Shortcut: FERRONEMATIC_ORDER

Module	liquid_crystal
Description	Usage
Calculate the ferronematic order parameter.
output value	type
the modulus of the average vector	scalar

Details and examples

Calculate the ferronematic order parameter.

The ferronematic order parameter P depends on the relative orientations of the molecular axes. If the axes all point into the same direction, giving rise to a net polarization if the molecules have permanent dipole moments, P is close to 1. If the molecular axes are oriented isotropically or are aligned antiparallel so that there is no net polarization, P is close 0.

The nematic and ferronematic order parameters can be used to distinguish the isotropic, nematic and ferronematic phases of liquid crystals.

$P$ is length of the average of the molecular axes ( $\hat{u}_i$ for $i=1,\ldots,N$ ) $P = \vert \frac{1}{N} \sum_{i=1}^N \hat{u}_i \vert$ Since the molecular axes are unit vectors, P ranges from a minimum of 0 to a maximum of 1.

By adding a bias to the ferronematic order parameter, one can drive a liquid crystal from the isotropic to the ferronematic phase.

The axis of a rod-like molecule is defined as the distance vector between two atoms, it points from the tail atom to the head atom.

Click on the labels of the actions for more information on what each action computes

# Assume there are three molecules with 20 atoms each.
# In the first molecule the molecular axis vector points from atom 1 to atom 20,
# in the second molecule it points from atom 21 to atom 40
# and in the third from atom 41 to atom 60.
# The ferronematic order parameter for the three molecules is computed as
PThe FERRONEMATIC_ORDER action with label P calculates the following quantities: Quantity    Type    Description  
P scalar the modulus of the average vector: FERRONEMATIC_ORDERCalculate the ferronematic order parameter. This action is a shortcut. More details MOLECULE_STARTSThe atoms where the molecular axis starts=1,21,41 MOLECULE_ENDSThe atoms where the molecular axis ends=20,40,60
# PLUMED interprets the command:
# P: FERRONEMATIC_ORDER MOLECULE_STARTS=1,21,41 MOLECULE_ENDS=20,40,60
# as follows (Click the red comment above to revert to the short version of the input):
P_dvalsThe DISTANCE action with label P_dvals calculates the following quantities: Quantity    Type    Description  
P_dvals vector the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,20 ATOMS2the pair of atom that we are calculating the distance between=21,40 ATOMS3the pair of atom that we are calculating the distance between=41,60
P_dvecsThe DISTANCE action with label P_dvecs calculates the following quantities: Quantity    Type    Description  
P_dvecs.x vector the x-component of the vector connecting the two atoms
P_dvecs.y vector the y-component of the vector connecting the two atoms
P_dvecs.z vector the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details COMPONENTS calculate the x, y and z components of the distance separately and store them as label  ATOMS1the pair of atom that we are calculating the distance between=1,20 ATOMS2the pair of atom that we are calculating the distance between=21,40 ATOMS3the pair of atom that we are calculating the distance between=41,60
P_duxThe CUSTOM action with label P_dux calculates the following quantities: Quantity    Type    Description  
P_dux vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=P_dvecs.x,P_dvals FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
P_duyThe CUSTOM action with label P_duy calculates the following quantities: Quantity    Type    Description  
P_duy vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=P_dvecs.y,P_dvals FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
P_duzThe CUSTOM action with label P_duz calculates the following quantities: Quantity    Type    Description  
P_duz vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=P_dvecs.z,P_dvals FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
P_muxThe MEAN action with label P_mux calculates the following quantities: Quantity    Type    Description  
P_mux scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=P_dux PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
P_muyThe MEAN action with label P_muy calculates the following quantities: Quantity    Type    Description  
P_muy scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=P_duy PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
P_muzThe MEAN action with label P_muz calculates the following quantities: Quantity    Type    Description  
P_muz scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=P_duz PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PThe CUSTOM action with label P calculates the following quantities: Quantity    Type    Description  
P scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=P_mux,P_muy,P_muz FUNCthe function you wish to evaluate=sqrt(x*x+y*y+z*z) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details FILEthe name of the file on which to output these quantities=colvar ARGthe labels of the values that you would like to print to the file=P

# Add a bias to the ferronematic order parameter P.
The PRINT action with label  calculates somethingBIASVALUETakes the value of one variable and use it as a bias More details ARGthe labels of the scalar/vector arguments whose values will be used as a bias on the system=P

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
MOLECULE_STARTS	atoms	The atoms where the molecular axis starts
MOLECULE_ENDS	atoms	The atoms where the molecular axis ends

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
MOLECULE_STARTS	input	none	The atoms where the molecular axis starts
MOLECULE_ENDS	input	none	The atoms where the molecular axis ends

Quantity	Type	Description
P	scalar	the modulus of the average vector