Characterization of polymer networks by measurements of the freezing point depression

Abstract

Based on the phenomenon of freezing point depression of a solvent by AT, experimental evidence is presented to show that the distance between the junction points can be calculated from AT. Direct measurements of the temperature-time-curve of the cooling network and the Differential Scanning Calorimetry offer the determination of zl T. Except the mean distances dc in dependence on cross-linking density, swelling degree, and other network parameters, the distribution of the distance between the junction points H(dc) can be determined, which allows conclusions on the course of cross-linking reaction. This paper attempts to give experimental evidence of influences of the breadth of H(dc) on application-relevant properties.

Relation for Solid−Liquid Coexistence Systems and Its Application to Melting Point Depression of Benzene in Natural Rubber

“…According to the "tube" model, even if the tube space filled with solvent molecules is frozen, the crystal produced in the whole space can be partitioned into small crystal pieces that may cause an appreciable magnitude of ∆T. [10][11][12][13]37,38 In the present analysis, the elastic effects by swelling can be introduced through the ν, while the partition (or "mesh") 37 effects that may dominate the crystal size may be evaluated through the GT part in eq 3 with the interfacial energy term. From rheological measurements, a molecular weight between the entanglement coupling points (M e ) has also been estimated for various polymers.…”

“…On the other hand, one can find another available relation that has frequently been used to analyze melting depressions with varied crystal particle sizes or a solid-liquid interfacial energy of the crystal particles in the pure systems. 9 This relation can basically describe more lowered melting and freezing points of the small particles than those of the bulk solid, which is the so-called Gibbs-Thomson (GT) relation, 5,[9][10][11][12][13] Here σ o is the interfacial energy, ζ o is the crystal size, and q is the shape factor (e.g., q ) 2 for cylindrical crystals, and q ) 4 for cubic or spherical crystals), and the h o which represents the bulk heat of fusion is assumed to remain constant over a small range of (T m °-T m ). However, it is inconvenient to use eq 2 to deal with mixtures because it is not a function of composition.…”

“…Arndt and Zander also concluded from measurements of the spin-spin relaxation time of proton by NMR that an unfrozen solvent remained left in swollen systems up to around T g because of the great motion of polymer chains contained. 12 In the lattice theory, a Gibbs free energy of fusion (∆G m ), from which can be started for deriving basic temperaturecomposition equations which arrive finally at eq 3, was expressed as a function of the crystal size (ζ o ) and degree of crystallinity (ω o ), and the specific parameter (D o ) that will be associated later with the interfacial free energy of the crystal end. The Gibbs free energy of fusion, expressed in moles, is written as Here and N o is the total number of solvent molecules in the system, φ and φ o are the volume fractions of polymer and solvent, respectively, V o and V are the molar volumes of a solvent molecule and a polymer repeating unit, respectively, h o and s o are the molar heat and entropy of fusion, respectively, x is the ratio of the molar volumes of the polymer and solvent, and χ is the polymer-solvent interaction parameter.…”

A Frozen Tube Model of Melting Point Depression of Solvents in Entangled Polymer Systems

“…But, the GT model does not consider any effects induced by mixing between solvent and polymer for the case of binary mixtures. On the other hand, the presence of unfrozen solvent molecules in frozen polymer mixtures has been experimentally verified by different workers, 6,11,12 and in the case of the frozen NR-benzene mixtures, unfrozen benzene molecules surrounding the polymer chains were observed at lower temperatures than T m°u sing both NMR and differential scanning calorimetry (DSC) measurements. 6 The presence of the local solution phase is consistent with a melting model of solvent crystallites in a polymer solution, as proposed by Hoei, Yamaura, and Matsuzawa 13 and by Hoei, Ikeda, and Sasaki.…”

Anomalous melting behavior of cyclohexane and cyclooctane in poly(dimethyl siloxane) precursors and model networks

“…mckenna@ttu.edu) developed by some researchers to deduce the size and size distribution of nanoscale heterogeneities in polymer networks by using melting (or freezing) point depression of the solvents. [9][10][11][12][13][14][15] In this method, the Gibbs-Thomson (GT) equation 16 is used in conjunction with the Flory-Huggins (FH) model 17,18 to obtain the size and size distribution of solvent crystals, which are comparable with the nanoscale mesh size and distribution in polymer networks. Nevertheless, previous results on the melting (or freezing) behavior of swelling agents confined in polymer networks are complicated and contradictory, and the mechanisms of melting (or freezing) point depression are not well understood.…”