The persistence length of isotactic poly(hydroxy butyrate) was measured using small-angle neutron scattering. The value obtained from these measurements reflects a high degree of local chain persistence. If this local persistence is accounted for, scattering from these chains can be globally fit with Gaussian scaling. A global scattering function, the unified equation, is used, which decomposes the chain structure into two levels, one corresponding to the Gaussian regime and one to the persistence regime. The persistence length obtained using this global scattering function is compared to that obtained using the graphical approach of Kratky and Porod with good agreement. Additionally, the global fitting approach of Sharp and Bloomfield is also considered. The Kratky and the Sharp and Bloomfield approaches appear to yield different values for the persistence length. Additionally, the Sharp and Bloomfield function does not allow inspection of the component parts of the fit. One advantage of both global functions is that the level of statistical confidence in the persistence length can be determined in a least-squares fit. Another advantage is the removal of ambiguity concerning an apparent regime of non-Gaussian scaling between the persistence scaling regime and the Gaussian regime.
Arylene-bridged polysilsesquioxanes are an interesting class of porous materials prepared
by sol−gel processing of ethoxysilane monomers in which there are two or more trialkoxysilyl
groups positioned about an arylene bridging group. The majority of these materials are highly
porous with surface areas as high as 1880 m2/g. In an effort to understand the nature of
porosity in these materials, small-angle X-ray and neutron scattering were employed to
characterize phenylene-, biphenylene-, and terphenylene-bridged polysilsesquioxanes. Phenylene-bridged polysilsesquioxane xerogels and aerogels were also compared to understand
the effect of drying protocol on pore structure. The effect of catalyst concentration is also
reported for the base-catalyzed system. In all cases studied here, we find evidence for domains
in the nanometer range with distinct fractal character. We associate these domains with
porosity rather than microphase separation of organic and inorganic moieties. The nature
of this porosity depends on the bridging group in a systematic way, but is only weakly
dependent on other synthetic parameters such as catalyst type, catalyst concentration, and
drying protocol.
Neutron scattering experiments were performed on three molecular
weight pairs of
symmetric, isotopic blends of poly(dimethylsiloxane) (PDMS) of
near-critical composition. Scattering data
covering close to 3 decades in size were globally fit using the random
phase approximation (RPA) and
the Debye function for Gaussian polymer coils using the interaction
parameter, χ, and statistical segment
length, b, as free parameters. These wide q
range fits differ from the standard, narrow q range RPA
fits
in that the power-law scaling regime and exponential decay regimes,
related to b, are accounted for.
Values for χ showed a well-behaved linear dependence on inverse
temperature. Critical temperatures
were estimated from these data. Direct observations of the
miscibility limit, through neutron cloud points,
were made in several cases which agree to some extent with the
extrapolated critical points. Monotonic
dependencies in temperature of the coil expansion factor, α, as
calculated from the statistical segment
length, were observed. Under the assumption that the thermal
dependence of α can be described in a
Flory−Krigbaum form, this offers a second measure of the critical
point in these blends. If coil expansion
is accounted for in this way, the noncombinatorial entropic component
of χ is observed to vanish in the
high-molecular-weight limit in keeping with a
Flory−Huggins/Hildebrand description of χ as
B/T. The
molecular weight dependence of χ supports the view that, after
accounting for coil expansion, end-group
effects are the sole source of noncombinatorial entropy in this model
system.
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