Shoon K. Kim

On the critical behavior of the optical activity of a fluid

A statistical theory is given for the dielectric tensor of a fluid composed of chiral molecules. Explicit expressions for circular dichroism and the optical rotations as functions of the optical frequencies in the critical region are obtained.

Theory of localized and nonlocalized adsorption of gases on heterogeneous surfaces

A theory is developed for adsorption of gases on patchwise heterogeneous surfaces with the assumption of a discrete distribution of site energies. The lateral interactions between adatoms in the first layer are neglected, but those in the second layer are accounted by the cluster expansion theorem. The heterogeneity effect on the isotherm is studied via the renormalization of the first layer coverage. The representation of the first layer coverage in the form of a pade approximant is introduced to determine the distribution of site energies. There is established a set of inequalities for the coefficients of the Pade approximant, which is essential in the analysis of experimental data. The theory is successfully applied to the systems of gases adsorbed on rutile reported by Drain and Morrison. It is found that the rutile surface primarily consists of three kinds of patches, the relative extent of which is proportional to that of cleavage planes of rutile. The distribution of site energies is discussed in comparison with the distribution functions previously obtained by other authors. The cluster integrals for the second layer are determined. The theory is also applied to the systems of gases on porous silver given by Hobson.

Virial expansion of the second layer in physical adsorption. An ab initio calculation for helium on argon crystal

A theory of localized and nonlocalized adsorption is given by applying the virial expansion theorem to the second layer. An ab initio calculation of the thermodynamic functions is carried out for the system of helium on an argon crystal. The gas‐solid interaction potential is calculated using lattice summation. The periodic potential along the directions parallel to the solid surface is described by a polynomial φn (x/d)/V0 = 1−[1−(2x/d)2]n within a site spacing d, where V0 is the height of potential barrier and n is an integer to be determined from the minimum potential surface. The values of n used for the first and second layers in the present work are 7 and 4, respectively. The second virial coefficient under the external potential is very well approximated by that of the two dimensional gas in free space. The Boyle temperature is 16.3°K for the system which is close to the experimental temperatures (10–20°K) of Ross and Steele. The deviation from the ideality due to the second virial coefficient is s...

A new method of matrix transformation. I. Matrix diagonalizations via involutional transformations

It is shown that two matrices A and B of order n×n which satisfy a monic quadratic equation with two roots λ1 and λ2 are connected by ATAB=TABB where TAB=A+B−(λ1+λ2) I with I being the n×n unit matrix (Theorem 1). The condition for TAB to be involutional is that the anticommutator of ?=A−(1/2)(λ1+λ2) I and ?=B−(1/2)(λ1+λ2) is a c number (Theorem 2). A 2m×2m matrix Q(2m) is introduced as a typical form of a matrix which can be diagonalized by an involutional transformation. These theorems are further extended through the matrix representation of the group of the general homogeneous linear transformations, GL(n). IUH (involutional, unitary, and Hermitian) matrices are introduced and discussed. The involutional transformations are shown to play a fundamental role in the transformations of Dirac’s Hamiltonian and of the field Hamiltonians which are quadratic in particle creation and annihilation operators in solid state physics.

Fluctuation in adsorbed phases

A study has been made of fluctuations in adsorbed phase coverage based on a model which assumes localized adsorption for the first layer and nonlocalized mobile adsorption for the second layer. For a homogeneous surface the envelopes, extremum locations, and limiting knee point of the fluctuation are calculated. An s‐shaped semiloop exists in the fluctuation, if the adsorption strength c is larger than the critical value cK=28.43. The molar fluctuation (fluctuation divided by coverage) has always one minimum. In the case of adsorption on a heterogeneous surface with s‐different patches there exist s maxima and minima in the fluctuation provided that [Mi]ci/Mi−1ci−1≳cK=28.43, i=2, 3,..., s, where ci and Mi are the adsorption strength and the number of lattice sites for the ith patch, respectively, and [Mi]=Jsk=iMk. From these extrema in the fluctuation we can estimate the characteristic constants ci’s and Mi’s of an adsorbed phase. The theory is in excellent agreement with the observed fluctuations of argo...

Characteristic properties of thermodynamic functions for the theory of localized and nonlocalized adsorption

The maxima, minima, and inflection points of the thermodynamic functions are calculated from the theory of localized and nonlocalized adsorption. Experimental determinations of the molecular thermodynamic functions, which depend on temperature alone, are discussed. Existing empirical methods of determining monolayer capacity from entropies and isosteric heat are examined. The inflection point of isosteric heat or of differential entropy directly gives monolayer capacity within an error less then 5% for ordinary systems. Similar results obtained for the BET theory are given in the Appendix; it is noted that the inflection point of the isosteric heat occurs at the coverage θ = 1−2c−1.

A new method of matrix transformations. II. General theory of matrix diagonalizations via reduced characteristic equations and its application to angular momentum coupling

A general formalism is given to construct a transformation matrix which connects two matrices A and B of order n×n satisfying any given polynomial equation of degree r, p(r)(x) =0; r?n. The transformation matrix TAB is explicitly given by a polynomial of degree (r−1) in A and B based on p(r)(x). A special case where B is a diagonal matrix Λ equivalent to A leads to the general theory of matrix diagonalizations with the transformation matrix TAΛ, which can be made nonsingular with a proper choice of Λ. In another special case where B is a constant matrix with the constant being a simple root λν of p(r)(x), the transformation matrix TAB reduces to the idempotent matrix Pν belonging to the eigenvalue λν of A. Based on the relation which exists between TAΛ and Pν, one can construct a transformation matrix U which is more effective than TAΛ and becomes unitary when A is Hermitian. Illustrative examples of the formalism are given for the problem of angular momentum coupling.

On the critical behavior of optical activity of a nonpolar binary liquid mixture

A statistical mechanical theory is presented for the dielectric tensor of a multicomponent fluid composed of chiral molecules. Explict expressions are obtained for circular dichroism and optical rotation of a binary liquid mixture in the critical region. The expression for circular dichroism suggests an alternative method of determining the critical parameters of a fluid mixture.

A unified theory of the point groups. III. Classification and basis functions of improper point groups

This paper introduces a new system of classification of improper point groups which is most effective for describing their general irreducible representations. The complete set of the general angular momentum eigenfunctions is classified according to the general irreducible representations of the seven sets of the improper point groups corresponding to Cn(C∞) and Dn(D∞) for an aribtrary n.

The theory of spinors via involutions and its application to the representations of the Lorentz group

A simple theory of the spinor representations of the complex orthogonal group O(d,C) in the d‐dimensional Euclidean space V(d) is presented via a basic lemma on involutional transformations and Cartan’s theorem on O(d,C). The arbitrary gauge factors of the representations are reduced to ± signs by introducing appropriate phase conventions. The concept of an axial involution is introduced. The plane rotations in V(d) are introduced and used to construct the representations of the proper orthogonal group O+(d,C). The Lorentz group is treated as a subgroup of O(4,C). The general expression for the basic 2×2 irreducible representations A(L0) of the proper orthochronous Lorentz group G(L0) is obtained by direct reduction of the 4×4 spinor representation S(L0) by means of the basic lemma on the involutional transformations. It is completely parameterized by the angle and the axis of the spacial rotation and by the velocity of the pure Lorentz transformation. The finite dimensional irreducible representations of...