SMALL ANGLE X-RAY AND NEUTRON SCATTERING IN...

Proceeding of the 6th National Seminar on Neutron and X-Ray Scattering, ISSN 1410-76

SMALL ANGLE X-RAY AND NEUTRON SCATTERING IN CRYSTALLINE & LIQUID CRYSTALLINE POLYMERS

G. Ungar

Department of Engineering Materials University of Sheffield, Sheffield, United Kingdom

Email: [email protected]

ABSTRACT SMALL ANGLE X-RAY AND NEUTRON SCATTERING IN CRYSTALLINE & LIQUID CRYSTALLINE POLYMERS. SAXS has been used extensively in the study of semicrystalline polymers since the earliest days, since the typical dimensions of the lamellar or microfibrillar crystals encountered in such systems are intrinsically on the 10 - 50 nm scale. Although true one-dimensional long range order is not attainable, stacking of lamellar crystals can be highly periodic, so that Bragg diffraction is often used as an approximation to obtain the “long period”. With the advent of synchrotron radiation, with high brilliance and highly collimated beam, SAXS has gain unprecedented power, with numerous time-resolved and high-resolution applications. These will be illustrated on examples of conventional polymers, as well as on model monodisperse oligomers. A further area of application of SAXS is mesomorphic phases in block-copolymers and thermotropic and lyotropic liquid crystals, which includes liquid crystal polymers and dendrimers; some of these applications will be described briefly. Like SAXS, SANS has found numerous applications in polymer solutions and solid polymers, both amorphous crystalline and liquid crystalline. By isotopic labelling, particularly deuteration, information on the trajectory of a polymer chain in the bulk can be obtained. Following the change in the trajectory occurring upon crystallization, a number of hitherto contentious issues regarding polymer morphology and the crystallization process have been settled. Selective deuteration of parts of the chains, such as chain ends, can result in particularly informative SANS experiments, especially in combination with SAXS data. Carefully chosen labeling can even bring about a high enough contrast to allow real-time SANS monitoring of rapid polymer crystallization, with recording speeds comparable with those of synchrotron SAXS. Examples will be illustrated. Keywords : SAXS, SANS, synchrotron, crystallization, liquid crystals

SAXS AND SANS IN MODEL CRYSTALLINE POLYMERS

Structural hyerarchy in semicrystalline polymers

Atomic scale - crystal unit cell: - several Angstroms (<1 nm to a few nm) - detailed crystal structure, conformation of individual

bonds - wide-angle XRD Scale of crystal thickness: - 100 - 500 Å (10 - 50 nm) - electron microscopy, small-angle XRD Scale of crystal aggregates (spherulites etc.): - µm scale - optical microscopy

Polymer Single Crystals

70 µm 6 µm

9.5 nm

Figure 1. Polyethylene from 0.1% xylene solution (AFM – atomic force microscopy)

- 16 -

Small Angle X-Ray and Neutron Scattering in Crystalline & Liquid Crystalline Polymers G. Ungar

Structure of lamellar polymer crystals

- Lamellar crystals thickness 10 nm (typically from solution)

- Polymer chains normal to lamellar surface - Typical length of extended polymer chain: 1mm =

1000 nm - What is the structure?

Figure 2. Chain-folded lamellar crystal

What about melt-crystallized polymers?

- Also lamellar crystals? - Small-angle X-ray scattering (SAXS) suggests so. - Diffraction peak at small 2q corresponds to

d-spacing 20 – 50 nm = “long period” l o stacking of lamellar crystals

Stacked melt-crystallized lamellae

x=lc/l - Folds less regular - Amorphous phase more liquid-like - Tie-molecules – give mechanical integrity - Stacking often irregular:

o analysed via 1-d correlation function

Microfibrillar structure of drawn semicrystalline polymers

crystalline

amorphous

microfibril

Figure 3. SAXS of oriented i-PP

Lamellar structure in melt-crystallized PE

Figure 4. SEM of surface of PE from which low MW fraction

was extracted

Ultralong Monodisperse n-Alkanes

- Very long, up to C390H782 - Strictly uniform in length - Ideal models for studying fundamental physical

properties of crystalline polymers, e.g. polyethylene

chain conform.

paraffinC102H206

C150H302

C198H398

C246H494

C294H590

C390H782

E F3 F4 F5F2

++++++ + + + +

+ + +++

+ ++

+

- 17 -


Figure 5. AFM micrograph of fracture surface of extended

C390. Note chain tilt.

Paths to Integer Folding from Solution

Solution

High Tc

Extended(E)

Once-Folded(F2)

Low Tc

SolutionSolution

High Tc

Extended(E)

Once-Folded(F2)

Low Tc

Quantized thickening of C390H782 lamellae

heat

ing

0.02 0.06 0.10 0.14 0.220.18

q (Å-1)

I q2

(a.u

. )

169Å 83Å

48Å

95 °C

105 °C

115 °C

125 °C

97Å

heat

ing

heat

ing

0.02 0.06 0.10 0.14 0.220.18

q (Å-1)

I q2

(a.u

. )

169Å 83Å

48Å

95 °C

105 °C

115 °C

125 °C

97Å

heat

ing

C210H422isothermal crystallization at 110ºCSAXS

q (Å-1)

I q2

0s

240s

6s/frame

0.02 0.06 0.10 0.14 0.18 0.22

C210H422isothermal crystallization at 110ºCSAXS

q (Å-1)

I q2

0s

240s

6s/frame

0.02 0.06 0.10 0.14 0.18 0.22

Nature of the Non-Integer Form (NIF)?

Initial proposal

NIF structure according to electron density from SAXS

x

Density

Crystal

Amorphous

Crystal

Subsequent transformation to a mixed integer form

NIF Folded-Extended (FE)Triple-Layer Superlattice

NIF Folded-Extended (FE)Triple-Layer Superlattice

- 18 -


True nature of NIF and its transformations

Melt

NIF

E F2 FE

high Tc

low Tc from time-resolved SAXS and SANS

Melt

NIF

E F2 FE

high Tc

low Tc from time-resolved SAXS and SANS

Fast real-time SANS on end-deuterated alkanes to complement real-time SAXS

D25C12------------C192H384-----------C12D25

(C216D)

D25C12------------C192H384-----------C12D25

(C216D)

T-jump Cell

Heating cell 1

Heating cell 2

Sample frame

motor

Incident neutron beam

Heating cell 1

Heating cell 2

Sample frame

motor

Incident neutron beam

Real-time SANS of isothermal crystallization of C216D at 4 temperatures

- 19 -


ED and SLD profiles of the final folded-extended form

Binary mixtures of long alkanes Model polymer systems with controlled polydispersity. C162H326 + C246H494 1:1 w:w C162H326 (208Å): C246H494 (315Å): Short alkanes (<50 C-atoms) do not co-crystallize. SAXS, C162H326+C246H494, cooling

9984 58

45 3550 C°

60 C°

70 C°

80 C°

90 C°

100 C°

110 C°

120 C°

I q 2 (a

.u.)

q ( )-1

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26208 105 70 52 42

Selective Deuteration

C168D-C242 C162-C216D

Semicrystalline (high T)

Superlattice (low T)

SAXS and SANS compared

high T semicrystalline (SCF)

low T superlattice

Combined SANS/SAXS on Semicrystalline Form C168D-C242

Inte

nsit y

0.00 0.04 0.08 0.12 0.16 0.20

SANS

SAXS

q (Å)-1

1 2 3 4 5 6

C168D-C242 50:50120 °C

7

Inte

nsit y

0.00 0.04 0.08 0.12 0.16 0.20

Inte

nsit y

0.00 0.04 0.08 0.12 0.16 0.20

SANS

SAXS

q (Å)-1

1 2 3 4 5 6

C168D-C242 50:50120 °C

7

Sc a

tterin

gL e

ngth

Ele

ctro

nD

ensi

ty

x (Å)-160 -120 -80 -40 0 40 80 120

(a)

(b)

(c)

216 Å

163 Å

131 Å 21 Å32 Å

142 Å 38 Å

18 ÅS

c atte

ring

L eng

thE

lect

ron

Den

sity

x (Å)-160 -120 -80 -40 0 40 80 120

Sc a

tterin

gL e

ngth

Ele

ctro

nD

ensi

ty

x (Å)-160 -120 -80 -40 0 40 80 120

(a)

(b)

(c)

216 Å

163 Å

131 Å 21 Å32 Å

142 Å 38 Å

18 Å

C162-C216D

Inte

nsity

0.00 0.04 0.08 0.12 0.16 0.20

SANS

SAXS

C162-C216D 50:50115 ºC

q (Å)-1

1 2

Inte

nsity

0.00 0.04 0.08 0.12 0.16 0.20

Inte

nsity

0.00 0.04 0.08 0.12 0.16 0.20

SANS

SAXS

C162-C216D 50:50115 ºC

q (Å)-1

1 2

- 20 -


(b) (c)

66Å

30Å

66Å

8Å

(d) (e)

ED SLD(b) (c)

66Å

30Å

66Å

8Å

(d) (e)

ED SLD

Increasing amorphous layer thickness in semicrystalline form by increasing chain length difference C122 C122 + C162 C198 C216 C246

• Chain tilt is confirmed. • Accurate detail of “rough” crystalline-

amorphous interface. • Gradual dissipation of orientational order of

chains emanating from crystal.

Triple-layer Superlattice

Iq2

(a.u

.)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

SANS

SAXS

q (Å)-1

C168D + C242 (50:50 w/w)r. t.

1 2 3 4 5 6 7 8 9 11 12

Iq2

(a.u

.)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

SANS

SAXS

q (Å)-1

Iq2

(a.u

.)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

SANS

SAXS

q (Å)-1

C168D + C242 (50:50 w/w)r. t.

1 2 3 4 5 6 7 8 9 11 12

Sca

tterin

g Le

ngth

Ele

ctro

n D

ensi

ty

-240 -160 -80 0 80 160 240

x (Å)

173Å 66Å

182Å 182Å48Å

173Å(a)

(b)

(c)

- 21 -


C192H385-COOH

double layer(odd orders)

single layer(even orders)

double layer(odd orders)

single layer(even orders)

SOME APPLICATIONS OF SMALL-ANGLE X-RAY SCATTERING IN COMPLEX LIQUID CRYSTALLINE SYSTEMS Contents:

1. 3d L.C. phases in molecules with low taper 2. 3d L.C. phases in molecules with high taper

(dendrons) 3. 2d columnar honeycombs

Common Liquid Crystal Phases

Nematic Smectic A Smectic C

“Lyotropic” series

BA

A

Thermotropic: Increasing proportion of highly tapered dendronLyotropic: Increasing proportion of oil in water(after Tschierske et al.)

BA

A

Thermotropic: Increasing proportion of highly tapered dendronLyotropic: Increasing proportion of oil in water(after Tschierske et al.)

Low-taper molecules

CH2OHCH2O

CH2OC12H25O

C12H25O

CH2CO2CH3

or

D20

OH

OC12H25 OCH2C12H25 O O

O

O

II-43

O CH2O

OC12H25 OOH

OC12H25 Electron Density Maps

136C

133C

79C

D20electron density

Hexagonalp6mm

Rectangularc2mm

- 22 -


II-43electron density

111C

66C

6C

Hexagonalp6mm

Rectangularc2mm

Obliquep2

ab

Colr : c2mm

Rectangularc2mm

Hexagonalp6mm

Tem

pera

ture

(a)

(b)

(c)

OH

OC12H25 OCH2C12H25 O O

O

O

Hexagonalp6mm

Rectangularc2mm

Obliquep2

Tem

pera

ture

(a)

(b)

(c)

O CH2O

OC12H25 OOH

OC12H25

Molecular Dynamics Simulation

O CH2O

OC12H25 OOH

OC12H25

Polymethylsiloxanes with hemiphasmid side chains

-CH3-CH3

n 5: Sm-A2

n = 7: high T - Sm-A2low T - Colh

intermediate T - mesh phase (R3m)- gyroid cubic (Ia3d)

n 9: Colh

n 5: Sm-A2

n = 7: high T - Sm-A2low T - Colh

intermediate T - mesh phase (R3m)- gyroid cubic (Ia3d)

n 9: Colh

R3m Mesh Phase

siloxanearomaticaliphatic

Sections through hole -Increasing hole diameter

- 23 -


Directly reconstructed electron density of R3m

higher

lower

highest electron density regions- polysiloxane backbones

(4 unit cells)

highest electron density regions- polysiloxane backbones

(4 unit cells) The three “bicontinuous” (double network) phases in liquid crystals and block copolymers

Ia3d bicontinuous cubic (“gyroid”) El. density from XRDblue: siloxane (high)yellow: alkyl chain ends (G-surface)

water channels ininverse lyotropic(schematic)

Im3mI - First Triple Network LC Phase

Nature Materials, 2005 4 562

Highly tapered molecules (Dendrimers)

dendron

dendrimer

dendron

dendrimer

O

O

RORO

RORO

O

O

OO

O O

O

O

RO

O

RO

O

X

R=C12H25

RO

RO

RO

O

O

O

RO

RO

RO

O

O

O

I: X=CH2OHII: X=COOH

R

RRIm3m (BCC)

Pm3n

P42/mnm

Im3m (BCC)Pm3n

P42/mnm BCC phase, dendronized polyoxazoline Electron density map

- 24 -


TEM of BCC in Polyoxazoline

Chem. Eur. J., 2001 7 4134 Alternative Pm3n Structures- different phase combinations

SpheresScience, 1997 278 449

Interlocking Columns

Semifluorinated SDOBOB

Rubidium salt (20%)

Rb+

“Isomorphous replacement” - targeted labeling with electron-rich atoms

q / Å -1

2

12-G2-COOH

12F8-G2-COOH

12F8-G2-COORb

Location of rubidium

JACS 2003 125 15974 The two tetrahedrally close packed (TCP) – or Frank-Kasper phases in thermotropic LC

Small-angle XRD of a monodomain of the tetragonal P42/mnm phase

h00

h10

h20

h30

h40

h50

h60

h70

h80

1k02k03k04k05k06k07k08k0

0k0

h00

h01

h02

h04

h03

10l20l30l40l

00lc*

a*a*

a*

Science, 2003 299 1208 tetragonal, P42/mnm Electron Density Maps

z=1/2

z=1/4 z=3/4

z=0hi

lo

z=1/2

z=1/4 z=3/4

z=0hi

lo

- 25 -


Analogues in Transition-Metal Alloys

BCC

α-iron

Pm3n

Cr3Si

P42/mnm

Fe-Cr σ−phase

BCC

α-iron

BCC

α-iron

Pm3n

Cr3Si

Pm3n

Cr3Si

P42/mnm

Fe-Cr σ−phase

P42/mnm

Fe-Cr σ−phase

A single atom in alloys A 103-104-atom micelleA single atom in alloys A 103-104-atom micelle Inverse micelles Soft spheres: d < 2r Inverse micelles and dendrimers: holes are very costly

tetrahedral holes cheapest TCP structures

Compromise for hard spheres: FCC or HCP. Include large octahedral interstices.

Temperature-induced transition

R

RRIm3m (BCC)

Pm3n

P42/mnm

Im3m (BCC)Pm3n

P42/mnm

increasing Tlow alkyl surface area

high alkyl surface area

LC Phases in 3,4,5-Trialkoxygallates

Pm3n

Im3m (BCC)

hex. columnar

??O(CH2)nH

O(CH2)nH

O(CH2)nHOCO

M+ -

Unknown Phase Found between 2-d columnar and 3-d micellar phases

q (Å )-1

Iq2

0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.450.05

q (Å )-1

Iq2

0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.450.05

Small Angle X-ray Powder Diffraction Pattern

- 26 -


Dodecagonal Phase: Single Domain X-ray Diffraction

Pattern repeats every 30o on rotation around horizontal axis.

12-fold symmetry?

Pattern repeats every 30o on rotation around horizontal axis.

12-fold symmetry?

X-ray parallel to axis:- clear 12-fold symmetry.

Dodecagonal liquid quasi-crystal.

X-ray parallel to axis:- clear 12-fold symmetry.

Dodecagonal liquid quasi-crystal.

Penrose tilings

2-D 3-D Indexing of Single Crystal Diffraction Pattern

d

q1q2

q3q4

(12210)

(13310)

(23200)

(24200)

(12100)

(1210 )n5

(2320 )n5(2420 )n5

(1110 )n5

(0000 )n5

( 0 )111 n5

( 0 )121 n5

( 0 )232 n5

( 0 )242 n5

n5 : 4 3 2 1 0 1 2 3 4

q5

q2 (1010 )n5

(2220 )n5

( 0 )222 n5

( 0 0 )1 1 n5

X.B.Zeng et al. Nature, 2004, 428, 157

Yellow circles – calculated from model

z = 1/4, 3/4 z = 1/2z = 0, 1

Pm3n

z = 1/4, 3/4 z = 1/2z = 0, 1

Pm3nPm3n

Dodecagonal Liquid QuasicrystalDodecagonal Liquid Quasicrystal

P42/mnmP42/mnm

C12 axis

Why do different dendrons form different 3-d phases?

radial distribution of volume

P42/mnm cage

Non-ionic surfactant C12EO12 + water

water C12EO12water C12EO12

alkylEO

alkylEO

- 27 -


2-d columnar honeycombs P42/mnmP42/mnm

columnarquasicrystal?

LC molecules containing 3 types of incompatible blocks Triblock Amphiphiles

Rigid aromatic

unit

Flexible non-polar chain

Polar group

BolaamphiphileBolaamphiphile FacialAmphiphile

FacialAmphiphile

COWORKERS Sheffield

• X.B. Zeng • Y. Liu • D.R. Dukeson

• V.S.K. Balagurusamy decreasing polar chain length (purple) • D. Yeardley • J. Hobbs

Science, 2005 307 96

Pennsylvania • V. Percec • W.D. Cho • G. Johansson • N.M. Holerca • A. Dulcey

Halle

• C. Tschierske • S. Diehle • U. Baumeister • B. Chen

CONCLUSIONS • Of the three “micellar” 3-d ordered phases (BCC,

Pm3n and P42/mnm) two are TCP structures (Frank-Kasper phases).

Topological duals on 32434 net

• First nanoscale quasicrystal. Potential scale-up to self-assembled photonic (wide isotropic PBG) materials.

• Radial volume didtribution function – allows prediction of phase structure from molecular architecture

• Pentagonal columnar phase observed. Possibility of columnar liquid quasicrystal.

- 28 -

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