Hole arrayed metal-insulator-metal structure for surface enhanced Raman scattering by self-assembling polystyrene spheres

A fabrication process based on the self-assembling polystyrene spheres is proposed to obtain hole arrayed metal-insulator-metal （HA-MIM） structure for surface enhanced Raman scattering （SERS）. The localized field enhancement aroused by the gap resonance in the HA-MIM structure is analyzed by finite-different time domain （FDTD） method. With reference to the theory result, the structure is experimentally fabricated and the Raman scattering spectrum of rhodamine 6G （R6G） is measured by a miniaturized Raman spectrometer. The results shows that the enhancement factor is 3.85 times higher than the control sample with single layered metal hole array. The fabrication process to obtain the HA-MIM SERS substrate is reproducible, fast, large area and low cost.     

The self-consistent mean spherical approximation for the one-component plasma

The consequences of choosing the adjustable hard-core diameter in the mean spherical approximation for the one-component plasma so as to achieve thermodynamic consistency between the energy and compressibility equations are investigated. Such a choice is found to be possible only for >8.5 and, although the resulting correlation functions are discontinuous, the height of the main peak in the static structure factor is remarkably accurate. Two especially noteworthy aspects of the thermodynamic results are that the compressibility equation is much more accurate than in any previous approximation free of input from computer simulations and that the nonstatic part of the internal energy has a ^1/4 dependence in the strong coupling limit in agreement with Monte Carlo data.     

Formation of soliton-like light beams in an aqueous suspension of polystyrene particles

A Kerr nonlinear medium consisting of an aqueous suspension of dielectric nanoparticles is used for the observation of continuous self-focusing of laser light. The minimum width of the soliton-like beam is measured in relation to the radiation power and the particle concentration. The possibilities of maximum narrowing of the beam in such a medium are discussed.     

A solution of the multiple-binding mean spherical approximation for ionic mixtures

The mean spherical approximation (MSA) for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the Wertheim formalism. Any number of bonds is allowed. It is shown that the general solution is given in terms of a screening MSA-like parameter ^T , a cross-interaction parameter that will depend on the binding association equations, the set of binding association fractions, and an additional algebraic equation. The equation for ^T is given for the general case. The equation for , however, depends strongly on the particular closure that is used to compute the contact pair correlation function. The full solution requires, as in the dimer case recently solved by Blum and Bernard, solvingm+2 equations and additionally the inversion of a matrix of size [(–1)m] for a system withm components and bonds. We recall that when =1, only dimers are allowed; for =2, only linear chains are formed: and when 3, branching of the polymers occurs. It can be shown that the excess entropy for the polymer case is as before,S ^MSA=( ^T )³/3 + sticky terms, where the sticky terms depend on the model and will be given in future work.     

Low angle structure factor of liquid aluminium in the mean density approximation

The low angle structure factor of liquid Al is calculated in the mean density approximation. It agrees with the recently observed data of Waseda out to k≈0.4 Å^?1.     

The general solution of the binding mean spherical approximation for pairing ions

The mean spherical approximation (MSA) for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the Wertheim formalism. Only pairs are allowed. It is shown that the general solution is given in terms of two scaling parameters and the set of binding fractions. One of the scales is the screening parameter, and the other is a coupling parameter analogous to that of the simple MSA, but that now is found solving a cubic equation. Therefore the full solution requires solvingm+2 nonlinear algebraic equations for a system withm components. A brief discussion of the thermodynamics is given.     

The temperature dependence of the refractive index of an aqueous suspension of polystyrene microspheres

We report an experimental measurement, based on an interferometric technique, for the determination of the temperature dependence of the refractive index n _L of a liquid suspension of dielectric spheres in the thermal range 20–52° C. In this range we have measured values of n _L /T of order of magnitude 10^–4° C^–1. The observed values are compared with those obtained for water.     

Variational extension of the mean spherical approximation to arbitrary dimensions

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limitT ΔS ^MSA /ΔE ^MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1. On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681.     

Solution of the mean spherical approximation for hard ions and dipoles of arbitrary size

The general solution of the mean spherical approximation (MSA) for an arbitrary mixture of hard spherical ions and dipoles, in which the ions can be of different size, is found. This solution is given in terms of three parameters that are calculated by solving an algebraic equation. Two of these parameters are scaling parameters required to satisfy the general symmetry of the pair correlation functions, and are similar to the one introduced in the solution of the MSA for an ionic mixture in earlier work. For equal size and low ionic concentration, we get a rather explicit solution of the MSA, which is formally similar to the Waisman-Lebowitz solution of the restricted primitive model, but with a concentration-dependent dielectric constant.Supported in part through NSF grant 77-04597.     

Comments on the mean spherical approximation for hard-core and soft potentials and an application to the one-component plasma

The thermodynamic properties of the mean spherical (MSA), Percus-Yevick (PY), and hypernetted-chain (HNC) approximations are derived by a simple and unified approach by considering the RPA free-energy functionalF and employing an Ewald-type identity. It is demonstrated that with decreasing relative contribution of the hard-core insertion to the thermodynamic functions, the MSA changes its nature from PY-like to HNC-like, withF changing its role from excess pressure to excess free energy, respectively. It is found that the condition of continuity of the MSA pair functions is equivalent to a stationarity condition forF and leads to thermodynamic consistency between the virial and energy equations of state for the (thus defined) soft-MSA (SMSA), withF playing the role of the excess free energy. It is shown that the PY-compressibility and virial equations of state forD-dimensional hard spheres may be simply obtained one from the other without knowing any details of the solution of the model. Using this relation we find an indication that the PY approximation for hard spheres becomes less accurate with increasing dimensionality. A general variational formulation is presented for the application of the MSA for soft potentials, and results for the one-component plasma are discussed and extended.On sabbatical leave from the Nuclear Research Center-Negev, P.O. Box 9001, Beer Sheva, Israel.     

Analytic solution of the mean spherical approximation for ion-dipole model in a neutralizing background

The analytic solution of the mean spherical approximation (MSA) for a multicomponent mixture of hard ions and hard dipoles with arbitrary valences and sizes of particles in a uniform neutralizing background is found. Expressions for the pair correlation functions and thermodynamics in the MSA are obtained.     

An analytic solution for the magnetization of two-dimensional ferrofluids based on the mean spherical approximation

An analytic formula is derived for the magnetization of a two-dimensional dipolar hard disk fluid using a variational functional series expansion of the free energy as a function of the orientational distribution function. The excess term expressing the effect of the intermolecular forces is calculated on the basis of the mean spherical approximation. Comparison with our own Monte Carlo simulation data shows excellent agreement for large external fields and for the zero-field susceptibility. At intermediate field strengths, the agreement is satisfactory for moderate dipole moments and densities.     

On the freezing and structure of hard spheres under spherical confinement

The equation of state and the structure of hard spheres confined in spherical pores have been investigated via molecular dynamics for different pore radii ranging from 5.0 to 10.0?σ, where σ is the particle diameter. The hard boundary is chosen to capture the pure geometric effect of spherical confinement. A discontinuity in the equation of state was observed, indicating the onset of a freezing-like phase transition, which was similar to that of the bulk hard-sphere fluids. The behaviour of confined particles resembles that of the bulk with increase in the pore size, while its deviation from the bulk is found to be larger at the solid-like phase. For the pore radius below 5.0, FCC-like crystal clusters are not formed in spherically confined hard spheres.     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.     

膨胀着的球面的相对论变换

分析了膨胀着的球面的相对论变换.