Advanced rare-event sampling technique named as the string method was used to investigate the kinetic energy variation during the defect annihilation in BCP thin films, in combination with the TICG model. The TICG model takes advantage of having explicit polymer chains expressed with Gaussian bead spring model, while nonbonded Hamiltonian is evaluated based on polymeric field theoretic form: Hnb=ρ0kBTNVdr(χNϕA(r)ϕB(r)+κN2(ϕA(r)+ϕB(r)1)2), where ϕα=ραρ0 denotes the normalized number density of species α and ρ0, χ, and κ are the average bulk number density of beads, Flory parameter, and the inverse compressibility, respectively. A string connecting defective and defect-free structures with a contour variable (reaction coordinate α) varying from 0 and 1 was defined on a multidimensional collective variable (CV) space constructed with density fields on a spatial grid over the simulation box. Each component of CV m is defined by normalized order parameter ϕA(ri)ϕB(ri)ϕA(ri)+ϕB(ri), where ϕA(ri) and ϕB(ri) are density values of A and B segments at the grid of ri. Among many possible strings connecting two states, the MFEP was defined with a string along which the gradient of free energy disappears. At each iteration of updating the string, a free energy gradient at 128 nodes uniformly distributed along the string was evaluated by umbrella sampling restraining TICG Monte Carlo simulations to be around corresponding CV m by adding the additional potential, Hc(rnN m)=λkBT2ΔL3[mm^]2. m^ is the CV value for particle coordinates, rnN. Then, the free energy gradient can be estimated by λΔL3kBT[mm^c]λFm. The string was updated using Euler technique, m1=m0τλ[m0m^c], at every node. Once the string was converged, free energy values at every node were estimated from ΔF[α]=0αdsFmm(s)dm(s)ds. Our simulations were conducted for lamellar-forming symmetric BCP thin films, which is shown to have qualitatively similar defect annihilation behavior as cylinder-forming cases (52). Simulation box size in the lateral direction was chosen to be six times of various periodicity L (d-spacing) of 1.655, 1.728, 1.8, 1.9, 2.0, and 2.1Re, end-to-end distance, while Ly and Lz (film thickness) were fixed at 8.275 and 1.655Re, respectively. For our calculations, we used the values N¯=ρ0Re3N=128, χN = 20, κN = 50, and λ=3000Re3. The step size for string update, τ, was chosen to vary depending on the systems from 0.025 to 0.08. While our calculation was conducted for lamellar structures, qualitative behavior of defect annihilation is expected to be similar to cylinder-forming cases (52).

Note: The content above has been extracted from a research article, so it may not display correctly.



Q&A
Please log in to submit your questions online.
Your question will be posted on the Bio-101 website. We will send your questions to the authors of this protocol and Bio-protocol community members who are experienced with this method. you will be informed using the email address associated with your Bio-protocol account.



We use cookies on this site to enhance your user experience. By using our website, you are agreeing to allow the storage of cookies on your computer.