OPTICAL PROPERTIES OF METALLIC NANOPARTICLES, MOLECULES AND POLYMERS

Transcription

1 OPTICAL PROPERTIES OF METALLIC NANOPARTICLES, MOLECULES AND POLYMERS Dr. Mca Grujcc Aprl, 004 Department of Mechancal Engneerng

2 Me Theory - Dlute Collodal Soluton Lmt

3 Sphercal Partcles Ref: C. F.Bohren and D. R. Huffman, Absorpton and Scatterng of Lght by Small Partcles, Wley: New York, 983.

4 Extncton Cross-secton secton of Sphercal Partcles C ext 4π R λ 3 p ε 3/ m ( ) ε + ε + ε p ε ε m Delectrc Functon of the Medum p m p R p - Partcle Radus λ - Incdent Wavelength ε p Real Part of Delectrc Functon of Partcles ε p Imagnary Part of Delectrc Functon of Partcles Delectrc Functon of the Nanopartcles ε ε + ε p p p

5 Complex Delectrc Functon For Bulk Materal ε bulk ( ω) me ω P ( ω + ωγ) ε bulk ( ε ) + ε ( ε ) bulk m e Mass of Electron ω Exctaton Angular Frequency

6 ω P ne meε 0 Bulk Plasmon Frequency e Electron Charge n Densty of Free Electrons ε 0 Permttvty of Free Space Γ v l F e τ Dampng Frequency v F Ferm Velocty l e Mean Free Path τ Relaxaton Tme

7 Real Part of Delectrc Functon of Bulk Materal ε bulk ( ) P ω ω ω + Γ Imagnary Part of Delectrc Functon of Bulk Materal ε bulk ( ω) ω Γ P ( + Γ ) ω ω Corrected Real Part of Delectrc Functon of Bulk Materal ε ( ) P ω ε bulk ω ω + Γ ε Hgh Frequency Delectrc Constant

8 Effect of the Small Partcle Sze Partcle Sze Effectve Mean-Free Path l eff l e + R p Effectve Dampng Frequency Γ eff v l F eff

9 Effect of Intrabound Transtons Free-electron electron Real Part of the Delectrc Functon of Sphercal Partcles ε ( ) P ω ε p ω ω + Γ eff Free-electron electron Imagnary Part of the Delectrc Functon of Sphercal Partcles ε p ( ω) ω Γ P eff ( + Γ ) ω ω eff

10 ε Total Complex Delectrc Functon ( ) free ( ) nt erband ω ε ω + ε ( ω) ( bulk, p) Delectrc Constant n Metallc Nanopartcles ε p ( ) free ( ) ( ) free ω ε ω + ε ω ε ( ω) p bulk bulk Dlute-dsperson Lmt Adsorpton Coeffcent α ddl Cext ρ N ρ N Number Densty of Partcles

11 Non-sphercal Partcles Ref: R. Gans,, Ann. Phys., 47 (95) 70

12 Extncton Cross Secton of Extncton Cross Secton of Non Non-Sphercal Partcles Sphercal Partcles ( ) c b a j P P P R C j p m j j p p j m ext,, ε ε ε ε λ ε π ; ln a c b a P P P r r r r r P + ( ) a b r Depolarzaton Vector for Nanorod (a>bc) Depolarzaton Vector for Nanorod (a>bc) where where

13 Input: Real and Imagnary Parts of the Delectrc Constants For Gold and Slver as a Functon of the Photon Wavelength 4370 Gold Slver Gold Slver Ref: P. B. Johnson and R. W. Chrsty, Phys. Rev. B, 6 (97) 4370

14 Results 5000 Extncton Coeffcent, M - cm Delectrc Constant of Water n.334 Sphercal Partcles Wavelength, nm Calculated Absorpton Spectra of Au Partcles n Water

15 Normalzed Absorbance Medum Delectrc Constant.4 Sphercal Partcles.376 n Wavelength, nm H O (n.334) Cyclohexane (n.376) Dodecane (n.4) Decaln (n.47) CS (n.60) Calculated Absorpton Spectra of Au Partcles Meda wth DfferentDelectrc Constant

16 Experment 5 nm Au Sphercal Partcles n Water and n Mxtures of Butyl Acetate and Carbon Dsulfde Ref: S. Underwood and P. Mulvaney, Langmur, 0 (994) Theory n.334 n.407 n.48 n.55 n.583 Sphercal Partcles Me Theory Transmsson Colors Sphercal Gold Partcles Effect of Delectrc Constant of the Medum

17 Medum Delectrc Constant 4.0 Partcle Aspect Rato Absorbance, a.u Transverse Plasmons,, Blue Shft.6 Longtudnal Plasmons,, Red Shft Wavelength, nm Elongated Ellpsodal Partcles

18 Absorbance, a.u Aspect Rato 3.3 Transverse Plasmons,, Red Shft Medum Delectrc Constant Longtudnal Plasmons,, Red Shft Wavelength, nm Elongated Ellpsodal Partcles

19 λ Regresson Analyss of the Wavelength at the Longtudnal Plasmon Peak ( ) R ε + max m

20 Maxwell Garnett Theory Non-Dlute Collodal Solutons Ref: J. C. Maxwell Garnett, Phlos.. Trans. R. Soc. London,03 (904) 385.

21 Au Core SO Shell (a) (b) (a) Slca Coated Gold Partcle; (b) Ideal Packng of Slca Coated Gold Partcles n the Flm to Form FCC Lattce wth Volume Fracton 0.74.

22 Average Electrc Feld n Composte Materal E av ( ) Em φe p φ + E p Electrcal Feld n the Partcle E m Electrcal Feld n the Matrx Materal Partcle Volume Fracton φ 0.74R 3 Au ( R + R ) 3 Au SO R Au Radus of the Gold Core R SO Thckness of SO Shell

23 Average Polarzaton n Composte Materal ( φ )( ε ) ( ) ( ) m ε Em + φ ε p ε E p ε av ε Eav Pav Electrc Feld Insde the Partcles (Lorentz Cavty Feld) 3ε m E p Em ε p + ε m ε m Delectrc Functon of the Matrx Materal

24 Fnal Form of the Equatons Average Electrc Feld n Composte Materal E av ( ) m φ Em + Em ε 3φε p + ε m Average Delectrc Functon n Composte Materal ε av ε α m ε p ε ( + φ ) + ε ( φ) p ( φ) + ε ( + φ) Average Absorpton Coeffcent n Composte Materal av ω Im c n ( ε ) av av m m 4πk λ av

25 Complex Delectrc Functon ε ε + ε ( ) n + k ( ddl, av) Complex Refractory Index n ε + ε + ε ( ddl, av) k ε + ε ε ( ddl. av)

26 Optcal Reflectance R ( n ) ( n + ) + + k k ( ddl, av) Optcal Transmttance T R exp ( ) R + 4R sn ψ ( α h) + exp( α h) R cos( ξ + ψ ) ( ddl, av) h Thckness of the Au@SO Flm

27 Optcal Reflectance R ( n ) ( n + ) + + k k ( ddl, av) Optcal Transmttance T R exp ( ) R + 4R sn ψ ( α h) + exp( α h) R cos( ξ + ψ ) ( ddl, av) h Thckness of the Au@SO Flm Functons n the Above Equaton 4π n h, λ k tan n + k ξ ( ddl av) ψ 0 ψ π ( ddl, av)

28 4 Results Flm Thckness 00nm Normalsed Absorbance nm 60nm 40nm 0nm 5nm Wavelength, nm Effect of Flm Thckness on the Calculated Absorpton Spectra of Au@SO Flms at the Partcle Volume Fracton φ 0.05.

29 . Normalsed Absorbance Partcle Volume Fracton Wavelength, nm Calculated Absorpton Spectra of Au Partcles Wth Dfferent Partcle Volume Fractons.

30 700 Surface Plasmon Peak Poston, nm MG Theory Expermental Volume Fracton of Au Effect of the Partcle Volume Fracton on the Calculated Peak Postons of the Coupled Plasmon Bands n Au@SO Flms

31 Experment 5 nm Gold Sphercal Partcles Coated wth Slca Shells of Varous Thckness Ref: T. Ung, L. M. Lz-Marzan and P. Mulvaney, J. Phys. Chem., B05 (00) t7.5nm t.5nm t4.6nm t.9nm t.5nm Theory Maxwell- Garnett Theory Transmsson Colors Sphercal Gold Partcles Effect of Delectrc Constant of the Medum

32 Experment 5 nm Gold Sphercal Partcles Coated wth Slca Shells of Varous Thckness Ref: T. Ung, L. M. Lz-Marzan and P. Mulvaney, J. Phys. Chem., B05 (00) t7.5nm t.5nm t4.6nm t.9nm t.5nm Theory Maxwell- Garnett Theory Reflecton Colors Sphercal Gold Partcles Effect of Delectrc Constant of the Medum

33 Dscrete Dpole Approxmaton Ref: J. J. Goodman, B. T. Drane,, and P. J. Flateau,, Opt. Lett.. 6 (99) 98.

34 Polarzaton of Each Dpole P α E α Polarzablty of the Dpole at r Total Electrcl Feld at Poston r E + Enc, Eself,

35 Electrc Feld of Incdent Plan Wave E nc, E exp r 0 ( k ω t) E o The Ampltude of the Incdent Electrc Feld k Wave Vector t Tme ω Frequency Electrc Feld From Other Dpoles E self, N j A j P j

36 Fnal Equaton for Polarzaton N ( ) α P A j P j Enc, + j Dyadc Green s Functon Approach ( kr ) ( kr ) j ( ) j A j P exp j k rj rj P j + j j 3 3 rj rj [ ( )] r P r r P j j j

37 j j j j 0 A A Matrx A Matrx A j j j j N j N j N j j x x y y z z P A P A Y Convoluton Convoluton + + z z z y y y x x x n N n N n N n exp ˆ Y Y Dscrete Fourer Transform Dscrete Fourer Transform

38 Extncton Cross Secton C ext N 4πk Im E 0 ( E P ) E * Complex Conjugate of Total Electrc Feld at r Absorpton Cross Secton C abs 4πk E 0 N Im [ ( ) ] P α P 3 k 3 P Scatterng Cross Secton C sca C ext C abs

39 R Reflectvty [ ( ) ( )] cos θ mcos θ r [ cos( θ ) + mcos( θ )] θ Incdent Angle r θ r Refractve Angle Complex Refractory Index m n + k

40 Imagnary Part of Refractory Index k ( ) m n Real Part of Refractory Index n sn ( θ ) sn( θ ) r

41 0.8 Partcle Volume Fractons 0.05 Normalsed Absorbance DDA MG Wavelength, nm Comparson of the Calculated Results from DDA and MG Effectve Medum Method

42 UV Spectra of Molecules Ref: Accelrys VAMP Tutoral

43 Cnnamate Molecule

44 Although self-consstent feld calculatons are adequate for the vast majorty of normal molecules, bradcals and excted states requre a more sophstcated treatment. Ths s often acheved usng confguraton nteracton methods (CI). In CI calculatons, the molecular orbtals for the ground state are calculated and then used unchanged to construct a seres of further electronc confguratons (mcrostates) that are mxed to form new electronc states. CI calculatons gve not only the ground state, but also the excted states that result from mxng the mcrostates used. They can therefore be used for the calculaton of UV/vs spectra, optmzaton of excted states, second order hyperpolarzabltes (sum-over-states method) etc. CI calculatons are avalable only for RHF wavefunctons. Any spn state (sngle, doublet, etc.) can be requested.

45 Confguraton Interacton Results Confguraton Interacton Results Osc Osc. Str Str. r r Dpole Length, A Dpole Length, A Del Del Mu Mu Energes Energes z z y y x x nm nm ev ev Excted Excted State State Ground Ground State State Accelrys Accelrys VAMP VAMP

46 Adsorpton Spectrum for Cnnamate Expermental Absorbance Calculated Wavelength, nm

47 IR Spectra of Polymers Ref: A. Soldera and J.-P. Dognon, Optcal Coeffcents of Polymers Versus Wavelength Calculated From Classcal Molecular Smulatons,, ACS Dvson of Polymerc Materals, Scence and Engneerng, 75 (996)

48 Methyl- Metha- Acrylate (MMA)

49 Poly- Methyl- Metha- Acrylate (PMMA)

50 Intensty Intensty km/mol km/mol Frequency Frequency /cm /cm Mode Mode Normal Mode Analyss Normal Mode Analyss Accelrys Accelrys Dscover Dscover

51 Infra Red Absorpton Coeffcent (Ramsay Functon) S ( ) K ν ν V ( ) m.303π 4 ν ν + ν ν Wavenumber ν / Half Wdth V m Molar Volume S Integrated Intensty

52 Infrared Absorpton Spectra of PMMA 5 Absorpton Coeffcent, a.u Expermental Calculated Frequency, cm - 000

53 Real Part of Refractve Index of PMMA Real Part of Refractve Index Calculated Expermental Wavelength, mcrons

54 Polymer Collodal Crystal Photonc Bandgap Structure S.H. Foulger, D.W. Smth, Jr. and J. Ballato Clemson Unversty A.L. Reynolds Translght : A Transfer Matrx Code gla.ac..ac.uk/groups/opto/photonccrystphotonccryst al/photoncs Photoncs/photoncsman.htm htm

55 Structural and Optcal Parameters of Polymer Encapsulated FCC Crystallne Collodal Arrays Type Partcles Partcle Dameter (nm) Partcle Dstance (nm) Cappng Medum CCA Polystyrene Water, n.344 Water + Poly(ethylene glycol) methacrylate (PEG-MA) + CCA/PEG Polystyrene Poly(ethylene glycol) dmethacrylate (PEG-DMA),-dethoxyacetophenone(DENP) n.367 PCCA Polystyrene Polymerzed State of the Above n.368 Ref: S. H. Foulger, et. al., Langmur, 7 (00) 603

56 Mechanochromc Response of PCCA Composte 0% Compressed Stress Free Calculated Reflectance, a.u. Expermental Wavelength, nm

57 Structural and Optcal Parameters of Polymer Encapsulated FCC Crystallne Collodal Arrays Type Partcles Partcle Dameter (nm) Partcle Dstance (nm) Cappng Medum Poly(ethylene glycol) + MOEA Polystyrene Poly(-methoxyethyl acrylate (MOEA)),(n c.489) MOEA+ Poly(ethylene glycol) + MOEM Polystyrene Poly(-methoxyethyl acrylate)-co- (50:50) poly(-methoxyethyl methacrylate) Poly(ethylene glycol) + MOEM Polystyrene Poly(-methoxyethyl methacrylate (MOEM)) Ref: S. H. Foulger, et. al., Adv. Mater., 5 (003) 685

58 Calculated/Measeured Reflectance Spectra for Dfferent Compressve Stress. Normalzed Reflectance, a.u % Compresson 30% Compresson Expermental Calculated 0% Compresson Wavelength, nm

59 A Comparson of the Measured and Calculated Reflected Colors Experment 0% Compresson 30% Compresson 48% Compresson Theory

60 One-Dmensonal Photonc Bandgap Structures A.L. Reynolds Translght : A Transfer Matrx Code gla.ac..ac.uk/groups/opto/photonccrystphotonccryst al/photoncs Photoncs/photoncsman.htm htm

61 Transfer Matrx Method

62 One-dmenson Planar Perodc Structure

63 () k k x () y z a b Wave Vectors: k, k Perod: d a + b N d () Two-layer Planar Structure () Perodc Two-layer Planar Structure

64 x X B: Boundary y z B B K K k k k 0 Z a b a φ [φ (z<0), φ (0<z<b), φ 3 (z>b)] Defnton of the Problem

65 Maxwell Electromagnetc Equatons E ( ω c)h H ( ω c) ε( r)e E Electrcal Feld H Magnetc Feld ω Angular Frequency c Lght Speed ε(r) Delectrc Constant

66 One-Dmensonal Case E ( r) ( E,0,0) H( r) ( 0, H,0) E ( ω c)h E z ω H c H ( ω c) ε( r)e H z ω ε( z) E c E z ω + ε( z) c E 0

67 Boundary Condtons At Boundary B: φ φ φ z φ z C D M A B At Boundary B: φ φ 3 φ z φ z 3 F G M C D

68 Soluton Form - Wave Functons φ kz kz A e + B e A, C, F Incdent Waves Magntude φ kz kz C e + D e B, D, G Reflected Waves Magntude φ 3 kz kz F e + G e k, k Wave Vector n Materals and φ [E,H] E, H Electrcal, Magnetc Felds

69 Wave Vectors After Substtuton of φ and φ nto the Governng Equaton one Obtans: k ε ( ω / c k ε ( ω / c ) )

70 Transfer Matrx Transfer Matrx B A T G F T T T T T T T k - k - k k T ) ) ) ) ) ) ) ) a exp(-k - k a exp(k k a exp(-k a exp(k a exp(-k - k a exp(k k a exp(-k a exp(k T

71 Bloch Theorem φ ( K d ) φ 0 z d z exp F G exp( K A d) B A A T (ω) exp( K d) B B Egevalue Problem

72 Band Structure Calculaton det T( ω) exp( K d) I 0 cos( K d) Func( ω) ω Func [cos( K d)] Func - A Mult-valued Functon

73 Transmsson Coeffcent C trans F A C trans Re al ( T )

74 Band Structure Calculaton 7E+5 6E+5 Radal Frequency, rad/s 5E+5 4E+5 3E+5 E+5 E Normalzed Recprocal Vector

75 Transmsson Spectrum Transmsson Coeffcent Wavelength, nm

76