Chinmay Das

Computational linear rheology of general branch-on-branch polymers

We present a general algorithm for predicting the linear rheology of branched polymers. While the method draws heavily on existing theoretical understanding of the relaxation processes in entangled polymer melts, a number of new concepts are developed to handle diverse polymer architectures including branch-on-branch structures. We validate the algorithm with experimental examples from model polymer architectures to fix the parameters of the model. We use experimentally determined parameters to generate a numerical ensemble of branched metallocene-catalyzed polyethylene resins. Application of our algorithm shows the importance of branch-on-branch chains in the system and predicts the linear rheology with good quantitative agreement over a wide range of branching density and molecular weight.

Linking models of polymerization and dynamics to predict branched polymer structure and flow.

The complex flow behavior of a branched polymer can be predicted from its chemical structure. We present a predictive scheme connecting the topological structure of highly branched entangled polymers, with industrial-level complexity, to the emergent viscoelasticity of the polymer melt. The scheme is able to calculate the linear and nonlinear viscoelasticity of a stochastically branched “high-pressure free radical” polymer melt as a function of the chemical kinetics of its formation. The method combines numerical simulation of polymerization with the tube/entanglement physics of polymer dynamics extended to fully nonlinear response. We compare calculations for a series of low-density polyethylenes with experiments on structural and viscoelastic properties. The method provides a window onto the molecular processes responsible for the optimized rheology of these melts, connecting fundamental science to process in complex flow, and opens up the in silico design of new materials.

Simulation Studies of Stratum Corneum Lipid Mixtures

We present atomistic molecular dynamics results for fully hydrated bilayers composed of ceramide NS-24:0, free fatty acid 24:0 and cholesterol, to address the effect of the different components in the stratum corneum (the outermost layer of skin) lipid matrix on its structural properties. Bilayers containing ceramide molecules show higher in-plane density and hence lower rate of passive transport compared to phospholipid bilayers. At physiological temperatures, for all composition ratios explored, the lipids are in a gel phase with ordered lipid tails. However, the large asymmetry in the lengths of the two tails of the ceramide molecule leads to a fluidlike environment at the bilayer midplane. The lateral pressure profiles show large local variations across the bilayer for pure ceramide or any of the two-component mixtures. Close to the skin composition ratio, the lateral pressure fluctuations are greatly suppressed, the ceramide tails from the two leaflets interdigitate significantly, the depression in local density at the interleaflet region is lowered, and the bilayers have lowered elastic moduli. This indicates that the observed composition ratio in the stratum corneum lipid layer is responsible for both the good barrier properties and the stability of the lipid structure against mechanical stresses.

Nanoscale mechanical probing of supported lipid bilayers with atomic force microscopy

We present theory and experiments for the force-distance curve F(z(0)) of an atomic force microscope (AFM) tip (radius R) indenting a supported fluid bilayer (thickness 2d). For realistic conditions the force is dominated by the area compressibility modulus κ(A) of the bilayer and, to an excellent approximation, given by F=πκ(A)Rz(0)(2)/(2d-z(0))(2). The experimental AFM force curves from coexisting liquid ordered and liquid disordered domains in three-component lipid bilayers are well described by our model, which provides κ(A) in agreement with literature values. The liquid ordered phase has a yieldlike response that we model as due to the breaking of hydrogen bonds.

Water permeation through stratum corneum lipid bilayers from atomistic simulations

Stratum corneum, the outermost layer of skin, consists of keratin filled rigid non-viable corneocyte cells surrounded by multilayers of lipids. The lipid layer is responsible for the barrier properties of the skin. We calculate the excess chemical potential and diffusivity of water as a function of depth in lipid bilayers with compositions representative of the stratum corneum using atomistic molecular dynamics simulations. The maximum in the excess free energy of water inside the lipid bilayers is found to be twice that of water in phospholipid bilayers at the same temperature. Permeability, which decreases exponentially with the free energy barrier, is reduced by several orders of magnitude as compared with phospholipid bilayers. The average time it takes for a water molecule to cross the bilayer is calculated by solving the Smoluchowski equation in the presence of the free energy barrier. For a bilayer composed of a 2:2:1 molar ratio of ceramide NS 24:0, cholesterol and free fatty acid 24:0 at 300 K, we estimate the permeability P = 3.7 × 10−9 cm/s and the average crossing time τav = 0.69 ms. The permeability is about 30 times smaller than existing experimental results on mammalian skin sections.

Lamellar and inverse micellar structures of skin lipids: effect of templating.

The outermost layer of skin comprises rigid nonviable cells (corneocytes) in a layered lipid matrix. Using atomistic simulations we find that the equilibrium phase of the skin lipids is inverse micellar. A model of the corneocyte is used to demonstrate that lamellar layering is induced by the patterned corneocyte wall. The inverse micellar phase is consistent with in vivo observations in regions where corneocyte walls are well separated (lacunar spaces) and in the inner layers of skin, and suggests a functional role in the lipid synthesis pathway in vivo.

Numerical prediction of nonlinear rheology of branched polymer melts

In a recent short communication [Read, D. J. et al., Science 333, 1871 (2011)], we showed that a computational scheme can describe the nonlinear flow properties for a series of industrial low-density polyethylene (LDPE) resins starting from the molecular architecture. The molecular architecture itself is determined by fitting parameters of a reaction kinetics model to average structural information obtained from gel-permeation chromatography and light scattering. Flow responses of these molecules in transient uniaxial extension and shear are calculated by mapping the stretch and orientation dynamics of the segments within the molecules to effective pom-pom modes. In this paper, we provide the details of the computational scheme and present additional results on a LDPE and a high-density polyethylene resin to illustrate the dependence of segmental maximum stretch variables on the flow rate.

BOND-ORIENTATIONAL ORDERING AND SHEAR RIGIDITY IN MODULATED COLLOIDAL LIQUIDS

From Landau–Alexander–McTague theory and Monte Carlo simulation results we show that the modulated liquid obtained by subjecting a colloidal system to a periodic laser modulation has long range bond-orientational order and non-zero shear rigidity. From infinite field simulation results we show that in the modulated liquid phase, the translational order parameter correlation function decays to zero exponentially while the correlation function for the bond-orientational order saturates to a finite value at large distances.

Pom-pom-like constitutive equations for comb polymers

In analogy with the pom-pom model, we introduce a simple model for comb polymers with multiple side-arms attached to a linear backbone by considering a set of coupled equations describing the stretch in the individual interbranch backbone segments. The stretch equations predict a sudden onset of backbone stretch as the flow rate is increased. Drag-strain coupling smooths this transition to some extent. For a series of well characterized polyisoprene and polystyrene combs, we find good agreement with the experimentally determined transient stress growth coefficients in uniaxial extension.

The physics of stratum corneum lipid membranes.

The stratum corneum (SC), the outermost layer of skin, comprises rigid corneocytes (keratin-filled dead cells) in a specialized lipid matrix. The continuous lipid matrix provides the main barrier against uncontrolled water loss and invasion of external pathogens. Unlike all other biological lipid membranes (such as intracellular organelles and plasma membranes), molecules in the SC lipid matrix show small hydrophilic groups and large variability in the length of the alkyl tails and in the numbers and positions of groups that are capable of forming hydrogen bonds. Molecular simulations provide a route for systematically probing the effects of each of these differences separately. In this article, we present the results from atomistic molecular dynamics of selected lipid bilayers and multi-layers to probe the effect of these polydispersities. We address the nature of the tail packing in the gel-like phase, the hydrogen bond network among head groups, the bending moduli expected for leaflets comprising SC lipids and the conformation of very long ceramide lipids in multi-bilayer lipid assemblies. This article is part of the themed issue ‘Soft interfacial materials: from fundamentals to formulation’.