The swelling of polyelectrolyte hydrogels has been {often|frequently|usually|typically|generally|normally} explained {using|utilizing|making use of|employing|working with|applying} {simple|easy|straightforward|basic|uncomplicated|very simple} models derived {from the|in the} Flory-Rehner model.{While|Whilst|Although|Even though|When|Though} these models qualitatively predict the experimentally observed trends, {they also|additionally they|in addition they} introduce {strong|powerful|robust|sturdy} approximations and neglect some {important|essential|crucial|critical|significant|vital} contributions.Consequently, they {sometimes|occasionally|at times|often|from time to time|in some cases} incorrectly ascribe the observed trends to contributions {which are|that are} of minor {importance|significance|value} {under|below|beneath} the {given|offered|provided} {conditions|circumstances|situations}.{In this|Within this} {work|function|perform|operate}, we investigate the swelling properties of weak (pH-responsive) polyelectrolyte gels at {various|numerous|different|a variety of|several|many} pH and salt concentrations, {using|utilizing|making use of|employing|working with|applying} a hierarchy of models, {gradually|steadily|progressively} introducing {various|numerous|different|a variety of|several|many} approximations.For {the first|the very first|the initial} time, we introduce a three-dimensional particle-based model which accounts for the topology {of the|from the|in the|on the|with the|of your} hydrogel network, for electrostatic interactions {between|in between|among|amongst|involving} gel segments and {small|little|tiny|modest|smaller|compact} ions and for acid-base equilibrium coupled {to the|towards the|for the} Donnan partitioning of {small|little|tiny|modest|smaller|compact} ions.This model {is the|will be the|may be the|would be the|could be the|is definitely the} most {accurate|correct|precise} {one|1|a single|one particular}, {therefore|consequently|as a result|for that reason|thus|hence}, we use it as a reference when assessing the {effect|impact} of {various|numerous|different|a variety of|several|many} approximations.{As the|Because the} {first|initial|very first|1st|initially} approximation, we introduce the affine deformation, which {allows|enables|permits|makes it possible for} us to replace the network of {many|numerous|several|a lot of|quite a few|lots of} chains by a single chain, {while|whilst|although|even though|when|though} retaining the particle-based representation.{In the|Within the|Inside the} {next|subsequent} step, we {use the|make use of the} mean-field approximation to replace particles by density fields, combining the Poisson-Boltzmann equation with elastic stretching {of the|from the|in the|on the|with the|of your} chain.{Finally|Lastly|Ultimately}, we introduce {an ideal|a perfect} gel model by neglecting the electrostatics {while|whilst|although|even though|when|though} retaining all other {features|attributes|functions|characteristics|capabilities|options} {of the|from the|in the|on the|with the|of your} {previous|prior|earlier|preceding} model.Comparing predictions from all {four|4} models {allows|enables|permits|makes it possible for} us {to understand|to know} which contributions dominate at {high|higher} or low pH or salt concentrations.We observe that the field-based models overestimate the ionization degree {of the|from the|in the|on the|with the|of your} gel {because they|since they|simply because they} underestimate the electrostatic interactions.{Nevertheless|Nonetheless}, a cancellation of effects {on the|around the} electrostatic interactions and Donnan partitioning causes that {both|each} particle-based and field-based models {consistently|regularly} predict the swelling {of the|from the|in the|on the|with the|of your} gels as a function of pH and salt concentration.{Thus|Therefore|Hence|As a result}, {we can|we are able to} conclude that any {of the|from the|in the|on the|with the|of your} employed models can rationalize the {known|recognized|identified} experimental trends in gel swelling, {however|nevertheless|nonetheless|even so|on the other hand|having said that}, only the particle-based models {fully|totally|completely} account for the {true|accurate|correct} effects causing these trends.The {full|complete} understanding of {differences|variations} {between|in between|among|amongst|involving} {various|numerous|different|a variety of|several|many} models {is important|is essential|is very important|is vital|is significant} when interpreting experimental {results|outcomes|final results|benefits} {in the|within the|inside the} framework of {existing|current} theories and for ascribing the observed trends to {particular|specific|certain|distinct|unique} contributions, {such as|like|including|for example|for instance|which include} the Donnan partitioning of ions, osmotic {pressure|stress} or electrostatic interactions. 4-Aminobenzo-12-crown-4 Purity Price of 94-75-7 PMID:24733396
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