Abstract:Small-angle neutron scattering (SANS) studies of binary mixtures provide χNS, a measure
of thermodynamic interactions between dissimilar polymer chains, one of which is usually labeled with
deuterium. For polymers differing only in isotopic substitution (isotope blends), χNS is seen to diverge
strongly upward (or sometimes downward) at low concentrations of either blend component. This
concentration dependence seems to vanish in the limit of large degree of polymerization N. Experimental
results can be describ… Show more
“…Additional complications in computing the binodal arise due to the composition dependence of χ that is found in many systems. − This is also not relevant for our system. The composition independence of χ (within experimental error) in PMB/PEB blends has been clearly established in several studies. − ,,, The effects of a subtle composition dependence of χ that might exist in our system is mitigated by our use of the same blend for determining the binodal and χ. 9 Comparison of the experimentally determined binodal temperature (solid circles) to the binodal temperature calculated from Flory−Huggins theory (curve) as a function of pressure for the B3 blend with no adjustable parameters.…”
The Flory−Huggins interaction parameter, χ, of an off-critical poly(methylbutylene)/poly(ethylbutylene) blend was measured over a wide temperature (T) and pressure (P) range by comparing
small-angle neutron scattering (SANS) profiles from single-phase systems with predictions based on the
random phase approximation (RPA). We show that χ, which is a nonlinear function of 1/T at low pressures,
becomes a linear function of 1/T at elevated pressures (above 2.5 kbar). The pressure dependence of the
phase boundary (i.e., binodal temperature) of our blend was determined from a series of dissolution
experiments wherein a phase-separated sample was heated under isobaric conditions until the SANS
profiles were identical to calculations based on the RPA. The binodal, thus obtained, was in quantitative
agreement with that computed using the Flory−Huggins theory. The agreement was obtained without
any adjustable parameters. Binodals determined by the more traditional cloud point measurements are
erroneous due to the presence of large nucleation barriers.
“…Additional complications in computing the binodal arise due to the composition dependence of χ that is found in many systems. − This is also not relevant for our system. The composition independence of χ (within experimental error) in PMB/PEB blends has been clearly established in several studies. − ,,, The effects of a subtle composition dependence of χ that might exist in our system is mitigated by our use of the same blend for determining the binodal and χ. 9 Comparison of the experimentally determined binodal temperature (solid circles) to the binodal temperature calculated from Flory−Huggins theory (curve) as a function of pressure for the B3 blend with no adjustable parameters.…”
The Flory−Huggins interaction parameter, χ, of an off-critical poly(methylbutylene)/poly(ethylbutylene) blend was measured over a wide temperature (T) and pressure (P) range by comparing
small-angle neutron scattering (SANS) profiles from single-phase systems with predictions based on the
random phase approximation (RPA). We show that χ, which is a nonlinear function of 1/T at low pressures,
becomes a linear function of 1/T at elevated pressures (above 2.5 kbar). The pressure dependence of the
phase boundary (i.e., binodal temperature) of our blend was determined from a series of dissolution
experiments wherein a phase-separated sample was heated under isobaric conditions until the SANS
profiles were identical to calculations based on the RPA. The binodal, thus obtained, was in quantitative
agreement with that computed using the Flory−Huggins theory. The agreement was obtained without
any adjustable parameters. Binodals determined by the more traditional cloud point measurements are
erroneous due to the presence of large nucleation barriers.
“…However, the question is then raised, "is the variation in χ eff with star concentration itself an artifact of imperfect experimental procedure?" Experimental reports of concentration dependences [44][45][46][47] for χ isotopic have reported values for χ eff which are either larger on both sides of φ h ) 0.5 than at φ h ) 0.5 or smaller on both sides, except for a study of high 1,2-addition PB blends by Sakurai et al 2 which showed neither an upturn nor a downturn with concentration. In the present study χ isotopic is found to be smaller away from the symmetric composition.…”
Section: Resultsmentioning
confidence: 98%
“…If this is true and values of χ ε are estimated at all concentrations using a single value for χ isotopic , then the monotonic decrease in χ ε with star concentration is recovered, as shown in the last column of Table . However, the question is then raised, “is the variation in χ eff with star concentration itself an artifact of imperfect experimental procedure?” Experimental reports of concentration dependences − for χ isotopic have reported values for χ eff which are either larger on both sides of φ h = 0.5 than at φ h = 0.5 or smaller on both sides, except for a study of high 1,2-addition PB blends by Sakurai et al . which showed neither an upturn nor a downturn with concentration.…”
Values of the bulk thermodynamic interaction parameter, χeff, for blends of anionically polymerized star (number of arms ) 4, 6, 8, 12) and linear polybutadienes (PB) of well-defined architecture and molecular weight were measured as a function of temperature using small-angle neutron scattering. Comparison of these measured values of χeff with results from comparable polystyrene (PS) blends suggests the existence of nonuniversal aspects in the thermodynamic interaction due to entropic contributions, χ , arising from architectural differences in chains. While the value of χ for PS star/linear blends increases monotonically with number of arms in the star, the value of χ in the PB star/linear blends does not, a result which cannot be anticipated by the Gaussian field theory (GFT) of Fredrickson et al. 1 An important discrepancy between theory and experiment is also found for the variation of χ with linear chain length. Theory anticipates the value of χ should decrease with increasing linear chain size, but in fact it increases. Qualitative agreement with the GFT is found on two counts: χ decreases with increasing concentration of star (when assuming χisotopic for linear/linear blends is constant with concentration), and χ decreases with increasing length of the star arm. In general, the value of χ for a PB blend of star and linear components is larger than the value of χ for a comparable PS blend. Indeed, phase separation is observed in one particular PB blend of a six-arm star with a sufficiently large linear chain.
“…Here, b D and b H are the scattering lengths of deuterium and hydrogen, respectively, and v 0 is a reference volume of approximately four (CH 2 ) units, equal to 123 Å 3 at 200 °C. , The scattering length density of a slice, ρ i , is calculated based on the number of protons and deuterons in this reference volume. N i and φ i are the volumetric degree of polymerization and volume fraction of component i , and a is the statistical segment length of linear polyethylene, adjusted to the 200 °C experiment temperature. , The Flory–Huggins interaction parameter, χ ij , was estimated using the measurement of Londono et al (for fully labeled and unlabeled chains) combined with the random mixing hypothesis to adjust for partial labeling. ,− Component n is arbitrarily used as a reference component. In our implementation, component n is the unlabeled polymer, which is described as a single component using the weight-averaged product ⟨ NP ( q , R g )⟩ w ; to model the scattering from dHDPE, this component is set to a minute volume fraction. , The off-diagonal elements of the matrix 0 are zero since no block architectures are present in the system.…”
Following a hydrogen−deuterium exchange reaction, size-exclusion chromatography with infrared detection (SEC-IR) was used to measure the distribution of deuterium with respect to molecular weight on a polyethylene resin. The SEC-IR method reveals significant heterogeneity in the distribution of deuterium across molecular weight, including a fraction of high molecular weight chains that are nearly or completely unlabeled. Small-angle neutron scattering (SANS) was performed on the labeled polymer and an isotopic blend; the random phase approximation model prediction for the scattering from an ncomponent blend was successfully used to model the measured SANS data. Additionally, a Monte Carlo algorithm was used to fit the measured SANS data to a deuterium distribution, yielding a measurement consistent with that obtained from SEC-IR. The methods are compared to literature approaches for describing nonideal deuterium labeling. These results demonstrate the value of including detailed information about the distribution of deuterium in a scattering model and provide methods for probing the structure and interactions of complex polyolefin resins that have been labeled via heterogeneous catalysis.
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