Analysis of Microsystems Summer 2010

Dr. Oswald Pruckerprucker@imtek.de

Part 3: Sorption of liquids and gases on surfaces

Definitions

• Adsorption is a process at surfaces. Molecules settle down on surfaces and get attached through relatively weak forces. They may over time be released again (= desorption). The entire process is dynamic.

• Adsorption is the temporary attachment of particles on surfaces.

• Absorption is the incorporation of a material (e.g. or liquid) in a body (such as a sponge). The absorbed material disappears inside the body.

… even more definitions

Substrate – often used to describe surfaces of solid state bodies, on which adsorbtion occurs (also: adsorbent) the orange bar

Adsorbate – general name of molecular species which is adsorbed onto a substrate the red balls

Adsorption – is a process in which a molecule will be adsorbed at a surface the „down arrow“

Desorption – the opposite of adsorption the „up arrow“

Absorption vs. Adsorption ... =)

Taken from: Carsten Schmuck, Bernd Engels,Tanja Schirrmeister, Reinhold Fink, Chemie für Mediziner,Pearson Studium, 2008, S. 124

How do we describe sorption phenomena

Adsorption isotherms• coverage - measure for the part of the surface to which an adsorbate (species) is

adsorbed. Usually denoted using the ‘theta’ symbol, θ.

• θ=1 indicates complete coverage of the solid surface with a monolayer.

Chemistry is better ;-)

Two major types of adsorption:

• Physisorption

• Chemisorption

Physisorption

Physical adsorption (Physisorption) – attachment through vdW forces. There is no significant change in charge distribution, neither within the molecule nor at the surface. no chemistry involved.

Chemisorption

Chemical adsorption (chemisorption) – attachment through chemical reactions; significant charge redistribution.

Chemical bonds may be anything from ionic to covalent.

Chemisorption vs. Physisorption

Chemisorption Physisorption

Enthalpy of Adsorption

Variable depending on type of attachment: 40 - 800 kJ mol-1

Depends of molar mass and polarity: 5-40 kJ mol-1

Nature of adsorption irreversible reversible

Max. coverage only monolayers multilayers possible

Kinetic aspects activation barrier fast, no activation barrier

Influence on isotherms

Example one: chemisorption of O2 on charcoal monolayer

Example two: physisorption of N2 on silica gel multilayer

chemisorption/physisorption

physisorption

Understanding isotherms

Important factors describing the amount of gas molecules which adsorb to solid

surfaces at constant temperature and constant pressure [discret point on

isotherm].

Interaction energy between adsorbent and adsorbate (adsorption energy)

Interaction between adsorbate molecules (apparent in heat of condensation)

Mobility of the adsorbed molecules

Surface heterogenities

Existence of pores and pore size distribution

Understanding isotherms

Type I: relatively strong adsorption, resulting in monolayer formation

Typ II: polylayer formation with strong interaction

Typ III:polylayer formation with low interaction

Typ IV und V: adsorption at porous surfaces

Quantitative description of adsorption

How to we quantitatively describe isotherms? [Engineers like math]

Literature survey brings about around 50 different mathematical equations, which are based on different models and which are making different assumptions to describe an adsorption process.

At the moment no standard theory of adsorption

Henry isotherm

1903/07 Henry, Dalton

Monolayer adsorption at solid surfaces

Adsorption layer is mobile

No interactions between adsorbed molecules in the adsorbate

Θ = bcΘ: coverage

b : Adsorption coefficient

c: concentration of the volume

Henry

Dalton

Langmuir isotherms

Langmuir 1918

Accounts for footprint of molecules

Initially coverage increases linearily, then levels of to reach a plateau

des

ads

kkK

KcKc

=+

= ,1

θ

Equilibrium:

Adsorption: c + * c* (kads)

Desorption: c* c + * (kdes)

[with c: molecule, *: site, and k: rate constants]

Irving Langmuir (1881 – 1957)

Born in Brooklyn, New York

Nobel price in Chemistry: 1932

Langmuir isotherms

des

ads

kkK

KcKc

=+

= ,1

θ

Maximum coverage: 1

No adsorption beyond monolayer

Langmuir isotherms

des

ads

kkK

KcKc

=+

= ,1

θ

High K or c 1

Low K or c Kc (Henry)

Langmuir isotherms

KcKc+

=1

θ RTGeK /∆−=

Adsorption at a fixed concentration is governed by thermodynamics enthalpy and temperature are key

Langmuir isotherms

Shortcomings of the theory:

Chemists understand it.

Large molecules may occupy more than one adsorption site

Does not account for multilayer builtup.

Coverage does not influence the probability of adsorption to a site.

All sites are equal, i.e. not influenced by the neighbor. No site-dependent rate constants.

des

ads

kkK

KcKc

=+

= ,1

θ

Langmuir isotherms

Example: Adsorption of colloids or nanoparticlesCurrently heavily pursued field of research. Description is difficult because ... reality bites:

Substrates are rough

Bunch of interactions between particles and particle/substrate: electrostatic, vdW or steric arguments (entropic)

Transport mechanisms

Desorption processes? (often: irreversible adsorption)

Langmuir model yields only crude approximation

Random Sequential Adsorption (RSA model)

Sequential adsorption at free sites

No diffusion at the surface, no displacement

Monolayers only

New particle is admitted to a large enough site

θ=86.5%

“Random Car Parking” problem

Random Sequential Adsorption (RSA model)

( )( ) 56.0

56.0

≅∞

≅∞

spheres

squares

θ

θ

At t=0: empty substrate

Monotonic increase in coverage with t

Jammed state: remaining sites are too small

Coverage lower than in close-packed state

Random Sequential Adsorption (RSA model)

(a) Θ = 0.56,

(b) Θ = 0.5 (aspect ratio 4),

(c) Θ = 0.45

(d) Θ = 0.38

RSA – an example

Part 4: Surface tension

Surface tension

Reason for surface tension is the broken symmetry at the transition point from liquid to gas.

Definition:

TPAG

,

==

δδγσ

Surface tension

Measuring surface tension

Ring method (de Noüy)

Wilhelmy plate

drop shape method

Measurement of the force needed to pull a ring out of the liquid

γπ )(2 ai rrF +=

A wettable plate is immersed into the liquid and the force that acts on the plate is measured. This force minus gravity gives the surface tension.

γlFF g 2−=

A droplet falls from a capillary as soon as gravity mg exceeds the surface tension.

γπ krmg 2=

Part 5: Wetting of surfaces

Contact angles

The contact angle Θ is formed at the boundary of the three phases solid/liquid/gas and is a direct measure for the wettability of the surface by the test liquid.

Θ+= coslgσσσ

slsg

sgσ

Surface tension of solid (s=solid, g=gas)

lgσ

Surface tension of liquid

slσ

Interfacial tension between solid and liquid

lgσ

sgσ

slσ

Θ Liquid

SolidYoung‘s equation

Gas

Contact angles

Θ+= coslgσσσ

slsg

Young‘s equation

Θ=−= coslgσσσσ slsgBWetting tension:

The surface tension of the solid could be determined if only we could measure the interfacial tension (surface – liquid).

For Θ0) we get: σB > 0 wetting

For Θ >90°(cos Θ

Contact angles

Interfacial free energy of solids

Zisman plot Only valid for unpolar interactions

The cosine of the contact angle is plotted as a function of the surface tension of the liquid used.

At the intercept of the regression with cos θ = 1 we get a critical interfacial tension γcrit below which any liquid will spread on the solid.

This value denotes the interfacial free energy of the solid if the interactions between the liquid and the solid are entirely unpolar.

Interfacial free energy of solids

Method of Owens, Wendt, Rabel & Kaelbel(often used for polymeric surfaces)

The advancing contact angle of a liquid with known polar and dispersive fractions of the surface tension γLp & γLd are measured. The surface free energy is then taken as the geometric average of the interfacial tensions of the liquid and the solid:

γSL is then calculated as:

Taking this result back into Young‘s equation we can rewrite to generate a linear relation of the type y = ax + b:

pS

dSS

pL

dLL γγγγγγ +=+= &

( )pLpSdLdSLSSL γγγγγγγ +−+= 2

dS

pSd

L

pL

dL

L baxy γγγγ

γγθ

===+

= ,,,2cos1

Interfacial free energy of solids

pSa γ=

dL

pLx

γγ

=

dL

Lyγ

γθ2cos1+

=

dSb γ=

Method of Owens, Wendt, Rabel & Kaelbel(often used for polymeric surfaces)

Interfacial free energy of solids

Different methods lead to different results. Determination of absolute values is difficult if not impossible.

It is not possible to determine the interfacial free energy of a unknown surface using reference measurements on known materials.

The roughness of the surface of interest is very critical

Non-ideal surfaces

Welcome to the real world! Real surfaces teach us that wetting is a rather complex phenomenum.

On real surfaces one usually gets a range of contact angles both at the same spot or at different spots on the sample.

Dynamic contact angles

Advancing contact angle θadv Measured while liquid is added to the drop

Receeding contact angle θadv Measured while liquid is taken from the drop

Dynamic contact angles

Dynamic contact angles are measured directly at the moment before the contact line starts to move (i.e. while the drop is still pinned).

The advancing contact angle is usually much larger than the receeding contact angle. Differences are at least 5 – 20°, often a lot more.

Contact angle hysteresis

Reasons for CA hysteresis

Physical roughness

Chemical heterogeneities

Contamination in test liquid

On soft surfaces (some polymers) forces might be strong enough to deform the substrate

Adsorption or desorption of molecules during advancing or receeding motion

Absorption of liquid (e.g. swelling)

Most important: Surface topography and roughness and the respective length scales

Wetting on rough surfaces

Yr r θθ coscos ⋅=

1coscos −+⋅= φθφθ Yr

Wenzel model:

Cassie model:

Young's equation:

• T. Young Philos. Trans. R. Soc. London 1805, 95, 65.• A. Cassie, S. Baxter Trans. Faraday Soc. 1944, 40, 546.• R. N. Wenzel Ind. Eng. Chem. 1936, 28, 988

µ-engineering polymer chemistry

lssgY γγθγ −=⋅coslg

Wenzel wetting

r is a roughness coefficient that relates the actual geometric wetted area to the projected area

Because or r > 1 roughness will always amplify a given wetting behavior (hydrophilic more hydrophilic | hydrophobic more hydrophobic)

Yr r θθ coscos ⋅=

areaprojectedareageometricr =

Cassie & Baxter wetting

Cassie and Baxter assume the air is trapped underneath the droplet and define a wetted fraction φ

( ) ( ) 11cos180cos1coscos * −+=°−+= θφφθφθ SSS

Wetting on rough surface

How well do the theories of Wenzel and Cassie/Baxter describe the wetting of rough/microstructured surfaces?

Lithography + anisotropic siliconetching

10 µm

0.1 µm

1 µm

stru

ctur

e si

ze

Anisotropic siliconetching (nanograss)

PS

PDMAA PFA

PMMAPHEMA

PEGMEM

hydrophilichydrophobic

Static contact angles

PDMAA

0°

180°

90°

flat µ-structured

PFA (Fluoropolymer)

Wenzel wetting

post height = post distance d=s [µm]co

ntac

tang

le

[°] Wenzel theory

Comparison of theory with experiment:

extremely high CA hysteresisWenzel theory has no practical

relevance no thermodynamic equilibrium is

reached

Wenzel theory

Pinning dominates wetting behavior

Strong „pinning“ at post edges dominates receeding CAVariety of „local contact angles“

= Pinning

... More real life

Drop impact!

Printing with misalignment

xx

x

xx

x

xx

x

desired impact area

actual impact area

spot diameter: 3mmmisalignment: 2mm

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

Hydrophobic break valve

CCH3

CH2C nOO

CH2CH2

(CF2)7CF3

hydrophobic patch: perfluorinated network

Micronozzles

TopSpot printhead

Collaboration with R. Zengerle, R. Steger, G. Birkle, P. Koltay, T. Brenner, M. Grumann, J. Ducree

a) micronozzle

targetzone

a) micronozzle

targetzone

adhesionforce

a)

low surface energy liquids

b)micronozzle

adhesionforce

targetzone

Foliennummer 1Foliennummer 2Definitions… even more definitionsAbsorption vs. Adsorption ... =)How do we describe sorption phenomenaChemistry is better ;-)PhysisorptionChemisorptionChemisorption vs. PhysisorptionInfluence on isothermsUnderstanding isothermsUnderstanding isothermsQuantitative description of adsorptionHenry isothermLangmuir isothermsIrving Langmuir (1881 – 1957)Langmuir isothermsLangmuir isothermsLangmuir isothermsLangmuir isothermsLangmuir isothermsRandom Sequential Adsorption (RSA model)“Random Car Parking” problemRandom Sequential Adsorption (RSA model)Random Sequential Adsorption (RSA model)RSA – an exampleFoliennummer 28Surface tensionSurface tensionMeasuring surface tensionFoliennummer 32Contact anglesContact anglesContact anglesFoliennummer 36Interfacial free energy of solidsInterfacial free energy of solidsInterfacial free energy of solidsInterfacial free energy of solidsNon-ideal surfaces Dynamic contact anglesDynamic contact anglesReasons for CA hysteresisWetting on rough surfacesWenzel wettingCassie & Baxter wettingWetting on rough surfaceFoliennummer 49Foliennummer 50Static contact anglesWenzel wettingPinning dominates wetting behavior... More real lifePrinting with misalignmentHydrophobic break valveMicronozzlesFoliennummer 58Foliennummer 59Foliennummer 60