Confined Polymers: unity of thought * in the test tube * in polymer brushes * in mesoscopic channels - PowerPoint PPT Presentation

Confined Polymers: unity of thought * in the test tube * in polymer brushes * in mesoscopic channels

Adrian Parsegian and many friends:

Sergey Bezrukov, Joel Cohen, Per Lyngs Hansen, Rudi Podgornik, et al., et al.

Laboratory of Physical and Structural Biology,

National Institute of Child Health and Human Development,

National Institutes of Health

http://lpsb.nichd.nih.gov

~nm

~cm

~10 nm

~nm

Peter Rand, Don Rau & VAP (1973 - ?)measure osmotic pressures of neutral polymer solutionsused then to measure forces between molecules under osmotic stress

Posmotic

Rand, Rau et al

small

big

Noda et al

cp = molar concentration

Cp = weight concentration

Mm = monomer weight

N = degree of polymerization

Low concentration, van’t Hoff law

High conc, des Cloiseaux 9/4ths law

Cp* ~ polymer concentration at which there is one polymer occupying each "pervaded" volume of a random coil polymer whose size is that at infinite dilution.

~ 1, crudely speaking

Ansatz: Add these two limits

and

Neat trick (Joel Cohen): Take Cp/N = (Cp/Cp*) Cp*/N

Recall Cp*~ N-4/5 /V-bar from the constraint that dC shows no N dependence).

Plot N9/5 vs. Cp/Cp*

Scaled forms

 = .48 +- .01

 = .161 +-.002

Added van’t Hoff and des Cloiseaux forms.

Extracted N9 from each term, vH and dC.

Defined C# = -4/5 C*

All the  and N dependence factored out to give a new “universal” form.

(Maybe think of C# as what C* would have been if we had our lives to live over.)

Weird thought: If/when this procedure is reliable, we need only one osmotic pressure measurement - well into the des Cloiseaux regime - for the entire set of sizes and concentrations.

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~cm

~10 nm

~nm

Posmotic

~ cm

~nm

Equilibrate in high-concentration 9/4-power limit

~nm

+ Posmotic

% PEG-grafted lipids

Fit by Hansen et al. BJ (2003)

Des Cloizeaux

9/4 limit

Data from Kenworthy et al. BJ (1995)

Normal

exp(-df/3A) hydration forces

De Gennes, Adv. Coll. & Interf. Sci. 27:189 (1987)Two types of grafted surfaces: a) low grafting – the distance between heads D is larger than the coil size RF, (“mushroom”)b)high grafting density D < RF, (“brush”)

Fit by Hansen et al. BJ (2003)

9/4 des Cloizeaux 

plus 3/4 elastic grafting constraints

Normal

exp(-df/3A) hydration forces

Data from Kenworthy et al. BJ (1995)

~nm

~cm

~10 nm

~nm

~10 nm

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I

Bezrukov, et al.

conductance of channels between polymer solutions

~10 nm

~2nm

Conductance reduced

in proportion to bath conductivity

~10 nm

~2nm

~5 nm

Zero Partitioning big guys

1000

800

600

Conductance, pS

400

Equipartitioning small guys

200

0

5

10

15

20

25

30

PEG, weight %

PEG3400

PEG200

PEG1500

PEG2000

Bezrukov, Vodyanoy, Brutyan, Kasianowicz, Macromolecules 29:8517 (1996)

Bezrukov, Vodyanoy, Parsegian, Nature, 370:279-281, 1994

1.0

0.8

Partition Coefficient

(from conductance ratio)

0.6

0.4

c*

0.2

0.0

0

5

10

15

20

25

30

PEG 3400, weight %

~ 2/3 of a molecule inside

at 30 wt %

Krasilnikov & Bezrukov, Macromolecules 37 (2004)

MW 3400 ~ 77 monomers of length 3.4 Angstroms

Stretches to ~ 28 nm (vs. ~10 nm length of pore)

Rg ~ 2.5 nm in dilute solution ( vs. ~ 1 nm radius of pore)

Consider 30 wt % PEG solu, just at the concentration to fill the pore:

300 (gm/liter) /44 (gm/mole) = 6.8 molar monomer PEG

x 6x1023 x 103 litre/m3 ==> 4.1 monomers/nanometer3

2) Channel volume: radius = 1 nm, length = 5 nm; v = 5  = 16 nm3

3) 4.1 monomers/nm3 x 16 nm3 = 66 monomers/channel volume

4) 66 monomers x 44 gm/mole monomer =

2,948 -- the MW of a PEG that fills pore at 30 wt %.

MW 3400 PEG slightly more than fills channel at 30 wt %.

High-concentration regime as “ideal” limit (des Cloizeaux) Pressure of bath ==>* small correlation length, * drive into channel of similar dimensionMovement of molecules in cells

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~cm

~10 nm

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Test-tubes, brushes, pores new unity in thinking about * large molecules at high concentration *the interior of cells and pores