Transcript DIFFUSION OF A RODLIKE VIRUS IN POLYMER SOLUTIONS

Rigid Rod Probes of Concentrated
Polymeric Solutions
Randy Cush* & Paul Russo
Louisiana State University
*Current address:
Syngenta, North Carolina
You’re going to make it after all!
Marrucci Symposium—74th Society of Rheology Meeting
October 15, 2002 -- Twin Cities
DLS for Molecular Rheology of Complex Fluids:
Prospects & Problems
Studied a lot
Barely studied
+ + + Wide-ranging autocorrelators
> 10 decades of time in one measurement!
– – – Contrast stinks: everything scatters, esp.
in aqueous systems or most supercritical
fluids, where refractive index matching
cannot hide the matrix.
Solution: Use Polarizers to Hide Matrix
Dynamic Light Scattering
LASER
Uv = q2Dtrans

V
LASER

V
H
Hv = q2Dtrans + 6Drot
q
4n sin / 2
o
Uv Geometry
(Polarized)
Hv Geometry
(Depolarized)
Strategy
•Find polymer that should (???) “entangle”
Dextran
•Find polymer that should not “entangle”
Ficoll
•Find a rodlike probe that is visible in DDLS
TMV
•Measure its diffusion in solutions of
each polymer separately
•Random coil
•Polysaccharide
•Invisible in HvDLS
•Highly-branched
•Polysaccharide
•Invisible in HvDLS
•Rigid rod
•Virus
•Visible in HvDLS
BARELY
As expected…
BothViscosity
11
Dextran 670,000
Ficoll 420,000
10
9
8
hsp/c /dL-g
-1
7
6
5
4
3
2
1
0
0
5
10
15
20
c/g-dL
25
-1
30
35
40
DIY farming--keeping the “A” in LSU A&M
Seedlings
Sick Plants 
And close-up of
mosaic pattern.
TMV Characterization
Sedimentation, Electron Microscopy and DLS
•Most TMV is intact.
•Some TMV is fragmented
–(weaker, faster mode in CONTIN)
•Intact TMV is easy to identify
–(stronger, slower mode in CONTIN)
All measurements made at low TMV
concentrations—no self-entanglement
nL
0
1
3
6
5
-8
Dr /s
Translation
Dt /10 cm s
-1
500
400
Rotation
3
300
2
Experiments are
in dilute regime.
3
TMV overlap (1/L )
1
200
0
0.0
0.5
1.0
1.5
2.0
c/mg-mL
-1
2.5
3.0
2 -1
4
Matrix is invisible
TMV + Dextran 215 s acquisition
1.3
g
(2)
1.2
1.1
1.0
Dextran >6000 s acquisition
0.9
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
Hv correlation
functions for 14.5%
dextran and 28%
ficoll with and
without added
0.5 mg/mL TMV
t/s
g(2)
1.4
TMV + Ficoll 600s aquisition
The dilute TMV
easily “outscatters”
either matrix
1.2
Ficoll >6000 s acquisition
1.0
1E-6
1E-5
1E-4
1E-3
0.01
t/s
0.1
1
10
100
Hey, it works!
4000
3500
/s
-1
3000
Hv TMV / Buffer
2500
2000
Uv TMV / Buffer
1500
1000
Hv TMV / Dextran / Buffer
500
0
0
1
2
3
2
10
4
-2
q /10 cm
5
I didn’t think—I experimented.
---Wilhelm Conrad Roentgen
Early results—very slight errors
350
6
/10-8cm2 s-1
300
200
trans
150
100
5
4
3
2
D
rot
D / s-1
250
50
1
0
0
0
2
4
6
8
10
wt% dextran
rotation
12
14
16
0
2
4
6
8
10
12
14
16
wt% dextran
translation
Macromolecules 1997,30, 4920-6.
At the sudden transition: L/xc.m. ~ 13 and L/x ~ 120
x
Dextran overlap
5
10
15
20
9
8
80
6
60
4
40
2
20
h/cP
Dr/Dt /10 cm
-2
0
xcm
L
0
0
0
5
10
15
20
wt % dextran
Macromolecules 1997,30, 4920-6.
Stokes-Einstein Plots: if SE works, these
would be flat. Instead, apparent deviations in
different directions for Drot and Dtrans
2
4
6
8
10
12
14
16
1.5
-1
4
-9
hDt /10 g-cm-s
hDr /g-cm -s
-1
0
1.0
-2
2
0.5
0
0.0
0
2
4
6
8
wt% Dextran
10
12
14
16
350
300
END OF PUBLISHED DATA
D / s-1
200
rot
We believed that the
transition represented
topological constraints.
rotation
250
150
100
50
It was suggested that more
systems be studied.
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
wt% ficoll
trans
When we did Ficoll, many
more points were added!
D
BEGIN FICOLL
/10-8cm2 s-1
6
translation
5
4
3
2
1
0
0
2
4
6
8
10
12
14
16
18
wt% ficoll
20
22
24
26
28
30
Huh? Drot still diving in Ficoll?
3.5
0.8
2.5
0.6
-1
rotation
0.5
2.0
0.4
1.5
0.3
1.0
0.2
0.0
0.0
0
5
10
15
20
wt% ficoll
25
30
-1
0.1
-1
0.5
-9
hDrot /g-cm -s
-1
0.7
hDtrans /10 g-cm -s
3.0
translation
Maybe we should think now.
The chiral dextran and ficoll alter
polarization slightly before and
after the scattering center.
With a strongly depolarizing probe,
this would not matter, but…
rTMV = IHv/IUv ~ 0.003
While matrix scattering is minimal,
polarized scattering from TMV
itself leaks through a “twisted” Hv
setup.
Most damaging at low angles
Mixing in Polarized TMV Light
Uv light from misalign True Hv light



6Drot
q2
Drot too low
q2
6Drot
q2
Even at the highest concentrations,
only a few degrees out of alignment.
300
Optical Rotation / arc-minutes
250
Dextran
Ficoll
200
150
100
50
0
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
wt %
Slight, but important, improvement.
NewFicollRatio_PR
350
Right way
Wrong way
300
Drot / s
-1
250
200
150
100
50
0
0
5
10
15
20
wt% ficoll
25
30
35
Improved Drot/Dtrans Ratio Plots
NewDexConcStudy_PR
8
7
7
6
6
Drot/Dtrans/ 10 cm
-2
-2
8
5
5
9
9
Drot/Dtrans/ 10 cm
NewFic
4
3
2
1
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
wt% dextran
0
0
5
10
15
20
25
wt% ficoll
30
35
40
Improved Stokes-Einstein Plots
Black = TMV Translation
Blue = TMV Rotation
NewFicollRatio_PR
NewDexConcStudy_PR
5.0
5.0
0.8
4.5
2.0
1.5
0.5
0.6
3.0
2.5
0.4
2.0
1.5
0.2
1.0
0.5
0.0
0
2
4
6
8
10
wt% dextran
12
14
0.0
16
0.0
0.0
0
5
10
15
20
wt% ficoll
25
30
35
-2
1.0
-2
0.2
3.5
-9
0.4
-9
2.5
-1
3.0
hDrot/g-cm s
0.6
hDtrans/ 10 g-cm-s
3.5
-1
4.0
hDtrans/10 g-cm-s
-1 -1
4.0
hDrot/g-cm s
0.8
4.5
Check Dtrans by FPR a.k.a. FRAP
FPRtmvDex_PR
6
Hv DLS
FPR
-8
Dtrans/ 10 cm s
2 -1
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
wt% dextran
Hydrodynamic Ratio—Effect of Matrix M
at High Matrix Concentration
DextranMWStudy_PR
9
8
-2
5
Drot/Dtrans/10 cm
6
9
7
4
3
2
1
0
0
2
4
6
8
10
12
5
14
16
dextran MW/ 10 daltons
18
20
Effect of Dextran Molecular Weight—
High Dextran Concentration (~ 15%)
TMV Translation
TMV Rotation
DextranMWStudy_PR
DextranMWStudy_PR
100
10
-9
Drot / s
-1
2
Dtrans/ 10 cm s
-1
-0.62 ± 0.04
-0.72 ± 0.01
1
0.1
10000
100000
1000000
Dextran MW
1E7
10
1
10000
100000
1000000
Dextran MW
1E7
Depolarized DLS—new opportunities
in nanometer-scale rheology.
Randy Cush
David Neau
Ding Shih
Holly Ricks
Jonathan Strange
Amanda Brown
Zimei Bu
Zuhal & Savas Kucukyavuz--METU
Seth Fraden—Brandeis
Nancy Thompson—Chapel Hill
NSF
THE END
Behavior of Dextran Matrix
10000
5% w/w
30% w/w
35% w/w
40% w/w
1000
Expected
10
log G’
G' / Pa
100
1
0.1
log w
0.01
1
10
w / Hz
100
Misalignment from thick polarizer in “active” part
of detector train, exacerbated by tiny cells
used to squelch optical rotation & conserve TMV
shifted by thick polarizer element
correctly aligned scattered beam
Doi-Edwards-Onsager Reference Volumes for Rods
n = number density = # of rods per unit volume
d
LC formation
n* = 4/A2  5/dL2
L
Reduced # Density
n/n*  ndL2/5
3
2
L
dL
1
n 3
L
nL3  1
1
n 2
dL
ndL2  1
A2 
n
dL2
4
1
A2
nA2  1
Thank
you!
Randy Cush
David Neau
Ding Shih
Holly Ricks
L
S
U
Jonathan Strange
Amanda Brown
Zimei Bu
Zuhal & Savas Kucukyavuz--METU
Seth Fraden—Brandeis
Nancy Thompson—Chapel Hill
NSF
Conditions for use as a Probe
•Is the TMV Probe Dilute?
A TMV concentration of 0.5 mg/mL, well below the
theoretical overlap concentration, was chosen. See Figure 2.
•Does dilute TMV overwhelm the matrix scattering?
At 0.5 mg/mL the TMV easily “outscatters” both matrices.
See Figure 3.
•Is the probe compatible with the matrix?
-Solutions stable months after preparation
-Angle dependent Hv SLS
-Dtrans goes up, not down (Figures 6 & 8)
Effect of Dextran Concentration
• The dependence of Drot and Dtrans upon added
dextran
is shown in Figure 4.
• The quotient Drot/Dtrans is plotted against viscosity in Figure
5. By combining both transport coefficients, each inversely
proportional to viscosity in dilute solution, we can remove
the effect of solution viscosity.
• Figure 6 reveals like positive deviations from the
Stokes-Einstein continuum expectation that diffusion be
inversely proportional to viscosity (below 6.5%).
•Above 6.5% the deviations become greater for both Drot
and Dtrans but in opposite directions
There once was a theorist from France
who wondered how molecules dance.
“They’re like snakes,” he observed,
“As they follow a curve, the large ones
Can hardly advance.”
D ~ M -2
de Gennes
P.G. de Gennes
Scaling Concepts in Polymer Physics
Cornell University Press, 1979
Outline
• Characterize the TMV
– Is it intact and behaving properly?
• Establish conditions for use of TMV as probe
– Can the probe be dilute and still overwhelm the
matrix scattering?
– Will the probe stay mixed with the matrix solutions
without aggregating?
• Show the effect of the dextran and ficoll
matrices on TMV diffusion
An ear of corn has about as many kernels as TMV
has protein subunits (ca. 2130). The protein
subunits enfold a spiral-wound strand of RNA which
will encode the next generation. TMV is more
extended than an ear of corn.
Effect of Ficoll Concentration
• The dependence of Drot and Dtrans upon added dextran
is shown in Figure 4.
• The quotient Drot/Dtrans is plotted against viscosity in
Figure 7.
• Figure 8 shows slight like positive deviations from the
Stokes-Einstein continuum expectation (below 11%).
• Above about 11% ficoll the deviation slowly becomes
greater for Drot and slightly greater for Dtrans but in
opposite directions
• Figure 9 compares TMV behavior in ficoll to that in
dextran.
80
9
60
4
40
2
20
0
0
0
5
10
15
20
wt% ficoll
25
30
h/ cP
Drot /Dtrans /10 cm
-2
6
Ficoll
Dextran
9
Drot / Dtrans/ 10 cm
-2
8
7
6
5
4
3
2
1
0
-1
0
10
20
30
h/ cP
40
50
60
Too-Good-to-be-True Conclusion?
• Below 6.5% dextran the diffusion of the rodlike
TMV probe is controlled mostly by viscosity.
• Above 6.5% dextran a sharp transition suggests
topological constraint for TMV rotation while
translation is not much affected.
• The transition is more gradual in ficoll.
• The TMV probe senses something different for
linear vs. highly branched polymers in solution.
• Looks good for topological models!
Alternate Conclusion?
• The systems studied so far place (impossibly?)
strict demands on geometric & polarization
alignment.
– Revised polarization placement
– Difficult zero angle measurements requiring even more
TMV
• New systems must be studied:
– TMV is OK
– Dextran/Ficoll must go!
• Depolarized probe diffusion has the potential, as
yet unrealized, to assess strength of
hydrodynamic vs. topological effects.
To Do
Get Cush to estimate the total number
of TMV’s he produced.
Slopes of intrinsic viscosity plot don’t
meet the 0.5 rule.
What has Deutch & Pecora to do with
Dtrans vs. M?
What does regular viscosity have to
say about M-dependence?
At what concentration was that Mdependent stuff done?
Entanglement in solution?
Collander
To isolate spaghetti in "solution" with a fork is
difficult: hydrodynamic interactions interfere
with entanglement. After solvent is drained to
obtain a "melt" the entire blob is easily handled.