coating technology

4

-1

4

StructurePropertyRelationships in

Polymers

4.1 Structural Parameters .........................................................

4-

1

4.2 Properties of Wet Coatings.................................................

4-

2

4.3 Properties of Dried Films ...................................................

4-

4

References .......................................................................................

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6

Most of the binders used in paints, varnishes, lacquer lms, and photolithographic coatings are madeup of macromolecules. The nal dry coating consists predominately of a polymer, either cross-linked orun-cross-linked. The material may have been polymeric before application or cured to become a polymerafter application. In either case, a knowledge of the properties of polymers as related to structural featureshelps in obtaining coatings with desired performance characteristics.

4.1 Structural Parameters

We begin by dening some important structural parameters of polymers.

4.1.1 Molecular-Weight Averages

As all polymers contain a distribution of molecules of differing masses, it is customary to dene averagesof the distribution:

where

N

i

= number of molecules of molar mass

M

i

, and

w

i

their weight, and

is the MarkHouwinkexponent dened by

MN M

N

M

ni i

i

w

(

(

number average)

weight averag

=

ee)

viscosity average

=

=

w M

w

M w M

i i

i

v i ia( ) [ ]1//

Subbu Venkatraman

Raychem Corporation

DK4036_C004.fm Page 1 Thursday, May 12, 2005 9:39 AM

2006 by Taylor & Francis Group, LLC

Molecular-Weight Averages Molecular Weight Between

Viscosity of Polymer Solutions Viscosity of Suspensions

Cross-Links Particle Size and Particle Size Distribution

The Glass Transition Temperature Tensile and Shear Moduli Other Properties

4

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Coatings Technology Handbook, Third Edition

(4.1)

where [

] is the intrinsic viscosity.The number

M

n

is usually measured by nuclear magnetic resonance (NMR) spectrometry or osmom-etry;

M

w

can be obtained via light-scattering techniques, while intrinsic viscosity measurements yieldestimates of

M

v

, Size-exclusion chromatography or gel permeation chromatography (GPA) can, in prin-ciple, be used to obtain all the averages mentioned above; care must be taken to ensure proper calibrationof the column with standards that have the same molecular structure as the polymer of interest.

Although different denitions exist for the breadth of a distribution, we will use the most commonone involving the averages dened above:

A value of unity for this quantity denes a narrow distribution polymer; a value of 2 is obtained incondensation polymers, and higher values indicate considerable breadth of molecular weights. A measureof this quantity can be obtained via GPC, or a combination of NMR and light-scattering techniques.

4.1.2 Molecular Weight Between Cross-Links

This is dened as the average molar mass between successive cross-link sites in a network polymer andis denoted by the symbol

M

c

. It is a measure of the density of cross-linking and can be estimated frommeasurements of the equilibrium degree of swelling or of the modulus.

4.1.3 Particle Size and Particle Size Distribution

In the case of latexes, many properties of the wet and dry coatings are determined by the sizes of thelatex particles. Estimations can be obtained directly through scanning electron micrography (SEM) if alm can be made. For the suspension, however, it is more customary to use light-scattering techniques(Coulter model N4, Brookhaven model DCP-1000) or optical sedimentation techniques (Horiba CAPA-700). In either case, it is possible to obtain a major portion of the particle size distribution.

4.2 Properties of Wet Coatings

Described below are some of the more important properties of coatings that are relevant to their ease ofapplication, either in solution or as suspensions. Most wet coatings are brushed on (as with paints) orsprayed on (as with some epoxies used as insulation). The solution coatings are mostly polymer based,and thus a survey of the rheological properties of polymer solutions is given; in addition, some propertiesof suspensions are discussed.

4.2.1 Viscosity of Polymer Solutions

Although several theories of polymer solutions

1

examine the dependence of viscoelastic properties onmolecular parameters, we shall not discuss these here. Instead, we shall focus on some generally acceptedempirical relationships. Most of these are covered extensively by Ferry.

2

4.2.1.1 Dependence on Molecular Weight

For pure polymers, the molecular weight dependence is usually expressed by the following type ofrelationship:

[ ] = KM v

MWD (molecular weight dispersity) =M

Mw

n



StructureProperty Relationships in Polymers

4

-3

(4.2)

where

0

is the zero-shear viscosity, and

K

is a solvent- and temperature-dependent constant. The valueof the exponent

is determined by the molecular weight range under consideration:

for

M

<

M

c

,

= 1 and for M >

M

c

,

= 3.4 (4.3)

where

M

c

is a critical molecular weight that expresses the onset of entanglements between molecules. Themagnitude of

M

c

is characteristic of the polymer structure; Table 4.1 gives some representative numbers.Although

M

c

signals the onset of topological effects on the viscosity, it is not identical to the molecularweight between entanglements,

M

e

. (The latter quantity is estimated from the magnitude of the rubberyplateau modulus.) Approximately, we have

(4.4)

Also,

M

c

is a function of polymer concentration. In the pure polymer (denoted by superscript zero),it attains its lowest value, ; in a solution of concentration

C

, its magnitude varies as discussed inSection 4.2.1.2.

The exponent

assumes the values quoted in Equation 4.3 only if the measured viscosity is in the so-called zero-shear-rate limit. At higher rates,

assumes values lower than unity and 3.4, in the two regimes.

4.2.1.2 Concentration Dependence of the Viscosity

As mentioned in Section 4.2.1.1, below a certain concentration, C*, entanglement effects are not signif-icant. This concentration is estimated from the following:

(4.4a)

where

M

is the molecular weight of the polymer in the coating solution. The concentration C* cannot beestimated from a plot of

0

against concentration, however; the transition is not sharp, but gradual.

4

Nosingle expression for the concentration exists below C

*

; however, in the entangled regime, the expression

(4.5)

works well for some polymers.

5,6

This relation does not hold all the way to the pure polymer, wherehigher exponents are found.

6

Equation 4.5 also does not hold in the case of polymer solutions in whichthere are other specic attractive forces, such as in poly(

n

-alkyl acrylates).

7

TABLE 4.1

Critical Molecular Weight

of Source Polymers

Polymer M

c

Polyvinyl chloride 6,200Polyethylene 3,500Polyvinyl acetate 25,000Polymethyl acrylate 24,000Polystyrene 35,000

Source

: From D. W. Van Krevelen,

Proper-ties of Polymers

, Elsevier, New York, 1976.

3

0 = KM

M Mc e~ 2

Mc0

CM

Mc* = 0

0 5 3 4= C M .



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Coatings Technology Handbook, Third Edition

There are two reasons for a reduction in viscosity of a polymer upon dilution: (a) the dilution effect,which causes the solution viscosity to be between those of the two pure components, and (b) a decrease ofviscosity due to a lowering of

T

g

upon dilution. The latter is solvent-specic and is the main reason for theapparent difculty in establishing a universal viscosityconcentration relationship for polymer solutions.

4.2.2 Viscosity of Suspensions

Many latex paints are suspensions in water or in an organic solvent. Their rheological properties differfrom those of polymer solutions in several ways. The concentration dependence is of a different form,and in addition, there is a dependence on particle size. Also, at high concentrations, these suspensionstend to have structure, which usually refers to an aggregated network. The immediate consequences ofthe existence of a pseudonetwork are the phenomena of yield stress and thixotropy. We explore next therelationship of these quantities to the characteristics of the particles making up the suspension.

4.2.2.1 Concentration Dependence of the Viscosity

In dilute suspensions, the concentration dependence is expressed by an extension of the Einstein equation:

(4.6)

where

s

is the solvent viscosity, and

is the volume fraction of the suspension. Equation 4.6 is valid forspherical particles without any interparticle interaction. Inclusion of long-range interaction (such asvolume exclusion) merely changes the coefcient of the

2

term.Of greater interest are the rheological phenomena that occur in suspensions of particles that have

short-range interactions, attractive or repulsive. In a comprehensive study, Matsumoto et al.

8

haveestablished the conditions for the existence of yield stresses in suspension. Their conclusions are as follows:

1. For particles with repulsive interactions, no yield stresses exist.2. Suspensions of neutral particles, or particles with attractive forces, do exhibit yield stresses.3. The magnitude of the yield stress increases with the concentration of the particles and with

increasing ratio of surface area to volume.

In this study, the existence of the yield stress was inferred from the presence of a plateau in the elasticmodulus G

, at very low frequencies; the magnitude of the yield stress was deduced from the height ofthe plateau modulus. A detailed and critical survey of the literature is given by Meitz.

9

The other important rheological consequence of a pseudonetwork is thixotropy, dened elsewhere inthis volume. The phenomenon is attributed to a time-dependent but reversible breakdown of the network.

4.3 Properties of Dried Films

4.3.1 The Glass Transition Temperature

The

T

g

is dened in various ways, but in a broad sense, it signals the onset of small-scale motion in apolymer. It is heavily inuenced by the chemical structure, in particular, by the bulkiness (steric hin-drance) of pendant groups. (See Van Kreleven

10

for an excellent discussion.)The molecular weight dependence of the glass transition is fairly straightforward and is given by the

following:

(4.7)

where is the limiting value of

T

g

at high molecular weights.

rel = = + +s

1 2 5 14 1 2. .

T TM

Mg g

n

=

Tg



StructureProperty Relationships in Polymers

4

-5

The effect of plasticizers on

T

g

is well documented.

10

According to a theoretical treatment by Bueche,

11

the

T

g

reduction by plasticizers can be calculated from

(4.8)

where

T

g,p

and

T

g,s

are the glass transition temperatures of the polymer and solvent, respectively, and

s

is the volume fraction of solvent. Then we write

where

l

= volume expansion coefcient above

T

g

, and

g

= volume expansion coefcient below

T

g

.To calculate the

T

g

of a solution, the

T

g

of the solvent should be known

12

or estimated as 2

T

m

/3, and

K

is usually taken to be 2.5.

4.3.2 Tensile and Shear Moduli

Both tensile and shear moduli are functions of temperature, and of time in the case of viscoelasticpolymers. We shall restrict our discussion to the temperature dependence of the isochronal moduli.(Because the tensile and shear moduli are related to each other through the use of an equation involvingthe Poissons ratio, the comments made here on the shear modulus

G

can be extended to the tensilemodulus

E

, as well.)For semicrystalline polymers below

T

g

, the modulus can be estimated from

13

(4.9)

where

G

g

,

G

c

are the moduli for the fully amorphous and fully crystalline polymer, respectively, and

X

c

is the degree of crystallinity.Above

T

g

, the same equation can be used, but Gc far exceeds Gg, and Equation 4.9 reduces to

(4.10)

For amorphous polymers above Tg, the modulus is given by the rubber elasticity expression:

(4.11)

wherelinked polymers is observed only at molecular weights higher than .

For cross-linked amorphous polymers above Tg (elastomers), the modulus is given in analogousfashion:

(4.12)

where Mc is the molecular weight between permanent cross-linked junctions. When Mc exceeds Me,trapped entanglements also play a part in determining modulus:14

TKT T

Kg

p g s g p s

s

(solution)Tg,

=

+

+

( )

( ), ,

1 1

Ks gs

p gp

=

< <

1

1

, 1 K 3

G G X G Gg c c g= + 2( )

G X Gc c2( )

GM

e

RT

e

=

Me0

Me0

GM

RT

c



is the entanglement molecular weight (see Section 4.2.1.2). This rubbery plateau for un-cross-

4-6 Coatings Technology Handbook, Third Edition

(4.13)

where Ge is given by Equation 4.11 and fe is a probability factor for trapped entanglements.In the case of network imperfections, Equation 4.12 is modied.14,15 The quantity fe 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 lms inuence performance characteristics. Examples are the coefcientof thermal expansion, ultimate mechanical properties, stress relaxation and creep, and dielectric prop-erties. However, correlation of these properties with structure for polymeric lms 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).

GM

f GRT

ce e

+



Ref. 2, see discussion in Chapter 17.

Table of ContentsChapter 4: StructureProperty Relationships in Polymers4.1 Structural Parameters4.1.1 Molecular-Weight Averages4.1.2 Molecular Weight Between Cross-Links4.1.3 Particle Size and Particle Size Distribution

4.2 Properties of Wet Coatings4.2.1 Viscosity of Polymer Solutions4.2.1.1 Dependence on Molecular Weight4.2.1.2 Concentration Dependence of the Viscosity

4.2.2 Viscosity of Suspensions4.2.2.1 Concentration Dependence of the Viscosity

4.3 Properties of Dried Films4.3.1 The Glass Transition Temperature4.3.2 Tensile and Shear Moduli4.3.3 Other Properties

References

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