Many Faces of Entropy or Bayesian Statistical Mechanics

Some 80–90 years ago, George A. Linhart, unlike A. Einstein, P. Debye, M. Planck and W. Nernst, managed to derive a very simple, but ultimately general mathematical formula for heat capacity versus temperature from fundamental thermodynamic principles, using what we would nowadays dub a “Bayesian approach to probability”. Moreover, he successfully applied his result to fit the experimental data for diverse substances in their solid state over a rather broad temperature range. Nevertheless, Linhart’s work was undeservedly forgotten, although it represents a valid and fresh standpoint on thermodynamics and statistical physics, which may have a significant implication for academic and applied science.     

Influence of solvent quality on the growth of polyelectrolyte multilayers

The effect of solvent conditions on the growth of polyelectrolyte (PE) multilayer films comprising poly(allylamine hydrochloride) (PAH) and poly(styrenesulfonate sodium salt) (PSS) on planar substrates was investigated by means of surface plasmon resonance spectroscopy (SPRS), quartz crystal microbalance (QCM), and atomic force microscopy techniques. The solvent quality was varied by the addition of ethanol to the PE solutions used for deposition of the layers, thus tuning the relative strength of electrostatic and secondary intermolecular and intramolecular interactions. Experiments were performed with PE solutions both without added electrolyte and containing 0.5 M NaCl. Decreasing the solvent quality (i.e., increasing the amount of ethanol in the adsorption solution) resulted in a marked increase of both the multilayer film thickness and mass loading, as determined from the SPRS spectra and QCM frequency shifts, respectively. With the solution composition approaching the precipitation point, thick PAH/PSS films were formed due to the screening of the electrostatic intra- and interchain repulsions and enhanced hydrophobic interactions between the polyelectrolyte chains. However, the films formed from water/ethanol mixtures remained stable upon subsequent exposure to water or salt-containing solutions: no significant film desorption occurred after up to 24 h of exposure to water or 0.5 M NaCl solutions. In addition, the effect of postdeposition exposure to water/ethanol mixtures was investigated for PE multilayers assembled from aqueous solutions. In this case, the optical thickness of the films was determined during exposure to water/ethanol mixtures, and instead of swelling, the polyelectrolyte films collapse to the surface as a result of the unfavorable segment-solvent interactions.     

Surface interactions during polyelectrolyte multilayer build-up. 2. The effect of ionic strength on the structure of preformed multilayers

Interactions between surfaces bearing multilayer films of poly(allylamine hydrochloride) (PAH) and poly(styrenesulfonate sodium salt) (PSS) were investigated across a range of aqueous KBr solutions. Three layer films (PAH/PSS/PAH) were preassembled on mica surfaces, and the resulting interactions were measured with the interferometric surface force apparatus (SFA). Increasing the ionic strength of the medium resulted in a progressive swelling of the multilayer films. Interactions in solutions containing more than 10(-3) M KBr were dominated by a long-ranged steric repulsion originating from compression of polyelectrolyte segments extending into solution. In 10(-1) M KBr, repeated measurements at the same contact position showed a considerable reduction of the range and the strength of the steric force, indicating a flattening of the film during initial approach. Furthermore, this flattening was irreversible on the time scale of the experiments, and measurements performed up to 72 h after the initial compression showed no signs of relaxation. These studies aid in understanding the dominant interactions between polyelectrolyte multilayers, including polyelectrolyte films deposited on colloidal particles, which is important for the preparation of colloidally stable nanoengineered particles.     

Rate constants and hydrogen isotope substitution effects in the CH3 + HCl and CH3 + Cl2 reactions

The kinetics of the CH3 + Cl2 (k2a) and CD3 + Cl2 (k2b) reactions were studied over the temperature range 188-500 K using laser photolysis-photoionization mass spectrometry. The rate constants of these reactions are independent of the bath gas pressure within the experimental range, 0.6-5.1 Torr (He). The rate constants were fitted by the modified Arrhenius expression, k2a = 1.7 x 10(-13)(T/300 K)(2.52)exp(5520 J mol(-1)/RT) and k2b = 2.9 x 10(-13)(T/300 K)(1.84)exp(4770 J mol(-1)/RT) cm(3) molecule(-1) s(-1). The results for reaction 2a are in good agreement with the previous determinations performed at and above ambient temperature. Rate constants of the CH3 + Cl2 and CD3 + Cl2 reactions obtained in this work exhibit minima at about 270-300 K. The rate constants have positive temperature dependences above the minima, and negative below. Deuterium substitution increases the rate constant, in particular at low temperatures, where the effect reaches ca. 45% at 188 K. These observations are quantitatively rationalized in terms of stationary points on a potential energy surface based on QCISD/6-311G(d,p) geometries and frequencies, combined with CCSD(T) energies extrapolated to the complete basis set limit. 1D tunneling as well as the possibility of the negative energies of the transition state are incorporated into a transition state theory analysis, an approach which also accounts for prior experiments on the CH3 + HCl system and its various deuterated isotopic substitutions [Eskola, A. J.; Seetula, J. A.; Timonen, R. S. Chem. Phys. 2006, 331, 26].     

Chemical-to-mechanical energy conversion in biomacromolecular machines: a plasmon and optimum control theory for directional work. 1. General considerations

To rationalize coherence and mechanochemical aspects of proteins acting as molecular machines, a plasmon concept for dealing with protein nonequilibrium dynamics is introduced and tested with respect to thermodynamic consistency. A stochastic optimum-control theory for protein conformational diffusion is developed and the corresponding stochastic Newton's second law derived for optimum-controlled conformational diffusion in proteins. The plasmon concept is shown to be consistent with this theory, in that optical plasmons can pump entropy out of (or into) the protein, decreasing (or increasing) its conformational diffusion and, at the same time, help decrease intra- and intermolecular friction, as well as (potentially) break the symmetry of the latter. Instead, acoustic plasmons may break the spatial symmetry of a protein's "potential of mean force", thus converting it into an effective Brownian ratchet potential by applying quasistatic deformational corrections to the former. These concepts seem to be of rather general applicability and might also be useful when studying, for example, intercalation of cationic dyes into DNA duplexes, positively charged oligopeptide transduction through cell membranes, or even DNA translocation through nanopores.     

Alkylaminophosphanyl substituted half-sandwich complexes of vanadium(III) and chromium(III): preparation and reactivity in ethylene polymerisation

[Cp^R(RPNEt₂)]M (Cp^R=t-BuC₅H₃, C₅(CH₃)₄, indenyl, fluorenyl; M=Li, K) smoothly react with VCl₃(Me₃P)₂ and CrCl₃(THF)₃ systems giving paramagnetic complexes [Cp^R(R¹PNEt₂)]MCl₂ (M=V(Me₃P)₂, Cr). After reaction with MAO these complexes are active in the polymerisation of ethylene yielding highly crystalline, high-density products of high molecular weight (M_w ranging from 100 000 to 4.5×10⁶ g mol⁻¹, 20≤T_p≤100 °C). Polymerisation with chromium complexes leads to the formation of polyethylenes with broad molecular weight distribution.     

Adsorption characteristics of bottle-brush polymers on silica: effect of side chain and charge density

The adsorption behavior of bottle-brush polymers with different charge/PEO ratio on silica was studied using optical reflectometry and QCM-D. The results obtained under different solution conditions clearly demonstrate the existence of two distinct adsorption mechanisms depending on the ratio of charge/PEO. In the case of low-charge density brush polymers (0-10 mol %), the adsorption occurs predominantly through the PEO side chains. However, the presence of a small amount of charge along the backbone (as low as 2 mol %) increases the adsorption significantly above that of the uncharged bottle-brush polymer in pure water. As the charge density of the brush polymers is increased to 25 mol % or larger the adsorption occurs predominantly through electrostatic interactions. The adsorbed layer structure was studied by measuring the layer dissipation using QCM-D. The adsorbed layer formed by the uncharged brush polymer dissipates only a small amount of energy that indicates that the brush lie along the surface, the scenario in which the maximum number of PEO side chains interact with the surface. The adsorbed layers formed by the low-charge density brush polymers (2-10 mol %) in water are more extended, which results in large energy dissipation, whereas those formed by the high-charge density brush polymers (50-100 mol %) have their backbone relatively flat on the surface and the energy dissipation is again low.     

Chemical modification of poly(acrylonitrile) with amines

The chemical modification of poly(acrylonitrile) was carried out using monoethanolamine and 1,2-ethylenediamine. The effect of the reaction conditions on the content of basic groups was studied. Polymer analogous reactions were carried out by varying the amount of the starting reagents and the temperature. The amino-containing polymers were characterized by elemental analysis. The obtained water-soluble polymers were used as carriers of low-molecular substances. © 1996 John Wiley & Sons, Inc.