Excluded volume effect for solutions of cellulose derivatives evaluated by wormlike chain model

Third-power law type equations of the linear expansion factor α_s and of the excluded volume effect $\text{z}$h($\text{z}$), expressed by a conventional notation, are derived for a wormlike chain as an extension of the Yamakawa and Stockmayer theory [J. chem. Phys.57, 2843(1972)], in which the corresponding fifth-power law type equations were obtained. The literature data on 11 systems of solutions of cellulose and its derivatives are analysed, by using a penetration function method based on the derived equations, to evaluate an excluded volume effect for a wormlike chain model. The results are compared with those deduced for a pearl necklace model.     

Statistical mechanics of aliphatic chain layers,influence of chain-length mixing

A molecular model is used to simulate interfaces composed of surfactants and cosurfactants in microemulsions where molecules are anchored at the surface of spherical micelles. A Monte Carlo calculation of the conformational properties of the aliphatic layer is carried out taking into account the rotational isomerism of the chains and the binary random distribution of chain lengths. The thermodynamic behavior and the main structural features of the monolayer are analyzed in relation to some micellar properties.     

A breathing wormlike chain model on DNA denaturation and bubble: effects of stacking interactions

DNA stably exists as a double-stranded structure due to hydrogen-bonding and stacking interactions between bases. The stacking interactions are strengthened when DNA is paired, which results in great enhancement of bending rigidity. We study the effects of this stacking-induced stiffness difference on DNA denaturation and bubble formations. To this end, we model double-stranded DNA as a duplex of two semiflexible chains whose persistence length varies depending on the base-pair distance. Using this model, we perform the Langevin dynamics simulation to examine the characteristics of the denaturation transition and the statistics of the bubbles. We find that the inclusion of the stacking interactions causes the denaturation transition to be much sharper than otherwise. At physiological temperature, the stacking interactions prohibit the initiation of bubble formation but promote bubbles, once grown, to retain the large size.     

Statistical mechanics of a two-dimensional lattice model of benzene adsorption in zeolites

In this Letter, we present a mean field calculation of the statistical mechanics of a lattice model of benzene adsorption in the quasi two-dimensional network of pores in zeolites. A lattice fluid model is introduced with monomer states to represent molecules standing perpendicular to the principle axis of the pore, dimer states to represent molecules lying flat against the pore wall, and vacant sites or holes. For a wide range of interaction parameters the model gives steps in adsorption isotherms similar to those observed experimentally for benzene adsorption in silicalite. Our treatment attributes the experimentally observed steps in the level of adsorption with rising pressure, to orientational transitions amongst molecules in the adsorbed phase with two possible ground states arrangements of the benzene molecules in the zeolite pores energetically competing with each other.     

Statistical mechanics of three-dimensional vesicles

We consider a lattice model of three-dimensional vesicles in which the boundary of the vesicle is a self-avoiding plaquette surface, homeomorphic to a sphere. Surfaces with fixed area can enclose a variety of different volumes and we associate a fugacity with the enclosed volume to mimic the effect of a pressure difference across the surface. Pairs of plaquettes which share a common edge can be in the same plane or normal to each other and we associate a fugacity with adjacent pairs of plaquettes at right angles to represent a surface stiffness term. We discuss the behaviour of the surfaces in the infinite surface area limit, as a function of these two fugacities.     

Statistical mechanics and fluid structure

In the axiomatic approach to the derivation of statistical mechanics the theory is based upon the equations of motions of classical mechanics (Hamilton equations). Since these equations are unstable with respect to initial conditions, in the time τ ≈ 10^?12 s they generate chaos in the system of atoms and molecules. This chaos can be described by only probability theory laws. The laws of this theory are introduced into statistical mechanics as the second postulate. However, for both postulates (i.e., Hamilton equations and probability theory laws) to be compatible with each other, about one and a half ten of additional requirements defining in detail the matter model underlying the theory must be imposed on the system. This report analyzes only the restrictions imposed by probability theory. The main of them are: a transition to the thermodynamic limit, the condition of correlation attenuation, and a short-range character of the interaction potential. The matter model formulated based on these restrictions is a continuous medium in which a correlation sphere with a small radius R ≈ 10^?7 cm (physical point) is submerged. It is submerged in an infinite thermostat, the particles of which behave as the ideal gas relative to the particles forming the correlation sphere. Here all macroscopic parameters of matter in this physical point are determined by the state of the correlation sphere. Thus formulated model determines the macro- and microscopic structure of matter, and finally, results in thermodynamic and hydrodynamic equations.     

Theoretical determination of helix-coil parameter sigma from a model of partly helical polypeptide chain.

The Zimm and Bragg parameter sigma is calculated numerically for poly(L-alanine), polyglycine, and the copolymers of L-alanine and glycine using the molecular theory of s and sigma as developed by Go, Go, and Scheraga in a modified formulation. In this formulation, sigma is obtained from the partition function of the whole chain in the helix-coil transition region and represents therefore the contributions from the ends of helical and coil sequences and from the interactions between atoms in a coil sequence with those in the neighboring helical sequence. When the parameter sigma is calculated numerically from a hard-sphere potential, it appears that steric intractions between atoms in the coil sequence with atoms in the neighboring helical sequence, which have been neglected in previous calculations, contribute significantly to the value of sigma. Owing to these interactions the entropy of the coil sequence as well as sigma decrease, but the decrease of sigma is larger in poly(L-alanine) than in polyglycine, because of the higher flexibility of the monomer in polyglycine. The numerical value of sigma for polyglycine compared with that of poly(L-alanine) might be overestimated however by the model presented here due to approximations inherent in the hard-sphere treatment and because only regular helical sequences are considered.     

Stable helical peptoids via covalent side chain to side chain cyclization

Peptoids are oligomeric N-substituted glycines with potential as biologically relevant compounds. Helical peptoids provide an attractive fold for the generation of protein-protein interaction inhibitors. The generation of helical peptoid folds in organic and aqueous media has been limited to strict design rules, as peptoid-folding is mainly directed via the steric direction of alpha-chiral side-chains. Here a new methodology is presented to induce helical folds in peptoids with the aid of side chain to side chain cyclization. Cyclic peptoids were generated via solid-phase synthesis and their folding was studied. The cyclization induces significant helicity in peptoids in organic media, aids the folding in aqueous media, and requires the incorporation of only relatively few chiral aromatic side chains.     

Statistical mechanics of time independent nondissipative nonequilibrium states

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent nondissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming that the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the interdomain population distribution. Assuming that these domains are robust with respect to small changes in thermodynamic state variables we derive a variety of fluctuation formulas for these systems. We verify our theoretical results using molecular dynamics simulations on a model glass forming system. Nonequilibrium transient fluctuation relations are derived for the fluctuations resulting from a sudden finite change to the system's temperature or pressure and these are shown to be consistent with the simulation results. The necessary and sufficient conditions for these relations to be valid are that the domains are internally populated by Boltzmann statistics and that the domains are robust. The transient fluctuation relations thus provide an independent quantitative justification for the assumptions used in our statistical mechanical treatment of these systems.     

Statistical mechanics of quantum-classical systems with holonomic constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.     

Statistical mechanics of helix bundles using a dynamic programming approach

Despite much study, biomolecule folding cooperativity is not well understood. There are quantitative models for helix-coil transitions and for coil-to-globule transitions, but no accurate models yet treat both chain collapse and secondary structure formation together. We develop here a dynamic programming approach to statistical mechanical partition functions of foldamer chain molecules. We call it the ascending levels model. We apply it to helix-coil and helix-bundle folding and cooperativity. For 14- to 50-mer Baldwin peptides, the model gives good predictions for the heat capacity and helicity versus temperature and urea. The model also gives good fits for the denaturation of Oas's three-helix bundle B domain of protein A (F13W*) and synthetic protein alpha3C by temperature and guanidine. The model predicts the conformational distributions. It shows that these proteins fold with transitions that are two-state, although the transitions in the Baldwin helices are nearly higher order. The model shows that the recently developed three-helix bundle polypeptoids of Lee et al. fold anti-cooperatively, with a predicted value of DeltaHvH/DeltaHcal = 0.72. The model also predicts that two-helix bundles are unstable in proteins but stable in peptoids. Our dynamic programming approach provides a general way to explore cooperativity in complex foldable polymers.     

Statistical mechanics of order-disorder in the thiourea + cyclohexane adduct

An order-disorder model for the transition at 128.8 K in the adduct of c-C₆H₁₂ with thiourea is evaluated by statistical mechanics. It is assumed that each c-C₆H₁₂ molecule can occupy any of six positions and that it interacts with the “host” lattice and also with nearest-neighbour c-C₆H₁₂ molecules both in its own channel and in neighbouring channels. A “mean field” approximation is applied to the latter type of interaction. With values of the interaction parameters computed by summing atom-atom potentials the predicted curve for heat capacity against temperature is too broad and has its maximum at a temperature which is too low. The effects of modification of the parameters are examined.     

Statistical mechanics of worm-like polymers from a new generating function

We present a mathematical approach to the worm-like chain model of semiflexible polymers. Our method is built on a novel generating function from which all the properties of the model can be derived. Moreover, this approach satisfies the local inextensibility constraint exactly. In this paper, we focus on the lowest order contribution to the generating function and derive explicit analytical expressions for the characteristic function, polymer propagator, single chain structure factor, and mean square end-to-end distance. These analytical expressions are valid for polymers with any degree of stiffness and contour length. We find that our calculations are able to capture the fully flexible and infinitely stiff limits of the aforementioned quantities exactly while providing a smooth and approximate crossover behavior for intermediate values of the stiffness of the polymer backbone. In addition, our results are in very good quantitative agreement with the exact and approximate results of five other treatments of semiflexible polymers.