Primary Sequences of Protein-Like Copolymers: Levy Flight Type Long Range Correlations

We consider the statistical properties of primary sequences of two-letter HP copolymers (H for hydrophobic and P for polar) designed to have water soluble globular conformations with H monomers shielded from water inside the shell of P monomers. We show, both by computer simulations and by exact analytical calculation, that for large globules and flexible polymers such sequences exhibit long-range correlations which can be described by Levy-flight statistics.Comment: 4 pages, including 2 figures; several references added, some formulations improve

Large-scale atomistic and quantum-mechanical simulations of a Nafion membrane: Morphology, proton solvation and charge transport

Atomistic and first-principles molecular dynamics simulations are employed to investigate the structure formation in a hydrated Nafion membrane and the solvation and transport of protons in the water channel of the membrane. For the water/Nafion systems containing more than 4 million atoms, it is found that the observed microphase-segregated morphology can be classified as bicontinuous: both majority (hydrophobic) and minority (hydrophilic) subphases are 3D continuous and organized in an irregular ordered pattern, which is largely similar to that known for a bicontinuous double-diamond structure. The characteristic size of the connected hydrophilic channels is about 25–50 Å, depending on the water content. A thermodynamic decomposition of the potential of mean force and the calculated spectral densities of the hindered translational motions of cations reveal that ion association observed with decreasing temperature is largely an entropic effect related to the loss of low-frequency modes. Based on the results from the atomistic simulation of the morphology of Nafion, we developed a realistic model of ion-conducting hydrophilic channel within the Nafion membrane and studied it with quantum molecular dynamics. The extensive 120 ps-long density functional theory (DFT)-based simulations of charge migration in the 1200-atom model of the nanochannel consisting of Nafion chains and water molecules allowed us to observe the bimodality of the van Hove autocorrelation function, which provides the direct evidence of the Grotthuss bond-exchange (hopping) mechanism as a significant contributor to the proton conductivity

Nonmonotonic incommensurability effects in lamellar-in-lamellar self-assembled multiblock copolymers

Using the self-consistent-field theory numerical procedure we find that the period D of the lamellar-in-lamellar morphology formed in symmetric multiblock copolymer melts AmN/2(BN/2AN/2)nBmN/2 at intermediate segregations changes nonmonotonically with an increase in the relative tail length m. Therewith D reveals, as a function of the Flory χ-parameter, a drastic change in the vicinity of the internal structure formation, which can be both a drop and a rise, depending on the value of m. It is argued that the unusual behavior found is a particular case of a rather general effect of the incommensurability between the two length scales that characterize the system under consideration.

Nonconventional morphologies in two-length scale block copolymer systems beyond the weak segregation theory

The order-disorder and order-order transitions (ODT and OOT) in the linear multiblock copolymers with two-length scale architecture AfmN(BN/2AN/2)nB(1−f)mN are studied under intermediate cooling below the ODT critical point where a nonconventional sequence of the OOTs was predicted previously within the weak segregation theory (WST). To describe the ordered morphologies appearing in block copolymers (BCs) under cooling, we use the pseudospectral version of the self-consistent field theory (SCFT) with some modifications providing a good convergence speed and a high precision of the solution due to using the Ng iterations and a reasonable choice of the predefined symmetries of the computation cell as well as initial guess for the iterations. The WST predicted sequence of the phase transitions is found to hold if the tails of the BCs under consideration are symmetric enough (|0.5−f|≤0.05); the quantitative agreement between the WST and SCFT phase diagrams is reasonable in a narrow (both in f and χ~ = χN) region close to the critical point, though. For |0.5−f|>0.05, a large region of the face-centered cubic phase stability is found (up to our knowledge, first within the SCFT framework) inside of the body-centered cubic phase stability region. Occurrence of the two-dimensional and three-dimensional phases with the micelles formed, unlike the conventional diblock copolymers, by the longer (rather than shorter) tails, and its relationship to the BC architecture is first described in detail. The calculated spectra of the ordered phases show that nonmonotonous temperature dependence of the secondary peak scattering intensities accompanied by their vanishing and reappearance is rather a rule than exception.

Microphase separation of diblock copolymers with amphiphilic segment

We present a statistical mechanical approach for predicting the self-assembled morphologies of amphiphilic diblock copolymers in the melt. We introduce two conformationally asymmetric linear copolymer models with a local structural asymmetry, one of a ‘‘comb-tail’’ type and another that we call ‘‘continuous jackknife model.’’ The copolymers consist of amphiphilic and ‘‘monophilic’’ (non-amphiphilic) blocks, which have different segmental volume and tend to segregate into subphases. Using a self-consistent field theory (SCFT) framework, we explore the phase diagrams for these copolymers and compare them with that known for conventional, conformationally symmetric diblock copolymers. To determine the impact of structural effects on the self-assembly of copolymer melts, copolymers with a variation in both molecular architecture and chemical composition, f, are studied for different values of the Flory–Huggins parameter, χ. The composition dependence of the phase diagrams is shown to be basically determined by the conformational asymmetry. Remarkably, the stable lamellar structures exist even in the very compositionally asymmetric case, f < ¼. An interesting geometric distinction of the ‘‘direct’’ and ‘‘inverse’’ morphologies is introduced. The presence of an internal structure is found to influence the high χ behavior, where a stable two-scale (structure-in-structure) hexagonal morphology is found to be formed for some compositions. Therefore, the local chemical structure of monomer units can dictate the global morphology of copolymer melts.