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Density data or specific volume
Input dialogue
The rheological data of the material is entered in the ‘Density’ tab:
- Solids density: The density of the compact solid
- Bulk density: The bulk density of the granulate or flakes. Is inevitably lower than the solid density
- Calculation type: Optionally density function (with 3 parameters) or volume function (with 2 parameters). See below for details.
Theoretical basics
Both the density and the specific volume as well as the glass transition or crystalline melting point can be determined from the pvT-diagrams.
The crystallite melting temperature $T_K$ is defined by the inflection point of the specific volume function in the pvT diagram. The glass transition temperature $T_G$ can be determined as the intersection of the tangents at the upper and lower course of the volume function.
Density function
The density function requires the three input values
- Specific density $\rho_0$: Corresponds to the density extrapolated to 0 °C (by default for a pressure of 100 bar)
- Slope of the density function $\rho_m$: Corresponds (for positive value) to the decrease in density per 1 °C
- Compressibility value $\kappa$: Describes the pressure dependence of the density
The temperature-dependent density of the melt can be described by the following linear equation
\[ρ = ρ_0 - ρ_m \cdot T\]
If only one density value is available, make sure that this value corresponds to the mass temperature in the process and that the gradient $\rho_m$ is zero. Otherwise, the value $ρ_0$ at $0 °C$ should be entered with the corresponding temperature dependence $\rho_m$.
The compressibility factor $\kappa$ influences the density as a function of the pressure:
$$ \kappa = - \frac{1}{V} \frac{dV}{dp} $$ $$\text{with}$$ $$\frac{dV}{V} = - \frac{d \rho}{\rho}$$ $$\text{is}$$ $$\frac{\Delta \rho}{\rho} = \kappa \cdot \Delta p$$
The value kappa can be imported directly from PAM or entered manually. If the value 0 is set for kappa, the density is calculated without taking the pressure into account.
Volume function
The function of the specific volume as the reciprocal of the density contains only two parameters:
\[v = v_0 + v_m \cdot T\]
The two characteristic values $v_0$ and $v_m$ can also be determined from the pvT diagram, whereby the data must be determined at an average pressure corresponding to the process.
The modelling of the specific volume cannot take pressure dependency into account.