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Computers and Chemical Engineering 33 (2009) 1701–1710

Contents lists available at ScienceDirect

Computers and Chemical Engineering

journa l homepage: www.e lsev ier .com/ locate /compchemeng

ultiscale molecular modeling in nanostructured material design and processystem engineering

aurizio Fermeglia ∗, Sabrina Priclniversity of Trieste, Department of Chemical, Environmental and Raw Materials Engineering, Piazzale Europa 1, 34127 Trieste, Italy

r t i c l e i n f o

rticle history:eceived 6 September 2008eceived in revised form 13 February 2009ccepted 28 April 2009vailable online 5 May 2009

eywords:ultiscale modelingesoscale simulation

roduct design

a b s t r a c t

Atomistic-based simulations such as molecular mechanics, molecular dynamics, and Monte Carlo-basedmethods have come into wide use for material design. Using these atomistic simulation tools, we cananalyze molecular structure on the scale of 0.1–10 nm. However, difficulty arises concerning limitationsof the time and length scale involved in the simulation. Although a possible molecular structure can besimulated by the atom-based simulations, it is less realistic to predict the mesoscopic structure definedon the scale of 100–1000 nm, for example the morphology of polymer blends and composites, whichoften dominates actual material properties. For the morphology on these scales, mesoscopic simulationssuch as the dynamic mean field density functional theory and dissipative particle dynamics are availableas alternatives to atomistic simulations. It is therefore inevitable to adopt a mesoscopic simulation tech-nique and bridge the gap between atomistic and mesoscopic simulations for an effective material design.Furthermore, it is possible to transfer the simulated mesoscopic structure to finite elements modelingtools for calculating macroscopic properties for the systems of interest.

In this contribution, a hierarchical procedure for bridging the gap between atomistic and macro-

scopic modeling passing through mesoscopic simulations will be presented and discussed. The conceptof multiscale (or many scale) modeling will be outlined, and examples of applications of single scaleand multiscale procedures for nanostructured systems of industrial interest will be presented. In par-ticular the following industrial applications will be considered: (i) polymer-organoclay nanocompositesof a montmorillonite–polymer–surface modifier system; (ii) mesoscale simulation for diblock copoly-mers with dispersion of nanoparticels; (iii) polymer–carbon nanotubes system and (iv) applications of

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multiscale modeling for p

. Introduction

The main goal of computational materials science is the rapidnd accurate prediction of properties of new materials before theirevelopment and production. In order to develop new materialsnd compositions with designed new properties, it is essential thathese properties can be predicted before preparation, processing,nd characterization. This is of particular importance in the fieldf polymer nanocomposites, where the properties of the materialepend on the nanostructure.

In fact, polymers are complex macromolecules whose structurearies from the atomistic level of the individual backbone bond

f a single chain to the scale of the radius of gyration, which caneach tens of nanometres. Polymeric structures in melts, blendsnd solutions can range from nanometre scales to microns, mil-imetres and larger. The corresponding time scales of the dynamic

∗ Corresponding author.E-mail address: mauf@dicamp.units.it (M. Fermeglia).

098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2009.04.006

s systems engineering.© 2009 Elsevier Ltd. All rights reserved.

processes relevant for different materials properties span an evenwider range, from femtoseconds to milliseconds, seconds or evenhours in glassy materials, or for large scale ordering processes suchas phase separation in blends. This situation is further complicatedby the presence of nanoparticles (from few to tens nanometres insize). No single model or simulation algorithm currently availablecan encompass this range of length and time scales. In order tosimulate such systems one must consider models that range fromthose including quantum effects and electronic degrees of freedomto chemically realistic, classical models. One promising approachtowards the solution of these problems is the tight integration of dif-ferent methods and theories in the so-called multiscale molecularmodeling which became in recent years one of the most impor-tant issues in computational materials research. With this approachthe bridging of length and time scales, and the consequent link-

ing of computational methods are used to predict macroscopicproperties and behaviour from fundamental molecular processes(Charpentier, 2002; Glotzer & Paul, 2002).

In this paper, we will show hierarchical procedures forbridging the gap between atomistic and macroscopic model-

1 Chemical Engineering 33 (2009) 1701–1710

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702 M. Fermeglia, S. Pricl / Computers and

ng passing through mesoscopic simulations. In particular, weill present and apply to some cases of industrial interest the

oncept of “message passing multiscale modeling”. Examplesonsidered will be (i) polymer-organoclay nanocomposites of aontmorillonite–polymer–surface modifier system; (ii) mesoscale

imulation for diblock copolymers with dispersion of nanoparti-les; (iii) polymer–carbon nanotubes system and (iv) evaluation ofhe environmental impact of a process based on toxicological data.

The strategy described in this paper is based on an overlappingrray of successively coarser modeling techniques. At each plateaua range of length and time scales), the parameters of the coarseescription are based on representative results of the immediatelyner description, as it will be explained in the following sections.

. Multiscale molecular modeling

Molecular modeling and simulation combines methods thatover a range of size scales in order to study material systems. Theseange from the sub-atomic scales of quantum mechanics (QM),o the atomistic level of molecular mechanics (MM), molecularynamics (MD) and Monte Carlo (MC) methods, to the micrometer

ocus of mesoscale modeling.Quantum mechanical methods have undergone enormous

dvances in the past 10 years, enabling simulation of systems con-aining several hundred atoms. Molecular mechanics is a fasternd more approximate method for computing the structure andehaviour of molecules or materials. It is based on a series ofssumptions that greatly simplify chemistry, e.g., atoms and theonds that connect them behave like balls and springs. The approxi-ations make the study of larger molecular systems feasible, or the

tudy of smaller systems, still not possible with QM methods, veryast. Using MM force fields to describe molecular-level interactions,

D and MC methods afford the prediction of thermodynamic andynamic properties based on the principles of equilibrium and non-quilibrium statistical mechanics (Allen & Tildesley, 1987; Gubbins

Quirke, 1996; Haile, 1992). Mesoscale modeling uses a basicnit (an agglomeration of atoms, called bead, obtained through aoarse-graining procedure) just above the molecular scale, and isarticularly useful for studying the behaviour of polymers and softaterials. It can model even larger molecular systems, but with the

ommensurate trade-off in accuracy. Examples of mesoscale theo-ies are dynamic mean field density functional theory (Mesodyn)nd dissipative particle dynamics (DPD) (Altevogt, Evers, Fraaije,aurits, & van Vlimmeren, 1999; Fraaije et al., 1997; Groot &arren, 1997). Furthermore, it is possible to transfer the simulatedesoscopic structure to finite elements modeling tools for calcu-

ating macroscopic properties for the systems of interest (Gusev,001).

Fig. 1 shows the class of models that are available at each singlecale.

QM, MM and mesoscale techniques cover many decades ofoth length and time scale, and can be applied to arbitrary mate-ials: solids, liquids, interfaces, self-assembling fluids, gas phase

olecules and liquid crystals, to name but a few. There are a num-er of factors, however, which need to be taken care of to ensurehat these methods can be applied routinely and successfully.

First and foremost of course are the validity and usability of eachethod on its own, followed by their interoperability in a com-on and efficient user environment. Of equal importance is the

ntegration of the simulation methods with experiment.

Multiscale simulation can be defined as the enabling technol-

gy of science and engineering that links phenomena, models, andnformation between various scales of complex systems. The ideaf multiscale modeling is straightforward: one computes informa-ion at a smaller (finer) scale and passes it to a model at a larger

Fig. 1. Multiscale molecular modeling: characteristic times and distances.

(coarser) scale by leaving out (i.e., coarse graining) degrees of free-dom (Doi, 2002; Goddard et al., 2001; McGrother, Golbeck Wood,& Lam, 2004).

The ultimate goal of multiscale modeling is then to predict themacroscopic behaviour of an engineering process from first princi-ples, i.e., starting from the quantum scale and passing informationinto molecular scales and eventually to process scales.

Thus, based on accurate QM calculations, a force field (FF)is determined, which includes charges, force constants, polar-ization, van der Waals interactions and other quantities thataccurately reproduce the QM calculations. With the FF, the dynam-ics is described with Newton’s equations (MD), instead of theSchrödinger equation. The MD level allows predicting the struc-tures and properties for systems much larger in terms of number ofatoms than for QM, allowing direct simulations for the propertiesof many interesting systems. This leads to many relevant and usefulresults in materials design; however, many critical problems in thisfield still require time and length scales far too large for practicalMD. Hence, the need to model the system at the mesoscale (a scalebetween the atomistic and the macroscopic) and to pass messagesfrom the atomistic scale to the mesoscale and to the macroscale.This linking through the mesoscale in which the microstructure canbe described is probably the greatest challenge to develop reliablefirst principles method for practical materials’ design applications.Only by establishing this connection from microscale to mesoscaleit is possible to build first principles method for describing theproperties of new materials and (nano)composites.

The problem here is that the methods of coarsening the descrip-tion from atomistic to mesoscale or mesoscale to continuum is notas obvious as it is going from electrons to atoms (Glotzer & Paul,2002). For example, the strategy for polymers seems quite differentthan for metals, which seem different from ceramics or semicon-ductors. In other words, the coarsening from QM to MD relies onbasic principles and can be easily generalized in a method and in aprocedure, while the coarsening at higher scales is system specific.

One of the first breakthrough examples of multiscale model-ing of materials is the linking of quantum and classical molecularmethods with continuum methods to study crack propagation in

silicon (Abraham, Broughton, Bernstein, & Kaxiras, 1998). Heretight-binding MD was carried out near the crack tip, classical MDwas employed farther away, and finite element calculations wereperformed far enough from the crack that a continuum approxi-mation was valid. By developing clever schemes to link the three

M. Fermeglia, S. Pricl / Computers and Chemical Engineering 33 (2009) 1701–1710 1703

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ethods together both spatially and temporally, the entire hybridimulation could be carried out with all three techniques operatingimultaneously in the appropriate areas.

Multiscale simulation poses, in some sense, greater challengesor polymer materials than for metallic and ceramic systems due tohe larger range of length and time scales that characterize macro-

olecules. In this respect, for example, Doi (2002) has developed auite of state-of-the-art simulation tools that model polymers at theolecular and mesoscale level. Although each tool performs calcu-

ations using only one technique, the output from one level can besed directly as input for another, allowing an off-line bridging of

ength and time scales. To achieve what he and others refer to asseamless zooming”, namely the ability to spawn higher resolu-ion simulations using more detailed methods where needed, willequire additional theoretical and computational advances.

Along similar lines, off-line multiscale simulations of nanofilledolymers using coarse-grained molecular dynamics, mesoscopicime dependent Ginsburg–Landau theory, and macroscopic contin-um finite element techniques have been carried out. Significantdvances in uniquely mapping atomistic models of polymers ontooarse-grained models (Fermeglia & Pricl, 2007; Müller-Plathe,002; Scocchi, Posocco, Fermeglia, & Pricl, 2007) have been made

n recent years, in some cases providing nearly exact quantitativegreement between the two models for certain quantities, but theseappings, too, are performed off-line, and the various methods are

ot linked within a single simulation.Scale integration in specific contexts in the field of polymer

odeling can be done in different ways. Any ‘recipe’ for passingnformation from one scale to another (upper) scale is based onhe definition of multiscale modeling which consider ‘objects’ thatre relevant at that particular scale (Fig. 2), disregard all degrees ofreedom of smaller scales and summarize those degrees of freedomy some representative parameters.

All approaches are initially based on the application of a forceeld that transfers information from quantum chemistry to atom-

stic simulation.From atomistic simulation to mesoscale, one can use a tra-

itional approach based on the estimation of the characteristicatio, the Kuhn length, and the Flory Huggins interaction param-ter (Fermeglia & Pricl, 2007). This approach for determining thenput parameters for mesoscale simulation is based on the follow-ng information: (i) the bead size and Gaussian chain architecture,

ii) the bead mobility M, and (iii) the effective Flory–Huggins �nteraction parameters. With this approach, the Flory–Huggins �arameters between two components of the coarse-grained molec-lar models in the mesoscopic simulation are estimated throughhe atomistic simulation, and a mesoscopic structure is predicted

g from atomistic model.

using these parameters. Mesoscopic simulations are performedusing a coarse-grained molecular model as shown in Fig. 2: theparticle in mesoscopic simulation is related to a group of severalatoms in the atomistic simulation. Mesodyn and DPD mesoscaletheory and simulation protocols are fully described in the literature(Altevogt et al., 1999; Fraaije et al., 1997; Groot & Warren, 1997).

The traditional approach can be enhanced and improved by con-sidering the detailed structure at the interface polymer–nanofiller(Scocchi et al., 2007). If one resorts to a particle based method fordescribing the system at mesoscale, atomistic MD simulation givesthe necessary details of the interface with a particular attention tothe binding energies among components. Mapping of the bindingenergies on mesoscale beads by means of a combinatorial approachto repulsive parameter for particles is then carried out and the sys-tem is simulated at mesoscale. If both particle based and field basedmethods are to be used at mesoscale, then an hybrid method can beadopted (Fraaije, 2009) in which particles are treated as describedabove and field interaction is calculated from pair–pair distributionfunctions.

Mesoscale simulation typical result is the morphology and thestructure of the matter at nanoscale level at the desired conditionsof temperature, composition and shear.

For the description of flow of polymeric materials on a pro-cessing scale, one must employ a hydrodynamic description andincorporate phenomena occurring on mesoscopic to macroscopiclength and time scales. For example, to capture the non-Newtonianproperties of polymer flow behaviour one can either use specialmodels for the materials stress tensor, or obtain it from a molecularsimulation using the instantaneous flow properties of the hydrody-namic fields as input. In the area of high-performance materials anddevices, polymer composites are finding a widespread application,and the modeling of these materials was until recently done primar-ily through finite element methods (FEM), and are beyond the realmof application of molecular modeling approaches. Nonetheless, areal problem in using FEM is the definition of the physical propertyof a complex material such as a polymer blend with phase segrega-tion and/or a polymer with microinclusion of nanosized platelets(Groot & Warren, 1997; Gusev, 1997, 2004; Gusev & Lusti, 2001).Mesoprop is a method based on finite elements for estimating prop-erties of a complex material starting from the density distribution atmesoscale. The method uses the results of a mesoscale simulationunder the form of three-dimensional density maps, and transforms

such information into a fixed grid that is used for the integrationof the equations to determine macroscopic properties. Palmyra isa different method that allows the simulation at FEM level witha variable grid methodology that allows to extend the size of thesystem studied.

1704 M. Fermeglia, S. Pricl / Computers and Chemical Engineering 33 (2009) 1701–1710

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of SAN. Accordingly, in Table 1 the SAN copolymer is orientedwith the S block next to MMT surface and the ANS polymer isthe same macromolecule but oriented with AN block next to MMTsurface. Similarly, polyB-SAN presents the main chain of B ori-

Fig. 3. From mesoscale

Fig. 3 shows how the mapping from mesoscale to macroscale isone. At FEM level each finite element corresponds to one phase,ith property tensor Pi, at mesoscale (Mesodyn or DPD) each

lement contains mixture of phases, with concentration Ci. It is nec-ssary to perform a geometry mapping by converting mesoscaleubic elements to Palmyra tetrahedrons. Once this is done, theaplace equation is solved directly to obtain direct properties suchs electric conductance, diffusion, permeability, etc. Local deforma-ion allows the calculation of mechanical properties.

Integration between these methods (from mesoscale toacroscale) is of paramount importance for the estimation of the

roperties of the materials, as it will be described in the followingections with some illustrative examples of application.

. Multiscale modeling for nanostructured material design

In the following sections, some applications of the message pass-ng multiscale modeling, described in the previous sections, to theesign of nanostructured materials will be presented and discussed.

.1. Polymer-organoclay nanocomposites (PCN)

Polymer-organoclays are important materials since the additionf a small amount of nanoclay to a polymer matrix enhances theacroscopic properties of the nanostructured material (Alexandre

nd Dubois, 2000). To do this the nanofiller must be com-letely exfoliated in the polymer and this is normally achievedy modifying the surface of the nanofiller with a particularomponents that is responsible of the exfoliation (Alexandrend Dubois, 2000). For designing the best surface modifier its necessary to estimate binding energy and basal spacing of a

ontmorillonite–polymer–surface modifier system. This will alsollow the calculation of the necessary parameters to be passed athe upper scale for the estimation of the morphology at mesoscalend the mechanical properties at macroscale.

The system considered as an example is the acrylonitrile–butad-ene–styrene (ABS) with montmorillonite (MMT) (Cosoli, Scocchi,ricl, & Fermeglia, 2008). Atomistic simulations allowed us to rankifferent surface modifiers (quaternary ammonium salts – quats)

or the selected clay/polymer system. Fig. 4 shows a 3D periodic cellor ternary simulations of the ABS-based PCN, while Table 1 lists

he binding energies for the best quat resulting from the screen-ng, which is the quaternary, double-tailed ammonium salt Cloisite0A®, and the relevant spacing between the clay platelets.

ABS is a complex system, being constituted by an acrylonitrileAN)–styrene (S) block copolymer (SAN) and a branched copolymer

hology to FEM analysis.

(polyB-SAN) with a main butadiene (B) chain and lateral chains

Fig. 4. 3D periodic system of a ternary (MMT–quat–polymer) system.

M. Fermeglia, S. Pricl / Computers and Chemical Engineering 33 (2009) 1701–1710 1705

Table 1Binary binding energy (kcal/mol) and basal spacing (Å) with cloisite 20A® and MMT for homopolymers AN, S, B and block copolymer SAN and polyB-SAN/a.

Polymer EMMT–pol [kcal/mol] EMMT–quat [kcal/mol] Epol–quat [kcal/mol] Basal spacing [nm]

PS −24 −1216 −32 3.108PB −7 −1266 −16PAN −41 −1248 −100S −36A −146P −116P −71

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AN −9 −1165NS −15 −1102olyB-SAN −5 −1386olyB-SANa −19 −1230

nted parallel to MMT surface, while polyB-SAN is rotated withain chain of B oriented normal to MMT surface. All binding

nergies are favorable (i.e., negative values), indicating an overallhermodynamic compatibility among all system components, asxpected.

By looking at the values of the Epol–quat term in Table 1, its evident that the most polar AN homopolymer is more affineo quat than all other ABS homopolymer chain components. Inn analogous way, B homopolymer binding energies are smaller.inally, if one considers the mean binding energy of SAN and ANS91.0 kcal/mol) and the binding energy for AN, the correspondingalues are, respectively, very similar. The same can be noticed ifne compares the mean values of the binding energy for polyB-AN (93.5 kcal/mol), and SAN or AN. This can be sensibly explainedith a minor contribution afforded to the total binding energy by

he S and B blocks. This last consideration ultimately allow us toonsider the smaller, rigid and less ramified SAN block copolymernto MMT layers, as the most probable mode of insertion.

This conjecture was later confirmed by ABS mesoscale modelingnd by literature data (Stretz, Paul, & Cassidy, 2005): rubbery phasepolyB-SAN) seems to segregate, forming round islands. This can belso seen in Fig. 5, a 3D mesoscale volumetric visualization.

Once again, binding energies and literature data (Stretz et al.,005) confirm that these nanocomposites have the same structure,here only SAN partially exfoliates MMT layers, and polyB-SAN

reates islands outside the stacks, surrounded by a SAN bulk phase.

In Fig. 6, a scheme of our two-phases FEM Palmyra simulations

s presented: the MMT stack with SAN intercalation (where overalloung’s modulus has been calculated with the first Palmyra simula-ion), and the whole system with MMT stacks and rubbery phases.

ig. 5. ABS mesoscale simulation. PolyB-SAN tends to form black-and-white islands.

Fig. 6. 3D cell visualizations of Palmyra simulations, up: MMT stack with SAN anddown: whole system.

The pure polymer bulk properties have been taken from Cosoli etal. (2008).

Table 2 shows overall results for ABS and nanocomposite Young’smodulus predicted by Palmyra. The small discrepancy between theexperimental and the calculated data is due to the slightly differ-ent formulation of ABS used in the calculation, as ABS has a wide

Table 2Young’s modulus for ABS–MMT nanocomposite and comparison with Stretz et al.(2005).

Overall properties % MMT Calculated Experimental

G0 [GPa] 0 2.42 2.20G [GPa] 2 3.15 2.75G/G0 2 1.30 1.25

1706 M. Fermeglia, S. Pricl / Computers and Chemi

Fig. 7. Morphology of the PCN system made up by a MMT platelet, Nylon6, andM3C18 quat molecules obtained via DPD simulation.

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ig. 8. Morphology of the PCN system made up by a MMT platelet, Nylon6, and3C18 quat molecules obtained with Palmyra.

ange of compositions. For this reason, a comparison of G/G0 ratioratio of nanocomposite and pure ABS Young’s modulus) betweenimulations and experiments were also done.

Another example in the area of polymer clays is the polyamideased system. In this case, atomistic simulation allowed us to calcu-

ate binding energies between the different beads that we definedn order to fit the particular structure (polymer intercalated clay)

e wanted to simulate. We used mesoscale simulation to modelhe space between two intercalated clay layers and subsequentlymported the resulting density fields in Palmyra (see Fig. 7), in ordero calculate mechanical and barrier properties for small stacks ofntercalated particles. This clearly constitutes a different method

ith respect to the one discussed for ABS PCN. Finally, models ofhe whole PCN (a box containing 36 single layer and stack clay par-icles, see Fig. 8) have been modeled with Palmyra using different

egrees of exfoliation and different stack dimensions and proper-ies, according to literature data (Duncan & Izzo, 2005; Esfand &omalia, 2001) and DPD box analysis, respectively.

In this study, the interaction parameters needed as input for theesoscale level DPD calculations have been obtained by a mapping

able 3alues of the Young modulus (E) and O2 permeability (P) in the x, y, and z directions for th

xx [GPa] Eyy [GPa] Ezzx [GPa]

6 particle box for PCN with M2(C18)2

.85 × 102 3.76 × 102 3.20 × 100

6 particle box for PCN with M3C18

.04 × 102 4.03 × 102 3.23 × 100

cal Engineering 33 (2009) 1701–1710

procedure of the binding energy values between different speciesobtained from simulations at the atomistic scale, using a simplecombinatorial procedure described in details in our previous paper(Scocchi et al., 2007).

Calculations of the Young modulus yielded results which arecomparable to experimental data if we consider the values alongthe x and y directions (i.e., parallel to the simulated extrusion direc-tion). Discrepancies between virtual and experimental data couldbe due to a different degree of crystallinity or different crystallineforms of Nylon6 in presence of MMT nanofillers, as claimed by someauthors (Fraaije, 1993; Malik et al., 2000). All estimated values forthe nanocomposite with M3C18 as quat are higher than the corre-sponding ones relative to the PCN with M2(C18)2, in harmony withthe different degree of exfoliation that has been modeled. As far aspermeability is concerned, it is possible to note that, as expected,O2 diffusion is hindered only in the z direction, i.e., perpendicu-lar to platelet x–y plane. Permeability is anyway reduced only to asmall extent (approximately 10–15%), because of the low nanofillerscontent (less than 2% in volume). Data are reported in Table 3.

3.2. Mesoscale simulation for diblock copolymers with dispersionof nanoparticles

Mixing microphase-separating diblock copolymers andnanoparticles can lead to the self-assembly of organic/inorganichybrid materials that are spatially organized on the nanome-ter scale. Controlling particle location and patterns within thepolymeric matrix domains remains, however, an unmet need.Computer simulation of such systems constitutes an interestingchallenge since an appropriate technique would require the cap-turing of both the formation of the diblock mesophases and thecopolymer–particle and particle–particle interactions, which canaffect the ultimate structure of the material. In this example (Maly,Posocco, Pricl, & Fermeglia, 2008) we discuss the application ofdissipative particle dynamics (DPD) to the study of the distributionof nanoparticles in lamellar and hexagonal A–B diblock copolymermatrices. The DPD parameters of the systems were calculatedaccording to a multiscale modeling approach, i.e., from lower scale(atomistic) simulations.

In agreement with some experimental evidence, we foundthat, depending on the nature and type of nanoparticle cover-ing (e.g., only A- or B-type covering), the particles can segregateinto the centers of the corresponding compatible domains (thesebeing lamellae or cylinders), forming nanowire-like structures thatextend throughout the material. The density distribution of thespecies in Fig. 9 (left) shows clearly that the nanoparticles (blackline) density reaches their maximum in correspondence of the max-imum of A (in blue). In effect, the interplay between microphaseseparation and favorable interactions do result in the self-assemblyof spatially ordered nanocomposites.

Should these particles be, for instance, metals or semiconduc-

tors, these systems could constitute a sort of nanoelectrode array,which could be utilized to fabricate organized nanodevices. On theother hand, for a different covering type (e.g., A6B6), the particlessegregate at the interfaces instead of the centers of the lamellae (orcylinders). Fig. 10 (left) shows clearly how the density distribution

e 36 particles boxes of both PCNs considered.

Pxx [barrier] Pyy [barrier] Pzz [barrier]

1.52 × 10−2 1.52 × 10−2 1.37 × 10−2

1.52 × 10−2 1.54 × 10−2 1.34 × 10−2

M. Fermeglia, S. Pricl / Computers and Chemical Engineering 33 (2009) 1701–1710 1707

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ig. 9. Distribution of A covered nanoparticles in diblock copolymers: nanoparticleosition of the center of mass of the nanoparticles in the simulation box.

f nanoparticles is radically different from that of Fig. 9 and nowndicates that the nanoparticles are located at the interface, as it ishown in Fig. 10 (right).

In these cases, for instance, if the copolymer matrix was to beissolved from the system, the remaining inorganic phase couldive origin to a nonporous material, with a regular arrangementf uniform pores, which could find applications, for instance, ineparation or catalytic processes.

The results also indicate that the morphologies of therganic/inorganic hybrid materials can be tailored by adding par-icles of specific size and chemistry. The findings highlight the facthat, in such complex mixtures, it is not simply the ordering ofhe copolymers that templates the spatial organization of the par-icles: the particles do not play a passive role and can affect theelf-assembly of the polymeric chains. In fact, we detected a phaseransition from the hexagonal to lamellar morphology induced bynonselective (i.e., A6B6(h)) block–particle interaction, indication

hat the particles actively contribute to the determination of theystem structure.

In conclusion, the proposed multiscale computationalpproach, which combines atomistic and mesoscale simu-ations, can yield important information for the design ofanostructured materials with desired morphology for novelpplications.

ig. 10. Distribution of A and B equal coverage nanoparticles in diblock copolymers: nanhe species; right: 3D representation of the nanoparticles at the interface.

ocated in the center of each domain; left: density distribution of the species; right:

3.3. Polymer–carbon nanotubes system

Carbon nanotubes (CNT) are interesting for several applica-tions in different fields: structural, electromagnetic, chemical andmechanical. They have already been used as composite fibres inpolymers and concrete to improve the mechanical, thermal andelectrical properties of the bulk product. In this example we showone application of computer simulations involving CNT, namelythe simulation at mesoscale level of the structure of a polymerCNT system. For simulating the mesoscale morphology of thesystem, information at atomistic level is necessary. This infor-mation is obtained in a ‘multiscale’ fashion. Firstly an atomisticmodel of single wall CNT is used to determine the Flory–Hugginsinteraction parameters of the CNT for different diameters. This isobtained directly from the definition of cohesive energy by run-ning two different simulation, one of the CNT in a bundle andanother one with a single isolated CNT. The difference betweenthe two values of energy the energy that is necessary to extractone CNT out of the bundle, namely the ‘bundling–de-bundling

energy’. For the polymer the traditional approach to calculate theFlory–Huggins interaction parameter in MD and MC is followed(Toth et al., 2004).

A comparison of the interaction parameters obtained shows thatonly CNT of a given diameter are soluble in a given polymer. The

oparticles are located at the interface of the domains; left: density distribution of

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708 M. Fermeglia, S. Pricl / Computers and

alculations enable to predict the CNT diameter to be used forbtaining a good dispersion of CNT in a polymer matrix.

The Flory–Huggins interaction calculated by molecular model-ng are then used at mesoscale level with a particle based methodDPD) for determining the mesoscopic structure of a CNT–polymerystem. Recently these approaches have been used (Maiti, Wescott,

Goldbeck-Wood, 2005) for estimating the morphology of aolymer CNT system and simulate, with FEM code, the electriconductance as a function of copolymer morphology.

. Multiscale modeling for process systems engineering

In the previous examples, multiscale molecular modeling haseen applied to the material design rather than to process design.rocess system engineering is an interesting area in which the con-ept of multiscale molecular modeling can be successfully applied,articularly for the estimation of physical properties to be used atrocess engineering level into process simulation software (Gani,004; Vlachos, 2005).

The example reported here refers to the integration of molecularodeling within the Cape Open standard for providing toxicological

ata to be used in conjunction with results from process simu-ation software, for the estimation of the environmental impactf a given process. In fact, chemical process sustainability, a com-lex issue which has been investigated for more than 20 years, cane estimated using different sustainability indicators. The quan-itative estimation of those indicators is necessary for two maineasons: (i) for evaluating the environmental impact of a chemi-al process and (ii) for choosing the best design among differentvailable alternatives. In order to accomplish these goals, the com-uterized calculation of sustainability indicators requires the use ofhree advanced computer design tools: process simulation, molec-lar modeling and a sustainability indicators software code. Apecific and complete software tool, process sustainability predic-ion (PSP) framework, integrated with process simulator programs,hich support the Cape Open standard interfaces, has been recently

eveloped (Toma, 2008).The idea is to use molecular modeling techniques to estimate

ifferent toxicological data, which are furthermore consideredn the calculation of some sustainability indicators. With thebjective of providing an easy-to-implement method for apply-

ng indicators for the purpose of analyzing industrial systemsor sustainability, Sikdar (2003) proposed a typology of indica-ors, considering the three dimensions of sustainability in threeistinct hierarchical groups: (1) one-dimensional (1D) indicators,hich provide information about only one dimension of sustain-

bility: economical, ecological, or social; (2) two-dimensional (2D)ndicators, which provide information simultaneously about twoimensions of sustainability: socio-ecological, socio-economical, orconomic–ecological; (3) three-dimensional (3D) indicators, whichrovide information about all three dimensions of sustainabilityMartins, Mata, Costa, & Sikdar, 2007).

Fig. 11 reports the general scheme in which the different ele-ents for calculating the indicators are presented and integrated

n the process sustainability prediction framework (PSP) (Fermegliat al., in press). The two fundamental sources of information for theSP are (i) the material and energy balances of the process calcu-

ated by a process simulator and (ii) the database of toxicologicalroperties of each component involved in the process. These datare combined and the potential environmental indexes (PEI) are cal-ulated. All the software developed and summarized in Fig. 11 has

een included into Cape Open Unit Operation modules and testedersus the most used process simulators available in the market, asell as the public domain software COCO–COFE (Van Baten, 2007).

The PSP needs toxicological data for all the components involvedn the process, and in many cases such data are not available

cal Engineering 33 (2009) 1701–1710

in the database. In those cases it is impractical and expen-sive to perform toxicity tests for all the chemical compoundsin use (Ren, Frymier, & Schultz, 2003) and molecular simulationmethods became an important tool for toxicological data predic-tion. The calculation of the environmental impact categories canbe reduced to some thermo-physical properties, some of whichcan be estimated using different molecular modeling techniques(see Fig. 12).

Atmospheric Oxidation Program (AOP), based on structure activ-ity relationship (SAR) calculation, was developed by U.S.EPA. Theprogram has been used in the present work for the estimation oflifetime a compound in the atmosphere, for the reaction rate withozone and reaction rate with hydroxyl.

For the calculation of the octanol–water partition coefficient,Kow, different molecular modeling methods can be used. Forexample KOWWIN, the Log Octanol–Water Partition CoefficientProgram, is a software developed by U.S.EPA which is based onSAR. ClogP is a program, based on group-contribution methods,which can be also used for the octanol–water partition coeffi-cient. ALOGPS is a software based on neural networks developedby the Virtual Computational Chemistry Laboratory. COSMOTh-erm (conductor like screening model thermodynamics) is anadvanced software tool based on quantum mechanics, whichcalculates different thermo-physical properties such as: vapourpressures, boiling points, activity coefficients, excess enthalpy andentropy, Henry’s law constants, solubility, octanol–water partitioncoefficient, vapour–liquid equilibrium, liquid–liquid equilibrium,solid–liquid equilibrium, density and viscosity for pure compounds(COSMOTherm, 2006). COSMOTherm is one of the software used,in the present work, for the estimation of octanol–water partitioncoefficient.

ECOSAR, developed by the Risk Assessment Division of theU.S.EPA, is a computer program based on SAR, used to predict theaquatic toxicity of chemicals based on their similarity of structureto chemicals for which the aquatic toxicity has been previouslymeasured.

TOPKAT, a computer program developed by Accelrys, employsrobust and cross-validated Quantitative Structure Toxicity Rela-tionship (QSTR) models for estimating 16 toxicity endpoints (i.e.,Mutagenicity, Rat Oral LD50, Carcinogencity, Developmental Toxi-city, etc.) (Accelrys, 2009).

It is evident, from Fig. 12, that some properties are of fundamen-tal importance for the calculation of the eight environmental impactcategories. As it can be noticed, human toxicity potential by inhala-tion and dermal exposure (HTPE), human toxicity potential byingestion (HTPI), aquatic toxicity potential (ATP) and terrestrial tox-icity potential (TTP) impact categories are related to an equilibriumproperty, the octanol–water partition coefficient. The other fourimpact categories: global warming potential (GWP), ozone deple-tion potential (ODP), photochemical oxidation potential (PCOP) andacidification potential (AP) are related to some transport propertiessuch as release rate of H+ or to reactivity properties such as: reactionrate with hydroxyl, reaction rate with ozone, lifetime, and thereforecan be calculated using quantum mechanics (QM) or (Q)SAR meth-ods. Table 4 reports an indication of the accuracy of the methodsused to estimate the octanol–water partition coefficient, the life-time of a chemical compound in the atmosphere, the reaction ratewith ozone and the reaction rate with hydroxyl. The data reportedin Table 4 refer to the deviation between calculated and experimen-tal data for a set of compounds for which toxicological data wereavailable in the literature (Fermeglia et al., in press).

The estimation methods used gives satisfactory results consid-ering the large uncertainties in the experimental data. We checkedhow the uncertainties propagate to the final environmental indexescalculated by the PSP for several different real industrial processesand the difference between the indexes calculated from the exper-

M. Fermeglia, S. Pricl / Computers and Chemical Engineering 33 (2009) 1701–1710 1709

Fig. 11. Process sustainability prediction (Toma, 2008).

Fig. 12. Thermo-physical properties and software programs used in the calculation of the environmental impact categories (Toma, 2008).

1710 M. Fermeglia, S. Pricl / Computers and Chemi

Table 4Expected uncertainties in using molecular modeling methods to estimate toxicolog-ical properties.

Thermo-physical property Molecular modelingmethods used

Average deviationfrom exp. data

Octanol–water partitioncoefficient

QSAR 14.22%COSMO-RS 4.92%

Life time SAR 21.37%R

Rh

ii

ego

5

mimiiitnn

pecc

mgdsticadtc

A

Ls

Italy: University of Padua.Toth, R., Coslanich, A., Ferrone, M., Fermeglia, M., Pricl, S., Miertus, S., et al. (2004).

Polymer, 45, 8075–8083.Van Baten, J. (2007). AIChE Annual Meeting. In Conference Proceedings, 2007 AIChE

Annual Meeting.Vlachos, D. G. (2005). Advances in Chemical Engineering, 30, 1–61.

eaction rate with ozone SAR 25%

eaction rate withydroxyl

GCM 22%QSAR 20%

mental data end form the data estimated by molecular modelings within 1%.

The PSP framework has been applied to the analysis of thenvironmental impact of several processes and it proved to be aenerally applicable tool for evaluating the environmental impactf a given process at design time (Fermeglia, Longo, & Toma, 2009).

. Conclusions

In this paper we have reviewed the concept of multiscaleolecular modeling and discussed the general guidelines for its

mplementation. The multiscale molecular modeling is applied inany fields of the material science, but it is particularly important

n the polymer science, due to the wide range of phenomena accru-ng at different scales (from quantum chemistry to the mesoscale)nfluencing the final property of the materials. In this context, mul-iscale molecular modeling can play a crucial role in the design ofew materials whose properties are influenced by the structure atanoscale.

Multiscale molecular modeling can also be successfully used inrocess system engineering applications for the estimation of prop-rties for pure components and mixtures in all cases in which theomponent data banks properties and interaction parameters ofonstitutive equations are missing.

Several examples have been reported in this paper showing theethodology and describing the simulation protocols. A general

ood agreement in the comparison with experimental literatureata of mechanical properties and morphologies is obtained, thushowing that the multiscale molecular modeling is a mature toolhat may be used in the design and development of new coat-ngs. Advances in computational materials science in general willontinue to facilitate the understanding of materials and materi-ls processing, the prediction of properties and behaviour, and theesign of new materials and new materials phases, thus facilitatinghe application of process system engineering to more sophisti-ated and innovative processes.

cknowledgements

The authors thank, Marco Ferrone, Paolo Cosoli, Giulio Scocchi,etitia Toma, Paola Posocco, Radovan Toth and Marek Maly for theupport in the calculations.

cal Engineering 33 (2009) 1701–1710

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