#!python
from __future__ import division,print_function
from pyPRISM.potential.Potential import Potential
import numpy as np
[docs]class Exponential(Potential):
r'''Exponential attractive interactions
**Mathematical Definition**
.. math::
U_{\alpha,\beta}(r \geq \sigma_{\alpha,\beta}) = \epsilon_{\alpha,\beta} \exp\left(- \frac{r-\sigma_{\alpha,\beta}}{\alpha}\right)
.. math::
U_{\alpha,\beta}(r < \sigma_{\alpha,\beta}) = C^{high}
**Variable Definitions**
:math:`\alpha`
Width of exponential attraction
:math:`\sigma_{\alpha,\beta}`
Contact distance of interactions between sites
:math:`\alpha` and :math:`\beta`.
:math:`\epsilon_{\alpha,\beta}`
Interaction strength between sites
:math:`\alpha` and :math:`\beta`.
:math:`C^{high}`
High value used to approximate an infinite potential due to overlap
**Description**
This potential models an exponential-like attraction between sites with
a specified site size and contact distance. For example, in Reference
[1] this potential is used to model the attraction between a
nanoparticle and monomers of a polymer chain.
References
----------
#. Hooper, J.B. and K.S. Schweizer, Theory of phase separation in polymer
nanocomposites. Macromolecules, 2006. 39(15): p. 5133-5142.
[`link <https://doi.org/10.1021/ma060577m>`__]
Example
-------
.. code-block:: python
import pyPRISM
#Define a PRISM system and set the A-B interaction potential
sys = pyPRISM.System(['A','B'],kT=1.0)
sys.domain = pyPRISM.Domain(dr=0.1,length=1024)
sys.potential['A','B'] = pyPRISM.potential.Exponential(epsilon=1.0,sigma=8.0,alpha=0.5,high_value=10**6)
.. warning::
If sigma is specified such that it does not fall on the solution grid
of the :class:`~pyPRISM.core.Domain.Domain` object specified in
:class:`~pyPRISM.core.System.System`, then the sigma will effectively
be rounded. A warning should be emitted during the construction of a
:class:`~pyPRISM.core.PRISM.PRISM` object if this occurs.
'''
[docs] def __init__(self,epsilon,alpha,sigma=None,high_value=1e6):
r''' Constructor
Arguments
---------
epsilon: float
Strength of attraction
alpha: float
Range of attraction
sigma: float, *optional*
Contact distance. If not specified, sigma will be calculated from
the diameters specified in the :class:`~pyPRISM.core.System.System`
object.
high_value: float, *optional*
High value used to approximate an infinite potential due to overlap
'''
self.epsilon = epsilon
self.sigma = sigma
self.alpha = alpha
self.high_value = high_value
self.funk = lambda r,sigma: - epsilon * np.exp(-(r-sigma)/(alpha))
def __repr__(self):
return '<Potential: Exponential>'
[docs] def calculate(self,r):
r'''Calculate the value of the potential
Attributes
----------
r: float np.ndarray
Array of pair distances at which to calculate potential values
'''
assert (self.sigma is not None), 'Sigma must be set before evaluating potential!'
magnitude = self.funk(r,self.sigma)
magnitude = np.where(r>self.sigma,magnitude,self.high_value)
return magnitude