Mushroom Regime Research Articles

Addressing Nanocomposite Systems via 3D-SCFT: Assessment of Smearing Approximation and Irregular Grafting Distributions

We develop a three-dimensional self-consistent field-theoretic approach (3D-SCFT) for polymer matrix nanocomposites of arbitrary geometries, e.g., polymer-grafted nanoparticles (PGNPs), polymer brushes, and particle solids. The spatio-temporal discretization of Edwards’s diffusion equation is realized with the finite element method (FEM). Unidimensional implementations for PGNPs (1D-SCFT) invoke the smearing approximation (SA), which treats the grafting points as being delocalized across a spherical shell. By conducting detailed comparisons between 1D-SCFT and 3D-SCFT, we assess the accuracy of the SA in terms of reproducing key structural and thermodynamic properties of dilute grafted silica/polystyrene NPs in molten polystyrene. The SA yields accurate radially averaged structural features such as the mean brush thickness and its scaling with grafting density, chain length, and particle size. The free energy is reproduced accurately as well, albeit noticeable deviations are observed when transitioning toward the mushroom regime. In the SA, the stretching free energy is a function of the radial distance of the free end of a grafted chain from the particle surface. In 3D-SCFT, the grafting points are fixed in space, and thus chain stretching is described more accurately. 3D-SCFT offers direct access to the spatial distribution of the segment density of a chain and affords detailed visualization of the mushroom-to-dense brush transition, at the levels of both the whole system and individual grafted chains. By taking advantage of the single-chain representation in 3D-SCFT, we explore NPs with arbitrary grafting distributions (e.g., rings, tadpoles, and dual-poles) and the corresponding variation of the free energy and structural properties. To the best of the authors’ knowledge, this is the first time that the grafting distribution is examined as an additional degree of freedom in a 3D field-theoretic framework. Our work constitutes a step toward the computational design of nanocomposites with tailor-made self-assembly properties, achieved by controlling the interactions of nanoparticles through modulation of the distribution of points of attachment of grafted chains on their surface (e.g., Janus particles).

Paclitaxel-Loaded Cationic Fluid Lipid Nanodiscs and Liposomes with Brush-Conformation PEG Chains Penetrate Breast Tumors and Trigger Caspase-3 Activation.

Novel approaches are required to address the urgent need to develop lipid-based carriers of paclitaxel (PTX) and other hydrophobic drugs for cancer chemotherapy. Carriers based on cationic liposomes (CLs) with fluid (i.e., chain-melted) membranes (e.g., EndoTAG-1) have shown promise in preclinical and late-stage clinical studies. Recent work found that the addition of a cone-shaped poly(ethylene glycol)-lipid (PEG-lipid) to PTX-loaded CLs (CLsPTX) promotes a transition to sterically stabilized, higher-curvature (smaller) nanoparticles consisting of a mixture of PEGylated CLsPTX and PTX-containing fluid lipid nanodiscs (nanodiscsPTX). These CLsPTX and nanodiscsPTX show significantly improved uptake and cytotoxicity in cultured human cancer cells at PEG coverage in the brush regime (10 mol % PEG-lipid). Here, we studied the PTX loading, in vivo circulation half-life, and biodistribution of systemically administered CLsPTX and nanodiscsPTX and assessed their ability to induce apoptosis in triple-negative breast-cancer-bearing immunocompetent mice. We focused on fluid rather than solid lipid nanodiscs because of the significantly higher solubility of PTX in fluid membranes. At 5 and 10 mol % of a PEG-lipid (PEG5K-lipid, molecular weight of PEG 5000 g/mol), the mixture of PEGylated CLsPTX and nanodiscsPTX was able to incorporate up to 2.5 mol % PTX without crystallization for at least 20 h. Remarkably, compared to preparations containing 2 and 5 mol % PEG5K-lipid (with the PEG chains in the mushroom regime), the particles at 10 mol % (with PEG chains in the brush regime) showed significantly higher blood half-life, tumor penetration, and proapoptotic activity. Our study suggests that increasing the PEG coverage of CL-based drug nanoformulations can improve their pharmacokinetics and therapeutic efficacy.

Material Properties, Dissolution and Time Evolution of PEGylated Lipid-Shelled Microbubbles: Effects of the Polyethylene Glycol Hydrophilic Chain Configurations.

Polyethylene glycol (PEG) is often added to the lipid coating of a contrast microbubble to prevent coalescence and improve circulation. At high surface density, PEG chains are known to undergo a transition from a mushroom configuration to an extended brush configuration. We investigated the effects of PEG chain configuration on attenuation and dissolution of microbubbles by varying the molar ratio of the PEGylated lipid in the shell with three (0%, 2% and 5%) in the mushroom configuration and two (10% and 20%) in the brush configuration. We measured attenuation through the bubble suspensions and used it to obtain the characteristic rheological properties of their shells according to two interfacial rheological models. The interfacial elasticity was found to be significantly lower in the brush regime (∼0.6 N/m) than in the mushroom regime (∼1.3 N/m), but similar in value within each regime. The dissolution behavior of microbubbles under acoustic excitation inside an air-saturated medium was studied by measuring the time-dependent attenuation. Total attenuation recorded a transient increase because of growth resulting from air influx and an eventual decrease caused by dissolution. Microbubble shell composition with varying PEG concentrations had significant effects on dissolution dynamics.

Boundary Conditions and Polymeric Drag Reduction for the Navier–Stokes Equations

Reducing wall drag in turbulent pipe and channel flows is an issue of great practical importance. In engineering applications, end-functionalized polymer chains are often employed as agents to reduce drag. These are polymers which are floating in the solvent and attach (either by adsorption or through irreversible chemical binding) at one of their chain ends to the substrate (wall). We propose a PDE model to study this setup in the simple setting where the solvent is a viscous incompressible Navier–Stokes fluid occupying the bulk of a smooth domain \(\Omega \subset {\mathbb {R}}^d\), and the wall-grafted polymer is in the so-called mushroom regime (inter-polymer spacing on the order of the typical polymer length). The microscopic description of the polymer enters into the macroscopic description of the fluid motion through a dynamical boundary condition on the wall-tangential stress of the fluid, something akin to (but distinct from) a history-dependent slip-length. We establish the global well-posedness of strong solutions in two-spatial dimensions and prove that the inviscid limit to the strong Euler solution holds with a rate. Moreover, the wall-friction factor \(\langle f\rangle \) and the global energy dissipation \(\langle \varepsilon \rangle \) vanish inversely proportional to the Reynolds number \(\mathbf{Re } \). This scaling corresponds to Poiseuille’s law for the friction factor \(\langle f\rangle \sim 1/\mathbf{Re } \) for laminar flow and thereby quantifies drag reduction in our setting. These results are in stark contrast to those available for physical boundaries without polymer additives modeled by, for example, no-slip conditions, where no such results are generally known even in two-dimensions.

Structure and thermodynamics of grafted silica/polystyrene dilute nanocomposites investigated through self-consistent field theory.

Polymer/matrix nanocomposites (PNCs) are materials with exceptional properties. They offer a plethora of promising applications in key industrial sectors. In most cases, it is preferable to disperse the nanoparticles (NPs) homogeneously across the matrix phase. However, under certain conditions NPs might lump together and lead to a composite material with undesirable properties. A common strategy to stabilize the NPs is to graft on their surface polymer chains of the same chemical constitution as the matrix chains. There are several unresolved issues concerning the optimal molar mass and areal density of grafted chains that would ensure best dispersion, given the nanoparticles and the polymer matrix. We propose a model for the prediction of key structural and thermodynamic properties of PNC and apply it to a single spherical silica (SiO2) nanoparticle or planar surface grafted with polystyrene chains embedded at low concentration in a matrix phase of the same chemical constitution. Our model is based on self-consistent field theory, formulated in terms of the Edwards diffusion equation. The properties of the PNC are explored across a broad parameter space, spanning the mushroom regime (low grafting densities, small NPs and chain lengths), the dense brush regime, and the crowding regime (large grafting densities, NP diameters, and chain lengths). We extract several key quantities regarding the distributions and the configurations of the polymer chains, such as the radial density profiles and their decomposition into contributions of adsorbed and free chains, the chains/area profiles, and the tendency of end segments to segregate at the interfaces. Based on our predictions concerning the brush thickness, we revisit the scaling behaviors proposed in the literature and we compare our findings with experiment, relevant simulations, and analytic models, such as Alexander's model for incompressible brushes.

Effects of graft locations on dispersion behavior of polymer-grafted nanorods: A molecular dynamics simulation study

In this paper, we present the effects of graft locations on the dispersion behavior of polymer-grafted nanorods using molecular dynamics simulations. Four graft locations of chains on nanorods, i.e., end-grafted, quarter-grafted, middle-grafted and uniformly grafted, are specially designed, and the effects of graft locations are examined in both sparsely grafted case and densely grafted case. Simulation results show that the end-grafted nanorods exhibit the poorest dispersion in the matrix, whilst the body-grafted (quarter-grafted and middle-grafted) ones show the best dispersion. At low grafting density in the mushroom regime, the middle-grafted disperse slightly better than the quarter-grafted, whereas at high grafting density in the brush regime, the situation is reversed. By analyzing the conformations of graft chains (mushroom height and brush height) and the behavior of grafted nanorods, it is inferred that the inter-rod cohesive energy provides a great contribution to the dispersion, as reflected by the significant role of the center region of nanorods. In general, a dense and wide coverage of the center/middle region of nanorods by graft chains can effectively improve the nanorod dispersion. This work is expected to provide some guidance on controlling and improving the dispersion of nanorods in polymer nanocomposites.

Effects of shell chemistry on acoustic response and dissolution behavior of lipid-coated microbubbles

Microbubbles have been widely used as contrast agents for ultrasound imaging. They are also being investigated for therapeutic applications including as a vehicle for ultrasound activated targeted drug delivery. Here the effects of the shell chemistry on the acoustic response and dissolution behavior of microbubbles have been investigated. Microbubbles encapsulated by a lipid shell (DPPC and DPPE-PEG2000) were prepared with different PEG molar ratios (0% to 20%) investigating their concentration, size distribution, stability and material properties. Note that different PEG concentrations were previously shown to result in different PEG surface configuration: mushroom for lower PEG concentrations and brush for higher ones. The microbubbles in the brush regime seem to generate higher fundamental and subharmonic scattering components at 2.25 MHz excitation, while the higher harmonics seems unaffected. Microbubbles in the mushroom regime showed different dissolution behavior with longer growth period before dissolution. This is believed to be resulted from a less permeable shell in comparison to shells in brush regime. The relation between acoustic response, dissolution behavior and material properties of the shell will be discussed.

Small-Angle Neutron Scattering Reveals the Structural Details of Thermosensitive Polymer-Grafted Cellulose Nanocrystal Suspensions.

Thanks to the use of small-angle neutron scattering (SANS), a detailed structural description of thermosensitive polymer-grafted cellulose nanocrystals (CNCs) was obtained and the behavior of aqueous suspensions of these derivatized biosourced particles upon temperature increase was revealed. Although literature data show that the surface grafting of thermosensitive polymers drastically enhances the colloidal properties of CNCs, direct space microscopic investigation techniques fail in providing sufficient structural information on these objects. In the case of CNCs decorated with temperature-sensitive polyetheramines following a peptide coupling reaction, a qualitative and quantitative analysis of SANS spectra shows that CNCs are homogeneously covered by a shell comprising polymer chains in a Gaussian conformation with a thickness equal to their radius of gyration in solution, thus revealing a mushroom regime. An increase of the temperature above the lower critical solution temperature (LCST) of the polyetheramine results in the formation of finite size bundles whose aggregation number depends on the particle concentration and suspension temperature deviation from the LCST. SANS analysis further reveals local changes at the CNC surface corresponding to a release of water molecules and a related denser polymer shell conformation. Noticeably, data show a full reversibility at all length scales when a sample was cooled down to below the LCST after being heated above it. Overall, the results obtained by SANS allow an in-depth structural investigation of derivatized CNCs, which is of high interest for the design of functional materials comprising these biosourced colloids.

Tuning the Multifunctionality of Iron Oxide Nanoparticles Using Self-Assembled Mixed Lipid Layers.

We present an approach to tuning the multifunctionality of iron oxide nanoparticles (IONs) using mixed self-assembled monolayers of cationic lipid and anionic polyethylene glycol (PEG) lipid. By forming stable, monodispersed lipid-coated IONs (L-IONs) through a solvent-exchange technique, we were able to demonstrate the relationship between surface charge, the magnetic transverse relaxivity (r2 from T2-weighted images), and the binding capacity of small interfering ribonucleic acids (siRNAs) as a function of the cationic-to-anionic (PEG) lipid ratio. These properties were controlled by the cationic charge and the PEG conformation; relaxivity and siRNA binding could be varied in the mushroom and brush regimes but not at high brush densities. In vitro results combining cell viability, uptake, and transfection efficiency using HeLa cells suggest that the functional physicochemical and biological properties of L-IONs may be best achieved using catanionic lipid coatings near equimolar ratios of cationic to anionic PEG-lipids.

End-anchored polymers in good solvents from the single chain limit to high anchoring densities.

An increasing number of applications utilize grafted polymer layers to alter the interfacial properties of solid substrates, motivating refinement in our theoretical understanding of such layers. To assess existing theoretical models of them, we have investigated end-anchored polymer layers over a wide range of grafting densities, σ, ranging from a single chain to high anchoring density limits, chain lengths ranging over two orders of magnitude, for very good and marginally good solvent conditions. We compare Monte Carlo and molecular dynamics simulations, numerical self-consistent field calculations, and experimental measurements of the average layer thickness, h, with renormalization group theory, the Alexander-de Gennes mushroom theory, and the classical brush theory. Our simulations clearly indicate that appreciable inter-chain interactions exist at all simulated areal anchoring densities so that there is no mushroom regime in which the layer thickness is independent of σ. Moreover, we find that there is no high coverage regime in which h follows the predicted scaling, h ∼ Nσ1/3, for classical polymer brushes either. Given that no completely adequate analytic theory seems to exist that spans wide ranges of N and σ, we applied scaling arguments for h as a function of a suitably defined reduced anchoring density, defined in terms of the solution radius of gyration of the polymer chains and N. We find that such a scaling approach enables a smooth, unified description of h in very good solvents over the full range of anchoring density and chain lengths, although this type of data reduction does not apply to marginal solvent quality conditions.

Influence of Chain Stiffness, Grafting Density and Normal Load on the Tribological and Structural Behavior of Polymer Brushes: A Nonequilibrium-Molecular-Dynamics Study.

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work.

Quantitative analyses of PEGylated phospholipids adsorbed on single walled carbon nanohorns by high resolution magic angle spinning 1H NMR

Adsorption of polyethylene glycol conjugated phospholipids with various PEG chain length (DSPE-PEG5000, 2000, 750) onto single-walled carbon nanohorns (SWCNH), a type of graphene nano-tubule, in aqueous solution was investigated by means of high-resolution magic angle spinning (HRMAS) 1H NMR. Peak integral ratio of PEG chains and alkyl chains of DSPE-PEGs in the NMR spectra linearly decreased to zero with the increase of SWCNH quantity, indicating that the adsorption of DSPE-PEGs on SWCNH was virtually irreversible. The area of SWCNH surface allocated to the individual DSPE-PEG5000, 2000, 750 molecule were estimated to be 7.06, 5.18, and 4.45 nm2, respectively. Coverages of the alkyl chains on the surface area of SWCNH were about 28%, 39% for DSPE-PEG5000, 2000 and 46% for DSPE-PEG750, suggesting single layer adsorption. We presumed that the electrostatic repulsion may prevent DSPE-PEGs from multiple layer and keep away neighbouring DSPE-PEGs on the surface. According to the molecular areas of the DSPE-PEGs, PEG5000 and 2000 chains were considered to be in brush-regimes, while PEG750 was considered to be in mushroom regime on the SWCNH surface.

Study of Dynamic Rheological, Dynamic Mechanical and Creep Properties of Acrylonitrile Styrene Acrylate (ASA)/Zn+2poly(ethylene-co-methacrylic acid) Ionomer Blend

A new class of blend system comprising weather resistant acrylonitrile/styrene/acrylate (ASA) terpolymer and Zn-ionomer was developed. Based on Zn-ionomer content, the blend system either forms ‘mushroom’ or ‘brush’ type conformation which affected dynamic rheology, DSC, DMA and creep properties differently. Formation of ionic crosslinkings by Zn-ionomer in ‘brush regime’ as well as limited ionic crosslinkings in ‘mushroom regime’ resulted in different nature molecular chain relaxation response. The DSC endotherm peak and glass transition temperature were also influenced by the type of conformation and ion-dipole interaction between the blend components. The tan δ from DMA study also reflected the similar trend. The creep deformation behavior of the blend was found to be dependent on highly deformable Zn-ionomer content and with temperature. The Findley model analysis suggests the ionic crosslinkings may be the possible reason for controlled creep deformation of the blend.

Quantitative study of fluctuation effects by fast lattice Monte Carlo simulations: Compression of grafted homopolymers

Using fast lattice Monte Carlo (FLMC) simulations [Q. Wang, Soft Matter 5, 4564 (2009)] and the corresponding lattice self-consistent field (LSCF) calculations, we studied a model system of grafted homopolymers, in both the brush and mushroom regimes, in an explicit solvent compressed by an impenetrable surface. Direct comparisons between FLMC and LSCF results, both of which are based on the same Hamiltonian (thus without any parameter-fitting between them), unambiguously and quantitatively reveal the fluctuations/correlations neglected by the latter. We studied both the structure (including the canonical-ensemble averages of the height and the mean-square end-to-end distances of grafted polymers) and thermodynamics (including the ensemble-averaged reduced energy density and the related internal energy per chain, the differences in the Helmholtz free energy and entropy per chain from the uncompressed state, and the pressure due to compression) of the system. In particular, we generalized the method for calculating pressure in lattice Monte Carlo simulations proposed by Dickman [J. Chem. Phys. 87, 2246 (1987)], and combined it with the Wang-Landau-Optimized Ensemble sampling [S. Trebst, D. A. Huse, and M. Troyer, Phys. Rev. E 70, 046701 (2004)] to efficiently and accurately calculate the free energy difference and the pressure due to compression. While we mainly examined the effects of the degree of compression, the distance between the nearest-neighbor grafting points, the reduced number of chains grafted at each grafting point, and the system fluctuations/correlations in an athermal solvent, the θ-solvent is also considered in some cases.

Observing the Mushroom-to-Brush Transition for Kinesin Proteins

The height of polymers grafted to a surface is predicted to be constant at low densities ("mushroom" regime) and increase with the third root of the polymer surface density at high densities ("brush" regime). This mushroom-to-brush transition is explored with kinesin-1 proteins adhered to a surface at controlled densities. The kinesin height is measured by attaching fluorescently labeled microtubules to the kinesins and determining their elevation using fluorescence interference contrast microscopy. Our measurements are consistent with a mushroom regime and a brush regime and a transition near the theoretically predicted density. The mushroom-to-brush transition may play a role in protein behavior in crowded cellular environments and may be exploited as a signal in intracellular regulation and mechanotransduction.

Influence of Shell Composition on the Resonance Frequency of Microbubble Contrast Agents

The effect of variations in microbubble shell composition on microbubble resonance frequency is revealed through experiment. These variations are achieved by altering the mole fraction and molecular weight of functionalized polyethylene glycol (PEG) in the microbubble phospholipid monolayer shell and measuring the microbubble resonance frequency. The resonance frequency is measured via a chirp pulse and identified as the frequency at which the pressure amplitude loss of the ultrasound wave is the greatest as a result of passing through a population of microbubbles. For the shell compositions used herein, we find that PEG molecular weight has little to no influence on resonance frequency at an overall PEG mole fraction (0.01) corresponding to a mushroom regime and influences the resonance frequency markedly at overall PEG mole fractions (0.050–0.100) corresponding to a brush regime. Specifically, the measured resonance frequency was found to be 8.4, 4.9, 3.3 and 1.4 MHz at PEG molecular weights of 1000, 2000, 3000 and 5000 g/mol, respectively, at an overall PEG mole fraction of 0.075. At an overall PEG mole fraction of just 0.01, on the other hand, resonance frequency exhibited no systematic variation, with values ranging from 5.7 to 4.9 MHz. Experimental results were analyzed using the Sarkar bubble dynamics model. With the dilatational viscosity held constant (10–8 N·s/m) and the elastic modulus used as a fitting parameter, model fits to the pressure amplitude loss data resulted in elastic modulus values of 2.2, 2.4, 1.6 and 1.8 N/m for PEG molecular weights of 1000, 2000, 3000 and 5000 g/mol, respectively, at an overall PEG mole fraction of 0.010 and 4.2, 1.4, 0.5 and 0.0 N/m, respectively, at an overall PEG mole fraction of 0.075. These results are consistent with theory, which predicts that the elastic modulus is constant in the mushroom regime and decreases with PEG molecular weight to the inverse 3/5 power in the brush regime. Additionally, these results are consistent with inertial cavitation studies, which revealed that increasing PEG molecular weight has little to no effect on inethe rtial cavitation threshold in the mushroom regime, but that increasing PEG molecular weight decreases inertial cavitation markedly in the brush regime. We conclude that the design and synthesis of microbubbles with a prescribed resonance frequency is attainable by tuning PEG composition and molecular weight.

Polymer–polymer adhesion with mobile promoters: Connector length dependence

The adhesion between two immiscible polymers stitched together via mobile chains is studied with large scale molecular simulations employing a coarse-grained bead-spring model. An adhesion model is presented that incorporates both connector molecular slipping out viscously and bulk dissipation in two dissimilar glassy polymers, in which one is dense melt and another is loose. The contributions to the separation work from thermodynamics and chain suction are studied in dependence of the connector length, at constant temperature, and at fixed basic molecular parameters. It is shown that connector length relative to its entanglement length can enhance the adhesion toughness and interfacial strength. Bulk dissipation is not considerable with low connector areal density in mushroom regime, while becomes more evident in the loose melt with increasing connector length when the coverage density is increased up to overlapping brush regime. The results provide insight into the structure evolution of adhesion interface with mobile promoter molecular, which are useful for future developments of continuum cohesive models for fracture of polymer–polymer interfaces.

Polymer-polymer adhesion with mobile promoters: Connector areal density dependence

The adhesion between two immiscible polymers stitched together via mobile promoters is studied with large scale molecular simulations employing a coarse-grained bead-spring model. An adhesion model is presented that enables both connector molecular slipping out viscously and bulk dissipation in two dissimilar glassy polymers, in which one is dense melt and another is loose. The contributions to the separation work from thermodynamics and chain suction are studied in dependence of the connector areal density, at constant temperature, and at fixed basic molecular parameters. It is shown that high connector coverage, but below saturation areal density, can enhance the adhesion toughness and interfacial strength. Bulk dissipation is not considerable with low connector areal density in mushroom regime, while becomes more evident in the loose block when the coverage density is increased up to overlapping brush regime. With increasing connector length, both bulk melts are enhanced by the segments of connector chains that penetrated in. The results provide insight into the structure evolution of adhesion interface coupled with promoter molecular, which are useful for future developments of continuum cohesive models for fracture of polymer- polymer interfaces.

Substrate-Independent Method for Growing and Modulating the Density of Polymer Brushes from Surfaces by ATRP

We describe a method for grafting PEG-based polymer chains of variable surface density using a substrate independent approach, allowing grafting from virtually any material substrate. The approach relies upon initial coupling of a macroinitiator to plasma polymer treated surfaces. The macroinitiator is a novel random terpolymer containing ATRP initiator residues, strongly negatively charged groups, and carboxylic acid moieties that facilitate covalent surface anchoring. Surface-initiated ATRP (SI-ATRP) using polyethylene glycol methyl ether methacrylate (PEGMA) at different concentrations led to grafted surfaces of controlled thickness in either the "brush" or "mushroom" morphology, which was controlled by the abundance of initiator residues in the macroinitiator. Grafted polymer layer structure was investigated via direct interaction force measurements using colloid probe atomic force microscopy (AFM). Equilibrium, hydrated graft layer thicknesses inferred from the highly repulsive AFM force data suggest that the polymer brush graft layer contained polymer chains which were fully stretched. Since the degree of stretching resulted in layer thicknesses approaching the polymer contour length, the polymer brushes studied must be very close to maximum graft density. Grafted layers where the polymer molecules were in the mushroom regime resulted in much thinner layers but the chains had greater chain entropic freedom as indicated by strongly attractive bridging interactions between tethered chains and the silica colloid probe. Use of this experimental methodology would be suitable for preparing grafted polymer layers of a preferred density free from substrate-specific linking chemistries.

Bursting Bubbles and Bilayers

This paper discusses various interactions between ultrasound, phospholipid monolayer-coated gas bubbles, phospholipid bilayer vesicles, and cells. The paper begins with a review of microbubble physics models, developed to describe microbubble dynamic behavior in the presence of ultrasound, and follows this with a discussion of how such models can be used to predict inertial cavitation profiles. Predicted sensitivities of inertial cavitation to changes in the values of membrane properties, including surface tension, surface dilatational viscosity, and area expansion modulus, indicate that area expansion modulus exerts the greatest relative influence on inertial cavitation. Accordingly, the theoretical dependence of area expansion modulus on chemical composition - in particular, poly (ethylene glyclol) (PEG) - is reviewed, and predictions of inertial cavitation for different PEG molecular weights and compositions are compared with experiment. Noteworthy is the predicted dependence, or lack thereof, of inertial cavitation on PEG molecular weight and mole fraction. Specifically, inertial cavitation is predicted to be independent of PEG molecular weight and mole fraction in the so-called mushroom regime. In the “brush” regime, however, inertial cavitation is predicted to increase with PEG mole fraction but to decrease (to the inverse 3/5 power) with PEG molecular weight. While excellent agreement between experiment and theory can be achieved, it is shown that the calculated inertial cavitation profiles depend strongly on the criterion used to predict inertial cavitation. This is followed by a discussion of nesting microbubbles inside the aqueous core of microcapsules and how this significantly increases the inertial cavitation threshold. Nesting thus offers a means for avoiding unwanted inertial cavitation and cell death during imaging and other applications such as sonoporation. A review of putative sonoporation mechanisms is then presented, including those involving microbubbles to deliver cargo into a cell, and those - not necessarily involving microubbles - to release cargo from a phospholipid vesicle (or reverse sonoporation). It is shown that the rate of (reverse) sonoporation from liposomes correlates with phospholipid bilayer phase behavior, liquid-disordered phases giving appreciably faster release than liquid-ordered phases. Moreover, liquid-disordered phases exhibit evidence of two release mechanisms, which are described well mathematically by enhanced diffusion (possibly via dilation of membrane phospholipids) and irreversible membrane disruption, whereas liquid-ordered phases are described by a single mechanism, which has yet to be positively identified. The ability to tune release kinetics with bilayer composition makes reverse sonoporation of phospholipid vesicles a promising methodology for controlled drug delivery. Moreover, nesting of microbubbles inside vesicles constitutes a truly “theranostic” vehicle, one that can be used for both long-lasting, safe imaging and for controlled drug delivery.