Viscosity liquid-glass transition

The three most important factors in the equation are the viscosity and the thermodynamic parameters G and Gm- The viscosity can be approximated between the liquidus temperature, Tuq, and the liquid-+glass transition temperature, Tg, by a Doolittle expression involving the relative free volume (Ramachandrarao et al. 1977) while G can be calculated using the relationship... 

It can be instructive to compare the two rather different mode coupling theory expressions for the viscosity one valid near the critical point and other near the liquid-glass transition point. 

The above expression has been used by Leutheusser [34] and Kirkpatrick [30] in the study of liquid-glass transition. Leutheusser [34] has derived the expression of the dynamic structure factor from the nonlinear equation of motion for a damped oscillator. In their expression they refer to the memory kernel as the dynamic longitudinal viscosity. 

Liquid viscosity near glass transition temperature. Rpt. Surface Sci. 2, 51 (1962). 

The liquid-glass transition has been intensively studied for many years. Despite the many papers on the subject, both experimental and theoretical, there is still no clear understanding of this transition. However a few relatively simple phenomenological theories have been developed to explain an extensive body of observations, especially those of viscosity, heat capacity, and volume. The focus of one set of these theories is on the temperature dependence of the diffusion in dense liquids. 

The limitations of the PGSS process are that the substances to be processed have to be in a liquid state. But most of the products used in the pharmaceutical and food industries will distort before reaching their melting point. Its use is mainly restricted to polymers since the dissolution of supercritical fluid reduces both viscosity and glass transition temperature. The polymer becomes spray able through a conventional nozzle. 

Solution Polymers. Acryflc solution polymers are usually characterized by their composition, solids content, viscosity, molecular weight, glass-transition temperature, and solvent. The compositions of acryflc polymers are most readily determined by physicochemical methods such as spectroscopy, pyrolytic gas—liquid chromatography, and refractive index measurements (97,158). The solids content of acryflc polymers is determined by dilution followed by solvent evaporation to constant weight. Viscosities are most conveniently determined with a Brookfield viscometer, molecular weight by intrinsic viscosity (158), and glass-transition temperature by calorimetry. 

As the temperature is decreased, free-volume is lost. If the molecular shape or cross-linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled further, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. 

The most common type of glass transition is one that occurs for many liquids when they are cooled quickly below their freezing temperature. With rapid cooling, eventually a temperature region is reached where the translational and rotational motion associated with the liquid is lost, but the positional and orientational order associated with a crystal has not been achieved, so that the disorder remains frozen in. The loss of both translational and rotational motion leads to a large increase in viscosity and a large decrease in heat capacity. 

In liquids, and in glasses at temperatures above their glass transition (T > Tg), the shear stresses are usually very small. The equation for the viscosity T can be derived if xv kT is a reasonable assumption... 

Figure 7. Experimental data (symbols) for TNB s viscosity [78] superimposed on the results of the fitting procedure (line) from Lubchenko and Wolynes [47] are shown. Ta is diown by a tickmark. (TNB = trinaphthyl benzene). The temperature Ter signifies a crossover from activated to collisional viscosity, dominant at the lower and higher temperatures, respectively (see text). The temperature is varied between the boiling point and the glass transition. The right-hand side panel depicts the temperature dependence of the length scales of cooperative motions in the liquid. The thick solid and dashed lines are the critical radius and the cooperativity length respectively. Taken from Ref. [47] with permission.

Liquids lower the glass transition temperature, and according to the WLF theory, the viscosity and relaxation times are decreased. 

The so-called glass transition temperature, Tg, must be considered below this temperature the liquid configuration is frozen in a structure corresponding to equilibrium at Tg. Around Tg a rather abrupt change is observed of several properties as a function of temperature (viscosity, diffusion, molar volume). Above 7 , for instance, viscosity shows a strong temperature dependence below Tg only a rather weak temperature dependence is observed, approximately similar to that of crystal. Notice that 7 is not a thermodynamically defined temperature its value is determined by kinetic considerations it also depends on the quenching rate. 

The lower limit of the elastic range, the glass transition temperature, can be easily determined by refractometric, volumetric, or other well known methods. The upper limit suffers from an exact definition the transition from the fixed liquid to the liquid state occurs without transformation. But as the viscosity decreases exponentially with the temperature it is very convenient to define a 1 flow-temperature by penetrometer measurements. If the rate of temperature rise is kept constant, this temperature is reproducible within 1° or 2°C. The penetrometer indicates a temperature where macroscopically one would call the substance liquid. ... 

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