Mathematical modelling in batch emulsion polymerization

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Living cationic polymerization

The kinetics of the polymerization of styrene iniated by 1-chloro-1-phenyltehane/tin (IV) chloride in the presence of tetrabutylammonium chloride have been studied. Dilatometry studies at 25 °C were conducted and the orders of reaction were established. Molecular weight studies were conducted for these experiments using size exclusion chromatography. These studies indicated that transfer/termination reactions were present. The observed kinetics may be explained by a polymerization mechanism involving a single propagating species which is present in low concentrations. Reactions at 0 °C and -15 °C have shown that a "living" polymerization could be obtained at low temperatures. A method was derived to study the kinetics of a "living" polymerization by following the increase in degree of polymerization with time. Polymerizations of styrene were conducted using 1,4-bis(bromomethyl)benzene as a difunctional co-catalyst. These reactions produced polymers with broad or bimodal molecular weight distributions. These observations may be explained by the rate of initiation being slower than the rate of propagation or the presence of transfer/termination reactions. Reactions were conducted using a co-catalyst using a co-catalyst produced by the addition of 1,1-diphenylethane to 1,4-bis(bromomethyl)benzene. Size exclusion chromatography studies showed that the polymers produced had a narrower molecular weight distribution than those produced by polymerizations initiated by 1,4-bis(bromomethyl)benzene alone. However the polydispersity was still observed to increase with reaction time. This may also be explained by slow initiation compared to the rate of propagation. Polymerizations initiated by both bifunctional initiators were examined using the method of studying reaction kinetics by following the change in number average degree of polymerization. The results indicated that a straight line relationship could also be obtained with a non-living polymerization.

Studies in the anionic polymerization of methyl methacrylate

A study has been made of the anionic polymerization of methyl methacrylate using butyllithium and polystyryl lithium as initiators and using aluminium triisobutyl as a cocatalyst. The aspects of the polymerization that were examined were the effect of changing the order of addition of reagents, the temperature at which polymerization takes place and the polarity of the solvent. Trends were assessed in terms of molecular weight, molecular weight distribution and tacticity. In addition, a second monomer addition test was carried out to verify that the polymerization was truly a living one, and a kinetic study was attempted. Studies to investigate the effect of changing the order of addition of reagents showed that polymer with similar polydispersities and tacticities are produced whether the pre-mixing (mixing initiator and cocatalyst before addition of monomer) or the post-mixing (mixing monomer and cocatalyst before addition of initiator) method were used. However, polymerizations using the post-mixing mixing method demonstrated lower initiator efficiencies, possibly indicating a different initiating species. Investigations into the effect of changing the polymerization temperature show the molecular weight distribution to narrow as the temperature decreases, although a small amount of low molecular weight tailing was also observed at low temperature. A clear relationship between tacticity and temperature was observed with syndiotacticity increasing with decreasing temperature. Changes in solvent polarity were achieved by using mixtures of the standard solvent, toluene, with varying amounts of cyclohexane, tetrahydrofuran or dichloromethane. Experiments at low solvent polarity (using toluene/cyclohexane mixtures) showed problems with initiator solubility but produced polymer with lower polydispersity and higher syndiotacticity than in toluene alone. Experiments using toluene/THF mixtures yielded no polymer, thought to be owing to a side reaction between THF and aluminium triisobutyl. Increased solvent polarity, achieved using toluene/dichloromethane mixtures produced polymer with higher polydispersity and at lower yields than the conventional system, but also with higher syndiotacticity. Second monomer addition reactions demonstrated that the polymerization was 'living' since an increase in molecular weight was observed with no increase in polydispersity. Kinetic studies demonstrated the high speed of the polymerization but yielded no useful data.

Living cationic polymerization of isobutene

The polymerization of isobutene initiated by 1-chloro-1-phenylethane has been investigated, and molecular weight studies conducted using size exclusion chromatography. Polymerizations carried out in a 40/60 (v/v) mixture of dichloromethaneIcyclohexane, using titanium (IV) chloride as a catalyst in the presence of pyridine at -30 °C were found to be controlled and living. The number average molecular weights of the polymers increased linearly with monomer conversion, and the molecular weight distributions were between 1.15 and 1.20. Efficiencies of initiation were between 80 and 100%, and evidence was found to suggest that backbiting to the initiator had occurred, resulting in the formation of cyclic oligomers during the early stages of polymerization. The kinetics of polymerization can be explained in terms of active species in. equilibrium with dormant species. The effects of temperature. and dielectric constant on this equilibrium were studied and a model based upon the Fuoss equation was developed. Pyridine was found to behave as proton trap in the system, and when it was used in excess the rate of polymerization was retarded. By assuming that the catalyst and pyridine formed a one to one complex, it was possible to show that the reaction was second order with respect to the catalyst. The synthesis of low molecular weight polyisobutenes was studied. When the concentration of initiator was increased relative to that of the isobutene, such that the theoretical degree of polymerization was 20 or less, the rate of initiation was slow compared to propagation. The efficiency of initiation in these polymerizations was typically between 30 and 40 %. Optimal conditions of temperature. and.catalyst concentration were established, leading to a 60 % efficiency of initiation. A one-pot synthesis of phenol end-capped polyisobutene was attempted by adding phenol at the end of a living polymerization. Evidence to substantiate the existence of capped polymer chains in the resultant product was inconclusive. Block copolymerizations of oxetane and isobutene were conducted using 1-chloro-1phenylethane/TiCl4, but no copolymer or oxetane homopolymer could be isolated.

Living cationic polymerization of styrene monomers

This thesis describes an experimental investigation of synthesis of polystyrene under various polymerization conditions such as solvent polarity, temperature, initial concentrations of initiator, catalyst, monomer and added salts or co-catalyst, which was achieved using the living cationic polymerization technology in conjunction with gel permeation chromatography (GPC) and NMR spectroscopy. Polymerizations of styrene were conducted using 1-phenyl ethylchloride (1-PEC) as an initiator and tin tetrachloride (SnCI4) as a catalyst in the presence of tetra-n-Butylammonium chloride (nBu4NCI). Effects of solvent polarity varied by mixing dichloromethane (DCM) and less polar cyclohexane (C.hex), temperature, initial concentrations of SnC14, 1-PEC and nBu4NCI on the polymerizations were examined, and the conditions under which a living polymerization can be obtained were optimised as: [styrene]o ~ 0.75 - 2 M; [1-PEC]o ~ 0.005 - 0.05 M; [SnCI4Jo ~ 0.05 - 0.4 M; [nBu4NCIJo ~ 0.001 - 0.1 M; DCM/C.hex ~ 50/0 - 20/30 v/v; T ~ 0 to -45°C. Kinetic studies of styrene polymerization using the Omnifit sampling method showed that the number average molecular weight (Mn) of the polymers obtained increased in direct proportion to monomer conversion and agreed well with the theoretical Mn expected from the concentration ratios of monomer to initiator. The linearities of both the 1n([MJoI[M]) vs. time plot and the Mn vs. monomer conversion plot, and the narrow molecular weight distribution (MWD) measured using GPC demonstrated the livingness of the polymerizations, indicating the absence of irreversible termination and transfer within the lifetimes of the polymerizations. The proposed 'two species' propagation mechanism was found to apply for the styrene polymerization with 1-PEC/SnCI4 in the presence of nBu4NCl. The further kinetic experiments showed that living styrene polymerizations were achieved using the 1-PEC/SnCI4 initiating system in mixtures of DCM/C.hex 30/20 v/v at -15°C in the presence of various bromide salts, tetra-n-butylammonium bromide, tetra-n-pentylammonium bromide, tetra-n-heptylammonium bromide, and tetra-n-octylammonium bromide, respectively. The types of the bromide salts were found to have no significant effect on monomer conversion, Mn, polydispersity and initiation efficiency. Living polymerizations of styrene were also achieved using titanium tetrachloride (TiCI4) as a catalyst and 1-PEC as an initiator in the presence of a small amount of 2,6-di-tert-butylpyridine or pyridine instead of nBu4NCl. GPC analysis showed that the polymers obtained had narrow polydispersities (P.D. < 1.3), and the linearities of both the In([MJo/[MJ) vs. time plot and the Mn vs. monomer conversion plot demonstrated that the polymerizations are living, when the ratio of DCM and C.hex was less than 40 : 10 and the reaction temperature was not lower than -15°C. The reaction orders relative to TiCl4 and 1-PEC were estimated from the investigations into the rate of polymerization to be 2.56 and 1.0 respectively. lH and 13C NMR analysis of the resultant polystyrene would suggest the end-functionality of the product polymers is chlorine for all living polymerizations.

Block co-polymerization by transformation reactions

The aim of this study was to use the transformation of anionic to metathesis polymerization to produce block co-polymers of styrene-b-pentenylene using WC16 /PStLi and WC16/PStLi/ AlEtC12 catalyst systems. Analysis of the products using SEC and 1H and 13C NMR spectroscopy enabled mechanisms for metathesis initiation reactions to be proposed. The initial work involved preparation of the constituent homo-polymers. Solutions of polystyryllithium in cyclohexane were prepared and diluted so that the [PStLi]o<2x10-3M. The dilution produced initial rapid decay of the active species, followed by slower spontaneous decay within a period of days. This was investigated using UV / visible spectrophotometry and the wavelength of maximum absorbance of the PStLi was found to change with the decay from an initial value of 328mn. to λmax of approximately 340nm. after 4-7 days. SEC analysis of solutions of polystyrene, using RI and UV / visible (set at 254nm.) detectors; showed the UV:RI peak area was constant for a range of polystyrene samples of different moleculor weight. Samples of polypentenylene were prepared and analysed using SEC. Unexpectedly the solutions showed an absorbance at 254nm. which had to be considered when this technique was used subsequently to analyse polymer samples to determine their styrene/ pentenylene co-polymer composition. Cyclohexane was found to be a poor solvent for these ring-opening metathesis polymerizations of cyclopentene. Attempts to produce styrene-b-pentenylene block co-polymers, using a range of co-catalyst systems, were generally unsuccessful as the products were shown to be mainly homopolymers. The character of the polymers did suggest that several catalytic species are present in these systems and mechanisms have been suggested for the formation of initiating carbenes. Evidence of some low molecular weight product with co-polymer character has been obtained. Further investigation indicated that this is most likely to be ABA block copolymer, which led to a mechanism being proposed for the termination of the polymerization.

The cationic ring-opening polymerization of cyclic ethers

The kinetics and mechanisms of ring opening polymerization and copolymerizntion of different cyclic ethers were studied using mainly a cationic system of iinitiation. BF30Et2/ethanediol. The cyclic ethers reacted differently showing that ring strain and basicity are the main driving forces in cationic ring opening polymerizaion. In most cases it was found that the degree of polymerization is controlled kinetically via terminations with the counterion and the monomers, and that the contribution of each type of reaction to the overall termination differs markedly. The Gel permeation chromatography studies showed that the molecular weight distribution of the samples of polyoxetanes were bimodal. This was in accordance with previous work establishing that the cyclic tetramer is found in much higher proportions than any of the other cyclic oligomers. However the molecular weight distribution of the copolymers made from oxetane and THF or from oxetane and oxepane were shown to be unimodal. These observations could be explained by a change in the structure of the growing end involved in the cationic polymerization. In addition crown ethers like dibenzo-crown-6 and compounds such as veratrole are believed to stabilise the propagating end and promote the formation of living polymers from oxetane.

The polymerization of lactic acid anhydrosulphite by anionic initiators

This thesis is primarily concerned with the synthesis and polymerization of 5-methyl-1;3, 2-dioxathiolan-4-one-2-oxide (lactic acid anhydrosulphite (LAAS)) using anionic initiators under various conditions. Poly(lactic acid) is a biodegradable polymer which finds many uses in biomedical applications such as drug-delivery and wound-support systems. For such applications it is desirable to produce polymers having predictable molecular weight distributions and crystallinity, The use of anionic initiators offers a potential route to the creation of living polymers. The synthesis of LAAS was achieved by means of an established route though the procedure was modified to some extent and a new method of purification of the monomer using copper oxides was introduced, Chromatographic purification methods were also examined but found to be ineffective. An unusual impurity was discovered in some syntheses and this was identified by means of 1H and 13C NMR, elemental analysis and GC-MS. Since poly-α-esters having hydroxyl-bearing substituents might be expected to have high equilibrium water contents and hence low surface tension characteristics which might aid bio-compatibility, synthesis of gluconic acid anhydrosulphite was also attempted and the product characterised by 1H and 13C NMR. The kinetics of the decomposition of lactic acid anhydrosulphite by lithium tert-butoxide in nitrobenzene has been examined by means of gas evolution measurements. The kinetics of the reaction with potassium tert-butoxide (and also sec-butyl lithium) in tetrahydrofuran has been studied using calorimetric techniques. LAAS was block co-polymerized with styrene and also with 1,3-butadiene in tetrahydrofuran (in the latter case a statistical co-polymer was also produced).

The ring opening polymerization of ring strained cyclic ethers

The kinetics and mechanisms of the ring-opening polymerization of oxetane were studied using cationic and coordinated anionic catalysts. The cationic initiators used were BF30Et2!/ethanol, BF30Et2!/ethanediol and BF30Et2/propantriol. Kinetic determinations with the BF30Et2/diol system indicated that a 1: 1 BF3:0H ratio gave the maximum rate of polymerization and this ratio was employed to detenmne the overall rates of polymerization. An overall second-order dependence was obtained when the system involved ethanediol or propantriol as co-catalyst and a 3/2-order dependence with ethanol, in each case the monomer gave a first-order relationship. This suggested that two mechanisms accounted for the cationic polymerization. These mechanisms were investigated and further evidence for these was obtained from the study of the complex formation of BF30Et2 and the co-catalysts by 1H NMR. Molecular weight studies (using size-exclusion chromatography) indicated that the hydroxyl ion acted as a chain transfer reagent when the [OH] > [BF3]. A linear relationship was observed when the number average molecular weight was plotted against [oxetane] at constant [BF3:0H], and similarly a linear dependency was observed on the BF3:0H 1:1 adduct at constant oxetane concentration. Copolymerization of oxetane and THF was carried out using BF30Et2/ethanol system. The reactivity ratios were calculated as rOXT = 1.2 ± 0.30 and rTHF = 0.14 ± 0.03. These copolymers were random copolymers with no evidence of oligomer formation. The coordinated anionic catalyst, porphinato-aluminium chloride [(TPP)AICl], was used to produce a living polymerization of oxetane. An overall third-order kinetics was obtained, with a second-order with respect to the [(TPP)AICl] and a first-order with respect to the [oxetane] and a mechanism was postulated using these results. The stereochemistry of [(TPP)AlCl] catalyst was investigated using cyclohexene and cyclopentene oxide monomers, using extensive 1H NMR, 2-D COSY and decoupling NMR techniques it was concluded that [(TPP)AlCl] gave rise to stereoregular polymers.

Reversible addition–fragmentation chain transfer polymerization of 2-chloro-1,3-butadiene

Controlled polymerization of 2-chloro-1,3-butadiene using reversible addition–fragmentation chain transfer (RAFT) polymerization has been demonstrated for the first time. 2-Chloro-1,3-butadiene, more commonly known as chloroprene, has significant industrial relevance as a crosslinked rubber, with uses ranging from adhesives to integral automotive components. However, problems surrounding the inherent toxicity of the lifecycle of the thiourea-vulcanized rubber have led to the need for control over the synthesis of poly(2-chloro-1,3-butadiene). To this end, four chain transfer agents in two different solvents have been trialed and the kinetics are discussed. 2-Cyano-2-propylbenzodithioate (CPD) is shown to polymerize 2-chloro-1,3-butadiene in THF, using AIBN as an initiator, with complete control over the target molecular weight, producing polymers with low polydispersities (Mw/Mn < 1.25 in all cases).

The pH-induced swelling and collapse of a polybase brush synthesized by atom transfer radical polymerization

We have used neutron reflectometry to characterize the swelling behaviour of brushes of poly[2-(diethyl amino)ethyl methacrylate], a polybase, as a function of pH. The brushes, synthesized by the "grafting from" method of atom transfer radical polymerization, were observed to approximately double their thickness in low pH solutions, although the pK is shifted to a lower pH than in dilute solution. The composition-depth profile obtained from the reflectometry experiments for the swollen brushes reveals a region depleted in polymer between the substrate and the extended part of the brush.

Controlled RAFT polymerization and zinc binding performance of catechol-inspired homopolymers

Incorporation of catechols into polymers has long been of interest due to their ability to chelate heavy metals and their use in the design of adhesives, metal-polymer nanocomposites, antifouling coatings, and so on. This paper reports, for the first time, the reversible addition-fragmentation chain transfer (RAFT) polymerization of a protected catechol-inspired monomer, 3,4-dimethoxystyrene (DMS), using commercially available trithiocarbonate, 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT), as a chain transfer agent. Our identified RAFT system produces well-defined polymers across a range of molecular weights (5-50 kg/mol) with low molar mass dispersities (Mw/Mn < 1.3). Subsequent facile demethylation of poly(3,4-dimethoxystyrene) (PDMS) yields poly(3,4-dihydroxystyrene) (PDHS), a catechol-bearing polymer, in quantitative yields. Semiquantitative zinc binding capacity analysis of both polymers using SEM/EDXA has demonstrated that both PDMS and PDHS have considerable surface binding (65% and 87%, respectively), although the films deposited from PDMS are of a better quality and processability due to solubility and lower processing temperatures. © 2014 American Chemical Society.

The enantioselective population pharmacokinetics of intravenous ketorolac in children using a stereoselective assay suitable for microanalysis

Objective: To describe the effect of age and body size on enantiomer selective pharmacokinetic (PK) of intravenous ketorolac in children using a microanalytical assay. Methods: Blood samples were obtained at 0, 15 and 30 min and at 1, 2, 4, 6, 8 and 12 h after a weight-dependent dose of ketorolac. Enantiomer concentration was measured using a liquid chromatography tandem mass spectrometry method. Non-linear mixed-effect modelling was used to assess PK parameters. Key findings: Data from 11 children (1.7–15.6 years, weight 10.7–67.4 kg) were best described by a two-compartment model for R(+), S(−) and racemic ketorolac. Only weight (WT) significantly improved the goodness of fit. The final population models were CL = 1.5 × (WT/46)0.75, V1 = 8.2 × (WT/46), Q = 3.4 × (WT/46)0.75, V2 = 7.9 × (WT/46), CL = 2.98 × (WT/46), V1 = 13.2 × (WT/46), Q = 2.8 × (WT/46)0.75, V2 = 51.5 × (WT/46), and CL = 1.1 × (WT/46)0.75, V1 = 4.9 × (WT/46), Q = 1.7 × (WT/46)0.75 and V2 = 6.3 × (WT/46)for R(+), S(−) and racemic ketorolac. Conclusions: Only body weight influenced the PK parameters for R(+) and S(−) ketorolac. Using allometric size scaling significantly affected the clearances (CL, Q) and volumes of distribution (V1, V2).

Competitive processes in controlled cationic ring-opening polymerization of oxetane:a Lotka-Volterra predator-prey model of two growing species competing for the same resources

The activation-deactivation pseudo-equilibrium coefficient Qt and constant K0 (=Qt x PaT1,t = ([A1]x[Ox])/([T1]x[T])) as well as the factor of activation (PaT1,t) and rate constants of elementary steps reactions that govern the increase of Mn with conversion in controlled cationic ring-opening polymerization of oxetane (Ox) in 1,4-dioxane (1,4-D) and in tetrahydropyran (THP) (i.e. cyclic ethers which have no homopolymerizability (T)) were determined using terminal-model kinetics. We show analytically that the dynamic behavior of the two growing species (A1 and T1) competing for the same resources (Ox and T) follows a Lotka-Volterra model of predator-prey interactions. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.