Liquid Structure, Thermodynamics, and Mixing Behavior of Saturated Hydrocarbon Polymers. 2. Pair Distribution Functions and the Regularity of Mixing (original) (raw)
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Macromolecules, 1998
The role of liquid structure in the mixing properties of saturated hydrocarbon polymers was investigated using the intermolecular pair distribution functions obtained by molecular dynamics simulations. A correlation was noted between specific geometric features of the pure component distribution functions and various observations on macroscopic mixing characteristics relative to the solubility parameter formalismsregularity, attractive irregularity, repulsive irregularitysfound earlier from neutron scattering studies of their blends. Ten component pairs are represented in these comparisons, and without exception they support the correlation. To our knowledge, it is the first relationship that provides an unambiguous connection between the pure component properties of polymers and how they mix.
Microscopic Solubility-Parameter Theory of Polymer Blends: General Predictions
Macromolecules, 1995
A microscopic solubility parameter theory for polymer blends is developed based on liquidstate polymer reference interaction site model (PRISM) integral equation methods. The well-defined approximations to obtain such a description are identified, and tractable schemes to go beyond them are discussed. Analytical predictions for the purely enthalpic X-parameter are derived using the Gaussian thread model. Many novel, non-Flory-Huggins effects are predicted including the failure of mean-field theory for random copolymer alloys, strong deuteration swap effects, nonadditivity of chemical and conformational asymmetry contributions to the %-parameter, and unusual and subtle temperature dependences of x due to thermally-induced density and chain dimension changes. Both general model calculations and applications to specific polyolefins are presented. The simple enthalpy-based theory accounts for the absolute magnitude of olefinic pparameters and a wide range of "anomalousn non-Flory-Huggins phenomena observed in recent small-angle neutron scattering and cloud-point experiments. New, experimentally testable predictions are also made. The fundamental origin of the non-mean-field behavior is the dependence of local intermolecular packing, and hence cohesive energy density, on the chain aspect ratio or effective stiffness. Numerical studies using more realistic semiflexible chain models are also presented and are in qualitative agreement with the analytic predictions. The influence of nonlocal, excess entropy of mixing processes is investigated and found to be a relatively small effect for chain aspect ratios characteristic of flexible polymers. Moreover, for blends which can be studied in the miscible phase at experimentally relevant temperatures, the enthalpic contribution to x arising from conformational asymmetry is generally orders of magnitude larger than the excess entropic contribution. These conclusions provide support for a fundamental assumption of regular solution theory that spatially local enthalpic effects make the dominant contribution to the excess mixture free energy.
Fluid Phase Equilibria, 2003
Blending (or mixing) of macromolecules is widely used to tailor the properties of polymeric materials and small-angle neutron scattering (SANS) has provided detailed information at the molecular level on the ability of different polymer species to mix or segregate at various thermodynamic conditions. For two decades, SANS data have been analyzed via the de Gennes "random phase approximation" (RPA) [P.-G. de Gennes, Scaling Concepts in Polymer Physics, second ed., Cornell University Press, Ithaca, London, 1979], which is based on the assumption that the dimensions of polymer chains remain unchanged on mixing for all concentrations and temperatures. Here we investigate the effect of temperature and concentration on the dimensions of macromolecules in blends using SANS and high-concentration labeling methods and construct a generic phase diagram, which specifies the range of validity of the RPA. Using scaling arguments, we demonstrate a parallel between the structure-property relationships in blends and solutions of polymers in small molecule solvents and reveal the impact of the chain length of the polymeric solvent on the phase behavior of polymer blends. The results offer new insights into the universality of the thermodynamic properties and structure of macromolecules in polymeric, liquid and supercritical solvents.
Computers & Chemical Engineering, 1998
Thermodynamic and structural properties of polymers are investigated using the molecular dynamics technique to simulate chain-like hydrocarbon molecules. Miscibilities of hydrocarbon blends can be in some instances be predicted from the cohesive energy densities of the constituent pure components. This approach holds great promise; however a number of obstacles must first be overcome. It is not currently known in which instances the mixture miscibility/pure component property relation is valid. In addition, although differences in polymeric cohesive energy densities can be estimated experimentally, measurements of individual polymeric cohesive energy densities are not possible and individual values must be estimated from internal pressure data. These simulations address both of these obstacles. The cohesive energy density, internal pressure, and for the first time their ratio are assessed for chain like hydrocarbons. Intermolecular pair distribution functions are determined, and a correlation between them and those instances where miscibility may be predicted from pure component properties is identified. Correlations between chain architecture, cohesive energy density and intermolecular pair distribution functions are also investigated. 0
50th Anniversary Perspective: Phase Behavior of Polymer Solutions and Blends
Macromolecules, 2017
We summarize our knowledge of the phase behavior of polymer solutions and blends using a unified approach. We begin with a derivation of the Flory− Huggins expression for the Gibbs free energy of mixing two chemically dissimilar polymers. The Gibbs free energy of mixing of polymer solutions is obtained as a special case. These expressions are used to interpret observed phase behavior of polymer solutions and blends. Temperature-and pressure-dependent phase diagrams are used to determine the Flory−Huggins interaction parameter, χ. We also discuss an alternative approach for measuring χ due to de Gennes, who showed that neutron scattering from concentration fluctuations in one-phase systems was a sensitive function of χ. In most cases, the agreement between experimental data and the standard Flory−Huggins−de Gennes approach is qualitative. We conclude by summarizing advanced theories that have been proposed to address the limitations of the standard approach. In spite of considerable effort, there is no consensus on the reasons for departure between the standard theories and experiments.
Equations of state and predictions of miscibility for hydrocarbon polymers
Macromolecules, 1992
The pressure-volume-temperature properties of a number of hydrocarbon polymers, including a series of ethylene-propylene copolymers, have been memured. These data, in the melt state, have been fit to equations of state. The characteristic parameters from the equations of state are related to thermodynamic properties of the polymers and have been correlated with their structure. The pure component data have been used to make predictions about the miscibility of the polymers with each other. It was found that, even in these nonpolar materials the enthalpy of mixing should dominate the behavior. The ethylene-propylene copolymers are predicted to be miscible for less than 15% differences in monomer contenta at molecular weights of lo5.
Journal of Polymer Science Part B: Polymer Physics, 1990
This research Contribution addresses mixing phenomena in a polymer blend that exhibits strong intermolecular association and bieutectic phase behavior. Molecular-level observations of specific interactions between dissimilar blend components have been obtained from high-resolution solidstate proton and carbon-13 nuclear magnetic resonance (N M R) experiments at ambient temperature. Results illustrate mixing effects on the isotropic chemical shifts of the critical component in a completely or partially phase-mixed blend. Perturbations in the NMR spectra result from conformational changes, hydrogen bonding, molecular complexation, or altered packing geometries that occur concomitantly with the mixing process. More convincing evidence that two components of a strongly interacting blend reside in a near-neighbor environment is obtained from the measurement of proton spin diffusion between dissimilar species. Proton spin diffusion is measured directly via the high-resolution CRAMPS experiment (Combined Rotation and Multiple Pulse Spectroscopy) in a molecular complex of poly(ethylene oxide) and resorcinol. A primary objective of this research endeavor is to bridge the gap between macroscopic and molecular-level probes of phase behavior and intermolecular association in mixtures that form molecular complexes. In this respect, the temperature-composition projection of the thermodynamic phase diagram is generated for binary mixtures of poly (ethylene oxide) and resorcinol, whose interaction sites are characterized via solid-state NMR. Under fortuitous conditions that are related to the overall mixture composition, two morphologically and crystallographically inequivalent phenolic I3C NMR signals are identified for resorcinol when the blends exist in a two-phase region below the eutectic solidification temperature. The success of this proposed structure-property relationship scheme, which bridges molecular-level mixing phenomena (via NMR) with solid-state phase behavior (via differential scanning calorimetry) depends on our ability to understand material properties at a level where continuum hypotheses are no longer valid.
Ind Eng Chem Res, 1995
The group contribution-Flory equation of state (GC-Flory EoS) is applied to the prediction of the phase behavior of monodisperse polymer/single solvent systems. The model is capable of predicting with satisfactory accuracy the most common types of phase diagrams typical of liquidliquid equilibria of polymer solutions (i.e., phase diagrams of the UCST, LCST, combined (UCST + LCST), and hourglass types). Combinatorial effects derived from differences in size, shape, and structure of the polymer and the solvent molecules strongly influence the phase behavior of the systems, but the type of a phase diagram of a specific polymerholvent system is primarily governed by the nature of the molecular energy interactions. The GC-Flory EoS predicts the significant effect of the free-volume contributions at high temperatures, which is in very good agreement with the nature of the liquid-phase separation at temperatures near the gas-liquid critical temperature of the solvent, where the highly expanded state of the solvent leads to LCST behavior.
Thermodynamic interactions in multicomponent polymer blends
Macromolecules, 1996
Small-angle neutron scattering (SANS) was used to probe the thermodynamic interactions in multicomponent polymer blends including ternary blends containing two homopolymers and a block copolymer, mixtures of a homopolymer and a block copolymer, and a blend of two block copolymers. The polymers used for this study were model polyolefins poly (ethylbutylene) and poly (methylbutylene) homopolymers and a poly (ethylbutylene)-block-poly (methylbutylene) copolymer. SANS profiles from homogeneous blends were ...
Effect of deuterium substitution on thermodynamic interactions in polymer blends
Macromolecules, 1993
We have investigated the effect of deuterium labeling on the thermodynamic interactions in blends of labeled and unlabeled saturated hydrocarbon polymers. Small-angle neutron scattering (SANS) was u e d to evaluate the Flory-Huggins interaction parameter x at several temperatures and compositions. Light scattering was also used in several cases to confirm the location of phase boundaries. We find that deuterium labeling changes x relative to the value for hydrogenous components and that the direction of the change depends on which of the two components is labeled. For blends of hydrogenated polybutadienes, x always increases when the more branched component is labeled, a pattern first noted by Crist and Rhee and also consistent with the expectation that deuterium substitution reduces the cohesive energy density (solubility parameter) of hydrocarbon substances. A solubility parameter formalism is developed by which x for hydrogenous componenta can be estimated with reasonable accuracy from SANS data obtained for the two combinations of singly-labeled components. It also provides a method for assigning relative values of the solubility parameter for a wide class of saturated hydrocarbon polymers.