Polystyrene empirical equation

In summary, the thermodynamic Model I based on Morton s theory has been used to successfully fit experimental data and obtain semi-empirical equations for the swelling of polystyrene and polymethyl methacrylate latexes. The semi-empirical equations offer a quick method for estimating swelling ratio from particle size and interfacial tension. The generalized form of Model II might prove to be more suitable for describing the swelling phenomena of relatively hydrophilic systems. ... 

The comprehensive set of the surface tension data of polystyrene in supercritical carbon dioxide at various temperatures and pressures was obtained successfully. Based on the obtained data, an empirical equation was developed that predicts the surface tension value at a given temperature and pressure. Within the experimental limits on temperature (< -385X) and pressure (< -2153 psi), the trends of surface tension dependence on temperature and pressure can be quantified with partial derivatives of the empirical equation. 

An empirical correlation was also proposed by Malek and Lu, whose experiments were restricted to particles of uniform size, in a range (dp = 0.8-3.7 mm) somewhat coarser than that used by Reddy et al. Their own results for wheat, brucite, sand, polyethylene, polystyrene, millet, and timothy seed (pa = 57-166 Ib/ft ), obtained in 4-, 6-, and 9-in. columns, as well as previous data (B3, MIO) for several other materials of size and density roughly within the same range, were all correlated within 11% by the equation... 

The above empirical relationship was tested for the sedimentation of polystyrene latex suspensions with i = 1.55 pm in 10 moldm NaCl the results are shown in Figure 9.13. In this case the circles are the experimental points, whereas the solid line is calculated using Equation (9.48) with =0.58 and fe= 5.4 [41]. 

A model for calculating viscosities of concentrated polymer solutions has been formulated and used successfully to predict viscosities of alkyd resin solutions in both pure aromatic solvents and in mixtures of hydrocarbons and oxygenated materials. It was also found to describe viscosity trends in polystyrene-diethylbenzene solutions accurately. The formulation explicitly accounts for the observation that concentrated solution viscosities increase markedly with decreasing compatibility between resin and diluent. The proposal of an empirical relationship which interprets the viscosity enhancement in poorer solvents in terms of increased chain-chain interactions is of interest. The model contains three constants which are fixed for a particular resin and are independent of diluent type. These are the Mark-HouuAnk constant, the parameter in the Martin viscosity equation, and the constant relating the postulated clustering to the solution thermodynamics of a particular solution. 

An increase in side group bulkiness generally serves to raise Tg. Ring-substituted polystyrenes show this effect and, in the case of polyacenaphthalene, the motions of the chain are so severely restricted that the Tg occurs at 264 °C. Chain microstructure is clearly important in determining chain mobility. We have already discussed the case of random copolymers on the basis of the Gibbs-DiMarzio theory and have developed equation (5-19), which shows that the Tg of a random copolymer is intermediate between the Tg s of the corresponding homopolymers. Equation (5-19) is similar in form to the empirical expression of Wood7... 

Kleintjens et al. have obtained spinodal and critical point expressions from equation (12) and applied these to data for polystyrene in cyclohexane. They obtain values for ko and kp which can be related to empirical correction terms introduced by Flory et al." Few conclusions could be drawn, however, as to either the effectiveness or the underlying molecular nature of the orientation correction parameters. ... 

Typical behavior is shown in Fig. 3.12(a), where the storage modulus in the plateau and terminal regions for a commercial polystyrene melt is plotted against frequency at several temperatures [17]. A reference temperature is selected, in this case To = 160 °C, and best-fit scale factors for data obtained at other temperatures are determined empirically to form Fig. 3.12(b). The timescale can shift very rapidly, as indicated by the plot of ar versus T in Fig. 3.13 [17]. The Williams-Landel-Ferry (WLF) equation, introduced in Chapter 2 and shown for this particular sample and choice of reference temperature in Fig. 3.13, describes rather well the temperature dependence of aj for most polymer melts and concentrated solutions. 

Measurements of stress relaxation of polystyrenes and poly(a-metliylsty-rene)s as well as dynamic moduli of polystyrenes have shown that ti is proportional to as predicted for Th> by equation 53 or for tj by 57 of Chapter 10 together with the empirically established dependence of tjo on M. 

If the viscosity is not corrected for the concentration dependence of fb or Ug as in equations 29 and 30, it is found empirically that tjo can be represented as a single function of cM"/ over wide ranges of c and M. The exponent y is 0.68 for polyisobutylene in several different solvents and cellulose tributyrate in 1,2,3-trichloropropane for various solutions of polystyrene, poly(vinyl acetate), polyisobutylene, and other polymers it was found to range from 0.50 to 0.74. - When t]Q is proportional to M -, as frequently observed at sufficiently high values of M and c, and y = 0.68, tjq is then proportional to c . Fifth-power dependence on c has been observed over limited concentration ranges, but must be considered as an empirical approximation because it includes a concentration dependence of or Og which should preferably be described by a relation of the form of equation 12. 

Adsorption isotherms of linear polymer molecules are found to be of the Langmuir type [55,56]. Many workers assume that the molecules are adsorbed in the shape of a random coil [57,58] and have developed equations to give the area occupied by a molecule. Some workers assume a modified Langmuir equation to be necessary since pwlymers may occupy more than one site [59]. Others adopt a more empirical approach [60]. An estimate of the inner and outer surface areas of porous solids has also been obtained by using a set of polystyrene fractions having narrow ranges of molecular weights [61]. 

We note that according to Eq. 2.34 for a good solvent at high molecular weight, becomes proportional to while it is now generally agreed that the exponent on M is very close to 3/5. Nonetheless, Baumann s equation has been used to estimate small deviations from the theta state. For example, Fetters et a/. [19] compiled (-Rg)o data for a number of polymers and summarized their results in the form of empirical, power-law equations. For example, for polystyrene in cyclohexane at 34.5 °C, they reported ... 

The long time mode corresponds to the liquid-liquid transition. The relaxation time follows a Fulcher-Vogel equation, the mobility is frozen at a critical temperature, T. Such behavior is characteristic of the vitreous state since it has also been observed in inorganic glasses and even in spin glasses. The departure of from Tg is given by the empirical WLF value in polymers like polystyrene it may be very different in odier polymers like poly(cyclohexyl methacrylate). This departure is also dependent upon the thermodynamic history of the polymer. 

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