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We experimentally investigated the correlation between local structures and phonon modes in quasi-2D colloidal glasses. The glass samples consist of thermo-sensitive poly-N-isopropylacrylamide microgel (PNIPAM) particles, whose diameter can be tuned by small changes of sample temperature. A binary mixture of these particles is confined between two coverslips and forms a monolayer of quasi-2D glass. By changing the number ratio between large and small particles, the structure or the overall degree of disorder of the samples can be systematically tuned. We employ a video microscopy to record the motion of the colloidal particles in the sample for 11 min at a rate of 60 fps. The trajectories of individual particles are obtained by particle tracking software. Dynamical matrix is constructed using covariance matrix analysis, from which the eigenfrequency and eigenvector of vibrations are extracted. In this study, we focus on the evolution of the low-frequency quasi-localized phonon modes in glasses, as the system becomes more and more disordered from the increased dopants. To compare the results from different samples, we choose those with packing fraction of 86%, and rescale the eigenfrequencies by the median frequency of each sample. For the four doping levels investigated (2%, 9%, 29%, 61%), the density of states at low frequencies increases with the doping level, suggesting that the fraction of low-frequency modes increases with disorder, which is corroborated by the higher boson peaks at higher dopant fractions. We have measured the participation ratio of the obtained phonon modes, and find that the boson peak corresponds to quasi-localized vibration modes, or soft modes. We also examine the correlation between the soft modes and local structural parameter. Specifically, we have calculated the local orientational order parameter in our samples, and computed the correlation coefficients between the relative amplitude and the local orientational order parameter for each mode. The soft modes are found to have a significantly negative correlation with the local orientational order parameter, which implies that the soft modes are concentrated in regions with poor local order. We therefore conclude that the local disorder is probably the structural origin of soft modes in glasses.
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Keywords:
- colloidal glass /
- Boson peak /
- quasi-localized modes
[1] Xu N, Vitelli V, Liu A J, Nagel S R 2010 Europhys. Lett. 90 56001
[2] Chen K, Ellenbroek W G, Zhang Z X, Chen D T N, Yunker P J, Henkes S, Brito C, Dauchot O, Saarloos W V, Liu A J, Yodh A G 2010 Phys. Rev. Lett. 105 025501
[3] Liu H M, Lu C L, Wang K F, Liu J M, Wang Q, Dong C 2010 Chin. Phys. B 19 017102
[4] Pohl R O, Liu X, Thompson E 2002 Rev. Mod. Phys. 74 991
[5] Zhang Z X, Xu N, Chen D T N, Yunker P, Alsayed A M, Aptowicz K B, Habdas P, Liu A J, Nagel S R, Yodh A G 2009 Nature 459 230
[6] Ghosh A, Chikkadi V K, Schall P, Kurchan J, Bonn D 2010 Phys. Rev. Lett. 104 248305
[7] Kaya D, Green N L, Maloney C E, Islam M F 2010 Science 329 656
[8] Chumakov A I, Monaco G, Monaco A, Crichton W A, Bosak A, Rffer R, Meyer A, Kargl F, Comez L, Fioretto D, Giefers H, Roitsch S, Wortmann G, Manghnani M H, Hushur A, Williams Q, Balogh J, Parliński K, Jochym P, Piekarz P 2011 Phys. Rev. Lett. 106 225501
[9] Graebner J E, Golding B 1979 Phys. Rev. B 19 964
[10] Xu N 2011 Front. Phys. China 6 109
[11] Souslov A, Liu A J, Lubensky T C 2009 Phys. Rev. Lett. 103 205503
[12] Mao X M, Xu N, Lubensky T C 2010 Phys. Rev. Lett. 104 085504
[13] Hiltner P A, Krieger I M 1969 J. Phys. Chem. 73 2386
[14] Hiltner P A, Papir Y S, Krieger I M 1971 J. Phys. Chem. 75 1881
[15] Kose A, Ozaki M, Takano K, Kobayashi Y, Hachisu S 1973 J. Colloid Interface Sci. 44 330
[16] Lu K Q, Liu J X 2006 Introduction to soft Matter Physics (Beijing:Pecking University Press) p309 (in Chinese) [陆坤全, 刘寄星 2006 软物质物理学导论(北京:北京大学出版社) 第309页]
[17] Tan P, Xu N, Schofield A B, Xu L 2012 Phys. Rev. Lett. 108 095501
[18] Shintani H, Tanaka H 2008 Nature Mater. 7 870
[19] Shintani H, Tanaka H 2006 Nature Phys. 2 200
[20] Saunders B R, Vincent B 1999 Adv. Colloid Interface Sci. 80 1
[21] Pelton R 2000 Adv. Colloid Interface Sci. 85 1
[22] Still T, Chen K, Alsayed A M, Aptowicz K B, Yodh A G 2013 J. Colloid Interface Sci. 405 96
[23] Wyart M 2005 Ann. Phys. (Paris) 30 1
[24] Xu N, Wyart M, Liu A J, Nagel S R 2007 Phys. Rev. Lett. 98 175502
[25] Wyart M, Liang H, Kabla A, Mahadevan L 2008 Phys. Rev. Lett. 101 215501
[26] Crocker J C, Grier D G 1996 J. Colloid Interface Sci. 179 298
[27] Yunker P, Chen K, Zhang Z X, Yodh A G 2011 Phys. Rev. Lett. 106 225503
[28] Chen K, Still T, Schoenholz S, Aptowicz K B, Schindler M, Maggs A C, Liu A J, Yodh A G 2013 Phys. Rev. E 88 022315
[29] Zhang G H, Sun Q C, Shi Z P, Feng X, Gu Q, Jin F 2014 Chin. Phys. B 23 076301
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[1] Xu N, Vitelli V, Liu A J, Nagel S R 2010 Europhys. Lett. 90 56001
[2] Chen K, Ellenbroek W G, Zhang Z X, Chen D T N, Yunker P J, Henkes S, Brito C, Dauchot O, Saarloos W V, Liu A J, Yodh A G 2010 Phys. Rev. Lett. 105 025501
[3] Liu H M, Lu C L, Wang K F, Liu J M, Wang Q, Dong C 2010 Chin. Phys. B 19 017102
[4] Pohl R O, Liu X, Thompson E 2002 Rev. Mod. Phys. 74 991
[5] Zhang Z X, Xu N, Chen D T N, Yunker P, Alsayed A M, Aptowicz K B, Habdas P, Liu A J, Nagel S R, Yodh A G 2009 Nature 459 230
[6] Ghosh A, Chikkadi V K, Schall P, Kurchan J, Bonn D 2010 Phys. Rev. Lett. 104 248305
[7] Kaya D, Green N L, Maloney C E, Islam M F 2010 Science 329 656
[8] Chumakov A I, Monaco G, Monaco A, Crichton W A, Bosak A, Rffer R, Meyer A, Kargl F, Comez L, Fioretto D, Giefers H, Roitsch S, Wortmann G, Manghnani M H, Hushur A, Williams Q, Balogh J, Parliński K, Jochym P, Piekarz P 2011 Phys. Rev. Lett. 106 225501
[9] Graebner J E, Golding B 1979 Phys. Rev. B 19 964
[10] Xu N 2011 Front. Phys. China 6 109
[11] Souslov A, Liu A J, Lubensky T C 2009 Phys. Rev. Lett. 103 205503
[12] Mao X M, Xu N, Lubensky T C 2010 Phys. Rev. Lett. 104 085504
[13] Hiltner P A, Krieger I M 1969 J. Phys. Chem. 73 2386
[14] Hiltner P A, Papir Y S, Krieger I M 1971 J. Phys. Chem. 75 1881
[15] Kose A, Ozaki M, Takano K, Kobayashi Y, Hachisu S 1973 J. Colloid Interface Sci. 44 330
[16] Lu K Q, Liu J X 2006 Introduction to soft Matter Physics (Beijing:Pecking University Press) p309 (in Chinese) [陆坤全, 刘寄星 2006 软物质物理学导论(北京:北京大学出版社) 第309页]
[17] Tan P, Xu N, Schofield A B, Xu L 2012 Phys. Rev. Lett. 108 095501
[18] Shintani H, Tanaka H 2008 Nature Mater. 7 870
[19] Shintani H, Tanaka H 2006 Nature Phys. 2 200
[20] Saunders B R, Vincent B 1999 Adv. Colloid Interface Sci. 80 1
[21] Pelton R 2000 Adv. Colloid Interface Sci. 85 1
[22] Still T, Chen K, Alsayed A M, Aptowicz K B, Yodh A G 2013 J. Colloid Interface Sci. 405 96
[23] Wyart M 2005 Ann. Phys. (Paris) 30 1
[24] Xu N, Wyart M, Liu A J, Nagel S R 2007 Phys. Rev. Lett. 98 175502
[25] Wyart M, Liang H, Kabla A, Mahadevan L 2008 Phys. Rev. Lett. 101 215501
[26] Crocker J C, Grier D G 1996 J. Colloid Interface Sci. 179 298
[27] Yunker P, Chen K, Zhang Z X, Yodh A G 2011 Phys. Rev. Lett. 106 225503
[28] Chen K, Still T, Schoenholz S, Aptowicz K B, Schindler M, Maggs A C, Liu A J, Yodh A G 2013 Phys. Rev. E 88 022315
[29] Zhang G H, Sun Q C, Shi Z P, Feng X, Gu Q, Jin F 2014 Chin. Phys. B 23 076301
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