water–water and water–macromolecule interactions in food dehydration and the effects of the pore...

Journal of Food Engineering 110 (2012) 514–524

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Journal of Food Engineering

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Water–water and water–macromolecule interactions in food dehydrationand the effects of the pore structures of food on the energetics of the interactions

J.-C. Wang, A.I. Liapis ⇑Department of Chemical and Biological Engineering, Missouri University of Science and Technology, 400 West 11th Street, Rolla, MO 65409-1230, USA

a r t i c l e i n f o

Article history:Received 20 September 2011Received in revised form 10 January 2012Accepted 14 January 2012Available online 31 January 2012

Keywords:Food dehydrationPorous structures of foodsMolecular dynamics modeling andsimulationsWater–water interactionsWater–macromolecule interactionsPore-size distributionsPolysaccharides

0260-8774/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2012.01.008

⇑ Corresponding author.E-mail address: [email protected] (A.I. Liapis).

a b s t r a c t

A molecular dynamics (MD) modeling and simulations approach has been rationally built and developedto study porous food systems constructed with amylose and dextran chains. The findings from our MDstudies indicate that the presence of food macromolecules decreases the energetics of the water–waterinteractions for the nearby water molecules in the pore space, but provides additional water–macromol-ecule interactions that can significantly outweigh the partial loss of water–water interactions to make theadjacent water molecules strongly bound to the food macromolecules so that the water activity andwater removal rate are decreased as dehydration proceeds and, thus, the dehydration energy require-ment would be increased. The effects of pore structures are greater in systems with higher densities offood macromolecules, smaller in size pores, and stronger water–macromolecule interactions. Dehydra-tion of food materials can thus be reasonably expected to start from the largest pores and from the mid-dle of the pores, and to have non-uniform water removal rates and non-planar water–vapor interfacesinside individual pores as well as across sections of the food materials. The food porous structures arefound to have good pore connectivity for water molecules. As dehydration proceeds, water contentand the support from water–water and water–macromolecule interactions both decrease, causing thefood porous structures to adopt more compact conformations and their main body to decrease in size.Dehydration in general also reduces pore sizes and the number of pore openings, increases the water–macromolecule interactions, and leads to the reduction of the overall thermal conductivity of the system,so that more energy (heat), longer times, and/or greater temperature gradients are needed in order to fur-ther dehydrate the porous materials. Our thermodynamic analysis also shows that the average minimumentropy requirement for food dehydration is greater when the water–macromolecule interactions arestronger and the food macromolecular density is higher. The importance of the physicochemical affinityof food molecules for water and of the compatibility of the resultant porous structures with water con-figurational structures in determining food properties and food processing through the water–macromol-ecule interactions, is clearly and fundamentally verified by the results and discussion presented in thiswork.

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1. Introduction

From a fundamental perspective, various food materials areconsisted mainly of edible and digestible biopolymers. These foodmacromolecules can be understood not to occupy the space contin-uously but to form structures with seams and pores that physicallyor chemically accommodate other food components. Water (mois-ture) is a major component of food materials and can act as a sol-vent, medium for heat and mass transfer, or participant in chemicalor biological reactions in food systems. Water is thus a major factor(Franks, 1985; Barbosa-Canoras et al., 2007) in determining theproperties of foods in the various stages of processing and packag-

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ing (Maroulis and Saravacos, 2003; Barbosa-Canoras et al., 2007).Food scientists and engineers have employed since 1953 the con-cept of equilibrium relative humidity (ERH) or, as is most oftencalled, water activity, aw, in order to construct phenomenologicalrelations for food materials so that they could study as a functionof aw (i) moisture adsorption/desorption, (ii) water migration andtextural changes, (iii) glass transition, (iv) microbial growth, (v)degradation rates of chemical and enzymatic reactions, and (vi)powder state changes (Chen and Mujumdar, 2006; Jayaramanand Das Gupta, 2006; Labuza, 2011).

From a fundamental phenomenological point of view, waterowes its ubiquity in foods and its effects on food structures andprocessing to its indispensable and unique interactions with themacromolecules and dissolved solute species of foods. These waterinteractions are constantly present in foods and responsible for

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J.-C. Wang, A.I. Liapis / Journal of Food Engineering 110 (2012) 514–524 515

making the values of aw different from that of the pure bulk waterunder the same temperature. Reflecting these interactions, the val-ues of the water activity variable, aw, in foods provide a practicaland possibly useful measure of the equilibrium thermodynamicstate of water in foods which could be correlated in a phenomeno-logical way with the observed physicochemical and biologicalstates of the foods, and could then be used in phenomenologicalcontinuum material and energy balance models to study thebehavior of the food material during processing. But the variableof water activity, aw, cannot provide information, for a given foodmaterial, about the force fields and relative importance of theinteractions among (a) water–water molecules, (b) macromole-cules and water molecules, (c) dissolved solute species and watermolecules, (d) macromolecule–macromolecule, and (e) macromol-ecules and dissolved solute species, as a food material is being pro-cessed (i.e., during the dehydration process) or is being packaged.These intermolecular interactions in which the water moleculesplay a very important role, can determine the structure of the foodmaterial at the beginning of a given process and during the pro-cessing of the food, as well as the distributions of water moleculesin the food material and in different energetic states so that thewater molecules can be properly categorized as liquid-like,weakly-bound, strongly-bound, and non-freezable in the evolving,during processing, structure of the food material. Furthermore, theproperties of water in the food are very sensitive to changes in thetemperature and concentration of the dissolved solute species inthe food. This type of sensitivity may well become larger in the re-sponses of biological (food) structures to changes in the hydrogenbonding patterns that exist in water during the processing or pack-aging of food. The phenomenological variable of water activity, aw,cannot provide information with respect to the changes of theproperties of water and their effect on the properties of the fooddue to changes in the hydrogen bonding patterns that occur inthe water of the food during processing or packaging.

Food dehydration (drying) refers to water removal from foodand represents a very important process in the preparation andpreservation of foods (Maroulis and Saravacos, 2003). It is a processthat requires energy to be supplied through heat conduction, con-vection, and/or radiation to enable water molecules to break loosefrom their interactions from the dissolved solutes and the biopoly-mers that form the porous structures of the foods. Food dehydra-tion is a process involving both energy (heat) transfer and masstransfer. The process of food dehydration and the preservation ofdehydrated foods can thus be directly related to the interactionsof water molecules with the macromolecules of food, because thewater–macromolecule and the water–water interactions dictatethe removal of water molecules during food dehydration, thestructures of foods before, during, and after dehydration, and thedehydration strategy and efficiency by which the supplied heat isutilized. It is apparent from items (a)–(e) above that the wateractivity variable, aw, cannot provide the relationship of the evolu-tion of the structural changes of the food material with the changesof the water–macromolecule and water-water interactions that oc-cur during dehydration. This aspect of food science and engineer-ing remains largely unexplored due mainly to the limitations ofcurrent experimental techniques and theoretical methods.

Molecular dynamics (MD) is a modeling approach (Allen andTildesley, 1987; Rapaport, 1997) that employs molecular-basedinteraction potentials to construct a model system that providesa satisfactory representation of the real system and allows variousproperties to be studied at a molecular level. Over the years MDhas been demonstrated to be a methodology capable of investigat-ing systems with complex geometries and molecules as well asstudying structural and dynamic properties that include the trans-port and interaction (e.g., adsorption) of molecules at interfaces.For multi-scale studies, MD is capable of characterizing micro-

scopic, mesoscopic, and even macroscopic porous media, identify-ing responsible mechanisms and evaluating their relativeimportance, which can make significant contributions to the for-mulation of appropriate constitutive equations for use in macro-scopic systems described by continuum mechanics models. Thesecapabilities can be employed to complement both experimentaland theoretical approaches and to conceive and design new pro-cesses. When properly applied (Riccardi et al., 2008, 2009a,b,2010a; Wang and Liapis, 2011a), MD can also provide the capabil-ity to probe and obtain detailed information at the molecular leveland scientific understanding with regard to the water–macromol-ecule and water–water interactions in foods. In this respect, our re-cent MD modeling and simulation studies which have constructedand employed atomistic and coarse-grain models to investigate thebehavior and structure of polymeric porous adsorbent mediaformed by dextran chains (Riccardi et al., 2009a,b; Wang andLiapis, 2011a,b) can be considered to represent original and novelapproaches that demonstrate the feasibility of MD for this purpose.The main task of the present work is to extend our MD modelingand simulations to elucidate the water–water and water–macro-molecule interactions in model food materials and examine thedependence of such interactions on the evolving pore structuresof foods during dehydration.

2. Molecular dynamics simulation models and methods

Polysaccharides are one of the main ingredients in many foodsand are also biopolymers of great importance with applications inmany fields. They have good affinity with water to enable them todissolve or disperse in water. Molecular systems constructed withmultiple polysaccharide chains that form realistic porous struc-tures and filled with different water contents are thus consideredphysicochemically appropriate model systems for representingfood materials and their dynamic stages of dehydration for thepurpose of this work. Two common polysaccharides are employedin this work, namely a-D(1 ? 4)-linked amylose and a-D(1 ? 6)-linked dextran. Although computer modeling studies of saccharidemolecules have been attempted before, they are mostly concernedwith conformations of single simple saccharide molecules and usu-ally without water (French and Brady, 1990). For the purpose ofthis work that involves MD simulations and large computationaltime and length scales, coarse-grain models are considered a sen-sible choice and hence employed. For modeling amylose, a recentlydeveloped M3B model (Molinero and Goddard, 2004) is used. Sincethe details are available in the literature, only a brief summary isgiven here. In the M3B model, each glucose monomer is repre-sented by three beads denoted as B1, B4, and B6 that correspondto the C1, C4, and C6 carbons and the glucose monomers are linkedtogether via inter-monomeric B1–B4 bonds. Between these M3Bbeads, the bond lengths are constrained in this work by the SHAKEalgorithm (Allen and Tildesley, 1987; Rapaport, 1997) and thebending and torsional motions are treated by the following poten-tials for proper conformational representation,

UbðhÞ ¼12

Khðhi � h0Þ2 ð1Þ

Utorð/Þ ¼X3

j¼1

12

Bj½1þ cosðj/� /0j Þ� ð2Þ

As part of the M3B model, water molecules are also coarsegrained into spherical beads with a proper size (3.77 Å) and inter-action strength (Molinero and Goddard, 2004). It should be notedthat the coarse grain size of water molecules is not meant to rep-resent the diameter of a single water molecule, but rather an effec-tive diameter that, together with the fitted interaction strength,

516 J.-C. Wang, A.I. Liapis / Journal of Food Engineering 110 (2012) 514–524

reproduces the density and interaction energetics of water whichare actually determined by the hydrogen bonds between watermolecules. The non-bonded interactions among water and M3Bbeads are treated with differently fitted Morse potentials. For mod-eling dextran, a modified M3B model has been developed and re-ported in our recent works (Riccardi et al., 2008, 2009a,b, 2010a)where different values were used for the angular and energeticparameters in Eqs. (1) and (2), and the glucose monomers arelinked together via inter-monomeric B1–B6 bonds. To facilitatecomparison, both amylose and dextran chain are consisted of 40monomers per main polymeric chain, of which 5% of the glucosemonomers have side branches that are one-monomer long. Theside branches are linked to randomly selected B6 sites in the caseof amylose chains and B4 sites in the case of dextran chains, asshown in Fig. 1(b) and (c) where the B1, B4, and B6 beads are indi-cated by the red, green, and blue balls, respectively, because theother M3B sites have already been used for inter-monomeric bon-dings. For comparison, an atomistic representation of a segment ofdextran chain is also included in Fig. 1.

In order to create stable realistic porous structures in the MDsimulation systems (Riccardi et al., 2008, 2009a,b, 2010a), the amy-lose and dextran chains are immobilized on a non-flat surface rep-resented by the following model,

Uisðx;y;zÞ¼2peisris

R0s

� �2 25

ris

zs

� �10

� ris

zs

� �4

�ffiffiffi2p

3 R0sris

� �zsrisþ 0:61ffiffi

2p R0s

ris

� �3

264

375

ð3aÞ

zs ¼ z� a 2þ cosð2pb

xÞ þ cosð2pb

yÞ� �

; ð3bÞ

where Uis is the interaction potential energy between the non-flatsurface and a particle i at (x,y,z) whose size and interaction strengthare denoted by ri and ei. The interaction parameters are determinedby the mixing rules, ris = (ris + R0s)/2 and eis ¼

ffiffiffiffiffiffiffiffiffiffieie0sp

, where R0s ande0s represent the nearest distance and the interaction strength,respectively, between the pseudomonomers adopted as the buildingblocks of the model surface (Riccardi et al., 2008, 2009a,b, 2010a).Here R0s is taken to be the same as the diameter of a glucose mono-

Fig. 1. (a) Atomistic representation of a-D(1 ? 6)-linked dextran chain. (b) M3B coarse-gmain chain via a (1 ? 4) bond. (c) M3B coarse-grain representation of amylose chain w

mer and e0s ¼maxðeB1; eB4; eB6Þ: The values of a, b, R0s, and e0s used inthis work are the same as in our previous studies (Riccardi et al.,2008, 2009a,b, 2010a).The model surface has 100 � 100 Å lineardimensions in the lateral directions where periodic boundary condi-tions are applied. For each polysaccharide, three cases were studiedwith one, ten, or twenty polysaccharide chains immobilized at ran-domly selected sites on the non-flat surface. As shown in Fig. 2, thepolysaccharide chains in their initial conditions have helical struc-tures and perpendicular orientations with respect to the local sur-face sites. In order to prevent pathological cases where thepolysaccharide chains may collapse onto the surface with dimin-ished pore structures, the first two monomers of each chain are heldrigid throughout every MD simulation. To complete the constructionof the initial conditions, the immobilized polysaccharide chains aresuperimposed with a separately equilibrated aqueous phase andany water molecule overlapping with the polysaccharide chainswas discarded. The MD simulations in this work are carried outusing the leap frog integration algorithm together with a Gaussianthermostat method for controlling temperature at 298 K. Beforedehydration, the model food systems are filled with water to thehighest Z positions (the Z direction is perpendicular to the surfacewith Z = 0 corresponding to the lowest points of the non-flat surface)of the polysaccharide chains and extra water molecules are removedfrom the top at the beginning of system equilibration. In this maxi-mally hydrated state with zero water removal from the pore spaces,the model systems are labeled to have 100% water content. To rep-resent different stages of food dehydration, water is removed fromthe top by different amounts and the systems are then re-equili-brated before data are collected and analyzed.

3. Results and discussion

We first studied the model systems with single amylose or dex-tran chain to establish references for comparison. In these systems,the single polysaccharide chain and the surface are completelycovered in water and there exist many water molecules sufficientlyaway from the polysaccharide chain to behave very similarly tothose in bulk conditions. Such reference systems can also be con-sidered to effectively present very large pores that result from verylow densities of food macromolecules. The energetics of water

rain representation of dextran chain with a side branch encircled and linked to theith a side branch encircled and linked to the main chain via a (1 ? 6) bond.

Fig. 2. Side views of the initial food porous structures formed by (a) 10 amylose chains, (b) 20 amylose chains, (c) 10 dextran chains, and (d) 20 dextran chains withoutshowing the water molecules in the porous structures for visual clarity.


molecules in these reference systems are analyzed as a function oftheir Z position as well as of their nearest distance to the polysac-charide chain. It should be noted here that in order to preventpossible complications caused by the water interactions with thenon-flat surface whose main purpose is to provide a templateand indirect control for generating stable porous structures, onlywater molecules above Z = 31.7 Å (corresponding to the highestpoint of the non-flat surface plus 2.5 times the water–water inter-action equilibrium distance) are included in both energetic analy-ses. The results from the amylose reference system are presentedin multiples of kBT in Fig. 3 where negative numbers are used in or-der to reflect the attractive nature of the interactions and kBT,equivalent to 2.478 kJ/mol, is used to facilitate the comparison be-tween the interaction energies and the thermal energy. The resultsin Fig. 3 indicate that the coarse-grain models employed in thiswork produce an average potential energy of �24 kBT per watermolecule for water molecules at sufficiently large distances fromthe amylose chain. This energy can be taken to be the water–waterinteraction energy in large pores and approximate DUdeh, theinternal energy change of water molecules entering the vaporphase from large pores. It also suggests a dehydration enthalpyof DHdeh = 3166 � 103 J/kgH2O, which is about 11.5% larger thanthe experimental value of 2840 � 103 J/kgH2O determined bySheehan and Liapis (1998). Water molecules close to the macro-molecule can be seen in Fig. 3 to have reduced water–water inter-actions, which can be attributed to reduced coordination numbersof water molecules within the hydration interaction range in theproximity of the macromolecule. However, the energetic gain inthe water–macromolecule interactions significantly outweighsthe partial loss of the water–water interactions, leading to muchstronger overall interactions and strongly-bound water moleculesadjacent to the macromolecule. The reference system with a singledextran chain has similar results as can be seen in Fig. 3. From thepoint of view that these strongly-bound water molecules aretrapped in deep energetic wells and subject to impedance caused

by nearby macromolecules that have different structures, theycan be understood not to be easily rearranged into configurationsthat resemble the ice structures and thus very likely to remainnon-freezable in the food under normal conditions. Following thisperspective and as suggested by the energetic data presentedabove, water molecules sufficiently away from the food macromol-ecules are either weakly bound to the macromolecules or in liquid-like states.

Before dehydration, the polysaccharide chains in the model foodsystems are all hydrated with water molecules filling the spaces ofthe pores to their highest Z positions, which for simplicity can be la-beled as having 100% water content in the pore spaces. Other thanthe first two monomers, the polysaccharide chains are not rigid butexhibit significant structural flexibility in their responses to theinteractions among themselves and with water. Shown in Fig. 4are the side views of the porous structures formed by the amyloseand dextran chains with 100% water content but no water moleculeis included for visual clarity. It can be seen that the porous struc-tures with 20 polysaccharide chains that represent food systemswith a higher density of polysaccharide chains have smaller pores.To probe the effects of pore structures on the water–water andwater–macromolecule interactions, the energetics of water mole-cules as a function of their Z position and of their distance to thenearest macromolecule are examined and shown in Figs. 5 and 6,respectively. Compared with Fig. 3 that shows the energetics ofwater molecules in very large pores or in bulk phase, it is apparentfrom Fig. 5 that the porous structures have reduced the water-water interactions by about 2–3 kBT per water molecule and the le-vel of reduction is more significant with smaller in size pores in thehigher density systems. This effect of pore structures can be attrib-uted with certainty to the reduction of water–water hydrationnumbers due to the presence of the polysaccharide chains. How-ever, the polysaccharide chains provide new water–macromoleculeinteractions in return that make the water overall potential energystronger than that of bulk water. This energetic aspect could be

Perpendicular distance Z(Å) from surface

Nearest distance r (Å) from polysaccharide chain

Inte

ract

ion

pote

ntia

l ene

rgy

per w

ater

mol

ecul

e ( k

BT)

water-water interaction water-macromolecule interaction total interaction potential interaction potential in bulk phase

-30.0

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

1101009080706050403020100

water-water interaction water-macromolecule interaction total interaction potential interaction potentail in bulk phase

-30.0

-25.0

-20.0

-15.0

-10.0

-5.0

0.0 water-water interaction water-macromolecule interaction total interaction potential interaction potentail in bulk phase

1101009080706050403020100

water-water interaction water-macromolecule interaction total interaction potential interaction potentail in bulk phase

(a)

(b)

(c)

(d)

Fig. 3. Energetics of water molecules at different perpendicular distances from the surface with (a) one amylose chain and (b) one dextran chain, and at different nearestdistances to the (c) one amylose chain and (d) one dextran chain in the reference systems. The numbers on the ordinate axes are multiples of kBT (equivalent to 2.478 kJ/mol).

Fig. 4. Side views ofthe porous structures formed by (a) 10 amylose chains, (b) 20 amylose chains, (c) 10 dextran chains, and (d) 20 dextran. All porous structures are 100%hydrated but the water molecules are not shown in the porous structures for visual clarity.


used to explain why food dehydration tends to be more difficult andmore energy consuming than simple water evaporation. Thewater–macromolecule interaction energetics shown in Fig. 5 canalso be related to certain pore structure characteristics. In the high-er density systems, the pore sizes are generally smaller and theycan be readily seen to result in greater water–macromolecule inter-actions. Between the amylose and dextran systems, the water–

macromolecule interactions in the dextran porous structures, espe-cially when the chain density is higher, tend to decrease as Z in-creases, while they are much less dependent on the Z position inthe amylose porous structures. The former suggests that the dex-tran porous structures have larger pores toward the upper regionsof their structures, while the latter suggests that the amylose por-ous structures have more uniform pore sizes in the Z direction.

Inte

ract

ion

pote

ntia

l ene

rgy

per w

ater

mol

ecul

e (k

BT)

Perpendicular distance Z (Å) from surface1101009080706050403020100

water-water interaction

water-macromolecule interaction total interaction potential

water-water interaction water-macromolecule interaction total interaction potential

-30.0

-25.0

-20.0

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0.0

1101009080706050403020100


-30.0

-25.0

-20.0

-15.0

-10.0

-5.0

0.0


(a)

(b)

(c)

(d)

Fig. 5. Energetics of water molecules at different perpendicular distances from the surface in the porous structures with 100% water content and (a) 10 amylose chains, (b) 20amylose chains, (c) 10 dextran chains, and (d) 20 dextran chains. The numbers on the ordinate axes are multiples of kBT (equivalent to 2.478 kJ/mol).

10 chains

-35.0-30.0-25.0-20.0-15.0-10.0-5.00.0


-35.0-30.0-25.0-20.0-15.0-10.0-5.00.0

3020100



3020100


Inte

ract

ion

pote

ntia

l ene

rgy

per w

ater

mol

ecul

e ( k

BT)

(a)

(b)

(c)

(d)

Nearest distance r(Å) from polysaccharide chain

Fig. 6. Energetics of water molecules as a function of their distance to the nearest chain in the porous structures with 100%water content and (a) 10 amylose chains, (b) 20amylose chains, (c) 10 dextran chains, and (d) 20 dextran chains. The numbers on the ordinate axes are multiples of kBT (equivalent to 2.478 kJ/mol).


These inferred characteristics appear to be consistent with visualexamination of the pore structures shown in Fig. 4.

A commonly used parameter that represents the state of foodduring dehydration is water activity, aw, which by its definition isa macroscopic empirical thermodynamic property. During fooddehydration, as water content decreases, water activity also de-creases and exhibits very non-linear relationships (Marinos-Kourisand Maroulis, 2006; Bhandari and Adhikari, 2008). Empirically,strongly-bound water refers to the last small amount of watermolecules that remain trapped until very low water vapor pres-

sures or equivalently very low aw values are realized. Based onthe results and discussion presented above and in Figs. 3–5, strongwater–macromolecule interactions underlie the strongly-boundwater in foods and hence are a cause of the lowering of the wateractivity aw in foods. From this point of view, the decreased poresizes resulting from higher food macromolecular densities canhave a twofold effect that depresses aw: increased capillary effect(e.g. Barbosa-Canoras et al., 2007, pp. 116) and enhanced water–macromolecule interactions as shown in this work. Since theformer cannot completely explain the significant aw changes


observed during water adsorption and desorption and between dif-ferent food systems, the latter must play a very important role indetermining aw and be included in our pursuit of an adequateunderstanding of food science and engineering. This aspect alsopoints out the possibility of non-uniform ‘‘microscopic or local’’water activity within the same food system during dehydrationdue to distributions of pore sizes and water–macromoleculeinteractions. It is also worth noting here that the capillary effect oc-curs due to a combination of surface tension (caused by cohesionwithin the liquid or more fundamentally attractive liquid–liquidintermolecular interactions) and adhesion between the liquid andsurrounding pore surface (caused by attractive liquid–pore inter-molecular interactions). The potential models employed in thiswork include both proper water–water interaction potential forthe former and water–macromolecule interaction potential forthe latter. Thus, the potential models employed in the MD simula-tions of this work have an adequate capability to generate andinvestigate the capillary effect in molecular detail in model foodsystems where food macromolecules are closely aligned togetherto form walled pores.

Different states of water molecules in food porous structurescan be further elucidated by the distribution of water energeticsas a function of distance to the food macromolecules and theresults are presented in Fig. 6. Again, it is observed that the magni-tude of the water-water interactions in the porous food structuresis weaker than that in the bulk phase (cf. Fig. 3) and that the watermolecules adjacent to the polysaccharide chains acquire strongwater–macromolecule interactions, which cause them to bestrongly bound, less available for other activities, and related tosmaller aw values. Such phenomena are more noticeable in thefood structures constructed with amylose chains (cf. Fig. 6) andin particular when the pores decrease in size due to higher polysac-charide density (cf. Figs. 3 and 6). As indicated by the strongerwater–amylose interactions in Fig. 6, the amylose-based porousstructures tend to accommodate water better than the dextran-based porous structures. In accordance with this differentiation isthe finding that the amounts of water molecules in the first hydra-tion shells (within a distance equivalent to the effective waterdiameter, 3.77 Å) around the amylose chains are larger than thosearound the dextran chains by approximately a factor of three. It isthus reasonable to conclude here that, in addition to the effects ofpore structures on water energetics and water activity, foodmacromolecules with different molecular architectures can imparttheir influences into different aspects of food properties and fooddehydration.

To complement the insight and understanding from the ener-getics and analyses on a per water molecule basis, quantitativechanges in the amounts of water molecules due to changes ofporous structures are examined. As the number of polysaccharidechains increases from 10 to 20 within the same simulation box,the number of water molecules filling the pore structures under-standably decreases significantly, but the number of strongly-bound water molecules within the first hydration shell from theamylose chains increases by �90% and within the second hydra-tion shell by �45%. In the case of dextran porous structures, thenumbers of water molecules in the first and second hydrationshells increase by �110% and �60%, respectively. In addition, abody of experimental studies and data (King, 1971; Liapis andBruttini, 2006) have also clearly shown that food macromoleculeshave very low thermal conductivities and in effect they representexcellent insulators. Based on these facts and the numbers andthe energetics of water molecules discussed above, we could thusconclude that it is more energy consuming and more difficult todehydrate food systems with higher polysaccharide densities.Because of their strong water–macromolecule interactions andbecause of the presence of chain macromolecules in close proxim-

ity, strongly-bound water molecules can be understood to be con-figurationally hindered and hence their dehydration would beaccompanied by larger entropy changes as compared to those ofweakly-bound water located away from the food macromoleculesor in the middle of the pores. However, because the last amounts ofwater to be dehydrated from foods are strongly-bound watermolecules with the macromolecules, it could be concluded thatthe enthalpic effect is more important than the entropic effect dur-ing food dehydration. This is a very important result with signifi-cant implications in the design of food engineering systems forfood dehydration. It is also worth mentioning here that thephenomenological macroscopic continuum models (Chen andMujumdar, 2006) cannot provide the explanation on why the fooddehydration process is found experimentally to be driven by en-thalpy changes. From this perspective, water removal during fooddehydration could be considered to start from the largest poresand from the middle regions of the pores. As a result of these ten-dencies coupled with water surface tension, the water–vapor inter-faces during food dehydration could be expected to be non-planarinside individual pores as well as across sections of a food materialdue to variable water dehydration rates that depend on the lateraldistributions of pore sizes. The phenomenological macroscopiccontinuum models used in food engineering practice to describethe dehydration behavior of foods, assume that the water–vaporinterfaces across sections of a food material during food dehydra-tion have a planar geometry. But the results obtained from ourmolecular dynamics modeling and simulations clearly indicatethat the water–vapor interfaces inside individual pores as well asacross sections of a food material have non-planar geometriesdue to variable water dehydration rates that depend on the lateraldistribution of pore sizes. Thus, the information obtained from ourwork can be used to modify significantly the structure and consti-tutive equations employed in the phenomenological macroscopicmodels used in food engineering practice.

To study food dehydration more directly, three dehydratedstages are prepared with 20%, 40%, and 60% of water removed fromthe top of the polysaccharide porous structures, which are labeledas having 80%, 60%, and 40% water contents, respectively. It isobserved that as the upper parts of the polysaccharide chainsbecome dehydrated without support from the water–macromole-cule and water–water interactions, they are energetically drivento form more compact conformations locally and some would evenbend downward so as to retain interactions with water. Conse-quently, the structural changes of the polysaccharide porous struc-tures in response to food dehydration are in such a direction thatthe main body of the porous structures becomes shorter in sizeand the pore sizes generally become smaller, as illustrated byFig. 7. It has been found experimentally that the structure of thefood changes size (its size is most often reduced) during dehydra-tion and when sample slices of the same dehydrated food entity atdifferent dehydration stages are examined by a microscope arefound that they have different pore structures. Our theoretical re-sults agree with the behavior observed experimentally and, fur-thermore, provide quantitative information about the pore-sizedistribution and pore connectivity characterizing the pore struc-ture of the food material at different stages of the dehydration pro-cess. To provide a more detailed and quantitative picture, thenumber of pore openings of different sizes as a function of distancefrom the non-flat surface is quantified by employing a two-levellattice representation (Zhang et al., 2005; Riccardi et al., 2008,2009a,b, 2010a). In this approach, the volume element of eachsystem is first divided into a lattice of bigger square prisms whoselateral dimensions along the x and y directions are 5 Å. The volumeof each square prism is then divided into a lattice of smaller squareprisms whose lateral dimensions are 1 Å. Cylindrical disks withvarying radii and a fixed thickness equivalent to the effective

Fig. 7. Side views ofthe porous structures formed by (a) 10 amylose chains, (b) 20 amylose chains, (c) 10 dextran chains, and (d) 20 dextran, all with 60% water content (40%water removal).


molecular diameter of water (3.77 Å) are tested at each of the lat-tice points in the two-level lattice representation. By knowing thecoordinates of the M3B beads from the MD simulations and byexcluding their radii from their distances to the centers of thecylindrical disks, this approach can efficiently and rigorously locateand assess the pores openings three-dimensionally. The results for

Fig. 8. Distributions of the number of pore openings in porous structures formed by (a)content, (c) 10 dextran chains and 100% water content, and (d) 10 dextran chains and 6

systems with 10 and 20 polysaccharide chains filled with 100% and60% water contents are shown in Figs. 8 and 9, respectively, wherethe smallest Z position corresponds to the highest point of thenon-flat surface and the pores are grouped into different size cate-gories to facilitate comparison. Judging by the significant levels ofinterception among curves that represent pores of different size

10 amylose chains and 100% water content, (b) 10 amylose chains and 60% water0% water content.

Fig. 9. Distributions of the number of pore openings in porous structures formed by (a) 20 amylose chains and 100% water content, (b) 20 amylose chains and 60% watercontent, (c) 20 dextran chains and 100% water content, and (d) 20 dextran chains and 60% water content.


groups, the model food porous structures can be described to havereasonably good pore connectivity (Meyers and Liapis, 1999;Zhang et al., 2005; Riccardi et al., 2008, 2009a,b,c, 2010a,b). Inaddition, it can be seen from Figs. 8 and 9 that (i) increased densityof food macromolecules indeed results in more pores and inparticular in pores of smaller sizes, and (ii) dehydration in generaltends to decrease the number of pores in the model food systemsbecause it reduces the support from water–water and water–mac-romolecule interactions for the pore structures and increases thecompactness of the conformations and configurations of the foodmacromolecules.

Inte

ract

ion

pote

ntia

l ene

rgy

per w

ater

mol

ecul

e (k

BT)

-35.0-30.0-25.0-20.0-15.0-10.0

-5.00.0

3020100

water-water interaction water-macromolecule interac total interaction potential

-35.0-30.0-25.0-20.0-15.0-10.0

-5.00.0

water-water interaction water-macromolecule interac total interaction potential

(b)

(a)

Nearest distance r(Å)

Fig. 10. Energetics of water molecules as a function of their distance to the nearest chaamylose chains, (b) 20 amylose chains, (c) 10 dextran chains, and (d) 20 dextran chains.

The changes in pore sizes due to dehydration are also reflectedin Fig. 10 where after 60% of the total amount of water is removed,the distance spans from water to the nearest polysaccharide chainsare significantly shorter than those shown in Fig. 6for the samesystems prior to dehydration. Fig. 10 also shows that the lowerdensity polysaccharide systems consistently have larger pores thantheir high density counterparts during dehydration. More impor-tantly, a comparison between Figs. 6 and 10 indicates that byreducing the pore sizes, dehydration increases the water–macro-molecule interactions while slightly decreases the water–waterinteractions. Therefore, while the overall thermal conductivity of

tion

tion water-water interaction water-macromolecule interaction total interaction potential

3020100


(d)

(c)

from polysaccharide chain

in in the porous structures with 40% water content (60% water removal) and (a) 10The numbers on the ordinate axes are multiples of kBT (equivalent to 2.478 kJ/mol).


the food material decreases as the removal of water proceedsduring dehydration (the thermal conductivity of water is much lar-ger than that of the macromolecules of food), the results of thiswork show that food dehydration further strengthens the interac-tion energies and lowers the aw values of the remaining water mol-ecules. Consequently, the difficulty of removing water moleculesfrom the deeper regions of the food materials would increase asdehydration progresses. Thus, one could use the quantitative infor-mation that our theoretical approach provides to design an engi-neering control system that can supply at any given time theappropriate amount of heat during food dehydration so that theamount of time required for dehydration can be minimized, andthis could also have beneficial effects for the stability and qualityof the dehydrated food material.

Since the pore structures of food materials can vary with type,depth, and dehydration time, and because these variations affectsignificantly the energetics of the water–water and water–macro-molecule interactions, it could be beneficial to adjust heat supplydynamically during food dehydration. Relevant to this topic inour current work is the average interaction potential energy ofwater molecules in the food structures at different dehydrationstages. In general, an upward or downward trend of this averagepotential energy indicates a higher or lower amount of heat fluxneeded for dehydration at similar rates. The average interactionpotential energy per water molecule calculated for the model foodsystems with 100%, 80%, 60%, or 40% water content is presented inFig. 11(a). Not surprisingly, the results confirm the previous find-ings discussed above that (i) the porous systems constructed withamylose chains give rise to greater water interaction potentialenergies and would thus require more heat to dehydrate thanthe ones constructed with dextran chains and (ii) the systems withhigher polysaccharide chain densities also result in greater waterinteraction potential energies and require more heat to dehydrate

(b)

(a)

45.0

40.0

35.0

30.01009080706050403020

10 amylose chains 20 amylose chains 10 dexran chains 20 dextran chains

Min

imum

ΔS de

h /R

for

spon

tane

ous

dehy

drat

ion

Water content (%) in pore space

-30.0

-25.0

-20.0

-15.0

1009080706050403020

10 amylose chains 20 amylose chains 10 dexran chains 20 dextran chains

Aver

age

pote

ntia

l ene

rgy

per w

ater

mol

ecul

e (k

BT)

Water content (%) in pore space

Fig. 11. (a) Average interaction potential energy per water molecule where thenumbers on the ordinate axis are multiples of kBT (equivalent to 2.478 kJ/mol) and(b) average minimum entropy requirement for spontaneous dehydration underdifferent water contents in the pore space of the model food systems where thenumbers on the ordinate axis are multiples of R (equivalent to 8.314 J/mol-K).

than the ones with lower chain densities. In addition, while the en-ergy requirement for dehydrating the higher density systems with20 chains increases as dehydration proceeds because of reducedpore sizes and enhanced water–macromolecule interactions, it ap-pears to remain constant for the lower density systems, which canbe taken to imply that the distributions of water potential energyand dehydration energy requirement per unit volume are muchmore uniform in food systems with low polysaccharide densities.However, it would be misleading if such constant energy require-ments are directly compared to that of pure water because theyare averaged over all water molecules in the pore space, includingstrongly-bound, weakly-bound, and liquid-like water molecules. Infact, it is highly possible that in all food systems where the rate ofwater removal is not uniform, the results of this work would sug-gest that water removal in such systems depends strongly on thedistributions of pore sizes and locations of water molecules withrespect to the polysaccharide chains. It could be further inferredthat because of the chain flexibility and strong water–macromole-cule interactions, certain residual amount of water molecules canbe trapped in small pores or by narrow bottlenecks and, thus, theymight not be removed by typical dehydration means.

If we consider the Gibbs free energy, DGdeh, for dehydrationwhere DGdeh � DHdeh � TDSdeh � DUdeh + RT � TDSdeh and ideal gasbehavior for low-pressure water vapor, we could estimate theaverage minimum entropy requirement, DSdeh, for dehydration tobe spontaneous (DGdeh 6 0). The results of this thermodynamicanalysis based on our model food systems and simulation dataare plotted in Fig. 11(b), where we can see that (i) dehydration ofthe amylose-based food systems that have stronger water–macro-molecule interactions involves higher entropy changes and (ii)dehydration of the higher density food systems is accompaniedby increased minimum entropy requirements as water content de-creases, while it has relatively little effect in the lower density foodsystems. These trends of DSdeh are insightful and agree with theprevious results and discussion. This type of thermodynamicanalysis is both insightful and beneficial for providing an averagedentropic overview of the dehydration of different food systems, butit is worth noting that the local entropy requirements across indi-vidual pores and systems vary with the distributions of pore sizesand distances to the pore wall formed by food macromolecules.

4. Conclusions

A molecular dynamics (MD) modeling and simulations ap-proach has been rationally developed to construct and studyamylose and dextran porous layers that could be considered goodphysicochemical representations of food materials. This approachcould also be adopted in the construction and subsequent studyof food materials with varying numbers and types of monomersper polymer chain. The findings from our MD studies indicate thatthe presence of food macromolecules lowers the water–waterinteractions for the nearby water molecules by reducing theirhydration numbers and disturbing their configurations, but alsoprovides new water–macromolecule interactions that can signifi-cantly outweigh the partial loss of water–water interactions tomake the water molecules adjacent to the macromoleculesstrongly bound and very likely non-freezable and correspondingto low values of water activity aw. As a result, water molecules inthe pore space in porous food systems are not in the sameenergetic and configurational states and, thus, most likely do nothave uniform distributions of water activity aw, water removalrate, and dehydration energy and entropy requirements withinindividual pores and cross-sectionally. These effects of porestructures are found to be greater in food systems with higher den-sities of food macromolecules, smaller in size pores, and strongerwater–macromolecule interactions. Based on the results and


discussion presented in this work, dehydration of food materialscan be reasonably expected to be driven more by enthalpic effectthan by entropic effect, and to start from the largest pores and fromthe middle regions of individual pores where the values of thewater activity locally are higher. As a result of these tendenciesand water surface tension, the water–vapor interfaces could be ex-pected to be non-planar inside individual pores as well as cross-sectionally and the water removal rates dependent on the lateraldistributions of pore sizes during food dehydration.

The model food porous materials are found to have good poreconnectivity for water molecules. As dehydration proceeds, theirwater contents decrease and their porous structures become morecompact due to lack of support from water–water and water–macromolecule interactions, causing the main body of the porouslayers to decrease in size. Dehydration also reduces pore sizesand the number of pore openings, increases the water–macromol-ecule interactions, and decreases the value of the overall thermalconductivity, so that more energy (heat), longer times, and/orgreater temperature gradients are needed in order to dehydratefurther the porous materials. In addition, the minimum entropyrequirement for food dehydration is found to be greater in foodsystems with stronger water–macromolecule interactions andhigher densities of food macromolecules. These results and discus-sion also confirm the important effects on food properties and fooddehydration of the physicochemical affinity of food molecules forwater and the compatibility of the resultant porous structures withwater configurations.

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