Fox-Flory Equation Research Articles

Relationships between glass transition temperature and conversion

The Couchman approach to the expression of the compositional variation of glass transition temperature (or the Di-Benedetto equation) can be used to evaluate the effect of molecular weight on Tg for a stepwise linear polymer. An expression for the KL constant in the Fox-Flory equation is proposed. It is also possible to estimate the TgL corresponding to the hypothetical linear structure defined in a three-dimensional network. For different epoxy-diamine systems, we have found a good concordance with the results obtained previously using an additive law.

Engineering plastics from lignin. XVII. Effect of molecular weight on polyurethane film properties

AbstractA series of five fractions with number average molecular weights (M̄n) between 1500 and 10,000 daltons were isolated from a Kraft hydroxypropyl lignin (HPL). From 1H‐NMR and UV analysis the chemical properties of the HPLs were found to vary slightly with molecular weight. The hydroxyl content decreased while the glass transition temperature (Tg) increased as the HPL molecular weight increased. The Fox‐Flory equation adequately described the M̄n vs. Tg relationship. The HPL fractions were used as polyols for the preparation of solvent‐cast polyurethane networks (PU) in film form. The Tg of the PUs increased from 40° to 120°C as the M̄n of the polyol rose from 1500 to 10,000 daltons. The molecular weight between crosslinks (M̄c) of the networks was determined by swelling. An observed decrease in M̄c with an increase in M̄n was related to the functionality of the system. The strength properties of films prepared from fractionated HPLs were superior to those prepared from nonfractionated HPLs.

Composition and molecular-weight dependence of the glass transition in polystyrene-poly(2,6-dimethylphenylene ether) blends

The glass transition behaviours of a series of poly(2,6-dimethylphenylene ethers) with various molecular weights and their blends with polystyrene have been studied. The data are analysed according to the Fox-Flory equation ( M n dependence) and the Gordon-Taylor equation (composition dependence). A more rigorous treatment according to the theory developed by Kanig is presented and data of polystyrene-poly(vinyl methyl ether) blends, as well as polystyrene-poly(methyl vinylether) blends which do not obey the Gordon-Taylor equation, are discussed in the framework of this theory. The theory allows the estimation of the energy required to separateA-B contacts.

Synthesis and characterization of Tg for pyrene end-labelled polystyrene having no ester linkages

A series of pyrene end-labelled polystyrene (PS) samples having molecular weights ranging from 2000 to 40 000 have been synthesized anionically. Complete characterization data are provided. The end-labelling reaction is performed by coupling the living polystyryl anion with 1-bromobutylpyrene, with coupling efficiencies ranging from 72 to 90%. The resulting pyrene end-labelled PS has no ester linkage in the backbone, a common structure resulting from alternative end-labelling reactions proceeding via terminal hydroxyl units. This leads to a potential enhancement in thermal and hydrolytic stability; in fact, the samples have the same thermal stability as unlabelled PS. The glass transition temperatures ( T g) of our samples vary linearly with M ̄ −1 n , consistent with the Fox-Flory equation. However, the T g values of the labelled PS samples are higher than the unlabelled ones with the difference widening as M ̄ n decreases. This difference is explained by a decrease of chain end mobility and hence of free volume caused by bulky end groups.

Structure-Property Relationships of Perfectly Alternating Polycarbonate-Polydimethylsiloxane Block Copolymers, Part II

Abstract The relationships between the properties and microstructures of two series of perfectly alternating bisphenol A-polycarbonate-polydimethylsiloxane block copolymers were studied. In the first series, the polycarbonate (PC) block length was kept constant while the block length of polydimethylsiloxane (PDMS) was varied. The tensile properties of these block copolymers were found to be a function of composition. Dynamic mechanical properties measured as a function of temperature revealed the two-phase nature of these materials. Transmission electron micrographs showed that all samples had a sponge-like morphology independent of composition. The rheological maximum viscosity for the sample containing PC and PDMS blocks of equal molecular weight and extrudate swells increased with PC content. Takayamagi's mechanical coupling model was used to predict the maximum loss tangent at the glass transition temperature of PDMS using the known properties of pure components. The predictions agreed fairly well with the experimental results. In a second series of block copolymers, the block molecular weights of both PC and PDMS were varied to keep the composition constant. The tensile strength of these samples was found to increase with block molecular weights, except for the sample having the highest block molecular weights. The lower tensile strength of this material was attributed to its lamellar type morphology. Cold crystallization of PDMS blocks was found for samples having high PDMS block molecular weight (greater than 8000 g/mole). The Tg of PC blocks followed the Fox-Flory equation with a higher K value than expected. The PDMS content in PC domains was calculated to range from 11% for material of low block molecular weights to about 1.3% for high block molecular weight material.

The effect of the molecular weight on the glass transition temperature in amorphous poly(ethylene terephthalate)

The glass transition temperature of amorphous and fractionated poly(ethylene terephthalate) has been measured by differential scanning calorimetry. The application of the Fox-Flory equation for the range of molecular weights between 37100 and 4500 gives the values of Tg∞=342.4 K and Kg=51200. The low value of Kg is interpreted by the free volume theory. The flex energy of the chain is evaluated by the Gibbs-Di Marzio theory with a value of 1483 cal/mol. These results are compared with those obtained by other authors for the poly(ethylene adipate) and the poly(diethylene terephthalate).

Viscosities of sodium polyacrylate in aqueous sodium chloride

Dilute solution viscosity data were obtained for a 98.1% neutralized sodium salt of polyacrylic acid having a viscosity-average degree of polymerization of about 1.9 × 10 4, over a wide range of added salt (NaCl) concentrations. It was found that: 1. 1. The shape of the η sp C curve in pure water is of an entirely different type from that expected from the folding-chain theory of Fuoss and others, but is essentially similar to that which we observed with sodium carboxy methyl celluloses of high degrees of polymerization. The curve increases steadily with increasing C, exhibiting a rather wide plateau region. 2. 2. A marked decrease of the reduced viscosity is brought about by the addition of NaCl, but no indication for the appearance of a maximum in η sp C is observed for the added salt concentration ranges studied. 3. 3. With increasing ionic strength of the medium, the Huggins constant, starting with a value of about 0.6, initially decreases, reaches a minimum with a value of about 0.33, increases again, and tends to 0.85 at the limit of zero ionic strength. This behavior is discussed in connection with the change in degree of coiling of the polyelectrolyte molecule as caused by the change in the ionic strength. In particular, the behavior at sufficiently high ionic strengths is interpreted as a result of hypercoiling of the molecule. 4. 4. The application of the method of Pals and Hermans to our data leads to too high a value for the length of a statistical segment in Kuhn's sense. In contrast to this, the Flory-Fox equation, when applied at the limit of very high ionic strength, gives a very reasonable value for this length, being about 38 A.