Glass transition data polymers

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

Figure 7.72 illustrates a large number of glass transition data of polymer solutions with comparisons to the Gibbs-DiMarzio (DM), Fox (F), and Schneider (S) equations described in Fig. 7.69 [30]. The upper left displays two sets of literature data on poly(vinylidene fluoride)-poly(methyl methacrylate) solutions (B,A). The glass transition shows a positive deviation from simple additivity of the properties of the pure components, which can only be represented with the help of the indicated interaction parameters of the Schneider equation. The lower left set of data illustrates poly(oxyethylene)-poly (methyl methacrylate) solutions (, o). They are well described by all three of the equations, indicating rather small specific interactions and great similarity between volume and entropy descriptions.

It is difficult to calculate thermal conductivity of oriented filled polymers, all the more to ascertain the temperature dependence of thermal conductivity ( ), thermal diffusivity (a), and specific heat (c). The calculation formulae cannot allow for such phenomena as the glass-transition of polymers, the possible lamination of polymer films due to the great discrepancy between the coefficients of linear expansion of the binder and filler, the effect of multiple thermal loading, etc. Therefore, most valuable are the experimental data on thermophysical properties of composite polymers in a wide temperature range (between 10 and 400 K). 

Tremendous interest has arisen in recent years regarding die issues of chain mobility and glass transition at polymer surfaces (1-4). Keddie et al used ellipsometric measurements of thermal expansivity to study Tg of polystyrene on silicon as a function of film thickness (1). The observed Tg asymptotically approached the bulk value of 100 C as thickness was increased, but for thinner films lO s of nm), Tg was significantly depressed. Clearly, such effects are of critical importance in the application of ultrathin polymer films as lubricants and protective coatings in magnetic data storage devices and micromechanical systems (5). Until recently, however, direct mechanical measurements of polymer behavior at the nanoscopic scale (which is necessary for mechanical analysis of ultrathin films) and at elevated temperatures has not been possible. 

Glass transition data for the commercially available Biopol polymers is shown in Fig. 5.3. Increasing the HV incorporation leads to small reduction in the copolymer 7g. 

Over 10000 papers contain glass transition data (43). This section of Polymer Handbook represents a fraction of these... 

In this section we resume our examination of the equivalency of time and temperature in the determination of the mechanical properties of polymers. In the last chapter we had several occasions to mention this equivalency, but never developed it in detail. In examining this, we shall not only acquire some practical knowledge for the collection and representation of experimental data, but also shall gain additional insight into the free-volume aspect of the glass transition. 

Reproduced, with minor revisions in the light of data now available, from chapter on Tlie Glass Transition, Melting Point and Structure by the author in Polymer Science edited by Professor A, D. Jenkins. with permission of Nonh Holland Publishing Company. 

Another important characteristic aspect of systems near the glass transition is the time-temperature superposition principle [23,34,45,46]. This simply means that suitably scaled data should all fall on one common curve independent of temperature, chain length, and time. Such generahzed functions which are, for example, known as generalized spin autocorrelation functions from spin glasses can also be defined from computer simulation of polymers. Typical quantities for instance are the autocorrelation function of the end-to-end distance or radius of gyration Rq of a polymer chain in a suitably normalized manner ... 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

A simple algorithm [17] makes it possible to find the probability of any fragment of macromolecules of Gordonian polymers. Comparison of these probabilities with the data obtained by NMR spectroscopy provides the possibility to evaluate the adequacy of a chosen kinetic model of a synthesis process of a particular polymer specimen. The above-mentioned probabilities are also involved in the expressions for the glass transition temperature and some structure-additive properties of branched polymers [18,19]. 

Bueche (16,172) proposed that the viscosity is proportional to the fourth power of the polymer concentration and a complex function of the free volume of the mixture. Kraus and Gruver (170) find that the 3.4 power fits experimental data better than does the fourth power. They used equation (58) with (r2) replaced by the mean-square radius of gyration (s2). The term r2)/(rf) indicates that poor solvents should lower the viscosity more than a good solvent. As the temperature increases, the factor increases as a function of the ratio (T - 7 (tJJ)/(7 - 7 ). The glass transition temperatures of the polymer and diluent are andT o, respectively. 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

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