Hydrogels Based on Polyacrylamide and Calcium Alginate: Thermodynamic Compatibility of Interpenetrating Networks, Mechanical, and Electrical Properties.

The synthesis and physicochemical properties of hydrogels with interpenetrated physical and chemical networks were considered in relation to their prospective application as biomimetic materials in biomedicine and bioengineering. The study was focused on combined hydrogels based on natural polysaccharide-calcium alginate (CaAlg) and a synthetic polymer-polyacrylamide (PAAm). The series of hydrogels with varying proportions among alginate and polyacrylamide have been synthesized, and their water uptake has been characterized depending on their composition. The equilibrium swelling and re-swelling in water after drying were considered. The compatibility of alginate and polyacrylamide in the combined blend was studied by the thermodynamic approach. It showed a controversial combination of negative enthalpy of mixing among PAAm and CaAlg with positive Gibbs energy of mixing. Mechanical and electrical properties of the combined gels with double networking were studied as relevant for their prospective use as scaffolds for tissue regeneration and working bodies in actuators. The storage modulus and the loss modulus were determined in the oscillatory compression mode as a function of proportions among natural and synthetic polymers. Both moduli substantially increased with the content of CaAlg and PAAm. The electrical (Donnan) potential of hydrogels was measured using the capillary electrode technique. The Donnan potential was negative at all compositions of hydrogels, and its absolute values increased with the content of CaAlg and PAAm.

Quantum-Chemical Study of the Assembly Mechanism of 1-Pyrrolines from N-Benzylaldimines and Arylacetylenes in KOtBu/DMSO Superbasic Medium.

By using a quantum-chemical approach, B2PLYP-D2/6-311+G**//B3LYP/6-31+G*, we have carried out a detailed study of the assembly of 1-pyrrolines from N-benzyl-1-phenylmethanimine and phenylacetylene in the superbasic medium KOtBu/dimethyl sulfoxide (DMSO). In this way, we have considered, both theoretically and experimentally, the mechanisms of the assembly through a concerted and stepwise nucleophilic cycloaddition and have addressed the side processes accompanying the assembly. It is found that the assembly via the concerted cycloaddition is kinetically more favorable than that via the stepwise cycloaddition. At the same time, the reaction of C-vinylation of aldimine with phenylacetylene occurs with a similar activation energy as the concerted cycloaddition and leads to the formation of 2-aza-1,4-pentadiene. The anion of 2-aza-1,4-pentadiene is an intermediate for the side processes leading to the formation of triarylpyridines and 1,3-diarylpropan-1-ones. Triarylpyridines are formed through the concerted cycloaddition of the next phenylacetylene molecule to 2-aza-1,4-pentadiene, while 1,3-diarylpropan-1-ones are formed as a result of the hydrolysis of 2-aza-1,4-pentadienes. It is found out that the mild conditions for the assembly of 1-pyrrolines (60 °C, 15 min) relate to the formation of complexes in the KOtBu/DMSO superbasic medium, where the anion is readily accessible for the nucleophilic attack by the phenylacetylene molecule.

Mechanical Force Acting on Ferrogel in a Non-Uniform Magnetic Field: Measurements and Modeling.

The development of magnetoactive microsystems for targeted drug delivery, magnetic biodetection, and replacement therapy is an important task of present day biomedical research. In this work, we experimentally studied the mechanical force acting in cylindrical ferrogel samples due to the application of a non-uniform magnetic field. A commercial microsystem is not available for this type of experimental study. Therefore, the original experimental setup for measuring the mechanical force on ferrogel in a non-uniform magnetic field was designed, calibrated, and tested. An external magnetic field was provided by an electromagnet. The maximum intensity at the surface of the electromagnet was 39.8 kA/m and it linearly decreased within 10 mm distance from the magnet. The Ferrogel samples were based on a double networking polymeric structure which included a chemical network of polyacrylamide and a physical network of natural polysaccharide guar. Magnetite particles, 0.25 micron in diameter, were embedded in the hydrogel structure, up to 24% by weight. The forces of attraction between an electromagnet and cylindrical ferrogel samples, 9 mm in height and 13 mm in diameter, increased with field intensity and the concentration of magnetic particles, and varied within 0.1-30 mN. The model provided a fair evaluation of the mechanical forces that emerged in ferrogel samples placed in a non-uniform magnetic field and proved to be useful for predicting the deformation of ferrogels in practical bioengineering applications.

Transport phenomena in complex systems (part 2).

This theme issue, in two parts, continues research studies of transport phenomena in complex media published in the first part (Alexandrov & Zubarev 2021 Phil. Trans. R. Soc. A 379, 20200301. (doi:10.1098/rsta.2020.0301)). The issue is concerned with theoretical, numerical and experimental investigations of nonlinear transport phenomena in heterogeneous and metastable materials of different nature, including biological systems. The papers are devoted to the new effects arising in such systems (e.g. pattern and microstructure formation in materials, impacts of external processes on their properties and evolution and so on). State-of-the-art methods of numerical simulations, stochastic analysis, nonlinear physics and experimental studies are presented in the collection of issue papers. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Modelling of hemodynamics in bifurcation lesions of coronary arteries before and after myocardial revascularization.

Modelling of patient-specific hemodynamics for a clinical case of severe coronary artery disease with the bifurcation stenosis was carried out with allowance for standard angiographic data obtained before and after successfully performed myocardial revascularization by stenting of two arteries. Based on a non-Newtonian fluid model and an original algorithm for fluid dynamics computation operated with a limited amount of initial data, key characteristics of blood flow were determined to analyse the features of coronary disease and the consequences of its treatment. The results of hemodynamic modelling near bifurcation sites are presented with an emphasis on physical, physiological and clinical phenomena to demonstrate the feasibility of the proposed approach. The main limitations and ways to minimize them are the subjects of discussion as well. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Theory of static magnetization of magnetopolymer composites: The second virial approximation.

This paper deals with a theoretical study of the static magnetization of a composite, consisting of nanodisperse single-domain ferromagnetic particles immobilized in a nonmagnetic medium. This situation is typical for magnetopolymer systems-smart materials, which found applications in high industrial and biomedical applications. It is supposed that the composite was polymerized without an external magnetic field; after curing the particles retain the spatial distribution and orientation of their axes of easy magnetization that they had before the host medium polymerization. Our results demonstrate that, in contrast to ferrofluids with a liquid host medium, a magnetic interparticle interaction provokes a decrease of the macroscopic magnetization of the system.

Transport phenomena in complex systems (part 1).

The issue, in two parts, is devoted to theoretical, computational and experimental studies of transport phenomena in various complex systems (in porous and composite media; systems with physical and chemical reactions and phase and structural transformations; in biological tissues and materials). Various types of these phenomena (heat and mass transfer; hydrodynamic and rheological effects; electromagnetic field propagation) are considered. Anomalous, relaxation and nonlinear transport, as well as transport induced by the impact of external fields and noise, is the focus of this issue. Modern methods of computational modelling, statistical physics and hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Special attention is paid to transport phenomena in biological systems (such as haemodynamics in stenosed and thrombosed blood vessels magneto-induced heat generation and propagation in biological tissues, and anomalous transport in living cells) and to the development of a scientific background for progressive methods in cancer, heart attack and insult therapy (magnetic hyperthermia for cancer therapy, magnetically induced circulation flow in thrombosed blood vessels and non-contact determination of the local rate of blood flow in coronary arteries). The present issue includes works on the phenomenological study of transport processes, the derivation of a macroscopic governing equation on the basis of the analysis of a complicated internal reaction and the microscopic determination of macroscopic characteristics of the studied systems. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Nonlinear theory of macroscopic flow induced in a drop of ferrofluid.

We present results of theoretical modelling of macroscopic circulating flow induced in a cloud of ferrofluid by an oscillating magnetic field. The cloud is placed in a cylindrical channel filled by a nonmagnetic liquid. The aim of this work is the development of a scientific basis for a progressive method of addressing drug delivery to thrombus clots in blood vessels with the help of the magnetically induced circulation flow. Our results show that the oscillating field can induce, inside and near the cloud, specific circulating flows with the velocity amplitude about several millimetres per second. These flows can significantly increase the rate of transport of the molecular non-magnetic impurity in the channel. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution.

In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long-time limit describing non-uniform distribution due to a space-dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Effect of ring-shaped clusters on magnetic hyperthermia: modelling approach.

Experiments demonstrate that magnetic nanoparticles, embedded in a tissue, very often form heterogeneous structures of various shapes and topologies. These structures (clusters) can significantly affect macroscopical properties of the composite system, in part its ability to generate heat under an alternating magnetic field (so-called magnetic hyperthermia). If the energy of magnetic interaction between the particles significantly exceeds the thermal energy of the system, the particles can form the closed ring-shaped clusters. In this work, we propose a relatively simple model of the heat production by the particles united in the 'ring' and immobilized in a host medium. Mathematically, this model is based on the phenomenological Debye equation of kinetics of the particles remagnetization. Magnetic interaction between all particles in the cluster is taken into account. Our results show that the appearance of the clusters can significantly decrease the thermal effect. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Cutaneous Squamous Cell Carcinoma in Patients with Hidradenitis Suppurativa.

Background: Cutaneous squamous cell carcinoma (cSCC) is a rare complication of hidradenitis suppurativa (HS). Objectives: To conduct a systematic review and an individual patient data (IPD) meta-analysis to describe the clinical characteristics of HS patients developing cSCC and determine predictors of poor outcome. Methods: Medline/PubMed, Embase, and Web of Science were searched for studies reporting cSCC arising in patients with HS from inception to December 2019. A routine descriptive analysis, statistical hypothesis testing, and Kaplan-Meier survival curves/Cox proportional hazards regression models were performed. Results: A total of 34 case reports and series including 138 patients were included in the study. The majority of patients were males (81.6%), White (83.3%), and smokers (n = 22/27 reported) with a mean age of 53.5 years. Most patients had gluteal (87.8%), Hurley stage 3 HS (88.6%). The mean time from the diagnosis of HS to the development of cSCC was 24.7 years. Human papillomavirus was identified in 12/38 patients tested. Almost 50% of individuals had nodal metastasis and 31.3% had distant metastases. Half of the patients succumbed to their disease. Conclusions: cSCC is a rare but life-threatening complication seen in HS patients, mainly occurring in White males who are smokers with severe, long-standing gluteal HS. Regular clinical examination and biopsy of any suspicious lesions in high-risk patients should be considered. The use of HPV vaccination as a preventive and possibly curative method needs to be explored.

Correction: Borin, D., et al. Magnetorheological Effect of Magnetoactive Elastomer with a Permalloy Filler. Polymers 2020, 12, 2371.

The authors wish to make a change to the published paper [...].

Magnetorheological Effect of Magnetoactive Elastomer with a Permalloy Filler.

Within the frames of this study, the synthesis of a permalloy to be used as a filler for magnetoactive and magnetorheological elastomers (MAEs and MREs) was carried out. By means of the mechanochemical method, an alloy with the composition 75 wt.% of Fe and 25 wt.% of Ni was obtained. The powder of the product was utilized in the synthesis of MAEs. Study of the magnetorheological (MR) properties of the elastomer showed that in a ~400 mT magnetic field the shear modulus of the MAE increased by a factor of ~200, exhibiting an absolute value of ~8 MPa. Furthermore, we obtained experimentally a relative high loss factor for the studied composite; this relates to the size and morphology of the synthesized powder. The composite with such properties is a very perspective material for magnetocontrollable damping devices. Under the action of an external magnetic field, chain-like structures are formed inside the elastomeric matrix, which is the main determining factor for obtaining a high MR effect. The effect of chain-like structures formation is most pronounced in the region of small strains, since structures are partially destroyed at large strains. A proposed theoretical model based on chain formation sufficiently well describes the experimentally observed MR effect. The peculiarity of the model is that chains of aggregates of particles, instead of individual particles, are considered.

Chain Formation and Phase Separation in Ferrofluids: The Influence on Viscous Properties.

Ferrofluids have attracted considerable interest from researchers and engineers due to their rich set of unique physical properties that are valuable for many industrial and biomedical applications. Many phenomena and features of ferrofluids' behavior are determined by internal structural transformations in the ensembles of particles, which occur due to the magnetic interaction between the particles. An applied magnetic field induces formations, such as linear chains and bulk columns, that become elongated along the field. In turn, these structures dramatically change the rheological and other physical properties of these fluids. A deep and clear understanding of the main features and laws of the transformations is necessary for the understanding and explanation of the macroscopic properties and behavior of ferrofluids. In this paper, we present an overview of experimental and theoretical works on the internal transformations in these systems, as well as on the effect of the internal structures on the rheological effects in the fluids.

On the theory of magnetic hyperthermia: clusterization of nanoparticles.

Experiments show that clusters consisting of nano-sized ferromagnetic particles strongly affect the intensity of heat production during magnetic hyperthermia. In this paper, a theoretical study and mathematical modelling of the heat production by clusters of single-domain ferromagnetic particles, immobilized in a host medium, are presented. Two situations of strong and weak magnetic anisotropy of the particles are considered. Our results show that, in the case of strong anisotropy, the clusterization weakens the thermal effect, whereas in the case of weak anisotropy it enhances it. This article is part of the theme issue 'Patterns in soft and biological matters'.

Role of particle clusters on the rheology of magneto-polymer fluids and gels.

Even in the absence of cross-linking, at large enough concentration, long polymer strands have a strong influence on the rheology of aqueous systems. In this work, we show that solutions of medium molecular weight (120 000-190 000 g mol-1) alginate polymer retained a liquid-like behaviour even for concentrations as large as 20% w/v. On the contrary, solutions of alginate polymer of larger (and also polydisperse) molecular weight (up to 600 000 g mol-1) presented a gel-like behaviour already at concentrations of 7% w/v. We dispersed micrometre-sized iron particles at a concentration of 5% v/v in these solutions, which resulted in either stable magnetic fluids or gels, depending on the type of alginate polymer employed (medium or large molecular weight, respectively). These magneto-polymer composites presented a shear-thinning behaviour that allowed injection through a syringe and recovery of the original properties afterwards. More interestingly, application of a magnetic field resulted in the formation of particle clusters elongated along the field direction. The presence of these clusters intensely affected the rheology of the systems, allowing a reversible control of their stiffness. We finally developed theoretical modelling for the prediction of the magnetic-sensitive rheological properties of these magneto-polymer colloids. This article is part of the theme issue 'Patterns in soft and biological matters'.

Patterns in soft and biological matters.

The issue is devoted to theoretical, computer and experimental studies of internal heterogeneous patterns, their morphology and evolution in various soft physical systems-organic and inorganic materials (e.g. alloys, polymers, cell cultures, biological tissues as well as metastable and composite materials). The importance of these studies is determined by the significant role of internal structures on the macroscopic properties and behaviour of natural and manufactured tissues and materials. Modern methods of computer modelling, statistical physics, heat and mass transfer, statistical hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Non-equilibrium patterns which appear during macroscopic transport and hydrodynamic flow, chemical reactions, external physical fields (magnetic, electrical, thermal and hydrodynamic) and the impact of external noise on pattern evolution are the foci of this issue. Special attention is paid to pattern formation in biological systems (such as drug transport, hydrodynamic patterns in blood and pattern dynamics in protein and insulin crystals) and to the development of a scientific background for progressive methods of cancer and insult therapy (magnetic hyperthermia for cancer therapy; magnetically induced drug delivery in thrombosed blood vessels). The present issue includes works on pattern growth and their evolution in systems with complex internal structures, including stochastic dynamics, and the influence of internal structures on the external static, dynamic magnetic and mechanical properties of these systems. This article is part of the theme issue 'Patterns in soft and biological matters'.

Field-induced circulation flow in magnetic fluids.

In this paper, we present results of a theoretical study of circulation flow in ferrofluids under the action of an alternating inhomogeneous magnetic field. The results show that the field with the amplitude of about 17 kA m-1 and angular frequency 10 s-1 can induce mesoscopic flow with a velocity amplitude of about 0.5 mm s-1. This mechanism can be used for intensification of drag delivery in blood vessels. This article is part of the theme issue 'Patterns in soft and biological matters'.

Ferrogels Ultrasonography for Biomedical Applications.

Ferrogels (FG) are magnetic composites that are widely used in the area of biomedical engineering and biosensing. In this work, ferrogels with different concentrations of magnetic nanoparticles (MNPs) were synthesized by the radical polymerization of acrylamide in stabilized aqueous ferrofluid. FG samples were prepared in various shapes that are suitable for different characterization techniques. Thin cylindrical samples were used to simulate the case of targeted drug delivery test through blood vessels. Samples of larger size that were in the shape of cylindrical plates were used for the evaluation of the FG applicability as substitutes for damaged structures, such as bone or cartilage tissues. Regardless of the shape of the samples and the conditions of their location, the boundaries of FG were confidently visualized over the entire range of concentrations of MNPs while using medical ultrasound. The amplitude of the reflected echo signal was higher for the higher concentration of MNPs in the gel. This result was not related to the influence of the MNPs on the intensity of the reflected echo signal directly, since the wavelength of the ultrasonic effect used is much larger than the particle size. Qualitative theoretical model for the understanding of the experimental results was proposed while taking into account the concept that at the acoustic oscillations of the hydrogel, the macromolecular net, and water in the gel porous structure experience the viscous Stocks-like interaction.

Heterogeneous materials: metastable and non-ergodic internal structures.

This issue is concerned with structural and phase transitions in heterogeneous and composite materials, the effects of external magnetic fields on these phenomena and the macroscopic properties and behaviour of materials with isotropic and anisotropic internal structures. Using experimental, theoretical and computer methods, these transitions are studied at the atomic and mesoscopic levels. The fundamental specific feature of structural transitions in many heterogeneous media consists of the fact that these transitions are stacked for a long time in non-equilibrium states that appear due to either macroscopic dissipative processes (an alternating magnetic field or hydrodynamic flow, for instance) or system lifetime in a metastable state. It is important to explain and describe these transitional states using the general approach of non-equilibrium physical mechanics. The review and research articles in the issue will cover the whole spectrum of scales (from nano to macro) and materials (from metastable liquids to biological polymers) in order to exhibit recently developed trends in the field of heterogeneous materials. Atomistic modelling, structuring induced by external magnetic fields and hydrodynamic flows, metastable and non-ergodic states, mechanical properties and phenomena in heterogeneous materials-all these are covered. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.