*Collect. Czech. Chem. Commun.*
**1996**, *61*, 59-69

https://doi.org/10.1135/cccc19960059

### The Model of Linear Aggregate of Ag Colloidal Particles with Variable Inter-Particle Distances

**Ondřej Šesták, Pavel Matějka and Blanka Vlčková**

*Department of Physical and Macromolecular Chemistry, Charles University, 128 40 Prague 2, Czech Republic*

### Abstract

A simplified method of calculation of the surface plasmon energy states of the Ag colloidal aggregates characterized by varying inter-particle (inter-sphere) distance has been developed. Ag colloidal aggregate is approximated by a linear (one-dimensional) assembly of *N* silver spheres (of identical radii *r* and identical inter-sphere distances *D*) mutually interacting by a dipole-dipole interaction. The calculations use the following parameters: *N* from 1 to 25, *r* = 2, 5 and 10 nm, *D* = 0, 0.5, 1 and 2 nm, water and/or vacuum embedding media. The perturbation energies *V*_{min} (stabilization energy) and *V*_{max} (destabilization energy) of the excited plasmon state of a linear aggregate of *N* spheres interacting by the dipole-dipole interaction were calculated as the eigenvalues of perturbation matrix using the above-mentioned parameters. The stabilization energy *V*_{min} increases with increasing number of spheres in the aggregate and with increasing sphere radius, while it decreases with increasing inter-particle (inter-sphere) distance. Calculations of the square values of the eigenvector coefficients show that the contribution of a particular single sphere to the total energy of the aggregate is the highest for the central sphere in the odd-*N* aggregates and for the two central spheres in the even-*N* aggregates. The results of the model calculations support the hypothesis that the differences between the surface plasmon absorption curves of the Ag colloid/monomeric adsorbate and of the Ag colloid/polymeric (oligomeric) adsorbate systems have their origin in the difference in the inter-particle distance distributions.

**Keywords:**
Ag-colloid;
Linear aggregates;
Aggregation theory;
SERS;
Surface plasmon states.