Scattering functions of semidilute solutions of polymers in a good solvent

Expressions for analyzing small-angle scattering data from semidilute solutions of polymers in a good solvent over a broad range of scattering vectors are examined. Three different scattering function expressions are derived from Monte Carlo simulations. The expressions are similar to those of polymer reference interaction site models, with a scattering-vector-dependent direct correlation function. In the most advanced model, the screening of excluded-volume interactions beyond the overlap concentration is taken into account. Two simpler expressions, in which the screening of excluded-volume interactions is not included, are also applied. The three models are tested against small-angle neutron scattering (SANS) experiments on polystyrene in deuterated toluene for a broad range of molar masses and concentrations over a wide range of scattering vectors. For each model, simultaneous fits to all the measured scattering data are performed. The most advanced model excellently reproduces the SANS data over the full range of the parameters. The two simpler models fit the data almost equally well. On the basis of an extensive study, an optimal fitting strategy can be recommended for experimentalists, who want to analyze small-angle scattering data from polymers at any concentration. For data sets that do not contain data on the single-chain scattering function, the simpler model is recommended; it uses a direct correlation function equal to the form factor of an infinitely thin rod, which is independent of the concentration and molar mass. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3081–3094, 2004     

Phase behavior of the polybutadiene–polystyrene diblock copolymer with the addition of the nonselective solvent dichlorobenzene in temperature and pressure fields

Thermal composition fluctuations were measured in a polybutadiene–polystyrene diblock copolymer with small-angle neutron scattering as a function of the temperature, pressure, and solvent content. The solvent was dichlorobenzene. In particular, we determined the phase diagram, the Flory–Huggins parameter, and the Ginzburg parameter. The two latter parameters were determined in terms of a theory by Fredrickson and Helfand from the susceptibility at an elevated temperature in the disordered regime. These parameters showed an overall linear decrease with pressure and a minimum at a 10% solvent content. The ordering temperature could be sufficiently well described by the theory of concentrated solutions. These results were consistent with corresponding experiments on a polybutadiene–polystyrene blend, for which the compensation of the free volume was observed by the solvent molecules. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3179–3190, 2004     

Small-angle neutron scattering studies of dynamics and hierarchical pattern formation in binary mixtures of polymers and small molecules

We present the dynamics of the composition fluctuations and pattern formation of two-component systems in both single-phase and two-phase states as studied by time-resolved small-angle neutron scattering and light scattering. Two-component systems to be covered here include not only dynamically symmetric systems, in which each component has nearly identical self-diffusion coefficients, but also dynamically asymmetric systems, in which each component has different self-diffusion coefficients. We compare the dynamic behaviors of the two systems and illuminate their important differences. The scattering studies presented for dynamically asymmetric systems highlight that stress–diffusion coupling and viscoelastic effects strongly affect the dynamics and pattern formation. For dynamically symmetric systems, we examine the universality existing in both polymer systems and small-molecule systems as well as new features concerning the time evolution of hierarchical structures during phase separation via spinodal decomposition over a wide range of wave numbers (up to four orders of magnitude). For both systems, we emphasize that polymers provide good model systems for studying the dynamics and pattern formation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3027–3062, 2004     

Does conventional nucleation occur during phase separation in polymer blends?

The kinetics of liquid–liquid phase separation in off-critical polymer blends was studied with time-resolved small-angle neutron scattering. Our objective was to study the nature of the nuclei that formed during the initial stages of the phase transition. The blends were composed of model polyolefins—deuterium-labeled poly(methyl butylene) (PMB) and poly(ethyl butylene) (PEB)—with molecular weights of about 200 kg/mol. A direct examination of the initial clustering of molecules before macroscopic phase separation was possible because of the large size of the polymer chains and concomitant entanglement effects. We discovered that the scattering profiles obtained during nucleation merged at a well-defined critical scattering vector. We propose that this is the signature of the critical nucleus and that the size of the critical nucleus is inversely proportional to the magnitude of the critical scattering vector. The kinetic studies were preceded by a thorough characterization of the equilibrium thermodynamic properties of our PMB/PEB blends. The locations of the binodal and spinodal curves of our system are consistent with predictions based on the Flory–Huggins theory. This combination of thermodynamic and kinetic experiments enabled the quantification of the dependence of the size and structure of the critical nuclei on the quench depth. Our results do not agree with any of the previous theories on nucleation. Some aspects of our results are addressed in recent theoretical work by Wang in which the effects of fluctuations on the classical binodal and spinodal curves in polymer blends are incorporated. Both theory and experiment support the notion that the traditional stability limit (spinodal) should be replaced by a metastability limit. Although Wang's theory provides an explanation for some of our observations, many fundamental issues regarding nucleation in polymer blends remain unresolved. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1793–1809, 2004     

Probing multiple melting behaviors in poly(ethylene naphthalene 2,6‐dicarboxylate) with different thermal histories by simultaneous wide‐angle and small‐angle X‐ray scattering

A simultaneous wide‐angle and small‐angle X‐ray scattering study of two poly(ethylene naphthalene 2,6‐dicarboxylate) samples crystallized from the glassy state at different annealing temperatures for different annealing times was carried out with synchrotron radiation. Either single or dual melting was induced in the samples, as confirmed by differential scanning calorimetry (DSC). The correlation function and interface distribution function were calculated to evaluate microstructural parameters such as the long spacing, the thickness of the amorphous and crystalline phases, and the width of the size distributions. The sample with dual melting behavior exhibited an abrupt increase of all microstructural parameters at temperatures above the melting of the lowest endotherm, whereas the sample revealing a single melting endotherm did not show such a sudden change. This finding agrees with the concept that the appearance of two melting peaks in DSC traces can be explained by the dual lamellar stacking model. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 881–894, 2001     

Equilibrium structure of hydrogen-bonded polymer blends

Deuterium-labeled polystyrene modified by random distributions of the comonomer p-(1,1,1,3,3,3-hexaflouro-2-hydroxyisopropyl)-α-methyl-styrene [DPS(OH)] has been blended with poly(butyl methacrylate) (PBMA) and studied with small-angle neutron scattering (SANS). Miscibility is induced via hydrogen bonding between the DPS(OH) hydroxyl group and PBMA carbonyl groups. The data suggest that the nature of the miscible-phase structure in these blends differs from that of the usual homopolymer blends at small scattering angles, which we attribute to the short-range site specific nature of the hydrogen bond interaction. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2745–2750, 1998     

The equatorial small‐angle scattering during the straining of poly(ether ester) and its analysis

A method for the quantitative analysis of two‐dimensional (2D) small‐angle X‐ray scattering (SAXS) patterns with fiber symmetry by successive information filtering is proposed and applied to a series of images recorded during a straining experiment of a two‐phase polymer sample at a synchrotron beamline. The studied equatorial scattering is similar to the frequently discussed void scattering, but originates from an ensemble of rodlike soft domains (needles) in the sample, orientated in the direction of strain. The intensity is extracted and projected onto the equatorial plane, the ideal two‐phase structure is extracted, and the 2D chord distribution is computed. This curve describes a 2D two‐phase morphology made from needle cross‐sections embedded in matrix material. Because interparticular correlation is found to be weak in the chord distribution, pure particle scattering is assumed. Modeling the needle cross‐sections by circular disks leads to a simple theory, which allows the deconvolution of a disk diameter distribution from the chord distribution. It is shown how parameters of the disk diameter distribution can be computed without deconvolution. For the selected poly(ether ester) thermoplastic elastomer the study of the soft domain needles indicates strain‐induced hardening. While for low elongation ϵ the soft needles are more compressible than the microfibrillar matrix, saturation is observed for ϵ > 2.5. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 975–981, 1999     

Analysis of the morphology of hectorite by use of small-angle X-ray scattering

An analysis of the three-dimensional correlation function of small-angle scattering is applied for the direct determination of stereological parameters of hectorite samples. Beside characteristic lengths and volume fractions the specific order distances are given. The samples can be described by homogeneous particles of different order magnitudes up to the size of the secondary particles, which were estimated to have maximum dimensions of about 450 nm. Beside traditional stereological formulas, including the interpretation of the derivatives of the small-angle correlation function, the so-called transformed correlation function is applied in order to detect distinctive characteristic lengths. Received: 2 December 1999 Accepted: 9 March 2000     

Small-angle scattering from hexagonal liquid crystals

In this paper, we discuss the scattering behavior of two-dimensional hexagonal liquid crystals with micellar cylinders as a building unit. We treat the hexagonal phase as an accumulation of ordered domains of finite size that typically consists of one hundred parallel cylinders whose axes are perpendicular to the lattice plane. When we suppose that no specific orientation is preferred, the lengths of the cylinders are rather large compared to their diameter, and the polydispersity of the size of the cylinders is negligible; it is therefore possible to split the scattering intensity into a product of the so-called form factor and the structure factor. This product approximation is the basic condition for the use of the generalized indirect Fourier transformation (GIFT) method and the deconvolution (DECON) method to evaluate the small-angle scattering data of hexagonal phases. The GIFT method provides the parameters of the structure factor model and the pair distance distribution function of the cylinders. Via the DECON technique, we can calculate the radial contrast profile of the cylinders from the pair distance distribution function that is obtained by the GIFT method.     

Temperature dependent phase behavior of PNIPAM microgels in mixed water/methanol solvents

Temperature dependent phase behavior of poly(N-isopropylacylamide) (PNIPAM) microgels in water/methanol mixtures of different composition was studied with dynamic light scattering (DLS) and small-angle neutron scattering (SANS). Using DLS, it is possible to measure the diffusion coefficient, and thus the size of particles exactly and directly; the variation of the phase transition temperature in the different solvents is also easy to detect by this method. With SANS measurements in D₂O/MeOD mixtures, some of the DLS results were confirmed. Moreover, SANS measurements give valuable information on the particle structure in different solvents. The experiments were compared with the theory of competitive hydration introduced by Tanaka et al. We found a good agreement of theory and experiment, and obtained the theoretical predictions: around the transition temperature, the composition of the bound methanol along the chains is higher than that of the outer solution, while the whole methanol composition inside the gel is lower. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym. Phys. 2013, 51, 1100–1111     

Thermodynamic interactions in blends of poly(4-tert-butyl styrene) and polyisoprene by small-angle neutron scattering

The thermodynamic interactions between poly(4-tert-butyl styrene) [P(4tBS)] and 1,4-polyisoprene (PI; both hydrogenous) were obtained as functions of the temperature, PI molecular weight, and blend composition through the examination of miscible ternary blends of these two components with a common miscible labeled polymer [90% 1,2-deuterated polybutadiene (dPBD)] with small-angle neutron scattering. The thermodynamic interaction parameters between P(4tBS) and dPBD and between P(4tBS) and PI increased with increasing temperature and were consistent with lower critical solution temperature behavior. Although the binary blends of P(4tBS) and dPBD exhibited phase separation at elevated temperatures, the thermodynamic interaction parameters between P(4tBS) and PI remained large and negative and independent of the PI molecular weight. Finally, the thermodynamic interactions for PI and P(4tBS) depended strongly on the ratio of PI to P(4tBS) and were also sensitive to the amount of dPBD present in the ternary blend. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3204–3217, 2004     

Formation of deprotected fuzzy blobs in chemically amplified resists

The requirement of nanometer dimensional control in photolithographic patterning underlies the future of emerging technologies, including next-generation semiconductors, nanofluids, photonics, and microelectromechanical systems. For chemically amplified resists, dimensional control is mediated by the diffusion and reaction of photogenerated acids within a polymer-based photoresist matrix. The complex nature of the combined processes of reaction and diffusion prohibit the routine measurement of this phenomenon. Using small-angle neutron scattering, we have measured the form of the diffusion–reaction path of a photogenerated acid within a model photoresist matrix with a labeled protection group on the polymer side group. During the deprotection reaction, changes in the scattering form factor result from the shape and form of the deprotected regions. The individual volumes or blobs of reacted material are diffuse, with a fuzzy boundary between the reacted and unreacted regions. The impact of these results on the pattern quality is also discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3063–3069, 2004     

Investigation of molecular order and phase transitions of smectic poly(ester imide)s by means of small-angle X-ray scattering

The molecular order and phase transitions of two smectic poly(ester imide)s based on aminobenzoic acid trimellitimide (PEI 1) or aminocinnamic acid trimellitimide (PEI 2) and α,ω-dihydroxydodecane were investigated by X-ray scattering. During cooling, the polymers pass through monotropic smectic liquid-crystalline (LC) phases (S_A, S_C), which transform into higher-ordered smectic-crystalline phases (S_E, S_H). The smectic layer structure of about 3 nm gives rise to a sharp reflection at 2θ ≅ 3°. Peak shape analysis and analysis of the interface distribution function revealed long-range longitudinal correlation among the mesogens in the LC phase but short-range lateral correlation. The development of a broad reflection in the small-angle X-ray scattering (SAXS, 2θ < 1°) indicates the formation of a lamellar two-phase system. The long-period changes reversibly between 10 and 30 nm with increasing temperature. The crystalline lamellae comprise a number of smectic-crystalline layers with packed mesogens, while the noncrystalline interlamellar regions keep their smectic-LC order. In the metastable S_B phase, formed during annealing of quenched PEI 1, the diffuse SAXS indicates a random distribution of small, probably fringed, crystals with hexagonal-packed mesogens. In the lamellar S_E and S_H phases, tie molecules play an important role, but chain folding cannot be excluded. Received: 16 July 1999/Accepted: 28 April 2000     

Interactions of cartilage extracellular matrix macromolecules

Articular cartilage is a low-friction, load-bearing tissue located at joint surfaces. The extracellular matrix (ECM) of cartilage consists of a fibrous collagen network, which is prestressed by the osmotic swelling pressure exerted by negatively charged proteoglycan (PG) aggregates embedded in the collagen network. The major PG is the bottlebrush-shaped aggrecan, which forms complexes with linear hyaluronic acid (HA) chains. We quantify microscopic and macroscopic changes resulting from self-assembly between aggrecan and HA using a complementary set of physical measurements to determine structure and interactions by combining scattering techniques, including small-angle X-ray scattering, small-angle neutron scattering, and dynamic light scattering with macroscopic osmotic pressure measurements. It is demonstrated that the osmotic pressure that defines the load-bearing ability of cartilage is primarily governed by the main macromolecular components (aggrecan and collagen) of the ECM. Knowledge of the interactions between the macromolecular components of cartilage ECM is essential to understand biological function and to develop successful tissue engineering strategies for cartilage repair. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Porod scattering study of coarsening in immiscible polymer blends

Studies of immiscible blend compatibilization often involve laborious microscopy methods to characterize changes in the particle size distribution with time in the melt. Here we explore a simple alternative approach based on Porod scattering from the two-phase structure. Although micron-sized particles in immiscible polymer blends are too large to be fully characterized by small-angle scattering, Porod scattering measurements of the interfacial area combined with knowledge of the blend volume fraction allows determination of an average particle diameter from a single scattering measurement. This technique is illustrated in experiments monitoring coarsening of particle size in polystyrene/poly(methyl methacrylate) blends prepared either by melt blending or solid-state shear pulverization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3413–3420, 2005     

聚丙烯酰胺凝胶结构非均匀性的动态光散射研究

利用动态光散射技术研究了聚丙烯酰胺 (PAAm)凝胶结构的非均匀性 ,分析了PAAm凝胶结构非均匀性的形成原因及凝胶动态光散射的数据处理方法和分析结果的物理意义 .研究结果表明 ,PAAm凝胶中含有动态相关长度 (LC)不同的两相 ,其中 ,LC 为 10～ 2 0nm的区域是聚合物稀疏相 ,LC 为 85nm左右的区域是聚合物密集相 ,两相的不均匀分布形成了PAAm凝胶结构的非均匀性 .分析表明 ,PAAm凝胶存在两相主要是由于单体和交联剂的溶解度存在差异所致 .随交联度增大 ,PAAm凝胶结构的非均匀性显著增强     

Orientation and relaxation of polymer–clay solutions studied by rheology and small-angle neutron scattering

The influence of shear on viscoelastic solutions of poly(ethylene oxide) (PEO) and clay [montmorillonite, i.e., Cloisite NA+ (CNA)] was investigated with rheology and small-angle neutron scattering (SANS). The steady-state viscosity and SANS were used to measure the shear-induced orientation and relaxation of the polymer and clay platelets. Anisotropic scattering patterns developed at much lower shear rates than in pure clay solutions. The scattering anisotropy saturated at low shear rates, and the CNA clay platelets aligned with the flow, with the surface normal parallel to the gradient direction. The cessation of shear led to partial and slow randomization of the CNA platelets, whereas extremely fast relaxation was observed for laponite (LRD) platelets. These PEO–CNA networklike solutions were compared with previously reported PEO–LRD networks, and the differences and similarities, with respect to the shear orientation, relaxation, and polymer–clay interactions, were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3102–3112, 2004     

相关函数法计算原位担载型煤直接液化催化剂的粒径分布

分别测定了纯煤样和浸浸煤样的小角Ｘ线射线散射,基于ＧＢＣ理论假设,采用相关函数法计算了原位担载于两种烟烟上ＦｅＳＯ４的粒径分布,考察了助剂ＮａＳ和尿素的添加对其粒径分布的影响。计算结果与ＸＲＤ表征结果相似,ＦｅＳＯ４在两种煤样上的最可几粒径为４ｎｍ左右,分布范围０．５～８ｎｍ。助剂对ＦｅＳＯ４粒径分布的影响较小,它们的添加主要是改变了催化剂前驱体的活性组成。     

Time-resolved small-angle neutron scattering study of polyethylene crystallization from solution

With time-resolved small-angle neutron scattering (TR-SANS), the crystallization kinetics of polyethylene from deuterated o-xylene solutions upon a temperature jump have been investigated. On the basis of a morphological model of coexisting lamellar stacks and coil chains in solution, experimental data have been quantitatively analyzed to provide structural information, such as the lamellar long period, the lamellar crystal thickness, the thickness of the amorphous layers between lamellae, the degree of crystallinity, and the crystal growth rate at various degrees of undercooling. The viability of TR-SANS for studying polymer crystallization is demonstrated through the consistency of these measurements and well-established knowledge of polyethylene crystallization from xylene solutions. One unique feature of this experimentation is that both the growth of lamellar crystals and the condensation of coil chains from solution are monitored simultaneously. The ratio of the crystal growth to the chain consumption rate decreases rapidly with a decreasing degree of undercooling. The Avrami analysis suggests that the growth mechanism approaches two-dimensional behavior at higher temperatures, and this is consistent with the observation of an increasing ratio of the sharp-surface area to the bulk crystal growth rate with temperature. The limitations, possible remedies, and potentials of TR-SANS for studying polymer crystallization are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3133–3147, 2004