Polymer Permeability

386 Pages·1985·28.557 MB·English

by  J. Comyn (auth.), J. Comyn (eds.)

POLYMER PERMEABILITY
POLYMER
PERMEABILITY
Edited by
J. COMYN
School of Chemistry, Leicester Polytechnic, UK
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First edition 1985
Reprinted 1994
© 1985 Chapman & Hall
Softcover reprint of the hardcover 1st edition 1985
ISBN·13:978-94-010-8650-9 e-ISBN-13:978-94-009-4858-7
DOl: 10.1007/978-94-009-4858-7
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Preface
Polymers are permeable, whilst ceramics, glasses and metals are gener
ally impermeable. This may seem a disadvantage in that polymeric
containers may allow loss or contamination of their contents and
aggressive substances such as water will diffuse into polymeric struc
tures such as adhesive joints or fibre-reinforced composites and cause
weakening. However, in some cases permeability is an advantage, and
one particular area where this is so is in the use of polymers in drug
delivery systems. Also, without permeable polymers, we would not
enjoy the wide range of dyed fabrics used in clothing and furnishing.
The fundamental reason for the permeability of polymers is their
relatively high level of molecular motion, a factor which also leads to
their high levels of creep in comparison with ceramics, glasses and
metals.
The aim of this volume is to examine some timely applied aspects of
polymer permeability. In the first chapter basic issues in the mathema
tics of diffusion are introduced, and this is followed by two chapters
where the fundamental aspects of diffusion in polymers are presented.
The following chapters, then, each examine some area of applied
science where permeability is a key issue. Each chapter is reasonably
self-contained and intended to be informative without frequent outside
reference. This inevitably leads to some repetition, but it is hoped that
this is not excessive.
J. COMYN
v
Contents
Preface v
List of Contributors viii
1. Introduction to Polymer Permeability and the Mathematics
of Diffusion 1
J. COMYN
2. Permeation of Gases and Vapours in Polymers 11
C. E. ROGERS
3. Case II Sorption 75
A. H. WINDLE
4. Effects of Oxygen Permeation and Stabiliser Migration on
Polymer Degradation 119
J. Y. MOISAN
5. Diffusion and Adhesion. 177
J. COMYN
6. The Role of Polymer Permeability in the Control of Drug
Release . 217
JOHN H. RICHARDS
7. Permeability and Plastics Packaging . . 269
R. J. ASHLEY
vi
Contents vii
8. Permeability of Coatings and Encapsulants for Electronic
and Optoelectronic Devices 309
M. T. GOOSEY
9. The Role of Water Transport in Composite Materials. 341
GAD MAROM
Index 375
List of Contributors
R. J. ASHLEY
Research and Development Division, Metal Box Ltd, Denchworth
Road, Wantage, axon OX12 9BP, UK
J. COMYN
School of Chemistry, Leicester Polytechnic, PO Box 143, Leicester
LEI9BH, UK
M. T. GODSEY
Morton Thiokol Inc, Dynachem Corporation, 2631 Michelle Drive,
Tustin, California 92680, USA
GAD MAROM
Casali Institute of Applied Chemistry, School of Applied Science and
Technology, The Hebrew University of Jerusalem, 91904 Jerusalem,
Israel
J. Y. MOISAN
ROC-TAC, Centre National d'Etudes de Telecommunications, BP
40, 22301 Lannion, France
JOHN H. RICHARDS
School of Pharmacy, Leicester Polytechnic, po Box 143, Leicester
LEI 9BH, UK
C. E. ROGERS
Department of Macromolecular Science, Case Western Reserve Uni
versity, Cleveland, Ohio 44106, USA
A. H. WINDLE
Department of Metallurgy and Materials Science, University of
Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK
viii
Chapter 1
Introduction to Polymer Permeabllity and the
Mathematics of Diffusion
1. COMYN
School of Chemistry, Leicester Polytechnic, UK
1. Fick's Laws of Diffusion . . . . . . 1
2. Film Permeation. . . . . . . . . . 3
3. Dimensions of Transport Parameters. 6
4. Diffusion into a Film or Slab . . 7
S. Diffusion into a Fibre . . . . . 8
6. Diffusion at a Concentration Step 9
References . . . . . . . . . . 10
1. FICK'S LAWS OF DIFFUSION
Fick's first law is the fundamental law of diffusion. It states that (eqn
(1» the flux in the x-direction (FJ is proportional to the concentration
gradient (ac/ax).
Fx = -D(ac/ax) (1)
Flux is the amount of substance diffusing across unit area in unit time
and D is the diffusion coefficient. The first law can only be directly
applied to diffusion in the steady state, that is, where concentration is
not varying with time.
Fick's second law of diffusion describes the non-steady state and it
has several forms; first to be examined is diffusion into a box shaped
element in Cartesian coordinates. A point P is at the centre of a
volume element which has edges of length 2 dx, 2 dy and 2 dz (Fig. 1).
The fluxes which cross the six faces of the element control the build-up
or decay of diffusant. If there is a flux gradient aF/ax in the x-direction
and the x-direction flux at P is F, then the actual flux at the face
ABCD is (Fx -(aF)ax)) dx and at the face abcd it is (Fx + (aFx/ax» dx.
2 1. Comyn
B
,\-0 '\
A a
----+
p
2dz 0
d
2dx
dr
dz
rd8
Fig. 1. Volume elements for the derivation of Fick's second law of diffusion.
So the material entering face ABeD in unit time is 4 dy dz(Fx-·
(aF)ax» dx and that leaving face abcd is 4 dy dz(Fx + (aF)ax» dx.
Hence the material accumulating in the volume element due to diffu
sion in the x -direction is
Rx = -8 dx dy dz(aFxfax) (2)
Similarly, eqns (3) and (4) can be derived for the y- and z-directions.
R" = - 8 dx dy dz(aF)ay) (3)
R = -8 dx dy dz(aFz/az) (4)
z
So the rate of concentration increase in the element is given by
ac Rx + Rv + Rz
(5)
at 8 dx dy dz
So
ac _ aFx_ aFy _ aFz
(6)
at ax ay az
Introduction to polymer permeability and the mathematics of diffusion 3
The flux gradients are obtained by differentiating eqn (1), for example
aFxfax = - D a2e/ax2, so that
2 2 2
ae D(a e + ae + ae)
at = ax2 ay2 az2 (7)
Equation (7) is known as Fick's second law of diffusion. Under
circumstances where diffusion is limited to the x-direction it simplifies
to
(8)
However, if D depends upon the concentration of the diffusant and
hence on location, it may be written as
(9)
If the volume element is a segment cut from a cylinder with sides dr,
r de and dz (Fig. 1) then the appropriate form of the second equation
IS
1[ a ( (D a (
ae ae) a ae) ae)]
at = -; ar rD ar + ae --;. ae + az rD az (10)
but if diffusion is entirely radial this reduces to
ae _!~ (rD ae)
(11)
at r ar ar
In any situation, the problem is to find a solution to the appropriate
form of the second equation. Solutions can be found in Crank's book 1
on the mathematics of diffusion or in that by Carslaw and Jaeger2 on
the analogous situation of heat conduction in solids. Some of the more
frequently used solutions are examined below.
2. FILM PERMEATION
If a film of thickness I and area A separates two chambers containing a
permeable gas or vapour at different pressures, then the gas will
permeate from the high pressure chamber to the low pressure
chamber. This situation is of particular interest in that it illustrates the