Macromolecules 1986, 19, 2665-2666
Polymer Probe Dynamics Entanglements of polymer coils in solution make the macromolecule-containing fluid non-Newtonian at relatively low shear rates. Thus, rheological studies of semidilute polymer solutions and melts closely complement light scattering characterization of the structure and dynamics of polymer pseudonetworks. Diffusion of probe polymer coils or particles in highly congested solutions (or gels) has been investigated by a variety of techniques, including radioactive tracers,' infrared spectroscopy from deuterium-labeled chains? pulsed field gradient nuclear magnetic re~onance,~'~ luminescence q ~ e n c h i n gand , ~ "forced Rayleigh scatteringn6 (or holographic grating spectroscopy'). In addition, two relaxation modes have been observed by means of photon correlation spectroscopy in the spectrum of scattered light from semidilute polymer solution^.^^^ Although the fast relaxation is characteristic of the cooperative or mutual diffusion, the origin of the slow mode has been a subject of some controversy, even though we have established its translational nature.s In addition to the slow mode, a still slower mode has been reported? It is unlikely that this very slow mode, if it exists, is representative of the self-diffusive motions of a single polymer coil in the semidilute solution regime because results from forced Rayleigh scattering yield a value for the self-diffusion coefficient of labeled polymer chains 1or 2 orders of magnitude higher than that based on the very slow mode from light scattering data. The existence of the very slow mode (as distinguished from the slow mode that we report here) also appears to be sample dependent'OJ' and may be the result of transient cluster formation.12 Isorefractive scattering is the optical analogue of isotopic substitution in neutron scattering and of photochromic (or fluorescence) labeling in forced Rayleigh scattering (or fluorescence photobleaching recovery). Translational diffusion coefficients of macroparticle (or molecular) probe species of many systems have been reported.13-15 Most commonly, the isorefractive solvent consists of either poly(methy1 methacrylate) (PMMA) in toluene or poly(vinyl methyl ether) (PVME) in o-fluorotoluenels and the "labeled" polymer probe is polystyrene (PS). We have chosen a quaternary system consisting of PMMA, PS, toluene (TOL), and a-chloronaphthalene (CNA). The introduction of a fourth component, the cosolvent achloronaphthalene, permits us to study the pseudonetwork structure by varying either the solvent composition or the temperature and to match the refractive index of either PS or PMMA. The effects of preferential adsorption from the mixed solvents can be taken into account, since we know the true polymer molecular weight used in the experiments. As PMMA and PS are immiscible, the PMMA probe in the PS solvent matrix is essentially surrounded by cosolvents.17 The light scattering spectrometer, using an argon ion laser at Xo = 488.0 nm, photon counting for integrated scattered intensity, and full correlation (Brookhaven Instruments, BI-2030 4Xn 136-channeldigital correlator) for Rayleigh line width measurements, was calibrated for absolute scattered intensity and line width studies over the angular range of 15O I0 I150O. The solution was prepared by adding a dilute solution of PMMA (probe) + mixed solvent of TOL and CNA (isorefractive with PS) to PS and clarified by centrifugation. At a fixed cosolvent composition, plots of the square root of Rayleigh ratio/concentration, (Rw/C)'l2,vs. temperature could determine the temperature at which the polymer (PS) and the cosolvent (CNA/TOL) become isorefractive.
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Our pseudogel-solvent mixture has been characterized by means of a correlation length L defined by R,(C) = Ro,(C)/(l + P L 2 / 3 ) ,with K being the magnitude of the momentum transfer vector. We have separately characterized the fractionated PMMA probe in dioxane. From the PMMA behavior in the pure solvent (dioxane), the mixed solvent (MS CNA/TOL with #CNA = 0.72) and the pseudogel "solvent" (PS(C > C*)/MS with volume fraction #CNA = 0.72), we have been able to determine the static and dynamic properties of the probe PMMA in a PS pseudonetwork dissolved in an isorefractive solvent mixture (MS) of CNA and TOL at 38 OC. The dynamic behavior of the probe PMMA in the PS pseudonetwork can be quite different from that in a pure solvent, especially when the probe size is greater than the mesh size of the pseudonetwork. For probe PMMA (M, 5.69 X lo6,M,/M,, 1.2, and R, 144 nm) at 1.2 X lo4 g/mL in a ternary solution of isorefractive polystyrene (M, 2 x 107, M,/M, 1.8, cps= 3.76 x 10-3 g/ mL)/toluene and a-chloronaphthalene (with r$cNA = 0.72) at 38 OC, the characteristic decay rates exhibit a very strong deviation from a single-exponential behavior even for a polymer probe of fairly narrow molecular weight distribution, in agreement with recent experiments on PS in PVME/o-fluoroto1uene,l6poly(styrene-co-acrylonitrile)in PMMA/TOL,ls and PS in PMMA/benzene.lg For the overall line width distribution of the probe PMMA, p2/F2 0.5, using a third-order cumulant fit, where p2 = J G(I')(I' - F)2 d r and T = 1 G(I')I' d I', with G(r) being the normalized characteristic line width distribution. The physical meaning of this line width broadening at KR, < 1for the polymer probe (PMMA in our case) is the main subject of this Communication. While Lodge et al.l* proposed that probe polydispersity plays a dominating role, Numasawa et. al.lQinterpreted their results in terms of hydrodynamic screening. We realize the multiplicity of possible effects due to hydrodynamic screening, entanglements, pseudonetwork cooperative motions, etc. Further, we want to emphasize a neglected observation to the interpretation of polymer probe dynamics by means of photon correlation spectroscopy (PCS). From our data analysis, we conclude that the broadening is not only due to the probe polydispersity effect and the fact that for self-diffusion Ds M-2. More importantly, it suggests a possible coupling between dynamical motions of the PS polymer pseudonetwork and the PMMA polymer probe. By using the CONTIN method of data analysis20 we have resolved G(r) to a minimum of two peaks. With A, = 0.45 and Af = 0.55 denoting the intensity ratio of the slow peak and the fast peak and an average line width separation distance of rf/rS 8, the nonunimodal characteristic line width behavior is well established. The slow mode can be identified with the translational (self) diffusive motion of the polymer probe while the fast mode is coupled mainly to the cooperative pseudonetwork motions and the overall macroscopic viscosity. As PCS cannot resolve all the complex dynamical motions exhibited by the pseudonetwork and the probe polymer coil, interpretation of the intensity-intensity time correlation function requires us to reexamine polymer dynamics as observed by PCS. If we consider a single polymer probe dissolved in small solvent molecules, PCS probes essentially only the translational diffusive motions of the polymer at small scattering angles. At KR,
