*Article* **Surface Energy of Au Nanoparticles Depending on Their Size and Shape**

#### **David Holec 1,\*, Phillip Dumitraschkewitz 2, Dieter Vollath 3 and Franz Dieter Fischer 4**

Received: 14 February 2020; Accepted: 5 March 2020; Published: 8 March 2020

**Abstract:** Motivated by often contradictory literature reports on the dependence of the surface energy of gold nanoparticles on the variety of its size and shape, we performed an atomistic study combining molecular mechanics and ab initio calculations. We show that, in the case of Au nanocubes, their surface energy converges to the value for (001) facets of bulk crystals. A fast convergence to a single valued surface energy is predicted also for nanospheres. However, the value of the surface energy is larger in this case than that of any low-index surface facet of bulk Au crystal. This fact can be explained by the complex structure of the surface with an extensive number of broken bonds due to edge and corner atoms. A similar trend was obtained also for the case of cuboctahedrons. Since the exact surface area of the nanoparticles is an ill-defined quantity, we have introduced the surface-induced excess energy and discuss this quantity as a function of (i) number of atoms forming the nano-object or (ii) characteristic size of the nano-object. In case (i), a universal power-law behaviour was obtained independent of the nanoparticle shape. Importantly, we show that the size-dependence of the surface energy is hugely reduced, if the surface area correction is considered due to its expansion by the electronic cloud, a phenomenon specifically important for small nanoparticles.

**Keywords:** surface energy; nanoparticles; gold; ab initio; molecular mechanics

#### **1. Introduction**

Surface energy is an important thermodynamic quantity. Particularly in cases where the volume-to-surface ratio becomes small, as is the case of nanoparticles, its relevance must not be underestimated [1,2].

There has been a vivid discussion concerning the qualitative trend of the surface energy as a function of the nanoparticle size. On the one hand, in many cases one finds reports on decreasing surface energy with decreasing particle size, e.g., in a study by Vollath and Fischer [3] or earlier studies [4,5]. This trend has been conventionally explained with an increasing tendency to form a liquid-like structure at the surface of the particles [6]. On the other hand, there exists a number of primarily theoretical papers finding a significant increase of the surface energy with decreasing particle size, see, e.g., Refs. [7–9]. Furthermore, there are also some heavily disputed experimental results indicating an increasing surface stress (and hence, due to a conventional assumption, also surface energy) with decreasing particle size [10,11]. Nanda et al. [11] pointed out that the difference between various reported trends stems from the nanoparticle nature. The surface energy is expected to increase for free nanoparticles with decreasing particle size, while the opposite trend is obtained for nanoparticles embedded in a matrix.

Wei and Chen [12] pointed out that, from the theoretical point of view, the trend could be qualitatively altered by changing the definition of a nanoparticle surface area. Unlike the energy change related to forming the free surface of a nanoparticle, the area is not well defined. Consequently, small changes of the radius/size yield large changes of the surface area, especially for nanometre-sized particles [12]. The rather geometrical argumentation of Ref. [12] was later linked to a physical quantity, a spatial expansion of the electronic cloud [13]. Using a refined, physically-based surface for small nanoparticles consequently leads to a weak-to-no size dependence of surface energy [14,15]. The latter reference also provided a thermodynamical-based model with predictive capabilities, hence seemingly resolving the enigma regarding the size dependence of the surface energy.

Nanoparticles, and particularly gold nanoparticles, nonetheless present a rich area of application as well as curiosity-driven research. Their applications span from biomimetic materials, over printed electronics to electrochemical biosensors [16,17]. Quite counterintuitively, the most preferable structure of a 55 Au atoms cluster was shown to be an amorphous structure even at 0 K [18], being a consequence of the small nanoparticle size. This prediction, however, was experimentally corroborated [18]. Ali et al. [9] predicted a rapid increase of the surface energy upon the nanoparticle melting. In agreement with earlier work of Shim et al. [19], they also predicted the decrease of melting temperature with decreasing nanoparticle size. Spontaneous segregation to some facets has been reported for Au-Ni nanoparticles, leading to an overall isotropic elastic response [20]. Another interesting effect is the shape variety of nanoparticles, accessible via solution synthesis modifying the surface energy in its very essence [17,21].

In the present study we, therefore, employ atomistic simulations to study the impact of nanoparticle shape on the resulting surface energy estimation. We focus on shapes ranging from rather artificial but geometrically simple nanocubes, over cuboctahedrons (special members of the truncated octahedrons, which have been reported as equilibrium shapes of Au nanoparticle), to nanospheres. In the final section we discuss how is the shape and size dependence of the surface-induced excess energy (i.e., the total nanoparticle surface energy) are related to number of broken bonds due to the creation of the free surface.

#### **2. Methodology**

Molecular mechanics (MM) simulations were performed using the LAMMPS package [22] together with an interatomic potential describing the gold interatomic interaction within the embedded atom method (EAM) as parametrised by Grochola et al. [23]. The individual idealised nanoparticles with well-defined shapes were cut out from bulk fcc structure with lattice constants of 4.0694 Å. This was obtained from fitting calculated total energies corresponding to different bulk volumes with Birch-Murnaghan equation of state [24], and agrees well with the values 4.0701 Å obtained by Grochola et al. [23]. All models were structurally relaxed using conjugate-gradient energy minimisation scheme at 0 K with force-stopping convergence criterion set to 10−12 eV/Å.

Additionally, a few ab initio runs were performed to benchmark our MM calculations. We used Vienna Ab initio Simulation Package (VASP) [25,26] implementation of Density Functional Theory (DFT) [27,28]. Two common approximations of the electronic exchange and correlation effects were considered: local density approximation (LDA) [28] and the Perdew–Wang parametrisation of the generalised gradient approximation (GGA) [29]. The contribution of ions and core electrons were described by projector augmented wave (PAW) pseudopotentials [30]. The plane wave cut-off energy was set to 400 eV, and the reciprocal space sampling was equivalent to 10 × 10 × 10 *k*-mesh for the fcc-conventional cell. In directions, where periodicity should be avoided (e.g., the direction of the slab, all 3 directions in the case of nanoparticles), only a single *k*-point was used. In other directions, the number of *k*-points was scaled so that the *k*-point spacing in the reciprocal space was kept constant, i.e., ≈ *π*/(10 · 4.069) Å−1 = 0.077 Å−1, where 4.069 Å is the lattice parameter of fcc-Au. Due to the employed periodic boundary conditions, we used a simulation box ≈20 Å larger than the actual (unrelaxed) nanoparticle to avoid any undesired interactions through the vacuum separating neighbouring nanoparticles. Similarly, ≈15 Å vacuum in the direction perpendicular to a free surface was used to separate slabs for calculating the surface energies of bulk Au. The electron charge was considered converged when the total energy of two subsequent self-consistency cycles differed by less than 10−4 eV, whereas structural optimisations were stopped when the total energy of two subsequent configurations differed by less than 10−3 eV. These criteria provide a total energy accuracy in the order of 1 meV/at. or better.

Finally, the qhull program [31] was used to calculate an area of a convex hull of ionic positions for each nanoparticle, to be used as an estimate of the surface area.

#### **3. Results**

#### *3.1. Low-Index Facets of Bulk Au*

The results presented in this chapter serve the subsequent discussion of the MM results, and their accuracy with respect to first principles calculations. Surface energy, *γ*, of a surface facet (*hkl*) can be calculated as

$$\gamma = \frac{1}{2A} \left( E\_{\text{slab}} - N E\_{\text{bulk}} \right) \,, \tag{1}$$

where *E*slab is energy of a slab composed of *N* layers. *E*bulk is the energy of the bulk material per one layer of cross-section *A*. The factor 2 results from the fact that the slab has two surfaces. A layer is understood as a surface primitive cell, i.e., when the desired facet (*hkl*) is perpendicular to one of the lattice vectors (for a detailed description of the surface primitive cells, see e.g., Ref. [32]). Due to the interaction of the two free surfaces, either through the vacuum (i.e., not well separated slabs in the case of periodic boundary conditions) or the bulk of the slab (i.e., too thin slab), the value *γ* has to be converged with respect to both of these. In the case of MM simulations, only the latter convergence needs to be tested if the simulation is run in a box without periodic boundary conditions in the direction perpendicular to the free surface.

Test calculations revealed that vacuum of 10 Å is sufficient to get surface energy results converged to well below 1 meV/Å2 . Similarly, a slab thickness of about 40 Å is needed in order to avoid interactions of the free surfaces through the gold layer. The obtained values from the DFT benchmarks and MD simulations are summarised in Table 1. The here obtained DFT values are comparable with data from the literature. They exhibit the same ordering (*γ*(110) > *γ*(100) > *γ*(111)) as reported earlier [33]. In a simplified picture, the surface energy expresses energy penalty related to the areal density of broken bonds [32,34]. This is 8/*a*2 0 for the (100) surface, 7.07/*a*2 0 for (110), and 4.33/*a*2 0 for the (111) surface (*a*0 being the fcc lattice constant). The density of broken bonds is similar for the (100) and (110) surfaces, while it is significantly lower for the (111) orientated facet, hence providing a qualitative explanation for the surface energy ordering.

**Table 1.** Calculated surface energies for three low-index facets, including data from the literature for comparison.

† FCD = full charge density.

The DFT and MM values exhibit an almost constant difference between the corresponding surface energies. Moreover, the MM values are very close to the DFT-LDA results. This is a somewhat surprising result since the EAM potential has been fitted to the DFT-GGA data using the same parametrisation by Perdew and Wang [29] as used here. We speculate that this is caused by fixing 4.07 Å as the lattice constant during the EAM potential fitting [23], as our LDA and GGA calculations yielded 4.061 and 4.176 Å, respectively. Nevertheless, since LDA and GGA are known to overestimate and underestimate, respectively, binding [38], and since the MM values are in between the two DFT-based estimations, we conclude that the interatomic potential used here is suitable for studying trends in surface energies. Moreover, the resulting values are expected to be very close to DFT-LDA calculations.

#### *3.2. Impact of Shape and Size on the Nanoparticles Surface Energy*

The surface energy of a gold nanoparticle consisting of *N* atoms is defined as an excess energy with respect to the energy of *N* atoms of bulk fcc gold, normalised to the nanoparticle surface area, *A*:

$$\gamma = \frac{E\_{\text{nanopparticle}} - NE\_{\text{bulk}}}{A} \,. \tag{2}$$

In the above, *E*nanoparticle is the total energy of the nanoparticle, while *E*bulk is energy per atom of bulk fcc Au. Unlike the total energies, the surface area *A* is not a well defined quantity. In the following sections, an area of a convex hull of the relaxed ionic positions is consistently used as an estimate for *A*.

#### 3.2.1. Nanocubes

In order to calculate the total energy of {100}-faceted nanocubes, structural models with a side length up to 20 nm were fully structurally relaxed. As a consequence of the surface tension, the apexes "popped in" as is apparent from the snapshot of relaxed atomic positions shown in Figure 1.

Supercells up to 3 × 3 × 3 conventional fcc cell (172 atoms) were treated using the DFT, while nanocubes up to 50 × 50 × 50 (515 151 atoms) were calculated using MM. A nanocube formed from *n* × *n* × *n* conventional cubic fcc cells (4 atoms per cell) contains *N* = 4*n*3 + 6*n*2 + 3*n* + 1 of atoms. The calculated surface energy values shown in Figure 2 were fitted with an exponential relationship

$$
\gamma = \gamma\_0 \exp\left(\frac{\mathcal{L}}{a}\right) \,, \tag{3}
$$

where *a* = *n* · *a*0 is the side length of a cube formed by *n* × *n* × *n* conventional fcc cells with the lattice parameter *a*0. The quantities *γ*0 and L are used as two fitting parameters. The thus obtained values of the pre-exponential parameter, *γ*GGA 0 = 57.4 meV/Å2 , *γ*LDA 0 = 89.8 meV/Å2 , and *γ*MM 0 = 81.4 meV/Å2 agree well with the bulk surface energies for the (100) facets (*γ*GGA (100) = 54.5 meV/Å2 ,

*γ*LDA (100) = 83.5 meV/Å2 , and *γ*MM (100) = 80.9 meV/Å2 ). This is an expected result as the bulk values are limits for infinitely large cubes. It is, however, surprising, that such a good agreement is obtained for the DFT data where only three data points are available for the fitting procedure. The same fitting procedure yielded for the parameter L (Equation (3)) values of 0.397 nm, 0.392 nm, and 0.661 nm for DFT-GGA, DFT-LDA, and MM data sets, respectively.

**Figure 1.** Relaxed structure of a nanocube with side *a* = 2.035 nm (666 atoms). The dashed line is a guide for the eye showing an ideal square shape.

**Figure 2.** Surface energy of nanocubes calculated by DFT and MM. The calculated datapoints were fitted with Equation (3). The dashed lines are (100) surface energies as listed in Table 1.

#### 3.2.2. Nanospheres

Nanospheres with all possible facet orientations were considered as an opposite extreme to the nanocubes with only a single orientation of their facets. They were constructed by cutting material contained in an ideal sphere of a given radius out of an infinitely large fcc Au crystal. The DFT calculations were performed up to *r* = 0.9 nm (152 atoms), while the MM calculations allowed easily for spheres up to *r* = 20.3 nm (2 094 177 atoms) (Figure 3). In comparison to the case of nanocubes, the surface energy of the nanospheres converges faster to a constant value of ≈94 meV/Å2 . This is a slightly higher value than *γ* of any low-index facet (cnf. Table 1) reflecting the fact that a spherical surface composes (from the atomistic point of view) of a large number differently orientated facets. Places where these facets meet (i.e., edges) are composed of atoms with the same or higher number of broken bonds than atoms in the surrounding planar facets, thus, further increasing the surface energy.

**Figure 3.** Surface energy of nanospheres calculated by DFT and MM. The dashed lines are the MM values for single-orientated (100) and (111) surfaces as listed in Table 1.

#### 3.2.3. Cuboctahedrons

The last class of objects studied in this work are cuboctahedrons, i.e., (100)-faceted cubes with all apexes cut by (111) planes (see inset in Figure 4b). Cuboctahedrons are a special subset of truncated octahedrons with the all sites equally long. Figure 4a shows the total energy per atom plotted against the nanoparticle size in terms of the number of forming atoms for cuboctahedrons together with more general truncated octahedrons. The latter were generated with a build-in function of Atomic Simulation Environment toolkit [39] for various sizes of the truncated octahedron apexes. Obviously, the cuboctahedrons are not always the most convenient shape for a given number of atoms.

The surface energy of cuboctahedrons (Figure 4b) oscillates between two values, ≈78 and ≈90 meV/Å2 . This behaviour is caused by the changing ratio of surface atoms forming the (100) and (111) facets and the edges and corners, which directly corresponds with the atomistic nature of the nanoparticle. A detailed analysis of the coordination of the surface atoms reveals that the number of 9-coordinated surface atoms, corresponding to ideal (111) facets, is in anti-phase with the surface energy as shown in Figure 4b. The 8-coordinated (100) surface atoms also show small steps hence causing a non-monotonous increase of their number as a function of the cuboctahedron size. At the same time, the numbers of 10-, 7-, 6-, and 5-coordinated surface atoms forming edges and corners (i.e., atoms with even smaller coordination and, consequently, more broken bonds than those on ideal (100) and (111) facets, and hence increasing the overall surface energy), exhibit the same "oscillations" concerning the cuboctahedron size as the surface energy itself. Therefore, the oscillations are expected to decrease with increasing cuboctahedron size. It is interesting to note that the two limit values for the surface energies, ≈90 and ≈80 meV/Å2 , represent approximately the same range as the two values, 80.9 and 72.5 meV/Å2 for pure (100) and (111) facets, respectively. Similarly to the case of nanospheres, the values are somewhat higher than the ideal single-orientated facets due to the presence of the edges and corners.

**Figure 4.** (**a**) Total energy per atom as a function of the nanoparticle size (in terms of number of forming atoms) for cuboctahedrons (full circles) and general truncated octahedrons (open circles). (**b**) Surface energy of cuboctahedrons calculated by MM and showed as a function of the size of "parent" cube. The dashed lines are the MM values for single-orientated (100) and (111) surfaces as listed in Table 1.

#### **4. Discussion**

#### *4.1. Correction of the Surface Area for Electronic Cloud*

The surface areas calculated in the previous parts corresponds to the convex hull of ionic positions. In our recent paper [13] dealing with predicting surface energy of Au55 cluster, we have discussed the error made by neglecting extend of the electronic cloud. There, a radius correction of 1.3–1.4 Å has been proposed under the assumption that the mass density of the nanocluster is the same as that of bulk fcc-Au. Note that, radius corrections of 0.5–0.8 Å have been proposed by de Heer [40].

In order to see how neglecting the electronic cloud layer actually influences the predicted surface energies, we re-evaluate the surface areas. Let {- *Ri*} be a set of the atomic (ionic) positions defined with respect to the nanoparticle centre of mass, i.e.,

$$\sum\_{i} \mathcal{R}\_{i} = \vec{0} \, , \tag{4}$$

where the sum is performed over all atoms in the nanoparticle. Subsequently, a new set of coordinates, {- *R*˜*i*}, is defined as

$$
\vec{\mathcal{R}}\_i = \left( |\mathcal{R}\_i| + \Delta \right) \mathcal{R}\_i^0 \tag{5}
$$

where - *R*0 *i* = - *Ri*/|- *Ri*| is a unit vector along the direction of - *Ri*. This means that all atoms, and in particular those on the convex hull envelope, are shifted by Δ away from the nanoparticle centre of mass. A new surface area is calculated as a convex hull of {- *R*˜*i*} positions for several representative values of Δ.

The results are summarised in Figure 5 for all three nanoparticle geometries considered in the present work. In all cases, the surface energy decreases with increasing values of Δ, which is a simple consequence of the surface energy definition in Equation (2). It is, however, remarkable to notice that even for the largest nanoparticle sizes the surface energy reduction is still larger than 1% for the DFT-based electron cloud thickness. We, therefore, conclude that, especially for nanoparticles with specific sizes below 5 nm, the correction of the surface area due to the electronic cloud is essential. Moreover, it is likely that for the small nanoparticle sizes, the surface energies calculated here are overestimated due to that fact that even a lower energy can be obtained for a different atomic ordering than fcc (e.g., Mackay icosahedrons as in the case of Au55) or even amorphous liquid-like structures [13]. Finally, it is worth noting that the problem of electronic cloud is not an issue in standard calculations of single orientated flat single crystal facets since it does not influence the actual surface area.

**Figure 5.** Corrected absolute (upper row) and relative values (lower row) of the surface energies for (**a**,**d**) nanocubes, (**b**,**e**) cuboctahedrons, and (**c**,**f**) nanosheres. The relative surface energies are calculated with respect to the values without correction for the electronic cloud thickness (Δ = 0).

#### *4.2. Surface Induced Excess Energy*

As mentioned above and discussed in the literature, the surface area of nanoparticles is an ill-defined quantity. In order to eliminate this problem, we introduce a new quantity, *E*excess, expressing the surface-induced excess energy with respect to the bulk energy corresponding to the same number, *N*, of atoms as in the nanoparticle, normalised to 1 atom, as

$$E\_{\text{excess}} = \frac{E\_{\text{nanopparticle}} - NE\_{\text{fcc}\cdot\text{Au}}}{N} \,\text{.}\tag{6}$$

A similar concept has been previously demonstrated to work also for energetics of carbon fullerenes [41], or even for elasticity of nanoporous gold [42]. If the excess energy, *E*excess, is evaluated for nanocubes, nanospheres, and cuboctahedrons, a linear relationship between log *E*excess and log *N* is obtained independent of the nanoparticle shape (Figure 6a). This suggests that the excess energy is a power law function of the total number of atoms (nanoparticle size). This fit (the dashed line in Figure 6a) gives

$$E\_{\text{excess}} = 3523.3 \,\text{meV/atom} \times N^{-0.346} \,\text{.}\tag{7}$$

**Figure 6.** Excess energy, *E*excess, of nanoparticles with respect to the bulk fcc Au as a function of the number, *N*, of atoms forming the nanoobject. *E*excess is normalised to (**a**) number of the atoms forming the nanoparticle, and (**b**) to the number of broken bonds. The dashed lines in (b) show the difference between the actual value of *E*excess as calculated by MM, and a fitted value using Equation (10).

Recalling the idea that the surface energy is genuinely connected with the broken bonds (bb), we now establish the energy needed to "break" a bond. Let us consider an *n* × *n* × *n* nanocube containing atoms with 4 different nearest neighbour coordinations: 8 atoms with 9 bb forming corners (i.e., 3-coordinated atoms), (12*n* − 12) atoms with 7 bb forming the edges (i.e., 5-coordinated atoms), (12*n*2 − 12*n* + 6) atoms with 4 bb forming the surface facets (i.e., 8-coordinated atoms), and (4*n*3 − 6*n*2 + 3*n* − 1) bulk atoms with no bb (i.e., fully 12-coordinated atoms). If we simply assume that all bonds "cost" the the same energy *E*bond to break them, the excess energy, *E*excess, i.e., the sum of the contributions described above, follows as

$$E\_{\text{excess}} = \left[ 9 \times 8 + 7 \times (12n - 12) + 4 \times (12n^2 - 12n + 6) \right] E\_{\text{bond}} \tag{8}$$

yielding *E*bond = 168.1 meV/bond from fitting the nanocubes data.

However, the red triangles in Figure 6b, showing the nanocubes excess energy normalised to the number of broken bonds, clearly exhibit a non-constant value for *E*bond. Consequently, we propose a slightly modified description in which the energy needed to break a bond is a (non-linear) function of the coordination. Hence, it costs different energy to create, e.g., a corner atom (9 broken bonds) than a facet atom (4 broken bonds). Thus the excess energy becomes

$$E\_{\text{excess}} = 72E\_{\text{corner}} + 84(n-1)E\_{\text{edge}} + 24(2n^2 - 2n + 1)E\_{\text{face}} \,. \tag{9}$$

Fitting yields *E*corner = 272.1 meV/bond, *E*edge = 215.2 meV/bond, and *E*facet = 166.0 meV/bond. It turns out that for nanocubes with side 5 nm, Equation (9) provides predictions with an accuracy better than ≈1 meV/bond. Energy of a broken bond, corresponding to an infinitely large (100) facet, can be estimated from the surface energies as given in Table 1. This value is 167.5 meV/bond, which is close to *E*bond = 168.1 meV/bond (Equation (8)) as well as *E*facet = 166.0 meV/bond (Equation (9)).

The complex shapes of cuboctahedrons and nanospheres somewhat restrict the intuitive analysis of the excess energy above presented. When the excess energy is fitted with a single valued energy per broken bond (equivalent to Equation (8)), values of 172.8 meV/bond and 181.9 meV/bond are obtained for cuboctahedrons and nanospheres, respectively. These values represent an excellent estimation of the excess energies in the limit of large nanoparticles, as shown in Figure 6b. Moreover, the excess energy value for cuboctahedrons lies between the values estimated for (100) (*E*(100) = 167.5 meV/bond) and (111) (*E*(111) = 173.3 meV/bond) facets. This fact further illustrates that the surface energy values, as presented in Section 3.2, are remarkably influenced by the evaluation of the actual surface area (which is, from the atomistic point of view, ill-defined). Consequently, the mean value of the surface energy of cuboctahedrons as shown in Figure 4b lies outside the range bounded by *γ*(100) and *γ*(111) values.

Finally, in order to obtain a non-constant behaviour, we fit the excess energy with

$$E\_{\text{excess}} = \sum\_{i=1}^{11} (12 - i) N(i) E(i) \tag{10}$$

where *N*(*i*) is the number of *i*-coordinated atoms (i.e., those having (12 − *i*) broken bonds) and *E*(*i*) is the corresponding excess energy contribution. Equation (10) is a generalised formulation of Equation (9) reflecting that all possible coordinations may occur due to the shape of nanoparticles. We note that the smallest coordination obtained was 3 and 4 for the case of cuboctahedrons and nanospheres, respectively. The fitted values of *E*(*i*) are given in Table 2, and the difference between the actual *E*excess from MM and values predicted using Equation (10) is shown in Figure 6b with dashed lines. Obviously, the fit provides excellent agreement for nanoparticles containing ≈104 atoms and more.

**Table 2.** Fitted coefficients *E*(*i*) for the excess energy expression according to Equation (10). The index *i* expresses the coordination of atoms (i.e., (12 − *i*) is the number of broken bonds, bb).

Our analysis provides an insight into the here predicted trends. Regardless of the nanoparticle shape, the surface energy decreases with the increasing particle size. The reason is that the smaller is the nanoparticle, the larger is the fraction of the surface atoms with small coordination, i.e., those with lots of broken bonds. Moreover, the energy to break a bond increases (generally) with the decreasing atom coordination.

#### *4.3. Contribution of Surface Stress State*

As it has been recently stressed out [43], the excess energy due to a free surface has two contributions: the surface energy contribution related to the energy penalty of broken bond and the contribution due to the elastic strain energy generated by the surface stress state. The latter depends on the surface curvature. As an illustrative example let us assume a spherical body and a homogeneous surface stress state with the value *σ* leading to a pressure with value 2*σ*/*R* in the whole spherical body. From this description it becomes clear that the energetic surface stress contribution is zero for the slab approach. Similarly, the energetic surface stress contribution will be negligible for rather large nanocubes with only a marginal amount of corner and edge atoms (see discussion in the Section 4.2).

We now try to estimate the energetic surface stress contribution to the excess energy for the case of a spherical nanoparticle using classical continuum mechanics. Let us denote *R* the nanosphere's radius, and *γ* its surface energy. Furthermore, let us keep to the reasonable assumption that the value of *σ* and *γ* are of the same order of magnitude. The corresponding total surface energy is then

$$
\mathcal{E}\_{\mathcal{I}} = 4 \pi R^2 \gamma \,. \tag{11}
$$

For sake of simplicity, we further assume isotropic elastic properties of the nanoparticle, with *ν* and *E* being its Poisson's ratio and Young's modulus, respectively. The elastic strain energy caused by the surface stress *σ*, activating an internal pressure 2*σ*/*R*, is

$$\mathcal{E}\_{\mathcal{T}} = \frac{4}{3} \pi R^3 \frac{6(1 - 2\nu)}{E} \frac{\sigma^2}{R^2} \, , \tag{12}$$

for details, see, e.g., Ref. [1], Appendix 3. The ratio of the energetic surface stress contribution to the surface energy follows with *σ* = *γ* as

$$\frac{\mathcal{E}\_{\sigma}}{\mathcal{E}\_{\gamma}} = \frac{2(1 - 2\nu)}{E} \frac{\gamma}{R} \,. \tag{13}$$

Taking a representative values for gold, *γ* = 1 J/m2 , *E* = 78 GPa, *ν* = 0.44, and *R* = 1 nm, Equation (13) yields 0.359 × 10−2, i.e., the energetic surface stress contribution to the total excess energy is less than 1% of the surface induced excess energy. This ratio becomes even smaller (negligible) for larger nanospheres.

To corroborate this rather simplistic estimation, we plot the excess energy distribution over a cross section including the centre for a nanosphere (Figure 7a) and a nanocube (Figure 7b) as obtained from the MM simulations. Several observations can be made. Firstly, the excess energy is concentrated at the nanoparticle surface irrespective of its shape. The surface stress (and hence the corresponding elastic strain energy) could be only of relevance for a nanosphere. However, we can conclude that this contribution is effectively zero (or negligible). A similar situation can be expected for a nanocube, where the excess energy is concentrated to the nanocube edges (corner of the cross section in Figure 7b). This fact nicely agrees with the fitted values of *E*edge = 215.2 meV/bond being larger than *E*facet = 166.0 meV/bond, estimated in Section 4.2.

Even though the term surface energy was used in a slightly imprecise way throughout the Section 3.2 (more accurate would be to talk about surface induced excess energy), we conclude that the energy contribution of surface stress can be neglected and the two quantities, surface energy and surface induced excess energy, are equivalent (or at least of the same order of magnitude) for practical cases with nanoparticles larger than ≈1 nm.

**Figure 7.** Contour plots of the distribution of the surface stress induced excess energy (in eV/at.) contribution for a cross section of (**a**) a nanoshere (*R* = 3.25 nm) and (**b**) a nanocube (*a* = 6.92 nm). Both cross sections include the nanoparticle centre. The dots represent actual atoms in the cross section, e.g., real locations, where the excess energy is stored. For sake of clear demonstration, the discrete data were interpolated over the whole cross sectional area.

#### **5. Conclusions**

A molecular mechanics study, complemented by first principles Density Functional Theory calculations, was performed to obtain surface energy of small gold nanoclusters of various sizes and (geometrically well defined) shapes. The employed interatomic pair potential was shown to give structural parameters and surface energies comparable with DFT-LDA calculations. The surface energy of nanocubes and nanospheres has been shown to converge to a constant value. The convergence was faster in the case of nanospheres compared with nanocubes. The surface energy, *γ*, is practically constant for any particles with radius larger than ≈3 nm. Truncated cubes (cuboctahedrons) did not achieve a single value for the surface energy within the studied range of nanoparticle sizes but, instead, an oscillating behaviour between two values. The range of these oscillations equals to the difference between *γ* of (100) and (111) facets. Finally, the surface-induced excess energy obviously follows a universal power-law dependence on the number of atoms forming the nanoparticle and is, to a large extent, related to the number of broken bonds (reduced coordination of the surface atoms). Importantly, the size-dependence of surface energy becomes significantly reduced when the actual surface area is corrected by the thickness of the electronic cloud, leading to almost constant values particularly for nanocube and nanosphere sizes of about 5 nm and more.

As outlined above, this study has found an increase of the surface energy with decreasing particle size (which is in agreement with other theoretical studies). Two remarks may be useful in this regard. Firstly, this fact should not be confused with experimental works on liquid solution–solid nanoparticle interface energies of gold nanoparticles, moreover often having irregular shapes or even liquid-like surface layer. Secondly, we note that small nanoparticles, specifically the Au55, were shown to be amorphous rather than crystalline. Hence the values predicted here for the smallest particle sizes of a few nanometers are not relevant for amorphous or glassy particles.

In conclusion, this work contributes to understanding of surface energy (solid phase–vacuum interface) of crystalline nanoparticles and its relation to the their structure.

**Author Contributions:** Conceptualization, D.H., D.V., and F.D.F.; methodology, D.H. and P.D.; software, D.H.; investigation, D.H. and P.D.; resources, D.H.; writing—original draft preparation, D.H.; writing—review and editing, D.H., D.V. and F.D.F.; visualization, D.H. and P.D.; supervision, D.H.; funding acquisition, D.H. and F.D.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** F.D.F. and D.H. appreciate financial support by the Austrian Federal government (in particular from the Bundesministerium für Verkehr, Innovation and Technologie and the Bundesministerium für Wirtschaft und Arbeit) and the Styrian Provincial Government, represented by Österreichische Forschungsförderungsgesellschaft mbH and by Steirische Wirtschaftsförderungsgesellschaft mbH, within the research activities of the K2 Competence Centre on "Integrated Research in Materials, Processing and Product Engineering", operated by the Materials Center Leoben Forschung GmbH in the framework of the Austrian COMET Competence Centre Programme, Projects A1.23 and A2.32.

**Acknowledgments:** The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC).

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

#### **References**

c 2020 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/).


Red and Purple Flesh Potatoes a Healthy and Attractive Alternative Associated with New Market Trends

*María-Teresa Pino and Cristina Vergara*

### **Abstract**

The potato is the fourth most important crop in the world in terms of human food, after maize, wheat and rice (FAOSTAT, 2019). The cultivated potato is a vital food-security crop considering its worldwide growth, from latitudes 65° Lat N to 53° Lat S, high yield, and great nutritive value. The potato is a good source of dietary energy and micronutrients, and its protein content is high in comparison with other roots and tubers. The cultivated potato is also a concentrated source of vitamin C and some minerals such as potassium and magnesium. Tuber flesh color generally ranges from white to dark yellow in cultivated potato; however, the high potato diversity shows tuber flesh color varies from white to dark purple. Red and purple-flesh potatoes are an interesting alternative for consumers due to phenolic compounds and antioxidant capacity. The goal of this publication is to show the advances in red and purple flesh potato, in terms of anthocyanin profile, color extraction and stability in simulated *in vitro* digestion.

**Keywords:** Antioxidant activity, Anthocyanins, *in vitro* digestion, Red and purple flesh potato, *Solanum tuberosum*

#### **1. Introduction**

The cultivated potato (*Solanum tuberosum* L.) is the fourth most important crop in the world, after maize, wheat, and rice. The cultivated potato is a vital food-security crop considering its worldwide growth and nutritional value. This crop is cultivated from latitudes 65° Lat N to 53° Lat S. However, the major potatoproducing regions are in the relatively temperate zones, but it is also cultivated in Andean tropical highlands and in tropical and sub-tropical environments as a winter crop [1]. In the last decade, the developing world's potato production exceeded that of the developed world, showing a significant increase and demand in Asia, Africa, and Latin America, however in these areas it is often cultivated in marginal areas with limited access to farm inputs [2]. Potato is a very efficient food crop and produces more dry matter and proteins per unit area in comparison to cereals. In addition, potato is an efficient water user, however drought susceptible crop, because under rainfed conditions, it yields more food per unit of water than other major crops. For every m3 of water applied to the crop, potato

produces 5600 kcal of dietary energy, compared to 3860 in maize, 2300 in wheat and 2000 in rice [3]. Because of its high nutritional value and yield, cultivated potatoes constitute the bulk of the economically and agronomically important crop production. It accounts for large quantities of dietary daily energy intake compared to other crops and contributes to hunger reduction and improved nutrition. In addition, potato is also a good source of protein content, micronutrients, a concentrated source of vitamin C and potassium in comparison with other roots and tubers [4]. However, depending on potato flesh color, the nutritional value may be higher or different, because the color is associated to unique metabolite profile on phenolics, flavonoids, and carotenoids. These compounds are directly associated with antioxidant activity, and highly desirable in diet because of their beneficial effects on human health [5]. The present chapter will be focused on red and purple flesh potatoes as a healthy and attractive alternative associated with new market trends.

#### **2. Color fleshed potatoes high in anthocyanins and antioxidant activity is promising food**

#### **2.1 Potato diversity in Chile**

Chile is one of the countries with the largest potato diversity in the world and is also recognized as a center of origin (or center of diversity). Potato migration from the Andes to coastal Chile caused its adaptation to long-day conditions, this process contributed to the development of commercial cultivars worldwide [6]. Chile is the origin of the *Solanum tuberosum* group *Chilotanum* corresponding to lowland tetraploid landraces. Several Chilean potato genetic diversity and population structure studies have shown the close genetic distance between Chiloe Island landraces and the modern potato group. This germplasm appears to represent an interesting gene pool that could be exploited in potato breeding programs or also used for niche markets, by the specific needs and preferences. A collection of *S. tuberosum* consisting of 30 accessions of native landraces originating from the island of Chiloe, nine commercial cultivars commonly used in Chile and one accession of *S. fernandezianum* from Robinson Crusoe Island, located at 257 m altitude (33°39′9.03" S, 78°50′45.9" W) was evaluated; the results showed that commercial cultivars do not present the same genetic variability as native potatoes, and the allelic richness of commercial cultivars is lower than that of native *S. tuberosum ssp. tuberosum*. Most of the native potato were clustered in accordance with their geographical location, while commercial cultivars, were clustered in accordance with their breeding programs in Chile and Europe [7, 8]. The most complete morphological description of the Chilean germplasm was published in 2008 in the Catalog of Native Potatoes from Chile. Two institutions of the Chilean government, INIA, and SAG (Agricultural and Livestock Service of Chile), among 589 native accessions analyzed, 320 different allelic phenotypes were found indicating that there are at least 320 different genotypes in the collections. Of these, 158 belonging to the INIA collection were not found in the SAG collection. These 158 new genotypes should increase the number of known Chilean potatoes. As expected, different genotypes were known under the same popular name [9]. The genetic diversity and heterozygosity contain invaluable genetic, physiological, and biochemical attributes, that can guarantee new healthy food and safe global food productivity. The INIA (Agriculture Research Institute of Chile) is working to preserve that biodiversity, identifying the attributes of each landrace for further crop improvement, in terms of nutrition, flesh color, disease resistance, and other attributes.

#### **2.2 Cultivated potato and red-purple fleshed potatoes**

Cultivated potato is a high valued crop because of its nutritional properties and biochemical composition, rich in starch, reducing sugars, non-reducing sugars, proteins, and carotenoids. Other important nutrients in potatoes include minerals and vitamins such as potassium, magnesium, vitamin C as well as vitamin B6, among others [10, 11]. Potatoes are a reliable source of ascorbic acid – ranged from to 5.8 to 21 mg of vitamin C per 100 g tuber on a fresh weight (FW) basis–, however several studies have reported changes in the content of vitamin C in potato tubers depending on variety [12, 13]. Potato flesh color ranged from white to dark yellow cultivars are the most common, a recent review showed that the total carotenoids content of tubers is influenced by location, season, genotype, and their interactions, with values between 5 and 10 mg kg−1 FW of total carotenoids, for white-fleshed potatoes, to over 100 mg kg−1 FW of total carotenoids for darkyellow potatoes [14]. Total carotenoids expression was observed in the mid of the tuber maturation process rather than in ready-to-harvest tubers. The predominant carotenoid forms found in cultivated potato were lutein, violaxanthin, zeaxanthin, and neoxanthin [15].

Today, with a major market shift for antioxidant-rich foods, the traders are also seeing an increase in the demand for red and purple fleshed potatoes, because these contain an important group of secondary plant metabolites associated with positive health benefits: phenolics, flavonoids, and anthocyanins [16]. Red and purple fleshed potatoes provide a natural source of anthocyanins and antioxidant activity [17]. Anthocyanins are recognized as natural flavonoid colorants ranged from orange-red (pelargonidin), reddish to blue-violet (malvidin), for use in food industry and pharmaceutical ingredients, because of their potential health benefits. The six predominant anthocyanidins found in higher plants (including root and tubers) are cyanidin, delphinidin, pelargonidin, peonidin, petunidin, and malvidin [18]. The phenolics compounds, flavonoids, and anthocyanins are potent antioxidants which contribute to the physiological defense against oxidative and free-radicalreactions. Food containing anthocyanins have been associated with a reduction in inflammation markers and a lower risk of chronic diseases, including obesity, diabetes, cardiovascular disease, and cancer [19, 20]. In addition, a recent study showed that anthocyanins ameliorate neurodegeneration at a molecular and clinical level and dietary anthocyanin's supplement prevents neurodegenerative diseases [21]. Colored fleshed potatoes contain relatively low amount of total phenolic acids, but its flavonoids and flavones extracts showed high scavenging activities toward oxygen compared to other fruits and vegetables [16].

In relation to the predominant anthocyanidins, a study in four potato cultivars ("Hermanns Blaue", "Highland Burgundy Red", "Shetland Black", and "Vitelotte") identified Petunidin derivatives in all of them except in "Highland Burgundy Red". Malvidin was the predominant on the "Vitelotte" cultivars. "Shetland Black" was the only one containing minor peonidin [22]. The evaluation of anthocyanin phenolic compounds of potato peels from ten colored potato cultivars (red and purple) the most prominent were pelargonidin, peonidin, and malvidin aglycones. All samples revealed antioxidant and antitumor activities, and no toxic effect [23]. Another recent study on colored potato (three red-fleshed, three-purple fleshed, and one marble-fleshed) showed that red and purple-fleshed potatoes are rich sources of anthocyanins. Pelargonidin and petunidin were the main anthocyanidin forms, and all aqueous extracts presented *in vitro* antioxidant, antibacterial and antifungal activities, and no toxic effects [24].

Because most native color fleshed potatoes have low yield, wide phenotypic variations and uneven flesh color, the INIA Chile's Potato breeding program has developed new putative color flesh potato cultivars as raw material to food coloring and ingredient extraction, with high anthocyanins flesh concentration and high yield. **Table 1** shows significant differences in color intensity (E1%), total anthocyanins (CAT), total polyphenol content (TPC), and antioxidant activity (FRAP), for selected red flesh potato (INIA RS58-3), purple flesh potato (INIA RQ12-521), blue-violet flesh potato (INIA RÑ98-9). Principal component analysis and matrix of correlation coefficients showed a good fit between color intensity (E1%) and total anthocyanins (CAT) with values from 0.63 between E1% and CAT-based in tuber dry weight between 0.90 for E1% and CAT-based in tuber fresh weight. Both red (INIA RS58-3) and blue-violet (INIA RÑ98-9) fleshed potatoes showed higher color intensity and higher total anthocyanins (CAT), also these two potato lines showed higher values in total polyphenol content (TPC), and antioxidant activity (FRAP). Conversely, the light purple flesh potato (INIA RQ12-521) showed lowest color intensity and consequently lower CAT, TPC, and antioxidant activity. Thus, selected red flesh potato (INIA RS58-3) and blue-violet flesh potato (INIA RÑ98-9) are promising raw material for natural color extraction and food coloring ingredients.

In term of Anthocyanin profile (**Table 2**), in these color fleshed potatoes, the predominant anthocyanins identified were Pelargonidin-3-glucoside, Peonidin-3-glucóside, Peonidin-3-arabinósido, Delphinidin 3-glucoside, Delphinidin 3-galactoside, Delphinidin 3-rutinoside, Delfinidina-3,5-diglucósido, Delphinidin 3-galactoside, Delphinidin 3-glucoside, Delphinidin 3-rutinoside, Malvidin-3-glucóside, and Malvidin-3,5-diglucóside. The major picks in red flesh potato (INIA RS58-3) were in Peonidin and Delphinidin derivatives, while in blue-violet flesh potato (INIA RÑ98-9) the picks were in Delphinidin and Malvidin.

#### **2.3 Stability and Bioaccesibility: potato anthocyanins**

The concentration and stability of these anthocyanins are affected by several parameters such as agronomic factors and postharvest storage. However, the stability of acylated anthocyanins is still not well addressed, and few studies in anthocyanins contents (CAT) in colored-flesh potato tubers during processing and digestion have been published [25, 26]. The stability of anthocyanins is affected by pH, temperature, and light. During the digestion process, anthocyanins stability is affected because undergo variation in pH and in digestive enzymatic activity. Therefore, the anthocyanins stabilization is needed to maintain their health effects in the human body and increase its positive effects. The anthocyanins stability could be improved by using micro-encapsulation technology such as spray-drying [26–28]. Micro-encapsulation is a technique wherein a bioactive compound is encapsulated by a biopolymer, to protect the compound from oxygen, water, or other conditions, thereby improving its stability and release in the desired stage [26, 28]. In order to know bio stabilization of anthocyanins extract from purple flesh cultivated potato, a study was addressed on the encapsulation anthocyanins' efficiency and bioaccesibility. The anthocyanin extract from INIA purple flesh potato (PPE) was micro-encapsulated by spray-drying [29] (**Figure 1**). Maltodextrin (MD) was used as the encapsulating agent, due to its high solubility in water, low viscosity, bland flavor, and colorlessness. Briefly, the mixture (extract PPE-maltodextrin) was fed into spray dryer at 130°C. The encapsulation efficiency (EE) was 86%, due the high anthocyanins-MD interactions caused by hydrogen bonding and/or electrostatic interactions. The total anthocyanins were 1.34 ± 0.02 mg cy-3-glug−1 and antioxidant activity (FRAP) was 10.1 ± 0.6 mg trolox equivalentg−1. The moisture (5.6 ± 0.4%), water activity (aw = 0.225 ± 0.001), and particle size (6.51 ± 0.1 um)

#### *Red and Purple Flesh Potatoes a Healthy and Attractive Alternative Associated… DOI: http://dx.doi.org/10.5772/intechopen.99181*

*Where, Red = RF, PF = Strong purple, PS = Light purple, VB = blue-violet; Tuber shape Rd = Round, O = Oval. Anthocyanin profile by HPLC analysis was carried out in Jasco Intelligent Quaternary Gradient PumpPU-2089 Plus, UV/VIS detector e interface LC-NetII/ADC, C18 Kromasil 100***-***5 de 150 mm at 30C°. Detection: UV @ 520 nm.*

#### **Table 2.**

*Anthocyanin profile of tubers, for selected red flesh potato (INIA RS58-3), purple fleshed potato (INIA RQ12- 521), blue-violet flesh potato (INIA RÑ98-9) cultivated in Osorno (40°34′26.22"S, 73°8′0.53"W.) Chile, during two seasons (2019-2020 and 2020-2021).*

were within the range described for anthocyanin encapsulated obtained by spraydrying [27, 30, 31].

PPE-MD encapsulation improved its anthocyanins stability due to anthocyanin extract and encapsulating agent interaction that may occur by hydrogen bonding and/or electrostatic interactions. Reduced damage of active anthocyanins was observed under adverse storage conditions. The time-course of the storage stability assay during 140 days at 60°C showed that encapsulated extract (PPE-MD) showed significantly higher anthocyanins retention than non-encapsulated PPE (**Figure 2**), thereby extending shelf life, color, and antioxidant capacity [29]. These results agree with earlier reports on use of spray drying technique on black-carrot, black berry, maqui and plum [27, 32–34].

Other important aspect is the *in vitro* bio accessibility (BA) of anthocyanins. Bio accessibility is defined as the amount of bioactive compound (anthocyanins) that was released from the food matrix after digestion [35]. The BA of encapsulated anthocyanins extracts of purple flesh potato (PPE-MD) was significantly higher than non-encapsulated extract (**Figure 3**). Micro-encapsulation protects PPE-MD during *in vitro* digestion, against environmental conditions, especially pH. The BA of the PPE and PPE-MD was higher than previous similar studies in maqui extract [27] and blueberry extract [28]. The encapsulation technology is a useful strategy to protect anthocyanins from purple flesh cultivated potato, during storage and *in vitro* gastrointestinal digestion model, as well. The anthocyanins micro-encapsulation contributes to the development of new purple potato products in powder formulation, potentially useful as colorants for the food industry or health ingredients (antioxidant and anti-inflammatory properties).

#### **2.4 Red and purple flesh potato-based food and natural ingredients responding to new global food market trends**

The global consumer trend preferences and the health and wellness market in the next coming years, show a promising future for non-traditional color fleshed potato, as red, purple, and blue fleshed potato, because their antioxidant activity

*Red and Purple Flesh Potatoes a Healthy and Attractive Alternative Associated… DOI: http://dx.doi.org/10.5772/intechopen.99181*

**Figure 1.**

*(a) Microencapsulated powders (anthocyanin extract from INIA purple flesh potato (PPE + maltodextrin) and (b) scanning electron microscopic (SEM) for anthocyanins microencapsulated powders.*

and health benefit are capturing the consumers' attention. Most studies about market trends have projected that "the global health and wellness food market" would grow at a CAGR of over 6% (6–8%) during the next years. This forecast is explained in part, because the world, upon COVID-19 pandemic impact, will face the growing incidences of chronic diseases, stress, obesity, aging and other adverse health conditions, see more detail in [36–38] reports. In potato, some reports about its market under the COVID-19 pandemic situation shows that potatoes become popular due to their long shelf-life. In relation to global market, most potatoes are consumed as fresh vegetable, however, is shifting from fresh potatoes to processed potato-based foods. Based on application, the processed potato market is segmented into readyto-cook, snacks, potato flour-gluten free, and other potato-based food additives for soups, gravies, bakery, and desserts driven by urbanization and changes in eating habits among many other factors. Thus, these global food market trends, raises further questions for food industry and R&D institutions, would be capable to develop new color fleshed potato-based foods and potato-based ingredients keeping its nutritional value and color.

#### **Figure 2.**

*Time-course storage stability assay for anthocyanins retention at 60°C for 140 days storage from nonencapsulated extract (PPE, ©) and encapsulated extract (PPE-MD,* ∆*), and the visual degradation of anthocyanins for liquid (analysis solution) on non-encapsulated PPE (source: Adapted Vergara et al. [29]).*

#### **Figure 3.**

*Bio accessibility (%) of non-encapsulated (PPE) and encapsulated (PPE-MD) anthocyanins extract after simulated in-vitro digestion.*

*Red and Purple Flesh Potatoes a Healthy and Attractive Alternative Associated… DOI: http://dx.doi.org/10.5772/intechopen.99181*

A recent research studied how the anthocyanin degradation and anthocyanin profile were influenced in red-fleshed potatoes (cv Herbie 26) after different methods of processing (dried cubes, French fries, chips, semi-finished products, and finished products); most evaluated processes showed losses on anthocyanin content. Chip products showed higher retention anthocyanins. Pelargonidin-3 feruloylrutinoside-5-glucoside, and pelargonidin-3-caffeoylrutinoside-5-glucoside, were most thermally stable [25]. To reduce the loss of effectiveness of plant-based compounds as anthocyanins, and polyphenols from color fleshed potatoes, microencapsulation arise as an alternative. This technique allows the development of novel plant-based ingredients able to keep their functionality after processing.

**Figure 4.**

*(a) Potato-based ingredient, flakes elaborated from red flesh potato (INIA RS58-3), purple fleshed potato (INIA RQ12-521), blue-violet flesh potato (INIA RÑ98-9). (b) Flakes elaborated from light purple fleshed potato (INIA RQ12-521).*

However, commercial product development depends on financial and operational viability. In the previous section of this chapter, anthocyanins' stability and bioaccesibility from color fleshed potatoes were discussed with emphasis in microencapsulation for INIA purple flesh potato and *in vitro* digestion. Thus, microencapsulated spray dried powder from purple-fleshed potato could be applied in drinks, in snacks, and in milk products because its stability and bioaccesibility [29]. The application of aqueous extracts from color fleshed potato was also tested and validated as natural colorants in a soft drink during 30-days shelf-life when compared with the commercial colorant E163 [24].

Potato flake is an ingredient with multiple applications in processed food and long shelf life. A recent study compared the convective tray drying method with a refraction-based drying method for producing potato flakes (cv. Kufri Pukhraj, a light yellow to gold flesh potato). The results showed that those flakes obtained by refraction-based drying had better nutritive value, color and acceptability. It recommended its application for the fortification of flour, baby foods, and extruded products [39]. Previously, a study in anthocyanin-rich red potato flakes showed that might improve the antioxidant system by enhancing hepatic SOD (superoxide dismutase) mRNA in mice [40]. The replacement of part of the wheat flour with purple fleshed potato powder (from freeze-dried) and albedo showed an enhancement antioxidant activity of fortified breads, and longer shelf life [41]. In addition to the previous reported health benefits, the purple fleshed potato powder (from freeze-dried) has the potential to aid in the amelioration of ulcerative colitis symptoms, a major form of inflammatory bowel disease [42].

Potato-based ingredients (flakes, spray dried powder, and freeze-dried powder) were elaborated from red flesh potato (INIA RS58-3), purple fleshed potato (INIA RQ12-521), and blue-violet flesh potato (INIA RÑ98-9) because their application in food industry (**Figure 4**). The spray dried powder shows better physical properties when compared to the freeze-dried powder. Conversely, freeze-dried powder

**Color intensity (E1%)** *is the optical density of a 1% juice solution at the wavelength of maximum absorbance intensity (INIA RÑ98-9: Abs = 522 nm, INIA RQ12-521: Abs = 521 y RS58-3: Abs = 506 nm) by spectrophotometer (Jasco V-700).* **Total anthocyanin content (TAC)** *by pH differential method expressed as mg of cyanidin-3 glucoside equivalents per fresh weight (FW).* **Antioxidant activity (FRAP)** *measured by the FRAP method as described as Trolox equivalent by spectrophotometer (Jasco V-700). Different letters in the same column indicate statistical difference (p* ≤ *0.05) among ingredient and potato lines. Three replicates were analyzed (with 3 instrumental measures per sample). Data were analyzed by one-way ANOVA followed by the Tukey test (p < 0.05) by InfoStat version 2020. http://www.infostat.com.ar).*

#### **Table 3.**

*Color intensity (E1%), total anthocyanins (CAT) and antioxidant activity (FRAP) of potato-based ingredients (flakes and freeze-dried powder) elaborated from red flesh potato (INIA RS58-3), and purple flesh (RQ12-521).*

*Red and Purple Flesh Potatoes a Healthy and Attractive Alternative Associated… DOI: http://dx.doi.org/10.5772/intechopen.99181*

preserves better the nutritional value such as naturally occurring. And, in spray dried powder the high temperature of heat may cause the loss of nutritional value. Red flesh potato (INIA RS58-3) and purple flesh potato (INIA RQ12-521) were selected for further evaluation because they fresh tubers show greater differences in color intensity. Potato-based ingredients as flakes and freeze-dried powder were compared (**Table 3**) for color intensity (E1%), total anthocyanins (CAT), and antioxidant activity (FRAP). As expected, freeze-dried powder preserved better the color intensity (E1%), total anthocyanins (CAT) and antioxidant activity (FRAP), however the flakes values were also attractive. These potato-based flakes and freezedried powder are food coloring because both ingredients provide color and bioactive compounds, with different applications.

#### **3. Conclusion**

All these antecedents, suggest that red and purple fleshed potatoes are not only a promising crop for starvation problem, also their consume promote health and may prevent chronic diseases. Anthocyanin-rich extracts from red and purple fleshed potatoes have high potential as natural colorants with multiple applications in food industry. Also, these potatoes contain an important group of secondary plant metabolites associated with antioxidant activity and positive health benefits, as phenolics, flavonoids, and anthocyanins. INIA's new putative color flesh potato cultivars (red flesh potato (INIA RS58-3), purple flesh potato (INIA RQ12-521), blue-violet flesh potato (INIA RÑ98-9)) are promising raw materials for natural color extraction and food coloring ingredients.

#### **Acknowledgements**

This chapter is a review the latest research on color fleshes potato and recent results of the authors on red to purple fleshed potato foodcoloring ingredients as well. We would like to acknowledge all authors cited in the references.

Acknowledgments to CONICYT-PAI I7817020005 and FIA PYT-2017-0488 grants.

#### **Conflict of interest**

The authors declare no conflict of interest.

#### **Appendices and nomenclature**

INIA Instituto de Investigaciones Agropecuarias de Chile (Institute of Agricultural Research of Chile). CAGR Compound annual growth rate.

Solanum tuberosum *- A Promising Crop for Starvation Problem*

#### **Author details**

María-Teresa Pino\* and Cristina Vergara Food for the Future Department, Instituto de Investigaciones Agropecuarias de Chile (Institute of Agricultural Research of Chile), Chile

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 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.

*Red and Purple Flesh Potatoes a Healthy and Attractive Alternative Associated… DOI: http://dx.doi.org/10.5772/intechopen.99181*

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Section 4 Potato Breeding

#### **Chapter 8**


**1. Introduction**

Magnesium (Mg) alloys have been widely applied as lightweight engineering materials due to their unique properties [1–8]. As commercial Mg-Zn-based alloys, ZK60 (Mg–Zn–Zr) alloys [9] have attracted great interest from researchers due to their high strength [10–12]. The microstructure [13,14], mechanical properties [15–17], and biological applications [18,19] of ZK60 alloys have been studied widely in recent decades. It has been verified that microstructure evolution is essential for the mechanical properties of ZK60 alloys, grain refinement, and stable precipitates, having vital effects on improving the mechanical properties [20–23]. Nevertheless, the weak corrosion resistance of ZK60 alloys limits their further applications.

 The second phases of Mg alloys may have a dual role in their corrosion, i.e., a galvanic acceleration effect or a corrosion blocking effect, depending on their quantities and distribution [24–26]. In Mg-Al alloys, when the amount of aluminum (Al) is low (e.g., Mg-5Al), the β-phase (Mg12Al17) is relatively discontinuous in the Mg matrix and mainly acts as a cathode

phase to accelerate the dissolution of the matrix. As the content of the Al element increases (e.g., Mg-10Al), the β-phase precipitates are tiny and continuously distributed along the grain boundaries, producing a barrier to prevent corrosion [27]. The similar effect of the second phase was reported in other Mg alloys [28,29]. However, the effect of the second phase in ZK60 alloys on their corrosion behaviors is barely reported. Some researchers tried to enhance the corrosion resistance of ZK60 alloys by modifying their microstructure through heat treatment [30,31], deformation processing [32], and alloying [33–36]. Even so, the relationship between the microstructure and corrosion behavior of ZK60 alloys needs more studies for it to be investigated.

Some studies reported the corrosion behavior of ZK60 alloys on different occasions. Cheng et al. [37] pointed out that the Zr element in ZK60 alloys refined the grain and purified the alloy composition, which could improve its corrosion resistance in 1 M NaCl. Zeng et al. [38] investigated the effects of the microstructure and concentration of NaCl (3.5 and 5.0 wt.%) on the corrosion behavior of an extruded ZK60 alloy. They found that an increase in the grain size of the ZK60 alloy accelerated its corrosion rate. The alloy microstructure played a crucial role in the pitting and intergranular corrosion. Xu et al. [39] reported that the corrosion rate of a cast ZK60 alloy decreased with the immersion time in solutions containing 3.5 wt.% NaCl, NaBr, and NaI, while it displayed passivation in 3.5 wt.% NaF solution. Apart from the above reports, some studies focused on the biodegradation behavior of ZK60 alloys in Hank's solution, Ringer's solution, simulated body fluid, and artificial urine for biomedical applications [40–43]. The biodegradable property of the ZK60 alloys is the interesting issue in these investigations. In general, the above research usually concentrated on the uniform corrosion of ZK60 alloys, and little attention was paid to the development of their local corrosion. The influence of microstructure on the local corrosion of ZK60 alloys is still not clearly understood, especially the effect of the second phase.

In this study, a commercial cast ZK60 alloy was selected as the test material. Its microstructure was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), and scanning Kelvin probe force microscopy (SKPFM) analysis. The general and local corrosion of the alloy in 0.1 M NaCl was investigated using weight loss tests, hydrogen evolution tests, and electrochemical measurements, as well as corrosion morphology monitoring with an optical microscope and SEM. The effect of the microstructure of the cast ZK60 alloy, especially the second phase and the distribution of alloying elements, on the corrosion initiation and developmental features of the alloy were investigated, and the mechanisms involved were studied. This work will help to verify the relationship between the microstructure and the corrosion behavior of ZK60 alloys. Moreover, it may also provide a theoretical basis for improving the corrosion resistance of ZK60 alloys by adjusting the microstructure in future research.

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

#### *2.1. Test Material and Solution*

A commercial as-cast ZK60 alloy was used in this study. Table 1 presents its chemical composition, analyzed by inductively coupled plasma-atomic emission spectrometry (ICP-AES, SPECTRO, Kleve, Germany). All the solutions used in this work were prepared with analytical-grade reagents and distilled water. The test solution was 0.1 M NaCl under an open-air condition, which was controlled at 25 ± 1 ◦C with a water bath.

**Table 1.** Chemical composition of the cast ZK60 alloy (wt.%).


**2. Transitions of educational psychology from simplicity to complexity**

It is possible to establish that its birth and development is mainly generated in the twentieth century, spite the identification of a varied range of European precursors such as North Americans [1] in the previous centuries. The birth and consolidation of this discipline, found between the years 1900 and 1920, is sustained and guided by ideologies and conceptual frameworks linked to the behavioral and functionalist perspective of psychology [1, 2], that will print an unmistakable seal of scientificity, evaluation and intervention of the medium to guide such behavior. This seal will be maintained throughout the twentieth century as part

These perspectives of psychology and their cognitivist derivation (cognitive behavioral psychology) were developed on the basis of the conception of the world and the human being of the paradigm of simplicity, which aims to value objectivity, control and reduction of variables [3, 4]. Even though other psychological views populated the twentieth century (psychoanalysis, humanistic psychology, transpersonal or systemic psychology, etc.), they have not had the same impact on educational psychology, as well as on education as a socio-cultural phenomenon, perhaps due to the fact that they search exactly the opposite, that is, the integrity, the

With a discipline inspired by the eighteenth and nineteenth centuries, and materialized in the twentieth century, I think it is fair, at the dawn of the twenty-first century, to establish a reflexive, innovative and transformative review of the educational psychology. This is necessary because even with the great amount of knowledge and expertise that has accumulated, educational psychology has not significantly impacted the educational process or contributed

What kind of educational psychology does the twenty-first century need? This is a great ques-

In this chapter we propose a resignification of the work of the educational psychologist in order to establish a complex and non-simplistic discipline that allows facing the essential tensions and dilemmas that have never been clarified [6] such as: what is the identity of educational psychology, and what is the purpose in the generation of knowledge. This desirable horizon, educational psychology from the complexity, requires a crucial tool: the availability of critical thinking. The nature of a professional is to use criticality to generate change, both of themselves as a professional and as a person, as well as of the educational community in

The critical concept has different acceptations, on the one hand, it is seen as something decisive or of priority, which must be resolved in a timely manner, and on the other hand, as the constant evaluation of an idea or situation (definition from the Royal Spanish Academy or RAE in Spanish) [7]. In this way, and from a superficial synthesis of these acceptations, critical thinking is a tool that would allow facing relevant situations of the person or the community through questioning and reflection, in order to achieve a change in said situation, and therefore, should be the strategy that allows the work of educational psychologists to promote change as a part of the sociocultural interaction in the educational community, a focus that

to the sociocultural change that is required in these times to learn and teach [5].

subjectivity, the emotional; in other words, the complexity.

tion to answer. However, little has been done about it [6].

of the professional role.

8 Educational Psychology - Between Certitudes and Uncertainties

which they are located.

César Coll was already pointing out in 2001.

Munné [8] has pointed out that the discussion of simplicity and complexity is linked to the search for knowledge, which relates this discussion with an ontological and epistemological analysis with which human beings have explained reality. The preceding is due to the fact that it is a search for knowledge that has guided the development of scientific and professional disciplines. The way in which this search has been based has been to a great extent, although not in a single dimension, on the rationality and reductionism that are characteristics of the traditional and positivist scientific outlook. This has allowed the capturing and understanding of reality in a sequential and orderly manner, and with basic processes of cognition that promote the processing of information in an expeditious and efficient manner, in order to achieve clear, measurable and unambiguous knowledge.

This perspective is oriented by the human need of seeing this reality as something ordered, perfect and harmonious [4, 8], where even the knowledge of the people and the educational theory should also be equally ordered, structured, and specified in stereotyped actions, with a hierarchical, clear and objective management, that leaves out the problems and noises that arise in the educational level (such as learning difficulties, school demotivation, violence and power) as they cannot be explained nor adequately controlled [4, 9].

According to the perspective of the simplistic paradigm, psychology as a scientific discipline (as well as the traditional educational psychology) would fit greatly in that model, as it would present characteristics that are focused on individual attention (preferably), on the assessment of technical knowledge, in the functionality of a pathology, in the standardization of behaviors to behavioral standards (norms), and in the hierarchical relation between the fields of knowledge [6].

Even the history of educational psychology has been influenced by the characteristics of simplicity, as its birth and consolidation seemed to have responded more to pragmatic-conceptual determinations, such as the adherence to the behavioral theory of the 1920s and 1930s, rather than an academic reflection [6]. This adoption of the scientific position (uncritical and amoral), has established a reductionist approach that is focused on the teaching and learning process as a central object of educational psychology [1].

It is necessary to properly recognize the contribution of a scientific view of simplicity that has allowed the conceptual and empirical field of psychology to develop as a serious and respectable discipline, thus, producing the same result in educational psychology. However, nowadays this view has been imposed as the only acceptable paradigm for the development of knowledge and professional performance, generating difficulties in the theoretical, paradigmatic and even technical evolution that this discipline presents in its link with the educational process, which results in an inability to provide adequate answers for the challenges that arise [10].

Therefore, it is necessary to direct our practices toward the development of a perspective centered on complexity, as it is part of our everyday reality, and can give an account of our most human characteristics, the solidary interconnection of the phenomena, and the uncertainty and the contradiction [3]. Its nature is holistic and evolutionary, in constant transformation, and includes the subject as an integral part of the construction of change. It sees knowledge as a multidimensional aspect, integrated by diverse approaches, which allow the integration of diversity, error, interculturality, emotionality and uncertainty [11].

result of cultural valuation, being an ideal that combines the main values of social constructionism, in clear opposition to the reductionism and disciplinary focus that has been gener-

A Critical Role of the Psychologist: A Way to Achieve Complexity in Educational Psychology

http://dx.doi.org/10.5772/intechopen.80509

11

The critical perspective is a position in the search for knowledge that allows us to reveal other different perspectives, which opens our understanding toward interpretations different from those given to us by tradition. Critical psychology has its roots in the critical theory of the Frankfurt School, with thinkers such as Horkheimer, Adorno, Marcuse, or Habermas [14].

In this view the acceptance of the world as it is was rejected, with its inequalities and injustices, and with the domination of classes, indicating that reality is not determined by natural reasons, but by historical and particular reasons that lead to a certain order [15]. Some of the most significant, worldwide known, authors of this perspective are Michel Foucault and Paulo Freire. Foucault is mainly known for the redefinition of concepts such as power, knowledge and discourse, as power is not exercised only with sovereignty or laws, nor with weapons or force, but with knowledge. In this sense, knowledge refers to all our opinions and knowledge about reality, to our convictions about basic facts of daily life, as well as to the value parameters we give to such events, good and evil, what is normal, and right or wrong,

Freire rescues the human sphere in a more social sense, politically committed with education, and argues that the traditional powers as well as authority impose an inequitable system in which the poor are deprived of their opportunity to participate and change the schemes that maintain said inequity. In addition, he advocates an education that breaks the culture of silence and generates awareness in the oppressed of the cultural and economic causes of their situation, that is, to free the human being through the awareness of their reality and their potential. For this purpose, education must be changed, because this is one of the great mechanisms that reproduce the established order and domesticates individuals in those reali-

Critical psychology does not act only on dominant theories, it also deals with methods, and its central task is to face the values and practices of psychology that do not review or question the forms of oppression that could be being transmitted or reproduced by them. The questioning, through critical judgment, of the different ways of exercising power, as well as its explicit and implicit manifestations in psychological practice and in daily life, are subject of critical studies, due to the fact that they can be presented as natural ways of being of some situations not

Criticism as a reflective activity, in a kind of thinking that allows us to analyze the level of foundation of an information or idea, based both on reflection itself and on the reflection of others [16, 17]. In this way, psychology has been developed into two flows, on one hand, from social critical psychology, that is, a more theoretical approach that questions the processes

discussed or, in some cases, argued as the only appropriate form of social existence.

ated in some fields of knowledge that are born from the simplistic view.

whether that is to an individual or social organization level.

ties that do not allow them to evolve as human beings [15].

**psychology**

**3. Critical thinking as a strategy for the evolution of educational**

This paradigm is characterized by a transdisciplinary conception of knowledge and praxis, which is achieved through an intricate conformation that must modify itself and, at the same time, modify the subjects that integrate its action, in a constant and participatory manner. In particular, it would allow the generation of a complex, dynamic and non-linear methodology that centrally deals with variability. This paradigm should be endowed with characteristics that are simultaneously so general as to explain phenomena in a vast variety of human situations, which is what science requires, and, at the same time, be able to accept specificities that rescue individuality and subjective contextualization [12].

Thus, in educational psychology, a view that comes from this paradigm is needed to a great extent, due to the fact that education is, precisely, one of the eminently complex areas of human interaction that requires balancing community needs such as discipline, coexistence and the curriculum, with individual needs, motivation and learning demand.

It would imply constructing from psychoeducational knowledge, with awareness, participation and meaning, aiming for a change and allowing it to change us, that is, with a tension between the technical and the critical versus knowledge and practice. In other words, generating knowledge, tools and techniques from theoretical and empirical bases as it has traditionally been done, but reflecting and modifying said elements from experience and interdisciplinary collaboration [6].

The preceding would also imply understanding and valuing the teaching-learning process as a tension between stability and change, given the need to transmit knowledge (what we call recurrence), in order to maintain the culture and, at the same time, to generate new knowledge, to produce what should lead us to change and transformation. In addition, it implies the establishment of a tension between the expertise, with all the knowledge and power that it can grant a person, and the inexperience, with all its ingenuity and dependence, while also valuing the social interaction and feedback that we generate with the other members of the educational community [13]. Finally, it would involve promoting the tension between the construction of knowledge, the techniques and professional identity, and the construction of knowledge based on the expert and inexperienced collaboration of the views, professional and non-professional, of those who share the educational framework.

To achieve this perspective from the complexity, it is of great importance to discuss the tensions of the discipline, as it is through reflection and dialog that we define the limits of knowledge and its adaptation to everyday reality. This does not involve leaving out research and disciplinary conceptualization, but establishing a balance between the latter and the social and cultural reality.

Through this, it would be possible to channel one of the greatest challenges promoted by the perspective of complexity, that is, transdisciplinarity [3]. This concept has been recently developed, due to the evolution that disciplinary groups have experienced in research, as a result of cultural valuation, being an ideal that combines the main values of social constructionism, in clear opposition to the reductionism and disciplinary focus that has been generated in some fields of knowledge that are born from the simplistic view.