Symmetry Breaking in Block Copolymer Thin Films

Transcription

1 Experimets Symmetry Breakig i Block Copolymer Thi Films Eric Cochra, Gila E. Stei, 2 Kirill Katsov, 2 Gle H. Fredrickso, 2 Edward Kramer 2 Chemical & Biological Egieerig Iowa State Uiversity 2 Materials Research Lab Uiversity of Califoria Sata Barbara 2007 CFDC Meetig

2 Outlie Experimets Experimets Motivatio & Itroductio 2 Pheomeology & Numerical Issues

3 Outlie Experimets Motivatio & Itroductio Experimets Motivatio & Itroductio 2 Pheomeology & Numerical Issues

4 Experimets Motivatio & Itroductio How does bulk BCP phase behavior relate to that i cofiemet? Coectio Betwee Bulk Block Copolymers Ad BCP Thi Films Bulk State Diblock Copolymer 3D-Periodicity Cofiig Iterfaces Pseudo-2D Behavior χn 40 Q 229 Q 229 H L H? 20 CPS Q 230 DIS CPS f

5 Experimets Motivatio & Itroductio How does bulk BCP phase behavior relate to that i cofiemet? D 2D Commesurate with 2D cofiemet 3D Icommesurate with 2D cofiemet

6 Experimets Motivatio & Itroductio How does bulk BCP phase behavior relate to that i cofiemet? χn 40 Q 229 Q 229 H L H? Q CPS CPS DIS f How do 3D spheres adapt to 2D cofiemet?

7 Experimets How ca BCP spheres pack? Withi a sigle layer Motivatio & Itroductio I the plae, oly 2 legth scales defie the geometry a The earest-eighbor distace a 2 The 2 d -earest-eighbor distace We combie these ito a sigle order parameter, η a 2 a Hexagoal close-packig a a 2 η = BCC-packig a a 2 η = Square packig a a 2 η = 2

8 Experimets How ca BCP spheres pack? From layer-to-layer Motivatio & Itroductio HCP-stackig (P6 3 /mmc) 3-D View 2-D Projectio (00 directio)

9 Experimets How ca BCP spheres pack? From layer-to-layer Motivatio & Itroductio BCC-stackig 3-D View 2-D Projectio (0 directio)

10 Experimets Motivatio & Itroductio Block Copolymer Thi Films Experimetal Studie Experimetal Studies by Gila Stei a Poly(2-viyl pyridie-b-styree) PS-PVP PS-PVP poly(viyl characteristics pyridie-b-styree) poly(viyl pyridiefpvp = 0.2 N = 626 T = 220 C χn 60 CH2 CH N Film preparatio CH2 CH CH2 CH PS PVP N Experimetal Studies by Gila Stei ad Ed Kramer poly(viyl pyridie-b-styree) CH2 CH CH2 CH N Substrate = Silico Bulk Phase = BCC Spi cast from Thi films fromspi spi castigcastig Thi films from Thi fi Discrete layer thickess toluee solutio PS at iterdiscrete layer thickess Thickess cotrol Discr face Cocetratio 5 wt% Spi rate RPM layers PVP brush at substrate (W

11 Outlie Experimets Motivatio & Itroductio Experimets Motivatio & Itroductio 2 Pheomeology & Numerical Issues

12 Experimets Film Thickess vs. Motivatio & Itroductio Thickess of aealed films coforms to a costat discrete layer thickess of 22 m

13 Experimets Grazig Icidece SAXS Motivatio & Itroductio FIG. : GISAXS geometry.

14 Experimets Motivatio & Itroductio Grazig Icidece SAXS average FIG. 2: a. GISAXS patters collected at α < α All-layer, measurig oly the top surface, for L=,6, All-layer average : Itesity lie profiles of data collected at αi.05α Top-layer oly C,P (full film thickess (AboveFIG. critical agle) (Above critical agle) lie at 2Θ 0.24 marks the positio of the i-plae scatterig for =. Oly a segmet of the (Below critical agle) ad 23. b. GISAXS patters collected at αi > αc,p, measurig the full film thickess. The black i C,P ad 23. patters b. GISAXS pattersatcollected at α, i measurig > αc,p, measurig fullsurface, film thickess. The black FIG. 2: a. GISAXS collected αi < αc,p oly thethetop for L=,6, GISAXS patters is show i each image. RESULTS lie at 2Θ 0.24 marks the positio of the i-plae scatterig for =. SCFT Oly a segmet of the GISAXS patters show eachagle image. thatiswith theismall approximatio, qk = k2θ ad is idepedet of αf. I summary, AND DISCUSSION we fid a complex trasitio from 2D to 3D packig as a fu The geeral model describes the lattice as a fuctio of vectors a = {a cos φ, a si φ} that with the small agle approximatio, qk = k2θ ad is idepedet of αf. thickess. 2D hexagoal ad a2 = {0, a2 }, where ay poit i the 2D lattice is defied by rk = v a +vthe 2 a2 with itegers The geeral describes the lattice askramer, astructure fuctio of&vectors =a {a cos φ, a si φ} the vmodel, v2. This model defies the HEX whe φ Fredrickso is 30 aad Eric Cochra, Stei, Katsov, Symmetry /a2 =, ad defies symmetry is preserved through 4 layers. Films 5 Breakig i Block Copolymer Thi Films exhibit a orthorhombic phase with symmetry itermediate to that of the HE

15 Experimets Motivatio & Itroductio η vs. -layers GI-SAXS data iterpreted η= a p (BCC 0 Plae).6 a2 η.2.08 HCP P63 /mmc Fmmm (Itermediate Orthorhombic) BCC-like Im3m.04 a a , # Layers A discotiuous trasitio from HCP Fmmm occurs. Ca theory help explai this? a a 2

16 Outlie Experimets Pheomeology & Numerical Issues Experimets Motivatio & Itroductio 2 Pheomeology & Numerical Issues

17 Experimets Pheomeology & Numerical Issues Structure of the thi-film free eergy Cosider a thi film with layers of spheres The total (extesive) free eergy is: F film = F bulk + F surface We argue that F F : F film F bulk F film F bulk We calculate free eergy per chai: f film,bulk Ffilm,bulk d film,bulk

18 Experimets Pheomeology & Numerical Issues Structure of the thi-film free eergy Cosider a thi film with layers of spheres The total (extesive) free eergy is: F film = F bulk + F surface We argue that F F : F film F bulk F film F bulk We calculate free eergy per chai: f film,bulk Ffilm,bulk d film,bulk 2 surface Bulk layers 2 surface Air-Polymer Substrate-Polymer

19 Experimets Pheomeology & Numerical Issues Structure of the thi-film free eergy Cosider a thi film with layers of spheres The total (extesive) free eergy is: F film = F bulk + F surface We argue that F F : F film F bulk F film F bulk We calculate free eergy per chai: f film,bulk Ffilm,bulk d film,bulk 2 surface Bulk layers 2 surface Air-Polymer Substrate-Polymer

20 Experimets Pheomeology & Numerical Issues Structure of the thi-film free eergy Cosider a thi film with layers of spheres For a -layer film we estimate the film thickess d film (η) = d film (η) + ( )d bulk (η) The itesive free eergy i terms of the sigle-layer quatities f (η) = f b (η)+ d (η) d (η) (f (η) f b (η)) We ca calculate these quatities usig SCFT 2 surface Bulk layers 2 surface Air-Polymer Substrate-Polymer

21 Experimets Pheomeology & Numerical Issues Structure of the thi-film free eergy Cosider a thi film with layers of spheres For a -layer film we estimate the film thickess d film (η) = d film (η) + ( )d bulk (η) The itesive free eergy i terms of the sigle-layer quatities f (η) = f b (η)+ d (η) d (η) (f (η) f b (η)) We ca calculate these quatities usig SCFT 2 surface Bulk layers 2 surface Air-Polymer Substrate-Polymer

22 Experimets Pheomeology & Numerical Issues Structure of the thi-film free eergy Cosider a thi film with layers of spheres For a -layer film we estimate the film thickess d film (η) = d film (η) + ( )d bulk (η) The itesive free eergy i terms of the sigle-layer quatities f (η) = f b (η)+ d (η) d (η) (f (η) f b (η)) We ca calculate these quatities usig SCFT 2 surface Bulk layers 2 surface Air-Polymer Substrate-Polymer

23 Experimets SCFT & Cavity Fields Thi-film geometry ad Naocomposites Pheomeology & Numerical Issues SCFT ca model o-periodic geometries ad polymer aocomposites with a simple modificatio H k B T = V dr( χ AB Nρ A (r)ρ B (r) V }{{} segmet-segmet iteractios 0.8 w A (r)ρ A (r) w B (r)ρ B (r) + p(r)(ρ A (r) + ρ B (r) ) }{{} icompressibility ) l Q ρb(r) ρ A(r) r

24 Experimets SCFT & Cavity Fields Thi-film geometry ad Naocomposites Pheomeology & Numerical Issues SCFT ca model o-periodic geometries ad polymer aocomposites with a simple modificatio H k B T = V dr( χ AB Nρ A (r)ρ B (r) V }{{} segmet-segmet iteractios + χ Ai Nρ A (r)ρ i (r) }{{} cavity-segmet iteractios w A (r)ρ A (r) w B (r)ρ B (r) + p(r)(ρ A (r) + ρ B (r) + ρ i (r) ) }{{} icompressibility ) l Q ρb(r) ρ i(r) ρ A(r) r

25 Experimets SCFT & Cavity Fields Numerical Challeges Pheomeology & Numerical Issues The impositio of a cavity field creates a sharp polymer/cavity iterface This requires good cotour resolutio Pressure field p(r) exhibits early sigular behavior at iterfaces desity desity r 0 0 r pressure pressure -60 r -800 r

26 Experimets SCFT & Cavity Fields Numerical Challeges Pheomeology & Numerical Issues Pressure field updates Pressure field updates force : p ew = p old + force + force = F p = ρ A (r) ρ B (r) ρ i (r) p ew = p old +, but p(r) max p(r) mi 000

27 Experimets SCFT & Cavity Fields Numerical Challeges Pheomeology & Numerical Issues Pressure field updates Pressure field updates force : p ew = p old + force + force = F p = ρ A (r) ρ B (r) ρ i (r) p ew = p old +, but p(r) max p(r) mi 000

28 Experimets SCFT & Cavity Fields Numerical Challeges Pheomeology & Numerical Issues Pressure field updates Pressure field updates force : p ew = p old + force + force = F p = ρ A (r) ρ B (r) ρ i (r) p ew = p old +, but p(r) max p(r) mi pressure -800 r

29 Experimets SCFT & Cavity Fields Numerical Challeges Pheomeology & Numerical Issues Pressure field updates Pressure field updates force : p ew = p old + force + force = F p = ρ A (r) ρ B (r) ρ i (r) p ew = p old +, but p(r) max p(r) mi pressure -800 r Example Two calculatios with the same radom iitial coditio: covergece parameter # iteratio No cavity field With cavity field

30 Experimets Pheomeology & Numerical Issues SCFT & Cavity Fields Groud State Domiace Ca we aticipate the form of p(r)? Re-write the diffusio equatio for a homopolymer i liear operator form: q(r, s) = 2 q(r, s) p(r)q(r, s) s = ( 2 p(r))q(r, s) = Lq(r, s) Formulate the eigevalue problem: Λi i th eigevalue of L Lψ i = Λ i ψ i ψ i i th eigefuctio of L Assert groud-state domiace: ρ polymer (r) [ψ 0 (r)] 2

31 Experimets Pheomeology & Numerical Issues SCFT & Cavity Fields Groud State Domiace Ca we aticipate the form of p(r)? Re-write the diffusio equatio for a homopolymer i liear operator form: q(r, s) = 2 q(r, s) p(r)q(r, s) s = ( 2 p(r))q(r, s) = Lq(r, s) Formulate the eigevalue problem: Λi i th eigevalue of L Lψ i = Λ i ψ i ψ i i th eigefuctio of L Assert groud-state domiace: ρ polymer (r) [ψ 0 (r)] 2

32 Experimets Pheomeology & Numerical Issues SCFT & Cavity Fields Groud State Domiace Ca we aticipate the form of p(r)? Re-write the diffusio equatio for a homopolymer i liear operator form: q(r, s) = 2 q(r, s) p(r)q(r, s) s = ( 2 p(r))q(r, s) = Lq(r, s) Formulate the eigevalue problem: Λi i th eigevalue of L Lψ i = Λ i ψ i ψ i i th eigefuctio of L Assert groud-state domiace: ρ polymer (r) [ψ 0 (r)] 2

33 Experimets Pheomeology & Numerical Issues SCFT & Cavity Fields Groud State Domiace Ca we aticipate the form of p(r)? ψ 0 satisfies: Lψ 0 = 0 2 ψ 0 = p(r)ψ 0 Geeral solutio is: p gd (r) = 2 ρ 2 ((ρ )2 + ρ ) p(r) p gd (r) looks much like p(r) i bulk case

34 Experimets Pheomeology & Numerical Issues SCFT & Cavity Fields Groud State Domiace Ca we aticipate the form of p(r)? ψ 0 satisfies: Lψ 0 = 0 2 ψ 0 = p(r)ψ 0 Geeral solutio is: p gd (r) = 2 ρ 2 ((ρ )2 + ρ ) p(r) p gd (r) looks much like p(r) i bulk case pgd(r), p(r) p(r)-pgd(r) r d r 4 d

35 Experimets Pheomeology & Numerical Issues SCFT & Cavity Fields Groud State Domiace Accelerated Covergece usig p(r)? Covergece Parameter # Iteratios No cavity field With cavity field o p gd(r) With cavity field accelerated covergece usig p gd(r)

36 Outlie Experimets Pheomeology & Numerical Issues Experimets Motivatio & Itroductio 2 Pheomeology & Numerical Issues

37 Experimets Pheomeology & Numerical Issues Structure of the thi-film free eergy Cosider a thi film with layers of spheres For a -layer film we estimate the film thickess d film (η) = d film (η) + ( )d bulk (η) The itesive free eergy i terms of the sigle-layer quatities f (η) = f b (η)+ d (η) d (η) (f (η) f b (η)) We ca calculate these quatities usig SCFT 2 surface Bulk layers 2 surface Air-Polymer Substrate-Polymer

38 SCFT Free Eergies Experimets Pheomeology & Numerical Issues Fbulk,kBT Bulk Phase Eergy x η HCP-Packig BCC-Packig Fsurf,kBT -Layer Free Eergy x η χn = 4 (ear ODT) χn = 50 χn = 60

39 Experimets Pheomeology & Numerical Issues 5 x 0 4 f (η), kt η χn = 50 The free eergy of ay value of may be composed from F bulk ad F film

40 Experimets Pheomeology & Numerical Issues f (η), kt 5 x = 2 (full SCFT) η χn = 50 The free eergy of ay value of may be composed from F bulk ad F film

41 Experimets Pheomeology & Numerical Issues SCFT predicts the experimetally observed discotiuity By fidig the value of η that miimizes F film we arrive at: η η η χn = 4 χn = 50 χn = 60

42 Experimets Pheomeology & Numerical Issues SCFT predicts the experimetally observed discotiuity η. η , # Layers χn = 60 χn 60 a a2 SCFT agrees well with this experimetally observed discotiuity

43 Ackowledgemets Experimets Pheomeology & Numerical Issues Fudig NSF Mitsubishi Chemical Ceter For Advaced Materials Computatioal Facilities Califoria NaoSystems Istitute (CNSI) Jeffrey Barteet for support of UCSB-MRL facilities Iowa State Uiversity Partership for High-Performace Computig Collaborators & Frieds Fredrickso Group Kramer Group