add Flory_Af

HugoMVale · Feb 25, 2024 · d6fc753 · d6fc753
1 parent d19fb0a
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diff --git a/docs/reference/stepgrowth/solutions.md b/docs/reference/stepgrowth/solutions.md
@@ -1,17 +1,18 @@
 # Solutions (polykin.stepgrowth)
 
-| Equation                                                 | Case                                                            |
-|----------------------------------------------------------|-----------------------------------------------------------------|
-| [`Case_1`](#polykin.stepgrowth.solutions.Case_1)         | AA  + BB                                                        |
-| [`Case_3`](#polykin.stepgrowth.solutions.Case_3)         | AA + BB'                                                        |
-| [`Case_5`](#polykin.stepgrowth.solutions.Case_5)         | AA + BB + B'                                                    |
-| [`Case_6`](#polykin.stepgrowth.solutions.Case_6)         | AA + A'B                                                        |
-| [`Case_7`](#polykin.stepgrowth.solutions.Case_7)         | AB + A'B'                                                       |
-| [`Case_8`](#polykin.stepgrowth.solutions.Case_8)         | AA + BB + B'B'                                                  |
-| [`Case_9`](#polykin.stepgrowth.solutions.Case_9)         | AA + A'A' + BB + B'B'                                           |
-| [`Case_10`](#polykin.stepgrowth.solutions.Case_10)       | AA + BB' + B''B''                                               |
-| [`Case_11`](#polykin.stepgrowth.solutions.Case_11)       | AA + A'B' + BB                                                  |
-| [`Stockmayer`](#polykin.stepgrowth.solutions.Stockmayer) | A + A$_2$ + A$_3$ + A$_4$ + ... + B + B$_2$ + B$_3$ + B$_4$ ... |
+| Equation                                                 | Case                                                              | $M_n$  | $M_w$ | $M_z$ |
+|----------------------------------------------------------|-------------------------------------------------------------------|--------|-------|-------|
+| [`Case_1`](#polykin.stepgrowth.solutions.Case_1)         | AA  + BB                                                          | ✓      | ✓    |       |
+| [`Case_3`](#polykin.stepgrowth.solutions.Case_3)         | AA + BB'                                                          | ✓      | ✓    |       |
+| [`Case_5`](#polykin.stepgrowth.solutions.Case_5)         | AA + BB + B'                                                      | ✓      |       |       |
+| [`Case_6`](#polykin.stepgrowth.solutions.Case_6)         | AA + A'B                                                          | ✓      |       |       |
+| [`Case_7`](#polykin.stepgrowth.solutions.Case_7)         | AB + A'B'                                                         | ✓      |       |       |
+| [`Case_8`](#polykin.stepgrowth.solutions.Case_8)         | AA + BB + B'B'                                                    | ✓      |       |       |
+| [`Case_9`](#polykin.stepgrowth.solutions.Case_9)         | AA + A'A' + BB + B'B'                                             | ✓      |       |       |
+| [`Case_10`](#polykin.stepgrowth.solutions.Case_10)       | AA + BB' + B''B''                                                 | ✓      |       |       |
+| [`Case_11`](#polykin.stepgrowth.solutions.Case_11)       | AA + A'B' + BB                                                    | ✓      |       |       |
+| [`Flory_Af`](#polykin.stepgrowth.solutions.Flory_Af)     | A$_f$                                                             | ✓      | ✓    | ✓     |
+| [`Stockmayer`](#polykin.stepgrowth.solutions.Stockmayer) | A + A$_2$ + A$_3$ + ... + A$_f$ + B + B$_2$ + B$_3$ + ... + B$_g$ | ✓      | ✓    |      |
 
 ::: polykin.stepgrowth.solutions
     options:
@@ -25,4 +26,5 @@
             - Case_9
             - Case_10
             - Case_11
+            - Flory_Af
             - Stockmayer
diff --git a/src/polykin/stepgrowth/solutions.py b/src/polykin/stepgrowth/solutions.py
@@ -7,7 +7,8 @@
 import numpy as np
 from numpy import dot
 
-from polykin.utils.types import FloatArray, FloatArrayLike, FloatVectorLike
+from polykin.utils.types import FloatArray, FloatArrayLike, FloatVectorLike, \
+    IntVectorLike
 
 __all__ = ['Case_1',
            'Case_3',
@@ -659,8 +660,8 @@ def Case_11(pB: Union[float, FloatArrayLike],
 
 def Stockmayer(A: FloatVectorLike,
                B: FloatVectorLike,
-               f: FloatVectorLike,
-               g: FloatVectorLike,
+               f: IntVectorLike,
+               g: IntVectorLike,
                MA: FloatVectorLike,
                MB: FloatVectorLike,
                pB: Union[float, FloatArrayLike]
@@ -698,9 +699,9 @@ def Stockmayer(A: FloatVectorLike,
         Vector (N) with relative mole amounts of A monomers.
     B : FloatVectorLike
         Vector (M) with relative mole amounts of B monomers.
-    f : FloatVectorLike
+    f : IntVectorLike
         Vector (N) with functionality of A monomers.
-    g : FloatVectorLike
+    g : IntVectorLike
         Vector (M) with functionality of B monomers.
     MA : FloatVectorLike
         Vector (N) with molar mass of reacted A monomers.
@@ -759,3 +760,49 @@ def Stockmayer(A: FloatVectorLike,
           (1 - pA*pB*(fe - 1)*(ge - 1)))/(pB*(sMA/sfA) + pA*(sMB/sgB))
 
     return (Mn, Mw)
+
+
+def Flory_Af(f: int,
+             MA: float,
+             p: Union[float, FloatArrayLike]
+             ) -> tuple[Union[float, FloatArray],
+                        Union[float, FloatArray],
+                        Union[float, FloatArray]]:
+    r"""Flory's analytical solution for the hopolymerization of an Af monomer.
+
+    The expressions for the number-, mass-, and z-average molar masses are:
+
+    \begin{aligned}
+    M_n &= M_{A_f}\frac{1}{1 - (f/2)p} \\
+    M_w &= M_{A_f}\frac{1 + p}{1 - (f-1)p} \\
+    M_z &= M_{A_f}\frac{(1 + p)^3 - f(3 + p)p^2}{(1 + p)[1 - (f-1)p]^2}
+    \end{aligned}
+
+    **References**
+
+    *   P. J. Flory, Molecular Size Distribution in Three Dimensional
+        Polymers. I. Gelation, J. Am. Chem. Soc. 1941, 63, 11, 3083.
+    *   M. Gordon, Proc. R. Soc. London, Ser. A, 1962, 268, 240.
+
+    Parameters
+    ----------
+    f : int
+        Functionality.
+    MA : float
+        Molar mass of reacted Af monomer.
+    p : float | FloatArrayLike
+        Conversion of A groups. 
+
+    Returns
+    -------
+    tuple[float | FloatArray, ...]
+        Tuple of molar mass averages, ($M_n$, $M_w$, $M_z$).
+    """
+
+    p = np.asarray(p)
+
+    Mn = MA/(1 - (f/2)*p)
+    Mw = MA*(1 + p)/(1 - p*(f - 1))
+    Mz = MA*((1 + p)**3 - (3 + p)*f*p**2)/((1 + p)*(1 - p*(f-1))**2)
+
+    return (Mn, Mw, Mz)
diff --git a/tests/stepgrowth/test_solutions.py b/tests/stepgrowth/test_solutions.py
@@ -172,10 +172,10 @@ def test_StockMayer():
     pB = 0.998
     r_BB_AA = 0.98
     A = [1.]
-    f = [2.]
+    f = [2]
     MA = [MAA]
     B = [r_BB_AA]
-    g = [2.]
+    g = [2]
     MB = [MBB]
     Mn0, Mw0 = Case_1(pB, r_BB_AA, MAA, MBB)
     Mn, Mw = Stockmayer(A, B, f, g, MA, MB, pB)
@@ -187,10 +187,10 @@ def test_StockMayer():
     pB = 0.978
     r_BC_AA = 0.95
     A = [1.]
-    f = [2.]
+    f = [2]
     MA = [MAA]
     B = [r_BC_AA]
-    g = [1.]
+    g = [1]
     MB = [MBC]
     Mn0, Mw0 = Case_3(pB, 0, r_BC_AA, MAA, MBC)
     Mn, Mw = Stockmayer(A, B, f, g, MA, MB, pB)