Intermolecular collisions, gases

The Stefan-Maxwell equations have been presented for the case of a gas in the absence of a porous medium. However, in a porous medium whose pores are all wide compared with mean free path lengths it is reasonable to guess that the fluxes will still satisfy relations of the Stefan-Maxwell form since intermolecular collisions still dominate molecule-wall collisions. 

UV photolysis (Chapman et al., 1976 Chedekel et al., 1976) and vacuum pyrolysis (Mal tsev et al., 1980) of trimethylsilyldiazomethane [122]. The silene formation occurred as a result of fast isomerization of the primary reaction product, excited singlet trimethylsilylcarbene [123] (the ground state of this carbene is triplet). When the gas-phase reaction mixture was diluted with inert gas (helium) singlet-triplet conversion took place due to intermolecular collisions and loss of excitation. As a result the final products [124] of formal dimerization of the triplet carbene [123] were obtained. 

We spent quite a lot of time looking at the concept of an ideal gas in Chapter 1. The simplest definition of an ideal gas is that it obeys the ideal-gas equation (Equation (1.13)). Most gases can be considered as ideal most of the time. The most common cause of a gas disobeying the ideal-gas equation is the formation of interactions, and the results of intermolecular collisions. 

The attraction of the gas particles for each other tends to lessen the pressure of the gas, because the attraction slightly reduces the force of gas particle collisions with the container walls. The amount of attraction depends on the concentration of gas particles and the magnitude of the particles intermolecular force. The greater the intermolecular forces of the gas, the higher the attraction is, and the less the real pressure. Van der Waals compensated for the attractive force with ... 

Chemical processes, in contrast, are processes that are not limited by rates of energy transfer. In thermal processes, chemical reactions occur under conditions in which the statistical distribution of molecular energies obey the Maxwell-Boltzmann form, i.e., the fraction of species that have an energy E or larger is proportional to e p(—E/RT). In other words, the rates of intermolecular collisions are rapid enough that all the species become thermalized with respect to the bulk gas mixture (Golden and Larson, 1984 Benson, 1976). 

Now it is worth recalling that in the theory of gas phase collisions between two molecules, the motion of both species A and B can be separated into their mutual approach along the intermolecular axis and the motion of the centre of mass of the pair of molecules [475]. After collision, though the relative velocity of A and B has changed, that of the centre of mass has not. The centre of mass X is determined by weighting the positions of A and B by the fractional mass of A and B, and X = (mArA + mBrB)/(mA + mB). The relative position of B about A is r =... 

At sufficiently high pressure, kum is typically independent of pressure. The high-pressure limit of the rate constant will be denoted kunji00. Intermolecular collisions of C with other C molecules or with other chemical species present in the gas provide the energy needed to surmount the barrier to reaction, such as the breaking of a bond. The partner in such collisions will be genetically denoted M. 

The appearance of the IR spectrum of a compound depends somewhat on the sample s phase. Under high resolution, gas-phase IR bands consist of closely spaced lines—the rotational fine structure however, IR bands of liquids and solids very rarely show rotational fine structure. In most solids, the molecules are held in fixed lattice positions and are not free to rotate. In liquids, the high rate of intermolecular collisions and the substantial intermolecular interactions cause random shifts in the rotational energies, thereby broadening the rotational lines of a band sufficiently to merge them into one another, and eliminate the rotational fine structure. (Broadening of fine structure lines is also observed in gas-phase spectra when the pressure is increased.)... 

A PVD-type reactor can be one in which molecules reach the surface directly in a molecular beam from some source or sources in which raw materials are vaporized. At the pressures commonly used (<10 6 Pa), the vaporized material encounters few intermolecular collisions while traveling to the substrate. Historically, higher pressure processes, such as sputtering and close-spaced vapor transport, have been classified as PVD (I). These processes also use physical means to generate the gas-phase species. However, the transport phenomena that need to be modeled for such higher pressure processes are more similar to CVD than PVD because of the diffusive-convective nature of transfer from the gas phase to the substrate. 

It may be noted that all the above formulae for heavier molecules, which take into account only the repulsive part of the intermolecular potential, give rot as independent of temperature. This is in striking contrast to vibrational relaxation rotational relaxation times, which depend also on the gas-kinetic collision frequency, would thus be expected to show weak temperature dependence varying... 

About 1.5 g of nickel was vaporized at 1823 K over 30 min from a resistively heated alumina-coated molybdenum wire spiral inside an evacuated 200-mm diameter glass vessel which was partly immersed in liquid nitrogen. About 20 g of the allyl halide was simultaneously vaporized into the vessel and condensed with the nickel vapor on the cold walls. During this cocondensation, the pressure in the vessel was below 2 x 10 4Torr so that few gas-phase intermolecular collisions occurred. 

Intermolecular collisions do not cause large deviations from the ideal gas law at STP for molecules such as N2 or He, which are well above their boiling points, but they do dramatically decrease the average distance molecules travel to a number which is far less than would be predicted from the average molecular speed. Collisions randomize the velocity vector many times in the nominal round trip time, leading to diffusional effects as discussed in Chapter 4. If all of the molecules start at time t = 0 at the position x = 0, the concentration distribution C(x,t) at later times is a Gaussian ... 

The uniformity of the deposited layer (Table 9.1, no. 3) also differs in both deposition technologies. In OVPD the organic molecules are randomly distributed by intermolecular collisions with carrier gas molecules which results in a very uniform and quantitative coverage of the substrate. OVPD thus also has the potential to cover unintended substrate non-uniformities, for example defects or particles. Consequently OVPD can also be applied to complex three-dimensional structured substrates. A single layer of Alq3, deposited by OVPD on a silicon wafer had a thickness uniformity of only 0.6% standard deviation, and surface roughness analysis by AFM confirmed, with an RMS value of 0.6 nm, that the thickness deviation of the Alq3 -layer is already in the molecular dimension [20]. 

Most of the chemical reactions occur in the condensed phase or in the gas phase under conditions such that the number of intermolecular collisions during the reaction time is enormous. Internal energy is quickly distributed by these collisions over all the molecules according to the Maxwell-Boltzmann distribution curve. 

At normal deposition pressures, the mean free path of the gas molecules is 10" -10" cm and is much smaller than the dimensions of the reactor, so that many intermolecular collisions take place in the process of diffusion to the substrate. An understanding of the growth is made particularly difficult by these secondary reactions. In a typical low power plasma, the fraction of molecular species that is radicals or ions is only about 10" , so that most of the collisions are with silane. An important process is the formation of larger molecules, for example... 

Calculate the intermolecular collision frequency and the mean free path in a sample of helium gas with a volume of 5.0 L at 27°C and 3.0 atm. Assume that the diameter of a helium atom is 50. pm. 

It has been generally recognized since about 1920 that thermal unimolecu-lar reactions are activated by intermolecular collisions. The key idea is that the chemical reaction does not follow immediately after energization, but competes with collisional deactivation of the energized molecule. This idea, and the associated mechanism, were suggested independently by Lindemaim [4] and Christiansen [5]. In the first step of this mechanism a molecule A is energized to A by collision with a bath gas molecule M. 

Gaseous flow has usually been investigated by theoretical means. Some experiments were also performed to verify the theoretical results. When gases are at low pressures, or are flowing in small geometries, the interaction of the gas molecules with the wall becomes as frequent as intermolecular collisions, which makes the boundaries and the molecular structure more effective on flow. This type of flow is known as rarefied gas flow. 

Knudsen flow is characterized by the mean free path (A) of the molecules, which is larger than the pore size, and hence collisions between the molecules and the pore walls are more frequent than intermolecular collisions. A lower limit for the significance of the Knudsen mechanism has usually been set at dp> 20 A [28]. The classical Knudsen equation for diffusion of gas is... 

Basic mechanisms involved in gas and vapor separation using ceramic membranes are schematized in Figure 6.14. In general, single gas permeation mechanisms in a porous ceramic membrane of thickness depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collisions. In membranes with large mesopores and macropores the separation selectivity is weak. The number of intermolecular collisions is strongly dominant and gas transport in the porosity is described as a viscous flow that can be quantified by a Hagen-Poiseuille type law ... 

With decreasing pore size the desorption energy from the wall to the gas phase within the pores (the maximum in the curves in Fig. 9.20) becomes smaller but remains positive. This implies that the molecules in the central part of the pore behave in a Knudsen-like marmer (i.e. no intermolecular collision) and can pass each other (region Cj, upper part of Fig. 9.20) but nevertheless are not free and follow curved trajectories (see Ref. [83] and Sections 9.4.3.1-2). In this region c we can speak of a surface flow enhanced micropore diffusion (SEMP). Because in surface diffusion the activation energy is a fraction of the adsorption heat (see... 

Pi is inlet pressure, microns pe is exit pressure, microns pm is mean pressure, microns n is viscosity at atmospheric pressure, poises Equation (3) reverts to Poiseuille s Law at sufficiently high pressures, where the second term in the large parenthetical factor becomes negligible compared to unity. As the pressure is decreased and intermolecular collisions become less frequent, a flow velocity profile is established where the forward velocity component near the wall becomes a finite value which increases with lower pressures. The reason for this condition is that at these pressures many molecules can stream from the bulk of flow, where the forward velocity is relatively high, to the wall, without suffering collisions with molecules having low forward velocities. Gas flow under such conditions is termed slip flow. Pressures corresponding to this type of flow are such that the second term of the correction factor in equation (3) is finite compared to unity. At lower pressures, where the mean free... 

With reduction of pressure the mean free path grows larger, and with it the resistance to mass transfer due to intermolecular collision is progressively diminished. At pressures corresponding to mean free paths larger than the dimensions of the vessel in question, the gas phase resistance to mass transfer is negligible and the only limiting factor on the rate of material movement is the rate of emission from the interface. 

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