Molecular Collision Processes

Type of physical science: Chemistry

Field of study: Chemical reactions

Molecular collision processes encompass the range of phenomena by which gaseous molecules and atoms exchange energy, momentum, and motional information through interactive encounters. These encounters, when averaged over the entire gaseous sample, describe the mechanisms for physical phenomena such as heat flow, sound propagation, and diffusion, but also provide the basis for understanding chemical reactions in microscopic detail.

Overview

A molecule traveling alone in an absolute vacuum proceeds along a path, or trajectory, described by a straight line and maintains a constant velocity, or speed, and so its kinetic energy (the product of one-half of its mass times its velocity squared, 1/2 mv²) is a constant. Since molecules are composed of a group of atoms arranged in a specific geometry and held together by bonds that are not entirely rigid, molecules can also possess internal energy in the form of vibration, the oscillatory motion of the atoms about their bonds, and rotation, or the tumbling of the molecule as it moves along. In the absence of external forces, as might be caused by any neighboring molecules (or even light), a lone molecule proceeding along such a trajectory will also maintain constant rotational and vibrational energies. If, however, the molecule encounters another molecule, an atom, or even a wall, it will experience a force caused by this species, and this force will alter (through either a push or pull on the molecule) the straight-line, constant energy path it was previously following. This experience of a new and temporary force and the subsequent alteration of path are consequences of having undergone a molecular collision. The study of molecular collision processes attempts to understand the nature of these temporary forces and the nature of the paths, or trajectories, followed by molecules in the presence of these forces--that is, before, during, and after they have acted.

A very simple, but quite instructive, example is obtained by considering a game of marbles or billiards. If one shoots or rolls a marble along a surface that is void of other marbles (ignoring friction), the marble shot (or shooter) proceeds along a path at constant speed and continues rolling in a straight line, unobstructed. If, however, one repeats the experiment, this time having placed a handful of other marbles in its path, the shooter will roll at constant velocity in a straight line until it encounters (or feels the force of) another marble. The force experienced between these marbles, because of their hard, rigid nature, will, through Newton's laws, lead to a partial conversion of the first marble's momentum (the product of its mass and velocity, mv) into momentum for both particles in new and opposite directions. Thus, the first marble may be deflected to the left at a somewhat slower speed, and the other marble, or collision partner, will be accelerated to a specific momentum in the rightward direction and continue rolling. Since the marbles can be thought of as having no internal structure, and thus have no ability to store internal energy, all the incoming kinetic energy of the shooter is transferred, but divided between, the new kinetic energies of the outgoing pair of marbles. This is an example of an elastic collision, in which not only is total energy conserved (not lost), but the sum of the total momentum for both particles before and after the collision is the same; thus, momentum is also conserved.

In the case of hard marbles colliding, no forces between them are felt until precisely the moment they physically touch. At this point, a strong repulsive force is encountered, which instantaneously leads to their deflection. In this example, the collision itself is described as occurring at precisely the point of impact. For molecules undergoing collision, the description is necessarily more complicated because molecules possess internal motions, or degrees of motional freedom (that is, a molecule can bend or rotate on impact), and a molecule does not possess a well-defined surface, as does a marble. Thus, molecules are fuzzy, or diffuse, species as regards the forces they may impart. This is a consequence of the electron clouds that surround the atomic nuclei and form the bonds between them in the molecule. As two molecules approach, they begin to feel each other's presence, or forces, at distances much greater than any distance associated with the "size" one would normally attribute to a single molecule based on the lengths of its bonds (think of what happens as two magnets are brought together). As two molecules approach at this long distance, typically five to ten times the molecular size, their forces begin to cause deflections in their paths. As they get closer, these forces increase in strength and the deflections increase, until eventually the forces overcome the incoming energy and the particles are deflected away from each other. As they initially depart, they continue to experience each other, until finally their separation is complete. This whole series of events, including possible changes in rotation and vibration or even bonding within the molecule, from the beginning of the action of forces to complete separation, is described by the collision trajectory and is the focus of molecular collision studies.

It will be helpful, before considering molecules further, to return to the example of two billiard balls. If one ball is sent directly at another one, the two are certain to collide, and if done precisely head-on, both will continue moving after collision along the original straight-line path.

This is an example of a collision with an impact parameter of zero. The first ball was following an original path that was destined to go right through the center of the other ball. The impact parameter is a physical measure of how close the centers of the species would have approached had no forces been present, and in the above example, they would have overlapped had not the forces of the balls prevented this at impact. If one starts a collision with an impact parameter greater than the diameter of the balls, one sees that the two miss and no collision occurs, since here their centers must approach to within one diameter (the sum of their radii) in order to experience the collision force. At impact parameters between zero and one ball diameter, we get side-on types of collisions, which lead to deflections at various angles; thus, the game of billiards is almost solely one of selecting the proper impact parameter to get the collisional angle desired (and send the collision partner toward one of the pockets).

In molecular collisions, the outcome of the collision is also strongly influenced by the incoming impact parameter and kinetic energy; however, the complexity of the forces makes the resulting trajectories much more complicated, as well as much more interesting. Unlike the billiard balls, most molecules at large distances feel an attractive dispersion force between them (much like opposite poles of magnets), and this force pulls the molecules in toward each other, aiding in the collision. Thus, molecules that start out at impact parameters that would seemingly suggest they will miss may get pulled in sufficiently at moderate approach distances to ensure collision. As the molecules approach to closer distances, the nature of the force turns repulsive because of the repulsion between the electron clouds of the two species. It is this repulsion that will eventually lead to the end of the collision, with a subsequent departure. It is the exact nature of the species that will depart that makes molecular collisions so intriguing.

Molecules have shape, and consequently their forces do not point in all directions equally. Molecules also are not rigid; thus, their forces can yield, like springs, when encountered in a sufficiently strong or violent manner. Consider the collision of an atom (a kind of microscopic billiard ball) and a diatomic, or two-atom, molecule. The diatomic molecule, for this example, is well characterized by two balls held together by a stiff spring (the bond). There are now several ways to consider having the atom hit the molecule. If the atom hits the molecule directly side-on (and the spring is stiff enough), an inelastic collision would occur, simply pushing the molecule as a whole into translational motion. Now consider a purely end-on collision. The oncoming atom hits only one of the atoms in the molecule in a direction right along the spring's axis. This will initially push that atom into the spring, and then this spring force will transmit energy to the other end of the molecule. The colliding atom will depart and most likely leave the two atoms in the molecule oscillating, or vibrating, with respect to each other, and the molecule as a whole will also have been accelerated to some small velocity. This is an example of an inelastic collision, in which some of the incoming atom's kinetic energy has been transferred into internal vibration of the molecular collision partner. Since energy is always conserved, the departing atom must have left with less kinetic energy than it came in with and, furthermore, when internal energy changes, momentum is no longer conserved. Another example of an inelastic collision is one that converts translational energy into molecular rotation; this would result from a collision in which an atom strikes only one end of a molecule, but from side-on, swinging that end of the molecule around and inducing molecular rotation. In samples of molecules, all these types of collisions are constantly at play, and energy is continuously being transferred between the translational, rotational, and vibrational degrees of freedom.

If these were the only consequences of a molecular collision, scientists would still be at a loss as to how to explain the reaction between two chemical species. In fact, the nature of the forces between two molecules is a bit more complicated than simply a weak attraction followed by a strong repulsion as they approach. Between these acting forces, there is an intimate range of forces, or interactions, between the molecules that are associated with the electrons from one molecule and the atoms of the other, or a mixing up of the electrons between the species.

This mixing is termed a covalent, or bonding, interaction, and during the close-in portion of the trajectory (in which the molecules are separated by a distance of the magnitude of a typical bond length), this mixing can lead to a rearrangement of the bonds within and between the two colliding molecules. Thus, as they separate, the two departing species may have a different arrangement of atoms or include more or less atoms than when they went in. No atoms are created or lost, so the net result is simply a scrambling of the atoms (in a very precise manner) between fragments. This is an example of a chemically reactive collision. Since the sum of all the bond strengths, or energies, in the reactant (incoming) pair is not typically equal to that in the product (departing) pair, some kinetic energy (or rotational and vibrational energy) must be gained or lost in the process; thus, chemically reactive collisions are necessarily inelastic in nature. If the bonds are stronger in the products, then kinetic energy is lost (converted to chemical potential energy in the form of bonds), and the collision is called an endothermic (from the Greek root endon, meaning "within") reaction. In order for this to occur, the reactants must bring in at least the critical amount of kinetic energy for conversion into chemical potential energy. If the product bonding is weaker, then potential energy is released into product kinetic energy and rotational and vibrational motion is an exothermic reaction. In the case of chemically reactive collisions, the trajectories are quite complex, having been formed by forces between many different atoms in each molecule, and the study of these processes forms an entirely separate branch of collisional investigation (called reaction dynamics).

Applications

Molecular collision processes play an important role in many of the natural phenomena experienced in daily life. The earth is continuously bathed in a gas, the atmosphere, and the collisions occurring between the molecules forming this gas determine the majority of its properties. The simplest of these collisional properties is that of molecular diffusion. The atmosphere is a complex mixture of naturally occurring (as well as some man-made) molecular species, and it is the action of diffusion that ensures that the gas remains relatively homogeneous, or mixed. Since humans rely on the oxygen component for life, they are critically dependent upon this mixing to ensure that each breath they take contains a suitable amount of oxygen.

Diffusion ensures this by forcing the molecules to continuously alter their directions through collisions and by subsequently dispersing them to fill all available regions of space.

If one considers a process that rapidly produces a species (a visible species such as smoke particles aids our visual example) in a well-localized region of space--say, an explosion or a smoky fire--one sees in watching those species over time that, ignoring wind, the cloud disperses slowly until finally it blends in with the surrounding gas and disappears. This action is a result of finite and nonzero velocities that all molecules possess when their temperature is not zero (as thermodynamics guarantees us). If the size, or cross section, of the molecules were infinitesimally small and there were no forces in action, the cloud would disperse spherically outward at a rate comparable to an average molecular speed (approximately 40 meters per second at room temperature). In this case, one would never see a cloud but for a fleeting moment. In fact, collisions moderate this dispersal by randomizing this outward flow, and a single molecule is found to follow a zigzag trajectory, commonly referred to as a random walk. At the same time the cloud is dispersing outward, oxygen and nitrogen molecules are diffusing inward, eventually leading to a homogeneous mixture.

The propagation of sound is another consequence of molecular collisions. Sound is registered in the ear when molecules strike the eardrum. This is occurring continuously even in a still room; however, this "white" noise is filtered out by the brain. What one can hear, however, is concentrated waves of arriving molecules that originate at some transmitting device, say, a speaker or vocal cord. The motion of the transmitter strikes gas molecules and sets them in outward motion. These molecules strike others, and the information is propagated outward toward your ear, with mild dissipation caused by the randomizing nature of collisions. There are several important consequences. In the absence of molecules, nothing can carry the information; thus, sound doesn't propagate in a vacuum. Were there not collisions between molecules, sound would propagate in a straight path from the transmitter; yet it is the trajectory-altering nature of collisions that ensures that the sound spreads spherically outward from the source (but has difficulty, that is, is rapidly dissipated, when going around objects). Sound velocity does not depend on the strength of the transmitter. Like diffusion, sound speed is determined by the velocity of molecules between collisions, moderated by the randomizing effects in the trajectories. Indeed, if an object is set in motion through a gas at faster than this mean molecular velocity, it will push molecules in front of it faster than the relative speed with which these molecules would normally communicate this information. This results in the object traveling faster than the sound it produces, and a large cone of sound information follows it, reaching one's ear as a sonic boom after the object has passed. This phenomenon is solely a consequence of the collisional nature of molecules and the fact that they cannot traverse the atmosphere without randomization of energy and trajectory.

Finally, heat or energy is transmitted through gas samples by collisions; however, this phenomenon is strongly dependent upon the inelastic nature of molecular collisions. The thermal energy emitted by a radiator appears as molecular motion of the first layers of gas molecules surrounding it. For this heat to be transmitted to the surrounding gas, and eventually to the accepting body, numerous collisions must occur, eventually delivering kinetic energy to the source as heat. The nature of inelastic collisions allows for a significant portion of this energy to be taken up into rotational and vibrational motions of the molecules. The rate at which this energy is communicated into the molecules and eventually across the gas depends on the nature or properties of the collisions; however, the amount left behind (as warmed gas) depends on the number of ways the molecules can vibrate or rotate, and is a measure of the molecules' heat capacity. Energy is transmitted through an atomic gas (with no vibrational or rotational motions possible) much more efficiently than it is through a molecular gas, which possesses a high internal heat capacity.

The study of molecular collision phenomena at the microscopic scale has progressed to a point where scientists can now understand the detailed and specific mechanisms by which collisions can be used to direct energy into very useful forms. This knowledge has been put to use in converting electrical energy into light in devices such as fluorescent bulbs and gaseous lasers. It has also been used to convert chemical energy into directed propulsion in rocket engines with maximum conversion efficiency. The understanding of chemical collision phenomena, although far from complete, is having ever-greater impact upon the use of energy to produce chemical compounds and material structures.

Context

The understanding of molecular collisions certainly has its roots in the early Greeks' concept that matter is composed of discrete particles, in this case atoms, and in the later concept of molecules existing as bound ensembles of these atoms. The first quantitative descriptions of how these might interact, however, were not possible before the description of forces and their consequences, first quantified by Sir Isaac Newton in the eighteenth century. His laws still provide the fundamental foundation for the simplest accurate description of most molecular collision processes.

To use Newton's laws, however, one must understand the nature of the molecular forces that are operative during a collision. It was not until late in the nineteenth or early in the twentieth century that our understanding of molecular composition and the interaction of matter progressed to a point where this could be attempted. James Clerk Maxwell's development of electromagnetic theory and Ludwig Boltzmann's detailed work on the nature of inelastic collisions in the late 1800's laid crucial groundwork for the detailed advances soon to be made in the understanding of molecular collisions with the advent of quantum theory in the 1920's and 1930's. It was only at this point that theoretical understanding of molecular interactions became sufficiently well-grounded that a theory of molecular collisions became an optimistic endeavor.

Indeed, as a graduate student in the early 1930's, Joseph Herschfelder, who was later to become one of the preeminent fathers of the field, first applied quantum theories to calculate (for many hours on a hand-driven calculating device) trajectories for the reactive collisions between a hydrogen atom and a hydrogen molecule.

At the same time, much progress was being made in the laboratory toward allowing the study of single molecules and very low-pressure samples of gases, and this work permitted some of the first detailed observations of the consequences of elastic and inelastic molecular collisions.

The greatest experimental advances, however, were made from the early 1960's through today, with the advent of sophisticated molecular beam machines capable of firing streams of molecules at one another and detecting the collisional outcome, and with the invention and subsequent development of the laser, with its unprecedented ability to detect, select, or even alter the behavior of discrete molecules in complex mixtures.

With these tools, it has become possible to study selectively the beginning and end result of numerous types of collisions of a wide variety of species. Coupled with the tremendous advances recently made in theory (quantum mechanical as well as classical), aided by the explosive increases in our computing capabilities, the actions that result when two molecules collide are beginning to be thoroughly understood. Perhaps the final frontier in this area lies in being able to describe the collisions of even more complicated molecules. This is mainly a problem of bookkeeping, since the forces are essentially the same; there are merely more of them. As more is understood about these collisions, however, questions must continue to be asked about how they may be put to work, and this challenge to both experiment and theory will persist long into the future.

Principal terms

COLLISION RATE: the average number of collisions per second in a gaseous sample, usually specified to be one cubic centimeter

COVALENT FORCE: the strong attractive or repulsive force felt between two molecules at close range as a result of electron-electron and electron-nuclei interactions between the species; this force can lead to molecular bonding

CROSS SECTION: the area surrounding a molecule (when looked at in projection--that is, two dimensions) that guarantees collision for all species that pass through

DISPERSION FORCE: the mutually attractive force felt between two molecules at moderately large distances, caused by interaction between their electron clouds

IMPACT PARAMETER: the distance of closest approach within which two potentially colliding species could pass if they had no forces acting between them

INELASTIC COLLISION: a collision with a species (usually a molecule)

in which energy is converted from kinetic energy to internal energy (rotation or vibration) or vice versa and momentum is not conserved

INTERACTION POTENTIAL: the energy stored or released as a result of forces (repulsive or attractive) that act between two species in close proximity

TRAJECTORY: a path describing the complete passage of two particles during a collisional event, originating at approach, going through the collisional motion, and terminating on complete separation

Bibliography

Kovalenko, Laurie J., and Stephen R. Leone. "Innovative Laser Techniques in Chemical Kinetics." JOURNAL OF CHEMICAL EDUCATION 65 (August, 1988): 681-687. A pedagogical discussion of the use of lasers to investigate the nature of molecular collision processes, with particular emphasis on inelastic and reactive processes.

Levine, R. D., and R. B. Bernstein. MOLECULAR REACTION DYNAMICS. Oxford, England: Oxford University Press, 1974. This superbly written book is the quintessential treatise on molecular reaction dynamics, bridging the gap between a simple, elementary understanding of chemistry and physics and the modern thought and experiments as they are practiced in the field. Perhaps moderately advanced, but not to be missed by the serious student wishing to continue study.

Polanyi, John C. "Some Concepts in Reaction Dynamics." SCIENCE 236 (May 8, 1987): 680-690. A condensed version of the author's Nobel Prize address, detailing the investigation of reaction mechanisms and molecular dynamics through the study of energy release in reaction products, the role of reagent energy, and the findings expected from future direct studies of transition states.

Waite, Boyd A. "A Gas Kinetic Explanation of Simple Thermodynamic Processes." JOURNAL OF CHEMICAL EDUCATION 62 (March, 1985): 224-227. A discussion concerning the relationship between microscopic collision behavior and the bulk, macroscopic observations of thermodynamics such as pressure and equilibrium.

Dynamics of Chemical Reactions

Chemical Reactions and Collisions