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signals arising from the source [41,43,44]. The array response is steered by forming a linear combination of the element outputs, as will be shown mathematically later. The Pattern of the Antenna Array. In an antenna array, if the distance between the elements-sensors is larger than the wavelength of radiation, several main lobes will be formed in the visible space. Conversely, if the element spacing is less than a wavelength, and all signals from elements are summed without any delay (see Fig. 9.2), then the produced array output signal will have a symmetric pattern about y 0 (see Fig. 9.4a). On the contrary, if in this case the output of each element is

public class Customer { private string m_Name; public string Name { get { return m_Name; } set { m_Name = value; } } private string m_ID; public string CustomerID { get { return m_ID; } set { m_ID = value; } } public List<Customer> GetCustomers() { List<Customer> results = new List<Customer>(); CustomersTableAdapter adapter = new CustomersTableAdapter(); CustomersDataSetCustomersDataTable custs = adapterGetData(); foreach (CustomersDataSetCustomersRow row in custs) {

B group) units and fewer dendritic (no unreacted B groups) units. The polydispersity in molecular weight and isomerism, the intramolecular cyclization, and the molecular shape variations due to steric crowding contribute to the random nature of hyperbranched polymers. Hyperbranched polymers can also be synthesized from the following systems [Jikei and Kakimotoa, 2001]:

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The AB2 AB system is equivalent to AB2 except that AB2 units are separated from each other by AB units. The AB2 B3 system modi es the AB2 system by using B3 as a central core from which polymerization radiates and offers greater control of molecular shape. The A2 B3 system is one of the standard systems used to produce crosslinked polymers (Sec. 2-10). It is useful for synthesizing hyperbranched polymers only when crosslinking is minimized by limiting conversion and/or diluting the reactants with solvent. Hyperbranched polymers can also be synthesized by chain polymerization, ring-opening polymerization, and combinations of ring-opening and step polymerization [Kim, 1998; Voit, 2000] (Secs. 3-6e, 3-15b-4, 3-15b-5, 3-15c, 5-4c).

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Dendrimers are dendritic (highly branched) polymers with a more controlled structure than the hyperbranched polymers [Bosman et al, 1999; Fischer and Vogtle, 1999; Grayson and Frechet, 2001; Hecht, 2003; Newkome et al, 1999; Simanek and Gonzalez, 2002; Tomalia, 2001; Tomalia and Frechet, 2002; Vogtle et al, 2000] Other terms have also been used to describe various dendritic polymers arborol, cascade, cauli ower, starburst The synthesis of dendrimers differs greatly from the one-pot proces for hyperbranched polymers Dendrimers are synthesized by more complicated processes involving sequential reactions There are two different methods: divergent and convergent The divergent method starts with a core molecule and builds outward by attaching to the core successive layers (or generations) of monomer units one at a time A large variety of reactions (organometallic as well as organic) have been used in synthesizing dendrimers The divergent method is illustrated in Fig.

d (a)

2-22 for the synthesis of polyamidoamine (PAMAM) dendrimers [Tomalia et al, 1990] A repetitive sequence of two reactions are used the Michael addition of an amine to an a,b-unsaturated ester followed by nucleophilic substitution of ester by amine Ammonia is the starting core molecule The rst step involves reaction of ammonia with excess methyl acrylate (MA) to form LXIII followed by reaction with excess ethylenediamine (EDA) to yield LXIV LXV is a schematic representation of the dendrimer formed after four more repetitive sequences of MA and EDA Dendrimers are characterized by the number of generations, the number of layers or shells of repeat units, analogous to the layering of an onion The number of generations is the number of repetitive sequences of the Michael addition and nucleophilic substitution reactions LXIV and LXV correspond to generations 1 and 5, respectively LXIV has three arms or three NH2 groups.

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Each generation doubles the number of arms or NH2 groups The fth-generation dendrimer (LXV) has 48 arms or NH2 groups..

Customer c = new Customer(); cName = rowCompanyName; cCustomerID = rowCustomerID; resultsAdd(c); } return results; } }

The convergent method of dendrimer synthesis is shown in Fig. 2-23 for a dendrimer of ve generations. Dendrimeric fragments are synthesized by repetitive reactions, and then several (three for the dendrimer in Fig. 2-23) are joined together in the last step by using a central core molecule to form the dendrimer. The method requires the use of appropriate reactants and chemical reactions. The functional group Z has an identity such that smaller fragments can be linked together to form a larger fragment, either by direct reaction with each other or with a coupling agent. The larger fragment also has a Z group because of the choice of appropriate reactants or coupling agent, and the linking of fragments continues in a repetitive manner. In some systems Z is a protected functional group that is deprotected at the appropriate time.

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