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Molecular Weight Scaling of the Transport Properties of Polyacrylamide in Water Patricia M. Patterson and Alex M. Jamieson* Department of Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106. Received November 14, 1983 ABSTRACT: Measurements of single-chain z-average translational diffusion coefficients, Dt,2, and radii of gyration, R, by photon correlation spectracopy and intrinsic viscosities, [TI, of several polyacrylamide (PAAm) fractions in 0.1 M NaCl with 0.02 w t % NaN3 are reported. Intrinsic viscosity data are insensitive to NaCl concentration up to 0.5 M, suggesting that the chain expansion of PAAm is independent of ionic strength. Our results are compared with recent literature data in which a variety of anomalous excluded-volume exponents for these quantities have been reported. We find good agreement between our data for [7] and R,,* with the earlier results but significant discrepancies when comparing our Dt/ results with the weight-average values, Dt$, in the literature. The effect of polydispersity on the experimental data is discussed in terms of the Schulz-Zimm distribution. In agreement with our observations, z-average diffusion coefficients are expected to be numerically consistent with the intrinsic viscosity data and, to a lesser extent, with experimental measurements of R,,, provided the weight-average molecular weight M , is used as a scaling paramete_r. Substantial discrepancies in scaling exponents are liable to occur from the comparison of Dt,,O against M , for polydisperse systems. Within experimental uncertainties our data Dt,z and [a] data for the PAAm-O.l M NaCl system are consistent with typical literature data for flexible-chain molecules in good solvents.
Introduction Modern theories of chain statistics' lead to a variety of simple scaling laws for the molecular weight, temperature, and concentration dependence of the structural and dynamic properties of chain molecules i n dilute2p3and semidilute solutions.M In the present paper, we are interested in the prediction of statistical theories for single-chain properties. The relevant experimental quantities are the radius of gyration, RG, and the Stokes hydrodynamic radius, RH, the latter being derived from the limiting translational diffusion coefficient, 02, the limiting sedimentation coefficient, So, or the intrinsic viscosity, [ a ] . Scaling laws for these properties are expressed i n terms of characteristic excluded-volume exponents:
RH [a1 - Na RG
and
N"G
(1)
N"H
(2)
sponding to crossover from ideal statistics at short distances to excluded-volume contribution at large distances (higher molecular weight). Experimentally, for polymers in the asymptotic regimes of good and 8 conditions, the predicted behavior of VG has been confirmed' i n the molecular weight range 250 OOO
