Field File - 1D Fields (pscf_fd)

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The pscf_fd program is designed for problems in which fields depend on only a single variable, and uses a a regular one-dimensional mesh to discretize the solutions. This program uses a simple file format for w and c fields that contains a header and data section.

Header: The header provides values for

• nx , the number of number of grid points
• nm , the number of monomer types.

Data section: Each row in the data section starts with the index of a grid point, followed by values of all fields at that grid point. Each column after the first gives the values of the field associated with a specific monomer type, listed in order of increasing monomer type index. The first row (index 0) contains field values at the lower bound of the coordinate (xmin), while the last row (index nx-1) contains values at the upper bound (xmax).

Example:

An example of a w (chemical potential) file is shown below. A large part of the data section has beem omitted, as indicated by vertical dots.

nx     401
nm     2
    0  -5.96942303323e+00   6.85191697162e-11
    1  -5.96942323364e+00  -5.38187402422e-07
    2  -5.96942383533e+00  -2.15872253218e-06
    3  -5.96942483954e+00  -4.87886942524e-06
    4  -5.96942624815e+00  -8.72758497848e-06
    5  -5.96942806338e+00  -1.37455598333e-05
    6  -5.96943028740e+00  -1.99853784445e-05
    7  -5.96943292171e+00  -2.75117227864e-05
    8  -5.96943596656e+00  -3.64016335715e-05
    9  -5.96943942006e+00  -4.67448371504e-05
   10  -5.96944327724e+00  -5.86441323650e-05
   11  -5.96944752894e+00  -7.22158673119e-05
              .                  .
              .                  .
              .                  .
  390  -5.96944327722e+00  -5.86440492859e-05
  391  -5.96943942004e+00  -4.67447613751e-05
  392  -5.96943596654e+00  -3.64015646109e-05
  393  -5.96943292169e+00  -2.75116589759e-05
  394  -5.96943028738e+00  -1.99853197974e-05
  395  -5.96942806337e+00  -1.37455050264e-05
  396  -5.96942624813e+00  -8.72753318994e-06
  397  -5.96942483952e+00  -4.87882055732e-06
  398  -5.96942383532e+00  -2.15867540140e-06
  399  -5.96942323357e+00  -5.38083020152e-07
  400  -5.96942303333e+00   0.00000000000e+00

Boundary Conditions:

The pscf_fd program solves the underlying modified diffusion equation using a boundary condition that requires the 1D spatial derivative of the propagator to vanish at both endpoints.

An additional constraint is applied when a problem is solved in canonical ensemble, in which values of volume fraction phi (rather than chemical potential mu) are specified for all polymer and solvent species. In this case, the value of the chemical potential is taken to zero for the last monomer type at the last grid point, by convention. This convention is why a value of 0.0000 is shown for the last column of the last row in the above example.

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