Coupling Effect between Mechanical Loading and Chemical Reactions

Pattern formation revisited within nonequilibrium thermodynamics: Burgers'-type equation

We revisit the description of reaction-diffusion phenomena within nonequilibrium thermodynamics and investigate the role of a nonstandard splitting of the entropy balance into the entropy production and the divergence of entropy flux. As previously reported by Pavelka et al. (Int J Eng Sci 78:192-217, 2014), a new term is identified following from the kinetic energy of diffusion. This newly appearing term acts as a thermodynamic force driving the reaction kinetics. Using the standard constitutive relations within the linear nonequilibrium thermodynamics, the governing equations for a reaction-diffusion problem in a two-species system are derived. They turn out to be linked to Burgers' equation. It is shown that the onset of stability is not altered, but a non-periodic pattern can emerge. The latter follows from the relation of the governing equation to Burger's equation with a source term. Hence, transients formed by glued and merging parabolic profiles are expected to appear at least in certain parameter regimes. We explore the significance of this effect and observe that for a comparable magnitude of the diffusion and of the new term stemming from the kinetic energy of diffusion, the solution is expected to be linked to the saw-tooth like solution to Burger's equation rather than to the eigenmodes of the Laplacian. We conclude that the reaction-diffusion model proposed by Turing is robust to the addition of this effect of the kinetic energy of diffusion, at least when this new term is sufficiently small. As the governing equations can be rewritten into the classical reaction-diffusion problem but with reaction kinetics outside of the classical law of mass action, the analysis presented in this study suggests that a yet richer behaviour of the classical reaction-diffusion problems can be expected, if nonstandard reaction kinetics are considered.

Processing and Investigation Methods in Mechanochemical Kinetics

The present work focuses on the challenges that emerge in connection with the kinetics of mechanically activated transformations. This is an important topics to comprehend to enable the full exploitation of mechanical processing in a broad spectrum of areas related to chemistry and materials science and engineering. Emerging challenges involve a number of facets regarding materials and material properties, working principles of ball mills and milling conditions, and local changes occurring in series in processed materials. Within this context, it is highly desirable to relate the nature and rate of observed mechanochemical transformations to individual collisions and then to the processes induced by mechanical stresses on the molecular scale. Hence, it is necessary to characterize the milling regimes that can establish in ball mills regarding frequency and energy of collisions, map the relationship between milling dynamics and transformation kinetics, and obtain mechanistic information through proper time-resolved investigations in situ. A few specific hints are provided in this respect.

Mechanical stress promotes cisplatin-induced hepatocellular carcinoma cell death

Cisplatin (CisPt) is a commonly used platinum-based chemotherapeutic agent. Its efficacy is limited due to drug resistance and multiple side effects, thereby warranting a new approach to improving the pharmacological effect of CisPt. A newly developed mathematical hypothesis suggested that mechanical loading, when coupled with a chemotherapeutic drug such as CisPt and immune cells, would boost tumor cell death. The current study investigated the aforementioned mathematical hypothesis by exposing human hepatocellular liver carcinoma (HepG2) cells to CisPt, peripheral blood mononuclear cells, and mechanical stress individually and in combination. HepG2 cells were also treated with a mixture of CisPt and carnosine with and without mechanical stress to examine one possible mechanism employed by mechanical stress to enhance CisPt effects. Carnosine is a dipeptide that reportedly sequesters platinum-based drugs away from their pharmacological target-site. Mechanical stress was achieved using an orbital shaker that produced 300 rpm with a horizontal circular motion. Our results demonstrated that mechanical stress promoted CisPt-induced death of HepG2 cells (~35% more cell death). Moreover, results showed that CisPt-induced death was compromised when CisPt was left to mix with carnosine 24 hours preceding treatment. Mechanical stress, however, ameliorated cell death (20% more cell death).

Time reversal in nonequilibrium thermodynamics

The general equation of nonequilibrium reversible-irreversible coupling (GENERIC) is studied in light of time-reversal transformation. It is shown that Onsager-Casimir reciprocal relations are implied by GENERIC in the near-equilibrium regime. A general structure which gives the reciprocal relations but which is valid also far from equilibrium is identified, and Onsager-Casimir reciprocal relations are generalized to far-from-equilibrium regime in this sense. Moreover, reversibility and irreversibility are carefully discussed and the results are illustrated in Hamiltonian dynamics, classical hydrodynamics, classical irreversible thermodynamics, the quantum master equation, and the Boltzmann equation.

Predicting Bone Remodeling in Response to Total Hip Arthroplasty: Computational Study Using Mechanobiochemical Model

Periprosthetic bone loss following total hip arthroplasty (THA) is a serious concern leading to the premature failure of prosthetic implant. Therefore, investigating bone remodeling in response to hip arthroplasty is of paramount for the purpose of designing long lasting prostheses. In this study, a thermodynamic-based theory, which considers the coupling between the mechanical loading and biochemical affinity as stimulus for bone formation and resorption, was used to simulate the femoral density change in response to THA. The results of the numerical simulations using 3D finite element analysis revealed that in Gruen zone 7, after remarkable postoperative bone loss, the bone density started recovering and got stabilized after 9% increase. The most significant periprosthetic bone loss was found in Gruen zone 7 (−17.93%) followed by zone 1 (−13.77%). Conversely, in zone 4, bone densification was observed (+4.63%). The results have also shown that the bone density loss in the posterior region of the proximal metaphysis was greater than that in the anterior side. This study provided a quantitative figure for monitoring the distribution variation of density throughout the femoral bone. The predicted bone density distribution before and after THA agree well with the bone morphology and previous results from the literature.

Mechano-chemical coupling in Belousov-Zhabotinskii reactions

Mechano-chemical coupling has been recently recognised as an important effect in various systems as chemical reactivity can be controlled through an applied mechanical loading. Namely, Belousov-Zhabotinskii reactions in polymer gels exhibit self-sustained oscillations and have been identified to be reasonably controllable and definable to the extent that they can be harnessed to perform mechanical work at specific locations. In this paper, we use our theoretical work of nonlinear mechano-chemical coupling and investigate the possibility of providing an explanation of phenomena found in experimental research by means of this theory. We show that mechanotransduction occurs as a response to both static and dynamic mechanical stimulation, e.g., volume change and its rate, as observed experimentally and discuss the difference of their effects on oscillations. Plausible values of the quasi-stoichiometric parameter f of Oregonator model are estimated together with its dependence on mechanical stimulation. An increase in static loading, e.g., pressure, is predicted to have stimulatory effect whereas dynamic loading, e.g., rate of volume change, is predicted to be stimulatory only up to a certain threshold. Further, we offer a physically consistent explanation of the observed phenomena why some Belousov-Zhabotinskii gels require an additional mechanical stimulation to show emergence of oscillation or why "revival" of oscillations in Belousov-Zhabotinskii reactions is possible together with indications for further experimental setups.

Hallmarks of mechanochemistry: from nanoparticles to technology

The aim of this review article on recent developments of mechanochemistry (nowadays established as a part of chemistry) is to provide a comprehensive overview of advances achieved in the field of atomistic processes, phase transformations, simple and multicomponent nanosystems and peculiarities of mechanochemical reactions. Industrial aspects with successful penetration into fields like materials engineering, heterogeneous catalysis and extractive metallurgy are also reviewed. The hallmarks of mechanochemistry include influencing reactivity of solids by the presence of solid-state defects, interphases and relaxation phenomena, enabling processes to take place under non-equilibrium conditions, creating a well-crystallized core of nanoparticles with disordered near-surface shell regions and performing simple dry time-convenient one-step syntheses. Underlying these hallmarks are technological consequences like preparing new nanomaterials with the desired properties or producing these materials in a reproducible way with high yield and under simple and easy operating conditions. The last but not least hallmark is enabling work under environmentally friendly and essentially waste-free conditions (822 references).

Coupling between chemical kinetics and mechanics that is both nonlinear and compatible with thermodynamics

Motivated by biological applications (e.g., bone tissue development and regeneration) we investigate coupling between mesoscopic mechanics and chemical kinetics. Governing equations of both dynamical systems are first written in a form expressing manifestly their compatibility with microscopic mechanics and thermodynamics. The same form is then required from governing equations of the coupled dynamics. The main result of the paper is an admissible form of the coupled dynamics.

Ag nanoparticles from the mechanochemical decomposition of Ag oxalate

The present work focuses on the chemical reactivity of Ag oxalate powders under mechanical processing conditions. The powders were submitted to mechanical loads in the presence of an aqueous solution containing a polymeric surfactant. A gradual decrease of the total mass of powders was observed, ascribable to the occurrence of a decomposition process. X-ray diffraction and UV-vis spectrophotometric analyses indicated that the Ag oxalate decomposes into metallic Ag and gaseous carbon dioxide. Transmission electron microscopy showed that metallic Ag exists in the form of particles with average size of about 5 nm. The formation of nanometer-sized Ag particles can be related to the plastic deformation and attrition processes taking place at the points of contacts between neighboring particles during the mechanical loading at collision.

Investigation of stress shielding around the Stryker Omnifit and Exeter periprosthetic hip implants using an irreversible thermodynamic-based model

This study investigates stress shielding by predicting bone density around two different implants following total hip arthroplasty using a new thermodynamic-based model for bone remodeling. This model is based on chemical kinetics and irreversible thermodynamics in which bone is treated as a self-organizing system capable of exchanging matter, energy, and entropy with its surroundings. Unlike the previous works in which mechanical loading is regarded as the only stimulus for bone remodeling, this model establishes a coupling between mechanical loading and the chemical reactions involved in the process of bone remodeling. This model is incorporated into the finite element software ANSYS by means of a macro to investigate stress shielding around two different implants: Stryker Omnifit and Exeter periprosthetic hip stems. The results of the simulation showing bone density reductions of 17% in Gruen zone 1 and 27% in Gruen zones 7 around the Omnifit hip stem agree well with dual-energy X-ray absorptiometry (DEXA) measurements reported in the literature. On the other hand, the Exeter implant is found to result in more severe resorption in the proximal femur. This is consistent with clinical studies, which report a higher survivorship rate for HA-coated Omnifit hip stems.

Computation of bone remodelling after Duracon knee arthroplasty using a thermodynamic-based model

The present study utilizes a recently developed literature model for the bone remodelling process to predict the evolution of bone density following Duracon total knee arthroplasty (TKA). In this model, which is based on chemical kinetics and irreversible thermodynamics, bone is treated as a self-organizing system capable of exchanging matter, energy, and entropy with its surroundings. Unlike previous models in which mechanical loading is regarded as the only stimulus for bone remodelling, the present model establishes a unique coupling between mechanical loading and the chemical reactions involved in the process of bone remodelling. This model was incorporated into the finite element software ANSYS by means of a macro to compute density distribution in distal femoral bone both before and after TKA. Consistent with dual-energy X-ray absorptiometry (DEXA) scans reported in the literature, the results showed that the most severe bone loss occurs in the anterior region of the distal femur and that there is more bone resorption in the lateral than the medial condyle following TKA. Furthermore, the bone density distribution predicted using the present model showed a gradual and uniform pattern and thus a more realistic bone evolution contrary to the strain energy density model, where there is no gradual bone density evolution.

Comparison of the effects of possible mechanical stimuli on the rate of biochemical reactions

The aim of this work is to address the question of what constitutes a mechanical stimulation of biochemical reactions in general and further to compare the importance of the two possible mechanical stimulations: shear rate and the rate of volume variation. Using linear nonequilibrium thermodynamics, the Curie principle (the relation for coupling phenomena) is retrieved for a phenomenological relation for a scalar flux in an isotropic system. From these phenomenological relations for the rate of chemical reaction, it is established that the only scalar quantity related to the rate of deformation tensor D that cannot be neglected is the rate of volume variation D((1)). This leads us to the conclusion that, although tissues are exposed to all variety of mechanical factors: straining, shear, pressure, and even dynamic electric fields, the volume variation rate D((1)) is the most important mechanical stimulus driving the processes in them.