5 The Theory of Adhesion 5.1 Contact Angle Equilibrium ...5-1 5.2 Forces of Attraction ...5-3 5.3 Real and Ideal Adhesive Bond Strengths ...5-8 References ...5-9 When pressure-sensitive
Trang 24-6 Coatings Technology Handbook, Third Edition
(4.13)
where G e is given by Equation 4.11 and f e is a probability factor for trapped entanglements
In the case of network imperfections, Equation 4.12 is modified.14,15 The quantity f e can be calculated
if the reaction parameters for network formation are known.14,16,17
4.3.3 Other Properties
Several other properties of dried films influence performance characteristics Examples are the coefficient
of thermal expansion, ultimate mechanical properties, stress relaxation and creep, and dielectric prop-erties However, correlation of these properties with structure for polymeric films is not well established; some of the more successful attempts are treated in Refs 2 and 3
References
1 R B Bird, R C Armstrong, and O Hassager, Dynamics of Polymeric Fluids, Vol 2 New York:
Wiley-Interscience, 1987
2 J D Ferry, Viscoelastic Properties of Polymers New York: Wiley, 1980.
3 D W Van Krevelen, Properties of Polymers New York: Elsevier, 1976.
4
5 J W Berge and J D Ferry, J Colloid Sci., 12, 400 (1957).
6 G Pezzin and N Gligo, J Appl Polym Sci., 10, 1 (1966).
7 Ref 2, p 510
8 T Matsumoto, O Yamamoto, and S Onogi, J Rheol., 24, 279 (1980).
9 D W Meitz, Ph.D thesis, Carnegie-Mellon University, December 1984
10 Ref 3, p 383
11 F Bueche, Physical Properties of Polymers New York: Wiley, 1962.
12 Ref 3, p 384
13 Ref 3, p 266
14 E M Valles and C W Macosko, Macromolecules, 12, 673 (1979).
15 P J Flory, Principles of Polymer Chemistry Ithaca, NY: Cornell University Press, 1953, p 458.
16 M Gottlieb, C W Macosko, G S Benjamin, K O Meyers, and E W Merill, Macromolecules, 14,
1039 (1981)
17 D S Pearson and W W Graessley, Macromolecules, 13, 1001 (1980).
G
RT
c
e e
ρ +
DK4036_C004.fm Page 6 Thursday, May 12, 2005 9:39 AM
Ref 2, see discussion in Chapter 17
Trang 35
The Theory of Adhesion
5.1 Contact Angle Equilibrium 5-1 5.2 Forces of Attraction 5-3 5.3 Real and Ideal Adhesive Bond Strengths 5-8 References 5-9
When pressure-sensitive adhesive is applied to a smooth surface, it sticks immediately The application pressure can be very slight, not more than the pressure due to the weight of the tape itself The adhesive
is said to “wet” the surface, and, indeed, if the tape is applied to clear glass and one views the attached area through the glass, it is found that in certain areas the adhesive–glass interface looks like a liquid–glass interface From this one would infer that a pressure-sensitive adhesive, even though it is a soft, highly compliant solid, also has liquidlike characteristics Some knowledge of the interaction between liquids and solids is beneficial to the understanding of adhesion
5.1 Contact Angle Equilibrium
When a drop of liquid is placed on a surface of a solid that is smooth, planar, and level, the liquid either spreads out to a thin surface film, or it forms a sessile droplet on the surface The droplet has a finite between the solid and the liquid and the surface tension of the liquid The contact angle equilibrium has received a great deal of attention, principally because it is perhaps the simplest direct experimental approach to the thermodynamic work of adhesion
Many years ago Young1 proposed that the contact angle represents the vectorial balance of three tensors, the surface tension of the solid in air (γsa), the surface tension of the liquid in equilibrium with the vapor (γlv), and the interfacial tension between the solid and the liquid (γsl), The force balance can be written
Young’s equation has come under criticism on the grounds that the surface tension of a solid is ill defined, but most surface chemists find his equation acceptable on theoretical grounds
The equation can be written as a force equilibrium or as an energy equilibrium, because the surface tension, expressed as a force per unit of length, will require an energy expenditure of the same numerical value when it acts to generate a unit area of new surface
Harkins and Livingston2 recognized that Young’s equation must be corrected when the exposed surface
of the solid carries an adsorbed film of the liquid’s vapor The solid–“air-plus-vapor” tensor, γsv, is less than the solid–air tensor, γsa Harkins and Livingston introduced a term, πe, to indicate the reduction thus:
Carl A Dahlquist
3M Company
DK4036_book.fm Page 1 Monday, April 25, 2005 12:18 PM
angle of contact (Figure 5.1) The magnitude of the contact angle depends on the force of attraction
Trang 45-4 Coatings Technology Handbook, Third Edition
where r is the center-to-center distance between the dipoles
If the rotational energy is less than the thermal energy of the system, then
where k is Boltzmann’s constant (0.0821 1·atm/mol deg), and T is absolute temperature (K)
There may be dipole-induced dipoles, where the potential energy of interaction is given by
where α2 and α1 are the molecular polarizabilities
There may be acid–base interactions7,8 across the interface that can lead to strong bonding Examples are hydrogen bonding, Lewis acid–base interactions, and Brønsted-type acid–base interactions
Covalent bonding between adhesive and adherend, if achievable either by chemical reactions or by high energy radiation, can lead to very strong bonds
Interdiffusion, usually not achievable except between selected polymers, can also lead to high adhesion The force of attraction between planar surfaces has been derived from quantum mechanical consid-erations by Casimir, Polder,9 and Lifshitz.10
Lifshitz calculated the attractive forces between nonmetallic solids at distances of separation sufficiently large that the phase lag due to the finite velocity of electromagnetic waves becomes a factor He obtained the following relationship between the attractive force and the known physical constants:
where F is the attractive force per unit of area, h is Planck’s constant, C is the velocity of light, d is the distance of separation, e o is the dielectric constant, and φ(e o) is a multiplying factor that depends on the dielectric constant as follows:
Strictly speaking, the dielectric constant in this expression should be measured at electron orbital frequency, about 1015 Hz However, if we assume handbook values of the dielectric constant at 106 Hz, which for nylon, polyethylene, and polytetrafluoroethylene, are 3.5, 2.3, and 2.0, respectively, the corre-sponding φ(e o) values are 0.37, 0.36, and 0.35 The force values then stand in the ratios 0.11 to 0.056 to 0.039 When normalized to F (nylon) = 1.0, they fall to the following ratios:
F(nylon), = 1.00; F(PE), 0.51; F(PTFE), 0.35 When the γc values (dynes/cm) of these three materials are similarly normalized to the γc values for nylon, the values fall in remarkedly similar ratios
γc
γc(norm)
56 1.00
31 0.55
18.5 0.33
U r
nt
3
µ µ
U
kTr
K =Keesom potential= −2
3
1 1 6
µ µ
U
r
6
= −µ α +µ α
d e
o
+
4
1
DK4036_book.fm Page 4 Monday, April 25, 2005 12:18 PM
Trang 5The Theory of Adhesion 5-5
In the Lifshitz equation, the force of attraction is shown to decrease as the inverse fourth power of the
distance of separation However, when the separation becomes so small that the phase lag in the
inter-action no longer is significant (it is of the order of 6° at a separation of 50 Å), the attractive force varies
as the inverse third power of the distance of separation This has been verified experimentally,11 although
the direct measurement is extremely difficult (Figure 5.4) The forces existing at separations greater than
50 Å contribute very little to adhesion
Some 30 years ago Good and Girifalco reexamined the interfacial tensions between dissimilar liquids
and developed a theory of adhesion.12 They found that the work of adhesion, given by
could be approximated quite well by the geometric mean of the works of cohesion of the two liquids
when the only attractive forces of cohesion are dispersion forces:
However, in some liquid pairs (e.g., water and hydrocarbons), this did not hold, and they coined an
“interaction parameter,” Φ, given by
Thus,
FIGURE 5.4 Attraction between ideally planar solids.
250 200
100
50
20
Force Constant
D 4.07
1
F ∝
D 2.94
1
F ∝
W a=γL1+γL2−γL L1 2
W a= 2 L1 L2
1 2
(γ γ )/
γ γ
1 2 1 2
1 2
W a= 2 L1 L2
1 2
Φ(γ γ )/
DK4036_book.fm Page 5 Monday, April 25, 2005 12:18 PM
Trang 65-6 Coatings Technology Handbook, Third Edition
For water on a paraffinic hydrocarbon, where the contact angle is 108°, Φ would have a value of about
0.55 For hexadecane on polyethylene, Φ is very near unity Good and his associates11,12 have provided
directions for calculating Φ, and they give experimental and calculated values for several combinations
of water and organic liquids
Fowkes13 approached the problem from a different point of view He reasoned that the only forces
operable at the interface between water and an aliphatic hydrocarbon molecule contain no hydrogen
bonding groups and no fixed dipoles
Fowkes also assumed that the work of adhesion would be given by twice the geometric mean of the
surface energies of the two liquids on either side of the interface but now taking into consideration only
the dispersion force components of the surface energies For the work of adhesion between water (L1)
and n-octane (L2), we have
where the superscript D stands for the dispersion energy component of the total surface energy Accepted
values for the surface energies and interfacial energies are as follows:
If these values are substituted into the equation above to solve for we get 22.0 ergs/cm2 Fowkes
evaluated several water-aliphatic hydrocarbon systems and found that they all yielded essentially the same
value for the dispersion energy component of the surface energy of water, 21.8 ± 0.7 ergs/cm2
Turning now to the work of adhesion and the interfacial energy between mercury and aliphatic
hydrocarbon, Fowkes calculated the dispersion energy component of the surface energy of mercury Using
n-octane as the hydrocarbon liquid having a surface energy of 21.8 ergs/cm2 (all of it attributed to
dispersion forces), the surface energy of mercury, 484 ergs/cm2, and the interfacial energy, 375 ergs/cm2,
we have
The average for a series of mercury–aliphatic hydrocarbon systems yielded 200 ± 7 ergs/cm2 for
the dispersion energy component of the surface energy of mercury
Since the remaining forces that contribute to the surface energy of mercury are metallic forces, the
only interacting forces at the water–mercury interface are the dispersion forces, and the work of adhesion
is given by
from which
This compares very favorably with the measured value of 426 ergs/cm2
D L D
=2(γ γ1 2)1 2/ =γ 1−γ 1 2
D
L
1=72 8 ergs/cm2; 2 = 2 =21 8 ergs/cm2;
1
1 2L = ergs/cm50 8 2
γH O2
D
,
W a
D n D
( ,
W a
D
D
=
196 2
1 2
/
γ γ
Hg
Hg
γHg
D
W a=2 200 21 8× 1 2=484 72 8+ − H g H O
2
( , )
γ
γ(H g,H O2 )=424 7 ergs/cm2 DK4036_book.fm Page 6 Monday, April 25, 2005 12:18 PM
Trang 7The Theory of Adhesion 5-7
The work of adhesion due to dispersion forces is numerically small in work or energy units For example, the work of adhesion of methylene iodide on polyethylene is 82 ergs/cm2 (θ = 52°) This small value is not, however, indicative of a small force of attraction across the interface Keep in mind that the work is the product of force and displacement, and that the attractive force, at separation distances less than 50 Å (5 × 10−7 cm) increases as the inverse of displacement raised to the third The molecules at the interface are at an equilibrium distance of separation where attractive forces and repulsive forces balance The variation in the repulsive forces with distance of separation has a dependence several orders of magnitude higher than the attractive forces (of the order of 1012 for atom pairs and 108
for repulsion forces across a hypothetical plane) We can calculate the maximum force of attraction by equating the work of adhesion to the work of separation
Let F a indicate the attractive force, F r the repulsive force, x the distance separation, and d the equilibrium distance We cannot measure d directly, but we can estimate it from calculations of the distance between
molecular centers in a liquid of known specific gravity and molecular weight In the case of methylene iodide (sp g 3.325, mol 267.9), we calculate the separation to be about 5 × 10−8 cm between the centers
of adjacent molecules
If we take 5 × 10−8 cm as a reasonable distance of separation across the interface between methylene
iodide and polyethylene, and we accept the force versus distance relationships for attraction (a) and repulsion (r), we can write:
where the subscript e stands for “equilibrium.” At equilibrium we have the condition that (F a)e = (F r)e
We can then express the work of adhesion as
The solution is
For methylene iodide on polyethylene, W a is 82 ergs/cm2 Taking d as 5 × 10−8 cm, F e = F = F r= 4.92
× 109 dynes/cm2
The maximum attractive force is encountered where the difference between the attractive forces and
the repulsive forces maximizes as separation proceeds This occurs where (d/x)3− (d/x)8 maximizes, at
about x = 1.22d.
At this displacement, F = 0.347F e, or, in the case of methylene iodide and polyethylene, at 1.71 × 109
dynes/cm2 (about 25,000 psi) This would be the maximum attractive force experienced when separation
of the materials is attempted; it far exceeds the average stresses that are typically observed when adhesive bonds are broken
Others have calculated theoretical forces of adhesion by other approaches All yield results that predict breaking strength far exceeding the measured breaking strengths
x
x
=
( )
( )
3
8
d
x dx
d d
∞
∞
∫
W a=F ed−d
DK4036_book.fm Page 7 Monday, April 25, 2005 12:18 PM
power (Figure 5.4)
Trang 86
Adhesion Testing
6.1 Fundamentals of Adhesion 6-1 6.2 Standardization of Adhesion Tests 6-3 6.3 Delamination Procedures 6-4 6.4 Local Debonding Systems 6-7 6.5 Flaw Detection Methods 6-10
6.6 Outlook 6-12 References 6-13
6.1 Fundamentals of Adhesion
Without sufficient adhesion, a coating of otherwise excellent properties in terms of resistance to weather, chemicals, scratches, or impact would be rather worthless It is therefore necessary to provide for good adhesion features when paint materials are formulated There must also be adequate means for controlling the level of adhesion strength after the coating has been spread and cured on the substrate Moreover, methods should be available that allow for the detection of any failure in the case of the dissolution of the bond between coating and substrate, under any circumstances whatsoever
6.1.1 Components at the Interface
In chemical terms, there is a considerable similarity between paints on one side and adhesives or glues
in this chapter to concentrate on the behavior of paint materials Adhesion is the property requested in either case, though perhaps with different emphasis on its intensity, according to the intended use Such a coating is, in essence, a polymer consisting of more or less cross-linked macromolecules and
a certain amount of pigments and fillers Metals, woods, plastics, paper, leather, concrete, or masonry,
to name only the most important materials, can form the substrate for the coating
It is important, however, to keep in mind that these substrate materials may inhibit a rigidity higher than that of the coating Under such conditions, fracture will occur within the coating, if the system experiences external force of sufficient intensity Cohesive failure will be the consequence, however, if the adhesion at the interface surpasses the cohesion of the paint layer Otherwise, adhesive failure is obtained, indicating a definite separation between coating and substrate
Ulrich Zorll
Forschungsinstitut für Pigmente and Lacke
DK4036_book.fm Page 1 Monday, April 25, 2005 12:18 PM
Components at the Interface • Causes of Failure • Measures of
Cross-Cut Test • Tensile Methods Adhesion
Scratch Technique • Indentation Debonding • Impact Tests Ultrasonic Pulse-Echo System • Acoustic Emission Analysis • Knife-Cutting Method • Peel Test • Blister Method
Thermographic Detection of Defects
on the other (Figure 6.1) Both materials appear in the form of organic coatings; thus, it is appropriate
Trang 97
Coating Calculations
7.1 Introduction 7-1 7.2 Resins 7-1 7.3 Pigments 7-2 7.4 Solvents 7-2 7.5 Additives 7-2 7.6
7.7 Calculations 7-2
7.8 Converting to a 100 Gallon Formulation 7-4 7.9 Cost 7-4 7.10 Coverage 7-5 7.11 Computer Use 7-5 Bibliography 7-5
7.1 Introduction
Coatings are defined as mixtures of various materials The questions arise as to how much of which materials, and how do these things relate The materials fall into four general categories, as follows:
• Resins
• Pigments
• Solvents
• Additives
7.2 Resins
These are the generally solid, sticky materials that hold the system together They are also called binders, and when in a solvent, they are the vehicles for the system They may come as a “single-package” or “two-package” system Single package is just the liquid resin or the resin in solvent Two package means that
an “A” part was blended with a “B” part to cause a chemical reaction In both systems, we need to know the amount of solid resin present This dry material divided by the total of the dry plus the solvent is frequently called a “resin solid.” With the two-package systems, we need to know not only the solids but also the ratio of these solids to form the desired film This ratio may be designated as a simple ratio of
1 to 1 Or it may be based on 1 or 100, as 0.3 to 1, or 30 parts per hundred, or a total of 100 as 43 to
57 These ratios determine the film properties We will also need to know the density (weight per unit volume, usually as pounds per gallon) of the resin or vehicle to help calculate volume
Arthur A Tracton
Consultant
DK4036_book.fm Page 1 Monday, April 25, 2005 12:18 PM
Formulation Weight • Formulation Volume • Formulation Density • Formulation of “Nonvolatile by Weight” • Ratio (Weight) • Pigment Volume Content (Volume)
Conventions 7-2
Formulation “Nonvolatile by Volume” • Pigment to Binder
Trang 10Coating Calculations
TABLE 7.1 Paint Formulation Calculations
No.
7
8
9
10
Factor = 1.96
On Total Formulation
© 2006 by Taylor & Francis Group, LLC