The use of Group Interaction Modelling (GIM) to predict the properties of polymers is becoming more widespread. One of the major reasons for this is the relatively low computing time required to provide reliable predictions, due in part to the definition of the polymer in terms of its characteristic mer unit. This negates the need for exact structural details of the typically highly crosslinked 3D network present in many high performance polymers. The mer unit is parameterised using functional group contributions dependent on the chemical structure of the components. The parameters used are the degrees of freedom, the cohesive energy at absolute zero, the van der Waal's volume, the mer unit length, and the molecular weight.

GIM assumes a hexagonal geometry where each polymer is surrounded by six neighbouring polymers that interact via van der Waal's forces. The energy of the system is defined by a modified Lennard-Jones potential that characterises the balance between attractive cohesive energy and repulsive thermal energy terms. Other thermodynamic terms for configurational and mechanical energy are incorporated as necessary.

Figure 1. Chemical structures of TGDDM, TGAP and DDS.
Schematic representation of the mer unit interaction sites with the hexagonal packing configuration..

Secondary transitions which occur in the loss history of viscoelastic polymers are modelled using normal distribution functions. The molecular rearrangements that cause irreversible loss of energy during the glass and beta transition are used to predict the peak temperature of each transition. The ratio of elastic energy stored to plastic energy lost is used to predict the cumulative loss tangent through each transition. Strain rate dependence in GIM is included via the frequency dependence of the glass and beta transitions.

The prediction of properties of a given polymer begins by calculating the thermal and cohesive energy contributions to the equation of state using the mer unit parameters. This is followed by using a series of linked constitutive equations for the prediction of non-linear properties such as the volume, heat capacity, coefficient of thermal expansion and bulk modulus. The loss tangent associated with the secondary transitions is then used to predict the Young's modulus and Poisson's ratio as a function of temperature. Finally the stress and strain can be predicted including any yield events as a function of strain rate.

In GIM, it is possible to formulate the representitive mer-unit for any combination of epoxy - amine cured blends. Here, we are showing only three epoxy resins: diglycidyl ether of bisphenol A (DGEBA, sold as Epon 828) triglycidyl p-aminophenol (TGAP, sold as MY0510) and tetraglycidyl 4,4' diaminodiphenylmethane (TGDDM, sold as MY721) and three amine curing agents: diaminodiphenylsulphone (DDS), diamine - diphenylmetane (DDM) and triethylenetetramine (TETA). As can be seen in the figure below, TGDDM, DDM and DDS are tetrafunctional whilst TGAP is trifunctional and DGEBA is bifuntional.

Chemical structures of DDS, DDM, TETA and DGEBA, TGAP, TGDDM.
Chemical structures of DDS, DDM, TETA and DGEBA, TGAP, TGDDM.

Further details of the GIM process can be found in the publications listed on this website.