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A Review of Methods, Data and Applications of State Diagrams of Food Systems

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Abstract

Understanding of the amorphous glassy state of food systems is often crucial in determining physicochemical characteristics and predicting stability of dehydrated and frozen foods. At the glass transition temperature (T g) of food components, transformation from the amorphous glassy state to the liquid-like rubbery state occurs. T g and ice-melting temperatures (T m) of food systems are used to construct their state diagrams, in which the different physical states/phases and state/phase transitions of food components are presented in relation to temperature and concentration. A state diagram may be used to identify the appropriate processing and storage conditions of food systems. An overview of determination methods is carried out for glass transition temperature, ice-melting temperature and conditions of maximum-freeze-concentration (glass transition temperature of maximum-freeze-concentrated solution, T g′ and onset of ice-melting temperature, T m′) for food systems. The data as T g, T m, T g′ and T m′ are necessary for construction of state diagrams of foods. The advantages and limitations of the determination methods are discussed. Combined data for glass transition temperature, ice-melting temperature and conditions of maximum-freeze concentration for selected food systems are presented in this study. The effect of food composition on glass line, freezing/melting curve and maximum-freeze-concentration conditions is evaluated. The significance of the state diagrams in predicting the physical, chemical and microbial stability in foods is briefly examined. Glass transition concept and state diagrams are useful for describing the physical and structural stability of food systems at specific conditions, yet they are not considered as the only determining factors of chemical, biochemical and microbial stability of food systems.

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References

  1. Abiad MG, Carvajal MT, Campanella OH (2009) A review on methods and theories to describe the glass transition phenomenon: applications in food and pharmaceutical products. Food Eng Rev 1(2):105–132

    Article  Google Scholar 

  2. Ablett S (1992) Overview of NMR applications in food science. Trends Food Sci Technol 31:246–250

    Article  Google Scholar 

  3. Ablett S, Izzard MJ, Lillford PJ, Arvannitoyannis I, Blanshard JMV (1993) Calorimetric study of the glass transition occurring in fructose solutions. Carbohydr Res 246:13–22

    Article  CAS  Google Scholar 

  4. Adhikari B, Howes T, Lecomte D, Bhandari BR (2005) A glass transition temperature approach for the prediction of the surface stickiness of a drying droplet during spray drying. Powder Technol 149:168–179

    Article  CAS  Google Scholar 

  5. Aguilera JM, del Valle JM, Karel M (1995) Caking phenomena in amorphous food powders. Trends Food Sci Technol 6:149–155

    Article  CAS  Google Scholar 

  6. Akkose A, Aktas N (2008) Determination of glass transition temperature of beef and effects of various cryoprotective agents on some chemical changes. Meat Sci 80:875–878

    Article  CAS  Google Scholar 

  7. Allen SG (1993) A history of the glassy state. In: Blanshard JMV, Lillford PJ (eds) The glassy state in foods. Nottingham University Press, Loughborough

  8. Arvanitoyannis I, Blanshard JMV, Ablett S, Izzard MJ, Lillford PJ (1993) Calorimetric study of the glass-transition occurring in aqueous glucose—fructose solutions. J Sci Food Agric 63:177–188

    Article  CAS  Google Scholar 

  9. Bai Y, Rahman MS, Perera CO, Smith B, Melton LD (2001) State diagram of apple slices: glass transition and freezing curves. Food Res Int 34:89–95

    Article  Google Scholar 

  10. Bell LN, Touma DE, White KL, Chen Y (1998) Glycine loss and Maillard browning as related to the glass transition in a model food system. J Food Sci 63(4):625–628

    Article  CAS  Google Scholar 

  11. Bell LN, Bell HM, Glass TE (2002) Water mobility in glassy and rubbery solids as determined by oxygen-17 nuclear-magnetic resonance: impact on chemical stability. Lebensm-wiss Technol 35(2):108–113

    Article  CAS  Google Scholar 

  12. Bell LN, White KL (2000) Thiamin stability in solids as affected by the glass transition. J Food Sci 65(3):498–501

    Article  CAS  Google Scholar 

  13. Bell LN (1995) Kinetics of non-enzymatic browning in amorphous solid systems: distinguishing the effects of water activity and the glass transition. Food Res Int 28(6):591–597

    Article  CAS  Google Scholar 

  14. Bell LN, Hageman MJ (1996) Glass transition explanation for the effect of polyhydroxy compounds on protein denaturation in dehydrated solids. J Food Sci 61(2):372–374

    Article  CAS  Google Scholar 

  15. Bell LN (2007) Moisture effects on food’s chemical stability. In: Barbosa-Canovas GV, Fontana AJ Jr, Schmidt SJ, Labuza TP (eds) Water activity in foods: fundamentals and applications. Blackwell Publishing Ltd, Ames

  16. Bengoechea C, Arrachid A, Guerrero A, Hill SE, Mitchell JR (2007) Relationship between the glass transition temperature and the melt flow behavior for gluten, casein and soya. J Cereal Sci 45:275–284

    Article  CAS  Google Scholar 

  17. Beristain CI, Azuara E, Tamayo T, Vernon-Carter EJ (2003) Effect of caking and stickiness on the retention of spray-dried encapsulated orange peel oil. J Sci Food Agric 83(15):1613–1616

    Article  CAS  Google Scholar 

  18. Bhandari BR, Howes T (1999) Implication of glass transition for the drying and stability of dried foods. J Food Eng 40:71–79

    Article  Google Scholar 

  19. Bhandari BR, Howes T (2000) Glass transition in processing and stability of food. Food Aust 52(12):579–585

    Google Scholar 

  20. Bidstrup SA, Day DR (1994) Assignment of glass transition temperature using dielectric analysis: a review. In: Seyler RJ (ed) Assignment of the glass transition. ASTM, Philadelphia

  21. Biliaderis CG, Swan RS, Arvannitoyannis I (1999) Physicochemical properties of commercial starch hydrolyzates in the frozen state. Food Chem 64(4):537–546

    Article  CAS  Google Scholar 

  22. Bindzus W, Livings SJ, Gloria-Hernandez HG, Fayard G, Van Lengerich B, Meuser F (2002) Glass transition of extruded wheat, corn and rice starch. Starch 54:393–400

    Article  CAS  Google Scholar 

  23. Blanshard JMV (1995) The glass transition, its nature, and significance in food processing. In: Becket ST (ed) Physico-chemical aspects of food processing, Blackie Academic & Professional, Glasgow

  24. Blond G, Simatos D, Catte M, Dussap CG, Gros JB (1997) Modeling of the water-sucrose state diagram below 0 degrees C. Carbohydr Res 298:139–145

    Article  CAS  Google Scholar 

  25. Boonyai P, Bhandari B, Howes T (2006) Applications of thermal mechanical compression tests in food powder analysis. Int J Food Prop 9:127–134

    Article  Google Scholar 

  26. Boonyai P, Howes T, Bhandari B (2007) Instrumentation and testing of a thermal mechanical compression test for glass-rubber transition analysis of food powders. J Food Eng 78:1333–1342

    Article  Google Scholar 

  27. Brake NC, Fennema OR (1999) Glass transition values of muscle tissue. J Food Sci 64(1):10–15

    Article  CAS  Google Scholar 

  28. Brent JL, Mulvaney SJ, Cohen C, Bartsch JA (1997) Thermomechanical glass transition of extruded cereal melts. J Cereal Sci 26:301–312

    Article  CAS  Google Scholar 

  29. Buera MP, Jouppila K, Roos YH, Chirife J (1998) Differential scanning calorimetry glass transition temperatures of white bread and mold growth in the putative glassy state. Cereal Chem 75(1):64–69

    Article  CAS  Google Scholar 

  30. Buera MP, Chirife J, Karel M (1995) A study of acid-catalyzed sucrose hydrolysis in an amorphous polymeric matrix at reduced moisture contents. Food Res Int 28(4):359–365

    Article  CAS  Google Scholar 

  31. Buitink J, Hemminga MA, Hoekstra FA (1999) Characterization of molecular mobility in seed tissues: an electron paramagnetic resonance spin probe study. Biophys J 76:3315–3322

    Article  CAS  Google Scholar 

  32. Buitink J, van den Dries IJ, Hoekstra FA, Alberda M, Hemminga MA (2000) High critical temperature above T-g may contribute to the stability of biological systems. Biophys J 79:1119–1128

    Article  CAS  Google Scholar 

  33. Champion D, Le Meste M, Simatos D (2000) Towards an improved understanding of glass transition and relaxations in foods: molecular mobility in the glass transition range. Trends Food Sci Technol 11:41–55

    Article  CAS  Google Scholar 

  34. Chartoff RP, Weissman PT, Sircar A (1994) The application of dynamic mechanical methods to T g determination in polymers: an overview. In: Seyler RJ (ed) Assignment of the glass transition. ASTM, Philadelphia

  35. Chen CS (1986) Effective molecular-weight of aqueous-solutions and liquid foods calculated from the freezing-point depression. J Food Sci 51:1537–1539

    Article  CAS  Google Scholar 

  36. Chen YH, Aull JL, Bell LN (1999) Solid-state tyrosinase stability as affected by water activity and glass transition. Food Res Int 32(7):467–472

    Article  CAS  Google Scholar 

  37. Chen YH, Aull JL, Bell LN (1999) Invertase storage stability and sucrose hydrolysis in solids as affected by water activity and glass transition. J Agric Food Chem 47(2):504–509

    Article  CAS  Google Scholar 

  38. Chiou D, Langrish TAG (2007) Crystallization of amorphous components in spray-dried powders. Dry Technol 25(9):1427–1435

    Article  CAS  Google Scholar 

  39. Chirife J, Buera MP (1994) Water activity, glass-transition and microbial stability in concentrated/semimoist food systems. J Food Sci 59(5):921–927

    Article  CAS  Google Scholar 

  40. Chung H, Woo K, Lim S (2004) Glass transition and enthalpy relaxation of cross-linked corn starches. Carbohydr Polym 55:9–15

    Article  CAS  Google Scholar 

  41. Cnossen AG, Siebenmorgen TJ, Yang W (2002) The glass transition temperature concept in rice drying and tempering: effect on drying rate. Trans ASAE 45(3):759–766

    Google Scholar 

  42. Coleman NJ, Craig DQM (1996) Modulated temperature differential scanning calorimetry: a novel approach to pharmaceutical thermal analysis. Int J Pharm 135:13–29

    Article  CAS  Google Scholar 

  43. Cordella C, Antinelli JF, Aurieres C, Faucon JP, Cabrol-Bass D, Sbirrazzuoli N (2002) Use of differential scanning calorimetry (DSC) as a new technique for detection of adulteration in honeys. 1. Study of adulteration effect on honey thermal behavior. J Agric Food Chem 50:203–208

    Article  CAS  Google Scholar 

  44. Couchman PR, Karasz FF (1978) A classical thermodynamic discussion of the effect of composition on glass-transition temperatures. Macromolecules 11:117–119

    Article  CAS  Google Scholar 

  45. Cuq B, Gontard N, Guilbert S (1997) Thermal properties of fish myofibrillar protein-based films as affected by moisture content. Polymer 38(10):2399–2405

    Article  CAS  Google Scholar 

  46. Cuq B, Lcard-Verniere C (2001) Characterization of glass transition of durum wheat semolina using modulated differential scanning calorimetry. J Cereal Sci 33:213–221

    Article  CAS  Google Scholar 

  47. D’Cruz NM, Bell LN (2005) Thermal unfolding of gelatin in solids as affected by the glass transition. J Food Sci 70(2):E64–E68

    Article  Google Scholar 

  48. de Graaf EM, Madeka H, Cocero AM, Kokini JL (1993) Determination of the effect of moisture on gliadin glass-transition using mechanical spectrometry and differential scanning calorimetry. Biotechnol Prog 9:210–213

    Article  Google Scholar 

  49. De Graaf RA, Karman AP, Janssen LPBM (2003) Material properties and glass transition temperatures of different thermoplastic starches after extrusion processing. Starch 55:80–86

    Article  Google Scholar 

  50. Delgado AE, Sun D (2002) Desorption isotherms and glass transition temperature for chicken meat. J Food Eng 55:1–8

    Article  Google Scholar 

  51. del Valle JM, Cudros TRM, Aguilera JM (1998) Glass transitions and shrinkage during drying and storage of osmosed apple pieces. Food Res Int 31(3):191–204

    Article  Google Scholar 

  52. Diab T, Biliaderis CG, Gerasopoulos D, Sfakiotakis E (2001) Physicochemical properties and application of pullulan edible films and coatings in fruit preservation. J Sci Food Agric 81:988–1000

    Article  CAS  Google Scholar 

  53. Di Gioia L, Cuq B, Guilbert S (1999) Thermal properties of corn gluten meal and its proteic components. Int J Biol Macromol 24:341–350

    Article  CAS  Google Scholar 

  54. Dlubek G, Fretwell HM, Alam MA (2000) Positron/positronium annihilation as a probe for the chemical environment of free volume holes in polymers. Macromolecules 33(1):187–192

    Article  CAS  Google Scholar 

  55. Drusch S, Serfert Y, Van Den Heuvel A, Schwarz K (2006) Physicochemical characterization and oxidative stability of fish oil encapsulated in an amorphous matrix containing trehalose. Food Res Int 39(7):807–815

    Article  CAS  Google Scholar 

  56. Earnest CM (1994) Assignment of the glass transition temperatures using thermomechanical analysis. In: Seyler RJ (ed) Assignment of the glass transition. ASTM, Philadelphia

  57. Farhat IA (2004) Measuring and modeling the glass transition temperature. In: Steele R (ed) Understanding and measuring the shelf-life of food. CRC Press, New York

  58. Farkas J, Mohacsi-Farkas C (1996) Application of differential scanning calorimetry in food research and food quality assurance. J Therm Anal 47:1787–1803

    Article  CAS  Google Scholar 

  59. Ferrero C, Zaritzky N (2000) Effect of freezing rate and frozen storage on starch-sucrose-hydrocolloid systems. J Sci Food Agric 80:2149

    Article  CAS  Google Scholar 

  60. Ferry JD (1980) Viscoelastic properties of polymers. Wiley, NewYork

    Google Scholar 

  61. Fessas D, Schiraldi A (2001) State diagrams of arabinoxylan-water binaries. Thermochim Acta 370(1–2):83–89

    Article  CAS  Google Scholar 

  62. Fitzpatrick JJ, Hodnett M, Twomey M, Cerqueira PSM, O’Flynn J, Roos YH (2007) Glass transition and the flowability and caking of powders containing amorphous lactose. Powder Technol 178:119–128

    Article  CAS  Google Scholar 

  63. Fonseca F, Obert JP, Beal C, Marin M (2001) State diagrams and sorption isotherms of bacterial suspensions and fermented medium. Thermochim Acta 366:167–182

    Article  CAS  Google Scholar 

  64. Forssel PM, Mikkila JM, Moates GK, Parker R (1997) Phase and glass transition behavior of concentrated barley starch-glycerol-water mixtures, a model for thermoplastic starch. Carbohdr Polym 34:275–282

    Article  Google Scholar 

  65. Foster KD, Bronlund JE, Paterson AHJ (2006) Glass transition related cohesion of amorphous sugar powders. J Food Eng 77:997–1006

    Article  CAS  Google Scholar 

  66. Fox TG, Flory PJ (1950) Second order transition temperatures and related properties of polystyrene .1. Influence of molecular weight. J Appl Phys 21:581–591

    Article  CAS  Google Scholar 

  67. Franks F (1986) Metastable water at subzero temperatures. J Microsc 141(3):243–249

    CAS  Google Scholar 

  68. Franks F (1986) Unfrozen water—yes—unfreezable water—hardly—bound water—certainly not. Cryoletters 7(4):207–211

    Google Scholar 

  69. Franks F (1991) Water activity: a credible measure of food safety and quality? Trends Food Sci Technol 2:68–72

    Article  Google Scholar 

  70. Gedde UW (1995) Polymer physics. Chapman and Hall, London

    Google Scholar 

  71. Gibbs JH, DiMarzio EA (1958) Nature of the glass transition and the glassy state. J Chem Phys 28:373–383

    Article  CAS  Google Scholar 

  72. Goff HD, Caldwell KB, Stanley DW, Maurice TP (1993) The influence of polysaccharides on the glass-transition in frozen sucrose solutions and ice-cream. J Dairy Sci 76:1268–1277

    Article  CAS  Google Scholar 

  73. Goff HD, Sahagian ME (1996) Glass transitions in aqueous carbohydrate solutions and their relevance to frozen food stability. Thermochim Acta 280/281:449–464

    Article  CAS  Google Scholar 

  74. Goff HD (1995) The use of thermal-analysis in the development of a better understanding of frozen food stability. Pure Appl Chem 67(11):1801–1808

    Article  CAS  Google Scholar 

  75. Gordon M, Taylor JS (1952) Ideal copolymers and the second order transitions of synthetic rubbers. I. Noncrystalline copolymers. J Appl Chem 2:493–500

    Article  CAS  Google Scholar 

  76. Goswami TK, Gupta SK (2008) Detection of dilution of milk with the help of glass transition temperature by differential scanning calorimetry (DSC). Afr J Food Sci 2:7–10

    Google Scholar 

  77. Goula AM, Karapantsios TD, Achilias DS, Adamopoulos KG (2008) Water sorption isotherms and glass transition temperature of spray dried tomato pulp. J Food Eng 85(1):73–83

    Article  Google Scholar 

  78. Gray R (1995) Electron spin resonance spectroscopy for detection of irradiated foods. In: Dickinson E (ed) New physico-chemical techniques for the characterization of complex food systems. Chapman and Hall, London

  79. Hancock BC, Zografi G (1997) Characteristics and significance of the amorphous state in pharmaceutical systems. J Pharm Sci 86(1):1–12

    Article  CAS  Google Scholar 

  80. Hansen E, Lauridsen L, Skibsted LH, Moawad RK, Anderson ML (2004) Oxidative stability of frozen pork patties: effect of fluctuating temperature on lipid oxidation. Meat Sci 68:185–191

    Article  CAS  Google Scholar 

  81. Hashimoto T, Suzuki T, Hagiwara T, Takai R (2004) Study on the glass transition for several processed fish muscles and its protein fractions using differential scanning calorimetry. Fish Sci 70:1144–1152

    Article  CAS  Google Scholar 

  82. Hutchinson JM (1995) Physical aging of polymers. Prog Pol Sci 20(4):703–760

    Article  CAS  Google Scholar 

  83. Israkarn K, Charoenrein S (2006) Influence of annealing temperature on Tg′ of cooked rice stick noodles. Int J Food Prop 9:759–766

    Article  Google Scholar 

  84. Johari GP, Hallbrucker A, Mayer E (1987) The glass liquid transition of hyperquenched water. Nature 330:552–553

    Article  CAS  Google Scholar 

  85. Jouppila K, Roos YH (1994) Glass transitions and crystallization in milk powders. J Dairy Sci 77:2907–2915

    Article  CAS  Google Scholar 

  86. Jouppila K, Roos YH (1997) The physical state of amorphous corn starch and its impact on crystallization. Carbohydr Polym 32:95–104

    Article  CAS  Google Scholar 

  87. Jouppila K, Kansikas J, Roos YH (1997) Glass transition, water plasticization, and lactose crystallization in skim milk powder. J Dairy Sci 80:3152–3160

    Article  CAS  Google Scholar 

  88. Kaletunc G, Breslauer KJ (1996) Construction of a wheat–flour state diagram: application to extrusion processing. J Therm Anal 47(5):1267–1288

    Article  CAS  Google Scholar 

  89. Kaletunc G, Breslauer KJ (2003) Calorimetry of pre and postextruded cereal flours. In: Kaletunc G, Breslauer KJ (eds) Characterization of cereals and flours. Marcel Dekker Inc, New York

  90. Kalichevsky MT, Jaroszkiewicz JM, Ablett S, Blanshard JMV, Lillford PJ (1992) The glass transition of amylopectin measured by dsc, dmta and nmr. Carbohydr Polym 18(2):77–88

    Article  CAS  Google Scholar 

  91. Kalichevsky MT, Blanshard JMV, Tokarczuk PF (1993) Effect of water content and sugars on the glass-transition of casein and sodium caseinate. Int J Food Sci Technol 28(2):139–151

    CAS  Google Scholar 

  92. Kantor Z, Pitsi G, Thoen J (1999) Glass transition temperature of honey as a function of water content as determined by differential scanning calorimetry. J Agric Food Chem 47(6):2327–2330

    Article  CAS  Google Scholar 

  93. Karathanos V, Angelea S, Karel M (1993) Collapse of structure during drying of celery. Dry Technol 11:1005–1023

    Article  Google Scholar 

  94. Karel M, Anglea S, Buera P, Karmas R, Levi G, Roos YH (1994) Stability related transitions of amorphous foods. Thermochim Acta 246:249–269

    Article  CAS  Google Scholar 

  95. Karmas R, Buera MP, Karel M (1992) Effect of glass-transition on rates of nonenzymatic browning in food systems. J Agric Food Chem 40(5):873–879

    Article  CAS  Google Scholar 

  96. Kasapis S, Rahman MS, Guizani N, Al-Aamri M (2000) State diagram of temperature vs date solids obtained from the mature fruit. J Agric Food Chem 48:3779–3784

    Article  CAS  Google Scholar 

  97. Kasapis S, Sablani SS (2005) A fundamental approach for the estimation of the mechanical glass transition temperature in gelatin. Int J Biol Macromol 36:71–78

    Article  CAS  Google Scholar 

  98. Kasapis S (2004) Definition of a mechanical glass transition temperature for dehydrated foods. J Agric Food Chem 52(8):2262–2268

    Article  CAS  Google Scholar 

  99. Kasapis S (2008) Recent advances and future challenges in the explanation and exploitation of the network glass transition of high sugar/biopolymer mixtures. Crit Rev Food Sci Nutr 48(2):185–203

    Article  CAS  Google Scholar 

  100. Katayama DS, Carpenter JF, Manning MC, Randolph TW, Setlow P, Menard KP (2008) Characterization of amorphous solids with weak glass transitions using high ramp rate differential scanning calorimetry. J Pharm Sci 97(2):1013–1024

    Article  CAS  Google Scholar 

  101. Katekawa EK, Silva MA (2007) On the influence of glass transition on shrinkage in convective drying of fruits: a case study of banana drying. Dry Technol 25:1659–1666

    Article  Google Scholar 

  102. Kelley FN, Bueche F (1961) Viscosity and glass–temperature relations for polymer-diluent systems. J Pol Sci 50:549–556

    Article  CAS  Google Scholar 

  103. Khalloufi S, El-Maslouhi Y, Ratti C (2000) Mathematical model for prediction of glass transition temperature of fruit powders. J Food Sci 65(5):842–848

    Article  CAS  Google Scholar 

  104. Kokini JL, Cocero AM, Madeka H, de Graaf E (1994) The development of state diagrams for cereal proteins. Trends Food Sci Technol 5:281–288

    Article  CAS  Google Scholar 

  105. Kokini JL, Cocero AM, Madeka H (1995) State diagrams help predict rheology of cereal proteins. Food Technol 49(10):74–82

    CAS  Google Scholar 

  106. Kou Y, Molitor PF, Schmidt SJ (1999) Mobility and stability characterization of model food systems using NMR, DSC, and conidia germination techniques. J Food Sci 64(6):950–959

    Article  CAS  Google Scholar 

  107. Krokida MK, Karathanos VT, Maroulis ZB (1998) Effect of freeze-drying conditions on shrinkage and porosity of dehydrated agricultural products. J Food Eng 35:369–380

    Article  Google Scholar 

  108. Kwei TK (1984) The effect of hydrogen bonding on the glass transition temperatures of polymer mixtures. J Polym Sci Lett Edit 22:307–313

    Article  CAS  Google Scholar 

  109. Labrousse S, Roos YH, Karel M (1992) Collapse and crystallization in amorphous matrices with encapsulated compounds. Sci Aliments 12(4):757–769

    CAS  Google Scholar 

  110. Laaksonen TJ, Roos YH (2000) Thermal, dynamic-mechanical, and dielectric analysis of phase and state transitions of frozen wheat doughs. J Cereal Sci 32(3):281–292

    Article  CAS  Google Scholar 

  111. Laaksonen TJ, Roos YH (2003) Water sorption and dielectric relaxations of wheat dough (containing sucrose, NaCl, and their mixtures). J Cereal Sci 37:319–326

    Article  Google Scholar 

  112. Lai VMF, Lii CY (1999) Effects of modulated differential scanning calorimetry (MDSC) variables on thermodynamic and kinetic characteristics during gelatinization of waxy rice starch. Cereal Chem 76(4):519–525

    Article  CAS  Google Scholar 

  113. Lazaridou A, Biliaderis CG (2002) Thermophysical properties of chitosan, chitosan-starch and chitosan-pullulan films near the glass transition. Carbohydr Polym 48:179–190

    Article  CAS  Google Scholar 

  114. Lazaridou A, Biliaderis CG, Bacandritsos N, Sabatini AG (2004) Composition, thermal and rheological behavior of selected Greek honeys. J Food Eng 64:9–21

    Article  Google Scholar 

  115. Le Meste M, Champion D, Roudaut G, Blond G, Simatos D (2002) Glass transition and food technology: a critical appraisal. J Food Sci 67(7):2444–2458

    Article  CAS  Google Scholar 

  116. Le Meste M, Huang V (1992) Thermomechanical properties of frozen sucrose solutions. J Food Sci 57(5):1230–1233

    Article  CAS  Google Scholar 

  117. Levine H, Slade L (1986) A polymer physicochemical approach to the study of commercial starch hydrolysis products. Carbohydr Polym 6:213–244

    Article  CAS  Google Scholar 

  118. Li Y, Kloeppel KM, Hsieh F (1998) Texture of glassy corn cakes as a function of moisture content. J Food Sci 63(5):869–872

    Article  CAS  Google Scholar 

  119. Li S, Dickinson LC, Chinachoti P (1998) Mobility of “unfreezable” and “freezable” water in waxy corn starch by H-2 and H-1 NMR. J Agric Food Chem 46:62–71

    Article  CAS  Google Scholar 

  120. Lim M, Wu H, Breckel M, Birch J (2006) Influence of the glass transition and storage temperature of frozen peas on the loss of quality attributes. Int J Food Sci Technol 41:507–512

    Article  CAS  Google Scholar 

  121. Lin AA, Kwei TK, Reiser A (1989) On the physical meaning of the Kwei equation for the glass-transition temperature of polymer blends. Macromolecules 22:4112–4119

    Article  CAS  Google Scholar 

  122. Lin X, Ruan RR, Chen P, Chung M, Ye X, Yang T, Doona C, Wagner T (2006) NMR state diagram concept. J Food Sci 71(9):136–144

    Article  CAS  Google Scholar 

  123. Madeka H, Kokini JL (1996) Effect of glass transition and cross-linking on rheological properties of zein: development of a preliminary state diagram. Cereal Chem 73(4):433–438

    CAS  Google Scholar 

  124. Maltini E, Torreggiani D, Venir E, Bertolo G (2003) Water activity and the preservation of plant foods. Food Chem 82:79–86

    Article  CAS  Google Scholar 

  125. Martinez-Navarrete N, Moraga G, Talens P, Chiralt A (2004) Water sorption and plasticization effect in wafers. Int J Food Sci Technol 39:555–562

    Article  CAS  Google Scholar 

  126. Matveev YI, Grinberg VY, Tolstoguzov VB (2000) The plasticizing effect of water on proteins, polysaccharides and their mixtures. Glassy state of biopolymers, food and seeds. Food Hydrocoll 14:425–437

    Article  CAS  Google Scholar 

  127. Matveev YI, Ablett S (2002) Calculation of the C′g and T′g intersection point in the state diagram of frozen solutions. Food Hydrocoll 16:419–422

    Article  CAS  Google Scholar 

  128. Matveev YI (2004) Modification of the method for calculation of the C′(g) and T′(g) intersection point in state diagrams of frozen solutions. Food Hydrocoll 18:363–366

    Article  CAS  Google Scholar 

  129. Micard V, Guilbert S (2000) Thermal behavior of native and hydrophobized wheat gluten, gliadin and glutenin-rich fractions by modulated DSC. Int J Biol Macromol 27:229–236

    Article  CAS  Google Scholar 

  130. Modulated DSC™ Compendium. Theory and experimental conditions, TA applications brief, TA Instruments, New Castle

  131. Morales A, Kokini JL (1999) State diagrams of soy globulins. J Rheol 43(2):315–325

    Article  CAS  Google Scholar 

  132. Mousia Z, Farhat IA, Blachot JF, Mitchell JR (2000) Effect of water partitioning on the glass-transition behaviour of phase separated amylopectin-gelatin mixtures. Polymer 41(5):1841–1848

    Article  CAS  Google Scholar 

  133. Nelson KA, Labuza TP (1994) Water activity and food polymer science: implications of state on arrhenius and WLF models in predicting shelf-life. J Food Eng 22(1–4):271–289

    Article  Google Scholar 

  134. Nikolaidis A, Labuza TP (1996) Glass transition state diagram of a baked cracker and its relationship to gluten. J Food Sci 61:803–806

    Article  CAS  Google Scholar 

  135. Noel TR, Parker R, Ring SG, Tatham AS (1995) The glass-transition behavior of wheat gluten proteins. Int J Biol Macromol 17(2):81–85

    Article  CAS  Google Scholar 

  136. Ohkuma C, Kawai K, Viriyarattanasak C, Mahawanich T, Tantratian S, Takai R, Suzuki T (2008) Glass transition properties of frozen and freeze-dried surimi products: effects of sugar and moisture on the glass transition temperature. Food Hydrocoll 22(2):255–262

    Article  CAS  Google Scholar 

  137. Paterson AHJ, Brooks GF, Bronlund JE, Foster KD (2005) Development of stickiness in amorphous lactose at constant T-Tg levels. Int Dairy J 15(5):513–519

    Article  CAS  Google Scholar 

  138. Peleg M (1996) On modeling changes in food and biosolids at and around their glass transition temperature range. Crit Rev Food Sci Nutr 38(1–2):49–67

    Article  Google Scholar 

  139. Perdon A, Siebenmorgen TJ, Mauromoustakos A (2000) Glassy state transition and rice drying: development of a brown rice state diagram. Cereal Chem 77:708–713

    Article  CAS  Google Scholar 

  140. Pouplin M, Redl A, Gontard N (1999) Glass transition of wheat gluten plasticized with water, glycerol, or sorbitol. J Agri Food Chem 47(2):538–543

    Article  CAS  Google Scholar 

  141. Rahman MS (1995) Food properties handbook. CRC Press, Boca Raton

    Google Scholar 

  142. Rahman MS (2006) State diagram of foods: its potential use in food processing and product stability. Trends Food Sci Technol 17:129–141

    Article  CAS  Google Scholar 

  143. Rahman MS (2004) State diagram of date flesh using differential scanning calorimetry (DSC). Int J Food Prop 7(3):407–428

    Article  Google Scholar 

  144. Rahman MS, Sablani SS, Al-Habsi N, Al-Maskri S, Al-Belushi R (2005) State diagram of freeze-dried garlic powder by differential scanning calorimetry and cooling curve methods. J Food Sci 70(2):135–141

    Article  Google Scholar 

  145. Rahman MS, Labuza TP (1999) Water activity and food preservation. In: Rahman MS (ed) Handbook of food preservation. Marcel Dekker, New York

  146. Rahman MS, Kasapis S, Guizani N, Al-Amri OS (2003) State diagram of tuna meat: freezing curve and glass transition. J Food Eng 57:321–326

    Article  Google Scholar 

  147. Rahman MS, Al-Marhubi IM, Al-Mahrouqi A (2007) Measurement of glass transition temperature by mechanical (DMTA), thermal (DSC and MDSC), water diffusion and density methods: a comparison study. Chem Phys Lett 440:372–377

    Article  CAS  Google Scholar 

  148. Rahman MS, Guizani N, Al-Khaseibi M, Al-Hinai SA, Al-Maskri SS, Al-Hamhami K (2002) Analysis of cooling curve to determine the end point of freezing. Food Hydrocoll 16:653–659

    CAS  Google Scholar 

  149. Rahman MS (2009) Food stability beyond water activity and glass transtion: macro-micro region concept in the state diagram. Int J Food Prop 12:726–740

    Article  CAS  Google Scholar 

  150. Rahman MS, Machado-Velasco KM, Sosa-Morales ME, Velez-Ruiz JF (2009) Freezing point: measurement, prediction and data. In: Rahman MS (ed) Food properties handbook, 2nd edn. CRC Press, Taylor and Francis Group, New York

  151. Rasanen J, Blanshard JMV, Mitchell JR, Derbyshire W, Autio K (1998) Properties of frozen wheat doughs at subzero temperatures. J Cereal Sci 28:1–14

    Article  Google Scholar 

  152. Reid DS (1990) Optimizing the quality of frozen foods. Food Technol 44(7):78–84

    Google Scholar 

  153. Reid DS, Fennema O (2007) Water and ice. In: Damodaran S, Parkin KL, Fennema O (eds) Fennema’s food chemistry, 4th edn. CRC Press, Taylor and Francis Group, New York

  154. Righetto AM, Netto FM (2005) Effect of encapsulating materials on water sorption, glass transition and stability of juice from immature acerola. Int J Food Prop 8:337–346

    Article  CAS  Google Scholar 

  155. Rizzolo A, Nani RC, Viscardi D, Bertolo G, Torreggiani D (2003) Modification of glass transition temperature through carbohydrates addition and anthocyanin and soluble phenol stability of frozen blueberry juices. J Food Eng 56:229–231

    Article  Google Scholar 

  156. Rolee A, LeMeste M (1999) Effect of moisture content on thermomechanical behavior of concentrated wheat starch-water preparations. Cereal Chem 76(3):452–458

    Article  CAS  Google Scholar 

  157. Roos YH, Karel M (1991) Applying state diagrams to food-processing and development. Food Technol 45(12):66–71

    CAS  Google Scholar 

  158. Roos YH, Karel M (1991) Water and molecular-weight effects on glass transitions in amorphous carbohydrates and carbohydrate solutions. J Food Sci 56(6):1676–1681

    Article  CAS  Google Scholar 

  159. Roos YH, Karel M (1991) Amorphous state and delayed ice formation in sucrose solutions. Int J Food Sci Technol 26:553–566

    Google Scholar 

  160. Roos YH (1993) Water activity and physical state effects on amorphous food stability. J Food Process Preserv 16:433–447

    Article  Google Scholar 

  161. Roos YH (1993) Melting and glass transitions of low-molecular-weight carbohydrates. Carbohydr Res 238:29–48

    Article  Google Scholar 

  162. Roos YH (1995) Glass transition-related physicochemical changes in foods. Food Technol 49(10):97–102

    CAS  Google Scholar 

  163. Roos YH (1995) Characterization of food polymers using state diagrams. J Food Eng 24:339–360

    Article  Google Scholar 

  164. Roos YH (1995) Phase transitions in foods. Academic press, San Diego, CA

    Google Scholar 

  165. Roos YH, Karel M, Kokini JL (1996) Glass transitions in low-moisture and frozen foods: effects on shelf life and quality. Food Technol 50(11):95–108

    Google Scholar 

  166. Roos YH (1997) Frozen state transitions in relation to freeze drying. J Therm Anal 48(3):535–544

    Article  CAS  Google Scholar 

  167. Roos YH (2003) Thermal analysis, state transitions and food quality. J Therm Anal Calorim 71(1):197–203

    Article  CAS  Google Scholar 

  168. Roos YH (2007) Phase transitions and transformations in food systems. In: Heldman DR, Lund DB (eds) Handbook of food engineering. CRC Press, Boca Raton

  169. Roos YH (2010) Glass transition temperature and its relevance in food processing. Annu Rev Food Sci Technol 1:469–496

    Article  CAS  Google Scholar 

  170. Roudaut G, Dacremont C, Valles Pamies B, Colas B, Le Meste M (2002) Crispness: a critical review on sensory and material science approaches. Trends Food Sci Technol 13:217–227

    Article  CAS  Google Scholar 

  171. Rouilly A, Orliac O, Silvestre S, Rigal L (2001) DSC study on the thermal properties of sunflower proteins according to their water content. Polymer 42:10111–10117

    Article  CAS  Google Scholar 

  172. Ruan RR, Long Z, Song A, Chen PL (1998) Determination of the glass transition temperature of food polymers using low field NMR. Lebensm Wiss uTechnol 31:516–521

    Article  CAS  Google Scholar 

  173. Ruan RR, Chen PL (1998) Water in foods and biological materials—a nuclear magnetic resonance approach. Technomic. Lancaster

  174. Ruan RR, Long Z, Chang K, Chen PL, Taub IA (1999) Glass transition temperature mapping using magnetic resonance imaging. Trans ASAE 42(4):1055–1059

    CAS  Google Scholar 

  175. Sa MM, Sereno AM (1994) Glass transitions and state diagrams for typical natural fruits and vegetables. Thermochim Acta 246:285–297

    Article  CAS  Google Scholar 

  176. Sablani SS, Rahman MS (2002) Pore formation in selected foods as a function of shelf temperature during freeze drying. Dry Technol 20(7):1379–1391

    Article  Google Scholar 

  177. Sablani SS, Kasapis S, Rahman MS, Al-Jabri A, Al-Habsi N (2004) Sorption isotherms and the state diagram for evaluating stability criteria of abalone. Food Res Int 37:915–924

    Article  Google Scholar 

  178. Sablani SS, Kasapis S (2006) Glass transition and water activity of freeze-dried shark. Dry Technol 24:1003–1009

    Article  CAS  Google Scholar 

  179. Sablani SS, Al-Belushi K, Al-Marhubi I, Al-Belushi R (2007) Evaluating stability of vitamin C in fortified formula using water activity and glass transition. Int J Food Prop 10:61–71

    Article  CAS  Google Scholar 

  180. Sablani SS, Kasapis S, Rahman MS (2007) Evaluating water activity and glass transition concepts for food stability. J Food Eng 78(1):266–271

    Article  Google Scholar 

  181. Sablani SS, Rahman MS, Al-Busaidi S, Guizani N, Al-Habsi N, Al-Belushi R, Soussi B (2007) Thermal transitions of king fish whole muscle, fat and fat-free muscle by differential scanning calorimetry. Thermochim Acta 462:56–63

    Article  CAS  Google Scholar 

  182. Sablani SS, Bruno L, Kasapis S, Syamaladevi RM (2009) Thermal transitions of rice: development of a state diagram. J Food Eng 90(1):110–118

    Article  Google Scholar 

  183. Sacha GA, Nail SL (2009) Thermal analysis of frozen solutions: multiple glass transitions in amorphous systems. J Pharm Sci 98:3397–3405

    Article  CAS  Google Scholar 

  184. Schebor C, Buera MD, Chirife J (1996) Glassy state in relation to the thermal inactivation of the enzyme invertase in amorphous dried matrices of trehalose, maltodextrin and PVP. J Food Eng 30(3–4):269–282

    Article  Google Scholar 

  185. Schebor C, Buera MD, Chirife J, Karel M (1995) Sucrose hydrolysis in glassy starch matrix. Food Sci Technol 28(2):245–248

    CAS  Google Scholar 

  186. Schmidt SJ (1999) Probing the physical and sensory properties of food systems using NMR spectroscopy. In: Belton PS, Hills BP, Webb GA (eds) Advances in magnetic resonance in food science. The Royal Society of Chemistry, UK

  187. Schmidt SJ (2007) Water mobility in foods. In: Barbosa-Canovas GV, Fontana AJ, Schmidt SJ, Labuza TP (eds) Water activity in foods: principles and applications. Blackwell publishing, USA

  188. Schmidt SJ (2004) Water and solids mobility in foods. In: Taylor S (ed) Advances in food and nutrition research. Academic Press, London

  189. Sherwin CP, Labuza TP, McCormick A, Chen B (2002) Cross-polarization/magic angle spinning NMR to study glucose mobility in a model intermediate-moisture food system. J Agric Food Chem 50(26):7677–7683

    Article  CAS  Google Scholar 

  190. Shimada Y, Roos YH, Karel M (1991) Oxidation of methyl linoleate encapsulated in amorphous lactose-based food model. J Agric Food Chem 39:637–641

    Article  CAS  Google Scholar 

  191. Shrestha AK, Howes T, Adhikari BP, Bhandari BR (2008) Spray drying of skim milk mixed with milk permeate: effect on drying behavior, physicochemical properties, and storage stability of powder. Dry Technol 26:239–247

    Article  CAS  Google Scholar 

  192. Silva MA, Sobral PJA, Kieckbusch TG (2006) State diagrams of freeze-dried camu-camu (Myrciaria dubia (HBK) Mc Vaugh) pulp with and without maltodextrin addition. J Food Eng 77:426–432

    Article  CAS  Google Scholar 

  193. Simatos D, Faure M, Bounjour E, Couch M (1975) The physical state of water at low thermal analysis and differential scanning calorimetry. Cryobiology 12:202–208

    Article  CAS  Google Scholar 

  194. Simatos D, Blond G, Le Meste M (1989) Relation between glass-transition and stability of a frozen product. Cryo-Letters 10:77–84

    Google Scholar 

  195. Simatos D, Blond G, Roudaut G, Champion D, Perez J, Faivre AL (1996) Influence of heating and cooling rates on the glass transition temperature and the fragility parameter of sorbitol and fructose as measured by DSC. J Therm Anal 47:1419–1436

    Article  CAS  Google Scholar 

  196. Singh KJ, Roos YH (2005) Frozen state transitions of sucrose-protein-cornstarch mixtures. J Food Sci 70(3):198–204

    Article  Google Scholar 

  197. Slade L, Levine H (1987) Structural stability of intermediate moisture foods—a new understanding. In: Mitchell JR, Blanshard JMV (eds) Food structure—its creation and evaluation. Butterworths, London

  198. Slade L, Levine H (1988) Non-equilibrium melting of native granular starch.1. Temperature location of the glass-transition associated with gelatinization of a-type cereal starches. Carbohydr Polym 8:183–208

    Article  CAS  Google Scholar 

  199. Slade L, Levine H (1988) Non-equilibrium behavior of small carbohydrate-water systems. Pure Appl Chem 60:1841–1864

    Article  CAS  Google Scholar 

  200. Slade L, Levine H (1991) Beyond water activity: recent advances based on an alternative approach to the assessment of food quality and safety. Crit Rev Food Sci Nutr 30:115–360

    Article  CAS  Google Scholar 

  201. Syamaladevi RM, Sablani SS, Tang J, Powers J, Swanson BG (2009) State diagram and water adsorption isotherm of raspberry (Rubus idaeus). J Food Eng 91:460–467

    Article  CAS  Google Scholar 

  202. Syamaladevi RM, Sablani SS, Tang J, Powers J, Swanson BG (2010) Water sorption and glass transition temperatures in red raspberry (Rubus idaeus). Thermochim Acta. doi: 10.1016/j.tca.2010.03.013

  203. Tan I, Wee CC, Sopade PA, Halley PJ (2004) Investigation of the starch gelatinization phenomena in water-glycerol systems: application of modulated temperature differential scanning calorimetry. Carbohydr Polym 58:191–204

    Article  CAS  Google Scholar 

  204. Telis VRN, Sobral PJA (2001) Glass transitions and state diagram for freeze-dried pineapple. Lebensm-wiss Technol 34:199–205

    Article  CAS  Google Scholar 

  205. Telis VRN, Sobral PJA (2002) Glass transitions for freeze-dried and air-dried tomato. Food Res Int 35:435–443

    Article  CAS  Google Scholar 

  206. Telis VRN, Sobral PJD, Telis-Romero J (2006) Sorption isotherm, glass transitions and state diagram for freeze-dried plum skin and pulp. Food Sci Technol Int 12(3):181–187

    Article  Google Scholar 

  207. Terefe NS, Hendrickx M (2002) Kinetics of the pectin methylesterase catalyzed de-esterification of pectin in frozen food model systems. Biotechnol Prog 18(2):221–228

    Article  CAS  Google Scholar 

  208. Tolstoguzov VB (2000) The importance of glassy biopolymer components in food. Nahr Food 44(2):76–84

    Article  CAS  Google Scholar 

  209. Torreggiani D, Forni E, Guercilena I, Maestrelli A, Bertolo G, Archer GP, Kennedy CJ, Bone S, Blond G, Contreras-Lopez E, Champion D (1999) Modification of glass transition temperature through carbohydrates additions: effect upon color and anthocyanin pigment stability in frozen strawberry juices. Food Res Int 32:441–446

    Article  CAS  Google Scholar 

  210. Toufeili I, Lambert IA, Kokini JL (2002) Effect of glass transition and cross-linking on rheological properties of gluten: development of a preliminary state diagram. Cereal Chem 79(1):138–142

    Article  CAS  Google Scholar 

  211. Truong V, Bhandari BR, Howes T, Adhikari B (2002) Analytical model for the prediction of glass transition temperature of food systems. In: Levine H (ed) Amorphous food and pharmaceutical systems. The Royal society of chemistry, Cambridge

  212. Van Nieuwenhuijzen NH, Primo-martin C, Meinders MBJ, Tromp RH, Hamer RJ, Van Vliet T (2008) Water content or water activity: what rules crispy behavior in bread crust? J Agric Food Chem 56:6432–6438

    Article  CAS  Google Scholar 

  213. Vassilikou-Dova A, Kalogeras IM (2009) Dielectric analysis (DEA). In: Menczel JD, Prime RB (eds) Thermal analysis of polymers. Wiley, New Jersey

  214. Vuataz G (2002) The phase diagram of milk: a new tool for optimizing the drying process. Lait 82:485–500

    Article  CAS  Google Scholar 

  215. Wang H, Zhang S, Cuen G (2008) Glass transition and state diagram for fresh and freeze-dried Chinese gooseberry. J Food Eng 84:307–312

    Article  Google Scholar 

  216. Ward IM, Hadley DW (1993) An introduction to the mechanical properties of solid polymers. Wiley, Chichester

    Google Scholar 

  217. Welti-Chanes J, Guerrero JA, Barcenas ME, Aguilera JM, Vergara F, Barbosa-Canovas GV (1999) Glass transition temperature (T g ) and water activity (a w ) of dehydrated apple products. J Food Process Eng 22(2):91–101

    Article  Google Scholar 

  218. White GW, Cakebread SH (1966) The glassy state in certain sugar containing food products. J Food Technol 1:73–82

    Article  CAS  Google Scholar 

  219. Wolfe J, Bryant G, Koster KL (2002) What is ‘unfreezable water’, how unfreezable is it and how much is there? CryoLetters 23:157–166

    Google Scholar 

  220. Wu X, Zhu Z (2009) Dynamic crossover of alpha relaxation in poly(vinyl acetate) above glass transition via mechanical spectroscopy. J Phys Chem B 113:11147–11152

    Article  CAS  Google Scholar 

  221. Yang W, Jia C, Siebennorgen TJ, Pan Z, Cnossen AG (2003) Relationship of kernel moisture content gradients and glass transition temperatures to head rice yield. Biosyst Eng 85(4):467–476

    Article  Google Scholar 

  222. Yang W, Jia C (2004) Glass transition mapping inside a rice kernel. Trans ASAE 47(6):2009–2015

    Google Scholar 

  223. Yu X, Kappes SM, Bello-Perez LA, Schmidt SJ (2008) Investigating the moisture sorption behavior of amorphous sucrose using a dynamic humidity generating instrument. J Food Sci 73(1):E25–E35

    Article  CAS  Google Scholar 

  224. Zasypkin D, Porzio M (2004) Glass encapsulation of flavors with chemically modified starch blends. J Microencapsul 21(4):385–397

    Article  CAS  Google Scholar 

  225. Zhong Z, Sun XS (2005) J Food Eng 69:453–459

    Article  Google Scholar 

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Acknowledgments

This activity was funded, in part, with an Emerging Research Issues Internal Competitive Grant from the Agricultural Research Center and with a Biological and Organic Agriculture (BioAg) Program Grant from the Center for Sustaining Agriculture and Natural Resources at Washington State University.

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  1. Department of Biological Systems Engineering, Washington State University, P.O Box 646120, Pullman, WA, 99164-6120, USA

    Shyam S. Sablani & Roopesh M. Syamaladevi

  2. School of Food Science, Washington State University, P.O Box 6463760, Pullman, WA, 99164-6376, USA

    Barry G. Swanson

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  1. Shyam S. Sablani
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Sablani, S.S., Syamaladevi, R.M. & Swanson, B.G. A Review of Methods, Data and Applications of State Diagrams of Food Systems. Food Eng. Rev. 2, 168–203 (2010). https://doi.org/10.1007/s12393-010-9020-6

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