This analyzer calculates the derivative of free energy with respect to parameter \(c_0 = 1/v \) at fixed united cell, fixed polymer volume fraction, and fixed \( \chi_b \) for AB diblock copolymer system.

See also: ConcentrationDerivative (Class API)

Mathematical Formula

\[ \frac{\partial F}{\partial c_0} = -\frac{\partial \ln Z}{\partial c_0} = \left\langle \frac{\partial H}{\partial \chi_b} \right\rangle + \frac{\partial \ln N}{\partial c_0} \]

\[ \frac{\partial H}{\partial c_0} = \left\langle \frac{H}{c_0} \right\rangle \]

\[ \frac{\partial \ln N}{\partial \chi_b} = - \frac{\text{MeshSize}}{2 c_0} \]

where \( v \) denote the monomer reference volume and \(\text{MeshSize} \) denotes the total number of mesh size.

Parameter File

The full parameter file format, including all optional parameters, is shown below:

ConcentrationDerivative{
  interval           int
  outputFileName     string
  hasAverage*        bool     (default true)
}

Meanings of the parameters are described briefly below:

Label	Description
interval	number of steps between data samples
outputFileName	name of output file
hasAverage	whether the average and error analysis are needed?

Output

During the simulation, \( c_0 \) and corresponding \( \frac{\partial F}{\partial c_0} \) are output to the file {outputFileName} every interval simulation steps.

At the end of the simulation, if hasAverage is true:

average info and error analysis are output to {outputFileName}.ave
error analysis info are output to {outputFileName}.aer