Modeling & optimisation of coarse multi-vesiculated particles

Clarke, Stephen Armour (2012-03)

Thesis (MScEng)--Stellenbosch University, 2012.

Thesis

ENGLISH ABSTRACT: Multi-vesiculated particles (MVP) are synthetic insoluble polymeric particles containing a multitude of vesicles (micro-voids). The particles are generally produced and used as a suspension in an aqueous fluid and are therefore readily incorporated in latex paints as opacifiers. The coarse or suede MVP have a large volume-mean diameter (VMD) generally in the range of 35-60μm, the large VMD makes them suitable for textured effect paints. The general principle behind the MVP technology is as the particles dry, the vesicles drain of liquid and fill with air. The large refractive index difference between the polymer shell and air result in the scattering of incident light which give the MVP their white opaque appearance making them suitable as an opacifier for the partial replacement of TiO2 in coating systems. Whilst the coarse MVP have been successfully commercialized, insufficient understanding of the influence of the MVP system parameters on the final MVP product characteristics coupled with the MVP’s sensitivity towards the unsaturated polyester resin (UPR) resulted in a product with significant quality variation. On the other hand these uncertainties provided the opportunity to model and optimise the MVP system through developing a better understanding of the influence of the MVP system parameters on the MVP product characteristics, developing a model to mathematically describe these relationships and to optimise the MVP system to achieve the product specifications whilst simultaneously minimising the variation observed in the product characteristics. The primary MVP characteristics for this study were the particle size distribution (quantified by the volume-mean diameter (VMD)) and the reactor buildup.1 The approach taken was to analyse the system determining all possible system factors that may affect it, and then to reduce the total number of system factors by selecting those which have a significant influence on the characteristics of interest. A model was then developed to mathematically describe the relationship between these significant factors and the characteristics of interest. This was done utilising a set of statistical methods known as design of experiments (DoE). A screening DoE was conducted on the identified system factors reducing them to a subset of factors which had a significant effect on the VMD & buildup. The UPR was characterised by its acid value and viscosity and in combination with the identified significant factors a response surface model (RSM) was developed for the chosen design space, mathematically describing their relationship with the MVP characteristics. Utilising a DoE method known as robust parameter design (specifically propagation of error) an optimised MVP system was numerically determined which brought the MVP product within specification and simultaneously reduced the MVP’s sensitivity to the UPR. The validation of the response surface model indicated that the average error in the VMD prediction was 2.16μm (5.16%) which compared well to the 1.96μm standard deviation of replication batches. The high Pred-R2 value of 0.839 and the low validation error indicates that the model is well suited for predicting the VMD characteristic of the MVP system. The application of propagation of error to the model during optimisation resulted in a MVP process and formulation which brought the VMD response from the standard’s average of 44.56μm to the optimised system’s average of 47.84μm which was significantly closer to the desired optimal of 47.5μm. The most notable value added to the system by the propagation of error technique was the reduction in the variation around the mean of the VMD, due to the UPR, by over 30%1 from the standard to optimised MVP system. In addition to the statistical model, dimensional analysis, (specifically Buckingham-Π method) was applied to the MVP system to develop a semi-empirical dimensionless model for the VMD. The model parameters were regressed from the experimental data obtained from the DoE and the model was compared to several models sited in literature. The dimensionless model was not ideal for predicting the VMD as indicated by the R2 value of 0.59 and the high average error of 21.25%. However it described the VMD better than any of the models cited in literature, many of which had negative R2 values and were therefore not suitable for modelling the MVP system.

AFRIKAANSE OPSOMMING: Sintetiese polimeer partikels wat veeltallige lugblasies huisves en omhul, staan beter bekend as MVP (verkort vanaf die Engelse benaming, "multi-vesiculated particles"). Tipies word hierdie partikels berei en gestabiliseer in 'n waterige suspensie wat dit mengbaar maak met konvensionele emulsie sisteme en dit dus in staat stel om te funksioneer as 'n dekmiddel in verf. Deur die volume gemiddelde deursnee (VGD) te manipuleer tot tussen 35 en 60μm, word die growwe partikels geskik vir gebruik in tekstuur verwe, soos byvoorbeeld afwerkings met 'n handskoenleer (suède) tipe tekstuur. Die dekvermoë van MVP ontstaan soos die partikels droog en die water in die polimeer partikel vervang word met lug. As gevolg van die groot verskil in brekingsindeks tussen die polimeer huls en die lugblasies, word lig verstrooi in alle rigtings wat daartoe lei dat die partikels wit vertoon. Dus kan die produk gebruik word om anorganiese pigmente soos TiO2 gedeeltelik te vervang in verf. Alhoewel growwe MVP al suksesvol gekommersialiseer is, bestaan daar nog net 'n beperkte kennis oor die invloed van sisteem veranderlikes op die karakteristieke eienskappe van die finale produk. Dit volg onder andere uit waarnemings dat die kwaliteit van die growwe MVP baie maklik beïnvloed word deur onbekende variasies in die reaktiewe poliëster hars wat gebruik word om die partikels te maak. Dit het egter die geleentheid geskep om die veranderlikes deeglik te modeleer en te optimiseer om sodoende 'n beter begrip te kry van hoe eienskappe geaffekteer word. 'n Wetenskaplike model is opgestel om verwantskappe te illustreer en om die sisteem te optimiseer sodat daar aan produk spesifikasies voldoen word, terwyl produk variasies minimaal bly. Die oorheersende doel in hierdie studie was om te fokus op partikelgrootte en verspreiding (bepaal met behulp van die VGD) as primêre karakteristieke eienskap, asook die graad van aanpaksel op die reaktorwand gedurende produksie. Vanuit eerste beginsel is alle moontlike veranderlikes geanaliseer, waarna die hoeveelheid verminder is na slegs dié wat die karakteristieke eienskap die meeste beïnvloed. Deur gebruik te maak van eksperimentele ontwerp is die wetenskaplike model ontwikkel wat die effek van hierdie eienskappe statisties omsluit. 'n Afskerms eksperimentele ontwerp is uitgevoer om onbeduidende veranderlikes te elimineer van dié wat meer betekenisvol is. Die hars is gekaraktiseer met 'n getal wat gebruik word om die aantal suur groepe per molekuul aan te dui, asook die hars se viskositeit. Hierdie twee eienskappe, tesame met ander belangrike eienskappe is gebruik om 'n karakteristieke oppervlakte model te ontwikkel wat hul invloed op die VGD van die partikels en reaktor aanpakking beskryf. Deur gebruik te maak van 'n robuuste ontwerp, beter beskryf as 'n fout verspreidingsmodel, is die MVP sisteem numeries geoptimiseer. Dit het tot gevolg dat die MVP binne spesifikasie bly en die VGD se sensitiwiteit vir variasie in die hars verminder het. Geldigheidstoetse op die oppervlakte model het aangetoon dat die gemiddelde fout in VGD 2.16μm (5.16%) was. Dit is stem goed ooreen met die 1.96μm standaard afwyking tussen herhaalde lopies. Hoë Pred-R2 waardes (0.839) en lae geldigheidsfout waardes het getoon dat die voorgestelde model die VGD eienskappe uiters goed beskryf. Toepassing van die fout verspreidingsmodel gedurende optimisering het tot gevolg dat die VGD vanaf die standaard gemiddelde van 44.56μm verskuif het na die geoptimiseerde gemiddelde van 47.84μm. Dit is aansienlik nader aan die verlangde optimum waarde van 47.5μm. Die grootste waarde wat toegevoeg is na afloop van hierdie studie, is dat die afwyking rondom die gemiddelde VGD, toegeskryf aan die eienskappe van die hars, verminder het met oor die 30%1 (vanaf die standaard tot die optimiseerde sisteem). Verdere dimensionele analise van die sisteem deur spesifiek gebruik te maak van die Buckingham-Π metode het gelei tot die ontwikkeling van 'n semi-empiriese dimensielose VGD model. Regressie op eksperimentele data verkry uit die eksperimentele ontwerp is vergelyk met verskeie modelle beskryf in ander literatuur bronne. Hierdie dimensionele model was nie ideaal om die VGD te beskryf nie, aangesien die R2 waarde 0.59 was en die gemiddelde fout van 21.25% relatief hoog was. Nietemin, hierdie model beskryf die VGD beter as enige ander model voorgestel in die literatuur. In talle gevalle is negatiewe R2 waardes verkry, wat hierdie literatuur modelle geheel en al ongeskik maak vir toepassing in die MVP sisteem.

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