polykin.kinetics.emulsion

kentry_collision

kentry_collision(r: float, C: float) -> float

Radical entry coefficient assuming irreversible collision-controlled entry.

The entry coefficient is given by:

\[ k_e = 4 \pi r^2 C N_A \]

where \(r\) is the particle radius, \(C\) is the collision coefficient, and \(N_A\) is Avogadro's number.

References

• Gardon, J. L. Emulsion Polymerization. I. Recalculation and Extension of the Smith-Ewart Theory. J. Polym. Sci., Part A-1: Polym. Chem. 1968, 6, 623-641.

PARAMETER	DESCRIPTION
r	Particle radius [m]. TYPE: float
C	Collision coefficient [m/s]. TYPE: float

RETURNS	DESCRIPTION
float	Radical entry coefficient [m³/(mol·s)].

Examples:

Evaluate the radical entry coefficient for a particle radius of 100 nm and a collision coefficient of 1e-2 m/s.

>>> from polykin.kinetics import kentry_collision
>>> ke = kentry_collision(r=100e-9, C=1e-2)
>>> print(f"ke = {ke:.2e} m³/(mol·s)")
ke = 7.57e+08 m³/(mol·s)

Source code in src/polykin/kinetics/emulsion/entry.py

def kentry_collision(
    r: float,
    C: float,
) -> float:
    r"""Radical entry coefficient assuming irreversible collision-controlled entry.

    The entry coefficient is given by:

    $$ k_e = 4 \pi r^2 C N_A $$

    where $r$ is the particle radius, $C$ is the collision coefficient, and $N_A$ is
    Avogadro's number.

    **References**

    *   Gardon, J. L. Emulsion Polymerization. I. Recalculation and Extension of the
        Smith-Ewart Theory. J. Polym. Sci., Part A-1: Polym. Chem. 1968, 6, 623-641.

    Parameters
    ----------
    r : float
        Particle radius [m].
    C : float
        Collision coefficient [m/s].

    Returns
    -------
    float
        Radical entry coefficient [m³/(mol·s)].

    Examples
    --------
    Evaluate the radical entry coefficient for a particle radius of 100 nm and a collision
    coefficient of 1e-2 m/s.
    >>> from polykin.kinetics import kentry_collision
    >>> ke = kentry_collision(r=100e-9, C=1e-2)
    >>> print(f"ke = {ke:.2e} m³/(mol·s)")
    ke = 7.57e+08 m³/(mol·s)
    """
    return 4 * pi * (r**2) * C * NA