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TABLE OF CONTENTS

• module rpa_mod
• procedure S_block
• procedure S_chain
• procedure S_ideal
• procedure S_inc
• procedure S_rpa

rpa_mod

MODULE

     rpa_mod

PURPOSE

     Provides procedures to calculate response/correlation functions 
     for a homogenous polymer mixture at a specified wavenumber

SOURCE

module rpa_mod
use const_mod
use chemistry_mod
implicit none

private
public :: S_block   ! correlation function matrix for one chain
public :: S_chain   ! correlation function matrix for one chain
public :: S_ideal   ! ideal gas correlation function matrix
public :: S_inc     ! Incompressible correlation function matrix, chi=0
public :: S_rpa     ! RPA correlation function matrix, arbitrary chi

S_block

FUNCTION

     S_block(i_chain, i_block, j_block, q)

PURPOSE

     Return dimensionless cross correlation function for blocks
     i_block and j_block on a chain of species i_chain at a single
     wavenumber q
 
     Convention: S_{ij}(k=0) = N_i N_j, where N_i is the number of i
     monomers in the chain of interest.
 

ARGUMENTS

     i_chain  - chain species index
     i_block  - block index
     j_block  - block index
     q        - wavenumber

SOURCE

   real(long) function S_block(i_chain, i_block, j_block, q)
   integer, intent(IN)     :: i_chain             ! chain species index
   integer, intent(IN)     :: i_block, j_block    ! block indices
   real(long), intent(IN)  :: q                   ! wavenumber

S_chain

SUBROUTINE

     S_chain(i_chain, q, S)

PURPOSE

     Calculate dimensionless single-chain correlation function.
     Use convention such that S_{a,ij}(k=0) = N_{ai}N_{aj} 

ARGUMENTS

     i_chain  - chain species index
     q        - wavenumber
     S(:,:)   - Correlation matrix (N_monomer x N_monomer)

SOURCE

   subroutine S_chain(i_chain, q, S)
   integer, intent(IN)     :: i_chain ! chain species index
   real(long), intent(IN)  :: q       ! wavenumber
   real(long), intent(OUT) :: S(:,:)  ! correlation function

S_ideal

SUBROUTINE

     S_ideal

PURPOSE

     Calculate correlation function for an ideal gas with compositon
     specified in chemistry. Includes contributions of all chain
     and solvent species.
      
     Convention: Fuction S_{ij}(k) is the dimensionless function:
 
     S_{ij}(k) = v \int dr e^{ik.r} <\delta c_{i}(r)\delta c_{j}(0)>
 
     where v is monomer reference volume.
 

ARGUMENTS

     q      - wavenumber
     S(:,:) - Correlation matrix (N_monomer x N_monomer)

SOURCE

   subroutine S_ideal(q, S, N)
   real(long), intent(IN)  :: q       ! wavenumber
   real(long), intent(OUT) :: S(:,:)  ! correlation function 
                                      ! (N_monomer,N_monomer)
   integer, intent(IN)     :: N       ! physical dimension of S

S_inc

SUBROUTINE

     S_inc

PURPOSE

     Calculates RPA correlation function for an incompressible liquid
     with the composition specified in chemistry, but chi_{ij}=0.

COMMENT

     Uses the convention:
     S_{ij}(k) = v \int dr e^{ik.r} <\delta c_{i}(r)\delta c_{j}(0)>
     The resulting matrix is singular, due to incompressibility.

ARGUMENTS

     q      wavenumber
     S(:,:) correlation matrix (N_monomer x N_monomer)
     N      physical dimensions of matrix S

SOURCE

   subroutine S_inc(q, S, N)
   real(long), intent(IN)  :: q       ! wavenumber
   real(long), intent(OUT) :: S(N,N)  ! correlation function matrix
                                      ! (N_monomer,N_monomer)
   integer, intent(IN)     :: N       ! physical dimension of S

S_rpa

SUBROUTINE

     S_rpa

PURPOSE

     Return RPA correlation function for incompressible mixture
     specified in chemistry module. 

COMMENT

     Uses the convention:
     S_{ij}(k) = v \int dr e^{ik.r} <\delta c_{i}(r)\delta c_{j}(0)>
     The resulting matrix is singular, due to incompressibility

ARGUMENTS

     q      wavenumber
     S(:,:) correlation matrix (N_monomer x N_monomer)
     N      physical dimensions of matrix S

SOURCE

   subroutine S_rpa(q, S, N)
   real(long), intent(IN)  :: q       ! wavenumber
   real(long), intent(OUT) :: S(:,:)  ! correlation function 
                                      ! (N_monomer,N_monomer)
   integer, intent(IN)     :: N       ! physical dimension of S