New paradigm for configurational entropy in glass-forming systems
Aleksandra Drozd-Rzoska, Sylwester J. Rzoska, Szymon Starzonek
Abstract
Abstract We show that on cooling towards glass transition configurational entropy exhibits more significant changes than predicted by classic relation. A universal formula according to Kauzmann temperature $${T}_{K}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>K</mml:mi> </mml:msub> </mml:math> is given: $$S={S}_{0}{t}^{n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math> , where $$t=\left(T-{T}_{K}\right)/T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mi>T</mml:mi> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>K</mml:mi> </mml:msub> </mml:mfenced> <mml:mo>/</mml:mo> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> . The exponent $$n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> is hypothetically linked to dominated local symmetry. Such a behaviour is coupled to previtreous evolution of heat capacity $$\Delta {C}_{P}^{config.}\left(T\right)=\left(nC/T\right){\left(1-{T}_{K}/T\right)}^{n-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>o</mml:mi> <mml:mi>n</mml:mi> <mml:mi>f</mml:mi> <mml:mi>i</mml:mi> <mml:mi>g</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:msubsup> <mml:mfenced> <mml:mi>T</mml:mi> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mi>n</mml:mi> <mml:mi>C</mml:mi> <mml:mo>/</mml:mo> <mml:mi>T</mml:mi> </mml:mfenced> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>K</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>T</mml:mi> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> associated with finite temperature singularity. These lead to generalised VFT relation, for which the basic equation is retrieved. For many glass-formers, basic VFT equation may have only an effective meaning. A universal-like reliability of the Stickel operator analysis for detecting dynamic crossover phenomenon is also questioned. Notably, distortions-sensitive and derivative-based analysis focused on previtreous changes of configurational entropy and heat capacity for glycerol, ethanol and liquid crystal is applied.