Satas D., Tracton A.A. (ed.). Coatings Technology Handbook
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32
CHAN AND VENKATRAMAN
Bernard cells usually appears as hexagonal cells with raised edges and depressed
centers?"" The increase in the polymer concentration and the cooling due to solvent
evaporation cause the surface tension and surface density to exceed those
of
the bulk.
This creates an unstable configuration, which tends to move into a more stable one in
which the material at the surface has a lower surface tension and density. Theoretical
analysis'" has established two characteristic numbers: the Raleigh number
R,,
and the
Marangoni number
M,,,
given by
where
p
is the liquid density.
g
is the gravitational constant,
CY
is the thermal expansion
coefficient,
T
is the temperature gradient on the liquid surface,
h
is the film thickness,
K
is the thermal diffusivity, and
T
is the temperature. If the critical Marangoni number is
exceeded, the cellular convective flow is formed by the surface tension gradient.
As
shown
in Figure
1
la, the flow is upward and downward beneath the center depression and the
raised edge, respectively. But
if
the critical Raleigh number is exceeded, the cellular
convective flow, which is caused by density gradient, is downward and upward beneath
the depression and the raised edge, respectively (Fig.
1
1
b).
In general, the density-gradient-
driven flow predominates in thicker liquid layers
(>4
mm), while the surface tension
gradient is the controlling force for thinner films.
Cratering is similar to the Bernard cell formation in many ways. Craters, which are
circular depressions on a liquid surface, can be caused by the presence of a low surface
tension component at the film surface. The spreading
of
this low surface tension component
causes the bulk transfer
of
film materials. resulting in the formation of a crater. The flow
q
of
material during crater formation
is
given by'"
h'
Ay
4=2r\
where
Ay
is the surface tension difference between the regions of high and low surface
(a)
(
b)
1
CONVECTIVE
FLOW
DIRECTION
Figure
11
Schcmatie illustration
of
the formation
of
the Bernard cells due
to
(a)
the surface
tension gradient and
(h)
the density gradicnt.
COATING
RHEOLOGY
33
SURFACE TENSION ACCEPTABLE APPEARANCE
SAGGING
CRATERING
l
TIY
POOR FLOW
(SURFACE TENSION TOO LOW)
LOW
LOW
HIGH
MELT VISCOSITY
Figure
12
The effects
of
surface tension
and
melt viscosity
on
coating appearance.
tension. The crater depth
d,.
is given byJ7
The relationship between the cratering tendency and the concentration of surfactant was
investigated by Satoh and Takano.JX Their results indicate that craters appear whenever
paints contain silicon oils
(a
surfactant)
in
an amount exceeding their solubility limits.
In the discussion above, high surface tension and low viscosity are required for good
flow-out and leveling. But high surface tension can cause cratering, and excessively low
viscosity would result in sagging and poor edge coverage. To obtain an optimal coating.
the balance between surface tension and viscosity is important. Figure
12
illustrates coating
performance
as
a
function of surface tension and melt viscosity. Coating is
a
fairly complex
process; achieving an optimal result calls for the consideration of many factors.
ACKNOWLEDGMENTS
We are grateful to Steve Trigwell for preparing the figures.
REFERENCES
1.
A.
W. Adamson,
Phy.sicd
Chrrllisfrv
of
Sur-rc~es.
4th ed. New
York:
Wiley.
1982.
2.
L.
Du
Nouy,
J.
Get].
Physiol.
1,
521
(1910).
3.
R.
H.
Dettre
and
R.
E.
Johnson, Jr.,
J.
Colloid
Inrrrfme
Sci..
21,
367
(1966).
34
CHAN AND VENKATRAMAN
4.
D.
S.
Ambwani and T. Fort, Jr.,
Su@rce
Colloid
Sci..
11,
93 (1979).
5.
J. R. J. Harford and E.
F.
T.
White,
Plnst. Polyn.,
37, 53 (1969).
6.
J. Twin,
Phil. Trans..
29-30, 739 (1718).
7.
J. W. Strutt (Lord Rayleigh).
Proc. R.
Soc.
London,
A92, 184 (1915).
8.
S.
Sugden,
J.
Chem.
Soc.,
1483 (1921).
9.
J. M. Andreas,
E.
A. Hauser, and W. B. Tucker,
J.
Phys.
Chenr..
42,
1001
(1938).
10.
S.
WU,
J.
PO!\VJl.
sci..
c34, 19 (1971).
11.
R.
J. Roe,
J.
Colloid
Intetface
Sci.,
31, 228 (1969).
12.
S.
Fordham,
Pmc. R.
Soc.
London.,
A194,
1
(1948).
13.
C.
E.
Stauffer,
J.
Phys.
Cheln.,
69, 1933 (1965).
14.
J.
F.
Padday and
A.
R. Pitt,
Phil. Trms. R.
Soc.
London,
A275, 489 (1973).
15.
H.
H.
Girault,
D.
J.
Schiffrin. and B. D.
V.
Smith,
J.
Colloid
Interfke
Sci.,
101, 257 (1984).
16.
C.
Huh and R. L. Reed,
J.
Colloid
Interfirce
Sci.,
91, 472 (1983).
17.
Y. Rotenberg, L. Boruvka, and
A.
W. Neumann,
J.
Colloid
Interfrrce
Sci.,
93, 169 (1983).
18.
0.
C. Lin,
Clzemteck,
January
1975,
p.
15.
19.
L.
Komum,
Rheol.
Acta,
18,
178 (1979).
20.
0.
C. Lin,
J.
Apl.
Po/yn.
Sci..
19. 199
(
1975).
21.
H.
Freundlich
and
A.
D.
Jones,
J.
Phys.
Chem.,
4, 40. 1217 (1936).
22.
W.
H.
Bauer and E.
A.
Collins,
in
Rheology
4,
F. Eirich, Ed. New York: Academic press,
23.
P.
S.
Roller,
J.
Phys.
Chenr.,
43, 457 (1939).
24.
S.
Reiner and G. W. Scott Blair. in
Rheology
Vol
4,
F. Eirich, Ed. New York: Academic
25.
S.
LeSota,
Pfritlt
Vrrrnish.
Prod.,
47, 60 (1957).
26.
R.
B.
Bird,
R.
C.
Armstrong, and
0.
Hassager,
Dyrwnics
of
Polweric
Fluids,
Vol.
1.
New
27.
S.
J. Storfer, J. T. DiPiazza, and R.
E.
Moran.
J.
Corrting
Technol.,
60, 37 (1988).
28.
V.
G. Nix and J.
S.
Dodge,
J.
Pcrint
Techrral..
45, 59 (1973).
29.
T. C. Patton,
Pcrinr
Flow
and
Pipent Dispersion,
2nd ed. New York: Wiley-Interscience,
30.
A. G. Frederickson,
Principles
and
Applications
cfRheology,
Prenticc Hall, Englewood Cliffs,
31.
S.
Wu,
J.
Appl.
Polynr.
Sci.,
22, 2769 (1978).
32.
J. F. Rhodes and
S.
E.
Orchard,
J.
Appl.
Sci.
Res.
A,
1
I,
451 (1962).
33.
R. K. Waring,
Rheology,
2, 307 (1931).
34.
N.
0.
P. Smith,
S.
E.
Orchard, and A.
J.
Rhind-Tutt,
J.
Oil
Colour.
ChelJl.
Assoc..
44, 618
35.
S.
Wu,
J.
A~pl.
Polym.
Sci.,
22, 2783 (1978).
36.
J.
S.
Dodge,
J.
Paint
Technol.,
44, 72 (1972).
37.
K. Walters and R. K. Kemp, in
Polymer
Systetns:
D<fbrnrcrtion
md
Flow.
R. E. Wetton and
R. W. Wharlow, Eds. New York: Macmillan,
1967,
p.
237.
38.
A. Quach and C. M. Hansen,
J.
Puint Tecllnol..
46, 592 (1974).
39.
L.
0.
Kornum and H.
K.
Raaschou Nielsen,
Progr.
Org.
Cmtings,
8,
275 (1980).
40.
L. Weh,
Plaste
Kmtsch.
20, 138 (1973).
41.
C.
G. M. Marangoni,
Nuo)~
Cimerrto.
2, 239 (l97
1
).
42.
C.
M. Hansen and
P.
E.
Pierce,
Incl.
Eng.
Chem.
Prod. Res.
De)).,
12, 67 (1973).
43.
C.
M.
Hansen and Pierce,
Incl.
Brg,
Cllenr.
Prod. Res.
Del,.,
13, 218 (1974).
44.
J. N. Anand and H. J. Karma,
J.
Colloid
lnterfnce Sci.,
31, 208 (1969).
45.
J. R.
A.
Pearson,
J.
Fluid
Mech..
4,
489 (1958).
46.
P. Fink-Jensen,
Fwbr
Lrrck.
68, 155 (1962).
47.
A.
V.
Hersey,
Phy. Ser.,
2,
56, 204 (1939).
48.
T. Satoh and N. Takano,
Colour
Mcrter.,
47, 402 (1974).
1967,
Chapter
8.
Press,
1967,
Chapter
9.
York: Wiley-Interscience,
1987,
p.
61.
1979.
NJ.
1964.
(1961).
Leveling
1
.O
INTRODUCTION
A
coating is applied
to
a surface by a mechanical force: by
a
stroke of
a
brush, by transfer
from
a
roll, by removing the excess with
a
knife’s edge, or by other means. Most of these
coating processes leave surface disturbances: a brush leaves brush marks;
a
reverse roll
coater leaves longitudinal striations; knife coating leaves machine direction streaks; roll
coating leaves
a
rough surface, when the coating splits between the roll and the substrate;
and spraying may produce a surface resembling orange peel.
2.0
YIELD VALUE
These surface disturbances may disappear before the coating is dried, or they may remain,
depending
on
the coating properties and time elapsed between the coating application and
its solidification. The surface leveling process is driven by surface tension and resisted
by viscosity. Some coatings, especially thickened aqueous emulsions, may exhibit pseu-
doplastic flow characteristics and may have
a
yield value: minimum force required to
cause the coating to flow (see Fig.
I).
For such coating to level, the driving force (surface
tension) must be higher than the yield value. Solution coatings are usually Newtonian
(have no yield value) and level rather well. Hot melt coatings solidify fast and may not
level adequately. Some typical yield values for various coatings are given in Table
1.
Viscosity measurements at very low shear rates are required to determine the yield
value. Some of the shear rates experienced in various processes are shown in Table
2.
A
Brookfield viscometer, which operates at shear rates of
0.6-24
sec-’, is not suitable
for investigating the leveling effects that appear at much lower shear rates. Shear rates
experienced during various coating processes are very high, and the viscosity measure-
ments at low shear rates might not disclose coating behavior at these high shear rates.
A
yield value
of
0.5
dyneskm’ produces very fine brush marks, while
a
yield value
of
20
dyneskm’ produces pronounced brush marks. The yield stress necessary to suppress
t
Deceased
35
36
SATAS
4t
I
0
100
200
300
400
500
SHEAR
RATE,
SEC'
Figure
1
Viscosity
of
pseudoplastic emulsion coating as a function of shear rate compared
to
Newtonian oil.
Table
1
Yield Values and Thixotropy Ratings
for
Various Coatings
Coating type Yield Value (dyneskm') Thixotropy rating
Enamels, glossy
0-30
None to slight
Enamels, semiglossy
50-
120
Slight
Flat paints
20-
100 Slight to marked
Aqueous
wall
coatings
10-100 Slight
to
marked
Metal primcrs
0-
100
None to marked
Varnishes
0
None
Table
2
Shear Rates
for
Various Processcs
Process Shear rate (sec
~
')
Leveling
0.01
-0.10
Pouring if solution
10-100
Mixing
so-
1000
Reverse roll coating
100-10,000
Knife over
roll
coating
1000-
10,000
Brushing
10,000-50,000
Spraying
10,000-70.000
LEVELING
37
sagging is estimated at
5
dyneskm', which is not compatible with the best leveling proper-
ties. Therefore, to produce both adequate leveling and nonsagging behavior, thixotropic
properties must be introduced to
a
coating.
3.0
LEVELING
AND
VISCOSITY
The driving force of the leveling process is surface tension. The force that resists leveling
is viscosity and to a lesser degree, the elasticity of the coating. To facilitate leveling,
therefore, it is desirable
to
employ coating of low viscosity. Low viscosity coatings, how-
ever, cannot always be used. It is difficult to deposit heavy coatings if the viscosity is
low.
If
the coating is applied on
a
vertical surface,
a
high viscosity is needed
to
prevent
sagging.
Aqueous coatings are often pseudoplastic: they exhibit
a
rate-dependent viscosity.
They may have a low viscosity
(20-30
mPa.sec) at high shear rates
(
10'
sec"), such
as
experienced in roll coating operations, and
a
much higher viscosity (1-3 Pa.sec) at low
shear rates (0.01-10 sec". prevalent during leveling. Such coatings do not level well
because
of
the high viscosity at
low
shear rates.
The rheology index is sometimes used as an indicator of the leveling capabilities
of
a
coating. The rheology index is defined
as
the ratio of high shear rate viscosity
to
low
shear rate viscosity. If the rheology index is one, the coating is Newtonian; if it is larger
than one, the coating is dilatant; if it is smaller than one, the coating is pseudoplastic. A
large rheology index favors good leveling; it should exceed
0.25
for aqueous systems of
acceptable leveling properties.
3.1
Thixotropy
Thixotropic behavior of some coatings is utilized to circumvent the dilemma
of
having a
coating of sufficiently low viscosity that levels well and
a
coating
of
sufficiently high
viscosity that does not sag. Thixotropy is the dependence of viscosity on time. There are
coatings that retain a low viscosity for
a
short period after shearing, thus allowing good
leveling, but thicken fast enough to prevent sagging.
The thixotropic behavior of
a
coating is usually characterized by the thixotropy loop
as
shown in Figure
2.
At the beginning, the coating is sheared at
a
continuously increasing
Figure
2
Thixotropic
loop.
38
SATAS
shear rate, producing curve
a.
Then the coating is sheared at a constant shear rate
until constant viscosity (curve
b)
is reached. The shear rate is then gradually decreased,
producing curve
c.
The area enclosed by the thixotropy loop indicates the degree of
thixotropy: the larger the area, the more pronounced is the thixotropic behavior
of
the
coating. A pseudoplastic coating that exhibits no thixotropy would form no loop and
curve
U
would coincide with curve
c.
Curve
b
would not be formed, because the
viscosity is not time dependent in nonthixotropic coatings. Thixotropic behavior is
quite common in many aqueous coatings and high viscosity inks, and it is utilized to
improve the coatability.
4.0
LEVELING AND SURFACE TENSION
If the coating contains ingredients of differing surface tension and volatility, a surface
tension gradient may be formed during drying, which results
in
poor leveling.' This behav-
ior was observed when a drop of alkyd resin was dried in heptane solution. A high surface
tension are is created around the outer edges, because of
a
faster solvent evaporation rate
in that region. This causes a flow of the solution from the center of the drop, resulting in
formation of a donut-shaped resin deposit. When xylene is employed as the solvent, the
result is the opposite.
A
region of lower surface tension is produced around the outer
perimeter of the drop, resulting in
a
thicker center of the dried deposit. The addition
of
a
solvent-soluble surface active agent eliminates the formation of the surface tension gra-
dient, resulting in a dried deposit of uniform thickness.
5.0
LEVELING OF
BRUSH
AND STRIATION MARKS
Brush application produces brush marks dependent
on
the rush fineness. Reverse roll and
other roll coaters in which the coating splits between the rolls produce regular longitudinal
striation marks in the coating. Knife coaters produce longitudinal streaks, which are caused
by the restriction of the flow under the knife by gel and other particles. The geometry
of
such coating striations or brush marks is shown schematically in Figure
3.
According to Orchard's' mathematical model of the leveling process, the leveling
half-time may be expressed in the following manner:
where
y
is the surface tension and
T\L
the viscosity (at
low
shear rate).
The equation states that a low viscosity and a high surface tension favor the rate of
-7
t
Figure
3
Profile
of
coating striation marks.
LEVELING
39
leveling. The geometry of the coating (distance between striation marks and the coating
thickness) has a very large effect
on
leveling. Decreasing the distance between the striation
or brush marks is very effective
in
accelerating leveling, as is an increase
in
coating
thickness. It has also been stated by some authors3 that coating elasticity has a retarding
effect
on
leveling, although the effect is less important than that
of
viscosity.
REFERENCES
1.
D.
A. Bultman and M. T. Pike,
J.
Chertl.
Spec.
Mmuf
Assoc.,
January
1981.
2.
S.
Orchard,
Appl.
Sci.
Res..
A1
1.
45
1
(1962).
3.
M. Bierman,
Rheol.
Acta.
138 (1968).
BIBLIOGRAPHY
Beeferman,
H.
L.,
and
D.
A. Bregren,
J.
Paint
Technol..
38(492), 9-17 (1966).
Kooistra, M.
F.,
“Film formation phenomena: Fundamentals and Applications,” in
Third
Interna-
tioml
Corfererlce
~II
Organic
Contings
Science
and
Technology,
G.
D.
Parfitt and
A.
V.
Patsis, Eds., Westport,
CT:
Technomic,
1979.
Matsuda, T., and
W.
H.
Brendly, Jr.,
J.
Cotrtir~g
Techno/..
51(658). 46-60 (1979).
Overdiep, W.
S.
“The leveling of paints,’’ in
Proceedings
ofthe
Corzjiererlce
011
Physiccrl
Cheni~trv
Patton, T.
C.,
Paint
Flow
and
Pigrtlent
Dispersiort,
2nd ed. New
York:
Wiley,
1979.
Satas,
D.,
“Surface appearance,” in
Plastics
Firlisllirlg
crrzd
Decorcrtion.
D.
Satas,
Ed.
New
York:
Smith, N.
D.
P.,
S.
E.
Orchard, and A. J. Rhind-Tutt,
J.
Oil
Chem
Colour.
Assoc..
44,
618-633
trnd
H?ldrr,cl~rltrr,lic.~,
Oxford, July
1
-
13, 1977.
Van Nostrand Reinhold,
1986,
pp.
17-20.
(September
1961
).
This Page Intentionally Left Blank
Structure-Property
Relationships in Polymers
Subbu
Venkatraman
Rqdwnl
Corporation,
Menlo
Park, Cnlifornin
Most
of
the binders used in paints, varnishes, lacquer films, and photolithographic coatings
are made up of macromolecules. The final dry coating consists predominately
of
a
polymer,
either cross-linked or un-cross-linked. The material may have been polymeric before appli-
cation, or cured to become a polymer after application. In either case,
a
knowledge
of
the
properties
of
polymers
as
related
to
structural features helps in obtaining coatings with
desired performance characteristics.
1.0
STRUCTURAL PARAMETERS
We begin by defining some important structural parameters
of
polymers.
1
.l
Molecular-Weight Averages
Since all polymers contain
a
distribution
of
molecules
of
differing masses, it is customary
to define averages of the distribution
C
N;M,
C
N;
M,,
(number
-
average)
=
-
M!,,
(weight
-
average)
=
~
C
w;M,
C
W;
M,.
(viscosity
-
average)
=
[C
wiM:']''"
where
N,
=
number of molecules of molar mass
M,,
and
W;
their weight, and
a
is the
Mark-Houwink exponent defined by
[q]
=
Km
(1)
where
[q]
is the intrinsic viscosity.
41