Molar glasses

It became evident in work of Van Krevelen and Hoftyzer (1975) that the product Tg-M behaves in general as an additive function, which was called the Molar Glass Transition Function. 

In analogy to the Molar Glass Transition Function, defined by Eq. (6.4), we shall define the equivalent Molar Melt Transition Function by ... 

Figure 1.1. Calculation of glass transition temperature Tg and density p at room temperature of polystyrene as an example of the application of group contribution techniques, (a) The structure of a polystyrene repeat unit, (b) Fonnal breakdown of this structure into two "groups", (c) Each group makes a contribution to the molecular weight M of the repeat unit, to the "molar glass transition function" Yg, and to the amorphous molar volume V [3a], M, Yg and V arc sums of these contributions ...

A simple graph theoretical distinction was made between "extensive" (molar) properties which depend on the amount of material present and "intensive" properties which do not. (The molecular weight per repeat imit, the molar volume, and the molar glass transition function, are examples of extensive properties. The density and the glass transition temperature are examples of intensive properties.)... 

On the other hand, many important properties of materials are intensive properties. The values of intensive properties are essentially independent of the amount of material present, provided of course that this amount is not zero. An intensive property can usually be expressed in terms of the quotient of a pair of extensive properties. For example, the density equals the molecular weight per repeat unit divided by the molar volume. The solubility parameter equals the square root of the cohesive energy density (defined as the cohesive energy divided by the molar volume). As shown in Chapter 1, the glass transition temperature (an intensive property) can often be estimated in terms of the molar glass transition function divided by the molecular weight of a repeat unit of the polymer. 

Equation 6.24 is isomorphous to Equation 1.1, which van Krevelen [30] had developed to estimate Tg in terms of the molar glass transition function. The calculation of Ym is done by... 

Figure 10.6 The Hruby parameter of glass stability (Tci,onset - Fg) gap versus weight % [O] for 70Ga2S3-30La2S3 (molar %) glass [11, 16).

Figure 10.7 Transmission electron micrograph of the intergrowth of two phases A and B, resembling a eutectic or eutectoid microstructure obtained when 70Ga2S3-30La2S3 (molar %) glasses with [O] between 0.49 and 2.12 wt % (Tg 560°C) were heated at 630°C. A is a new phase of unknown identity and B is Ga6Laio/3Si4, melilite [17],...

The reagent is conveniently stored as a solution in isopropyl alcohol. The molten (or solid) alkoxide is weighed out after distillation into a glass-stoppered bottle or flask and is dissolved in sufficient dry isopropyl alcohol to give a one molar solution. This solution may be kept without appreciable deterioration provided the glass stopper is sealed with paraffin wax or cellophane tape. Crystals of aluminium isopropoxide separate on standing, but these may be redissolved by warming the mixture to 65-70°. 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

The second largest use at 21% is for unsaturated polyester resins, which are the products of polycondensation reactions between molar equivalents of certain dicarboxyhc acids or thek anhydrides and glycols. One component, usually the diacid or anhydride, must be unsaturated. A vinyl monomer, usually styrene, is a diluent which later serves to fully cross-link the unsaturated portion of the polycondensate when a catalyst, usually a peroxide, is added. The diacids or anhydrides are usually phthahc anhydride, isophthahc acid, and maleic anhydride. Maleic anhydride provides the unsaturated bonds. The exact composition is adjusted to obtain the requked performance. Resins based on phthahc anhydride are used in boat hulls, tubs and spas, constmction, and synthetic marble surfaces. In most cases, the resins contain mineral or glass fibers that provide the requked stmctural strength. The market for the resins tends to be cychcal because products made from them sell far better in good economic times (see Polyesters,unsaturated). 

Photochromic silver—copper haUde films were produced by vacuum evaporation and deposition of a mixture of the components onto a sUicate glass substrate (13). The molar ratio of the components was approximately 9 1 (Ag Cu) and film thicknesses were in the range of 0.45—2.05 p.m. Coloration rate upon uv exposure was high but thermal fade rates were very slow when compared with standard silver haUde glass photochromic systems. 

Ionic Equilibria.. The ion product constant of D2O (see Table 3) is an order of magnitude less than the value for H2O (24,31,32). The relationship pD = pH + 0.41 (molar scale 0.45 molal scale) for pD ia the range 2—9 as measured by a glass electrode standardized ia H2O has been established (33). For many phenomena strongly dependent on hydrogen ion activity, as is the case ia many biological contexts, the difference between pH and pD may have a large effect on the iaterpretation of experiments. 

In addition to the normal methylene linkage formation involved in polymerization with both resoles and novolaes, other, usually less desirable, eondensation by-products are also seen in novolac synthesis. Among these are benzodioxanes and dibenzyl ethers. The reaction pH has significant effect on the relative amounts produced. Fig. 15 shows typical structures for these by-products. When such byproducts are present, the meaning of the molar ratio changes and variability with respect to molecular weight development, glass transition point, and solubility may be seen. They also lead to poor raw material utilization. 

As with resoles, the central issue in design of novolacs is molecular weight. The effects of formaldehyde-to-phenol molar ratio and formaldehyde conversion on molecular weight of novolacs has been well studied and reported [192,193]. The effects of molecular weight on most of the important properties are also available [193]. These include Tg, melt viscosity, gel time, hot-plate flow, glass-plate flow. 

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. 

Experimental data for Van der Waals volumes Molar volumes Heat capacities Solubility parameter and glass transition temperature... 

Figure 25 ANN model (5-8-6) training and testing results for van der Waals volume, molar volume, heat capacity, solubility parameter, and glass transition temperature of 45 different polymers.

Suppose we dissolved LO.O g of cane sugar in enough water to make 200. mL of solution, which we might do (with less precision) if we were making a glass of lemonade. Cane sugar is sucrose (C H On), which has a molar mass of 342 g-mol" 1. What is the molarity of sucrose molecules in the solution ... 

An old bottle labeled Standardized 6.0 m NaOH was found at the back of a shelf in the stockroom. Over time, some of the NaOH had reacted with the glass and the solution was no longer 6.0 M. To determine its purity, 5.0 mL of the solution was diluted to 100. mL and titrated to the stoichiometric point with 11.8 mL of 2.05 M HCl(aq). What is the molarity of the sodium hydroxide solution in the bottle ... 

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