Rigid Rod Probes of Concentrated Polymeric Solutions

Randy Cush* & Paul RussoLouisiana State University

Marrucci Symposium—74th Society of Rheology MeetingOctober 15, 2002 -- Twin Cities

*Current address: Syngenta, North Carolina You’re going to make it after all!

DLS for Molecular Rheology of Complex Fluids:Prospects & Problems

+ + + 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.

Studied a lot

Barely studied

Solution: Use Polarizers to Hide Matrix

Dynamic Light ScatteringDynamic Light Scattering

Hv = q2Dtrans + 6Drot

LASER

VV HH

PMT

Hv Geometry Hv Geometry (Depolarized)(Depolarized)

Uv Geometry Uv Geometry (Polarized)(Polarized)

VV

Uv = q2Dtrans

o

nq

2/sin4

PMT

LASER

StrategyStrategy

•Find polymer that should not “entangle”

•Find a rodlike probe that is visible in DDLS

•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

Dextran

Ficoll

TMV

•Find polymer that should (???) “entangle”

BARELYBARELY

0 5 10 15 20 25 30 35 400

1

2

3

4

5

6

7

8

9

10

11

BothViscosity

sp/c

/dL

-g-1

c/g-dL-1

Dextran 670,000 Ficoll 420,000

As expected…

Seedlings

Sick Plants And close-up of mosaic pattern.

DIY farming--keeping the “A” in LSU A&M

TMV CharacterizationTMV 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)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

200

300

400

500D

t /10-8cm

2s-1

Dr /

s-110 L3

c/mg-mL-1

0

1

2

3

4

5

6

Rotation

Translation

Experiments are in dilute regime. TMV overlap (1/L3)

All measurements made at low TMV concentrations—no self-entanglement

Hv correlation Hv correlation functions for 14.5% functions for 14.5% dextran and 28% dextran and 28% ficoll with and ficoll with and without added without added 0.5 mg/mL TMV0.5 mg/mL TMV

The dilute TMV The dilute TMV easily “outscatters” easily “outscatters” either matrixeither matrix

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10 100

1.0

1.2

1.4

Ficoll >6000 s acquisition

TMV + Ficoll 600s aquisition

g(2

)

t/s

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10 1000.9

1.0

1.1

1.2

1.3

Dextran >6000 s acquisition

TMV + Dextran 215 s acquisition

g(2

)

t/s

Matrix is invisible

0 1 2 3 4 5

0

500

1000

1500

2000

2500

3000

3500

4000

Hv TMV / Dextran / Buffer

Uv TMV / Buffer

Hv TMV / Buffer

/s-1

q2/1010 cm-2

Hey, it works!

I didn’t think—I experimented.

---Wilhelm Conrad Roentgen

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

Dtr

ans/1

0-8 c

m2

s-1

wt% dextran0 2 4 6 8 10 12 14 16

0

50

100

150

200

250

300

350

Dro

t/ s-

1

wt% dextran

Early results—very slight errors

rotation translationMacromolecules 1997,30, 4920-6.

0 5 10 15 20

0

2

4

6

8 /cP

Dr/D

t /1

09 cm-2

wt % dextran

0 5 10 15 20

0

20

40

60

80

Dextran overlap

Macromolecules 1997,30, 4920-6.

At the sudden transition: L/c.m. ~ 13 and L/ ~ 120

L

cm

Stokes-Einstein Plots: if SE works, thesewould be flat. Instead, apparent deviations in

different directions for Drot and Dtrans

0 2 4 6 8 10 12 14 16

0.0

0.5

1.0

1.5

Dt /10

-9g-cm

-s-2

Dr /

g-cm

-1-s

-1

wt% Dextran

0

2

4

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 300

1

2

3

4

5

6

Dtr

an

s/10-

8 cm

2 s-

1

wt% ficoll

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

0

50

100

150

200

250

300

350

Dro

t/ s-

1

wt% ficoll

rotation

translation

END OF PUBLISHED DATA

We believed that the transition represented topological constraints.

It was suggested that more systems be studied.

BEGIN FICOLL

When we did Ficoll, many more points were added!

0 5 10 15 20 25 300.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Dtra

ns /10

-9g-cm-1-s

-1

Dro

t /g-

cm-1-s

-1

wt% ficoll

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Huh? Drot still diving in Ficoll?

rotationtranslation

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…

TMV = 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

q2 q2 q2

Drot too low

6Drot6Drot

Even at the highest concentrations, only a few degrees out of alignment.

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 360

50

100

150

200

250

300

Op

tica

l Ro

tatio

n /

arc

-min

ute

s

wt %

Dextran Ficoll

0 5 10 15 20 25 30 35

0

50

100

150

200

250

300

350

NewFicollRatio_PR

Right way Wrong way

Dro

t / s

-1

wt% ficoll

Slight, but important, improvement.

Improved Drot/Dtrans Ratio Plots

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160

1

2

3

4

5

6

7

8

NewDexConcStudy_PR

Dro

t/Dtr

ans/

109 cm

-2

wt% dextran0 5 10 15 20 25 30 35 40

0

1

2

3

4

5

6

7

8

NewFicollRatio_PR

Dro

t/Dtr

ans/

109 c

m-2

wt% ficoll

Improved Stokes-Einstein PlotsBlack = TMV Translation

Blue = TMV Rotation

0 2 4 6 8 10 12 14 160.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0

0.2

0.4

0.6

0.8

NewDexConcStudy_PR

Dro

t/g-c

m-1s-1

wt% dextranD

trans /10-9g-cm

-s-2

0 5 10 15 20 25 30 350.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0

0.2

0.4

0.6

0.8

NewFicollRatio_PR

Dro

t/g-c

m-1 s

-1

wt% ficoll

Dtrans / 10

-9g-cm-s

-2

Check Dtrans by FPR a.k.a. FRAP

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160

1

2

3

4

5

6

FPRtmvDex_PR

Hv DLS FPR

Dtr

ans/

10-8

cm2 s-1

wt% dextran

Hydrodynamic Ratio—Effect of Matrix M at High Matrix Concentration

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

8

9DextranMWStudy_PR

Dro

t/Dtr

ans/

109 cm

-2

dextran MW/ 105 daltons

Effect of Dextran Molecular Weight—High Dextran Concentration (~ 15%)

10000 100000 1000000 1E71

10

100

DextranMWStudy_PR

-0.62 ± 0.04

Dro

t / s

-1

Dextran MW10000 100000 1000000 1E7

0.1

1

10

DextranMWStudy_PR

-0.72 ± 0.01

Dtr

ans/

10-9

cm

2 s-1

Dextran MW

TMV Translation TMV Rotation

Randy CushDavid Neau

Ding Shih

Holly Ricks

Jonathan Strange

Amanda Brown

Zimei Bu

Zuhal & Savas Kucukyavuz--METU

Seth Fraden—Brandeis

Nancy Thompson—Chapel Hill

NSF

Depolarized DLS—new opportunities in nanometer-scale rheology.

THE END

1 10 100

0.01

0.1

1

10

100

1000

10000

G' /

Pa

/ Hz

5% w/w 30% w/w 35% w/w 40% w/w

Behavior of Dextran Matrix

log

log

G’

Expected

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

Ld

1

1

3

3

3

L

L

L

1

1

2

2

2

dL

dL

dL

1

14

2

2

2

2

A

A

dLA

LC formation = 4/A2 5/dL2

Reduced # Density dL2/5

Doi-Edwards-Onsager Reference Volumes for Rods = number density = # of rods per unit volume

Thank you!

LSU

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

Conditions for use as a ProbeConditions 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 ConcentrationEffect 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 Francewho wondered how molecules dance.“They’re like snakes,” he observed, “As they follow a curve, the large onesCan hardly advance.”

D ~ M -2

P.G. de GennesScaling Concepts in Polymer Physics

Cornell University Press, 1979

de Gennes

OutlineOutline• 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 TMVhas protein subunits (ca. 2130). The protein

subunits enfold a spiral-wound strand of RNA whichwill encode the next generation. TMV is more

extended than an ear of corn.

Effect of Ficoll ConcentrationEffect 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.

0 5 10 15 20 25 300

2

4

6D

rot /

Dtr

ans

/109 cm

-2

wt% ficoll

0

20

40

60

80/ cP

0 10 20 30 40 50 60

-1

0

1

2

3

4

5

6

7

8 Ficoll Dextran

Dro

t / D

tran

s/ 1

09 cm-2

/ cP

Too-Good-to-be-True Conclusion?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 M-dependent stuff done?

Entanglement in solution?Entanglement in solution?

To isolate spaghetti in "solution" with a fork is To isolate spaghetti in "solution" with a fork is difficult: hydrodynamic interactions interfere difficult: hydrodynamic interactions interfere with entanglement. After solvent is drained to with entanglement. After solvent is drained to obtain a "melt" the entire blob is easily handled. obtain a "melt" the entire blob is easily handled.

Collander