLP-SEC experiment, the conversion of monomer to polymer remains rather low, and it is difficult to measure the degree of branching directly (defined as the ratio of the quaternary carbons to the total polymerization events). Generally, the cumulative determination of the degree of branching is carried out by 13C-NMR spectroscopy [22–25], which requires some milligrams of polymer, which is not easy to obtain in a standard PLP-SEC experiment; otherwise, the error in the 13C-NMR determination invalidates such a measurement. Plessis et al. were able to measure experimentally the branching density in a PLP experiment using a reactor with larger volumes of reactants than in conventional PLP set-ups [26]. They studied the effect of temperature and monomer concentration on branching density in a PLP experiment. To the best of our knowledge, no experimental study has been done to investigate the effect of frequency on the branching level.

Now the question is why do reaction temperatures close to 70 ◦C, using a laser frequency of 500 Hz, lead to a PLP-MMD, allowing an adequate *kp* determination for *n*-butyl acrylate? It is reported in the literature: "Diminishing the effects from the MCRs is hence a prerequisite for a successful PLP-SEC experiment" [18,27]. Nikitin et al. [7] stated that the fraction of radicals that are not subjected to backbiting is proportional to exp(−kbbt), where kbb is the backbiting rate coefficient and *t* is the time after generation of these radicals by a laser pulse. Therefore, as the laser frequency increases, the fraction of growing chains that undergoes backbiting decreases. Such explanation has been used to explain the PLP-MMD-recovering of other acrylic monomers at higher temperatures than previous experiments [21]. On the other hand, in a PLP Monte Carlo simulation, the concept of competitive processes was used to explain the recovery of PLP-MMD at high laser frequencies [28]. In this simulation, the events that each of the radicals undergo were selected based on the probability of the corresponding reaction mechanism, with the condition that the time needed to undergo the chosen reaction could not exceed the life expectancy of the radical. This assumption led to a decrease in the degree of branching and recovery of PLP-MMD distributions at high temperatures and laser frequencies [28]. Additionally, in a deeper study of reversible addition-fragmentation chain transfer polymerization (RAFT), the concept of competitive processes was used to explain the decrease in the degree of branching in such a controlled radical polymerization. In this process, the deactivation time of growing radicals (adjusted by changing the amount of the RAFT agent) is typically faster than the characteristic time for backbiting. Following the same idea, the authors explained that the reduction of the radical lifetime to chain termination induced by fast laser pulse can result in a decrease in backbiting rate and, hence, the branching level in the PLP process, allowing the recovery of the PLP-MMD [29]. In summary, there are two possible explanations for the recovering of the PLP-MMD as the laser frequency increases. According to the latest explanation, reduction in the backbiting rate and, hence, the branching level is a crucial requisite for recovery of the PLP-MMD. However, in the first explanation, only decreasing the fraction of the radicals that undergo backbiting while maintaining the same backbiting rate leads to recovery of PLP-MMD.

In this study, PLP-SEC experiments are simulated using the polymerization kinetics of BA (the most studied acrylic monomer); the behavior of backbiting and the degree of branching are analyzed during PLP-SEC experiments carried out at different temperatures, laser frequencies, and concentration of radicals generated in the laser pulse. The degree of branching of the polymer obtained in a PLP is studied and discussed under different experimental conditions; and finally, the simulation results are used to study the validity of different explanations for the recovery of PLP-MMD at high laser frequency. It is shown whether reduction of the backbiting rate/branching level is an essential requisite for recovery of the PLP-MMD.

#### **2. Simulation Details**

BA PLP experiments at different reaction conditions were simulated in the present study. The detailed kinetic scheme used in these simulations, and relevant kinetic parameters which were taken from the literature, are presented in Supporting Information. It includes all relevant reactions in homopolymerization of acrylates, such as inter/intra molecular transfer to polymer. β-scission was not included in the kinetic scheme due to its negligible effect at the simulated temperatures (maximum 60 ◦C) [30]. The simulated PLP experiments were implemented in Predici commercial

software package [31]. To simulate the PLP polymerization by using an isothermal process at a given time (that is fixed by the laser frequency), the concentration of new radicals generated by the laser pulse ([R0]) sharply increased to 10−5 moL L−1. The total time of the simulation was 1 s in these simulations. Three different temperatures (20, 40, and 60 ◦C) and four laser frequencies (50, 100, 250, and 500 Hz) were employed. The monomer concentration was 7 moL/L. Also, in order to analyze the effect of radical concentration generated in the laser pulse on the CLD and on the degree of branching, PLP-SEC experiments at 20 ◦C with frequencies of 100 and 500 Hz and at two additional [R0], 10−4 moL L−1 and 10−6 moL L−1, were simulated.

Instead of using the MMD of the polymer chains and polymeric radicals, the analysis was done using the CLD calculated by Predici in the Gel Permeation Chromatography (GPC) mode, size exclusion chromatography-chain length distribution (SEC-CLD). This simplified the analysis of the results, and the transformation process to the MMD was straightforward. Moreover, it should be pointed out that measuring the absolute molar mass of branched polymer chains by SEC is not trivial [20], and the calibration might introduce some error in the experimental measurements; such analysis is beyond the scope of the present study.

In addition to SEC-CLD of the inactive polymer chains, the simulation allows the calculation of the SEC-CLD of the chain-end radicals and of the MCR, the degree of branching, the fraction of MCRs that terminates with radicals generated by the laser pulse, and the ratio of the formed MCRs to the total propagation steps, among others.

#### **3. Results and Discussion**

In Figure 1 (left side), the final SEC-CLD of the polymer chains is presented for the simulations with [R0] = 10−5 moL L−1. Each row of Figure 1 shows a different temperature. In the same figure (right side), the first derivative of each SEC-CLD is presented; the derivate was calculated by averaging the slopes of two adjacent points for each data point using the raw data, i.e., no smoothing was applied. At 20 ◦C and 50 Hz, it can be seen that there is a single peak in the CLD. The presence of this peak was confirmed in its corresponding derivative, which showed a sharp peak that resembles a PLP polymerization; however, a second peak was not observed. By increasing the frequency to 100 Hz, the peak at short chain-length became more visible and it shifted to nearly half of the value of chain-length of the previous condition; in the corresponding derivative, one can see that there is another small peak at larger chain-length, and this last peak is at the chain-length of the previous experiment at 50 Hz. In the SEC-CLD of the simulation at 250 Hz, two defined peaks can be seen in the CLD that were also present in the corresponding derivative. At the highest frequency, 500 Hz, two peaks at shorter chain-length were clearly observed, and in the derivative there were up to three peaks. For this temperature, the PLP-shape of the CLD was obtained at frequencies higher than, or equal to, 100 Hz. The higher the frequency of the laser pulse, the shorter the chains (shorter dark period) and the more defined the peaks in the SEC-CLD and in the correspondent derivative. From an experimental point of view, the acceptable *kp* calculations were carried out up to this temperature at 100 Hz due to the presence of more than one peak in the derivative of the SEC-CLD [4], which was observed in the present results as well.

Next, we analyzed the results at 40 ◦C; it should be recalled here that at such temperature, it was not possible to obtain reliable experimental PLP-MMDs to properly calculate the *kp* using frequencies up to 100 Hz. At 50 Hz, there were no defined peaks in the SEC-CLD or in its derivative, and a broad, featureless distribution was obtained. At 100 Hz, although the SEC-CLD was broad, there was a rather small peak in the SEC-CLD that was also observable in its derivative. The peak in the derivative resembles a PLP polymerization. In principle, this peak could be used to determine the *kp* [7], but for the reliability of the results, the presence of at least a second peak at larger chain lengths is desired. Such second peak in the derivative of the SEC-CLD appeared when the frequency was 250 Hz, along with the formation of a broad peak at even larger chain lengths. For the simulation with 500 Hz, a PLP-shape of the CLD was totally recovered, and in the derivative it was possible to observe the

presence of three peaks. Therefore, the information of the experiment with 500 Hz could be used to calculate *kp*.

The highest temperature considered in the simulations was 60 ◦C (third row in Figure 1). For this temperature, the SEC-CLD at 50 and 100 Hz did not have the shape of a PLP experiment, i.e., there were no peaks in the SEC-CLD nor in the corresponding derivatives. At 250 Hz, only one peak in both graphs was formed, therefore, the use of such information to calculate the *kp* would not be recommended. However, at 500 Hz, the SEC-CLD recovered the PLP-shape and in the derivative two peaks were present. Therefore, it was possible to use this information to calculate the *kp* at such a temperature.

**Figure 1.** (**left**) Final size exclusion chromatography-chain length distributions (SEC-CLDs), and (**right**) the correspondent derivatives of the polymer chains for different temperatures and laser frequencies. Take into account that the conversion is not the same in each experiment, leading to different area under the curve.

The most relevant information presented in Figure 1 is summarized in Table 1. The chain lengths reported in this table were obtained by reading the maximum of each peak in the derivative of the SEC-CLD (if observable); the first peak is the one at the shortest chain length. In the same table, the *kp* was calculated by using the chain length of each peak (*kp1* corresponds to the peak L1, and so on) and Equation (1). The concentration of monomer was 7 moL L−1. The last column of Table 1 reports the *kp* used as an input in the simulation at the given temperature (calculated with Arrhenius' parameters of Table S1). In all cases, the error between the calculated value of *kp* using the data reported in Table 1, along with Equation (1), and the *kp* calculated through Arrhenius' parameters was less than 7%. Additionally, the ratio *kpi*/*kpi*+*1* was rather close to 1 in all cases.

**Table 1.** Chain lengths at which the chain length distribution (CLD) shows critical points, Li, determined at the maximum of the derivatives of the CLD of Figure 1. kpi calculated with this information and Equation (1) and *kp* the input at the given temperature.

Figure 2 shows the degree of branching, which was calculated as the cumulative fraction of polymerized acrylic units that have a quaternary carbon for different temperatures and laser frequencies. The quaternary carbons are mainly formed by the MCR propagation (termination by combination also contributes to the formation of quaternary carbons). It is worth mentioning that in order to separate the effect of the patching reaction from the branching level, the quaternary carbons created in the patching reaction were not considered in the degree of branching. In all cases, once the polymerization begins, the degree of branching increases and, after some time, a plateau with positive slope is observed. The degree of branching increases as the temperature becomes higher, which is a reasonable result due to the higher activation energy of the backbiting reaction compared to propagation of the chain-end radicals. By a totally different simulation approach of the PLP of BA at 500 Hz (kinetic Monte Carlo), it has been determined that the degree of branching reaches a value of 0.14% at 32.85 ◦C and 0.21% at 51.85 ◦C after 100 pulses [32]. At 51.85 ◦C and monomer concentration of 6.76 moL L−1, the simulation used in this work reached 0.18% after 1 s, showing a good agreement between both simulation approaches. The differences between both simulation approaches were due to the different kinetic scheme used in the kinetic Monte Carlo simulations (two types of initiator radicals and time dependent initiator concentration). As observed in Figure 2, although slightly lower values of the degree of branching were calculated as the laser frequency increased at constant temperature, there was not a significant decrease of the degree of branching at a fixed temperature. At 20 ◦C, degree of branching was between 0.10 and 0.08% at 50 and 500 Hz, respectively; at 60 ◦C, the variation was between 0.22 and 0.21% at 50 and 500 Hz, respectively. From these results, it can be concluded that the degree of branching at a constant temperature does not depend on the laser frequency. In the same figure, for each temperature, the instantaneous probability of backbiting, calculated by kbb/(kp[*M*] + kbb), is plotted as a solid line, where [*M*] is the monomer concentration. The ratio of backbiting events to the total propagation events obtained during the simulations at 500 Hz was plotted as a dashed gray line (both values were

multiplied by a factor of 100). The instantaneous probability of backbiting under the quasi-steady-state conditions is related to the degree of branching, that is why these calculations were plotted in the same figure. As observed, the degree of branching has approached the instantaneous probability of backbiting at 500 Hz, but within the simulation time they never touched each other; the same behavior was observed with the kinetic Monte Carlo simulation [32]. Regarding these results, the reason for such a difference is that an MCR can terminate with the radicals generated in the laser pulse; the faster the laser pulse, the larger the MCRs that are terminated by this reaction, as discussed below.

**Figure 2.** Degree of branching as a function time obtained during the simulation at different temperature and laser frequencies. The solid gray line is the instantaneous probability of backbiting and the dashed line is the ratio of the backbiting events to the total propagation events during the simulation; both calculations multiplied by a factor of 100.

Additionally to MCR's propagation and (cross) termination with another polymeric radical, it might be possible for an MCR to react with the radicals generated during the laser pulse (see Kinetic Scheme S1). It is worth mentioning that in the simulations, initiation rate coefficient was assumed equal to the propagation rate coefficient. Therefore, the difference between the calculated degree of branching in the simulations and the instantaneous probability of backbiting could be explained by the fraction of MCRs that react with the radicals generated in the pulse, giving place to patched MCRs. As the laser frequency increases, the number of radicals at the same interval of time also increases, leading to a larger fraction of patched MCRs. Figure 3 shows the percentage of patched MCRs at different temperatures and laser frequencies. As explained above, it can be seen that increasing laser frequency leads to a larger fraction of patched MCRs. On the other hand, the fraction of patched MCRs decreases by increasing temperature.

**Figure 3.** Percentage of mid-chain radicals (MCRs) that are patched by the radicals generated in the laser pulse.

As it was shown in Figure 2, increasing the laser frequency does not significantly change the degree of branching at a constant temperature, and the slight difference can be explained by patching of the MCRs as discussed above. However, the PLP-CLD is recovered by increasing the laser pulse frequency. Nikitin et al. claimed that there is a minimum fraction of chain-end radicals, with respect to total radical concentration, at a constant temperature and time that still allows the observation of the peaks in the CLD [7]. This fraction is proportional to the exp(−kbb/f), where f is the laser frequency. They also showed that this minimum fraction is independent of polymerization conditions at constant temperature. As a consequence, if the reaction temperature increases, the backbiting rate coefficient

will also increase and, therefore, to have a significant fraction of secondary radicals that do not undergo backbiting the laser frequency should increase.

It is worth mentioning here that all the simulations have the same duration (1 s) and monomer concentration. Thus, the number of polymer chains is lower at low frequencies than at high ones. On the other hand, the ratio of backbiting events to propagation is nearly independent of the laser frequency. Therefore, at low laser frequency a larger fraction of chains undergoes backbiting, creating MCRs that could distort the CLD by breaking the time correlation of Equation (1) due to the stability of the MCRs. When the number of polymer chains increases (as in a high frequency experiment with the same duration), nearly the same number of backbiting to propagation events takes place, but affecting a relatively lower fraction of chains; therefore, the PLP-MMD is recovered. This is supported by the results presented in Figure 4, in which the zeroth moment of the chain-end radical species, or the concentration of the chain-end radicals and MCRs, for 20 and 60 ◦C and different laser frequencies is shown. In this figure, the concentration of each radical is divided by the concentration of radicals generated in each laser pulse (10−5 moL L−1). At 20 ◦C and 50 Hz, immediately after the laser pulse, the concentration of the chain-end radicals starts to decay during the dark period as they mainly undergo termination reaction. Moreover, a fraction of them undergoes backbiting reaction; the concentration of MCRs increases, and then decreases in the last part of the dark period. Towards the end of the dark period, the concentration of MCRs is greater than that of the chain-end radicals. Nevertheless, since some chains did not undergo backbiting during the dark period, they could be terminated in the next laser pulse, leading to a peak in the SEC-CLD. Increasing the laser frequency to 100 Hz leads to a greater concentration of both types of radicals because, in this case, the dark period has half the duration of the previous simulation. Thus, it can be seen that concentration of chain-end radicals is greater, leading to a well-defined peak in the SEC-CLD. It is true that the MCRs are also in greater number but affecting a relatively lower fraction of chains. At 250 Hz, although the concentration of chain-end radicals decreases during the dark period, the next laser pulse hits the reacting mixture when the concentration of chain-end is enough to produce a PLP-CLD of the polymer chains. Again, because there are more radicals, the MCR concentration also increases, but it seems not to affect a significant fraction of chains. With the highest frequency, the concentration of chain-end is even greater, resulting in a higher concentration of MCRs. For this case, such concentration of chain-end radicals leads to a well-structured PLP-CLD. As the laser frequency increases, the fraction of chain-end radicals close to the next laser pulse also increases. At 60 ◦C, the behavior is rather similar to the previous description; however, as the temperature is higher, a larger fraction of MCRs is present [26]. Nevertheless, as the dark period diminishes and before the next laser pulse hits the sample, a larger fraction of chain-end radicals is present, leading to the recovery of the PLP-CLD.

Additional information that can be extracted from the simulation is the CLD of chain-end radicals, which of course is not obtained by experimental procedures. The results are presented in Figure 5, which show the final SEC-CLD of the chain-end radicals (at 1 s of integration time, before the last laser pulse is applied). It is worth mentioning that it is a cumulative distribution that contains the information of all of the chain-end radicals that were generated at different times during the reaction, and some of the chains might have multiple branching points. For example, at 20 ◦C, it is observed that increasing the laser frequency leads to the formation of peaks in the SEC-CLD of the chain-end radicals. As the frequency increases, a multimodal CLD is obtained, i.e., some of the chain-end radicals can grow by more than one dark period. These chains would terminate among them or, preferentially, with the radicals generated in the next laser pulse, leading to a well-defined PLP-CLD of the polymer. By increasing the temperature to 40 ◦C, the multimodal SEC-CLD of the growing chain-end radicals is obtained with frequencies greater than 250 Hz. Because more chain-end radicals undergo backbiting, it is necessary to have enough chains that are not affected by such reaction to recover the PLP-CLD. Increasing the frequency to 500 Hz leads to well-defined peaks in the CLD, because the accumulation of unaffected chain-end radicals is greater. The same behavior is observed at 60 ◦C, but in this temperature, the multimodality (actually, bimodality) of the CLD is presented only at

500 Hz, in which the accumulation of growing chain-end radicals that are not affected by backbiting is enough to recover the PLP-CLD of the final polymer.

**Figure 4.** Ratio of the concentration of the radicals i (i: Chain-end radicals in black and MCRs in red), divided by the concentration of the radicals generated in the laser pulse. [R0] = 10−5 moL L−1.

**Figure 5.** Final SEC-CLD of the chain-end radicals at different temperatures and laser frequencies.

The last part of the results is shown in Figure 6. This figure summarizes the results at 20 ◦C for laser frequencies of 100 and 500 Hz, but the radical concentration produced in the laser pulse [R0] is changing. In all cases, a PLP-CLD is obtained, meeting the IUPAC criteria for a good *kp* determination (more than one peak in the CLD and its derivative, and *kpi*/*kpi*+1 close to 1). Moreover, the deviation with respect to the *kp* used as input at 500 Hz and [R0] = 1 × 10−4 moL L−1 is around 15%; at 100 Hz and the same [R0], the deviation is around 7%. In the other cases, such deviation is smaller, with the smallest being at [R0] = 1 × 10−6 moL L−1 and 500 Hz. Actually, many peaks can be seen at the CLD and its derivative. These results are in agreement with the simulation results of Nikitin et al. [7], in which they demonstrated that at a minimum laser frequency and constant temperature, there is sufficient population of chain-end radicals to produce sharp peak(s) in the CLD, that is indeed independent of [R0]. Also, in the CLD obtained with the largest concentration of radicals, [R0] = 1 × 10−4 moL L−1, one can see the formation of polymer chains with low molecular mass. The concentration of chains with such low molar mass decreases as [R0] becomes lower. The reason is that due to the high concentration of growing radicals (chain-end and MCR), the cross termination of these radicals is enhanced during the dark period, still having a fraction of radicals that are terminated at the next laser pulse.

**Figure 6.** Effect of [R0] on different parameters. Left side column is at 20 ◦C and 100 Hz, whereas left side is at 20 ◦C and 500 Hz. First row, final SEC-CLDs; second row, the correspondent derivatives; third row, the degree of branching (and patched MCR in the inset) at 20 ◦C, 100 Hz (left side column) and 500 Hz (right side column). At 500 Hz and [R0] = 1 × 10−6 mol L−1, the simulation was stopped at 0.5 s due to computer memory limitations. Inserts in each graph is a zoom in a desired area.

Regarding the backbiting-to-propagation ratio, the results show that this ratio is not significantly affected. However, the degree of branching decreases as [R0] increases. Such a decrease is larger at high laser frequency of 500 Hz. In this case, the reduction of the degree of branching is due to the larger fraction of pathed MCR as [R0] increases. From these results, in order to have reliable *kp* determinations, it could be recommended to produce a low concentration of radicals in the laser pulse (by lowering the laser power and/or using a low initiator concentration), but having in mind the necessity of producing enough polymer chains for an adequate SEC measurement.

#### **4. Conclusions**

PLP-SEC experiments of *n*-butyl acrylate were simulated at different temperatures, laser frequencies, and radical concentrations produced at laser pulses. At all temperatures, the PLP-CLD was recovered as the laser frequency increased. It was shown that the recovery of PLP-CLD by increasing laser frequency is a consequence of increasing the fraction of chain-end radicals that does not undergo backbiting, which is in line with the explanation given by Nikitin et al. [7]; therefore, the degree of branching does not significantly decrease as the laser frequency increases at a fixed temperature. According to the simulation results, the ratio of backbiting to propagation reaction was not affected by the increment of the laser frequency; the ratio of quaternary carbons to the total propagation steps was rather close to the instantaneous degree of branching in all conditions. These results did not give support to other explanations given in the literature, which related the recovery of the PLP-MMD only with the decrease in the backbiting rate and, consequently, the decrease of branching density. The difference between the degree of branching with respect to the instantaneous probability of backbiting was explained by the patching of MCRs (termination reaction of the MCRs with the radicals generated in the laser pulse). By increasing laser frequency or the radical concentration at laser pulses, the patched MCRs' percentage increased, which consequently led to a lower degree of branching.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2227-9717/7/8/501/s1, Table S1 and Scheme S1: kinetic scheme and rate coefficients used in the simulations of the PLP-SEC of BA.

**Author Contributions:** Authors contributed equally.

**Funding:** This research received no external funding.

**Acknowledgments:** Yuri Reyes acknowledges the financial support of CONACyT (México). Shaghayegh Hamzehlou acknowledges the University of the Basque Country (UPV/EHU) for the "Contratación para la especialización de personal investigador doctor" postdoctoral grant.

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

#### **References**

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**1. Introduction**

Plastics are a versatile class of materials which can be found in products ranging from single-use packaging to components used in automotive and durable goods. Unfortunately, plastics are also identified as an environmental pollutant due to poor recycling rates and poor end-of-life waste management [1, 2]. This has led to many organizations, such as the Ellen MacArthur Foundation, to promote a circular economy for plastic [3].

The circular economy for plastic is based on three tenets: reducing the use of plastics, reusing a product multiple times and recycling at end of life. The first two components are directed more toward plastic packaging but recycling at end of life can be applied to all types of products and industries. Post-consumer recycled (PCR) resin is the recycled product of waste created by consumers and is defined by ISO 14021 [4]. It is commercially available from multiple suppliers, but not all grades are created equal. However, there needs to be a demand for recycled plastics for the circular economy to work properly. Regrettably, there is a misperception that recycled plastics are always inferior to virgin plastics and therefore can only be used in "down-cycled" applications. As engineers and scientists interested in both the production of high-quality products and environmental sustainability, we questioned the validity of this misperception and initiated this study to answer the following questions:

Although there are many factors associated with completely answering the questions above, the factor which we will be evaluating in this paper is strength. Strength of plastics can be quantified by measuring tensile, bending, shear, compression, flexural, and impact properties, among others. Each molded plastic resin's mechanical properties can vary depending on molecular weight, crystallinity, molding parameters, and additives/fillers. The mechanical properties can be defined by testing specimens in compliance with ASTM [5, 6] or ISO [7] testing standards. The advantages of mechanical property testing following ASTM or ISO testing standards are

A. Standard specimens can be obtained from material supplier

Since a plastic's strength degrades over time as it ages in the environment, it is crucial to take this degradation into account when designing parts. Therefore, the aging behavior of plastics needs to be understood thoroughly. As real-time aging can take a significant time (i.e., years), most aging studies are performed using accelerated aging tests utilizing temperature, temperature and humidity, temperature cycling, UV exposure, and/or chemical exposure [8]. The Arrhenius-based accelerated life model is the most popular model to understand the acceleration of aging due to temperature. The rate of reaction, *R,* based on the Arrhenius model can be explained by

$$R(T) = A e^{-\frac{E\_a}{kT}} \tag{1}$$

where *A* is a material constant; *Ea* is the activation energy (eV), *K* is the Boltzmann's constant (eV/K), and *T* (K) is the absolute temperature. Based on this model, the acceleration factor (AF) can be calculated as

$$AF = \exp\left[\frac{E\_a}{K}\left(\frac{1}{T\_u} - \frac{1}{T\_t}\right)\right] \tag{2}$$

where,

Tu is unit localized temperature during field usage (K).

Tt is unit localized temperature in the test (K).

*Effect of Environmental Aging on Tensile Properties of Post-Consumer Recycled (PCR)… DOI: http://dx.doi.org/10.5772/intechopen.99528*

Ea is activation energy.

K is Boltzmann's constant (8.617385 x10–5 eV/K).

The acceleration factor for temperature and humidity-based acceleration is derived from Peck's Model:

$$AF = \left(\frac{RH\_u}{RH\_t}\right)^{-n} \exp\left[\frac{Ea}{k}\left(\frac{1}{T\_u} - \frac{1}{T\_t}\right)\right] \tag{3}$$

where,

RHu is relative humidity in field (%).

RHt is relative humidity in the test (%).

n is a constant.

Finally, the acceleration factor for aging due to thermal cycling comes from the modified Coffin-Manson model:

$$AF = \left(\frac{\Delta T\_{test}}{\Delta T\_{field}}\right)^m \tag{4}$$

where,

ΔTtest = temperature difference in TC test (°C);

ΔTfield = temperature difference in field usage (°C);

m = Coffin-Manson exponent.

Any acceleration-based model depends on the distribution of the data that best fits. The life of a consumer product follows a bathtub curve under variable stress and can be explained better by the Weibull distribution, for which the probability density function can be explained as

$$f(t) = \frac{\beta}{a} \left(\frac{t-\gamma}{a}\right)^{\beta-1} e^{-\left(\frac{t-\gamma}{a}\right)^{\beta}}\tag{5}$$

where β is the shape parameter or slope of the curve, α is the characteristic orWeibull life, and α is the location parameter. This is true for 3 parameter Weibull distribution. Typically, γ is considered to be zero and hence the equation can be derived as

$$f(t) = \frac{\beta}{a} \left(\frac{t}{a}\right)^{\beta - 1} e^{-\left(\frac{t}{a}\right)^{\beta}} \tag{6}$$

In this chapter, the scope of the research is to focus on the performance variation of different grades of PCR compared to conventional or virgin PC after thermal cycling and high temperature & high humidity aging. The reason behind picking thermal cycling and high temperature & high humidity aging is because these two are the most common environmental exposures for consumer hardware. The effects of chemical, UV and solar aging will be reported at a later date.


**5. Dielectric relaxation and conductivity**

66 Polyurethane

compounds.

(3); Eu(fod)3 (4)

Eu(fod)3 also is considerably lower.

of europium chelate compounds on the intensity of their luminescence. The fig. 10, a illustrates the luminescent spectra of isolated Eu (3+) chelate compounds. The fig. 10, b represents the spectra of luminescence of CPU films, modified with 1%wt. of Eu (3+)

**Figure 10.** The luminescence spectra (λex. = 365 nm) of the europium (3+) chelate compounds (a) and of CPU films with 1%wt. of these chelate compounds (b): Eu(TTA)3phen (1); Eu(TTA)3ТРРО (2); Eu(TTA)3

(a) (b)

As it can be seen the luminescence of Eu (3+) chelate compounds introduced into PU matrix (only 1%wt.) is more intensive than luminescence of isolated metal chelate compounds (100% wt). In addition, the intensity of luminescence of tetra coordinated Eu(3+) chelate compounds (Eu(TTA)3phen and Eu(TTA)3TPPO) both isolated and introduced into CPU matrix, considerably exceeds such intensity for 3-coordinated Eu(3+) chelate compound Eu(TTA)3 that does not contain additional ligands The intensity of photoluminescence of

Estimation of Eu (3+) environment symmetry in various complexes via the coefficient of asymmetry (*η*) defined as ratio of intensity of 5D0 → 7F2 –transition to intensity of 5D0 → 7F1 transition. (Haopeng et al., 2008) shows that the greatest coefficient of asymmetry (*η* = 9) has CPU-1%Eu(TTA)3phen characterized by the greatest intensity of luminescence. Consequently, the presence of additional ligand in the external coordination sphere of Eu (3+) favours increasing of luminescence intensity. Then increasing of Eu-chelate compounds luminescence intensity in PU can be explained in particular by additional coordination of lanthanide ion with the functional groups of PU and/or by formation of The dielectric properties of PU were studied by broad band DRS measurements in wide range of temperature (-40 to 120 oC). The data are analyzed within the various formalisms. The direct current conductivity was both measured using two-electrode method and was estimated using DRS complex electric resistance dс =d/(ARdc) and Z"(Z') isotherms (Cole-Cole diagram). Figure 11-13 illustrate obtained dielectric spectra. Calculated conductivity values are listed in Table 5.

According to two-electrode method the direct current conductivity of PU can drastically change in the presence of some metal chelate compounds. At the room temperature dc for the CPU-5%Eu increases by one order as compared with CPU-0. In the presence of polyheteronuclear metal chelate compounds *d* enlarges from 2 to 3 orders (fig. 13, table 5). DRS analysis of complex dielectric permittivity as well as complex admittance σ\*, complex electrical modulus М\* and impedances Z', Z" allows reveal the nature of the observed conductivity.

\* The PU films synthesized with PPG-2000

a) dc measured using two-electrode method and b) dc obtained using DRS data

**Table 6.** PUs conductivity at a direct current

**Figure 11.** Log-log plots of the imaginary part of complex electrical modulus M" *vs.* frequency for CPU–5%Eu at several temperatures

Bottom-Up Nanostructured Segmented Polyurethanes with Immobilized in situ Transition and Rare-Earth Metal Chelate Compounds – Polymer Topology – Structure and Properties Relationship 69

2 max

*τ*

metal-containing PU are linear indicating the Arrhenius-type of temperature dependence of

Decreasing of max value with the increasing of Eu(3+) content in PU confirm increasing of macro chains mobility in metal-containing CPU (Kozak et al., 2006). The activation energy of conductivity relaxation for CPU-0, CPU-0,5%Eu, CPU-1%, CPU-5% are approximately similar. Experimental dependences of logdc vs. 1/T are non-Arrenius both for PU-0 and metal containing PUs. It fit the theoretical curves of Vogel–Tamman-Fulcher (VTF) equation σdc=σoexp(-B/(T-To) (fig. 13) indicating influence of the PU free volume on charge transport. The results obtained give evidence of significant influence of structural organization in the

As it can be seen PU's direct current (σdc) conductivity grows with increasing of temperature and that is characteristic to ionic conductivity. The metal ion participation as current carrier is unlikely because to small amounts of metal ion in the modified PUs (~ 0.025-0.25% wt.). That fact and coordination immobilization of the modifiers in polymer makes unlikely increasing of the conductivity due to the metal chelate compound conductive properties. On the other hand ionic mechanism of conductivity and adequate amount of protons presented in PU matrix as well as observed increasing of polymer chain mobility in modified PU

Comparison of direct current conductivity of CPU based on PPG-2000 with conductivity of CPU based on PPG-1000 shows increasing of conductivity at the direct current of such system up to 10-7Sm/sm at the 40оС due "softening" of PU. Nevertheless it can be seen that conductivity level of maximum soft LPU is at least one order lower then conductivity of CPU.

**6. "Metal chelate compound - polymer" complexing and formation of the**

Mutual influence of metal chelate compound and polymer matrix due to complex formation is a decisive reason of observed changes of structural, dynamic, relaxation etc. characteristics of the metal contained PU. The complexing of metal chelate compounds with

**6.1. The complexing of the metal chelate compound with PU matrix according to**

The electron spectroscopy allows analyse both character of complexing of metal chelate compound with the polymer matrix and state of metal chelate compound in PU. The electron spectra of transition and rare-earth metal chelate compound in PU indicate presence of the band of *d-d*-transitions for the transition metal chelate compound introduced into PU (fig.14) and band of π-π-transitions for the rare-earth metal chelate compounds

**additional network of coordination bonds in metal containing PU**

PU matrix was analysed using electron spectroscopy and EPR.

**the electron spectroscopy**

allows us to suppose proton participation in the process of charge transport.

max

*πf* ) in log scale *vs.* 1/T (fig. 12) for

Experimental dependences of relaxation time ( 1

modified PU on its conductivity level.

*τmax*.

**Figure 12.** The thermal dependence of the relaxation time (τmax) for the CPU with various content of Eu (3+) chelate compound.

**Figure 13.** The logdc vs. 1/T for CPU: (a) CPU with various length of flexible component: CPU (PPG-2000) – 1%Cu2Zn (1); CPU (PPG-1000) – 1% Cu(eacac)2 (2); CPU (PPG-2000) – 1% Cu(eacac)2 (3); CPU (PPG-2000) – 0 (4); CPU (PPG-1000) – 0 (5) and (b) CPU-0 (1) and CPU-Cu2Zn formed in the presence of various solvents: 1, 4-dioxane (2); dichloromethane (3) and DMFA (4).

The curves on the fig. 11 have well defined maxima in temperature region of 60 to 120oC. According to (Pathmanatham & Johari, 1990; Kyritsis & Pissis, 1997) these maxima correspond to conductivity relaxation. Increasing of temperature is accompanied with shift of conductivity relaxation maxima to higher frequencies (fig. 11). The fact concerned to increasing of segmental mobility in PU. The metal chelate compounds introduction and increasing of their content in the system result in increasing of PU segmental mobility.

Experimental dependences of relaxation time ( 1 2 max max *τ πf* ) in log scale *vs.* 1/T (fig. 12) for metal-containing PU are linear indicating the Arrhenius-type of temperature dependence of *τmax*.

68 Polyurethane

120 110 100 90 80 70

T,C0

0,5% Eu(fod)3

1% Eu(fod)3

1000/T,K-1

**Figure 12.** The thermal dependence of the relaxation time (τmax) for the CPU with various content of

1

lgdc(S/cm)

1000/T,K-1

presence of various solvents: 1, 4-dioxane (2); dichloromethane (3) and DMFA (4).

**Figure 13.** The logdc vs. 1/T for CPU: (a) CPU with various length of flexible component: CPU (PPG-2000) – 1%Cu2Zn (1); CPU (PPG-1000) – 1% Cu(eacac)2 (2); CPU (PPG-2000) – 1% Cu(eacac)2 (3); CPU (PPG-2000) – 0 (4); CPU (PPG-1000) – 0 (5) and (b) CPU-0 (1) and CPU-Cu2Zn formed in the

The curves on the fig. 11 have well defined maxima in temperature region of 60 to 120oC. According to (Pathmanatham & Johari, 1990; Kyritsis & Pissis, 1997) these maxima correspond to conductivity relaxation. Increasing of temperature is accompanied with shift of conductivity relaxation maxima to higher frequencies (fig. 11). The fact concerned to increasing of segmental mobility in PU. The metal chelate compounds introduction and increasing of their content in the system result in increasing of PU segmental

2,6 2,8 3,0

0% Eu(fod)3

10-4

2,5 3,0

Eu (3+) chelate compound.

mobility.

lg

dc, S/c

m

10-3

10-4

4

3 2

1

2,4 2,6 2,8 3,0 3,2 3,4

1000/T(K-1 )

5% Eu(fod)3

10-3

Decreasing of max value with the increasing of Eu(3+) content in PU confirm increasing of macro chains mobility in metal-containing CPU (Kozak et al., 2006). The activation energy of conductivity relaxation for CPU-0, CPU-0,5%Eu, CPU-1%, CPU-5% are approximately similar. Experimental dependences of logdc vs. 1/T are non-Arrenius both for PU-0 and metal containing PUs. It fit the theoretical curves of Vogel–Tamman-Fulcher (VTF) equation σdc=σoexp(-B/(T-To) (fig. 13) indicating influence of the PU free volume on charge transport. The results obtained give evidence of significant influence of structural organization in the modified PU on its conductivity level.

As it can be seen PU's direct current (σdc) conductivity grows with increasing of temperature and that is characteristic to ionic conductivity. The metal ion participation as current carrier is unlikely because to small amounts of metal ion in the modified PUs (~ 0.025-0.25% wt.). That fact and coordination immobilization of the modifiers in polymer makes unlikely increasing of the conductivity due to the metal chelate compound conductive properties. On the other hand ionic mechanism of conductivity and adequate amount of protons presented in PU matrix as well as observed increasing of polymer chain mobility in modified PU allows us to suppose proton participation in the process of charge transport.

Comparison of direct current conductivity of CPU based on PPG-2000 with conductivity of CPU based on PPG-1000 shows increasing of conductivity at the direct current of such system up to 10-7Sm/sm at the 40оС due "softening" of PU. Nevertheless it can be seen that conductivity level of maximum soft LPU is at least one order lower then conductivity of CPU.


Preface

Chapter 7 **Estrogenic Compounds in Estuarine and Coastal Water**

Maria João Rocha and Eduardo Rocha

and Daniel Junqueira Dorta

**VI** Contents

**Environments of the Iberian Western Atlantic Coast and Selected Locations Worldwide — Relevancy, Trends and Challenges in View of the EU Water Framework Directive 153**

Chapter 8 **Impact of Pesticides on Environmental and Human Health 195**

Mariana Furio Franco Bernardes, Murilo Pazin, Lilian Cristina Pereira

Since the thalidomide tragedy in the 1960s, the theme of toxicology has advanced rapidly over the past decade with emerging innovative toxicity testing protocols, techniques, and regulation being placed. While the discipline of toxicology can be rather complex, having a comprehensive understanding of the principles and mechanisms of foreign substances that can cause toxicity is important for consumers to make decisions about the risks and benefits inherent to issues pertaining to human diseases. Since the bioactivation of many toxins and toxicants and its consequences on human health are not clearly known, special emphasis is devoted by scientists worldwide to understanding how drugs, environmental chemicals and industrial pollutants can cause adverse heath effects. This book provides a unique, integrat‐ ed approach addressing the theory and mechanisms of toxicity, current cutting-edge meth‐ odologies of toxicology, and applications from the latest toxicological studies relevant to human diseases.

Toxicology studies on cell, drug and environment bring the most current state of evidence regarding the role of distinctive toxicants in different living systems. There are three main sections in this book concerning the bases of mitochondrial dysfunction, drug toxicology and environmental toxicology. In the first section, the book puts singular prominence on the effects of toxicants, mainly reactive oxidative species in the cellular level ("Pathological As‐ pects with Global Impact Induced by Toxicants at Cellular Level") leading to mitochondrial dysfunction induced by anticancer agents ("Mitochondrial Dysfunction on the Toxic Effects of Anticancer Agents— From Lab Bench to Bedside") and drug development targeting the mitochondria ("Mitochondrial Targeting for Drug Development") in the pathophysiology of various diseases.

The second section, entitled "Drug Toxicology", explores the effects of xenobiotics under the forensic perspective ("Forensic Toxicology"), introducing different methods and approaches in biological and non-biological matter. In the same section, the clinical manifestations and life-threatening signs/symptoms of tramadol poisoning are also discussed ("Tramadol Poi‐ soning"), bringing important aspects of drug administration.

Finally, the third section explores environmental toxicology. Three chapters are included in this section about the potential deleterious environmental impacts on human health. The first chapter ("How to Answer the Question — Are Drugs Real Threats to Biological Sys‐ tems or Overrated Innocuous Chemicals?") explores a wide-spectrum of the effects of sub‐ stances and its interactions with the biota. The effects of estrogenic endocrine disruptors compounds in water environments are also discussed ("Estrogenic Compounds in Estuarine and Coastal Water Environments of the Iberian Western Atlantic Coast and Selected Loca‐ tions Worldwide — Relevancy, Trends and Challenges in View of the EU Water Framework

Directive), followed by the impact of pesticides on human health ("Impact of Pesticides on Environmental and Human Health").

In this book, 20 prominent experts have equally contributed to develop and explore the sci‐ entific progress that has been made over the last decades in the toxicology field. We are con‐ fident that this book will serve as a guide for researchers and students.

**Ana Cristina Andreazza and Gustavo Scola**

University of Toronto Canada **Bases of Mitochondrial Dysfunction**

Directive), followed by the impact of pesticides on human health ("Impact of Pesticides on

In this book, 20 prominent experts have equally contributed to develop and explore the sci‐ entific progress that has been made over the last decades in the toxicology field. We are con‐

**Ana Cristina Andreazza and Gustavo Scola**

University of Toronto

Canada

fident that this book will serve as a guide for researchers and students.

Environmental and Human Health").

VIII Preface