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### Thermally Driven Migration in LBE

### Thermal Diffusion Coefficient

### Fluid Stress Near Particles

### Particle Thermal Diffusion Coefficient

陳彥龍Yeng-Long Chen

Institute of Physics and Research Center for Applied Science

Academia Sinica

To understand and manipulate the structure and dynamics of biopolymers with statistical physics

Micro- and Nano-scale Building Blocks

Diameter: 7nm

Persistence length : ~10 mm

Endothelial Cell

F-Actin

DNA

Rg

3.4 nm

Nuclei are stained blue with DAPI

Actin filaments are labeled red with phalloidin Microtubules are marked green by an antibody

xp

Persistence length : ~ 50 nm

Mironov et al. (2003)

Boland et al. (2003)

Forgacs et al. (2000)

- Cells deposited into gel matrix fuse when they are in proximity of each other
- Induce sufficient vascularization
- Embryonic tissues are viscoelastic
- Smallest features ~ O(mm)

Organ printing and cell assembly

Fluid plug reactor from Cheng group, RCAS

Advantages of microfluidic chips

Channel dimension ~ 10nm - 100 mm

- High throughput
- Low material cost
- High degree of parallelization

Efficient device depends on controlled transport

Theory and simulations help us understand dynamics of macromolecules

Coarse graining

Microchannels

1 nm

1 mm

10 mm

C-C bond length

Radius of gyration

l

l

l

l

3.4 nm

F

F

F

F

1

1

1

1

F

F

F

F

2

2

2

2

2 nm

Multi-Scale Simulations of DNAMulti-component systems : multiple scales for different components

Nanochannels

10 nm

100 nm

Persistence length ≈ 50nm

Essential physics :

DNA flexibility

Solvent-DNA interaction

Entropic confinement

Molecular Dynamics

- Model atoms and molecules using Newton’s law of motion

Monte Carlo

- Statistically samples energy and configuration space of systems

Cellular Automata

- Complex pattern formation from simple computer instructions

Large particle in a granular flow

Polymer configuration sampling

Sierpinksi gasket

- If alive, dead in next step
- If only 1 living neighbor, alive

l

F

1

T

4

F

2

5

m

m

R||

m

2

m

DNA Trapped in Nanoslit

Does the shape of the molecule change as it grows longer ?

R1

R2

Monte Carlo N=256 SAW H=2s slit

Po-keng Lin et al. PRE (2007)

Rg2 ~ Nn

Virtual & Real Experiments

Real Experiments

Rg ~ N0.68

trelax~N2.2

rod

slit(H=5s) 2D Slit(2D proj)

R12 n=1.21 1.51 1.33

R22n=1.20 1.51 1.33

Rg2n=1.19 1.53 1.35

sphere

Coarse-grained DNA Dynamics

DNA is a worm-like chain

2a

f ev(t)

l-DNA 48.5 kbps

f W(t)

DNA as Worm-like Chain

L = 22 m

Ns = 10 springs

Nk,s = 19.8 Kuhns/spring

f S(t)

Marko and Siggia (1994)

Model parameters are matched to TOTO-1 stained l-DNA

Parameters matched in bulk are valid in confinement !

Chen et al., Macromolecules (2005)

v1

v2

v3

Brownian DynamicsHow to treat solvent molecules ??

Explicit inclusion of solvent molecules on the micron scale is extremely computational expensive !!

solvent = lattice fluid (LBE)

Brownian motion through fluctuation-dissipation

z: particle friction coef.

Replace continuum fluid with discrete fluid positions xiand discrete velocity ci

3D, 19-vector model

Hydrodynamic fields are moments of the velocity distribution function

ni(r,v,t) = fluid velocity distribution function

Ladd, J. Fluid Mech (1994)

Ahlrichs & Dünweg, J. Chem. Phys. (1999)

Boltzmann eqn.

Fluid particle collisions relaxes fluid to equilibrium

Lij = local collision operator

=1/t in the simplest approx.

Hydrodynamic Interactions (HI)

Particle motion perturbs and contributes to the overall velocity field

Free space

Wall correction

Force

Stokes Flow

Solved w/

Finite Element Method

For Different Channels

z

DNA Separation in Microcapillary

T2 DNA after 100 s oscillatory Poiseuille flow

detector

25 mm

l-DNA in microcapillary flow

40mm

Sugarman & Prud’homme (1988)

Chen et al.(2005)

Detection points at 25 cm and 200 cm

Parabolic Flow

Longer DNA higher velocity

h

Dilute DNA in Microfluidic Fluid Flow

l-DNA Nc=50, cp/cp*=0.02

We=( trelax)

geff = vmax / (H/2)

Chain migration to increase as We increases

Ld

Non-dilute DNA in Lattice Fluid Flow

Lattice Size = 40 X 20 X 40, corresponding to 20 x 10 x 20 mm3 box

Nc=50, 200, 400

We=100 Re=0.14

As the DNA concentration increases, the chain migration effect decreases

40mm

H = 10 mm

- Tcold

- Thot

Thermal-induced DNA Migration

y

Migration of a species due to temperature gradient

Thermal Diffusion

Mass Diffusion

Particle Current

Soret Coefficient

Thermal fractionation has been used to separate molecules

Many factors contribute to thermal diffusivity –

a “clean” measurement difficult

Hydrodynamic interactions

Wiegand, J. Phys. Condens. Matter (2004)

Factors that affect DT:

Colloid Particle size

DT ↑ as R ↑ (Braun et al. 2006)

DT↓ as R ↑ (Giddings et al. 2003, Schimpf et al., 1997)

Polymer molecular weight

DT ~ N0(Schimpf & Giddings, 1989, Braun et al. 2005, Köhler et al., 2002, …)

DT ↓ as N ↑ (Braun et al. 2007)

Electrostatics ?

Solvent quality :

DT changes sign with good/poor solvent (Wiegand et al. 2003)

DT changes sign with solvent thermal expansion coef.

Tcold

Thot

T=10

T=2

T=0

TH

TC

g(y)

0

2

4

6

8

10

y,m

T(y)=temperature at height y

Thermal migration is predicted with a simple model

Simple model appears to quantitatively predict DT

DT is independent of N – agrees with several expt’s

What’s the origin of this ?

T=7

T=4

T=2

T=0

Thot

Tcold

Momentum is exchanged between monomer and fluid through friction

Dissipation of Y-dependent fluctuations leads to a hydrodynamic stress in Y

DT decreases with particle size 1/R

– agrees with thermal fractionation device experiments

DT independent of temperature gradient

(Many) Other factors still to include …

DT=4

g(y)

1.0

2.0

0.2

0

0.4

0.8

y/H

1.0

0

0.2

0.4

0.6

0.8

1.0

y/H

Thermal and Shear-induced DNA Migration

Thermal gradient can modify the shear-induced migration profile

Thermal diffusion occurs independent of shear-induced migration

TH

TC

DT=4

As N ↑, D ↓, ST↑

stronger shift in g(y) for larger polymers

40mm

σm

f r(t)

f bend(t)

~2nm

f ev(t)

f vib(t)

Summary and Future Directions

- Shear and thermal gradient can be used to control the position of DNA in the microchannel and their average velocity
- Shear and thermal driving forces for manipulating DNA appear to have weak or no coupling => two independent control methods.
- Inclusion of counterions and electrostatics will make things more complicated and interesting.

- How “solid” should the polymer be when it starts acting as a particle ?
- As we move to nano-scale channels, what is the valid model?
--can we choose the coarse-graining dynamically ?

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