Concerning the problem of the isokinetic relationship. II. The physical significance of the degrees of freedom in the statistical-mechanical model

1984 ◽  
Vol 37 (6) ◽  
pp. 1139 ◽  
Author(s):  
W Linert ◽  
AB Kudrjawtsev
Keyword(s):  
Degrees Of Freedom ◽  
Potential Barrier Height ◽  
Physical Significance ◽  
Reaction Series ◽  
Isokinetic Relationship ◽  
Fitting Procedure ◽  
Statistical Mechanical Model ◽  
Complete Form ◽  
Statistical Mechanical ◽  
The Relationship

The statistical model presented recently for the isokinetic relationship is developed. The physical meaning of the degrees of freedom (s) is explained in terms of ∆Cp‡, i.e. the change in the specific heat between ground and activated states: ∆Cp‡ =-(s-1)R In the case where (s-1)/(E/kBT) cannot be neglected the relationship is ∆Cp‡=-(s-1)(1-kBT/E)R where E denotes the potential barrier height. The results from a digital fitting procedure for the complete form of the model are compared with those obtained from the simplified equations for 'energy-barrier-controlled' reaction series.

Concerning the problem of the isokinetic relationship. I. A statistical mechanical model

1983 ◽  
Vol 36 (10) ◽  
pp. 1903 ◽  
Author(s):  
W Linert ◽  
AB Kudrjawtsev ◽  
R Schmid
Keyword(s):  
Frequency Factor ◽  
Isokinetic Temperature ◽  
Reaction Series ◽  
Empirical Coefficient ◽  
Isokinetic Relationship ◽  
Exponential Factor ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
The Common

The equation for the rate constant derived from the statistical theory of kinetics is compared with the common Arrhenius equation. Thereby the pre-exponential factor and the activation energy can be expressed by means of the theoretical quantities, frequency factor (Z0), oscillator number (s), and potential barrier height (E). In these terms the isokinetic relationship can be represented by the equation (c- c) = b(E-E) where c is s- 1 and the bars denote the means in the reaction series under consideration. The empirical coefficient b, in connection with the numerical value of the isokinetic temperature, is proposed to be used as a criterion for the classification of reaction series. The model is exemplified by means of an organic SN2 reaction.

Physics of Granular Systems

2015 ◽  
Author(s):  
Raphael Blumenfeld ◽  
Sam F. Edwards ◽  
Stephen M. Walley
Keyword(s):  
Degrees Of Freedom ◽  
Granular Matter ◽  
Granular Systems ◽  
Mechanical Theory ◽  
Micro Structure ◽  
Fundamental Physics ◽  
Granular Assemblies ◽  
Stress Transmission ◽  
Statistical Mechanical ◽  
The Relationship

This article discusses the fundamental physics of granular systems. It begins with an overview of the science of granular matter, followed by a description of the ‘micro’-structure on the granular level. It then considers stress transmission in mechanically equilibrated granular assemblies, focusing on conditions for marginal rigidity, isostaticity theory, and limitations of linear stress theories. It also examines the use of statistical mechanics to analyse and classify granular materials, taking into account the micro-canonical volume ensemble, structural degrees of freedom, the canonical volume ensemble and the quasi-particles of the volume ensemble, the stress ensemble, and the relationship between the volume and stress ensembles. The article concludes with an assessment of recent advances in the ongoing attempt to construct a statistical mechanical theory of granular systems.

Concerning the Problem of the Isokinetic Relationship. III. The Temperature-Dependance of the hammett Equation

1985 ◽  
Vol 38 (5) ◽  
pp. 677 ◽  
Author(s):  
W Linert ◽  
R Schmid ◽  
AB Kudrjawtsev
Keyword(s):  
Benzoic Acid ◽  
Hammett Equation ◽  
Reaction Series ◽  
Temperature Dependent ◽  
Isokinetic Relationship ◽  
A Value ◽  
The Common ◽  
Point Of Intersection ◽  
Temperature Dependance ◽  
The Relationship

It is shown that the temperature-dependence of the Hammett equation is, in contrast to tradition, both physically and experimentally better described by means of temperature-dependent σ and temperature- independent ρ (termed ρo). The relationship between ρo and the customary (temperature dependent) ρ is ρT = ρo(1/T-1/Tbiso)/(1/T-1/Tbiso) where Tbiso , is the isoequilibrium temperature of the benzoic acid ionization, for which the present analysis suggests a value of -255 K, and T is 298 K. In these terms, the temperature variation of the Hammett equation can be evaluated by supplying merely E(u)a (the activation energy for the reaction of the unsubstituted reactant) and ρo, in that the σ value for the isokinetic substituent , i.e., the abscissa of the common point of intersection in the Hammett plot, is σiso = (1/T-1/Tbiso)E(u)a/(2.303Rρo) = E(u)a/(2630po) Further, ρo I related to energies ρo = E(u)a/(ΔH°u-ΔH°s(iso))where ΔH°u and ΔH°s(iso) are the ionization enthalpies of the parent benzoic acid and that bearing the isokinetic substituent , respectively. Analogous equations apply to thermodynamic reaction series when substituting E(u)a for ΔH°u(series). Along these lines the interpretation of the customary Hammett plot is advanced.

Footbridges as an important part of a system: the context as an experience

2021 ◽  
Author(s):  
Toon Maas ◽  
Mohamad Tuffaha ◽  
Laurent Ney
Keyword(s):  
Design Process ◽  
Degrees Of Freedom ◽  
The Other ◽  
Infrastructure Projects ◽  
Good Design ◽  
Cultural Processes ◽  
The Relationship

<p>“A bridge has to be designed”. Every bridge is the exploration of all degrees of a freedom of a project: the context, cultural processes, technology, engineering and industrial skills. A successful bridge aims to dialogue with these degrees of freedom to achieve a delicate equilibrium, one that invites the participation of its users and emotes new perceptions for its viewers. In short, a good design “makes the bridge talk.”</p><p>Too often, the bridge, as an object, is reduced to its functionality. Matters of perceptions and experiences of the users are often not considered in the design process; they are relegated to levels of chance or treated as simple decorative matter. The longevity of infrastructure projects, in general, and bridges, in particular, highlights the deficiencies of such an approach. The framework to design bridges must include historical, cultural, and experiential dimensions. Technology and engineering are of paramount importance but cannot be considered as “an end in themselves but a means to an end”. This paper proposes to discuss three projects by Ney &amp; Partners that illustrate such a comprehensive exploration approach to footbridge design: the Poissy and Albi crossings and the Tintagel footbridge.</p><p>The footbridges of Poissy and Albi dialogue most clearly with their historical contexts, reconfiguring the relationship between old and new in the materiality and typology use. In Tintagel, legend replaces history. Becoming a metaphor for the void it crosses, the Tintagel footbridge illustrates the delicate dialogue of technology and engineering on one side and imagination and experience on the other.</p>

A statistical mechanical model for inverse melting

2003 ◽  
Vol 119 (8) ◽  
pp. 4582-4591 ◽  
Author(s):  
Melissa R. Feeney ◽  
Pablo G. Debenedetti ◽  
Frank H. Stillinger
Keyword(s):  
Mechanical Model ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical

scholarly journals Cooperativity and modularity in protein folding

2016 ◽  
Author(s):  
Masaki Sasai ◽  
George Chikenji ◽  
Tomoki P. Terada
Keyword(s):  
Protein Folding ◽  
Mechanical Model ◽  
Energy Landscape ◽  
Native Conformation ◽  
Folding Nucleus ◽  
Modern Methods ◽  
Complex Topology ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
Dynamical Features

AbstractA simple statistical mechanical model proposed by Wako and Saitô has explained the aspects of protein folding surprisingly well. This model was systematically applied to multiple proteins by Muñoz and Eaton and has since been referred to as the Wako-Saitô-Muñoz-Eaton (WSME) model. The success of the WSME model in explaining the folding of many proteins has verified the hypothesis that the folding is dominated by native interactions, which makes the energy landscape globally biased toward native conformation. Using the WSME and other related models, Saitô emphasized the importance of the hierarchical pathway in protein folding; folding starts with the creation of contiguous segments having a native-like configuration and proceeds as growth and coalescence of these segments. The ϕ-values calculated for barnase with the WSME model suggested that segments contributing to the folding nucleus are similar to the structural modules defined by the pattern of native atomic contacts. The WSME model was extended to explain folding of multi-domain proteins having a complex topology, which opened the way to comprehensively understanding the folding process of multi-domain proteins. The WSME model was also extended to describe allosteric transitions, indicating that the allosteric structural movement does not occur as a deterministic sequential change between two conformations but as a stochastic diffusive motion over the dynamically changing energy landscape. Statistical mechanical viewpoint on folding, as highlighted by the WSME model, has been renovated in the context of modern methods and ideas, and will continue to provide insights on equilibrium and dynamical features of proteins.

scholarly journals Statistical Mechanical Model of Gas Adsorption in a Metal-Organic Framework Harboring a Rotaxane Molecular Shuttle

2020 ◽  
Author(s):  
Jonathan Carney ◽  
David Roundy ◽  
Cory M. Simon
Keyword(s):  
Mechanical Model ◽  
Gas Adsorption ◽  
Adsorption Properties ◽  
Temperature Sensitive ◽  
Adsorption Model ◽  
Adsorption Sites ◽  
Statistical Mechanical Model ◽  
Metal Organic ◽  
Statistical Mechanical ◽  
Molecular Shuttle

Metal-organic frameworks (MOFs) are modular and tunable nano-porous materials with applications in gas storage, separations, and sensing. Flexible/dynamic components that respond to adsorbed gas can give MOFs unique or enhanced adsorption properties. Here, we explore the adsorption properties that could be imparted to a MOF by a rotaxane molecular shuttle (RMS) in its pores. In the unit cell of an RMS-MOF, a macrocyclic wheel is mechanically interlocked with a strut of the MOF scaffold. The wheel shuttles between stations on the strut that are also gas adsorption sites. At a level of abstraction similar to the seminal Langmuir adsorption model, we pose and analyze a simple statistical mechanical model of gas adsorption in an RMS-MOF that accounts for (i) wheel/gas competition for sites on the strut and (ii) gas-induced changes in the configurational entropy of the shuttling wheel. We determine how the amount of gas adsorbed, position of the wheel, and differential energy of adsorption depend on temperature, pressure, and the interactions of the gas/wheel with the stations. Our model reveals that, compared to a rigid, Langmuir material, the chemistry of the RMS-MOF can be tuned to render gas adsorption more or less temperature-sensitive and to release more or less heat upon adsorption. The model also uncovers a non-monotonic relationship between the temperature and the position of the wheel if gas out-competes the wheel for its preferable station.

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