Купить СНПЧ А7 Архангельск, оперативня доставка


Considerações Temodinâmicas das Isotermas

DOI: http://dx.doi.org/10.15871/1517-8595/rbpa.v10n1p83-94



Kil J. B. Park1, Kil J. Park2, Félix E. P. Cornejo3 & Inácio M. D. Fabbro4


Abstract: Apresentam-se as considerações termodinâmicas das isotermas e as equações empíricas mais usuais na literatura. Uma das importantes aplicações das equações de isotermas é a energia de relacionamento da água com a matriz sólida que é traduzida na energia de adsorção. A outra importante consideração é acerca dos valores de monocamada molecular de água, que indicam a relação com as reações químicas que determinam a deterioração dos materiais biológicos, através das áreas expostas da matriz sólida.

Key words: atividade de água, modelos teóricos, modelos empíricos, energia de sorção, superfície exposta.


Resumo: The thermodynamic considerations of the isotherms and the more usual empirical equations in literature are presented. One of the important applications of the isotherm equations is the energy of water relationship with matrix solid that is translated in the adsorption energy. The other important consideration is concerning the values of water molecular monolayer, which indicate the relation with the chemical reactions that determine the deterioration of the biological materials, through the displayed areas of the solid matrix.

Palavras-chave: water activity, theoretical models, empirical models, sorption energy, exposed surface.


1 Doutorando em Engenharia Agrícola da Faculdade de Engenharia Agrícola da Universidade Estadual de Campinas. Caixa Postal 6011. CEP: 13083-875. Campinas-SP, Brasil. E-mail: kil.park@agr.unicamp.br.
2 Professor Titular - Faculdade de Engenharia Agrícola – Universidade Estadual de Campinas. Caixa Postal 6011. CEP: 13084-971. Campinas-SP, Brasil. E-mail: kil@agr.unicamp.br.
3 Pesquisador da Embrapa Agroindústria de Alimentos. Felix@ctaa.embrapa.br.
4 Professor Titular - Faculdade de Engenharia Agrícola – Universidade Estadual de Campinas. Caixa Postal 6011. CEP: 13084-971. Campinas-SP, Brasil. E-mail: inacio@agr.unicamp.br.


Literatura Citada

Aguerre, R.J.; Suarez, C.; Viollaz, P.Z. New BET type multi-layer sorption isotherms. - Part II: Modelling water sorption in foods. In: Lebensm - Wiss u. Tech. [s.n.], v. 22, p.192-195, 1989.

American Society of Agricultural Engineers – ASAE. ASAE Standard: D245.4: Moisture Relationship of Grains, 1991.

Armbruster, M.H.; Austin, J.B. The adsorption of gases on smooth surfaces of steel. Joural of American Chemistry Society, v.66, n.2, p.159-171, 1944.

Berezin, G.I.; Kiselev, A.V. Dependence of heat capacity of adsorbate on surface coverage on the basis of BET theory assumptions. Journal of Colloid and Interface Science. V.22, p.161-164, 1966.

Brunauer, S.; Emmet, T.H.; Teller, F. Adsorption of gases in multimolecular layers. In: G. Am. Chem. Soc., [s.n.], v. 60, n. 2, p. 309-319, 1938.

Cervenka, L.; Rezkova, S,; Kralovsky, J. Moisture adsorption characteristics of gingerbread, a traditional bakery product in Pardubice, Czech Republic. Journal of Food Engineering, v.84, n.4, p.601-607, 2008. Disponível online.

Chen, C.S. Equilibrium moisture curves for biologica materials. Transactions of the ASAE, v. 14, p. 924-926, 1971.

Chen, C.S.; Clayton, J.T. The effect of temperature on sorption isotherms of biological materials. Transactions of the ASAE, v. 14, p. 927-929, 1971

Chinnan, M.S.; Beauchat, L.R. Sorption isotherms of whole cowpeas and flours. In: Lebensm - Wiss u. Tech., [s.n.], v. 18, p. 83-88, 1985.

Chung, D.S.; Pfost, H.B. Adsorption and desorption of water vapor by cereal grains and their products. Transactions of the ASAE, v. 10, p. 549-557, 1967.

Delgado, A.E.; Sun, Da-W. Influence of surface water activity on freezing/thawing times and weight loss prediction. Journal of Food Engineering, v.83, n.1, p.23-30, 2007.

Goula, A.M.; Karapantsios, T.D.; Achilias, D.S.; Adamopoulos, K.G. Water sorption isotherms and glass transition temperature of spray dried tomato pulp. Journal of Food Engineering, v.85, n.1, p.73-83, 2008. Disponível on line.

Halsey, G. Physical adsorption on uniform surfaces. In: The Journal of Chemical Physics, v. 16, n. 10, p. 931-937, 1948.

Hill, T.L. Statistical mechanics of adsorption. VII thermodynamic functions for the BET theory. The Journao of Chem. Physics. V.17, n.9, p.772-774, 1949.

Kavitha, S.; Modi, V.K. Effect of water activity and temperature on degradation of 5′-inosine monophosphate in a meat model system. LWT – Food Science and Technology, v. 40, n. 7, p. 1280-1286. 2007.

Labuza, T.P. Sorption phenomena in foods. In: Food Technol. [s.n.], 1968. v. 22, n.3, p. 15- 24.

Labuza, T.; Roe, K.; Payne, C.; Panda, F.; Labuza, T. J.; Labuza, P. S.; Krusch, L. Storage stability of dry food systems: influence of state changes during drying and storage. In: International Drying Symposium IDS’2004, 14th, 2004, São Paulo, Brazil. Proceedings...São Paulo: Ourograf Gráfica e Editora, v. A, p. 48-68, 2004.

Langmuir, I. The adsorption of gases in a plane surfaces of glass, mica and platinum. In: J. Am. Chem. Soc., [s.n.], 1918. v. 46, p. 1361-1403.

Leite, J.T.De C.; Murr, F.E.X.; Park, K.J. Transições de fase em alimentos: Influência no processamento e na armazenagem. Revista Brasileira de Produtos Agroindustriais, Campina Grande/PB, v.7, n.1, p.83-96, 2005.

Lomauro, C.J.; Bakshi, A.S.; Labuza, T.P. Evaluation of food moisture sorption isotherm equations. Part I: Fruit, vegetable and meat products. In: Lebensm. - Wiss. u.- Technol. [s.n.], v. 18, n. 2, p. 111-117, 1985.

Maroulis, Z.B.; Tsami, E.; Marinos-Kouris, D.; Saravacos, G.D. Application of the GAB model of the moisture sorption isotherms for dried fruits. In: Journal of Food Science. [s.n.], v. 7, n. l, p. 63-78, 1988.

Park, K. J.; Antonio, G.C.; Oliveira, R.A. De; Park, K.J.B. Conceitos de processo e equipamentos de secagem. 121p. 2007. Disponível em: <http://www.feagri.unicamp.br/ctea/manuais/concproceqsec_07.pdf>. Acesso em: 09 de out. 2007.

Park, K.J.; Nogueira, R.I. Modelos de ajuste de isotermas de sorção de alimentos. In: Engenharia Rural, Piracicaba: ESALQ/USP, v. 3, n. 1, p.81-86, 1992.

Peleg, M. Assessment of a semi-empirical four parameter general model for sigmoid moisture sorption isotherms. In: J. Food Proc. Eng., Connecticut-USA: Food and Nutrition Press, Inc., v. 16, n. 1, p. 21-37, 1993.

Rizvi, S.S.H.; Benado, A.L. Thermodynamic properties of dehydrated foods. Food Technology, march, p.83-92, 1984.

Samapundo, S.; Devlieghere, F.; Geeraerd, A.F.; Meulenaer, B. De; Impe, J.F.; Debevere, J. Modelling of the individual and combined effects of water activity and temperature on the radial growth of Aspergillus flavus and A. parasiticus on corn. Food Microbiology, v. 24, n. 5, p. 517-529, 2007.

Saravacos, G.D.; Stinchfield, R.M. Effect of temperature and pressure on the sorption of water vapor by freeze-dried food materials. J. of Food Science, Chicago: Inst Food Technologists, v. 30, p. 779-7786, 1965.

Saravacos, G.D.; Tsiourvas, D.A., Tsami, E. Effect of temperature and pressure on the water adsorption isotherms of sultan. rainsins. J. of Food Science, Chicago: Inst Food Technologists, v. 51, p. 381 -94, 1986.

Shrestha, A.K.; Howes, T.; Adhikari, B.P.; Bhandari, B.R. Water sorption and glass transition properties of spray dried lactose hydrolysed skim milk powder. LWT – Food Science and Technology, v. 40, n. 9, p. 1593-1600. 2007.

Spiess, W.E.L.; Wolf, W.F. The results of the COST 90 project on water activity. In: JOWITT, R. Physical Properties of Foods. London: Applied Science Publishers, p.65- 91, 1983.

Suárez, C.; Aguerre, R.; Violaz, P.E. Analysis of the desorption isotherms of rough rice. Lebensm. Wiss. U. Thecnol., v.16, p.176- 179, 1983.

Treyball, R.B. Drying. mass tranfer operations. New York: McGraw-Hill, 1968, p. 569-575.

Toupin, C.J.; Le Mauger, M., McGregor, J.R. The evaluation of BET constants from sorption isotherms data. In: Lebensm.-Wiss. u.- Technol. [s.n.], v. 16, n. 3, p. 153-156, 1983.

Van der Berg, C. Description of water activity of foods for engineering purposes by means of the GAB model of sorption. In: Engineering and Food. London: B. M. Mckenna Elsevier Applied Science, v. 1, p.311-321, 1984.

Wang, N.; Brennan, J. G. Moisture sorption isotherm characteristics of potatoes at four temperatures. In: Journal of Food Engineering, [s.n.], v. 14, p. 269-287, 1991.