Zippelius, Annette

[["dc.bibliographiccitation.artnumber","214905"],["dc.bibliographiccitation.issue","21"],["dc.bibliographiccitation.journal","The Journal of Chemical Physics"],["dc.bibliographiccitation.volume","124"],["dc.contributor.author","Wald, Christian"],["dc.contributor.author","Goldbart, Paul M."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T09:41:48Z"],["dc.date.available","2018-11-07T09:41:48Z"],["dc.date.issued","2006"],["dc.description.abstract","We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent cross-links are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerge upon sufficient cross-linking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of cross-linking, provided the mesh size is smaller than the correlation length of phase separation. The mixed get becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellas or random structures with a unique wavelength, can be energetically favorable. (c) 2006 American Institute of Physics."],["dc.identifier.doi","10.1063/1.2200697"],["dc.identifier.isi","000238758700049"],["dc.identifier.pmid","16774440"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/33812"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Inst Physics"],["dc.relation.issn","1089-7690"],["dc.relation.issn","0021-9606"],["dc.title","Glassy correlations and microstructures in randomly cross-linked homopolymer blends"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","051802"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","Physical Review. E"],["dc.bibliographiccitation.volume","77"],["dc.contributor.author","Xing, Xiangjun"],["dc.contributor.author","Pfahl, Stephan"],["dc.contributor.author","Mukhopadhyay, Swagatam"],["dc.contributor.author","Goldbart, Paul M."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T11:15:48Z"],["dc.date.available","2018-11-07T11:15:48Z"],["dc.date.issued","2008"],["dc.description.abstract","A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media."],["dc.identifier.doi","10.1103/PhysRevE.77.051802"],["dc.identifier.isi","000256885400084"],["dc.identifier.pmid","18643092"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/54445"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1539-3755"],["dc.title","Nematic elastomers: From a microscopic model to macroscopic elasticity theory"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","843"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","EPL"],["dc.bibliographiccitation.lastpage","849"],["dc.bibliographiccitation.volume","70"],["dc.contributor.author","Wald, C."],["dc.contributor.author","Zippelius, Annette"],["dc.contributor.author","Goldbart, Paul M."],["dc.date.accessioned","2018-11-07T10:36:39Z"],["dc.date.available","2018-11-07T10:36:39Z"],["dc.date.issued","2005"],["dc.description.abstract","The physical properties of blends of distinct homopolymers, cross-linked beyond the gelation point, are addressed via a Landau approach involving a pair of coupled order-parameter fields: one describing vulcanisation, the other describing local phase separation. Thermal concentration fluctuations, present at the time of cross-linking, are frozen in by cross-linking, and the structure of the resulting glassy fluctuations is analysed at the Gaussian level in various regimes, determined by the relative values of certain physical length scales. The enhancement, due to gelation, of the stability of the blend with respect to demixing is also analysed. Beyond the corresponding stability limit, gelation prevents complete demixing, replacing it by microphase separation, which occurs up to a length scale set by the rigidity of the network, as a simple variational scheme reveals."],["dc.identifier.doi","10.1209/epl/i2004-10522-9"],["dc.identifier.isi","000230210600021"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/45379"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Edp Sciences S A"],["dc.relation.issn","0295-5075"],["dc.title","Glassy states and microphase separation in cross-linked homopolymer blends"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","26004"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","EPL"],["dc.bibliographiccitation.volume","80"],["dc.contributor.author","Mao, Xiaoming"],["dc.contributor.author","Goldbart, Paul M."],["dc.contributor.author","Xing, Xiangjun"],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T11:06:29Z"],["dc.date.available","2018-11-07T11:06:29Z"],["dc.date.issued","2007"],["dc.description.abstract","Spatial heterogeneity in the elastic properties of soft random solids is examined via a semi-microscopic model network using replica statistical mechanics. The elastic heterogeneity is characterized by random residual stress and Lam ecoefficient fields, and the statistics of these quantities is inferred. Correlations involving the residual-stress field are found to be long ranged and governed by a universal parameter that also gives the mean shear modulus. Copyright (C) EPLA, 2007."],["dc.identifier.doi","10.1209/0295-5075/80/26004"],["dc.identifier.isi","000250409700016"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/52324"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Epl Association, European Physical Society"],["dc.relation.issn","0295-5075"],["dc.title","Elastic heterogeneity of soft random solids"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","49"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","EPL"],["dc.bibliographiccitation.lastpage","55"],["dc.bibliographiccitation.volume","67"],["dc.contributor.author","Mukhopadhyay, S."],["dc.contributor.author","Goldbart, Paul M."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T10:47:38Z"],["dc.date.available","2018-11-07T10:47:38Z"],["dc.date.issued","2004"],["dc.description.abstract","Goldstone modes in the amorphous solid state, resulting from the spontaneous breaking of translational symmetry due to random localisation of particles, are discussed. Starting from a microscopic model with quenched disorder, the broken symmetry is identified to be that of relative translations of the replicas. Goldstone excitations, corresponding to pure shear deformations, are constructed from long-wavelength distortions of tire order parameter. The elastic free energy is computed, and it is shown that Goldstone fluctuations destroy localisation in two spatial dimensions, yielding a two-dimensional amorphous solid state characterised by power law correlations."],["dc.identifier.doi","10.1209/epl/i2003-10278-8"],["dc.identifier.isi","000223424900008"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/48007"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","E D P Sciences"],["dc.relation.issn","0295-5075"],["dc.title","Goldstone fluctuations in the amorphous solid state"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","677"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","EPL"],["dc.bibliographiccitation.lastpage","682"],["dc.bibliographiccitation.volume","76"],["dc.contributor.author","Ulrich, S."],["dc.contributor.author","Mao, Xiaoming"],["dc.contributor.author","Goldbart, Paul M."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T09:00:44Z"],["dc.date.available","2018-11-07T09:00:44Z"],["dc.date.issued","2006"],["dc.description.abstract","Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Landau-Wilson free energy S for arbitrary cross-link densities. Considering pure shear deformations, S takes the form of the elastic energy of an isotropic amorphous solid state, from which the shear modulus can be identified. It is found to be a universal quantity, not depending on any microscopic length-scales of the model."],["dc.identifier.doi","10.1209/epl/i2006-10310-7"],["dc.identifier.isi","000242210900021"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/24246"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Edp Sciences S A"],["dc.relation.issn","0295-5075"],["dc.title","Elasticity of highly cross-linked random networks"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","031140"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Physical Review. E"],["dc.bibliographiccitation.volume","80"],["dc.contributor.author","Mao, Xiaoming"],["dc.contributor.author","Goldbart, Paul M."],["dc.contributor.author","Xing, Xiangjun"],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T11:25:24Z"],["dc.date.available","2018-11-07T11:25:24Z"],["dc.date.issued","2009"],["dc.description.abstract","Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the structure of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their elastic properties. Vulcanization theory studies semimicroscopic models of random-solid-forming systems and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids in terms of residual stress and Lame-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long ranged and governed by a universal parameter that also gives the mean shear modulus."],["dc.identifier.doi","10.1103/PhysRevE.80.031140"],["dc.identifier.isi","000270383400055"],["dc.identifier.pmid","19905095"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/56612"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1539-3755"],["dc.title","Soft random solids and their heterogeneous elasticity"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","184201"],["dc.bibliographiccitation.issue","18"],["dc.bibliographiccitation.journal","Physical Review. B"],["dc.bibliographiccitation.volume","70"],["dc.contributor.author","Goldbart, Paul M."],["dc.contributor.author","Mukhopadhyay, S."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T10:44:28Z"],["dc.date.available","2018-11-07T10:44:28Z"],["dc.date.issued","2004"],["dc.description.abstract","In sufficiently high spatial dimensions, the formation of the amorphous (i.e., random) solid state of matter, e.g., upon sufficent crosslinking of a macromolecular fluid, involves particle localization and, concomitantly, the spontaneous breakdown of the (global, continuous) symmetry of translations. Correspondingly, the state supports Goldstone-type low energy, long wavelength fluctuations, the structure and implications of which are identified and explored from the perspective of an appropriate replica field theory. In terms of this replica perspective, the lost symmetry is that of relative translations of the replicas; common translations remain as intact symmetries, reflecting the statistical homogeneity of the amorphous solid state. What emerges is a picture of the Goldstone-type fluctuations of the amorphous solid state as shear deformations of an elastic medium, along with a derivation of the shear modulus and the elastic free energy of the state. The consequences of these fluctuations-which dominate deep inside the amorphous solid state-for the order parameter of the amorphous solid state are ascertained and interpreted in terms of their impact on the statistical distribution of localization lengths, a central diagnostic of the state. The correlations of these order parameter fluctuations are also determined, and are shown to contain information concerning further diagnostics of the amorphous solid state, such as spatial correlations in the statistics of the localization characteristics. Special attention is paid to the properties of the amorphous solid state in two spatial dimensions, for which it is shown that Goldstone-type fluctuations destroy particle localization, the order parameter is driven to zero, and power-law order-parameter correlations hold."],["dc.identifier.doi","10.1103/PhysRevB.70.184201"],["dc.identifier.isi","000225477300040"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/47271"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","American Physical Soc"],["dc.relation.issn","1098-0121"],["dc.title","Goldstone-type fluctuations and their implications for the amorphous solid state"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]