6/12/2012

1

SANS BASICS

Boualem Hammouda

National Institute of Standards and Technology Center for Neutron Research

hammouda@nist.gov

OUTLINE• 1. The SANS Technique

• 2. SANS Data AnalysisStandard Plots (Guinier, Porod)SANS ModelsInverse Fourier TransformShape Reconstruction Method

• 3. SANS Research TopicsA- Phase Transitions in Pluronic P85 SolutionsB- Role of Chirality in Peptide BiogelsC- Structure of SDS Micelles

• 4. Final PointsVSANS and USANSFinal Words

6/12/2012

2

1 – The SANS Technique

The NIST Center For Neutron Research

6/12/2012

3

Incident Beam

Area Detector

Scattered BeamSample Q

SourceAperture

SampleAperture

MonochromaticNeutron Beam

Monochromation Collimation Scattering Detection

2

sin4

Qneutron 

wavelength

scattering angle

Small-Angle Neutron Scattering

Nanoscale Structures

0.010.001 0.1 1

Scattering Variable Q (Å-1)

Length Scale (Å)

1001000 10

10-410-5

104105106

Polymers

ComplexFluids

Biology

SANSUSANS

6/12/2012

4

d

d

d

)Q(d)Q(I incohcoh

COHERENT INCOHERENT

- Q-independent- no info. about structure

~ Contrast factor = (A‐B)2- Info. about structure

Scattering length density:volume

length scattering

v

b

A

AA

SANS Cross Sections

Zero contrast

Multiple contrasts Contrast match

Finite contrast

The Contrast Match Method

6/12/2012

5

2 –SANS Data Analysis

• Standard Plots (Guinier Plot, Porod Plot)

• SANS Models

• Inverse Fourier Transform

• Shape Reconstruction Method

SANS Data Analysis

6/12/2012

6

0.0001

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1

Cylinder with Rg2

= 100 Å and Rg1

= 10 Å

Fo

rm F

act

or

P(Q

)

Scattering Variable Q (Å-1)

1/Q1

1/Q4

1/Q0 Low-Q Guinier Region

Intermediate-Q Guinier Region

Porod Region

Guinier-Porod Regions Guinier Plots

2

R

12

LRg

yields slope22

22

-1

-0.8

-0.6

-0.4

-0.2

0

0 0.0001 0.0002 0.0003 0.0004

Ln

[P(Q

)]

Q2

2

RRg

yields slope2

21

-7

-6.5

-6

-5.5

-5

-4.5

0 0.01 0.02 0.03 0.04

Ln

[Q*P

(Q)]

Q2

SANS Models

cross section

volume fraction

contrastfactor

Macromolecules Particles

Structure FactorSI(Q)

Form FactorP(Q)

Structure FactorSI(Q)

Form FactorP(Q)

form factor

structure factor

Random Phase Approximation Ornstein Zernike

particle volume

)Q(S )Q(PVd

)Q(dIA

2BAA

6/12/2012

7

U(r)

r

Hard Sphere

Screened Coulomb

Square Well

Particle Structure Factor –The Ornstein-Zernike Equation

)Q(S )Q(PVd

)Q(dIA

2BAA

Form FactorP(Q)

StructureFactorSI(Q)

10-5

0.0001

0.001

0.01

0.1

1

10

0.1 1 10

Percus-Yevick Model for Sphere

Form Factor P(Q) Struct. Fact. S

I(Q)

P(Q)*SI(Q)

Fo

rm F

acto

r an

d S

tru

ctu

re F

acto

r

QR

Fourier Transform

)r(PQr

)Qrsin(r4dr

V

1)r(P ]r.Qiexp[rd)Q(P 2

0P

3

3

R

r

16

1

R

r

4

31)r(P

r

r’

R

Fourier transform:

Radial pair correlation function:

Density-density correlation function:

)]r'r.(Qiexp[n

)'r(n)r(n'rdrd

n

)Q(n)Q(n)Q(P

22

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

Sphere

P(r)

(r/R)2*P(r)

Pai

r C

orr

ela

tio

n F

un

ctio

n

r/R

6/12/2012

8

A- Phase Transitions in Pluronic P85 Solutions

B- Role of Chirality in Peptide Biogels

C- Structure of SDS Micelles

3. SANS Research Topics

A - Phase Transitions in Pluronic P85 Solutions

6/12/2012

9

Dissolved Unimer(low temperature)

Formed Micelle(high temperature)

PEO

PEO

PPO

hydrophobic

hydrophilic

PEO PPO

PEO

P85: EO26PO40EO26

Pluronics

EO:-CH2CH2-O-

PO:-CH(CH3)CH2-O-

0.1

1

10

100

0.01 0.1

0.5 % P85 in d-Water

100 oC

90 oC

70 oC

50 oC

10 oC

Sca

tter

ing

Inte

nsi

ty (

cm-1

)

Scattering Variable Q (Å-1)

1/Q4

1/Q1

1/Q2

1/Q0

unimers

sphericalmicelles

cylindricalmicelles

lamellarmicelles

1/Q5/3

Pluronic Micelles

lamellarmicelles

cylindricalmicelles

sphericalmicelles

unimers

6/12/2012

10

0

20

40

60

80

100

120

140

0 0.05 0.1 0.15 0.2 0.25 0.3

P85/d-Water

demixed lamellae formation linecylindrical-to-lamellar micellesspherical-to-cylindrical micellesunimers-to-spherical micelles

Tem

per

atu

re (

oC

) P85 Fraction

unimers

spherical micelles

cylindrical micelles

lamellar micelles demixed lamellae

paracrystallinespherical micelles

paracrystallinecylindrical micelles

Phase Diagram

0.1

1

10

100

1000

20 30 40 50 60 70 80 90 100

0.5 % P85/d-Water

Gu

inie

r F

acto

r

Temperature (oC)

26 oC 62 oC 82 oC

sphericalmicelles

cylindricalmicelles

lamellarmicelles

Core-Shell Spherical Particles Model

core region A

shell region Bsolvent region C

10% P85 Pluronic/D2O, 40 oC

RA=43.9 Å

RB=72.0 Å

C = 6.4*10-6 Å-2

B = 5.9*10-6 Å-2

A = 1.7*10-6 Å-2

Fits yield

)Q(SQR

)QR(j3V

QR

)QR(j3V

V

N

d

)Q(dI

2

B

B1BACB

A

A1ABA

6/12/2012

11

Core-Shell Spherical Particles

3A

AODEOPOagA

R3

4

]y.f.b52f.b.52b40[N2

)RR3

4

]y).f1.(b.52)f1.(b.52[N

3A

3B

BODEOagB

2

AODEOPOag3

A y.v.f.52v.f.52v.40.NR3

42

BODEOag3

AB y.v).f1.(52v).f1.(52.N)RR(3

42

In the core:2,795 PPO monomers690 PEO monomers490 D2O molecules

In the shell:2,943 PEO monomers34,167 D2O molecules

Material Balance Equations: Results for 10% P85 at 40 oC:

B- Role of Chirality in Peptide Biogels

6/12/2012

12

Faraday Rotation

Substances rotate linearly polarized light to the left (L-type) or to the right (D-type)

- A molecule is chiral if it is different from its mirror image

- Human hands are chiral

- Non-biological substances are heterochiral . They can be of the L-type or D-type

- Biological substances are homochiral. They are either of the L-type or of the D-type

- Proteins are of the L-type. Sugars are of the D-type. DNA is of the D-type. The reason is still a mystery

Chirality

Right handedLeft handed

6/12/2012

13

- Proteins are responsible for most biological function. They are made out of peptides. Peptides are made out of amino acids. There are 20 amino acids.

- Examples of amino acids include Lysine (K), Glutamate (E), Tryptophan (W) and Alanine (A)

- Most proteins rotate polarized light to the left. They are left handed or L-type

Proteins

DNA- DNA is the blueprint for life. It is the template for the synthesis of proteins

- DNA is made out of nucleotides. There are 4 DNA nucleotides: A, C, T and G

- The human genone contains 6 billion nucleotides making up some 23,000 genes

- Most DNA rotate polarized light to the right. They are right handed or D-type

- Peptides can be synthesized to be L-type or D-type

- Series of L-type and D-type short peptide sequences (11 amino acids) were synthesized.

- These were combined to give L-D- or D-L- heterochiral mixtures and L-L- or D-D- homochiral mixtures

- The resulting gels were investigated using mechanical testing (shear response) and SANS measurements

Peptide Biogels

6/12/2012

14

Mechanical Testing

- Heterochiral samples gel faster. Homochiral samples are slow to gel.

- Homochiral gels are initially weaker then become stronger

0 10 20 30 40 50100

101

102

103

104

105

Ela

stic

Modulu

s, P

a

Time, hrs

heterochiral

homochiral

SANS Data

Homochiral

Heterochiral

- Heterochiral gels scatter differently from homochiral ones

- They are all characterized by fibrilar structure

6/12/2012

15

SANS Data Analysis

Homochiral

Heterochiral

Heterochiral

Homochiral

- Homochiral fibers are thicker and denser than heterochiral ones

Shape ReconstructionFiber cross sections

Inverse FourierTransform

heterochiralhomochiral

webFiber

- Peptide biogel is formed of fibers joined by a web

Fiber-Web Structure

6/12/2012

16

- Chirality plays a role in the mechanical properties and structure of biogels

- Homochirality confers higher strength (shear modulus) and yield stress value. Right-right hand-shake is stronger.

- Heterochirality confers faster gelation kinetics

- Biogel structure consists of main fibers held together by a web of cross fibers

- Fibers for homochiral biogels are thicker and denser

- Advantages conferred to homochirality lead to enhanced stability

Results

C- Structure of SDS Micelles

6/12/2012

17

- Surfactants are formed of a hydrophilic head and a hydrophobic tail

- Micelles form when enough surfactants aggregate (above the critical micelle concentration or CMC)

- SDS surfactants form micelles in water (or deuterated water)

Micelle Formation

0.1

1

10

0.01 0.1

68 oC

20% SDS10% SDS5% SDS2% SDS1% SDS0.5% SDS

Sca

tte

red

In

ten

sit

y (

cm-1

)

Scattering Variable Q (Å-1)

SANS from SDS Micelles

- Ellipsoidal micelles form

6/12/2012

18

0.1

1

10

0.01 0.1

5 % SDS, 49 oC

Model FitSANS Data

Sca

tte

red

In

ten

sit

y (

cm-1

)

Scattering Variable Q (Å-1)

Bd

)Q(d

Q

A)Q(I

ellipsoidsn

)Q(S)Q(PV2

ellipsoidsd

)Q(dIP

Ellipsoid Micelles Model Fit

- Power law (low-Q) + ellipsoidal micelles (high-Q) model fits well

1.5 104

2 104

2.5 104

3 104

3.5 104

4 104

4.5 104

280 300 320 340 360

10 % SDS5 % SDS 2 % SDS 1 % SDS 0.5 % SDS

Elli

ps

oid

Vo

lum

e (Å

3 )

Temperature (K)

Some Fit Results

- Micelles become smaller at higher temperatures and lower volume fraction

6/12/2012

19

10

15

20

25

30

35

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

1% SDS/d-Water, 21 oC

Ra Rb

Elli

pso

id H

alf

Ax

es (

Å)

NaCl Salt Fraction (mol/L)

More Fit Results

- Salt addition affects lateral growth only

-0.2

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

1 % SDS/d-Water

SDS fraction in the micellesD

2O fraction in the micelles

SD

S a

nd

D2O

Fra

cti

on

s in

th

e M

icel

les

Temperature (oC)

Material Balance Equations

- SDS surfactant fraction remains constant above the CMC

6/12/2012

20

SDS MASS FRACTION (%)

T E M P E R A T U R E

(oC)

25

50

75

100

25 50 75 10000

lamellar phase

intermediates

spherical micelles

hydrated SDS crystals

hexagonalphase

intermediates+ crystals

hexagonal phase+ crystals

lamellar phase+crystals

Phase Diagram

- SDS/water phase diagram from calorimetry

4. Final Points

6/12/2012

21

Upgrade and VSANS

30 m SANS

Present Guide Hall

New Guide Hall

30 m SANS

40 m VSANS

10 m SANS

USANS

ConfinementBuilding

USANS Instrument

SANS, VSANS and USANS Ranges

VSANS

0.01

1

100

104

106

108

1010

10-5 0.0001 0.001 0.01 0.1 1

4% PEO/d-Ethanol,

Mw=42,900 g/mole, T=25oC

USANS DataSANS Data

Sca

tte

red

In

ten

sity

(cm

-1)

Q (Å-1)

SANS

USANS

6/12/2012

22

0.0001

0.01

1

100

104

106

108

1010

10-5 0.0001 0.001 0.01 0.1 1

Crosslinked CTVB Micelles

gel with no excess oil gel with excess octane gel with excess toluene

Sca

tte

red

In

ten

sity

(c

m-1

)

Q (Å-1)

SANS and USANS Data

VB-

CTA+

Final Words

THE SANS PROGRAM AT NIST

200 experiments per year

15 theses per year

80 publications per year

REFERENCES- B. Hammouda, “Probing Nanoscale Structures – The SANS Toolbox”, (2009). Book available online.- M. Taraban, Y. Feng, B. Hammouda, L. Hyland and B. Yu, “Chirality-Mediated Mechanical and Structural Properties ofOligopeptide Hydrogels”, Chemistry of Materials (2012)

ACKNOWLEDGMENTSSteve Kline, Marc Taraban, Bruce Yu

http://www.ncnr.nist.gov/staff/hammouda/