The kinetics of direct nonradiative energy transfer between dyes confined to the 2.6 nm wide interface region of polyisoprene-poly(methyl methacrylate) block copolymer films are reported. This system differs from restricted geometry systems examined previously because of the diffuse nature of the edges of the confining space. The interface thickness is similar in magnitude to the characteristic distance for energy transfer (R 0 ) 2.3 nm) for the donor-acceptor dye pair (phenanthrene-anthracene) employed here. Samples were prepared from matched pairs of block copolymers, one containing a donor dye and the other an acceptor dye, at the PI-PMMA junction. Donor fluorescence decay profiles were fitted to the Klafter-Blumen expression [I D (t) ) A 1 exp{-(t/τ D ) -P(t/τ D ) } + A 2 exp(-t/τ D )] containing the additional A 2 term to account for donors (ca. 3%) outside the interface. The parameters obtained followed the predicted behavior, namely, that the preexponential term P was proportional to the acceptor concentration, whereas the stretched-exponential parameter was independent of the global acceptor concentration C A for acceptor-to-donor ratios C A /C D > 1. One of the most unusual features of the data is a crossover in observed as a function of a global acceptor concentration C A for a certain range of donor-acceptor composition, C A /C D < 1.

The fluorescence and fluorescence decay profiles of pyrene and 1-ethylpyrene in solutions of a hydrophobic alkali-swellable emulsion (HASE) polymer were examined to characterize the association structure formed from the hydrophobic substituents. The HASE polymer was obtained by the copolymerization of ethyl acrylate (EA), methacrylic acid, and a macromonomer containing a C20H41 group separated from the backbone by 32 ethylene oxide units. We examine solutions neutralized with 1 equiv of NaOH, at polymer concentrations where virtually all of the added probe is partitioned into hydrophobic domains of the polymer. Both monomer and excimer emission are observed, and I E/I M increases in proportion to the amount of probe added to the system. Individual monomer fluorescence decay profiles fit well to the traditional micelle Poisson quenching model, but attempts to calculate the hydrophobe aggregation number N R led to values that changed markedly with the ratio of probe to polymer. These results were rationalized in terms of a polymer structure in water containing various hydrophobic domains of different composition. These domains vary from nonionic micelle like structures containing upward of 60−80 C20H41 groups, where the first probes added to the system are located, to mixed structures containing both C20H41 and EA groups from the polymer backbone.

Simulations of energy-transfer kinetics were carried out for a lamellar block copolymer system in which donor and acceptor dyes were attached to the block junction. In such a system, the distribution of donors and acceptors follows P J (z), which describes the distribution of the junctions across the interface. We use these simulations to examine the type of information about the block copolymer morphology available from analysis of fluorescence decay profiles generated by these systems. Within the context of a Helfand-Tagami distribution for P J (z), one can obtain reliable estimates of the ratio of the period spacing to interface thickness (H/δ) but not the individual parameters H and δ. Since H can be determined independently in a scattering experiment, this approach is useful for obtaining values of δ with better than 5% accuracy. Attempts to distinguish a Helfand-Tagami profile from a Gaussian profile were not successful. The energy-transfer experiment may be employed to reject the wrong morphology only if prior values of H and δ are determined by other methods.

We carried out simulations of energy transfer kinetics for lamellar block copolymer systems in which donor and acceptor dyes were attached to the block junctions. We considered blocks of homopolymers that were sufficiently immiscible and of sufficiently high molecular weight to employ the Helfand−Tagami distribution of block junctions. The morphology of such block copolymers has been frequently discussed in terms of an apparent dimension parameter, which is recovered from the analysis of fluorescence decay curves, using the Klafter−Blumen (KB) formalism. Here, we investigate how such apparent dimensions are influenced by the interface thickness between the two blocks (which is dependent on the Flory−Huggins χ parameter of the system). We also probe the dependence of this apparent dimension on the concentration of the dyes in labeled samples. This kind of dependence has been experimentally observed but never explained, perhaps because of the approximations inherent in using the KB model to analyze fluorescent decay curves for block copolymer systems. We have found that apparent dimensions approach three for reasonably broad interfaces, but decrease to near two for very narrow interfaces, in accordance with asymptotic formulas that we propose for strongly segregated, lamellar block copolymer melts. Global analysis of the decay curves, as well as weighted linear regression of the parameters obtained from individual analyses of the decays, suggest linear relationships between the apparent dimensions from KB analyses and acceptor concentrations. We discuss the dependence on interface thickness in terms of the basic (Förster) theory of direct energy transfer, and indicate why the KB model is a reasonable representation of lamellar block copolymers.