Isaac C. Sanchez

Temperature, composition and molecular-weight dependence of the binary interaction parameter of polystyrene/poly(vinyl methyl ether) blends

Abstract The binary interaction parameter χ eff has been obtained for deuterated polystyrene/poly(vinyl methyl ether) blends as a function of temperature, composition and molecular weight from small-angle neutron scattering experiments. The consistency of the correlation length ξ, the zero-wavenumber scattering intensity S (0) and the χ eff parameter with the mean-field prediction has been demonstrated by the q dependence of the static structure factor S ( q ) and the 1/T dependence of ξ −2 , S (0) −1 and χ eff . The effective interaction parameter χ eff can be related to the Flory-Huggins interaction parameter χ eff can be related to the Flory-Huggins interaction parameter χ F . The free-energy function as well as the spinodal curve and cloud-point curve have been constructed.

Order—disorder transitions in polytetrafluoroethylene

Abstract The phase diagram of polytetrafluoroethylene is enlarged by differential scanning calorimetry to include the concentration of hexafluoropropylene comonomer units. The two transitions near 292 and 303 K in the homopolymer move to lower temperatures and apparently become one at small concentrations. Analysis of the data yields 295 K for the temperature and 13.2 J/g for the heat of transition of an infinitely large homopolymer crystal. The heat of transition associated with the formation of a crystal defect is 0.021 eV. The qualitative features of the transition can be accounted for by a mean-field model which involves two order parameters corresponding to planar units and helix reversals. This model yields two transitions which move closer together and to lower temperatures with increasing comonomer concentration. Decreasing lamella thickness will have a qualitatively similar effect.

Relationships between polymer interaction parameters

Abstract Experimental methods that determine binary polymer-polymer χ interaction parameters may probe the mixtures free energy, its first derivative, or its second derivative. In general, there are four different χ parameters that are required to describe a binary polymer mixture, but if one is determined experimentally, the other three can be calculated. This allows for the determination of both the spinodal and two-phase coexistence curves. Theoretical Henrys law constants that govern gas sorption in polymers are derived which can be used to facilitate the determination of polymer-polymer interaction parameters by inverse gas chromatography.

A universal coexistence curve for polymer solutions

Coexistence curves for binary polymer/solvent solutions are asymmetric when volume fraction is used as the concentration variable. Coexistence curves for polystyrene/methylcyclohexane solutions can be symmetrized by a simple transformation of variables; in the new dimensionless variable ψ, all of the data satisfy a universal scaling law: ‖ψ−ψc‖=ψ0(eN0.313)β; e≡(Tc−T)/Tc, where N is the degree of polymerization and ψc and ψ0 are constants independent of N. The experimental value of the critical exponent β (0.327±0.002) agrees well with recent renormalization group calculations for the Ising model. The exponent on N(0.102±0.002) may be universal and should be compared with its mean‐field value of 1/4; a calculation of its nonclassical value remains a challenging theoretical problem.

Liquids: Surface tension, compressibility, and invariants

A new equation has been dervied which relates the surface tension (σ) to a liquid’s isothermal compressibility (κ) and mass density (ρ). The derivation is based on a generalized square‐gradient approximation for the free energy density of a nonuniform fluid. The equation is σ(κ/ρ)1/2=A1/20=constant in the normal liquid range. Except for water, A0 is temperature independent for a variety of inorganic, organic, and polymer liquids. Among 50 nonpolar and polar organic liquids, including hydrogen bonding liquids, A1/20 appears to be an invariant with a value of 2.78±0.13×10−4 (erg cm2/g)1/2. Among the diatomic elements (except hydrogen), A1/20 is an invariant with a value of 1.8×10−4. Among the heavy noble elements, A1/20 is an invariant with a value of 1.36×10−4. For the quantum noble elements helium and neon, A1/20=1.0×10−4. The constant A0 is shown to be proportional to a second moment of a direct correlation function. A semiempirical formula has been derived for A0 relating it to the parameters e0 and...

Concentration fluctuations in polymer blend thermodynamics

Monomer concentration fluctuations in high molecular weight polymer blends are investigated. The fluctuations reduce the value of the χ interaction term in the Flory–Huggins free energy by a factor of (1‐6/π2) and add a concentration and molecular weight contribution which decreases phase stability for off‐critical compositions. Except at the critical point, the spinodal values are smaller than those predicted from a Flory–Huggins‐type free energy. For an incompressible blend with components of equal size N, the corrections to the spinodal were found to vary as ‖1−2φ0‖4/3N−1/3, where φ0 is the mean concentration.

A closed‐form, free‐energy functional for a binary polymer mixture

A new, closed‐form, free‐energy functional is derived for a binary polymer mixture. When the free‐energy functional is expanded in series form around the mean concentration, the leading term in the expansion is the usual Flory–Huggins free energy. The Fourier transform of the coefficients of this expansion are approximate vertex functions Γ(n). A useful and tractable form for Γ(n) is obtained for all n which only depends on the magnitudes of the n wave vectors. It is shown that Γ(2) is exact and Γ(3) and Γ(4) reduce to the correct limiting values in the small and large wave vector limits.

Statistical thermodynamics of bulk and surface properties of polymer mixtures

Abstract A generalized version of the lattice fluid theory of solutions is considered. Necessary and sufficient conditions for phase stability in a binary mixture are defined by a spinodal inequality. From the general properties of the spinodal, the necessary conditions for polymer/polymer miscibility and bimodal behavior of the spinodal are defined. A general theory of interfacial tension in phase separated multi-component mixtures is formulated. The interfacial tension theory can be combined with lattice fluid theory to obtain a unified theory of bulk and interfacial properties.

Self-consistent Fields and Critical Exponents for Polymers

A self-consistent field (SCF) is constructed for a polymer chain with excluded volume modeled as a self-avoiding random walk (SAW) of N steps (N →∞). The SCF requires the introduction of a second exponent \(\bar \theta \) in addition to the usual ν exponent that characterizes the size of a SAW. The SCF equals N times the probability \({\bar P_N}\) of an interaction of the chain end with a distant part of the chain. In d-dimensional space \({\bar P_N}\) scales as \({N^{ - \gamma \left( {d + \bar \theta } \right)}} \left( {d \leqslant 4} \right);\); self-consistency of the field yields the relations θ = (4 - d)/3 and \(\upsilon \left( {d + \bar \theta } \right) = 2.\). It is shown that \({\theta _0} 1 is the exponent associated with the probability of a SAW forming a large loop with a long tail. A SCF ( Φ ) is also determined for a semidilute solution of polymer volume fraction φ. The number of binary interactions scales as Φ φ ∼ φ9/4