Condensation of molecules

It has long been known from statistical mechanical theory that a Bose-Einstein ideal gas, which at low temperatures would show condensation of molecules into die ground translational state (a condensation in momentum space rather than in position space), should show a third-order phase transition at the temperature at which this condensation starts. Nonnal helium ( He) is a Bose-Einstein substance, but is far from ideal at low temperatures, and the very real forces between molecules make the >L-transition to He II very different from that predicted for a Bose-Einstein gas. 

When extended to the second layer, the Langmuir mechanism requires that the rate of condensation of molecules from the gas phase on to molecules already adsorbed in the first layer, shall be equal to the rate of evaporation from the second layer, i.e. 

An alternative way of deriving the BET equation is to express the problem in statistical-mechanical rather than kinetic terms. Adsorption is explicitly assumed to be localized the surface is regarded as an array of identical adsorption sites, and each of these sites is assumed to form the base of a stack of sites extending out from the surface each stack is treated as a separate system, i.e. the occupancy of any site is independent of the occupancy of sites in neighbouring stacks—a condition which corresponds to the neglect of lateral interactions in the BET model. The further postulate that in any stack the site in the ith layer can be occupied only if all the underlying sites are already occupied, corresponds to the BET picture in which condensation of molecules to form the ith layer can only take place on to molecules which are present in the (i — l)th layer. 

In chapter 7, all works discussed on model molecular systems for conjugated polymers refer to condensed molecular solid ultra-thin films, generally prepared by condensation of molecules from the effusion of a Knudsen-type cell, in UHV, on to clean metallic substrates held at low temperatures. Clean is defined as atomically clean as determined by core-electron level XPS, such that there is intimate contact between the molecules at the substrate-film interface, without the influence of, for example, a metallic oxide, hydrocarbon... 

When the crystal surface contains sites of different adsorption energies the adsorbate will condense area by area. According to Predali and Cases89) the adsorption isotherm will be steplike in relation to condensation of molecules on areas i, and each step i is compared with sites having the same energy 0 j. Developing the isotherm with condensation on inhomogenous surfaces they start with the definition of the fraction of sites a and /S on which condensation occurs between undersaturation Afi and dAft. When all the... 

The second type is the construction of a heterocyclic system from units containing perfluoroalkyl groups or their fragments. Each type has its own advantages and weaknesses. Thus, reactive species used in processes of the first type are perfluoroalkyl radicals and carbocations, and the processes are conducted by elaborate methods (thermolysis, photolysis, electrolysis, one-electron oxidation, etc.), whereas reactions of the second type use condensation of molecules with suitable groups and nucleophilic reactions of perfluoroolefins. 

Molecular self-assembly is defined as the spontaneous condensation of molecules into ordered arrays by noncovalent forces [refs. 20,24]. For molecular self-assembly to be reversible, the free energy of interaction, AG°, between two molecules must be comparable to the average thermal energy, kT, of molecules. Molecular self-assembly ordinarily involves weak interactions (e.g. hydrogen bonds, van der Waals interactions, and hydrophobic interactions). Although one, two, or all three dimensions of the final array may extend into the millimeter... 

In a series of experiments designed to explore further the role of polarity in affecting retention time in reversed-phase chromatography, we developed chemical procedures for the condensation of molecules of known polarity,... 

Another interesting phenomenon is homogeneous nucleation. In the process of condensation of molecules to form an embryonic drop, new surface is created. During this accretion stage the system passes from the molecular size, where an interface cannot yet be defined, to that where it has macroscopic dimensions with a well-defined interfacial tension. In sec. 1.2.23d we presented the classic picture in which y was considered constant. This approach is of course too simple a statistical analysis of the growing body is needed, whereby some of the models discussed in this chapter may appear helpful. Control of this process is very relevant for the... 

Table 7-5. Total Surface Area, Total Effective Surface Area Available for Collisions with Molecules for Three Important Aerosols, and the Associated Time Constant for the Condensation of Molecules with Molecular Weight M, = 0.1 kg/mol (v, = 2.5 x 102 m/s)...

Clusters are generally observed in molecular beam expansions. The low-temperature characteristic of this environment permits the condensation of molecules into dimers, trimers and, if the cooling is sufficient, veritable snowballs with thousands of monomer units. These broad distributions of clusters in a beam cause major problems in detection. While it is possible to control the expansion so that dimers are the dominant cluster (in the presence of a large excess of monomers), the trimers can only be studied in the presence of an excess of dimers, etc. Thus a major experimental problem in the study of neutral clusters is the detection of a particular cluster in the presence of many other sized clusters. 

In general the forces which cause the condensation of molecules to solids and liquids are much weaker than those of valency. The heat of the reaction 2H2-I-O2 = SHgO, which involves the making and breaking of valency bonds, is of the order 10 cal., while the latent heat of vaporization of water is of the order 10 cal. for a gram molecule. 

For equilibrium the rate of condensation of molecules on to vacant sites equals the rate of evaporation from occupied sites. Thus... 

In many publications my colleagues and myself have attempted to give quite an unequivocal answer to this question. The polymer state" may be considered to be a peculiar form of condensation of molecules, and the transition into this state may be regarded as a special fundamental phase transition on the background of which usual phase transitions take place. I his concept may be proven and developed just for flexible-chain fmlymers capable of the manifestation of rubber-like elasticity, i.e. of reversible 1000-fold and greater deformations which involve forces of the entropy nature. 

In a confined area above a liquid, equilibrium is established between the evaporation and condensation of molecules from the liquid. For a given temperature, this results in a steady-state level of the vapor, which can be described as a pressure. Such a pressure is called the vapor pressure of the liquid (Figure 2.8). 

Jochim, S., Bartenstein, M., Altmeyer, A., Hendl, G., Riedl, S., Chin, C., Denschlag, J.H., and Grimm, R., Bose-Einstein condensation of molecules. Science,... 

The different degree of stability of bosons and fermions leads to a surprising result. One might think that the best way to achieve mBEC is the direct conversion of an atomic BEC. However, the stability of fermions turned out to be a key ingredient to experimentally achieve the condensation of molecules see Section 9.4.4. For attaining a collisionally stable mBEC of boson-composed molecules, their transfer into the rovibrational ground state (Section 9.5) may be the only feasible way. 

Zwierlein, M.W., Stan, C.A., Schunck, C.H., Raupach, S.M.F., Gupta, S., Hadzibabic, Z., and Ketterle, W., Observation of Bose-Einstein condensation of molecules, Phys. 

The above mentioned formulae are based on the assumption that a vdW interaction of the atoms at any distance do not affect their polarizabilities. In fact, the observed polarizabilities of rare gases and molecular substances vary, depending on the aggregate state. The relative variations range from 0.3 % for Ar to 16.8 % for I2 [19]. On condensation of molecules, the polarizability can decrease (e.g., by 3.2 % for CF4 or SnBr4) or increase (by 3.0 % for CI2, 6.6 % for Br2, 16.8 % for I2) [20]. Given that the effective molecular volume always decreases on condensation, this increase of polarizability can be caused only by accumulation of electron density between molecules. Some clue can be provided by the so-called Muller s factor, the ratio between the (relative) changes of refraction, E, and of volume, V [21],... 

Jochim S, Bartenstein M, Altmeyer A, Hendl G, Reidl S, Chin C, Denschlag JM, Grimm R. (2003) Bose-Einstein condensation of molecules. Science 302 2101-2103. 

Zwierlein MW, Stan CA, Schunck CH, Raupach SMF, Gupta S, Hadzibabic Z, Ketterle W. (2003) Observation of Bose-Einstein condensation of molecules. Phys. Rev. Lett. 91 250401-1-4. 

If 6 is the fraction of the total catalyst surface covered by adsorbed molecules at any instant, then the fraction of bare catalyst surface available for adsorption is (1 — 6). According to kinetic theory, since the rate at which molecules strike a unit area of a surface is proportional to the pressure of the gas, the rate of condensation of molecules should be determined both by the partial pressure and the fraction of bare catalyst surface or i(l — 6)p, where ki is a proportionality constant. If 2 is the rate at which molecules evaporate from a unit surface when the surface is fully covered, then for a fraction 0 of a fully covered surface, the rate of evaporation will be k2d. For adsorption equilibrium, these rates must be equal. Therefore,... 

A gel results from a condensation of molecules or particles in a solvent. It is constituted by tenuous and entangled chains of solid wetted by a liquid which occupies the whole volume located between soUd chains. The liquid is a mixture of solvent, unreacted molecules inducing gelation and by-products of chemical reactions. It is obvious that only the network is of interest for material applications. There are many ways to remove the liquid located within the pores of the gel. A dried gel is named xerogel (from the Greek workxeppof that means dried). 

As mentioned above, in principle, aU materials obtained by the hydrolysis and condensation of molecules from the type RSiX3 (X=C1, OR) lead to polysilsesquioxane. Therefore many sol-gel based materials formed from these precursors would also belong to this material class if the intermediately formed Si-OH groups completely condensed to Si-O-Si groups. In recent years particularly bridged polysilsesquioxanes starting from precursors of the type X3Si-R- iX3 attracted much scientific interest. This type of compounds will not be covered by this article and interested readers are pointed to other review articles [38, 39]. 

The extent to which solid surfaces become heterogeneous by condensation of molecules evaporating from the liquid drop... 

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