The present invention relates to branched polymers and methods of preparing them. In particular the present invention relates to polymers prepared by non free radical reactions involving controlled chain growth polymerisation. The reactions can involve the polymerisation of vinyl-containing monomers. Alternatively the reactions can involve other types of controlled chain growth polymerisation including ring opening polymerisation of cyclic monomers such as for example lactones.

Many different types of branched polymers, and many different ways of preparing branched polymers, are known.

Some branched polymers are cross-linked or gelled, whereas others are soluble and non- gelled. The present invention is generally concerned with polymers which fall within the latter group.

The properties and potential applications of branched polymers are governed by several characteristics including the architecture of the polymers, the type of monomers from which they are made, the type of polymerisation, the level of branching, the functional groups on the polymers, the use of other reagents, and the conditions under which polymerisation is carried out. These characteristics can in turn affect the hydrophobicity of the polymers or parts of them, viscosity, solubility, and the form and behaviour of the polymers on a nanoparticulate level, in bulk and in solution.

Various methods have been used to achieve controlled levels of branching within vinyl polymers in order to avoid extensive cross-linking and gelation. There has been extensive activity in the area of free radical polymerisation. For example, the“Strathclyde route”, as described in N. O’Brien, A. McKee, D.C. Sherrington, A.T. Slark, A. Titterton, Potymer20Q0, 41, 6027-6031 involves the controlled radical polymerisation of predominantly monofunctional vinyl monomer in the presence of lower levels of difunctional (di)vinyl monomer and chain transfer agent. In other methods, the use of controlled or living polymerisation removes the need for chain transfer agent. In general, gelation can be avoided if a vinyl polymer made from predominantly a monofunctional monomer is branched by virtue of a difunctional vinyl monomer so that there is on average one branch or fewer per vinyl polymer chain, as disclosed, for example, in WO 2009/122220, WO 2014/199174 and WO 2014 199175. As a result of further experimentation and investigations using various polymerisation methods and conditions, we have now discovered a new method of polymerisation which is surprisingly effective, which results in a new type of polymer architecture and which addresses several of the issues associated with known polymerisation methods.

From a first aspect the present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a multifunctional monomer in the presence of an initiator, wherein the extent of polymerization of multifunctional monomer is controlled relative to the extent of reaction of multifunctional monomer with initiator, to prevent gelation of the polymer.

By“multifunctional monomer” we mean that the monomer has more than one site at which polymerisation may occur. Thus, for example, in the case of vinyl polymerisation the multifunctional monomer is a multivinyl monomer (MVM), i.e. a monomer which has more than one polymerisable double bond. A subset of multivinyl monomers is divinyl monomers (DVMs), i.e. monomers which have two polymerisable double bonds. In the case of ring- opening polymerisation (ROP) the multifunctional monomer is a monomer which has a plurality of, e.g. two, rings (e.g. lactones, amongst other possibilities), the ring-opening of which propagates polymerisation.

Thus, because each (multifunctional) monomer can be polymerised at (at least) two sites, each monomer residue can be present within not just one polymer chain but more than one polymer chain. The multifunctional monomer can therefore act as a brancher. The default situation is that the multifunctional monomer will act as a brancher unless there is residual unreacted functionality (e.g., in the case of vinyl polymers, unreacted double bonds in the product even after vinyl polymerisation) or unless the functionality reacts with some other material, e.g. initiator or impurities or other material in the system.

The brancher thus acts as a bridger, i.e. forms a bridge between the polymer chains.

One or more multifunctional monomer may be used, for example a mixture of difunctional monomers or a mixture of difunctional monomer(s) with tri- and/or higher functional monomer(s).

The polymerisation is controlled. Monomer residues are incorporated under controlled conditions whereby polymerisation does not occur to such an extent that excessive crosslinking occurs; branching is controlled so that gelation does not occur. This can be achieved by titration of multifunctional monomer into initiator.

Thus, for example, a reaction vessel can be provided with initiator and optionally other material e.g. solvent, and/or other material, e.g. a catalyst to activate the initiator. The initiator or reactive species formed from the initiator may be, and commonly is, a very reactive species. Accordingly, if appropriate the reaction may be carried out under inert conditions, e.g. after heating the vessel, sealing, and/or purging with inert gas. Multifunctional monomer may then be added to the reaction vessel. This may be done slowly (e.g. dropwise, if under laboratory conditions). This will typically mean that, at least at the start of the reaction, there will be an excess of initiator relative to multifunctional monomer, such that multifunctional monomer will react with initiator in preference to the formation of polymer chains. Sufficient multifunctional monomer may be added so as to achieve the desired structure and desired level of reaction and branching, without adding so much as to cause gelation.

It will be understood that the reaction vessel could be a reactor of any suitable kind. The skilled person will understand that at industrial scale various types of reactor including batch or continuous may be used. An important feature of the present invention is that the polymerisable monomer is added to the initiator, regardless of what form the reactor takes.

Thus, the present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a multifunctional monomer in the presence of an initiator, wherein a reactor is charged with initiator or wherein initiator is generated in situ in said reactor, and wherein multifunctional monomer is added to said initiator so that the extent of polymerization of multifunctional monomer is controlled relative to the extent of reaction of multifunctional monomer with initiator.

The present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a multifunctional monomer in the presence of an initiator, wherein a reactor is charged with initiator or wherein initiator is generated in situ in said reactor, and wherein multifunctional monomer is added to said initiator so that the extent of polymerization of multifunctional monomer is controlled relative to the extent of reaction of multifunctional monomer with initiator, to prevent gelation of the polymer.

Thus, cross-linking and insolubility are avoided by controlling the way in which a difunctional monomer, or other multifunctional monomer, reacts.

Consistent with certain theoretical considerations regarding numerical relationships between amounts of initiator and amounts of multifunctional monomer, as discussed in more detail below, and in particular relating to ways of avoiding gelation of the product, we have found that certain ratios work particularly effectively.

Thus, for example, where the multifunctional monomer is a difunctional monomer, 0.5 to 2 equivalents of difunctional monomer may be added per equivalent of initiator. This may optionally be 0.75 to 1.5, 0.85 to 1.2, 0.85 to 1.1 , 0.85 to 1 , 0.9 to 1 , 0.95 to 1 , 0.98 to 1 , 0.99 to 1 , up to 1 , less than 1 , or about 1 equivalents of difunctional monomer per equivalent of initiator.

Where the multifunctional monomer is a trifunctional monomer, 0.33 to 1 equivalents of trifunctional monomer may be added per equivalent of initiator. This may optionally be 0.33 to 0.75, 0.4 to 0.7, 0.4 to 0.6, 0.4 to 0.55, 0.45 to 0.5, 0.48 to 0.5, 0.49 to 0.5, up to 0.5, less than 0.5, or about 0.5 equivalents of trifunctional monomer per equivalent of initiator

Where the multifunctional monomer is a tetrafunctional monomer, 0.25 to 0.67 equivalents of tetrafunctional monomer may be added per equivalent of initiator. This may optionally be 0.28 to 0.5, 0.3 to 0.4, 0.3 to 0.35, 0.3 to 0.33, 0.31 to 0.33, 0.32 to 0.33, up to 0.33, less than 0.33, or about 0.33 equivalents of tetrafunctional monomer per equivalent of initiator.

The skilled person will however understand that the conditions, in particular the level of dilution, can influence the reaction and hence the amount of monomer per initiator in non- gelled products.

The skilled person will also understand that different types of monomer and/or different levels of functionality (e.g. combinations of di- with tri- and/or tetra- or other combinations) may be used. The relative amounts of multifunctional monomer and initiator can be adjusted accordingly.

The polymerisation may be living. The chain ends may remain active throughout the process. There are two notable ramifications of this.

A first ramification of the living polymerisation is that termination will not necessarily occur in the absence of impurities or other materials or certain conditions; therefore the process can be tailored by choosing the amount of multifunctional monomer to add, and termination can be carried out when desired, by the addition of a species which can react with the active chain ends. The second ramification of the living polymerisation is that post functionalisation can be carried out. This active chain ends can react with various compounds to add functionality (in one example - as exemplified herein - reaction with epoxides can yield hydroxy-functionalised materials) prior to, or as part of, termination of the reaction. Such reaction is different from mere termination of the reaction because it adds a further moiety to the product rather than for example merely quenching (the latter, in the case of anionic vinyl polymerisation for example, typically comprising incorporation of protons).

The titration method of the present invention means that specific amounts of polymerisable monomer are added to initiator until a desired level of reaction has occurred. This brings about structures of particular characteristics which can be measured and monitored. In some cases a visual change is observed. The addition may take place slowly. The process allows considerable tuning, monitoring and reproducibility. For a particular set of reagents and conditions, appropriate ratios can be determined without undue burden.

The polymerisation may be vinyl polymerisation.

The vinyl polymerisation may be anionic vinyl polymerisation. This relies on the use of an initiator which is an anion, for example a carbanion. Sources of carbanionic initiator may include for example alkyllithium reagents, e.g. butyl lithium, e.g. sec-butyl lithium.

The vinyl polymerisation may be oxyanionic vinyl polymerisation. This relies on the use of an initiator which is oxyanionic. The oxyanion may for example be an organic oxyanion which has been formed (optionally in situ) from an alcohol. Sources of oxyanionic initiator may include for example alkoxy potassium compounds, e.g. compounds formed in situ from the reaction of potassium tert-butoxide with an alcohol e.g. benzyl alcohol.

The polymerisation may be ring-opening polymerisation (ROP).

The ring-opening polymerisation may comprise the opening of rings such as for example lactones, lactams, cyclic ethers or cyclic amines using a suitable initiator.

ROP can result in functionality which can act as cleavable sites (e.g. esters) and therefore the resultant products can be degradable.

The polymer contains a multiplicity of polymer chain segments, and controlling the amount or rate of propagation relative to the incorporation of initiator affects the average length of those polymer chains. Therefore, from a further aspect the present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a multifunctional monomer in the presence of an initiator, wherein the extent of polymerization of multifunctional monomer is controlled relative to the extent of reaction of multifunctional monomer with initiator, to achieve a polymer having a multiplicity of polymer chain segments wherein the average number of multifunctional monomer residues per primary polymer chain is between 1 and 3.

The multifunctional monomer may be a difunctional monomer.

Therefore, from a further aspect the present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a difunctional monomer in the presence of an initiator, wherein the extent of polymerization of difunctional monomer is controlled relative to the extent of reaction of difunctional monomer with initiator, to achieve a polymer having a multiplicity of polymer chain segments wherein the average number of difunctional monomer residues per primary polymer chain is between 1 and 3.

The multifunctional monomer may be a trifunctional monomer, or higher.

Therefore, from a further aspect the present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a trifunctional monomer in the presence of an initiator, wherein the extent of polymerization of trifunctional monomer is controlled relative to the extent of reaction of trifunctional monomer with initiator, to achieve a polymer having a multiplicity of polymer chain segments wherein the average number of trifunctional monomer residues per primary polymer chain is between 1 and 2.

The skilled person is able to control the propagation reaction relative to the incorporation of initiator by known techniques. This may be done by controlling the amount of multifunctional monomer added and by the termination. The initiator is present in a considerable amount and accordingly can contribute to the chemistry of the structure. Various initiators are suitable and of low cost, and impart versatility to the method and resultant product.

The primary chains (of the polymer) are kept very short so that gel formation is avoided, whilst at the same time a high level of branching is achieved.

Optionally the only reagents used in the method of the present invention are one or more multifunctional monomer (for example a difunctional monomer), an initiator, optionally a solvent, and optionally, at the end of the process, material for terminating the reaction (e.g., in the case of anionic vinyl polymerisation, a source of protons). Thus the present invention allows the homopolymerisation of multifunctional monomers.

Monofunctional monomers are not required in the method of the present invention.

Optionally, however, monofunctional monomers may be used, i.e. optionally a copolymerisation may be carried out. For example, the method may comprise the incorporation of not only a difunctional monomer but also an amount, optionally a lesser amount, of monofunctional monomer. The molar amount of difunctional monomer relative to monofunctional monomer may be greater than 50%, greater than 75%, greater than 90% or greater than 95%, for example. Optionally, the ratio of difunctional monomer residues to monofunctional monomer residues may be greater than or equal to 1 : 1 , or greater than or equal to 3: 1 , greater than or equal to 10: 1 or greater than or equal to 20: 1.

Alternatively, in some scenarios, more monofunctional monomer may be used. Optionally, the method may comprise the incorporation of not only one or more difunctional monomer but also monofunctional monomer, wherein for example 20% or more, 30% or more, 40% or more, 50% or more, 60% or more, 70% or more, 80% or more, 90% or more, or 95% or more, of the functional monomers used are difunctional monomers. Optionally, the method may comprise the incorporation of not only one or more difunctional monomer but also monofunctional monomer, wherein for example 20% or more, 30% or more, 40% or more, 50% or more, 60% or more, 70% or more, 80% or more, 90% or more, or 95% or more, of the functional monomer residues in the product are difunctional monomer residues.

The possible incorporation of monofunctional monomers is applicable not just with difunctional monomers but also with other types of multifunctional monomers. Accordingly, the method may comprise the incorporation of not only one or more multifunctional monomer but also monofunctional monomer, wherein for example 10% or more, 20% or more, 30% or more, 40% or more, 50% or more, 60% or more, 70% or more, 80% or more, 90% or more, or 95% or more, of the functional monomers used are multifunctional monomers. Optionally, the method may comprise the incorporation of not only one or more multifunctional monomer but also monofunctional monomer, wherein for example 10% or more, 20% or more, 30% or more, 40% or more, 50% or more, 60% or more, 70% or more, 80% or more, 90% or more, or 95% or more, of the functional monomer residues in the product are multifunctional monomer residues. The monofunctional monomer may optionally be incorporated as a block. For example, as exemplified herein, one or more multivinyl monomer (e.g. a divinyl monomer) may first be added to an initiator, and then subsequently a monovinyl monomer may be added. Or, in the case of ring-opening polymerisation, one or more multifunctional monomer (e.g. a difunctional monomer, i.e. a monomer containing two connected rings each of which is suitable for or susceptible to ring-opening polymerisation) may first be polymerised, and then subsequently a monomer containing one ring which is suitable for or susceptible to ring- opening polymerisation may then be polymerised. Conversely the monofunctional monomer may be added first and then a multifunctional monomer (or more than one type of multifunctional monomer) subsequently. Alternatively the procedure may be copolymerisation, e.g. statistical copolymerisation, rather than block copolymerisation.

Thus, in accordance with the present invention, either sequential polymerisation of different types of monomer, or copolymerisation (e.g. statistical polymerisation) of different types of monomer, or both, is possible. The different types of monomer may include monofunctional monomer as well as multifunctional monomer (including possibly different types of multifunctional monomer).

Anionic and oxyanionic polymerisations using divinyl monomers

One type of polymerisation which is of particular interest is anionic (which includes oxyanionic) vinyl polymerisation. In this context, “multifunctional monomer” should be understood as“multivinyl monomer” and“difunctional monomer” should be understood as “divinyl monomer”.

The divinyl monomer contains two double bonds each of which is suitable for anionic polymerisation. It may contain one or more other group which may optionally be substituted, subject to the monomer being compatible with anionic polymerisation conditions.

Each vinyl group in the divinyl monomer may for example be an acrylate, methacrylate, vinyl aliphatic, or vinyl aromatic (e.g. styrene) group.

Due to the large amount of initiator in the reaction, the vinyl polymer chains in the final product are generally quite short and the chemistry of the longest chains in the polymer may be governed by the other chemical species in the monomer. Thus, for example, monomers which contain, in addition to two vinyl groups, ester linkages [e.g. dimethacrylates, such as ethylene glycol dimethacrylate (EGDMA)] polymerise to form polyester structures, wherein the longest repeating units comprise esters. Thus the present invention opens up new ways of making polyesters or other polymers, allowing the formation of different types of architecture to those previously considered possible.

Optionally a mixture of divinyl monomers may be used. Thus two or more different divinyl monomers may be copolymerised.

Other types of multivinyl monomer

Multivinyl monomers other than divinyl monomers may be used, for example, trivinyl monomers, tetravinyl monomers and/or monomers with more vinyl groups. Trivinyl monomers, in particular, are useful, as they can be sourced or prepared without significant difficulty, and allow further options for producing different types of branched polymers. The discussion, disclosures and teachings herein in relation to divinyl monomers also apply where appropriate, mutatis mutandis, to other multivinyl monomers.

Initiator

Any suitable initiator may be used.

In the case of anionic vinyl polymerisation, these include anionic and oxyanionic initiators.

The chain-end chemistry can be tailored by the choice of initiator. Thus, hydrophobic/ hydrophilic behaviour and other properties can be influenced.

Optionally, a mixture of initiators may be used. Thus, two or more different initiator residues may be incorporated into the product.

Further considerations regarding reaction conditions and reagents for anionic polymerisation

The skilled person will be aware of reaction conditions and reagents which are suitable for anionic polymerisations. In particular, certain groups or substituents may interfere with or stop the reaction and the skilled person without undue burden can select or modify the reagents to achieve effective polymerisation. For example, in some contexts and under some conditions acrylate and methacrylate (multi)vinyl monomers may be suitable, but in other contexts they may not, due to the presence of the carboxyl functionality. Therefore, optionally, the vinyl monomer(s) used is not an acrylate or methacrylate monomer. Optionally the vinyl monomer does not contain a carboxylate group, an imine group, a nitrile, a hydroxyl group, an amine, or other heteroatom-containing functional group or other functional group which interferes with the polymerisation.

Optionally the vinyl monomers may comprise aryl groups (e.g. benzene rings), which may be adjacent to the double bonds. For example the present invention is particularly effective with divinyl benzene and similar monomers, e.g. multivinyl benzene, and monomers (which may optionally be substituted or derivatised) which contain within their structures moieties selected from divinyl benzene, multivinyl benzene, styrene and other related structures. Thus, optionally, the vinyl monomer may be a vinyl aromatic monomer. Optionally the vinyl monomer may be a vinyl aliphatic monomer (e.g. a saturated aliphatic monomer).

As exemplified below, the polymerisations of the present invention may conveniently and cost-effectively be carried out at room temperature, or at temperatures which are not far removed from room temperature or ambient temperature. For example, the temperature may optionally be between -5 and 70 degrees C, optionally between -5 and 50 degrees C, optionally between 0 and 40 degrees C, or optionally between 20 and 30 degrees C. Nevertheless, the use of temperatures outside these ranges is possible.

As exemplified below, the polymerisation may be carried out in a three component system, i.e. the system may contain initiator, monomer(s) and solvent, and optionally only these three components. This is an effective and economical system, particularly when carried out at room temperature or temperatures which are not far removed from room temperature. In other words it may be the case that other species which may affect (or are intended to affect) the reactivity of the monomer(s) or initiator are not present; for example, optionally, the system may exclude lithium chloride, or may exclude alkali metal halides, or may exclude alkali metal inorganic salts, and/or may exclude alkaline earth metal inorganic salts.

Where not only multivinyl monomer(s) but also monovinyl monomer(s) are incorporated, one useful way of doing this is to copolymerise the multivinyl and monovinyl components concurrently. Alternatively the components may be polymerized sequentially.

Whilst the comments above are relevant in particular to anionic polymerisation, the skilled person will also be able to choose and tailor appropriate components and conditions for oxyanionic systems without undue burden. Relative amounts of initiator and divinyl monomer

The relative amounts of initiator and divinyl monomer can be modified easily and optimised by routine procedures to obtain non-gelled polymers without undue burden to the skilled person. The analysis of the products can be carried out by routine procedures, for example the relative amounts of initiator and divinyl monomer can be determined by NMR analysis.

Regarding the reagents used, optionally at least 1 equivalent, or between 1 and 10 equivalents, or between 1.2 and 10 equivalents, or between 1.3 and 10 equivalents, or between 1.3 and 5 equivalents, or between 1 and 5 equivalents, or between 1 and 3 equivalents, or between 1 and 2 equivalents, or between 1.2 and 3 equivalents, or between 1.2 and 2 equivalents, or between 1 and 1.1 equivalents, or approximately 1 equivalent, of initiator may be used relative to divinyl monomer. This procedure amounts to telomerisation, i.e. the formation of short chains with small numbers of repeat units.

In the final product, there may be n+1 initiator moieties per n divinyl monomer moieties (thus tending to a 1 : 1 ratio as the molecular weight increases): this is based on a scenario where a theoretically ideal macromolecule of finite size is formed. Other scenarios are however possible, for example intramolecular loop reactions may occur: in practice, therefore, ratios other than (n+1):n are possible. Optionally, on average between 0.5 and 2 initiator moieties are present per divinyl monomer moiety, optionally between 0.7 and 1.5, optionally between 0.75 and 1.3, or between 0.8 and 1.2, or between 0.9 and 1.1 , or between 1 and 1.05, or approximately 1.

Without wishing to be bound by theory, the (n+1):n relationship of this idealized scenario can be rationalized as follows. There may be one initiator per vinyl polymer chain [e.g. if the initiator is an alkyllithium (“RLi”) then an R group is incorporated at one end of the chain and (ultimately, after termination) a H atom or other terminating group at the other]. The simplest theoretical product contains a single divinyl monomer wherein each of the two double bonds is capped by an initiator (such that each of the two double bonds can be considered a vinyl polymer chain having a length of only one vinyl group). Thus, in this simplest theoretical product there is one more initiator than divinyl monomer (2 vs. 1). For each additional propagation (i.e. for each further divinyl monomer which is incorporated) there needs to be one further initiator incorporated if there is to be a product of finite size and if there is to be no intramolecular crosslinking: this is because one double bond of the further divinyl monomer can be incorporated into one existing chain which does not need further initiator, whereas the other double bond of the further divinyl monomer requires a further initiator. Therefore, according to this theoretical assessment, some examples of the ratio of initiator residues to divinyl monomer residues in the product are as follows:

It can be seen that the ratio of initiatonDVM tends towards 1 as the molecular weight increases.

Relative amounts of initiator and trivinyl monomer

Where the multivinyl monomer used is a trivinyl monomer, the following may optionally apply.

Regarding the reagents used, optionally at least 2 equivalents, or between 2 and 20 equivalents, or between 2.4 and 20 equivalents, or between 2.6 and 20 equivalents, or between 2.6 and 10 equivalents, or between 2 and 10 equivalents, or between 2 and 6 equivalents, or between 2 and 4 equivalents, or between 2.4 and 6 equivalents, or between

2.4 and 4 equivalents, or between 2 and 2.2 equivalents, or approximately 2 equivalents, of initiator may be used relative to trivinyl monomer.

In the final product, there may be 2n+1 initiator moieties per n trivinyl monomer moieties (thus tending to a 2: 1 ratio as the molecular weight increases): this is based on a scenario where a theoretically ideal macromolecule of finite size is formed. Other scenarios are however possible, for example intramolecular loop reactions may occur: in practice, therefore, ratios other than (2n+1):n are possible. Optionally, on average between 1 and 4 initiator moieties are present per trivinyl monomer moiety, optionally between 1.4 and 3, optionally between

1.5 and 2.6, or between 1.6 and 2.4, or between 1.8 and 2.2, or between 2 and 2.1 , or approximately 2. Without wishing to be bound by theory, the (2n+1):n relationship of this idealized scenario can be rationalized as follows. There may be one initiator per vinyl polymer chain [e.g. if the initiator is an alkyllithium (“RLi”) then an R group is incorporated at one end of the chain and (ultimately, after termination) a H atom or other terminating group at the other]. The simplest theoretical product contains a single trivinyl monomer wherein each of the three double bonds is capped by an initiator (such that each of the three double bonds can be considered a vinyl polymer chain having a length of only one vinyl group). Thus, in this simplest theoretical product there are two more initiators than trivinyl monomer (3 vs. 1). For each additional propagation (i.e. for each further trivinyl monomer which is incorporated) there needs to be two further initiators incorporated if there is to be a product of finite size and if there is to be no intramolecular crosslinking: this is because one double bond of the further trivinyl monomer can be incorporated into one existing chain which does not need further initiator, whereas the other two double bonds of the further trivinyl monomer each require a further initiator.

Therefore, according to this theoretical assessment, some examples of the ratio of initiator residues to trivinyl monomer residues in the product are as follows:

It can be seen that the ratio of initiator : trivinyl monomer tends towards 2 as the molecular weight increases.

Relative amounts of initiator and tetravinyl monomer

Where the multivinyl monomer used is a tetravinyl monomer, the following may optionally apply. Regarding the reagents used, optionally at least 3 equivalents, or between 3 and 30 equivalents, or between 3.6 and 30 equivalents, or between 3.9 and 30 equivalents, or between 3.9 and 15 equivalents, or between 3 and 15 equivalents, or between 3 and 9 equivalents, or between 3 and 6 equivalents, or between 3.6 and 9 equivalents, or between 3.6 and 6 equivalents, or between 3 and 3.3 equivalents, or approximately 3 equivalents, of initiator may be used relative to tetravinyl monomer.

In the final product, there may be 3n+1 initiator moieties per n tetravinyl monomer moieties (thus tending to a 3: 1 ratio as the molecular weight increases): this is based on a scenario where a theoretically ideal macromolecule of finite size is formed. Other scenarios are however possible, for example intramolecular loop reactions may occur: in practice, therefore, ratios other than (3n+1):n are possible. Optionally, on average between 1.5 and 6 initiator moieties are present per tetravinyl monomer moiety, optionally between 2.1 and 4.5, optionally between 2.25 and 3.9, or between 2.4 and 3.6, or between 2.7 and 3.3, or between 3 and 3.15, or approximately 3.

Without wishing to be bound by theory, the (3n+1):n relationship of this idealized scenario can be rationalized as follows. There may be one initiator per vinyl polymer chain [e.g. if the initiator is an alkyllithium (“RLi”) then an R group is incorporated at one end of the chain and (ultimately, after termination) a H atom or other terminating group at the other]. The simplest theoretical product contains a single tetravinyl monomer wherein each of the four double bonds is capped by an initiator (such that each of the four double bonds can be considered a vinyl polymer chain having a length of only one vinyl group). Thus, in this simplest theoretical product there are three more initiators than tetravinyl monomer (4 vs. 1). For each additional propagation (i.e. for each further tetravinyl monomer which is incorporated) there need to be three further initiators incorporated if there is to be a product of finite size and if there is to be no intramolecular crosslinking: this is because one double bond of the further tetravinyl monomer can be incorporated into one existing chain which does not need further initiator, whereas the other three double bonds of the further tetravinyl monomer each require a further initiator.

Therefore, according to this theoretical assessment, some examples of the ratio of initiator residues to tetravinyl monomer residues in the product are as follows:

It can be seen that the ratio of initiator : tetravinyl monomer tends towards 3 as the molecular weight increases. Relative amounts of initiator and multivinyl monomer

Numerical relationships and theoretical assessments have been presented above for each of divinyl monomers, trivinyl monomers and tetravinyl monomers. In summary, without wishing to be bound by theory, in certain idealised scenarios the number of initiator residues per n MVM residues in the final product may be as follows:

Thus it can be seen that, as the valency of the monomer increases, more and more initiator is required to be present in the final product to cap the chains, unless some other mechanism (e.g. intramolecular reaction) does that.

In general the following may optionally apply across the various types of multivinyl monomers discussed herein. Regarding the reagents used, optionally at least 1 equivalent, or between 1 and 30 equivalents, or between 1.2 and 30 equivalents, or between 1.3 and 30 equivalents, or between 1.3 and 15 equivalents, or between 1 and 15 equivalents, or between 1 and 9 equivalents, or between 1 and 6 equivalents, or between 1.2 and 9 equivalents, or between 1.2 and 6 equivalents, or between 1 and 3 equivalents, of initiator may be used relative to multivinyl monomer. In the final product, optionally, on average between 0.5 and 6 initiator moieties are present per multivinyl monomer moiety, optionally between 0.7 and 4.5, optionally between 0.75 and 3.9, or between 0.8 and 3.6, or between 0.9 and 3.3, or between 1 and 3.15, or between approximately 1 and approximately 3.

Relative amounts of initiator and multifunctional monomer in the case of other types of polymerisation (e.g. ring-opening polymerisation)

The numerical relationships outlined above are applicable to not just vinyl polymerisation but also other types of polymerisation, e.g. ring-opening polymerisation. Thus for example when dilactones, trilactones and tetralactrones are subjected to ring-opening polymerisation in accordance with the principles of the present invention, the ratio of incorporated initiator residues to monomer residues tends towards 1 : 1 , 2: 1 and 3: 1 respectively, as the size of the product increases.

Extent of vinyl polymerization

We believe that one important feature of the vinyl polymerisation method of the present invention is that the average length of the vinyl polymer chains within the overall polymer is short. A typical polymeric molecule prepared in accordance with the present invention will contain many vinyl polymer chains (each of which is on average quite short) linked together by the moiety which in the multivinyl monomer is between the double bonds.

This is achieved by adding the monomer to the initiator in a controlled way and by adjusting the conditions and the relative amounts reagents. The identities of the multivinyl monomer and the initiator, as well as other factors, affect this balance, but the progress of the reaction can be easily monitored and the properties of the resultant polymer easily determined, by known, routine, techniques. Therefore there is no undue burden to the skilled person in carrying out a method in accordance with the present invention, or in determining which methods fall within the scope of the present invention.

Extent of vinyl polymerisation when using divinyl monomers

The number of propagation steps (i.e. how many divinyl monomers are added) before termination of the growing vinyl polymer chain needs to be high enough to generate a branched polymer but low enough to prevent gelation. It appears that an average vinyl polymer chain length of between 1 and 3, between 1 and 2.5, between 1 and 2.2, between 1 and 2, between 1.3 and 2, between 1.5 and 2, between 1.7 and 2, between 1.8 and 2, between 1.9 and 2, or between 1.95 and 2, or of approximately 2, divinyl monomer residues, is suitable. Whilst the average may optionally be between 1 and 3, a small number of vinyl polymer chains may contain significantly more divinyl monomer residues, for example as many as 10, 15, 18, 20 or more.

Optionally 90 % of the vinyl polymer chains contain fewer than 10 DVM residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer.

Without wishing to be bound by theory, the average vinyl polymer chain length, in a scenario which assumes that there is no intramolecular reaction, can be calculated as follows. If, as discussed above there are n+1 initiator moieties per n divinyl monomer moieties, and one initiator per vinyl polymer chain, then, because there are 2n double bonds per n divinyl monomers, the number of double bond residues per chain will on average be 2n/(n+1) which will tend towards 2 as the molecular weight increases.

Therefore, according to this theoretical assessment, some examples of average vinyl chain length are as follows:

It can be seen that the range, for the average chain length under certain theoretical conditions, is between 1 and 2. In practice the value may fall outside this range: other reactions, for example intramolecular polymerisation, may occur. The skilled person will understand that the process makes a range of products which, depending on the conditions, can include low molecular weight products (the smallest being the product containing just one DVM, i.e. wherein the vinyl chain length is 1) up to high molecular weight products. Whether the product mixture is purified, and how it is purified, will of course affect the composition of the product and accordingly the length of vinyl polymer chains present. Thus, in some scenarios, where lower molecular weight products are removed, the average vinyl polymer chain length in the resultant purified product may be higher.

Empirically, the appropriate extent of polymerization has been determined by 1) taking a representative monofunctional monomer that resembles the multifunctional monomer chemically, 2) taking the initiator of interest, 3) conducting a range of linear polymerizations at varying initiator/monomer ratios, 4) analysing the products and 5) determining the average chain length.

The process can be tailored, and polymerisation can proceed effectively, regardless of whether DVM is homopolymerised or DVM is polymerised with some monovinyl monomer present.

Optionally, the product may contain a large amount of divinyl monomer residues wherein one of the double bond residues is bonded to an initiator residue (as opposed to being part of a chain), i.e. has a nominal chain length of 1. The other double bond residues of those divinyl monomer residues may be part of a longer chain. This may be the most common form of the vinyl residue in the product. Optionally the most common vinyl“chain” is that which contains only one divinyl monomer residue. Optionally the two most common vinyl chains are (i) the vinyl“chain” which contains only one divinyl monomer residue and (ii) a vinyl chain which contains an integer selected from between 2 and 8, e.g. between 2 and 7, e.g. between 2 and 6, e.g. between 3 and 8, e.g. between 3 and 7, e.g. between 3 and 6, e.g. between 3 and

5, e.g. 4 or 5, e.g. 5, divinyl monomer residues. Optionally the most common vinyl“chain” is that which contains only one divinyl monomer residue, and the second most common vinyl chain contains an integer selected from between 2 and 8, e.g. between 2 and 7, e.g. between 2 and 6, e.g. between 3 and 8, e.g. between 3 and 7, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 4 or 5, e.g. 5, divinyl monomer residues. Optionally the distribution of chain lengths may be bimodal, e.g. the maxima may be at chain length 1 and at a second chain length which may optionally be between 3 and 8, e.g. between 3 and 7, e.g. between 3 and

6, e.g. between 3 and 5, e.g. 4 or 5, e.g. 5. Extent of vinyl polymerisation when using trivinyl monomers

The number of propagation steps (i.e. how many trivinyl monomers are added) before termination of the growing vinyl polymer chain needs to be high enough to generate a branched polymer but low enough to prevent gelation. It appears that an average vinyl polymer chain length of between 1 and 2, between 1 and 1.8, between 1 and 1.7, between 1 and 1.5, between 1.1 and 1.5, between 1.2 and 1.5, between 1.25 and 1.5, between 1.3 and 1.5, between 1.4 and 1.5, or between 1.45 and 1.5, or of approximately 1.5, trivinyl monomer residues, is suitable.

Whilst the average may optionally be between 1 and 2, a small number of vinyl polymer chains may contain significantly more trivinyl monomer (TVM) residues, for example as many as 5, 10, 15, 18, 20 or more.

Optionally 90 % of the vinyl polymer chains contain fewer than 8 TVM residues, or 90% have a length of 5 or fewer, or 90% have a length of 4 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 8 or fewer, or 95% have a length of 5 or fewer, or 75% have a length of 8 or fewer, or 75% have a length of 6 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer.

Without wishing to be bound by theory, the average vinyl polymer chain length, in a scenario which assumes that there is no intramolecular reaction, can be calculated as follows. If, as discussed above there are 2n+1 initiator moieties per n trivinyl monomer moieties, and one initiator per vinyl polymer chain, then, because there are 3n double bonds per n trivinyl monomers, the number of double bond residues per chain will on average be 3n/(2n+1) which will tend towards 1.5 as the molecular weight increases.

Therefore, according to this theoretical assessment, some examples of average vinyl chain length are as follows:

It can be seen that the range, for the average chain length under certain theoretical conditions, is between 1 and 1.5. In practice the value may fall outside this range: other reactions, for example intramolecular polymerisation, may occur.

The skilled person will understand that the process makes a range of products which, depending on the conditions, can include low molecular weight products (the smallest being the product containing just one TVM, i.e. wherein the vinyl chain length is 1) up to high molecular weight products. Whether the product mixture is purified, and how it is purified, will of course affect the composition of the product and accordingly the length of vinyl polymer chains present. Thus, in some scenarios, where lower molecular weight products are removed, the average vinyl polymer chain length in the resultant purified product may be higher.

Optionally, the product may contain a large amount of trivinyl monomer residues wherein two of the double bond residues are bonded to an initiator residue (as opposed to being part of a chain), i.e. have a nominal chain length of 1. The other double bond residues of those trivinyl monomer residues may be part of a longer chain. This may be the most common form of the vinyl residue in the product. Optionally the most common vinyl“chain” is that which contains only one trivinyl monomer residue. Optionally the two most common vinyl chains are (i) the vinyl“chain” which contains only one trivinyl monomer residue and (ii) a vinyl chain which contains an integer selected from between 2 and 7, e.g. between 2 and 6, e.g. between 2 and 5, e.g. between 3 and 7, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3 or 4, e.g. 3 or e.g. 4, trivinyl monomer residues. Optionally the most common vinyl“chain” is that which contains only one trivinyl monomer residue, and the second most common vinyl chain contains an integer selected from between 2 and 7, e.g. between 2 and 6, e.g. between 2 and 5, e.g. between 3 and 7, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3 or 4, e.g. 3 or e.g. 4, trivinyl monomer residues. Optionally the distribution of chain lengths may be bimodal, e.g. the maxima may be at chain length 1 and at a second chain length which may optionally be between 3 and 7, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3 or 4, e.g. 3 or e.g. 4. Extent of vinyl polymerisation when using tetravinyl monomers

The number of propagation steps (i.e. how many tetravinyl monomers are added) before termination of the growing vinyl polymer chain needs to be high enough to generate a branched polymer but low enough to prevent gelation. It appears that an average vinyl polymer chain length of between 1 and 1.7, between 1 and 1.5, between 1 and 1.4, between 1 and 1.33, between 1.1 and 1.33, between 1.2 and 1.33, between 1.25 and 1.33, or between 1.3 and 1.33, or of approximately 1.33, tetravinyl monomer residues, is suitable.

Whilst the average may optionally be between 1 and 1.7, a small number of vinyl polymer chains may contain significantly more tetravinyl monomer residues, for example as many as 3, 5, 10, 15, 18, 20 or more.

Optionally 90 % of the vinyl polymer chains contain fewer than 6 tetravinyl monomer residues, or 90% have a length of 4 or fewer, or 90% have a length of 3 or fewer, or 90% have a length of 2 or fewer, or 95% have a length of 8 or fewer, or 95% have a length of 6 or fewer, or 95% have a length of 4 or fewer, or 95% have a length of 3 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer.

Without wishing to be bound by theory, the average vinyl polymer chain length, in a scenario which assumes that there is no intramolecular reaction, can be calculated as follows. If, as discussed above there are 3n+1 initiator moieties per n tetravinyl monomer moieties, and one initiator per vinyl polymer chain, then, because there are 4n double bonds per n tetravinyl monomers, the number of double bond residues per chain will on average be 4n/(3n+1) which will tend towards 1.33 as the molecular weight increases.

Therefore, according to this theoretical assessment, some examples of average vinyl chain length are as follows:

It can be seen that the range, for the average chain length under certain theoretical conditions, is between 1 and 1.33. In practice the value may fall outside this range: other reactions, for example intramolecular polymerisation, may occur.

The skilled person will understand that the process makes a range of products which, depending on the conditions, can include low molecular weight products (the smallest being the product containing just one tetravinyl monomer residue i.e. wherein the vinyl chain length is 1) up to high molecular weight products. Whether the product mixture is purified, and how it is purified, will of course affect the composition of the product and accordingly the length of vinyl polymer chains present. Thus, in some scenarios, where lower molecular weight products are removed, the average vinyl polymer chain length in the resultant purified product may be higher.

Optionally, the product may contain a large amount of tetravinyl monomer residues wherein three of the double bond residues are bonded to an initiator residue (as opposed to being part of a chain), i.e. have a nominal chain length of 1. The other double bond residues of those tetravinyl monomer residues may be part of a longer chain. This may be the most common form of the vinyl residue in the product. Optionally the most common vinyl“chain” is that which contains only one tetravinyl monomer residue. Optionally the two most common vinyl chains are (i) the vinyl“chain” which contains only one tetravinyl monomer residue and (ii) a vinyl chain which contains an integer selected from between 2 and 6, e.g. between 2 and 5, e.g. between 2 and 4, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3 or 4, e.g. 3 or e.g. 4, tetravinyl monomer residues. Optionally the most common vinyl“chain” is that which contains only one tetravinyl monomer residue, and the second most common vinyl chain contains an integer selected from between 2 and 6, e.g. between 2 and 5, e.g. between 2 and 4, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3 or 4, e.g. 3 or e.g. 4, tetravinyl monomer residues. Optionally the distribution of chain lengths may be bimodal, e.g. the maxima may be at chain length 1 and at a second chain length which may optionally be between 3 and 6, e.g. between 3 and 5, e.g. 3 or 4, e.g. 3 or e.g. 4. Extent of vinyl polymerisation when using multivinyl monomers in general

Numerical relationships and theoretical assessments have been presented above for each of divinyl monomers, trivinyl monomers and tetravinyl monomers.

In summary, without wishing to be bound by theory, in certain idealised scenarios the average number of multivinyl monomer residues per vinyl polymer chain may be as follows, where the product contains n multivinyl monomer residues:

Thus it can be seen that, as the valency of the monomers increases, the average vinyl chain length is required to decrease.

In general the following may optionally apply across the various types of multivinyl monomers discussed herein.

The average vinyl polymer chain length may contain the following number of multivinyl monomer residues: between 1 and 3, between 1 and 2.5, between 1 and 2.2, between 1 and

2, between 1.1 and 2, between 1.2 and 2, between 1.3 and 2, between 1.33 and 2, between 1.5 and 2, between 1.8 and 2, between 1.9 and 2, between 1.95 and 2, between 1.2 and 1.5, between 1.3 and 1.5, between 1.4 and 1.5, between 1.45 and 1.5, between 1.1 and 1.4, between 1.2 and 1.4, between 1.2 and 1.33, or between 1.3 and 1.33.

Whilst the average may optionally be between 1 and 3, a small number of vinyl polymer chains may contain significantly more multivinyl monomer residues, for example as many as

3, 5, 8, 10, 15, 18, 20 or more.

Optionally 90 % of the vinyl polymer chains contain fewer than 10 multivinyl monomer residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 90% have a length of 4 or fewer, or 90% have a length of 3 or fewer, or 90% have a length of 2 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 95% have a length of 5 or fewer, or 95% have a length of 4 or fewer, or 95% have a length of 3 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer.

Optionally, the product may contain a large amount of multivinyl monomer residues wherein all but one of the double bond residues in the multivinyl monomer residue is bonded to an initiator (as opposed to being part of a chain), i.e. has a nominal chain length of 1. The remaining double bond residue of the multivinyl monomer residues may be part of a longer chain. This may be the most common form of the vinyl residue in the product. Optionally the most common vinyl“chain” is that which contains only one multivinyl monomer residue. Optionally the two most common vinyl chains are (i) the vinyl“chain” which contains only one multivinyl monomer residue and (ii) a vinyl chain which contains an integer selected from between 2 and 8, e.g. between 2 and 7, e.g. between 2 and 6, e.g. between 2 and 5, e.g. between 3 and 8, e.g. between 3 and 7, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3, e.g. 4 or e.g. 5 multivinyl monomer residues. Optionally the most common vinyl“chain” is that which contains only one multivinyl monomer residue, and the second most common vinyl chain contains an integer selected from between 2 and 8, e.g. between 2 and 7, e.g. between 2 and 6, e.g. between 2 and 5, e.g. between 3 and 8, e.g. between 3 and 7, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3, e.g. 4 or e.g. 5, multivinyl monomer residues. Optionally the distribution of chain lengths may be bimodal, e.g. the maxima may be at chain length 1 and at a second chain length which may optionally be between 3 and 8, e.g. between 3 and 7, e.g. between 3 and 6, e.g. between 3 and 5, e.g. 3, 4 or 5.

Extent of polymerisation in other cases (e.g. in the case of ring-opening polymerisation)

The numerical relationships outlined above in relation to vinyl polymerisation are also applicable to other types of polymerisation e.g. ring-opening polymerisation. Thus, in the case of ROP of dilactones, trilactones and tetralactones in accordance with the principles of the present invention, the average number of dilactone residues, trilactone residues and tetralactone residues, per polymer chain, may tend towards 2, 1.5 and 1.33 respectively as the size of the product increases.

Conversion

In accordance with the present invention, polymerization may proceed to the extent that the polymer product contains very little, substantially no, or no, residual polymerisable functionality (e.g. vinyl functionality, in the case of vinyl polymerisation). In the case of vinyl polymerisation, optionally, no more than 20mol%, no more than 10mol%, no more than 5mol%, no more than 2mol%, or no more than 1 mol%, of the polymerizable double bonds of the multivinyl monomer, e.g. of the divinyl monomer, remain in the polymer.

Similarly, in the case of ring-opening polymerisation, optionally, no more than 20mol%, no more than 10mol%, no more than 5mol%, no more than 2mol%, or no more than 1 mol%, of the polymerizable rings, e.g. of the difunctional monomer, remain unopened in the polymer.

This is advantageous in controlling the chemistry and consequent properties of the product.

By using a large amount of initiator, and/or controlling other aspects of the reaction, by titrating multifunctional monomer into initiator (e.g. multivinyl monomer into anionic initiator), the present invention not only avoids gelation but also allows substantially complete conversion.

Whilst, from the first aspect above, reference has been made to preventing gelation, from other aspects it is instead possible to define the invention in terms of the other features described above, solely or in combination, e.g. the amount of initiator, extent of conversion, and/or extent of polymerisation. For example, the present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a difunctional monomer in the presence of an initiator, wherein 1 to 10 molar equivalents of initiator are used relative to difunctional monomer, and/or wherein the polymer product contains on average 0.9 to 1.1 initiator moieties per difunctional monomer moiety, and/or wherein the average polymer chain length is between 1.8 and 2 difunctional monomer residues, and/or wherein conversion of difunctional monomer to polymer is 80% or more. In other examples, the present invention provides a method of preparing a branched polymer comprising the non free radical polymerisation of a multifunctional monomer in the presence of an initiator, wherein 1 to 6 molar equivalents of initiator are used relative to multifunctional monomer, and/or wherein the polymer product contains on average 1 to 3 initiator moieties per multifunctional monomer moiety, and/or wherein the average polymer chain length is between 1.33 and 2 multifunctional monomer residues, and/or wherein conversion of multifunctional monomer to polymer is 80% or more. Polymer products

The present invention relates not only to a new method of polymerisation but to corresponding polymerisation products. The process imparts particular distinguishing characteristics (particularly in terms of architecture, branching and solubility).

Therefore, from a further aspect the present invention provides a polymer obtainable by the process of the present invention.

From a yet further aspect the present invention provides a polymer obtained by the process of the present invention.

Nevertheless it is also possible to define the polymers of the present invention in terms of their structure rather than in terms of the process used to make them.

Vinyl polymer products

Accordingly, from a further aspect the present invention provides a branched polymer product comprising divinyl monomer residues and initiator residues, wherein the molar ratio of initiator residues to divinyl monomer residues is between 0.5 and 2. The ratio is optionally between 0.7 and 1.5, optionally between 0.75 and 1.3, optionally between 0.8 and 1.2, optionally between 0.9 and 1.1 , optionally between 1 and 1.05, optionally approximately 1.

Some of the vinyl polymer chains (i.e. the primary polymer chains) may contain as many as 18, or 15, divinyl monomer residues. Only a small proportion are this long, however: the average, for high molecular weight materials, may be around 2.

Optionally 90 % of the vinyl polymer chains contain fewer than 10 DVM residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer).

Thus the present invention provides a branched polymer product comprising divinyl monomer residues and initiator residues, wherein 90 % of the vinyl polymer chains contain fewer than 10 DVM residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer.

During the reaction, it is possible that neither of the two carbon atoms of a vinyl group forms a bond to another vinyl group (instead they could form a bond to an initiator residue or hydrogen, or, in some cases, other moiety), or it is possible that one of the two carbon atoms of a vinyl group forms a bond to another vinyl group, or it is possible that both carbon atoms of a vinyl group form bonds to other vinyl groups. Therefore, in the product, each vinyl residue may be directly linked to 0, 1 or 2 other vinyl residues as closest neighbours. We have found that where the mean of this number is within particular ranges, then effective branched polymers are obtained. Therefore, from a further aspect the present invention provides a branched polymer product comprising divinyl monomer residues and initiator residues, wherein each vinyl residue is directly vinyl polymerised to on average 0.5 to 1.5 other divinyl monomer residue. Optionally this may be 0.8 to 1.2, 0.8 to 1.1 , 0.9 to 1 , or approximately 1 , on average.

Thus the polymers of the present invention are characterised by having a large amount of initiator incorporation, and also by having short distinct vinyl polymer chains. Whereas, conventionally, a vinyl polymer chain will normally comprise a long saturated backbone, in the present invention - even though the polymers are built up using vinyl polymerisation - most of the double bonds only react with one other double bond, or react with no other double bonds, rather than react with two other double bonds. This means that the linkages between the two double bonds in the monomer, which linkages conventionally bring about branching between polymer chains in the prior art, instead form the backbone of the longest polymer chains in the present invention. This is conceptually different from the prior art and represents a step change in how branched polymerisation may be achieved.

As discussed above, a further way of defining the present invention is in terms of the limited length of vinyl chain segments within the polymer.

Therefore, from a further aspect the present invention provides a branched polymer product comprising divinyl monomer residues and initiator residues, wherein the branched polymer product comprises a multiplicity of vinyl polymer chain segments having an average length of between 1 and 3 divinyl monomer residues.

The average length may be between 1 and 2.5, between 1 and 2.2, between 1 and 2, between 1.3 and 2, between 1.5 and 2, between 1.7 and 2, between 1.8 and 2, between 1.9 and 2, between 1.95 and 2, or approximately 2. The skilled person will understand how the number of double bond residues affects the carbon chain length of the resultant vinyl polymer segment. For example, where a polymer chain segment comprises 2 double bond residues, this equates to a saturated carbon chain segment of 4 carbon atoms.

The incorporation of monovinyl monomers as well as divinyl monomers may affect the average vinyl chain length but does not affect the average number of divinyl monomer residues per chain. It can be a way of increasing the length of the vinyl chains without increasing branching.

The product can also be defined in terms of the amount of residual vinyl functionality.

Thus, from a further aspect the present invention provides a branched polymer product comprising divinyl monomer residues and initiator residues wherein the divinyl monomer residues comprise less than 20mol% double bond functionality.

In other words, in such polymer products, at least 80% of the double bonds of the divinyl monomers have reacted to form saturated carbon-carbon chains.

The residues may comprise less than 10mol%, or less than 5mol%, or less than 2mol%, or less than 1mol%, or substantially no, double bond functionality. In other words, in some cases, less than 1 % of the polymerisable groups remain unreacted in the product.

Another way of defining the product is in terms of its Mark Flouwink alpha value. Optionally, this may be below 0.5.

The above description of polymer products relates in particular to vinyl polymers containing divinyl monomer residues. Analogously, the present invention provides polymer products containing other multivinyl monomer residues including for example trivinyl monomer residues and tetravinyl monomer residues. Disclosures herein relating to the polymerisation methods are applicable also to the resultant products.

Thus, the present invention provides a branched polymer product comprising multivinyl monomer residues and initiator residues, wherein the molar ratio, on average, of initiator residues to multivinyl monomer residues may optionally be: for multivinyl monomers generally: between 0.5 and 6, between 0.7 and 4.5, between 0.75 and 3.9, between 0.8 and 3.6, between 0.9 and 3.3, between 1 and 3.15, or between approximately 1 and approximately 3;

- for trivinyl monomers:

between 1 and 4, between 1.4 and 3, between 1.5 and 2.6, between 1.6 and 2.4, between 1.8 and 2.2, between 2 and 2.1 , or approximately 2;

- for tetravinyl monomers:

between 1.5 and 6, between 2.1 and 4.5, between 2.25 and 3.9, between 2.4 and 3.6, between 2.7 and 3.3, between 3 and 3.15, or approximately 3.

Furthermore the present invention provides a branched polymer product comprising multivinyl monomer residues and initiator residues, wherein optionally:

- for multivinyl monomers generally:

90 % of the vinyl polymer chains contain fewer than 10 multivinyl monomer residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 90% have a length of 4 or fewer, or 90% have a length of 3 or fewer, or 90% have a length of 2 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 95% have a length of 5 or fewer, or 95% have a length of 4 or fewer, or 95% have a length of 3 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer;

- for trivinyl monomers:

90 % of the vinyl polymer chains contain fewer than 8 TVM residues, or 90% have a length of 5 or fewer, or 90% have a length of 4 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 8 or fewer, or 95% have a length of 5 or fewer, or 75% have a length of 8 or fewer, or 75% have a length of 6 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer;

- for tetravinyl monomers:

90 % of the vinyl polymer chains contain fewer than 6 tetravinyl monomer residues, or 90% have a length of 4 or fewer, or 90% have a length of 3 or fewer, or 90% have a length of 2 or fewer, or 95% have a length of 8 or fewer, or 95% have a length of 6 or fewer, or 95% have a length of 4 or fewer, or 95% have a length of 3 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer The present invention also provides a branched polymer product comprising multivinyl monomer residues and initiator residues, wherein optionally each vinyl bond is directly vinyl polymerised to on average:

- for multivinyl monomers generally:

0.1 to 1.5, 0.2 to 1.2, 0.825 to 1.1 , or approximately 0.3 to 1 , other multivinyl monomer residue;

- for trivinyl monomers:

0.2 to 1.3, 0.25 to 1.2, 0.3 to 1 , 0.4 to 0.7, or approximately 0.5, other trivinyl monomer residue;

- for tetravinyl monomers:

0.1 to 1 , 0.2 to 0.8, 0.25 to 0.5, or approximately 0.3, other tetravinyl monomer residue.

Furthermore the present invention provides a branched polymer product comprising multivinyl monomer residues and initiator residues, wherein the branched polymer product comprises a multiplicity of vinyl polymer chain segments having an average length of:

- for multivinyl monomers generally:

between 1 and 3, between 1 and 2.5, between 1 and 2.2, between 1 and 2, between 1.1 and 2, between 1.2 and 2, between 1.3 and 2, between 1.33 and 2, between 1.5 and 2, between 1.8 and 2, between 1.9 and 2, between 1.95 and 2, between 1.2 and 1.5, between 1.3 and 1.5, between 1.4 and 1.5, between 1.45 and 1.5, between 1.1 and 1.4, between 1.2 and 1.4, between 1.2 and 1.33, or between 1.3 and 1.33 multivinyl monomer residues;

- for trivinyl monomers:

between 1 and 2, between 1 and 1.8, between 1 and 1.7, between 1 and 1.5, between 1.1 and 1.5, between 1.2 and 1.5, between 1.25 and 1.5, between 1.3 and 1.5, between 1.4 and 1.5, or between 1.45 and 1.5, or of approximately 1.5, trivinyl monomer residues;

- for tetravinyl monomers:

between 1 and 1.7, between 1 and 1.5, between 1 and 1.4, between 1 and 1.33, between 1.1 and 1.33, between 1.2 and 1.33, between 1.25 and 1.33, or between 1.3 and 1.33, or of approximately 1.33, tetravinyl monomer residues. The incorporation of monovinyl monomers as well as multivinyl monomers may affect the average vinyl chain length but does not affect the average number of multivinyl monomer residues per chain. It can be a way of increasing the vinyl chains without increasing branching.

From a further aspect the present invention provides a branched polymer product comprising multivinyl monomer residues and initiator residues wherein the multivinyl monomer residues comprise less than 20mol% double bond functionality. The residues may comprise less than 10mol%, or less than 5mol%, or less than 2mol%, or less than 1 mol%, or substantially no, double bond functionality.

The above discussion is particularly applicable to anionic or oxyanionic vinyl polymerisation.

Other polymer products including products of ring-opening polymerisation

The principles of the present invention are applicable not just to vinyl polymerisation but also mutatis mutandisXo other polymerisation e.g. ring-opening polymerisation.

Accordingly, from a further aspect the present invention provides a branched polymer product comprising difunctional monomer residues and initiator residues, wherein the molar ratio of initiator residues to difunctional monomer residues is between 0.5 and 2. The ratio is optionally between 0.7 and 1.5, optionally between 0.75 and 1.3, optionally between 0.8 and 1.2, optionally between 0.9 and 1.1 , optionally between 1 and 1.05, optionally approximately 1.

The difunctional monomers may be monomers containing two rings which are suitable or susceptible to ring-opening polymerisation.

Some of the polymer chains may contain as many as 18, or 15, difunctional monomer residues. Only a small proportion are this long, however: the average, for high molecular weight materials, may be around 2.

Optionally 90 % of the polymer chains contain fewer than 10 difunctional monomer residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer. Thus the present invention provides a branched polymer product comprising difunctional monomer residues and initiator residues, wherein 90 % of the polymer chains contain fewer than 10 difunctional monomer residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer.

From a further aspect the present invention provides a branched polymer product comprising difunctional monomer residues and initiator residues, wherein each difunctional monomer residue is directly polymerised to on average 0.5 to 1.5 other difunctional monomer residue. Optionally this may be 0.8 to 1.2, 0.8 to 1.1 , 0.9 to 1 , or approximately 1 , on average.

As discussed above, a further way of defining the present invention is in terms of the limited length of polymer chain segments within the polymer.

Therefore, from a further aspect the present invention provides a branched polymer product comprising difunctional monomer residues and initiator residues, wherein the branched polymer product comprises a multiplicity of polymer chain segments having an average length of between 1 and 3 difunctional monomer residues.

The average length may be between 1 and 2.5, between 1 and 2.2, between 1 and 2, between 1.3 and 2, between 1.5 and 2, between 1.7 and 2, between 1.8 and 2, between 1.9 and 2, between 1.95 and 2, or approximately 2.

The incorporation of monofunctional monomers as well as difunctional monomers may affect the average polymer chain length but does not affect the average number of difunctional monomer residues per primary chain. It can be a way of increasing the length of the polymer chains without increasing branching.

The monofunctional monomers may for example be monomers containing one ring which is suitable for or susceptible to ring-opening polymerisation.

The product can also be defined in terms of the amount of residual polymerisable functionality. Thus, from a further aspect the present invention provides a branched polymer product comprising difunctional monomer residues and initiator residues wherein the difunctional monomer residues comprise less than 20mol% residual functionality.

In other words, in such polymer products, at least 80% of the polymerisable functionality of the difunctional monomers has reacted.

The residues may comprise less than 10mol%, or less than 5mol%, or less than 2mol%, or less than 1 mol%, or substantially no, residual functionality.

Another way of defining the product is in terms of its Mark Houwink alpha value. Optionally, this may be below 0.5.

The above description of polymer products relates in particular to polymers containing difunctional monomer residues. Analogously, the present Invention provides polymer products containing other multifunctional monomer residues including for example trifunctional monomer residues and tetrafunctional monomer residues. In the case of ring- opening polymerisation, trifunctional monomers and tetrafunctional monomers contain, respectively, three and four ring-openable and polymerisable rings. Disclosures herein relating to the polymerisation methods are applicable also to the resultant products.

Thus, the present invention provides a branched polymer product comprising multifunctional monomer residues and initiator residues, wherein the molar ratio, on average, of initiator residues to multifuncational monomer residues may optionally be:

- for multifunctional monomers generally:

between 0.5 and 6, between 0.7 and 4.5, between 0.75 and 3.9, between 0.8 and 3.6, between 0.9 and 3.3, between 1 and 3.15, or between approximately 1 and approximately 3;

- for trifunctional monomers:

between 1 and 4, between 1.4 and 3, between 1.5 and 2.6, between 1.6 and 2.4, between 1.8 and 2.2, between 2 and 2.1 , or approximately 2;

- for tetrafunctional monomers:

between 1.5 and 6, between 2.1 and 4.5, between 2.25 and 3.9, between 2.4 and 3.6, between 2.7 and 3.3, between 3 and 3.15, or approximately 3. Furthermore the present invention provides a branched polymer product comprising multifunctional monomer residues and initiator residues, wherein optionally:

- for multifunctional monomers generally:

90 % of the polymer chains contain fewer than 10 multifunctional monomer residues, or 90% have a length of 7 or fewer, or 90% have a length of 5 or fewer, or 90% have a length of 4 or fewer, or 90% have a length of 3 or fewer, or 90% have a length of 2 or fewer, or 95% have a length of 15 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 7 or fewer, or 95% have a length of 5 or fewer, or 95% have a length of 4 or fewer, or 95% have a length of 3 or fewer, or 75% have a length of 10 or fewer, or 75% have a length of 7 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer;

- for trifunctional monomers:

90 % of the polymer chains contain fewer than 8 trifunctional monomer residues, or 90% have a length of 5 or fewer, or 90% have a length of 4 or fewer, or 95% have a length of 10 or fewer, or 95% have a length of 8 or fewer, or 95% have a length of 5 or fewer, or 75% have a length of 8 or fewer, or 75% have a length of 6 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer;

- for tetrafunctional monomers:

90 % of the polymer chains contain fewer than 6 tetrafunctional monomer residues, or 90% have a length of 4 or fewer, or 90% have a length of 3 or fewer, or 90% have a length of 2 or fewer, or 95% have a length of 8 or fewer, or 95% have a length of 6 or fewer, or 95% have a length of 4 or fewer, or 95% have a length of 3 or fewer, or 75% have a length of 5 or fewer, or 75% have a length of 4 or fewer, or 75% have a length of 3 or fewer, or 75% have a length of 2 or fewer

Furthermore the present invention provides a branched polymer product comprising multifunctional monomer residues and initiator residues, wherein the branched polymer product comprises a multiplicity of polymer chain segments having an average length of:

- for multifunctional monomers generally:

between 1 and 3, between 1 and 2.5, between 1 and 2.2, between 1 and 2, between 1.1 and 2, between 1.2 and 2, between 1.3 and 2, between 1.33 and 2, between 1.5 and 2, between 1.8 and 2, between 1.9 and 2, between 1.95 and 2, between 1.2 and 1.5, between 1.3 and 1.5, between 1.4 and 1.5, between 1.45 and 1.5, between 1.1 and 1.4, between 1.2 and 1.4, between 1.2 and 1.33, or between 1.3 and 1.33 multifunctional monomer residues; - for trifunctional monomers:

between 1 and 2, between 1 and 1.8, between 1 and 1.7, between 1 and 1.5, between 1.1 and 1.5, between 1.2 and 1.5, between 1.25 and 1.5, between 1.3 and 1.5, between 1.4 and 1.5, or between 1.45 and 1.5, or of approximately 1.5, trifunctional monomer residues;

- for tetrafunctional monomers:

between 1 and 1.7, between 1 and 1.5, between 1 and 1.4, between 1 and 1.33, between 1.1 and 1.33, between 1.2 and 1.33, between 1.25 and 1.33, or between 1.3 and 1.33, or of approximately 1.33, tetrafuncational monomer residues.

The incorporation of monofunctional monomers as well as multifunctional monomers may affect the average primary polymer chain length but does not affect the average number of multifunctional monomer residues per chain. It can be a way of increasing the polymer chain lengths without increasing branching.

From a further aspect the present invention provides a branched polymer product comprising multifunctional monomer residues and initiator residues wherein the multifunctional monomer residues comprise less than 20mol% residual polymerisable functionality. The residues may comprise less than 10mol%, or less than 5mol%, or less than 2mol%, or less than 1 mol%, or substantially no, residual polymerisable functionality.

Drawings

The present invention will now be described in further non-limiting detail and with reference to the drawings in which:

Figure 1 shows a schematic representation of a branched polymer in accordance with one embodiment of the present invention, resulting from the anionic vinyl polymerisation of divinyl benzene using sec-butyl lithium as anionic initiator;

Figure 2 shows a schematic representation of a branched polymer in accordance with another embodiment of the present invention, resulting from the anionic vinyl polymerisation of divinyl benzene using sec-butyl lithium as anionic initiator, with post functionalisation using 1 ,2-butylene oxide;

Figure 3 shows proton NMR spectra for the products of Figures 1 and 2 with signals characteristic of the latter (hydroxy-functionalised) material highlighted; Figure 4 shows a schematic representation of a branched polymer in accordance with another embodiment of the present invention, resulting from the oxy-anionic vinyl polymerisation of ethylene glycol dimethacrylate using an initiator derived from benzyl alcohol and potassium tert-butoxide, and the proton NMR spectrum thereof;

Figure 5 shows a reaction scheme for a ring-opening polymerization in accordance with a further embodiment of the present invention, comprising the homopolymerisation of the dilactone BOD (4,4’-bioxepanyl-7,7’-dione) using an alcohol initiator and catalyst;

Figure 6 shows an NMR spectrum for a degradable product prepared by ring opening polymerization; and

Figure 7 shows GPC traces for degradable product prepared by ring opening polymerization.

Examples

Abbreviations:

BO: 1 ,2-butylene oxide

sec-BuLi: sec-butyllithium

DVB: divinylbenzene

GPC: gel permeation chromatography

¹ H NMR: proton nuclear magnetic resonance

MeOH: Methanol

THF: tetrahydrofuran

ABuOK: potassium fert-butoxide

EGDMA: ethylene glycol dimethacrylate

HCI: hydrochloric acid

Example 1 - Polymerisation of multivinyl monomer (i.e. synthesis of polyMVM) by anionic polymerisation

Experimental (for a ~0.5 g scale reaction based on monomer):

In a typical experiment, 2.78 ml_ (2.539 g, 19.5 mmol) of DVB were placed in a flask containing 3 A molecular sieve pellets. 30 ml_ of anhydrous toluene were added to the DVB, the flask was sealed and the mixture left over the molecular sieve for a minimum of 12 hours prior to use in order to ensure complete moisture removal. Under an atmosphere/flow of argon, 2.5 ml_ of sec-BuLi solution (1.3 M in hexane, 3.25 mmol of sec-BuLi) were placed in a 2 necks round bottomed flask (oven dried at >100 °C prior to use) fitted with a stirrer bar. 5 ml_ (~0.4 g of DVB, -3 mmol) of the anhydrous toluene/DVB mixture were then very slowly added, dropwise, with a syringe under argon, to the sec-BuLi solution. After addition of the first few drops, a deep orange/red colour immediately appeared which is characteristic of the formation of styryl lithium species. As a result of the very slow addition, no significant release of heat was noticeable at that point.

After complete addition of 5 ml_ of the toluene/DVB mixture, the reaction was left to stir for 15 minutes and then terminated by slow addition of -0.2 ml_ (5 mmol) of anhydrous degassed methanol. A significant release of heat was noticeable at this stage and the red/orange colour disappeared to give a turbid mixture. THF was added to the mixture to yield a cloudy dispersion. This turbidity is believed to be due to the presence of methoxy lithium salt species. The THF solution was then filtered and precipitated in MeOH. The supernatant was discarded and the precipitate dried in a vacuum oven at 50 °C for at least 24 hours. The resulting material was analysed by ¹ H NMR and triple detection GPC (results below).

A schematic representation of the structure of the product is shown in Figure 1.

Example 2 - Polymerisation of multivinyl monomer (i.e. synthesis of polyMVM) by anionic polymerisation followed by functionalisation by reaction with epoxide to provide hydroxy- functional material

Experimental (for a -0.25 g scale reaction based on monomer):

In a typical experiment, 0.8 g (6.14 mmol) of DVB were placed in a flask containing 3 A molecular sieve pellets. 20 g of anhydrous toluene were added to the DVB, the flask was sealed and the mixture left over the molecular sieve for a minimum of 12 hours prior to use in order to ensure complete moisture removal.

Under an atmosphere/flow of argon, 1.15 mL of sec-BuLi solution (1.3 M in hexane, 1.5 mmol of sec-BuLi) were placed in a 2 necks round bottomed flask (oven dried at >100 °C prior to use) fitted with a stirrer bar. 5 g of the anhydrous toluene/DVB mixture (-0.19 g of DVB, -1.5 mmol) were then very slowly added, dropwise, with a syringe under argon, to the sec-BuLi solution. After addition of the first few drops, a deep orange/red colour immediately appeared which is characteristic of the formation of styryl lithium species. As a result of the very slow addition, no significant release of heat was noticeable at that point.

After complete addition of 5 g of the toluene/DVB mixture, the reaction was left to stir for 15 minutes. 3 mL of THF (25 eq. per active species, 37.5 mmol) were then added to the reaction medium, followed by the addition of 0.6 mL of 1 ,2-butylene oxide (BO, 4.6 eq. per active species, 7 mmol). The reaction mixture colour changed from deep red to yellow, getting lighter over time. The reaction was left to stir for 4 hours and then terminated by addition of -2 mL of degassed MeOH/HCI mixture (17 v % HCI). The reaction mixture was then opened to air, diluted with about 15 mL of THF and then precipitated in about 200 mL of de-ionised water. The precipitate was collected and dried in a vacuum oven at 50 °C for at least 24 hours. The resulting material was analysed by ¹ H NMR and GPC.

A schematic representation of the structure of the product is shown in Figure 2.

Example 3 - Polymerisation of multivinyl monomer and polymerisation of monovinyl monomer by anionic polymerisation - preparation of star-like material

Experimental (for a ~0.5 g scale reaction based on monomer):

In a typical experiment, 1.6 g (12.3 mmol) of DVB were placed in a flask containing 3 A molecular sieve pellets. 40 g of anhydrous toluene were added to the DVB, the flask was sealed and the mixture left over the molecular sieve for a minimum of 12 hours prior to use in order to ensure complete moisture removal.

Under an atmosphere/flow of argon, 2.5 mL of sec-BuLi solution (1.3 M in hexane, 3.25 mmol of sec-BuLi) were placed in a 2 necks round bottomed flask (oven dried at > 100 °C prior to use) fitted with a stirrer bar. 10 g of the anhydrous toluene/DVB mixture (-0.387 g of DVB, -2.92 mmol) were then very slowly added, dropwise, with a syringe under argon, to the sec-BuLi solution. After addition of the first few drops, a deep orange/red colour immediately appeared which is characteristic of the formation of styryl lithium species. As a result of the very slow addition, no significant release of heat was noticeable at that point.

After complete addition of 10 g of the toluene/DVB mixture, the reaction was left to stir for 15 minutes and a sample of the material (the“core”) was taken and analysed by GPC. 3.74 mL of styrene (3.385 g, 32.5 mmol, 10 eq. per active species) were then added dropwise to the reactor. After complete addition of styrene, the reaction was terminated by slow addition of -0.4 mL (10 mmol) of anhydrous degassed methanol. A significant release of heat was noticeable at this stage and the red/orange colour disappeared to give a turbid mixture. The reaction mixture was then opened to air, diluted with about 20 mL of THF and then precipitated in about 250 mL of de-ionised water. The precipitate was collected and dried in a vacuum oven at 50 °C for at least 24 hours. The resulting material was analysed by ¹ H NMR and GPC.

Entry Mw Mn D MH a dn/dc

(kg/mol) (kg/mol) (mL/g)

Core 392.6 5L 72.58 0.356 0.1666

Star 2,018 53.6 37.68 0.366 0.1804

Example 4 - Polymerisation of multivinyl monomer (i.e. synthesis of polyMVM) by oxy-anionic polymerisation

Experimental (for a ~1 g scale reaction based on monomer; @ room temperature):

In a typical experiment, 9 g of ethylene glycol dimethacrylate (EGDMA) were placed in a flask containing 3 A molecular sieve pellets. 9 g of anhydrous tetrahydrofuran (THF) were added to the EGDMA, the flask was sealed and the mixture left over the molecular sieve for a minimum of 12 hours prior to use in order to ensure complete moisture removal.

Under an atmosphere/flow of dry nitrogen, 0.5661 g of potassium fert-butoxide (t- BuOK, 5.04 mmol) were placed in a round bottomed flask (oven dried at >100 °C prior to use) fitted with a stirrer bar. 0.8 mL of anhydrous THF were added to the flask and the mixture was allowed to stir at room temperature until complete dissolution of FBuOK. 0.52 mL of benzyl alcohol (BzOH, 0.5450 g, 5.04 mmol) were then added dropwise to the t-BuOK/THF solution and the reaction was left to stir at room temperature for a minimum of 1 hour until obtaining a homogeneous, transparent pale yellow solution.

1.83 g of the anhydrous EGDMA/THF solution previously prepared (@ 50 wt % i.e. 0.91 g of EGDMA, 4.6 mmol) were then added dropwise over 45 min to the reactor. Through EGDMA addition, the reaction mixture colour turned from pale yellow to deep orange/brown and became viscous. After complete addition, the reaction mixture was left to stir for 60 minutes to ensure full monomer conversion.

The reaction was terminated by addition of 0.4 mL of degassed MeOH. The colour changed from deep orange/brown to light orange.

The reaction mixture was then opened to air, diluted with about 10 mL of THF, filtered to remove possible salt and then precipitated in about 200 mL of MeOH. The precipitate was collected and dried in a vacuum oven at 50 °C for at least 24 hours. The resulting material was analysed by ¹ H NMR and GPC. A schematic representation of the structure of the product is shown in Figure 4.

Example 5 - Polymerisation of multivinyl monomer (i.e. synthesis of polyMVM) by oxy-anionic polymerisation (larger scale, higher temperature)

Experimental (for a ~4 g scale reaction based on monomer; @ 55 °C):

In a typical experiment, 9 g of ethylene glycol dimethacrylate (EGDMA) were placed in a flask containing 3 A molecular sieve pellets. 9 g of anhydrous tetrahydrofuran (THF) were added to the EGDMA, the flask was sealed and the mixture left over the molecular sieve for a minimum of 12 hours prior to use in order to ensure complete moisture removal.

Under an atmosphere/flow of dry nitrogen, 2.261 1 g of potassium fert-butoxide (t- BuOK, 20.15 mmol) were placed in a round bottomed flask (oven dried at >100 °C prior to use) fitted with a stirrer bar. 5 mL of anhydrous THF were added to the flask and the mixture was allowed to stir at 55 °C until complete dissolution of FBuOK. 2.08 mL of benzyl alcohol (BzOH, 2.1736 g, 20.1 mmol) were then added dropwise to the t-BuOK/THF solution and the reaction was left to stir at 55 °C (minimum of 15 minutes) until obtaining a homogeneous, transparent pale yellow solution.

7.8 g of the anhydrous EGDMA/THF solution previously prepared (@ 50 wt % i.e. 3.9 g of EGDMA, 19.7 mmol) were then added dropwise over 30 min to the reactor at 55 °C. Through EGDMA addition, the reaction mixture colour turned from pale yellow to deep dark orange/brown. After complete addition, the reaction mixture was left to stir for 30 minutes to ensure full monomer conversion.

The reaction was terminated by addition of 5 mL of degassed HCI/MeOH solution (33 v % HCI). The colour changed from dark orange/brown to light orange and a white precipitate appeared.

The reaction mixture was then opened to air, diluted with about 30 mL of THF and then precipitated in about 500 mL of de-ionised water. The precipitate was collected and dried in a vacuum oven at 50 °C for at least 24 hours. The resulting material was analysed by ¹ H NMR and GPC.

Example 5 - Polymerisation of multifunctional monomer by ring opening of dilactone to form hyperbranched polymer

With reference to Figure 5, in accordance with the present invention not only vinyl polymerisation but also other types of living polymerisation can result in hyperbranched polymers - in this case, ring-opening telomerisation of BOD (4,4’-bioxepanyl-7,7’-dione).

Preparation of difunctional monomer (BOD)

BOD was synthesised via a Baeyer-Villiger oxidation of 4,4’-bihexanone, as proposed by Irvine and co-workers (N. T. Nguyen, K. J. Thurecht, S. M. Flowdle and D. J. Irvine, Polym. Chem., 2014, 5, 2997-3008).

The Baeyer-Villiger oxidation of 4,4’-bihexanone to form BOD using performic acid as the oxidant.

Urea hydrogen peroxide (15 g) and formic acid (100 mL) were added to a 250 mL round bottom flask (RBF) equipped with a magnetic stirrer bar. The solution was stirred for 2 h to allow the formation of performic acid and the RBF then placed in an ice bath. 4,4’- Bicyclohexanone (5 g) was added gradually, over the course of 1 h, with constant stirring, to the RBF in an ice bath. The solution was then left to stir over night at room temperature. The reaction was quenched with water (100 mL). A liquid-liquid extraction was then performed with CHCb (four washes, each 100 mL). The CHCI ₃ phase was collected and washed with saturated NaHC0 ₃ solution (three washes, each 100 mL). The CHCb phase was dried with Na ₂ S0 ₄ and left to stir overnight. The mixture was filtered by gravity and the filtrate was rotary evaporated to yield a white solid, BOD (2.22 g, 38 %). The white solid was analysed by ¹ H NMR and ¹³ C NMR. dH (400 MHz; CDCI ₃ ; Me ₄ Si) 4.25 (4H, ddd, J22.3, 12.7 and 7.2 - OC/¾CH ₂ -), 2.81 - 2.49 (4H, m, -C(0)C//iCH ₂ -), 2.04 - 1.74 (4H, m, -CHC//iCH ₂ 0-), 1.76 - 1.58 (4H, m, -CHC//iCH ₂ C(0)-), 1.49 (2H, dd, J24.3 and 12.2 -CH ₂ C/* H _2- ). 5C (400 MHz; CDCh; Me ₄ Si) 24.87 (-C(0)CH ₂ CH ₂ CH-), 31.13 (-OCH ₂ OH ₂ CH-), 32.30 (-CH ₂ OHCH ₂ -), 67.06 (-CFi ₂ CH ₂ 0-) and 174.40 (-CH ₂ C(0)0-).

Ring opening polymerisation: Poly(BOD) synthesis

In a typical acid catalysed ring opening polymerisation, methane sulfonic acid (MSA) (7 mg, 7.3 mΐtioI) and BzOH (0.12 g, 1.1 mmol) were weighed into a dry 10 ml_ RBF equipped with a dry magnetic stirrer. The RBF was then sealed with a septum and dry DCM (4 ml_) was injected into the RBF under a nitrogen atmosphere using a nitrogen Schlenk line. The solution was then heated to 32 °C. BOD (0.25 g, 1.1 mmol) was dissolved in DMC (2 ml_). The BOD solution was then titrated into the RBF over 185 mins at a rate of 0.01 ml_ min ¹ using an automatic syringe. The polymerisation was then terminated 5 mins after the final addition of BOD by the addition of alumina (Brockmann, activated, basic) (6 g). The mixture was filtered by gravity and the basic alumina left in the filter paper rinsed with DCM (three washes, each 2 ml_). The resulting solution was then passed through a 0.2 mΐti syringe filter and added dropwise into cold petroleum ether (100 ml_), yielding a white dispersion. After allowing to settle at room temperature for 2 h, the supernatant was poured away and the precipitate was air dried then dried under vacuum at room temperature, yielding a highly viscous clear liquid. The polymer was characterised by triple detection size exclusion chromatography (TD-SEC) and ¹ FI NMR.

The homopolymerisation of BOD exemplifies how ROP can be used in the context of the present invention to produce hyperbranched (HB) polymers with a high density of surface functionality and branching, which are degradable.

a) Reaction scheme showing the initial product formed by the slow addition of BOD to the BzOH initiator in the presence of a catalyst, b) ROP of BOD with the intermediate produced by the slow addition of BOD to an activated intitator solution.

Polv(BOD) Characterisation

Figure 6 shows a ¹ FI NMR spectrum (CDCI3; 400 MFIz) of Poly(BOD) at ca. 80 % ring conversion.

The ¹ FI NMR of purified poly(BOD) (Figure 20) showed that there was significant incorporation of BzOH initiator into the polymer which produces an aromatic signal at 7.35 ppm. The ¹ H NMR also showed that not all of the rings reacted, with ring conversions being observed as ca. 80 %. This suggests that there is a potential for further reaction of the material to reach greater ring conversions and higher molecular weight species.

The incomplete conversion, i.e. the presence of some unopened rings in the product, can be useful because they can subsequently be reacted or functionalised. For example, the residual lactones can be subjected to reaction with certain compounds (e.g. amines, to form amides).

Therefore, optionally, and in general, in accordance with the present invention, the polymerisation of the multifunctional monomer may be incomplete, i.e. some reactive functionality may remain. For example, in the case of ring opening polymerisation, some rings (e.g. lactone rings) may remain which are suitable for or susceptible to ring-opening reaction. For example, in the case of anionic or oxyanionic vinyl polymerisation, some vinyl groups may remain which are suitable for or susceptible to reaction. Alternatively the polymerization can be carried out so that there is complete polymerisation of multifunctional monomer, or substantially complete conversion, or conversion above a certain amount, e.g. 10% or more, 20% or more, 50% or more, 80% or more, 90% or more, 95% or more, 98% or more, or 99% or more. Thus the present invention permits the preparation of a range of products.

There can also be observed a broad alcohol peak that corresponds to the chain ends of the poly(BOD) at 3.12 ppm.

The table below shows the results of GPC analysis of polyBOD. Each of the samples of poly(BOD) had the same dn/dc which was 0.1 18 mL g ^_1 . For the samples in which BOD was successfully homopolymerized to form a soluble HB polymer, there was found to be a trend between the conversion and M _n , M _w and the M-H. a value. As the conversion increases, both Mn and M _w increase. M _w increases by a much larger amount than M _n as the number of reactive ends on larger poly(BOD) structures is greater than that of smaller poly(BOD) structures. Hence, the larger poly(BOD) structures will grow faster, creating a fewer number of very high molecular weight species that will strongly affect M _w .

Table of monomer conversion, M _n , M _w , B, and M-H a for poly(BOD).

a: Determined by ¹ H NMR, b: determined by GPC

Entry Ring conversion M _n M _w ^b D ^b M-H. a ^b

Figure 7 shows GPC traces of poly(BOD) samples (Entry 1 and Entry 2 correspond to the entries in the table above). These GPC traces show that there is a multimodal distribution of the polymer. This is indicative of the formation of HB polymers, as there is a“step-growth” like increase in the growth of the polymer which leads to a highly uneven MWD.

Polv(BOD) Degradation Study

Samples of poly(BOD) materials were placed in pre-weighed vials containing a solution of lipase {pseudomonas cepacian) in a buffered phosphate saline solution (pH 7.2) with sodium azide (0.02 wt%) at 37 °C with constant agitation for 10 days. The clear homogeneous aqueous phase was then carefully removed from the vials ensuring all solids were kept inside. The vials and solids were then washed with deionised water and the aqueous phase removal procedure was repeated. The vials and their content were then placed in a vacuum oven at 50 °C for 24 hours and the mass loss was assessed by weight difference.

The degradation study used a control of commercially available PCL (M _n = 80 kg mol ¹ ) in lipase solution to ensure the enzyme solution was active.

Table : Results of the degradation study of the poly(BOD). The table contains the initial mass of the film, the mass lost through degradation and the percentage mass lost with the error based on the equipment which was ± 1 mg.

a: determined by ¹ H NMR b: determined by degradation study

Entry Ring Initial Mass ^b Mass Loss ^b Percentage Mass Loss

Given the very high branching density of the poly(BOD) it might have been expected that ester bonds would be inaccessible. Nevertheless, the results show that significant degradation occurred. 10-20% weight loss, as shown in the table below, indicates not merely proof of concept but also a useful level of degradation. These experiments relate to a specific set of conditions for a limited (ten day) time period: under industrially relevant or commercially relevant conditions, for various different time periods, the degradation may be significantly greater.

Furthermore, without wishing to be bound by theory, it may be that the numerical percentage mass loss data do not give a completely meaningful indication of the extent of degradation. The hyperbranched nature of the products may mean that cleavage may result initially in conversion of very large polymer products to fragments which are still large, before said large fragments break down into small components.

It should also be noted that these experiments relate to lipase degradation but other modes of degradation are possible, for example in the presence of other enzymes (e.g. cutinases) or other systems. Breakdown of the polymers by cleavage at the esters may occur under enzymatic or non-enzymatic conditions, for example by hydrolysis under natural or environmental conditions, or under various chemical conditions wherein the nature of the conditions (e.g. pH conditions) may be varied according to the requirements.