990 resultados para REGIME-III CRYSTALLIZATION
Resumo:
In this paper, the isothermal crystallization kinetics of polypropylene (iPP) during self-nucleation was studied by means of differential scanning calorimetry(DSC). The iPP was melted at 438 K and then isothermally crystallized in the range of temperature between 421 and 425 K. The mechanism of nucleation and growth of iPP was discussed. The Avrami equation was applied to analyzing the process of isothermal crystallization of iPP from the melt. The average value of Avrami exponent is n=3.01, suggesting that the primary crystallization maybe corresponds to three-dimensional spherulitic growth. The K-g value obtained from Lauritzen-Hoffman equation is 1.128 X 10(5) K-2, which suggests that crystallization species should be regime I. The decrease of crystallization active energy and chain folding work indicates that the self-nucleation can greatly promote the overall crystallization of iPP.
Resumo:
Isothermal crystallization kinetics in the melting of poly(ethylene oxide) (PEO) were investigated as a function of the shear rate and crystallization temperature by optical microscopy. The radial growth rates of the spherulites are described by a kinetics equation including shearing and relaxation combined effects and the free energy for the formation of a secondary crystal nucleus. The free-energy difference between the liquid and crystalline phases increased slightly with rising shearing rates. The experimental findings showed that the influence of the relaxation of PEO, which is related to the shear-induced orientation and stretch in a PEO melt, on the rate of crystallization predominated over the influence of the shearing. This indicated that the relaxation of PEO should be more important so that the growth rates increase with shearing, but it was nearly independent of the shear rate within the measured experimental range.
Resumo:
Crystallization and melting behavior of short ethylene sequence of metallocene ethylene/alpha -olefin copolymer with high comonomer content have been studied by standard DSC and modulated-temperature differential scanning calorimetry (M-TDSC) technique. In addition to high temperature endotherm around 120 degreesC, a low temperature endotherm is observed at lower temperatures (40-80 degreesC), depending on time and temperature of isothermal crystallization. The peak position of the low temperature endotherm T-m(low) varies linearly with the logarithm of crystallization time and the slope, D, decreases with increasing crystallization temperature T-c. The T-m(low) also depends on the thermal history before the crystallization at T-c, and an extrapolation of T-m(low) (30.6 degreesC) to a few seconds has been obtained after two step isothermal crystallization before the crystallization at 30 degreesC. The T-m(low) is nearly equal to T-c, and it indicates that the initial crystallization at low temperature is nearly reversible. Direct evidence of conformational. entropy change of secondary crystallization has been obtained by using M-TDSC technique. Both the M-TDSC result and the activation energy analysis of temperature dependence suggest that crystal perfection process and conformational entropy decreasing in residual amorphous co-exist during secondary crystallization.
Resumo:
Isothermal crystallization kinetics in the miscible mixtures of poly(epsilon-caprolactone) (PCL) and poly(styrene-co-acrylonitrile) (SAN) have been investigated as a function of the composition and the crystallization temperature by optical microscopy. The radial growth rates of the spherulites have been described by a kinetic equation including the interaction parameter and the free energy for the formation of secondary crystal nuclei. Fold surface free energies decrease slightly with the increase of SAN content. The experimental findings show that the influence of the glass transition temperature of the mixture, which is related to the chain mobility, on the rate of crystallization predominates over the influence of the surface free energies. This indicates that the glass transition temperature of the mixture should be of more importance, so that the growth rates decrease when the content of the noncrystallizable component increases. In addition, the Flory-Huggins interaction parameter obtained by fitting the kinetic equation with experimental data is questionable.
Resumo:
A study has been made of the crystallization behavior of polypropylene (PP) filled with rare earth oxides under isothermal conditions. These rare earth oxides include lanthanum oxide (La2O3), yttrium oxide (Y2O3), and a mixture of rare earth oxides containing 70% Y2O3 (Y2O3-0.70). A differential scanning calorimeter was used to monitor the energetics of the crystallization process from the melt. During isothermal crystallization, dependence of the relative degree of crystallinity on time was described by the Avrami equation. It has been shown that the addition of any of the three rare earth oxides causes a considerable increase in the overall crystallization rate of PP but does not influence the mechanism of nucleation and growth of the PP crystals. The analysis of kinetic data according to nucleation theories shows that the increase in crystallization rate of PP in the composites is due to the decrease in surface energy of the extremity surfaces. The relative contents of the beta-form in the composites are somewhat higher than that in the plain PP. However, the contents of the beta-form in the plain PP and the composites are all very low relative to those of the alpha-form and the influence of the formation of the beta-form on the crystallization kinetics can be neglected.
Resumo:
The crystallization and melting behaviour of poly(aryl-ether-ether-ketone) (PEEK) in blends with another polymer of the same family containing a bulky pendant phenolphthalein group (PEK-C) have been investigated by thermal methods. The small interaction energy density of the polymer pair (B = -8.99 J/cm3), evaluated from equilibrium melting point depression, is consistent with the T(g) data that indicate partial miscibility in the melt. Two conjugated phases are in equilibrium at 430-degrees-C: one is crystallizable and contains about 35 wt% of PEK-C; the other, containing only 15 wt% of PEEK, does not form crystals upon cooling and it interferes with the development of spherulites in the sample. The analysis of kinetic data according to nucleation theories shows that crystallization of PEEK in the explored temperature range takes place in Regime III and that a transition to Regime II might be a consequence of an increase in the amount of non-crystallizable molecules in the PEEK-rich phase. A composition independent value of the end surface free energy of PEEK lamellae has been derived from kinetic data (sigma-e = 40 +/- 4 erg/cm2) in excellent agreement with previous thermodynamic estimates. A new value for the equilibrium melting temperature of PEEK (T(m)-degrees = 639 K) has been obtained; it is about 30-degrees-C lower than the commonly accepted value and it explains better the "memory effect" in the crystallization from the melt of this high performance polymer.
Resumo:
“Por lo tanto, la cristalización de polímeros se supone, y en las teorías se describe a menudo, como un proceso de múltiples pasos con muchos aspectos físico-químicos y estructurales influyendo en él. Debido a la propia estructura de la cadena, es fácil entender que un proceso que es termodinámicamente forzado a aumentar su ordenamiento local, se vea obstaculizado geométricamente y, por tanto, no puede conducirse a un estado de equilibrio final. Como resultado, se forman habitualmente estructuras de no equilibrio con diferentes características dependiendo de la temperatura, presión, cizallamiento y otros parámetros físico-químicos del sistema”. Estas palabras, pronunciadas recientemente por el profesor Bernhard Wunderlich, uno de los mas relevantes fisico-quimicos que han abordado en las ultimas décadas el estudio del estado físico de las macromoléculas, adelantan lo que de alguna manera se explicita en esta memoria y constituyen el “leitmotiv” de este trabajo de tesis. El mecanismo de la cristalización de polímeros esta aun bajo debate en la comunidad de la física de polímeros y la mayoría de los abordajes experimentales se explican a través de la teoría LH. Esta teoría clásica debida a Lauritzen y Hoffman (LH), y que es una generalización de la teoría de cristalización de una molécula pequeña desde la fase de vapor, describe satisfactoriamente muchas observaciones experimentales aunque esta lejos de explicar el complejo fenómeno de la cristalización de polímeros. De hecho, la formulación original de esta teoría en el National Bureau of Standards, a comienzos de la década de los 70, sufrió varias reformulaciones importantes a lo largo de la década de los 80, buscando su adaptación a los hallazgos experimentales. Así nació el régimen III de cristalización que posibilita la creacion de nichos moleculares en la superficie y que dio pie al paradigma ofrecido por Sadler y col., para justificar los experimentos que se obtenian por “scattering” de neutrones y otras técnicas como la técnica de “droplets” o enfriamiento rapido. Por encima de todo, el gran éxito de la teoría radica en que explica la dependencia inversa entre el tamaño del plegado molecular y el subenfriamiento, definido este ultimo como el intervalo de temperatura que media entre la temperatura de equilibrio y la temperatura de cristalización. El problema concreto que aborda esta tesis es el estudio de los procesos de ordenamiento de poliolefinas con distinto grado de ramificacion mediante simulaciones numéricas. Los copolimeros estudiados en esta tesis se consideran materiales modelo de gran homogeneidad molecular desde el punto de vista de la distribución de tamaños y de ramificaciones en la cadena polimérica. Se eligieron estas poliolefinas debido al gran interes experimental en conocer el cambio en las propiedades fisicas de los materiales dependiendo del tipo y cantidad de comonomero utilizado. Además, son modelos sobre los que existen una ingente cantidad de información experimental, que es algo que preocupa siempre al crear una realidad virtual como es la simulación. La experiencia en el grupo Biophym es que los resultados de simulación deben de tener siempre un correlato mas o menos próximo experimental y ese argumento se maneja a lo largo de esta memoria. Empíricamente, se conoce muy bien que las propiedades físicas de las poliolefinas, en suma dependen del tipo y de la cantidad de ramificaciones que presenta el material polimérico. Sin embargo, tal como se ha explicado no existen modelos teóricos adecuados que expliquen los mecanismos subyacentes de los efectos de las ramas. La memoria de este trabajo es amplia por la complejidad del tema. Se inicia con una extensa introducción sobre los conceptos básicos de una macromolecula que son relevantes para entender el contenido del resto de la memoria. Se definen los conceptos de macromolecula flexible, distribuciones y momentos, y su comportamiento en disolución y fundido con los correspondientes parametros caracteristicos. Se pone especial énfasis en el concepto de “entanglement” o enmaranamiento por considerarse clave a la hora de tratar macromoléculas con una longitud superior a la longitud critica de enmaranamiento. Finaliza esta introducción con una reseña sobre el estado del arte en la simulación de los procesos de cristalización. En un segundo capitulo del trabajo se expone detalladamente la metodología usada en cada grupo de casos. En el primer capitulo de resultados, se discuten los estudios de simulación en disolución diluida para sistemas lineales y ramificados de cadena única. Este caso mas simple depende claramente del potencial de torsión elegido tal como se discute a lo largo del texto. La formación de los núcleos “babys” propuestos por Muthukumar parece que son consecuencia del potencial de torsión, ya que este facilita los estados de torsión mas estables. Así que se propone el análisis de otros potenciales que son igualmente utilizados y los resultados obtenidos sobre la cristalización, discutidos en consecuencia. Seguidamente, en un segundo capitulo de resultados se estudian moleculas de alcanos de cadena larga lineales y ramificados en un fundido por simulaciones atomisticas como un modelo de polietileno. Los resultados atomisticos pese a ser de gran detalle no logran captar en su totalidad los efectos experimentales que se observan en los fundidos subenfriados en su etapa previa al estado ordenado. Por esta razon se discuten en los capítulos 3 y 4 de resultados sistemas de cadenas cortas y largas utilizando dos modelos de grano grueso (CG-PVA y CG-PE). El modelo CG-PE se desarrollo durante la tesis. El uso de modelos de grano grueso garantiza una mayor eficiencia computacional con respecto a los modelos atomísticos y son suficientes para mostrar los fenómenos a la escala relevante para la cristalización. En todos estos estudios mencionados se sigue la evolución de los procesos de ordenamiento y de fusión en simulaciones de relajación isoterma y no isoterma. Como resultado de los modelos de simulación, se han evaluado distintas propiedades fisicas como la longitud de segmento ordenado, la cristalinidad, temperaturas de fusion/cristalizacion, etc., lo que permite una comparación con los resultados experimentales. Se demuestra claramente que los sistemas ramificados retrasan y dificultan el orden de la cadena polimérica y por tanto, las regiones cristalinas ordenadas decrecen al crecer las ramas. Como una conclusión general parece mostrarse una tendencia a la formación de estructuras localmente ordenadas que crecen como bloques para completar el espacio de cristalización que puede alcanzarse a una temperatura y a una escala de tiempo determinada. Finalmente hay que señalar que los efectos observados, estan en concordancia con otros resultados tanto teoricos/simulacion como experimentales discutidos a lo largo de esta memoria. Su resumen se muestra en un capitulo de conclusiones y líneas futuras de investigación que se abren como consecuencia de esta memoria. Hay que mencionar que el ritmo de investigación se ha acentuado notablemente en el ultimo ano de trabajo, en parte debido a las ventajas notables obtenidas por el uso de la metodología de grano grueso que pese a ser muy importante para esta memoria no repercute fácilmente en trabajos publicables. Todo ello justifica que gran parte de los resultados esten en fase de publicación. Abstract “Polymer crystallization is therefore assumed, and in theories often described, to be a multi step process with many influencing aspects. Because of the chain structure, it is easy to understand that a process which is thermodynamically forced to increase local ordering but is geometrically hindered cannot proceed into a final equilibrium state. As a result, nonequilibrium structures with different characteristics are usually formed, which depend on temperature, pressure, shearing and other parameters”. These words, recently written by Professor Bernhard Wunderlich, one of the most prominent researchers in polymer physics, put somehow in value the "leitmotiv "of this thesis. The crystallization mechanism of polymers is still under debate in the physics community and most of the experimental findings are still explained by invoking the LH theory. This classical theory, which was initially formulated by Lauritzen and Hoffman (LH), is indeed a generalization of the crystallization theory for small molecules from the vapor phase. Even though it describes satisfactorily many experimental observations, it is far from explaining the complex phenomenon of polymer crystallization. This theory was firstly devised in the early 70s at the National Bureau of Standards. It was successively reformulated along the 80s to fit the experimental findings. Thus, the crystallization regime III was introduced into the theory in order to explain the results found in neutron scattering, droplet or quenching experiments. This concept defines the roughness of the crystallization surface leading to the paradigm proposed by Sadler et al. The great success of this theory is the ability to explain the inverse dependence of the molecular folding size on the supercooling, the latter defined as the temperature interval between the equilibrium temperature and the crystallization temperature. The main scope of this thesis is the study of ordering processes in polyolefins with different degree of branching by using computer simulations. The copolymers studied along this work are considered materials of high molecular homogeneity, from the point of view of both size and branching distributions of the polymer chain. These polyolefins were selected due to the great interest to understand their structure– property relationships. It is important to note that there is a vast amount of experimental data concerning these materials, which is essential to create a virtual reality as is the simulation. The Biophym research group has a wide experience in the correlation between simulation data and experimental results, being this idea highly alive along this work. Empirically, it is well-known that the physical properties of the polyolefins depend on the type and amount of branches presented in the polymeric material. However, there are not suitable models to explain the underlying mechanisms associated to branching. This report is extensive due to the complexity of the topic under study. It begins with a general introduction to the basics concepts of macromolecular physics. This chapter is relevant to understand the content of the present document. Some concepts are defined along this section, among others the flexibility of macromolecules, size distributions and moments, and the behavior in solution and melt along with their corresponding characteristic parameters. Special emphasis is placed on the concept of "entanglement" which is a key item when dealing with macromolecules having a molecular size greater than the critical entanglement length. The introduction finishes with a review of the state of art on the simulation of crystallization processes. The second chapter of the thesis describes, in detail, the computational methodology used in each study. In the first results section, we discuss the simulation studies in dilute solution for linear and short chain branched single chain models. The simplest case is clearly dependent on the selected torsion potential as it is discussed throughout the text. For example, the formation of baby nuclei proposed by Mutukhumar seems to result from the effects of the torsion potential. Thus, we propose the analysis of other torsion potentials that are also used by other research groups. The results obtained on crystallization processes are accordingly discussed. Then, in a second results section, we study linear and branched long-chain alkane molecules in a melt by atomistic simulations as a polyethylene-like model. In spite of the great detail given by atomistic simulations, they are not able to fully capture the experimental facts observed in supercooled melts, in particular the pre-ordered states. For this reason, we discuss short and long chains systems using two coarse-grained models (CG-PVA and CG-PE) in section 3 and 4 of chapter 2. The CG-PE model was developed during the thesis. The use of coarse-grained models ensures greater computational efficiency with respect to atomistic models and is enough to show the relevant scale phenomena for crystallization. In all the analysis we follow the evolution of the ordering and melting processes by both isothermal and non isothermal simulations. During this thesis we have obtained different physical properties such as stem length, crystallinity, melting/crystallization temperatures, and so on. We show that branches in the chains cause a delay in the crystallization and hinder the ordering of the polymer chain. Therefore, crystalline regions decrease in size as branching increases. As a general conclusion, it seems that there is a tendency in the macromolecular systems to form ordered structures, which can grown locally as blocks, occupying the crystallization space at a given temperature and time scale. Finally it should be noted that the observed effects are consistent with both, other theoretical/simulation and experimental results. The summary is provided in the conclusions chapter along with future research lines that open as result of this report. It should be mentioned that the research work has speeded up markedly in the last year, in part because of the remarkable benefits obtained by the use of coarse-grained methodology that despite being very important for this thesis work, is not easily publishable by itself. All this justify that most of the results are still in the publication phase.
Resumo:
Microwave (MW) thawing of 2D frozen cylinders exposed to uniform plane waves from one face, is modeled using the effective heat capacity formulation with the MW power obtained from the electric field equations. Computations are illustrated for tylose (23% methyl cellulose gel) which melts over a range of temperatures giving rise to a mushy zone. Within the mushy region the dielectric properties are functions of the liquid volume fraction. The resulting coupled, time dependent non-linear equations are solved using the Galerkin finite element method with a fixed mesh. Our method efficiently captures the multiple connected thawed domains that arise due to the penetration of MWs in the sample. For a cylinder of diameter D, the two length scales that control the thawing dynamics are D/D-p and D/lambda(m), where D-p and lambda(m) are the penetration depth and wavelength of radiation in the sample respectively. For D/D-p, D/lambda(m) much less than 1 power absorption is uniform and thawing occurs almost simultaneously across the sample (Regime I). For D/D-p much greater than 1 thawing is seen to occur from the incident face, since the power decays exponentially into the sample (Regime III). At intermediate values, 0.2 < D/D-p, D/lambda(m) < 2.0 (Regime II) thawing occurs from the unexposed face at smaller diameters, from both faces at intermediate diameters and from the exposed and central regions at larger diameters. Average power absorption during thawing indicates a monotonic rise in Regime I and a monotonic decrease in Regime III. Local maxima in the average power observed for samples in Regime II are due to internal resonances within the sample. Thawing time increases monotonically with sample diameter and temperature gradients in the sample generally increase from Regime I to Regime III. (C) 2002 Elsevier Science Ltd. All rights reserved.
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This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.
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The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitative model is presented which predicts three different regimes of behaviour depending upon the jet Weissenberg number Wi and extensibility of the polymer molecules. In regime I (Wi < ½) the polymer chains are relaxed and the fluid behaves in a Newtonian manner. In regime II (½ < Wi < L) where L is the extensibility of the polymer chain the fluid is viscoelastic, but the polymer do not reach their extensibility limit. In regime III (Wi > L) the chains remain fully extended in the thinning ligament. The maximum polymer concentration at which a jet of a certain speed can be formed scales with molecular weight to the power of (1-3ν), (1-6ν) and -2ν in the three regimes respectively, where ν is the solvent quality coefficient. Experimental data obtained with solutions of mono-disperse polystyrene in diethyl phthalate with molecular weights between 24 - 488 kDa, previous numerical simulations of this system, and previously published data for this and another linear polymer in a variety of “good” solvents, all show good agreement with the scaling predictions of the model.
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A quantum chemistry based Green's function formulation of long-range charge transfer in deoxyribose nucleic acid (DNA) double helix is proposed. The theory takes into account the effects of DNA's electronic structure and its incoherent interaction with aqueous surroundings. In the implementation, the electronic tight-binding parameters for unsolvated DNA molecules are determined at the HF/6-31G* level, while those for individual nucleobase-water couplings are at a semiempirical level by fitting with experimental redox potentials. Numerical results include that: (i) the oxidative charge initially at the donor guanine site does hop sequentially over all guanine sites; however, the revealed rates can be of a much weaker distance dependence than that described by the ordinary Ohm's law; (ii) the aqueous surroundings-induced partial incoherences in thymine/adenine bridge bases lead them to deviate substantially from the superexchange regime; (iii) the time scale of the partially incoherent hole transport through the thymine/adenine pi stack in DNA is about 5 ps. (C) 2002 American Institute of Physics.
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A partir de uma visão contemporânea do contrato o trabalho procurou, (i) reconstruir o marco teórico sobre qual se funda o contrato de concessão comercial no Brasil, registrando uma nota histórica sobre a criação da Lei nº 6.729/1979; (ii) avaliar a validade da lei estudada sob o enfoque do regime constitucional vigente; (iii) analisar o regime jurídico das convenções de marca previstas na lei e a utilização dessas convenções como mecanismos de incentivo de atuação dos concessionários dentro de suas respectivas áreas operacionais, conceituando-as; (iv) sugerir mecanismos de solução de conflitos decorrentes da atuação, pelos concessionários, fora de sua respectiva área operacional, especialmente a cláusula de mediação e arbitragem
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After 20 years of reestablished democracy in Brazil, what do the state legislators think about the regime? The goal of the article is to show the views of state legislators of the Legislative Assemblies of the States of São Paulo and Paraná on democracy. For the views we use a structured and self-administered questionnaire. The results show that for the state legislators: i) democracy is stable, ii) it is superior to any other kind of regime, iii) it's support comes from some public policy and the use of voting and iv) parties and elections are important for democracy.
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This paper analyzes the opinions of legislators members of parliamentaries elites of Legislative Assemblies of the States of São Paulo, Paraná and Santa Catarina on democracy. The opinions of legislators paulistas were collected using a questionnaire selfadministered and structured, while the opinions of legislators paranaenses and catarinenses were collected with the surveys “As elites administrativas, parlamentares e partidárias do Paraná, 1995-2006” and “Elites políticas e a democracia: os valores políticos dos parlamentares catarinenses da 16º Legislatura, 2007”. The results were: i) democracy is stable, ii) it is superior to any other type of regime, iii) is supported by some social policies and the use of voting and iv) democracy has support of various ideological currents.
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The objective of this paper is to analyze the values of democracy in the opinions of the councillors of the cities of São Bernardo do Campo, Santo André and São Caetano do Sul. This paper analyzes the period of 2010 and the technique of collection and analysis data were based on the main research methods in the Social Sciences. The results were: i) democracy is stable, ii) it is superior to any other type of regime, iii) content support in some public policy and the use of voting and iv) democracy has the support of the various ideological options.