Starting from the fundamental equations of the statistical rate theory of interfacial transport (SRTIT), a set of
three equations has been developed, resulting in a new description of the kinetics of localized gas adsorption/desorption on energetically heterogeneous solid surfaces. For the Langmuir model of adsorption, these equations
take the following form: dθt/dt = 2kTχc(εc)K̃
gs[Kpeε
c
/
kT
− 1/(Kp)e-εc/kT
], θt(εc,T) =
χ(ε)[{exp((ε − εc)/kT)}/{1 + exp((ε − εc)kT)}] dε, and χc(εc) =
χ(ε)[{(1/kT) exp((ε − εc)/kT)}/{[1 + exp((ε − εc)/kT)]2}] dε,
where θt is the average surface coverage, t is time, T and k are the absolute temperature and Boltzmann
constant, respectively, p is the nonequilibrium pressure in the experiment, K̃
gs is an expression depending on
the conditions at which the experiment is carried out, K is a temperature-dependent constant, and χ(ε) is the
normalized differential distribution of the number of adsorption sites at various values of the adsorption
energy ε. Two adsorption energy distributions, one Gaussian-like and one rectangular, were taken into
consideration since they lead to the two well-known isotherm equations, the Langmuir−Freundlich and the
Temkin isotherms, commonly used to describe adsorption equilibria. By accepting these energy distributions,
one arrives at two kinetic expressions θt(t) which after several simplifying assumptions reduce to the well-known power-law and Elovich equations. The new equations have been subjected to an exhaustive numerical
analysis, and then used to interpret some experimental data reported in the literature. Both the constant K and
the adsorption energy distribution χ(ε) can be calculated from equilibrium adsorption isotherms by this analysis.
We have therefore shown that by measuring just the adsorption equilibria it is possible to predict the related
behavior of adsorption kinetics. In the theoretical procedures available in the literature, only the reverse operation
was possible.
The
release dynamics of cisplatin from the interior of a carbon nanotube
is studied using molecular dynamics simulations. The nanotube is initially
capped by magnetic nanoparticles which, upon exposure to an external
magnetic field, detach from the nanotube tips, and the initially encapsulated
cisplatin molecules leave the nanotube interior according to the diffusion
mechanism. Diffusivities of cisplatin in bulk water and inside the
nanotube were determined by analyzing the mean-square displacements,
and they take the values 2.1 × 10–5 and (0.6–0.9)
× 10–5 cm2 s–1, respectively, at 310 K. The release of cisplatin was found to be
an activated process with the activation barrier ∼25 kJ mol–1 in an ideal system. Analysis of experimental data
allowed for the estimation of the diffusion barrier in the actual
system which was found to be ca. 85 kJ mol–1. The
difference between these two estimations is attributed to the existence
of numerous surface defects in the case of experimental system. The
release dynamics proceeds according to a simple 1D Fick’s mechanism,
and either simulation or experimental data follow a very simple equation
derived from the above assumption. That equation predicts that the
release of simple molecules from carbon nanotubes should obey the
second-order kinetic equation. The time scale of the release depends
on the nanotube length, initial amount of drug, and diffusivity of
drug molecules inside the nanotube. Simulations predict that, for
the studied ideal architecture, the release completes in a few milliseconds.
Experimental data show that that process is, due to surface defects,
definitely slower; i.e., it needs about 3 h.
Carbon nanotubes (CNTs) have emerged as promising drug delivery systems particularly for cancer therapy, due to their abilities to overcome some of the challenges faced by cancer treatment, namely non-specificity, poor permeability into tumour tissues, and poor stability of anticancer drugs. Encapsulation of anticancer agents inside CNTs provides protection from external deactivating agents. However, the open ends of the CNTs leave the encapsulated drugs exposed to the environment and eventually their uncontrolled release before reaching the desired target. In this study, we report the successful encapsulation of cisplatin, a FDA-approved chemotherapeutic drug, into multi-walled carbon nanotubes and the capping at the ends with functionalised gold nanoparticles to achieve a “carbon nanotube bottle” structure. In this proof-of-concept study, these caps did not prevent the encapsulation of drug in the inner space of CNTs; on the contrary, we achieved higher drug loading inside the nanotubes in comparison with data reported in literature. In addition, we demonstrated that encapsulated cisplatin could be delivered in living cells under physiological conditions to exert its pharmacological action.
Theoretical analysis of thermodesorption from energetically heterogeneous solid surfaces is commonly based on the absolute rate theory in the form of the Wigner-Polanyi (W-P) equation, which neglects readsorption. As a consequence, the results of such analyses contain errors of unknown type and magnitude.Here we show that the application of the statistical rate theory of interfacial transport, instead of the W-P equations, leads to adsorption/desorption rate equations which simplify taking readsorption effects into account. An extensive model investigation is presented to show how neglecting readsorption can affect the theoretical analysis of experimental TPD peaks. Our investigation shows that readsorption can mimic effects which are actually due to surface energetic heterogeneity and/or to interactions between the adsorbed molecules. In addition to illustrative model calculations, the role of readsorption is also demonstrated by a quantitative analysis of spectra of hydrogen thermodesorption from a nickel catalyst.
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