SORPTION ISOTHERMS CONSTRUCTION & EVALUATION Jiri Blahovec, Stavros Yanniotis

WATER INTERNAL ENERGY

COHESIVE FORCES Bond Energies: Covalent triple ~ 800 kJ.mol -1 double kJ.mol -1 single kJ.mol -1 Hydrogen kJ.mol -1 Group electrostatic kJ.mol -1 Van der Waals 1-2 kJ.mol -1 Hydrophobic 1-5 kJ.mol -1 Thermal energy (R.T.)2.5 kJ.mol -1 - regular structure - conservative character - elasticity - hard matter - irregular net formation - dissipative character - flowing - soft matter - instability (T, solvents)

DRY MATTER AND WATER

CELLULAR STRUCTURE In cellular structure the state properties are done: 1.Properties of cell walls and intercellular bonding 2.Turgor stress inside cells Generally by bonding among the rigid structural units

SORPTION Chemical (Strong) reactants Solutions (softer) Physical (Soft) Surfaces (stronger) pores

EQUILIBRIUM MOISTURE

WATER ACTIVITY a w – water activity  =  w -  wr = RT ln( a w )

SORPTION ISOTHERM Relation between water activity and moisture content at constant temperature

SORPTION ISOTHERMS ( POTATO TUBERS – ROLE OF TEMPERATURE)

ISOSTERIC HEAT OF SORPTION (kJ/mol)

SORPTION ISOTHERMS (Brunauer’s Classification)

SIGMOIDAL SORPTION ISOTHERMS (Brunauer’s Type II) Point of Inflexion

THE BASIC SIGMOIDAL TYPES BET (two parameters) Brunauer-Emmet-Teller (Brunauer et al.,1938) based on multilayer surface sorption GAB (three parameters) Guggenheim-Anderson-de Boer (Van den Berg, 1984) - corrected BET HH (four parameters) Hailwood Horrobin (Hailwood and Horrobin, 1946) based on monolayer surface combined with solution sorption

BET ISOTHERM w – moisture content (d.b.) a w – water activity C and w m parameters, where w m - monomolecular moisture content, C - strength of water bond to DM surface

BET ISOTHERM (Linearized Form & Internal Surface) Linear in coordinates y = a w /[w(1 – a w )] and x = a w : y = A + Bx; C = 1 + B/A; w m = 1/(AC) Internal Surface Area (ISA in m 3 per kg of DM):

MODEL RIGIDITIES Model importance for data cleaning and/or smoothing Model discrepancy with data due to the model rigidity Solving by further models with more parameters Van den Berg, C. & Bruin, S. (1981): 77 most important models: theoretical (48), partially theoretically based (15), and fully empirical (14).

GAB ISOTHERM

GAB ISOTHERM (Transformation & Evaluation) Haiworth-Horrobin transformation: Native Wheat Starch a = 0.560, b = 9.352, c = , R 2 = a w less than 0.91

GAB ISOTHERM (Discrepancies in Approximation) Native Wheat Starch R 2 = 0.887

GAB ISOTHERM (Polynomial Generalization) Polynomial of Fourth Order R 2 = (GAB)

HH ISOTHERM a 1 ’ and a 2 ’ are parameters the term on the right side can be understood as a sum of surface and solution bonding of water the equation can be rearranged to the GAB one The equation can be easy generalized into the four parameter equation with less rigidity to general data

HH ISOTHERM (Generalized) Native Wheat Starch R 2 = 0.953

CONSTRUCTION OF SORPTION MODELS Assumption: Different mechanisms of sorption are independent, i.e. parallel (without interaction) Then where w i are moisture contents corresponding to i-th mechanisms, This attempt was also applied in the HH model

STRUCTURAL SORPTION MODELS (chemical reactions and interaction between different sources are omitted) MC = MC adsorbed at solid surfaces (surfaces in pores with radius less then monolayer thickness are excluded) + MC in water solutions + MC in pores with radius higher than the monolayer thickness Thickness of water monolayer is about 1 nm.

CONCLUSIONS Knowledge of water activity so important for storing is the main cause of studies of the sorption isotherms Model sorption isotherms are important for clearing and smoothing data Simple model isotherms are too rigid to be able to describe well the complicated sorption data of foods and agro-products More complicated models with more free parameters help to solve the problems The way for building more complicated structural models is given

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