Skip to content

polykin.kinetics.emulsion¤

kdesorption_Asua ¤

kdesorption_Asua(
    kfmp: float,
    kpp: float,
    Mp: float,
    K0: float,
    beta: float,
) -> float

Radical desorption coefficient according to Asua's model.

The desorption coefficient is given by:

\[ k_{des} = k^p_{fm}[M^p] \left( \frac{K_0}{\beta K_0 + k^p_p [M^p]} \right) \]

where \(k^p_{fm}\) is the transfer-to-monomer rate coefficient in the particle phase, \(k^p_p\) is the propagation rate coefficient in the particle phase, \([M^p]\) is the monomer concentration in the particle phase, \(K_0\) is the monomeric radical desorption rate coefficient, and \(\beta\) is the probability that the desorbed monomeric radical reacts in the aqueous phase by propagation or termination .

Note

Nomura and Harada's model can be seen as a particular case of Asua's model where \(\beta=\bar{n}\).

References

  • Asua, J.M., Sudol, E.D. and El-Aasser, M.S. (1989), Radical desorption in emulsion polymerization. J. Polym. Sci. A Polym. Chem., 27: 3903-3913.
  • Nomura, M. and Harada, M. (1981), Rate coefficient for radical desorption in emulsion polymerization. J. Appl. Polym. Sci., 26: 17-26.
PARAMETER DESCRIPTION
kfmp

Transfer-to-monomer rate coefficient in the particle [L/(mol·s)].

TYPE: float

kpp

Propagation rate coefficient in the particle phase [L/(mol·s)].

TYPE: float

Mp

Monomer concentration in the particle phase [mol/L].

TYPE: float

K0

Monomeric radical desorption coefficient [s⁻¹].

TYPE: float

beta

Probability that the desorbed monomeric radical reacts in the aqueous phase by propagation or termination.

TYPE: float

RETURNS DESCRIPTION
float

Radical desorption rate coefficient [s⁻¹].
See Also

Examples:

Evaluate the radical desorption coefficient for a system with a transfer-to-monomer rate coefficient of 1e-3 L/(mol·s), a propagation rate coefficient of 1e2 L/(mol·s), a monomer concentration in the particle phase of 10 mol/L, a monomeric radical desorption coefficient of 1e3 s⁻¹, and a probability of 20% that the desorbed monomeric radical reacts in the aqueous phase.

>>> from polykin.kinetics import kdesorption_Asua
>>> kdes = kdesorption_Asua(kfmp=1e-3, kpp=1e2, Mp=10, K0=1e3, beta=0.20)
>>> print(f"kdes = {kdes:.2e} s⁻¹")
kdes = 8.33e-03 s⁻¹
Source code in src/polykin/kinetics/emulsion/desorption.py 
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
def kdesorption_Asua(
    kfmp: float,
    kpp: float,
    Mp: float,
    K0: float,
    beta: float,
) -> float:
    r"""Radical desorption coefficient according to Asua's model.

    The desorption coefficient is given by:

    $$ k_{des} = k^p_{fm}[M^p] \left( \frac{K_0}{\beta K_0 + k^p_p [M^p]} \right) $$

    where $k^p_{fm}$ is the transfer-to-monomer rate coefficient in the particle phase,
    $k^p_p$ is the propagation rate coefficient in the particle phase, $[M^p]$ is the
    monomer concentration in the particle phase, $K_0$ is the monomeric radical desorption
    rate coefficient, and $\beta$ is the probability that the desorbed monomeric radical
    reacts in the aqueous phase by propagation or termination .

    !!! note

        Nomura and Harada's model can be seen as a particular case of Asua's model where
        $\beta=\bar{n}$.


    **References**

    *   Asua, J.M., Sudol, E.D. and El-Aasser, M.S. (1989), Radical desorption in emulsion
        polymerization. J. Polym. Sci. A Polym. Chem., 27: 3903-3913.
    *   Nomura, M. and Harada, M. (1981), Rate coefficient for radical desorption in
        emulsion polymerization. J. Appl. Polym. Sci., 26: 17-26.

    Parameters
    ----------
    kfmp : float
        Transfer-to-monomer rate coefficient in the particle [L/(mol·s)].
    kpp : float
        Propagation rate coefficient in the particle phase [L/(mol·s)].
    Mp : float
        Monomer concentration in the particle phase [mol/L].
    K0 : float
        Monomeric radical desorption coefficient [s⁻¹].
    beta : float
        Probability that the desorbed monomeric radical reacts in the aqueous phase by
        propagation or termination.

    Returns
    -------
    float
        Radical desorption rate coefficient [s⁻¹].

    See Also
    --------
    * [`K0_Nomura`](K0_Nomura.md): Associated method for $K_0$.

    Examples
    --------
    Evaluate the radical desorption coefficient for a system with a transfer-to-monomer
    rate coefficient of 1e-3 L/(mol·s), a propagation rate coefficient of 1e2 L/(mol·s),
    a monomer concentration in the particle phase of 10 mol/L, a monomeric radical
    desorption coefficient of 1e3 s⁻¹, and a probability of 20% that the desorbed
    monomeric radical reacts in the aqueous phase.

    >>> from polykin.kinetics import kdesorption_Asua
    >>> kdes = kdesorption_Asua(kfmp=1e-3, kpp=1e2, Mp=10, K0=1e3, beta=0.20)
    >>> print(f"kdes = {kdes:.2e} s⁻¹")
    kdes = 8.33e-03 s⁻¹
    """
    return (kfmp * Mp * K0) / (beta * K0 + kpp * Mp)