Surface Tension and its measurements - University of BabylonSurface Tension and its measurements...

Surface Engineering Dr. Ammar Al-kawaz

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Surface Tension and its measurements

Surface Tension

Surface tension is a fundamental property by which the gas–liquid interfaces are

characterized. The zone between a gaseous phase and a liquid phase looks like a

surface of zero thickness. The surface acts like a membrane under tension.

It reflects in principle directly the strength of bonding within the bulk material.

Due to very different binding forces, hard solids (covalent, ionic, metallic)

typically reveal “high-energy” surfaces (surface tension ~500–5000 mJ/m2) in

contrast to weak molecular solids and liquids (soft matter) with “low-energy”

surfaces (surface tension < 100 mJ/m2).

Most polymers belong to the second class of materials where interactions

between chains are dominated by van der Waals forces and hydrogen bonds.

Surface and interfacial tensions of polymers play a key role in wetting and

coating processes, in biocompatibility or polymer blending, and in corrosion and

adsorption processes. The behavior of colloidal dispersions, adhesion, and

friction is influenced by surface and interface tension.

A molecule in the bulk liquid is subjected to attractive forces(also known as

cohesion forces) from all directions by the surrounding molecules. It is

practically in a uniform field of force. But for the molecule at the surface of the

liquid, the net attraction towards the bulk of the liquid is much greater than the

attraction towards the vapor phase, because the molecules in the vapor phase are

more widely dispersed.

Figure 1

This indicates that the molecules at the surface are pulled inwards. This causes

the liquid surfaces to contract to minimum areas, which should be compatible


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with the total mass of the liquid. The droplets of liquids or gas bubbles assume

spherical shape, because for a given volume, the sphere has the least surface

area.

If the area of the surface is to be extended, one has to bring more molecules

from the bulk of the liquid to its surface. This requires expenditure of some

energy because work has to be done in bringing the molecules from the bulk

against the inward attractive forces. The amount of work done in increasing the

area by unity is known as the surface energy.

If the molecules of a liquid exert large force of attraction, the inward pull will be

large. Therefore, the amount of work done will be large.

Surface tension of polymers can be divided into two components, polar (𝛾𝑃)

and dispersion (𝛾𝑑) to account the type of attraction forces at the interfaces. The

chemical constitution of the surface determines the relative contribution of each

component to surface tension. The polar component is comprised of various

polar molecular interaction including hydrogen bonding, dipole energy and

induction energy, while the dispersion component arises from London

dispersion attractions. The attractive forces (van der waals and London

dispersion) are additive, which results in the surface tension component being

additive: 𝛾 = 𝛾𝑝 + 𝛾𝑑.

Equivalence between surface tension and surface energy

The natural tendency of the surface of a liquid is to contract to minimize the

surface area. Therefore, if we attempt to increase the area, work will be required.

Consider a thin film of liquid, ABCD, contained in a rectangular wire-frame, as

shown in (Fig.2).

Figure 2 Illustration of the work done in increasing the surface area

The boundary BC (length = l) is movable. Imagine now that the film is stretched

by moving the boundary BC by ΔX to the new position EF. If 𝛾 be the surface


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tension, the force acting on the film is (2 𝛾l), because the film has two surfaces.

The work done in stretching the film is:

W=2γlΔX = γ ΔA ------------------------------------1

Where ΔA= 2lΔX is the change in total area on the two sides of the film.

Therefore,

γ =W

𝚫𝐀 ---------------------------------------2

Calculation of surface tension

Parachor method

Sugden proposed the following equation to calculate surface tension from the

physical properties of the compound:

γ = [φ(ρl−ρv)

M]

4 -----------------------------------------3

Where 𝜌𝑙 and 𝜌𝑣 are the densities of the liquid and vapor, respectively, and M is

the molecular weight. 𝜑 is known as parachor, which means comparative

volume.

If we neglect the density of vapor in comparison with the density of the liquid,

we have 𝜑 = vl ∗ 𝛾1/4 where vl is the molar volume of the liquid.

A comparison of the parachors of different liquids is equivalent to the

comparison of their molar volumes under the condition of equal surface tension.

𝜑 is a weak function of temperature for a variety of liquids over wide ranges of

temperature, and generally assumed to be a constant. Additive procedures exist

for calculating 𝜑.

Equation (3) suggests that surface tension is very sensitive to the value of

parachor and the liquid density. The structural contributions for calculating 𝜑

are given in Table 1 .The total value of 𝜑 for a compound is the summation of

the values of the structural units.


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Example:

Calculate the surface energy of PS using Parachor method. Use table below

Density(g/cm3) Parachor No Atomic Mass

0.91

C H Double bond 6-membered

ring

C H

4.8 17.1 23.2 6.1 12.01 1.007

Solution:

The surface tension is given by:

𝛾 = [𝜑(𝜌𝑙)

𝑀]

4

M=8×1.007+8×12.01= 104.136 g/mol

𝜌 = 0.91 g/cm3

vl = M

ρ = 104.136 /0.91 = 114.435

𝜑 = (8×17.1)+(8×4.8)+(3×23.2)+6.1 = 250.9

γ = [φ

vl]

4 = [

250.9

114.435]

4= 23.1 J/mol


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Effect of temperature on surface tension The surface tension of most liquids decreases with increasing temperature. Since

the forces of attraction between the molecules of a liquid decrease with

increasing temperature, the surface tension decreases with increasing

temperature.


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One of the classical equations correlating the surface tension and temperature is

the Eotvos-Ramsay-Shields equation:

γ(vl)2/3 = Ke(TC − T − 6) ----------------------------------4

Where vl is the molar volume of the liquid which can be represented by (𝑀

𝜌𝑙),

𝑇𝐶 is the critical temperature and 𝐾𝑒 is a constant. For non-associated liquids,

the value of 𝐾𝑒 is 2.12, and for associated liquids, its value is less than this

value.

Example

Calculate critical temperature (Tc) of Co2 using Ramsay-Shield Equation if you

know:

Temperature Cᵒ Density (g/cm3) SurfaceTension (Dyne/cm)

0 0.926 5.4

20 0.772 1.16

Solution:

γ(vl)2/3 = Ke(TC − T − 6)

At 0 Cᵒ

MCo2 = 12+ (2×16) =44 g/mol

0 Cᵒ =273 K

5.4(44

0.927)2/3= Ke(Tc − 273 − 6)

71.712 = Ke(Tc − 279) ------------------------------1

At 20 Cᵒ

1.1(44

0.772)2/3= Ke(Tc − 293 − 6)

16.29 = Ke(Tc − 299) ----------------------------------2

From (Eq. 1) and (Eq. 2) :

𝟕𝟏. 𝟕𝟏𝟐

𝟏𝟔. 𝟐𝟖=

𝑲𝒆(𝑻𝒄 − 𝟐𝟕𝟗)

𝑲𝒆(𝑻𝒄 − 𝟐𝟗𝟗)

𝑻𝒄 =


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According to the equation [𝛾(𝑣𝑙)2/3 = 𝐾𝑒(𝑇𝐶 − 𝑇 − 6)], the surface tension

will become zero at a temperature six degrees below the critical temperature,

which has been observed experimentally.

Theoretically, the value of surface tension should become zero at the critical

temperature, since at this temperature; the surface of separation between a liquid

and its vapor disappears. However, it has been observed that the meniscus

disappears a few degrees below the critical temperature for some liquids.

The Brock-Bird correlation relates surface tension to the critical properties of

the liquid by the relationship,

-----------------------------------(5)

Where Q is given by:

------------------(6)

Where Tb is the normal boiling point of the liquid, Pc is the critical pressure and

Tr is the reduced temperature.

The quantity 𝛾𝑃𝑐−1/3

𝑇𝑐−1/3

𝑘−1/3 (where k is Boltzmann’s constant) is

dimensionless. It was suggested by van der Waals that this group may be

correlated with the quantity (1-Tr). This method of estimation of surface tension

is also known as corresponding states method.

The Brock-Bird method is not suitable for liquids which exhibit strong hydrogen

bonding (such as alcohols and acids). Sastri and Rao (1995) have presented the

following correlations for surface tension of such liquids.

For alcohols, they proposed:

--------------------------- (7)

For acids, the Sastri–Rao correlation is,

--------------------------- (8)


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For any other type of liquid, the following correlation was suggested by them.

----------------------------- (9)

Other equations which are represented the mechanical relationships between

surface tension of the liquid and the change that occurs on the temperature:

1. Van Der Waals Equation γ = γ° [1 −T

Tc]

1.5

2. Katayama’s Equation γ [M

dL−dV]

2/3= K(Tc − T)

3. Maclecod’s Equation γ = C(dL − dV)4


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The Wetting of Surfaces by Liquids

The energetics of solid surfaces and their effect on the interaction with liquids

play an important role in a variety of applications such as adhesive bonding,

polymer coatings, printing, etc., where a high degree of wetting is desired. In

other applications such as water and ice repellency and anti-sticking, easy-

cleaning or self-cleaning surfaces, wetting is undesirable.

Surface Free Energy

Suppose a box with a sliding cover is filled with a liquid ( Fig.3) the sliding

cover is assumed to have no interfacial tension with liquid. If the cove is slid

back to uncover a surface area of dA, the necessary reversible work will be

(𝛾𝑑𝐴), for a pure substance, the increase in the free energy of the system at

constant temperature and pressure s defined by Equation:

dG = 𝛾𝑑𝐴----------------------1

Figure 3 An ideal liquid box

The total free energy of the system is comprised of the energy of the bulk liquid

and the surface liquid. The latter is equal to the surface free energy per unit area

(𝐺𝑠) multiplied by the surface area as shown in ( Eq.2). Combining (Eq.1) and (

Eq.2) results in (Eq.3) which illustrates that the free energy of a pure substance

is equal to its surface tension.

dG = 𝐺𝑠𝑑𝐴 ---------------------2

𝐺𝑠 = [𝑑𝐺

𝑑𝐴]

𝑇∙𝑃=γ ------------------------3

Work of adhesion

The work of adhesion is defined as the reversible thermodynamic work requires

separating the interface from the equilibrium state of two phases to a saparation

distance of infinity. (Eq.4) show the work of the adhesion for a liquid-solid

combination. This definition is attributed to the French scientist A. Dupre.


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𝑾𝒂 = 𝜸𝑳 + 𝜸𝑺 − 𝜸𝑺𝑳 -------------------4

𝜸𝑳 is the surface energy (tension) of the liquid phase, 𝜸𝑺 is the surface energy

(tension) of the solid phase, 𝜸𝑺𝑳 is the interfacial surface tension, and 𝑾𝒂 is the

work of adhesion. A rise in the interfacial attraction results in an increase in the

work of adhesion. Eq.4 can be rewritten to determine the work of cohesion

( 𝑾𝒄) when the two phases are identical and no interface is present as shown in

Eq.5 for a solid phase:

𝑾𝒄 = 𝟐𝜸𝒔 ------------------------------5

The contact angle

When a small amount of liquid is placed on the surface of a solid, it forms a

drop which covers a limited area of the surface. This is illustrated in (Figure 4),

in which the contact angle, θ, is the angle between the tangent to the liquid

surface at the contact line and the solid surface. The limiting condition is that

0◦ <θ<180◦.

1. If we take the condition where the contact angle approaches zero, we have

a surface that is completely wetted by the liquid. Water on clean glass is

an example of this. The glass is hydrophilic due to the silica surface,

which is made up of a large number of oxygen atoms and surface silanol

groups that can hydrogen bond with the water surface.

Figure 4 The contact angle, θ, formed by a drop of liquid on a solid surface

2. Mercury on a polytetrafluoroethylene (PTFE) surface forms drops with a

contact angle of about 150◦ and this can be considered to be complete

non-wetting of the surface.

3. If the value of contact angle is θ ≥90◦, the droplet does not spread readily.

Generally, when the water contact angle is less than 90◦ the surface is

considered hydrophilic. When the water contact angle is greater than 90◦ the

surface is considered hydrophobic.


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Figure 5 Illustration of contact angles formed by sessile liquid drops on a smooth homogeneous solid

surface

Controlling the contact angle

The surface tension and contact angle can be controlled by different methods:

1. Surface roughness: if the surface is rough and water penetrates into the

roughness, whatever trend the flat surface showed will be enhanced, a

hydrophobic surface will become even more hydrophobic and a

hydrophilic surface will become more hydrophilic.

Figure 6 Definition of contact angles, (a) Contact angle on ideal surface is called Young contact angle, (b)

Apparent or measured contact angle on rough (Wenzel) surface.

2. Electro-wetting: when a potential difference is applied between the liquid

and the solid surface, the electric force at the corners of the drop pulls it

down onto the surface, lowering the contact angle.

3. Chemical modification: chemical modification of the suface can lead to

change in its surface tension. For example, adding polar, hydrophilic

groups to the surface will lead to a lower contact angle.

4. Temperature: The surface tension of most liquids decreases with

increasing temperature

The Young Equation

Thomas Young in 1805, suggested that the contact angle of a liquid drop on an

ideal solid surface is defined by the mechanical equilibrium of the drop under

the action of three interfacial tensions.

γvs = γls + γvl cos θ -----------------------------(1)


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This usually referred to as Young’s equation, and θ is Young’s contact angle.

Contact Angle Hysteresis

In practice, however, there exist many metastable states of a droplet on a solid,

and the observed contact angles are usually not equal to θ. The phenomenon of

wetting is more than just a static state. The liquid moves to expose its fresh

surface and to wet the fresh surface of the solid in turn. The measurement of a

single static contact angle to characterize wetting behavior is no longer

adequate. If the three-phase contact line is in actual motion, the contact angle

produced is called a “dynamic” contact angle.

In particular, the contact angle formed by expanding and contracting the liquid

are referred to as the advancing contact angle θa and the receding contact angle

θr, respectively (Fig.7).

Figure 7 Illustration of advancing and receding contact angle

These angles fall within a range, with the advancing angles approaching a

maximum value, and the receding angles approaching a minimum value.

Dynamic contact angles can be measured at various rates of speed. At a low

speed, it should be close or equal to a properly measured static contact angle.

The difference between the advancing angle and the receding angle is called the

hysteresis (H):

H = θa + θr ----------------------- ()

The significance of contact angle hysteresis has been extensively investigated ,

and the general conclusion is that it arises from surface roughness and/or

heterogeneity.


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Surface Tension Measurements Surface tension measurement techniques are divided into methods for solids and

liquids. There are two methods for measuring surface tension of liquids: static

and dynamic.

Table 1 Static surface tension measurement methods for liquids

Table 2 Dynamic Surface tension Measurement Methods for liquids


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Table 3 Surface Tension Measurement Methods for Solids

Reference

1. Manfred Stamm, “Polymer Surfaces and Interfaces ", First edition, Springer-Verlag Berlin Heidelberg

(2008).

2. Sina Ebnesajjad “ Surface Treatment of materails for adhesion Bonding”William Andrew Puplishing,

USA, 2006.

3. Pallab Ghosh,” lecture Surface Tension”, Department of Chemical Engineering, India.

4. Yuehua Yuan and T. Randall Le, “Surface Science Techniques”, chapter one, Springer-Verlag Berlin

Heidelberg, 2013.

5. Krister Holmberg, “HANDBOOK OF APPLIED SURFACE AND COLLOID CHEMISTRY”, John

Wiley & Sons Ltd, 2002.


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METHODS FOR THE MEASUREMENT OF CONTACT ANGLE

Several methods are available for measuring the contact angle and suitable

equipment may be purchased ‘off the shelf’. The technique chosen will depend

on the surface.

Sessile Drop

Figure 8 Schematic of the sessile drop experiment. In this approach, liquid is added or removed via the

syringe and the drop profile is photographed

Captive Bubble

In this experiment, the solid is immersed in the liquid and a bubble is produced

from a gas-tight syringe and brought into contact with the surface.


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Figure 9 Schematicofthecaptivebubbleexperiment.Expandingthebubblegives θR and contraction gives θA

Wilhelmy Plate

Figure 10 Schematic of the Wilhelmy plate experiment, where h is the depth of immersion of a plate of

width w and thickness t. The net force is measured with a balance.

Measurement of surface tension (liquid) The surface tension of liquid can be experimentally measured by several

methods. The drop-weight method, du Noüy ring method, Wilhelmy plate

method and the maximum bubble pressure method are discussed in this module.


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Drop-weight method

In this method, a drop is allowed to form slowly at the end of a tube having a

fine capillary inside it. Then it is slowly released and collected in a container.

Several drops (e.g., 100 drops, at the rate of one drop in about 200 s) are

collected in the same manner and the weight of the liquid is measured. From this

weight, the average weight of a drop is calculated.

The classical instrument for carrying out this measurement in the laboratory is

Stalagmometer. Now days, computer-controlled instruments can form precise

drops.

The principle behind the drop-weight method is as follows. As the size of the

drop at the tip of the tube grows, its weight goes on increasing. It remains

attached to the tube due to surface tension, which acts around the circumference

of the tube in the upward direction. When the downward force due to gravity

acting on the drop becomes slightly greater than the surface tension force, the

drop detaches from the tube. Therefore:

Upward force = 2𝜋𝑟° 𝛾 ---------------------------- (11)

Downward = mg ------------------------------- (12)

Where 𝑟° is the outer radius of the tip of the tube

At the point of detachment

mg = 2𝜋𝑟° 𝛾 ------------------------------(13)

Equation (13) is known Tate’s law.

The use of this equation requires the value of 𝑟°. To avoid this, a relative method

is usually used. A liquid whose surface tension is known is used as a reference

liquid. Highly-purified water or an ultrapure organic liquid may be used for this

purpose. The surface tension is calculated from the following equation:

𝛾 = [𝑚

𝑚𝑟𝑒𝑓] 𝛾𝑟𝑒𝑓 ---------------------------------- (14)

where 𝛾𝑟𝑒𝑓 is the surface tension of the reference liquid, and the weight of a

drop of this liquid is 𝑚𝑟𝑒𝑓.


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Du Nouy ring method

This is one of the most widely-used methods for measuring the surface tension.

The advantage of the ring method is that it is rapid, very simple and does not

need to be calibrated using solutions of known surface tension. When applied to

pure liquids with due precautions, the error can be reduced to ± 0.25%.

The measurement is performed by an instrument known as Tensiometer. This

instrument has an accurate micro-balance and a precise mechanism to vertically

move the sample liquid in a glass beaker. The modern tensiometer has a

computer-controlled arrangement that can move the table holding the liquid very

slowly (~100 μm/s). The procedure is illustrated in Fig.

The micro-balance continuously records the force applied on the ring when it

pulls through the air-liquid interface. The surface tension is the maximum force

needed to detach the ring from the liquid surface. The detachment force is equal

to the surface tension multiplied by the periphery of the surface detached.

Therefore, for a ring,

F=4πRr𝛾 -------------------------------------------------(15)

Where Rr is the radius of the ring. The force measured by the balance includes

the weight of the ring. In actual practice, the weight of the ring is first recorded

before it is immersed in the liquid. Sometimes, a calibration is made with a

known weight.

Usually the results obtained from Eq. (15) are in error. Harkins and Jordan

(1930) derived a correction factor 𝑓 such that the correct surface tension can be

obtained from the following equation.


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-------------------------------------------- (16)

The correction factor appears due to the weight of the liquid film immediately

beneath the ring, which is also raised when the ring pulls.

Wilhelmy plate method

In this method, a thin plate (usually made of platinum and iridium) is used. It is

dipped into the liquid whose surface tension is to be measured, as shown in Fig.

The vessel containing the liquid is gradually lowered and the force measured by

the balance at the point of detachment (F) is noted.

The Wilhelmy plate is sometimes used in another way. In this approach, the

liquid level is raised until it just touches the hanging plate. The force recorded

on the balance is noted.

The Wilhelmy equation is:

𝛾𝐹

𝑃 cos 𝜃 ------------------------------ (17)

Where P is the wetted perimeter of the plate, and 𝜃 is the contact angle.

The contact angle is reduced to near-zero values (so that the liquid wets the plate

completely) by cleaning the plate by burning it in the flame of Bunsen burner

before each experiment. If the contact angle is close to zero, Eq. (17) simplifies

to:


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𝛾 =𝐹

𝑃

The Wilhelmy plate method does not need any correction because the weight of

the film hanging from the plate is negligibly small.

Maximum bubble-pressure method (MBPM)

The Wilhelmy plate method gives the equilibrium (static) surface tension.

Surfactant solutions require a significantly higher amount of time than the pure

liquids to achieve this equilibrium. The surface tension of the surfactant solution

decreases with time. An example is shown in Fig.

In applications such as foaming, cleaning or coating, the interfaces are formed

very quickly. For such applications, the dynamics of rapid formation of interface

is important, which depends on the mobility of the surfactant molecules.

The maximum bubble pressure method (MBPM) is an easy-to-use technique for

measuring the dynamic surface tension (DST).

In the MBPM method, the gas bubbles are produced in the sample liquid at an

exactly-defined rate of generation. The bubble blown at the end of a capillary is

stable, and expands with the increasing pressure of the gas in the bubble. The

pressure reaches a maximum when the bubble is hemispherical and its radius is

equal to the radius of the capillary. The procedure is illustrated un Fig.


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If the maximum pressure is pmax (whose value is recorded by the instrument),

and the hydrostatic pressure is 𝑝°, then the following equation gives the dynamic

surface tension.

Where 𝑟𝑐 is the inner radius of the capillary. After reaching the maximum, the

pressure decreases, and the size of the bubble increases. As the size of the

bubble becomes larger than a hemisphere, it becomes unstable because the

equilibrium pressure within it decreases as it grows. Such a bubble expands

further, escapes and rises through the liquid. The entire cycle of bubble

formation, its growth and release is repeated.

The growth of the bubble and its separation can be divided into two time

periods. During the first period, the surfactant molecules adsorb on the surface

of the bubble and the surface tension varies accordingly. This period is termed

surface lifetime. The second period is the time in which the bubble grows

rapidly and finally separates from the capillary. This period is termed dead time.

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