Molecular Weight and Compositional Dependence of Isotopic Blends

Abstract

The chain length and compositional dependence of the effective chi parameter, χs, in model isotopic polyethylene blends were determined at two different temperatures using our recently developed optimized cluster theory for polymer mixtures. χs was found to have a concave-up compositional dependence that decreased with increasing temperature and molecular weight, in agreement with neutron scattering measurements. A best fit to the chain length dependence of χs at constant temperature and composition had the form, χs = χs(∞) + D/N, where N is the number of segments comprising the polymers. In addition, the calculated compositional dependence of χs could be accurately described by a simple functional form that was previously proposed to fit experimental data on isotopic blends. However, the theory underestimates the breadth of the compositional dependence reported in the literature.

Thermodynamic interactions in blends of poly(4‐tert‐butyl styrene) and polyisoprene by small‐angle neutron scattering

“…Interestingly, the changes in χ PI/P(4tBS) with the dPBD composition are comparable to the changes in the PI [or P(4tBS)] composition in Figure 6(a,c). Such linear (or parabolic) compositional dependences for χ, with the values for compositions at the wings being considerably larger than those in the middle of the range, are similar to data for mixtures of isotopes,2, 39 mixtures of polybutadienes,10 mixtures of polybutadiene and polyisoprene,11, 22, 38 and many mixtures of polyolefins 40. For the cases in which linear compositional dependences have been observed (i.e., mixtures of polybutadienes and mixtures of polybutadiene and polyisoprene11, 22, 38, 41), the origins are thought to be equation‐of‐state effects (i.e., volume changes upon mixing).…”

A Theoretical Study of Isotope Blends: No Concentration Dependence of the SANS χ Parameter

“…Fourier transforms of the intramolecular correlations s i ( r ) are contained in the (block diagonal) elements of ŝ ( q ), and monomer number densities ρ i are the elements of ρ . Details are given in ref .…”

“…The result establishes the Fourier transforms of the three pair correlation functions ĥ ij ( q ) = ĥ o ij ( q ) + δ ĥ ij ( q ), which are used to write the partial structure factors of the blend: The reader is reminded that OCT is an approximate theory that is most accurate at high density and temperature, where the effects of short-range tail potentials are small. More complete descriptions of the theory and input parameters (pair potentials, intrachain correlation function matrix ŝ ( q ), reference system correlation function matrices ĥ o ( q ) and ĉ o ( q )) may be found in refs and .…”

“…Note furthermore that χ app is very close to χ bare = 2.086 × 10 -4 . Also included in Figure are results from a previous OCT study of precisely the same N = 8746 blend . In that work the monomer volumes v 1 and v 2 and reference volume v 0 were mistakenly set at π d 3 /6 = 0.03106 nm 3 (based on hard core diameter d ), which is larger than the monomer volume used here.…”

Thermodynamic Interactions in Isotope Blends: Experiment and Theory

“…More importantly, there is no indication that χ NS (φ) diverges at low φ, contrary to observed behavior. Quite interesting in this regard is the recent work of Melenkevitz 32,33 using off-lattice optimized cluster theory (OCT) to model isotope blends, specifically the PE/d-PE system of Londono et al 7 Here again fluctuations and constant compressibility are included. The model mimics experiment in many ways, with χ NS (φ,N) described by the empirical eq 5; both the divergence of χ NS (φ) and the 1/N dependence of χ NS (N) are captured.…”