Thermodynamics and Kinetics of a Brownian Motor.pdf

7/30/2019 Thermodynamics and Kinetics of a Brownian Motor.pdf

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Thermodynamics and Kinetics of

a Brownian Motor

R Dean Astumian

Shreya Ray 20091069Prashant Beeraka 20091032


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Langevins Thermal Noise

Brownian Motion of Particles in solvent has two components:

Fluctuating force that changes direction and magnitude very fast, averages to zero over

time = THERMAL NOISEViscous drag force damps the motion induced by these fluctuations

The amplitude of thermal noise depends on:

Viscosity (which again dampens it)

Temperature


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Feynmans Ratchet and Pawl

Allows motion only in onedirection (sawtooth potential)

Diffusion acts in both directions,

but ratchet moves only in one

direction: So can we have a

perpetual motion machine thatviolates the Second Law of

Thermodynamics? (Can

anisotropy drive a motor?)

NO. Despite the anisotropy, without an energy supply, probabilities of moving in either

direction are exactly EQUAL. (counterintuitive?)

We need to couple diffusion to thermal gradient/gravity/electrostatic or any other force field

in order to extract work.


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Noise harms, Noise heals

Electrophoresis, centrifugation, chromatography: Long-range gradients used. Thermal noisecauses band-broadening. Must be turned off each time a new batch of particles is added.

Coupling short-range non-equilibrium fluctuations in an anisotropic medium with diffusive

Brownian motion can bias the direction of motion. In fact, the thermal noise provides part

of the energy required to for transport across energy barrier!

So, small voltages are required; can be used continuously.

Fluctuation-driven transport requires:

Thermal Noise to cause Brownian motion

Anisotropy arising from the structure of the medium

Energy supplied either by external variation of constraints or by a chemical reaction far

from equilibrium (the fluctuation)


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The Anisotropic Periodic Potential

Interdigitated electrodes

deposited on glass usingphotolithography

Linear array of dipoles aligned

head-to-tail, via

aggregation/polymerisation

Alpha=anisotropy parameter


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Flashing Ratchet : Fluctuating Potential

Uphill transport against sufficiently small Fext

Sawtooth potential is periodically turned on

and off

On-state favours trapping inside well- going

back is difficult

Off-state favours thermal diffusion to the right

side too, although gaussian probability

distribution drifts downhill.

Toffshould be sufficient for this diffusion to

occur. It should however not be high enough

for velocity drift.

Larger particles diffuse slowly- principle of

separation? Too broad

Assisted by tilting (gravity) or constant electric

field.


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Rocking Ratchet: Fluctuating Force

Square wave modulation of sawtooth potential

Overall, favours motion in the direction of

sharper edge of sawtooth because of

appearance of traps in the other direction.

Mean velocity increases with the push given by

the square wave, but this shouldnt be so largeas to mask the effects of sawtooth.

Mean velocity increases when this process is

assisted by thermal noise upto an optimum T,

beyond which again noise becomes unwanted.

(too shallow wells)


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Chemical Modulation

Our particle catalyses hydrolysis of SH

Local conc. Of S and H vary with position

because of dipole array, hence a sawtooth

potential

Away from eqm transition probability is same

in all directions

Near eqm we have trabsitions from charged to

uncharged form and vice-versa

Charged state is affected by dipole, neutral

state is not: an on-off switch

Mean velocity increases away from eqm, as

delG produces the sawtooth. Larger barriers,

however, disfavour the process.


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Molecular Pumps and Motors

External oscillating fields have been shown to drive transport by the sodium-potassium

triphosphatase ion pump

Externally imposed electric oscillations can substitute for energy from ATP-hydrolysis to

power uphill transport of ions

It is not clear whether molecular motors too use this mechanism

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Thermodynamics and Kinetics of a Brownian Motor.pdf