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Thermodynamic data
Material data - Thermodynamics
The rheological data of the material are entered in the ‘Thermodynamics’ tab:
- Crystallite melting/glass transition temperature: The crystallite melting temperature (thermoplastic) corresponds to the temperature of the peak of the enthalpy curve. The glass transition temperature (amorphous plastic) corresponds to the temperature at which the amorphous plastic changes from a rigid, amorphous state to a soft state.
- Thermal conductivity: The thermal conductivity of the solid $\lambda_F$ is assumed to be constant. The thermal conductivity of the melt is specified for a value extrapolated to 0 °C ($\lambda_0$) with a gradient of $\lambda_m$ per 1 °C.
- Molecular structure: For semi-crystalline thermoplastics, a distinction is made between solid enthalpy and melting enthalpy. In the case of amorphous plastics, there is only an enthalpy of solids.
- Specific heat capacity: This is only required for the melting range. It is modelled as a straight line with a constant gradient with a value extrapolated to 0 °C ($c_{p,0}$) and a gradient of $c_{p,m}$ per 1 °C.
- Melting enthalpy: The enthalpy for melting the crystalline areas (only partially crystalline plastics)
- Solid enthalpy: The enthalpy up to the crystallite melting/glass transition temperature, which is required for heating
Theoretical principles
Thermal conductivity
\[λ(T) = λ_0 + λ_m \cdot T\]
$λ_0$ represents the thermal conductivity resulting from the straight line describing the melting range at 0 degrees. The gradient of the thermal conductivity $λ_m$ can also be negative and must then be entered with a negative sign. The effective thermal diffusivity of the solid is required for the melting calculation. To determine this value, the thermal conductivity of the solid $λ_F$ must be entered.
Specific heat capacity
The function curve of the specific heat capacity $c_p$ at ambient pressure is shown for amorphous and semi-crystalline thermoplastics in the following figure. In the melt range, the specific heat capacity behaves almost linearly and can therefore be calculated using a linear equation:
\[c_p(T) = c_{p,0} + c_{p,m}\cdot T\]
can be described.
The peak in the curve for semi-crystalline thermoplastics describes the temperature $T_K$ and thus the melting temperature.
Specific Enthalpy
The specific enthalpy results from the integral of the specific heat capacity $c_p (T)$ between the limits $T_1$ and $T_2$:
\[Δh = \int \limits_ {T_1}^{T_2} c_p(T)dT\]
This gives the amount of heat related to the unit mass that is required to increase the temperature of the polymer from $T_1$ to $T_2$.
Semi-crystalline materials, on the other hand, exhibit a gradual increase due to the phase transformation. The additional amount of heat is referred to as the melting enthalpy $∆h_A$. The following figure shows the specific enthalpy as a function of temperature.
With indicating amorphous thermoplastics the field for melting enthalpy is not editable. In case of semi-crystalline thermoplastics the increase in enthalpy $∆h$ is formed by an enthalpy increase of the solid material $∆h_F$ and the melting enthalpy $∆h_A$ :
Amorphous thermoplastics: \[∆h=∆h_F\]
Semi-crystalline thermoplastics: \[∆h=∆h_F+ ∆h_A\]
Plus the enthalpy increase in the melting range: $$∆h_{melt}=\frac{1}{2} c_{p,m} \cdot (T^2-{T_{K,G}}^2) + c_{p,0} \cdot (T-T_{K,G})$$