## 1 Introduction  
The oligomerization of ethylene is an important industrial reaction, and megatons of \(\alpha\)-olefins are produced in this way every year. Depending on the chain length of the alkene, these materials are used for manufacturing various products, ranging from plastics to lubricants and linear low-density polyethylene (LLDPE). Among the industrial processes used for ethylene oligomerization usinghomogeneous catalysis, many processes were developed by companies such as Shell (Shell High Olefins Process (SHOP)) [1] and the IFP--Institut Francais du Petrole (Dimersol and Alfabutol) [2,3]. These systems allow the production of products with high activities and selectivities; however, the separation of the products from the reaction medium makes catalyst recycling a challenge. The use of heterogeneous catalytic systems may be an interesting way to address the issue of separating the catalyst from the reaction products, increase the catalysts' resistance and facilitate its reuse [4].  
Currently, a wide variety of molecular sieves are available, including zeolites, and these materials have become important as catalysts and adsorbents [5, 6, 7]. Molecular sieves are most commonly used in processes that employ relatively small molecules due to the sizes of their pores, which are approximately 8 A [8]. The \(\beta\)-zeolite described by Mobil Oil Corporation is an example of a zeolite structure that is applicable in such a situation. The zeolite is a \(\beta\)-zeolite, which has a three-dimensional system of channels and micropores (diameters of 7.5 A) that are circumscribed by rings of 12 tetrahedra that can be directly synthesized with a considerably high Si/Al ratio. Its high acidity, thermal stability, and hydrothermal stability and the ease by which relatively large molecules can diffuse through the channels make this a very interesting material from the perspective of developing new catalytic zeolites.  
Other supports used with the same propose are the mesoporous MCM-41 (Mobil Composition of Matter 41) solids. These supports represent a new platform because their morphological characteristics and pore diameters of between 2 and 50 nm allow the introduction of compounds with greater steric hindrance into the cavities. The solids [Si]-MCM-41 and [Si,Al]-MCM-41 [9] have high thermal stability and a hexagonal arrangement of pores with linear and parallel channels and are constructed with a beehive-type silica matrix. Use of MCM-41 as support of several metal complexes that are catalysts of ethylene, propylene or 1-hexene oligomerization reactions was described in the literature [6, 10, 11, 12, 13, 14]. In all cases, the reported oligomer selectivity was affected by the presence of MCM-41.  
We have used ionic liquids as solvents in several types of catalytic reactions (biphasic catalysis) [15,16]. Recently, a new type of tether was described in the literature in which the complex is anchored to the ionic liquid that is supported on mesoporous silica; this technique has been employed in hydroformylation [17, 18, 19], carbonylation [20], hydrogenation [21], Heck [22] and epoxidation [23] reactions.  
In this work, a nickel-\(\beta\)-dimine complex was immobilized on \(\beta\)-zeolite, [Si]-MCM-41 and [Si,Al]-MCM-41 modified with the tetrafluoroborate of 1-(3-trimetoxisillpropil)-3-methylimidazolium ionic liquid in the presence of the tetrafluoroborate of 1-butyl-3-methylimidazolium (BMI.BF4). The catalyst obtained was used in ethylene oligomerization reactions.