#### Polymerization Kinetics: Screencast

Describes the reaction steps in addition polymerization, using free radical polymerization as an example.

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An introduction to step-growth polymerization.

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Calculates the number-averaged and weight-averaged molecular weights of a polymer, along with its polydispersity.

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##### Important Equations:

\(P_j\) = concentration of polymer with \(j\) monomer units

\(j\) = number monomer units in the polymer

\(\overline{M_n} = MW_m \dfrac{\sum_j jP_j}{\sum_j P_j} = MW_m \dfrac{\Gamma_1}{\Gamma_0} =\) number average molecular weight

\(\overline{M_w} = MW_m \dfrac{\sum_j j^2P_j}{\sum_j jP_j} = MW_m \dfrac{\Gamma_2}{\Gamma_1} =\) weight average molecular weight

\( \overline{MW_m}\) = molecular weight of monomer

\(\Gamma_0 = \sum_j P_j =\) zero moment of distribution

\(\Gamma_1 = \sum_j jP_j =\) first moment of distribution

\(\Gamma_2 = \sum_j j^2P_j = \) second moment of distribution

\(PD = \dfrac{\overline{M_w}}{\overline{M_n}} = \dfrac{\Gamma_2 \Gamma_0}{\Gamma_1 ^2} =\) polydispersity

\(\overline{DP} = \dfrac{\overline{M_n}}{MW_m} =\) degree of polymerization

\(\overline{DP} =\) average number of repeat units (i.e., average number of monomers in a polymer

Alternate ways to express average molecular weights

\(\overline{M_n} = \sum x_i (iMW_m)\)

\(x_i\) = mole fraction of polymer \(i\)

\(\overline{M_w} = \sum w_i (iMW_m)\)

\(w_i\) = weight fraction of polymer \(i\)

Addition polymerization

\[r_p = k_p \left( \frac{f\,k_d}{k_t} \right) [I_2]^{\frac{1}{2}} [M]\]

where \(r_p\) = rate of polymer formation

\(k_p\) = rate of constant for propagation

\(f\) = initiator efficiency (number less than one)

\(k_d\) = rate constant for dissociation of initiator

\(k_t\) = rate constant for termination

\( [I_2] \) = concentration of initiator

\( [M] \) = concentration of monomer