Elasticity, one of the most important properties of a soft material, is difficult to quantify in polymer networks because of the presence of topological molecular defects in these materials. Furthermore, the impact of these defects on bulk elasticity is unknown. We used rheology, disassembly spectrometry, and simulations to measure the shear elastic modulus and count the numbers of topological "loop" defects of various order in a series of polymer hydrogels, and then used these data to evaluate the classical phantom and affine network theories of elasticity. The results led to a real elastic network theory (RENT) that describes how loop defects affect bulk elasticity. Given knowledge of the loop fractions, RENT provides predictions of the shear elastic modulus that are consistent with experimental observations.

We report the synthesis of Janus bottlebrush block copolymers by graft-through polymerization of branched diblock macromonomers. Self-assembly of the bottlebrushes was characterized by small-angle X-ray scattering, atomic force microscopy, and scanning electron microscopy. Phase separation and packing models of the bottlebrushes were computed, and their self-assembly behavior was corroborated experimentally in bulk and in thin films. Lamellar, hexagonal cylinder, and gyroid phases were observed and modeled. The A-branch-B Janus bottlebrush structure provides several unique advantages in the context of bottlebrush polymer assembly, including access to the first examples of gyroid phases.

Through the use of macromolecular design and efficient chemical reactions it is now possible to control the composition of polymer networks and gels with excellent precision. In contrast, topological defects are still impossible to avoid and are generally difficult to quantify. For example, primary loops that form when a bifunctional monomer (A 2 ) reacts twice with the same f functional ( f > 2) monomer (B f ) during formation of an end-linked A 2 + B f network represent a pervasive defect that has a detrimental effect on mechanical integrity. Methods for the quantitative analysis of primary loops in such materials have recently emerged; however, these methods have only been applied to the simplest network structure: A 2 + B 3 . Herein, we report strategies for counting primary loops in tetrafunctional (A 2 + B 4 ) networks and networks with mixed tri-and tetrafunctional (A 2 + B 3 /B 4 ) junctions. We apply these strategies to the quantitative analysis of primary loops in a series of endlinked poly(ethylene glycol) hydrogels synthesized via copper-catalyzed azide−alkyne cycloaddition "click" chemistry. Our results show that A 2 + B 4 networks are particularly susceptible to cyclic defects compared to A 2 + B 3 networks and that higher-order cyclic species must play a significant role in the gel point of the former materials. Our experimental results were compared to rate theory and Monte Carlo simulations. This work reveals new structural insights into a widely studied family of materials and sets the stage for the development of strategies to tune network defects in such gels.

Controlling the molecular structure of amorphous cross-linked polymeric materials is a longstanding challenge. Herein, we disclose a general strategy for precise tuning of loop defects in covalent polymer gel networks. This "loop control" is achieved through a simple semibatch monomer addition protocol that can be applied to a broad range of network-forming reactions. By controlling loop defects, we demonstrate that with the same set of material precursors it is possible to tune and in several cases substantially improve network connectivity and mechanical properties (e.g., ∼600% increase in shear storage modulus). We believe that the concept of loop control via continuous reagent addition could find broad application in the synthesis of academically and industrially important cross-linked polymeric materials, such as resins and gels.

Accurate description of the soil water retention curve (SWRC) at low water contents is important for simulating water dynamics and biochemical vadose zone processes in arid environments. Soil water retention data corresponding to matric potentials of less than −10 MPa, where adsorptive forces dominate over capillary forces, have also been used to estimate soil specific surface area (SA). In the present study, the dry end of the SWRC was measured with a chilled‐mirror dew point psychrometer for 41 Danish soils covering a wide range of clay (CL) and organic carbon (OC) contents. The 41 soils were classified into four groups on the basis of the Dexter number (n = CL/OC), and the Tuller‐Or (TO) general scaling model describing water film thickness at a given matric potential (<−10 MPa) was evaluated. The SA estimated from the dry end of the SWRC (SA_SWRC) was in good agreement with the SA measured with ethylene glycol monoethyl ether (SA_EGME) only for organic soils with n > 10. A strong correlation between the ratio of the two surface area estimates and the Dexter number was observed and applied as an additional scaling function in the TO model to rescale the soil water retention curve at low water contents. However, the TO model still overestimated water film thickness at potentials approaching ovendry condition (about −800 MPa). The semi–log linear Campbell‐Shiozawa‐Rossi‐Nimmo (CSRN) model showed better fits for all investigated soils from −10 to −800 MPa and yielded high correlations with CL and SA. It is therefore recommended to apply the empirical CSRN model for predicting the dry part of the water retention curve (−10 to −800 MPa) from measured soil texture or surface area. Further research should aim to modify the more physically based TO model to obtain better descriptions of the SWRC in the very dry range (−300 to −800 MPa).