Browsing by Subject "Simulations of Diblock Copolymers"

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    Investigation of Universal Behavior in Symmetric Diblock Copolymer Melts
    (2015-12) Medapuram, Pavani
    Coarse-grained theories of dense polymer liquids such as block copolymer melts predict a universal dependence of equilibrium properties on a few dimensionless parameters. For symmetric diblock copolymer melts, such theories predict a universal dependence on only $\chi_e N$ and $\Nbar$, where $\chi_e$ is an effective interaction parameter, $N$ is the degree of polymerization, and $\Nbar$ is a measure of overlap. This thesis focuses on testing the universal behavior hypothesis by comparing results for various properties obtained from different coarse-grained simulation models to each other. Specifically, results from pairs of simulations of different models that have been designed to have matched values of $\Nbar$ are compared over a range of values of $\chi N$. The use of vastly different simulation models allows us to cover a vast range of $\Nbar \simeq$ 200 - 8000 that includes most of the experimentally relevant range. Properties studied here include collective and single-chain correlations in the disordered phase, block and chain radii of gyration in the disordered phase, the value of $\chi_e N$ at the order-disorder transition (ODT), the free energy per chain, the latent heat of transition, the layer spacing, the composition profile, and compression modulus in the ordered phase. All results strongly support the universal scaling hypothesis, even for rather short chains, confirming that it is indeed possible to give an accurate universal description of simulation models that differ in many details. The underlying universality becomes apparent, however, only if data are analyzed using an adequate estimate of $\chi_e$, which we obtained by fitting the structure factor $S(q)$ in the disordered state to predictions of the recently developed renormalized one-loop (ROL) theory. The ROL theory is shown to provide an excellent description of the dependence of $S(q)$ on chain length and thermodynamic conditions for all models, even for very short chains, if we allow for the existence of a nonlinear dependence of the effective interaction parameter $\chi_e$ upon the strength of the $AB$ repulsion. The results show that behavior near the ODT exhibits a different character at moderate and high values of $\Nbar$, with a crossover near $\Nbar \simeq {10}^4$. Within the range $\Nbar \lesssim {10}^4$ studied in this work, the ordered and disordered phases near the ODT both contain strongly segregated domains of nearly pure $A$ and $B$, in contrast to the assumption of weak segregation underlying the Fredrickson–Helfand (FH) theory. In this regime, the FH theory is inaccurate and substantially underestimates the value of $\chi_e N$ at the ODT. Results for the highest values of $\Nbar$ studied here agree reasonably well with FH predictions, suggesting that the theory may be accurate for $\Nbar \gtrsim {10}^4$. Self-consistent field theory (SCFT) grossly underestimates ${\left(\chi_e N\right)}_{\mathrm{ODT}}$ for modest $\Nbar$ because it cannot describe strong correlations in the disordered phase. SCFT is found, however, to yield accurate predictions for several properties of the ordered lamellar phase. A detailed quantitative comparison of experimental results to theoretical predictions and obtained simulations results is also presented. Experimental results for structure factor obtained from small-angle neutron and X-ray scattering (SANS and SAXS) measurements are analyzed using methods closely analogous to those used to analyze simulation results. Peak scattering intensity results of different chain lengths of a $AB$ pair are fitted to the ROL theory predictions in order to estimate the effective interaction parameter $\chi_e(T)$ of the chemical system. The resulting $\chi_e(T)$ estimates are used to obtain ODT values $(\chi_e N)_{\mathrm{ODT}}$ of different experimental systems, which we compare to the scaling law obtained from simulation results and to theoretical predictions. The results are largely consistent with the expected systematic decrease with increasing $\Nbar$ and lie closer to the simulations scaling law than to any theoretical prediction. These results confirm the overwhelming importance of fluctuation effects in systems with modest values of $\Nbar = 10^{2} - 10^{3}$, and the usefulness of coarse-grained simulations as a starting point for quantitative modeling.
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    Structure and Dynamics of Micelle-Forming Asymmetric Diblock Copolymer Chains
    (2021-09) Chawla, Anshul
    Experiments on micelle-forming asymmetric diblock copolymer melts have shown the existence of a liquid-like state of micelles at temperatures greater than the order-disorder transition temperature (ODT).These micelles have been hypothesized to appear at an even greater temperature called the critical micelle temperature (CMT). The regime between the CMT and ODT, called the disordered micellar regime, has been known to affect the formation of many exotic phases like the Frank-Kasper and the Laves phases due to its slow dynamics. Self-Consistent Field Theory (SCFT), one of the most commonly employed theoretical tools, only predicts the appearance of micelles in stationary and periodic configurations, and hence is incapable of capturing the disordered micellar regime. Some previous theoretical studies do provide predictions of the structural properties of the disordered micelles, however, these studies used SCFT predictions of free energies of isolated micelles to approximate the free energy of disordered micelles. We have used coarse-grained classical molecular dynamics to simulate melts of asymmetric diblock copolymer chains having a minority block volume fraction, $f = 0.125$.At high $\chi N$, where $\chi$ is the Flory-Huggins interaction parameter and $N$ is the degree of polymerization, SCFT predicts the formation of ordered micellar phases for this volume fraction. Our simulations show the existence of a disordered micellar regime for $\chi N$ above the $\cNso$, where $\cNso$ is the value of $\chi N$ corresponding to the ODT predicted from SCFT. We study melts having two significantly different invariant degree of polymerization, $\overline {N} = 960$ and $3820$, that span the disordered homogenous phase, disordered micellar regime, and the ordered body-centered cubic (BCC) phase. The first part of this thesis pertains to analyzing the evolution of the structure of these melts as a function of $\chi N$.By using a cluster identification algorithm, we show that micelle-like clusters appear at a CMT with the appearance being much more sudden for the higher $\overline {N}$ simulations. Moreover, micelles appear when $\chi N$ is near $\cNso$. We also show that the signature of the presence of disordered micelles in scattering experiments (SAXS and SANS) arises at a somewhat higher $\chi N$ as compared to $\cNso$. Comparisons of the free energy derivative, peak wavenumber, micelle aggregation number and the free chain fraction obtained from simulations with these quantities calculated from SCFT show close agreement, thus emphasizing similarities in the structure of the disordered micelles and the ordered micelles predicted by SCFT at the same $\chi N$. Analysis of the shape of the identified clusters also reveal a rapid formation/breaking of bridges between micelles present in both disordered and ordered phases. The latter part of this thesis considers the dynamics of these melts, namely single chain diffusion and structural relaxation.Signatures of the sudden appearance of micelles at the CMT is also reflected in the analysis of the dynamic properties as a sudden slowdown in the molecular relaxation and an even more significant slow down in the structural relaxation. We measure the rate at which polymers are expelled from micelles, and relate this to the polymer diffusivity.