Lec12_Surfaces.pdf

7/28/2019 Lec12_Surfaces.pdf

http://slidepdf.com/reader/full/lec12surfacespdf 1/34

Biomaterials Lecture 12Surfaces: Surface Tension and Young

Laplace Equation

Unless otherwise noted, source Information for the following slides:

1) B. Ratner, A. Hoffman, F. Schoen, and J. Lemons: Biomaterials Science,2nd edition (San Diego: Elsevier Academic Press. 2004).

2) Butt, H‐J.; Graf, K.; Kappl Physics and Chemistry of Interfaces, 2nd Edition (Wilet‐VCH: Weinheim 2006).



“Today…I propose to tell you of a real two‐

dimensional world in which phenomena

occur that are analogous to those described in ‘Flatland’. I plan to tell you about the

behavior of molecules and atoms that are

held at the surface of solids and liquids”.

– I. Langmuir, Science 1936, 84, 379.

In 1932 he received the Nobel Prize in Chemistry "for his discoveries

and investigations in surface chemistry.“

1st industrial scientist to win the Nobel Prize



Surfaces of Biomaterials

• Why are surfaces important in biomaterials

applications?• The surface of a material strongly dictates

performance in vivoSurface Properties Influencing Cell Adhesion

•

Wettability• Roughness

• Electrical Charge

•

Crystallinity• Composition

• Mobility



What constitutes a surface?

An interface is the boundary region between two adjacent bulk phases

We recognize (S/G), (S/L), and (L/V) as surfaces

L

L

V

G

S

S

L

L

L = Liquid

G = Gas

S = Solid

V = Vapor

S

S

We recognize (S/G), (S/L), and (L/V) as surfaces

http://www.bioen.utah.edu/faculty/pat/Courses/biomaterials/coursenotes.html



What’s so special about a surface?

1. Inherently small number of atoms

a) Bulk vs. Surface

1 cm3 material

≈ 1023 atoms

Surface ≈ 1015 atoms

Modified from:Anne Mayes 3.051J/20.340J Materials for Biomedical Application, MIT, http://ocw.mit.edu,




2. Enhanced mobility

a) Fewer bonds

b) Gradient in density

→ Facilitates rate limited processes (phase transformations,

crystallization, corrosion,…)

“Ideal” 2‐D surfaces exist only

as mathematic constructs





3. Higher energy state

– Atoms/molecules with unsatisfied (“dangling”) or

strained bonds

– → High reacvity and suscepbility to adsorbates




Physical Description of Biomaterial Surfaces

Biomaterial surfaces exhibit remarkable heterogeneity in physical structure:

Material dependant: Metals vs. Polymers vs. Ceramics vs. Gels

Chemistry: Polar vs. Apolar, Charge, Reactivity, Patterned

Morphology: Smooth, Rough, Stepped, Patterned, Diffuse

Order: Crystalline, Amorphous, Semi‐Crystalline, Phases

Environment: Hydration, Solvent Quality

Bumpy with Phases

Hydration

Glassy




Crystal Surface Defects




Crystal Surface Dynamics



Polymer Surface Dynamics

Given sufficient mobility, polymer surfaces will reorient or restructure in

response to their local micro‐environment so as to minimize their interfacial free

energy with the surrounding phase.

CH3

OH

CH3

OH

CH3 CH3

OH OH

OH OHOH OH

CH3 CH3CH3 CH3

Bulk Bulk

Polar Solvent Apolar Solvent / Air




Biological Surfaces




Surface Energetics

Molecules in the bulk of a material (e.g. crystal lattice) have a low relative energy

state due to nearest neighbor interactions (e.g. bonding).

Performing sufficient work on the system to create an interface can disrupt this

harmony...




Molecules at a surface are in a state of higher free energy than those in the bulk.

This is in large part due to the lack of nearest neighbor interactions at a surface.

(Excess) Surface Free Energy




The same thing occurs regardless of material (e.g. polymers).

(Excess) Surface Free Energy




Important Point

Systems move toward lowering their free energy

Surfaces do so by:Geometric changes (if possible)

Bonding (strong and weak interactions)

Dynamic rearrangement

Protein

CH3

OH

CH3

OH CH3

OH

CH3

OH




Surface Tension• Surface tension acts to decrease the free energy of the system, hence

some observed effects:

• Liquid droplets form spheres

• Meniscus effects in capillaries



Surface Energy and Tension in Liquids

• The cohesive forces between molecules

down into a liquid are shared with all

neighboring atoms.

• Those on the surface have no

neighboring atoms above, and exhibit

stronger attractive forces upon their

nearest neighbors on the surface.

• This enhancement of the

intermolecular attractive forces at the

surface is called surface tension.



Surface Tension: Intermolecular Forces




In order to develop some concepts related to surfaces we will first look at the surface properties of liquids.

The work (w) required to create a new surface is proportional to the # molecules at the

surface, hence the area (A):

Where is the proportionality constant defined as the specific surface free energy. It has

units of (energy/unit area, mJ/m2).

acts as a restoring force to resist any increase in area, for liquids it is numerically equal

to the surface tension.

When considered as a force rather than an energy, the force is called "surface tension“ and

has units of (force/unit length, mN/m)

AW





acts as a restoring force to resist any increase in area, for liquids it is numerically equal to the surface tension.

Surface tension can also be defined by the force required to hold the slider in place and to

balance the surface tensional force

Ldx

W F

2




Surface Tension of Solids

Bottomline:

The surface tension of solids is experimentally inaccessible.

Why?

Creation of new area in a solid is not reversible – you end up stretching or cleaving the

sample. Interfacial stress during elastic enlargement can be measured and related to

interfacial tension only if the relationship of interfacial tension as a function of strain is

independently known.



Surface Tension of Example Materials

Trends:

• high materials (> 200 dyn/cm) – metals, carbides, oxides

• Low materials: polymers and organics



Examples: Surface Tension of Liquids in Contact

with Air



The Young‐Laplace Equation

In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface

between two static fluids, such as water and air, due to the phenomenon of surface

tension.

for the radius of curvature in directions 1 (R1) and 2 (R2). Hence is balanced by

P, or the surface tension tends to compress the droplet, increasing the internal

pressure.

An interesting consequence:

21

11

R RP

Δ p for water drops of different radii at STP

Droplet radius 1 mm 0.1 mm 1 μm 10 nm

Δ p (atm) 0.0014 0.0144 1.436 143.6

The pressure difference (P ) across the

surface of a liquid is related to the surface

curvature:





• In a sufficiently narrow (i.e., low Bond number) tube of circular cross‐

section (radius a), the interface between two fluids forms a meniscus that

is a portion of the surface of a sphere with radius R. The pressure jump across this surface is:

RP

2




Young‐Laplace has several fundamental implications:

• If we know the shape of a liquid surface we know its curvature and we can

calculate the pressure difference

• In the absence of external fields, the pressure is the same everywhere in

the liquid; otherwise there would be a flow of liquid to regions of lower

pressure. Thus, P is constant and Young‐Laplace equation tells us that in this case the surface of the liquid has the same curvature everywhere

• With the help of Young‐Laplace equation, it is possible to calculate the equlibrium shape of a liquid surface. If we know the pressure difference

and some boundary conditions (volume of liquid and its contact line), then

we can calculate the geometry of the liquid surface



Applications to Biomaterials

• Consequence for the alveolar network during breathing

• Presence of pulmonary surfactants lower surface tension and

stabilize the system…related to respiratory distress syndrome





Measuring Surface Energy of Solids

Fracture Method

• A crack is opened up by forces pulling the edges

apart.

• A "double cantilever" forms. The work done by the

applied force is equal to the potential energy of the

"leaf springs" and the surface energy. Solving for the

surface energy (eventually) gives:



Measuring Surface Energy of Solids

Indentation Method

With small specimens an indentation method is used.

•A diamond point is forced into the surface and microcracksappear at the sharp edges.

• It can be shown (but not in this course) that the surface

energy is given by:

• Measuring the lengths, a, and c, and the indenting force, F,

will give the surface energy.



Measuring Surface Tension of Liquids

Winhelmy Plate Method

• A thin plate that is used to measure

equilibrium surface or interfacial tension at

an air‐liquid or liquid‐liquid interface.

• The plate is oriented perpendicular to the

interface, and the force exerted on it is

measured

• L the wetted perimeter (2w + 2d) of the

Wilhelmy plate and θ is the contact angle

between the liquid phase and the plate

• The force on the plate due to wetting is

measured via a tensiometer or microbalance

• Plate is usually platinum (easy to clean in a

flame)

coslF




Measuring Surface Tension of LiquidsPendant

Drop

Method

• A drop of liquid is suspended from the end of a tube by surface tension.

• The force due to surface tension is proportional to the length of the boundary between the liquid and the tube, with the proportionality

constant usually denoted γ. Since the length of this boundary is the circumference of the tube, the force due to surface tension is given by:

• The mass m of the drop hanging from the end of the tube can be found by equating the force due to gravity (F g = mg) with the component of the surface tension in the vertical direction (F

γ

sinα) giving the formula

• Where α is the angle of contact with the tube, and g is the acceleration due to gravity.

• The limit of this formula, as α goes to 90°, gives the maximum weight of a pendant drop for a

liquid with a given surface tension, γ.

d F

d mg




Measuring Surface Tension

• Other Methods include:

• Du Noüy ring tensionmeter

• Bubble Pressure Method

•Sessile Drop Method


Documents

Lec12_Surfaces.pdf