Translationally invariant colloidal crystal templates

Popli, Pankaj; Ganguly, Saswati; Sengupta, Surajit

doi:10.1039/c7sm01877k

Cited by 10 publications

(14 citation statements)

References 51 publications

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“…For solids where individual particles can be distinguished and tracked, one should be able to realise h X in the laboratory and check our predictions in the full h X − ε plane. Indeed, it has already been discussed in detail [15,17,20] how this may be accomplished in the future for colloidal particles in 2d using dynamic laser traps. Briefly, the set of reference coordinates is read in and a laser tweezer is used to exert additional forces, F χ (r i ) = −∂H X /∂r i to each particle i which bias displacement fluctuations.…”

Section: Discussionmentioning

confidence: 99%

“…The ensemble average X can be tailored using h X consistent with standard fluctuation response relations [15] and h X can also modify the probability of defects. Note that since X is defined in terms of relative displacements, the term proportional to h X in H does not explicitly break translational invariance [20]. Positive values of h X help create non-affine rearrangements away from the reference configuration.…”

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confidence: 99%

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On the existence of thermodynamically stable rigid solids

Nath

Ganguly

Horbach

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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Customarily, crystalline solids are defined to be rigid since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the metastable state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then used to obtain the equilibrium free energy as a function of this variable. Our results lead to a unique view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable when an external field, which penalizes particle rearrangements, is switched on. This produces a line of first-order phase transitions in the field-strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

On the existence of thermodynamically stable rigid solids

Nath

Ganguly

Horbach

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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“…Using the non-affine formalism it is also possible to describe the non-trivial singular deformations like pleats and ripplocations 20,21 undergone by solids having atoms bound by strong chemical bonds, which disallow any kind of dislocations. Also it has been shown, 18,22 that colloids can be ordered in any given crystal structure by suppressing the non-affine displacements, with the help of special feedback-control laser traps. Using a similar projection formalism as described in Ganguly et al, 15 for large bio macrolecules lacking any kind of long-range structural order it has been shown by Dube et al, 23 that important conformational changes are always accompanied by non-affine fluctuations and that regions in proteins with high susceptibility for non-affine fluctuations correlate with binding hotspots and the magnitude of the spatial correlations reveal allosteric connections in different locations of protein molecules.…”

Section: Optimisationsmentioning

confidence: 99%

Nonaffine Displacements Encode Collective Conformational Fluctuations in Proteins

Prakashchand

Ahalawat

Bandyopadhyay

et al. 2020

J. Chem. Theory Comput.

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Identifying subtle conformational fluctuations underlying the dynamics of bio macromolecules is crucial for resolving their free energy landscape. We show that a collective variable, originally proposed for crystalline solids, is able to filter out essential macromolecular motions more efficiently than other approaches. While homogenous or 'affine' deformations of the biopolymer are trivial, biopolymer conformations are complicated by the occurrence of in-homogenous or 'non-affine' displacements of atoms relative to their positions in the native structure. We show that these displacements encode functionally relevant conformations of macromolecule and, in combination with a formalism based upon time-structured independent component analysis, quantitatively resolve the free energy landscape of a number of macromolecules of hierarchical complexity. The kinetics of conformational transitions among the basins can now be mapped within the framework of a Markov state model. The non-affine modes, obtained by projecting out homogenous fluctuations from the local displacements, are found to be responsible for local structural changes required for transitioning between pairs of macro states.

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“…Special, dynamic, feedback controlled laser traps have been proposed, though not yet experimentally realized, which may be able to perform this feat. Unlike static traps, the structures stabilized by such a process are translationally invariant and possess all allowed zero modes [21].…”

Section: Introductionmentioning

confidence: 99%

Exploring the link between crystal defects and nonaffine displacement fluctuations

et al. 2019

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We generalize, and then use, a recently introduced formalism to study thermal fluctuations of atomic displacements in several two and three dimensional crystals. We study both close packed as well as open crystals with multi atom bases. Atomic displacement fluctuations in a solid, once coarsegrained over some neighborhood may be decomposed into two mutually orthogonal components. In any dimension d there are always d 2 affine displacements representing local strains and rotations of the ideal reference configuration. In addition, there exists a number of non-affine localized displacement modes that cannot be represented as strains or rotations. The number of these modes depends on d and the size of the coarse graining region. All thermodynamic averages and correlation functions concerning the affine and non-affine displacements may be computed within a harmonic theory. We show that for compact crystals, such as the square and triangular in d = 2 and the simple, body-centered and face-centered cubic crystals in d = 3, a single set of d−fold degenerate modes always dominate the non-affine sub-space and are separated from the rest by a large gap. These modes may be identified with specific precursor configurations that lead to lattice defects. In open crystals, such as the honeycomb and kagome lattices, there is no prominent gap although soft non-affine modes continue to be associated with known floppy modes representing localized defects. Higher order coupling between affine and non-affine components of the displacements quantify the tendency of the lattice to be destroyed by large homogeneous strains. We show that this coupling is larger by almost an order of magnitude for open lattices as compared to compact ones. Deformation mechanisms such as lattice slips and stacking faults in close packed crystals can also be understood within this framework. The qualitative features of these conclusions are expected to be independent of the details of the atomic interactions.

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Translationally invariant colloidal crystal templates

Cited by 10 publications

References 51 publications

On the existence of thermodynamically stable rigid solids

On the existence of thermodynamically stable rigid solids

Nonaffine Displacements Encode Collective Conformational Fluctuations in Proteins

Exploring the link between crystal defects and nonaffine displacement fluctuations

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