Molecular interactions

Levente NovákIstván BányaiZoltán Nagy

Department of Physical Chemistry

Surfaces and Interfaces

● Definition of interfacial region● Types of interfaces: surface vs interface● Surface tension● Contact angle, weting, and spreading● Adsorption● Biological interfaces

Surfaces and interfaces (IUPAC definitions)

● “A boundary between two phases is called a surface or interface.”● “interface is preferred for the boundary between two condensed

phases and in cases where the two phases are named explicitly”● “in some instances the word surface is limited to its geometrical

meaning”● “interface is used to describe the thin three dimensional layer

(surface layer or interfacial layer) between the phases in contact”● area of a surface/interface: A or AS (in m2)● specific area (a or aS, in m2/g): area A proportional to the mass m of

the sample

aS=Am

Definition of interfacial layer (what does “thin” mean?)

Interfacial layer or interfacial region:

● The region of finite thickness where two homogeneous bulk phases meet and where the properties change markedly.

● At a molecular level the thickness of the interfacial region is significant and can not be neglected

Interfacial region of a soap solutionInterfacial region of a soap solution

surface excess concentration

Liqu

idG

as

Interfacial layer and dispersity

● Properties of the interfacial region● For coarse disperse system or bulk phases, the efect on the

properties is rather small● For colloidal systems (high degree of dispersion) the efect is large,

and its properties are very important due to the large specific surface

1E-006 1,257E-011 4,189E-018 30000001E-005 1,257E-009 4,189E-015 3000001E-004 1,257E-007 4,189E-012 300001E-003 1,257E-005 4,189E-009 30001E-002 1,257E-003 4,189E-006 3001E-001 1,257E-001 4,189E-003 30

1 1,257E+001 4,189E+000 3

r (mm) A (mm2) V (mm3) A/V (mm-1)

Types of interfaces

Two main types:● Fluid interfaces

● Gas—liquid (G—L)● Liquid—liquid (L1—L2)

● Non-fluid interfaces (one phase is solid)● Gas—solid (G—S)● Liquid—solid (L—S)● Solid-solid (S1—S2)

Surface tension

● The atractive forces acting on molecules at the surface are anisotropic

● Molecules in the bulk of the phase are at a lower energy level than molecules at the surface● Molecules at the surface are subject to an inward force of

molecular atraction (unit: N/m)● The surface decreases until it reaches the minimum value

possible

Surface tension, 1st definition

γ =( dGdA )

n , p ,T

Thermodynamic definition of surface tension:

● Gibbs free energy of unit area (J/m2)● γ must be positive → interface tends to a minimum (minimal surface)

Surface tension (γ) is the energy required to increase the surface area of a chemically pure liquid by a unit amount (J/m2)

G=γ×A + other terms

Surface tension, 2nd definition

Surface tension (γ) is defined as the force along an imaginary line of unit length of the surface. The force is parallel to the surface but perpendicular to the imaginary line (N/m).

length l

F⃗

γ =Fl

γ =F2 l

Special case:

For two-sided thin films (e.g. soap bubbles), due to the action of the two surfaces, the equation becomes

The Dupré-experiment

Independently of the pull length S, the force F1 required to pull the soap layer is always the same until the layer “pops” → surface tension is not function of the pull length S.

S

Surface tension in everyday life

γ =dFdx

=dGdA

The air-water surface tension is larger than that of air-hair or water-hair surface (another example is sand castle which stands together when wet but falls apart when dry). Air—waterAir—hair Hair—water

The surface becomes the minimal possible due to the surface tension → falling drops become spherical

A needle has a length of 3.2 cm. When placed gently on the surface of the water (γ =0.073 N/m) in a glass, this needle will float if it is not too heavy.

What is the weight of the heaviest needle that can be used in this demonstration?

Three forces act on the needle, its weight W and the two forces F1 and F2 due to the surface tension of the water. The forces F1 and F2 result from the surface tension acting along the length of the needle on either side. ATTENTION! Here θ denotes the supplemen tary angle of the contact angle.

Example: efects of surface tension

ΣF=0

“Walking” on water

Water striders are insects able to run on the surface of water.

If γ is lowered by the use of surfactants, when it becomes low enough, it can not keep the strider on the surface anymore.

Surface tension and intermolecular interactions

If the interaction between water molecules and and between an immiscible liquid's molecules is stronger than that between each other the interfacial tension is lower. The interfacial tension is approximately the diference of the respective surface tensions of the two liquids saturated with each other (Antonov's rule) → valid mostly for liquids interacting with van der Waals forces

γL1/L2=γL2

−γL1

e.g. for water and octane:γn-Octane/Water = γWater - γn-Octane = 72.8 - 21.8 = 51.0 mN/m

Δ=45.3Δ=54.4Δ=51.0Δ=412Δ=46.0

Δ=43.9

Measurement of surface tension

Wilhelmy plate du Noüy ring

The maximum force is measured to pull out the ring or plate from the surface

Capillary rise, capillary depression

● If a narrow capillary tube is dipped into a liquid the level of liquid in the tube is usually diferent from that in the larger vessel● Water in glass capillary → capillary rise● Mercury in glass capillary → capillary depression

● Importance of capillarity● Weting and water drainage of soils● Drying of wall paints● Water uptake in plants● Thorny dragon (Australian lizard species)

Capillary rise/depression

h=2γ cosθρ grcap

h=2γ

ρ grcap

⇔ γ =12

Δ ρ ghrcap

If a tube is suficiently narrow and the liquid adhesion to its walls is suficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action. The height the column is lifed to is given by

If there is perfect weting:

Capillary action is the result of adhesion and surface tension. Adhesion of water to the walls of a vessel will cause an upward force on the liquid at the edges and result in a meniscus which turns upward. The surface tension acts to hold the surface intact, so instead of just the edges moving upward, the whole liquid surface is dragged upward.

Temperature and surface tension

Loránd Eötvös ( Hungarian physicist who introduced the concept of molecular surface tension); Ramsay and Shields:

γV 2 /3=k E (T c−T )

γV 2/3=k E (T c−T−6) Ramsay and Shields

Eötvös

γ : surface tension (N/m)VM : molar volume (m3·mol-1)kE : Eötvös “constant” (J·K-1·mol2/3)Tc : critical temperature (K)T : actual temperature (K)

( dγ

dT )p

=−( dSdA )

T

kE=d (γ (

Mρ )

2/3

)

dT=2.12×10−7 J⋅mol2/3

⋅K−1

kE is not a true constant, it somehow depends on e.g. association and dissociation efects

Curved surfaces, Laplace pressure

pout

pin

surface

pout

pin

surface1surface2

Laplace pressure

For curved surfaces the pressures are diferent on either side → a pressure diference Δp results (Laplace pressure). The pressure is always larger at the concave face of the curvature. The Laplace pressure depends on the radius and the surface tension.

pin−pout=Δ p=2γ

rpin−pout=Δ p=

4γ

rBubble or drop in liquid: 1 surface Two-walled bubble: 2 surfaces

Soap bubbles

Atentione A hollow (e.g. soap) bubble has not one but two spherical surfaces (inside and outside)

Δ p=4γ

r

circumference (=length)

circumference (=length)

area

area

inside and

outside surfaces

The Laplace equation for a spherical liquid drop:

The Laplace equation for a spherical soap bubble:

If the bubble and drop had the same radius, the pressure diference between the inside and outside of the bubble is twice as large as that for the drop. The reason is that the bubble has two surfaces, whereas the drop has only one. Thus, the bubble would have twice the force due to surface tension, and so the pressure inside the bubble would have to be twice as large to counteract this larger force.

http://www.youtube.com/watch?v=kvrsAhuvs3M

Δ p=2γ

r

Δ p=4γ

r

Which bubble will grow and which one shrink if we open the tap?

Experiment: surface tension-propelled boat

Phenomena at curved interfaces:The Kelvin equation

The efect of surface curvature on the vapor pressure of a liquid

ln( pr

pr=∞)=(γ V L

RT )( 2rm)

pr : pressure over the surface of radius r (Pa)Pr=∞ : pressure over a flat surface (Pa)γ : surface tension (N/m)VM : molar volume (m3/mol)R : gas constant (J·K-1·mol-1)T : temperature (K)r > 0 when the center of curvature lies in the

liquid phase and r < 0 (negative sign) when it lies in the vapor phase

Consequences:

● Ostwald ripening● Self-nucleation of a new phase● Heterogeneous nucleation● Capillary condensation

pr > pr=∞ pr < pr=∞

r < 0

pr

r > 0

pr

Consequences

● The smaller the radius, the higher the vapor pressure● In a population of various size droplets the smaller ones will tend to

evaporate while the larger ones will tend to grow → in clouds the larger droplets grow until they are heavy enough to fall as rain.

● In small capillaries vapor can condense below the saturation vapor pressure → capillaries fill first with liquid (discussed in Lecture 3)

Ostwald ripening● Ostwald ripening

● A similar mechanism exists for crystals in a solution: the larger crystals tends to grow at the expense of smaller ones. The equilibrium between a small liquid droplet and its vapor unstable.

● Same mechanism for emulsions → ageing (spontaneous slow, irreversible change) → coarsening (droplets get bigger)

● Very important mechanism during the preparation of e.g. photographic “emulsions” (in fact suspensions), creams, paints, glues, etc.

cr : concentration in the droplet/particle of radius r (mol/m3)c

m: concentration in the medium (mol/m3)

pr : pressure in the droplet/particle of radius r (Pa)pm : pressure in the medium (Pa)μr : chemical potential in the droplet/particle of radius r (J/mol)μ

m: chemical potential in the medium (J/mol)

γ : surface tension (N/m)r : radius of curvature (m)VM : molar volume (m3/mol)

ln(cr

cm

)=2γV m

RT r

ln(pr

pm

)=2γV m

RT r

ln(μ rμm

)=2γV m

RT r

Self-nucleation

● Self nucleation of a new phase● Formation of very small nuclei or “embryos” of the new

phase inside the old phase: – Supersaturation– Critical nucleus size → minimal nucleation concentration– Critical nucleation concentration

● To be discussed in Lecture 10