 We will come back to this course in polymer chemistry and in this lecture number 22, we are going to continue. The first half of our discussion on chain copolymerization will cover the remaining part of the chain copolymerization discussion we are having and then take from there we start new topic or new synthetic procedure namely ring opening polymerization. Now, if you look at the slides, you know we had during last two lectures that in our discussion on chain copolymerization, we basically covered these topics different types of copolymers importance of copolymerization and copolymer composition, the micro structures alternate random block is structure how the reactivity difference between the monomers actually give this type of copolymer microstructure and we have talked about copolymerization composition drift with time and then we talked about how the monomer reactivities and different types of chain initiation, you know types of chain initiation actually determine these values of the reactivity ratios. In today's lecture, we will just cover this treat of peak, we talk about QE scheme and then very briefly about ionic copolymerization how that is different from radical copolymerization and just a brief idea about the type of application this copolymers goes. Now, in the last lecture, we talked about different factors contributing to the reactivities of this the monomers and in turn the reactivity ratio, the value of the reactivity ratios of this monomers, we talked about the resonance stabilization of the substituted group, we talked about the electron charge density, electronic charge density, we talked about the steric effect and so on. Now, all these factors actually contribute to the reactivity of the monomer in such a way that it is very difficult to distinguish the contribution from each of these factors in the reactivity of the monomers. Hence, it is very difficult to get a quantitative idea or it is very difficult to predict the reactivity ratios of the monomers from a given structure. Nonetheless, one semi empirical method proposed by Price and Alfre is often used very commonly to sort of get the reactivity ratios of different monomers and a ranking between different monomers in terms of their reactivities. There is a semi empirical approach and this is the QE scheme we are talking about and this is a we are talking continue our discussion on radical copolymerization. So, it is applicable for radical copolymerization and this scheme is based on the assumption that the rate constant rate constant of reaction between a propagating radical P, this is a propagating radical P with a monomer M. Now, this rate constant can write K P M, this rate constant for reaction between a propagating polymeric radical P and a monomer M is given by this expression where these two terms are the reactivity measure of the reactivity of the polymeric radical and this is the measure of reactivity of the monomer. And these two term E P and E M, they are the measure of electronic charges dextrostatic charges on the polymer radical and the monomer respectively. So, if I write from this the expression for R 1 which will given by K 11 by K 12, I should write. Now, this both cases the polymer radical is the same. So, this will get cancelled. So, I can write Q for M 1, Q for M 2, for 1, 1, 1, E M 2. You can get the expression from K 11 and K 2 and if you do the ratio, you get these two, this because this is the same radical one and one. So, this cancel out. So, you get this where this is the measure of reactivity of monomer 1 and this is the measure of reactivity of monomer 2. This is the charges, electrostatic charges on the polymer radical and the monomer. Now, another assumption is made in this approach is that E P 1 is same as E M 1 and we can we write this as E 1. The assumption is that the electrostatic charge on the polymer radical which has at the end monomer 1 structure and the electrostatic charge on monomer is same and which we writing as E 1. So, similarly we can write E P 2 E M 2 as E 2. So, again the assumption is that the electrostatic charge on the polymer radical and the monomer are same if the monomeric residue end of the polymer radical is same as the monomer we are talking about. So, if I can write similarly for R 2 Q, now because Q is always talking about always related to monomer. So, we can you know ignore or we can remove this term monomer M. We can just write Q 1 and Q 2. So, now we can write Q 1 and Q 2 and we have seen R 1 is Q 1 by Q 2 exponential minus E 1 E 1 minus E 2. Essentially these two relates the reactivity ratios of the monomers to the electrostatic charge on the monomer. We do not have any term which is related to the polymer radicals. These all the terms are related to the monomer. So, basically this relates to the reactivities of the two monomers and the electrostatic charge on the two monomers. If we multiply these two, we get this value for R 1 and R 2 which is basically the measure of we have seen earlier is measure of alternative tendency. If it is close to 0, then the monomers will produce a alternative microstructure. If they are close to 1, then the two monomers will produce a random copolymer. And if they are equals both are equals to 1, then obviously R 1, R 2 will be equal to 1, then that will be exactly random copolymers. So, R 1, R 2 will be given by if we can multiply these two, it will be given by exponential minus E 1 minus E 2 square. Now, this expression is in sync with our understanding till now. Now, if E 1 is very close to E 2, that means the electronics charges of the double bond in the monomers are very close. Then obviously, this will become close to 1 and we get a random copolymers, random copolymer. Now, if the double bond for the two monomers has different electrostatic charge, if they are then they are what will happen R 1, R 2 will be close to 0. That means their reactivity, you know they will produce a more a copolymer which is more closer in alternate copolymer rather than a random copolymer. So, if E 1 minus E 2 goes up, then it will be an an extreme for say E 1 is E 2, we will get R 1, R 2 close to 1 which will give ideal copolymerization as we expect. And if they are if this is goes down, so they are equal and then you get this, if they are different then R 1, R 2 will be closer to 0 producing a alternate copolymer which is in sync with our understanding whatever we have discussed till now. Now, how do you get this values for Q and E? Now, arbitrarily it has been assigned, the styrene has been assigned sort of arbitrarily a value of Q is 1 and E is 0.8 and you and rest of the monomers are compared with the value of styrene. What happened? You individual monomers are copolymerized with styrene and from the experimental values of R 1 and R 2, you can use these expressions where if you consider one as styrene, then you know Q 1, you know E 1, hence you will from these two expression and you also know R 1 from experiment, R 1, R 2 from experiment. So, from using these two expression, you will be able to find out the values for Q 2 and E 2. So, monomers are copolymerized with styrene and you get experimental values of R 1 and R 2 and from known values of styrene, having Q is 1 and E is minus 0.8, you can get the unknown values for the second monomer and once you get the individual values for different monomers, they are those values of Q and E are further defined by copolymerizing monomers other than styrene. Basically, if first copolymerized with styrene, get the experiment values of R 1 and R 2 and get from the expression, you get Q and E for the unknown monomers and then it refine further these values of Q 1, Q and E for the other monomers by making copolymers between them. Now, this is Q is a measure of reactivity as we have seen and E is a measure of electrostatic charge. So, if Q goes up, the reactivity will go up and E goes down, the value of Q goes down because it is a measure of electron density electrostatic charge. So, basically electron density on the double bond, if there is electron donating group, then the electronic density electrostatic charge will go up, then key value will be going up and if there is electron withdrawing group, which basically reduces the electron density on the double bond and hence the electrostatic charge, it will be more of a lower number. So, electron density Q goes down and Q goes down and electron density goes up and the value is negative, E is negative when the double bond in say this monomer, the double bond is electronic reach compared to a ethylene molecule, it is a simple and double bond. So, if you look at few datas of the numbers for Q and E, styrene is a arbitrarily taken as 1 and minus 8, minus 0.8 and if you compare with other monomers, say like other conjugate diene like isoprene and butadiene, because they can easily stabilize the radical by resonance, their reactivity is high. So, Q is high and they also basically act as the electron donating group. So, increase the electron density in the double bond. So, basically this value is negative and negative means is equal to electron reach, negative is the charge for electron. So, negative means electron reach. Now, if you compare the monomers having electron withdrawing groups like MMA and acrylonitrile, the reactivity comes down compared to styrene, because they cannot stabilize as much as styrene can do a propagating radical. Whereas, because they have electron withdrawing group, the charge on the double bond actually lower is more of a positive charge. So, you get a positive value and acrylonitrile is more strong electron withdrawing group. So, it has a higher positive value compared to MMA. And compare this vinyl chloride and vinyl acetate, which is basically as we have known for earlier discussions done in several times, their reactivity is very low, because they cannot stabilize the radical propagating radicals. So, their reactivities are low. So, Q values are low and they are basically very weakly donating or electro withdrawing groups. So, the values are very low either positive or negative depending upon what is the net electron withdrawing effect or electron donating effect. Look at this monomer malic anhydride. We know the structure of malic anhydride. Now, this is a very too very strong electron withdrawing group. So, basically the electric charge will be much more positive compared to a ethylene group. And that is why the value for E is quite high positive 2.25. And these values will vary is not that these values are very fixed values, but this value might vary little bit depending upon the condition of the reaction also, but the trend will remain same. So, absolute values of this monomer Q and E value might change, but the trend will always remain same depending irrespective of the condition. And because it cannot stabilize the radical much, their reactivities also comes down. So, in general we can write that if your monomer can stabilize the resonance, the propagating radical by resonance, the reactivity is high, then Q would be greater than 5 if they cannot stabilize by resonance, then Q would be lower. So, basically Q is a measure of resonance stabilization. So, now we can say if you know these values, then we know that if the two monomers which are having very electrostatic charge, having very positive charges like acrylonitrile and malic anhydride, they will be difficult to co-polymerize. Other hand if you take malic anhydride, the monomers are very much electrostatically positive. So, homo polymerization of malic anhydride is very difficult, it does not happen. Now, if you take malic anhydride and co-polymerize with something which has a negative value of E, that means they have a electro positive, electron rich double bond, then obviously there will be attraction between the two polar polarities and there will be possibilities for, I know the co-polymerization will be much easier. So, whereas malic anhydride does not homo polymerize, but it can easily co-polymerize with butylene or styrene, because their charges are opposite. So, the monomers can attract each other and do the reaction. So, basically now we know that with this how to, what are Q and E and how, what is the basis of these values Q and E, how to experimentally or semi-empty get these values of Q and E in comparison to arbitrarily assigned values of styrene. And from the, these values of Q and E, we now can predict whether two monomers can co-poly, will co-polymerize or not and they are sort of ranking in their reactivities and so. So, with this we will move to, we will basically completed our discussion on radical co-polymerization. We will move and discuss very briefly about ionic co-polymerization and the ionic co-polymerization are not very often done, you know. Typically, as we have said earlier in our discussion earlier lectures that carrying out ionic polymerization is always difficult. So, unless there is a specific requirement like you are making a, a, a, a specialty polymers like then there is no point of making this polymers by this ionic method. That is why these co-polymers are not usually synthesized by doing ionic co-polymerization from a mixture of two or more monomers. But co-polymerization is done by ionic polymerization to make block co-polymers where you first make a block of one monomer and then add the second block to get a block co-polymers. Nonetheless, if we compare ionic co-polymerization and have with radical co-polymerization, we can understand the differences and in that way we can understand several characteristics of ionic co-polymerization. Now, unlike radical co-polymerization, this ionic co-polymerization is much more selective. You know not many monomer pair undergo co-polymerization. So, the number of co-monomer pair you can choose which you can use to make a co-polymer by ionic method is limited and we come, we know that in case of radical co-polymerization basically there are numerous options where you can choose two monomers and make co-polymer from there. And we know that cationic co-polymer, the monomers which are having electron donating group as a substituent co-polymer will co-polymerize by cationic method and the monomers having electron withdrawing group as a substituent will undergo co-polymerization with an ionic method. Typically, generally the tendency of this co-polymerization are towards ideal behavior because when as I said that the number of monomers are limited. So, only those monomers which are having reactivity towards a cation, they undergo cationic co-polymerization. The monomers which have reactivity reactivity towards anion they go, they undergo anionic co-polymerization. So, where the monomers which undergo ionic co-polymerization their reactivities are not too different. So, they typically or generally have a ideal type co-polymer, they make typically ideal co-polymers. And of course, like the homo-polymerization we have discussed the reactivity of a ionic polymerization will depend upon the initiator you are choosing and the medium polarity solvent polarity and the temperature. So, if you are talking about co-polymerization the values of R will change with the different types of initiator medium polarity and temperature. Some examples of the commercial co-polymers as we said earlier the styrene is very styrene homopolymer or polystyrene. Polystyrene is a very brittle polymer which breaks easily and also it is very having poor, very poor solvent resistance or chemical resistance. So, to improve what is done styrene is co-polymers will acrylonoitrile where the amount of acrylonoitrile is limited to 10 to 40 percent by which you can or the solvent resistance property of styrene is improved. So, this co-polymer has much improved solvent resistance property compared to polystyrene, but acrylonoitrile also are brittle. So, polyacrylonoitrile also brittle. So, if this co-polymer does not have a significant improvement over the polystyrene molecule homopolymer in terms of brittleness. What is done? Styrene butadiene rubber is used where a rubber butadiene having low T g it gives a rubbery domains in the co-polymers and as a result this co-polymer becomes rubbery or elastomeric and this co-polymers are typically synthesized by emulsion or ionic polymerization. This co-polymers with high styrene containing high amount of styrene can are used as a latex paint where the styrene is costly little bit with unsaturated di carboxylic acid and to combine or to improve both the solvent resistance and impact properties of styrene one very common approach is taken is a making it for the tar polymer where you have acrylonoitrile which improve the solvent resistance butadiene we improve the impact properties and styrene which gives you the heat resistance properties. So, this is a very commonly used co-polymer. So, this is a very commonly used co-polymer as a homopolymer or as a as such or as a blend with some other homopolymers like polystyrene and polycarbonate and others. Styrene can be cross linked with a small amount of divinyl benzene cross linker that will make cross linked spheres cross link product which can be used as a packing material for the columns in size exclusion comatography. And there are other examples of co-polymers which are available commercial like ethylene, vinyl acetate, co-polymers and polystyrene. So, under other examples but I am not spending much time on discussing those applications here. What we will do now? We will move to the next polymerization method which is ring opening polymerization or in short ROP. ROP by name as the name suggest is a ring opening polymerization. So, you have a ring the monomer in having ring structure and you polymerize it and make a linear polymer. Now, the feasibility of this polymerization from a ring to linear product linear ring monomer to or cyclic monomer to a linear product like all other reactions depends both on thermodynamic and thermodynamic and last kinetic factor. We have discussed this thermodynamic factor earlier also while discussing in ring formation, cyclic formation in step growth polymerization if you can recollect from about 4 or 5th or 6th lecture where we talked about the tendency of cyclic ring formation in step growth polymerization. The same logic applies here about the thermodynamic factor. Now, if you look the data if you compare let us talk about the data and then we can understand the thermodynamic factor in more clearly. Now, these are the data of all the three del G, gas free energy change, enthalpy change and entropy change. Now, I have made it T del S to compare and put it in the same scale. This is from cyclo-alkane liquid cyclo-alkane to linear crystalline polymers. Now, when we are talking about cyclo-action these are basically we are talking about polyethylene. These are all polyethylene whether you start from a 3 member ring or 4 member or 5 member this all gives you polyethylene. Now, these are these values here shown here these are all semi empirical values. They are not experiment with them and they are semi empirical values. Now, if you look at the data as the ring size increases from 3 to 4, 5, 6, 7, 8. Now, the ring the lower member ring 3 and 4 member ring they are quite highly strained. 3, 4 membered are strained because of bond angle strain. They are having high energy because of bond angle strain. Whereas, 5 membered ring are strained due to eclipse conformation and 7, 8 membered ring having also strain because of trans-anumeral conformation. Now, if you look at these numbers the enthalpy change on polymerization from a 3 membered cyclic ring to a linear polymers it is highly negative. And, if you just talk about linear polymers what about first let us talk about del S. Now, del S will be negative because the monomers are getting joined making a linear linear polymer. Now, in if you talk about the same molecular weight obviously, if you have a larger ring less number of monomers you require to make the same length of polymers. So, your del S would be less negative your if your ring size is larger. So, if you can and if you see that if your ring size increases your del S value is much less than the decreasing is a becoming less and less negative. But, if you follow the del G value, Gibbs free energy value and del H value they are almost having same trend. So, basically the polymerization, this polymerization is dictated mainly by the enthalpy change because 3 and 4 membered ring are highly strained. When they open up and polymerize the Gibbs have lot of this energy which was already this which is getting released because of ring opening. Similar also true for high high the rings with size of 7 8 carbon. 6 membered ring are highly strained ring is actually little higher than 0 if you compare it is slightly higher than 0. Basically 6 membered ring is not thermodynamically feasible the opening ring opening polymerization of 6 membered ring is not thermodynamically feasible. So, basically now from this thermodynamic data we know that it is easy to ring open polymerize ring opening is to carry out ring opening polymerization on 3, 4 membered ring and say 7 membered ring 5 membered ring also will polymerized by ring opening method whereas 6 membered ring is not that feasible to or basically is not feasible to polymerize thermodynamically. However, can you make take a say 3 membered ring or a 4 membered ring and or say 5 membered ring can you make polyethylene by this route this way can you make polyethylene from either of this either of this by ring opening polymerization the answer is no because it is not only determining by thermodynamic feasibility there has to be some kinetic pathway through which you can carry out the polymerization. Basically this is saturated ring and there is no place where you can carry out a say electrophilic or nucleophilic attack by external and open the ring and then carry out the polymerization. So, this is this molecules even if they are thermodynamically feasible they do not undergo ring opening polymerization. So, what you need you need a say you need a heteroatom in the ring in the cyclic ring which if you have a ring like say ether molecule Z is ether or say A star or say A amide then what you can do there is a if you use acid or base they can actually do nucleophilic or electrophilic attack on this ring and ring open and then which can react with another ring cyclic molecules and let the chain propagate. So, what we what you basically need what you basically now know that simple cyclic rings like cyclo cyclopentane or cyclobutane they do not undergo ring opening polymerization you require a heteroatom which will actually enable a electrophilic or a nucleophilic attack by external agents by which the ring will open and then start the propagation reaction and which will finally lead to a polymer molecule. So, the types of monomers we there is a different structure where basically these are the types of monomers you can you can do a ring opening polymerization. So, basically all have a heteroatom in the ring where it is a ether group or a A star or a amide whatever is the case now that actually enables a electrophilic or nucleophilic attack from external agents which will ring open first and then propagate. This is this will form and give polyphosphazine if you have a cyclic siloxane molecule it can open up to give you linear polysiloxane. If you have a lactone give you polyester if you have a lactam it will in cyclo lactam it will give you a linear polyamide molecules. Now, the chart of the thermodynamic feasibility which we shown that was for ring cycloalkanes not this type of monomers where you have a heteroatom. So, the absolute value in this graph will change if we consider now a cyclic ring having heteroatom or the trains more or less remain same. So, again the the trend of you know thermodynamic feasibility will decrease as you increase from 3 to 6 and then again you can go up if you increase the ring size. So, basically if you have cyclic ethers say tetrahydro pyrone or a 1 4 dioxane they do not undergo polymerization whereas this actually undergo ring opening polymerization. Now, let us talk about few characteristics of ring opening polymerization and we will talk about the mechanism and kinetics of ring opening polymerization. Now, as we discussed if you have a cyclic ring here then you need first to ring open the ring to open up and then start the propagation reaction. Now, if you have a radical initiator say if you have a radical initiator now it is unlikely that this will interact or react with this and ring open that is not very feasible. So, you either need a cation or anion to sort of initiate a ring opening polymerization. So, initiation by in case of ring opening polymerization the initiation is done by the same types of ionic initiators as in the case of ionic polymerization of carbon carbon double bonds. We have discussed in length about the cationic polymerization and anionic polymerization of carbon carbon double bond and those are the same types of initiators will be used to basically polymerize the cyclic rings and make a ring opening polymerization. So, radical initiator is not basically applicable in terms of in case of ring opening polymerization. Now, because we are talking about initiation by ionic initiator. So, you have those different types of species covalent species between the ion and the counter ion with it present as a covalent species or ion pair or free ion those different types of association between the reactant center and the counter impossible. Hence, there is a tremendous effect of the solvent and the counters ion in case of ring opening polymerization as well as was in the case of the linear ionic polymerization of the double bond. Now, this is a chain polymerization that is interesting because the polymers you are making see if you have a lactone you are opening up and making a polyester or you have a lactone you are opening up and making a polyester polyamide. Now, polyester polyamides are typically synthesized what we have discussed earlier they are synthesized by step polymerization. But in this case we are making the same types of polymers which we knew till now that they are typically synthesized by step growth polymerization. They can be synthesized by ring opening polymerization of the cyclic monomers as well and the mechanism here is chain polymerization. So, basically a propagating chain propagates and the monomers get added and the chain ends. So, the chain keep on propagating. There is no reaction between two monomers or there is no reaction between two high molecular polymeric chain as well the same as mechanism same as chain polymerization and in because you are talking about ionic polymerization in most cases they are leaving and we know that by molecular termination is not possible for ionic polymerization. So, there is in if you take care of the reaction medium very well. So, that there is no impurities then these polymers are leaving. So, you can make block polymers or functional polymers at the end of the reaction and in this case unlike the linear polymerization of the vinyl molecules polymerization depolymerization equilibrium is very important. Now, one different this ring opening polymerization with the normal chain polymerization we know is that the rate constant for propagation is in its several order of magnitude lower than normal chain polymerization. It is actually of same order like in case of step growth polymerization. So, though this is a chain polymerization, but the reaction rate or the propagation rate constant is having much lower value compared to several order of magnitude lower in comparison to normal chain polymerization and the values are similar to the step growth polymerization values. So, the reaction is lower compared to your normal chain polymerization and as you know that we discussed this is most cases these are leaving. So, the molecular weight of ring opening polymerization is dependent on the conversion. So, higher the conversion the higher the molecular weight and also you can control the or estimate or predict the molecular weight from the ratio of monomer and the initiator as in the case of other leaving polymerization we know. So, unlike step growth polymerization here you have control you can control the molecular weight by the ratio of monomer and initiator and like the step growth polymerization the the molecular weight will depend upon the conversion, but in case of step growth the high molecules only get a higher conversion or in case of ring opening you get slow increase in the molecular weight with the or the linear increase of the molecular weight with the conversion of monomer. So, examples of what will before we come to examples let us talk about the mechanism part how what are the ways this ring opening polymerization done. If we know this is ionic polymerization so let us first talk about an ionic ROP. Now the initiator it is initiated by as I said the same similar ionic initiators as in the case of linear chain anionic polymerization like metal hydroxides or alkoxide metal hydroxides or metal ankoxides or metal oxides etcetera or like we discussed earlier alkyl metal like alkyl lithium or aryl metal you can use to initiate the anionic chain polymerization or radical anion also anionic species like sodium naphthalene they also there are same types of initiator as we talked about the our discussion on anionic chain polymerization. So, what happened say you talk about say alkyl metal initiator you have a alkyl metal initiator it say I take an anionic take an ethylene oxide now there is a nucleophilic attack by this initiator and the ring will open up. So, you have this now if this will again react with another monomer again similar way. So, you can write as a general you can increase the number of state and you get a your polymerization. Now, as I said that like other anionic polymerization this is a leaving polymerization. So, this at the end of the reaction it remains like this. So, you can add a second monomer and make a block of polymer if you want to terminate reaction you can exchange this with say adding some water or alcohol and then you can exchange like other we discussed earlier. Now, if we talk about cationic ring opening polymerization now here typically strong protonic acids like say trifluoroacetic acid or fluorosulfonic acid or say triflic acid which are where these are acids which are very strong acid are required to initiate a ring opening polymerization. Now, let us have so this will say talk about now a four-membered ether. Now, in this case there is a nucleophilic attack of the oxygen to the proton and you get you actually form secondary oxonium ion in all these cases you have a counter ion associated with that you this will react with another monomer and propagate the chain. So, you can make a polymer like this will form secondary oxonium ion this is tertiary oxonium ion. Now, we have been talking that you need a very strong acid because if your counter ion have sufficient if your acid is not that strong then this counter ion will have sufficient nucleophilicity to either attack the oxonium ion or a proton and stop the reaction there itself. So, for that you require a very high level strong acid. So, that the nucleophilicity of the counter ion will not be enough to compete with the addition of monomer or the reaction of monomer with the oxonium ion. Similarly, if you have little bit of moisture present in the medium or if you have water molecule then this will easily compete with your monomer with the oxonium ion and then terminate or disrupt the reaction immediately. So, like earlier when you talked about cationic polymerization here also you need to have a very stringent requirement of. So, that you do not have a moisture any moisture present in the system. Now, other types of initiators will be talked about those catalyst and co-catalyst like BF3 and H2O catalyst and other type this can be also used in this ring opening poly cationic ring opening polymerization also. Now, at the end as this will remain leaving the only thing in case of cationic polymerization as you can imagine that if your chain is having is your linear chain at the end you have a cationic group and an anionic counter ion then you can if you have oxygen here then it can do intramolecular reaction and form a linear molecule plus a ring molecule and where it can also react with another linear molecules and then stop this chain and form a site in in in middle of another chain. So, from there a branching can happen. So, this this is this are the side reaction where chain transfer takes place intramolecularly within the chain forming a ring structure and another linear molecule or if there are intramolecular chain transfer reaction happen then there will be possibility of branching in in this case and in this case also if you want to stop the reaction you can add agents which by which it can external agents which will terminate the cationic chain. Now, with this I think we have discussed the ring opening polymerization. Now, let us talk about few examples of commercial ring opening polymerization. These are the typically these are polymers which are available commercially which are made by ring opening polymerization. For example, polyethylene oxide and polypropylene oxide they are synthesized by anionic ring opening or corresponding cycling model if polypropylene oxide and polypropylene oxides poly tetrahydro furan can be synthesized or we use synthesized by cationic ring opening polymerization of tetrahydro furan polyacetyls a synthesis by cationic ring opening polymerization of tioxin and as I gave examples of aliphatic polyesters from lactones and polyamides from lactons and this is also very common where linear polysiloxins or silicones are synthesized by anionic or cationic ring opening polymers of cyclic siloxins. So, with this we end our discussion of ring opening polymerization and in the next lecture we will start our discussion on stereochemistry of polymerization and subsequently in another lecture we will talk about coordination polymerization. So, we will start stereochemistry of polymers and polymerization process in our next lecture.