Considering the general composition of a RAFT polymer, the average number of monomer units per polymer chain (degree of polymerisation, DPn) and therefore the
(number) average molar mass of the polymer (Mn) may be inferred from the ratio of consumed monomer to CTA, as shown in equations 1.1 and 1.2:
Where [M]0 is the initial monomer concentration; p is the monomer conversion; [CTA]0 is the initial concentration of CTA; n is the number of radicals generated by one initiating species (for example, an azoinitiator thermally decomposes to generate two initiating radicals, so n would equal 2); f is the initiator efficiency; [I]0 is the initial concentration of initiator; kd is the decomposition rate coefficient of the initiator; the term (1-fc/2) describes the average number of chains generated in a radical-radical termination event, where fc is the
DP𝑛= M 0 . 𝑝 CTA 0 + n𝑓 I 0 1 − e−𝑘d𝑡 1 −𝑓2 c 𝑀n,th= M 0 . 𝑝 . 𝑀M CTA 0 + n𝑓 I 0 1 − e−𝑘d𝑡 1 −𝑓2 c + 𝑀CTA 1.1 1.2
Page | 5 coupling factor; MM and MCTA are the molar masses of the monomer CTA, respectively. Provided that the number of initiator-derived chains is negligible in comparison to CTA- derived chains the equations 1.1 and 1.2 may be simplified to equations 1.1b and 1.2b. However, while the ratio of CTA/monomer dictates the average molar mass of the resulting polymeric population, the nature of the CTA is crucial since this will influence how well- defined the population is in terms of molar mass distribution.
DP𝑛= M 0 . 𝑝 CTA 0 𝑀n,th= M 0 . 𝑝 . 𝑀M CTA 0 + 𝑀CTA 1.1b 1.2b
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1.3.3 – Control of molar mass distribution
In order to ensure control over the molar mass distribution two principal criteria must be satisfied in the RAFT mechanism. Firstly, the pre-equilibrium step should proceed rapidly and quantitatively towards R• (which should then react efficiently with monomer). Secondly, exchange of radical centres between polymer chains should be rapid relative to the rate of propagation. These criteria may be met through careful consideration of the R- and Z- groups of the RAFT agent relative to the monomer of choice. The nature of the Z-group determines the reactivity of the C=S bond towards addition and fragmentation.54 For a well-controlled RAFT polymerisation, the rate at which the polymeric radicals add to the thiocarbonylthio moiety should be greater than the rate at which they propagate (kaddP >> kp), allowing chains to grow at a more uniform rate. The reactivity of a CTA is expressed in terms of its chain transfer coefficient (Ctr) which describes the relative rates of chain transfer (ktr) to propagation (kp), and is shown in equation 1.3:
The rate constant of transfer (ktr), which is described in equation 1.4, is dependent on the addition-fragmentation behaviour during the pre-equilibrium. The term ϕ, which is introduced in equation 1.5, describes the tendency for the pre-equilibrium to proceed towards the formation of R•. A number of different Z-group structures have been employed in RAFT polymerisation, such as dithioesters, trithiocarbonates, xanthates and dithiocarbamates.55, 56 The two latter examples are less reactive towards radical addition and are therefore better suited for the control of highly reactive propagating radicals, derived from monomers such as vinyl esters and vinyl amides.57, 58 Meanwhile, for less reactive propagating radicals, derived from monomers such as (meth)acrylates, (meth)acrylamides and styrenic derivatives, the more active CTAs such as dithioesters and trithiocarbonates are preferred to ensure Ctr is high.41, 59, 60 A range of Z-group structures are shown in Scheme 1.2, in order of their reactivity towards radical addition.
𝐶tr = 𝑘tr 𝑘p 𝑘tr= 𝜙𝑘add 1.3 1.4
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Scheme 1.2 – Structures of various Z-groups used in RAFT polymerisation; addition rates
decrease and fragmentation rates increase from left to right. * are used to highlight the activated
(pyridinium) and deactivated (pyridine) forms of a switchable N-methyl-N-(4-pyridinyl) dithiocarbamate
RAFT agent.
As previously stated, the pre-equilibrium step should proceed rapidly and to completion in order for main equilibrium to begin. This requires that fragmentation of the intermediate radical 2 proceeds preferentially towards the CTA-derived R-group radical R• (kβ) as opposed to the polymeric radical Pn• (k-add), and that this favoured R• radical may efficiently add with monomer (kiR > kp), thereby exiting the pre-equilibrium. The tendency for fragmentation of intermediate 2 towards R• is defined by the partition coefficient, ϕ, according to equation 1.5:
Where the rate constants are defined in Scheme 1.1. For the pre-equilibrium to proceed towards the desired products (R• and 3), ϕ should be ≥ 0.5 (kβ > k-add) which dictates that R• must be a better homolytic leaving group than Pn
•
. Radical stability, polarity and steric effects will impact the leaving group ability of R• relative to Pn• as well as its efficiency for adding to monomer, and therefore must be carefully considered with respect to the monomer used.61 Many different R-groups have been reported representing a spectrum of leaving group ability (Scheme 1.3).55, 56 The broad range of both R- and Z-group chemistries enables the behaviour of a RAFT agent to be readily tuned and it is this versatility that affords
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𝜙 = 𝑘𝛽 𝑘−𝑎𝑑𝑑+ 𝑘𝛽 1.5Page | 8 control over such an impressive range of monomer types compared to other RDRP approaches.
Scheme 1.3 – Structures of various R- groups used in RAFT polymerisation; the homolytic
leaving group ability (kβ) decreases from left to right.
Fortunately, the influence of the R- and Z- group in RAFT polymerisation has been extensively reviewed and general guidelines for selecting an appropriate RAFT agent based on monomer type are available.54-57, 61