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Moisture diffusion in porous broccoli florets and stalks is modeled using the free volume and Maxwell-Eucken theories. These theories are based on the mobility of water and concern the variation of the effective diffusion coefficient for a wide range of temperature and moisture content during product drying. Mass and heat transport, shrinkage, and vitamin C degradation during drying of broccoli are simulated by a spatial model. The effective diffusion coefficient varies strongly with product moisture content and temperature. Vitamin C degradation is high at moisture contents around 2 kg water/kg dry matter. The influence of the size of broccoli on the drying rate is evaluated for several types of broccoli florets and stalks.

Water sorption and dynamical properties of bread crust were studied using gravimetric sorption experiments. Water uptake and loss were measured while relative humidity (RH) was step-wise in- or decreased. Experimental results were compared with Fickian diffusion models and empirical models like the exponential and power-law model. From comparison of experimental sorption curves and the power-law model for short times it followed for all bread crust that the diffusional coefficient n is close to one. It turned out that this is not due to so-called case II diffusion and water transport that is limited by relaxation of the solid material but due to the fact that RH did not instantaneously but gradually increased to the set value. Sorption curves of isotherm experiments could be best described by the Fickian diffusion model for low RH and by the exponential model for large RH. Transport rates depend on moisture content and show a maximum around RH = 0.7, corresponding to a water mass fraction ω1 = 0.12. Diffusion rates could be well described by free volume theory up to the maximum, but this theory could not explain the strong decrease at higher ω1. Indications for a local glass-rubber transition at room temperature were found near a water mass fraction ω1 ≈ 0.09. This corresponds very well to the start of the crisp–non-crisp transition as measured by a sensory panel, but not to the glass-rubber transition at ω1 ≈ 0.12 as measured by other techniques like Differential Scanning Calorimetry. So it seems that more than one glass-rubber like transitions may be important to describe the properties of heterogeneous cellular food systems.

In this work, we propose a model for describing the dynamics in polymer blends or polymer-solvent blends close to and below Tg. The model is solved on a 2D lattice corresponding to spatial scales from 10 nm up to a few micrometers and incorporate the heterogeneous nature of the dynamics at the scale of a dynamic heterogeneity (3-5 nm). In case of polymer blends, we apply this model to study phase separation close to and below Tg upon cooling, and rejuvenation in miscible range upon heating. In the course of phase separation, we observe slow structures forming in coexistence with faster ones. In the same time, the global dynamics of the system slows down and domains grow like the logarithm of the time. During rejuvenation, we observe that morphologies melt much faster the elapsed time required to build them during aging. In the case of polymer-solvent blends, the system is put in contact with a solvent reservoir and is at temperatures far below the pure polymer glass transition. We consider situations where the activity of the solvent reservoir is varied in order to describe either films drying or swelling. Our model allows for explaining case-II diffusion in the context of the plasticisation of a glassy polymer by penetrating solvent during swelling. Regarding the process of film drying, we show that films up to 1 micrometer thick can be completely dried. When drying a thicker film, we show that a glassy crust may appear on the free surface, as shown experimentally, Dans ce travail, nous proposons un modèle qui décrit la dynamique dans les mélanges de polymères et polymère-solvant à l'approche de la transition vitreuse. Le modèle est résolu sur un réseau 2D sur des échelles de 10 nm à plusieurs microns. Ce modèle incorpore l'aspect hétérogène de la dynamique à l'échelle d'une hétérogénéité dynamique (3-5 nm). Dans le cas des mélanges de polymères, nous appliquons ce modèle afin d'étudier la séparation de phase lorsque le système est refroidi proche ou sous Tg, et le rajeunissement lorsque le système est réchauffé dans un état miscible et fondu. Pendant la séparation de phase, nous observons que des morphologies lentes se forment en coexistence avec des morphologies rapides. Pendant ce temps, la dynamique globale du système se ralentit et les domaines croissent comme le logarithme du temps. Lors de la réchauffe en revanche, nous observons que les domaines vitreux fondent plus vite que le temps nécessaire pour qu'ils se forment lors de la séparation de phase. Dans le cas des mélanges polymère-solvant, le système est en contact avec un réservoir de solvant et est en dessous de la température de transition vitreuse du polymère pur. L'activité du réservoir peut être changée afin de décrire le séchage ou le gonflement de films. Notre modèle permet de décrire la diffusion cas-II lorsqu'un polymère vitreux est plastifié par du solvant qui pénètre le système. Concernant le processus inverse de séchage, nous montrons que des films ayant des épaisseurs inférieures à 1 micron peuvent être séchés entièrement. Pour des films plus épais, en revanche, une croûte vitreuse se forme sur la surface libre du film

Vapor–liquid equilibrium data were determined for five polymer + toluene systems at isothermal conditions between 333.15 and 373.15 K. Polymers comprise copolymers and terpolymers of octadecyl acrylate (ODA), acrylic acid (AA), styrene (St), and 1-vinyl-2-pyrrolidone (VP) because of their practical importance as flow improvers for crude oil and/or derivatives. The need to measure these systems has emerged because relevant phase equilibrium data are not available in literature. All-glass micro-ebulliometer with circulation of liquid phase was used for measurement of total pressure over polymer + toluene mixtures, as described in our earlier study.1 To analyze the obtained data, we opted for the prediction of phase behavior, as the data of two experimental points, including concentration end points, could not be reduced with use of the UNIQUAC equation, as is e.g. in the Polymer Solution Data Collection by Hao et al.2 We used two predictive models, the Entropic-FV activity coefficient model3 and the GC-Flory EOS model, 4 to estimate the activity of toluene in a mixture with a polymer. Both models are based on the group contribution method. Two terpolymers, namely poly(ODA0.79–AA0.11–VP0.10) and poly(ODA0.82–St0.05–AA0.13) in mixtures with toluene were chosen as examples of solvent activity predictions, because values of all necessary group parameters for both models were at hand. Figures 1 and 2 show the prediction of toluene activities in both the terpolymer solutions, respectively. It is obvious that the models are mutually comparable and in a good agreement. Moreover, the dependence of solvent activity on concentration provides a qualitative description of particular system behavior over the whole concentration range including activity trends, since the prediction is based on group contributions, which comprises the structure of components involved. It is necessary to point out, that prediction procedures were not used for validation of experimental data, but to give an idea about the trend in activity vs. concentration dependence. As it can be seen, good agreement with experimental data was achieved. Figure 1. Activity of toluene in poly(ODA0.82–St0.05–AA0.13) at 363.15 Figure 2. Activity of toluene in poly(ODA0.79–AA0.11–VP0.10) at 353.15 K. References: 1. J. Pavlíček, G. Bogdanić and I. Wichterle, Fluid Phase Equilib., 2010, 297 (1), 142–148. 2. W. Hao, H. S. Elbro and P. Alessi, Polymer Solution Data Collection. 1: Vapor–liquid Equilibrium, Chemistry Data Series XVI, Part 1, DECHEMA: Frankfurt/M., 1992. 3. G. M. Kontogeorgis, Aa. Fredenslund and D. P. Tassios, Ind. Eng. Chem. Res., 1993, 32 (2), 362–372. 4.G. Bogdanić and Aa. Fredenslund, Ind. Eng. Chem. Res. 1994, 33 (5), 1331–1340.

Water sorption of gluten and wheat starch films as a function of water activity was studied using gravimetric step-change sorption experiments. Films of different thicknesses were used with the aim to vary the characteristic diffusion time and to get insights in the contribution of the polymer-chain rearrangement in the sorption behaviour. It is shown that both starch and gluten are in the glassy state for a water activity aw below 0.9. From comparison of the dynamical sorption curves with a Fickian diffusion model, it is shown that water diffusion in gluten films seems Fickian for aw 0.7, while for starch films, non-Fickian sorption behaviour is observed for aw > 0.1. The results show that polymer-chain rearrangement and the stress built up in the matrix play an important role in the sorption dynamics of these films. Even when the material is in the glassy state matrix relaxation phenomena play a role in the sorption behaviour of starch and gluten.

All-glass micro-ebulliometers with circulation of liquid phase has been constructed for determination of vapour–liquid equilibria ; charge of liquid phase is approximately 8 mL. Vapour pressure of toluene was measured to prove its proper functioning, and then vapour liquid equilibria were determined in the polymer + solvent (toluene) mixtures.

Transport of oil products, namely crude oil, gas condensate and derivatives, requires flow improver additives for optimal realization. These compounds, already in low concentrations, are able to improve significantly flow properties of transported material. It was found [1, 2] that one class of efficient additives consists of copolymers and terpolymers synthesized by polymerization of long chain acrylate (ODA) with styrene (St) and acrylic acid (AA) and St or 1-vinyl-2-pyrrolidone (1V2P). Chemical structure of the synthesized compounds is shown in Fig. 1. Fig. 1. Structural representation of a) copolymer of ODA-St ; b) copolymer of ODA-AA ; c) terpolymer of ODA-St-AA ; d) terpolymer of ODA-AA-1V2P ; e) terpolymer of ODA-St-1V2P Such polymeric improver additives have already been exploited with excellent results as the means for separation of paraffinic fractions and their effect on the pour point and rheological properties of crude oil samples in the northern Croatia. For future development of better additives, the group contribution method represents a powerful tool ; however the evaluation of particular group increments must be based on thermodynamic data on systems which are not hitherto available. The five structurally different additives, poly(ODA0.85-St0.15), poly(ODA0.95-AA0.05), poly(ODA0.82-St0.05-AA0.13), poly(ODA0.79-AA0.11-1V2P0.10), poly(ODA0.78-St0.05-1V2P0.17 were selected for vapor– liquid equilibrium (VLE) measurement because they decrease considerably pour point of all crude oils, i.e. they are improving rheological properties of crude oils. In this work, VLE were determined ebulliometrically by the micro-method described in [3] in toluene as solvent, at different temperatures and pressures. Prediction of phase equilibrium compositions will be carried out with use of both the Entropic-FV model [4] and the GC-Glory EOS [5] group contribution models. The results will be completed shortly before the conference and shown during the presentation. References [1] A. Erceg Kuzmić, M. Radošević, G. Bogdanić, R. Vuković, Fuel 86 (2007) 1409. [2] A. Erceg Kuzmić, M. Radošević, G. Bogdanić, V. Srića, R. Vuković, Fuel 87 (2008) 2943. [3] I. Wichterle, G. Bogdanić, A. Erceg Kuzmić, 23rd European Seminar on Applied Thermodynamics – ESAT 2008, Proceedings, 572-573, Cannes, France, 2008. [4] G. M. Kontogeorgis, Aa. Fredenslund, D. P. Tassios, Ind. Eng. Chem. Res. 31 (1993) 362. [5] G. Bogdanić, Aa. Fredenslund, Ind. Eng. Chem. Res. 33 (1994) 1331. The authors acknowledge the partial support of the Ministry of Science, Education and Sports of the Republic of Croatia (Grant No. 061-0000000-3029) and of the Czech Science Foundation (Grant No. 104/07/0444).

Transport of oil products, namely crude oil, gas condensate and derivatives, requires flow improver additives for optimal realization. These compounds, already in low concentrations, are able to improve significantly flow properties of transported material. It was found [1, 2] that one class of efficient additives consists of copolymers and terpolymers synthesized by polymerization of long chain methacrylates with styrene and (meth)acrylic acid and styrene or 1-vinyl-2-pyrrolidone. Such polymeric improver additives have already been exploited with excellent results as the means for separation of paraffinic fractions being responsible for increased viscosity and pour point. For future development of better additives, the group contribution method represents a powerful tool ; however the evaluation of particular group increments must be based on thermodynamic data on systems which are not hitherto available. In this work, liquid– vapor equilibria were determined ebulliometrically for several systems consisting of the above mentioned terpolymer + organic solvent at different temperatures and pressures. Subsequently, this data base is used for evaluation of the first approximation of necessary input data. Prediction of phase equilibrium compositions has been carried out with use of three group contribution models: the Entropic-FV model [3], the GC-Glory EOS [4] and the GC-LF EOS [5, 6]. References [1] A. Erceg Kuzmić, M. Radošević, G. Bogdanić, R. Vuković, Fuel 86 (2007) 1409. [2] A. Erceg Kuzmić, M. Radošević, G. Bogdanić, V. Srića, R. Vuković, Fuel, in press. [3] G. M. Kontogeorgis, Aa. Fredenslund, D. P. Tassios, Ind. Eng. Chem. Res. 31 (1993) 362. [4] G. Bogdanić, Aa. Fredenslund, Ind. Eng. Chem. Res. 33 (1994) 1331. [5] M. S. High, R. P. Danner, AIChE J. 36 (1990) 1625. [6] M. S. High, R. P. Danner, Fluid Phase Equilib. 53 (1989) 323. The authors acknowledge the partial support of the Grant Agency of the Czech Republic (Grant No. 104/07/0444) and of the Ministry of Science, Education and Sports of the Republic of Croatia.

There are numerous examples of the importance of small molecule migration in polymeric materials, such as in drying polymeric packing, controlled drug delivery, formation of films, and membrane separation, etc. The Chapman-Enskog kinetic theory of hard-sphere fluids with the Weeks-Chandler-Andersen effective hard-sphere diameter (Enskog-WCA) has been the most fruitful in diffusion studies of simple fluids and mixtures. In this work, the ability of the Enskog-WCA model to describe the temperature and concentration dependence of the mutual diffusion coefficient, D, for a polystyrene-toluene system was evaluated. Using experimental diffusion data, two polymer model approaches and three mixing rules for the effective hard-sphere diameter were tested. Some procedures tested resulted in models that are capable of correlating the experimental data with the refereed system well for a solvent mass fraction greater than 0.3.

The Vrentas/Duda proposal for the diffusion of polymer-solvent systems, which is based on the free-volume theory, was employed in correlating and predicting mutual diffusion coefficients in highly concentrated polymer solutions. It has been observed that the predictive version of the model is capable of qualitatively representing the experimental data, while the use of an adjustable parameter greatly improves the performance of the model. The systems studied were poly(vinyl) acetate-toluene and Neoprene-acetone, and a comparison between experimental data and calculated values from the Vrentas/Duda model is reported. A new experimental apparatus based on the sorption technique was built to provide reliable diffusivity data on the Neoprene-acetone system.

The segmental interaction model containing the combinatorial, free-volume and energetic contributions to the excess Gibbs energy for correlation/prediction of liquid-liquid equilibria (LEE) of polymer solutions has been developed1,2. The energetic contribution is based on the solution of segment concept. The groups are defined as the polymer or copolymer segments (repeating units) or solvent molecules, as is usually done when applying the mean field theory3. Group activity coefficients are calculated through the UNIQUAC model. The informations used to determine the parameters include the experimental LLE data, the densities of the solvent and the polymer at the temperature of the mixture, the van der Waals volumes for the calculation of the free volume-combinatorial contribution, and the molecular surface parameters of the segments for the application of the UNIQUAC model. The densities are estimated using the DIPPR data bank4 for the solvent and the Polymer Solution Handbook5 for the Tait equation parameters. The van der Waals volumes and molecular surface parameters are calculated through additive group contributions6,7. Previous application of the model was related to the LLE correlation/prediction of nonpolar and moderately polar systems and the present work shows that the extension to a system with strong specific interactions is possible. The lower and upper critical solution temperatures as well as the closed loop diagrams for numerous systems are correlated/predicted, using weakly temperature dependent UNIQUAC parameters. The main limitation is probably the immediate proximity of the critical point of the solvent, where the excess volume of the solution cannot be described. ________________________________ 1. G.Bogdanić, J.Vidal, 16th European Seminar on Applied Thermodynamics, Abbaye des Premontres, Pont-a-Mousson, France, 19th-22th June 1997, Proceedings, p.73. 2. E.Panagou, J.Vidal, G.Bogdanić, Polym.Bull., 40,117-123(1998). 3. G. ten Brinke, F.E. Karasz, W.J. MacKnight, Macromolecules, 16,1827-1832(1983). 4. T.E.Daubert, R.P.Danner, Data Compilation Tables of Properties of Pure Compounds, Design Institute for Physical Property Data, AIChE, 1985. 5. R.P.Danner, M.S.High, Polymer Solution Handbook, AIChE, Pennsylvania State University, 1992. 6. Aa.Fredenslund, J.Gmehling, P.Rasmussen, Vapor-Liquid Equilibria Using UNIFAC, Elsevier Scientific, New York, 1997. 7. A.Bondi, Physical Properties of Molecular Crystals, Liquid and Glasses, Wiley, New York, 1968.