Viscosity of strong and fragile glass-forming liquids investigated by means of principal component analysis

TLDR: In this article, the Vogel-Fulcher-Tammann-Hesse (VFTH) equation has been used for describing the temperature dependence with viscosity for strong, moderate and fragile glass-forming liquids.

About: This article is published in Journal of Physics and Chemistry of Solids.The article was published on 2007-01-01 and is currently open access. It has received 69 citations till now. The article focuses on the topics: Viscosity.

Figures

Table 2 Total and cumulative percentages and respective eingenvalues of each axis considered

Table 3 Values of B, T0, Tg and Tm of the corresponding four PC axis

Fig. 5. Plot of principal component 1 (related to B parameter) versus principal component 3 (Tg).

Table 1 VFTH viscosity parameters B and T0 (A was fixed as 5, Z in Pa s unities, plus w2 test), Tg and Tm values, the measured viscosity temperature range and the corresponding parameters m and D

Fig. 1. Frequency distribution of A from VFTH equation (in Pa s) in 38 silicate and borate systems (the same presented in Table 1), considering it as a free parameter (as also B and T0). Dashed vertical line represents the average value. Results from Ref. [8].

Fig. 2. Experimental viscosity of silicate (a) and borate (b) systems as a function of the normalized temperature Tg/T, showing the range from ‘‘strong’’, characteristic of open tetrahedral network liquids, to ‘‘fragile’’, typical of ionic and molecular liquids.

Frequently asked questions

Q1. What are the contributions in "Viscosity of strong and fragile glass-forming liquids investigated by means of principal component analysis" ?

In this work, the VFTH equation was applied over a wide temperature range ( between the glass transition temperature, Tg, and the melting point, Tm ) for 38 oxide glasses, considering simple, binary and ternary compositions of silicate and borate systems. Principal component analysis ( PCA ) was used in the present study to verify the correlation between the B and T0 parameters [ J. F. Mano, E. Pereira, J. Phys. 

Q2. What is the main reason for the distribution observed in the map?

The main reason for the distribution observed in the map may be related to the weight of the PCs: in the first PCA, the highest weights come from the high B values of SiO2, albite and B2O3. 

Q3. What is the effect of the B parameter on the viscosity of the glass?

The B parameter also diminishes with alkali content in the lithia–silica, soda–silica and potassium–silica systems, showing the influence of depolymerization degree. 

Q4. What is the eigenvalue of the system of equations?

Once an eigenvalue is known, the system of equations can be solved for the components of M by setting one component equal to an arbitrary non-zero value and solving for the rest. 

Q5. What is the sensitivity of the liquid structure to temperature changes?

A useful measure of the viscosity dependence on temperature is the fragility parameter m, proposed by Angell [15,16] and is defined by:m ¼ dðlog10 ZÞ dðTg TÞT¼Tg. (13)Eq. (1) indicates the sensitivity of the liquid structure to temperature changes. 

Q6. What is the first order condition for a minimum with respect to the elements of P?

MTM ¼ 1. (5) The first–order condition for a minimum with respect to the elements of P is, in matrix formPT ¼MTZ (6) or, equivalently,P ¼ ZTM. (7) The first–order condition for a minimum with respect to the elements of M is, in matrix form,lMT ¼ ZP, (8) or, equivalently, since P ¼ ZTM,lM ¼ ZZTM. 

Q7. What is the main reason to consider A fixed?

the main physical reason to consider A fixed is that at high temperatures there is a decrease in structural complexity of the glassy melts [14]. 

Q8. What is the determinant of the coefficient matrix?

Luis Ferreira Nascimento, C. Aparicio / Journal of Physics and Chemistry of Solids 68 (2007) 104–110106have a non-trivial solution, the determinant of the coefficient matrix (N lI) must be zero.