neutrons in soft matter 2...neutrons in soft matter joão t. cabral & julia s higgins department...
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Neutrons in soft matter
João T. Cabral & Julia S Higgins Department of Chemical Engineering
Imperial College London
Lecture 2 – Reflectometry & Dynamics
David G Bucknall Heriot-Watt, UK
14th Oxford School on Neutron Scattering, 17 September 2015
Outline
Single chain polymer conformation (solution and blends)
Polymer blends: interactions, conformation & dynamics (equilibrium and phase separation)
Introduction soft matter & relevance of neutron scattering
Single objects: spheres, coils, rods...
Lecture 1 – Structure & kinetics – SANS
Lecture 2 – Interfaces and dynamics
Reflectivity and diffusion
Dynamics in soft matter, QENS, BS, Spin-echo
Forster et al (2011)
• Interdiffusion, e.g., welding
Miscible systems
Immiscible systems
• Copolymers, e.g., di-blocks
• Reduce interfacial tension
• Entangle with homopolymers
smaller dispersed phase
increase strength
Reflectometry: study of interfaces
Reflectometry
CRISP (ISIS)
Significance of the interfacial width
Theoretical width
Infinite molecular weight limit
E Helfand & AM Sapse
J Chem Phys 62 (1975) 1327
Finite molecular weight limit
2
1
12
11
2
t NN66
a2w
M Stamm & DW Schubert
Ann Rev Mater Sci
25 (1995) 325
Measure interfacial width to find
wt = 2a
(6)0.5
where a (statistical segment length)
Basics of Reflectivity
q < qcrit
q qcrit
q > qcrit
only reflection
critical angle
reflection and refraction
q
I(q)
qcrit
Reflection
Reflection
&
Refraction
The Reflectivity Profile
Information
Content
r
d
Simplest Case
Complex Case
r
d
What about lateral
information?
Off-specular !
Evaluating Reflectivity Data
qz (Å
-1)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Refl
ecti
vit
y,
R(q
z)
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
qz (Å
-1)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
R(q
z)q
z
4
(Å-4
)
10-11
10-10
10-9
10-8
10-7
qc
q2
q1
(a)
(b)
r
d
fft
Ideal
r
d
Real world
r
21
21
22
zdj
bNn
nj+1
nj
refracted
beam
incident
beamreflected
beam
qj
qj+1
qj
11 qq jjjj cosncosn
11
11
1
jjj
jjj
j,jsinnsinn
sinnsinnr
*
j,jj,j rrR 11
q
sinkq
42
1
1
1
j,zj,z
j,zj,z
j,jqq
qqr
0
1
2
m-1
m
m+1
n0
n2
nm-1
nm
n1
nm+1
Air
layer
number
refractive
index
substrate
d1
d2
dm-1
dm
mm,mm,m
mm,mm,m
m,miexprr
iexprrr
21
2
11
11
1
q sindn mmm 2
mmm
mmm
mcossini
sinicosc
m
m
mMM
MMcM
0 2221
1211
2
12221011211
12221011211
mm
mm
MMMM
MMMMR
Snell’s Law
Fresnel’s law
Single layers and bilayers
Normalised Distance
-3 -2 -1 0 1 2 3
Vo
lum
e F
racti
on
,
0.0
0.2
0.4
0.6
0.8
1.0
Interfacial Width - Definition
Polymer 2 Polymer 1
w
1
21
2tanh
z
w
z
Momentum Transfer, Q (Å-1
)
0.01 0.1
Re
fle
ctiv
ity
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
w = 0 nm
w = 5 nm
w = 10 nm
Effect of Interdiffusion on
Reflectivity Profiles
Momentum Transfer, Q (Å-1
)
0.01 0.1
Re
fle
ctiv
ity
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Effect of Limiting
Q range on Observation Window
Momentum Transfer, Q (Å-1
)
0.01 0.1
Re
fle
ctiv
ity
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
q = 0.25
q = 0.65
q = 1.5
Effect of Angle on the Q Range
q
sin
4Q
q
0.05 < (nm) < 0.65
Horizontal Distance (m)
0 100 200 300 400
Vert
ical D
ista
nce (
m
)
-0.04
-0.02
0.00
0.02
0.04
Roughness causes off-specular scattering
and increased resolution term.
Surface profile of i-PP
at RT
Momentum Transfer, Q (Å-1)
0.02 0.03 0.04 0.05 0.06
Ref
lect
ivit
y
0.001
0.01
0.1
1
Measured reflectivity
of d(i-PP) at 180 C
Calculated reflectivity
of i-PP assumimg small
surface roughness
Effect of Crystallinity
on reflectivity
Brewster angle micrograph
of surface of i-PP (bar 20m
Thermally Excited Capillary Waves
Mean field theory assumes thatthe interface is flat.
At equilibrium capillary wavesare thermally excited.
According to the equipartition theorem each mode increases the surface energy by 0.5 kT. The actual surface is roughened by a superposition
of all possible capillary wave modes.
wt
w0
w
z
x
y
z
Projection onto z-y plan
w = (wt2 + w0
2)0.5
Definition of w0 dominates derivation of wt
NR Measured Interfacial Width
s
As made
t = 0
Annealed
t > 0
s
Polymer Interdiffusion
s
s
Non-Fickian Diffusion - Case II Diffusion
8 s t
n n =
1
2
Non-Fickian Diffusion
t = 0 t > 0
s
The Tube Model
Polymer chains in the melt
Each chain can be considered to be constrained within a tube
Polymer Motion
t
t = te
Entanglement time
t = tR
t = td
Rouse relaxation
time
Reptation time
t = 0
Polymer Diffusion
t < te
te < t < tR
t > td
tR < t < td
aT
t (mins)
0.001 0.01 0.1 1 10 100 1000 10000
s (
Å)
10
100
te
tR t
d
A Karim et al, Phys Rev B 42 (1990) 6846
NR Results 4
1
ts
41
ts
81
ts
21
ts
Momentum Transfer, Q (A-1)
0.01 0.1
Ref
lect
ivit
y
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 5
32
63
93
124
155
186 212
t (mins)
Real Time Reflectivity Measurements
Si / PS (50k) / dPS (40k) @ 115 C
‘225’
Dtw 4
Calculating a Diffusion Coefficient
For dPS-PS system:
D = (1.7 0.2) 10-17 cm2s-1
D
Nbr 2
2
3t
tr = 3223 363 s (dPS) = 4333 489 s (hPS)
Reptation time:
M Doi and SF Edwards
The Theory of Polymer Dynamics (1986) 22
2
3 bN
dTkD TB
D = 2.81 10-17 cm2s-1
When (115C) = 0.199 dyne.s.cm-1
and dT = 5.7 nm
Rouse time:
D
dTR 2
2
9t
tR = 215 23 s
Polymer-Oligomer Interdiffusion Reflectivity Cell
Motor
Heatable fixed top plate
Heatable moveable base plate
Polymer coated silicon
‘Fluid’ container
Neutron Reflectivity Melt Cell
heated brass
base plate
thermocouple
Neutron
beam
aluminium plate
dPS film
bulk PE layer
silicon block
retaining screw
heaters
Momentum Transfer, Q (Å-1
)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Refl
ect
ivit
y
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
Si
dPMMA
OMMA d
w
dPMMA(100k) / OMMA(510) @ 45 C
0.5
20.5
43.0
64.5
84.5 106.0
127.5
t (mins)
Momentum Transfer, Q (Å-1)
0.00 0.02 0.04 0.06 0.08 0.10
Refle
ctivit
y
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
3
27
47
65
101
123
135
t (mins)
dPS (101k) / OSt (1100) Interdiffusion @ 65C
t (mins)
0 20 40 60 80 100 120 140
Inte
rfa
ce
Po
sitio
n, x
0 (
nm
)
88
90
92
94
96
t (mins)
0 20 40 60 80 100 120 140
Inte
rfa
cia
l w
idth
, w
i (n
m)
0
2
4
6
10
12
14
16
dPS (101k) / OSt (1100) Interdiffusion @ 65C
w1
w
2
Off-specular reflection
Grazing incidence: wide and small angle
P Muller (2011)
substrate
h
h = 5-500 nm
1 nm Rg = 2–20 nm
Polymer:Fullerene
?
Adv. Mater. 25 985-991 (2013)
Polymer-fullerene blends
PS+5% C60 h = 100nm
PS (2k), 30 nm 1% C60, 30 nm
140C
Thin films
500 μm
a b
PS PS + 5%C60 2
k, 3
0 n
m
c d
500 m
2k
, 15
0 n
m
‘Spinodal nucleation’
140oC
180oC
180oC
Phys. Rev. Lett. 105, 038301 (2010) Macromolecules 44, 4530-4537 (2011) GISANS & reflectometry
Organic Solar Cell lifetime?
N2
Light exposure Thermal annealing Device testingSpin casting
time-
+
PCElight
Nature Communications 4, 2227 (2013) Angew. Chem. Int. Ed. 53, 12870-12875 (2014)
Summary
• study and design interfaces
Reflectivity
• investigate diffusion mechanisms
• engineer ‘functional’ surfaces / devices
Neutrons in soft matter
João T. Cabral Department of Chemical Engineering
Imperial College London
Lecture 2 (II) – Dynamics
Scattering theory reminder Scattering cross section
coherent incoherent
Dynamic structure factor
Intermediate scattering function
FT (t,w)
Pair correlation function
FT (r,q)
RHH
R
vibrations
rotations
motion decomposition
)]0()([)]0()([)]0()([1),( RtRiQTtTiQ
i
VtViQ
self eeeN
tQI
vibrations
CM
translation rotations
single-particle dynamics
RHH
R
vibrations
rotations
single-particle tools
motion decomposition )]0()([)]0()([)]0()([1
),( RtRiQTtTiQ
i
VtViQ
self eeeN
tQI
22
31 uQ
e
frozen for polymers T<<Tg.
vibrations
CM
translation rotations
2210rot2/3
2/31)Q(A)()Q(A),Q(S
wt
t
ww
)3Qr(j21)Q(A 031
0
)Q(A1)Q(A 01 with
Methyl protons 3-fold jumps
relevant proton reorientations: methyl and phenyl rotations about group’s axis.
CM translation
Proton delocalisation DW factor:
2210rot/2
/21)Q(A)()Q(A),Q(S
wt
t
ww
)Qr2(j1)Q(A 021
0
RHH
R
with
Phenyl proton 2-fold jumps
R
R 1.032 Å
R 2.28 Å
22
31 uQ
e
frozen for polymers T<<Tg. CM translation:
Proton delocalisation: DW factor:
2210rot2/3
2/31)Q(A)()Q(A),Q(S
wt
t
ww
)3Qr(j21)Q(A 031
0
)Q(A1)Q(A 01 with
Methyl protons 3-fold jumps
RHH
R R 1.032 Å
3-fold CH3 potential
Side group rotations:
motion decomposition in the glass
vibrations
CM
translation rotations
single-particle dynamics
example:
distribution tcorrelation
RT
EA
e
0
2E
20i
2
)EE(
E
i e2
1)E(g
s
s
glassy polymers: no single relaxation time
variety local molecular
environments
Eo: average barrier height
s: distribution width
V()
V3
intra-
inter-
(Gaussian) distribution of potential barriers:
(log-Gaussian) distribution of reorientation times:
if
2
0i2
2
)(ln
i e2
1)(lng s
s
wwwN
1iii10rot )(Lg)Q(A)()Q(A),Q(SDynamic structure factor:
Case study: Polycarbonates
C OC
OCH3
CH3
O
BPA-PC
Bisphenol-A polycarbonate
thermoplastic polymer with remarkable
• optical clarity
• mechanical properties
• commercial applications
– high Tglass transition
– large impact strength
– ductility.
depend strongly on architecture
impact strength
BPA-PC: ~2400 J/m
TMPC: ~70 J/m
(Fried et al. 1990) C
Rp
Rp Rp
Rp
OC
ORc
Rc
O
PC modified
Toughness
C
CH3
CH3 CH3
CH3
OC
OCH3
CH3
O
TMPC
C OC
OCH3
CH3
O
BPA-PC
TMPC
BPA-PC Stress (N/m2)
Strain (m/m)
Polycarbonates
CH2 CH
PS
r(PC) = 1.198g/cm3
r(TMPC) =1.084g/cm3
Glassy BPAPC tough co-operative phenyl motion,
involve 1 monomer
(account for dielectric/mechanical activity).
Glassy TMPC most brittle PC substituted CH3 hinder backbone mobility;
poor chain packing (large free volume).
Packing
C OC
OCH3
CH3
O
BPA-PC
QENS: characterise dynamics of local reorientation.
C
CH3
CH3 CH3
CH3
OC
OCH3
CH3
O
TMPC
quantitative window scans
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500
Temperature (K)
S(Q
,w~
0)
(T)/
S(Q
,w~
0)
(T~
0)
Q=1.82A-1
C
CH3
CH3 CH3
CH3
OC
OCH3
CH3
O
TMPC
Elastic scans
w res
00 arctan)Q(A12
)Q(A)0~,Q(S
RT
EA
e
0
0
')'()',()0~,(
w
wwwww dRQSQS
for a Lorenztian resolution
PARAMETERS
• <u2>(T) initial slope
• distribution: EA and s
• o
ASSUMED
• geometry EISF
• activation ansatz:
TMPC
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0 100 200 300 400 500
Temperature (K)
ln [
S(Q
,w~
0)
(T)/
S(Q
,w~
0)
(T~
0)]
Q=1.82A-1
Q=1.43A-1
Q=0.86A-1
124
2
KA106dT
ud .
Ea1~6
kJ/mol s1~1
Ea2=15
kJ/mol s1~5
C
CH3
CH3 CH3
CH3
OC
OCH3
CH3
O
TMPC
T
g
0
200
400
600
800
1000
-0.01 -0.005 0 0.005 0.01energy (meV)
S(Q
, w)
elasticquasielasticdatafit
Q=1.82Å-1
0.00
0.01
0.10
1.00
10.00
2 6 10 14
1000/T (K-1)
(
me
V)
IN10
1e
V
Mibemol
50eV
low temperature relaxation
E (meV)-0.005 0.000 0.005
Inte
nsity (
au)
0
4K
11
TMPC first relaxation step:
3-fold CH3 potential
)()(9
))Qr(jo1(2)(
9
)Qr(jo45),Q(S ttrot wwww
w
w
(Colmenero et al, PRL 1998)
TMPC BPA-PC
• very low T low Eo
• rather sharp narrow
s
Mathiew equation: inelastic lines
candidate: rotational tunneling
AE4/3
At eE
wwith
Distribution of EA
highly asymmetric distribution of wt
-2.5
-2
-1.5
-1
-0.5
0
0 100 200 300 400 500
Temperature (K)
ln [
S(Q
,w~
0)
(T)/
S(Q
,w~
0)
(T~
0)]
BPA-PC
C OC
OCH3
CH3
O
BPA-PC
Tg
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400 500
Temperature (K)
I(w
~0
,T)/
I(w
~0
,T=
0K
)
TMPC
BPA-PC
Q=1.82Å-1
0
0.05
0.1
0.15
0.2
0 200 400 600Temperature (K)
Apparent <u2>/Å
2
Ephenyl~37
kJ/mol s1~6
Ech3=15 kJ/mol
s1~3
(after Spiess et al. 1987)
compatible with TMPC
Distribution?
C
CH3
CH3 CH3
CH3
OC
OCH3
CH3
O
TMPC
CH2 CH
PS
TMPC: only PC miscible with PS, large FH
1st step: no resolvable perturbation
2nd step: broadened distribution
Glassy
polymers:
backbone chain conformation
Structural disorder
Blending
inter-
intra-
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400 500
Temperature (K)
I(w
~0
,T)/
I(w
~0
,T=
0K
)
TMPC
TMPC/PSd
50:50
Q=1.82Å-1
molecular potential.
intramolecular environment
•average EA
•architectural
considerations
intermolecular limited effect on s
Conclusions: CASE STUDY
Characterisation local dynamics of PCs:
two architectures toughest (BPA-PC) & most brittle (TMPC)
exhibits two methyl relaxations of rather
different distribution of potentials
Phenyl + methyl
combined backscattering window scans, inelastic BS & TOF Technique
TMPC
BPA-PC
Blending affects s(EA)
E