ΣΥΓΧΡΟΝΕΣ ΥΠΟΛΟΓΙΣΤΙΚΕΣ ΜΕΘΟ ΟΙ ΓΙΑ ΤΟΝ ΠΡΟΣ ΙΟΡΙΣΜΟ ΘΕΡΜΟ ΥΝΑΜΙΚΩΝ Ι ΙΟΤΗΤΩΝ ΠΡΟΗΓΜΕΝΩΝ ΥΛΙΚΩΝ. Ιωάννης Γ. Οικονόµου

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1 ΣΥΓΧΡΟΝΕΣ ΥΠΟΛΟΓΙΣΤΙΚΕΣ ΜΕΘΟ ΟΙ ΓΙΑ ΤΟΝ ΠΡΟΣ ΙΟΡΙΣΜΟ ΘΕΡΜΟ ΥΝΑΜΙΚΩΝ Ι ΙΟΤΗΤΩΝ ΠΡΟΗΓΜΕΝΩΝ ΥΛΙΚΩΝ Ιωάννης Γ. Οικονόµου Εργαστήριο Μοριακής Θερµοδυναµικής και Μοντελοποίησης Υλικών Ινστιτούτο Φυσικοχηµείας ΕΚΕΦΕ «ηµόκριτος» Θερινό Σχολείο ΕΚΕΦΕ «ηµόκριτος» Ιούλιος 005 Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos ΣΥΓΧΡΟΝΕΣ ΤΑΣΕΙΣ ΤΗΣ ΠΑΓΚΟΣΜΙΑΣ ΒΙΟΜΗΧΑΝΙΑΣ ΧΗΜΙΚΩΝ ΙΕΡΓΑΣΙΩΝ Κατά τα τελευταία χρόνια, παρατηρείται µία µεταστροφή της ΧΒ από την παραγωγή προϊόντων χαµηλού µοναδιαίου κόστους σε εξειδικευµένα προϊόντα υψηλής προστιθέµενης αξίας (φαρµακευτικά προϊόντα, καλλυντικά, πρόσθετα τροφίµων, ειδικά πολυµερή κλπ.). Τα προϊόντα αυτά βασίζονται σε υλικά µε σηµαντική πολυπλοκότητα ως προς: τη χηµική τους δοµή, τη µοριακή και υπερµοριακή αρχιτεκτονική, τη µίκρο και µέσο-δοµή, και την συµπεριφορά τους κατά την τελική τους χρήση. Αυστηροί περιβαλλοντικοί κανονισµοί στην Ε.Ε., τις ΗΠΑ και αλλού απαιτούν την υιοθέτηση νέων διεργασιών παραγωγής φιλικών προς το περιβάλλον οι οποίες συνάδουν µε το στόχο της αειφόρου ανάπτυξης. Η παγκοσµιοποίηση της οικονοµίας αυξάνει τον ανταγωνισµό σε όλα τα επίπεδα υποχρεώνοντας την υιοθέτηση άριστων πρακτικών στο σχεδιασµό διεργασιών και προϊόντων. Συνεπώς, η θεµελιώδης κατανόηση των σχέσεων µοριακών µηχανισµών µικροσκοπικής δοµής µακροσκοπικών ιδιοτήτων είναι υψίστης σηµασίας. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 1

2 COMPUTATIOAL MATERIALS SCIECE AD EGIEERIG chemcal Molecular geometry & electronc propertes Molecular nteracton potentals Molecular Smulatons, Appled Statstcal Mechancs e.g. Monte Carlo, Molecular Dynamcs, Molecular Mechancs, Transton-State Theory Quantum Mechancal Calculatons consttuton Coarsegraned nteracton parameters Rate constants, frcton coeffcents Molecular organzaton and moton Mcrosopc mechansms underlyng macroscopc behavor Processng Mesoscopc Smula- Tons e.g. Knetc MC, Self-consstent feld theory, Dynamc densty functonal theory, Dsspatve partcle dynamcs Morphology Mcrostructure Macroscopc Calculatons, Desgn Appled Thermodynamcs, Transport phenomena, Chemcal knetcs, Contnuum mechancs, Electromagnetc theory Materal Propertes Equatons of State, Consttutve relatons Product performance under specfc applcaton condtons Calculatons gude and complement expermental efforts for the development of new materals, processes, and products. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos ΘΕΩΡΙΑ ΠΕΙΡΑΜΑ - ΠΡΟΣΟΜΟΙΩΣΗ Προσοµοίωση Φυσικό Σύστηµα Θεωρία Πείραµα Για συστήµατα όπου οι πειραµατικές µετρήσεις είναι δύσκολες (πχ. υψηλές θερµοκρασίες και πιέσεις, τοξικά ή εύφλεκτα συστατικά) η προσοµοίωση µπορεί να χρησιµοποιηθεί ως ψευδο-πειραµατική πληροφορία. Η προσοµοίωση µπορεί να χρησιµοποιηθεί για τον έλεγχο της ορθότητας και της ακρίβειας µίας θεωρίας. Μέσω της προσοµοίωσης είναι δυνατός ο ποσοτικός προσδιορισµός της επίδρασης κάποιων παραµέτρων στις ιδιότητες του συστήµατος. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos

3 PROJECT OUTLIE Synthess, characterzaton, property measurements and molecular modellng of novel slcon polymers wth promsng propertes as membrane materals for flud mxture separaton. Tentatve large-scale applcatons nclude: Reducton of dew pont of natural gas for safer and more effcent long dstance transport. Producton of natural gas lquds from the heavy hydrocarbon fractons. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos MEMBRAE SEPARATIO TECHOLOGY Separaton of mxtures usng membranes s a fast growng technology due to: Low energy consumpton, Mld operatng condtons, o envronmental polluton, Process contnuty and flexblty, Easy scalablty, Space savngs, Modular plant desgn. MEMBRAE TECHOLOGY MARKET Membrane technology market (n mllon $) natural gas total Year Baker, Ind. Eng. Chem. Res., 41, 1393 (00) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 3

4 MEMBRAE SEPARATIO MECHAISM Feed Drvng Force P, C Permeate Retentate Permeablty : P = D S P1 D1S1 a = = = asa P D S D Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos MEMBRAE SELECTIVITY vs. PERMEABILITY Robeson et al., Polymer, 35, 4970 (1994) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 4

5 COMPOSITIO OF ATURAL GAS (n vol. %) 90 % methane, 4 % ethane, 3 % propane, 0.6 % -butane, 0.5 % n-butane, 1 % C 5+, 0.4 % ntrogen, 0.4 % CO, % H S. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos ATURAL GAS SEPARATIO WITH MEMBRAES Most ndustral applcatons utlze glassy polymerc FROM COMMERCIAL MEMBRAE membranes (dffuson controllng mechansm). H 3 C CH 3 Here, the heavy component s S recovered, so rubbery membranes are preferred (solublty drven mechansm). O O Separaton of heavy hcs n TO A EWLY DEVELOPED MEMBRAE natural gas ncreases safety and effcency of gas transport. The hc lqud fracton can be used locally. H 3 C CH 3 S Commercal elastomer membranes are vulnerable to sulfur contanng compounds. CH CH Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 5

6 CHEMICAL SYTHESIS OF POLYMERS Me S SMe ο C Me S CH x Me Temperature affects MW Polymerzaton temperature ( o C) 160 Polymer MW 800,000 Effect of stop-reagent concentraton at 175 o C C 6 H 5 OH conc. (wt %) 0.01 Polymer MW 360, ,000, ,500, ,000, ,600,000 Alentev et al., Polymer, 45, 6933 (004) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos PERMEABILITY OF POLYSILMETHYLEES at 5 O C and P P = 0.4 bar Polymer P (Barrer) O CH 4 C H 6 C 3 H 8 n-c 4 H 10 PDMSM PDMSTM PDMSM/PDMSTM (50:50) PDMSM/PDMSTM (75:5) PDMS [10] [6] Alentev et al., Polymer, 45, 6933 (004) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 6

7 MOLECULAR DYAMICS SIMULATIO umercal soluton of ewton s equaton of moton: mr = f= rv( r1,... r) = 1,,..., Calculaton of thermodynamc, dynamc, transport and other tme dependent propertes, Wth current computng facltes, smulaton up to ~100 ns of real tme. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos ATOMISTIC FORCE FIELDS FOR CHAI FLUIDS V( r,..., ) ) ( ) ( ) ) 1 r = Vl ( + V θ + V φ + Vr (, j all bonds all bond all torsonal all pars angles angles k V l l l k l, ( ) ( ) θ, =, o ( ) ( ) φ V θ = θ θ, o V ( φ ) = o ( 1 cos3φ ) V 1 6 σ, j σ, j Vr (, j) = 4ε, j r, j r, j Parameters are obtaned from: ab nto quantum mechancs calculatons (bonded parameters), or ft to spectroscopc or thermodynamc data (non-bonded parameters). Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 7

8 DESITY FUCTIO THEORY (DFT) CALCULATIOS FOR FORCE-FIELD FIELD DEVELOPMET DFT calculatons determne mnmum energy confguraton, and energy dfferences between confguratons. B3LYP functonal wth 6-311G bass set was used. A model dmer molecule was examned. MIIMUM EERGY STRUCTURE COFORMATIOAL EERGY MAP o o o o 1.916Å 1.91Å 1.915Å V V 1 cos3 V = 1.075kcal/mol φ,o ( φ ) = ( φ ) φ,o Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos MOLECULAR DYAMICS SIMULATIO DETAILS MD calculatons were performed n the PT ensemble (osé and Klen statstcal ensemble technque). Equatons of moton for MD n the PT ensemble: LJ ζ ζ ζ ζ Vbendng ( ) + V Vj r r torson j ζ ζ ms r mssr = s λn( r rl ) ζ ζ ζ r r j r rj l s s = ( nt ext ) + L L P P L LW s L s = r s s m fkt + Q s System examned: Polymer melt conssts of 3 chans of 80 monomerc unts (MW = 5775). Typcal smulaton tme: 1 ns for equlbraton + 5 ns for producton (tme step = 0.5 fs). Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 8

9 PVT PROPERTIES OF PDMSM Densty (g/cm 3 ) Ko and Mark, 1975 Bhde and Stern, 1991 Shah et al., 1993 Maer et al (0 MPa) Maer et al (80 MPa) Maer et al (160 MPa) Fnkelshten, 1999 MD, 0 MPa MD, 80 MPa MD, 160 MPa Temperature (K) Rapts et al., Macromolecules 37, 110 (004) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos MICROSCOPIC STRUCTURE of PDMSM: RADIAL DISTRIBUTIO FUCTIO at 300 K and 0.1 MPa CH 3 -CH 3 CH -CH 1 S-CH -CH S-S 0.8 S-CH 3 g(r) 0.6 g(r) r (Å) r (Å) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 9

10 DIHEDRAL AGLE DISTRIBUTIO FOR PDMSM Probablty Densty x Constant, 300 K Varable, 300 K Constant, 400 K Dhedral angle (degrees) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos CHARACTERIZATIO OF FREE VOLUME PDMSM at 300 K and 0.1 MPa Penetrant: 1.4 Å 31.5 Å (a) (b) a) Delaunay tetrahedron, defned by four neghbor atoms of the polymer. b) Accessble volume wthn the Delaunay tetrahedron (shown n green). Penetrant: 1.84 Å (methane) Greenfeld and Theodorou, Macromolecules, 6, 5461 (1993) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 10

11 TIME EVOLUTIO OF ACCESSIBLE VOLUME Penetrant: Methane (1.84 Å) Penetrant: Sphercal molecule (1.4 Å) 31.5 Å t = 0 ps t = 10 ps t = 0 ps t = 0 ps t = 10 ps t = 0 ps t = 30 ps t = 40 ps t = 50 ps t = 30 ps t = 40 ps t = 50 ps t = 60 ps t = 70 ps t = 80 ps t = 60 ps t = 70 ps t = 80 ps Rapts et al., Macromolecules 37, 110 (004) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos CHEMICAL POTETIAL CALCULATIO: TEST PARTICLE ISERTIO (WIDOM METHOD) A A( + 1, V, T) A(, V, T) 1 Q( + 1, V, T) µ ( ρ, T ) = ln = =, ( + 1 ) β Q( V,, T TV ) 3 1 ( + 1) Λ 1 Z( + 1, V, T) = ln ln nt β Vq β VZ (, V, T ) g µ ( ρ, T ) exp( βu ) ghost g ex 1 µ ρ, T µ ρ, T µ ρ, T = ln exp βu ghost β A ghost molecule s nserted n the smulaton box and ts energy wth the remanng molecules, U ghost, s calculated. For accurate estmate of µ ex of complex fluds, usually several hundred thousands of nsertons are needed. ( ) ( ) ( ) ( ) Wdom, J. Chem. Phys. 39, 808 (1963) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 11

12 HERY S LAW COSTAT: CALCULATIO DETAILS Two dfferent force-felds (constant and varable bond models). Constant bond length model: 8 dfferent PDMSM confguratons at 300 K, 4 dfferent PDMSM confguratons at 400 K. Varable bond length model: 3 dfferent PDMSM confguratons at 300 K. 5,000 pctures stored from every run. Attempted nsertons per pcture : 10,000 to 400,000. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos ln(h'/mpa) SORPTIO OF n-alkaes n I PDMSM Henry s law constant ρpol ex Halk pol = lm exp( βµ alk ) xalk 0 β Exp (300 K) Sm (Const, 300 K) Sm (Var, 300 K) Sm (Const, 400 K) carbon number Enthalpy of sorpton (kcal/mol) Rapts et al., Macromolecules 37, 110 (004) Enthalpy of sorpton lns H = s 1 R T Experment Smulaton carbon number Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 1

13 DIFFUSIO COEFFICIET OF n-alkaes n I PDMSM System: 3 PDMSM chans + 5 / 10 n-alkane molecules. Montor the dsplacement of n-alkane molecules wth tme. In the fckan regme (normal dffuson): r t From the slope of the curve, D s calculated. Very long MD smulatons are needed for relable estmate of D of long n- alkanes (more than 0 ns). dstance (A) <r*r> (A) 10 methane molecules n PDMSM tme (ns) tme (ns) D =.3x10-6 cm s -1 Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos S: orange CH : gray CH 3 : whte PDMSM n-butae MIXTURE: A typcal snapshot DIFFUSIO COEFFICIET OF n-alkaes n I PDMSM 300 K and 0.1 MPa D (x10 7 cm /sec) Experment (RAS) Experment (D) Experment (Stern et al.) MD Smulaton carbon number Economou et al., Flud Phase Equl., n press (005) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 13

14 CORRELATIO OF COFORMATIOAL TRASITIO WITH TRASLATIOAL JUMP Tme (ps) Molecular Dsplacement (n Å) Dhedral Angle Transton (n rad) Translatonal jump: Move of center of mass by more than 3.75 Å wthn less than 6 ps. Conformatonal transton: From gauche to trans and vce versa. n-alkane n-butane <t cæt > (ps) 373 <t uæt > (ps) Tme (ps) n-pentane n-hexane Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos COCLUSIOS A new atomstc force-feld was developed for a slconcontanng rubbery polymer based on ab nto calculatons and expermental PVT data. Molecular Dynamcs was used to elucdate the molecular mechansms that control sorpton and dffuson of n-alkanes n the polymer. Smulaton calculatons and expermental data for the solublty and dffuson coeffcent of n-alkanes n the polymer are n excellent agreement. Atomstc smulaton s a relable tool for advanced materals desgn. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 14

15 WORK I PROGRESS Systematc nvestgaton of polymer chemcal structure on permeablty propertes: Homopolymers H 3 C CH 3 CH S CH CH CH Copolymers H 3 C CH 3 S H 3 C CH 3 CH S CH CH x CH CH CH y Calculaton of permeablty propertes for mxed gases (.e. methane n-butane): Evaluaton of the plastczaton effects. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos MOTIVATIO Dendrmer topology hghly ordered, well-defned branched polymers H H H H G4 H H H H H H Potental use dendron H H H H nanocatalyss, cotrolled release agents, lght harvestng, chemcal sensors, supramolecular buldng blocks Lmtaton of structure: sterc hnderance fully extended surface G number of end groups G+1 dense core vs. dense shell models H H H H H H H branch ponts (g) H H H H H H H H H spacers H H end groups Zacharopoulos and Economou, Macromolecules, 35, 1814 (00) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 15

16 ECAPSULATIO AD RELEASE OF PHARMACEUTICALLY ACTIVE COMPOUDS acl + OH = O OH Me H Me H F H O C C 4H 9 O C O Me H Paleos et al., Bomacromolecules, 5, 54 (004) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos SIMULATIO METHOD H Molecular model G1 PPI H H H H H unted atom methylene groups H Perodc boundary condtons G5 dendrmer melt Force feld Dredng E kb ( b ) (cos cos ) {1 cos[ ( )]} b kθ θ θ kφ n φ φ 1 6 σ j σ j εj j, rj r j = Molecular mechancs, smulated annealng Molecular dynamcs (PT) ns Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 16

17 DEDRIMER RELAXATIO C Rg () t = ( R () )( (0) g t Rg Rg Rg ) R R 4 g g autocorrelaton of the squared radus of gyraton t Rg = 4 ps (G), 9 ps (G3), 0 ps (G4) and 45 ps (G5) Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos DEDRIMER COFORMATIOS (T = 400 K, t = 500 ps) G G3 G4 Dfferent colors represent dfferent dendra G5 κ = 1-3I /I 1 ; I 1, I : frst and second nvarants of the radus of gyraton tensor ; κ [0,1] Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 17

18 OVERALL DIMESIOS <R g >.9 Fractal dmenson r ( ) 4π ρ( ) M r = r r dr 0 exponent measured from a log-log plot of M(r):.56,.95,.88, 3.09 Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos ITRAMOLECULAR STRUCTURE g+1 Ig+1 g Ig+1 g+1 Ig g-1 crtcal generaton: extended spread of dendra vs. back-foldng Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 18

19 ED GROUPS transton from unmodal to trmodal end group dstrbuton Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 0( unoccuped) ψ α = 1 ( occuped) O = t DEDRO OVERLAP ψαψ β jkα β {, jk, } Or ( ) = 3 ψαψ β {,, } 3 {, jk, } α= β α β {, jk, } α= β ψψ α ψψ α β β δ δ rr, jk,, rr, jk,, overlap saturaton consstent wth space-fllng arrangement Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 19

20 D = t {, jk, } A {, jk, } A DEDRIMER OVERLAP A A {, jk, } A Dr ( ) = ψ ϕ ψ ψ A A {, jk, } A ψϕ A ψψ A A A δ δ rr, jk,, rr, jk,, overlap decay consstent wth denser packng Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos DEDRIMER AQUEOUS SOLUTIOS System nvestgated: PPI dendrmer (blue molecule) n water (small molecules). Applcatons: Controlled release of actve molecules (drugs etc.), anocatalyss, Separatons. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 0

21 ΣΥΜΠΕΡΑΣΜΑΤΑ Η µοριακή προσοµοίωση αποτελεί ένα ιδιαίτερα χρήσιµο και αξιόπιστο εργαλείο πρόβλεψης δοµικών, θερµοδυναµικών και άλλων ιδιοτήτων µη ιδανικών υλικών συστηµάτων. Με τη χρήση κατάλληλων µοριακών µοντέλων (πεδίων δυνάµεων) είναι δυνατός ο προσδιορισµός ιδιοτήτων µε ακρίβεια που προσεγγίζει την πειραµατική ακρίβεια. Κατά συνέπεια, η µοριακή προσοµοίωση σε συνδυασµό και µε πειραµατικές µετρήσεις µπορεί να χρησιµοποιηθεί ως εργαλείο σχεδιασµού νέων προϊόντων και διεργασιών της χηµικής, φαρµακευτικής και πετρελαϊκής βιοµηχανίας καθώς και της βιοµηχανίας νέων υλικών. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos A VIEW TO THE FUTURE Today, molecular smulaton s a relable desgn tool for novel complex functonal materals and optmum chemcal process desgn. Addtonal work s needed for the development of accurate force felds for a wde range of soft (fluds) and hard materals. Despte the contnuous ncrease of computng power, there s always need for further development of novel molecular modelng strateges (possbly by nvokng mesoscopc modelng) that wll allow tacklng more complex systems and, hopefully, reduce computng tme requrements. Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos 1

22 Η ΥΠΟΛΟΓΙΣΤΙΚΗ ΙΣΧΥΣ ΣΥΝΕΧΙΖΕΙ ΝΑ ΑΥΞΑΝΕΙ ΑΠΟ ΟΣΗ ΤΩΝ ΙΣΧΥΡΟΤΕΡΩΝ ΥΠΕΡΥΠΟΛΟΓΙΣΤΩΝ 1.E+09 Today Speed (Mflops) 1.E+07 1.E+05 1.E+03 1.E+01 1.E-01 1.E-03 Πηγή: IBM 704 Cray - 1 IBM ASCI Whte Moore's law Cray Y - MP IBM Blue Gene Year Molecular Thermodynamcs and Modellng of Materals Laboratory, RCPS Demokrtos