Reptation Analysis of Interdiffusing Chromophore-Labeled Polymers
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REPTATION ANALYSIS OF INTERDIFFUSING CHROMOPHORE-LABELED POLYMERS
W.W. MERRILL*, M. TIRRELL* AND S. PRAGER** * Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455 ** Department of Chemistry, University of Minnesota, Minneapolis, MN 55455
1. INTRODUCTION Understanding the dynamics of the microscopic mixing of polymer across an interface is crucial in determining the dependence of the fracture yield stress on healing time, and on the dynamics of polymer blending. Previous theoretical analyses of healing by Prager, Tirrell and Adolf [1,2,3] and Kim and Wool [4] have been helpful in interpreting the results of crack healing experiments. These models have asserted strict reptation dynamics and then postulated simple relationships between microstructure and fracture stress. The underlying microstructure can be probed directly by fluorescence measurements on interdiffusing chromophore-labeled polymers. 2.
DONOR-ACCEPTOR ELECTRONIC EXCITATION TRANSFER
The excitation of donor chromophores in solution can be transferred non-radiatively, through dipole-dipole interaction, to acceptor chromophores which do not directly absorb the incident radiation. If donor-donor excitation exchange is negligible and donor-acceptor exchange is essentially irreversible then the ratio of the intensities of the emitted acceptor to donor fluorescence is: IA
ID
_
A -
qD
-
1
(2.1)
where qA and qD are the respective quantum efficiencies of fluorescence in the absence of the other species. The probability that a given donor excitation does not eventually transfer to any acceptor before deactivation or donor fluorescence, , has been derived by F6rster [5] for the case of a homogeneous mixture of chromophore labels: = 1
-
2 (7E/2) Xo exp(ICX 0 /4)
erfc( 4
Xo/2)
(2.2)
where Xo is the average number of acceptor chromophores in a sphere of Fdrster radius, Ro, and is therefore proportional to acceptor chromophore concentration. The rate of excitation transfer between any given donor and acceptor pair decreases according to an inverse sixth law in separation distance. Were only a single pair in solution, the probability would be one-half at a separation distance of Ro.
Mat. Res. Soc. Symp. Proc. Vol. 79. 1987 Materials Research Society
422
Thus the probability is sensitive to microscopic concentration inhomogeneities. 3.
THE EXPERIMENT
The intensity signal ratio is reduced below the expected homogeneous value if the donor chromophores are microscopically Probing the segregated from the acceptor chromophores. interdiffusion of polymer chains using freeze-drying as a method to microscopically segregate the individual chains (and hence the tagged chromophores on them) was first suggested by Morawetz [6]. A dilute solution of polystyrene, some labeled with the donor phenanthrene and others labeled with the acceptor anthracene, is freeze-dried, causing collapse of the chains into individual globules. Since only donor or acceptor labels are tagged to any individual chain, these are ini
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