Anisotropic formation theory

Anisotropic formation theory Stratified or anisotropic formations are assumed to possess different drillabilities parallel and normal to the bedding planes with the result that the bit does not drill in the direction of the resultant force. 

Hasinoff noted that the rate coefficient of formation of encounters pairs, fcD, was smaller than predicted from the Smoluchowski—Stokes—Einstein rate coefficient [eqn. (29)]. In aqueous glycerol, this reduction was by 0.14 times, in aqueous polyethylene glycol by 0.30 times, and in aqueous ethylene glycol by 0.11 times. Hasinoff compared these reductions in rate of diffusive rate of formation of encounter pairs with three theories of anisotropic reactivity due to Weller [262], Schmitz and Schurr [257] and... 

The complexity of the system implies that many phenomena are not directly explainable by the basic theories of semiconductor electrochemistry. The basic theories are developed for idealized situations, but the electrode behavior of a specific system is almost always deviated from the idealized situations in many different ways. Also, the complex details of each phenomenon are associated with all the processes at the silicon/electrolyte interface from a macro scale to the atomic scale such that the rich details are lost when simplifications are made in developing theories. Additionally, most theories are developed based on the data that are from a limited domain in the multidimensional space of numerous variables. As a result, in general such theories are valid only within this domain of the variable space but are inconsistent with the data outside this domain. In fact, the specific theories developed by different research groups on the various phenomena of silicon electrodes are often inconsistent with each other. In this respect, this book had the opportunity to have the space and scope to assemble the data and to review the discrete theories in a global perspective. In a number of cases, this exercise resulted in more complete physical schemes for the mechanisms of the electrode phenomena, such as current oscillation, growth of anodic oxide, anisotropic etching, and formation of porous silicon. 

Main chain polymers. Due to the rigidity of the monomer units stiff polymer chains are obtained which according to the theory should have a tendency towards the formation of anisotropic melts The properties... 

The second or alternative mechanism is used by the Maier-Saupe mean field theory in which the stability of the nematic phase is derived from an anisotropic potential. Picken has developed a theory for the nematic phase formation of liquid crystalline polymers, which is based on the Maier-Saupe mean field theory [37, 38], A molecule in a nematic domain, with its axis at an angle

average orientation axis of the domain, is assumed to feel the influence of the surrounding medium only in terms of an anisotropy potential... 

Pursuing this last thought, can the elastic energy be incorporated into any of the statistical theories for the formation of liquid crystal formation (e.g., Onsager, Flory. Meier-Saupe, Doi) to predict an equilibrium between isotropic and anisotropic phases that is different from that in the defect-free state ... 

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