Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- en:materialdaten:dichtedaten_bzw._spezifisches_volumen [2024/10/17 17:18] – [Compressibility factor kappa] neelest
+++ en:materialdaten:dichtedaten_bzw._spezifisches_volumen [2025/05/15 15:06] (aktuell) – [Theoretical basics] cschall
@@ Zeile 1: / Zeile 1: @@
 ======Density data or specific volume======
+===== Material data - density =====
+The following 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 method**: Optionally density function (with 3 parameters) or volume function (with 2 parameters). See below for details.
 {{ :materialdaten:rex171_mat_en_003.png?nolink |}}
-===== Density data or specific volume =====
+===== 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.
+melting point can be determined from the pvT-diagram.
 {{ :materialdaten:abb_pvt_diagramm_en.svg?600 |}}
-Here, the crystalline melting point $T_K$ is defined by the point of inversion of the
+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.
-specific volume function in the pvT-diagram. The glass transition point $T_G$ can be
-determined as the point of intersection of the tangents to the upper and lower volume
-function. The temperature-dependent density of the melt is described by the following
-straight-line equation:
-**Density function:**  \[ρ = ρ_0 - ρ_m \cdot T\]
+==== Density function ====
-If only one density value is available, it must be ensure that this value corresponds to
+The density function requires the three input values
-the melt temperature. Otherwise the value $ρ_0$ at $0 °C$ should be entered. In
+  * **Specific density** $\rho_0$: Corresponds to the density extrapolated to 0 °C (by default for a pressure of 100 bar)
-order to simplify the data input it is alternatively possible to enter a temperaturedependent change in the specific volume $v$ by aid of a switch.
+  * **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
-**Volume function:** \[v = v_0 + v_m \cdot T\]
+The temperature-dependent density of the melt can be described by the following linear equation
-The two characteristic values $v_0$ und $v_m$ can also be established by the pvT-diagram. The values are to be established at a medium pressure corresponding
+\[ρ = ρ_0 - ρ_m \cdot T\]
-to the process.
-==== Compressibility factor kappa ====
+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 specific volume or rather the density
+The compressibility $\kappa$ (order of magnitude 0.0001 1/bar, reciprocal of the bulk modulus K) influences the density as a function of the pressure:
-in dependence of the pressure. The value refers to an average temperature and an
-average pressure of the pvT-data. Changing the specific volume by the pressure is
-described with the following equation.
-\[kappa = - \frac{1}{v} (\frac{dv}{dp}) _{T=const}\]
+$$ \kappa = \frac{1}{K} = - \frac{1}{V} \frac{dV}{dp} $$
+$$\text{with}$$
+$$\frac{dV}{V} = - \frac{d \rho}{\rho}$$
+$$\text{is}$$
+$$\frac{\Delta \rho}{\rho} = \kappa \cdot \Delta p$$
-The value kappa can be imported directly from PAM or entered manually. If 0 is
+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.
-entered as the value for kappa, the specific volume or rather the pressure is
-calculated without considering the pressure.
-In addition to this, the solid and bulk density can be entered.
+==== 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.
 ===Further topics===
   * [[en:materialdaten:datenbankanbindung_an_pam|]]
   * [[en:materialdaten:allgemeineangaben|]]
-  * [[en:materialdaten:rheologische_materialdaten|]]
   * [[en:materialdaten:thermodynamische_daten|]]
   * [[en:materialdaten:dichtedaten_bzw._spezifisches_volumen|]]
-  * [[en:materialdaten:tribologische_daten|]]
+  * [[en:materialdaten:rheologische_materialdaten|]]
   * [[en:materialdaten:technologische_daten|]]
+  * [[en:materialdaten:tribologische_daten|]]
+  * [[en:materialdaten:zusatzstoffe|]]
   * [[en:materialdaten:molekulargewicht|]]
   * [[en:materialdaten:faserabbau|]]
   * [[en:materialdaten:eingabe_von_mischungen|]]
-  * [[en:materialdaten:polymer-polymer_mischung|]]
-  * [[en:materialdaten:gefuelltes_polymer|]]