Engineering single-polymer micelle shape using nonuniform spontaneous surface curvature.

Conventional micelles, composed of simple amphiphiles, exhibit only a few standard morphologies, each characterized by its mean surface curvature set by the amphiphiles. Here we demonstrate a rational design scheme to construct micelles of more general shape from polymeric amphiphiles. We replace the many amphiphiles of a conventional micelle by a single flexible, linear, block copolymer chain containing two incompatible species arranged in multiple alternating segments. With suitable segment lengths, the chain exhibits a condensed spherical configuration in solution, similar to conventional micelles. Our design scheme posits that further shapes are attained by altering the segment lengths. As a first study of the power of this scheme, we demonstrate the capacity to produce long-lived micelles of horseshoe form using conventional bead-spring simulations in two dimensions. Modest changes in the segment lengths produce smooth changes in the micelle's shape and stability.

Predicting tensorial electrophoretic effects in asymmetric colloids.

We formulate a numerical method for predicting the tensorial linear response of a rigid, asymmetrically charged body to an applied electric field. This prediction requires calculating the response of the fluid to the Stokes drag forces on the moving body and on the countercharges near its surface. To determine the fluid's motion, we represent both the body and the countercharges using many point sources of drag known as Stokeslets. Finding the correct flow field amounts to finding the set of drag forces on the Stokeslets that is consistent with the relative velocities experienced by each Stokeslet. The method rigorously satisfies the condition that the object moves with no transfer of momentum to the fluid. We demonstrate that a sphere represented by 1999 well-separated Stokeslets on its surface produces flow and drag force like a solid sphere to 1% accuracy. We show that a uniformly charged sphere with 3998 body and countercharge Stokeslets obeys the Smoluchowski prediction [F. Morrison, J. Colloid Interface Sci. 34, 210 (1970)JCISA50021-979710.1016/0021-9797(70)90171-2] for electrophoretic mobility when the countercharges lie close to the sphere. Spheres with dipolar and quadrupolar charge distributions rotate and translate as predicted analytically to 4% accuracy or better. We describe how the method can treat general asymmetric shapes and charge distributions. This method offers promise as a way to characterize and manipulate asymmetrically charged colloid-scale objects from biology (e.g., viruses) and technology (e.g., self-assembled clusters).

How long must humans live?

Species are defined by biological criteria. This characterization, however, misses the most unique aspect of our species; namely, an ability to invent technologies that reduce mortality risks. Old animals are rare in nature, but survival to old age has become commonplace in humans. Science now asks how long can humans live, but we suggest a more appropriate question is: How long must humans live? Three lines of evidence are used to identify the biological equivalent of a warranty period for humans and why it exists. The effective end of reproduction, the age when the sex ratio is unity, and the acceleration of mortality reveal that approximately 50-55 years is sufficient time for our species to achieve its biological mandate-Darwinian fitness. Identifying this boundary is biomedically important because it represents a transition from expected health and vigor to a period when health and vigor become progressively harder to maintain.

Orientational ordering of colloidal dispersions by application of time-dependent external forces.

We discuss a method of organizing incoherent motion of a colloidal suspension to produce synchronized, coherent motion, extending the discussion of our recent Letter [Moths and Witten, Phys. Rev. Lett. 110, 028301 (2013)]. The method does not require interaction between the objects. Instead, the effect is controlled by the "twist matrix" which gives the angular velocity of an asymmetric object in a fluid resulting from a weak external force. We analyze the two types of forcing considered in the Letter: a force alternating between two directions and a continuously rotating force. For the alternating force, we justify the claim of the Letter that under appropriate forcing conditions, the orientational entropy of the objects decreases indefinitely with time, on average. We provide a bound on that rate in terms of the twist matrix. For the case of rotating force, we derive conditions for phased-locked motion of the objects to the force and prove that there is only one stable phase-locked orientation under these conditions. We find numerically that the fastest alignment typically occurs for tilt angles of order unity. We discuss how the alignment effect scales with the object size for external forcing caused by gravity or an electric field. Under practical forcing conditions we estimate that the alignment should persist despite rotational diffusion for objects larger than about 10 microns. Potential misalignment owing to hydrodynamic interaction of the objects is estimated to be negligible at volume fractions smaller than about 10(-4.5) (10(-3)) when the forcing is gravitational (electrophoretic).

Full alignment of colloidal objects by programed forcing.

By analysis and simulation, we demonstrate two methods for achieving complete orientational alignment of a set of identical asymmetric colloidal objects dispersed randomly in a fluid. Sedimentation or electrophoresis in a constant field can lead to partial alignment, in which the objects rotate about a common body axis, but the phases of rotation for these objects are random. We show that this phase disorder can be removed by two forms of programed forcing. First, simply alternating the forcing between two directions reduces the statistical entropy of the orientation arbitrarily. Second, the addition of a small rotating component to the applied field in analogy to magnetic resonance can lead to phase locking of the objects' orientation. We identify conditions for alignment of a broad class of generic objects and discuss practical limitations.

Wilhelmy plate artifacts in elastic monolayers.

A recent article [L. Pocivavsek et al., Soft Matter4, 2019 (2008)] by some of us pointed out difficulties in interpreting Wilhelmy plate measurements on elastic Langmuir monolayers that support anisotropic stress. Using a simplified geometry it showed conditions in which the Wilhelmy plate measures significantly different stress from the ambient stress. We correct a serious error in this analysis and strengthen its conclusion, showing that the Wilhelmy stress and the ambient stress can have opposite signs.

Spontaneous free-boundary structure in crumpled membranes.

We investigate the strong curvature that appears at the boundaries of a thin crumpled elastic membrane. We account for these high-curvature regions in terms of the stretching-ridge singularity believed to dominate the structure of strongly deformed elastic membranes. Using a membrane fastened to itself to form a bag shape with a single stretching ridge, we show that the creation of points of high boundary curvature lowers the interior ridge's energy. In the limit of small thickness, the induced curvature becomes arbitrarily strong on the scale of the object size and results in sharp edges connecting interior vertices to the boundary. We analyze these edges as conical sectors with no stretching. As the membrane size diverges, the edge energy grows as the square root of the central ridge energy. For comparison, we discuss the effect of truncating a stretching ridge at its ends. The effect of truncation becomes appreciable when the truncation length is comparable to the width of the untruncated ridge.

Validation of photographic food records in children: are pictures really worth a thousand words?

BACKGROUND/OBJECTIVES: Self-reported food records are commonly used to estimate dietary intake. However, diet diaries are time consuming for participants and children are often unfamiliar with standard portion sizes or weights/volume of foods that can add to the error associated with self-reported intake. We hypothesize that photographic food records to assess dietary intake will be as accurate as a standard food diary and will decrease participant/family burden. SUBJECTS/METHODS: A total of 28 healthy subjects, 10-16 years, consumed a weighed diet for 3 days and returned any uneaten items for weigh back on day 4. During the 3 days of weighed diet, subjects recorded all intake both using a standard diet diary and taking photographs before and after consumption. Photographs were analyzed by two independent dieticians for estimation of serving size. The actual amount consumed was compared to the diary and photographic estimates through Spearman's correlation coefficients and confidence intervals. RESULTS: There was no difference between the diet diary and photographic estimates of total energy, carbohydrate, fat, protein, fiber, vitamins A, D and E, calcium, iron or zinc compared to actual intake. However, both participants and their parents reported that the photographic method was quicker, simpler and would be preferred if they were to record dietary intake in the future. In this study cohort, 36% of subjects accurately reported actual daily energy intake (+/-5% of actual intake), only 29% underreported energy intake and 35% overreported energy intake. CONCLUSIONS: Photographic food records can be used to accurately estimate dietary intake in a pediatric population. In addition, this method is less burdensome for the participants and their family.

Microscopic wrinkles on supported surfactant monolayers.

We discuss mechanical buckling instabilities of a rigid film under compression interacting repulsively with a substrate through a thin fluid layer. The buckling occurs at a characteristic wavelength that increases as the one-fourth power of the bending stiffness, such as the gravitational instability studied previously by Milner However, the potential can affect the characteristic buckling wavelength strongly, as predicted by Huang and Suo. If the potential changes sufficiently sharply with thickness, this instability is continuous, with an amplitude varying as the square root of overpressure. We discuss three forms of interaction important for the case of Langmuir monolayers transferred to a substrate: Casimir-van der Waals interaction, screened charged double-layer interaction, and the Sharma potential. We verify these predictions numerically in the van der Waals case.

Microscopic folds and macroscopic jerks in compressed lipid monolayers.

We report hitherto unrecognized cooperative behavior in the stochastic collapse of certain compressed lipid monolayers implicated in pulmonary function. The cooperativity emerges from a statistical analysis of the collapse events captured using fluorescence microscopy and digital image analysis. The collapse events involve folding of the monolayer on a micron scale, yet each event produces a macroscopic jerk of the layer. The cooperative collapse is striking for its temporal sharpness and large spatial extent.

Surface charge relaxation and the pearling instability of charged surfactant tubes.

The pearling instability of bilayer surfactant tubes was recently observed during the collapse of fluid monolayers of binary mixtures of Dimyristoylphosphocholine (DMPC): Palmitoyloleoylphosphoglycerol (POPG) and Dipalmitoylphosphocholine (DPPC):POPG surfactants. It can be explained by a Rayleigh-like instability under the action of the bilayer surface tension. The magnitude of surface tension is dictated by the electrostatic interaction between charged surfactants. Relaxation of charged molecules is proposed here as an additional mechanism driving the instability. We find the functional dependence of the electrostatic surface tension and relaxation energies on the screening length kappa(-1) explicitly. Relaxation lowers the cost of bending a tube into pearls making the cylindrical tube even more unstable. It is known that for the weak screening case in which the tube radius is smaller than the screening length of the solution, this effect is important. However, for the case of strong screening it is negligible. For the experiments mentioned, the situation is marginal. In this case, we show that the effect of relaxation remains small. It contributes about 20% to the total electrostatic energy.

Confined multilamellae prefer cylindrical morphology. A theory of myelin formation.

By evaporating a drop of lipid dispersion we generate the myelin morphology often seen in dissolving surfactant powders. We explain these puzzling nonequilibrium structures using a geometric argument: the bilayer repeat spacing increases and thus the repulsion between bilayers decreases when a multilamellar disk is converted into a myelin without gain or loss of material and with number of bilayers unchanged. Sufficient reduction in bilayer repulsion can compensate for the cost in curvature energy, leading to a net stability of the myelin structure. A numerical estimate predicts the degree of dehydration required to favor myelin structures over flat lamellae.

Defect formation and kinetics of atomic terrace merging.

Pairs of atomic scale terraces on a single crystal metal surface can be made to merge controllably under suitable conditions to yield steps of double height and width. We study the effect of various physical parameters on the formation of defects in a kinetic model of step doubling. We treat this manifestly nonequilibrium problem by mapping the model onto a 1D random sequential adsorption problem and solving this analytically. We also do simulations to check the validity of our treatment. We find that our treatment effectively captures the dynamic evolution and the final state of the surface morphology. We show that the number and nature of the defects formed is controlled by a single dimensionless parameter q . For q close to one we show that the fraction of defects rises linearly with epsilon identical with 1-q as 0.284epsilon . We also show that one can arrive at the final state faster and with fewer defects by changing the parameter with time.

Trapping of vibrational energy in crumpled sheets.

We investigate the propagation of transverse elastic waves in crumpled media. We set up the wave equation for transverse waves on a generic curved, strained surface via a Langrangian formalism and use this to study the scaling behavior of the dispersion curves near the ridges and on the flat facets. This analysis suggests that ridges act as barriers to wave propagation and that modes in a certain frequency regime could be trapped in the facets. A simulation study of the wave propagation qualitatively supported our analysis and showed interesting effects of the ridges on wave propagation.

Singularities, structures, and scaling in deformed m-dimensional elastic manifolds.

The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges that meet in vertices. Elastic energy condensation should occur in response to compressive strain in elastic objects of any dimension greater than 1. We study elastic energy condensation numerically in two-dimensional elastic sheets embedded in spatial dimensions three or four and three-dimensional elastic sheets embedded in spatial dimensions four and higher. We represent a sheet as a lattice of nodes with an appropriate energy functional to impart stretching and bending rigidity. Minimum energy configurations are found for several different sets of boundary conditions. We observe two distinct behaviors of local energy density falloff away from singular points, which we identify as cone scaling or ridge scaling. Using this analysis, we demonstrate that there are marked differences in the forms of energy condensation depending on the embedding dimension.

The polymer mat: arrested rebound of a compressed polymer layer.

Compression of an adsorbed polymer layer distorts its relaxed structure. Surface force measurements from different laboratories show that the return to this relaxed structure after the compression is released can require tens of minutes and that the recovery time can grow rapidly with molecular weight. We argue that the arrested state of the free layer before relaxation can be described as a Guiselin brush structure (O. Guiselin, Europhys. Lett. 17, 225 (1992)), in which the monomer density falls off only weakly with distance from the surface. This brush structure predicts an exponential falloff of the force at large distance with a decay length that varies as the initial compression distance to the 6/5 power. This exponential falloff is consistent with surface force measurements. We propose a relaxation mechanism that accounts for the increase in relaxation time with chain length.

Anomalous strength of membranes with elastic ridges.

We report on a simulational study of the compression and buckling of elastic ridges formed by joining the boundary of a flat sheet to itself. Such ridges store energy anomalously: their resting energy scales as the linear size of the sheet to the 1/3 power. We find that the energy required to buckle such a ridge is a fixed multiple of the resting energy. Thus thin sheets with elastic ridges such as crumpled sheets are qualitatively stronger than smoothly bent sheets.

Topography and instability of monolayers near domain boundaries.

We theoretically study the topography of a biphasic surfactant monolayer in the vicinity of domain boundaries. The differing elastic properties of the two phases generally lead to a nonflat topography of "mesas," where domains of one phase are elevated with respect to the other phase. The mesas are steep but low, having heights of up to 10 nm. As the monolayer is laterally compressed, the mesas develop overhangs and eventually become unstable at a surface tension of about K(deltac(0))(2) (deltac(0) being the difference in spontaneous curvature and K a bending modulus). In addition, the boundary is found to undergo a topography-induced rippling instability upon compression, if its line tension is smaller than about Kdeltac(0). The effect of diffuse boundaries on these features and the topographic behavior near a critical point are also examined. We discuss the relevance of our findings to several experimental observations related to surfactant monolayers: (i) small topographic features recently found near domain boundaries; (ii) folding behavior observed in mixed phospholipid monolayers and model lung surfactants; (iii) roughening of domain boundaries seen under lateral compression; (iv) the absence of biphasic structures in tensionless surfactant films.

Pain perception and utility: a comparison of the syringe and computerized local injection techniques.

Thirty patients received maxillary infiltration and mandibular inferior alveolar nerve block injections with both a traditional syringe and a computerized system, the Wand. Patients noted their preference for either system and rated their injection pain and postoperative discomfort on a ten-point scale for each type of injection. Mean injection discomfort ratings with the Wand were lower than with the syringe but were not statistically significant. Reduced postoperative discomfort using the Wand for the inferior alveolar nerve block was significant. Both of the dentists in the study and those patients who stated a preference favored the Wand system.

Mortality-rate crossovers and maximum lifespan in advantaged and disadvantaged populations: accelerated-mortality and sudden-death models.

One population is advantaged relative to another by our definition if its survival function is greater at all ages. A population has a lifespan maximum if there is an age at which its survival function becomes exactly zero. Earlier work concerned conditions under which the mortality-rate functions of advantaged and disadvantaged populations displaying lifespan maxima always crossed. Here two survival models of populations having lifespan maxima are presented in which mortality-rate crossings between advantaged and disadvantaged subpopulations may fail to appear. One, the accelerated-mortality model, has a continuous survival function; in the other, the sudden-death model, the survival function is discontinuous. Both differ from examples examined previously in that their mortality-rate functions become infinite at their lifespan maxima.