Activation Energy for Carbohydrate solutions

Table 1: Activation energy data is obtained by fitting the Arrhenius model (equation) to the viscosity data. The viscosity of the carbohydrates in the rheometer was calculated from the slope of shear stress versus shear rate plots, with the internal cylinder rotating at 44 different speeds in the range of 0.028 to 243 rpm. The tabulated values of the parameter Ea, correspond to the fitting of the Arrhenius model.

ID Name Concentration (% w/w) Volumetric molar fraction φ Ea (kJ/mol) RMS (%)
1 sucrose 10 0.075 16.05832 9.16
2 sucrose 20 0.155 19.96957 6.4
3 sucrose 30 0.239 22.28966 3.32
4 sucrose 40 0.329 26.0641 15.4
5 sucrose 50 0.424 33.04732 8.46
6 sucrose 60 0.524 40.69629 12.36
7 glucose 10 0.078 16.56387 14
8 glucose 20 0.161 19.95477 6.51
9 glucose 30 0.247 22.16732 2.64
10 glucose 40 0.338 26.06795 16.02
11 glucose 50 0.434 33.12279 13.43
12 glucose 60 0.535 40.24821 16.8
13 fructose 10 0.078 16.3683 9.03
14 fructose 20 0.161 20.08474 6.71
15 fructose 30 0.247 22.4675 9.58
16 fructose 40 0.338 26.05844 16.01
17 fructose 50 0.434 32.72751 6.6
18 fructose 60 0.535 40.28572 14.92

NOMENCLATURE:

Ea = Activation Energy (J/mol)
RMS = Root mean square (%)

NOTE: The experimental reference temperature was 45°C (318.15 K).

Reference: Telis V. R. N. Telis-Romero J. Mazzotti H. B. & Gabas A. L. (2007). Viscosity of Aqueous Carbohydrate Solutions at Different Temperatures and Concentrations. International Journal of Food Properties 10(1) 185–195. DOI: https://doi.org/10.1080/10942910600673636


Table 2: Activation energy data is obtained from acid-catalyzed hydrolysis experiments of the carbohydrates with 0.998 N sulfuric acid.

ID Name k (x 105 s-1) at 40°C k (x 105 s-1) at 60°C k (x 105 s-1) at 80°C Ea (kcal/mol) ΔH (kcal/mol) ΔS (cal/mol/degree)
1 Maltose 0.0361 0.600 10.2 33.1 32.4 +14.7
2 Maltitol 0.0361 0.506 7.28 31.2 30.5 +8.6
3 Maltose phenylosotriazole 0.0250 0.439 7.55 33.2 32.5 +14.5
4 Maltobionic acid 0.0222 0.369 6.00 32.6 31.9 +12.1
5 Maltose cyanohydrin 0.0417 0.550 7.34 30.3 29.6 +6.2
6 Maltose I-phenylflavazole 0.308 0.892 2.58 12.4 11.7 -46.7

NOMENCLATURE:

Ea = Activation Energy (kcal/mol)
ΔH = Enthalpy of activation (kcal/mol)
ΔS = Entropy of activation (cal/mol/degree)

NOTE: Hydrolytic Rate Data (In 0.998N sulfuric acid).

Reference: BeMiller, J. N., & Mann, R. K. (1966). Acid-catalyzed hydrolysis of maltose and selected maltose derivatives. Carbohydrate Research, 2(1), 70–79. DOI: https://doi.org/10.1016/s0008-6215(00)81779-6


Table 3: Rate constants obtained from the kinetic equation at various temperatures for D- and L-fucose are presented, along with activation energies derived from the Arrhenius fits.

ID Name T (K) k (x 105 s-1) Ea (kJ/mol)
1 D-fucose 313 3.12 ± 0.07 140 ± 20
2 D-fucose 318 5.52 ± 0.08
3 D-fucose 323 13.8 ± 0.1
4 D-fucose 328 25.4 ± 0.5
5 L-fucose 313 1.71 ± 0.07 124 ± 9
6 L-fucose 318 6.47 ± 0.08
7 L-fucose 323 14.6 ± 0.2
8 L-fucose 328 27.1 ± 0.2

Reference: Wlodarczyk, P., Cecotka, A., Adrjanowicz, K., Kaminski, K., & Paluch, M. (2013). Mutarotation in biologically important pure L-fucose and its enantiomer. Journal of Physics: Condensed Matter, 25(37), 375101. DOI: https://doi.org/10.1088/0953-8984/25/37/375101


Table 4: Activation energies are calculated by first preparing aqueous solutions of carbohydrate polymer blends, drying them isothermally at different temperatures, and measuring their effective diffusivity. The effective diffusivity, influenced by moisture content, drop volume shrinkage, and temperature, is fitted to an Arrhenius-type relationship. The activation energy is then determined from the slope of the Arrhenius plot.

ID Biopolymer blend code Ea (kJ/mol) r SD
1 GA100 18.1 −0.95 0.01
2 MG100 24.5 −0.99 0.04
3 MD100 30.2 −0.98 0.11
4 GA50-MG50 19.6 −0.99 0.03
5 GA50-MD50 25.3 −0.99 0.07
6 MG50-MD50 25.7 −0.99 0.07
7 GA33-MG33-MD33 27.6 −0.90 0.30
8 GA66-MG17-MD17 33.5 −0.99 0.11
9 GA17-MG66-MD17 30.6 −1.00 0.16
10 GA17-MG17-MD66 19.9 −0.94 0.16

NOMENCLATURE:

Ea = Activation Energy (kJ/mol)
r = Correlation coefficient
SD = Standard deviation (Assumed, please verify with the Authors)
GA = gum arabic, MG = mesquite gum, MD = maltodextrin DE 10

NOTE: Solutions of carbohydrate polymers blends were prepared in accordance to a Simplex Centroid experimental design, and a drop of each blend was dried isothermally at 50, 60 and 80°C in a thermogravimetric analyzer.

Reference: Pérez-Alonso, C., Báez-González, J. G., Beristain, C. I., Vernon-Carter, E. J., & Vizcarra-Mendoza, M. G. (2003). Estimation of the activation energy of carbohydrate polymers blends as selection criteria for their use as wall material for spray-dried microcapsules. Carbohydrate Polymers, 53(2), 197–203. DOI: https://doi.org/10.1016/s0144-8617(03)00052-3


Table 5: To obtain the activation energy, the rate constants for the degradation of sugars and amino acids in subcritical water were determined by fitting the concentration changes over time to a first-order reaction model. The relationship between these rate constants and temperature was then analyzed using the Arrhenius law, which connects the rate constant to the activation energy, pre-exponential factor, and temperature. Finally, the activation energies were derived by solving the kinetic equations using a Runge-Kutta method and optimizing the parameters to minimize the error between experimental and calculated concentrations.

ID Name Temperature (°C) k0 (min-1) Ea (kJ/mol)
1 Glucose decomposition (G) 150 1.59×10-8 90.8
2 Glucose decomposition (G) 180 3.19×10-8 90.8
3 Glucose decomposition (G) 200 5.80×10-8 90.8
4 Glucose + Proline decomposition (G + Pro) 150 2.61×10-8 97.0
5 Glucose + Proline decomposition (G + Pro) 180 5.57×10-8 97.0
6 Glucose + Proline decomposition (G + Pro) 200 1.07×10-7 97.0
7 Xylose decomposition (X) 150 3.59×10-9 95.4
8 Xylose decomposition (X) 180 8.39×10-9 95.4
9 Xylose decomposition (X) 200 1.67×10-8 95.4
10 Xylose + Aspartic acid decomposition (X + Asp) 150 1.94×10-10 104.5
11 Xylose + Aspartic acid decomposition (X + Asp) 180 4.61×10-10 104.5
12 Xylose + Aspartic acid decomposition (X + Asp) 200 8.25×10-10 104.5
13 Proline decomposition (Pro) 150 5.73×10-6 85.4
14 Proline decomposition (Pro) 180 1.28×10-5 85.4
15 Proline decomposition (Pro) 200 2.57×10-5 85.4
16 Proline + Glucose decomposition (Pro + G) 150 1.67×10-3 55.1
17 Proline + Glucose decomposition (Pro + G) 180 3.72×10-3 55.1
18 Proline + Glucose decomposition (Pro + G) 200 7.09×10-3 55.1
19 Proline + Xylose decomposition (Pro + X) 150 5.88×10-7 74.8
20 Proline + Xylose decomposition (Pro + X) 180 1.31×10-6 74.8
21 Proline + Xylose decomposition (Pro + X) 200 2.50×10-6 74.8
22 Aspartic acid decomposition (Asp) 150 3.21×10-9 90.8
23 Aspartic acid decomposition (Asp) 180 7.48×10-9 90.8
24 Aspartic acid decomposition (Asp) 200 1.43×10-8 90.8
25 Aspartic acid + Xylose decomposition (Asp + X) 150 6.53×10-10 67.4
26 Aspartic acid + Xylose decomposition (Asp + X) 180 1.52×10-9 67.4
27 Aspartic acid + Xylose decomposition (Asp + X) 200 2.89×10-9 67.4

NOTE: The kinetic study was conducted in subcritical water medium in the temperature range from 150 to 200°C.

Reference: Alonso-Riaño, P., Illera, A. E., Benito-Román, O., Melgosa, R., Bermejo-López, A., Beltrán, S., & Sanz, M. T. (2024). Degradation kinetics of sugars (glucose and xylose), amino acids (proline and aspartic acid) and their binary mixtures in subcritical water: Effect of Maillard reaction. Food Chemistry, 442, 138421. DOI: https://doi.org/10.1016/j.foodchem.2024.138421


Table 6: Activation energies from different literatures.

ID Name Temperature (°C) Ea (kJ/mol) Ref
1 Dextran -94 32 I
2 Pullulan -73 39 I
3 Amylose -59 52 I
4 Dextran hydrolysis 60 52.7 ± 0.4 II
5 Sucrose 36.9 109.2 III

Reference (I): Scandola, M., Ceccorulli, G., & Pizzoli, M. (1991). Molecular motions of polysaccharides in the solid state: dextran, pullulan and amylose. International Journal of Biological Macromolecules, 13(4), 254–260. DOI: https://doi.org/10.1016/0141-8130(91)90082-6

Reference (II): Virgen-Ortíz, J. J., Ibarra-Junquera, V., Escalante-Minakata, P., Ornelas-Paz, J. de J., Osuna-Castro, J. A., & González-Potes, A. (2015). Kinetics and thermodynamic of the purified dextranase from Chaetomium erraticum. Journal of Molecular Catalysis B: Enzymatic, 122, 80–86. DOI: https://doi.org/10.1016/j.molcatb.2015.08.020

Reference (III): Tombari, E., Salvetti, G., Ferrari, C., & Johari, G. P. (2007). Kinetics and Thermodynamics of Sucrose Hydrolysis from Real-Time Enthalpy and Heat Capacity Measurements. The Journal of Physical Chemistry B, 111(3), 496–501. DOI: https://doi.org/10.1021/jp067061p