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1.
Opt Express ; 32(4): 5659-5670, 2024 Feb 12.
Artigo em Inglês | MEDLINE | ID: mdl-38439286

RESUMO

The synthesis of laser coherence and the accuracy of beam scanning, which are based on an optical phased array (OPA), are severely constrained by phase noise. This limitation hampers their applications in various fields. Currently, the most widely utilized calibration method is adaptive optics, which can effectively mitigate phase noise and enhance the quality of the output beam. However, because of the multiple array elements of the OPA and the large optimization range for each element, the adaptive optimization method experiences slow convergence and a high risk of falling into local optima. We propose a narrowing search range algorithm that can quickly reduce phase noise by narrowing the search range of the optimal value. After initial optimization, the SPGD algorithm was used. This study was verified through simulations and experiments utilizing the OPA of various array elements. These findings indicate that the hybrid algorithm expedites the calibration process, requires simple experimental equipment, and can be broadly utilized.

2.
Phys Med Biol ; 69(4)2024 Feb 05.
Artigo em Inglês | MEDLINE | ID: mdl-38198716

RESUMO

Objective.The high-precision segmentation of retinal vessels in fundus images is important for the early diagnosis of ophthalmic diseases. However, the extraction for microvessels is challenging due to their characteristics of low contrast and high structural complexity. Although some works have been developed to improve the segmentation ability in thin vessels, they have only been successful in recognizing small vessels with relatively high contrast.Approach.Therefore, we develop a deep learning (DL) framework with a multi-stage and dual-channel network model (MSDC_NET) to further improve the thin-vessel segmentation with low contrast. Specifically, an adaptive image enhancement strategy combining multiple preprocessing and the DL method is firstly proposed to elevate the contrast of thin vessels; then, a two-channel model with multi-scale perception is developed to implement whole- and thin-vessel segmentation; and finally, a series of post-processing operations are designed to extract more small vessels in the predicted maps from thin-vessel channels.Main results.Experiments on DRIVE, STARE and CHASE_DB1 demonstrate the superiorities of the proposed MSDC_NET in extracting more thin vessels in fundus images, and quantitative evaluations on several parameters based on the advanced ground truth further verify the advantages of our proposed DL model. Compared with the previous multi-branch method, the specificity and F1score are improved by about 2.18%, 0.68%, 1.73% and 2.91%, 0.24%, 8.38% on the three datasets, respectively.Significance.This work may provide richer information to ophthalmologists for the diagnosis and treatment of vascular-related ophthalmic diseases.


Assuntos
Algoritmos , Aprendizado Profundo , Compostos de Espiro , Vasos Retinianos/diagnóstico por imagem , Aumento da Imagem , Processamento de Imagem Assistida por Computador/métodos
3.
Polymers (Basel) ; 15(24)2023 Dec 15.
Artigo em Inglês | MEDLINE | ID: mdl-38139972

RESUMO

A combination of starch and hydrocolloids is a facile method for physically modifying native starch. Bletilla striata polysaccharide (BSP) is a glucomannan with various applications in the food and cosmetic industries as a thickening agent. This study focused on investigating the impact of BSP on the pasting, rheological and adhesive properties of wheat starch (WS). Results from a Rapid Visco-Analyzer (RVA) revealed that the addition of BSP (below 0.2%) resulted in increases in peak viscosity, breakdown and setback values. However, for the addition of BSP at a higher concentration (0.3%), the opposite trend was observed. Rheological measurements indicated that the presence of BSP increased the viscoelastic properties of WS-BSP gels. TGA results demonstrated that the presence of BSP promoted the thermal stability of starch. FTIR results indicated the short-range order structure decreased at low addition concentrations of BSP (0.05% and 0.1%) and increased with higher BSP addition concentrations (0.2% and 0.3%). SEM observation showed that the BSP improved the hydrophilic property of starch gels and decreased the size of pores in the starch gels. Further, the mechanical properties of paper samples unveiled that the present of BSP in starch gels obviously increased its bonding strength as an adhesive.

4.
Molecules ; 28(19)2023 Sep 25.
Artigo em Inglês | MEDLINE | ID: mdl-37836634

RESUMO

Invaluable paper relics that embody a rich traditional culture have suffered damage, requiring urgent restoration. In this context, the utilization of soymilk as a sizing agent holds great significance and reverence. This study investigates the use of soymilk as a sizing agent for Xuan paper and evaluates its effects on various properties and the long-term behavior of the paper. The findings reveal that the application of soymilk as a sizing agent for Xuan paper imparts distinct properties, including hydrophobicity, improved mechanical properties, and unique chromaticity. These characteristics-arising from the papillae on the surface of the Xuan paper, the protein folding of the soy protein, and hydrogen-bonding interactions between the soy protein and paper fibers-play a crucial role in shaping the paper's unique attributes. From a physicochemical perspective, the aging process leads to multiple changes in paper properties. These changes include acidification, which refers to a decrease in pH, as well as a decline in mechanical strength, an increase in chromaticity, and a decrease in the degree of polymerization (DP) of the paper. The Ekenstam equation is employed to predict the lifespan of the paper, showing longer lifespans for Sheng Xuan paper and a negative correlation between soymilk concentration and lifespan in soymilk-sized paper. Our work provides valuable insights for the preservation and maintenance of paper, highlighting the potential benefits and challenges of using soymilk for surface sizing.


Assuntos
Leite de Soja , Proteínas de Soja , Proteínas de Soja/química , Leite de Soja/química , Fenômenos Químicos
5.
Molecules ; 28(18)2023 Sep 17.
Artigo em Inglês | MEDLINE | ID: mdl-37764445

RESUMO

Wheat starch (WS) is a common adhesive material used in mounting of calligraphy and paintings. Potassium alum (PA) has indeed been used for many centuries to modify the physicochemical properties of starch. Thermal analysis revealed that the presence of PA led to an increase in the gelatinization temperature and enthalpy of the starch gels. The leached amylose and the swelling power of the starch gels exhibited a maximum at the ratio of 100:6.0 (WS:PA, w/w). The rheological properties of starch gels were consistent with changes in the swelling power of starch granules. SEM observations confirmed that the gel structure became more regular, and the holes grew larger with the addition of PA below the ratio of 100:6.0 (WS:PA, w/w). The short-range molecular order in the starch gels was enhanced by the addition of PA, confirmed by FT-IR analysis. Mechanical experiments demonstrated that the binding strength of the starch gels increased with higher PA concentrations and decreased significantly after the aging process. TGA results revealed that PA promoted the acid degradation of starch molecules. This study provides a detailed guide for the preparation of starch-based adhesive and its applications in paper conservation.

6.
Phys Chem Chem Phys ; 25(3): 1642-1648, 2023 Jan 18.
Artigo em Inglês | MEDLINE | ID: mdl-36510818

RESUMO

In this work, we systematically study an immiscible binary system undergoing thermal/photo reversible reactions in theory. For the thermal reaction case, no dissipative structures can be formed and only uniform equilibrium states are observed but the dynamical evolution to these trivial states witnesses a new type of sophisticated phase amplification phenomenon-temporary phase separation (TPS). Linear analysis and light-scattering calculations confirm that TPS is predominated either by spinodal decomposition or nucleation and growth mechanism, or by both successively. For the photo reaction case, steady dissipative patterns exist and are maintained by the external energy input of lights. Linear analysis together with simulations reveals that the characteristic wavelength (ξ) of these structures shortens as the input energy density increases and they obey the relation of ln ξ∝ 1/Tb with Tb the effective temperature of lights. The TPS phenomenon and length-scale dependency of dissipative patterns observed in this simple binary system might have rich implications for the non-equilibrium thermodynamics of biological systems.

7.
Vaccine ; 39(29): 3871-3878, 2021 06 29.
Artigo em Inglês | MEDLINE | ID: mdl-34088505

RESUMO

Quadrivalent influenza inactivated vaccine (IIV4) is more likely to provide wider protection against yearly circulating influenza viruses than trivalent inactivated influenza vaccine (IIV3). In this study, a total of 320 participants were allocated to four age cohorts (6-35 months, 3-8 years, 9-17 years, and ≥ 18 years; 80 participants/cohort) according to their actual date of birth. Participants in each cohort were randomly assigned to two groups to receive intramuscular injection of the trial vaccine or the comparative vaccine in a one-dose (3-8 years, 9-17 years,and ≥ 18 years) schedule on day 0 or two-dose (6-35 months cohort) schedule on day 0 and 28. The first objective is to evaluate the safety and immunogenicity of the full-dose subunit non-adjuvanted IIV4 (FD-subunit NAIIV4) we developed versus an active-control, China-licensed split-virion NAIIV4, in people ≥ 3 years. The second objective is to evaluate the safety and immunogenicity of FD-subunit NAIIV4 versus the half-dose (HD-subunit NAIIV4) in toddlers aged 6-35 months. Results showed that all adverse reactions noted were rare, mild, and self-limited. In ≥ 3 years cohorts, systemic adverse reactions in FD-subunit NAIIV4 groups were less than the active control split-virion NAIIV4 groups ([Systemic adverse reaction rates (95%CI)], 15.0 (8.6-21.4) versus 19.2(12.1-26.2), p = 0.391). The overall seroprotection efficacy after vaccination were comparable between FD-subunit NAIIV4 and the active control split-virion NAIIV4([Seroprotection rates (95%CI)], H1N1, 99.2(81.3-100.0) versus 94.9(90.9-98.9), p = 0.117; H3N2, 81.7(74.7-88.6) versus 82.1(75.1-89.0), p = 0.939; BV, 75.8(68.2-83.5) versus 74.4(66.4-82.3), p = 0.793; BY, 94.2(90.0-98.4) versus 92.3(87.5-97.1), p = 0.568). Additionally, FD-subunit NAIIV4 has comparable safety and better seroprotection versus that of the half-dose in 6-35 months toddlers groups ([Total adverse reaction rates (95%CI)], 37.5(18.5-56.5) versus 47.5(26.1-68.9), p = 0.366) ([Seroprotection rates (95%CI)], H1N1, 85(56.4-100.0) versus 75.7(47.6-100.0), p = 0.117; H3N2, 50(28.1-71.9) versus 29.7(12.2-47.3), p = 0.070; BV, 75(48.2-100.0) versus 29.7(12.2-47.3), p < 0.001; BY, 75(48.2-100.0) versus 56.8(32.5-81.0), p = 0.091). As a result, the FD-subunit NAIIV4 we developed is safe and effective to provide broader and adequate protection against the circulating influenza viruses during 2018-2019, which could be an essential component of the global preventive strategy for influenza pandemic.


Assuntos
Vírus da Influenza A Subtipo H1N1 , Vacinas contra Influenza , Influenza Humana , Anticorpos Antivirais , China , Método Duplo-Cego , Testes de Inibição da Hemaglutinação , Humanos , Imunogenicidade da Vacina , Lactente , Vírus da Influenza A Subtipo H3N2 , Vacinas contra Influenza/efeitos adversos , Influenza Humana/prevenção & controle , Vacinas de Produtos Inativados/efeitos adversos
8.
IEEE Trans Haptics ; 13(2): 312-324, 2020.
Artigo em Inglês | MEDLINE | ID: mdl-31603800

RESUMO

Achieving high stiffness and low inertia is a big challenge for current haptic devices. Impedance-based devices are limited in providing high stiffness while, in contrast, admittance-based devices are limited in generating low inertia. Thus, it is difficult to simulate hard contact and small inertia simultaneously in virtual environments. In this paper, we introduce a co-actuation module to overcome this difficulty. The module is a one degree-of-freedom (DOF) revolute joint which consists of a link and a physical constraint with a clearance between the two components. A motor controls the physical constraint moving cooperatively with the link. In free space, the constraint has no contact to the link and thus, users can move the link freely without feeling the inertia of the motor. In constrained space, the constraint comes into contact with the link and thus, users can feel a resistance from the motor. By means of a direct physical contact between the link and the constraint, users can feel a hard virtual surface. This paper describes the principle and the implementation of the proposed co-actuation module. Performance evaluation was conducted using a two-DOF haptic device in a task workspace of 100 mm × 100 mm. The effective inertia of the device is 64-142 g within the task workspace. The device can stably render a virtual wall with stiffness as high as 65 N/mm. The penetration to the virtual wall was 0.02-0.41 mm when tapping the wall with a speed range of 80-320 mm/s. The maximum back driving force was about 0.19 N when moving within 4.5-8.6 mm/s. The experimental results demonstrate that the concept of co-actuation is feasible in achieving high force, high stiffness range and low inertia for haptic devices.


Assuntos
Desenho de Equipamento , Retroalimentação Sensorial , Desempenho Psicomotor , Percepção do Tato , Interface Usuário-Computador , Adulto , Desenho de Equipamento/normas , Estudos de Viabilidade , Humanos , Estudo de Prova de Conceito
9.
ACS Omega ; 4(23): 20367-20380, 2019 Dec 03.
Artigo em Inglês | MEDLINE | ID: mdl-31815241

RESUMO

We apply the string method to the self-consistent mean-field theory framework of the rod-coil block copolymer system to calculate the minimum energy pathways in the rearrangement transitions of lamellae and cylinders with different orientations under certain epitaxial growth relationship. Metastable phases appearing in the reordering transition pathway tend to form the structure at low χN side of the order-order transition boundary compared with the initial phase. In particular, for complex network, metastable phases, such as single gyroid and perforated lamellae, need to select a rearrangement transition between lamellae or cylinders near the order-disorder transition boundary with the same epitaxial growth relationship but different orientations. It is confirmed that this strategy for obtaining complex metastable phases by rational design of rearrangement transition between specific phases in the phase diagram can be applied to a wide range of χN as well as the coil-coil block copolymer system. We further investigate the rearrangement transition behavior combining with the analysis of contribution from the free energy, entropy, degree of mixing between different blocks, and the average orientation degree of rods during the phase transitions. Based on this mechanism, we have developed a target-directed design strategy for constructing self-assembled metastable structures of rod-coil block copolymers.

10.
Phys Rev Lett ; 123(10): 108002, 2019 Sep 06.
Artigo em Inglês | MEDLINE | ID: mdl-31573310

RESUMO

Macromolecules contain molecular units as the coding information for their correlated structures in physical dimensions. The relationship between these two features is governed by the interaction energies of the involved molecular units and their encoded sequences. We present a neural network algorithm that treats molecular units themselves as neural networks, which has the flexibility to allow each unit to respond to its own environment and to influence others in the system. Through a deep neural network and a self-consistent procedure, molecular units in the network establish a strong correlation to produce the desirable features in the physical world. The proposed framework is applied to the HP model. Both the forward problem of predicting folded structures from given sequences and the inverse problem of predicting required sequences for a given structure are examined.

11.
J Phys Chem B ; 122(36): 8601-8613, 2018 09 13.
Artigo em Inglês | MEDLINE | ID: mdl-30114905

RESUMO

Polymer crystallization is the most important part in determining the performance of polymeric materials. The twin-lattice model originally provided by Lennard-Jones and Devonshire, developed by Pople and Karasz and other researchers, is extended for describing the thermodynamics of polymer crystallization. The positional order of segments and the orientational order of bonds are considered in this model. The free energy of polymers is obtained by further introducing the conformational energy and entropy, and thus a new parameter is defined, which is the ratio of conformational energy and positional diffusion energy. We studied two kinds of processes in polymer crystallization, including the process with plastic crystal phase and without any mesophases. The choice of crystallizing process is determined by the magnitude of lattice energy and conformational energy. The solid-solid transition from crystal to plastic crystal shows a significant dependence on the conformational energy. Considering data reliability, n-paraffins are chosen as the representation of polymers to compare the predictions of the model with experimental observations. We predict the number of carbons beyond which the rotator phase disappears, which is quite in agreement with the experiments. These calculations and results show this model can provide a new understanding to the crystallization of polymers.

12.
Macromol Rapid Commun ; 39(11): e1800048, 2018 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-29744954

RESUMO

An intriguing morphological transition from poly(3-hexylthiophene) (P3HT) 1D nanofibers to 2D nanoribbons enabled by the addition of a series of alkylthiols is reported. First, P3HT 1D nanofibers are formed due to strong anisotropic π-π stacking between planar rigid backbones. Upon the addition of alkylthiols, P3HT nanofibers are transformed into nanoribbons associated with the crystallographic transition from edge-on orientation to flat-on orientation. The content of alkylthiols has a great influence on the P3HT morphology in the solution. The mechanism of such a morphological transformation is discussed based on the interaction between alkylthiols and P3HT chains. This work offers an effective strategy to tailor the crystal morphology and dimension of P3HT, which not only improves the understanding of P3HT crystallization but also may enable such discovery into conjugated polymer-based optoelectronic devices.


Assuntos
Nanofibras/química , Nanotubos de Carbono/química , Tiofenos/química , Microscopia de Força Atômica , Microscopia Eletrônica de Transmissão , Teoria Quântica , Espectrofotometria , Compostos de Sulfidrila/química
13.
J Biol Phys ; 44(1): 1-16, 2018 03.
Artigo em Inglês | MEDLINE | ID: mdl-29019015

RESUMO

Endocytotic and exocytotic processes are usually studied using particle-vesicle systems in theory, but most of them are electroneutral. Nevertheless, charged particle-vesicle systems are much closer to real biological systems. Therefore, wrapping behaviors of a negatively charged vesicle wrapping a positively charged particle are systematically investigated by a series of 2D dynamical simulations in this article. The competition between the elastic bending energy and the electrostatic energy dictates the vesicle configuration and charge distribution. It is found that only for intermediate charge concentrations and small particle sizes a vesicle can completely engulf the particle. When the charge density is high, the interaction between vesicle and particle is unexpectedly weakened by both the hardening effect of the charged membrane and the effective-transportation-frozen effect of the charged components. When the particle is strongly charged, multi-layer folding conformations are observed. These studies may provide important insights into mechanism of endocytotic and exocytotic processes in biological systems.


Assuntos
Endocitose , Modelos Moleculares , Conformação Molecular , Vesículas Transportadoras/química , Vesículas Transportadoras/metabolismo , Tamanho da Partícula , Termodinâmica
14.
Soft Matter ; 13(44): 8250-8263, 2017 Nov 15.
Artigo em Inglês | MEDLINE | ID: mdl-29071322

RESUMO

We employ a rod-coil multiblock molecular chain model to investigate chain folding behavior, which is a significant characteristic in semicrystalline polymers, by using the method of self-consistent field theory (SCFT). Polymer chains with different conformations in crystalline and amorphous regions are described by rigid rod chains and flexible Gaussian chains, respectively. At present, we concentrate on the thermodynamic behaviors of polymer semi-crystals after the formation of the initial lamellar crystals. A new mechanism for lamellar thickening is proposed to realize that the end of lamellar thickening depends on the crystallinity degree. In other words, it is impossible for lamellae to develop into extended-chain crystals by means of lamellar thickening if crystallinity is limited to a certain degree. We further discuss the competition between crystalline and amorphous regions and its influence on crystallization behaviors, such as the formation of double lamellae, chain tilt, the anomalies and adjacent re-entry. The synergistic influences of the driving force of crystallization, interfacial energy and crystallinity degree on chain folding behavior are also investigated when the density anomalies in amorphous regions are excluded. Our model demonstrates advantages in accurately describing the mesoscopic layered structures of semicrystalline polymers based upon a microscopic chain model and provides at least a semi-quantitative thermodynamic picture for chain folding.

15.
Polymers (Basel) ; 8(5)2016 May 11.
Artigo em Inglês | MEDLINE | ID: mdl-30979280

RESUMO

The effect of geometrical asymmetry ß (described by the length-diameter ratio of rods) on the rod-coil diblock copolymer phase behavior is studied by implementation of self-consistent field theory (SCFT) in three-dimensional (3D) position space while considering the rod orientation on the spherical surface. The phase diagrams at different geometrical asymmetry show that the aspect ratio of rods ß influences not only the order-disorder transition (ODT) but also the order-order transition (OOT). By exploring the phase diagram with interactions between rods and coils plotted against ß, the ß effect on the phase diagram is similar to the copolymer composition f. This suggests that non-lamellae structures can be obtained by tuning ß, besides f. When the rods are slim compared with the isotropic shape of the coil segment (ß is relatively large), the phase behavior is quite different from that of coil-coil diblock copolymers. In this case, only hexagonal cylinders with the coil at the convex side of the interface and lamella phases are stable even in the absence of orientational interaction between rods. The phase diagram is no longer symmetrical about the symmetric copolymer composition and cylinder phases occupy the large area of the phase diagram. The ODT is much lower than that of the coil-coil diblock copolymer system and the triple point at which disordered, cylinder and lamella phases coexist in equilibrium is located at rod composition fR = 0.66. In contrast, when the rods are short and stumpy (ß is smaller), the stretching entropy cost of coils can be alleviated and the phase behavior is similar to coil-coil diblocks. Therefore, the hexagonal cylinder phase formed by coils is also found beside the former two structures. Moreover, the ODT may even become a little higher than that of the coil-coil diblock copolymers due to the large interfacial area per chain provided by the stumpy rods, thus compensating the stretching entropy loss of the coils.

16.
J Chem Phys ; 145(21): 214902, 2016 Dec 07.
Artigo em Inglês | MEDLINE | ID: mdl-28799373

RESUMO

The surface interaction between substrates and block copolymers is one of the most important factors that control the alignment of self-assembled domains under thin film confinement. Most previous studies simply modeled substrates modified by grafting polymers as a hard wall with a specified surface energy, leading to an incomplete understanding of the role of grafted polymers. In this study, we propose a general model of surface interactions where the role of grafted polymers is decomposed into two independent contributions: the surface preference and the surface softness. Based on this model, we perform a numerical analysis of the stability competition between perpendicular and parallel lamellae of symmetric diblock copolymers on substrates modified by homopolymers using self-consistent field theory. The effects of the surface preference and the surface softness on the alignment of lamellar domains are carefully examined. A phase diagram of the alignment in the plane of the surface preference parameter and the surface softness parameter is constructed, which reveals a considerable parameter window for preparing stable perpendicular lamellae even on highly preferential substrates.

17.
Soft Matter ; 11(9): 1788-93, 2015 Mar 07.
Artigo em Inglês | MEDLINE | ID: mdl-25608843

RESUMO

We report on the first systematic study of vesicle conformational change caused by Coulomb interaction between surface charges on a lipid vesicle. The equilibrium configuration of a charged vesicle is found, as the result of the competition between the local bending elastic energy and the long-range electrostatic interaction within the membrane where the counter-ion effects are neglected. Because of the Rayleigh instability, a charged vesicle undergoes conformational transitions as a function of the surface charge density.


Assuntos
Lipossomos/química , Eletricidade Estática
18.
J Chem Phys ; 140(22): 224101, 2014 Jun 14.
Artigo em Inglês | MEDLINE | ID: mdl-24929368

RESUMO

We present a fast and accurate numerical method for the self-consistent field theory calculations of confined polymer systems. It introduces an exponential time differencing method (ETDRK4) based on Chebyshev collocation, which exhibits fourth-order accuracy in temporal domain and spectral accuracy in spatial domain, to solve the modified diffusion equations. Similar to the approach proposed by Hur et al. [Macromolecules 45, 2905 (2012)], non-periodic boundary conditions are adopted to model the confining walls with or without preferential interactions with polymer species, avoiding the use of surface field terms and the mask technique in a conventional approach. The performance of ETDRK4 is examined in comparison with the operator splitting methods with either Fourier collocation or Chebyshev collocation. Numerical experiments show that our exponential time differencing method is more efficient than the operator splitting methods in high accuracy calculations. This method has been applied to diblock copolymers confined by two parallel flat surfaces.

19.
J Colloid Interface Sci ; 426: 137-44, 2014 Jul 15.
Artigo em Inglês | MEDLINE | ID: mdl-24863776

RESUMO

Oxidized carbon nanotubes (CNTOs) with hydrophilic oxygen-containing functional groups and hydrophobic conjugated structure are prepared by the oxidation of carbon nanotubes (CNTs). After the polymerization of styrene with CNTOs dispersed in aqueous phase, polystyrene (PS) microspheres with string-like structure are obtained. Thermogravimetic analysis (TGA), differential scanning calorimeter (DSC) and Raman results indicate the strong interaction between the separated PS chains from the oil phase and CNTOs during the initial stage of the polymerization. These adsorbed PS chains on the surface of CNTOs are quickly swollen by the monomer and they grow in size during the further polymerization. The pH value and the ion strength of aqueous phase obviously affect the stability of PS microspheres. The particle size of microspheres is also determined by the pH. We demonstrate that the one-dimensional structure of CNTOs is responsible for the formation of polymer microspheres with special architecture.

20.
Eur Phys J E Soft Matter ; 37(3): 18, 2014 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-24664410

RESUMO

In this work, we propose a theoretical framework based on the self-consistent field theory (SCFT) for the study of self-assembling block copolymers on a general curved surface. Relevant numerical algorithms are also developed. To demonstrate the power of the approach, we calculate the self-assembled patterns of diblock copolymers on three distinct curved surfaces with different genus. We specially study the geometrical effects of curved surfaces on the conformation of polymer chains as well as on the pattern formation of block copolymers. By carefully examining the diffusion equation of the propagator on curved surfaces, it is predicted that Gaussian chains are completely unaware of the extrinsic curvature but that they will respond to the intrinsic curvature of the surface. This theoretical assertion is consistent with our SCFT simulations of block copolymers on general curved surfaces.

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