All about Graphene

a.      Fabrication and Characteristics

Graphene is two-dimensional crystalline form of carbon: a single layer of carbon atoms arranged in hexagons, like a honeycomb, with sp² bonding, unlike diamond and amorphous carbon materials as having sp³ bonding. Chemical functionalization of the main graphene sheet (not the edges) is achieved by either covalent or non-covalent methods. Covalent functionalization requires the breaking of sp² bonds and can be achieved using a wide range of reactions. Non-covalent functionalization relies on van der Waals forces often due to  pi-pi stacking between aromatic molecules and the graphene lattice. Regarding its electronic properties, a good approximation to the band structure of mono-layer graphene can be obtained from a simple nearest neighbor tight-binding calculation. Inspection of this band structure immediately reveals three electronic properties of mono-layer graphene which have excited such interest in this material: the vanishing carrier density at the Dirac points, the existence of pseudo-spin and the relativistic nature of carriers [1].  In case of magnetic properties of graphene, weak paramagnetism at low temperatures is reported for relatively defect free graphene, and the use of ion irradiation to add vacancies can increase the paramagnetism [2].

Fourier’s Smart Tool: Altering a Problem to be Easily Solved

       Linear transforms, especially Fourier and Laplace transforms are widely used in solving problems in science and engineering, The Fourier transform is used in linear systems analysis, antenna studies, optics, random process modeling, probability theory, quantum physics, and boundary value problems and has been very successfully applied to restoration of astronomical data. The Fourier transform, a pervasive and versatile tool is used in many fields of science as a mathematical or physical tool to alter a problem into one that can be more easily solved. Some scientists understand Fourier theory as a physical phenomenon not simply as a mathematical tool. In some branches of science the Fourier transform of one function may yield another physical function.

From Force to Energy: Evolution of Classical Mechanics

      Newtonian mechanics is mathematically fairly straightforward, and can be applied to a wide variety of problems. It took the Apollo astronauts to the moon and the voyager spacecraft to the far reaches of the solar system. It is not a unique formulation of mechanics, however; other formulations are possible. Here we will look at two common alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics.

        Its original prescription rested on two principles. First, we should try to express the state of the mechanical system using the minimum representation possible and which reflects the fact that the physics of the problem is coordinate-invariant. Second, a mechanical system tries to optimize its action from one split second to the next; often this corresponds to minimizing its total energy as it evolves from one state to the next. These notes are intended as an elementary introduction into these ideas and the basic prescription of Lagrangian and Hamiltonian mechanics.

Revolution in Equation of State: Van der Waals’s Correction for Ideal Gas Equation

       The perfect gas equation of state PV = nRT is manifestly incapable of describing actual gases at low temperatures, since they undergo a discontinuous change of volume and become liquids. Van der Waals equation comes up to recognize the molecules that interact with each other. The equation puts two parameters to mimic this interaction. The first, an attractive intermolecular force at long distances, helps draw the gas together and therefore reduces the necessary outside pressure to contain the gas in a given volume (the gas is a little thinner near the walls). The second is to take account of the finite molecular volume. A real gas cannot be compressed indefinitely (it becomes a liquid, for all practical purposes incompressible).

Schrodinger and Wave Mechanics

      In mathematical physics, the Schrodinger equation, are the most fundamental equations in non-relativistic quantum mechanics, playing the same role as Hamilton’s laws of motion in non-relativistic classical mechanics. The Schrodinger equation has two ‘forms’, one in which time explicitly appears, and so describes how the wave function of a particle will evolve in time. In general, the wave function behaves like a wave, and so the equation is often referred to as the time dependent Schrodinger wave equation. The other is the equation in which the time dependence has been ‘removed’ and hence is known as the time independent Schrodinger equation and is found to describe, amongst other things, what the allowed energies are of the particle. These are not two separate, independent equations – the time independent equation can be derived readily from the time dependent equation.

Seeing Throughout Blood Circulatory to Understand Drugs Delivery System

それが十回と言われているように、ナノ粒子は生物医学アプリケーション内の多くの利点があります。薬物送達アプリケーションでは、ナノ粒子はテレサと、キャリアと、薬自体となることができます。

        Studying drug delivery system will combine some basic knowledge in Physics, Chemistry and Biology as interdisciplinary of science and engineering. Targeting medicines into specific tissue or part of body needs  some considerations such as in which way the drugs will be delivered, what kind of media that ensures the drugs reaching the their destination, drugs biocompatibility to not be detected as “alien or invader” by immune system, etc. So, it becomes necessity to understand blood circulatory since blood is main “transporter” in our body. 

How Can Magnetic Fields Interfere?

         It’s obvious whether we can also treat magnetic fields as a common wave. As doubtlessly known, two propagated waves can be interfered each other.  Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape resulted from the net effect of the two individual waves upon the particles of the medium.

        Consider two waves that are in phase, sharing the same frequency and with amplitudes A₁ and A₂. Their troughs and peaks line up and the resultant wave will have amplitude A = A₁ + A₂. This is known as constructive interference. If the two waves are π radians, or 180°, out of phase, then one wave's crests will coincide with another waves' troughs and so will tend to cancel it out. The resultant amplitude is A = |A₁ − A₂|. If A₁ = A₂, the resultant amplitude will be zero. This is known as destructive interference.

A Basic Chemical Reaction, REDOX

     化学反応（かがくはんのう）とは、原子間の結合の生成、あるいは切断によって異なる物質を生成する変化のことである。Any chemical reaction in which the oxidation numbers (oxidation states) of the atoms are changed is an oxidation - reduction reaction. Such reactions are also known as redox reactions, which is shorthand for reduction-oxidation reactions.

Oxidation and Reduction

Oxidation involves an increase in oxidation number, while reduction involves a decrease in oxidation number. Usually the change in oxidation number is associated with a gain or loss of electrons, but there are some redox reactions (e.g., covalent bonding) that do not involve electron transfer. Depending on the chemical reaction, oxidation and reduction may involve any of the following for a given atom, ion, or molecule:

Faraday’s Law of Induction and The Correlation between Biot-Savart Concept

        Faraday’s Law and Biot-Savart equation become 2 basic concepts respectively in designing electric generator or magnetic generator that have been used in many application field, for example, producing electric power by power generator to supply town’s electricity or especially producing high frequency AC magnetic field to cause heat loss in super paramagnetic magnetic nanoparticle for hyperthermia treatment. We’ve already learned about the Biot-Savart’s equation that simply said if the magnetic field can be produced along wire carrying an electric current. Now, Faraday’s concept tells reversely.

          Any change of magnetic environment in a coil of a wire will cause a voltage (Electromotive Force: EMF) to be induced in the coil. No matter the change is produced, the voltage will be generated. The change could be produced by changing  the magnetic field strength, moving magnet toward or away from  the coil, moving the coil into or out the magnetic field, rotating the coil relative to the magnet, etc.

Superparamagnetic: A Size Effect of Nanoparticles

ナノ粒子は、ポリマーと無機製剤とその両方の組み合わせに基づいて、先進的な生物医学研究のツールを提供することがあります。病気の早期発見のための診断テストのように、標的薬物送達システムとして、イメージングと創薬のためのツールとして、それは多くの生物医学アプリケーションで使うことができます。

         Nanoparticles used in biomedical applications include liposomes, polymeric micelles, block ionomer complexes, dendrimers, inorganic and polymeric nanoparticles, nanorods and quantum dots. All have been tested pre-clinically or clinically for targeted drug and gene delivery and as agents to enhance diagnostic imaging output like in MRI. Properties present only on the nanoscale level, like the increased intensity of fluorescent light emission of semiconductor crystals (quantum dots) or switchable magnetic properties of superparamagenetic nanoparticles (SPIONs), make these materials unique and useful for applications in the biomedical field of medical imaging and cell tracking. Other nanoparticles like water-soluble synthetic polymers (dendrimers) were tested in pre-clinical models for the delivery of drugs, genes, and as imaging agents showing a rich versatility for tailoring their binding properties to several requirements, among them facilitation of cellular uptake of drugs (e.g. cancer drugs).

From Normal Cell Into Cancer

 誰もが知っているように、いくつかのケースには、悪性腫瘍（あくせいしゅよう）は人間の死を引き起こすことができる。悪性腫瘍、がんと言うのは、他の組織との境界に侵入したり（浸潤）、あるいは転移し、身体の各所で増大することで生命を脅かす腫瘍である。どのように正常細胞は癌細胞になって、以下記載されています。

Carcinogenesis is process by which normal cells are transformed into cancer cells characterized by a progression of changes on cellular and genetic level that ultimately reprogram a cell to undergo uncontrolled cell division, thus forming a malignant mass. Carcinogenesis is caused by mutation of the genetic material of normal cells, which upsets the normal balance between proliferation and cell death. This results in uncontrolled cell division. The uncontrolled and often rapid proliferation of cells can lead to benign tumors; some types of these may turn into malignant tumors (cancer). Benign tumors do not spread to other parts of the body or invade other tissues, and they are rarely a threat to life unless they compress vital structures or are physiologically active, for instance, producing a hormone. Malignant tumors can invade other organs, spread to distant locations (metastasis) and become life-threatening.

Colligative Properties of Solution

束一的性質（そくいつてきせいしつ）とは不揮発性溶質の希薄溶液における相平衡の性質で、溶質を溶媒で希釈する際に化学ポテンシャルが減少することを原因として、蒸気圧降下、沸点上昇、凝固点降下、浸透圧といった現象を引き起こす。

化学ポテンシャルの強度は溶質のモル分率に依存する為、束一的性質を原因とする現象は溶質の種類によらずモル濃度（より正確には活量）の大小でその強度が決定付けられる。それ故、高分子化合物などの（平均）分子量は、束一的性質に基づいて沸点上昇、凝固点降下、浸透圧の変化量をもとに決定することが可能である。

         Colligative properties are those properties of solutions that depend on the number of dissolved particles in solution, but not on the identities of the solutes. For example, the freezing point of salt water is lower than that of pure water, due to the presence of the salt dissolved in the water. To a good approximation, it does not matter whether the salt dissolved in water is sodium chloride or potassium nitrate; if the molar amounts of solute are the same and the number of ion are the same, the freezing points will be the same. For example, AlCl ₃ and K ₃ PO ₄ would exhibit essentially the same colligative properties, since each compound dissolves to produce four ions per formula unit. The four commonly studied colligative properties are freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure. Since these properties yield information on the number of solute particles in solution, one can use them to obtain the molecular weight of the solute.

Magnetic Field along Current Carried Wires.

Biot-Savart Law

          The Biot-Savart Law relates magnetic fields to the currents which are their sources. In a similar manner, Coulomb's law relates electric fields to the point charges which are their sources. Finding the magnetic field resulting from a current distribution involves the vector product, and is inherently a calculus problem when the distance from the current to the field point is continuously changing.      

   

          We now use the Biot-Savart law to deal with problems in magnetostatics: this is the situation of steady currents leading to constant magnetic fields.  There are two simple cases where the magnetic field integrations are easy to carry out, and fortunately they are in geometries that are of practical use. We use the formula for the magnetic field of an infinitely long wire whenever we want to estimate the field near a segment of wire, and we use the formula for the magnetic field at the center of a circular loop of wire wheneverwe want to estimate the magnetic field near the center of any loop of wire. 

Pennes' Equation: 生体組織の熱伝達を 学ぶこと

          The transport of thermal energy in living tissue is a complex process involving multiple phenomenological mechanisms including conduction, convection, radiation, metabolism, evaporation, and phase change. The study of tissue heating processes at high temperatures is relevant to therapeutic applications (such as RF, microwave, and laser ablation and hyperthermia) and food processing applications (such as baking and frying).

 
         Pennes' bio-heat equation, based on the heat diffusion equation, is a much used approximation for heat transfer in biological tissue. Many publications have shown it is a valuable approximation, especially at hyperthermia temperatures. However, at the higher temperatures seen during ablation, the Pennes’ bio-heat equation does not incorporate all the physical processes affecting final tissue temperature. These processes include but are not limited to the effects of the movement and diffusion of tissue water due to temperature and changes in local water content due to heating, water evaporation at high temperatures, the diffusion of this generated water vapor, and its possible re-condensation.

         To add to the complexity, the thermal and other physical properties are a function of temperature, water content and the changes in the mechanical stresses on the tissue. Attempting to model this complex physical system, which involves electromagnetic (EM), thermal and mass transfer modeling, mechanical stresses, etc, is challenging due to the interdependent nature of the physical properties.

自分自身に信じることができるか？

Basic Concept of Improving Self-Capability

          Everyone has already agreed that stress is common problem, affecting our mental and physical health. We may think of stressful events as unpleasant ones, such as losing a job or having difficulties at home or at school. But changes for the better can also cause stress, like a new baby, a wedding, and a new house. In an ideal world, maybe we could get away from stressful situations, or change them. Too often we can't do that - but we can learn to control our response to those situations. And we can develop techniques that will reduce the effects of stress on our mental and physical health.

        Now, let's see how Physics explains about stress.

The Meaning Behind Coulomb’s Law and Ionic Bond

Introduction to Coulomb’s Law

         Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form as follows:

  

The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges.

and in vector form as:

ストイキオメトリ: Math Behind Chemistry

君たちは化学が好きでしょうか? 僕は良い文章を見付けた。その文章は基本化学に教えているんだ,ストイキオメトリ。何か思い出すのか? 我々が中学にあった時, ストイキオメトリを勉強した でしょう. じゃあ, 読みましょう。。。 ^_^ 

  

Stoichiometry is  branch of chemistry that deals with the quantitative relationships that exist among the reactants and products in chemical reactions. Given enough information, one can use stoichiometry to calculate masses, moles, and percents within a chemical equation.