Application of Light Scattering to Coatings: A User’s Guide

202 Pages·2014·12.82 MB·English

by  Michael P. Diebold (auth.)

Application of Light Scattering
to Coatings
Michael P. Diebold
Application of Light
Scattering to Coatings
A User’s Guide
1 3
Michael P. Diebold
DuPont Titanium Technologies
Wilmington
Delaware
USA
The information set forth herein is based on technical data that DuPont believes to be reliable.
It is intended for use by persons having technical skill, at their own risk. Since conditions of
use are outside our control, we make no warranties, expressed or implied and assume no li-
ability in connection with any use of this information. Nothing herein is to be taken as license
to operate under or a recommendation to infringe any patents.
ISBN 978-3-319-12014-0 ISBN 978-3-319-12015-7 (eBook)
DOI 10.1007/978-3-319-12015-7
Springer Cham Heidelberg New York Dordrecht London
Library of Congress Control Number: 2014954030
© E. I. du Pont de Nemours and Company 2014
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Preface
Paints are a ubiquitous and essential part of our everyday lives. One important role
they play is to alter or improve the appearance of an object. There are a number of
appearance attributes that coatings confer, including color, gloss, distinctness of
image, sheen, opacity, and the like. In this book we focus on the opacity of paints,
specifcally on white hide.
Opacity can come from two sources, either alone or together. They are light
absorption and light scattering. Both of these optical phenomena prevent light from
penetrating to the substrate surface and then returning to our eye, but they do so in
very different ways. Light absorption removes the light all together, resulting in a
black paint. Scattering, on the other hand, ideally redirects all of the light out of the
paint flm before it can penetrate as far as the substrate surface, resulting in a white
paint.
The scattering interactions between light and particles are of paramount impor-
tance to the Coatings Industry. However, the only mention of light in the curriculum
of many universities is as a theoretical construct based on wave equations. Scatter-
ing is given a mere footnote, if mentioned at all.
The intent of this book is to provide a detailed explanation of light scattering
and white opacity in a way that is useful to the coatings formulator. While some
concepts covered here date back a century or more, they have not yet, to the au-
thor’s knowledge, been assembled in one place. It is the specifc goal of this book
to provide a reference both for those new to the feld of Coatings Science as well as
longtime practitioners of the art.
This book approaches light scattering from both a theoretical and a practical
view point. The frst two chapters describe the physical phenomenon of light scat-
tering, frst by a single particle and then by an ensemble of particles. Chapter 1 is the
most theoretical in the book, and those readers less inclined to theory can skip all
but the summary and still follow the remaining chapters. After discussing the phe-
nomenon of light scattering, the book turns to the practical aspects of formulating a
paint with high opacity. A chapter is given on measuring white opacity, followed by
a number of chapters’ detailing factors that affect light-scattering strength in a paint
flm. The book concludes with a discussion on cost reduction using the principles
covered in previous chapters.
A list of references can be found at the end of each chapter. In general, these
are the frst reports of important concepts or results, rather than the most recent
v
vi Preface
paper on the subject. There are three reasons for this—frst, due to the high level of
research activity going on in the coatings industry, a list of the most recent refer-
ences would be obsolete very soon after publication of this book. Second, the initial
report is nearly always the most complete in terms of describing a new concept and
its underlying fundamentals. Finally, with the ease of electronic searches available
today, it is trivial for a researcher to fnd the most recent papers that reference back
to these original reports, whereas following the paper trail backward poses more of
a diffculty.
I thank Dr. Gabriela Burgos, Dr. Ricardo Abrahao, Dr. Muktha Bharathy,
Dr. Pablo Aragon, Dr. Guobin Shan, Steve Broadwater, Christopher Ahmer, Colin
Dickens, Bob Kwoka, and Julia Diebold for their helpful comments on various
drafts of this book. Throughout the writing process, I benefted from in depth dis-
cussions with Dr. John Crowther and Dr. James Sipe. Jason Boke measured the data
reported in chaps. 5 and 7, and in the process prepared more than 1000 drawdowns
from dozens of paints over a short four month period. Finally, I am especially grate-
ful to Dr. Austin H. Reid, Jr., whose expert editing skills early in the writing of this
book have much improved its readability, and whose kind and generous friendship
I have greatly enjoyed and benefted from over the last 30 years.
Contents
1 Scattering by a Single Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Introduction to Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Scattering Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
The Nature of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
The Effect of Particle Size and Light Wavelength . . . . . . . . . . . . . . . . . . . 7
Light Scattering by a Single, Isolated Particle . . . . . . . . . . . . . . . . . . . . . . 8
Comparing Scattering Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
The Magnitude of Light Defection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Light Scattering in Different Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
The Optimal TiO Particle Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2
Undertone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Exotic Particle Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Mie Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2 Scattering by Groups of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
The Need to go Beyond Mie Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Dependent Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
PVC and TiO PVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2
The CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Crowding Versus Nonideal Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Light Scattering in Paint Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Points of Possible Confusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
S and S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
TiO2 coat
Causes and Control of Nonideal Spacing . . . . . . . . . . . . . . . . . . . . . . . . . 46
State of TiO Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2
Resin Particle Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Effect of Extender Particle Size on Nonideal Spacing . . . . . . . . . . . . . 49
Formulating at High-Effective PVC . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Nano-Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
The Optimal TiO Particle Size Revisited . . . . . . . . . . . . . . . . . . . . . . . . 54
2
vii
viii Contents
Wet Hide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 The Kubelka–Munk Framework and Measuring Opacity . . . . . . . . . 59
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
The Kubelka–Munk Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
The Judd Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Opacity from Low-Quality TiO Pigments . . . . . . . . . . . . . . . . . . . . . . . . 70
2
Measuring Scattering Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Contrast Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Spread Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Hiding Power at Equal Brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
The Full Value of High-Quality TiO . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2
Computer-Assisted Spread Rate Determinations . . . . . . . . . . . . . . . . . 76
Tint Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
A Comparison Between Opacity Measurements . . . . . . . . . . . . . . . . . . . 79
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4 TiO Pigments in Liquid Paints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
The Behavior of Small Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Forces Present Between Particles in the Liquid Paint . . . . . . . . . . . . . . . 85
van der Waals Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Steric Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Electrostatic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Dispersion of Small Particles into a Liquid . . . . . . . . . . . . . . . . . . . . . . . 87
Paint Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Electrostatic Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
In the Absence of Organic Dispersant . . . . . . . . . . . . . . . . . . . . . . . . . 93
Electrostatic Dispersants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Steric Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
A Comparison of Stabilization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Surface Treatment of TiO Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2
The Drying Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Quantifying Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Optical Techniques: Liquid Paints . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Optical Techniques: Dry Paint Films . . . . . . . . . . . . . . . . . . . . . . . . . 104
Microscopic Techniques: Dry Paint Films . . . . . . . . . . . . . . . . . . . . . 104
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Contents ix
5 Effects of Extenders on Paint Optics Below the CPVC . . . . . . . . . . . 111
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
General Considerations When Using Extenders . . . . . . . . . . . . . . . . 113
Formulating with Extenders in Practice . . . . . . . . . . . . . . . . . . . . . . . 114
Paint Constituents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Replacement of Resin by Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Extender Use Below the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Small-Particle Extenders Replacing Resin . . . . . . . . . . . . . . . . . . . . 119
Small-Particle Extenders Replacing Pigment . . . . . . . . . . . . . . . . . . 122
Large-Particle Extenders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Replacing One Extender Particle with Another . . . . . . . . . . . . . . . . . 131
Revisiting the Effective PVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Revisiting the Window Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Intermediate-Sized-Particle Extenders and Dilution Effciency . . . . . . . 135
Hollow Sphere Polymer and Flash-Calcined Clay . . . . . . . . . . . . . . . . . 137
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6 Volume Relationships and the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . 141
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Volume Relationships in Paint Films . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Characterizing the Void Content of a Paint Film . . . . . . . . . . . . . . . . . . 145
Oiled Hide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Measuring the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Paint-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
OA and the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
The Nonadditivity of OA and CPVC . . . . . . . . . . . . . . . . . . . . . . . . . 150
The CPVC of Water-Borne Paints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Solvent Versus Latex Paints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
The Binding Power Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Controlling the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Effect of Extender Particle Size: Large and Small Particles . . . . . . . 155
Effect of Extender Particle Size: Nano and Highly Porous
Extender Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
TiO Pigments with Thick, Porous Coatings . . . . . . . . . . . . . . . . . . . 158
2
Mixtures of Small and Large Particles . . . . . . . . . . . . . . . . . . . . . . . . 160
Revisiting the SX Versus TiO PVC Curve . . . . . . . . . . . . . . . . . . . . . . . 161
2
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7 Effects of Extenders on Paint Optics Above the CPVC . . . . . . . . . . . 167
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
x Contents
General Considerations When Formulating Above the CPVC . . . . . . . . 168
The Role of Extenders Above the CPVC . . . . . . . . . . . . . . . . . . . . . . 169
The Utility of the Porosity Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Formulating Above the CPVC with Extender Particles . . . . . . . . . . . . . 172
Formulating Near the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8 Cost-Effective Paint Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Formulations Without Extenders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Formulations with Extenders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Below the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Above the CPVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Assessing Claims of Equal Opacity at Reduced TiO Loadings . . . . . . 192
2
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196