Application of molecular rotors to the determination of the molecular weight dependence of viscosity in polymer melts

The molecular dynamics of polymers have been studied through measurements of such properties as (tracer) diffusivity (D) and (zero-shear) viscosity ( η) in relation to the numberaverage molecular weight ( M) of the polymer. These measurements can be compared with established theories, for example, the Rouse or reptation model for the cases involving polymer melts. Although numerous techniques are available for direct molecular-level measurements of the diffusivities in polymers, the viscosities of polymers have been measured exclusively using bulk measurements techniques with the most common method being the use of a conventional viscometer or rheometer. In this report, we demonstrate for the first time that fluorescent molecular rotors, farnesyl-(2-carboxy-2-cyanovinyl)-julolidine (FCVJ), can be used as an active probe for precise determination of the M dependence of η and the entanglement molecular weight of a polymer by using a molecular weight series of poly(propylene oxide) (PPOX) as model polymers. Our results are consistent with previous measurements and also with theories. There are a couple of key distinguishing features of using the fluorescent molecular rotor to probe the M-dependent η behavior for a polymer-based fluid. First, the quantum yield (i.e., the ratio of the number emitted photons to that of absorbed photons) of FCVJ is dependent strongly on the local free volume of the medium; therefore, this technique allows measurement of the microviscosity of the medium surrounding the rotor probe. Also, unlike the conventional method of measuring η using a viscometer or rheometer, the FCVJ-based η measurement does not require any external mechanical perturbation. The term “molecular rotor” has been frequently referred to a group of intramolecular charge-transfer complexes that undergo nonradiative relaxation from the fluorescent excited state through intramolecular rotation. 1 In the excited singlet state of the molecule, the energy can be released either by fluorescence emission or by intramolecular rotation around a specific unit, which relaxes the molecule back to its ground state. For example, in FCVJ, this rotation occurs around the bond between the carboxy and cyanovinyl groups (as shown with an arrow in Scheme 1). With the two feasible mechanisms for energy relaxation, the quantum yield ( Φ) can be given in terms of the intrinsic radiative rate ( kf) and the nonradiative (rotational) rate (knr) asΦ ) kf/(kf + knr); in general,knr is much greater than kf, and thereforeΦ ≈ kf/knr. For molecular rotors,knr is dominated by a torsional motion. Therefore, in a highly viscous medium, the relatively small free volume ( Vf) in the matrix will restrict the intramolecular rotation, and the rotor will have a small knr and a largeΦ. The relationship between knr and Vf can be typically expressed as knr ) knr 0 exp[-x(V0/Vf)], where knr 0 is the intrinsic rate in the zeroV0 limit,2 V0 denotes the van der Waals volume of the solvent molecule, and x is a parameter that depends on the rotor chemistry. 3 Substituting the this relationship into the above equation for Φ yields Φ ) (kf/knr 0 ) exp[-x(V0/Vf)]. Using the relationη ) η0 exp(V0/Vf), the equation forΦ can be further simplified into an expression known as the Fo ̈rster-Hoffmann expression 4