Gradient copolymer

In the gradient copolymer, there is a continuous change in monomer composition along the polymer chain (see Figure 2). This change in composition can be depicted in a mathematical expression. The local composition gradient fraction ${\displaystyle g(X)}$ is described by molar fraction of monomer 1 in the copolymer ${\displaystyle (F_{1})}$ and degree of polymerization ${\displaystyle (X)}$ and its relationship is as follows:[6]

${\displaystyle g(X)={\frac {dF_{1}(X)}{dX}}}$

The above equation supposes all of the local monomer composition is continuous. To make up for this assumption, another equation of ensemble average is used:[6]

${\displaystyle F_{1}^{(loc)}(X)={\frac {1}{N}}\sum _{i=1}^{N}F_{1,i}(X)}$

The ${\displaystyle F_{1}^{(loc)}(X)}$ refers ensemble average of the local chain composition, ${\displaystyle X}$ refers degree of polymerization, ${\displaystyle N}$ refers number of polymer chains in the sample and ${\displaystyle F_{1,i}(X)}$ refers composition of polymer chain i at position ${\displaystyle X}$.

This second equation identifies the average composition over all present polymer chains at a given position, ${\displaystyle X}$.[6]

Prior to the development of controlled radical polymerization (CRP), gradient copolymers (as distinguished from statistical copolymers) were not synthetically possible. While a "gradient" can be achieved through compositional drift due to a difference in reactivity of the two monomers, this drift will not encompass the entire possible compositional range. All of the common CRP methods[8] including atom transfer radical polymerization and Reversible addition−fragmentation chain transfer polymerization as well as other living polymerization techniques including anionic addition polymerization and ring-opening polymerization have been used to synthesize gradient copolymers.[6]

The gradient can be formed through either a spontaneous or a forced gradient. Spontaneous gradient polymerization is due to a difference in reactivity of the monomers. The resulting change in composition throughout the polymerization creates an inconsistent gradient along the polymer. Forced gradient polymerization involves varying the comonomer composition of the feed being throughout the reaction time. Because the rate of addition of the second monomer influences the polymerization and therefore properties of the formed polymer, continuous information about the polymer composition is vital. The online compositional information is often gathered through automatic continuous online monitoring of polymerization reactions, a process which provides in situ information allowing for constant composition adjustment to achieve the desired gradient composition.

The wide range of composition possible in a gradient polymer due to the variety of monomers incorporated and the change of the composition results in a large variety of properties. In general, the glass transition temperature (Tg) is broad in comparison with the homopolymers. Micelles of the gradient copolymer can form when the gradient copolymer concentration is too high in a block copolymer solution. As the micelles form, the micelle diameter actually shrinks creating a "reel in" effect. The general structure of these copolymers in solution is not yet well established.

The composition can be determined by gel permeation chromatography(GPC) and nuclear magnetic resonance (NMR). Generally the composition has a narrow polydispersity index (PDI) and the molecular weight increases with time as the polymer forms.

• Mechanically gradient polymers

• http://torkelson.northwestern.edu/Research/GCP/gcp.html
• http://www.cmu.edu/maty/materials/index.html