MOISTURE SORPTION ISOTHERMS OF QUINOA SEEDS: THERMODYNAMIC ANALYSIS

Bustos-Vanegas, Jaime D.; Corrêa, Paulo C.; Zeymer, Juliana S.; Baptestini, Fernanda M.; Campos, Renata C.

doi:10.1590/1809-4430-Eng.Agric.v38n6p941-950/2018

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Sumário

Scientific Paper, Post-Harvest Science and Technology • Eng. agríc. (Online) 38 (6) • Nov-Dec 2018 • https://doi.org/10.1590/1809-4430-Eng.Agric.v38n6p941-950/2018 copy

MOISTURE SORPTION ISOTHERMS OF QUINOA SEEDS: THERMODYNAMIC ANALYSIS

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The present research aimed to study the water sorption behavior of quinoa seeds analyzing the hysteresis phenomenon and determining thermodynamic properties. Static gravimetric technique was used to obtain the equilibrium moisture content of quinoa seeds in different temperature conditions (15, 25, 35 e 50 °C) and relative humidity (between 11 and 96%). Equilibrium moisture content data were adjusted by eight mathematical models and the Modified Halsey model was the best one to describe the water sorption phenomena of quinoa seeds. Hygroscopic equilibrium moisture content of quinoa seeds is directly proportional to the water activity and decreases with increasing temperature. The hysteresis phenomena were observed throughout the range of water activity, showing more evident at low temperatures. Integral isosteric heat and differential entropy decreased with the increase of equilibrium moisture content. Gibbs free energy decreased with the increase of temperature and equilibrium moisture content. Compensation enthalpy-entropy theory was confirmed and the sorption mechanism is controlled by enthalpy.

KEYWORDS
entropy; Gibbs energy; hysteresis; isosteric heat; mathematical modeling

Model	Equation
Modified Oswin (Oswin, 1946Oswin CR (1946) The kinetic of package life. III Isotherm. Journal of Chemical Industry 65:419-421.)	$U_{e} = \frac{a + b T}{{[\frac{(1 - a_{w})}{a_{w}}]}^{1 / c}}$	(1)
Modified Halsey (Iglesias & Chirife, 1976Iglesias H, Chirife J (1976) Prediction of the effect of temperature on water sorption isotherms of food material. Journal of Food Technology (11):109-116.)	$U_{e} = {[\frac{exp (a - b T)}{- ln a_{w}}]}^{1 / c}$	(2)
Modified GAB (Anderson, 1946Anderson RB (1946) Modifications of the B.E.T. equation. Journal of American Chemical Society (68):686-691.)	$U_{e} = \frac{a b (\frac{c}{T}) a_{w}}{[1 - b a_{w}] [1 - b a_{w} + (\frac{C}{T}) a_{w}]}$	(3)
Copace (Corrêa & Almeida, 1999Corrêa PC, Almeida FAC (1999) Comparação de modelos matemáticos de equilíbrio higroscópico para semente e fibra de algodão herbáceo, cultivar Redenção. Revista de Oleaginosas e Fibrosas 3(1):1-6.)	$U_{e} = exp [a - (b T) + (c a_{w})]$	(4)
Sigma-Copace (Teixeira et al., 2015Teixeira LP, Andrade ET, Espíndola JZ, Pereira RG (2015) Determinação do equilíbrio higroscópico e do calor isostérico do bagaço de cana-de-açúcar. Journal of the Brazilian Association of Agricultural Engineering 35(3):555-566. DOI: http://dx.doi.org/10.1590/1809-4430-Eng.Agric.v35n3p555-566/2015 http://dx.doi.org/10.1590/1809-4430-Eng.... )	$U_{e} = exp [a - (b T) + (c exp (a_{w}))]$	(5)
Henderson (Resende et al., 2006Resende O, Corrêa PC, Goneli ALD, Ribeiro DM (2006) Isotermas e calor isostérico de sorção do feijão. Revista Ciência e Tecnologia de Alimentos 26(3):626-631. DOI: https://doi.org/10.1590/S0101-20612006000300022 https://doi.org/10.1590/S0101-2061200600... )	$U_{e} = {[\frac{\ln (1 - a_{w})}{[- a (T + 273.15)]}]}^{1 / c}$	(6)
Henderson-Thompson (Thompson et al., 1968Thompson TL, Peart RM, Foster GH (1968) Mathematical simulation of corn drying - a new model. Transaction of the ASAE 24:582-586.)	$U_{e} = {[\frac{\ln (1 - a_{w})}{[- a (T + b)]}]}^{1 / c}$	(7)
Smith (Corrêa et al., 2006Corrêa PC, Afonso Júnior PC, Ribeiro DM, Silva FS (2006) Equilíbrio higroscópico de milheto, alpiste e painço: Obtenção e modelagem 10(1):162-167.)	$U_{e} = a - (b T) - c \ln (1 - a_{w})$	(8)

Model	Parameters			R² (%)	SDE (% d.b.)	MRE (%)	Residual Distribution
Model	a	b	c	R² (%)	SDE (% d.b.)	MRE (%)	Residual Distribution
Oswin Modified	15.06278	-0.1436	3.01422	98.75	0.04	10.73	Biased
Halsey Modified	5.6083	-0.0317	2.1514	98.96	0,03	7.98	Random
GAB Modified	6.6989	0.8359	465.3184	97.94	1.98	13.13	Random
Copace	1.2677	0.0077	2.5143	96.63	2.52	15.10	Biased
Sigma-Copace	0.3802	0.0080	1.2833	97.34	1.99	9.85	Random
Henderson	0.000075	1.4195	–	97.05	2.36	15.35	Biased
Henderson-Thompson	0.00027	56.3612	1.4232	97.69	2.09	13.93	Biased
Smith	8.9201	0.1481	9.0100	98.66	1.49	8.45	Biased

Model	Parameters			R² (%)	SDE (% d.b.)	MRE (%)	Residual Distribution
Model	a	b	c	R² (%)	SDE (% d.b.)	MRE (%)	Residual Distribution
Oswin Modified	12.0144	-0.10487	2.81209	97.28	0.05	10.81	Biased
Halsey Modified	4.9313	-0.0275	2.0866	97.98	0.04	8.44	Random
GAB Modified	5.1515	0.8806	723.4795	97.83	1.82	12.15	Random
Copace	0.7423	0.0066	3.0135	96.81	2.44	19.82	Biased
Sigma-Copace	0.1949	0.0068	1.4829	97.85	1.90	11.85	Random
Henderson	0.000172	0.1868	–	97.13	2.31	18.72	Biased
Henderson-Thompson	0.00044	89.6080	1.1879	97.43	2.19	18.37	Biased
Smith	5,2673	0.1033	9.4625	98.00	1.93	14.03	Biased

Identification	Adjusted equation	R² (%)
Adsorption	Q_st = 2686.6314^* * Significant at 1% probability by t test. + 968249367^* * Significant at 1% probability by t test. exp(-1.0296^ * Significant at 1% probability by t test. *U_e)	99.87
Adsorption	ΔS = 0.7110^ Significant at 1% probability by t test. + 265.6857^* * Significant at 1% probability by t test. * exp(-1.0296^* * Significant at 1% probability by t test. *U_e)	99.87
Desorption	Q_st = 2954.3655^* * Significant at 1% probability by t test. + 403298^* * Significant at 1% probability by t test. exp(-1.1858^ * Significant at 1% probability by t test. *U_e)	99.94
Desorption	ΔS = 1.5105^ Significant at 1% probability by t test. +11562267^* * Significant at 1% probability by t test. exp(-1.1858^ * Significant at 1% probability by t test. *U_e)	99.94

Identification	T_B (K)	ΔG_B (kJ kg⁻¹)	R² (%)
Adsorption	364.43	1.214*10⁻¹³	99.99
Desorption	348.81	6.366*10⁻¹²	99.99

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[1] *Corresponding author. Universidade Federal de Viçosa/ Viçosa - MG, Brasil. E-mail: jdbustosv@gmail.com