京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22822号 / 理博第4632号 / 新制||理||1666(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 山本 潤, 教授 佐々 真一, 准教授 荒木 武昭 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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This thesis presents the investigation of the liquid crystal (LC) - particle suspensions. Particles from nano- to micro-size, spherical to two-dimensional shapes, with different functionality are dispersed into nematic and smectic phases. The aim is to create ordered nanoparticle (NP) assemblies and thereby modify the common properties of the liquid crystal, such as dielectric anisotropy and electro-optical, revealing any interaction between particles and LC properties. It is found that for concentrations (>0.5vol%), the ferroelectric NPs have increased the sensitivity of the nematic liquid crystal to the electric field through electro-optical responses, which is seen by an enhancement in the dielectric anisotropy. This could be induced by the coupling of the electrical dipole moments in the spherical NPs with the LC director field. The electro-optical properties of the chiral smectic (SmC*) phase (tilt angle Θ, switching time τ_s and spontaneous polarisation P_s) are found to be independent of the concentration and sizes of the doped NPs. The relaxation frequency f_R of the Goldstone mode is faster in the ferroelectric NPs suspensions of 2.0vol% compared to the paraelectric NPs. In the graphene oxide (GO) - nematic LC (5CB) suspensions, the small GO sizes of mean size 560 nm are more easily dispersible than larger flakes of 2.8 micro metre mean size. As the GO concentration is increased, each of the threshold voltage and splay elastic constant dramatically increases, reaching saturation at ≈1.0wt%. The field driven switching-on time is practically not affected, while the purely elastically driven switching-off time is strongly sped-up. Interestingly, thermotropic and lyotropic LC phases are exhibited in the GO-5CB suspensions when heating the thermotropic liquid crystal into its isotropic phase. The isotropic phase of 5CB acts as a solvent for the GO particles, forming a lyotropic nematic phase with largely reduced birefringence. It is found that the nematic to isotropic phase transition is shifted toward higher temperature for the GO-5CB system compared to the BaTiO3-5CB system. Dispersions of different sizes of GO flakes are prepared in isotropic and nematic fluid media. The dielectric relaxation behaviour of GO-dispersions was examined for a wide temperature range (25-60 ℃) and frequency range (100 Hz-2 MHz). The mixtures containing GO flakes were found to exhibit varying dielectric relaxation processes, depending on the size of the flakes and the elastic properties of the dispersant fluid. The relaxation frequencies in the isotropic media were lower compared to the nematic medium. Relaxation frequencies (~10 kHz) are observed in the GO-isotropic media, which are reduced as the size of the GO flakes are decreased, are anticipated to be inherited from GO flakes. However, the fast relaxations (~100 kHz) that are observed in the nematic suspensions could imply strongly slowed down molecular relaxation modes of the nematogenic molecules. Finally, the phase diagram of lyotropic LC as a function of the lateral dimensions of the GO flakes, their concentration, geometrical confinement configuration and solvent polarity was investigated. Polarising optical microscopy was used to determine isotropic-biphasic-nematic phase evolution. The confinement volume and geometry of the sample relative to the GO size are shown to be vital to the observation of the lyotropic phase. GO LCs have the potential for a range of applications from display technologies to conductive fibres. The confinement related LC phase transition is critical toward their applications. It is also found that the stability of the LC phase is higher for the solvent of higher dielectric constant.

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The present thesis reports computer simulation studies of several phase transition related phenomena in a range of soft-condensed matter systems. A coherent unifying theme of the thesis is the understanding of dynamics of phase transitions through free energy calculations using recently developed efficient non-Boltzmann sampling methods. Based on the system/phenomena of interest, the thesis has been classified into four major parts: I. Isotropic-nematic (IN) phase transition in liquid crystals. II. Nucleation phenomena in gas-liquid transition with particular emphasis on the systems close to the spinodal curve. III. Collapse transition in linear hydrocarbon (n-alkane) chains for a varying range of length, solvent and temperature. IV. Crystallization of unbranched polymer chains in dilute solution, with particular emphasis on the temperature dependent crossover between the rod-like crystalline state and spherical molten globule state. The thesis has been further divided into ten chapters running through the four parts mentioned before. In the following we provide a brief chapter-wise outline of the thesis. Part I deals with the power law relaxation and glassy dynamics in thermotropic liquid crystals close to the IN transition and consists of two chapters. To start with, Chapter I.1 provides an introduction to thermotropic liquid crystals. Here we briefly introduce various liquid crystalline phases, the order parameter used to characterize the IN transition, a few well established theoretical models, and we conclude with describing the recent experimental and computer simulation studies that have motivated the work described in the next chapter. In Chapter I.2, we present our molecular dynamics simulation studies on single particle and collective orientational dynamics across the IN transition for Lebwohl Lasher model, which is a well-known lattice model for thermotropic liquid crystals. Even this simplified model without any translational degrees of freedom successfully captures the short-tointermediate time power law decay recently observed in optical heterodyne detected optical Kerr effect (OHDOKE) measurements near the IN transition. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a sub-diffusive regime which is followed by a super-diffusive regime before the onset of the longtime diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in the orientational motion particularly at lower temperatures. Interestingly, this behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of recently developed transition matrix Monte Carlo (TMMC) method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order transition, hence allowing for large scale, collective, and correlated orientational density fluctuations. We attribute this large scale fluctuations as the reason for the observed power law decay of the orientational time correlation functions. Part II consists of three chapters, where we focus on the age old problem of nucleation and growth, both from the perspective of thermodynamics and kinetics. We account for the rich history of the problem in the introductory Chapter II.1. In this chapter we describe various types and examples of the nucleation phenomena, and a brief account of the major theoretical approaches used so far. We begin with the most successful Classical Nucleation Theory (CNT), and then move on to more recent applications of Density Functional Theory (DFT) and other mean-field types of models. We conclude with a comparison between the experiments, theories and computational studies. In the next chapter (Chapter II.2) we attempt to elucidate the mechanism of nucleation near the gas-liquid spinodal from a microscopic point of view. Here we construct a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. The free energy, as a function of the size of the largest cluster, develops a pronounced minimum at a subcritical cluster size close to the spinodal. This signifies a two step nature of the process of nucleation, where the rapid formation of subcritical nuclei is followed by further growth by slower density fluctuations on an uphill free energy surface. An alternative free energy pathway involving the participation of many subcritical clusters is envisaged near the spinodal where the growth of the nucleus is found to be promoted by a coalescence mechanism in contrast to the single particle addition assumption within CNT. The growth of the stable phase becomes progressively collective and spatially diffuse, and the significance of a “critical nucleus” is lost for deeper quenches. In this chapter we present our studies both in 3dimensional Lennard-Jones (LJ) system and Ising model (both 2and 3dimensions). Our general findings seem to be independent of the model chosen. While the previous chapter focuses on relatively well-studied 3-dimensional (3D) LJ system, in Chapter II.3 we present our studies on the characteristics of the nucleation phenomena in 2dimensional (2D) Lennard-Jones fluid. To the best of our knowledge this is the first extensive computer simulation study to check the accuracy of CNT in 2D. Using various Monte Carlo methods, we calculate the free energy barrier for nucleation, line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinoidal limit). In 2D, a surprisingly large cutoff (rc ≥ 7.0σ where σ is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. Note that typically 2.5σ is sufficient for 3D LJ fluids. We observe that in 2D system CNT fails to provide a reliable estimate of the free energy barrier. While it is known to slightly overestimate the nucleation barrier in 3D, it underestimates the barrier by as much as 50% at the saturation ratio S = 1.1(defined as S = P/Pc, where Pc is the coexistence pressure) and at the reduced temperature T* = 0.427(defined as T* = KBT/ ε, where ε is the depth of the potential well). The reason for the marked inadequacy of the CNT in 2D can be attributed to the non-circular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable non-circular nature remains even without any cutoff to make the simple CNT inaccurate. Part III again consists of three chapters and focuses on the conformational equilibria. Collapse transition and self-organized structures of n-alkanes in solution. In Chapter III.1 we carry out a brief survey of the existing theories of polymer in solution, with particular emphasis on the collapse process in poor solvents. We also introduce the concept of “hydrophobicity” and “hydrophobic collapse”, which is now a subject enormous interest, partly because it my help in understanding the initial processes involved in protein folding. We briefly discuss the subject of formation of beautiful self-organized structures by block copolymers, and also simple homopolymers which is essentially the focus of the work embodied in the next two chapters. In Chapter III.2 we demonstrated a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures o the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like(circular) for small chains(CnH2n+2; n ≤ 20) and spherical for very long ones( n = 100), we find the emergence of ordered helical structures at intermediate lengths (n ~ 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation(characterized by well-developed 1/f noise, where f is the frequency ) between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier. This appears to support a weakly first order phase transition between the extended and the collapsed states. Chapter III.3 extends the study of previous chapter to much longer chains (n ≥ 100), which irreversibly collapse in water into globular forms. Even though the collapsed form has a nearly spherical shape, close inspection shows a propensity towards local ordering in the alignment of the polymer segments. This tendency to maintain alignment in order to maximize the number of contacts leads to a core-shell like structure, where the shell is often characterized by a bent rod-like shape consisting of two adjacent segments running in parallel. A key event associated with the initial stage of collapse seems to be the formation of a skewed ring (or loop) that serves as a “nucleation center” for rest of the chain to collapse into. Time evolution of the radial distribution function of water surrounding the polymer, shows that the density of neighboring water decreases by only about 15-20% from that of bulk water. Even though interior of the ting-like structures is fully devoid of water, solvent accessible surface representation shows that these regions are geometrically/spatially inaccessible to water molecules. We suggest that the role of water is to stabilize such ring-like structures once formed by natural conformational fluctuations of the polymer chain. This view is confirmed by observation of spontaneous formation and melting away of such ring-like entities in a polar aprotic solvent(DMSO). We also comment on the role of the flexibility of polymer chains in determining the collapse kinetics. The last part(Part IV) of the thesis consists of two chapters that deal with the crystallization of linear polymer chains from dilute solution. The way long chain polymers crystallize is drastically different from their small molecule counterparts due to their topological connectivity. Linear polymers often crystallize from dilute solution in the form of thin lamellae with well-defined crystallographic features. In Chapter IV.1 we briefly survey the current theoretical understanding and confusions associated with the highly debated field of polymer crystallization. While the last few decades have seen the development of many successful phenomenological theories, the molecular mechanism of formation of such self-organized lamellae is extremely complex and very poorly understood. There are clearly two distinct steps in polymer crystallization. Firstly, the individual linear polymers must self-organize into bundles of somewhat regular structures. These structures then further aggregate to lamellar form and crystallize into a lattice. In this respect , it has marked similarity to the problem of protein crystallization. In chapter IV.2 we present Brownian dynamics simulation studies of a single polythelene chain of length 500. Such systems can reasonably mimic the process of crystallization from dilute solutions. Our simulations could successfully reproduce some of the interesting phenomena observed in experiments and very recent computer simulation studies, including multi-center nucleation of rod-like structures within a single polymer chain, an inverse relation between lamellar thickness and temperature etc. But our primary focus has been to understand the nature of the phase transition as one traverses along the melting temperature and the underlying free energy surface. Near the melting temperature we observe a very intriguing fluctuation between the disordered molten globule state and the ordered rod-like crystalline, where these two forms have highly different shape and structure. These fluctuations have strong signature of 1/f noise or intermittency. This clearly indicates the existence of a weakly first order transition, where two widely different states with large difference in values of order parameter are separated by a rather small free energy barrier. This can be related to the experimentally observed density fluctuations that resemble spinodal decomposition. It is important to note that very similar fluctuations have been observed in our previous studies on liquid crystals (Chapter 1.2) and intermediate sized alkalines in water(Chapter III.2) that signifies a universal underlying energy landscape for these systems. We have discussed the scope of future work at the end of each chapter whenever appropriate.

In dieser Arbeit werden Messungen der elektrischen und thermischen Transportkoeffizienten an einem antiferromagnetisch ordnenden Iridat und FeAs-basierten Hochtemperatursupraleitern vorgestellt und analysiert. Iridate sind Materialien mit starker Spin-Bahn-Kopplung. In dem zweidimensionalen Vertreter Sr_2IrO_4 führt diese Kopplung zu isolierendem Mott-Verhalten mit gleichzeitiger antiferromagnetischer Ordnung der gekoppelten Spin-Bahn-Momente. Somit stellt Sr2IrO4 ein Modellsystem für die Untersuchung magnetischer Anregungen dieser Momente in Iridaten dar. Die Analyse der Wärmeleitfähigkeit von Sr_2IrO_4 liefert erstmals klare Hinweise auf magnetische Wärmeleitung in den Iridaten. Die extrahierte magnetische freie Weglänge gibt Aufschluss über die Streuprozesse der zum Wärmetransport beitragenden Magnonen und lässt Schlüsse über die Anregungen des gekoppelten Spin-Bahnsystems zu. Die FeAs-Hochtemperatursupraleiter haben aufgrund ihrer geschichteten Kristallstruktur einen hauptsächlich zweidimensionalen Ladungstransport. Die Phasendiagramme dieser Materialien setzen sich aus Ordnungsphänomenen zusammen, die Magnetismus, Supraleitung und eine Strukturverzerrung umfassen. Das Hauptaugenmerk richtet sich auf die Reaktion der Transportkoeffizienten mit den sich ausbildenden Phasen in Vertretern der 111- und 122-Familien unter chemischer Dotierung innerhalb und außerhalb der Schichtstruktur. Mithilfe von Widerstand und magnetischer Suszeptibilität lassen sich Phasendiagramme der verschiedenen Supraleiterfamilien konstruieren. In ausgewählten Fällen werden der Hall-Koeffizient und elektrothermische Transporteffekte genutzt, um das Phasendiagramm näher zu erforschen. Der Großteil der Untersuchungen zeigt omnipräsente elektrische Ordnungsphänomene, die als nematische Phase bezeichnet werden. Die Messdaten zeigen, dass die Wärmeleitfähigkeit und der Nernst-Koeffizient dominant von Fluktuationen, die der nematischen Phase vorausgehen, beeinflusst werden. Aus den Ergebnissen der Nernst-Daten an dotiertem BaFe_2As_2 werden Schlüsse über die der nematischen Phase zugrunde liegenden Mechanismen des korrelierten Elektronensystems gezogen.

Nesta tese estudamos um modelo de spins do tipo Ising, modelo J1 J2, com interações competitivas J1 ferromagnéticas entre primeiros vizinhos na rede quadrada e J2 antiferromagnética entre segundos vizinhos. O diagrama de fases do modelo e as correlações de pares foram analisadas com o Método do Aglomerado Variacional nos casos sem e com um campo magnético externo. A campo nulo, construímos o diagrama de fases no plano T=J1 onde = jJ2j=J1. A transição ferromagnética-paramagnética é de segunda ordem quando < 1=2 e a transição stripes-paramagnética de primeira ordem para 1=2 < < 1 e de segunda ordem para valores de 1. Nossos resultados concordam com prévios estudos. Ao aplicarmos um campo magnético externo ao sistema, em regiões onde a campo nulo se observa a fase de stripes ( = 0:6 e = 1), as filas (ou colunas) de spins paralelos ao campo externo ganham estabilidade dando lugar a uma fase de stripes mista com magnetizações nas filas e colunas com magnitudes diferentes. A campos maiores, o sistema se encontra numa fase homogênea com uma magnetização remanente, a fase paramagnética saturada. Na interfase entre a fase de stripes e a paramagnética saturada, encontramos uma fase intermediária nemática do tipo Ising. Esta fase possui uma magnetização homogênea e correlações de pares anisotrópicas nas direções x e y quantificadas por um parâmetro de ordem orientacional. A fase nemática tem sido observada principalmente em sistemas com interações competitivas de longo alcance. O uso do Método do Aglomerado Variacional na aproximação de quatro pontos permitiu detectá-la no modelo J1 J2 clássico. A presença da fase nemática intermediária foi confirmada em simulações de Monte Carlo. As transições stripes-paramagnética saturada e stripes-nemática são de primeira ordem e a transição nemática-paramagnética saturada é uma transição de segunda ordem de acordo com a análise da energia livre. Na segunda parte do nosso estudo, calculamos o fator de estrutura na aproximação de quatro pontos do Método do Aglomerado Variacional válido tanto nas fases desordenada como ordenadas no modelo sem e com campo magnético. A partir desta análise, determinamos as linhas de estabilidade para a fase paramagnética no modelo sem campo e também mostramos a existência destas linhas na solução de stripes. No modelo com campo, estudamos o fator de estrutura e a susceptibilidade reduzida para = 0:6 e diferentes temperaturas. A susceptibilidade é descontínua nas transições stripes-paramagnética saturada e stripes-nemática compatível com uma transição de primeira ordem. Por sua vez, na transição nemática-paramagnética saturada de segunda ordem se observa um máximo em uma das componentes da susceptibilidade no espaço recíproco e um câmbio da simetria Z2 para a Z4 no fator de estrutura. / In this thesis, we studied a Ising model, the J1 J2 model, with nearest neighbors ferromagnetic interactions J1 and next-nearest antiferromagnetic neighbors interactions J2. The phase diagram and the pair correlations were analyzed with the Cluster Variation Method, with and without an external magnetic field. At zero field, we build the phase diagram in the plane T=J1 where = jJ2j=J1. The ferromagnetic-paramagnetic phase transition is a second order one at < 1=2. The stripes-paramagnetic is a first order transition when 1=2 < < 1 and second order for values bigger than one. Our results are in agreement with previous works. Applying an external magnetic field to the system, in regions where the ground state is stripes ( = 0:6 e = 1), the columns (or rows) of parallel spins to the field gain stability given place to a mixed phase with columns (or rows) magnetization with different magnitudes. At higher fields, the systems enters in a homogeneous phase with a remanent magnetization, the saturated paramagnetic phase. In the interface between the stripes and saturated paramagnetic phase we found a intermediate phase, the Ising-nematic. This phase has a homogeneous magnetization and anisotropic nearest-neighbor correlations in the directions x and y quantified by a orientacional order parameter. The nematic phase has been observed in systems with long range interactions. The Cluster Variation Method (CVM) in the four site approximation detected the nematic phase in the classical J1 J2 model. These results were confirmed by Monte Carlo simulations. The stripes-saturated paramagnetic and stripes-nematic transitions are found to be first order transitions. The nematic-saturated paramagnetic is of second order according to free energy analysis. In the second part, we computed the structure factor in the four-site approximation of the CVM. This expression is valid for order and disorder phases, with or without a magnetic field. Through this analysis we found the paramagnetic stability lines in the model at zero magnetic field, we also showed the existence of spinodal temperature for stripes solutions. In the model with a magnetic field, we studied the structure factor and susceptibility for = 0:6 and different temperatures. A discontinuity in susceptibility was observed in the stripes-saturated paramagnetic and stripes-nematic transitions compatible with a first order transition. In the nematic-saturated paramagnetic second order transition we found a maximum in one of the susceptibility components and a change of the Z2 symmetry to the Z4 in the structure factor.

Les nanocristaux de cellulose (NCC), obtenus par hydrolyse acide des microfibrilles de cellulose native sous forme de suspensions colloïdales aqueuses, sont des nanoparticules biosourcées ayant des propriétés mécaniques et optiques particulièrement séduisantes pour la conception de nanomatériaux à haute performance. Pour éliminer certaines de leurs limitations comme la sensibilité au sel et l'absence de contrôle de leurs interactions, nous nous sommes attachés au cours de ce travail à modifier chimiquement ces NCC par greffage de chaînes de polymère thermosensible de la famille de polyétheramines Jeffamine® sur leur surface. La première méthode de greffage utilisée faisait appel à une oxydation TEMPO suivie d'un couplage peptidique. Après l'optimisation de la réaction de greffage, les nouveaux systèmes (NCC-g-Jeffamine) ont été caractérisés et de nouvelles propriétés ont été identifiées notamment leur insensibilité au sel, leur capacité de redispersion dans des solvants organiques, leur caractère tensioactif, leur stabilité thermique améliorée ainsi que leur thermoagrégation réversible. L'étude structurale par diffusion des neutrons aux petits angles a permis d'avoir des informations sur les épaisseurs des couches de polymère greffé ainsi que sur la conformation des chaînes. De nouvelles caractéristiques de l'auto-organisation en phase chirale-nématique de ces nouveaux systèmes ont été notées concernant leur diagramme de phase et leur pas cholestériques. La deuxième méthode de greffage explorée consistait en une oxydation aux ions métapériodate suivie d'une amination réductrice. Les résultats ont montré un détachement partiel des chaînes de cellulose suite à l'oxydation puis leur détachement complet après le greffage du polymère pour obtenir des copolymères cellulose-Jeffamine ayant éventuellement des propriétés intéressantes à étudier. / Cellulose nanocrystals (CNC), obtained by acid hydrolysis of native cellulose microfibrils as colloidal aquous suspensions, are bioresourced nanoparticles that have great mechanical and optical properties well adapted for the conception of new nanomaterials with high performance. In order to eliminate some of their limitations like sensitivity to salt and absence of interactions control, we studied in this work the chemical modification of these CNC by grafting thermoresponsive polymer chains (polyetheramines Jeffamine®) on the their surface. A first grafting strategy used was a TEMPO oxidation followed by peptidic coupling. After the optimization of the grafting reaction, the new systems (CNC-g-Jeffamine) were characterized and new properties were identified particularly their insensitivity to salts, their ability to be redispersed in organic solvents, their surfactant character, their enhanced thermal stability and their reversible thermoagregation. The structural study using small angles neutrons scattering gave us information about thicknesses of the polymer corona and the chains conformation. New characteristics of their self-assembly into chiral-nematic phases were noticed more particularly concerning phase diagrams and cholesteric pitches. The second grafting strategy consisted in an oxidation using periodate ion followed by reductive amination. Results showed a partial detachment of cellulose chains after oxidation. A complete detachment was observed after grafting the polymer chains to finally obtain cellulose-Jeffamine copolymers which could have interesting properties to study.

Nesta tese estudamos um modelo de spins do tipo Ising, modelo J1 J2, com interações competitivas J1 ferromagnéticas entre primeiros vizinhos na rede quadrada e J2 antiferromagnética entre segundos vizinhos. O diagrama de fases do modelo e as correlações de pares foram analisadas com o Método do Aglomerado Variacional nos casos sem e com um campo magnético externo. A campo nulo, construímos o diagrama de fases no plano T=J1 onde = jJ2j=J1. A transição ferromagnética-paramagnética é de segunda ordem quando < 1=2 e a transição stripes-paramagnética de primeira ordem para 1=2 < < 1 e de segunda ordem para valores de 1. Nossos resultados concordam com prévios estudos. Ao aplicarmos um campo magnético externo ao sistema, em regiões onde a campo nulo se observa a fase de stripes ( = 0:6 e = 1), as filas (ou colunas) de spins paralelos ao campo externo ganham estabilidade dando lugar a uma fase de stripes mista com magnetizações nas filas e colunas com magnitudes diferentes. A campos maiores, o sistema se encontra numa fase homogênea com uma magnetização remanente, a fase paramagnética saturada. Na interfase entre a fase de stripes e a paramagnética saturada, encontramos uma fase intermediária nemática do tipo Ising. Esta fase possui uma magnetização homogênea e correlações de pares anisotrópicas nas direções x e y quantificadas por um parâmetro de ordem orientacional. A fase nemática tem sido observada principalmente em sistemas com interações competitivas de longo alcance. O uso do Método do Aglomerado Variacional na aproximação de quatro pontos permitiu detectá-la no modelo J1 J2 clássico. A presença da fase nemática intermediária foi confirmada em simulações de Monte Carlo. As transições stripes-paramagnética saturada e stripes-nemática são de primeira ordem e a transição nemática-paramagnética saturada é uma transição de segunda ordem de acordo com a análise da energia livre. Na segunda parte do nosso estudo, calculamos o fator de estrutura na aproximação de quatro pontos do Método do Aglomerado Variacional válido tanto nas fases desordenada como ordenadas no modelo sem e com campo magnético. A partir desta análise, determinamos as linhas de estabilidade para a fase paramagnética no modelo sem campo e também mostramos a existência destas linhas na solução de stripes. No modelo com campo, estudamos o fator de estrutura e a susceptibilidade reduzida para = 0:6 e diferentes temperaturas. A susceptibilidade é descontínua nas transições stripes-paramagnética saturada e stripes-nemática compatível com uma transição de primeira ordem. Por sua vez, na transição nemática-paramagnética saturada de segunda ordem se observa um máximo em uma das componentes da susceptibilidade no espaço recíproco e um câmbio da simetria Z2 para a Z4 no fator de estrutura. / In this thesis, we studied a Ising model, the J1 J2 model, with nearest neighbors ferromagnetic interactions J1 and next-nearest antiferromagnetic neighbors interactions J2. The phase diagram and the pair correlations were analyzed with the Cluster Variation Method, with and without an external magnetic field. At zero field, we build the phase diagram in the plane T=J1 where = jJ2j=J1. The ferromagnetic-paramagnetic phase transition is a second order one at < 1=2. The stripes-paramagnetic is a first order transition when 1=2 < < 1 and second order for values bigger than one. Our results are in agreement with previous works. Applying an external magnetic field to the system, in regions where the ground state is stripes ( = 0:6 e = 1), the columns (or rows) of parallel spins to the field gain stability given place to a mixed phase with columns (or rows) magnetization with different magnitudes. At higher fields, the systems enters in a homogeneous phase with a remanent magnetization, the saturated paramagnetic phase. In the interface between the stripes and saturated paramagnetic phase we found a intermediate phase, the Ising-nematic. This phase has a homogeneous magnetization and anisotropic nearest-neighbor correlations in the directions x and y quantified by a orientacional order parameter. The nematic phase has been observed in systems with long range interactions. The Cluster Variation Method (CVM) in the four site approximation detected the nematic phase in the classical J1 J2 model. These results were confirmed by Monte Carlo simulations. The stripes-saturated paramagnetic and stripes-nematic transitions are found to be first order transitions. The nematic-saturated paramagnetic is of second order according to free energy analysis. In the second part, we computed the structure factor in the four-site approximation of the CVM. This expression is valid for order and disorder phases, with or without a magnetic field. Through this analysis we found the paramagnetic stability lines in the model at zero magnetic field, we also showed the existence of spinodal temperature for stripes solutions. In the model with a magnetic field, we studied the structure factor and susceptibility for = 0:6 and different temperatures. A discontinuity in susceptibility was observed in the stripes-saturated paramagnetic and stripes-nematic transitions compatible with a first order transition. In the nematic-saturated paramagnetic second order transition we found a maximum in one of the susceptibility components and a change of the Z2 symmetry to the Z4 in the structure factor.