Effects of polymer polydispersity on the phase behaviour of colloid-polymer mixtures

We study the equilibrium behaviour of a mixture of monodisperse hard sphere colloids and polydisperse non-adsorbing polymers at their $\theta$-point, using the Asakura-Oosawa model treated within the free-volume approximation. Our focus is the experimentally relevant scenario where the distribution of polymer chain lengths across the system is fixed. Phase diagrams are calculated using the moment free energy method, and we show that the mean polymer size $\xi_{\rm c}$ at which gas-liquid phase separation first occurs decreases with increasing polymer polydispersity $\delta$. Correspondingly, at fixed mean polymer size, polydispersity favours gas-liquid coexistence but delays the onset of fluid-solid separation. On the other hand, we find that systems with different $\delta$ but the same {\em mass-averaged} polymer chain length have nearly polydispersity-independent phase diagrams. We conclude with a comparison to previous calculations for a semi-grandcanonical scenario, where the polymer chemical potentials are imposed, which predicted that fluid-solid coexistence was over gas-liquid in some areas of the phase diagram. Our results show that this somewhat counter-intuitive result arose because the actual polymer size distribution in the system is shifted to smaller sizes relative to the polymer reservoir distribution.Comment: Changes in v2: sketch in Figure 1 corrected, other figures improved; added references to experimental work and discussion of mapping from polymer chain length to effective radiu

Evolucao historica dos precos do suino, insumos e suas relacoes de troca na Regiao Oeste de Santa Catarina.

bitstream/item/67828/1/CUsersPiazzonDocumentsProntosCPATC-DOCUMENTOS-29-EVOLUCAO-HISTORICA-DOS-PRECOS-DO-SUINO-INSUMOS-E-SUAS-RELACOES-DE-TROCA-NA-RE.pd

Levantamento de reconhecimento dos solos da região sudeste do Estado do Paraná (áreas 4, 5 e 6).

bitstream/item/63300/1/BPD-13-2002-Parana-Sudeste-areas-4-5-6.pd

Guia para identificação dos principais solos do Estado do Paraná.

Conceitos e definições; Principais solos do Estado do Paraná.bitstream/item/36228/1/Guia-para-identificacao.pd

Caracterização dos solos do Município de Castro, PR.

O município de Castro, com uma superfície aproximada de 2.030km2, situa-se no Primeiro Planalto Paranaense, com uma pequena porção, a oeste da sede municipal, localizada no Segundo Planalto. O clima é do tipo Cfb, com precipitação da ordem de 1.400-1.600mm e com chuvas bem distribuídas durante o ano. O material de origem do solo está relacionado ao intemperismo de diferentes litologias, compreendendo desde granitos referidos ao Proterozóico/Paleozóico até arenitos da Formação Furnas, do Devoniano. Na porção sudeste da área, onde o relevo é mais vigoroso, a vegetação original predominante é do tipo floresta subtropical perenifólia, enquanto no restante da área predominava a vegetação de campo subtropical úmido. Ao todo foram estabelecidas 23 unidades de mapeamento, distribuídas pelas seguintes classes: Latossolos Brunos (13,77%), Latossolos Vermelhos (2,75%), Latossolos Vermelho-Amarelos (0,26%), Nitossolos Háplicos (25,39%), Cambissolos Háplicos (23,97%), Cambissolos Húmicos (2,71%), Organossolos Mésicos (15,14%) e Neossolos Litólicos + Afloramentos Rochosos (16,01%).bitstream/item/63306/1/BPD-09-2002-Parana-Castro.pd

Classificação e caracterização dos solos de testes de progenies de erva-mate (Ilex paraguariensis St. Hil.).

bitstream/CNPF-2009-09/16608/1/com_tec29.pd

Caracterização dos solos do Município de Piraí do Sul, PR.

bitstream/item/104763/1/Parana-Pirai.pd

Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energy expressions for the fluid and solid phases. Cloud and shadow curves, which determine the onset of phase coexistence, are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation effects. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or re-entrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus only be defined for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find in addition that coexistence of several solids with a fluid phase is also possible