Molar mass glass transition

Molar masses, glass transition temperatures, and fractional free volume (calculated from densities and Paul and Park s series of increments) of the polymers are summarized in Tables I and II (6-8). Fractional free volume (Vf) calculated by the method of Park and Paul (P) differs for different gases, depending on the diameters of the gas molecules. Here, the values for O2 and N2 are given as examples. As expected, the values for Vf increase with decreasing kinetic diameter of the gas molecules. 

Interestingly, our own studies have revealed that both the shape of the macromolecule and the glass transition temperature, Tg, change with irradiation time. For example, the irradiation of a bimodal commercial sample of polyvinylcarbazole (PNVK) (Fig. 5.31a) in dichloromethane occurred with an initial increase in (the number average) molar mass (M ) and an apparent loss in the bimodal nature of the polymer (Tab. 5.16, Fig. 5.31b). A similar initial increase in has been observed by Price [39] during a sonically induced polymerisation. 

The polymers are easily soluble in polar solvents like TFIF, DMAc, and DMSO, indicating that the solubility is enhanced by the large number of polar end groups and the branched structure. It is fully amorphous with a glass transition temperature between 90 and 110 C,depending on molar mass. 

When a chain with M= 200,000 g/mole is linked to other chains at four points, the average molar mass between cross-links, M., amounts to 40,000. The mass of one unit is 4x12 + 6x1 =54 g/mole so the number of units between cross-links is about 740. At the glass-rubber transition no whole chains obtain free mobility, as a result of the entanglements, but chain parts of 30 to 100 monomer units. The chemical cross-links, therefore, hardly contribute to the restriction in chain mobility the increase in Tg will, therefore, be negligible. 

Figure 10. LCT configurational entropy ScT as a function of the reduced temperature 5T = (T — To)/To for low and high molar mass F-F and F-S polymer fluids at constant pressure of P = 1 atm (0.101325 MPa). The product ScT is normalized by the thermal energy k To at the ideal glass transition temperature To- (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005 American Chemical Society.)...

Figure 17. Specific volume Vt and isothermal compressibility (at the glass transition temperature Tg) calculated from the LCT as a function of the inverse number l/M of united atom groups in single chains for constant pressure (P = I atm 0.101325 MPa) F-F and F-S polymer fluids. Both quantities are normahzed by the corresponding high molar mass limits (i.e., by...

Figure 22. The configurational entropy Sc per lattice site as calculated from the LCT for a constant pressure, high molar mass (M = 40001) F-S polymer melt as a function of the reduced temperature ST = (T — To)/Tq, defined relative to the ideal glass transition temperature To at which Sc extrapolates to zero. The specific entropy is normalized by its maximum value i = Sc T = Ta), as in Fig. 6. Solid and dashed curves refer to pressures of F = 1 atm (0.101325 MPa) and P = 240 atm (24.3 MPa), respectively. The characteristic temperatures of glass formation, the ideal glass transition temperature To, the glass transition temperature Tg, the crossover temperature Tj, and the Arrhenius temperature Ta are indicated in the figure. The inset presents the LCT estimates for the size z = 1/of the CRR in the same system as a function of the reduced temperature 5Ta = T — TaI/Ta. Solid and dashed curves in the inset correspond to pressures of P = 1 atm (0.101325 MPa) and F = 240 atm (24.3 MPa), respectively. (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005, American Chemical Society.)...

The systematic synthesis of non amphiphilic l.c.-side chain polymers and detailed physico-chemical investigations are discussed. The phase behavior and structure ofnematic, cholesteric and smectic polymers are described. Their optical properties and the state of order of cholesteric and nematic polymers are analysed in comparison to conventional low molar mass liquid crystals. The phase transition into the glassy state and optical characterization of the anisotropic glasses having liquid crystalline structures are examined. 

The linkage of conventional low molar mass Lc s to a linear polymer main chain via a flexible spacer provides a method to realize systematically the liquid crystalline state in linear polymers. Above the glass transition temperature Tg the polymer main chain can be assumed to exhibit, at least in the nematic state, an almost free motion of the chain segments, causing a tendency towards a statistical chain conformation. Due to their mobility, the polymer main chains are able to diffuse past each other, which is a condition to obtain the liquid state. Therefore such polymers can be classified as liquids of high viscosity10O). 

Two main transitions may take place during the formation of a polymer network gelation, a critical transition defined by the conversion at which the mass-average molar mass becomes infinite (Chapter 3) glass transition, or vitrification, characterized by the conversion at which the polymer begins to exhibit the typical properties of a glass. 

Polyurethane Networks. Andrady and Sefcik (1983) have applied the same relationship as Rietsch et al. (1976), to the glass transition temperature of networks based on poly(propylene oxide) diols with a controlled molar mass distribution, crosslinked by aromatic triisocyanates. They obtained a Kr value of 25 K kg mol-1, about twice that for PS networks. They showed that the length distribution of elastically active chain lengths, directly related to the molar mass distribution of the starting poly(propylene oxide), has practically no effect on Tg. 

Klc = critical stress intensity factor in mode I, MPam1/2 Km = stress concentration factor Me = average molar mass between crosslinks, kg mol 1 Mn = number-average molar mass, kg mol 1 p = hydrostatic pressure, Pa Tg = glass transition temperature, K... 

For miscible blend phases, these parameters need to be described as a function of the blend composition. In a first approach to describe the behavior of the present PPE/PS and SAN/PMMA phases, these phases will be regarded as ideal, homogeneously mixed blends. It appears reasonable to assume that the heat capacity, the molar mass of the repeat unit, as well as the weight content of carbon dioxide scale linearly with the weight content of the respective blend phase. Moreover, a constant value of the lattice coordination number for PPE/PS and for SAN/PMMA can be anticipated. Thus, the glass transition temperature of the gas-saturated PPE/SAN/SBM blend can be predicted as a function of the blend composition (Fig. 17). Obviously, both the compatibilization by SBM triblock terpolymers and the plasticizing effect of the absorbed carbon dioxide help to reduce the difference in glass transition temperature between PPE and SAN. 

If the molar mass is sufficiently high, the glass-rubber transition temperature is almost independent of the molar mass. On the other hand, the very diffuse rubbery-liquid transition... 

As is well known, the glass-rubber transition is of considerable importance technologically. The glass transition temperature (Tg) determines the lower use limit of a rubber and the upper use limit of an amorphous thermoplastic material. With increasing molar mass the ease of "forming" (shaping) diminishes. 

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