Volume recovery isobaric

Below Tg (4,5) co-operative molecular processes are usually assumed to be inactive. However, physical ageing implies that conformational changes may be still able to occur if rather infrequently. Structural relaxation processes are observed to be non-exponential and are represented by a continuous distribution or stretched exponential form (d). Thermorheologically simplicity (TRS) implies that the molecular relaxation process has the same form at different temperatures (7) and the validity of this assumption is addressed in this paper. Isobaric volume recovery (8,9) has been described by a single parameter mc el, however all fi ee volume models (10,11) have limitations and a distribution of hole sizes and relaxation times leading to a pseudo-linear theory is a more realistic model(72). Comparison of data fi om various techniques should throw light on the molecular nature of physical agdng. 

For the case of isobaric temperature jumps or isothermal pressure jumps, these equations revert to the KAHR equations for volume recovery using (dS/dP)r = -Ak and (dS/dT)p = Aa. Ak is the difference in the compressibilities of the liquid and glass at Tg. For enthalpy recovery, (d5/dP)r = VTAa and (dS/dT)p = ACp. 

For describing thermally stimulated current associated with transitions in amorphous polymers, the multiple order parameter concept has been used. This concept has been widely discussed in past years and a good fit of volume recovery under isothermal and isobaric conditions through the glass transition has been presented by Kovacs et al. The relative volume departure of the system from equilibrium, 5, has been assumed to have a rate of change t,- of... 

Kovacs AJ, Aklonis JJ, Hutchinson JM, Ramos AA (1979) Isobaric volume and enthalpy recovery of glasses II. A transparent multiparameter theory. J Polym Sci Polym Phys Ed 17 1097-1162... 

Kovacs, A. J., Hutchinson, J. M., Aklonis, J. J., and Ramos, A. R., Isobaric volume and enthalpy recovery of glasses 2. Transparent multi-parameter theory, J. Polym. Sci. Polym. Phys. Ed., 17,1097-1162(1979). 

Various phenomenological equations have heen used to describe the dependence of the characteristic relaxation time on temperature and structiu-e and sometimes pressure, including the TNM equation (120), equations derived hy Hodge (123) and Scherer (124), both based on the approach of Adam and Gibbs (125), the KAHR and similar equations (119,126), equations based on free volume, and several others (127,128). The essential idea in all of these equations is that the characteristic relaxation time depends on the instantaneous state of the material (ie, temperature, pressure, and some measure of structure— volume, 5, Tf, and/or Pf). The most widely used form is the TNM equation for isobaric structural recovery ... 

Isobaric energy recovery systems allow a small portion of the concentrate stream to mix with the raw seawater as part of the process. This volume of bypass water is necessary to lubricate the moving parts. This leakage results in a slight increase in the TDS of the seawater exposed to the membranes and must be included in the SWRO system design... 

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