# Storage Conditions and Adsorption Thermodynamic Properties for Purple Corn

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## Abstract

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_{e}) was determined by the continuous weight-change method. Seven mathematical models of isotherms were modeled, using the coefficient of determination R

^{2}, mean absolute error (MAE), and estimated standard error (ESE) as the convergence criterion. Thermodynamic parameters such as isosteric heat (q

_{st}), Gibbs Free Energy (ΔG), differential entropy (ΔS), activation energy (E

_{a}), and compliance with the isokinetic law were evaluated. It was observed that the adsorption isotherms presented cross-linking around 75% ERH and 17% X

_{e}, suggesting adequate storage conditions at these values. The GAB and Halsey models reported better fit (R

^{2}> 97%, MAE < 10%, ESE < 0.014 and random residual dispersion). The reduction of X

_{e}from 17 to 7%, increases q

_{st}, from 7.7022 to 0.0165 kJ/g, while ΔG decreases considerably with the increase in X

_{e}, presenting non-spontaneous endergonic behavior, and linear relationship with ΔS, evidencing compliance with the isokinetic theory, governed by q

_{st}. E

_{a}showed that more energy is required to remove water molecules from the upper layers bound to the monolayer, evaluated using C

_{GAB}. The models predicted the storage conditions, and the thermodynamic parameters show the structural stability of the purple corn grains of the Canteño variety during storage.

## 1. Introduction

_{e}) in food is reached when the partial vapor pressure of the material equals the vapor pressure of the air that contains it, to the ratio of the vapor pressure of the food. The ambient air is called water activity, a

_{w}and is a determining factor during storage [22,23].

_{w}and equilibrium moisture data [33,34]. These models, such as BET and GAB, provide information on the thermodynamic behavior of the water bound to the active sites [35,36], on the surface of the food.

## 2. Materials and Methods

#### 2.1. Samples

#### 2.2. Construction of Adsorption Isotherms

#### 2.3. Determination of Equilibrium Moisture

_{e}is the equilibrium moisture on a dry basis; m

_{eq}, is the mass of the sample at equilibrium, g; and m

_{s}is the mass of the dry sample, g.

#### 2.4. Adjustment of Adsorption Isotherms

^{2}, mean absolute error (MAE) (Equation (2)) and the estimated standard error (ESE) (Equation (3)), by considering good fit when MAE < 10% and ESE lower [47,48,49,50,51]. Likewise, the dispersion of the residuals of X

_{e}was taken as a convergence criterion, which evaluates the tendency of the systematic and random errors during the experimentation [51].

_{ei,exp}is the observed experimental equilibrium moisture content; M

_{ei,pre}is the predetermined moisture content in the observations; N is the number of experimental observations, n is the number of constants in the model.

#### 2.5. Thermodynamic Parameters

_{st}) (or differential enthalpy) evaluates the difference between the total heat of sorption in the purple corn and the heat of vaporization of water at the system temperature [52], and can be estimated using the Clausius-Clapeyron equation (Equation (11)) [53].

_{st}was obtained by plotting ln a

_{w}vs. 1/T, at their respective humidities, where q

_{st}/R is the slope.

_{st}is the isosteric heat of sorption (kJ/kg); and R is the universal gas constant (8.314 kJ/kmol·K) for water (0.4619 kJ/kg·K).

_{st}data X

_{e}, were fitted to the Tsami equation (Equation (12)) [53].

_{st}is the isosteric heat of sorption when the moisture content is constant; X

_{e}is the equilibrium humidity (g water/g dry sample), q

_{0}is the isosteric heat of adsorption (kJ/mol) of the first water molecule in the food and is defined as X

_{e}→ 0 $\Rightarrow $ q

_{st}→ q

_{0}; and X

_{0}is the characteristic moisture content for each product.

_{β}is the isokinetic temperature (K); ΔG

_{β}is the free energy (kJ/kg) at T

_{β}.

_{β}is an indicator in which it is assumed that all interactions within the purple corn grains occur with the same speed [57], while the term +ΔG

_{β}represents whether the adsorption process is spontaneous or not (−ΔG

_{β}).

_{β}with the harmonic mean temperature (T

_{hm}) (Equation (17)) [56,58,59], and it is valid when T

_{β}≠ T

_{hm}, likewise if T

_{β}> T

_{hm}, the process of sorption is governed by the isosteric heat of sorption (enthalpy of sorption), and if T

_{β}< T

_{hm}by the entropy [60,61].

_{0}is a pre-exponential factor, and E

_{a}is the activation energy (kJ/mol).

## 3. Results and Discussion

#### 3.1. Adsorption Isotherms

_{e}, of purple corn was reached after 15 days at 18 °C, and in 12 days at 25 °C and 30 °C. The behavior of X

_{e}at storage conditions is shown in Figure 1, and a crossover of the isotherms around a

_{w}0.75 is observed, due to the composition of purple corn of a higher content of carbohydrates and sugars compared to other corn varieties, this behavior is characteristic of fruits with a high sugar content [16,20,22,23,25,31,62].

#### 3.2. Adjustment of Adsorption Isotherms

^{2}values of 0.967 and 0.974, MAE of 5.149% and 5.902%, and ESE 0.013 and 0.011, respectively; at 25 °C, R

^{2}values of 0.973 and 0.976, MAE 8.795% and 8.628% and ESE 0.014 and 0.012 were found, while at 30 °C, R

^{2}values were reported to be 0.984 and 0.975, MAE 8.508% and 10.412% and ESE as 0.011 and 0.013, respectively (Table 3). In the same way, both models presented random residual dispersion at the study temperatures, which indicates that the models better attenuate systematic and experimental errors due to repetitiveness, better representing the adsorption phenomenon [22,25,34,66,67].

^{2}values > 0.90. In fact, these models are used as predictors of X

_{e}behavior at different relative humidities, generally for cereals and fruits [20,30,35,44,65].

_{GAB}values, these were greater than unity, which indicates that the adsorption in the monolayer is fast, that is, the humidity at the monolayer level is achieved quickly during the first days and, as a consequence, the purple corn is prone to rapid attack by molds and yeasts [26,27,68].

_{GAB}is high is because the surface of the purple corn grain is constituted by a large number of active centers, including polar groups of the −CO, −COO

^{−}and −NH

^{3+}, which allow it to establish a greater number of hydrogen bridge bonds.

_{GAB}, which is related to the standard chemical potential between the molecules of the second layer and those of the pure liquid state, was observed to increase with temperature (Table 3), which suggests a decrease in humidity at low a

_{w}values.

_{m}level of the GAB model, was found to be around 7% d.b., which is a usual behavior for corn varieties [39,69], the fact that X

_{m}decreases with temperature indicates that at higher temperatures, the moisture loss is greater at the monolayer level for a defined relative humidity [67,69], due to the breaking of the intermolecular bonds of the hydrogen bridge type between the surface of the corn grain and the water available at the X

_{e}level. This suggests that temperature is a critical condition for the attack of molds and yeasts, which is a typical behavior of foods that follow type II isotherms [24,34,36,39,54,64].

#### 3.3. Thermodynamic Parameters

_{st}of purple corn was determined considering a

_{w}values calculated using the Halsey equation, for X

_{e}between 0.07 and 0.17. Figure 2a, presents the behavior of q

_{st}as a function of X

_{e}, and it is observed that as the equilibrium humidity increases, the value of q

_{st}decreases from 7.7022 to 0.0165 kJ/g, meaning this behavior is a result of an initially high humidity at the monolayer level, requiring more energy to break the polar and hydrogen bonds on the surface of the corn grain, and as X

_{e}increases, the active sites that adsorb water are no longer available, which is usual in foods with a high carbohydrate content [39,67,69,70,71].

_{st}values found are higher than those reported for this cereal [39,69] due to the coloration of the purple corn grain, which is related to the presence of phenolic compounds and sugars [2,5,15], thereby giving it a greater number of functional groups, with the capacity to establish a greater number of bonds with water, for which it would require more energy to eliminate it from the monolayer.

_{e}increases, the availability to form bonds is lower, thereby requiring less energy, which is characteristic of non-spontaneous processes when they reach equilibrium, as evidenced by the adsorption systems of purple corn at different relative humidities [41,54,75].

_{e}interval between 7 to 15%, presenting a rapid drop up to X

_{e}11% (Figure 2c), this would be due to the greater availability of the active sites, and from this point, the mobility of the molecules decreases, related to ΔG [19,41,76].

^{2}> 0.99) was observed between q

_{st}and ΔS (Figure 2d), that is, there is a direct relationship between the energy needed to bind free water to the food surface, and the mobility of water molecules at the monolayer level, so the isokinetic theory, or enthalpy–entropy compensation, applies to this experimentation [36,45,55,56].

_{β}was 476.53 K, while T

_{hm}297.0 K, which suggests a sorption process governed by q

_{st}(T

_{β}> T

_{hm}) [60,61], which is usual behavior in seeds and grains [24,35,41,43], likewise, this comparison established that purple corn grains remain stable following structural modifications that could occur during water removal or drying in the range of the study temperatures [44,77].

_{a}), which represents the necessary energy of the phenomena occurring at the level of the water monolayer of the corn grain surface.

_{m}), and bind to the specific polar groups of corn, was 10.947 kJ/mol, for the interval from 18 to 30 °C (Table 4), on the other hand, the C

_{GAB}parameter is related to the difference in energy of the molecules adsorbed in the monolayer and the upper ones [27,44,56,68], whose value was 18.84 kJ/mol. Likewise, the parameter k

_{GAB}, which refers to the chemical potential, that is, the energy necessary to form the bond between the water molecules and the active sites [68], was 6.82 kJ/mol.

## 4. Conclusions

_{e}at 18, 25, and 30 °C, suggesting adequate storage conditions at these values. The GAB and Halsey models reported a better fit and would allow for a description of the behavior of corn grain moisture at different equilibrium relative humidities. The reduction of X

_{e}between 17 and 7% occurs with an increase in the isosteric heat of adsorption, q

_{st}, from 7.7022 to 0.0165 kJ/g, while the Gibbs free energy decreases considerably with the increase in X

_{e}at the study temperatures, showing a non-spontaneous endergonic behavior, and presents a positive linear relationship with the adsorption differential entropy, evidencing the compliance of the isokinetic theory, governed by q

_{st}, which suggests the structural stability of corn grains during storage and drying. The activation energy showed that more energy is required to remove water molecules from the upper layers bound to the monolayer, evaluated using C

_{GAB}.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**(

**a**) Isosteric heat of sorption; (

**b**) Gibbs free energy; (

**c**) Differential entropy for purple corn (

**d**) Relationship between differential entropy and isosteric heat of sorption (** evaluated at 5% significance).

Substance | Equation | R^{2} |
---|---|---|

Sodium hydroxide | ${a}_{w}=0.081-1.128\times {10}^{-3}T+3.929\times {10}^{-5}{T}^{2}-5.092\times {10}^{-7}{T}^{3}$ | 0.998 |

Lithium chloride | $Ln{a}_{w}=\left(\raisebox{1ex}{$500.95$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)-3.85$ | 0.980 |

Potassium Acetate | $Ln{a}_{w}=\left(\raisebox{1ex}{$861.39$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)-4.33$ | 0.970 |

Magnesium chloride | ${a}_{w}=0.365-2.523\times {10}^{-3}T+5.071\times {10}^{-5}{T}^{2}-4.166\times {10}^{-7}{T}^{3}$ | 0.963 |

Magnesium Nitrate | $Ln{a}_{w}=\left(\raisebox{1ex}{$356.60$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)-1.82$ | 0.990 |

Potassium iodide | $Ln{a}_{w}=\left(\raisebox{1ex}{$255.90$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)-1.23$ | 1.000 |

Sodium chloride | $Ln{a}_{w}=\left(\raisebox{1ex}{$228.92$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)-1.04$ | 0.960 |

Potassium chloride | $Ln{a}_{w}=\left(\raisebox{1ex}{$367.58$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)-1.39$ | 0.970 |

Barium chloride | ${a}_{w}=0.908-4.011\times {10}^{-4}T+2.786\times {10}^{-5}{T}^{2}-2.037\times {10}^{-7}{T}^{3}$ | 0.997 |

Model | ||
---|---|---|

Temperature dependent | ||

BET | ${x}_{e}=\frac{{x}_{m}{c}_{BET}{a}_{w}}{\left[\left(1-{a}_{w}\right)\left(1+\left({c}_{BET}-1\right){a}_{w}\right)\right]}$ | (2) |

GAB | ${x}_{e}=\frac{{x}_{m}{c}_{GAB}{k}_{GAB}{a}_{w}}{\left[\left(1-{k}_{GAB}{a}_{w}\right)\left(1-{k}_{GAB}{a}_{w}+{c}_{GAB}{k}_{GAB}{a}_{w}\right)\right]}$ | (3) |

Oswin | ${x}_{e}=A{\left[\frac{{a}_{w}}{1-{a}_{w}}\right]}^{B}$ | (4) |

Modified Henderson | $1-{a}_{w}=\mathit{exp}(-kT{x}_{e}^{{n}^{\prime}})$ | (5) |

Chung y Pfost | ${a}_{w}=\mathit{exp}(\frac{A}{RT}\mathit{exp}(-B{x}_{e}))$ | (6) |

Temperature independent | ||

Halsey | ${a}_{w}=\mathit{exp}\left[\frac{-A}{{x}_{e}^{B}}\right]$ | (7) |

Henderson | $1-{a}_{w}=\mathit{exp}(-k{x}_{e}^{n})$ | (8) |

_{BET}, k

_{GAB}, k, n, n′ are constants of the equations; X

_{e}is the equilibrium humidity (g water/g dry basis); X

_{m}is the humidity of the molecular monolayer (g water/g dry mass); R is the universal gas constant; and, T is the temperature (K).

Model | Parameters | R^{2} | SEE | MAE (%) | Residual Distribution | ||
---|---|---|---|---|---|---|---|

Temperature dependent | |||||||

GAB | 18 °C | X_{m} | 0.076 | 0.967 | 0.013 | 5.149 | Random |

C_{GAB} | 1,502,959 | ||||||

K | 0.755 | ||||||

25 °C | X_{m} | 0.068 | 0.973 | 0.014 | 8.795 | Random | |

C_{GAB} | 4,501,090 | ||||||

K | 0.825 | ||||||

30 °C | X_{m} | 0.064 | 0.984 | 0.011 | 8.508 | Random | |

C_{GAB} | 1,812,258 | ||||||

K | 0.842 | ||||||

BET | 18 °C | X_{m} | 0.028 | 0.301 | 0.056 | 33.845 | Trending |

C_{BET} | −19.315 | ||||||

25 °C | X_{m} | 0.030 | 0.604 | 0.049 | 26.359 | Trending | |

C_{BET} | −20.218 | ||||||

30 °C | X_{m} | 0.029 | 0.594 | 0.051 | 27.66 | Trending | |

C_{BET} | −21.015 | ||||||

Oswin | 18 °C | A | 0.132 | 0.959 | 0.014 | 6.657 | Random |

B | 0.264 | ||||||

25 °C | A | 0.127 | 0.957 | 0.016 | 9.171 | Slightly random | |

B | 0.323 | ||||||

30 °C | A | 0.121 | 0.966 | 0.015 | 9.870 | Slightly random | |

B | 0.345 | ||||||

Modified Henderson | 18 °C | k | 0.336 | 0.912 | 0.020 | 10.794 | Trending |

n | 2.518 | ||||||

25 °C | k | 0.130 | 0.903 | 0.024 | 12.346 | Trending | |

n | 2.005 | ||||||

30 °C | k | 0.095 | 0.927 | 0.022 | 12.53 | Trending | |

n | 1.809 | ||||||

Chun-Pfost | 18 °C | A | −24.266 | 0.948 | 0.015 | 7.443 | Random |

B | 19.759 | ||||||

25 °C | A | −16.300 | 0.929 | 0.021 | 12.428 | Trending | |

B | 16.826 | ||||||

30 °C | A | −13.974 | 0.940 | 0.020 | 13.612 | Trending | |

B | 16.113 | ||||||

Temperature independent | |||||||

Halsey | 18 °C | A | 0.002 | 0.974 | 0.011 | 5.902 | Random |

B | 2.867 | ||||||

25 °C | A | 0.004 | 0.976 | 0.012 | 8.628 | Random | |

B | 2.387 | ||||||

30 °C | A | 0.005 | 0.975 | 0.013 | 10.412 | Random | |

B | 2.276 | ||||||

Henderson | 18 °C | k | 97.702 | 0.912 | 0.020 | 10.794 | Trending |

n | 2.518 | ||||||

25 °C | k | 38.724 | 0.903 | 0.024 | 12.346 | Trending | |

n | 2.005 | ||||||

30 °C | k | 28.762 | 0.927 | 0.022 | 12.529 | Trending | |

n | 1.809 |

Parameters | 18 °C | 25 °C | 30 °C | E_{a} (kJ/mol) |
---|---|---|---|---|

X_{m} | 0.0764 | 0.0677 | 0.0640 | −10.947 |

C_{GAB} | 1,502,958.98 | 4,501,089.95 | 1,812,257.53 | 18.843 |

k | 0.7552 | 0.8252 | 0.8418 | 6.820 |

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**MDPI and ACS Style**

Choque-Quispe, D.; Ramos-Pacheco, B.S.; Choque-Quispe, Y.; Aguilar-Salazar, R.F.; Mojo-Quisani, A.; Calla-Florez, M.; Solano-Reynoso, A.M.; Zamalloa-Puma, M.M.; Palomino-Malpartida, Y.G.; Alcarraz-Alfaro, T.;
et al. Storage Conditions and Adsorption Thermodynamic Properties for Purple Corn. *Foods* **2022**, *11*, 828.
https://doi.org/10.3390/foods11060828

**AMA Style**

Choque-Quispe D, Ramos-Pacheco BS, Choque-Quispe Y, Aguilar-Salazar RF, Mojo-Quisani A, Calla-Florez M, Solano-Reynoso AM, Zamalloa-Puma MM, Palomino-Malpartida YG, Alcarraz-Alfaro T,
et al. Storage Conditions and Adsorption Thermodynamic Properties for Purple Corn. *Foods*. 2022; 11(6):828.
https://doi.org/10.3390/foods11060828

**Chicago/Turabian Style**

Choque-Quispe, David, Betsy S. Ramos-Pacheco, Yudith Choque-Quispe, Rolando F. Aguilar-Salazar, Antonieta Mojo-Quisani, Miriam Calla-Florez, Aydeé M. Solano-Reynoso, Miluska M. Zamalloa-Puma, Ybar G. Palomino-Malpartida, Tarcila Alcarraz-Alfaro,
and et al. 2022. "Storage Conditions and Adsorption Thermodynamic Properties for Purple Corn" *Foods* 11, no. 6: 828.
https://doi.org/10.3390/foods11060828