Surface properties of bottle-brush polyelectrolytes on mica: effects of side chain and charge densities

Surface properties of a series of cationic bottle-brush polyelectrolytes with 45-unit-long poly(ethylene oxide) side chains were investigated by phase modulated ellipsometry and surface force measurements. The evaluation of the adsorbed mass of polymer on mica by means of ellipsometry is complex due to the transparency of mica and its birefringence and low dielectric constant. We therefore employed a new method to overcome these difficulties. The charge and the poly(ethylene oxide) side chain density of the bottle-brush polymers were varied from zero charge density and one side chain per segment to one charge per segment and no side chains, thus spanning the realm from a neutral bottle-brush polymer, via a partly charged brush polyelectrolyte, to a linear fully charged polyelectrolyte. The adsorption properties depend crucially on the polymer architecture. A minimum charge density of the polymer is required to facilitate adsorption to the oppositely charged surface. The maximum adsorbed amount and the maximum side chain density at the surface are obtained for the polymer with 50% charged segments and the remaining 50% of the segments carrying poly(ethylene oxide) side chains. It is found that brushlike layers are formed when 25-50% of the segments carry poly(ethylene oxide) side chains. In this paper, we argue that the repulsion between the side chains results in an adsorbed layer that is non-homogeneous on the molecular level. As a result, not all side chains will contribute equally to the steric repulsion but some will be stretched along the surface rather than perpendicular to it. By comparison with linear polyelectrolytes, it will be shown that the presence of the side chains counteracts adsorption. This is due to the entropic penalty of confining the side chains to the surface region.     

Weighted allocations,their concomitant-based estimators,and asymptotics

Annals of the Institute of Statistical Mathematics - Various members of the class of weighted insurance premiums and risk capital allocation rules have been researched from a number of...     

Optimum Burn-in Time for a Bathtub Shaped Failure Distribution

An important problem in reliability is to define and estimate the optimal burn-in time. For bathtub shaped failure-rate lifetime distributions, the optimal burn-in time is frequently defined as the point where the corresponding mean residual life function achieves its maximum. For this point, we construct an empirical estimator and develop the corresponding statistical inferential theory. Theoretical results are accompanied with simulation studies and applications to real data. Furthermore, we develop a statistical inferential theory for the difference between the minimum point of the corresponding failure rate function and the aforementioned maximum point of the mean residual life function. The difference measures the length of the time interval after the optimal burn-in time during which the failure rate function continues to decrease and thus the burn-in process can be stopped.      

On Estimation of Poisson Intensity Functions

Under the presence of only one realization, we consider a computationally simple algorithm for estimating the intensity function of a Poisson process with exponential quadratic and cyclic of fixed frequency trends. We argue that the algorithm can successfully be used to estimate any Poisson intensity function provided that it has a parametric form.     

The influence of deterministic noise on empirical measures generated by stationary processes

We consider weak convergence of empirical measures generated by stationary random process perturbed by deterministic noise . We assume that the noise has asymptotic distribution. In particular, we demonstrate that if the process is ergodic, or satisfies some mixing assumptions, then the influence of deterministic noise on is the same as it would be if were stochastic. Such results are of importance when investigating fluctuations and convex rearrangements of stochastic processes.

     

The Shape of the Borwein–Affleck–Girgensohn Function Generated by Completely Monotone and Bernstein Functions

Fifteen years ago, J. Borwein, I. Affleck, and R. Girgensohn posed a problem concerning the shape (convexity, log-convexity, reciprocal concavity) of a certain function of several arguments that had manifested in a number of contexts concerned with optimization problems. In this paper we further explore the shape of the Borwein–Affleck–Girgensohn function as well as of its extensions generated by completely monotone and Bernstein functions.     

Heavy tailed capital incomes: Zenga index,statistical inference,and ECHP data analysis

Micro-data of European Union (EU) countries show that capital incomes account for a large part of disparity in populations and follow heavy-tailed distributions in many EU countries. Measuring and comparing the disparity requires incorporating the relative nature of ‘small’ and ‘large,’ and for this reason we employ the newly developed Zenga index of economic inequality. Its non-parametric estimator does not fall into any well known class of statistics. This makes the development of statistical inference a challenge even for light-tailed populations, let alone heavy-tailed ones, as is the case with capital incomes. In this paper we construct a heavy-tailed Zenga estimator, establish its asymptotic distribution, and derive confidence intervals. We explore the performance of the confidence intervals in a simulation study and draw conclusions about capital incomes in EU countries, based on the 2001 wave of the European Community Household Panel (ECHP) survey.     

Effect of polymer architecture on the adsorption properties of a nonionic polymer

The adsorption of a linear- and bottle-brush poly(ethylene oxide (PEO))-based polymer, having comparable molecular weights, was studied by means of quartz crystal microbalance with dissipation monitoring ability (QCM-D) and AFM colloidal probe force measurements. The energy dissipation change monitored by QCM-D and the range of the steric forces obtained from force measurements demonstrated that linear PEO forms a more extended adsorption layer than the bottle-brush polymer, despite that the adsorbed mass is higher for the latter. Competitive adsorption studies revealed that linear PEO is readily displaced from the interface by the bottle-brush polymer. This was attributed to the higher surface affinity of the latter, which is governed by the number of contact points between the polymers and the interface, and the smaller loss of conformational entropy.