Equilibrium and dynamics of ionic solutions
Massachusetts Institute of Technology. Dept. of Chemical Engineering.
Gregory J. McRae.
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The present work is motivated by the desire to understand the physical mechanism underlying the propagation of nervous influx in neurons as well as the modulation and summation of electrical signals during their progression in dendrites. The survey of existing literature shows that most studies model dendrites and axons as cables and simply ignore the physical basis of these electrical signals. Indeed in neurons as in any cell there exists a potential difference of about 70 mV across the plasmic membrane caused by differences in the concentrations of small ions between the inside and outside of the cell; nervous influx is a temporary alteration of this potential difference that can propagate along the plasmic membrane. Nervous influx is carried by ionic currents flowing both across the membrane and inside the neuron under the membrane. It propagates at velocities comprised between 0.1 m/s and 100 m/s. The present study ambitioned to build a model for the propagation of nervous influx based on ionic currents but the literature on electrolytes did not provide a good fundamental theory to construct such a model. Therefore the subject of the thesis evolved from modeling nervous influx to developing a new fundamental theory of ionic solutions and testing it against available experimental data. The reference theory was elaborated by Debye and Hickel in the 1930's and is the only full and consistent theory but it is valid only in dilute media because it is insufficient on two points: it considers ions as infinitesimally small and ignores their correlations. Consequently a new theory of small ions is developed in which ions are treated as hard spheres and their correlations are included locally. The new theory is consistent and can be reduced to the Debye-Hiickel theory when the radius of ions and the correlation length are taken to be zero. The theory assigns to each ion an ionic radius corresponding to the extent of its electronic cloud and a hydrated radius corresponding to the extent of its shell of hydration. The solution as a whole has a correlation length determining the volume around each ion in which correlations have a significant effect. The correlation length and the hydrated radii are determined from experimental data, whereas the ionic radii have a fixed value taken from the literature. The correlation length and the hydrated radii were determined for 75 binary electrolytes by calculating the osmotic coefficient and the mean ionic activity coefficient and by fitting the wealth of experimental data available. Usually three fits were made for each electrolyte. The general fit is always close to experimental points but underestimates the values in the semi-dilute region. The dilute fit and the semi-dilute fit approximate experimental points very well in their respective regions but markedly stray from them in the concentrated region. The main explanation for the need for three fits is that the correlation length and the hydrated radii actually change with the concentration of ions whereas the model assumes them to be constant. The rate of change being small, the whole set of experimental points can be approximated very well with three fits. et of experimental points can be approximated very well with three fits. The next step was to compare these three fits with the semi-empirical models of Meissner and Pitzer for the mean ionic activity coefficient. All three are good approximations. The Pitzer model is the most precise for almost all electrolytes; the Meissner model and the present model are equivalent in their accuracy. Afterwards a short study was performed on multicomponent electrolytes and it confirmed the behavior observed for binary electrolytes. The osmotic coefficient and the mean ionic activity coefficient are usually well approximated in the concentrated and dilute regions and slightly underestimated in the semi-dilute region. The last part of the present study examines the propagation of linear plane waves. In bulk solutions the propagation is generally conservative and the phase and group velocities are on the order of hundreds of meters per second. The group velocity in bulk solutions provides an upper bound for the velocity of nervous influx; the velocity resulting from diffusion provides a lower bound; the actual mechanism must be a combination of the two depending on local conditions. In a nutshell the principal objective has been fulfilled: a new theory for ionic solutions has been developed that is valid from infinite dilution to saturation; it reproduces experimental data at equilibrium well. The theory is then applied to describe the propagation of linear waves in bulk solutions and has found group velocities on the order of hundreds of meters per second. Nevertheless the equations studied thus far cannot be applied to describe the environment under the plasmic membrane of neurons because they assume that local concentrations are small perturbations from the bulk concentrations, which is not the case. Thus the other objective of the thesis is only partially fulfilled; ionic waves are a plausible mechanism for the propagation of nervous influx and the most probable one, but the demonstration is incomplete.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2009.Includes bibliographical references (leaves 194-201).
DepartmentMassachusetts Institute of Technology. Dept. of Chemical Engineering.
Massachusetts Institute of Technology