ABSTRACT:Small-angle X-ray scattering measurements have been made on seven polymacromonomer samples consisting of polystyrene with a fixed side chain length of 15 styrene residues in cyclohexane at 34.5C to obtain the z-average mean-square radius of gyration hS 2 i z and the particle scattering function PðÞ. The dependence of hS 2 i z on the weight-average molecular weight M w , which ranges from 5:1 Â 10 3 to 1:8 Â 10 5 , is described by the wormlike chain with the model parameters explaining previous light scattering hS 2 i z data for high molecular weights (6 Â 10 5 -7 Â 10 6 ), when the effect of the chain diameter d and that of side chains near the main-chain ends on the polymacromonomer contour length L are incorporated into analysis. Scattering profiles in the form of the Kratky plot are also explained by the recent theory for the wormlike chain with a circular cross section unless the axial ratio L=d is less than 2, i.e., unless M w is lower than 2:6 Â 10 4 . The conventional cross-section plot, i.e., the plot of ln½kPðÞ vs. k 2 with slope Àd 2 =16, is found to be applicable to samples with L=d > 2, where k denotes the magnitude of the scattering vector. It is concluded from further analysis of the hS 2 i z data combined with previous transport coefficient data that the wormlike cylinder model, a smeared model for regular comb polymers, consistently explains the molecular weight dependence of hS 2 i z , intrinsic viscosity, and translational diffusion coefficient for the polystyrene polymacromonomer in cyclohexane over a broad range of molecular weight. The applicability of a semiflexible comb model consisting of wormlike main and side chains to hS 2 i z and PðÞ is also examined.

Seven cyclic (1 --> 4)-alpha-D-glucan (cycloamylose) samples ranging in weight-average molecular weight from 5 x 10(3) to 1.8 x 10(4) and gamma-cyclodextrin have been studied by sedimentation equilibrium in dimethylsulfoxide (at 25 degrees C) and by dynamic light scattering in 0.5 N aqueous sodium hydroxide (at 25 degrees C), a good solvent for linear amylose. The measured translational diffusion coefficients D in the aqueous NaOH agree fairly closely with previous Monte Carlo results for cyclic (1 --> 4)-alpha-D-glucan chains with excluded volume, when correction is made for the effects of bead diameter and fluctuating hydrodynamic interaction (HI) on the Kirkwood theory on which the computation of D was based. These D data are also explained almost quantitatively by Yamakawa and Fujii's expression for the associated KP ring (based on the Kratky-Porod wormlike chain) with the molecular parameters for linear amylose if the fluctuating HI and excluded-volume effects are taken into account. It is concluded that the translational diffusion behavior of cycloamylose in the aqueous NaOH is consistent with the conformational characteristics derived from the conformational energy of maltose and dilute-solution data for linear amylose.

ABSTRACT:Synchrotron small-angle X-ray scattering (SAXS) measurements have been made on toluene solutions of six polystyrene polymacromonomer samples having a fixed side chain length of 15 styrene residues and ranging in the polymerization degree of the main chain N w from 6.5 to 106 (in weight average) at 25 C. The z-average meansquare radii of gyration hS 2 i z from the present SAXS and previous light scattering as a function of N w and the particle scattering functions PðÞ in the form of k 2 PðÞ against k (the magnitude of the scattering vector) are compared with theoretical values for three models: (a) the wormlike cylinder with a uniform cross section, (b) the wormlike chain with Gaussian density distribution within the cross-sectional plain, and (c) the touched-bead comb with wormlike main and side chains. Theoretical curves for the models (a) and (b) equally fit the data points for hS 2 i z and k 2 PðÞ (for k < 1 nm À1 ) with a set of model parameters consistent with that describing the previously determined N w -dependence of intrinsic viscosity in toluene, but the latter model explains the PðÞ behavior up to a slightly larger k. The model (c) allows similarly good fits to hS 2 i z and better fits to k 2 PðÞ over a wider k range if the Kuhn segment length of each side chain and the bead diameter are adjusted to values much larger than those expected for an isolated polystyrene molecule. The decoupling approximation to PðÞ invoked in the literature is also examined for the models (a) and (b).[doi:10.1295/polymj.PJ2007058] KEY WORDS Small-angle X-ray Scattering / Polymacromonomer / Comb Polymer / Radius of Gyration / Particle Scattering Function / Wormlike Chain / Dilute-solution studies 1-9 revealed that polymacromonomer molecules have considerably high stiffness in solution and can be modeled by the Kratky-Porod (KP) wormlike chain.10 Analyses of hydrodynamic properties such as the intrinsic viscosity [] and the translational diffusion coefficient D generally give information on the chain diameter d, but as was pointed out previously in relation to the estimation of d, available hydrodynamic theories involve a few problems in their accuracy (see ref 11). Thus, for the purpose of deducing geometrical features of polymacromonomer side chains, we commenced small-angle X-ray scattering (SAXS) experiments 11,12 on cyclohexane solutions of low molar mass polystyrene polymacromonomer F15 (with 15 styrene residues in each side chain) at the theta point 34.5 C using a laboratory scale apparatus. 12 The result showed that the measured z-average mean-square radii of gyration hS 2 i z and particle scattering functions PðÞ for k (the magnitude of the scattering vector) smaller than 1 nm À1 are essentially consistent with the structural information derived from [] and D on the wormlike cylinder model. With regard to the structural feature of the side chains, however, this uniform cylinder can be a coarse-grained model, at least, for low molecular weight samples.In the present study, we made synchrotron SAXS measuremen...