Double Donnan[ edit ] Note that Sides 1 and 2 are no longer in osmotic equilibrium i. In many instances, from ultrafiltration of proteins to ion exchange chromatography, the pH of the buffer adjacent to the charged groups of the membrane is different from the pH of the rest of the buffer solution. When the charged groups are positive acidic , then they will repel protons so that the pH will be higher than the surrounding buffer. Physiological applications[ edit ] Red blood cells[ edit ] When tissue cells are in a protein-containing fluid, the Donnan effect of the cytoplasmic proteins is equal and opposite to the Donnan effect of the extracellular proteins.
|Published (Last):||17 August 2009|
|PDF File Size:||17.74 Mb|
|ePub File Size:||16.92 Mb|
|Price:||Free* [*Free Regsitration Required]|
He belonged to an old Yankee family that had produced distinguished American clergymen and academics since the 17th century. He was the fourth of five children and the only son of Josiah Willard Gibbs Sr. On his father's side, he was descended from Samuel Willard , who served as acting President of Harvard College from to On his mother's side, one of his ancestors was the Rev.
Gibbs's given name, which he shared with his father and several other members of his extended family, derived from his ancestor Josiah Willard, who had been Secretary of the Province of Massachusetts Bay in the 18th century.
He is chiefly remembered today as the abolitionist who found an interpreter for the African passengers of the ship Amistad , allowing them to testify during the trial that followed their rebellion against being sold as slaves. At Yale, Gibbs received prizes for excellence in mathematics and Latin , and he graduated in , near the top of his class. At age 19, soon after his graduation from college, Gibbs was inducted into the Connecticut Academy of Arts and Sciences , a scholarly institution composed primarily of members of the Yale faculty.
He also suffered from astigmatism , whose treatment was then still largely unfamiliar to oculists , so that Gibbs had to diagnose himself and grind his own lenses. During the first two years, he taught Latin and during the third year, he taught "natural philosophy" i. At the time, German academics were the leading authorities in the natural sciences, especially chemistry and thermodynamics.
Gibbs, who had independent means and had yet to publish anything, was assigned to teach graduate students exclusively and was hired without salary. These papers introduced the use of different type phase diagrams, which were his favorite aids to the imagination process when doing research, rather than the mechanical models, such as the ones that Maxwell used in constructing his electromagnetic theory, which might not completely represent their corresponding phenomena.
Maxwell even made, with his own hands, a clay model illustrating Gibbs's construct. He then produced two plaster casts of his model and mailed one to Gibbs. That cast is on display at the Yale physics department. The joke later circulated in New Haven that "only one man lived who could understand Gibbs's papers. That was Maxwell, and now he is dead.
He described that research in a monograph titled " On the Equilibrium of Heterogeneous Substances ", published by the Connecticut Academy in two parts that appeared respectively in and That work, which covers about three hundred pages and contains exactly seven hundred numbered mathematical equations,  begins with a quotation from Rudolf Clausius that expresses what would later be called the first and second laws of thermodynamics : "The energy of the world is constant.
The entropy of the world tends towards a maximum. Nevertheless it was a number of years before its value was generally known, this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficult reading for anyone, and especially so for students of experimental chemistry whom it most concerns.
O'Connor and E. Gibbs's office was on the second floor, to the right of the tower in the picture. With this object in mind, Gibbs distinguished between the dot and cross products of two vectors and introduced the concept of dyadics. Similar work was carried out independently, and at around the same time, by the British mathematical physicist and engineer Oliver Heaviside.
Gibbs sought to convince other physicists of the convenience of the vectorial approach over the quaternionic calculus of William Rowan Hamilton , which was then widely used by British scientists. This led him, in the early s, to a controversy with Peter Guthrie Tait and others in the pages of Nature.
In other mathematical work, he re-discovered the " Gibbs phenomenon " in the theory of Fourier series which, unbeknownst to him and to later scholars, had been described fifty years before by an obscure English mathematician, Henry Wilbraham. The methods that he used were highly original and the obtained results showed decisively the correctness of Maxwell's electromagnetic theory.
He had a way, toward the end of the afternoon, of taking a stroll about the streets between his study in the old Sloane Laboratory and his home—a little exercise between work and dinner—and one might occasionally come across him at that time. In May, Yale organized a memorial meeting at the Sloane Laboratory. The eminent British physicist J. Thomson was in attendance and delivered a brief address.
According to his student Lynde Wheeler, of the existing portraits, this is the most faithful to Gibbs's kindly habitual expression. Gibbs was not a freak, he had no striking ways, he was a kindly dignified gentleman. Wilson,  According to Lynde Wheeler , who had been Gibbs's student at Yale, in his later years Gibbs was always neatly dressed, usually wore a felt hat on the street, and never exhibited any of the physical mannerisms or eccentricities sometimes thought to be inseparable from genius His manner was cordial without being effusive and conveyed clearly the innate simplicity and sincerity of his nature.
For many years, he served as trustee, secretary, and treasurer of his alma mater, the Hopkins School. Arthur appointed him as one of the commissioners to the National Conference of Electricians, which convened in Philadelphia in September , and Gibbs presided over one of its sessions. Bumstead referred to Gibbs's personal character: Unassuming in manner, genial and kindly in his intercourse with his fellow-men, never showing impatience or irritation, devoid of personal ambition of the baser sort or of the slightest desire to exalt himself, he went far toward realizing the ideal of the unselfish, Christian gentleman.
In the minds of those who knew him, the greatness of his intellectual achievements will never overshadow the beauty and dignity of his life. This shows a plane of constant volume, passing through the point A that represents the body's initial state. The curve MN is the section of the "surface of dissipated energy". AB is the "available energy" now called the Helmholtz free energy and AC the "capacity for entropy" i.
Thus, it was Gibbs who first combined the first and second laws of thermodynamics by expressing the infinitesimal change in the internal energy, dU, of a closed system in the form:  d.
Josiah Willard Gibbs