January 15, 2016 Fort Washington Chili Cincinnati

Hi Greg,

What I find worthwhile mentioning for sure that the FTIR technique still seems to be used in Pratsinis’ group for determining flame temperatures. This technique was developed and established by Phil.

Hope this helps, Best regards Hendrik

Dr. Hendrik Kammler

TRD Head of Operations and Global TRD CI Network Lead Novartis Pharma AG

Postfach CH-4002 Basel Switzerland

Phone +41 61 324 0591 Mobile +41 79 592 9157

hendrik.kammler@novartis.com www.novartis.com

January 15, 2016 Fort Washington Chili

Cincinnati

Nanoparticle Formation

Solution Route

-Separation

-Surface Tension

(Pore/Particle Collapse) -Solvent Disposal

-Reaction Rate is Slow -Transport is Slow -Batch Process

Aerosol Route

-Particles are Pre-Separated -No Surface Tension Issues -No Solvent Disposal

-Reaction Rate is Fast -Continuous Process

-Rapid Supersaturation & Dilution

Kelvin Laplace

Nano-particles form far from equilibrium.

T ~ 2500°K

Time ~ 100 ms

φ

~ 1 x 10

d

~ 5 to 50 nm

Kammler HK, Beaucage G, Kohls DJ, Agashe N. Ilavsky J J Appl. Phys. 97(2005) (Article 054309).

What is SAXS?

X-ray, λ θ

d = λ/(2 sin θ) = 2π/q

Branched Aggregates

What is SAXS?

Guinier’s Law

X-ray, λ θ

d = λ/(2 sin θ) = 2π/q

What is SAXS?

Guinier and

Porod Scattering

X-ray, λ θ

d = λ/(2 sin θ) = 2π/q

What is SAXS?

Polydispersity

Particle size distributions from small-angle scattering using global scattering functions, Beaucage, Kammler, Pratsinis J. Appl.

Cryst. 37 523-535 (2004).

X-ray, λ θ

d = λ/(2 sin θ) = 2π/q

What is SAXS?

Linear Aggregates

Beaucage G, Small-angle Scattering from Polymeric Mass Fractals of Arbitrary Mass- Fractal Dimension, J. Appl. Cryst. 29 134-146 (1996).

X-ray, λ θ

d = λ/(2 sin θ) = 2π/q

What is SAXS?

Branched Aggregates

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev. E 70 031401 (2004).

X-ray, λ θ

d = λ/(2 sin θ) = 2π/q

5mm LAT 16mm HAB Typical Branched Aggregate

d_p = 5.7 nm z = 350

c = 1.5, d_min = 1.4, d_f = 2.1

_br = 0.8

Branched Aggregates

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev. E 70 031401 (2004).

APS UNICAT

Silica Premixed Flames J. Appl. Phys 97 054309 Feb 2005

* same for all flames!

TiCl

Diffusion Flame Nucleation and Growth

( )

kT E

d d R

z

p f

D -

÷÷ ø ö çç

è æ

~

ln 2

~ ln

Activated growth for z

Titania Diffusion Flame from TiCl₄

Beaucage G, Agashe N, Kohls D, Londono D, Diemer B

Silica Diffusion Flame

Axial Particle Growth follows

Classic Diffusion Limited

Surface Growth, d ~ t

Kammler HK, Beaucage G, Kohls DJ, Agashe N. Ilavsky J J Appl. Phys. 97(2005) (Article 054309).

Summary:

1) SAXS as a tool for in situ observation of structure 2) Homogeneous nucleation

appears to be a common feature of flame growth.

3) A wide range of particle growth mechanisms can be involved

4) Branching can be monitored in terms of the mass fractal dimension but

5) A much richer description of

aggregate growth is give by

inclusion of new model for

branched structure.

Number Density and Primary Particle Size versus Height Above the Burner

Silica Premixed Flame

(Data agree with Choi Cho Lee and Kim 1999 Fig. 9.)

. . Nucleation, Issues:

“Chemical” Nucleation Homogeneous Nucleation Gibbs-Thompson (Kelvin)

 

r = 2gv RTln p pæ _s

è ö

ø

r is the critical size for stability. For high-T & low p_s (solid) in a typical flame r < 0.1 nm

Chemical reaction leads directly to solid particles of molecular scale that grow by coalescence continuously from about

r ~ 0.5 nm No Spontaneous Nucleation Event

. .

. . . .

Silica Volume Fraction (Conversion)

Height Above Burner Homogeneous

Nucleation

Surface Nucleation

Higher = Smaller

Narrower = Lower Polydispersity

_c

(_c )_surface

Girshick/Giesen Model May Explain This Behavior

In Flames and Other Aerosols

Growth

 

r ~ t

 

r ~ t

Axial Particle Size

and Growth for Titania Diffusion Flame

 

r = 2gv RTln p pæ _s

è ö

ø

Gibbs- Thompson

(Kelvin)

d_p ~ t Reaction limited growth.

Aggregation

Mass Fractal dimension,

d

, and degree of aggregation, z.

Nano-titania from Spray Flame df

d

z R ÷ ÷ ø ö ç ç

è

= a æ 2

Problem: Disk d

= 2; Gaussian Walk d

=2;

Random aggregation (right) d

~ 1.8;

Randomly Branched Gaussian d

~ 2.5;

Self-Avoiding Walk d

= 5/3

T_c

1.8 ms 1.25 ms

0.55 ms Zirconia Spray Flame

Fractal dimensions: d

, d

, c, the degree of

aggregation (z), and the molar branch fraction, 

-F F

-F F

R d

df

d

z R ÷ ÷ ø ö ç ç

è

~ æ

min

min

~

d

d

z R

p ÷ ÷

ø ö ç ç

è

= æ

~ p

p

z =

d

should effect perturbations & dynamics.

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev. E 70 031401 (2004).

Six Arm Polyurethane Star Polymers

Kulkarni A, Beaucage G using Data of Jeng, Lin et al App. Phys. A (2002)

5mm LAT 16mm HAB Typical Branched Aggregate

d_p = 5.7 nm z = 350

c = 1.5, d_min = 1.4, d_f = 2.1

_br = 0.8

Branched Aggregates

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev. E 70 031401 (2004).

APS UNICAT

Silica Premixed Flames J. Appl. Phys 97 054309 Feb 2005

Signatures of Possible Mechanisms for Structural Change

Premixed Silica Flame,

Hexamethyldisiloxane precursor

5mm LAT 16mm HAB

Typical Branched Aggregate d_v/s = 9.5 nm, z = 223, c = 1.10, d_min = 2.07, d_f = 2.28 _br = 0.38

Premixed Silica Flame

5 mm lateral 16 mm lateral

Silica Premixed Flame

Primary Particle Growth and Entrainment

Complicate the Situation

Surface Nucleation Homogeneous Nucleation

 

G = DHr³ + 6

g

 

G = DHr³ + 4

g

High particle density can be accommodated

by:

Structure Depends on Temperature & Concentration

T em pe ra tu re , C on ce nt ra ti on , N um be r

Height Above Burner Nucleation

Coalescence

Surface Nucleation

Aggregation Agglomeration (Hard)

(Soft)

1) coalescence and sintering 2) aggregation hard agglom.

3) agglomeration

soft agglom.

Particle Size Distribution Curves From SAXS:

(Persistence effects not observed) Unified Method

i) Global fit for B

and G.

ii) Calculate PDI (no assumptions &

unique “solution”)

iii) Assume log-normal distribution for 

and distribution curve (or other models)

iv) Data to unique solution Solution to distribution

Advantages

Generic PDI (asymmetry also) Global fit (mass fractal etc.) Direct link (data => dispersion) Use only available terms

Simple to implement

G R PDI B

62 . 1

4

=

( ) ^{( )}

12

ln ln úûù

êëé

=

= PDI





2 1 14

2

3

5

ú ú û ù ê ê

ë

= é

e

m R

Particle size distributions from small-angle scattering using global scattering functions, Beaucage, Kammler, Pratsinis J. Appl. Cryst.

37 523-535 (2004).

Particle Size Distribution Curves from SAXS

PDI/Maximum Entropy/TEM Counting

Outline:

1) Fractal dimensions and degree of aggregation 2) Persistence length and substructural scaling

3) Minimum number of features 4) Small-angle scattering for branched structures

5) Ceramic aggregates

6) Polymer chains in dilute conditions 7) Networks

8) Unfolded proteins 9) Summary

http://www.eng.uc.edu/~gbeaucag/Classes/IntrotoPolySci/PicturesDNA.html

Chain persistence

PHB = polyhydroxybutyrate (side chain = -CH3) PHV = polyhydroxyvalerate (side chain = -CH2CH3) These are short chain branching similar to branching in polyolefins

Persistence length of isotactic poly(hydroxyl butyrate) Beaucage G, Rane S, Sukumaran S, Satkowski MM, Schechtman LA, Doi Y Macromolecules 30 4158-4162 (1997).

Rheology and persistenc in polyhydroxy alkonates. Ramachrichnan R, Beaucage G, Satkowski M, Melik D in preparation J. Rheology.

Persistence length of isotactic poly(hydroxyl butyrate) Beaucage G, Rane S, Sukumaran S, Satkowski MM, Schechtman LA, Doi Y Macromolecules 30 4158-4162 (1997).

Rheology and persistenc in polyhydroxy alkonates. Ramachrichnan R, Beaucage G, Satkowski M, Melik D in preparation J. Rheology.

Chain persistence

Intrinsic and Topological Stiffness in branched polymers. Connolly R, Bellesia G, Timoshenko EG, Kuznetsov YA, Elli S, Ganazzoli G Macromolecules 38 5288-5299 (2005).

N = Length of Side Chain

S = Number of Flexible Spacers Longer Side Chain Causes

Stiffer Chain

(no helical structure)

Chain persistence

Determination of d

, c and d

.

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev. E 70 031401 (2004).

( )q B_fq^df

I = ^-

( ) _÷^÷

ø ö çç

è

= æ - exp 3

2 2

Rg

G q q I

There appears to be a quantifiable difference in scattering for different d_min and

the same d_f.

Determination of d

, c and d

.

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev. E 70 031401 (2004).

( )q B_fq^df

I = ^-

( ) _÷^÷

ø ö çç

è

= æ - exp 3

2 2

Rg

G q q

I

Gaussian

Chain 2 1 2 Disk 2 2 1

Static scattering can be used to obtain d_min.

Branched polystyrene in a good solvent

d

should be 5/3 (1.67) for self-avoiding walk

M_w/M_n ~ 2 Good Solvent Scaling for c = 1 and c > 1

Hyperbranched polyesteramides

Sample R_g,2 d_f d_min c Description M_n* M_w*

1 17.2 (15.5) 1.3 1 1.3 Regular 1.5 3.6

2 22.2 (21.6) 1.64 1.67 1 Linear 1.8 5.9 3 26.8 (30.5) 1.60 (1.63) 1.09 1.47 Close to Regular 2.4 11.0 4 57.5 1.74 (1.68) 1.59 1.09 Close to Linear 2.4 59.0 5 288.3 1.63 (1.63) 1.34 1.21 Branched 2.8 248

One pot synthesis semi-random Dendrimers

For samples 3 & 4 polydispersity is apparent due to linear

vs branched chains.

Linear is local persistent branching Regular is global structural branching

*M_n & M_w in kg/mole

Molecular Structure Characterization of Hyperbranched Polyesteramides ETF Gelade, B Goderis, K. Mortensen et al. Macromolecules 34 3552-58 (2001)

Outline:

1) Fractal dimensions and degree of aggregation 2) Persistence length and substructural scaling

3) Minimum number of features 4) Small-angle scattering for branched structures

5) Ceramic aggregates

6) Polymer chains in dilute conditions 7) Networks

8) Unfolded proteins 9) Summary

http://www.eng.uc.edu/~gbeaucag/Classes/IntrotoPolySci/PicturesDNA.html

8) Unfolded proteins

Is the molten golbule a third phase of proteins? VS Pande & DS Rohksar, PNAS 95 1490-94 (1998)

Simulation Results, g is denaturant

-Unfolded state is analogous to gas state (following Flory random walk model as applied by Pande) -Dense states not associated with biological activity could be analogous to glassy state (molten globule) -0 conformational entropy native state is analogous to crystalline state

-Unfolded state contains some:

Chain persistence associated with fluctuating helicies and -sheets

Crosslink/disulfide/cystine-cystine bonds that act as branching sites

hydrophobic interactins that may appear to be branching sites

-Conformational transitions should show increase in d_f and c towards a regular 3d structure

8) Unfolded proteins

“a Gaussian-like conformation”

Mapping the cytochrome C folding landscape

Julia G. Lyubovitsky

Caltech 2003 Biochemistry

R_g d_f d_min c

125Å 2.05 1.07 1.90

This is almost a regular structure with dimension 2:

A crumpled sheet!!

R_g PDI 94.0Å 1.08

This is and almost sperical domain of

24.3 nm diameter.

Deviation from PDI = 1 can be due to polydispersity or asymmetry.

Cytochrome C Native State

Space Filling Model

R_g PDI Native 94.0 Å 1.08

MG 99.0 Å 2.90

(Both also

Show Aggregates at Low-q)

Model of cytochrome b562 A) MG B) N

Cytochrome C

Molten Globule State

Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD. Chapter 5: Protein Function. Molecular Biology of the Cell 3rd Ed. Garland Publishing, New York. 1994. pg 213 & 215.

Summary:

-Two classes of branching effects:

persistence and scaling

-Statistical understanding of scaling can distinguish regular and fractal structures statically

-Examples from aggregated ceramics, branched polymers, and proteins.

-The proposed method would seem to have broad applicability

Swiss National Science Foundation, US NSF, Swiss Commission for Technology and Innovation

Polydispersity in aggregate size

( )q B_fq^df

I = ^-

( ) _÷^÷

ø ö çç

è

= æ - exp 3

2 2

Rg

G q q I

M

/M

~ 3

Large aggregates

Growth kinetics show d

=> 1

d

=> 1.8 for RLCA

Predicted previously

by Meakin

Monodisperse Fractal Aggregates M_w/M_n = 1

Constant Growth Conditions z = 8, 30, 100

d_min is constant, 1.15

Similar to Branched Polymers d_f increases

c increases

Construction of A Scattering Curve

I() is related to amount Nn²

 is related to size/distances

( )

q d 2

sin 2 4

p l 

p

=

= q

We can “Build” a Scattering Pattern from Structural

Components using Some Simple Scattering Laws



q = 2 d p ^{I ( q ) = N ( d ) n}

( ) ^d

n_e = Number of Electrons in “d” Particles Complex Scattering Pattern (Unified Calculation)

Particle with No Interface

( ) ^d

n d N q

I ( ) = ( )

÷ ÷ ø ö ç ç

è

= æ -

exp 3 )

(

2 1 , 2

1

R

G q q

I

6 2

2

V ~ R

N G = r

6 8 2

R

~ R R

Guinier’s Law

Spherical Particle With Interface (Porod)

Guinier and Porod Scattering

)

( q = B q

I

S N

B

= 2 p r

~ R

S

3 2

2

I ( q ) dq N R

q

Q = ò = r

2 3

2 R

R B

d Q

P

p

= =

p

Structure of Flame Made Silica Nanoparticles By Ultra-Small-Angle X-ray Scattering

Kammler/Beaucage Langmuir 2004 20 1915-1921

Polydisperse Particles

Polydispersity Index, PDI

G R PDI B

62 . 1

4

=

( ) ^{( )}

12 ln ln

úûù êëé

=

= PDI





2 1 14

2

3

5

ú ú û ù ê ê

ë

= é

e m R

Particle size distributions from small-angle scattering using global scattering functions, Beaucage, Kammler, Pratsinis J. Appl. Cryst. 37 523-535 (2004).

Linear Aggregates

Beaucage G, Small-angle Scattering from Polymeric Mass Fractals of Arbitrary Mass-Fractal Dimension, J. Appl. Cryst. 29 134-146 (1996).

÷ ÷ ø ö ç ç

è

= æ -

exp 3 )

(

2 2 , 2

2

R

G q q

I

df

R R G

z G ÷÷ ø çç ö

è

= æ

=

1 2 1

2

df

f

q B q

I ( ) =

( ) ²

2 , 2

d f g

f

f

d

R d B G

f

G

=

( ) ²

2 ,

min

2 d f

g

f

d

R d B G

f

G

= Branched Aggregates

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev.

E 70 031401 (2004).

c d

R z

p R

1 2

min

÷÷ = ø çç ö

è

= æ

df

d

Br

R

R

÷÷ ø çç ö

è - æ

=

min

1

1



d

c = d

Large Scale (low-q) Agglomerates

)

( q = B q

I

Small-scale Crystallographic Structure

2) Persistence length and substructural scaling

New Idea:

Long-chain branching

Effects chain scaling (d_f, d_min, c) Short-chain branching

Effects chain persistence (l_p and chain entropy, G)

(dendrimers may be an interesting case in this regard)

Old Idea:

Long-range interaction Effects chain scaling (SAW d_f = 5/3)

Short-range interaction Effects chain persistence (l_p and chain entropy, G) Flory RISM, C_

Intrinsic and Topological Stiffness in branched polymers. Connolly R, Bellesia G, Timoshenko EG, Kuznetsov YA, Elli S, Ganazzoli G Macromolecules 38 5288-5299 (2005).

Outline:

1) Fractal dimensions and degree of aggregation 2) Persistence length and substructural scaling

3) Minimum number of features 4) Small-angle scattering for branched structures

5) Growth kinetics

for ceramic aggregates 6) Summary

Kammler HK, Beaucage G, Kohls DJ, Agashe N. Ilavsky J J Appl. Phys. 97(2005) (Article 054309).

3) Minimum number of features

http://www.cs.ucl.ac.uk/staff/D.Jones/t42morph.html

a) <Persistence length>: l_p or d_p b) <z>

c) d_f mass scaling dimension d) d_min mass scaling for

minimum path, p

e) In some cases you may want the number of branches or the coordination number

With these features you can calculate:

branch fraction, _br connectivity, c

regularity of the structure (“disk/rod/sphere” -ness) & compare with simulations

Statistically, there are 2 distinct classes of consequences from branching:

chain persistence and structural scaling

Some Complexities of Fractal Growth

Fractal aggregates are springs

Ogawa K, Vogt T., Ullmann M, Johnson S, Friedlander SK, Elastic properties of nanoparticulate chain aggregates of TiO₂, Al₂O₃ and Fe₂O₃ generated by laser ablation, J. Appl. Phys. 87, 63-73 (2000).

Fractal aggregates can behave at times as semi-dilute polymers.

Overlap Concentration Tensile Blob

Low Elongation

df

d

BB

E

G

+

=

3 _min



High Elongation

E l

 =

Witten TA, Rubinstein M, Colby RH,

Reinforcement of rubber by fractal aggregates J. Phys. II France 3 367-383 (1993).

Kohls DJ Beaucage G, Rational design of reinforced rubber Cur. Op. Sol. St. Mat. Sci. 6 183-194 (2002).

d_f<2d_min d_f>2d_min weakly

branched strongly branched

-(d_min+d_f+1) (d_min+1)/(d_min-1)

2(d_f-1)/(d_min-d_f+2) -(3d_min+1)/(2d_min-d_f+1)

d_f=1.7-1.8 d_min=1.2-1.3

d_f=2.0-2.1 d_min=1.0-1.1

Polymers vs. Ceramic Aggregates Thermo. Equil. vs. Kinetic Growth

For Polymers d_min is the

Thermodynamically Relevant Dimension (5/3 = 1.67 or 2)

Branch fraction can be defined in this context

Hyperbranched Polymers Closer to Ceramic Aggregates

Kulkarni A, Beaucage G using data from:

Geladé ETF et al. (Mortensen), Macromolecules 34, 3552 (2001).

Data from:

E. De Luca, R. W. Richards, I. Grillo, and S. M. King, J. Polym. Sci.: Part B: Polym. Phys. 41, 1352 (2003).

Comparing simulated growth mechanisms for ceramic aggregates, minimum path, d

, is the most important structural feature.

Minimum path becomes more convoluted

Chains more branched

Branched Structures

http://www.eng.uc.edu/~gbeaucag/Classes/Properties.html

http://www.eng.uc.edu/~gbeaucag/Classes/MorphologyofComplexMaterials/Overview.html

-Non-space filling

Density is a function of size -Often display fractal scaling Fractal statics, d_f

Fractal dyamnics, d_min

-Often display a large-scale limit -Always display a small-scale limit -Substructure can also display fractal structure, that is

scaling transitions are possible -What is the minimum number of features needed to describe a branched structure? (This may depend on what you want.)

-2

( )

, min

2 ^f

f

d d

g

f

R

d

B = G G

Topological information can be extracted from this feature arising from combined Local Scattering Laws

( )

÷ ÷ ø ö ç ç

è

= æ -

exp 3 )

(

2

R

G q q

I

Guinier’s Law

f

q B

q

I ( ) =

Power Law

G Beaucage, Physical Review E (2004)

A S Kulkarni and G Beaucage, Journal of Polymer Science, Part B: Polymer Physics (2006)

( ) ²

2

2 , min

f d g f

d G

R d B

f

= G

Branch content from scattering

df

c

R z R

p ÷÷

ø çç ö

è æ

1

~

~

1 2

G z = G

d

c = d

R R z

p

z

÷÷ ø çç ö

è - æ - =

=

min

1

1



R₂

R₁

d_min p

G Beaucage, Physical Review E (2004)

A S Kulkarni and G Beaucage, Journal of Polymer Science, Part B: Polymer Physics (2006)

Figure 11. Schematic of particle nucleation and growth from in situ data analysis.

-Smallest Particle is not

Molecular Scale Predicted by Chemical Nucleation -Homogeneous Nucleation is Observed in Peak in N and Minimum in d

(~ 1/T)

-Hydrolysis/Condensation Mechanism is Supported -These Low T Flames may differ Significantly from High T Flames

SAXS Summary TiCl

Flame

Possible explanations for observations

Girshick Model (Giesen) matches data (except in SIZE)

On the interaction of coagulation and coalescence during gas-phase synthesis of Fe-nanoparticle agglomerates Giesen, Othner, Roth (Duisburg-Essen) Chem. Eng. Sci.

59 2201-2211 (2004) & Iron-atom condensation interpreted by a kinetic model and a nucleation model approach Giesen Kowalik Roth Phase Trans. 77 115-129 (2004)

Giesen & Roth