Entropy glass transition temperatures

The increase in the length of the side chain results normally in an internal plasticization effect caused by a lower polarity of the main chain and an increase in the configurational entropy. Both effects result in a lower activation energy of segmental motion and consequently a lower glass transition temperature. The modification of PPO with myristoyl chloride offers the best example. No side chain crystallization was detected by DSC for these polymers. 

Figure 2-13 Schematic drawing of (a) density as a function of temperature, and (b) entropy as a function of temperature for glasses with different cooling rates and hence different glass transition temperature (Martens et al., 1987). The entropy of the undercooled liquid is estimated assuming constant heat capacity.

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 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.)...

Figure 4.29 Changes in volume or entropy which can occur on cooling a liquid. Crystallization may occur at Tj- or, if the liquid is supercooled below jy, a glass is formed. The temperature corresponding to the break in slopes of V(oi S) versus T is termed the glass transition temperature, T. The value of varies with the cooling rate, R(Ri > f 2)-...

The conformational entropies of copolymer chains are calculated through utilization of semiempirical potential energy functions and adoption of the RIS model of polymers. It is assumed that the glass transition temperature, Tg, is inversely related to the intramolecular, equilibrium flexibility of a copolymer chain as manifested by its conformational entropy. This approach is applied to the vinyl copolymers of vinyl chloride and vinylidene chloride with methyl acrylate, where the stereoregularity of each copolymer is explicitly considered, and correctly predicts the observed deviations from the Fox relation when they occur. It therefore appears that the sequence distribution - Tg effects observed in many copolymers may have an intramolecular origin in the form of specific molecular interactions between adjacent monomer units, which can be characterized by estimating the resultant conformational entropy. 

It should be remembered, however, that the springs connecting the beads are entropy springs, and that the network chains are flexible either because they are above their glass transition temperature, or because they are imbedded in a solvent. 

The glass-transition temperature Tt is thought by some to be a second-order transition, so some data relevant to it are shown in the middle two sketches. The volume and entropy merely show a change in slope at Tr The second derivatives are shown in the bottom pair of sketches, with the expected discontinuities in the thermal expansion coefficient and heat capacity. 

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