Phase Behaviors of Block Copolymers - Part 3: Macrophase Separation

import Pkg
Pkg.activate(".")

using Polymer
using Scattering
using Polyorder
using PhaseDiagram
using PolymerArchitectureMakie
using CairoMakie
using LaTeXStrings

  Activating project at `~/SynologyDrive/Develop/Polyorder.jl/docs/tutorial`

# Suppressing displaying source code file location for @info
using Logging
global_logger(ConsoleLogger())

ConsoleLogger(IJulia.IJuliaStdio{Base.PipeEndpoint}(IOContext(Base.PipeEndpoint(RawFD(49) open, 0 bytes waiting))), ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (3, 3, 142704586847)), Info, Base.CoreLogging.default_metafmt, true, 0, Dict{Any, Int64}())

include("common.jl")

plot_density (generic function with 3 methods)

Macorphase separation may happen when there are more than one component in the polymer system. Moreover, macrophase separation and microphase separation may happen simultaneously when there are least one block copolymer component in the polymer system.

PhaseDiagram.jl provides the function macrophase to compute the phase coexistence point.

DIS-DIS coexistence

First, create an SCFT model. Note that for DIS calculations, only polymer system is imoportant because FH theory is used to calculate the free energy and the chemical potential.

The polymer system is a AB/A binary blend with a symmetric AB diblock copolymer and the length of homopolymer α=0.5, χN=20.0.

model_dis_dis = let
    uc = UnitCell(1.0)
    lat = BravaisLattice(uc)
    system = AB_A_system()
    # Lattice and ds are irrelavent here, because we only interested in DIS phase
    scft = NoncyclicChainSCFT(system, lat, 0.1)
    PolyorderModel(scft)
end;

Next, create a MacrophaseModel object with the intial guess of volume fractions for two DIS phases being 0.1 and 0.9. ϕ₀ is the initial volume fraction of the AB component before macrophase separation.

macro_dis_dis = MacrophaseModel(model_dis_dis, model_dis_dis;
                                phase1=DISPhase, phase2=DISPhase,
                                ϕ₁=0.1, ϕ₂=0.9, ϕ₀=0.6, cached=false);

Finally, using an optimization algorithm enclosed in OptimOptimizer together with the macrophase function to solve the coexistence point, which is (0.0193969, 0.927374). OptimOptimizer wraps all optimization algorithms provided by the Optim.jl package. It requires 18 SCFT evaluations.

macrophase(OptimOptimizer(), macro_dis_dis; lb=[0.01, 0.6], ub=[0.6, 0.99]);

[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.1     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.9     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.049477    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.925833    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.049477    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.925833    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.013965    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.909849    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.013965    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.909849    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.018031    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.938982    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.018031    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.938982    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.023692    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.924599    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.023692    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.924599    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.018071    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.926364    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.018071    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.926364    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019603    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927548    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019603    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927548    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019406    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927369    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019406    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927369    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019397    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927374    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019397    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927374    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019397    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927374    phase: DIS
[ Info: 
[ Info: ======================================================

Other coexistence solvers are available, including:

• JSOOptimizer: optimizers provided by the JSOSolvers.jl package
• OPSOptimizer: surrogate-based optimizers developed in our group.
• RootsOptimizer: root-finding algorithms provided by the Roots.jl package. Requires SurrogateMacrophaseModel instead of MacrophaseModel.

The JSOOptimizer requires 14 SCFT evaluations.

macrophase(JSOOptimizer(), macro_dis_dis; lb=[0.01, 0.6], ub=[0.6, 0.99]);

[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.1     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.9     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.01    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.99    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.015943    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.943026    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.024652    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.918515    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.01836     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.925487    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.020379    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.928707    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019262    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.92737     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019248    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927399    phase: DIS
[ Info: 
[ Info: ======================================================

The OPSOptimizer requires only 8 SCFT evaluations (the initial guess ignored), which reduces the computational cost by (18-8)/18=56% and (14-8)/14=43% with respect to OptimOptimizer and JSOOptimizer, respectively.

let
    vecϕ01 = [0.01, 0.2]  # list of initial guesses for phase 1
    vecϕ02 = [0.75, 0.95]  # list of initial guesses for phase 2
    tol_io = 1e-8  # tol for internal optimizer
    tol_oo = 1e-4  # tol for outside optimizer
    ϕ1 = 0.1  # initial guess of the solution for phase 1
    ϕ2 = 0.9  # initial guess of the solution for pahse 2
    ϕ0 = 0.6  # the initial volume fractions of the mixing system, critical for optimizing algorithms, but not used by root finding algorithms.

    io = RootsOptimizer(; x_abstol=tol_io)
    oo = OPSOptimizer(vecϕ01, vecϕ02; optimizer=io, x_abstol=tol_oo)
    ϕ₁, ϕ₂, _ = macrophase(oo, macro_dis_dis)
end;

[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.01    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.2     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.75    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.95    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.032363    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.919318    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019367    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.92758     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.019239    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927396    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.01925     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.927397    phase: DIS
[ Info: 
[ Info: ======================================================

Exercises

1. Choose either coexistence optimizer, compute the binodal line for A/B binary blend for χN\<10.0 where A and B have same length. Note that the critical point is χN=2.0 for this case.

2. Repeat 1 for A/B binary blend where the length ratio between A and B is 2.

LAM-DIS coexistence

In this demonstration, we will reproduce part of result reported in Fig.3 of Ref. Mester, Z.; Lynd, N. A.; Fredrickson, G. H. Numerical Self-Consistent Field Theory of Multicomponent Polymer Blends in the Gibbs Ensemble. Soft Matter 2013, 9 (47), 11288.

begin
    ds = 0.01
    uc = UnitCell(7.0)
    lattice = BravaisLattice(uc)
    system_lam = AB_A_system(; χN=10.0, ϕAB=0.5, fA=0.45, α=1.0)
    scft_lam = NoncyclicChainSCFT(system_lam, lattice, ds)
end;

Polyorder.solve!(scft_lam);

[ Info: ******* SCFT Simulation Start *******
[ Info: Algorithm: PicardMann iteration with α=0.2.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [7.0]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: number: 100                                                                     
[ Info: F: 0.1757755892                                                                 
[ Info: resediual norm: 0.00103                                                         
[ Info: number: 200                                                                     
[ Info: F: 0.1756234785                                                                 
[ Info: resediual norm: 0.000289                                                        
[ Info: number: 300                                                                     
[ Info: F: 0.1756127438                                                                 
[ Info: resediual norm: 8.32e-5                                                         
[ Info: number: 400                                                                     
[ Info: F: 0.1756118565                                                                 
[ Info: resediual norm: 2.43e-5                                                         
[ Info: number: 500                                                                     
[ Info: F: 0.1756117754                                                                 
[ Info: resediual norm: 7.22e-6                                                         
[ Info: number: 600                                                                     
[ Info: F: 0.1756117675                                                                 
[ Info: resediual norm: 2.18e-6                                                         
[ Info: final loss: 9.927483577453274e-7
[ Info: Stop triggered by EarlyStopping.Threshold(1.0e-6) stopping criterion. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()

[ Info: final F: 0.1756117669
[ Info: final loss: 9.93e-7
[ Info: final stress norm: 0.0020823856893135984
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [7.0]
└   * Angles: [0]
[ Info: iterations: 666
[ Info: time per iteration: 3 milliseconds, 72 microseconds, 151 nanoseconds
[ Info: Run time: 00:00:02.046052958
[ Info: =======================================

plot_density(scft_lam)

┌ Warning: Found `resolution` in the theme when creating a `Scene`. The `resolution` keyword for `Scene`s and `Figure`s has been deprecated. Use `Figure(; size = ...` or `Scene(; size = ...)` instead, which better reflects that this is a unitless size and not a pixel resolution. The key could also come from `set_theme!` calls or related theming functions.
└ @ Makie ~/.julia/packages/Makie/PpRC2/src/scenes.jl:264

Batch evaluations

We can compute the free energies for a list of $\phi_{AB}$ values.

begin
    ϕABs_AB_A_lam = [0.5, 0.6, 0.7, 0.8, 0.85, 0.9, 0.92, 0.94, 0.96, 0.98]
    ϕAs_AB_A_lam = 1 .- ϕABs_AB_A_lam
    ϕA_AB_A_control = ϕControlParameter(:hA, system_lam)
    Fs_AB_A_lam = similar(ϕAs_AB_A_lam)
    μs_AB_A_lam = similar(ϕAs_AB_A_lam)
    info_AB_A_lam = []
end;

using Polyorder: BB, SD, SIS

let
    scft = Polyorder.clone(scft_lam)
    for i in eachindex(ϕAs_AB_A_lam)
        system = Polymer.update!(scft.system, ϕAs_AB_A_lam[i], ϕA_AB_A_control)
        lat = Polyorder.lattice(scft)
        scft = Polyorder.reset(scft, lat, system)
        updater = VariableCell(BB(1.0), SIS(1.0))
        conv, _ = cell_solve!(scft, updater)
        Fs_AB_A_lam[i], μs_AB_A_lam[i] = Polyorder.F(scft), Polyorder.μ̃(scft, 1)
        # Store extra information
        info = (convgence=conv, ϕA=ϕAs_AB_A_lam[i],
                F = Polyorder.F(scft),
                Lx=first(Polyorder.unitcell(scft).edges),
                Nx=first(size(first(scft.ϕfields))))
        push!(info_AB_A_lam, info)
    end
end

[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.

[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [7.0]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 6.776239569878718e-7

[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.1753855179
[ Info: final loss: 6.78e-7
[ Info: final stress norm: 1.13e-7
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [7.2226103539773465]
└   * Angles: [0]
[ Info: iterations: 80
[ Info: time per iteration: 20 milliseconds, 56 microseconds, 96 nanoseconds
[ Info: Run time: 00:00:01.60448775
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [7.2226103539773465]
└   * Angles: [0]

[ Info: Final F: 0.17538551788070622
[ Info: Final loss: 6.776239569878718e-7
[ Info: Final stress: 1.1275764079807448e-7
[ Info: Total solve! calls: 8
[ Info: Total SCFT iterations: 80
[ Info: Total time: 00:00:02
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [7.2226103539773465]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 8.768184231380956e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.4215462056
[ Info: final loss: 8.77e-7
[ Info: final stress norm: 1.36e-9
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [5.861524102066409]
└   * Angles: [0]
[ Info: iterations: 150
[ Info: time per iteration: 529 microseconds, 675 nanoseconds
[ Info: Run time: 00:00:00.079451375
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [5.861524102066409]
└   * Angles: [0]
[ Info: Final F: 0.4215462056178785
[ Info: Final loss: 8.768184231380956e-7
[ Info: Final stress: 1.3576447730642472e-9
[ Info: Total solve! calls: 15
[ Info: Total SCFT iterations: 150
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [5.861524102066409]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 9.848856140002156e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.6673106306
[ Info: final loss: 9.85e-7
[ Info: final stress norm: 1.13e-7
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.929819985195713]
└   * Angles: [0]
[ Info: iterations: 140
[ Info: time per iteration: 96 microseconds, 281 nanoseconds
[ Info: Run time: 00:00:00.013479375
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.929819985195713]
└   * Angles: [0]
[ Info: Final F: 0.6673106306173366
[ Info: Final loss: 9.848856140002156e-7
[ Info: Final stress: 1.1327559347710169e-7
[ Info: Total solve! calls: 14
[ Info: Total SCFT iterations: 140
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.929819985195713]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 6.478339360058344e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.9135518668
[ Info: final loss: 6.48e-7
[ Info: final stress norm: 8.29e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.26390965953216]
└   * Angles: [0]
[ Info: iterations: 140
[ Info: time per iteration: 156 microseconds, 789 nanoseconds
[ Info: Run time: 00:00:00.0219505
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.26390965953216]
└   * Angles: [0]
[ Info: Final F: 0.9135518668182665
[ Info: Final loss: 6.478339360058344e-7
[ Info: Final stress: 8.286513809719884e-8
[ Info: Total solve! calls: 14
[ Info: Total SCFT iterations: 140
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.













[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.26390965953216]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 7.857013743313433e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 1.0379038192
[ Info: final loss: 7.86e-7
[ Info: final stress norm: 1.17e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.989219186554587]
└   * Angles: [0]
[ Info: iterations: 120
[ Info: time per iteration: 99 microseconds, 647 nanoseconds
[ Info: Run time: 00:00:00.01195775
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.989219186554587]
└   * Angles: [0]
[ Info: Final F: 1.037903819167518
[ Info: Final loss: 7.857013743313433e-7
[ Info: Final stress: 1.1662838494879982e-8
[ Info: Total solve! calls: 12
[ Info: Total SCFT iterations: 120
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.989219186554587]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 8.977770333507324e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 1.1643951406
[ Info: final loss: 8.98e-7
[ Info: final stress norm: 4.77e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.730272679467624]
└   * Angles: [0]
[ Info: iterations: 190
[ Info: time per iteration: 86 microseconds, 590 nanoseconds
[ Info: Run time: 00:00:00.016452167
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.730272679467624]
└   * Angles: [0]
[ Info: Final F: 1.1643951405881336
[ Info: Final loss: 8.977770333507324e-7
[ Info: Final stress: 4.77080237612934e-8
[ Info: Total solve! calls: 19
[ Info: Total SCFT iterations: 190
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.730272679467624]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 8.060993367930467e-7

[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 1.2161406052
[ Info: final loss: 8.06e-7
[ Info: final stress norm: 2.35e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.6263155222235377]
└   * Angles: [0]
[ Info: iterations: 270
[ Info: time per iteration: 79 microseconds, 771 nanoseconds
[ Info: Run time: 00:00:00.021538417
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.6263155222235377]
└   * Angles: [0]
[ Info: Final F: 1.216140605153019
[ Info: Final loss: 8.060993367930467e-7
[ Info: Final stress: 2.3505801695610388e-8
[ Info: Total solve! calls: 27
[ Info: Total SCFT iterations: 270
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.6263155222235377]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 9.173627260872319e-7

[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 1.2690935429
[ Info: final loss: 9.17e-7
[ Info: final stress norm: 5.28e-9
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.5191074541101033]
└   * Angles: [0]
[ Info: iterations: 550
[ Info: time per iteration: 440 microseconds, 246 nanoseconds
[ Info: Run time: 00:00:00.242135667
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.5191074541101033]
└   * Angles: [0]
[ Info: Final F: 1.269093542940276
[ Info: Final loss: 9.173627260872319e-7
[ Info: Final stress: 5.283438332023666e-9
[ Info: Total solve! calls: 55
[ Info: Total SCFT iterations: 550
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.5191074541101033]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: number: 100                                                                     
[ Info: F: 1.3242184592                                                                 
[ Info: resediual norm: 0.000394                                                        
[ Info: stress norm: 2.64e-10                                                           
[ Info: cell: [3.4088]                                                                  
[ Info: number: 200                                                                     
[ Info: F: 1.3242159065                                                                 
[ Info: resediual norm: 5.73e-5                                                         
[ Info: stress norm: 8.14e-12                                                           
[ Info: cell: [3.40874]                                                                 
[ Info: number: 300                                                                     
[ Info: F: 1.3242158534                                                                 
[ Info: resediual norm: 8.36e-6                                                         
[ Info: stress norm: 2.25e-13                                                           
[ Info: cell: [3.40874]                                                                 
[ Info: number: 400                                                                     
[ Info: F: 1.3242158523                                                                 



[ Info: resediual norm: 1.22e-6                                                         
[ Info: stress norm: 4.82e-15                                                           
[ Info: cell: [3.40874]                                                                 
[ Info: final loss: 9.88150980728329e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 1.3242158523
[ Info: final loss: 9.88e-7
[ Info: final stress norm: 3.16e-15
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.4087397638821413]
└   * Angles: [0]
[ Info: iterations: 4110
[ Info: time per iteration: 92 microseconds, 520 nanoseconds
[ Info: Run time: 00:00:00.380258125
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.4087397638821413]
└   * Angles: [0]
[ Info: Final F: 1.32421585228201
[ Info: Final loss: 9.88150980728329e-7
[ Info: Final stress: 3.155329510700846e-15
[ Info: Total solve! calls: 411
[ Info: Total SCFT iterations: 4110
[ Info: Total time: 00:00:01
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: 1S semi-implicit method (SIS-1) with α=1.0.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.4087397638821413]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 9.15586208483552e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 1.3867508867
[ Info: final loss: 9.16e-7
[ Info: final stress norm: 2.23e-12
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.4087397638821413]
└   * Angles: [0]
[ Info: iterations: 130
[ Info: time per iteration: 72 microseconds, 429 nanoseconds
[ Info: Run time: 00:00:00.009415834
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.4087397638821413]
└   * Angles: [0]
[ Info: Final F: 1.386750886724393
[ Info: Final loss: 9.15586208483552e-7
[ Info: Final stress: 2.2311562788070764e-12
[ Info: Total solve! calls: 13
[ Info: Total SCFT iterations: 130
[ Info: Total time: 00:00:01

Visualize the free energy curves of LAM and DIS phase.

begin
    ϕAs_AB_A_dis = 0.01:0.01:0.99
    ϕABs_AB_A_dis = 1 .- ϕAs_AB_A_dis
    Fs_AB_A_dis = similar(ϕAs_AB_A_dis)
    μs_AB_A_dis = similar(ϕAs_AB_A_dis)
    for i in eachindex(ϕAs_AB_A_dis)
        system = Polymer.update!(system_lam, ϕAs_AB_A_dis[i], ϕA_AB_A_control)
        Fs_AB_A_dis[i], μs_AB_A_dis[i] = Polyorder.F_DIS(system), Polyorder.μ̃_DIS(system, 1)
    end
end

let
    f = Figure()
    ax = Axis(f[1, 1],
        xlabel = L"$\phi_{AB}$",
        ylabel = L"$F$",
    )
    lines!(ax, ϕABs_AB_A_lam, Fs_AB_A_lam, label="LAM")
    scatter!(ax, ϕABs_AB_A_lam, Fs_AB_A_lam, label=nothing; markersize=2)
    lines!(ax, ϕABs_AB_A_dis[1:end], Fs_AB_A_dis[1:end], label="DIS")
    f
end

┌ Warning: Found `resolution` in the theme when creating a `Scene`. The `resolution` keyword for `Scene`s and `Figure`s has been deprecated. Use `Figure(; size = ...` or `Scene(; size = ...)` instead, which better reflects that this is a unitless size and not a pixel resolution. The key could also come from `set_theme!` calls or related theming functions.
└ @ Makie ~/.julia/packages/Makie/PpRC2/src/scenes.jl:264

The same straight line is subtracted from both the free energy curves of the LAM and DIS phases. It can be seen that

• when $\phi_A < 0.06$ ($\phi_{AB}>0.94$), LAM reduces to DIS. Thus in this region, the stable phase is DIS.
• A cotangent line can be constructed by connecting $\phi_{A} \approx 0.25$ ($\phi_{AB} \approx 0.75$) and $\phi_{A} \approx 0.93$ ($\phi_{AB} \approx 0.07$). Thus in this region, LAM and DIS coexist.
• When $0.06 < \phi_{A} < 0.25$ ($0.75 < \phi_{AB} < 0.94$), LAM is the stable phase.
• When $\phi_{A} > 0.93$ ($\phi_{AB} < 0.07$), DIS is the stable phase again.

These observations are consistent with the result presented in Fig. 3 of Ref. Mester, Z.; Lynd, N. A.; Fredrickson, G. H. Numerical Self-Consistent Field Theory of Multicomponent Polymer Blends in the Gibbs Ensemble. Soft Matter 2013, 9 (47), 11288.

let
    f = Figure()
    ax = Axis(f[1, 1],
        xlabel = L"$\phi_{AB}$",
        ylabel = L"$F$",
    )
    line = get_line(ϕABs_AB_A_dis[1], Fs_AB_A_dis[1], ϕABs_AB_A_dis[end], Fs_AB_A_dis[end])
    F_lam = subtract_line(line, ϕABs_AB_A_lam, Fs_AB_A_lam)
    lines!(ax, ϕABs_AB_A_lam, F_lam, label="LAM")
    scatter!(ax, ϕABs_AB_A_lam, F_lam, label=nothing)
    F_dis = subtract_line(line, ϕABs_AB_A_dis, Fs_AB_A_dis)
    lines!(ax, ϕABs_AB_A_dis, F_dis, label="DIS")
    f
end

┌ Warning: Found `resolution` in the theme when creating a `Scene`. The `resolution` keyword for `Scene`s and `Figure`s has been deprecated. Use `Figure(; size = ...` or `Scene(; size = ...)` instead, which better reflects that this is a unitless size and not a pixel resolution. The key could also come from `set_theme!` calls or related theming functions.
└ @ Makie ~/.julia/packages/Makie/PpRC2/src/scenes.jl:264

RootsOptimizer

RootsOptimizer is less robust than other optimizers. You have to make sure that the data range should not include any inflection point in the free energy curve.

The other important thing to bare in mind is that the chemical potential returned is for the first component in the polymer system, which is AB block copolymer in our AB_A_system(). Therefore, we have to use $\phi_{AB}$ as the independent variable.

The coexistence point in ϕAB is 0.0670242 and 0.751779 as computed.

let
    # ϕAB range for DIS phase is [0.02, 0.2]
    s1 = CHSplineSurrogate(reverse(ϕABs_AB_A_dis)[2:20] |> collect, reverse(Fs_AB_A_dis)[2:20] |> collect, reverse(μs_AB_A_dis)[2:20] |> collect)
    # ϕAB range for LAM phase is [0.7, 0.98]
    s2 = CHSplineSurrogate(ϕABs_AB_A_lam[3:end] |> collect, Fs_AB_A_lam[3:end] |> collect, μs_AB_A_lam[3:end] |> collect)
    smp = SurrogateMacrophaseModel(s1, s2, ϕA_AB_A_control; ϕ₁=0.1, ϕ₂=0.8, ϕ₀=0.6)

    # macrophase(JSOOptimizer(), smp; lb=[0.02, 0.7], ub=[0.2, 0.9])  # also works.
    # macrophase(OptimOptimizer(), smp; lb=[0.02, 0.7], ub=[0.2, 0.9])  # also works
    # RootsOptimizer's bound depends on the input surrogates, cannot be set separately.
    macrophase(RootsOptimizer(), smp)
end

(0.06703239288354801, 0.7527251272714819, nothing)

OPSOptimizer

Internal optimizer is used for computing the coexistence based on surrogates. The most robust internal optimizer is the OptimOptimizer. For this particular case, JSOOptimizer fails.

The coexistence point in ϕAB is 0.0.0670345 and 0.752099 as computed.

let
    ds = 0.01
    uc = UnitCell(5.0)
    lat = BravaisLattice(uc)
    system = AB_A_system(; χN=10.0, ϕAB=0.7, fA=0.45, α=1.0)
    ϕAB_control = ϕControlParameter(:AB, system)

    scft_dis = NoncyclicChainSCFT(system, lat, 0.1)

    scft = NoncyclicChainSCFT(system, lat, ds)
    Polyorder.solve!(scft)
    updater = VariableCell(BB(1.0), SIS(1.0))
    scft_lam = NoncyclicChainSCFT(system, lat, ds; updater)
    Polyorder.initialize!(scft_lam, scft.wfields)

    model_dis = PolyorderModel(scft_dis)
    model_lam = PolyorderModel(scft_lam)

    # All ϕs are for AB diblock copolymer
    ϕdis_init = [0.02, 0.2]
    # ϕlam_init = [0.6, 0.8]  # [0.6, 0.8] works for OptimOptimizer and RootsOptimizer
    ϕlam_init = [0.7, 0.9]
    tol_io = 1e-8
    tol_oo = 1e-4
    ϕ1, ϕ2, ϕ0 = 0.1, 0.8, 0.6

    m = MacrophaseModel(model_dis, model_lam, ϕAB_control;
                        phase1=DISPhase, phase2=LAMPhase,
                        ϕ₁=ϕ1, ϕ₂=ϕ2, ϕ₀=ϕ0, cached=true)
    # io = RootsOptimizer(x_abstol=tol_io)
    io = OptimOptimizer(x_abstol=tol_io)
    oo = OPSOptimizer(ϕdis_init, ϕlam_init; optimizer=io, x_abstol=tol_oo)
    ϕ₁, ϕ₂, _ = macrophase(oo, m)
end

[ Info: ******* SCFT Simulation Start *******
[ Info: Algorithm: PicardMann iteration with α=0.2.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [5.0]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: number: 100                                                                     
[ Info: F: 0.6673584304                                                                 
[ Info: resediual norm: 0.00213                                                         
[ Info: number: 200                                                                     
[ Info: F: 0.6673898126                                                                 
[ Info: resediual norm: 0.000322                                                        
[ Info: number: 300                                                                     
[ Info: F: 0.6673803223                                                                 
[ Info: resediual norm: 9.57e-5                                                         
[ Info: number: 400                                                                     
[ Info: F: 0.667379361                                                                  
[ Info: resediual norm: 2.95e-5                                                         
[ Info: number: 500                                                                     
[ Info: F: 0.6673792562                                                                 
[ Info: resediual norm: 9.6e-6                                                          
[ Info: number: 600                                                                     
[ Info: F: 0.6673792441                                                                 
[ Info: resediual norm: 3.18e-6                                                         
[ Info: number: 700                                                                     
[ Info: F: 0.6673792427                                                                 
[ Info: resediual norm: 1.06e-6                                                         
[ Info: final loss: 9.94933958466398e-7
[ Info: Stop triggered by EarlyStopping.Threshold(1.0e-6) stopping criterion. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.6673792427
[ Info: final loss: 9.95e-7
[ Info: final stress norm: 0.0019443753562810862
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [5.0]
└   * Angles: [0]
[ Info: iterations: 706
[ Info: time per iteration: 108 microseconds, 708 nanoseconds
[ Info: Run time: 00:00:00.076748
[ Info: =======================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.02    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.2     phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 

[ Info:      ϕ = 0.7     phase: LAM
[ Info: 
[ Info: ======================================================
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
┌ Warning: Timed out waiting for `Base.active_repl_backend.ast_transforms` to become available. Autoloads will not work.
└ @ BasicAutoloads ~/.julia/packages/BasicAutoloads/08hIo/src/BasicAutoloads.jl:117
[ Info: If you have a slow startup file, consider moving `register_autoloads` to the end of it.
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [5.0]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 9.489873107824222e-7

[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.6673105692
[ Info: final loss: 9.49e-7
[ Info: final stress norm: 6.26e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.929813126246492]
└   * Angles: [0]
[ Info: iterations: 110
[ Info: time per iteration: 7 milliseconds, 707 microseconds, 652 nanoseconds
[ Info: Run time: 00:00:00.847841791
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.929813126246492]
└   * Angles: [0]
[ Info: Final F: 0.667310569244048
[ Info: Final loss: 9.489873107824222e-7
[ Info: Final stress: 6.261105775724781e-8
[ Info: Total solve! calls: 11
[ Info: Total SCFT iterations: 110
[ Info: Total time: 00:00:01
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.9     phase: LAM
[ Info: 
[ Info: ======================================================
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.929813126246492]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 8.022386025172836e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 1.1643950602
[ Info: final loss: 8.02e-7
[ Info: final stress norm: 2.02e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.7302686839920463]
└   * Angles: [0]
[ Info: iterations: 380
[ Info: time per iteration: 74 microseconds, 826 nanoseconds
[ Info: Run time: 00:00:00.028434208
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [3.7302686839920463]
└   * Angles: [0]
[ Info: Final F: 1.1643950601764115
[ Info: Final loss: 8.022386025172836e-7
[ Info: Final stress: 2.0153536631018778e-8
[ Info: Total solve! calls: 38
[ Info: Total SCFT iterations: 380
[ Info: Total time: 00:00:01
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.077986    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.799925    phase: LAM
[ Info: 
[ Info: ======================================================
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.929813126246492]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 8.631423743886505e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.9133651077
[ Info: final loss: 8.63e-7
[ Info: final stress norm: 2.11e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.2643441034604335]
└   * Angles: [0]
[ Info: iterations: 230
[ Info: time per iteration: 84 microseconds, 108 nanoseconds
[ Info: Run time: 00:00:00.019344875
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.2643441034604335]
└   * Angles: [0]
[ Info: Final F: 0.9133651076678013
[ Info: Final loss: 8.631423743886505e-7
[ Info: Final stress: 2.1085240332141832e-8
[ Info: Total solve! calls: 23
[ Info: Total SCFT iterations: 230
[ Info: Total time: 00:00:01
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.063789    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.754828    phase: LAM
[ Info: 
[ Info: ======================================================
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.2643441034604335]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 8.688642019882246e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.8020999422
[ Info: final loss: 8.69e-7
[ Info: final stress norm: 7.55e-9
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.540241647935044]
└   * Angles: [0]
[ Info: iterations: 180
[ Info: time per iteration: 84 microseconds, 258 nanoseconds
[ Info: Run time: 00:00:00.015166458










[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.540241647935044]
└   * Angles: [0]
[ Info: Final F: 0.8020999421659334
[ Info: Final loss: 8.688642019882246e-7
[ Info: Final stress: 7.554323257942448e-9
[ Info: Total solve! calls: 18
[ Info: Total SCFT iterations: 180
[ Info: Total time: 00:00:01
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.067057    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.751812    phase: LAM
[ Info: 
[ Info: ======================================================
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.540241647935044]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 6.998750488834815e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.7946750378
[ Info: final loss: 7.0e-7
[ Info: final stress norm: 3.12e-8
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.5599649161212605]
└   * Angles: [0]
[ Info: iterations: 110
[ Info: time per iteration: 80 microseconds, 674 nanoseconds
[ Info: Run time: 00:00:00.008874208
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.5599649161212605]
└   * Angles: [0]
[ Info: Final F: 0.7946750377906326
[ Info: Final loss: 6.998750488834815e-7
[ Info: Final stress: 3.116529035851736e-8
[ Info: Total solve! calls: 11
[ Info: Total SCFT iterations: 110
[ Info: Total time: 00:00:01
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.067042    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.751693    phase: LAM
[ Info: 
[ Info: ======================================================
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.5599649161212605]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 7.952866312182435e-7



[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.7943829015
[ Info: final loss: 7.95e-7
[ Info: final stress norm: 5.83e-7
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.560725056792581]
└   * Angles: [0]
[ Info: iterations: 50
[ Info: time per iteration: 574 microseconds, 555 nanoseconds
[ Info: Run time: 00:00:00.028727792
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.560725056792581]
└   * Angles: [0]
[ Info: Final F: 0.7943829014723307
[ Info: Final loss: 7.952866312182435e-7
[ Info: Final stress: 5.832922876482787e-7
[ Info: Total solve! calls: 5
[ Info: Total SCFT iterations: 50
[ Info: Total time: 00:00:01
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.067042    phase: DIS
[ Info: 
[ Info: ======================================================
[ Info: ======================================================
[ Info: 
[ Info:      ϕ = 0.751693    phase: LAM
[ Info: 
[ Info: ======================================================
[ Info: ###### Cell Optimization Start ######
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: Cell optimization starts ...
[ Info: ******* SCFT Simulation Start *******
┌ Info: Algorithm: Variable cell method
│ * Cell updater: Barzilai-Borwein (BB2) method
│ * max step size: 1.0
│ * step size: 0.2.
│ * Fields updater: PicardMann iteration with α=0.2.
└ * Scheme: run fields updater 10 times per cell iteration.
[ Info: MDE solvers: ["OSF"]
[ Info: tolerance: 1.0e-5 (stress norm)
[ Info: tolerance: 1.0e-6 (Residual)
[ Info: initial F: Inf
[ Info: initial residual norm: 0.0
[ Info: initial stress norm: NaN
┌ Info: initial unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.560725056792581]
└   * Angles: [0]
[ Info: 
[ Info: Simulation starts > > > > > >
[ Info: final loss: 2.317180184347666e-7
[ Info: Stop triggered by a `ThresholdStress` control. 
[ Info: > > > > > > Simulation finished.
[ Info: 
[ Info: ------ SCFT Simulation Summary ------
[ Info: convergence: Polyorder.Successful()
[ Info: final F: 0.7943833434
[ Info: final loss: 2.32e-7
[ Info: final stress norm: 6.47e-7
┌ Info: final unit cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.560725186436381]
└   * Angles: [0]
[ Info: iterations: 20
[ Info: time per iteration: 84 microseconds, 489 nanoseconds
[ Info: Run time: 00:00:00.001689791
[ Info: =======================================
[ Info: Cell optimization finished.
[ Info: ------ Cell Optimization Summary ------
[ Info: Convergence: Polyorder.Successful()
┌ Info: Stress-free cell: UnitCell
│   * Crystal system: Line
│   * Edges: [4.560725186436381]
└   * Angles: [0]
[ Info: Final F: 0.7943833434464063
[ Info: Final loss: 2.317180184347666e-7
[ Info: Final stress: 6.468070334560042e-7
[ Info: Total solve! calls: 2
[ Info: Total SCFT iterations: 20
[ Info: Total time: 00:00:01

(0.06704172117731037, 0.7516931569494402, (10, [0.02, 0.2, 0.07798583826477423, 0.06378889438017175, 0.06705655939772899, 0.06704175426434512, 0.06704172117731037], [0.7, 0.9, 0.7999245104511178, 0.7548281267521397, 0.7518116984787448, 0.7516931270371734, 0.7516931569494402], [-0.989249113279732, -0.5214024235381877, -0.8632976230451874, -0.8987378390466816, -0.8907488410504592, -0.8907852827924947, -0.8907853642313469], [0.667310569244048, 1.1643950601764115, 0.9133651076678013, 0.8020999421659334, 0.7946750377906326, 0.7943829014723307, 0.7943833434464063]))

Exercises

1. Reproduce the whole Fig.3 of Ref. Mester, Z.; Lynd, N. A.; Fredrickson, G. H. Numerical Self-Consistent Field Theory of Multicomponent Polymer Blends in the Gibbs Ensemble. Soft Matter 2013, 9 (47), 11288.