Lecture 02 Colloids

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Colloids

Lecture 02

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Soft Condensed Matter (Spring 2019) Instructor: Jihoon Choi 77

Condensation and Freezing

Upon cooling, a collection of molecules exhibit its physical state changes (gas - liquid - solid).

• At high temperature,

→ the attractive forces between molecules are weak compared to the thermal energy gas (very little correlation between the motions of different molecules)

→

• As the temperature is reduced,

→ the attractive forces between molecules start to become more important.

on colliding, pairs of molecules stay together longer and correlations between the motion of different molecules start to appear, with clusters of molecules forming and breaking up.

→

new and dense phase of the material = liquid

→

kinetic E of motion + attractive E of interaction between the molecules

→

kinetic E of motion

→

• As the temperature is decreased further,

→ by packing the molecules together in a regular way, higher density of molecules; frozen

→ larger contribution from the attractive part of the potential

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Condensation and Freezing

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Viscous, Elastic, and Viscoelastic Behaviour

• Normal condensed matter comes in two forms, solid and liquid. Typical ‘soft condensed matter’ seems more difficult to classify.

solid or liquid ?

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Viscous, Elastic, and Viscoelastic Behaviour

(viscous liquid)

• Newtonian liquid (time and shear rate independent viscosity)

y u(h) = h

area A ∆x V

area A F

∆x F

y θ

y V

Force (F) resisting the relative motion of the plates:

(the coefficient η is the viscosity of the fluid)

The velocity gradient V/y is identical to the time derivative of the shear strain e′

F = Aη y V

shear strain (e) = ∆x / y

= σ A

shear stress (σ) = η e′

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Viscous, Elastic, and Viscoelastic Behaviour

(viscoelastic soft matter)

• Soft matter often behaves in a way that combines viscous and elastic response, with an additional dependence on timescale.

viscoelasticity

• If one applied a stress on a slow timescale, it flows like a very viscous liquid, but if one rolls it up into a ball and drops it on a hard surface it bounces elastically.

• A viscoelastic material responds to an applied stress in a time dependent way.

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Viscous, Elastic, and Viscoelastic Behaviour

(viscoelastic soft matter)

• imagine a stress being applied at time t = 0 and held constant.

shear strain

1/G0

initial elastic

response final viscous response

The material responds at first in an elastic way, with a constant strain, but after a certain time τ it begins to flow like a liquid, with the strain increasing linearly with time.

→

The time τ is the relaxation time; it is the time that separates the solid-like behaviour from the liquid-like behaviour.

→

If a stress is applied on a timescale t

→

t < τ : solid-like t > τ : liquid-like

Instantaneous modulus G0 characterizes the elastic response of the material at times much shorter than the relaxation time

→

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Viscous, Elastic, and Viscoelastic Behaviour

(viscoelastic soft matter)

strain rate

stress

strain rate

stress

strain rate

stress

effective viscosity

strain rate strain rate strain rate

effective viscosity effective viscosity

Newtonian shear thinning shear thickening

Both types of non-Newtonian behaviour are characteristic of concentrated dispersions of particles, and can be understood as being a consequence of the rearrangement of the particles in response to the flow.

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Viscous, Elastic, and Viscoelastic Behaviour

• 120 nm SiO2 nanoparticles (ϕ = 0.47) in polyethylene glycol

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Viscous, Elastic, and Viscoelastic Behaviour

(viscoelastic soft matter)

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Liquids and Glasses

• Relaxation time and viscosity in glass-forming liquids

→ oxide glasses, metallic glasses, organic molecules, polymer glasses, …

→ As the temperature is lowered, we reach a state at which the relaxation time becomes comparable to the timescale of the experiment. And, the system falls out of equilibrium with respect to configurational degree of freedom.

→ onset of the experimental glass transition at a temperature Tg

→ A glass is a material which is identical

in its state of order with a liquid (short-range order, but no-long range

order, but behaves mechanically like a solid)

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Glass Transition

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Liquids and Glasses

• Glass transition

→ The transition between a liquid state and a glass is marked by discontinuities in thermodynamics quantities that are second derivatives of a free energy.

→ As the temperature is lowered, we reach a state at which the relaxation time becomes comparable to the timescale of the experiment. And, the system falls out of equilibrium with respect to configurational degree of freedom.

V

glass (1)

glass (2)

crystal liquid

→ Glass transition temperature Tg

→ The glass transition is similar in appearance to a second-order phase transition, but it is not a true

thermodynamic phase transition because the transition temperature depends on the rate at which we do the experiment.

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Liquids and Glasses

• Discontinuity appears in :

First-order

Second-order

differential of G (= H - TS) corresponding

experimental quantities

S V

∂T

( )

∂S p

∂p

( )

∂S T

∂T

( )

∂V p

∂p

( )

∂V T

Cp β κ

isothermal

compressibility ∂p

( )

∂V T

V heat capacity at 1

constant pressure isobaric expansion

coefficient ∂T

( )

∂V p

V 1 Cp

∂T

( )

∂S p

= T

β =

κ =

S V