Popular Science Monthly/Volume 14/January 1879/Molecular Dynamics
By L. R. CURTISS.
DYNAMICS refers to force or power. It deals with the primary conceptions of energy in its relations to subjects that are susceptible of numerical estimation, such as time, space, and velocity. Or, again, dynamics is that branch of science which measures the energies producing motion as well as those produced by motion, and is divided into two parts—kinematics, which pertains to motion without regard to the bodies acted upon; and kinetics, which refers to the cause of energies whereby motion is given to bodies, each of which is the antithesis of static energy or energy at rest. Molecular dynamics has for its domain the actual working forces inherent in the atoms and molecules of matter. This branch of the subject bears the same relation to physics as the differential calculus does to mathematics, and by thus dealing with the physical molecules and atoms we are enabled to extend the kinetic chain of causation down toward the infinitely small with a certainty almost parallel to the accuracy with which the integral calculus defines the motion of the planets.
The text-books teach us that one of the properties of matter is inertia, including both that of rest and that of motion, the former being defined as the passive condition of bodies when at rest. This definition refers to matter as a mass. The new philosophy, however, teaches that, since molecular motion refers to the invisible movements of the particles of the mass, there is no such thing as complete rest of the ultimate particles of matter short of absolute zero of temperature, which, if universal, means total frigidity of every sun and orb in the universe.
The current of scientific thought tends to demonstrate that all the phenomena of Nature are to be regarded merely as varieties of motion, one guiding principle of which is conservation of energy. This being an established fact in science, it fortifies us in our position of reasoning downward in the direction of primary causes. By conservation of energy we are to understand that, while matter exists throughout the universe in definite quantity, there is also existing, as an attribute of matter, a definite amount of energy or force; and just so sure as matter is indestructible and unchangeable, just so sure is force or energy indestructible and interchangeable. That is, matter and force are both indestructible, but force or energy (synonymous terms) is convertible into the several modes of force. The attributes of matter are attraction of gravitation, attraction of cohesion, and chemical affinity. Attraction of gravitation is a force exerted upon each and every atom of matter throughout the universe, with a never-ending geometric ratio, varying directly as the mass and inversely as the square of the distance. The force known as chemical affinity binds the integral particles of compounds in an embrace many millions of times stronger than that of gravitation, but, like cohesive attraction, is incompetent to exert its power beyond very short distances, such as those measured by the limits of the molecule.
The correlation of physical forces has for its domain the interchangeableness and universality of the forces of Nature. It is competent to solve the dynamical problems of vital and physical phenomena, demanding from every antecedent its consequent, and exacting from every consequent an equivalency of antecedent. All sound experience of whatever kind justifies this affirmation. These views compel the idea of the universality of motion, and that force is the eternal causation of each and every phenomenon, and that the existing relations between matter and force remain constant throughout the universe. The same forces that whirl suns and planets in a restless march through shoreless space measure the phenomena of the moments of life.
The different consequents of molecular motion are sound, light, heat, etc., the antecedents of them all being some mode of motion. By the term "mode of motion" is meant the manner in which energies are made sensible to our understanding. Thus, the terms heat, light, etc., are but familiar ones by which we express the various modes in which force is exhibited to our senses in its action upon matter. Conservation of energy was denominated by Faraday as "the highest law in physical science which our faculties permit us to perceive." Its unfoldings mark an intellectual epoch which divides the old from the new. It teaches of the unity of the universe; it tells us how the sun's rays constitute the mighty energies of daily life and action upon every hand, warming, illuminating, and vivifying the surface of the globe.
As an illustration of this interchangeableness of force: suppose two files of men to be arranged in proper order, between which we roll a cannon-ball with a certain initial velocity. This ball runs the gantlet of those files of men, it being the individual duty of each man to retard the momentum of the ball by interposing his hand in its path. It is evident that each hand so interposed will receive a shock, the force of which is just equivalent to the amount parted with by the ball itself. Finally, the ball comes to rest. The original momentum of the ball has for its equivalency the sum total of the lesser energies imparted to the several hands interposed. Or again, if, instead of hands interposed, we substitute a row of smaller balls, and let them receive the impact of the moving one, the result will be just the same. Each and every ball interposed will have the motion of its constituent particles augmented by an amount of energy of motion exactly equivalent to that parted with by the larger ball; and, when the moving ball finally comes to rest, the sum total of molecular energies in the interior of each ball is exactly equal to the original momentum of the larger ball. Thus we have an illustration of the transference of molar into molecular motion, the molecular motion making its appearance as heat, one of the modes of force. If you push endwise against a stick of wood, the force applied will immediately appear at the other end. This is transmission of force by means of molecular action. The force being applied to one end of the bar is transmitted from particle to particle with great velocity its entire length. If a row of bricks be properly placed, any force applied to the first of the row, sufficient to topple it against the next, will be transmitted throughout from the first to the last of the series. Or again, if the bar of wood be pushed against one end of our imaginary row of bricks, we shall have in the rod and in the falling bricks a continuous chain of similar phenomena, the action of the bricks being a visible illustration of the transmission of force, and highly analogous to that invisible transmission along the molecules of the bar.
Apart from the different modes of force, we have energy in two forms—static or potential, and actual or dynamic. The potential has been likened to a weight wound up, and the actual to a weight in the act of falling. The amount of energy expended in winding up the weight, less the friction, is exactly equivalent to the potential energy of the weight so raised, also to the dynamic energy given out by its falling or running down. The inherent measure of force possessed by each and every atom is its kinetic energy, and this energy is the correlative and antecedent of all the modes of force which characterize the various phenomena of the visible universe. The condition in which matter presents itself to our senses depends upon the degree in which these several forces are made manifest. All the phenomena of Nature consist in transformations of energy only, the working force of the universe being previously invested in the kinetic energy of its atoms.
The potential energies of the atoms of matter, in their free condition, are almost beyond human comprehension. Thus, heat a pound of charcoal to the point of incandescence. The vibratory motion of the atoms of carbon will then have reached an amazing velocity; oxygen rushes in to form new compounds; the oxygen-atom, by its impact upon the coal, has its motion of translation converted into vibratory motion, which immediately appears as heat. The clash of these atoms makes up the sum total of the energies of the combustion. The actual amount of dynamical energy set free by the union of this pound of charcoal with atmospheric oxygen is equivalent to the mechanical raising of eleven and a quarter million pounds one foot high. Let us further consider the dynamical forces inherent in the molecules of free gases, and look to a molecular explanation of the three states of matter, the solid, fluid, and gaseous. In solids the atoms are held together with a rigidity that develops the full strength of cohesive force. In liquids the same attraction is so far lessened that a definite form can only be preserved in a limited degree, as in drops of water maintaining a spheroidal, shape against the force of gravity. In the gaseous form atoms do not cohere, the cohesive force having been translated into the energy of motion, and it is this energy of motion which constitutes the expansive force of confined gases.
Suppose we have a vessel containing eight pounds of oxygen and one pound of hydrogen. This mechanical mixture of gases, invisible though it be, and harmless as it appears, is the theatre of energies wholly beyond our conceptions. Figure to your imagination these gases made up of atoms so small that a billion times a billion would scarcely fill a cubic inch, and all these atoms vibrating among themselves without actual contact. Although the minute distances over which these atoms travel are utterly immeasurable by direct appliances, we shall presently see that the energies evolved by the clash of their chemical union is something prodigious. The concussion of atoms at the union of eight pounds of oxygen with one pound of hydrogen sets free an amount of energy, in the form of heat, equivalent in mechanical value to 47,246,400 pounds let fall one foot, or the crash of a ton's weight as an avalanche down a precipice of 23,623 feet.
The three states of matter have been likened to three planes, of which the gaseous is the uppermost, the fluid occupying the intermediate plane, and the solid state for the lower one. The clash of atoms at the union of the two gases has resulted in the liberation of the energy above mentioned, but a change of state has taken place, and we now have water in the vaporous condition occupying the intermediate plane. This nine pounds of steam in condensing to water sets free an energy, the mechanical equivalent of 6,722,000 pounds let fall through the space of one foot. The next change takes us past the reduction of the temperature of the water from the boiling to the freezing point, setting free both the specific and latent heat of the water. This final fall to the plane of congelation occasions a further dissipation of energy equivalent to 2,237,256 foot-pounds, making a grand total of 56,000,000 foot pounds as the measure of energy in our nine pounds of invisible gas.
The verity of these statements might be questioned were it not that the most refined researches give unvarying results. Suppose we reverse this experiment, and, commencing with nine pounds of ice, we will, by a process of mental abstraction, again bring our conceptions down to the immeasurably small, and fix our attention upon the molecules of the ice. Figure to yourself the atoms of each molecule as being in oscillation through points of equilibrium. And, while your attention is centred upon the motions taking place in the interior of the mass, we will let fall upon the block of ice a concentrated beam of sunlight, and see how it deals with the inherent forces of cohesion and chemical affinity. The solar undulations impinge upon the molecules of the ice, and, under this bombardment of heat waves, see how rapidly the atoms accelerate their motions! All this while the contest is going on between the dynamic energy of the sun's waves of heat and the cohesive force of the molecules. Beautifully and symmetrically the forces of Nature built up the crystalline mass, and as silently and surely the sun's competency of heat will effect its liquefaction. Thus far we have seen the atoms accelerating in velocity by virtue of the energy imparted by the solar-heat waves, and all this time they are vibrating within the definite limits of the molecule. A further increase of heat will increase the motion of the atoms, thus tending to a rupture of the bonds of cohesive attraction. The struggle goes on until the ice melts, by which process we have solar energy conserved in the latent heat of water. The molecules being thrown almost beyond the range of cohesive force, their movements are no longer confined to their former limits, but may extend throughout the length and breadth of the mass. This is the fluid state. The amount of energy required to swing the atoms so nearly beyond the range of cohesive attraction, or simply to melt the ice, is equal to 500 tons raised one foot high. This force still exists as transmuted energy, and is the latent heat of water. A further addition of heat takes the form of increased vibratory action up to the boiling-point. Then comes another struggle seven times greater than the first. This last remnant of cohesive force of water must; be surrendered, and the heat-energy necessary to perform the act is conserved or transmuted into the latent heat of steam. The last vestige of cohesive force now being gone, the molecules of steam are free to oscillate in all directions, and impinge against the walls of the containing vessel. If we continue the application of heat to the point of dissociation, the molecules of vapor will have acquired a momentum sufficient to rupture the bonds of chemical affinity. And here the energy required to separate the molecules of steam into its constituent atoms of oxygen and hydrogen is simply prodigious, being about forty-eight times as much as was necessary for the process of liquefaction. Thus the aggregated energies required to set free the oxygen and hydrogen in our nine pounds of ice are equivalent to the raising of a ton's weight 28,000 feet, and we now have the original nine pounds of gas, laden with the potential energies of 56,000,000 foot-pounds, which is just equivalent to the requisite liberation of force necessary to reduce the gases back again to the solid form of ice. A cubic foot of water yields 1,862 cubic feet of the separate gases when at normal condition, and no human device is competent to overcome this expansion by pressure sufficient to reduce them back again to the liquid condition. Upon the evidence of Faraday we have it that "the decomposition of a single drop of water by electricity calls for an expenditure of more electromotive force than would suffice to charge a thunder-cloud."
Our main source of dynamic energy is from the sun. His energy is exhibited in every wind that blows, in every shower that falls, and in the history of every snow-flake—in the glare of gaslights, in the heat of the furnace, in the colors of the rainbow, and in the gorgeous sunset, in the beauty of vegetation and its silent growth. Thus, in an almost infinite variety of physical phenomena we see this transmutation of solar energy. This energy, after doing its allotted work, is in time dissipated into space by radiation. And, were it not for the intermediate position of the vegetable kingdom to check this degradation of energy and raise the elementary constituents from the chemical to the organic plane, man's duration here would be short indeed. The locking up of potential energy in the protoplasmic cell of the plant requires the expenditure of a vast amount of energy, but the solar ray, aided by the subtile alchemy of the leaf, is competent for the task; and, while the chlorophyl of the leaf assists in weaving organic tissues from the air, this outward dissipation of energy is delayed for a while, giving us food for our bodies and fuel for our fires. This final process of combustion once more converts these potential energies into the dynamic form and sets them free to dissipate into space. All the mechanical power which comes from the combustion of fuel and all the muscular force of the animal kingdom is but the transmutation of solar energy through the mediumship of plant-life. Well might we say, as did the pagans of old, "We are children of the sun." This flood of solar force is unceasing. Waves of ether may conduct a store of energies across the universe and invest them in a wealth of carbonaceous flora; these energies may lie dormant in vegetable fossils for untold eras; man may delve in mines and exhume the coal, and enlist the aid of oxygen to break the bonds of chemical affinity, setting free those energies stored away in the countless ages of the past; he may unfold link after link of the great dynamic chain of causation, and subject them to the scrutinizing analysis of the physicist; he may survey the rocks and tell us of their radiations of internal heat, or by his calculus tell us for how long in the past this planet may have been the theatre of life and death; he may tell us, not only of the energies in the atoms of a drop of water, but of a world of atoms—nay, more, of a universe made up of atoms with their energies drifting out into measureless space; but he can tell us naught of that unseen universe into which the energies of the visible creation are ever tending.
While dealing with the forces of Nature from an atomic standpoint, we are treading upon the border-land of science, beyond which all sensible phenomena have their origin.
Science may, by spectrum analysis, determine the constitution of the irresolvable nebulæ; it may tell us of the millions upon millions of ethereal waves necessary to impinge upon the retina to produce a given chromatic effect; it may measure the waves of air that roll as music down upon the tympanum of the ear: but how undulations upon the retina or vibrations of the auditory nerve are converted into consciousness of sight or sound, is a question which, like the causation and mystery of life, belongs to that realm outside of the domain of science—a realm the infinite mystery of which transcends all analysis!
In conclusion, let us not be led into a rigid belief that the present views of molecular physics are competent to explain all the phenomena that may be presented for solution for all time to come. It is enough to say that it answers our purpose in giving a satisfactory explanation of a large class of natural phenomena as they are exhibited to us in daily life. But, as we know the favored ideas of scientists and scholars in generations preceding ours have given way to newer and better ones, so, in turn, the popular conceptions of to-day may serve as stepping-stones to coming ideas, each destined to take its place as the predecessor of a higher and better intelligence.