Modelling Data Better Approaches How to get useful information? - PowerPoint PPT Presentation

Modelling Data – Better Approaches How to get useful information? Adrian R. Rennie

Monolayers – Simple Interpretation Define g s (Q z ) in terms of measured 2.0E-07 reflectivity and R F (Q z ) (the Fresnel 8 Å 15 Å reflectivity for perfectly sharp 20 Å interface): 30 Å 60 Å -2 g s (Q) / Å g s ( Q ) = Q 2 (R − R F ) / (1 − R) 1.0E-07 ln g s ( Q ) ≈ – t 2 Q 2 /12 Roughly ln ( Q 2 R) ≈ – t 2 Q 2 /12 0.0E+00 0.00 0.01 0.02 0.03 0.04 0.05 Contrast match of two bulk phases 2 / Å -1 Q R F (Q) = 0

Real Interfaces are not just layers Slab models are easy to calculate but people are not very interested in just thickness and scattering length density Neutron beam Top Solid Roughness 1 Top 1 2 2 3 3 4 4 5 6 F reg 2 7 8 F reg 1 Sub Liquid

Surface Excess and Area per Molecule Volume per molecule: V m Neutrons Scattering length: b m Scattering length density:  T  = b m / V m  a t   l Thickness of layer: t  S  A m Scattering length density Area per molecule: A m V m = t A m Scattering length density:  = (b m / V m ) = b m /( t A m ) t  Area per molecule: A m = b m l

Adsorption of Surfactant Surface active molecules Amphiphilic Bind to surface – how? What are properties? Hexadecyl trimethyl ammonium bromide Tail Head C 16 H 33 N(CH 3 ) 3+ Br -

Some Possible Structures • Monolayer • Bilayer

Cationic Surfactant CTAB at 27° C on amorphous SiO 2 (a) D 2 O (b) cmSiO 2 at 6 ×10 -4 M Models Solid line – Bilayer Dashed line - Monolayer

Cationic Surfactant • CTAB 27 C on SiO 2 • Label heads & tails Head 6 +/- 2 Å Tail 28 +/- 4 Å Roughness ~ 8 Å Fractional Coverage 35% at 3 ×10 -4 M Langmuir 6 , 1031-1034 (1990). 80% at 6 ×10 -4 M J. Colloid Interf. Sci. 162 , 304-310 (1994).

Plotting Data 1.0E-02 Lipid DSPC Reflectivity 1.0E-03 Background Different representation is helpful 1.0E-04 1.0E-05 1.0E-06 0.0 0.1 0.2 0.3 Q / Å -1 Lipid DSPC - Bgd subtracted 1.0E-02 5.0E-08 Lipid DSPC - Bgd subtracted Reflectivity 1.0E-03 3.0E-08 RQ 4 1.0E-04 1.0E-08 1.0E-05 1.0E-06 -1.0E-08 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 Q / Å -1 Q / Å -1

How to Look at Data? Log 10 R vs Q RQ 4 vs Q

Effects of Resolution 0 1% 3%  Q/Q -1 5% 7% log 10 R -2 -3 -4 0.00 0.05 0.10 Q / Å -1 Silicon substrate: film thickness 1500 Å scattering length density 6.3 × 10 −6 Å -2

Non-Uniform Surfaces If you have patches of different layers at an interface do you average the density or average the reflectivity? Neutron beam Top Solid Roughness 1 Top 1 2 2 3 3 4 4 5 6 F reg 2 7 8 F reg 1 Sub Liquid What is the coherence length of a neutron?

Describing Polymers • Interdiffusion – is this roughness? • Brushes – parabolic density profile (E. P. K. Currie et al Physica B, 283 17 – 21) • Other scaling laws e.g. O. Guiselin J. Phys. 50 , 3407-3425 (1989). We expect smooth profiles!

Thermoresponsive polymer brush J. Zhang, et al., Soft Matter , 4, 500–509 (2008).

Repeating Layers A one dimensional Neutron beam crystal Solid Top Roughness Top 1 1 2 Bragg’s law 2 3 3 4 4 Bilayer Intensity of peaks may N repeats Depend on size and Liquid disorder Sub

Calculate reflectivity for a profile

Using Multiple Contrasts Simultaneous fits for multiple data sets

Off-specular Scattering, GISANS, Near- surface SANS Adrian R. Rennie

Interfaces are 3-dimensional Understanding rheology – shear flow Brown et al. Progress in Colloid and Polymer Science 98 , (1995) 99-102.

Fate of a Neutron at an Interface • Reflected • Scattered/Diffracted from surface Neutrons Neutrons Neutrons Neutrons Neutrons Neutrons • Absorbed • Scattered from bulk (either side of surface) • Other accidents

Evanescent Wave  c neutrons Below k c no travelling wave 0 enters the sample -500 Amplitude decays with depth in sample z / Å -1000 Decay length depends on (  c  ) - -1500 Evanescent wave can cause scattering -2000 -1 -0.5 0 0.5 1

Looking at Materials Anneli Salo - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=6746303

Looking at Materials Anneli Salo - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=6746303

Off-specular & Reflection Q z ≈ (2π/λ) (θ i + θ f ) Q x ≈ (2π/λ) (θ i + θ f ) (θ i - θ f ) ( 2012) , Frédéric Ott, Sergey Kozhevnikov ‘Off-specular data representations in neutron reflectivity’, J. Appl. Cryst. 44, (2011), 359-369.

Scattering from Surface Structures Peter Müller-Buschbaum ‘GISAXS and GISANS as metrology technique for understanding the 3D morphology of block copolymer thin films’ European Polymer Journal 81 , (2016), 470-493.

Strong Off-specular Scattering 96083 1.6 -2 1.4 1.5 1.5 1.2 -2.5 1 1.0 1.0 0.8 -3  f / degrees  (deg) 0.6 -3.5 0.4 0.5 0.5 0.2 -4 0 0.0 0.0 -0.2 -4.5 1 2 3 4 5 6 0 2 4 6  (Ang.)  / Å PS latex in D 2 O Liquid/Sapphire 10% vol. dispersion, Radius ~350 Å. Sapphire substrate,  i = 0.35 deg

PS latex in D 2 O Liquid/Sapphire 10 10 Transform to 5 Q x / 10 -5 Å -1 map of Q z Q x 5 0 0 -5 -5 0.01 0.02 0.03 0.04 Q z / Å -1 10% vol. dispersion, Radius ~350 Å, sapphire substrate,  i = 0.35 deg

Some Scattering at Interfaces X-ray scattering – glass Sinha et al., Phys. Rev. 38 , 2297, 1988 . B.

Incoherent background 80 70 Scattering from D 2 O 60 Average Counts 50 and from null reflecting water 40 30 20 (8% D 2 O) 10 0 -1 0 1 2 3 4 Rennie et al., Macromolecules 22 , (1989), 3466-3475. Angle,  / degrees

Interfacial structure: GISANS Nouhi et al. Journal of Applied Crystallography (2017)

Calculating Scattering Reflect and Scatter Distorted Wave Born Approximation (DWBA) Reflect only Simply allow for sequential events e.g. Reflection followed by weak scattering. Reflection then Scattering (a) Optical Matrix Calculation Refraction then Scattering (b) Weak Scattering (Born Scattering then Reflection approximation)

How deep is the evanescent wave? 2000 2000 Evanescent Wave Depth / Å Evanescent Wave Depth / Å 1500 0.37 degs 16 Å 1500 0.62 degs 14 Å 12 Å 1000 1000 10 Å 8 Å 6 Å 500 500 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 Incident Angle / degrees Wavelength / Å Silicon/D 2 O Interface

Copolymer films P. Müller Buschbaum et al. J. Appl. Cryst . 47 , (2014), 1228–1237

Changes with Depth Horizontal cuts • Used wavelength to probe different depths • Longer wavelength looks neare the surface J. Appl. Cryst . 47 , (2014), 1228–1237

Diffraction from Surface Layers Nouhi et al. Journal of Applied Crystallography (2017)

Penetration depth A depth sensitive technique: Wavelength Incident angle

Data at different angles

Data at different angles <z 1/e > z 1/e

Calculations & Intensity Data D22 - ILL QCM-D data: structure forms with a separation from the interface [Hellsing et al. 2017, manuscript ] NG3 SANS - NCNR

Scattering at Interfaces • Off-specular scattering • Near Surface SANS • GISANS What is the difference?

PS latex in D 2 O Liquid/Sapphire 10 10 Transform to 5 Q x / 10 -5 Å -1 map of Q z Q x 5 0 0 -5 -5 0.01 0.02 0.03 0.04 Q z / Å -1 10% vol. dispersion, Radius ~350 Å, sapphire substrate,  i = 0.35 deg

PS latex in D 2 O – sapphire surface 1 Sum along Q x 0.1 R(Q) 0.01 0.001 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Q / Å -1 10% vol dispersion, 0.35

PS latex in D 2 O – sapphire surface 0.04 y = 0.002820x - 0.000360 Assign Bragg 0.03 peaks (index) Qpeak / Å -1 0.02 Q 1 = 0.00282 Å -1 0.01 d = 2230 Å 0.00 0 2 4 6 8 10 12 14 3 first peaks Order of Peak outside range 10% vol dispersion, 0.35, 0.8 and1.5 deg

PS latex in D 2 O – sapphire surface 0.7 Sum along Q x 0.6 0.5 0.4 R(Q) 0.3 0.2 0.1 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Q / Å -1 10% vol dispersion, 0.35

Compare Qx and Qz M. S. Hellsing, et al. Applied Physics Letters , 100 , (2012), 221601.