Roland Horst

Complex miscibility behaviour for polymer blends in flow

Abstract Experimental observations of the effect of shear flow on the miscibility of binary polymer blends are compared to calculations based on a generalized Gibbs energy of mixing Gγ˙. This mixing free energy characterizes the steady state established at shear rateγ˙, as the sum of G z , the equilibrium Gibbs energy and E s , the energy the system stores while flowing.

Calculation of the phase separation behavior of sheared polymer blends

The influence of shear on the phase diagrams of model blends of polymer A end polymer B, exhibiting phase separation upon heating, was calculated on the basis of the generelized Gibbs energy of mixing G γ . , characterizing the study state established at shear rate γ . , as the sum of G z , the equilibrium Gibbs energy, end E a , the energy the system can store while flowing. The results obtained for the two model systems A150/B200 and A75/B200) the figures denote the molar masses in kg/mol) are qualitatively identical. With increasing shear drate the homogeneous region expands first, then shrinks below its equilibrium value within a certain γ . range

Pressure dependence of the miscibility of poly(vinyl methyl ether) and polystyrene: Theoretical representation

The present calculations were performed on the basis of the Sanchez-Lacombe-Balasz lattice fluid theory. The two system specific parameters e12* and δe* required for that purpose have been obtained from the spinodal temperatures measured (SANS) for mixtures of poly(vinyl methyl ether) (PVME) and deuterated polystyrenes (d-PS) by Schwahn and coworkers. The experimental data reported for atmospheric pressure and six representatives of the present system are well described theoretically, where e12* does not depend on molar mass and δe* decreases only slightly as the chain length of d-PS is raised. The measured pressure influences on the spinodal conditions correspond to an approximately linear reduction of δe* with increasing P; this observation should reflect the volume changes associated with the formation of specific interactions. According to the present calculations the critical composition shifts markedly towards pure PVME as P is raised. Since experimental data are commonly expressed in terms of the F...

Calculation of shear influences on the phase separation of polymer blends exhibiting upper critical solution temperatures

Calculations were performed on the basis of a generalized Gibbs energy of mixing Gγ, which is the sum of the Gibbs energy of mixing of the stagnant system and Es, the energy stored in the system during stationary flow. With increasing shear rate γ, the demixing temperatures shift to lower values (shear-induced mixing; diminution of the heterogeneous area), then to higher values (shear-induced demixing), and finally to lower values again before the effects fade out. The details of the rather complex phase diagrams resulting for a given shear rate are primarily determined by a band in the T/χ plane (χ = mole fraction) within which (∂2Es/∂χ2)T<0 (i.e., ES acts towards phase separation). There are two ranges of γ within which closed miscibility gaps can exist: The more common outer islands are partly or totally situated outside the equilibrium gap (and within the above mentioned band). As γ is raised they break away from the “mainland” at the upper end of the first region of shear-induced mixing and shift to T>UCST where they submerge. Bound to a suitable choice of parameters, a second kind of closed miscibility gaps, the inner islands, which always remain within the equilibrium solubility gap (and outside the band of negative curvature of ES) is additionally observed. This time the islands break away from the “mainland” at the lower end of the first region of shear-induced mixing where they also submerge. The present findings are compared with the results of previous calculations for LCSTs.

Phase diagrams calculated for quaternary polymer blends

A method is presented that allows the calculation of phase diagrams (spinodal, binodal, and tie lines) of quaternary mixtures on the basis of the Gibbs energy of mixing ΔG. No derivatives of ΔG with respect to the composition variables are required. This method is particularly useful in cases where the composition dependence of ΔG is very complex, and no analytical representation of ΔG can be found. Phase diagrams have been calculated on the basis of the Flory–Huggins theory for mixtures of four polymers. Blends that phase separate because of very favorable interactions (negative interaction parameters) were of particular interest. In this case miscibility gaps can be located inside the tetrahedron composed of the Gibbs phase triangles of the four completely miscible ternary subsystems. For symmetrical mixtures of K components (identical chain lengths and interaction parameters) equations are presented that allow the calculation of K‐phase and (K−1)‐phase regions for any value of K.

Phase diagrams calculated for sheared ternary polymer blends

Abstract On the basis of the generalized Gibbs energy of mixing G γ (which is the sum of the Gibbs energy for zero shear and the energy the system stores in steady flow) phase diagrams were calculated as a function of shear rate γ for ternary model blends. This modelling uses simple equations for the description of the stagnant systems (Flory-Huggins) and for the contributions resulting from flow. Surface and alignment effects are neglected. A new procedure, which does not require the derivatives of G γ with respect to composition, was used to that end. Choosing typical values for the binary interaction parameters and molar masses, four classes of ternary systems were studied in greater detail. Under equilibrium conditions, with two of them there only exist one-phase and two-phase regions in the temperature range of interest. At least one three-phase domain occurs with the other two types of ternary mixtures. In addition to all effects observed for binary systems, the following new phenomena were calculated: (i) twofold disappearance of closed loops of immiscibility and twofold reappearance; (ii) creation and annihilation of three phase areas; and (iii) creation and annihilation of islands of homogeneity in the centre of the ternary phase diagram.

Determination of interaction parameters for highly incompatible polymers

Abstract Experiments and calculations were performed for the ternary system cyclohexane/polystyrene/polyisobutylene (CH/PS/PIB) to study the possibilities of determining the Flory-Huggins interaction parameters χ PS/PIB between these highly incompatible polymers. To that end χ CH/PIB was determined (vapour pressure measurements and additional thermodynamic information) as a function of composition; χ CH/PS and its concentration dependence could be taken from earlier experiments. Furthermore, the cloud point curve and some tie lines of the ternary system were measured. In the subsequent evaluation of these data, the phase diagram was calculated and χ PS/PIB (as a function of concentration) adjusted until the theoretically calculated binodal line matches with the measured cloud points. The polymer/polymer interaction parameter thus obtained increases at 35°C from 0.416 in the limit of pure PS to 0.449 in the limit of pure PIB. This result agrees reasonably well with the prediction of the solubility parameter theory and is in good accord with information stemming from light scattering experiments in a ternary system under ‘optical theta conditions’.

Phase diagrams of the system tetrahydrofuran/γ-butyrolactone/poly(ether imide) and determination of interaction parameters

Abstract The thermodynamic interactions in the ternary mixture tetrahydrofuran/γ-butyrolactone/poly(ether imide) (THF/γ-BL/PEI) are investigated from 30 to 50°C. This is a membrane-forming system with a high He-selectivity. Cloud point measurements show that the two binary polymer solutions THF/PEI and γ-BL/PEI exhibit miscibility gaps which close towards the centre of the ternary phase diagram where the mixtures become homogeneous (cosolvency). Vapour pressures were determined for the subsystem THF/γ-BL. For the theoretical calculations the Gibbs energy of mixing is formulated according to the Flory-Huggins theory and the interaction parameter χ THF γ-BL calculated from the vapour pressures. The adjustment of theoretical phase diagrams to the experimental data (cloud point curves, tie lines and critical points) gives access to χ THF PEI and χ γ-BL PEI . For a satisfactory representation of the liquid-liquid demixing, a concentration dependent χ THF PEI is required, whereas concentration independent values for χ THF γ-BL and χ γ-BL PEI suffice.

Influence of Molar Mass Distribution on the Compatibility of Polymers

Abstract Phase equilibria were calculated by means of a new method (direct minimization of the Gibbs energy of mixing) for polymer blends consisting of monodisperse polymer A and polydisperse polymer B. The results obtained for a Schulz-Flory distribution of B (molecular nonuniformity U = (M w/M n) −1 = 1 and 100 components of model B) agree quantitatively with that of computations on the basis of continuous thermodynamics. The influence of U B on the miscibility of A and B in 1:1 mixtures was studied for constant M w of B, quantifying the incompatibility of the polymers by the length of the tie lines. The outcome of these calculations demonstrates that the typical effect of an augmentation of U B (keeping M w and the overall composition constant) consists in an enlargement of the mutual solubility of A and B. However, for an almost compatible pair of polymers (i.e., interaction parameters g are only slightly larger than the critical values for U B = 0), this statement remains true only in the case of suf...

Shear induced mixing/demixing: Blends of homopolymers, of homopolymers plus copolymers, and blends in solution

Shear may shift the phase boundary towards the homogeneous state (shear induced mixing, SIM), or in the opposite direction (shear induced demixing, SID). SIM is the typical behavior of mixtures of components of low molar mass and polymer solutions, SID can be observed with solutions of high molar mass polymers and polymer blends at higher shear rates. The typical sequence with increasing shear rate is SIM, then occurrence of an isolated additional immiscible area (SLD), melting of this island into the main miscibility gap, and finally SIM again. A three phase line originates and ends in two critical end points. Raising pressure increases the shear effects. For copolymer containing systems SID is sometimes observed at very low shear rates, preceding the just mentioned sequence of shear influences.