Force fields in colloidal systems

Force fields in colloidal systems

Forces

class pystokes.forceFields.Forces

Computes forces in a system of colloidal particles

Methods in the Forces class take input,
  • arrays of positions, forces
  • parameters for a given potential

The array of forces is then update by each method.

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Parameters:particles (int) – Number of particles (Np)
harmonicConfinement()

Forces on colloids in a harmonic trap

lennardJones()

The standard Lennard-Jones potential truncated at the minimum (aslo called WCA potential)

We choose phi(r) = lje/12 (rr^12 - 2*rr^6 ) + lje/12, as the standard WCA potential. ljr: minimum of the LJ potential and rr=ljr/r.

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • lje (float) – Strength of the LJ
  • ljr (float) – Range of the LJ
lennardJonesWall()

The standard Lennard-Jones potential truncated at the minimum (aslo called WCA potential)

We choose phi(r) = lje/12 (rr^12 - 2*rr^6 ) + lje/12, as the standard WCA potential. ljr: minimum of the LJ potential and rr=ljr/r.

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • lje (float) – Strength of the LJ
  • ljr (float) – Range of the LJ
lennardJonesXWall()

The standard Lennard-Jones potential truncated at the minimum (aslo called WCA potential)

We choose phi(r) = lje/12 (rr^12 - 2*rr^6 ) + lje/12, as the standard WCA potential. ljr: minimum of the LJ potential and rr=ljr/r. This force is only in z-direction due to wall at x=0

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • lje (float) – Strength of the LJ
  • ljr (float) – Range of the LJ
membraneBound()

Force on colloids in membraneSurface

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • r0 (np.array) – An array of trap centers An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • cn (float) – Stiffness of the trap
membraneConfinement()

Force on colloids in membraneSurface

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • r0 (np.array) – An array of trap centers An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • cn (float) – Stiffness of the trap
membraneSurface()

Force on colloids connected as a membrane

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • bondLength (float) – The size of natural spring
  • springModulus (float) – Stiffness of the trap
  • bendModulus (float) – Bending cost
multiRingpolymers()

Force on colloids connected by a spring in a ring polymer

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Parameters:
  • r (np.array) – An array of positions
  • F (np.array) – An array of forces An array of size 3*Np, An array of size 3*Np,
  • bondLength (float) – The size of natural spring
  • springModulus (float) – Stiffness of the trap
multipolymers()

Force on colloids in many polymers connected by a spring

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Parameters:
  • r (np.array) – An array of positions
  • F (np.array) – An array of forces An array of size 3*Np, An array of size 3*Np,
  • bondLength (float) – The size of natural spring
  • springModulus (float) – Stiffness of the trap
opticalConfinement()

Force on colloids in optical traps of varying stiffnesses

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • r0 (np.array) – An array of trap centers An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • k (float) – Stiffness of the trap
sedimentation()

Force on colloids in sedimentation

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Parameters:
  • r (np.array) – An array of positions An array of size 3*Np,
  • F (np.array) – An array of forces An array of size 3*Np,
  • g (float) – Gravity
softSpringWall()

F = -k(r-rmin)

spring()

Force on colloids connected by a spring in a single polymer

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Parameters:
  • r (np.array) – An array of positions
  • F (np.array) – An array of forces An array of size 3*Np, An array of size 3*Np,
  • bondLength (float) – The size of natural spring
  • springModulus (float) – Stiffness of the trap

Torques

class pystokes.forceFields.Torques

Computes torques in a system of colloidal particles

Methods in the Torques class take input,
  • arrays of positions, Torques
  • parameters for a given potential

The array of torques is then update by each method.

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Parameters:particles (int) – Number of particles (Np)
bottomHeaviness()

Torque due to bottom-heaviness

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Parameters:
  • p (np.array) – An array of Orientations An array of size 3*Np,
  • F (np.array) – An array of Torques An array of size 3*Np,
  • bh (float) – bottomHeaviness