A structural study of polyelectrolyte gels in a unidirectionally swollen state

We investigated the structures of polyelectrolyte gels, poly(N-isopropylacrylamide-co-2-acrylamido-2-methylpropane sulfonic acid) (NIPA/AMPS) hydrogels in a unidirectionally swollen state by using small-angle X-ray scattering (SAXS). The SAXS results show that the structure of the NIPA/AMPS gels strongly depends upon the composition of NIPA/AMPS. Increase in composition of AMPS causes suppression of concentration fluctuations in the long wavelength. As a consequence, a NIPA/AMPS hydrogel with a low composition of AMPS macroscopically phase-separated at high temperatures, while microphase separation occurred for a NIPA/AMPS gel with a higher composition of AMPS. The instability in the microphase separation initially occurred in the direction perpendicular to the swelling for the latter gel. In the disordered state near the microphase separation region, an elliptic scattering pattern was observed, and the scattering intensity around the peak position in the direction perpendicular to the unidirectionally swelling was larger than that in the direction parallel to it. The behavior became more remarkable, as the interaction parameter χ became larger. These behaviors are consistent with the prediction from the Rabin-Panukov theory. The scattering vector at the scattering maximum in the perpendicular direction q_m,⊥ significantly shifted to smaller q, where q represents the magnitude of the scattering vector, when the microphase separation occurred. It is shown that the periodicity of the microphase-separated structure ranged from 300 to 400 Å.     

Comparison of heat- and pressure-induced gelation of β-lactoglobulin aqueous solutions studied by small-angle neutron and dynamic light scattering

The gelation mechanism of β-lactoglobulin (bLG) aqueous solutions was investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). Temperature- and pressure-jump experiments, respectively, abbreviated as T-jump (from 20 to 75 °C; T-jump) and P-jump (from 0.1 to 315 MPa) were carried out and the time evolution of gel structure was monitored by DLS and SANS as a function of time. The gelation threshold was determined by DLS as the point when nonergodicity appeared. In the case of T-jump, a rapid increase of the time-average scattered intensity, 〈I〉_T, and a steep decrease of the initial amplitude of the intensity-intensity time correlation function, , were observed at the gelation threshold. On the other hand, P-jump showed a gradual increase of the 〈I〉_T and a continuous decrease of the . It was revealed by SANS that bLG underwent thermal denaturation, resulting in a formation of gels consisting of densely aggregated unfolded bLG oligomers. On the other hand, the pressure-induced gels were found to be a fractal aggregates consisting of primary particles of bLG monomers. The difference in the gel structure as well as gelation mechanism between bLGs treated by T-jump and P-jump is discussed in comparison with T-induced and P-induced microphase separation of amphiphilic block copolymers in water [Osaka N, Shibayama M. Phys Rev Lett 2006;96:048303].     

Silica reinforced triblock copolymer gels

The effect of silica and polymer coated silica particles as reinforcing agents on the structural and mechanical properties of polystyrene-poly(ethylene/butylene)-polystyrene (PS-PEB-PS) triblock gel has been investigated. Different types of chemically modified silica have been compared in order to evaluate the influence of the compatibility between gel and filler.Time-resolved SANS and small-angle X-ray scattering (SAXS) shows that the presence of silica particles affects the ordering of the polystyrene domains during gelsetting. The scattering pattern of silica-reinforced gels reveals strong scattering at very low q, but no structure and formfactor information. However, on heating above the viscoelastic to plastic transition, the ‘typical’ scattering pattern of the copolymer gel builds-up. All reinforced gels are strengthened by the addition of the reinforcing agent. The transitions from a viscoelastic rubber to a plastic fluid and from a plastic fluid to a viscoelastic liquid are shifted to more elevated temperatures when silica is added to the triblock copolymer gel.     

Structural and magnetic characterization of norbornene-deuterated norbornene dicarboxylic acid diblock copolymers doped with iron oxide nanoparticles

A series of iron oxide doped norbornene (NOR)/deuterated norbornene dicarboxylic acid (NORCOOH) diblock copolymers were synthesized and characterized by X-ray photoelectron spectroscopy (XPS), small angle neutron scattering (SANS) and superconducting quantum interference device (SQUID) experiments. γ-Fe₂O₃ nanoparticles were synthesized within the microdomains of diblock copolymers with volume fractions of NOR/NORCOOH 0.64/0.36, 0.50/0.50 and 0.40/0.60. A spherical nanoparticle morphology was displayed in the polymer with 0.64/0.36 volume fraction. Polymers with 0.50/0.50 and 0.40/0.60 volume fractions exhibited interconnected metal oxide nanostructures. The observed changes in the shape and peak positions of the small-angle neutron scattering profiles of polymers after metal doping were related to the scattering from the metal oxide particles and to the possible deformed morphologies due to the strong interparticle interactions between metal particles, which may influence the polymer microphase separation. The combined scattering from both polymer domains and magnetic particles was depicted in SANS profiles of metal oxide doped polymers. γ-Fe₂O₃ containing block copolymers were superparamagnetic at room temperature. An increase in the blocking temperature (T_b) of interconnected nanoparticles was observed and was related to the interparticle interactions, which depends on the average distance (d) between particles and individual particle diameter (2R). The sample with volume fraction of 0.4/0.6 have the lowest d/(2R) ratio and exhibit the highest T_b at 115 K.     

Polystyrene nanoparticles with tunable interfaces and softness

Polystyrene nanoparticles, cross-linked with divinylbenzene (PS-(DVB)_x) and having radii, R_p ≤ 10 nm, have been synthesized using batch and semi-batch radical microemulsion polymerizations. The nanoparticles were characterized thoroughly using ¹H NMR, size exclusion chromatography, differential scanning calorimetry, and various small-angle scattering techniques (light, X-rays, and neutrons). Control over network and interface morphologies of the PS-(DVB)_x nanoparticles is readily achieved by varying the concentration of divinylbenzene and the polymerization technique (batch vs. semi-batch). Small-angle neutron scattering (SANS) allowed us to identify three distinct nanoparticle morphologies: (i) fuzzy soft gels with flexible chain-segments tethered/looped at the interface of a homogeneous core, (ii) smooth soft gels without a fuzzy interfacial layer, and (iii) dendritic glassy gels exhibiting an inhomogeneous core with an ill-defined interface. Atomic force microscopy imaging supports the morphologies and the softness of the nanoparticles as indicated by SANS.     

Structural investigations of a neutralized polyelectrolyte gel and an associating neutral hydrogel

Small angle neutron scattering (SANS) measurements are used to differentiate the local organization of the polymer chains in two different classes of hydrogel. In neutral polyvinyl alcohol gels, hydrogen bonding gives rise to long range structural perturbations that are superimposed on the underlying chemically cross-linked network, thus producing excess scattering at small values of the scattering vector q. This secondary superstructure causes an increase in the elastic modulus. The intensity scattered by the thermal fluctuations in these gels can be described by an Ornstein-Zernike lineshape and is consistent with the osmotic modulus deduced from macroscopic osmotic and mechanical observations.Strongly charged polyacrylate hydrogels, however, display a qualitatively different scattering response. At low q a power law behavior is observed characteristic of a fractal surface. At intermediate q another component of osmotic origin is visible, which varies as q⁻¹, which indicates that the presence of divalent cations favors linear alignment of the network chains. Acceptable agreement is found between the estimate of the thermal fluctuations deduced from SANS and the results derived from independent osmotic observations.     

Small angle neutron scattering studies on structural inhomogeneities in polymer gels: irradiation cross-linked gels vs chemically cross-linked gels

A comparison of network structure in a solvent was made for two types of poly(N-isopropylacrylamide) gels cross-linked by chemical reaction with N,N′-methylenebisacrylamide (BIS) (chemical gels) and by γ-ray irradiation (γ-ray gels). The cross-linking density dependence for these gels was examined by small angle neutron scattering (SANS). The SANS results indicated an increase of frozen inhomogeneities with an introduction of cross-links for both chemical and γ-ray gels. However, it was found that the effect of cross-linking is much stronger in the chemical gels than in the γ-ray gels. The differences in the structure were successfully interpreted by a statistical-mechanical theory of gels proposed by Panyukov-Rabin (Phys. Rep. 269 (1996) 1). The degree of polymerization between cross-links, N, was a decreasing function of cross-linking content for both types of gels, while that for the γ-ray gels was a weak function of irradiation dose. Quantitative analyses on BIS concentration and γ-ray dose dependence led to an experimental evidence of the existence of cross-linking saturation threshold.     

Poly(ionic liquid)-derived nanoporous carbon analyzed by combination of gas physisorption and small-angle neutron scattering

The preparation of nanoporous carbon materials and their characterization combining small-angle neutron scattering (SANS) with gas physisorption is presented. Carbon with a porous structure and tunable form is obtained here by a salt-templating approach using poly(ionic liquid) as precursor. SANS in combination with contrast matching by deuterated p-xylene was used for a separation of the scattering component deriving from the density fluctuations of the carbon matrix and the inaccessible porosity. The resulting scattering curves could be used for an unambiguous characterization of the pore structure of the materials. SANS curves measured at different partial pressure of the matching agent p-xylene were used for a differential filling of the micro- and mesopores. The analysis using the chord length distribution (CLD) was employed to determine the specific surface area and the pore size at different adsorption steps. The SANS results were in good agreement with the quenched solid density functional theory (QSDFT) analysis of the nitrogen physisorption. By the comparison of both characterization methods the pore shape could be determined. The combination of both SANS and gas physisorption is thus shown to provide a comprehensive characterization of the pore structure of the carbon monoliths throughout the entire pertinent length scale.     

Structural aspects of the LCST phase behavior of poly(benzyl methacrylate) in room-temperature ionic liquid

The structure and lower critical solution temperature (LCST) phase behavior of well-defined poly(benzyl methacrylate) (PBnMA) solution using 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide, [C₂mim][NTf₂] ionic liquid (IL) as a solvent have been studied by dynamic light scattering (DLS) and small-angle neutron scattering (SANS) at various temperatures. The SANS profiles observed for fully deuterated IL ([C₂mim]-d₁₁[NTf₂]) containing PBnMA were kept practically unchanged in the temperature range between 298 and 363 K, while they suddenly changed at 363 K. This indicates that the LCST behavior of PBnMA-IL solution is a first-order phase transition, which is consistent with the DLS results. The SANS profiles below 363 K were well represented by the theoretical Debye scattering function with inter-molecular interaction and the radius of gyration, R_g was estimated to be almost constant, i.e., ∼45 Å. The SANS result obtained here was compared with those in aqueous PNIPAm solutions as a typical LCST system, and some differences between IL and aqueous solution systems are pointed out. It is found that thermodynamic quantities (ΔH_demix, ΔS_demix and ΔG_demix) from the homogeneous solution to the phase separation states strongly depend on the solvation of the PBnMA polymer by the IL ([C₂mim] cation and [NTf₂] anion). We propose an LCST phase separation mechanism in the polymer-IL solution.     

Synthesis of novel amphiphilic pH‐sensitive polyurethane networks through water‐in‐oil soap‐free emulsion polymerization process. I. Microstructural differences and swelling behaviors

pH‐sensitive amphiphilic networks are synthesized from urethane acrylate anionomer (UAA) precursor chains. The microstructures of these networks are very sensitive to the nature of and the amount of solvent used during crosslinking. Whereas dioxane forms relatively homogenous solution, water preferentially interacts with hydrophilic segment of UAA chains, causing the microphase separation between hydrophilic moieties and hydrophobic main chains. This microphase separation was locked‐in by crosslinking reaction, enhancing largely the hydrophilicity of UAA networks and the hydrophobic aggregation. The UAA gels, prepared with water (UAAG) and/or dioxane (UADG), exhibit quite different swelling behaviors in the same dissolution medium because of their completely different microstructures. The improved hydrophilicity of UAAG gels due to the hydrophilic/hydrophobic microphase separation is confirmed by measuring the contact angle to water. These microphase‐separated hydrophilic domains on UAA gel matrix, which are observed by scanning electron microscopy measurement, influence the mechanical property of dried UAA gels as well. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 2115–2127, 2000     

Effect of hydrolysis on spatial inhomogeneity in poly(acrylamide) gels of various crosslink densities

The spatial inhomogeneity in poly(acrylamide) (PAAm) gels of various crosslink densities has been investigated with the static light scattering measurements. The gels were prepared using N,N′-methylenebis(acrylamide) (BAAm) as a crosslinker at a fixed initial monomer concentration but at various crosslink densities. Ammonium persulfate-N,N,N′,N′-tetramethylethylenediamine (TEMED) redox initiator system was used to initiate the polymerization reactions as well as to create charged groups in the aged gels. The gels were characterized by elasticity tests and by light scattering measurements at a gel state just after their preparation. Elasticity measurements show that 91-94% of the crosslinker molecules used in the hydrogel preparation were wasted in ineffective crosslinks. Debye-Bueche analysis of the light scattering data indicates frozen concentration fluctuations within the gel samples, which increase continuously with increasing crosslink density of the hydrogels. This phenomenon was explained with the multiple crosslinking reactions leading to the formation of highly crosslinked regions in the final hydrogel. The extent of concentration fluctuations was found to decrease drastically with increasing time of aging of gels in the synthesis reactor, indicating that the hydrolysis of amide groups into carboxylate anions facilitates the homogenization of the gel samples. A thermodynamic model was developed to explain the experimental observations in terms of the osmotic pressure of counterions in the aged gels.     

Phase separation in randomly charged polystyrene sulphonate ionomer solutions

The dynamics of randomly charged polystyrene caesium-sulfonate ionomers in semi-dilute solutions were studied using a combination of dynamic light scattering (DLS), small angle neutron scattering (SANS), and bulk rheology. The samples were studied in toluene solutions where the aggregation of the dipolar groups is favoured. Evidence of aggregation in dilute solution is found using DLS and SANS with both the hydrodynamic and static radius of gyration indicating that there is a contraction of the chains due to intra-chain attractive forces. SANS experiments demonstrate the evolution of the aggregates into a network structure as a function of polymer concentration. The association process is caused by the dipolar attraction between the charged groups and introduces two static correlation lengths in the mesh structure of the network; the standard semi-dilute mesh size (ξ=1.12c^{−0.72±0.03}) and an inhomogeneity length (Ξ=24c^0.58±0.05) due to micro-phase separation. The scaling of the amplitudes of the correlation lengths I₁(0)∼c^{−0.33±0.07} and I₂(0)∼c^2.0±0.4 are consistent with good solvent conditions and micro-phase separation, respectively. An imposed shear causes the break up of the micro-phase separated micellar system with a characteristic yield stress for the Bingham step-like shear thinning.     

Light and neutron scattering studies of excess low-angle scattering in moderately concentrated polystyrene solutions

The light scattering (LS) and small-angle neutron scattering (SANS) behaviour of semi-dilute solutions of polystyrene has been determined in both ‘good’ and ‘theta’ solvents. Above a critical concentration related to chain overlap, an excess small-angle scattering component is in evidence for scattering vectors, q, such that qR_g < 1. Application of a number of recent solution scattering theories fails to account for the small-angle scattering observed. The inter- and intramolecular scattering functions are measured experimentally through characterization of the SANS behaviour of solutions containing mixtures of polystyrene and perdeuteropolystyrene. The resultant intermolecular scattering functions depend on the fraction of labelled chains, indicating clearly that the solutions contain large scale fluctuations. LS studies support this hypothesis and further show that the presence of these fluctuations is reproducible, yet dependent on the solution preparation procedure. Similar behaviour is observed in screening length measurements. The excess low-angle scattering is well characterized by the Debye—Bueche random two-phase model, which is subsequently used to estimate the characteristic dimensions of the long-range fluctuations.     

Small-angle neutron scattering characterization of the structure of nanoporous carbons for energy-related applications

We used small-angle neutron scattering (SANS) and neutron contrast variation to study the structure of four nanoporous carbons prepared by thermo-chemical etching of titanium carbide TiC in chlorine at 300, 400, 600, and 800 °C with pore diameters ranging between ∼4 and ∼11 Å. SANS patterns were obtained from dry samples and samples saturated with deuterium oxide (D₂O) in order to delineate origin of the power law scattering in the low Q domain as well as to evaluate pore accessibility for D₂O molecules. SANS cross section of all samples was fitted to Debye-Anderson-Brumberger (DAB), DAB-Kirste-Porod models as well as to the Guinier and modified Guinier formulae for cylindrical objects, which allowed for evaluating the radii of gyration as well as the radii and lengths of the pores under cylindrical shape approximation. SANS data from D₂O-saturated samples indicate that strong upturn in the low Q limit usually observed in the scattering patterns from microporous carbon powders is due to the scattering from outer surface of the powder particles. Micropores are only partially filled with D₂O molecules due to geometrical constraints and or partial hydrophobicity of the carbon matrix. Structural parameters of the dry carbons obtained using SANS are compared with the results of the gas sorption measurements and the values agree for carbide-derived carbons (CDCs) obtained at high chlorination temperatures (>600 °C). For lower chlorination temperatures, pore radii obtained from gas sorption overestimate the actual pore size as calculated from SANS for two reasons: inaccessible small pores are present and the model-dependent fitting based on density functional theory models assumes non-spherical pores, whereas SANS clearly indicates that the pore shape in microporous CDC obtained at low chlorination temperatures is nearly spherical.     

Suppression of inhomogeneities in hydrogels formed by free-radical crosslinking copolymerization

Network microstructures of poly(acrylamide) (PAAm) and poly(N,N-dimethylacrylamide) (PDMA) hydrogels were compared by static light scattering and elasticity measurements. The hydrogels were prepared by free-radical crosslinking copolymerization of the monomers acrylamide (AAm) or N,N-dimethylacrylamide (DMA) with N,N′-methylenebis(acrylamide) as a crosslinker. During the formation of PAAm gels, the reaction time dependence of the scattered light intensity exhibits a maximum at a critical reaction time, while in case of PDMA gels, both a maximum and a minimum were observed, corresponding to the chain overlap threshold and the gel point, respectively. This difference in the time-course between the two gelling systems is due to the late onset of gelation in the DMA system with respect to the critical overlap concentration. Compared to the AAm system, no significant scattered light intensity rise was observed during the crosslinking polymerization of DMA. It was shown that, regardless of the crosslinker ratio and of the initial monomer concentration, PDMA gel is much more homogeneous than the corresponding PAAm gel due to the shift of the gelation threshold to the semidilute regime of the reaction system. The results suggest that the spatial gel inhomogeneity can be controlled by varying the gel point with respect to the critical overlap concentration during the preparation of gels by free-radical mechanism.     

Dilute-solution structure of charged arborescent graft polymer

The solutions of charged G1 arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers in methanol-d4 and D₂O were investigated over a dilute concentration range ?=0.005-0.05 (?: mass fraction) using small-angle neutron scattering (SANS). Upon addition of acid (HCl) arborescent graft polymers became charged and a peak appeared in SANS data. The interparticle distance (d_exp) calculated from a peak position corresponded to the expected value (d_uni) for a uniform particle distribution. This indicates the formation of liquid-like ordering due to long-range Coulombic repulsions. The smaller dielectric constant of methanol-d4 resulted in long-range electrostatic repulsions persisting to lower polymer concentration than in D₂O. The slow mode scattering was observed by dynamic light scattering measurements for the same polymer solutions, indicating the presence of structural inhomogeneity in the solutions. Both the peak and slow mode disappeared by addition of NaCl or excess HCl into the solutions due to the screening of electrostatic interactions. The G1 polymer grafted with longer P2VP chains (M_w∼30,000 versus 5000 g mol) formed a gel on addition of HCl. This result reveals that molecular expansion is more significant for arborescent polymers with longer (M_w∼30,000) linear polyelectrolyte branches, resulting in gelation for ?>0.01. Upon addition of NaCl or excess HCl a gel transformed back to a liquid resulted from the screening of electrostatic interactions.     

Small-angle neutron scattering study on block and gradient copolymer aqueous solutions

The small-angle neutron scattering investigation was carried out on semi-dilute aqueous solutions of block and gradient copolymers comprising pEOVE and pMOVE, pEOVE₃₀₀-block-pMOVE₃₀₀ (Block) and p(EOVE-grad-MOVE)₆₀₀ (Grad). Here, pEOVE and pMOVE denote poly(2-ethoxyethyl vinyl ether) and poly(2-methoxyethyl vinyl ether), respectively, and the numbers indicate the degrees of polymerization. The monomer composition in the Grad had a gradient along the polymer chain. For 20.0 wt% solutions, a microphase-separated structure and physical gelation were observed both in Block and in Grad systems. In the case of the Grad system, a gradual microphase separation took place as a function of temperature via a micellization with a small radius of core, characterized by the “reel-in” process, i.e., a winding of polymer chains to the core of a micelle because of the gradient composition. On the other hand, the Block system underwent a stepwise transition with respect to temperature. The relationship between microphase separation and the rheological behavior is explained from the viewpoint of microscopic structure.     

On the nature of the second-order optical nonlinearity of nanoinhomogeneous glasses in the Li2O-Nb2O5-SiO2 system

The submicroscopic structure of lithium niobium silicate glasses of the compositions 2xLiNbO₃ · (1 ? x)(Li₂O · 2SiO₂) (x = 0.40, 0.45, 0.50) and 30Li₂O · 25Nb₂O₅ · 45SiO₂ in the initial state and after heat treatment for different times at temperatures in the vicinity of the glass transition point T _g are investigated using X-ray powder diffraction, small-angle neutron scattering (SANS), synchrotron small-angle X-ray scattering (SAXS), and electron microscopy. A nanostructure with inhomogeneities ～40 Å in size is formed in glasses at the initial stages of phase separation at temperatures in the range 600–670°C. This structure is responsible for the appearance of the second-order optical nonlinearity. The SANS, SAXS, and electron microscopic data on the inhomogeneity size are in good agreement with each other. According to the X-ray diffraction, SANS, and SAXS data, the ordering of the glass structure and the difference between the density of inhomogeneities and the density of the matrix increase in the course of heat treatment. At the initial stage of amorphous phase separation, the glass decomposes into regions enriched in SiO₂ and regions with an increased content of lithium and niobium. An increase in the temperature or time of heat treatment results in the precipitation of LiNbO₃ ferroelectric crystals. The results obtained allow us, for the first time, to make the inference that nanoscale changes in the glass structure lead to considerable changes (by one order of magnitude and more) in the quadratic optical nonlinearity, which can be controlled by heat treatment. The origin of the second-order optical nonlinearity is associated with both the nanosized modulations of the polarizability due to the inhomogeneous glass structure and the polarity of structural nanoinhomogeneities from which the LiNbO₃ phase precipitates at the later stages of phase separation.     

Frequency and temperature dependence of poly(N‐isopropylacrylamide) gel rheology

Poly(N‐isopropylacrylamide) or p‐NIPAAM gels undergo a prominent deswelling transition near physiological temperatures. Using passive microrheology, we have investigated the viscoelastic response of p‐NIPAAM gels over a frequency range not accessible to bulk rheological measurements. Overall, NIPAAM gels moderately shear stiffen with increasing frequency. More intriguingly, sample viscosity rapidly declines with increasing frequency before leveling off near the solvent viscosity. The frequency for this crossover coincides with the emergence of fast gel modes seen in dynamic light scattering (DLS) from the gel. Furthermore, we monitored viscoelastic responses on approach to the deswelling transition. Intrinsic light scattering indicates that experimental conditions are not near the critical point and that the deswelling transition is second order in nature. Nevertheless, the corresponding elastic and viscous moduli of p‐NIPAAM displayed power‐law decreases with temperature. These changes with temperature were independent of probe frequency. Power law exponents, however, are sensitive to details of the sample preparation suggesting that these viscoelastic responses vary with gel structure. Correlating our microrheological measurements with DLS from the gel matrix itself, we find that several of the observed microrheological features are closely related to the intrinsic dynamics of the p‐NIPAAM gels. In particular, the transition from gel‐ to solvent dominated dissipation coincides with a transition from fast to slow gel modes. Combining microrheology with intrinsic light scattering, therefore, provides a compelling approach to probe rheological responses and correlate them to the underlying network dynamics. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci., 2013     

Dynamic light scattering and small-angle neutron scattering studies on phenolic resin solutions

Solution properties of unfractionated phenolic resins prepared by polycondensation of phenol and formaldehyde using oxalic acid as a catalyst were investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The hydrodynamic radius, obtained by DLS experiments with 1 vol % solution in acetone, and the correlation length, ξ, of the Ornstein-Zernike equation, obtained by SANS experiments with 10 vol % solution in tetrahydrofuran, obey a power-law relation as a function of z-average molecular weight estimated by gel permeation chromatography, with scaling exponents of 0.57 and 0.27, respectively. These behaviors are unaffected by polymerization conditions, such as initial phenol-to-formaldehyde molar ratio in the range from 0.9 to 1.5, catalyst concentration with oxalic acid-to-phenol molar ratio from 0.01 to 0.1, and reaction time within the period in which the polymer remains soluble. SANS curves for polymers prepared under different conditions are sufficiently superimposed onto a single curve with the reduced variables, ξ⁻²I(q) and ξq. These results indicate that unfractionated phenolic resins have a self-similar structure with respect to the molecular weight.