Cross formulation

Borgis D, Hynes JT (1996) Curve crossing formulation for proton transfer reactions in solution. J Phys Chem 100 1118-1128... 

Cross formulates basic principles of revenue management (Cross 2001, p. 69) ... 

It is important to clarify here that the description of PT processes by curve crossing formulations is not a new approach nor does it provide new dynamical insight. That is, the view of PT in solutions and proteins as a curve crossing process has been formulated in early realistic simulation studies [1, 2, 42] with and without quantum corrections and the phenomenological formulation of such models has already been introduced even earlier by Kuznetsov and others [47]. Furthermore, the fact that the fluctuations of the environment in enzymes and solution modulate the activation barriers of PT reactions has been demonstrated in realistic microscopic simulations of Warshel and coworkers [1, 2]. However, as clarified in these works, the time dependence of these fluctuations does not provide a useful way to determine the rate constant. That is, the electrostatic fluctuations of the environment are determined by the corresponding Boltzmann probability and do not represent a dynamical effect. In other words, the rate constant is determined by the inverse of the time it takes the system to produce a reactive trajectory, multiplied by the time it takes such trajectories to move to the TS. The time needed for generation of a reactive trajectory is determined by the corresponding Boltzmann probability, and the actual time it takes the reactive trajectory to reach the transition state (of the order of picoseconds), is more or less constant in different systems. 

Fischer represented the structure of D-(-f)-glucose with the cross formulation (1) in Fig. 22.3. This type of formulation is now called a Fischer projection (Section 5.13) and is... 

The algorithm leads to computation of the width 2a, and the depths d, dj, dj, d, d , d at six equidistant points along the y -axis of the cross-section of a crack, as well as the surface density of charge m=4 ju c at the crack walls. In its formulation from Fig.3, the algoritlun is adapted to cracks with a constant width. 

We refer to this equation as to the time-dependent Bom-Oppenheimer (BO) model of adiabatic motion. Notice that Assumption (A) does not exclude energy level crossings along the limit solution q o- Using a density matrix formulation of QCMD and the technique of weak convergence one can prove the following theorem about the connection between the QCMD and the BO model ... 

Alkyds are formulated from polyester resins, cross-linking monomers, and fillers of mineral or glass. The unsaturated polyester resins used for thermosetting alkyds are the reaction products of polyfunctional organic alcohols (glycols) and dibasic organic acids. 

Anaerobic stmctural adhesives are typically formulated from acryhc monomers such as methyl methacrylate [80-62-6] C Hg02, and methacrylic acid [79-41-4] (see Acrylic ester polymers). Very often, cross-linking agents such as dimethacrylates are also added. A peroxide, such as cumene... 

Acryhc stmctural adhesives have been modified by elastomers in order to obtain a phase-separated, toughened system. A significant contribution in this technology has been made in which acryhc adhesives were modified by the addition of chlorosulfonated polyethylene to obtain a phase-separated stmctural adhesive (11). Such adhesives also contain methyl methacrylate, glacial methacrylic acid, and cross-linkers such as ethylene glycol dimethacrylate [97-90-5]. The polymerization initiation system, which includes cumene hydroperoxide, N,1S7-dimethyl- -toluidine, and saccharin, can be apphed to the adherend surface as a primer, or it can be formulated as the second part of a two-part adhesive. Modification of cyanoacrylates using elastomers has also been attempted copolymers of acrylonitrile, butadiene, and styrene ethylene copolymers with methylacrylate or copolymers of methacrylates with butadiene and styrene have been used. However, because of the extreme reactivity of the monomer, modification of cyanoacrylate adhesives is very difficult and material purity is essential in order to be able to modify the cyanoacrylate without causing premature reaction. 

Production of pentaerythritol in the United States has been erratic. Demand decreased in 1975 because of an economic recession and grew only moderately to 1980 (69). The range of uses for pentaerythritol has grown rapidly in lubricants (qv), fire-retardant compositions, adhesives, and other formulations where the cross-linking capabiUties are of critical importance. 

Pentaerythritol and trimethylolpropane acryUc esters are usefiti in solventiess lacquer formulations for radiation curing (qv), providing a cross-linking capabihty for the main film component, which is usually an acryUc ester of urethane, epoxy, or polyester. Some specialty films utilize dipentaerythritol and ditrimethylolpropane (94,95). 

THPC—Amide Process. The THPC—amide process is the first practical process based on THPC. It consists of a combination of THPC, TMM, and urea. In this process, there is the potential of polymer formation by THPC, melamine, and urea. There may also be some limited cross-linking between cellulose and the TMM system. The formulation also includes triethanolamine [102-71-6J, an acid scavenger, which slows polymerization at room temperature. Urea and triethanolamine react with the hydrochloric acid produced in the polymerization reaction, thus preventing acid damage to the fabric. This finish with suitable add-on passes the standard vertical flame test after repeated laundering (80). 

Fillers (qv) are occasionally used in flexible slab foams the two most commonly used are calcium carbonate (whiting) and barium sulfate (barytes). Their use level may range up to 150 parts per 100 parts of polyol. Various other ingredients may also be used to modify a flexible foam formulation. Cross-linkers, chain extenders, ignition modifiers, auxiHary blowing agents, etc, are all used to some extent depending on the final product characteristics desired. 

One of the first attempts to produce polyurethane was from the reaction of an intermediate polyol of 1,3- and l,4-bis(hydroxyhexa uoroisopropyl)benzene m- and -12F-diols) by reaction with epichlorohydrin. This polyol was subsequentiy allowed to react with a commercial triisocyanate, resulting in a tough, cross-linked polyurethane (129,135,139). ASTM and military specification tests on these polyurethanes for weather resistance, corrosion prevention, bUster resistance, and ease of cleaning showed them to compare quite favorably with standard resin formulations. 

The organic and aqueous phases are prepared in separate tanks before transferring to the reaction ketde. In the manufacture of a styrenic copolymer, predeterrnined amounts of styrene (1) and divinylbenzene (2) are mixed together in the organic phase tank. Styrene is the principal constituent, and is usually about 90—95 wt % of the formulation. The other 5—10% is DVB. It is required to link chains of linear polystyrene together as polymerization proceeds. DVB is referred to as a cross-linker. Without it, functionalized polystyrene would be much too soluble to perform as an ion-exchange resin. Ethylene—methacrylate [97-90-5] and to a lesser degree trivinylbenzene [1322-23-2] are occasionally used as substitutes for DVB. 

Formulations for acryHc copolymers involve monomers such as acryHc acid [79-10-7], methacrylic acid [79-14 ], or esters of these acids. Formation of a copolymer from a methylmethacrylate ester (3), where DVB serves as the cross-linker, gives the stmctures ... 

Surfactants evaluated in surfactant-enhanced alkaline flooding include internal olefin sulfonates (259,261), linear alkyl xylene sulfonates (262), petroleum sulfonates (262), alcohol ethoxysulfates (258,261,263), and alcohol ethoxylates/anionic surfactants (257). Water-thickening polymers, either xanthan or polyacrylamide, can reduce injected fluid mobiHty in alkaline flooding (264) and surfactant-enhanced alkaline flooding (259,263). The combined use of alkah, surfactant, and water-thickening polymer has been termed the alkaH—surfactant—polymer (ASP) process. Cross-linked polymers have been used to increase volumetric sweep efficiency of surfactant—polymer—alkaline agent formulations (265). 

Neoprene—phenohc contact adhesives, known for thein high green strength and peel values, contain a resole-type resin prepared from 4-/-butylphenol. The alkyl group increases compatibiHty and reduces cross-linking. This resin reacts or complexes with the metal oxide, eg, MgO, contained in the formulation, and increases the cohesive strength of the adhesive. In fact, the reactivity with MgO is frequently measured to determine the effectiveness of heat-reactive phenoHcs in the formulation. 

Waterborne contact adhesives contain an elastomer in latex form, usually an acryflc or neoprene-based latex, and a heat-reactive, cross-linkable phenohc resin in the form of an aqueous dispersion. The phenoHc resin improves metal adhesion, green strength, and peel strength at elevated temperature. A typical formulation contains three parts latex and one part phenohc dispersion (dry weight bases). Although metal oxides may be added, reaction of the oxide with the phenohc resin does not occur readily. 

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