Global Gibbs free energy combines bulk and surface free energies of void, where the bulk varies with the third power of radius compared to surface that changes with the second power only. Upon optimizing with respect to radius one obtains a critical radius as a linear function of their radio.

It turns out that you may obtain following expression for the critical void radius above which void grows otherwise void shrinks on the condition that the chemical potential of vacancies in the matrix is greater than in the vacuum state (void), which is also temperature and pressure dependent property.

rcrt = 2 Gama /[hsub (1- T/Tsub )]

where h sub is sublimation enthalpy and T is sublimation Temperature of matrix. Gama is the surface specific Gibbs free energy and assumed to be doesn't change. Here it is assumed that enthalpy doesn't vary but the entropy is obtained from: delG=hsub-Tsub del Ssub =0 at the equilibrium. Then delS(T) = h sub /T

Note: For vacancies below the sublimation temperature at atmospheric pressure above condition is satisfied. Otherwise existing voids shrinks regardless their sizes till the matrix reaches to the saturation limit. Similarly vacancy saturation concentration increases with temperature in the matrix reaches about 10**-4 (fraction) at the melting temperatures, TM. That means chemical potential of vacancies has negative temperature coefficient as can be seen above, which produces decrease in the critical radius upon cooling down to nil at the absolute zero, and approaches to infinity (the flat surface) at the sublimation temperature of the matrix. Any void having smaller radius then the initial critical size at the start temperature, it decreases its size till the dynamic critical size catches it up upon further cooling (This situation dependence on the Kinetics) . But those having larges sizes than the initial critical one just opposite takes place they rather grow much faster upon cooling.

İf cooling rate is extremely high (super cooling) then small void might grow up depending upon whether its size is larger than the critical size at final super cooled temperature.

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Dear Dr. Hidouri; The effect of PH level of the environment on the unfolding kinetics of ssDNA (Alpha Peptide) , which is also exposed to the hydrostatic pressure is investigated numerically using irreversible thermodynamic model combined with the torsional and bending deformations recently by us and compared with the experimental work. The results are reported as a WorkİNG PAPER in RG. Regards

Full Text is Available under the following Title;

• ELASTIC RESPONSE AND AGING KINETICS OF ALPHA POLYPEPTIDES [ssDNA] UNDER VARIOUS CONSTRANTS: SPECIAL REFERENCE TO THE SIMPLE SPRING MECHANICS

Vikash Kumar Singh Chauhan hello i want to investigate the effect of temperature on copper block with different values to see either it is expend or contract, kindly tell me how to see these changes in CST Microwave studio?