Journal of Non-Crystalline Solids 131-133 (1991) 703-708 703
North-Holland
Interdiffusion at the interface of polymeric bilayers"
evidence for reptation?
G.P. Felcher and A. Karim
Materials Science Division, Argonne National Laboratory, Argonne, I L 60439, USA
T.P. Russell
IBM Research Division, Almaden Research Center, San Jose, CA 95120, USA
Neutron reflection is used to study the interdiffusion in equal molecular weight polystyrene bilayer melts with a spatial
resolution of 10 ,~. Interracial widths and concentration profiles at the bilayer interface are obtained for annealing times up to
and beyond the reptation time, T d. For t < T0, the reptation model predicts a mean square displacement of monomers whose
time dependence is a power law, the exponent of which changes with time. For the relatively lightweight polymers of
M - 233000, the mean square displacements of monomers is in general agreement with predictions; the permanence of a
discontinuity at the interface - which also follows from the reptation model - is observed only for molecular weights
M - 10000001
1. Introduction for the motion over distances shorter than the size
of the molecule, which might be identified with
There is considerable interest in the basic the radius of gyration, gR" The mean square dis-
mechanism of diffusion in polymer melts: by con- placement of monomers is predicted [3,7] to fol-
trast with atoms or simple molecules, the long low a time dependent power law: 02= t ~, where
chains of monomers forming the polymer mole- a < 1 for t < 'I'd, becoming 1 at t = ~'d, in the limit
cules become entangled along their length. Of the of conventional diffusion. To observe such dis-
various models proposed [1], the most successful is placement requires a technique with a spatial reso-
the reptation model, first proposed by de Gennes lution less than the size of the diffusing molecule,
[2] and later developed by Edwards [3]. In the and unfortunately the above-mentioned tech-
reptation model the polymer molecules diffuse by niques have a resolution of 100 ,~, to be compared
sliding along their contour within a hypothetical with a radius of gyration gR -- 150 ,~, for a mole-
tube, which is defined by the locus of intersections cule with a typical weight of M = 300 000. With
of the molecule with its neighboring molecules, the powerful technique of neutron spin-echo [8],
The time taken by the molecule to move out of its the time dependence of the correlation function
initial tube is the reptation time, T d. The main has been determined, but only up to times that
success of this theory consists in giving the correct were a fraction of ~'d"
scaling of the bulk self-diffusion coefficient, D*, The diffusion in polymer melts can also be
with molecular weight, M: D*-M -2. This de- studied by observing the time evolution of the
pendence has been confirmed by a variety of profile at the interface of two polymer (say, A and
different techniques: infrared spectroscopy [4], B) layers put in contact at time zero. This is
forward recoil spectrometry [5] and secondary ion exactly the kind of measurement done by neutron
mass spectrometry [6]. reflection, with a resolution that may approach 10
The reptation theory gives further predictions ,~. Actually, neutron reflection can give the de-
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)