scholarly journals Exact matrix treatment of the statistical mechanics of adsorption of large aromatic molecules on graphene

2020 ◽  
Vol 22 (21) ◽  
pp. 12113-12119
Author(s):  
Lawrence J. Dunne ◽  
George Manos
Keyword(s):  
Statistical Mechanics ◽  
Adsorption Isotherms ◽  
Graphene Surface ◽  
Aromatic Molecules ◽  
Statistical Mechanical ◽  
Exact Matrix

Theoretical adsorption isotherms show plateaus reflecting the types of conformer on the graphene surface. Both catechol and phenyl hydroquinone adsorption can be described by our interconvertible statistical mechanical monomer–dimer–trimer model.

Surface modification of graphene-coated carbon steel using aromatic molecules for enhancing corrosion resistance; comparison between type of aryl substitution with different spatial situations

2018 ◽  
Vol 65 (3) ◽  
pp. 249-262 ◽  
Author(s):  
Zahra Shams Ghahfarokhi ◽  
Mojtaba Bagherzadeh ◽  
Ebrahim Ghiamati Yazdi ◽  
Abbas Teimouri
Keyword(s):  
Surface Modification ◽  
Carbon Steel ◽  
Corrosion Protection ◽  
Protection Efficiency ◽  
Graphene Surface ◽  
Content Type ◽  
X Ray ◽  
Aromatic Molecules ◽  
Proposed Modification ◽  
Coated Carbon

Purpose The purpose of this paper is study of the type of functional group and its situation on phenyl molecule, in increasing the corrosion protection of modified graphene layers by it. Corrosion protection efficiency of graphene was raised via modifying the surface of graphene-coated carbon steel (CS/G) by using aromatic molecules. Phenyl groups with three different substitutions including COOH, NO2 and CH3 grafted to graphene via diazonium salt formation route, by using carboxy phenyl, nitro phenyl and methyl phenyl diazonium salts in ortho, meta and para spatial situations. Design/methodology/approach Molecular bindings were characterized by using X-ray diffractometer, fourier-transform infrared spectroscopy (FTIR), Raman and scanning electron microscopy (SEM)/ energy dispersive X-ray analysis (EDXA) methods. Anti-corrosion performance of modified CS/G electrodes was evaluated by weight loss and electrochemical techniques, potentiodynamic polarization (Tafel) and electrochemical impedance spectroscopy, in 3.5 per cent NaCl solution. Findings The obtained results confirmed covalently bonding of phenyl groups to the graphene surface. Also, the observed results showed that substitution spatial situations on phenyl groups can affect charge transfer resistance (Rct), corrosion potential (Ecorr), corrosion current density (jcorr) and the slope of the anodic and cathodic reaction (ßa,c), demonstrating that the proposed modification method can hinder the corrosion reactions. The proposed modification led to restoring the graphene surface defects and consequently increasing its corrosion protection efficiency. Originality/value The obtained results from electrochemical methods proved that protection efficiency was observed in order COOH < NO2 < CH3 and MPD in the para spatial situation and showed the maximum protection efficiency of 98.6 per cent in comparison to other substitutions. Finally, the ability of proposed graphene surface modification route was further proofed by using surface methods, i.e. SEM and EDXA, and contact angles measurements.

Linear Response Theory

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Statistical Mechanics ◽  
Linear Response ◽  
Ad Hoc ◽  
Linear Response Theory ◽  
Perturbative Expansion ◽  
General Nature ◽  
Response Theory ◽  
Equilibrium Statistical Mechanics ◽  
Standard Application ◽  
Statistical Mechanical

Equilibrium statistical mechanics is a first principle theory whose fundamental statements are general and independent of the details associated with individual systems. No such general theory exists for nonequilibrium systems and for this reason we often have to resort to ad hoc descriptions, often of phenomenological nature, as demonstrated by several examples in Chapters 7 and 8. Equilibrium statistical mechanics can however be extended to describe small deviations from equilibrium in a way that preserves its general nature. The result is Linear Response Theory, a statistical mechanical perturbative expansion about equilibrium. In a standard application we start with a system in thermal equilibrium and attempt to quantify its response to an applied (static- or time-dependent) perturbation. The latter is assumed small, allowing us to keep only linear terms in a perturbative expansion. This leads to a linear relationship between this perturbation and the resulting response. Let us make these statements more quantitative. Consider a system characterized by the Hamiltonian Ĥ0.

ON THE EXTENSIVITY OF THE ENTROPY Sq FOR N ≤ 3 SPECIALLY CORRELATED BINARY SUBSYSTEMS

2006 ◽  
Vol 16 (06) ◽  
pp. 1727-1738 ◽  
Author(s):  
YUZURU SATO ◽  
CONSTANTINO TSALLIS
Keyword(s):  
Statistical Mechanics ◽  
Stationary States ◽  
Nonextensive Statistical Mechanics ◽  
Entropy Formula ◽  
Gibbs Entropy ◽  
Statistical Mechanical

Many natural and artificial systems whose range of interaction is long enough are known to exhibit (quasi)stationary states that defy the standard, Boltzmann–Gibbs statistical mechanical prescriptions. For handling such anomalous systems (or at least some classes of them), nonextensive statistical mechanics has been proposed based on the entropy [Formula: see text], with [Formula: see text] (Boltzmann–Gibbs entropy). Special collective correlations can be mathematically constructed such that the strictly additive entropy is now Sq for an adequate value of q ≠ 1, whereas Boltzmann–Gibbs entropy is nonadditive. Since important classes of systems exist for which the strict additivity of Boltzmann–Gibbs entropy is replaced by asymptotic additivity (i.e. extensivity), a variety of classes are expected to exist for which the strict additivity of Sq (q ≠ 1) is similarly replaced by asymptotic additivity (i.e. extensivity). All probabilistically well defined systems whose adequate entropy is S1 are called extensive (or normal). They correspond to a number W eff of effectively occupied states which grows exponentially with the number N of elements (or subsystems). Those whose adequate entropy is Sq (q ≠ 1) are currently called nonextensive (or anomalous). They correspond to W eff growing like a power of N. To illustrate this scenario, recently addressed [Tsallis, 2004] we provide in this paper details about systems composed by N = 2, 3 two-state subsystems.

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

scholarly journals Exact matrix treatment of an osmotic ensemble model of adsorption and pressure induced structural transitions in metal organic frameworks

2016 ◽  
Vol 45 (10) ◽  
pp. 4213-4217 ◽  
Author(s):  
Lawrence J. Dunne ◽  
George Manos
Keyword(s):  
Metal Organic Frameworks ◽  
Structural Transformations ◽  
Ensemble Model ◽  
Structural Transitions ◽  
One Dimensional ◽  
Metal Organic ◽  
Statistical Mechanical ◽  
Exact Matrix

Here we present an exactly treated quasi-one dimensional statistical mechanical osmotic ensemble model of pressure and adsorption induced breathing structural transformations of metal–organic frameworks (MOFs).

BET Adsorption Isotherm and Surface Heterogeneity

1992 ◽  
Vol 57 (6) ◽  
pp. 1201-1209
Author(s):  
Lydia Ethel Cascarini de Torre ◽  
Eduardo Jorge Bottani
Keyword(s):  
Distribution Function ◽  
Adsorption Isotherm ◽  
Statistical Mechanics ◽  
Adsorption Isotherms ◽  
Surface Heterogeneity ◽  
Adsorption Energies ◽  
Multilayer Formation ◽  
Effect Of Surface

The BET adsorption isotherm is modified in order to take account of surface heterogeneity. The adsorption isotherm is obtained following the statistical mechanics formalism, proposed by Steele, and the effect of surface heterogeneity is limited to the first layer. A Gaussian adsorption energies distribution function is used to describe surface heterogeneity. The variations of the C parameter, multilayer formation and the inversion of adsorption isotherms are analysed.

scholarly journals Statistical mechanical analysis of the electromechanical coupling in an electrically-responsive polymer chain

Soft Matter ◽  
2020 ◽  
Vol 16 (27) ◽  
pp. 6265-6284
Author(s):  
Matthew Grasinger ◽  
Kaushik Dayal
Keyword(s):  
Statistical Mechanics ◽  
Potential Application ◽  
Electromechanical Coupling ◽  
Mechanical Analysis ◽  
Soft Sensors ◽  
Sensors And Actuators ◽  
Responsive Polymer ◽  
Biomedical Technologies ◽  
Statistical Mechanical ◽  
Couple Deformation

Polymers that couple deformation and electrostatics have potential application in soft sensors and actuators for robotics and biomedical technologies. This paper applies statistical mechanics to study their coupled electromechanical response.

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