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Center for Neutron Science www.cns.che.udel.edu
Measuring the nanoscale to engineer nanomaterials for sustainable energy, protective materials, and improving
human health
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Surfactant
Oil Water
I1 I2
H1
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Uni- or Multi-Lamellar
Vesicles
Bicontinuous Cubic
Bicontinuous Microemulsion
Lamellar
Inverse Micelle Hexagonal
Micelle
Rod-like Micelle
Cubic
Surfactant Self-Assembly Hydrophilic �Water-loving�
Lyophilic �Oil-loving�
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'Applications require intimate knowledge of the structure and rheology of WLMs.
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Hu and Lips (2005) J. Rheology 45(1): 1001-10027.
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Decruppe et al. (1995) Coll. Polym. Sci. 273(4): 346-351.
Rehage and Hoffman (1991) Molecular Physics 74(5): 933-973.
Stress plateau
Birefringence banding Spatiotemporal fluctuations
Heterogeneous flow
Becu et al. (2004) Phys Rev. Lett. 93(1): 1-4
interface position
time!
6
applied shear rate
shea
r stre
ss
(a)
?*+#"-(#2(1*+."($.&I%&'(
Hypothesis: A non-monotonic constitutive relation results in segregation of the flow-field into two distinct shear �states�.
Questions: Are there microstructural changes driving this nonequilibrium instability? Are there concentration differences between the bands?
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Small Angle Neutron Scattering (SANS) 3-D real-space microstructure under shear
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1-2 plane
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Kim et al. JOR (2014), Gurnon et al. Soft Matter (2013) Lopez-Barron et al. Physical Review Letters, 108, 258301 (2012). Rogers, et al. Soft Matter, (2012), 8, 3831
velocity- velocity gradient plane LAOS time-resolved SANS LAOS time-resolved SANS
A. Kate Gurnon, P. Douglas Godfrin, Norman J. Wagner, Aaron P. R. Eberle, Paul Butler, Lionel Porcar. “Measuring Material Microstructure under flow using 1-2 plane flow- Small Angle Neutron Scattering,” JOVE (2014).
! = 0.42 s G0 = 103 Pa
10
Relevant length- and time- scales: 5.1% w/w cetylpyridinium chloride and 1.1% w/w sodium salicylate (2:1 molar ratio) in a 0.5 M NaCl and D2O brine
xm [nm] 34±5 (kbT/G0)1/3
lp [nm] 24±3 from birefringence measurements2
le [nm] 43±15 xm5/3/lp
2/3
Lc [nm] 334±100 G''min/G0= le/Lc
rcs [nm] 1.8±0.1 From SANS model fit
"SLD 6.08!10-6 #SLD,PLM - #SLD,solvent
2 F. Nettesheim, M. W. Liberatore, M. E. Helgeson, P. A. Vasquez, P. Cook, Y. T. Hu, N. J. Wagner, L. Porcar. Microstructural mechanisms for shear banding in semi-dilute wormlike micellar solutions. (in preparation).
Dimensionless groups: Deborah Number: De = $% = 0.23 and 2.3 Weissenberg Number: Wi = $%&0 = 1.2, 2.3 and 23
11
30.6+"%&'(.&'B+(R!S(T(KUG+&')*(In
tens
ity
�q� scattering angle
�-1� slope, rigid rods
Plateau intensity, overall length, or correlation length
Bending due to flexibility, persistence length
Micelle diameter (light)
(SANS)
(USANS)
�-1� slope, rigid rods
persistence length
Micelle diameter (light)
(SANS)
310 Å cL
xM
le
920 Ålp
rcs
21000 Å
2050 Å
21.4 Å
310 Å cL
xM
le
920 Ålp
rcs
21000 Å
2050 Å
21.4 Å
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14
Relevant length- and time- scales: 5.1% w/w cetylpyridinium chloride and 1.1% w/w sodium salicylate (2:1 molar ratio) in a 0.5 M NaCl and D2O brine
The WLMs persist for steady and oscillatory shear conditions.
q q
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•! 3 regions for steady shear •! Alignment and angle of orientation with respect to the shear flow of WLM
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]! 23I+#J7'N2hO'E9ZE'G%I+#&8\'o! 9GG+%#'%K+#'8:#+88'"<+#8-"":5'.L+L5'&"'ES>'
H3#.&*'.&.Q%0'+0%8Q/'#+8G"&8+L'
o! M8/.00%Q"&'.&'2h'.&:+&8.:7'%:'$'i':'i'Td$'
o! E:+%H7'2h'.&:+&8.:7'%:':'j'Td$5'/".&/.H+&:'?.:-'"&8+:'"='E2'8:%:+L'
"! Shear banding instability accompanied by SID driven by stress-concentration coupling.
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Inte
nsity
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q [A-1]
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T^'
26
Metastable states of WLMs created with LAOS [De = 0.23, Wi = 2.3]
B
Wi = 2.3 •! Steady shear = shear banding •! No banding instead a metastable
state created and interrogated using LAOS
•! Secondary loops associated with a stress overshoot during LAOS
Gurnon et al. Soft Matter, 2014
H,+IJ2LM2!.&-!B?%+J2LM2!L)),*%-!'+!2+S!E.N%$'9%#"&'6LaL'4P+#0+'1'Z."&+0'6"#/%#'
,3##L'MG.&L',"00L'S&:L'E/.L'KL'NT[ATO'UU]^U'
HYSICALEVIEWETTERS
PRL
American Physical Society
Member Subscription CopyLibrary or Other Institutional Use Prohibited Until 2017 Articles published week ending 22 JUNE 2012
Volume 108, Number 25Published by
!
!
SOR Rheology Bulletin, July 2012 Lopez-Barron et al. , PRL 108 258301 (2012)
38@O:3@83Nb(1*#71(&#(0#&0+&)".C#&('".I%+&)1(
Te'`3#&"&'+:'%0L'9,E'c%/#"'Z+IL'[YKc5'U5'TCDdTe['
c30Q0%$+00%#'W+8./0+'h"#$%Q"&'=#"$'%'60%&%#'Z%$+00%#'6-%8+'3&H+#'E-+%#'h0"?'
R#*F*!T%&U,%75;V5!E.&W.!L=!X%?$%&A;5!R*+&%,!>+$1.$Y5!>.#,!X#',%$45!M+$K.&!O=!Z.F&%$456!.&-!G,0!(,AA+&;'
'
29
VSANS!Very Small-Angle Neutron "Scattering Diffractometer'
!++H8]'0"?'l5'T>5'-.*-'J3F'
30
!++H8]'0"?'l5'T>5'-.*-'J3F'!++H8]'0"?'l5'T>5'-.*-'J3F'
M<%0P3$.&'`+08']j'6#":+.&',#78:%08'
UA'
!++H'="#'EG++HmL''
UT'
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g"?'40+/:#./'h.+0H'>E9')"#@8'•! 90:+#&%Q&*'/3##+&:'N9,O'+0+/:#./'R+0H'.&H3/+8'%':#%&8.+&:'H.G"0+''•! S&H3/+H'H.G"0+8'.&'G%#Q/0+8'.&:+#%/:':"'="#$'8:#3/:3#+8'
Electrode
Electrode
Electric Field: Off Electric Field: On
DSA Cell - Top View
FDEP
Electric Field: Off
Electric Field: On
Electrodes
DSA Cell - Side View
2.9�m Polystyrene in DI Water
FChain
Electric F
ield
T[n$' T[n$'
!+?'E%$G0+'4&<.#"&$+&:8\'4]E9!E'
U^'
>.#+/:+H'8+0=]%88+$P07'"='/"00".H%0'/#78:%08'P7'H.+0+/:#"G-"#+Q/'"#H+#.&*'"P8+#<+H'?.:-'8$%00'%&*0+'&+3:#"&'8/%I+#.&*'NE9!EOo'(%8"&'cL'c/c300%&'%&H'!"#$%&'(L')%*&+#p''E"K'c%I+#'T[A[''
Biotherapeutics: Next Generation of Pharmaceutics
https://www.pharmatching.com/blog/2011/01/what%E2%80%99s-the-matter-with-monoclonal-antibodies/'
o Immunological'and'allergic'disorders'as'well'as'oncology]related'abnormaliQes'
o Structural'specificity'and'low'toxicity'
' o Several'dozen'MAbs'have'
been'approved'by'the'FDA'for'clinical'use'and'several'hundred'are'currently'in'development'o New and exciting protein
constructs have entered the pipeline (e.g. diabodies, MAb fragments, drug conjugates)
Importance of biotherapeutics:
Unmet medical needs
35
• More convenient subcutaneous delivery is desired for the clinical or home setting
• Smaller volumes (<1.5 mL) require larger concentrations for same effectiveness • In some cases, larger concentrations lead to an undesirable viscosity
• Biopharmaceutical trend: even early stage development screens are now including techniques/methods to predict whether the candidates will exhibit elevated viscosities at high concentrations (light scattering techniques) • Also manufacturing process steps are impacted, such as concentration, filtration and fluid transport
Delivery and Manufacturing (CMC or Developability) Issues
hIp://www.glassdoor.com/Photos/Genentech]Office]Photos]E274_P2.htm'
hIp://pramlinQde.net/how]to]use]pramlinQde/'36
High Concentration MAb Viscosity
37
Fab
Fc
Genentech’s MAb1 and MAb2 Comparison!
S. Yadav, T. M. Laue, D. S. Kalonia, S. N. Singh, and S. J. Shire, Molecular Pharmaceutics, 2012, 9, 791–802.
CDR loops
MAb1 – more charged residues in the CDR loops MAb2 – more polar or hydrophobic residues in CDR loops
38!
MAb Cluster Characterization Procedure
! Incident beam
Scattered beam
Detector
q
( ) bkgqSqPVVNqI psp +!= )()()( 22 ""
s+#"]E-+%#'W.8/"8.:7'<8L',"&/+&:#%Q"&' E9!EVE9tE'(Interaction Potential Types)''
!+3:#"&'EG.&'4/-"'N,038:+#'k7G+8O',0+%#'6./:3#+'"='c9P'/038:+#':7G+8'
Ma'
39!
40!
Connection Between Interactions and Scattering!
+ salt
Neutron spin echo results, dimeric clusters • Neutron spin echo (NSE) data:
mAb2
mAb1
mAb1 cluster is about 1.7X that of mAb2 in 0mM NaCl case Extended'Dimers'
Cluster Formation and Enhanced Viscosity Combining NSE and SANS
43
Eric'J.'Yearley,'Isidro'E.'Zarraga*,'Steven'J.'Shire,'Thomas'M.'Scherer,'YaQn'Gokarn,'Norman'J.'Wagner,'Yun'Liu*,'“Small]Angle'Neutron'ScaIering'CharacterizaQon'of'Monoclonal'AnQbody'ConformaQons'and'InteracQons'at'High'ConcentraQons”,'Biophysical'Journal,'105,'720]731(2013)'
Acknowledgements & Co-authors"!
@."#&(_$+"B+(_ee#&5#$%B(
f.)+(g9"&#&(g_(=+1+."0*(
<."B#1(GhA+iNW.""h&(_ee#&5#$%B(
G%#&+B(!#"0."(>GG(g"+&#$B+((
5.6(j+B'+1#&(:<3W(
OB#"%.&(8+6+1*+%/(,9!#&)(@&.B-C0.B(
5.6(G%$+".)#"+(<35(
!.9B(W9)B+"(8<8=(8>3?(
^^'
MAb Neutron Spin Echo Data
MAb2 50mg/mL
MAb2 150mg/mL
MAb1 150mg/mL
MAb1 50mg/mL
45
MAb Neutron Spin Echo Data!
Ratio of DS Between MAb2 and MAb1
MAb2
MAb1
46!
• SANS is a very useful tool to investigate the interaction types in solution
• NSE is a powerful tool to study the formation and types of dynamic clusters in solutions. • MAb1 forms small clusters at low concentrations driven by an anisotropic attractive
interaction
• Small clusters doesn’t seem to grow with the increase of volume fraction.
• The large increase of viscosity of MAb1 is due to the formation of small dynamic clusters while MAb2 viscosity is dominated by the monomeric motions in solutions.
• What about SANS low-Q upturn in MAb1 150mg/mL at 150mM NaCl and the NSE data showing loss of long-lived dynamic clusters? Why doesn’t the viscosity of MAb1 collapse to the levels of MAb2 with the addition of salt
• One explanation: the viscosity decreases significantly (but not to the levels of MAb2) because the attractive electrostatic forces holding the cluster together is suppressed by the salt, but the ability of the MAb1 proteins to move closer to each other is enhanced due to the screening of the repulsion and increased in hydrophobic associations forming a larger, loose network (in comparison to MAb2)
Conclusions
47
Acknowledgements
• Yatin Gokarn and Rosalynn Tiang (Genentech Inc.)
• Lionel Porcar and Peter Falus (ILL) • Michihiro Nagao and Antonio Faraone (NIST Center for Neutron Research)
48
<#&0B91%#&1(a(@0EB+I'+/+&)1(
49
applied shear rate
shea
r stre
ss
(a)
`3#&"&'+:'%0L'L"2!E.1$+!R%NL'[YKc5'U5'TCDdTe['`3#&"&'+:'%0L''O(PD'[YKc5!e^5'+dA[De'`3#&"&'+:'%0=!2+S!E.N%$![YKc5'A[5'TeeB'Z"G+b]2%#"&'+:'%0L'>?@A=!B%C=!D=
I(Q) ~ P(Q)S(Q)
P(Q)
S(Q)
P(Q) or form factor – gives information on the shape and size of a protein S(Q) or structure factor – gives information on the interactions between proteins
OR OR
OR ~1000 Å ~10 Å
Typical MAb SANS Patterns!
50!
MAb Self-Associations
51!
MAb Self-Associations
52!
MAb Self-Associations
*Asymmetric shape and
charge
53!
54
,"&/038."&8\''Z9ME'"='8-+%#'P%&H.&*')Zc8'
55
•! 1,2 plane STR-SANS is available at the ILL Grenoble and at the NCNR NIST
•! RheoSALS with temperature control is available from TA Instruments
•! Region I Stress-SANS Rule demonstrated for entangled flowing WLMs
•! Region II Metastable states of flow-aligned, entangled WLMs with shear-induced concentration fluctuations as precursor to shear banding
•! Region III flow-aligned, shear demixed WLMs with different SSR coefficient
•! LAOS with STR-SANS are powerful tools to develop structure property relationships for complex fluids and to test nonequlibrium thermodynamic models
g9"&#&'%'!.,=!2+S!E.N%$'A[5'TeeB'NT[A^O'L"2!E.1$+,%N%$A!!NT[A^O'M5'TCDxTe['NT[A^O'!!!
38@O:3@83Nb(&#(0#&0+&)".C#&('".I%+&)1(
dD'
57
Nonlinear entangled WLM during LAOS [De = 0.23, Wi = 1.2]
A
Wi = 1.2
Arrows denote the average angle of orientation and the alignment factor at each condition given the SANS 2D scattering pattern.
Gurnon et al. Soft Matter, 2014
0.0 0.5 1.0-40
-30
-20
-10
0
10
20
30
40
0.0 0.5 1.00.0
0.1
0.2
0.3
0.4
0.5
0.0 0.5 1.0
-160-120-80-40
04080
120160
!/!0
" (o )
(A)
- 1
0
1
#
(B)
!/!0
Af
#0
inner wall [De =0.23, Wi = 2.3] outer wall [De =0.23, Wi = 2.3]
(C)
!/!0
$ (P
a)1 L. M. Walker, N. J. Wagner, SANS Analysis of the Molecular Order in Poly("-benzyl l-glutamate)/Deuterated Dimethylformamide (PBLG/d-DMF) under Shear and during Relaxation. Macromolecules 29, 2298 (1996/01/01, 1996). 2 M. E. Helgeson, M. D. Reichert, Y. T. Hu, N. J. Wagner, Relating shear banding, structure, and phase behavior in wormlike micellar solutions. Soft Matter 5, 3858 (2009).
( ) ( )1/2
0 sin 2fG CA! "=
Stress-SANS Rule
Good agreement for the local stress at both the inner and outer positions and the macroscopic stress response during rheology measurement.
Q
de'
0.0 0.5 1.0-40
-30
-20
-10
0
10
20
30
40
0.0 0.5 1.00.0
0.1
0.2
0.3
0.4
0.5
0.0 0.5 1.0
-160-120-80-40
04080
120160
!/!0
" (o )
(A)
- 1
0
1
#
(B)
!/!0
Af
#0
inner wall [De =0.23, Wi = 2.3] outer wall [De =0.23, Wi = 2.3]
(C)
!/!0
$ (P
a)
0.0 0.5 1.0-40
-30
-20
-10
0
10
20
30
40
0.0 0.5 1.00.0
0.1
0.2
0.3
0.4
0.5
0.0 0.5 1.0
-160-120-80-40
04080
120160
!/!0
" (o )
(A)
- 1
0
1
#
(B)
!/!0
Af
#0
inner wall [De =0.23, Wi = 2.3] outer wall [De =0.23, Wi = 2.3]
(C)
!/!0
$ (P
a)1 L. M. Walker, N. J. Wagner, SANS Analysis of the Molecular Order in Poly("-benzyl l-glutamate)/Deuterated Dimethylformamide (PBLG/d-DMF) under Shear and during Relaxation. Macromolecules 29, 2298 (1996/01/01, 1996). 2 M. E. Helgeson, M. D. Reichert, Y. T. Hu, N. J. Wagner, Relating shear banding, structure, and phase behavior in wormlike micellar solutions. Soft Matter 5, 3858 (2009). 3 R. H. Ewoldt, G. H. McKinley, On secondary loops in LAOS via self-intersection of Lissajous-Bowditch curves. Rheol. Acta 49, 213 (Feb, 2010).
'
( ) ( )1/2
0 sin 2fG CA! "=
Stress-SANS law
Neither the inner or outer positions neither capture the stress overshoot, the missing stress must be the result of larger length-scale structures.
Q
dB'
1 E. Helfand & G. Fredrickson, Large Fluctuations in Polymer Solutions under Shear, PRL 62 (21) 2468 (1989) 2Y.T. Hu et al. , Shear thickening in low-concentration solutions of wormlike micelles I., JOR 42(5) 1185 (1998)
3P. Thareja et al., Shear-induced phase separation (SIPS) with shear banding in solutions of cationic surfactant and salt. J. Rheol. 55, 1375 (Nov, 2011).'
60
Evidence of supra-molecular microstructure Rheo-Small Angle Light Scattering (SALS)
[De = 0.23, Wi = 1.2] [De = 0.23, Wi = 2.3]
•! Butterfly patterns during SALS caused by concentration fluctuations •! LAOS rheology - stress overshoot corresponds with butterfly patterns in rheo-SALS
which result from shear induced concentration fluctuations during LAOS. •! Shear banding microstructure origin is concentration fluctuations resulting in stress
overshoot
Hashimoto and Kume, J. Phys. Soc. Jap. 1992
`3#&"&5'9L'_L5'`"H=#.&5'6L'>L5')%*&+#5'!L'(L5'4P+#0+5'9L'6L'aL5'23:0+#5'6L5'6"#/%#5'ZL''c+%83#.&*'c%:+#.%0'c./#"8:#3/:3#+';&H+#'h0"?';8.&*'A]T'60%&+'h0"?]E$%00'9&*0+'!+3:#"&'E/%I+#.&*L ' ''O=!P*A=!DQ)='Ne^O5'+dA[De5'H".\A[LUCBAVdA[De'NT[A^OL'
DA'
,"&/038."&8\''Z9ME'"='8-+%#'P%&H.&*')Zc8'
62
•! 1,2 plane STR-SANS is available at the ILL Grenoble and at the NCNR NIST
•! RheoSALS with temperature control is available from TA Instruments
•! Region I Stress-SANS Rule demonstrated for entangled flowing WLMs
•! Region II Metastable states of flow-aligned, entangled WLMs with shear-induced concentration fluctuations as precursor to shear banding
•! Region III flow-aligned, shear demixed WLMs with different SSR coefficient
•! LAOS with STR-SANS are powerful tools to develop structure property relationships for complex fluids and to test nonequlibrium thermodynamic models
g9"&#&'%'!.,=!2+S!E.N%$'A[5'TeeB'NT[A^O'L"2!E.1$+,%N%$A!!NT[A^O'M5'TCDxTe['NT[A^O'!!!
DU'
_`+0)1(#2(5%0+BB."(W".&0*%&'J((5%0*+BB+(<.B.$"+1+(F)*%1(1+11%#&H((a(!#1)+"(k(W!MZY[(F?9+1l(MJMY(39//%)(>>H((
0.01 0.11
0.01% NaTos0.10% NaTos0.25% NaTos
Inte
nsity
[cm
-1]
q [A-1]
0.01
!"#$%&'()*+,-%,./0001(2*-3-045670()*+,-%,.08809.%(:#09;%(&0
0.0 0.5 1.00.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Inner wall Inner 45s-1 Outer wall Outer 45s-1
1,2
Alig
nmen
t Fac
tor
t/TAB'
j%'*(W".&0*%&'(m(0"?'=#+l3+&/75'$"H+#%:+'8-+%#'#%:+''
0
1
|!|
|d!/dt|
t
|Nor
maliz
ed A
pplie
d Exc
itatio
n|
LAOS inner max
Steady shear inner Steady shear outer
LAOS outer max
Rj-A+"N.B%'&/+&)S(((5.e%/9/(G@P3(.B%'&/+&)(bb(1)+.I-(1*+."(
(,+'"++(#2(*-A+"N.B%'&/+&)(%1(/.'&%n+I($-($".&0*%&'(
TT'
<#&0B91%#&1(Low Branching! "
Interaction peak!!Shear banding "# steady shear!!Simultaneous elastic, viscous!responses "across gap "# LAOS!!!!
0.01 0.1 1 10 100
0.1
1
10
! (P
a)
Shear rate (1/s)
Stress !
0.1 1 10 100
0.1
1
Vis
cosi
ty (P
a.s)
Shear Rate (1/s)
Viscosity !
0.0 0.5 1.0
0.0
0.2
0.4
1
,2 A
lignm
ent F
acto
r
t/T
0
100
|Str
ess|
(Pa)
0.0 0.5 1.0
0.0
0.1
0.2
0.3
1,2
Alig
nmen
t Fac
tor
|Str
ess|
(Pa)
t/T
0
2
4
6
High Branching" "
Screened interactions!!
Shear thinning only"#inhibits banding!
!Viscous response "
only across gap!#inhibits material
stratification!!
!"
0.01 0.11
0.01% NaTos0.10% NaTos0.25% NaTos
Inte
nsity
[cm
-1]
q [A-1]
Candau, S. J.; Khatory, A.; Lequeux, F.; Kern, F. J. Phys. IV 1993, 3, 197- 209.
66
Disentangled high shear state of WLMs [De = 2.3, Wi = 23] Please click on the movie below to play it: SANS arrow’s magnitude and direction defines the degree of alignment and angle of orientation respectively.
For LAOS of equivalent Wi as region III, a highly aligned, oriented microstructure persists throughout the oscillatory cycle. The materials is largely shear thinning and less viscoelastic than the previous two conditions.
C
Wi = 23 Microstructure at two positions across the gap for comparable steady shear Wi.
67
The stress-SANS rule using the segmental microstructure fails to predict the rheology stress however, the rheo-SALS experiments show a persistent butterfly pattern during the oscillation. Evidence of a supra-molecular state that cannot relax during the oscillation cycle indicates that shear induced demixing occurs during LAOS.
LAOS stress of the disentangled, high shear state of WLMs [De = 2.3, Wi = 23]
LAOS stress of the disentangled, Q
'f.)+(g9"&#&J()+H\''d\[[]d\AdG$'\MM*',"&Q&+&:%0'D5'g.0:"&(B?%+,+F@!.&-!E*1$+A'$#1'#$%!+0!"+&1%&'$.'%-5!M%.$![.$-J2)?%$%!
"+,,+*-.,!\*A)%$A*+&A!G&-%$!2'%.-@!2?%.$!.&-!R.$F%!LK),*'#-%!(A1*,,.'+$@!2?%.$!*&!L,,!]?$%%!>,.&%A!+0!2?%.$!
Z%-=!7;^Y8J7^88!>E ! !T+,-%&!T.'%!3!:[*,'+&< ! !!]?+K.A!X.$+&!LI.$-!R%1'#$%^'E-+%#'k-./@+&.&*'1'`+0%Q"&'.&',"00".H%0'>.8G+#8."&8']'!"&+l3.0.P#.3$'E:%:+8'%&H'k-+.#'9GG0./%Q"&8'.&'6+#8"&%0'6#":+/Q<+'4l3.G$+&:'
De'
;&H+#8:%&H.&*':-+'&"&0.&+%#'8-+%#'#-+"0"*7'"='/"$G0+F'J3.H8']'.&/03H.&*'G"07$+#85'8+0=]%88+$P0.&*'8"03Q"&85'/"00".H8'%&H'&%&"G%#Q/0+'838G+&8."&8']'.8'%H<%&/+H'P7'H.#+/:07'$+%83#.&*':-+'$./#"8:#3/:3#+N8O'#+8G"&8.P0+'="#':-+'8:#+88'3&H+#'H+="#$%Q"&L'a-+"]"GQ/85'H.#+/:'<.83%0.b%Q"&5'#-+"]!ca5'%&H'0.*-:'%&H'F]#%7'8/%I+#.&*'3&H+#'J"?'%#+'%$"&*':-+'<%#."38'$+:-"H8'%GG0.+H':"'%'?.H+'<%#.+:7'"='$"H+0'%&H'.&H38:#.%0'878:+$8':"'%.H'.&':-+'H+<+0"G$+&:'"='8:#3/:3#+]G#"G+#:7'#+0%Q"&8-.G8'%&H'"K+&5':"'#%Q"&%0.b+'8++$.&*07'%&"$%0"38'#-+"0"*./%0'P+-%<."#L'k-+8+'$+:-"H8'%#+'"K+&'878:+$'8G+/.R/5'-"?+<+#5'%&H'%'l3%&Q:%Q<+5'#"P38:5'%&H'P#"%H07'%GG0./%P0+'$+:-"H'/%G%P0+'"='$+%83#.&*':-+'=300':-#++]H.$+&8."&%0'$./#"8:#3/:3#+'#+$%.&8'%&'+FG+#.$+&:%0'/-%00+&*+L'S&H++H5'8"$+'"=':-+'$"#+'.&:+#+8Q&*'&"&0.&+%#'+y+/:85'83/-'%8'8-+%#]P%&H.&*'%&H'8-+%#].&H3/+H'G-%8+':#%&8="#$%Q"&85'?-+#+':-+'J"?]R+0H'%&H'$./#"8:#3/:3#+'%#+'.&Q$%:+07'/"3G0+H5'#+l3.#+':-+'%P.0.:7':"'#+8"0<+':-+'$./#"8:#3/:3#+'P":-'?.:-'8G%Q%0'%&H'Q$+'#+8"03Q"&L''S&':-.8'G#+8+&:%Q"&'?+'#+<.+?'%'#"P38:'%&H'P#"%H07'%GG0./%P0+'$+:-"H'38.&*'&+3:#"&'8/%I+#.&*':"'$+%83#+':-+'$./#"8:#3/:3#+'.&'%00':-#++'G0%&+8'"='J"?5'%&H'?.:-'8G%Q%0'%&H'Q$+]#+8"03Q"&L'!+3:#"&'8/%I+#.&*'-%8'%'H.8Q&/:'%H<%&:%*+'%8'$"8:'$%:+#.%08'%#+'%$+&%P0+':"'8:3H7'P7'&+3:#"&'8/%I+#.&*5'3&0.@+'F]a%7'%&H'0.*-:'8/%I+#.&*L'h3#:-+#5':#307'3&.l3+'+FG+#.$+&:8'%#+'G"88.P0+'P7'8+0+/Q<+'.8":"G./'83P8Q:3Q"&5'?-./-'%00"?8'G#"P.&*'/"$G"&+&:8'.&'%'$.F:3#+'P7'/"&:#%8:'$%:/-.&*L')+'-%<+'%HH#+88+H':-.8'/-%00+&*+'P7'H+<+0"G.&*'%',"3+I+'*+"$+:#7':"'%//+88':-+'A]T'N<+0"/.:7]<+0"/.:7'*#%H.+&:'G0%&+'"='J"?O'P7'8$%00'%&*0+'%&H'30:#%]8$%00'%&*0+'&+3:#"&'8/%I+#.&*L''h3#:-+#5'8G%Q%0'#+8"03Q"&'"='"#H+#'A[['$./#"&8'.8'%/-.+<+H'P7'%&'%G+#:3#+':-%:'8/%&8'%/#"88':-+'J"?L'',"$P.&+H'?.:-'%'&"?'/"$$+#/.%05'#-+"]E9!E',"3+I+'*+"$+:#7':-%:'+&%P0+8'#%H.%0'N<+0"/.:7]<"#Q/.:7O'%&H':%&*+&Q%0'N<+0"/.:7'*#%H.+&:]<"#Q/.:7O'$+%83#+$+&:85':-+8+'.&8:#3$+&:8'G#"<.H+':-+'R#8:'$+%83#+$+&:8'"='$./#"8:#3/:3#+'.&'%00':-#++'G#"z+/Q"&8'"=':-+'J"?'%&H':-385'#+/"&8:#3/Q&*':-+'=3005':-#++'H.$+&8."&%0'J"?.&*'$./#"8:#3/:3#+L'h3#:-+#5'Q$+'H+G+&H+&:'H+="#$%Q"&8':-%:'%#+'"K+&'38+H':"':+8:'G-78./%007]P%8+H'/"&8Q:3Q<+'$"H+085'83/-'%8'J"?'8:%#:]3G'%&H'0%#*+'%$G0.:3H+'"8/.00%:"#7'8-+%#'NZ9MEO5'%#+'G#"P+H'P7'8:#"P"8/"G./%007'87&/-#"&.b.&*':-+'H+="#$%Q"&'R+0H'%&H':-+'8/%I+#+H'&+3:#"&'/"00+/Q"&':-#"3*-'Q$+'8:%$G.&*'%&H'P.&&.&*'$+:-"H8L'h.&%0075'&+3:#"&'8/%I+#.&*'.8'%&'%P8"03:+'8/%I+#.&*'$+:-"H'83/-':-%:'0"/%0'/-+$./%0'/"$G"8.Q"&'/%&'%08"'P+'$+%83#+H'3&H+#'J"?L''k-.8'+&%P0+H'H+:+#$.&.&*'83/-'+y+/:8'%8'8-+%#].&H3/+H'/"&/+&:#%Q"&'*#%H.+&:8L'k-+8+'.&8:#3$+&:8'%#+'&"?'%<%.0%P0+'="#'38+'P7':-+'/"$$3&.:7'%:':-+'S&8Q:3:+'Z%3+'Z%&*+<.&'.&'43#"G+'%&H'%:':-+'!SEk',+&:+#'="#'!+3:#"&'a+8+%#/-'.&':-+';LEL''a+/+&:'#+830:8'="#':-+'8-+%#]/#78:%00.b%Q"&'"='8+0=]%88+$P0+H'P0"/@'/"G"07$+#'$./+00+8'.&'."&./'0.l3.H8'3&H+#'Z9ME5':-+'8-+%#'P%&H.&*'"='?"#$]0.@+'$./+00+8'3&H+#'8:%#:]3G'J"?5'%&H':-+'Q$+]H+G+&H+&:'$./#"8:#3/:3#+'"='8-+%#':-./@+&.&*'/"00".H%0'H.8G+#8."&8'%&H'/"00".H%0'*+08'3&H+#'Z9ME'%#+'G#+8+&:+H':"'H+$"&8:#%:+':-+'P#+%H:-'"=':-+'$+:-"H'%&H'-"?':-+8+'$+%83#+$+&:8'G#"<.H+'=3&H%$+&:%0'$./#"8:#3/:3#%0'H%:%'+88+&Q%0'="#'3&H+#8:%&H.&*':-+'#-+"0"*75'%8'?+00'%8'="#'/#.Q/%007':+8Q&*'#-+"0"*./%0'/"&8Q:3Q<+'$"H+08'"=':-+8+'/"$G0+F'J3.H8L''
DB'
a+0%F%Q"&'Q$+\''
60%:+%3'$"H3038\'
2#+%@%*+'Q$+\'
a+G:%Q"&'Q$+A\'
Linear viscoelastic response:
- Nearly Maxwellian behavior
4FG+#.$+&:%0'E78:+$'4FG+#.$+&:%0'E78:+$'D'?:{'/+:70G7#.H.&.3$'/-0"#.H+V8"H.3$'8%0./70%:+''NX!%E%0YVX,67,0Yf[LdO'.&'[Ldc'!%,0V>TM'P#.&+'
1 10 100
1
10
100
!"! !" # !" $ !" % !"& '"!
!"'
!"#
!"(
!"$
!")
+,,-+
!
+ ,-+!
G' G''
Dyn
amic
Mod
uli,
Pa
!, rad/s
1/"
1/"br
20
2
02
( )'( )1 ( )
( )''( )1 ( )
GG
GG
!""!"!"" # "!" $
=+
= ++
0.42 s! =
0G 103.2 Pa=
0.0019 sbr! =2 9.2 srep br! ! != =
A,%:+85'(L'6-78L\',"&H+&8L'cI+#'o5'BADC5'ABBD'
Rehage & Hoffman, Mol. Phys. 74, 933 1991
1 10 100
1
10
100
!"! !" # !" $ !" % !"& '"!
!"'
!"#
!"(
!"$
!")
+,,-+
!
+ ,-+!
G' G''
Dyn
amic
Mod
uli,
Pa
!, rad/s
1/"
1/"br
0.42 s! =
C['
71
,"&/038."&8'="#'8:%#:]3G'J"?8'"=')Zc8'
)"#$0.@+'c./+00%#'8"03Q"&8'N)Zc8O'WLM formation with ionic surfactants:
E/-3P+#:'+:'%0L5'Z%&*$3.#'Kp5'^[CB5'T[[U'
Relevant length scales in WLMs:
o! Contour Length, Lc
o! Entanglement length, le
o! Mesh size, �M
o! Persistence length, lp
o! WLM radius, rcs
Length scales have been and can be obtained from birefringence, linear rheology and small-angle neutron scattering CT'
E:%#:]3G'8-+%#'J"?'N6#+<."38')"#@O'E:%#:]3G'8-+%#'J"?'N6#+<."38')"#@O'dLB'?:{'!%E%0V,67,0'NX!%E%0YVX,67,0Yf[LdO''.&'[Ldc'!%,0V>TM'P#.&+'
?V/#"88]G"0%#.b+#8''''''''''?V"'G"0%#.b+#8' h0"?'<.83%0.b%Q"&'%&H'P.#+=#.&*+&/+'
E9ZE''NA]T'G0%&+O'
h0"?'<.83%0.b%Q"&'%&H'E9ZE\''
o! 2+="#+':-+'8:#+88'G+%@\'*#/#'+['8%$G0+'?.:-'&#(10.6+"%&'Z(
o! 9K+#'G+%@\'$"%'*)UI."E(1)"%A+1(.AA+."(%#+'&+.:-+#'8G%Q%007'&"#':+$G"#%007'RF+HL'23I+#J7'E9ZE'G%I+#&8'%GG+%#'.&'P":-'P%&H8L'
o! 9K+#'8:#+88'v8-"30H+#w\''>+/#+%8+'.&'8/%I+#.&*L'W96+"V-(I%1.AA+."'.&'"3:+#'P%&HL'k-+'P%&H+H'8:%:+'.8'+8:%P0.8-+HL'
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Hu & Lips, J . Rheol 49, 1001, 2005
CU'
74
E-+%#'P%&H.&*'%&H'/"&8Q:3Q<+'$"H+08'
!"
p = # 1$
I + %G0
!p&'(
)*+,!p + 2G0 !-
polymeric stress" #$$$$ %$$$$
+ D!"2!p
"diffusion""#$ %$
. ! = !p + /0 !-"solvent"&
[1] Helgeson et al. (2009) Journal of Rheology, 53(3): 727-756.
!: drag-orientation coupling parameter
1 (1 )B
Hk T
! "#= $# +% &' ( )QQ$1' *
10-1 100 101 102 103 10410-1
100
101
!=0.85
" 12 /
G0
#$.
!=0.45
%&#$.
Bead-spring chains with anisotropic friction:
Model couples non-monotonic stress to anisotropic drag through !.
'< 0.5 ! monotonic '> 0.5 ! non-monotonic
Q
The Giesekus-diffusion (G-D) model1:
75
Z.&@.&*'#-+"0"*7'%&H'"#.+&:%Q"&%0'"#H+#'M#.+&:%Q"&%0'"#H+#':+&8"#A\'''''E/%0%#'G%#%$+:+#8T\'
'•! M#.+&:%Q"&'%&*0+\'
•! 90.*&$+&:'=%/:"#\'
1Order tensor: tr 3
S IQQ
Kramers relation: = + pQQ I !
( ) 22 110
12
cot 2 2S SS
!" #$= % &' (
( ) ( ) 11 221 2 11 22
0 11 22
3 33 +fA k k S SG! !
! !+= + = + =
+
[1] H. Giesekus (1982) J. Non-Newt. Fluid Mech., 11(1-2): 69-109. [2] Helgeson et al. (2009) Journal of Rheology, 53(3): 727-756.
Q
Orientational ellipsoid
H,+IJ2LM2!.&-!B?%+J2LM2!L)),*%-!'+!2+S!E.N%$'9%#"&'6LaL'4P+#0+'1'Z."&+0'6"#/%#'
,3##L'MG.&L',"00L'S&:L'E/.L'KL'NT[ATO'UU]^U'
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HYSICALEVIEWETTERS
PRL
American Physical Society
Member Subscription CopyLibrary or Other Institutional Use Prohibited Until 2017 Articles published week ending 22 JUNE 2012
Volume 108, Number 25Published by
!
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*-A#)*+1%1(0#&0+"&%&'()*+(B#0.B(/%0"#1)"90)9".B(+^#B9C#&(#2(DG51()*.)(B+.I1()#(1*+."($.&I%&'Z(
(
CC'
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f.)+(g9"&#&(!*,(3)9I+&)(:,(
<."B#1(GhA+iNW.""h&(_ee#&5#$%B(
G%#&+B(!#"0."(>GG(g"+&#$B+((
5.6(j+B'+1#&(:<3W(
OB#"%.&(8+6+1*+%/(,9!#&)(@&.B-C0.B(
5.6(G%$+".)#"+(<35(
!.9B(W9)B+"(8<8=(8>3?(
Ce'
CB'XAY!9L'4P+#0+'%&H'ZL'6"#/%#'NT[ATO'"#$$%&'!()*&*+&!*&!"+,,+*-!.&-!/&'%$0.1%!21*%&1%'ACFKH\'UU]^UL'XTY'9L'_%:+'`3#&"&5'6L'>"3*0%8'`"H=#.&5'!"#$%&'(L')%*&+#5'9%#"&'6L'aL'4P+#0+5'6%30'23:0+#5'Z."&+0'6"#/%#'(MW4'T[A^'XUY'cL'Z.P+#%:"#+'+:'%0L'>?@A=!B%C=!D!LM5'[T[d[^'NT[[DOL
New sample environment: shear cell SpatioTemporal Resolved Small Angle Neutron Scattering (1-2 flow-STR SANS)1,2,3
Aaron Eberle
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HYSICALEVIEWETTERS
PRL
American Physical Society
Member Subscription CopyLibrary or Other Institutional Use Prohibited Until 2017 Articles published week ending 22 JUNE 2012
Volume 108, Number 25Published by
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Laser beam Lower Peltier plate
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http://www.tainstruments.com
Shear direction
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Incident light travels in the shear gradient direction, so that the scattering is in the plane of the shear and vorticity directions.
Removable neutral density filter
Beamstop
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•!Predicted for heterogeneous polymer networks by Bastide, Leibler and Prost, Macromol. 1990
•!Extended to explain shear-induced concentration fluctuations in polymer solutions by Hashimoto and Kume, J. Phys. Soc. Jap. 1992
•!Observed for shearing wormlike micelles by van Egmond (1997) and others…
Thareja et al. JOR 2012
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New sample environment: shear cell SpatioTemporal Resolved Small Angle Neutron Scattering (1-2 flow-STR SANS)1,2,3
Aaron Eberle
A$$'(1) Velocity (2) Velocity gradient (3) Vorticity
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