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polykin.kinetics¤

TerminationCompositeModel ¤

Composite model for the termination rate coefficient between two radicals.

This model implements the chain-length dependence:

\[ k_t(i,j)=\sqrt{k_t(i,i) k_t(j,j)} \]

with:

\[ k_t(i,i)=\begin{cases} k_t(1,1)i^{-\alpha_S}& \text{if } i \leq i_{crit} \\ k_t(1,1)i_{crit}^{-(\alpha_S-\alpha_L)}i^{-\alpha_L} & \text{if }i>i_{crit} \end{cases} \]

where \(k_t(1,1)\) is the temperature-dependent termination rate coefficient between two monomeric radicals, \(i_{crit}\) is the critical chain length, \(\alpha_S\) is the short-chain exponent, and \(\alpha_L\) is the long-chain exponent.

References

  • Smith, Gregory B., Gregory T. Russell, and Johan PA Heuts. "Termination in dilute-solution free-radical polymerization: a composite model." Macromolecular theory and simulations 12.5 (2003): 299-314.
PARAMETER DESCRIPTION
kt11

Temperature-dependent termination rate coefficient between two monomeric radicals, \(k_t(1,1)\).

TYPE: Arrhenius | Eyring

icrit

Critical chain length, \(i_{crit}\).

TYPE: int

aS

Short-chain exponent, \(\alpha_S\).

TYPE: float DEFAULT: 0.5

aL

Long-chain exponent, \(\alpha_L\).

TYPE: float DEFAULT: 0.2

name

Name.

TYPE: str DEFAULT: ''

Examples:

>>> from polykin.kinetics import TerminationCompositeModel, Arrhenius
>>> kt11 = Arrhenius(1e9, 2e3, T0=298.,
...        symbol='k_t(T,1,1)', unit='L/mol/s', name='kt11 of Y')

>>> ktij = TerminationCompositeModel(kt11, icrit=30, name='ktij of Y')
>>> ktij
name:    ktij of Y
icrit:   30
aS:      0.5
aL:      0.2
kt11:
  name:            kt11 of Y
  symbol:          k_t(T,1,1)
  unit:            L/mol/s
  Trange [K]:      (0.0, inf)
  k0 [L/mol/s]:    1000000000.0
  EaR [K]:         2000.0
  T0 [K]:          298.0

>>> ktij(T=25., i=150, j=200, Tunit='C')
129008375.03821689
Source code in src/polykin/kinetics/cldtermination.py 
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class TerminationCompositeModel(KineticCoefficientCLD):
    r"""Composite model for the termination rate coefficient between two
    radicals.

    This model implements the chain-length dependence:

    $$ k_t(i,j)=\sqrt{k_t(i,i) k_t(j,j)} $$

    with:

    $$ k_t(i,i)=\begin{cases}
    k_t(1,1)i^{-\alpha_S}& \text{if } i \leq i_{crit} \\
    k_t(1,1)i_{crit}^{-(\alpha_S-\alpha_L)}i^{-\alpha_L} & \text{if }i>i_{crit}
    \end{cases} $$

    where $k_t(1,1)$ is the temperature-dependent termination rate coefficient
    between two monomeric radicals, $i_{crit}$ is the critical chain length,
    $\alpha_S$ is the short-chain exponent, and $\alpha_L$ is the long-chain
    exponent.

    **References**

    *   Smith, Gregory B., Gregory T. Russell, and Johan PA Heuts. "Termination
        in dilute-solution free-radical polymerization: a composite model."
        Macromolecular theory and simulations 12.5 (2003): 299-314.

    Parameters
    ----------
    kt11 : Arrhenius | Eyring
        Temperature-dependent termination rate coefficient between two
        monomeric radicals, $k_t(1,1)$.
    icrit : int
        Critical chain length, $i_{crit}$.
    aS : float
        Short-chain exponent, $\alpha_S$.
    aL : float
        Long-chain exponent, $\alpha_L$.
    name : str
        Name.

    Examples
    --------
    >>> from polykin.kinetics import TerminationCompositeModel, Arrhenius
    >>> kt11 = Arrhenius(1e9, 2e3, T0=298.,
    ...        symbol='k_t(T,1,1)', unit='L/mol/s', name='kt11 of Y')

    >>> ktij = TerminationCompositeModel(kt11, icrit=30, name='ktij of Y')
    >>> ktij
    name:    ktij of Y
    icrit:   30
    aS:      0.5
    aL:      0.2
    kt11:
      name:            kt11 of Y
      symbol:          k_t(T,1,1)
      unit:            L/mol/s
      Trange [K]:      (0.0, inf)
      k0 [L/mol/s]:    1000000000.0
      EaR [K]:         2000.0
      T0 [K]:          298.0

    >>> ktij(T=25., i=150, j=200, Tunit='C')
    129008375.03821689
    """

    kt11: Union[Arrhenius, Eyring]
    icrit: int
    aS: float
    aL: float
    symbol: str = 'k_t (i,j)'

    def __init__(self,
                 kt11: Union[Arrhenius, Eyring],
                 icrit: int,
                 aS: float = 0.5,
                 aL: float = 0.2,
                 name: str = ''
                 ) -> None:

        check_type(kt11, (Arrhenius, Eyring), 'k11')
        check_bounds(icrit, 1, 200, 'icrit')
        check_bounds(aS, 0, 1, 'alpha_short')
        check_bounds(aL, 0, 0.5, 'alpha_long')

        self.kt11 = kt11
        self.icrit = icrit
        self.aS = aS
        self.aL = aL
        self.name = name

    def __repr__(self) -> str:
        return custom_repr(self, ('name', 'icrit', 'aS', 'aL', 'kt11'))

    @staticmethod
    def equation(i: Union[int, IntArray],
                 j: Union[int, IntArray],
                 kt11: Union[float, FloatArray],
                 icrit: int,
                 aS: float,
                 aL: float,
                 ) -> Union[float, FloatArray]:
        r"""Composite model chain-length dependence equation.

        Parameters
        ----------
        i : int | IntArray
            Chain length of 1st radical.
        j : int | IntArray
            Chain length of 2nd radical.
        kt11 : float | FloatArray
            Temperature-dependent termination rate coefficient between two
            monomeric radicals, $k_t(1,1)$.
        icrit : int
            Critical chain length, $i_{crit}$.
        aS : float
            Short-chain exponent, $\alpha_S$.
        aL : float
            Long-chain exponent, $\alpha_L$.

        Returns
        -------
        float | FloatArray
            Coefficient value.
        """

        def ktii(i):
            return np.where(i <= icrit,
                            kt11*i**(-aS),
                            kt11*icrit**(-aS+aL)*i**(-aL))

        return sqrt(ktii(i)*ktii(j))

    def __call__(self,
                 T: Union[float, FloatArrayLike],
                 i: Union[int, IntArrayLike],
                 j: Union[int, IntArrayLike],
                 Tunit: Literal['C', 'K'] = 'K'
                 ) -> Union[float, FloatArray]:
        r"""Evaluate kinetic coefficient at given conditions, including unit
        conversion and range check.

        Parameters
        ----------
        T : float | FloatArrayLike
            Temperature.
            Unit = `Tunit`.
        i : int | IntArrayLike
            Chain length of 1st radical.
        j : int | IntArrayLike
            Chain length of 2nd radical.
        Tunit : Literal['C', 'K']
            Temperature unit.

        Returns
        -------
        float | FloatArray
            Coefficient value.
        """
        TK = convert_check_temperature(T, Tunit, self.kt11.Trange)
        if isinstance(i, (list, tuple)):
            i = np.array(i, dtype=np.int32)
        if isinstance(j, (list, tuple)):
            j = np.array(j, dtype=np.int32)
        return self.equation(i, j, self.kt11(TK), self.icrit, self.aS, self.aL)

__call__ ¤

__call__(
    T: Union[float, FloatArrayLike],
    i: Union[int, IntArrayLike],
    j: Union[int, IntArrayLike],
    Tunit: Literal["C", "K"] = "K",
) -> Union[float, FloatArray]

Evaluate kinetic coefficient at given conditions, including unit conversion and range check.

PARAMETER DESCRIPTION
T

Temperature. Unit = Tunit.

TYPE: float | FloatArrayLike

i

Chain length of 1st radical.

TYPE: int | IntArrayLike

j

Chain length of 2nd radical.

TYPE: int | IntArrayLike

Tunit

Temperature unit.

TYPE: Literal['C', 'K'] DEFAULT: 'K'

RETURNS DESCRIPTION
float | FloatArray

Coefficient value.
Source code in src/polykin/kinetics/cldtermination.py 
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def __call__(self,
             T: Union[float, FloatArrayLike],
             i: Union[int, IntArrayLike],
             j: Union[int, IntArrayLike],
             Tunit: Literal['C', 'K'] = 'K'
             ) -> Union[float, FloatArray]:
    r"""Evaluate kinetic coefficient at given conditions, including unit
    conversion and range check.

    Parameters
    ----------
    T : float | FloatArrayLike
        Temperature.
        Unit = `Tunit`.
    i : int | IntArrayLike
        Chain length of 1st radical.
    j : int | IntArrayLike
        Chain length of 2nd radical.
    Tunit : Literal['C', 'K']
        Temperature unit.

    Returns
    -------
    float | FloatArray
        Coefficient value.
    """
    TK = convert_check_temperature(T, Tunit, self.kt11.Trange)
    if isinstance(i, (list, tuple)):
        i = np.array(i, dtype=np.int32)
    if isinstance(j, (list, tuple)):
        j = np.array(j, dtype=np.int32)
    return self.equation(i, j, self.kt11(TK), self.icrit, self.aS, self.aL)

equation staticmethod ¤

equation(
    i: Union[int, IntArray],
    j: Union[int, IntArray],
    kt11: Union[float, FloatArray],
    icrit: int,
    aS: float,
    aL: float,
) -> Union[float, FloatArray]

Composite model chain-length dependence equation.

PARAMETER DESCRIPTION
i

Chain length of 1st radical.

TYPE: int | IntArray

j

Chain length of 2nd radical.

TYPE: int | IntArray

kt11

Temperature-dependent termination rate coefficient between two monomeric radicals, \(k_t(1,1)\).

TYPE: float | FloatArray

icrit

Critical chain length, \(i_{crit}\).

TYPE: int

aS

Short-chain exponent, \(\alpha_S\).

TYPE: float

aL

Long-chain exponent, \(\alpha_L\).

TYPE: float

RETURNS DESCRIPTION
float | FloatArray

Coefficient value.
Source code in src/polykin/kinetics/cldtermination.py 
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@staticmethod
def equation(i: Union[int, IntArray],
             j: Union[int, IntArray],
             kt11: Union[float, FloatArray],
             icrit: int,
             aS: float,
             aL: float,
             ) -> Union[float, FloatArray]:
    r"""Composite model chain-length dependence equation.

    Parameters
    ----------
    i : int | IntArray
        Chain length of 1st radical.
    j : int | IntArray
        Chain length of 2nd radical.
    kt11 : float | FloatArray
        Temperature-dependent termination rate coefficient between two
        monomeric radicals, $k_t(1,1)$.
    icrit : int
        Critical chain length, $i_{crit}$.
    aS : float
        Short-chain exponent, $\alpha_S$.
    aL : float
        Long-chain exponent, $\alpha_L$.

    Returns
    -------
    float | FloatArray
        Coefficient value.
    """

    def ktii(i):
        return np.where(i <= icrit,
                        kt11*i**(-aS),
                        kt11*icrit**(-aS+aL)*i**(-aL))

    return sqrt(ktii(i)*ktii(j))