Variable hydration of small carbohydrates for prediction of equilibrium properties in diluted and concentrated solutions J.-B. Gros LGCB, Université B. Pascal, Clermont-Ferrand, France
Which thermodynamic properties in food processing, formulation and control? Water activity Osmotic pressure Activity of dissolved species Solubility of gases Solubility of solids in water Partition factors ph
Food products = nonideal complex mixtures Excess free energy f,p Osmotic properties g E Solid-liquid equilibrium properties T f, T m Solubility S K i LL Liquid-liquid equilibrium properties γ i Dissociation properties ph Vapor-liquid equilibrium properties K i LV,a w T b Solubility G
Our selected γ i model: main characteristics Group-contribution method glucose-water solution Hydration of ions NaCl solution CH 2 4 CH 5 OH CH-O Structural decomposition Hydration number
Our selected γ i model U L P D H S Unifac Larsen Pitzer Debye Hückel Solvation - the predictive group-contribution UNIFAC (975) model modified by Larsen (987) for short range physical interactions - for long range interactions : a Pitzer term (Debye-Hückel) - hydration of ions by water molecules No salt dependent coefficients Only ions or group dependent coefficients
Example: mean ionic activity coefficients for some salts in aqueous solutions gamma KCl, gamma NaCl Modèle ULPDHS Modèle ULPDHS g molal 0,7 0,6 gmolal 0,7 0,5 0,6 0 2 3 4 5 m KCl (mol/kg) 0 2 4 6 8 m NaCl (mol/kg),4,2 NaOH ULPDHS 4 3,5 3 gamma HCl Modèle ULPDHS gmolal g molal 2,5 2,5 0,6 0 2 4 6 8 m NaOH (mol/kg) 0,5 0 2 3 4 5 6 7 m HCl (mol/kg)
Example: water activity in sugar aqueous solutions aw aw 0,7 0,6 Modèle ULPDHS 0,5 Modèle ULPDHS 0,7 0 0, 0,2 0,3 0,4 0,5 0,6 0,7 Glucose weight fraction 0,4 0 0,2 0,4 0,6 Sucrose weight fraction aw aw 5 0,7 0,6 Modèle ULPDHS 0 0,2 0,4 0,6 Fructose weight fraction Modèle ULPDHS 0 0, 0,2 0,3 0,4 0,5 Maltose weight fraction
Scope Improve the estimation for aqueous system containing sugars Constraint: predict properties of aqueous solutions of single and multiple solutes including electrolytes: group-contribution method
What is to be done? Add new groups in the physical model: pyranose ring, furanose ring, osidic bond... Have a better description of the strong forces between molecules
Hydration of species Electrolytes Sugars Water molecules are bound to ions,forming stochiometric complexes Hydroxyl groups play a major role
Hydration number nh Glucose Fructose Sucrose Mannose Xylose nh 3,0 3,0 6,4 (literature) 3,26 3,26 3,7 8,4 c 8,8 c 8, c 6,8 c 5 Hydration varies with concentration hydration number 4 3 2 0 0 0,2 0,4 0,6 solute weight fraction
Chemical part of the model S + nh H O 2 K ( ) S, nh H O 2 S Free form: X SL Hydrated form : X SH Ideal mixture of the 3 species The equilibrium constant K is given by K = exp 0 G R T = X SL X SH nh W X X SH ; X SL : molar fractions nh : hydration number
Chemical part of the model: true composition?? Apparent composition True composition Mass balance X XS app = + SH + X n X SL SH X W app X = W and + n X K SH 3 equations and 3 unknowns X SH, X SL et X W
Physical part of the model - interaction between the true species At high concentrations, interactions exist between species X SH, X SL et X W : physical model size of the true molecules London dispersion forces, etc. K becomes: K = exp 0 G R T = X SH X SL γ γ SL SH a nh W
Example: water activity in sugar aqueous solutions: glucose, mannose, fructose K=,4 K=4 5 aw aw Modèle ULPDHS (nh=0) Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) Modèle ULPDHS (solv variable) 0,7 0 0, 0,2 0,3 0,4 0,5 0,6 0,7 Glucose weight fraction 5 0 0, 0,2 0,3 0,4 0,5 0,6 Mannose weight fraction K=,9 aw 0,7 0,6 Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) 0 0,2 0,4 0,6 Fructose weight fraction
Xylose, sucrose, maltose K=0,32 K=6,9 aw 5 aw 0,6 Modèle ULPDHS (nh=0) 0,4 Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) 0 0, 0,2 0,3 0,4 Xylose weight fraction 0,2 Modèle ULPDHS (solv variable) 0 0,2 0,4 0,6 Sucrose weight fraction K=6,9 aw 5 Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) 0 0, 0,2 0,3 0,4 0,5 Maltose weight fraction
Results: nh and K Glucose Fructose Sucrose Mannose Xylose nh (literature) 3,0 3,0 6,4 3,26 3,26 3,7 8,4 c 8,8 c 8, c 6,8 c nh (OH) = 0.4 2 2 3,2 2 2 K,4,9 6,9 4 0,32 nh,766 (0,35) 2,5 (0,5) 2,95 (0,35),34 (0,268) 06 () K,7,78 6,42,769,4
Water activity and molar activity coefficient of water 5 5 Sucrose: a w, g w, g s and average 0 20 40 60 80 Brix, % w/w sucrose 3 2,5 2,5 Molal activity coefficient of sucrose hydration number nh (sucrose) = 3.2 The apparent or average hydratation number varies with concentration average hydration number 3 2,5 2,5 0,5 0 n eq = n x sh xsh + x sp γsl n Ka w γ sh = n γ sl + Ka γ 0 0,2 0,4 0,6 sh Sucrose weight fraction n w
Solubility of sucrose and glucose Sucrose weight fraction 0,6 0,4 0,2 0 Experiments Model 20 40 60 80 00 Temperature ( C) Glucose weight fraction 0,6 0,4 0,2 0 Experiments Model 20 40 60 80 00 Temperature ( C) ln H C C ( ) f,s p m,s p γ = + + SXSapp ln R T Tm,S R T R Tm,S T T
Glucose: a w,g w and g s,4 Water activity and molar activity coefficient of water 5 5,35,3,25,2,5,,05 Molal activity coefficient of glucose 0 0 20 30 40 50 60 70 Brix, w/w glucose
Concentrated apple juice Water activity Fontan and Chirife 0,7 Model 0 0 20 30 40 50 60 70 Total sugar concentration (% w/w)
Honey: model honey and Geek honeys Water activity 0,7 0,6 0,5 0,4 Rüegg and Blanc Model 70 75 80 85 90 Total sugar concentration (% w/w) Botanic/Geographical origin Water activity 20 C after melting at 50 C Calculated water activity Honey-dew (pine)/thasos 0.60 0.62 0.65 0.600 0.570 0.55 Floral/Livadia 0.528 0.56 0.550 0.543 Floral(orange blossom)/argos 0.584 0.56 Lazaridou et al., J. Food Eng. (2004) 0.577 0.590
Conclusion We need reliable data for hydration of species, by experiments and/or by molecular modelling A second-approximation form of chemical solution theory (a chemical part and a physical part) gives better estimates at high concentration of solutes than classical physical models Sandler
Acknowledgements Former students: C. Achard, M. Catté PhD student: L. Ben Gaïda Prof. C.G. Dussap