We present a semianalytical continuum-space model of starlike polymer brushes in good solvent. Our approach is based on a modified Carnahan−Starling equation of state for hard spheres and accounts for finite extensibility of the bonds. No free fit parameters are required, and the model is able to reproduce the recently observed two-population structure of starlike polymer brushes. We further demonstrate why a simple approach, based on Gaussian chain elasticity, fails to approximate dendrimer brushes. The accuracy of our novel approach, which is filling a gap between oversimplified analytical models and numerically sophisticated, lattice-based codes, is verified through comparison with molecular dynamics simulations.
A central equation for the fiscal theory of the price level (FTPL) is the government budget constraint (or "government valuation equation"), which equates the real value of government debt to the present value of fiscal surpluses. In the past decade, the governments of most developed economies have paid very low interest rates, and there are many other periods in the past in which this has been the case. In this paper, we revisit the implications of the FTPL in a world where the rate of return on government debt may be below the growth rate of the economy, considering different sources for the low returns: dynamic inefficiency, the liquidity premium of government debt, or its favorable risk profile.
We present a systematic approach to characterize the stretching scenarios for dendrimer brushes. We compare mean-field theory for second-generation dendrimer brushes in good solvent, taking into account finite extensibility of chains, with direct molecular dynamics simulations. We analyze the stretching scenario of the dendrimers and find very broad distributions of forces acting on the free branches of individual molecules. Our results question the accuracy of a recently introduced method to determine the stretching scenario in terms of a simple scaling analysis of the monomer concentrations. Instead, the resulting scaling exponents appear to respond to model-dependent implementations of the molecular elasticityan observation which may open paths toward an improved theoretical modeling of polymers in numerical procedures. As a function of grafting density, dendrimer brushes are scaling in a similar manner as linear chain brushes, but systematic deviations exist which increase with the functionality and the number of generations of the dendrimers.
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