Mean-field theory of critical behaviour and first order transition: A comparison between the Master Equation and the nonlinear Fokker-Planck equation

In this paper, we demonstrate the usage of the Nernst–Planck equation in conjunction with mean-field theory to investigate particle-laden flow inside nanomaterials. Most theoretical studies in molecular encapsulation at the nanoscale do not take into account any macroscopic flow fields that are crucial in squeezing molecules into nanostructures. Here, a multi-scale idea is used to address this issue. The macroscopic transport of gas is described by the Nernst–Planck equation, whereas molecular interactions between gases and between the gas and the host material are described using a combination of molecular dynamics simulation and mean-field theory. In particular, we investigate flow-driven hydrogen storage inside doubly layered graphene sheets and graphene-oxide frameworks (GOFs). At room temperature and with slow velocity fields, we find that a single molecular layer is formed almost instantaneously on the inner surface of the graphene sheets, while molecular ligands between GOFs induce multi-layers. For higher velocities, multi-layers are also formed between graphene. For even larger velocities, the cavity of graphene is filled entirely with hydrogen, whereas for GOFs there exist two voids inside each periodic unit. The flow-driven hydrogen storage inside GOFs with various ligand densities is also investigated.

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Calculation of the thermodynamic quantities of perovskite metal organics DMAKCr and perovskite HyFe close to the weakly first-order relaxor-like structural transformation using the mean field theory

International Journal of Modern Physics B ◽

10.1142/s0217979219501030 ◽

2019 ◽

Vol 33 (11) ◽

pp. 1950103 ◽

Cited By ~ 4

Author(s):

H. Yurtseven ◽

Ö. Tarı

Keyword(s):

Field Theory ◽

Field Model ◽

Mean Field Theory ◽

Mean Field ◽

Excess Heat Capacity ◽

Mean Field Model ◽

First Order ◽

Entropy Formula ◽

Inverse Susceptibility ◽

The Mean

Weakly first-order or nearly second-order phase transitions occurring in metal–organic frameworks (MOFs), particularly in DMAKCr and perovskite HyFe, are studied under the mean field model by using the observed data from the literature. In this work, mainly thermal and magnetic properties among various physical properties which have been reported in the literature for those MOFs are studied by the mean field theory. By expanding the free energy in terms of the magnetization (order parameter), the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S), latent heat (L), magnetization (M) and the inverse susceptibility ([Formula: see text]) are calculated as a function of temperature close to the weakly first-order phase transition within the Landau phenomenological model which is fitted to the experimental data from the literature for C[Formula: see text] (DMAKCr and perovskite HyFe) and for magnetization M (HyFe). Our predictions of the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S) agree below T[Formula: see text] with the observed data within the temperature intervals studied for DMAKCr and perovskite HyFe. From our predictions, we find that magnetization decreases continuously whereas the inverse susceptibility decreases linearly with increasing temperature toward the transition temperature in those MOFs as expected for a weakly first-order transition from the mean field model.

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The Master equation in mean field theory

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2014.11.005 ◽

2015 ◽

Vol 103 (6) ◽

pp. 1441-1474 ◽

Cited By ~ 43

Author(s):

Alain Bensoussan ◽

Jens Frehse ◽

Sheung Chi Phillip Yam

Keyword(s):

Field Theory ◽

Master Equation ◽

Mean Field Theory ◽

Mean Field

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DNA thermal denaturation by polymer field theory approach: effects of the environment

Condensed Matter Physics ◽

10.5488/cmp.24.33603 ◽

2021 ◽

Vol 24 (3) ◽

pp. 33603

Author(s):

Yu. Holovatch ◽

C. von Ferber ◽

Yu. Honchar

Keyword(s):

Field Theory ◽

Scaling Laws ◽

Order Transition ◽

Theory Approach ◽

Random Lattice ◽

First Order ◽

Solvent Quality ◽

Dna Strands ◽

First Order Transition ◽

Dna Thermal Denaturation

We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the d = 3 case, the corresponding diverging ε = 4-d expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension d = 2, the exponents are deduced from mapping the polymer model onto a two-dimensional random lattice, i.e., in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations.

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