254 research outputs found

    Microphase separation in thin block copolymer films: a weak segregation mean-field approach

    Full text link
    In this paper we consider thin films of AB block copolymer melts confined between two parallel plates. The plates are identical and may have a preference for one of the monomer types over the other. The system is characterized by four parameters: the Flory-Huggins chi-parameter, the fraction f of A-monomers in the block copolymer molecules, the film thickness d, and a parameter h quantifying the preference of the plates for the monomers of type A. In certain regions of parameter space, the film will be microphase separated. Various structures have been observed experimentally, each of them characterized by a certain symmetry, orientation, and periodicity. We study the system theoretically using the weak segregation approximation to mean field theory. We restrict our analysis to the region of the parameter space where the film thickness d is close to a small multiple of the natural periodicity. We will present our results in the form of phase diagrams in which the absolute value of the deviation of the film thickness from a multiple of the bulk periodicity is placed along the horizontal axis, and the chi-parameter is placed along the vertical axis; both axes are rescaled with a factor which depends on the A-monomer fraction f. We present a series of such phase diagrams for increasing values of the surface affinity for the A-monomers. We find that if the film thickness is almost commensurate with the bulk periodicity, parallel orientations of the structures are favoured over perpendicular orientations. We also predict that on increasing the surface affinity, the region of stability of the bcc phase shrinks.Comment: 35 pages, 20 figure

    Coming Full Circle with Boyd\u27s OODA Loop Ideas: An Analysis of Innovation Diffusion and Evolution

    Get PDF
    The Observe-Orient-Decide-Act (OODA) Loop ideas of Air Force Colonel John Boyd have impacted the Department of Defense (DoD), influenced military thought, paved the way for operational change, and helped to shape fighting doctrines. A wide variety of OODA Loop ideas and interpretations exist in the literature, but are unorganized and have not undergone holistic study to determine how Boyd\u27s ideas have spread or changed over time. As such, this research analyzed a quarter century (1976-2003) sample of the OODA Loop literature to examine the diffusion and evolution of OODA Loop ideas since Boyd\u27s original conceptualizations. This research used qualitative data analysis to examine OODA Loop ideas in light of innovation diffusion theory. Ideas from Boyd\u27s original OODA Loop theories were compared and contrasted with subsequent literature instances to assess diffusion and evolution of OODA Loop ideas in the DoD. This research concluded with a proposed conceptual framework for collectively considering OODA Loop ideas

    The phase behavior of polydisperse multiblock copolymer melts : (a theoretical study)

    Get PDF
    Summary The main theme of this thesis is the influence of polydispersity on the phase behavior of copolymer melts. With “polydispersity” we do not only refer to polydispersity in overall chain length, but also to polydispersity in the composition and the monomer sequence of the chains. Study of the influence of polydispersity is important because synthesizing purely monodisperse copolymers is very difficult, and for most polymerization techniques the occurrence of a certain degree of polydispersity is inevitable. We start with a short discussion about phase separation. A homopolymer is a chain molecule consisting of only one sort of link (monomer). For many homopolymer blends, i.e. mixtures of different homopolymers, the homogeneous state becomes unstable on lowering the temperature, and the different molecule species tend to separate from each other. The result is a splitting of the system into coexisting phases. Each of these phases separately is homogeneous, but they differ in composition. The separation of a polymer blend into coexisting homogeneous phases is called macrophase separation. In a copolymer, on the other hand, different monomer types are chemically linked together. Therefore, a complete separation of the system into the different monomer types is impossible. Instead, on lowering the temperature the phase separation occurs on a microscopic length scale. Small domains rich in one monomer type are alternated by small domains rich in the other. Usually, these domains are arranged in a regular pattern. When in a copolymer system such domains arise, we talk about microphase separation. The research described in this thesis was restricted to copolymers consisting of two monomer types, henceforth denoted by A and B. Most attention was paid to the so-called random copolymers. In random copolymer chains, the correlation in chemical identity between two monomers decays exponentially with their mutual distance along the chain. It has been assumed that within the chains, like monomers tend to aggregate to form long sequences of identical monomers. Such sequences are called blocks. The block length distribution in random copolymers is very broad: the variation in the block lengths is of the same order of magnitude as the block lengths themselves. Homopolymers having such a length distribution can be formed by a polycondensation reaction, after which they can be linked together to form a multiblock copolymer chain. With the phase behavior of a polymer system we mean the phase of the system as a function of temperature. The phase contains information about the volumes and compositions of the coexisting phases in case of macrophase separation, and the size and the spatial arrangement of the microscopic domains in case of microphase separation. In chapter 1 we describe the theory which enables the calculation of the phase behavior of a large class of polydisperse copolymer melts. In chapter 2 we describe how the regular periodic spatial arrangement of the domains in a microphase separated copolymer melt can be described mathematically. In chapter 3 the phase behavior of the correlated random copolymer melt is calculated in the so-called meanfield approximation, which means that it is assumed that the concentration profile is static (the concentration profile describes the spatial dependence of the A-monomer fraction). This approximation becomes more accurate if the block lengths in the system increase. In chapter 3 we derive an expression for the free energy of a random copolymer melt, and using this expression it is shown that the system tends to microphase separate. The A-rich and B-rich domains appear to have a regular spatial arrangement despite the intrinsic disorder present in the sequence distribution along the chains. In chapter 4 the study of the correlated random copolymer is continued by taking into account the possibility of macrophase separation. It is shown that for certain values of the composition and temperature the melt can indeed separate into coexisting phases, but at least one of these phases has to be microphase separated. Nevertheless, it is very doubtful whether the system will ever reach this two-phase state under experimental conditions, because macrophase separation requires a complete spatial rearrangement of the molecules, which is a very slow process due to the restricted mobility of the chains. In chapter 5 we go beyond the mean-field approximation. As indicated above, in the mean-field approximation it is assumed that the profile is regular, smooth, and static. In reality, however, irregular, time-dependent disturbances are present. These disturbances are called fluctuations. It is to be expected that due to the intrinsic disorder in the monomer distribution along random copolymer chains, fluctuations will be rather important in systems consisting of these molecules. This expectation is confirmed by the analysis in chapter 5. It is shown that the regular structures predicted in chapter 3 are strongly distorted, giving the concentration profile a disordered appearance. In chapter 6 a more general class of copolymers is considered, namely polydisperse multiblock copolymers for which the average number of blocks per chain, and the average number of momomers per block are very large. The length distribution of the A-blocks is arbitrary, and may differ from the arbitrary length distribution of the B-blocks. The correlated random copolymer studied in the previous chapter belongs to this general class, if we choose a Flory distribution both for the lengths of the A-blocks, and for the lengths of the B-blocks. In chapter 6 we calculate and compare the mean-field phase diagrams for various realizations of the block length distributions. By changing continuously the degree of polydispersity, it is possible to study its influence on the phase behavior.

    Freezing in polyampholyte globules: Influence of the long-range nature of the interaction

    Full text link
    In random heteropolymer globules with short-range interactions between the monomers, freezing takes place at the microscopic length scale only, and can be described by a 1-step replica symmetry breaking. The fact that the long-range Coulomb interaction has no intrinsic length scale suggests that freezing in random polyampholyte globules might take place at all length scales, corresponding to an overlap parameter q(x) that increases continuously from zero to its maximum value. Study of the polyampholyte globule within the independent interaction approximation seems to confirm this scenario. However, the independent interaction model has an important deficiency: it cannot account for self-screening, and we show that the model is only reliable at length scales shorter than the self-screening length. Using the more realistic sequence model we prove that in the general case of a random heteropolymer globule containing two types of monomers such that unlike monomers attract each other, freezing at arbitrarily large length scales is not possible. For polyampholyte globules this implies that beyond the self-screening length, the freezing behavior is qualitatively the same as in the case of short-range interactions. We find that if the polyampholyte globule is not maximally compact, the degree of frustration is insufficient to obtain freezing.Comment: 28 pages, 5 figures, submitted to J.Chem.Phy

    Effects of polydispersity on the phase coexistence diagrams in multiblock copolymers with Laser block length distribution

    Full text link
    Phase behavior of AB-multiblock copolymer melts which consists of chains with Laser distribution of A and B blocks have been investigated in the framework of the mean-field theory, where the polydispersity of copolymer is a function of two parameters K and M. The influence of the Laser distribution on higher order correlation functions (up to sixth order) are computed for various values of K and M, and their contributions on the phase diagrams and phase coexistence are presented. It is shown that, with increasing polydispersity (decreasing K and increasing M) the transition lines of all phases shift upwards, consequently polydispersity destabilize the system.Comment: 15 pages, Late

    Menu-driven cloud computing and resource sharing for R and Bioconductor

    Get PDF
    Summary: We report CRdata.org, a cloud-based, free, open-source web server for running analyses and sharing data and R scripts with others. In addition to using the free, public service, CRdata users can launch their own private Amazon Elastic Computing Cloud (EC2) nodes and store private data and scripts on Amazon's Simple Storage Service (S3) with user-controlled access rights. All CRdata services are provided via point-and-click menus. Availability and Implementation: CRdata is open-source and free under the permissive MIT License (opensource.org/licenses/mit-license.php). The source code is in Ruby (ruby-lang.org/en/) and available at: github.com/seerdata/crdata
    • …
    corecore