From Liquid to Solid-Measurement of Mechanical Quantities Over More than 10 Decades

The change in mechanical behavior of more than 10 orders of magnitude is discussed using an isothermal curing reaction as an example.

The material passes through several different states (the low viscosity Newtonian liquid, non-Newtonian liquid, gel and glassy states).

Such changes can now be measured over the complete range using a DMA/SDTA861e and a Haake RheoStress 600.

Introduction

The mechanical properties of materials can change by many decades as a function of temperature or chemical structure. For example, when ice melts it changes from an elastic solid to a liquid with a viscosity of about 2 mPa·s. This represents a change of more than 12 decades in the mechanical properties. Similar changes of mechanical behavior occur with polymers. The two extremes in this case are the glassy state and the melt at high temperature. But reactive materials such as adhesives and polymeric coating materials can also exhibit changes in mechanical behavior of the same order during the reaction.

Knowledge of the mechanical properties provides information about structure and molecular interactions. In practical applications, for example adhesives or the production of composites, it is very important to have information about flow behavior, gelation and vitrification. To obtain this data, the mechanical quantities have to be determined over a range that is as wide as possible. From the point of view of measurement, this presents a problem because the change in material properties occurs on a logarithmic scale, but the sensors used in measuring instruments have a linear resolution.

The classical solution to this problem is to use several different instruments and different sample geometries, whereby one instrument typically covers 3 to 5 decades with one sample geometry. If measurements are required that cover a large range, several measurement curves have to be recorded that correspond to one another reasonably well in the range of overlap.

This problem was addressed in the development of the METTLER TOLEDO DMA/SDTA861e and particular attention was paid to expanding the measurement range. In the shear mode, the DMA can determine modulus changes of up to 8 decades in one measurement using the same sample geometry. This makes it possible to determine the mechanical behavior of a material from the glassy state to below the gel point in a single measurement. To obtain measurement data in the range from the gel point through to the low viscosity liquid state, the DMA measurements can be combined with rheometric data (measured with the Haake RheoStress 600). In this case, the large overlap range of the two instruments is very advantageous

This study shows how the results from a METTLER TOLEDO DMA/SDTA861e and the Thermo Electron Haake RheoStress 600 can be combined to determine the modulus change over 10 decades using the isothermal curing of an epoxy resin as an example.

As model substance, a two-component stoichiometric epoxy resin mixture consisting of the diglycidylether of bisphenol A (DGEBA) and diaminodiphenylmethane (DDM) as hardener or curing agent was used.

Mechanical Quantities during a Polymerization: From the Low Molecular Weight Liquid to the Polymeric Glass

The relationship between viscosity, η, and shear modulus, G, is given by the equations

G´ = ω η´ (1)

and

G˝ = ω η˝ (2)

where G´ is the storage modulus and G˝ the loss modulus, ω = 2π f the angular frequency, and f the frequency.

The curing of an epoxy resin system is a polymerization reaction. The change in mechanical behavior of such a system during the reaction is shown in Figure 1 using a stoichiometric reaction mixture of DGEBA-DDM as an example. The conversion is displayed on the abscissa and was measured during the isothermal reaction using a DSC822e [1].

Before the reaction begins, the sample consists of a low molecular weight mixture of resin and hardener. This is raised as quickly as possible to the reaction temperature. Initially relatively small molecules are formed in the reaction and the material behaves like a Newtonian liquid. This means that only the real part of the viscosity exists. For the shear modulus, it follows then from eqs (1) and (2) that the storage modulus is practically non-existent. The loss modulus is less than 100 Pa. As the molecules become larger, the viscosity increases.

At a conversion of 50%, the molecules are so large that the liquid loses its Newtonian behavior due to the stronger hydrodynamic interaction. The storage component of the shear modulus is now significant, but still much smaller than loss modulus. The material therefore still retains the characteristic behavior of a liquid (G˝ > G´).

^{From Liquid to Solid - Measurement of Mechanical Quantities over More than 10 Decades | Thermal Analysis Application No. UC 202 | Application published in METTLER TOLEDO Thermal Analysis UserCom 20}