A Molecular Motion Projector WILLIAM S. VON ARX Yale University, New Haven, Connecticut
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HIS instrument is offeredas a visual aid in teaching the concepts of the states of matter and their relationships. The projected image is a shadowgram of particles in motion which behave very much as atomic and molecular particles are supposed to behave in nature. The image produced is analogous to that which might be expected from a microscope having a linear resolving power of a b ~ u 0.1 t A. U. and a field of view of perhaps 500 A. U. diameter. A series of very simple, definite changes in the adjustment of the apparatus produces, with convincing realism, a remarkably large repertoire of demonstrations. A list of these is as follows: CONCEPTS The gross aspects of atoms and molecules: fuzzy concentrations of mass. The ceaseless motion of material particles. The energy of atomic and molecular motion as a function of temperature. The concept of mean free path. The concept of mean free time.
GENERAL
EQUILIBRIUM STATES Gas-liquid equilibrium including illustration of the critical point. Gassolid equilibrium. Liquid-solid equilibrium. The effects of changing pressure and temperature on these equilibria. THE GAS PHASE
Complete lack of organized position, or direction of particle motion. Gaussian velocity distribution. Shift of modal velocity as a function of temperature Mean free path as a function of pressure. Unilateral pressure on a membrane as a function of temperature. Bilateral pressure on a membrane-gage pressure. Osmotic pressure on a semipermeable membrane. . Dalton's Law of Partial Pressures. Brownian motion in gases. LIOUID - PHASE Transitory quasi-crystalline positioning of particles. Liquid-vapor equilibrium as a function of temperature. (Contrast of mean free oath in the two ohases). Transition from liquid properties to gasbropkties a t the critical point. Brownian motion in liquids.
THE
The annealing process. Ejection of impurities from growing crystal lattices. Rule of optical discontinuity in the development of new crystals. Hexagonal close packed layering Cubic close packed layering. Negative crystals.
The projection apparatus consists of two essential parts: a glass shaking table, and an optical system. THE SHAKING TABLE
plate The shaking table is made of a piece of glass 4 inches square mounted on a heavy brass frame surrounded by a molding of angle brass to act as walls. The particles roll about on the glass and rebound from the brass retaining walls. The whole tahle is suspended from the skeleton framework of the apparatus by four '/&nch brass rods 6 inches long. These are soldered to the shaking table a t one end and fitted with threaded leveling sleeves a t the other. The sleeves pierce comer braces of the framework and are equipped with lock nuts which bear upon the braces, locking the table once it is adjusted level. The shaking table is driven by a clockwork which is rigidly fixed to the table and moves with it. The clockwork has been stripped of all but the driving train and a heavy lead eccentric mounted on the last rotating arbor. Since the power a t this remote point is very small, the spring will have difficulty turning the movement except when the works is oscillated in such a way that the center of gravity of the eccentric contains the axis of rotation of the eccentric which remains stationary in space as the train unwinds. The eccentric will turn a t whatever rate the works is oscillated. The shaking table has two natural frequencies of vibration: (1) as a conical pendulum, (2) as a torsional pendulum. The eccentric will assume either frequency of rotation and the unwinding spring will supply energy to the system, keeping the amplitude constant. In each case the eccentric frequency is governed by the shaking tahle frequency and, once synchronized, the two will run without further attention until the spring is unwound. AUXILIARY APPARATUS AND ADJUSTMENTS
The shaking table is equipped with a tilting screw under one edge of the glass to rotate the table out of level by known amounts. This produces the liquid and solid phases, a technique to be discussed later. There is also a flexible membrane which may be swung in place to perform the pressure demonstrations. The membrane is simply a paper strip approximately ' / r inch high and slightly shorter than the width of the glass plate on the shaking table, to fit comfortably within t h e
THE SOLID PHASE
Development of crystals from the liquid phase and from the amorphous state. Idiomolecular transfer and the development of minimum surface forms. Fixed crystalline d o m a i n ~ a r i l l a t i o nof particles around mean positions. Development of intermolecular bonds as an inverse function of distance. Sublimation.
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retaining walls. This strip is held in smooth-running brass guides so that i t will move with the shaking table lengthwise, but not thickness-wise, acting as a flexible wall which prevents the particles from passing from one comoartment of the shaking table to the other. When projected on the screen the membrane is apparently fixed a t both ends but free to bow outward or inward according to the resultant pressures of the particles on either side. The brass guides are mounted on threaded columns so that they may be raised and lowered and swung aside, and locked by lock nuts in any position. When the membrane is lifted from the shaking table sufficiently for the smallest particles to pass under, by raising the guides, i t will remain a barrier to all larger particles and demonstrate osmotic pressure as a n idealized semipermeable membrane.
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THE OPTICAL SYSTEM
The optical system of the apparatus is essentially a periscope: a train of two mirrors with the transparent shaking table between. The bottom mirror reflects the inclined beam from an arc light upward through the shaking table while the top one reflects the beam toward the wall or a screen. The particles on the shaking table appear as shadows on the screen. The field of view is vignetted by a pair of adjustable masks in each of the two coordinates of the field. The light source is the anode of a carbon arc. Heavy anodes are used in order to develop a marked penumbra around the shadow of each particle. This gives the particles a fuzzy appearance a t the edges with a small dark central
condensation representing the modern picture of the electron fields surrounding atomic nuclei. As two particles come near each other the penumbrae are proximally occluded and the central dark condensation distorts by extension toward the approaching particle. simulating what might be a chemical bond. In crystal lattice images this bonding is very marked. The iutensity of the bond is represented by the blackness of the shadow which is an inverse function of the distance between adjacent particles. SOURCES OF PARTICLE ENERGY
The energy of particle motion on the shaking table is supplied in part by collisions with the other moving particles, the brass retaining walls, and in part by the moving glass. It is found that perfectly spherical particles are unsatisfactory for the operation of the instrument. Slightly flattened or irregular particles totter on the moving glass, thereby picking up enough energy from the table to roll away. A large number of impacts occur between particles, yet careful scrutiny shows that some particles move as though struck by "unseen particles in another plane." This produces an illusion of depth. The effect is very similar to observing Brownian motion of particles as they move through the focal plane of a microscope. The mean energy with which the particles move depends upon the total energy of the shaking table motion and the ratio between the periods of oscillation of the shaking table and the tottering aspherical particles. If these periods are identical, the maximum energy of
motion is supplied to the particles. If they are integral multiples of each other somewhat less energy is transmitted. If they are nonintegal multiples very little energy is transmitted. Similarly, a variation of shaking table amplitude has a marked effect, since the particle's topple period is a function of topple amplitude. To achieve complete control over the shaking table frequency, one or more of the lock nuts on the leveling screw sleeves may he loosened. This decreases the restoring force supplied by the brass suspension rods, reducing the frequency of tahle oscillation. The amplitude is reduced as well, since a great deal of energy is consumed in rocking the suspension rods in their mountings Both effects conspire to reduce the energy of particle motion. These changes in particle energy are used in demonstrating the response of the particles to changes of "temperature."
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1. Orient the instrument as it is to be used durine: projection. 2. Level the shaking table with the leveling screws bv watchinn the behavior of 20 or 30 shot while - t6e clockwirk runs. When there is no referential motion or grouping over a period of 10 or 15 seconds, the table is sufficiently level. 3. Turn on the arc light, making sure that the endon carbon is the anode and the larger of the two. Set it as close to the lower mirror of the instrument as possible. 4. Adjust the mirror so that the image falls on the desired area and then vignette the field with the substage masks until the motion of the shaking table is occulted.
These adjustments must precede demonstrations whenever the instrument has been moved to a new loTHE PARTICLES cation, since the shot responds strongly to small incliThe particles used are of several sizes and materials. nations of the shaking table. The reasons for the order The gas molecules are ordinary BB shot which are ir- of procedure are clearly these: orientation precedes regular enough in sphericity and smoothness to pick up leveling to avoid deleveliug the shaking table by turnlarge amounts of energy from the moving glass, and ing the instrument between adjustment and operating heavy enough to produce a considerable effect upon positions. Concerning step three, the anode is the larger particles during impact. For the Brownian mo- hotter of the two carbons in a d.-c. arc, hence the tion demonstration, larger smooth round steel ball brighter. A large bright circular and effectively single bearings are used in order that they may not pick up source will cause the shadows of the particles to be symenergy from the glass hut move entirely a t the mercy metrically diffuse, giving the desired picture of the of the colliding BB's. For the osmotic pressure dem- conventional electron clouds surrounding atomic nuclei. onstration, large steel ball bearings are used in order The shorter the optical path between the hot carbon that they may be readily distinguished from the smaller and the particles on the shaking table, the larger the lead particles. These particles are roughened so as to projected field and the fuzzier the appearance of the move energetically. Their large size prevents them particles. Lastly, step four; vignetting the field, so from passing under the pressure membrane as the that the shadow of the moving shaking table is ocsmaller particles do, consequently the membrane be- culted, increases the realism of the demonstration since haves semipermeably. The numbers of particles em- there is no apparent source for the energy of particle motion. The particles move busily about the field, ployed are as follows: which is defined by soft hut fixed boundaries. If sharp Gas phnse 50 BB's Rough boundaries are preferred the field masks may be inLiquid phase 200 BB'r Rough Solid phase Fill the shaking table Rough stalled near the top mirror where they cut the beam a t Bronnian partielrs Two Vrioeh hall hearings Smooth Osmotic particle3 Ten '/cinch ball hearings Rough the last possible instant before leaving the instrument. Sharpened field boundaries exaggerate the apparent To count the numbers of particles placed on the shaking table rapidly and easily, one of a set of brass fuzziness of the particles and are in that sense advanangles may be placed in the corners of the shaking tageous. table, enclosing a space capable of holding only the reDEMONSTRATIONS O F THE STATES OF MATTER quired number of BB shot. Three are required; one It should be remarked before describing the demonstrations in of 50-BB capacity for gas phase demonstrations, one of detail that the analogy between the demonstrations and their 350-BB capacity for liquids, and one of 200-BB ca- assumed physical mechanism in nature is very close for gases, pacity for liquid-gas equilibria. The solid phase em- only approximate for liquids, and theoretically impossible for ploys the entire area of the stage and as packing pro- solids. The particles on the stage are free moving and mutually nongresses more shot must be added to fill the frame. Efficient removal of large numbers of BB shot is best attractive. Upon contact with each other elastic farces of repulare present, and hygroscopic moisture induces short-range accomplished by a scoop with a long flat blade for sion forces of attraction. The conditions thus approximate all the close contact with the glass. By scooping the shot physical requirements for a real gas at all pressures. against the retaining walls of the shaking table the According to the Latest physical ideas, liquids are composed of quasi-crystalline groups and groups of groups as a result of intertahle can be cleared in a matter of seconds. OPERATIONAL TECHNIQUE
The procedure of setting up and adjusting the instrument follows a regular order:
particle forces of attraction. While the projector yields images of particles behaving in this manner, the cause of the behavior is not mutual attraction but merely physical crowding,so that the model is in that sense imperfect. At supercritical temperatures the analogy becomes perfect once more.
The solid state images are produced by a single layer of particles representing a monomolecular thin section through one of the principal planes of a crystal. The impossibility of a twodimensional lattice has been demonstrated theoretically and furthermore the strong attractive forces sustaining the lattice are absent. To be quite rigorous then, it should be stated whenever the instrument is used that the images are to be considered as monomolecular thin sections through the solids, liquids, and gasesrepresented and that the mechanism behind the effects shown is faithfully analogous to nature only in the case of gases, andliquids at supercritical temperatures.
Since the projected images of solids, liquids, and gases produced by the molecular motion projector are in effect enormously magnified, the ordinary criteria for the identification of the states of matter fail, and new ones must be supplied. Gas: Particles move freely from impact to impact in straight lines over mean free paths arbitrarily chosen to be greater in length than one particle diameter. The mean free time of motion is very much greater than the relatively instantaneous time of impact.
free-moving particles is small with respect to the time spent in near contact with adjacent particles. GASES, LIQUIDS, SOLIDS, AND POLYPHASE EQUILIBRIA
The gas, liquid, and amorphous solid states of matter can be reproduced by simply increasing the number of particles on the shaking table. Fifty particles of BB shot moving on a four-inch square shaking table yields a model of a gas. Increasing the number to 350 produces motion of the sort to be expected a t the critical point a t which both liquid and gas properties are manifest, &., a combination of independent particle motion characteristic of gases, with group motion of temporary quasi-crystalline aggregates composed of freemoving particles characteristic of liquids. Further increase in numbers of particles reduces the gas type of motion until liquid conditions prevail. The solid state begins when the temporary quasi-crystalline aggregates of the liquid phase become permanent. Particle exchange between aggregates diminishes until finally the stage is so crowded with particles that exchange ceases altogether. This state is characteristic of amorphous, isotropic solids. To induce crystallization a sorting process must be introduced whereby the low energy particles may be collected in one part of the stage and packed. This is accomplished by tilting the stage with one of the tilting screws under the glass plate. Once tilted, the particles pack on the stage with gratifying rapidity, often producing more than one crystal. When two crystals form they vie with each other for supremacy in size. An intercrystalline commissure exists between them in which the particles have vastly greater freedom of motion than their packed neighbors. The freedom of motion across the intercrystalline boundary is characteristic of the gas phase and therefore may be classified as idiomolecular transfer. Particles from the smaller lattice can be seen working across to the larger lattice in a manner which produces minimum area forms on the boundaries of each. POLYPHASE DYNAMIC EQUILIBRIUM
Liquid: Particles move freely and as individuals or couples from one quasi-crystalline group to another. The mean free time is arbitrarily chosen to be from only a little greater than, to considerably less than, the mean time spent in the company of other particles composing a quasi-crystalline group. A quasi-crystalline group is composed of rarely more than three or four particles in approximately cubic, rhombic, trigonal, or other simple geometric arrangement. Solids: Particle motion is restricted to local excnrsions of less than one particle diameter from a fixed point of mean position which may or may not bear systematic geometrical relationship to other fixed points of mean position. The mean free times of independent,
Stage tilting in addition to increasing the number of particles produces the equilibrium states between gases and liquids, gases and solids, liquids and solids, and amorphous and crystalline solids. Beginning with the gas phase on a level table (50 particles), very slight tilting causes the low energy particles to collect on the lower edge of the plate, producing the group and motion characteristics of the liquid phase. Occasionally some of the high-energy particles from the liquid phase break away and enter the gas phase region. Conversely, some of the gas particles lose their energy and fall back into the liquid phase region. Dynamic equilibrium is soon established. Loosening the lock nuts on one, two, then three of the leveling sleeves, the total energy of the shaking table system may be decreased with a corresponding change in the equilibrium proportions of liquid and solid. This demonstrates the change of vapor pressure over
liquids as a function of temperature. The vapor pressure may be shown to change by swinging the pressure membrane in place over the gas phase region of the stage. Increased vapor pressure will bow the membrane more sharply, demonstrating the pressure change. The gas-solid equilibrium may be demonstrated with about 200 particles by tilting the stage more than it is tilted for the gas-liquid equilibrium. In this case the low-energy particles are trapped by the packing process which prevents their picking up kinetic energy from the moving glass underneath. Once trapped they stay in lattice arrangement up to the boundary between the solid and gas phases. At the boundary the particles are only temporarily packed and may pick up enough energy to sublime. Few particles accomplish this, hence the gas phase is characteristically tenuous, but in equilibrium with the solid phase nevertheless. The vapor pressure may be increased by winding the spring of the driving clock thereby increasing the total energy of the system, or by lessening the tilt of the shaking table. Lessening the tilt reduces the restrictive bonding of the packed particles, the lattice becomes looser and the vapor pressure much higher, both of the latter effects being characteristic of hot solids and their vapor phases. Further relaxation of the tilt of the shaking table, bringing it almost level, allows the packing to loosen enough for the particles to gather energy. Soon the entire lattice is in a state of violent motion, breaking up at last into the liquid phase with a very dense gas phase above it. The melting process is thus illustrated. Freezing may be reproduced by reversing the procedure; viz., increasing the tilt of the shaking table by two steps; one, slight tilt to allow liquid-gas equilibrium to establish itself, and two, stronger tilt to induce crystallization of the liquid phase. Amorphous solids may be reproduced by nearly filling the leveled shaking table with particles and running the driving clock in synchronism with the torsional period of the shaking table. The freedom of qotion of the particles is so restricted that they pack in small groups but not in recognizable crystal systems. Particle motion is of the restricted variety around mean positions which characterizes solids, and is distinct from liquids in that the particles are not free to wander from group to group. The annealing process may be demonstrated after the amorphous solid is established, by tilting the table oery slightly and increasing the period of oscillation to that of conical motion. The mean free time of the particles is more nearly commensurate with this period, hence they have more opportunity to gather energy and "heating" results. Very slight tilting a t this point in/ the demonstration will induce packing, slow "cooling." As packing proceeds one or two centers will dominate the scene and gradually incorporate less competent centers, forming minimum surface crystalline forms. These forms enlarge a t the expense of all others until finally all the particles are packed and no longer free to transfer. The solid is then "cold" and coarsely crystalline-annealed.
GAS PHASE PHENOMENA
The gas phase phenomena of particular interest are demonstrations of unilateral pressure on a membrane,
DYNAMIC EQUILIBRIUM BETWEEX
A LIQUID AND ITS
VAPOR.THELINEARBOUNDARY IS THE SHADOW O P A WIRE WHICHHELPSTO EMPHASIZE THE DIPFERENCE BETWEEN GAS MOTION AND STRICTED QUASI-CRYSTALLINE LIQUIDMOTION.
FREE
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Dalton's law of partial pressure, bilateral pressure on a membrane, osmotic pressure, and Brownian motion. The membrane used in pressure demonstrations has been described earlier. I t acts as a flexible barrier dividing the shaking table into halves.
Unilateral pressure can be demonstrated by placing shot on only one side of the membrane. This pressure
can be shown to be a function of two independent variahles; the number of particles per unit area, and the
Dalton's law of partial-pressures is demonstrated by using particles of differing radii so that their roles are easily identified. Particles of one size alone will flex the membrane a certain amount. These particles are then cleared away and the other particles allowed to flex the memhrane. If the amplitudes of flexure are measured roughly in each case, it will he found that when both sizes of particles are introduced simultaneously the flexure will have an amplitude which is the sum of the two. Since the amplitude of flexure is a measure of the pressure upon the membrane, Dalton's law is shown to hold. Gage pressure, or bilateral pressure on a membrane, can be shown by putting particles on both sides of the
OSMOTICPRESSURE. WITH THE PAPERMEMBRANE LIFTED FROM TEE STAGE SUFFICIENTLY FOR THE SMALLER PARTICLES TO PASS UNDER. ONLYTHE LARGERPARTICLESMAY HIT IT AND PRODUCE
Panssrm~UPON
IT.
THIS1s AN IDEALIZED PICTURE
energy with which they move. The total energy of particle motion can be controlled by the tightness of the clock spring in the driving mechanism and also by
p .,.;,&"t ' ' 2 -
A ...
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. .
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CRYSTALLINE STATEREPRESENTED BY A SINGLE LAYER OF HEXAGONALLY CLOSE-PACKED PARTICLES. THE SHADOWS BETWEEN ADJACENT PARTICI.ES REPRESENT THE BONDINGOR ELECTRON FIELD D~sroRrloNC ~ A C T E R ~ S OF TIC LATTICEGROW-
BROWNIAN MOTIONILLUSTRATED BY Two LARGE Pnnrrc~esIN A MATRIX OF GASPARTICLES. THE LARGE PARTICLES RECEIVEENERGY PROM COLLIDING GASPARTICLES ALONEA N D THEREFORE REPRESENTTHE PHENOMENON FAITHFULLY. BROWNIAN MOTIONI N LIQUIDS MAY BE REPRESENTED BY ADDINGMOREPAETIUES TO THE MATRIX.
the frequency to which it is synchronized. Pressure observations of total energy will show that pressure is a direct function of the total energy of particle motion.
barrier. With particle population equal on both sides of the membrane, no deflection will be observed With unequal populations, however, the flexure can be shown to be proportional to the excess density on the heavily populated side. Removing all the particles from the stage and rep lac in^ the density excess on one side of the bamer, the deflection will be observed to be the same as for the measured excess in the first case. Osmotic pressure demonstrations require additional adjustment of the height of the memhrane from the shaking table. By means of the lock nuts on the columns supporting the membrane guides, the bottom of the membrane is lifted from the table sufficiently to allow the small BB shot to roll freely beneath. Larger particles are then placed on one side of the barrier. These are too large to pass under the barrier. consequently they alone exert an unbalanced pressure upon it. The elevation of the bamer is unnoticed in the pro-
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jected image. To begin with, the small particles and large particles may be separated by the barrier before it is raised. As soon as the stage is set in motion the small particles will distribute themselves all over the stage by rushing into the field occupied by the larger particles and unbalanced pressure is established. Brownian motion can be demonstrated in couuection with either the liquid or gas phase. The technique is the same for both. merelv the numbers of shot are different. The Brownian particles are relatively large smooth ball bearings. These particles spin easily on the moving glass of the shaking table but do not pick up energy of translation because of their large inertia and lack of ability to totter as the shot does. All their translational motion is supplied by collisions with the moving shot. Since the shot motion is completely random, occasional condensations of shot will crowd alongside one of the Brownian particles, accelerate it, and then break up on the rebound. Uneven concentric bombardment of these large particles by the shot gives them an erratic, ponderous motion of the Brownian sort Plotting these motions gives the same kinked traces as those reported for Brownian motion. Since the mechanical anaiogy is perfect, this demonstration may be shown before microscopic examination of actual Brownian particles so that the student may have an accurate
mental picture of the invisible details of the process. The Brownian motion particles may also be used in the solid state demonstrations as impurities to be ejected from a growing crystal lattice of BB's. Begin with the table nearly filled with BB shot in the amorphous solid state and then add the impurities. In the amorphous state the impurities are perfectly acceptable to the other particles. Then tilt the table to induce packing. As packing gradually encloses the large ball bearings they will be systematically ejected from the lattice along the principal crystallographic axes as is the case in natural crystals. Frequently in the process of crystallization the lattice will build around an unpopulated gap in the lattice pattern leaving a hole with crystallographic boundaries, a negative crystal. More rarely a few particles will remain in the hole possessing gas or liquid properties, or both. These are analogous to liquid inclusions and negative crystals so common in natural crystals. Unfortunately these demonstrations cannot be produced a t will They do occur frequently enough, however, to add greatly to the interest of many solid phase demonstrations. The author wishes to thank Mr. Alfred G. Pechar for his help in constrncting the experimental model of the instrument discussed and illustrated in this paper.
