LIGHT SCATTERING AND ADSORPTION ANOMALIES (Kandinski, 1926) - PowerPoint PPT Presentation

FRACTAL DUST PARTICLES: LIGHT SCATTERING AND ADSORPTION ANOMALIES (Kandinski, 1926) Robert Botet Laboratoire de Physique des Solides - Université Paris-Sud (France) IDMC 2011, Pune

ALMOST-KNOWN KNOWNS ABOUT FRACTAL DUST PARTICLES LIGHT SCATTERING IN VARIOUS DOMAINS OF PHYSICS ( AND POSSIBLE ASTROPHYSICAL APPLICATIONS ) (Kandinski, 1926) Robert Botet Laboratoire de Physique des Solides - Université Paris-Sud (France) IDMC 2011, Pune

WHY IS THE INVERSE SCATTERING PROBLEM SO DIFFICULT? direct problem  scattering is computed solving the Maxwell equations • with the correct limit conditions OUTPUT reciprocal space direct space q incident light INPUT INPUT = scatterer OUTPUT = 4 functions, e.g.: Stokes parameters S i ( q , l ) depend on a number of independent parameters ( q , l , m, distribution of the matter in the scatterer, size-distribution ) IDMC 2011, Pune

THE FREE NUMERICAL PROGRAMS TO DO SO… http://www.t-matrix.de/  300 free numerical codes of electromagnetic scattering by particles or surfaces! IDMC 2011, Pune

WHY IS THE INVERSE SCATTERING PROBLEM SO DIFFICULT? inverse problem  we know the Stokes parameters, what is the • scatterer? INPUT q incident light OUTPUT INPUT = Stokes parameters S i ( q , l ) OUTPUT = scatterer the information is spread over 4 functions of a number of variables and parameters IDMC 2011, Pune

THE FREE NUMERICAL PROGRAMS TO DO SO… NONE though all the information exists in the Stokes parameters functions…. IDMC 2011, Pune

WHY IS THE INVERSE SCATTERING PROBLEM SO DIFFICULT? inverse problem  we know the Stokes parameters, what is the • scatterer? INPUT q incident light OUTPUT • The inverse problem would be simple if we knew where is hidden the value of this or that parameter in the Stokes parameter functions actually, some examples are known but they are rare… IDMC 2011, Pune

EXAMPLE OF AN INVERSE SCATTERING PROBLEM: / ESTIMATE THE FRACTAL DIMENSION / / Inverse problem  we know the intensity scattered by fractal aggregate • of homogeneous grains, what is the value of the fractal dimension ? INPUT q incident light OUTPUT: D f IDMC 2011, Pune

INTERLUDE: WHAT IS A FRACTAL AGGREGATE? IDMC 2011, Pune

REMINDER OF WHAT IS A FRACTAL AGGREGATE • In a diluted cold fluid, grains tend to stick together to form fractal aggregates, following a process called: Cluster-Cluster Aggregation (CCA) N  D c R f • a fractal aggregate is entirely defined (in the statistical sense) by: – its reduced radius of gyration, R g / a – its fractal dimension, D f – Its prefactor, c IDMC 2011, Pune

FRACTAL AGGREGATE GALLERY 0. was it fractal before collection? at least  this is aggregate of grains! Brownlee particle IDMC 2011, Pune

FRACTAL AGGREGATE GALLERY 1. snowflakes ( Maruyama & Fujiyoshi, 2005 ) IDMC 2011, Pune

FRACTAL AGGREGATE GALLERY 2. numerical Au colloidal particles ( Weitz et al, 1985 ) IDMC 2011, Pune

FRACTAL AGGREGATE GALLERY 3. numerical Latex colloidal particles IDMC 2011, Pune

FRACTAL AGGREGATE GALLERY 4. Diesel smoke ( Xiong & Friedlander, 2001 ) laboratory generated meteoric smoke ( Saunders & Plane, 2006 ) IDMC 2011, Pune

THE SAS (SMALL-ANGLE SCATTERING) AS A TOOL TO MEASURE THE FRACTAL DIMENSION OF OPTICAL SOFT PARTICLES q incident light IDMC 2011, Pune

(INTRA) SINGLE- SCATTERING ASSUMPTION… • Scattering quantities for isotropic fractal aggregate of homogeneous grains of radius a under single-scattering assumption , must depend on:  q – the scattering angle single parameter: qa = 2 x sin ( q /2)  x = 2p a /l 5 parameters – the size parameter  R g / a – the shape parameter  D f phase at detector: e i qr – the fractal dimension  c – the prefactor k s q = k i - k s – the complex refractive index  m q k i incident light r = R g I ( q ) c I ( qa , m ) S ( qR , D ) N 1 g f 1-grain scattering structure factor p 4 = q = q q sin( ) / 2 l IDMC 2011, Pune

WHAT ABOUT THE STRUCTURE FACTOR? = I ( q ) c I ( qa , m ) S ( qR , D ) N 1 g f 1-grain scattering structure factor depends only on R g 1  2 = i q r = exp(- q 2 R g 2 /3) when qR g < 1 S e j 2 N j A = when 1 < qR g D   f qR     g scaling with exponent D f p 4 = q = q q sin( ) / 2 l IDMC 2011, Pune

PUTTING ALL TOGETHER (SAS = VERSUS q ) In terms of the quantities q et l , these results write: Rayleigh  (1+cos 2 q ) /l 4 Structure factor  S = total intensity/intensity scattered by a grain S  exp(-c( q R g /l ) 2 ) for the small values of q (Guinier regime)  ( l/ sin ( q /2) ) Df for the intermediate values of q (fractal regime) log [I( q )/(1+cos 2 q )] Guinier fractal  slope: -D f Porod  pente -4 varying the phase angle a= 180- q  q  10 l/ a ° q  10 l/ R g ° IDMC 2011, Pune log sin q/2

PUTTING ALL TOGETHER (SAS = VERSUS q ) most of the intensity goes in the forward direction log [I( q )/(1+cos 2 q )] Guinier fractal  pente -D f Porod  slope: -4 q  10 l/ R g ° q  10 l/ a ° log sin q/2 – Conditions : • |m-1|<<1 (optically soft particles) IDMC 2011, Pune • |2ka(m-1)|<<1 (small grains)

2 PARAMETERS CAN BE MEASURED IN SAS : R g AND D f D f log [I( q )/(1+cos 2 q )] Guinier fractal  slope: -D f R g Porod  slope: -4 q  10 l/ R g ° q  10 l/ a ° log sin q/2 – Conditions : • |m-1|<<1 (optically soft particles) IDMC 2011, Pune • |2ka(m-1)|<<1 (small grains)

PUTTING ALL TOGETHER (VERSUS l ) In terms of the quantities q et l , these results write: Rayleigh  (1+cos 2 q ) /l 4 Structure factor  S = total intensity/intensity scattered by a grain S  exp(-c( q R g /l ) 2 ) for the large values of l  ( l/ sin ( q /2) ) Df for the intemediate values of l log [ l 4 I( l )] Porod fractal  slope: D f - 4 Guinier varying the wavelength l  ultraspectral imaging could be used to have spatial maps of D f l  12 sin( q /2) R g l  12 sin( q /2) a log l IDMC 2011, Pune

CURRENT APPLICATION : SAXS q < 3° Soleil synchroton Guinier regime  exp(- q 2 R g 2 /3) log I( q ) fractal regime  q -Df Porod regime  q -4 q  1/ R g q  1/ a log q IDMC 2011, Pune

CURRENT APPLICATION : SAXS Pt fractal nanoparticles ( Min et al, 2007 ) Guinier regime  exp(- q 2 R g 2 /3) log I( q ) fractal regime  q -Df q  1/ R g q  1/ a log q IDMC 2011, Pune

…BUT WHAT ABOUT MULTIPLE -SCATTERING??? multiple-scattering is irrelevant for D f  2, in the mean-field approximation ( i.e. the em fields are similar inside each grain ) Berry & Percival, 1986 IDMC 2011, Pune

…BUT WHAT ABOUT MULTIPLE -SCATTERING??? multiple-scattering is irrelevant for D f  2, in the mean-field approximation ( i.e. the em fields are similar inside each grain ) Berry is correct! I ( N )/ I (1)  q -Df for D f  2 1/R g << q << 1/a  q -2 for D f > 2 within the mean-field assumption Berry & Percival, 1986 Botet et al, 1995 IDMC 2011, Pune

…BUT WHAT ABOUT MULTIPLE -SCATTERING??? multiple-scattering is irrelevant for D f <2, in the mean-field approximation ( i.e. the em fields are similar inside each grain ) Berry is correct! I ( N )/ I (1)  q -Df for D f  2 1/R g << q << 1/a  q -2 for D f > 2 within the mean-field assumption Berry & Percival, 1986 Botet et al, 1995 the mean-field assumption is valid when the material is far from optical resonance IDMC 2011, Pune Shalaev, 2000

…AND THE CONCLUSION ABOUT MULTIPLE -SCATTERING The fractal relation S( q )  q -Df is robust! It is valid whenever D f  2 and material far from resonance log [I( q )/(1+cos 2 q )] fractal  slope: -D f q  l/2p R g log sin q/2 when D f > 2, we lose the information about the fractal dimension because the light is ‘trapped’ inside loops of particles – Conditions : off-resonance and D f  2 • IDMC 2011, Pune • ka<<1 (small grains)

POSSIBLE APPLICATIONS q zodiacal light (photo: Beletsky) IDMC 2011, Pune

POSSIBLE APPLICATIONS q sungrazer comets (photo: SOHO Consortium) IDMC 2011, Pune

POSSIBLE APPLICATIONS q planetary nebula – infrared image ( photo: NASA's Spitzer Space Telescope) IDMC 2011, Pune

POSSIBLE APPLICATIONS q upper atmospheres in forward diffusion (photos: NASA-JPL) IDMC 2011, Pune

THE POLARIZATION OF FORWARD TRANSMITTED LIGHT AS A TOOL TO MEASURE SIZE OF ALIGNED ABSORBING AGGREGATES transmitted light incident light IDMC 2011, Pune

1) FRACTAL AGGREGATES DISPERSED IN A FIELD • anisotropy of aggregates can appear in 2 different conditions: – 1) fractal aggregates grow in a field-free region, then, are dispersed in a field growth dispersion IDMC 2011, Pune

THE NATURAL THE TURAL ANISO ANISOTR TROPY OPY OF OF DIS DISORDERED ORDERED FRA FRACT CTAL AL AGGREG GGREGATE TES • disordered fractal aggregates are statistically isotropic • but when placed in an oriented field, they can exhibit anisotropy due to irregularity in shape a same N=512 CCA aggregate of fractal dimension 2, with the axis of smallest inertia moment aligned along z • what about the polarization of the light transmitted through a cloud of such aligned aggregates?… IDMC 2011, Pune