1.2 Introduction to DNA copolymers
Polymers and their basic properties are at first shortly introduced.
A polymer is defined as a macromolecule which consists of several monomer units. The words of the president of the Royal Society and 1957 Nobel Prize Laureate, Lord Todd, uttered almost 35 years ago –“I am inclined to think that the development of polymerization is perhaps the biggest thing chemistry has done, where it has had the biggest effect on everyday life. The world would be a totally different place without artificial fibers, plastics, elastomers, etc. Even in the field of electronics, what would you do without insulation? And there you come back to polymers again”, seems to accurately present the importance of the polymer field in the technological progress . Polymers are ubiquitous, they can be found in natural material such as wood or shellfish shell as well as in synthetic materials such as gels and plastics .
Depending on the type and repeating unit, polymers can be divided in [28, 30, 31] (Figure 1-1);
1. Homopolymers, along which all monomer units are of the same composition (A being a monomer)
2) Copolymers, which are composed of a mixture of at least two monomers. In the class of copolymer, four classes can be distinguished;
a) Random (statistical), along which the sequence of polymer is incidental -A-A-A-B-A-B-A-A-B-B-A-B-B-B-
Notation of such a polymer includes stat or ran between the monomer names, e.g. poly(A-stat-B) or poly(A-ran-B)
b) Alternating, a regular pattern of the monomers can be found in the sequence -A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-
c) Block, when a continuous sequence of each monomer is implemented in the structure --A-A-A-A-A-A-A-A-A-B-B-B-B-B-B-B-B-B-B-A-A-A-A-A-A-A-A-A-A-
d) Graft, when the copolymer is branched, being composed of different building blocks in the backbone and in the side chain
Figure 1-1. Polymer configurations A) homopolymer, B) block copolymer, C) graft copolymer, D) random/statistical copolymer 
As a consequence of the polymerization process throughout which the chain growth is controlled by the availability of monomers, polymers molecular mass vary greatly from the chemistry of low molecular mass molecules. Polymers are regarded as polydisperse. In order to define the molecular mass of polymers, two definitions are commonly used;
The number average molar mass; defined as the ratio of Mw/Mn. Ideally a monodisperse polymer would have a polydispersity index value equal to one . Generally, molecular weights of polymers vary between 1000 and 106 Da.
The solvent choice is crucial. In a good solvent a chain expands to maximize interactions with solvent molecules. In this case the chain is swollen. In a poor solvent the chain minimizes the interactions with solvent molecules through chain contraction. In a so called theta solvent, these two effects are ideally balanced and polymer chains is in an unperturbed conformation [29, 32].
The conformation of solubilized chains depends on segment-segment and segment-solvent interactions. The radius of gyration (Rg) is the basic parameter which describes the polymer size. Rg averages the distance of a chain block from the center of mass of the coil [29, 33, 34];
14 𝑅𝑔 = 𝑅
Where, R is the average end-to-end distance, related to the length (l) of independent subunits through the following equation;
𝑅 = 𝑙√𝑁 Equation 4
Where, N is the total number of the monomer subunits.
Each independent subunit is composed of few monomers, exceeding the length lo of a single monomer l˃lo. The parameter which is related to the length of independent subunits is the Kuhn’s length l. In the example depicted in the figure below (Figure 1-2), the Kuhn’s length is equal to 4 monomers. Equation 3 is valid only in a theta solvent. The radius of gyration can be obtained from scattering measurements.
Figure 1-2. Difference between monomer length lo and the Kuhn’s length l
188.8.131.52 Block copolymers
Owing to constant developments in synthetic strategies, a broad library of block configurations has been achieved. Figure 1-3 depicts representative macromolecular configurations which can be classified taking under consideration two parameters; a) the number of chemically different moieties and b) linear versus branched sequencing. Linear configuration A-B, where A monomer is covalently bounded to monomer B is considered as the most common and the most explored category of block copolymers. Due to thermodynamic incompatibility, segments A and segments B gather in A-B diblock self-assembly where the analogous blocks maximize the contact in contrary to the blocks which are dissimilar . Nevertheless, macrophase separation is limited by entropic forces resulting from covalent linkage. As a consequence, the structure results from the equilibrium between repulsive and attractive forces. The free energy cost of contact between distinct segments is described by the temperature-dependent Flory-Huggins interaction parameter χAB. In bulk or solid state, constituent segments undergo self-assembly forming regularly-shaped and uniformly-sized compartments which are periodically distributed . The degree of polymerization N and relative composition fractions fA and fB where fA=NA/N and fA+fB=1 are two supplementary parameters which are determining the morphology of the system created by microphase separation . Over a certain critical molecular weight usually polymers are incompatible if there is no strong intermolecular interaction like hydrogen bonding or electrostatic attraction, which illustrates the delicate minimization of the free-energy. Figure 1-4 depicts equilibrium morphologies of diblock copolymers. The body-centered cubic spherical phase is formed when the content of the minority block reaches around 20%. At a volume fraction of ~30% of the minority block in a matrix of the majority block, hexagonally packed cylinders are formed. When the volume fraction of one segment reaches 38%, gyroid
or perforated layers are formed depending on the incompatibility degree. Roughly equal volume fraction of two segments leads to alternating lamellae . Morphological transitions mentioned above were obtained both experimentally [37-40] as well as by statistical thermodynamics theories [41-44].
Figure 1-3. BCs can be arranged into almost countless number of molecular structures composed of two, three or more monomer types. In the picture above structures are divided according to monomer type and linear versus branched sequencing. Different colors (A, B and C shown as green, orange and blue, respectively) stand for the same monomer type. A copolymer is represented by a joined linear sequence of monomers. The colored strands are joined as shown to form the block copolymer macromolecule. Typical monomer length scale is sketched in the upper-left inset 
ABC or other multicomponent molecular systems are obtained when three or more monomers are used in the synthesis procedure. These numerous synthetic strategies allow arranging multiple monomers in branched architectures (Figure 1-3). Alterations in morphology as well as in properties might be induced by slight modifications in the molecular topology like for
copolymers ABC can also self-assemble in the bulk state giving rise to even higher number of segregation patterns, being some of them visually wondrous and complex. Tetra and pentablocks self-assembled morphology patterns number should increase, however because of challenges in synthesis such structures were rarely reported .
In comparison to the bulk state, copolymers also self-assemble in a block-selective solvent, which is dissolving just one of the segments, giving birth to different morphologies, as will be discussed in the next subsection.
Figure 1-4.Thermodynamically stable segregation patterns .Two-color chain represents the A–B diblock copolymer. Structure is determined by the relative lengths of the two polymer blocks (fA). (Figure adapted with permission of Elsevier)