pyPRISM.potential.Exponential module¶
-
class
pyPRISM.potential.Exponential.
Exponential
(epsilon, alpha, sigma=None, high_value=1000000.0)[source]¶ Bases:
pyPRISM.potential.Potential.Potential
Exponential attractive interactions
Mathematical Definition
\[U_{\alpha,\beta}(r \geq \sigma_{\alpha,\beta}) = \epsilon_{\alpha,\beta} \exp\left(- \frac{r-\sigma_{\alpha,\beta}}{\alpha}\right)\]\[U_{\alpha,\beta}(r < \sigma_{\alpha,\beta}) = C^{high}\]Variable Definitions
- \(\alpha\)
- Width of exponential attraction
- \(\sigma_{\alpha,\beta}\)
- Contact distance of interactions between sites \(\alpha\) and \(\beta\).
- \(\epsilon_{\alpha,\beta}\)
- Interaction strength between sites \(\alpha\) and \(\beta\).
- \(C^{high}\)
- 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]
Example
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
Domain
object specified inSystem
, then the sigma will effectively be rounded. A warning should be emitted during the construction of aPRISM
object if this occurs.-
__init__
(epsilon, alpha, sigma=None, high_value=1000000.0)[source]¶ Constructor
Parameters: - 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
System
object. - high_value (float, optional) – High value used to approximate an infinite potential due to overlap