Influence of swelling on the elasticity of polymer networks cross-linked in the melt state: Test of the localization model of rubber elasticity.

The elasticity of polymer networks, formed by cross-linking high molecular mass polymers in the melt state and then swollen by a solvent, involves contributions from both the presence of cross-link network junctions and the interchain interactions associated with the combined effect of excluded volume interactions and topological constraints that become modified when the network is swollen. We test the capacity of the previously developed localization model of rubber elasticity, a mean field "tube model," to describe changes in elasticity observed in classical experimental studies of the mechanical properties of this type of network. In order to obtain a satisfactory comparison to the experiments, it was found to be necessary to account for the independently observed tendency of the network junctions to become localized in the network with appreciable swelling, as well as the interchain interactions emphasized in previous discussions of the localization model.

Coexistence of Crumpling and Flat Sheet Conformations in Two-Dimensional Polymer Networks: An Understanding of Aggrecan Self-Assembly.

We investigate the conformational properties of self-avoiding two-dimensional (2D) ideal polymer networks with tunable mesh sizes as a model of self-assembled structures formed by aggrecan. Polymer networks having few branching points and large enough mesh tend to crumple, resulting in a fractal dimension of d_{f}≈2.7. The flat sheet behavior (d_{f}=2) emerges in 2D polymer networks having more branching points at large length scales; however, it coexists with crumpling conformations at intermediate length scales, a feature found in scattering profiles of aggrecan solutions. Our findings bridge the long-standing gap between theories and simulations of polymer sheets.

Ion-induced changes in DNA gels.

Small angle neutron scattering (SANS) measurements are reported for DNA gels under near physiological conditions in which the concentration of monovalent and divalent counter-ions and the pH are varied. The scattering intensity I(q) is described by a two-term equation, one due to osmotic concentration fluctuations and the other coming from static inhomogeneities frozen in by the cross-links. SANS in the low q range indicates the presence of large clusters and the size of which exceeds the resolution of the experiment. In the intermediate q-range, the intensity increases with the CaCl2 concentration and the slope approaches -1, corresponding to linear (rod-like) scatterers. In the highest q region, the scattering response is governed by the local chain geometry. Screening of electrostatic interactions by sodium chloride causes a moderate increase in the SANS intensity that is accompanied by an increase in the mesh size L of the network. Addition of calcium chloride, or a decrease in pH, produces similar trends, and ultimately leads to phase separation. The scattering intensity at q = 0, estimated from independent measurements of the osmotic pressure Π, is in excellent agreement with I(0) from the SANS measurements. Anomalous small angle X-ray scattering (ASAXS) measurements on the uncross-linked DNA show that the monovalent ion cloud is only weakly influenced by the addition of divalent ions. Conversely, the divalent counter-ion cloud tightly follows the contour of polymer chains.

Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels.

We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.

Five-Year Outcomes after PCI or CABG for Left Main Coronary Disease.

BACKGROUND: Long-term outcomes after percutaneous coronary intervention (PCI) with contemporary drug-eluting stents, as compared with coronary-artery bypass grafting (CABG), in patients with left main coronary artery disease are not clearly established. METHODS: We randomly assigned 1905 patients with left main coronary artery disease of low or intermediate anatomical complexity (according to assessment at the participating centers) to undergo either PCI with fluoropolymer-based cobalt-chromium everolimus-eluting stents (PCI group, 948 patients) or CABG (CABG group, 957 patients). The primary outcome was a composite of death, stroke, or myocardial infarction. RESULTS: At 5 years, a primary outcome event had occurred in 22.0% of the patients in the PCI group and in 19.2% of the patients in the CABG group (difference, 2.8 percentage points; 95% confidence interval [CI], -0.9 to 6.5; P = 0.13). Death from any cause occurred more frequently in the PCI group than in the CABG group (in 13.0% vs. 9.9%; difference, 3.1 percentage points; 95% CI, 0.2 to 6.1). In the PCI and CABG groups, the incidences of definite cardiovascular death (5.0% and 4.5%, respectively; difference, 0.5 percentage points; 95% CI, -1.4 to 2.5) and myocardial infarction (10.6% and 9.1%; difference, 1.4 percentage points; 95% CI, -1.3 to 4.2) were not significantly different. All cerebrovascular events were less frequent after PCI than after CABG (3.3% vs. 5.2%; difference, -1.9 percentage points; 95% CI, -3.8 to 0), although the incidence of stroke was not significantly different between the two groups (2.9% and 3.7%; difference, -0.8 percentage points; 95% CI, -2.4 to 0.9). Ischemia-driven revascularization was more frequent after PCI than after CABG (16.9% vs. 10.0%; difference, 6.9 percentage points; 95% CI, 3.7 to 10.0). CONCLUSIONS: In patients with left main coronary artery disease of low or intermediate anatomical complexity, there was no significant difference between PCI and CABG with respect to the rate of the composite outcome of death, stroke, or myocardial infarction at 5 years. (Funded by Abbott Vascular; EXCEL ClinicalTrials.gov number, NCT01205776.).

Hydrogel composite mimics biological tissues.

A novel composite hydrogel was developed that shows remarkable similarities to load bearing biological tissues. The composite gel consisting of a poly(vinyl alcohol (PVA) matrix filled with poly(acrylic acid) (PAA) microgel particles exhibits osmotic and mechanical properties that are qualitatively different from regular gels. In the PVA/PAA system the swollen PAA particles "inflate" the PVA network. The swelling of the PAA is limited by the tensile stress Pel developing in the PVA matrix. Pel increases with increasing swelling degree, which is opposite to the decrease of the elastic pressure observed in regular gels. The maximum tensile stress Pmaxel can be identified as a quantity that defines the load bearing ability of the composite gel. Systematic osmotic swelling pressure measurements have been made on PVA/PAA gels to determine the effects of PVA stiffness, PAA crosslink density, and Ca2+ ion concentration on Pmaxel. It is found that Pmaxel increases with the stiffness of the PVA matrix, and decreases with (i) increasing crosslink density of the PAA and (ii) increasing Ca2+ ion concentration. Small angle neutron scattering (SANS) measurements indicate only a weak interaction between the PVA and PAA gels. It is demonstrated that the osmotic swelling pressure of PVA/PAA composite gels reproduces the osmotic behavior of healthy and osteoarthritic cartilage.

Molecular dynamics study of the swelling and osmotic properties of compact nanogel particles.

Owing to their great importance in materials science and other fields, we investigate the solution and osmotic properties of uncharged compact nanogel particles over a wide range of solvent quality and particle concentration by molecular dynamics (MD) simulations. We characterize the osmotic pressure by estimating the second and third virial coefficients, and by extension, we identify the θ-point where the second virial coefficient vanishes. Calculations of the structure factor indicate that these particles are similar to macrogels in that the particle-like scattering profile disappears at moderate concentrations. We also find that improving the solvent quality enhances the spatial segmental uniformity, while significant heterogeneous structure arises near the θ-point. Well below the θ-point where the second osmotic virial coefficient vanishes, these heterogeneous structures become less prevalent as the particles tend to collapse. We also investigate the degree of swelling and structure of compact nanogel particles with a variable excluded volume interaction and gel particle concentration. The osmotic modulus and the scaling exponents in good and θ-point conditions of these gels are characteristic of interacting randomly branched polymers, i.e., "lattice animals".

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles.

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Structure and conformational properties of ideal nanogel particles in athermal solutions.

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Comparative experimental and computational study of synthetic and natural bottlebrush polyelectrolyte solutions.

We systematically investigate model synthetic and natural bottlebrush polyelectrolyte solutions through an array of experimental techniques (osmometry and neutron and dynamic light scattering) along with molecular dynamics simulations to characterize and contrast their structures over a wide range of spatial and time scales. In particular, we perform measurements on solutions of aggrecan and the synthetic bottlebrush polymer, poly(sodium acrylate), and simulations of solutions of highly coarse-grained charged bottlebrush molecules having different degrees of side-branch density and inclusion of an explicit solvent and ion hydration effects. While both systems exhibit a general tendency toward supramolecular organization in solution, bottlebrush poly(sodium acrylate) solutions exhibit a distinctive "polyelectrolyte peak" in their structure factor, but no such peak is observed in aggrecan solutions. This qualitative difference in scattering properties, and thus polyelectrolyte solution organization, is attributed to a concerted effect of the bottlebrush polymer topology and the solvation of the polymer backbone and counterions. The coupling of the polyelectrolyte topological structure with the counterion distribution about the charged polymer molecules along with direct polymer segmental hydration makes their solution organization and properties "tunable," a phenomenon that has significant ramifications for biological function and disease as well as for numerous materials applications.

Screening lengths and osmotic compressibility of flexible polyelectrolytes in excess salt solutions.

We report results of small angle neutron scattering measurements made on sodium polystyrene sulfonate in aqueous salt solutions. The correlation length (ξ) and osmotic compressibility are measured as a function of polymer (c) and added salt (cS) concentrations, and the results are compared with scaling predictions and the random-phase approximation (RPA). In Dobrynin et al.'s scaling model the osmotic pressure consists of a counter-ion contribution and a polymer contribution. The polymer contribution is found to be two orders of magnitude smaller than expected from the scaling model, in agreement with earlier observations made on neutral polymers in good solvent condition. RPA allows the determination of single-chain dimensions in semidilute solutions at high polymer and added salt concentrations, but fails for cS≤ 2 M. The χ parameter can be modelled as the sum of an intrinsic contribution (χ0) and an electrostatic term: χ∼χ0 + K'/√cS, where χ0 > 0.5 is consistent with the hydrophobic nature of the backbone of NaPSS. The dependence of χelec∼ 1/√cS disagrees with the random-phase approximation (χelec∼ 1/cs), but agrees with the light scattering results in dilute solution and Dobrynin et al.'s scaling treatment of electrostatic excluded volume.

Systematic investigation of synthetic polyelectrolyte bottlebrush solutions by neutron and dynamic light scattering, osmometry, and molecular dynamics simulation.

There is a great interest in the synthesis and characterization of polyelectrolytes that mimic naturally occurring bottlebrush polyelectrolytes to capitalize on the unique properties of this class of macromolecules. Charged bottlebrush polymers form the protective mucus layer in the lungs, stomach, and orifices of animals and provide osmotic stabilization and lubrication to joints. In the present work, we systematically investigate bottlebrush poly(sodium acrylates) through a combination of measurements of solution properties (osmometry, small-angle neutron scattering, and dynamic light scattering) and molecular dynamics simulations, where the bottlebrush properties are compared in each case to their linear polymer counterparts. These complementary experimental and computational methods probe vastly different length- and timescales, allowing for a comprehensive characterization of the supermolecular structure and dynamics of synthetic polyelectrolyte bottlebrush molecules in solution.

Everolimus-Eluting Stents or Bypass Surgery for Left Main Coronary Artery Disease.

BACKGROUND: Patients with obstructive left main coronary artery disease are usually treated with coronary-artery bypass grafting (CABG). Randomized trials have suggested that drug-eluting stents may be an acceptable alternative to CABG in selected patients with left main coronary disease. METHODS: We randomly assigned 1905 eligible patients with left main coronary artery disease of low or intermediate anatomical complexity to undergo either percutaneous coronary intervention (PCI) with fluoropolymer-based cobalt-chromium everolimus-eluting stents (PCI group, 948 patients) or CABG (CABG group, 957 patients). Anatomic complexity was assessed at the sites and defined by a Synergy between Percutaneous Coronary Intervention with Taxus and Cardiac Surgery (SYNTAX) score of 32 or lower (the SYNTAX score reflects a comprehensive angiographic assessment of the coronary vasculature, with 0 as the lowest score and higher scores [no upper limit] indicating more complex coronary anatomy). The primary end point was the rate of a composite of death from any cause, stroke, or myocardial infarction at 3 years, and the trial was powered for noninferiority testing of the primary end point (noninferiority margin, 4.2 percentage points). Major secondary end points included the rate of a composite of death from any cause, stroke, or myocardial infarction at 30 days and the rate of a composite of death, stroke, myocardial infarction, or ischemia-driven revascularization at 3 years. Event rates were based on Kaplan-Meier estimates in time-to-first-event analyses. RESULTS: At 3 years, a primary end-point event had occurred in 15.4% of the patients in the PCI group and in 14.7% of the patients in the CABG group (difference, 0.7 percentage points; upper 97.5% confidence limit, 4.0 percentage points; P=0.02 for noninferiority; hazard ratio, 1.00; 95% confidence interval, 0.79 to 1.26; P=0.98 for superiority). The secondary end-point event of death, stroke, or myocardial infarction at 30 days occurred in 4.9% of the patients in the PCI group and in 7.9% in the CABG group (P<0.001 for noninferiority, P=0.008 for superiority). The secondary end-point event of death, stroke, myocardial infarction, or ischemia-driven revascularization at 3 years occurred in 23.1% of the patients in the PCI group and in 19.1% in the CABG group (P=0.01 for noninferiority, P=0.10 for superiority). CONCLUSIONS: In patients with left main coronary artery disease and low or intermediate SYNTAX scores by site assessment, PCI with everolimus-eluting stents was noninferior to CABG with respect to the rate of the composite end point of death, stroke, or myocardial infarction at 3 years. (Funded by Abbott Vascular; EXCEL ClinicalTrials.gov number, NCT01205776 .).

Effects of mono- and divalent cations on the structure and thermodynamic properties of polyelectrolyte gels.

Measurements are reported on the effect of monovalent and divalent salts on the swelling behavior and supramolecular structure of sodium polyacrylate gels (NaPA) made by osmotic swelling pressure and small angle neutron scattering measurements. The swelling response of the gels in solutions of ten different monovalent salts is found to be practically identical indicating that the principal effect of monovalent ions is screening the electrostatic repulsion among the charged groups on the polyelectrolyte chains; i.e., chemical differences between the monovalent ions do not play a significant role. Introducing Ca2+ ions into the equilibrium NaCl solution results in a sharp volume transition of the gels. The threshold Ca2+ ion concentration at which the transition occurs increases with increasing NaCl concentration in the surrounding bath. It is demonstrated that the swelling behavior of NaPA gels exhibits universal properties in solutions containing both NaCl and CaCl2. Osmotic swelling pressure measurements reveal that both the second and third virial coefficients decrease with increasing CaCl2 concentration until the volume transition is reached. The macroscopic measurements are complemented by small angle neutron scattering that reveals the variation of the thermodynamic length scales as the volume transition is approached. The thermodynamic correlation length L increases with increasing CaCl2 concentration.

Microscale mapping of extracellular matrix elasticity of mouse joint cartilage: an approach to extracting bulk elasticity of soft matter with surface roughness.

Cartilage is composed of cells and an extracellular matrix, the latter being a composite of a collagen mesh interpenetrated by proteoglycans responsible for tissue osmotic swelling. The matrix composition and structure vary through the tissue depth. Mapping such variability requires tissue sectioning to gain access. The resulting surface roughness, and concomitant proteoglycan loss contribute to large uncertainties in elastic modulus estimates. To extract elasticity values for the bulk matrix which are not obfuscated by the indeterminate surface layer, we developed a novel experimental and data analysis methodology. We analyzed the surface roughness to optimize the probe size, and performed high-resolution (1 µm) elasticity mapping on thin (∼12 µm), epiphyseal newborn mouse cartilage sections cut parallel to the bone longitudinal axis or normal to the articular surface. Mild fixation prevented the major proteoglycan loss observed in unfixed specimens but not the stress release that resulted in thickness changes in the sectioned matrix. Our novel data analysis method introduces a virtual contact point as a fitting parameter for the Hertz model, to minimize the effects of surface roughness and corrects for the finite section thickness. Our estimates of cartilage elasticity converge with increasing indentation depth and, unlike previous data interpretations, are consistent with linearly elastic material. A high cell density that leaves narrow matrix septa between cells may cause the underestimation of elastic moduli, whereas fixation probably causes an overestimation. The proposed methodology has broader relevance to nano- and micro-indentation of soft materials with multiple length scales of organization and whenever surface effects (including roughness, electrostatics, van der Waals forces, etc.) become significant.

Ionic effects in semi-dilute biopolymer solutions: A small angle scattering study.

Systematic investigations using neutron and X-ray small angle scattering in near-physiological salt solutions were made to reveal the effect of polymer concentration, pH, and calcium ion concentration on the structure of semi-dilute solutions of four model biopolymers [polyaspartic acid, DNA, chondroitin sulfate, and hyaluronic acid (HA)] representing typical backbone structures. In the low q range (<0.01 Å-1), the scattering response I(q) is dominated by scattering from large clusters. In the intermediate q range, I(q) varies approximately as q -1, exposing the linear nature of the scatterers. In these polyelectrolyte solutions, the correlation length L displays a power law dependence on the polymer concentration c that resembles that of neutral polymer solutions. L increases with increasing calcium chloride concentration and with decreasing pH. The effect of the different divalent cations, Ba, Mg, Ca, Sr, and Mn, on the structure of DNA solutions is practically identical. However, in mixed salt conditions at the same ionic strength, the combined effect of mono- and divalent counter-ions on the structure of the polymer solutions deviates significantly from additivity. Anomalous small angle X-ray scattering observations on both DNA and HA solutions reveal that the divalent strontium counter-ions form a tight sheath around the polymer chain. The shape of the divalent ion cloud is similar in these two systems.

[Evolution of the Hungarian adult heart transplantation program]. / A felnottszív-átültetés fejlodése Magyarországon.

The authors give a short introduction of the Hungarian and the international history of adult heart transplantation, and highlight the similarities in the evolution of the two programs. Their aim was to show how the Hungarian post-transplant survival changed in the last five years. They wanted to investigate how all the changes they had made in the program affected the post-transplant results. They investigated 496 heart transplantation data and compared to international data. Orv Hetil. 2018; 159(46): 1869-1875.

[The Semmelweis University extracorporeal membrane oxygenation program - 5 years' results and perspectives]. / A Semmelweis Egyetem extracorporalis membránoxigenizációs programja ­ az 5 éves Városmajori-eredmények függvényében.

The mechanical circulatory support (MCS) program of the Semmelweis University Heart and Vascular Centre has become established over the last five years. The main requirements of our MCS program to be developed first were the Heart Transplantation and Heart Failure Intensive Care Unit and a well trained medical team. The wide range of mechanical circulatory support devices provides suitable background for the adequate treatment of our patients in all indications. In this review, we present our results related to extracorporeal membrane oxygenation (ECMO) supports performed in the last five years. Between 2012 and 2017, we applied MCS support in 140 cases, among them 111 patients received ECMO support. The leading indications of ECMO support were the following: primary graft failure after heart transplantation (33 cases), postcardiotomy cardiogenic shock (18 patients), acute decompensation of end-stage heart failure (14 patients), acute myocardial infarction complicated with refractory cardiogenic shock (37 patients), cardiogenic shock developed after transcatheter aortic valve implantation (3 patients), malignant arrhythmia due to drug intoxication (1 patient) and acute respiratory distress syndrome (4 cases). The mortality of patients receiving ECMO support was 46%. The analysis of the results of ECMO support needs to change our approach. The mortality results show that we lost the half of our patients. However, the mortality in the conventionally treated patients would have been 100% without ECMO. In fact, we could save the life of half of these patients. Orv Hetil. 2018; 159(46): 1876-1881.

[Computer-assisted decision-making in cardiac surgery: from 3D preoperative planning to computational fluid dynamics in the design of surgical procedures]. / Számítástechnikai döntéstámogató rendszer kiépítése a szívsebészetben: a 3D tervezéstol a posztoperatív eredményekig.

INTRODUCTION: Although surgical specialties utilize static models for preoperative planning, the evolution of dynamic planning methods and computer simulations created the opportunity for the introduction of dynamic parameters in cardiac surgery. Our aim was to apply 3D models in cardiac surgical practice, predicting fluid dynamic results, ventricular shape, volume and function before the operation. METHODS: Using a script developed by us, the raw DICOM files were imported, the dilated left ventricle was modeled and fluid dynamic parameters were simulated, such as flow kinematic and profile analysis, turbulence calculation and myocardial response to shear stress. Then step-by-step simulation of the surgical ventricle restoration procedure was accomplished and the calculated variables were imbedded in silico model. The length of resection lines was modified based on the previous computer simulation and applied during the operation, if feasible. RESULTS: The sphericity and conicity indexes were improved significantly in postoperative period (0.42 vs. 0.67 and 0.36 vs. 0.72, p < 0.05). The occurred shear stress at endocardium decreased 83% due to the normalization of flow kinematic pattern of the ventricle in postoperative period (132.21 ± 29.5 dyne/cm2 vs. 22.92 ± 10.3 p < 0.05 dyne/|cm2). The postoperative turbulent flow pattern significantly decreased, according to our computational method (2712 vs. 1823, p < 0.0001). CONCLUSION: With our method, the standardization of the surgical ventricle reconstruction was achievable and the surgical steps were predictable. Therefore, a new decision making support system was established in cardiac surgery for high risk patients. A personalized surgical technique was offered to our patients, improving their life expectancy and quality of life.

Decisive test of the ideal behavior of tetra-PEG gels.

The objective of this work is to investigate the thermodynamic and scattering behavior of tetra-poly(ethylene glycol) (PEG) gels. Complementary measurements, including osmotic swelling pressure, elastic modulus, and small angle neutron scattering (SANS), are reported for a series of tetra-PEG gels made from different molecular weight precursor chains at different concentrations. Analysis of the osmotic swelling pressure vs polymer volume fraction curves makes it possible to separate the elastic and mixing contributions of the network free energy. It is shown that in tetra-PEG gels these free energy components are additive. The elastic term varies with the one-third power of the polymer volume fraction and its numerical value is equal to the shear modulus obtained from independent mechanical measurements. The mixing pressure of the cross-linked polymer is slightly smaller than that of the corresponding solution of the uncross-linked polymer of infinite molecular weight but it exhibits similar dependence on the polymer concentration. The observed deviation between the osmotic mixing pressures of the gel and the solution can be attributed to the presence of small amount of structural inhomogeneities frozen-in by the cross-links. SANS reveals that the scattering response of tetra-PEG gel is mainly governed by the thermodynamic concentration fluctuations of the network, i.e., the contribution from static inhomogeneities to the SANS signal is small.