Polymerization nonequilibrium

John A. Pojman is a professor in the Macromolecular Science Division of the Department of Chemistry at Louisiana State University. He earned his doctorate in chemical physics from the Univereity of Texas at Austin. Dr. Pojman was a faculty member at the University of Southern Mississippi for ISyeare. He has published over 100 peer-reviewed publications and coedited three monographs and coauthored another one. His interests include nonlinear dynamics with polymers, cure-on-demand polymerizations, nonequilibrium thermodynamics of miscible fluids, microgravity research, and the aquatic salamandei of Louisiana. He also claims the world s largest collection of pocket protectors. 

In addition, there is another interesting nonequilibrium mechanism that can produce one type of structure which then remains permanently. Suppose there was a far-from-equilibrium chemical system with three reactants X, Y, and Z that oscillate. As in the case of the Belousov-Zha-botinski reaction, let us assume that the concentrations of these variables reach their maxima in a well-defined order X reaches its maximum first followed by Y and Z successively. The order X — Y — Z is determined (and fixed) by the nonequilibrium kinetics. Now suppose that such a system is coupled to a polymerizing catalyst that can produce either of the following two unidentical polymers ... 

Jardine et al. (1985b) employed a two-site nonequilibrium transport model to study Al sorption kinetics on kaolinite. They used the transport model of Selim et al. (1976b) and Cameron and Klute (1977). Based on the above model, Jardine et al. (1985a) concluded that there were at least two mechanisms for Al adsorption on Ca-kaolinite. It appeared that there were equilibrium (type-1) reactions on kaolinite that involved instantaneous Ca-Al exchange and rate-limited reaction sites (type-2) involving Al polymerization on kaolinite. The experimental breakthrough curves (BTC) conformed well to the two-site model. 

Building of the adequate model (nonequilibrium thermodynamic approach, polymeric or pseudopolymeric models, fractal analysis, combinations of various methods, etc.). 

The thermodynamic approach considers micropores as elements of the structure of the system possessing excess (free) energy, hence, micropore formation processes are described in general terms of nonequilibrium thermodynamics, if no kinetic limitations appear. The applicability of the thermodynamic approach to description of micropore formation is very large, because this one is, in most cases, the result of fast chemical reactions and related heat/mass transfer processes. The thermodynamic description does not contradict to the fractal one because of reasons which are analyzed below in Sec. II. C but the nonequilibrium thermodynamic models are, in most cases, more strict and complete than the fractal ones, and the application of the fractal approach furnishes no additional information. If no polymerization takes place (that is right for most of processes of preparation of active carbons at high temperatures by pyrolysis or oxidation of primary organic materials), traditional methods of nonequilibrium thermodynamics (especially nonequilibrium statistical thermodynamics) are applicable. 

In some cases, when the polymerization appears, the energy distribution of micropores is negligible in comparison with the energy of polymerization. That is possible when the temperature of the treatment of the primary material (if this one can be polymerized, e.g., silica, alumina) is low (less 300-350 °C). In such cases, traditional methods of nonequilibrium thermodynamics are not effective, and the micropore formation can be considered as the result of the polymerization process which is described by methods of polymer science. However, models of macromolecular systems do not always give enough information about micropores as the empty space between polymers. For such systems, the application of fractal methods can allow us to obtain additional information, while one has to take into account the fact that they cannot be applied to very narrow pores (ultramicropores which are found, for instance, in some silica gels). 

We note that such problem does not appear in the nonequilibrium statistical thermodynamic approach (Sec. Ill), according to which micropores are considered together with their solid environment (micropore walls). Therefore, unlike the case of pyrolytic carbons, micropores in polymeric materials cannot be described in their own energy terms (chemical potential, etc.). 

Now, we will consider a nonequilibrium chemical process in a polymeric system described by equations of linear thermodynamics ... 

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

Assume as a model for a Ziegler-Natta system the diffusion of monomer to a site of catalytic activity—presumably one of a number of sites on a solid particle—where it is inserted into a growing polymer chain. For the bulk polymerization of a monomer such as 4-methylpentene-l where polymer is insoluble in monomer, the solid catalyst particle becomes the center of an expanding sphere of precipitated polymer chain (s) growing from the inside. On this molecular level, the rate of chain growth will be directly proportional to the monomer activity at the individual sites. At equilibrium the monomer activity at each site encapsulated in precipitated polymer will equal that of the surrounding bulk monomer, [Mo]. Under nonequilibrium conditions, where the rate of diffusion of monomer from the bulk monomer thru the precipitated polymer to the polymerization site becomes comparable to the rate of polymerization at that site, the localized activity will be lower, and the rate of polymerization will be correspondingly lower. 

We have reviewed the recent development of a nonequilibrium statistical mechanical theory of polymeric glasses, and have provided a unified account of the structural relaxation, physical aging, and deformation kinetics of glassy polymers, compatible blends, and particulate composites. The specific conclusions are as follows ... 

There is a close connection between molecular mass, momentum, and energy transport, which can be explained in terms of a molecular theory for low-density monatomic gases. Equations of continuity, motion, and energy can all be derived from the Boltzmann equation, producing expressions for the flows and transport properties. Similar kinetic theories are also available for polyatomic gases, monatomic liquids, and polymeric liquids. In this chapter, we briefly summarize nonequilibrium systems, the kinetic theory, transport phenomena, and chemical reactions. 

The complex interrelationships of three types of chemical equilibria, namely oxidation-reduction, hydrolysis, and complexa-tion, as well as polymerization, a nonequilibrium process, determine the nature and speciation of plutonium in aqueous environmental systems. This paper presents a selective, critical review of the literature describing these processes. Although most research has been conducted under non-environmental conditions— that is, macro concentrations of plutonium and high acidities—the results in some cases are applicable to environmental conditions. In other cases the behavior is different, however, and care should always be exercised in extrapolating macro data to environmental conditions. 

The microporous material exhibits in all cases a precisely controlled, reproducible and preselected morphology, because it is fabricated by the polymerization of a periodic liquid crystalline phase which is a thermodynamic equilibrium state, in contrast to other membrane fabrication processes which are nonequilibrium processes. 

Application As is well-known in the industry, any microporous material which is formed through a nonequilibrium process is subject to variability and nonuniformity, and thus limitations such as block thickness, for example, due to the fact that thermodynamics is working to push the system toward equilibrium. In the present material, the microstructure is determined at thermodynamic equilibrium, thus allowing uniformly microporous materials without size or shape limitations to be produced. As an example, the cubic phase consisting of 44.9 wt% DDAB, 47.6% water, 7.0% styrene, 0.4% divinyl benzene (as cross-linker), and 0.1% AIBN as initiator has been partially polymerized in the authors laboratory by themal initiation the equilibrated phase was raised to 8S°C, and within 90 minutes partial polymerization resulted S AXS proved that the cubic structure was retained (the cubic phase, without initiator, is stable at 65°C). When complete polymerization by thermal initiation is accomplished, then such a process could produce uniform microporous materials of arbitrary size and shape. 

Figure 1.3 clearly demonstrates the luminous gas phase created under the influence of microwave energy coupled to the acetylene (gas) contained in the bottle. This luminous gas phase has been traditionally described in terms such as low-pressure plasma, low-temperature plasma, nonequilibrium plasma, glow discharge plasma, and so forth. The process that utilizes such a luminous vapor phase has been described as plasma polymerization, plasma-assisted CVD (PACVD), plasma-enhanced CVD (PECVD), plasma CVD (PCVD), and so forth. 

V2 = 1). The transition (partial or complete) into the liquid crystalline state occurs only after the system is heated above the glass-transition point. For real polymeric systems with semiflexible chains, the liquid crystalline state in the initial solution often is not realized, so the formation of nonequilibrium amorphous polymer upon the introduction of a nonsolvent is quite probable. 

Nonequilibrium behavior during solute transport in soil may also result from time-dependent chemical and biological transformation reactions. Consideration of chemical fixation, dissolution, hydrolysis, and polymerization reactions in mathematical models are often necessary to correctly describe the transport of certain solutes in soil. Time-dependent biological reactions that transform solutes into a variety of chemical species may also need consideration during solute transport in some soils. 

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