is fitted to the spatial profile. Here, I is the normalized pixel intensity, x is the distance along the loop, B0 and B1 are appropriate constants, and A0, Ld, λ, and φ are the amplitude, damping length, wavelength and phase of the oscillation, respectively. Applying the Levenberg-Marquardt least-squares minimization technique (Markwardt, 2009), the best fitment to the data is shown as a black solid curve in **Figure 2A**. The damping length of the oscillation, as estimated from the fitted curve, is 3.7±0.4 Mm. The orange diamond symbols in **Figure 2B** display the damping lengths obtained from all 35 selected loop structures, plotted as a function of the corresponding localized temperature on a log-log scale. The vertical bars denote the respective uncertainties on damping length derived from the fit whereas the horizontal bars highlight the associated uncertainties on temperature propagated from the respective errors given by the regularized inversion method (Hannah and Kontar, 2012). Since the temperature is determined from a double-Gaussian fit to the individual DEMs (Krishna Prasad et al., 2018), the uncertainty on peak location is estimated by scaling the corresponding error on the nearest point by a factor of 1/ √ N, where, N is the number of data points involved in the fit. Subsequently, to get a representative temperature value for each loop, a weighted mean across all spatio-temporal locations near the foot point is considered. The associated uncertainty is then estimated from the weighted standard deviation of values across the same locations. It may be noted that the uncertainties on loop temperature reported by Krishna Prasad et al. (2018) are fairly small compared to those shown here (**Figure 2B**) which is because the authors did not incorporate the temperature errors given by the DEM inversion method but simply quoted the errors obtained from the Gaussian fit alone. The actual temperature values might also marginally differ because of the weighted averages employed here. Another important aspect to note here is that in about 5 cases, the damping lengths are measured from pairs of loops from the same active region some of which exhibit distinct values. The differences in values obtained in such cases reflect the different physical conditions of the loop structures despite belonging to the same active region.

### 3.2. Amplitude Tracking Method

Since the phase tracking method involves manually choosing a specific temporal location from each of the time-distance maps, it is possible that such human intervention naturally biases the obtained results. Also, it is not trivial to apply this technique to all temporal locations since the signal-to-noise at a large number of locations is low due to aspects of amplitude modulation. To circumvent this problem and verify the reliability of our results, we estimate the damping lengths using the alternative technique of amplitude tracking. In this method, the amplitude of the oscillation, A, at each spatial position is directly measured in relation to the standard deviation, σ, of the respective filtered time series using A = √ 2σ. This formula assumes that the observed oscillations can be represented by a pure sinusoidal signal. The time-averaged intensities from the original time series (i.e., collapsing the time domain in **Figure 1b**) are used as the background for normalization to obtain relative amplitudes as a function of distance along the loop. Since the amplitude at each spatial position is derived from the full time series, the median error on respective pixel intensities is used to estimate the corresponding uncertainty. The diamond symbols in **Figure 3A** show the spatial dependence of amplitude values thus obtained for the fan-like loop structure highlighted in **Figure 1a**. The vertical bars represent the associated uncertainties. These data were then fit with a decaying exponential model satisfying the functional form,

$$A(\mathbf{x}) = A\_0 \, e^{\left(\frac{-\mathbf{x}}{T\_d}\right)} + \mathbf{C} \,, \tag{2}$$

where x is the distance along the loop, A0 and C are appropriate constants, and Ld is the damping length.

The initial few locations where the wave amplitude is found to increase are ignored in order to isolate the purely decaying phase of the oscillation for fitment. The black solid line in **Figure 3A** represents the best exponential fit obtained. The corresponding damping length is 4.8 ± 1.5 Mm, which is on the same order as that obtained using the phase tracking method outlined in section 3.1. Following the same procedure, the damping lengths for the oscillations observed in all 35 selected loop structures have been estimated. For a handful of loop structures, it is found that the model does not converge properly, producing damping lengths either far greater than the loop length itself (> 1000 Mm) or far less than one pixel (< 0.1 Mm). Upon inspection of the time-distance maps corresponding to these individual cases, we found that there are unusual brightenings, perhaps in the form of transient events manifesting in the loop background, at certain spatiotemporal locations, which naturally contaminate the amplitude extraction process and thereby prevent a robust fitment of the data. While this could be avoided by manually restricting the time series for each particular case, the main strength of this method was in the alleviation of human intervention. As such, we chose to ignore specific loop structures where the model fitting did not converge to commonly expected values. The orange diamond symbols in **Figure 3B** represent the damping lengths obtained from the remaining 31 cases, plotted as a function of the loop temperature on a log-log scale. The vertical bars highlight the corresponding uncertainties on damping length whereas the horizontal bars denote the respective uncertainties on temperature. The loop temperature and the associated uncertainties are estimated in the same way as that described in section 3.1.

# 3.3. Theoretical Calculations

Theoretical and numerical calculations in the past have suggested that thermal conduction is the dominant physical mechanism responsible for the damping of slow magnetoacoustic waves in the solar corona (De Moortel and Hood, 2003; Klimchuk et al., 2004). Considering one-dimensional linear wave theory for slow magnetoacoustic waves with thermal conduction as the damping mechanism (e.g., De Moortel and Hood, 2003; Krishna Prasad et al., 2012b), the dispersion relation between the wave number, k, and the angular frequency, ω, can be shown to be,

$$
\rho \mathcal{L}\_s^4 k^4 + i\alpha \mathcal{c}\_s^2 k^2 - \mathcal{y} \, d\alpha^2 \mathcal{c}\_s^2 k^2 - i\alpha^3 = 0 \,. \tag{3}
$$

Here, cs is the sound speed, d = (γ −1)κkT0 γ c 2 s p0 is the thermal conduction parameter, κk = κ0T 5/2 0 is the parallel thermal conduction, and p0 = 2n0kBT0 is the gas pressure, where κ0 is the thermal conduction coefficient, T0 is the equilibrium temperature, and n0 is the number density. For propagating waves, the frequency, ω, is constant and in the limit of weak thermal conduction (i.e., when dω ≪ 1), the solutions for wave number, k, may be found as k = ω cs −i 1 Ld , where Ld = 2cs dω2 (γ −1) is the damping length. The interested reader is referred to Mandal et al. (2016) for a detailed derivation.

FIGURE 2 | (A) Spatial variation of the relative intensity at the temporal location marked by the white dashed line in Figure 1c. The vertical bars denote the respective uncertainties. The solid curve represents the best fit to the data for an exponentially decaying sine wave model following Equation (1). The obtained damping length value from the fitted curve is listed in the upper-right corner of the plot. (B) Damping lengths extracted from all of the selected loop structures, plotted as a function of the localized temperature on a log-log scale. The orange diamonds represent the values obtained following the phase tracking method shown in (A), whereas the green circles represent the theoretical values estimated from damping due to thermal conduction. The open and filled circles, respectively, highlight the values computed from a constant γ (= 5/3) and those computed using γ values extracted from observations (Krishna Prasad et al., 2018). The vertical and horizontal bars on the observed values denote the corresponding propagated uncertainties.

FIGURE 3 | (A) Relative amplitudes of the oscillations as a function of distance along the loop segment marked by the solid blue lines in Figure 1a. The vertical bars denote the respective uncertainties. The black solid line represents an exponential fit to the decaying phase of the data following Equation (2). The obtained damping length value from the fitted curve is listed in the plot. (B) Damping lengths extracted from all the selected loop structures plotted as a function of the local temperature on a log-log scale. The orange diamonds represent the observational values following the amplitude tracking method shown in (A), whereas the green circles represent the theoretical values estimated from the damping due to thermal conduction. The open and filled circles, respectively, highlight the values computed from a constant γ (= 5/3) and those computed using γ values extracted from observations (Krishna Prasad et al., 2018). The vertical and horizontal bars on the observed values denote the corresponding uncertainties.

As described in section 3, Krishna Prasad et al. (2018) studied the same set of loop structures that are presented here. They applied a regularized inversion method (Hannah and Kontar, 2012) on observed intensities in 6 coronal channels of SDO/AIA to compute corresponding DEM. Subsequently, by employing a double-Gaussian fit to the DEM curve, the temperature and the density of the plasma are calculated from the peak location and the area under the curve, respectively. The density is estimated by assuming the apparent width of the loop as equivalent to the emission depth along the line of sight effectively ignoring any background/foreground emission although a contribution to the latter from hot plasma is carefully discarded from the double-Gaussian fit. Using the theoretical relation between the relative oscillation amplitudes in temperature and density associated with a slow wave, the polytropic index of the plasma is determined after eliminating the corresponding phase shifts. The periodicity of the oscillations is also calculated through a simple Fourier analysis on the intensity fluctuations. Utilizing the respective values of these parameters computed by Krishna Prasad et al. (2018) for each loop, we estimate the expected damping lengths from the above theory.

The filled green circle symbols shown in **Figures 2B**, **3B** represent the theoretically computed values. It may be noted that the respective dω values were found to reside in the interval 0.01 − 0.16, so the assumption of weak thermal conduction (i.e., dω ≪ 1) is inherently valid across our range of coronal datasets. The classical Spitzer values for thermal conduction, following κk = 7.8 × 10−7T 5/2 0 ergs cm−1 s −1 K −1 , are employed in our calculations. As can be seen from the figures, the damping lengths are expected to be considerably shorter for hotter loops. Since it is very common to assume the polytropic index, γ , is equal to 5/3 in the solar corona, we additionally compute damping lengths arising from a constant (5/3) value for γ . The open green circles shown in **Figures 2B**, **3B** represent these values which suggest a similar but much shallower dependence on temperature. Moreover, the damping lengths in this case are shorter by up to an order of magnitude or more which clearly divulges the effect of polytropic index on the damping length. It is worth noting here that the scatter in the theoretically computed damping lengths is mainly due to the different physical conditions of the loop structures studied.

# 4. DISCUSSION AND CONCLUDING REMARKS

The spatial damping characteristics of propagating slow magnetoacoustic waves, observed in 35 fan-like loop structures selected from 30 different active regions, have been studied. The damping length, in particular, is measured using two independent methods: a phase tracking method and an amplitude tracking method. Employing the temperature information acquired from DEM analysis, the temperature dependence of the damping length has been investigated for the first time (**Figures 2B**, **3B**). These results do not indicate any apparent decrease in damping length with temperature as would be expected by the stronger thermal conduction in that case. It may be noted that the results from previous studies (e.g., Krishna Prasad et al., 2012b), who based their conclusions on the measurement of damping lengths for a single loop structure observed in multiple temperature channels, are inconsistent with the current findings. However, those studies are purely qualitative and the results are often based on just two temperature channels. Furthermore, the sensitivities of the measured damping lengths from the intensity perturbations to the filter/instrument used (e.g., Klimchuk et al., 2004) are also not taken into consideration in previous studies. In the present case, we employ damping length measurements from multiple loop structures observed in the same filter (SDO/AIA 171 Å). Hence, we naturally consider the current results more reliable due to the conservation of instrument characteristics across all independent measurements.

Utilizing the temperatures, densities, polytropic indices, and oscillation periods that have previously been derived for the same set of loop structures (Krishna Prasad et al., 2018), we calculated the theoretical damping lengths expected from the dissipation due to thermal conduction. In contrast to the observations, the theoretical calculations show a steep decrease in the damping length with temperature. Damping lengths were also computed assuming a fixed value, 5/3, for the polytropic index, in line with the previous studies. These values display a similar but shallower dependence. The discrepancy between the observational and theoretical dependences perhaps indicates that thermal conduction is suppressed in hotter loop structures. In fact, the increase in the polytropic indices of these loops with temperature, as reported by Krishna Prasad et al. (2018), also implies the suppression of thermal conduction in hotter loops (e.g., in accordance with Wang et al., 2015), although a direct conclusion could not be drawn from these results alone since the polytropic index of the coronal plasma is dependent on several other physical processes besides thermal conduction. The current results, on the other hand, appear to show direct evidence for the suppression of thermal conduction with increasing temperature.

Alternatively, one could argue that thermal conduction is perhaps not the dominant damping mechanism for slow magnetoacoustic waves, as previously reported by Marsh et al. (2011) and Wang et al. (2015). Indeed, as can be seen from **Figures 2B**, **3B**, the theoretical damping lengths are 2 − 3 orders of magnitude higher than those obtained from the observations. One may also note that a simple visual inspection of oscillation amplitudes, in **Figures 1b,c** for example, reveals significant damping within 10 Mm scales whereas the expected damping lengths due to thermal conduction are at least 100 Mm or more which clearly demonstrates the extent of mismatch between the observations and the theory. The differences in the temperature dependence would further add to this discrepancy. We note, however, that the incongruity between the theory and observations is less if we consider the calculations for γ = 5/3. Also, the distances measured along the observed loop structures are projected onto the image plane, meaning the obtained damping lengths are only lower limits. Nevertheless, the difference between the theoretical and the observed scales is too large to ignore, and would not likely be accounted for even if a fractional contribution from the other damping mechanisms (e.g., compressive viscosity and optically thin radiation) is included.

Lastly, we would like to bring out some of the major caveats of our results. The temperature range of the loops investigated is limited especially considering the large uncertainties on temperature. While the magnitude of change in the expected damping lengths over the same temperature range and the extent of mismatch between the observed and theoretical values still make our results valid, it is imperative to state that a larger temperature range would make the results more reliable. Additionally, it should be noted that different DEM inversion methods can result in different peak temperatures although the difference can be marginal depending on the temperature range investigated. Also, it can be argued whether the peak emission in a DEM sufficiently represents the plasma within the loop. Keeping these limitations in mind, we believe further investigations, both theoretical and observational, are necessary to understand the damping of slow magnetoacoustic waves in the solar corona. In particular, the impetus is on increasing the temperature range studied to include hotter loop structures to examine whether these traits are consistent across the full spectrum of coronal magnetism.

# DATA AVAILABILITY

The data analyzed in this study was obtained by the Atmospheric Imaging Assembly onboard NASA's Solar Dynamics Observatory. The data are not restricted, and requests to access these datasets should be directed to the Joint Science Operations Center (http://jsoc.stanford.edu/ajax/lookdata.html).

## AUTHOR CONTRIBUTIONS

SK and DJ planned and designed the study. SK processed the data, performed the analysis and wrote the first draft of the manuscript. TV assisted in theoretical calculations. DJ and TV contributed to the interpretation of the results. All authors took part in the manuscript revision, read and approved the submitted version.

#### REFERENCES

### FUNDING

The authors gratefully acknowledge the financial support from the following research grants: STFC—ST/K004220/1, ST/L002744/1, ST/R000891/1, Randox Laboratories Ltd.— 059RDEN-1, European Research Council (ERC)—724326, and KU Leuven—GOA-2015-014.

### ACKNOWLEDGMENTS

The authors thank all the referees for their valuable comments/suggestions. SK would like to thank the UK Science and Technology Facilities Council (STFC) for support. DJ gratefully acknowledges STFC for the award of an Ernest Rutherford Fellowship, in addition to Invest NI and Randox Laboratories Ltd. for the award of a Research & Development Grant (059RDEN-1). This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme and KU Leuven. The SDO/AIA imaging data employed in this work are courtesy of NASA/SDO and the AIA science team. We acknowledge the use of pipeline developed by Rob Rutten to extract, process, and co-align AIA cutout data.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Krishna Prasad, Jess and Van Doorsselaere. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.


**3. Addition of polymers or biopolymers**

Studies on additives as salts and cosolvents have been widely investigated in the past and will not be reported, unless this is strictly necessary. Conversely, studies on systems containing synthetic polymers or biopolymers are still a matter of debate and investigation and will be discussed in this section. The first efforts along this line go back to the 1950s and were essentially dealing with protein separation from biological membrane lipids. These efforts were led to convergence in a classical textbook of the early 1990s [22]. This induced many scientists to focus on new and, sometimes, controversial fields [23–25].

The underlying phenomenology can be understood by looking at **Figure 1**. In the plot the behavior of a ternary system containing water, surfactant, and polymer is reported. If the relative *wt%* of the latter substances is much lower than water, the ternary phase diagram can be simplified in a pseudo-binary one. As can be seen in **Figure 1**, a pseudo-phase behavior occurs in absence of polymer; the *cmc* is the point separating the micellar from the molecular regime. Added polymer induces the splitting of the solution phase into three regions. For finite amounts of polymer, the following areas are observed, from the left:

#### **Figure 1.**

*The surfactant behavior in presence of a nonionic polymer. The black line in the left bottom of the figure indicates the molecular solution region and the dotted one the micellar regime. The turquoise area indicates the molecular regime and is limited by the cac, above which the surfactant starts to interact with the polymer. The red area indicates the interaction regime; the yellow one, the saturation regime, occurs when the polymer is saturated. The line separating the red and yellow regions is indicated as cmc\* line.*

i. a molecular solution region, *I*;

ii. a polymer-surfactant one, *II*; and

iii. a region where free micelles coexist with polymer-surfactant adducts, *III*.

To build up the phase map, surface tension values are measured for a number of polymer *wt%* (**Figure 2**). There splitting of surface tension values in three regimes is evident. *Cac* and *cmc\** are easily determined form these and other experiments, as well [22].

On thermodynamic grounds, the line separating region *I* from *II* indicates the points above which polymer/surfactant interactions start to occur; the line position depends on polymer content and nature. There is an ensemble of critical points, whose location in the phase map depends on the polymer amount. Once the process has occurred, the surfactants located on the polymer backbone act as nucleation sites for the binding of more surface-active species. Thus, entities similar to micelles (*emi-micelles*) aggregate thereon: a sort of "pearl necklace" is formed [26]. Thus, the polymer backbone is decorated by a series of small aggregates, whose number is dictated by its length; the interacting polymer sections, the so termed "polymer

**47**

**Figure 2.**

assume during the flow.

*Surfactant Mixtures: Performances vs. Aggregation States DOI: http://dx.doi.org/10.5772/intechopen.85437*

binding sites", are a few kdalton long. Surfactant nucleation thereon continues until all possible sites are saturated. In consequence of that, the polymer tends to assume a different conformation with respect to the native one, with subsequent changes in viscosity. This is the reason why polymer/surfactant systems act as "viscosity modulators" [27, 28]. Another important consequence is the fact that they are "kinetic

*Plot indicating how to get the cac, the first minimum, and the cmc\*, at surface saturation, for a given amount of polymer vs. surfactant content. Black points refer to data in presence of polymer, the red ones to the surfactant alone.*

Ancillary effects are concomitant to the mentioned behavior. First, micelles of smaller size compared with free ones are formed; they behave as a whole kinetic entity with the polymer (i.e., the binding energy is significant). This is a feature similar to those occurring in biological systems, as in the binding of molecules to the protruding parts of a receptor. The line separating the two regions is defined as "critical aggregation concentration" or *cac* line. The nucleation of fat droplets on a cotton string is a pertinent example for the formation of polymer-surfactant adducts; their location thereon is energetically more favored than in free form. The *cmc\** one, conversely, is a polymer saturation threshold, above which there is no room for binding. As a consequence, free micelles do form and coexist with polymer-adsorbed ones. Technological applications find place in formulation. The viscoelastic properties that such systems exhibit are used in shampoos, eye-drop fluids, etc. [30, 31]. Viscoelasticity is simply detected by abruptly rotating the fluid-containing vials, with transient formation of ellipsoidal bubbles or, in a more quantitative way, by rheology [27, 28]. An alternative simple procedure requires pressing drops of these formulations between glass slides and looking by a polarizing microscope, to detect the preferred orientation that polymer-surfactant adducts

There is no significant difference when polyelectrolytes replace nonionic polymers. In cases like such, precipitation may also occur; cases are known [32], mostly as to biopolymers are concerned [33–36]. In mixtures containing proteins, precipitates or, eventually, two-phase regions are usually met. As a rule, these are centered around the charge neutralization line, where precipitates or gels may coexist (**Figure 3**). In such systems relevant are the modifications observed in

buffers" as to matter exchange with the bulk is concerned [29].

*Surfactant Mixtures: Performances vs. Aggregation States DOI: http://dx.doi.org/10.5772/intechopen.85437*

#### **Figure 2.**

*Surfactants and Detergents*

i. a molecular solution region, *I*;

experiments, as well [22].

ii. a polymer-surfactant one, *II*; and

*saturated. The line separating the red and yellow regions is indicated as cmc\* line.*

iii. a region where free micelles coexist with polymer-surfactant adducts, *III*.

*The surfactant behavior in presence of a nonionic polymer. The black line in the left bottom of the figure indicates the molecular solution region and the dotted one the micellar regime. The turquoise area indicates the molecular regime and is limited by the cac, above which the surfactant starts to interact with the polymer. The red area indicates the interaction regime; the yellow one, the saturation regime, occurs when the polymer is*

To build up the phase map, surface tension values are measured for a number of polymer *wt%* (**Figure 2**). There splitting of surface tension values in three regimes is evident. *Cac* and *cmc\** are easily determined form these and other

On thermodynamic grounds, the line separating region *I* from *II* indicates the points above which polymer/surfactant interactions start to occur; the line position depends on polymer content and nature. There is an ensemble of critical points, whose location in the phase map depends on the polymer amount. Once the process has occurred, the surfactants located on the polymer backbone act as nucleation sites for the binding of more surface-active species. Thus, entities similar to micelles (*emi-micelles*) aggregate thereon: a sort of "pearl necklace" is formed [26]. Thus, the polymer backbone is decorated by a series of small aggregates, whose number is dictated by its length; the interacting polymer sections, the so termed "polymer

**46**

**Figure 1.**

*Plot indicating how to get the cac, the first minimum, and the cmc\*, at surface saturation, for a given amount of polymer vs. surfactant content. Black points refer to data in presence of polymer, the red ones to the surfactant alone.*

binding sites", are a few kdalton long. Surfactant nucleation thereon continues until all possible sites are saturated. In consequence of that, the polymer tends to assume a different conformation with respect to the native one, with subsequent changes in viscosity. This is the reason why polymer/surfactant systems act as "viscosity modulators" [27, 28]. Another important consequence is the fact that they are "kinetic buffers" as to matter exchange with the bulk is concerned [29].

Ancillary effects are concomitant to the mentioned behavior. First, micelles of smaller size compared with free ones are formed; they behave as a whole kinetic entity with the polymer (i.e., the binding energy is significant). This is a feature similar to those occurring in biological systems, as in the binding of molecules to the protruding parts of a receptor. The line separating the two regions is defined as "critical aggregation concentration" or *cac* line. The nucleation of fat droplets on a cotton string is a pertinent example for the formation of polymer-surfactant adducts; their location thereon is energetically more favored than in free form. The *cmc\** one, conversely, is a polymer saturation threshold, above which there is no room for binding. As a consequence, free micelles do form and coexist with polymer-adsorbed ones. Technological applications find place in formulation. The viscoelastic properties that such systems exhibit are used in shampoos, eye-drop fluids, etc. [30, 31]. Viscoelasticity is simply detected by abruptly rotating the fluid-containing vials, with transient formation of ellipsoidal bubbles or, in a more quantitative way, by rheology [27, 28]. An alternative simple procedure requires pressing drops of these formulations between glass slides and looking by a polarizing microscope, to detect the preferred orientation that polymer-surfactant adducts assume during the flow.

There is no significant difference when polyelectrolytes replace nonionic polymers. In cases like such, precipitation may also occur; cases are known [32], mostly as to biopolymers are concerned [33–36]. In mixtures containing proteins, precipitates or, eventually, two-phase regions are usually met. As a rule, these are centered around the charge neutralization line, where precipitates or gels may coexist (**Figure 3**). In such systems relevant are the modifications observed in

**Figure 3.**

*Partial phase diagram for the system water-lysozyme-lithium perfluorononanoate (a stiff, fully fluorinated surfactant), at 25°C. The coexistence of a solution and precipitate occurs in the black area, whereas a pure gel, in dark gray, and one empty of particles, in light gray, are met. The charge neutralization limit is indicated as a blue line. This is the point at which all nominal charges on the protein, at the given pH, are fully neutralized. Partly redrawn from Ref. [26].*

protein conformation. Changes in the relative amounts of alpha-helix, beta-sheet, and random coil conformations are concomitant to protein-surfactant interactions in a wide part of the interaction regime. Such changes are responsible for significant variations in protein activity and three-dimensional structure of the "adducts" that are formed. All these systems are characterized by a not univocally defined stoichiometry, and the definition of "adduct" is more correct with respect to that of "complex." The rationale underlying that behavior finds origin in the fact that alkyl chains are essentially located in the protein hydrophobic tasks. Many possible locations are available in cases like such. The above statements are quite well acquainted from experiments on albumins and, more generally, on protein denaturation strategies [37]. Thus, biopolymer/surfactant systems offer the opportunity to prepare proteins in pure form from extensive dialysis of the corresponding mixtures. For these reasons they find extensive use in biochemically intended procedures.

## **4. Mixtures made of oppositely charged surfactants**

Pioneering studies in the field are due to Wennerstroem [38], who focused on the synthetic analogues of lipids and suggested that stoichiometric mixtures of oppositely charged surfactants could be good substitutes of lipids. The original hypothesis dealt with systems of 1–1 stoichiometry, in terms of charge. There, the electrostatic interactions between polar groups mimic charge separation among entities bound on a glycerol backbone, which is also joining two alkyl chains. The above systems are models of swelling, lamellar domains. The first experimental results were discouraging; in fact, these mixtures often show thermotropic rather than lyotropic behavior [39], due to the high "Krafft point" [40] of alkyl chains in such mixtures. Later work demonstrated that nonstoichiometric *Cat-An* mixtures were more promising. It was noticed there the presence of vesicular entities [41, 42]. Debates occurred on the stability of largely polydispersed in size vesicles. It is actually accepted that they are kinetically stable entities although thermodynamic stability is demonstrated in some cases [43, 44].

The phenomenology of such systems, defined by the acronym "cat-anionic," is extremely appealing from a bio-intended viewpoint. In the phase diagram, in particular, the vesicular areas are located in proximity of micellar ones and are clearly

**49**

*Surfactant Mixtures: Performances vs. Aggregation States DOI: http://dx.doi.org/10.5772/intechopen.85437*

distinguishable from them. The observation is in favor of a significant modification in the micellar structure induced by the second surfactant. Cat-anionic mixtures, hereafter termed *Cat-An*'s, are characterized by a bluish color and may turn to yellowish or opalescent appearance when vesicle sizes exceed some 100 nms. They are both positively and negatively charged. This fact gives the opportunity to use *Cat-An* vesicles as vehiculating/binding agents of DNA (for positively charged ones) and proteins. In the latter eventuality, both positively and negatively charged

Debates questioned on the possible protein denaturation that could be induced by the surfactants present in *Cat-An* formulations, until it was realized that the surfactant in molecular form is solely responsible for protein denaturation [45]. The amount of such species is orders of magnitude lower than in solutions of the single surfactants. The above behavior is supported by the following thermodynamic considerations. The mutual interactions between polar head groups and alkyl chain packing play a key role in such systems. The observed behavior is different from that expected if ideality of mixing holds. In words, when fluid chains are presumably miscible in all proportions, the effect of surface charges modulates the area on which alkyl chains insist and determines their optimal packing. This results in a strong nonideality of mixing. It is not surprising, therefore, that the *cmc* for an aggregate of given stoichiometry can be orders of magnitude lower than expected from primitive considerations. To quantify such effects, it was assumed the validity of regular solution theory, and it was imposed, accordingly, that "the free monomer has an activity coefficient of unity" [46]. This is an oversimplified viewpoint, since surfactant solutions are strongly nonideal even below the *cmc*. To proceed along, we assume that the concentration above which added surfactant preferentially enters into aggregates (disregarding their size and shape) is the saturation threshold for the molecular species. In this way, the difference in composition between molecular and micellar form is immaterial. In two-component surfactant mixtures, thus, the

vesicles may be used, depending on the demand dictated by protein charge.

*cmc* of the mixed system is defined according to the relation [47].

parameter, *b*, results to be [47].

*b* = ∆*Gexc*,*mixt*[(*X*2

cargos for proteins and DNA [49–51].

(1/*cmcmixt*) = [(*X*2/3 *cmc*3) + (1 − *X*2)/2 *cmc*2)] (2)

where *γ*2 and *γ*3 are the activity coefficients of the surfactants, having *cmc3* and *cmc2* as the corresponding critical values. *cmcmix*t is the critical concentration of the mixed system. *X*'s are the mole fraction of the given surface-active species. In the limits dictated by the regular solution theory [48], the solute-solute interaction

> 2 + *X*3 2 )/(*X*2 2*X*3 2

The underlying rationale is as follows. Micelles are in fluid state with freely moving polar head groups. They may change position, adsorb/desorb counterions, and so forth. The constraints acting on alkyl chains are such that polar head groups close each other attract/repel. In consequence of that, mixed systems show strong deviations from the ideal behavior. This tendency is quantified by the mentioned *b* parameter. The effect is substantial (**Figure 4**) and explains why the amount of both surfactants in molecular form is orders of magnitude lower than expected. In words, *Cat-An*'s are in equilibrium with their own counterions and with tiny amounts of free surfactants, as well. This is the basis for using cat-anionic vesicles as

Sizes of *Cat-An* vesicles strongly depend on the formulation stoichiometry. As mentioned above, 1–1 mixtures form indefinitely large smectic crystals; on both sides of this threshold, sizes depend regularly on composition and approach values

)] (3)

#### *Surfactant Mixtures: Performances vs. Aggregation States DOI: http://dx.doi.org/10.5772/intechopen.85437*

*Surfactants and Detergents*

**Figure 3.**

*Partly redrawn from Ref. [26].*

protein conformation. Changes in the relative amounts of alpha-helix, beta-sheet, and random coil conformations are concomitant to protein-surfactant interactions in a wide part of the interaction regime. Such changes are responsible for significant variations in protein activity and three-dimensional structure of the "adducts" that are formed. All these systems are characterized by a not univocally defined stoichiometry, and the definition of "adduct" is more correct with respect to that of "complex." The rationale underlying that behavior finds origin in the fact that alkyl chains are essentially located in the protein hydrophobic tasks. Many possible locations are available in cases like such. The above statements are quite well acquainted from experiments on albumins and, more generally, on protein denaturation strategies [37]. Thus, biopolymer/surfactant systems offer the opportunity to prepare proteins in pure form from extensive dialysis of the corresponding mixtures. For these reasons they find extensive use in biochemically intended procedures.

*Partial phase diagram for the system water-lysozyme-lithium perfluorononanoate (a stiff, fully fluorinated surfactant), at 25°C. The coexistence of a solution and precipitate occurs in the black area, whereas a pure gel, in dark gray, and one empty of particles, in light gray, are met. The charge neutralization limit is indicated as a blue line. This is the point at which all nominal charges on the protein, at the given pH, are fully neutralized.*

Pioneering studies in the field are due to Wennerstroem [38], who focused on the synthetic analogues of lipids and suggested that stoichiometric mixtures of oppositely charged surfactants could be good substitutes of lipids. The original hypothesis dealt with systems of 1–1 stoichiometry, in terms of charge. There, the electrostatic interactions between polar groups mimic charge separation among entities bound on a glycerol backbone, which is also joining two alkyl chains. The above systems are models of swelling, lamellar domains. The first experimental results were discouraging; in fact, these mixtures often show thermotropic rather than lyotropic behavior [39], due to the high "Krafft point" [40] of alkyl chains in such mixtures. Later work demonstrated that nonstoichiometric *Cat-An* mixtures were more promising. It was noticed there the presence of vesicular entities [41, 42]. Debates occurred on the stability of largely polydispersed in size vesicles. It is actually accepted that they are kinetically stable entities although thermodynamic

The phenomenology of such systems, defined by the acronym "cat-anionic," is extremely appealing from a bio-intended viewpoint. In the phase diagram, in particular, the vesicular areas are located in proximity of micellar ones and are clearly

**4. Mixtures made of oppositely charged surfactants**

stability is demonstrated in some cases [43, 44].

**48**

distinguishable from them. The observation is in favor of a significant modification in the micellar structure induced by the second surfactant. Cat-anionic mixtures, hereafter termed *Cat-An*'s, are characterized by a bluish color and may turn to yellowish or opalescent appearance when vesicle sizes exceed some 100 nms. They are both positively and negatively charged. This fact gives the opportunity to use *Cat-An* vesicles as vehiculating/binding agents of DNA (for positively charged ones) and proteins. In the latter eventuality, both positively and negatively charged vesicles may be used, depending on the demand dictated by protein charge.

Debates questioned on the possible protein denaturation that could be induced by the surfactants present in *Cat-An* formulations, until it was realized that the surfactant in molecular form is solely responsible for protein denaturation [45]. The amount of such species is orders of magnitude lower than in solutions of the single surfactants.

The above behavior is supported by the following thermodynamic considerations. The mutual interactions between polar head groups and alkyl chain packing play a key role in such systems. The observed behavior is different from that expected if ideality of mixing holds. In words, when fluid chains are presumably miscible in all proportions, the effect of surface charges modulates the area on which alkyl chains insist and determines their optimal packing. This results in a strong nonideality of mixing. It is not surprising, therefore, that the *cmc* for an aggregate of given stoichiometry can be orders of magnitude lower than expected from primitive considerations. To quantify such effects, it was assumed the validity of regular solution theory, and it was imposed, accordingly, that "the free monomer has an activity coefficient of unity" [46]. This is an oversimplified viewpoint, since surfactant solutions are strongly nonideal even below the *cmc*. To proceed along, we assume that the concentration above which added surfactant preferentially enters into aggregates (disregarding their size and shape) is the saturation threshold for the molecular species. In this way, the difference in composition between molecular and micellar form is immaterial. In two-component surfactant mixtures, thus, the *cmc* of the mixed system is defined according to the relation [47].

$$\left(\mathbf{1}/cmc\_{\rm mix}\right) = \left[\left(X\_2/\gamma\_3cmc\_3\right) + \left(\mathbf{1} - X\_2\right)/\gamma\_2cmc\_2\right] \tag{2}$$

where *γ*2 and *γ*3 are the activity coefficients of the surfactants, having *cmc3* and *cmc2* as the corresponding critical values. *cmcmix*t is the critical concentration of the mixed system. *X*'s are the mole fraction of the given surface-active species. In the limits dictated by the regular solution theory [48], the solute-solute interaction parameter, *b*, results to be [47].

$$b = \Delta G\_{\text{exc}, \text{mix}} \left[ \left( X\_2^{\ 2} + X\_3^{\ 2} \right) / \left( X\_2^{\ 2} X\_3^{\ 2} \right) \right] \tag{3}$$

The underlying rationale is as follows. Micelles are in fluid state with freely moving polar head groups. They may change position, adsorb/desorb counterions, and so forth. The constraints acting on alkyl chains are such that polar head groups close each other attract/repel. In consequence of that, mixed systems show strong deviations from the ideal behavior. This tendency is quantified by the mentioned *b* parameter. The effect is substantial (**Figure 4**) and explains why the amount of both surfactants in molecular form is orders of magnitude lower than expected. In words, *Cat-An*'s are in equilibrium with their own counterions and with tiny amounts of free surfactants, as well. This is the basis for using cat-anionic vesicles as cargos for proteins and DNA [49–51].

Sizes of *Cat-An* vesicles strongly depend on the formulation stoichiometry. As mentioned above, 1–1 mixtures form indefinitely large smectic crystals; on both sides of this threshold, sizes depend regularly on composition and approach values

#### **Figure 4.**

*Dependence of the cmc (in mol kg−1 ) on cetyltrimethylammonium bromide, CTAB, mole fraction for SDS-CTAB mixtures, at 25°C. The red line is for visual purposes; the full on the top refers to ideal mixing and the vertical to the nonideality of mixing. The blue area indicates the precipitation regime.*

#### **Figure 5.**

*Vesicle size (in nm) for SDS-CTAB mixtures, at 25°C, vs. the nominal surface charge excess of the vesicular aggregate. The light blue area in the center of the figure refers to the precipitation regime.*

**51**

provided the original work is properly cited.

applications on more conscious grounds.

\* and Gianfranco Risuleo2

1 Department Chemistry, Sapienza University, Rome, Italy

\*Address all correspondence to<EMAIL_ADDRESS>
2 Formerly at Department Biology, Sapienza University, Rome, Italy

*Surfactant Mixtures: Performances vs. Aggregation States DOI: http://dx.doi.org/10.5772/intechopen.85437*

accordingly retain their size for indefinitely long times.

**5. Conclusions**

**Author details**

Camillo La Mesa1

pertinent to the pure surfactant aggregates. In words, the excess surface charge determines vesicles sizes (**Figure 5**). It is worth to note that similar trends are also observed in mixtures of oppositely charged lipids [52]. The surface charge versatility is reminiscent of statements based on the relations between particles size and surface charge density. The higher the former, the lower the latter. This fact has important consequences on the links between (nominal) surface charge density and sizes. It is a sort of charge-based size tailoring and is quintessential in choosing the proper particles for transfection technologies. Another pertinent possibility along this line arises from thermal cycling procedures, which allow getting stable particles of proper size by raising the temperature above a certain value (which depends on the composition of the *Cat-An* mixture [53]. Thermally quenched vesicles obtained

Sound procedures based on the combination of the above features allow getting vesicles of the desired size and surface charge density. This allows using them for DNA transfection technologies and protein immobilization onto vesicles [54]. An interesting feature is that vesicles of a given composition are destroyed by adding amounts of surfactant required for the complete neutralization of the *Cat-An* mixture. In consequence of that, the biopolymer which is eventually bound onto vesicles is released in its

This contribution focuses on the possibilities offered by surfactants and their mixtures in selected bio-intended applications. The mentioned systems are niche fields, but are becoming of relevant impact in a lot of practical purposes. Think, for instance, that applications in shampoos and similar products almost always include silk proteins as adjuvants of hair state and health. Transfection, conversely, is quite appealing for biochemistry and molecular biology applications. In many aspects, thus, both fields of research are on the same line as those originally intended in the pre-Christian age. It is as if we were moving back to the roots of surfactancy. Luckily, we have much more knowledge in the field, and this allows us to exploit

pristine form [55]. This is a terrific possibility for bio-intended technologies.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Surfactant Mixtures: Performances vs. Aggregation States DOI: http://dx.doi.org/10.5772/intechopen.85437*

pertinent to the pure surfactant aggregates. In words, the excess surface charge determines vesicles sizes (**Figure 5**). It is worth to note that similar trends are also observed in mixtures of oppositely charged lipids [52]. The surface charge versatility is reminiscent of statements based on the relations between particles size and surface charge density. The higher the former, the lower the latter. This fact has important consequences on the links between (nominal) surface charge density and sizes. It is a sort of charge-based size tailoring and is quintessential in choosing the proper particles for transfection technologies. Another pertinent possibility along this line arises from thermal cycling procedures, which allow getting stable particles of proper size by raising the temperature above a certain value (which depends on the composition of the *Cat-An* mixture [53]. Thermally quenched vesicles obtained accordingly retain their size for indefinitely long times.

Sound procedures based on the combination of the above features allow getting vesicles of the desired size and surface charge density. This allows using them for DNA transfection technologies and protein immobilization onto vesicles [54]. An interesting feature is that vesicles of a given composition are destroyed by adding amounts of surfactant required for the complete neutralization of the *Cat-An* mixture. In consequence of that, the biopolymer which is eventually bound onto vesicles is released in its pristine form [55]. This is a terrific possibility for bio-intended technologies.

### **5. Conclusions**

*Surfactants and Detergents*

**50**

**Figure 5.**

**Figure 4.**

*Dependence of the cmc (in mol kg−1*

*Vesicle size (in nm) for SDS-CTAB mixtures, at 25°C, vs. the nominal surface charge excess of the vesicular*

*) on cetyltrimethylammonium bromide, CTAB, mole fraction for SDS-*

*CTAB mixtures, at 25°C. The red line is for visual purposes; the full on the top refers to ideal mixing and the*

*vertical to the nonideality of mixing. The blue area indicates the precipitation regime.*

*aggregate. The light blue area in the center of the figure refers to the precipitation regime.*

This contribution focuses on the possibilities offered by surfactants and their mixtures in selected bio-intended applications. The mentioned systems are niche fields, but are becoming of relevant impact in a lot of practical purposes. Think, for instance, that applications in shampoos and similar products almost always include silk proteins as adjuvants of hair state and health. Transfection, conversely, is quite appealing for biochemistry and molecular biology applications. In many aspects, thus, both fields of research are on the same line as those originally intended in the pre-Christian age. It is as if we were moving back to the roots of surfactancy. Luckily, we have much more knowledge in the field, and this allows us to exploit applications on more conscious grounds.

### **Author details**

Camillo La Mesa1 \* and Gianfranco Risuleo2

1 Department Chemistry, Sapienza University, Rome, Italy

2 Formerly at Department Biology, Sapienza University, Rome, Italy

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**ECOTOXICOLOGY**

Edited by **Ghousia Begum**

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http://dx.doi.org/10.5772/1185 Edited by Ghousia Begum

#### **Contributors**

Elvira Maria Gaspar, Sara Raquel Rato Pires, João Filipe Lopes, Inês Santos Nunes, Margarita Topashka-Ancheva, Tsvetelina Gerasimova, Elke Cardoso, Gian Luigi Mariottini, Sabria Barka, Petr Dvorak, Semra Soydam Aydin, Sümer Aras, Didem Aksoy Körpe, Çiğdem Dönmez

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First published in Croatia, 2012 by INTECH d.o.o. eBook (PDF) Published by IN TECH d.o.o. Place and year of publication of eBook (PDF): Rijeka, 2019. IntechOpen is the global imprint of IN TECH d.o.o. Printed in Croatia

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**Abstract**

The human skin is pivotal for protecting the body from various stresses and diseases, regulating several physiological aspects, and sensing any signal changes around the environment. To work and function optimally, the skin should be protected and cared regularly by using some treatments. Chalcone, as a privileged structure, exhibits wide and unique bioactivities related to several skin disorders such as in preventing and treating pigmentation disorders (melasma and vitiligo), cutaneous leishmaniasis, rashes (acne vulgaris, seborrheic dermatitis and dandruff, psoriasis and atopic dermatitis), and rosacea. In this chapter, the role of chalcone derivatives in treating several skin disorders as mentioned above is discussed to provide a brief and comprehensive perspective regarding the role of chalcone in dermatology including in vitro, preclinical, and clinical assays.

**Keywords:** chalcones, dermatology, skin disorder, bioactivity, skin treatment


**4. Angiotensin receptor blockers (ARBs)**

ARBs preferentially block AT1 and leave AT2 unopposed. Long-term administration of ARBs results in a several-fold increase in plasma Ang and thus a possible overstimulation of AT2. It is generally accepted that the effects of stimulation of AT2 on the cardiovascular system are beneficial and that no harm would result from increased activation of these receptors; indeed, activation of AT2 is believed to contribute to the benefits of blocking AT1 (Levy, 2004).

Various ARBs were screened for their role in the treatment of acute myocarditis and are found to have significant activity against acute myocarditis. ARBs prevent progression of systolic heart failure, thereby reducing cardiac morbidity and mortality (Lindholm et al., 2002; Cohn & Tognoni, 2001). They also reduce myocardial damage during myocarditis. The major cardiovascular actions of Ang II have been reported to be mediated by the AT1, and AT1 antagonists are therapeutically effective for the treatment of patients with heart failure by reducing cytokines and oxidative stress through their anti-inflammatory effects. Thus, the blockade of AT1 is an important way to interrupt the RAS (Sukumaran et al., 2010). Recently, an AT1 antagonist has been shown to ameliorate EAM by the suppression of myocardial damage and inflammatory events in the myocardium in addition to hemodynamic modifications, and it has been reported to inhibit nitric oxide (NO) production in macrophages and IL 1 production. ARB treatment decreased myocardial fibrosis and its marker molecules (i.e. RNA expression of TGF-1 and collagen-III), and improved the survival rate and cardiac function in rats with DCM after myocarditis in a dose dependent manner. Treatment with oral ARB improved both systolic and diastolic functions, increased neurohormonal parameter, such as plasma Ang II, and ameliorated myocardial remodeling and its marker molecules (Sukumaran et al., 2010, 2011a, 2011b; Shirai et al., 2005).


**3.1.4 Aminolysis**

Aminolysis is another method of chemical degradation of PET, which has been relatively little investigated, compared to the other techniques.

Fig. 7. Using of BHET (glycolysis product of PET waste) to obtain other materials.

Depolymerization of PET waste has been carried out using various amines, such as ethanolamine, benzylamine, hexamethylenediamine, aniline, methylamine hydrazine monohydrate and some polyamines. Catalysts such as lead acetate, glacial acetic acid, sodium acetate and potassium sulfate are usually used to facilitate the reaction. Aminolysis

waste have been well known to be utilized as a starting material in the manufacture of unsaturated polyesters, vinyl ester resins, epoxy resins, alkyd resins and polyurethanes. Glycolysis is carried out using different glycols like; ethylene glycol, propylene glycol, 1, 4 butanediol and triethylene glycol, diethylene glycol (DEG), dipropylene glycol (DPG), glycerol (Gly) and etc. During glycolysis reaction, the organic group R″ of an ester with the organic group R′ of an alcohol exchanges. (Shamsi R et al, 2009; Mohamadi et al, 2010 & M.

Methanolysis is the degradation of PET using methanol at high temperatures and high pressures with the main products being dimethyl terephthalate (DMT) and ethylene glycol. Methanolysis is the recycling process which has been practiced and tested on a large scale for many years in the past. In this case, polyester waste is transformed with methanol into DMT (Dimethyl terephthalate), under pressure and in presence of catalysts. Finally the crude DMT is purified by vacuum distillation. Degradation of PET using ethylene glycol at high temperatures and high pressures with the main products being BHET is used to produce some different materials such as polyester, polyurethane resins and esteric

Aminolysis is another method of chemical degradation of PET, which has been relatively

Fig. 7. Using of BHET (glycolysis product of PET waste) to obtain other materials.

Depolymerization of PET waste has been carried out using various amines, such as ethanolamine, benzylamine, hexamethylenediamine, aniline, methylamine hydrazine monohydrate and some polyamines. Catalysts such as lead acetate, glacial acetic acid, sodium acetate and potassium sulfate are usually used to facilitate the reaction. Aminolysis

M. Sadeghi G et al, 2011)

plasticizer, as shown in Fig. 7.

little investigated, compared to the other techniques.

**3.1.4 Aminolysis**

**3.1.3 Methanolysis**

products, such as BHETA, have the potential to undergo further reactions to yield secondary value-added products. In this direction, very recently the synthesis of unsaturated polyesters polyurethanes, epoxy resin hardeners and non-ionic polymeric surfactants has been reported.

$$\begin{array}{c} \text{O} \\ \text{-C-}\bigotimes \text{-C-}\bigotimes \text{-CH}\_{2}\text{-CH}\_{2}\text{-O-}\bigotimes \\ \qquad \Big\downarrow \\ \text{H}\_{3}\text{C-N-}\text{-C-}\bigotimes \text{-CH}\_{2}\text{-CH}\_{3}\text{-CH}\_{2}\text{-CH}\_{2}\text{-CH}\_{2}\text{-CH}\_{2}\text{-OH}-\text{H}\text{-}\text{H}\text{-}\text{CH}\_{2}\text{-CH}\_{2}\text{-OH} \end{array}$$

Fig. 8. Aminolysis reaction.

Zahn and Pfeifer carried out aminolysis of PET with solutions of hydrazine, benzyl amine, ethylene diamine, hexamethylene diamine, piperidine and aniline. They obtained different reaction products as the diamides of terephthalic acid, which do not possess any potential for further chemical reactions. According to Popoola the basicity of an amine relative to water as well as its steric hindrance due to size determines the rate of degradation of PET. During aminolysis of PET with methylamine, the methyl terephthalamide is obtained, which isn't enough reactive for its recycling into any useful product through further reactions. Shukla and Harad have been investigated the use of ethanolamine for the aminolytic degradation of PET waste in the presence of different simple chemicals such as glacial acetic acid, sodium acetate and potassium sulphate as catalysts. The product obtained, BHETA has potential for further reactions to obtain useful products.

#### **4. Polyurethane**

Polyurethane is any polymer composed of a chain of organic units joined by carbamate (urethane) links. Polyurethane polymers are formed through step-growth polymerization, by reacting a reactant (with at least two isocyanate functional groups) with another reactant (with at least two hydroxyl or alcohol groups) in the presence of a catalyst. Generalized formation reaction of the urethane group is:

$$\text{R}-\text{NCO} + \text{R}'-\text{OH} \quad \rightarrow \quad \text{R}-\text{NH}-\text{COO}-\text{R}'$$

Thermoplastic polyurethanes (TPUs) are linear polymers formed by the polymerization reaction of three basic components:

As shown in the above reactionurethane linkage is produced by reacting an isocyanate group,—N=C=O with a hydroxyl (alcohol) group,—OH. In fact, polyurethanes are produced by the polyaddition reaction of a polyisocyanate with a polyalcohol (polyol) in the presence of a catalyst and other additives. The reaction product is a polymer containing the urethane linkage, -RNHCOOR'-. A broad range of physical properties can be achieved by varying the chemistry and molecular weight of the various components, and through

From PET Waste to Novel Polyurethanes 365

**4.2.1. Hard Segments** which are segments formed by the reaction of the diisocyanate and the short-chain diol. They have a high density of urethane groups of high polarity, and for

**4.2.2. Soft Segments** which are segments formed by the reaction of the diisocyanate and the long-chain diol. They have a low polarity as they have a very low density of urethane groups, and therefore, they are flexible at room temperature (very low hardness). A general

The polarity of hard segments produces a strong attraction between them, which causes a high degree of aggregation and order in this phase, forming crystalline or pseudo-crystalline areas located in a soft and flexible matrix. This so-called phase separation between both blocks will be more or less important, depending on the polarity and molecular weight of the flexible chain, the production conditions, etc. The crystalline or pseudo-crystalline areas act as a physical crosslink, which accounts for the high elasticity level of TPUs, where as the flexible chains will impart the elongation characteristics to the polymer. The schematic representation of the segmented micro structure and two-phase morphology of polyurethane are shown in Figs. 10 and 11. These "pseudo crosslinks" , based on hydrogen bonding between carbonyl groups and –NH groups of various chains , however, disappear under the effect of heat, and thus the classical extrusion, injection molding and calendaring

Fig. 10. Schematic represent of microstructure of segmented polyurethane chains.

Consequently –and not less importantly- TPU scraps can be reprocessed. When TPUs are cold, the "pseudocrosslinks" reappear again, providing the elastic properties to the obtained

this reason, they are rigid at room temperature (high hardness).

structure of thermoplastic polyurethane's chain would be as Fig. 9:

Fig. 9. General structure of polyurethane's chain.

processing methods are applicable to these materials.

manipulation of the ratios in which they are reacted in polyurethanes. Therefore polyurethanes have received recent attention as regards the development of wide family of polymeric materials (paints, adhesives, elastomers, flexible, and rigid foams, etc.) and thus play an important and increasing role in our daily life. The greatest advantage offered by polyurethane is their versatility, both in finished product properties and ease of production and application. By the proper choice of isocyanate and polyol, products can be made with properties ranging from low viscosity resins used in printing to high modulus solids used in industrial parts. Polyurethanes are applied to the manufacture of flexible, high-resilience foam seating; rigid foam insulation panels; microcellular foam seals and gaskets; durable elastomeric wheels and tires; automotive suspension bushings; electrical potting compounds; high performance adhesives; surface coatings and surface sealants; synthetic fibers (e.g. Spandex); carpet underlay; and hard-plastic parts (i.e. for electronic instruments) and any other industrial parts.


4. Strategies to tailor the kinetic behavior of hydride compounds and systems

Investigations on the kinetic tailoring to improve the hydrogen storage properties of hydride compounds and hydride systems involve knowledge about the thermodynamic behavior and kinetic behavior of the hydride system. First, equilibrium pressures at different temperatures are needed to plan the experimental pressure and temperature for the characterization of the kinetic behavior. Second, some knowledge about the mechanism(s) that constraint the overall reaction rates is also required. For this reason, it is important to know or at least have clues about possible rate-limiting steps for the hydrogenation/dehydrogenation processes, as well as the influence of the temperature and pressure dependences on the reaction rates. In this regard, knowledge about K(T) allows quantifying in terms of Ea the effects of a tailoring strategy. In this line, knowledge of F(P) dependence is usually necessary to properly determine K(T). All these understanding about the thermodynamics and kinetics of the hydride compound or system matter of investigation enormously contribute to seek the best strategy to improve it hydrogenation/dehydrogenation reaction rates. Of course, there are several opportunities in which kinetic improvements for a hydride compound or system are proposed based just on a simple experimental procedure; without any previous systematic study about the thermodynamics and kinetics. This approach is also possible, but it leads to a superficial knowledge about the actual kinetic improvement and to a poor understanding of the behavior of the hydride compound or system.

The most relevant approaches to enhance the kinetic behavior of hydride compounds and systems are: (1) improving the microstructural refinement via mechanical milling, (2) doping with transition metal and transition metal compounds, (3) forming in situ catalyst, and (4) nanoconfinement. In this section, the concepts of these strategies are explained and examples for their practical application to hydride compounds and systems are also described [58–96].

In general, two or three of these strategies are applied together, as for example mechanical milling, transition metal, or transition metal compound addition and in situ catalyst formation or nanoconfinement and transition metal or compound addition, etc. However, it is possible to put emphasis on the each strategy in order to understand what the specific effects are on the hydride forming, regardless the combined application of them.

3.4 Pressure dependence F(P)

Gold Nanoparticles - Reaching New Heights

Table 5.

140

Pressure dependencies, their physical mining, and rate-limiting step.

At constant temperature, the hydrogenation/dehydrogenation reactions show a dependence on a functional relationship between the operative pressure (P) and the equilibrium pressure (Peq) for both hydrogenation and dehydrogenation processes. This dependence is called F(P). Table 5 describes the most relevant F(P) applied to different materials and their physical meaning. These functions were obtained from experimental investigations and proposed in pioneering works about the kinetic


**5. Conclusions**

RSA is a very good and reliable treatment option with low complication rates for proximal humerus head-split fractures in the older patient population. Patients who sustain a head-split fracture due to high-impact trauma have greater biological and regenerative potential that can lead to more promising outcomes. Comminution or multifragmentation of the articular face presents as a prognostic indicator for significantly poorer outcome.

**Author Contributions:** Conceptualization, J.-P.I., U.B. and M.S.; methodology, J.-P.I., U.B. and M.S.; formal analysis, T.I.; investigation, J.-P.I.; data curation, M.S., U.B.; writing—original draft preparation, J.-P.I.; writing—review and editing, U.B., F.F., D.E., M.S.; visualization, J.-P.I., T.I.; supervision, M.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding. **Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Institutional Review Board (or Ethics Committee) of Charité—Universitaetsmedicine Berlin (EA1/167/18; date of approval: 11 November 2018) and Ludwig-Maximilians-Universitaet Muenchen (22-0178; date of approval: 6 April 2022).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** Data available on request due to ethical restrictions. The data presented in this study are available on request from the corresponding author. The data are not publicly available.

**Acknowledgments:** The authors thank M. Wilhelmi, (medical writer at Schulthess Clinic) for manuscript proofreading.

**Conflicts of Interest:** J.-P.I., T.I., F.F. and D.E. declare no conflict of interest. M.S. and U.B. are consultants for Stryker Corporation.


**2. MALDI-MS**

MALDI-MS was developed from laser desorption/ionization mass spectrometry (LDI-MS). The first LDI-MS experiment for high-mass molecules was reported in 1987 (Tanaka et al., 1987). In this experiment, a powder of cobalt metal in glycerol was used for the observation of ions with a mass to charge (*m/z*) ratio of 34,000. Soon afterward, MALDI-MS results of serum albumin (67,000 Da) were reported using nicotinic acid as the matrix (Karas & Hillenkamp, 1988). It was reported that MALDI-MS can detect a wide range of molecules ranging from small (*m/z* <1000) to large molecules (*m/z* >1,000,000) (Yates, 1998). The schema of MALDI-MS is shown in Figure 1.

In routine MALDI-MS analysis (i.e., non-imaging analysis), the analyte can be mixed with an excess of matrix. On the other hand, molecular imaging of tissue sections using MALDI-IMS requires the tissue surface to be homogeneously covered by a matrix. On-tissue

Application of Matrix-Assisted Laser Desorption/Ionization Imaging Mass Spectrometry 439

sectioning, and washing), choice of matrix and matrix application, measurement, and data analysis. To obtain meaningful biological images, all steps need to be carefully controlled. In this section, the basic experimental MALDI-IMS procedures are described. The schema of

After biological study (a), the tissue of interest should be appropriately isolated (b). A thin section of isolated tissue is mounted on a glass slide (c), coated with matrix (d), and measured by a mass spectrometer (e). The resultant mass spectra (f) can be used for a data mining approach (g). Molecules of interest can be visualized (f) and identified by MS/MS on tissue (f).

The samples for MALDI-IMS come from a variety of biological sources, including organs, whole animal body dosed with a pharmaceutical compound, or pathological tissues. Optimization of the sample preparation procedure according to the chemical and physical properties of analytes is important. Here, the basic sample preparation steps for MALDI-

Collection and treatment procedures need to be sufficiently fast to prevent rapid tissue degradation, because the sample degradation process starts immediately after the cessation of blood flow. The most preferred sample for MALDI-IMS is a chemically unmodified freshfrozen one. Fresh-frozen samples can be prepared using dry ice, liquid nitrogen, or liquid nitrogen-chilled isopentane, and can be preserved in a deep freezer until required. The samples should be well sealed to prevent drying during storage, and it is important to

ensure that the tissue section morphology is well preserved before MALDI-IMS.

MALDI-IMS is presented in Figure 2.

Fig. 2. Schema of MALDI-IMS.

**3.1 Biological sample preparation**

**3.1.1 Sample condition for MALDI-IMS**

IMS are described.

application of matrix results in the *in situ* extraction of molecules from biological tissues. The cocrystal of matrix and analyte molecules in tissue is irradiated with a pulsed laser of appropriate energy, leading to desorption and ionization of the matrix and analyte molecules. The fragmentation of analyte molecules is prevented by the incorporation of the analyte molecules into matrix crystals. The role of the optical absorption of the matrix in the transfer of energy from the laser beam to the analyte molecules is governed by Beer's law, as described previously (Karas et al., 1985). However, the mechanisms underlying the formation of charged matrix and analyte molecules in the MALDI process are not fully understood.

Fig. 1. Schema of MALDI-MS.

The matrix molecules absorb the laser energy and facilitate desorption and ionization of analyte molecules in the tissue. The homogeneous matrix cover is important for MALDI-IMS, because a heterogeneous distribution of matrix results in different ionization efficiencies of analyte molecules based on their location.


**Joong-Ki Hwang**

School of Mechanical Engineering, Tongmyong University, Busan 48520, Korea<EMAIL_ADDRESS>Tel.: +82-51-629-1567

Received: 20 April 2020; Accepted: 15 July 2020; Published: 20 July 2020

**Abstract:** The effect of the roll design on the strain distribution of the flat surface, lateral spreading, and the strain inhomogeneity of a flat-rolled wire were investigated during the flat rolling process. Oval-grooved and cambered rolls with various radii were applied to the flat rolling process based on a numerical simulation. The effective strain on the flat surface of the wire increased when using a cambered roll due to the highly intensified contact pressure on the flat surface, while the effective strain on the flat surface of the wire decreased when using an oval-grooved roll. Lateral spreading decreased when using an oval-grooved roll because the spread in the free surface area of the wire was highly restricted by the oval-grooved roll shape. In contrast, the spread in the surface area increased when using a cambered roll due to the less-restricted metal flow at the free surface. Accordingly, a cambered roll with a small radius is highly recommended in order to improve the surface quality of flat-rolled wires. This is beneficial for industrial plants because the cambered roll can be easily applied in flat rolling plants.

**Keywords:** roll design; flat-rolled wire; strain inhomogeneity; normal pressure; macroscopic shear bands


*2.4. Homomorphic Filter*

In order to solve the localization task, typical situations may happen such as lighting variations and changes in the position of some objects (chairs, tables, open doors, etc.). Hence, descriptors must be robust against these circumstances.

Fernandez et al. [41] showed that some pre-treatments could improve the localization accuracy in indoor environments with different lighting levels. Among the studied techniques, the use of the homomorphic filter [42] can be highlighted. The homomorphic filter permits filtering the luminance and reflectance components from an image separately.

The use of this filter has proven to provide especially good results when it is used in combination with the HOG descriptor [31], whereas in the FS and *gist* cases, the results were similar to or worse than without this pre-treatment filter. Hence, in the present paper, the following configurations will be used throughout the experiments: FS without filter, HOG with filter, and *gist* without filter.


**2. Results and Discussion**

In the production of radioisotopes for nuclear medicine, automation of the radiochemical separation process of the radioisotope of interest from the target and contaminants is necessary to make the results reproducible, minimize losses of radioactive material, decrease process times, and maximize recovery yields. Not least, automation allows for drastic reduction of radiation exposure to the operator conducting the separation.

Recently, we developed a separation and purification module based on the liquid– liquid extraction method applied to the cyclotron-production of 99mTc from target of metallic molybdenum. Despite this system being extremely efficient, it requires rather long process times for the extraction of technetium with MEK with gas bubbling (helium or argon) within a glass separation column, and subsequent separation of the phases.

The purpose of this work was to develop a different, more compact, and efficient, automatic system for the extraction of 99mTc from molybdenum, based on the liquid–liquid in-flow extraction process and separation with a membrane separator device, which would allow for minimization of costs, times, dimensions and involved volumes, while keeping high yield and quality.

The Zaiput device (Figure 1), a membrane separator, was therefore selected as the heart of the automatic system that allows two immiscible phases to be separated, taking advantage of the interfacial tension between them and the affinity of one of the two phases for a microporous membrane. Thanks to a differential pressure applied inside the device from a simple diaphragm, the separation can take place continuously [32]. This system allows the macro process of solvent extraction to be reduced to a micro scale, and therefore follows flow chemistry laws.

While the device takes care of the phase's separation, the liquid–liquid extraction, in which the two phases are put in intimate contact allowing for solute transfer, takes place inside a capillary according to flow chemistry [38–41]. The capillary, optimized in terms of length and diameter and wrapped in a loop to minimize space, allows the two co-injected phases to alternate, forming a sort of train technically called the slug-flow regime. This typical micro-arrangement of phases is optimal for liquid–liquid extraction, as it allows the surface/volume ratio of the phases to be maximized, and therefore the ability to transfer solutes according to the chemical affinities involved [34,36,40].

In a preliminary phase, a prototype of the automatic system was assembled and tested with the aim of optimizing the flow rates of the biphasic system (NaOH 6 M/MEK) to achieve a proper separation. Subsequently, "cold" tests (without radioactivity) were performed to optimize the process conditions (volumes, transfer speed, slug-flow regime, loop dimensions, residence times of the sample in the loop, speed, and separation times). Capillary dimensions (ETFE capillary loop 1/8 inch, length = 106 cm; internal diameter 1.59 mm; internal volume about 2.1 mL) and flow rate (0.5 mL/min) are calibrated to maximize the contact between the two phases by achieving a slug-flow regime), the most suitable regime for liquid–liquid extraction on a micro-scale [40]. A schematic diagram of the overall system as it was assembled and installed is reported in Figure 2.

**Figure 2.** Diagram of the extraction and separation system.

In order to assess how the efficiency of the extraction and separation system concerned, three "hot" tests (with radioactivity) were performed. The separation tests were carried out by adding 99mTc-sodium pertechnetate eluted by a 99Mo/99mTc generator in order to trace the activity in the process phases and to determine its efficiency. The collected results, summarized in Table 1, show that the system is able to quantitatively and selectively extract and separate (91.0 ± 1.8% decay corrected) the [99mTc]TcO4Na in about 20 min.

After the phase separation, the 99mTcO4 − contained in the organic solution was purified through a silica and an alumina column, in order to remove molybdate traces and the MEK solvent, respectively. Finally, [99mTc]TcO4 − was collected from the alumina column with saline. In Table 2, chemical (CP) and radiochemical (RCP) purity values of the [99mTc]TcO4 − solution obtained at the end of the overall procedure is reported. Post-

separation purification with column cartridges allows a pharmaceutical product compliant with the Pharmacopoeia standards to be obtained.

**Table 2.** CP and RCP of [99mTc]TcO4 − obtained at the end of the overall procedure of this work compared with the European pharmacopeia requirements for injection, other solvent-extraction-based techniques from the literature, and the quality of [ 99mTc]TcO4 − eluted from a UTK generator (Curium). \* EU Phar. = European Pharmacopoeia.

Given the high 99mTc extraction yield and purity achieved, this system can be efficiently involved in the separation of technetium from both low and high specific activity molybdenum. In the case of indirect technetium production, the generator-like extraction of 99mTc from low specific activity 99Mo can be performed running the protocol described here. Moreover, following further decay of 99Mo into 99mTc, the molybdenum-rich aqueous phase coming out from the separator system, can be recirculated to the capillary loop and to the separator with fresh organic solvent for the extraction and separation of 99mTc in continuous. Finally, the extraction process, starting with an alkaline aqueous solution of molybdenum, allows extension of the application of the system to not only the treatment of molybdenum metal targets, but also to oxides.