Direct Nonradiative Energy Transfer Research Articles

Direct Energy Transfer Studies of the Domain−Boundary Interface in Polyisoprene−Poly(methyl methacrylate) Block Copolymer Films

Direct nonradiative energy transfer (DET) experiments were carried out on five polyisoprene−poly(methyl methacrylate) diblock copolymers with polyisoprene volume fractions ranging from 0.07 to 0.5 (polyisoprene microdomains dispersed in a poly(methyl methacrylate) matrix). These experiments yield the ratio R/δ of the microdomain size R to the thickness of the domain−boundary interface δ as a function of the block copolymer overall chain length N. A plot of ln(R/δ) vs ln N indicates that the microdomain size varies as N0.65, close to the N2/3 predicted by theory, while the interfacial thickness δ (26 A) is independent of the degree of polymerization covered in this work. In addition, the Flory−Huggins interaction parameter χ for PI−PMMA was determined from the DET data (0.077). We conclude from these experiments that PI−PMMA belongs to the class of strongly segregated systems.

Energy Transfer in Restricted Geometry: Polyisoprene−Poly(methyl methacrylate) Block Copolymer Interfaces

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 (R0 = 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 [ID(t) = A1 exp{−(t/τD) − P(t/τD)β} + A2 exp(−t/τD)] containing the additional A2 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 β was independent of the global acceptor concentration CA for acceptor-to-donor ratios CA/CD > 1. One of the most unusual features of the data is a crossover in β observed as a function of a global acceptor concentration CA for a certain range of donor−acceptor composition, CA/CD < 1.

Direct Nonradiative Energy Transfer in Polymer Interphases: Fluorescence Decay Functions from Concentration Profiles Generated by Fickian Diffusion

A model is presented describing direct nonradiative energy transfer (DET) occurring between energy donors and acceptors attached to polymer chains diffusing across a planar interface. The model considers the fact that each donor is surrounded by a nonuniform concentration of acceptors. Previous models of energy transfer in slowly diffusing systems have considered that both the donors and acceptors are distributed according to concentration profiles generated through diffusion but have simplified the problem by assuming that, in any thin slice through the profile, the acceptor concentration can be taken to be uniform. We show that this mean local concentration model provides a good description of the system when the concentration gradients are broad, but it fails when the concentration gradients are steep or when R 0 , the critical Forster distance, is large. The proposed model is expected to be particularly important for the description of the early stages of the diffusion process where one may wish to distinguish reptation effects from Fickian diffusion.

Dipole-dipole electronic energy transfer. Fluorescence decay functions for arbitrary distributions of donors and acceptors: systems with planar geometry

We derive an expression for direct non-radiative electronic energy transfer which accommodates the possibility of a distribution of donor environments. At present we deal with situations in which the sample has a plane of symmetry for the concentration profiles. The relation enables one to evaluate donor fluorescence decay functions I D( t) from a knowledge of donor/acceptor concentration profiles, C D( z) and C A( z), along the sample axis z. It reduces to known expression in the case of DET in infinite media, and allows simplified asymptotic solutions or facile numerical analysis in systems with more complicated concentration profiles.

Study of polymer diffusion across the interface in latex films through direct energy transfer experiments

Efforts have been made to improve the method of using direct nonradiative energy transfer to follow the interdiffusion of polymer molecules across an interface. Two data analysis techniques are developed. The first one presents the extent of interdiffusion in terms of an acceptor concentration distribution; the second one recovers the diffusion coefficient and the concentration profile based on a Fickian diffusion model. The first method is model independent while the second method can be readily extended for other diffusion models. Polydisperse systems are characterized by a distribution of molecular mobilities. The energy transfer experiment provides a mean diffusion coefficient averaged over the sample history. For such systems, the concept of ‘‘instantaneous’’ effective diffusion coefficient and a method to derive it are discussed. These techniques are examined using computer simulations and tested in the study of molecular diffusion process of a poly(butyl methacrylate) latex system.

Interdiffusion of polymer chains during latex coating

AbstractThe fluorescence method was used to study the interdiffusion of polymer chains during annealing of latex above its glass transition temperature (Tg). The latex film was prepared from mixture of naphthalene (N) (donor) and pyrene (P) (acceptor)‐labeled poly(methyl methacrylate) (PMMA) latex particles. Heptane was used as the coalescent agent. A steady‐state fluorescence technique was employed to measure the amount of direct nonradiative energy transfer from N to P during the interdiffusion of polymer chains across the particle–particle junction. Various latex films with different latex contents were used to measure the percentage critical occupation for the reliable steady‐state fluorescence measurements. Diffusions activation energies in these latex films were measured and found to be around 30 kcal/mol, which was attributed to the backbone motion of PMMA chains.

Recovery of acceptor concentration distribution in a direct energy transfer experiment

The Klafter-Blumen equation, describing the kinetics of direct non-radiative energy transfer (DET) by the Förster mechanism, is extended to the case of guest molecules distributed non-uniformly in a space of known dimensionality. We describe a technique to recover the distribution of acceptor molecules in the medium, based upon the theory of the Fredholm integral equation of the first kind and its numerical solutions. The technique has been tested by computer simulations, and applied to several sets of experimental data. Examples are chosen from experiments involving energy transfer between dyes absorbed to the surface of polymeric microspheres, between dyes attached to polymer chains diffusing across an interface, and between dyes which undergo particle aggregation when dissolved at high concentrations in polymer matrices. Based on a comparison of these results with those obtained from directly fitting donor fluorescence decay profiles to the Klafter-Blumen equation, the merit of this new approach and its limitation are discussed.

Molecular diffusion and latex film formation: An analysis of direct nonradiative energy transfer experiments

The diffusion of polymer molecules across an interface is an important topic in polymer physics. Measuring this diffusion process requires a labeling experiment so that the mixing of otherwise identical molecules can be followed. Here we examine the use of nonradiative energy transfer to follow the interdiffusion of polymer molecules during the annealing of latex films. Those films are prepared from a mixture of phenanthrene (Phe, the donor)- and anthracene(An, the acceptor)-labeled poly(butyl methacrylate) (PBMA) latex particles. We examine in some detail the kinetics of direct energy transfer (DET) at an interface and the evolution of the DET kinetics as the components mix. Time resolved and steady state measurement approaches are compared, and the former is employed to examine molecular diffusion in a series PBMA latex films. Various diffusion models are considered. Diffusion coefficients are calculated by treating the data in terms of a Fickian spherical diffusion model. A film from one set of samples is similar in molecular weight to that studied by small angle neutron scattering (SANS) [K. Hahn, G. Ley, H. Schuller, and R. Oberthur, Colloid Polym. Sci. 264, 1029 (1986)]. Diffusion coefficients calculated from both sets of experiments using similar Fickian diffusion models are very similar in magnitude.