Polystyrene free volume

In the methacrylate homologous series, the effect of side-chain bulkiness is just the opposite. In this case, however, the pendant groups are flexible and offer less of an obstacle to free rotation than the phenyl group in polystyrene. As chain bulk increases, molecules are wedged apart by these substituents, free volume increases, and Tg decreases. 

Fig. 15. Oxygen permeability versus 1/specific free volume at 25 °C (30). 1. Polybutadiene 2. polyethylene (density 0.922) 3. polycarbonate 4. polystyrene 5. styrene-acrylonitrile 6. poly(ethylene terephthalate) 7. acrylonitrile barrier polymer 8. poly(methyl methacrylate) 9. poly(vinyl chloride) 10. acrylonitrile barrier polymer 11. vinyUdene chloride copolymer 12. polymethacrylonitrile and 13. polyacrylonitrile. See Table 1 for unit conversions.

The results of [91] supply ample evidence in support of this qualitative picture. The authors determined the baric viscosity factor b = [0 In j/(0P)-1] T (where t] is viscosity, P is pressure) for impact-resistant polystyrene filled with antimony trioxide. The viscosity piezocoefficient is known to be related to the free volume. A very simple formula for this relationship has been proposed in [92] in this form ... 

As an example of composite core/shell submicron particles, we made colloidal spheres with a polystyrene core and a silica shell. The polar vapors preferentially affect the silica shell of the composite nanospheres by sorbing into the mesoscale pores of the shell surface. This vapor sorption follows two mechanisms physical adsorption and capillary condensation of condensable vapors17. Similar vapor adsorption mechanisms have been observed in porous silicon20 and colloidal crystal films fabricated from silica submicron particles32, however, with lack of selectivity in vapor response. The nonpolar vapors preferentially affect the properties of the polystyrene core. Sorption of vapors of good solvents for a glassy polymer leads to the increase in polymer free volume and polymer plasticization32. 

Equivalence of Temperature and Radiation in Increasing the Creep Rate. It is possible to calculate a temperature rise which would give the same free volume increase as that calculated for a given gas concentration. When this is done, the free volume increase caused by the gas in the 0.033-inch polystyrene sample is equivalent to a temperature rise of... 

Polyvinylchloride was the host polymer in a study of the diffusion of dimethyl-phthalate, dibutylphthalate, and dioctylphthalate, performed by Maklakov, Smechko, and Maklakov 60) between room temperature and 110 °C. Azancheev and Maklakov 61) extended this work to include polystyrene as host, and to dependences of diffusion on concentration. They concluded that the macromolecules did constrain and trap the phthalate molecules at high polymer concentration, but without inhibiting the mobility of these diluents at lower polymer concentrations, e.g., in the gel. They used a version of the free volume theory to give a semi-quantitative explanation of the temperature and molecular size dependence of phthalate diffusion. 

Tager and co-workers (51) have invoked bundle structures to explain correlations between the viscosities of concentrated polymer solutions and the thermodynamic interactions between polymer and solvent. They note, for example, that solutions of polystyrene in decalin (a poor solvent) have higher viscosities than in ethyl benzene (a good solvent) at the same concentration, and quote a number of other examples. Such results are attributed to the ability of good solvents to break up the bundle structure the bundles presumably persist in poor solvents and give rise to a higher viscosity. It seems possible that such behavior could also be explained, at least in part, by the effects of solvent on free volume (see Section 5). Berry and Fox have found, for example, that concentrated solution data on polyvinyl acetate in solvents erf quite different thermodynamic interaction could be reduced satisfactorily by free volume considerations alone (16). Differences due to solvent which remain after correction for free volume... 

In some reports83,84) the change in the fractional free-volume was calculated at temperatures above Tg for epoxy resin filled with polystyrene particles on the basis of the experimental value of the reduction factor aT and the universal value fg according to the equation... 

It was found that the total fraction of the free-volume in the system increases with increasing concentration of the polymeric filler. The temperature dependence of fg for the epoxy matrix was calculated on the supposition that free-volume is an additive value of the constituent components and using the temperature dependence of the fractional free-volume of polystyrene. It was found that with increasing filler concentration the fractional free-volume becomes greater than for pure epoxy resin. Since the fraction of the free-volume increases with increasing total surface area of the filler, it may be supposed that this effect is associated with the surface layers of polymer. It was found that the rate of free-volume expansion in a filled system is higher than in an unfilled one, which means that the expansivity of the free-volume... 

Figure I 1.7. Variation of viscoelastic scaling factors with gas content for PS-C02 and PDMS-C02 systems. Lower scaling factor values for PS-C02 system, compared with PDMS-C02 system, are due to the closer proximity of the experimental temperatures to Tg of the pure polymer. The top curve displaying results for iso-free volume dilution of high-Mw polystyrene by low-Af polystyrene represents the effect on viscosity of volumetric dilution of high-Mw chains. Viscosity reductions for polymer-gas systems are significantly lower than the iso-free volume dilution curve, indicating that viscosity reduction is primarily due to free volume contributed by dissolved gas.

Styrene-Divinylbenzene Networks. Using ionic polymerization methods, Rietsch et al. (1976) prepared polystyrene (PS) networks with a well-controlled length of elastically active chains and crosslinks of variable functionality. In a given series, the glass transition temperature obeys the classical free volume theory ... 

Fjuita (16) studied the viscosity behavior of a polystyrene/ethyl-benzene solution to obtain the variation of free volume with changing polymer concentration. This work suggested a value of v ... 

Larry Duda and Jim Vrentas were the first to systematically study the diffusion of small molecules in molten polymers, formulate a free volume-based theoretical model, and elucidate the sharp dependence of the diffusion coefficient on temperature and concentration.2 Figure 8.8 shows diffusivities of toluene in polystyrene as a function of concentration and temperature. The values were computed using the Vrentas and Duda (17) free volume model and, as shown, coincide well with available data. 

Figure 5-3 Test of predictive capabilities of proposed free-volume model using data for the toluene polystyrene system. Only data points represented by solid symbols were used to obtain free-volume parameters (73).

The temperature dependence of D for the n-pentane-polystyrene system both above and below Tg2 has been calculated using the formulae of this free-volume model (64). The results obtained are shown in Fig. 5-4 along with a few experimental data (94) for the same system at three temperatures below Tg2. 

Fig. 1. Interaction potential between two colloidal particles as a function of the reduced centre-to-centre separation R = r/2a, where a is the radius of the particles. Curve 1, steric repulsion due to the adsorbed layer (Vs) curve 2, attraction due to the free polymer (Vd) curve 3, van dcr Waals attraction (X7.,) curve 4, sum of the contributions given by curves 1—3. System polvisobutene-stabilized silica particles and polystyrene (free polymer) in cyclohexane at 308 K. Molecular weight of the free polymer = 82,000, volume fraction of polystyrene, 0 = 0.02, a = 48 nm, thickness of the adsorbed layer 6 = 5 nm, x = 0.5 for polystyrene—cyclohexane, x, = 0.47 and xs = 0.10 for polyisobutene— cyclohexane, AjkT 4.54 and v = 0.10.

Free volume in polystyrene and polyisobutylene. J. Polymer Sci. To be published (1963c). 

Free volume approach to polystyrene melt viscosity. J. Appl. Phys- 29, 1395-1398 (1958). 

Dynamic Mechanical Properties. Figure 15 shows the temperature dispersion of isochronal complex, dynamic tensile modulus functions at a fixed frequency of 10 Hz for the SBS-PS specimen in unstretched and stretched (330% elongation) states. The two temperature dispersions around — 100° and 90°C in the unstretched state can be assigned to the primary glass-transitions of the polybutadiene and polystyrene domains. In the stretched state, however, these loss peaks are broadened and shifted to around — 80° and 80°C, respectively. In addition, new dispersion, as emphasized by a rapid decrease in E (c 0), appears at around 40°C. The shift of the primary dispersion of polybutadiene matrix toward higher temperature can be explained in terms of decrease of the free volume because of internal stress arisen within the matrix. On the other... 

An alternative explanation of the VFT model (28) is based on the free volume concept introduced by Fox and Floury [66-68] to describe the relaxation kinetics of polystyrene. The main idea behind this approach is that the probability of movement of a polymer molecule segment is related to the free volume availability in a system. Later, Doolittle [69] and Turnbull and Cohen [70] applied the concept of free volume to a wider class of disordered solids. They suggested a similar relationship... 

For a fixed strain rate, a comparison of Eq. (74) and experimental data [51, 52] of miscible blends is shown in Fig. 32. Curves 1 and 2 represent, respectively, the PPO/PS blends in compression, and the PPO/PS-pCIS blends in tension.Table 2 lists the three parameters fjf2, CK, and A/f2 used in curves 1 and 2. The unique feature here is the presence of a maximum yield (or strength) for 0 <

nonequilibrium interaction (A < 0). Such phenomenon does not occur in incompatible blends or composite systems. Table 2 also reveals that the frozen-in free volume fractions which are equal to 0.0243 and 0.0211 for polystyrene and for PPO, respectively. These are reasonable values for polymers in the glassy state. In the search for strong blends, we prefer to have —A/f2 > 1, and a larger difference between the yield stresses of blending polymers. 

The affect of polymer stereoregularity in the chains on the PAL data has also been studied. Hamielec et al [56] found what appears to be an increased lifetime (hole size) with increased randomness of the chain configuration in a series of polyvinlychloride (PVC) polymers, despite the large degree of scatter in the sample (probably due to the fact that a series of commercially available products were used.). They however found little correlation with tacticity in polypropylene. More recently a PAL study on a series of very well characterized polystyrene and poly(p-methlystyrene) samples of differing tacticity [57] was performed. In addition to finding that the polystyrene samples have smaller free volume holes than the poly(p-methylstyrene) samples, they found that the syndiotactic samples had broader hole distributions than the attactic samples. 

The larger free volume and distribution also indicates a larger fraction of free volume near the surface than in the bulk. According to the WFL theory [43], a larger free volume leads to a lower Tg. Indeed a significant Tg depression (as much as 70 °C) has been reported in the surface of polystyrene by using PAL method [10]. Other studies of polymer surfaces have shown that the size of the free volume holes near the surface of polyethylene [47] and polypropylene [48] are larger than the bulk. 

Yu, Z., Yahsi, U., McGervey, J.D., Jamieson, A.M., Simha, R. (1994) Molecular weight-dependence of free volume in polystyrene studied by positron annihilation measurements . J. Poly. Sci. B. 32,2637. 

Bohlen, J., Kirchheim, R. (2001) Macroscopic volume changes versus changes of free volume as determined by positron annihilation spectroscopy for polycarbonate and polystyrene . Macromolecules 34,4210. 

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