We measure the fluctuations of the position of a silica bead trapped by an
optical tweezers during the aging of a Laponite suspension. We find that the
effective temperature is equal to the bath temperature

Ciliberto, Sergio

Jop, Pierre

Petrosyan, Artyom

English

arXiv

We measure the fluctuations of the position of a silica bead trapped by an optical tweezers during the aging of a Laponite suspension. We find that the effective temperature is equal to the bath temperature

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Comment on ”Measurement of Effective Temperaturesin an Aging Colloidal Glass”Pierre Jop, Artyom Petrosyan, Sergio CilibertoTo cite this version:Pierre Jop, Artyom Petrosyan, Sergio Ciliberto. Comment on ”Measurement of Effective Tem-peratures in an Aging Colloidal Glass”. 2007. <ensl-00145416>HAL Id: ensl-00145416https://hal-ens-lyon.archives-ouvertes.fr/ensl-00145416Submitted on 10 May 2007HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.ensl-00145416, version 1 - 10 May 2007Comment on ”Measurement of Effective Temperatures in an Aging Colloidal Glass”Pierre Jop, Artyom Petrosyan & Sergio CilibertoLaboratoire de Physique, CNRS UMR 5276, E´cole Normale Supe´rieure de Lyon, 46 alle´e d’Italie, 69364 Lyon cedex 7, France.PACS numbers: 64.70.Pf, 05.40.-a, 05.70.Ln, 82.70.DdIn a Letter [1], Greinert et al. reported an increase ofeffective temperature (Teff ) during the aging process ofa Laponite suspension measured from the fluctuationsof position of optically trapped beads. We think theirresults are not conclusive since there could be some arti-facts in the experiment.We measure the fluctuations of the position of a silicabead trapped by an optical tweezers during the aging ofthe Laponite. The laser beam (λ=980 nm) is focusedby a microscope objective (×63) 20 µm above the cover-slip surface to create a harmonic potential well wherea bead of 1 or 2 µm in diameter (d) is trapped. TheLaponite mass concentration is varied from 1.2 to 3% wtfor different ionic strengths.Following the method used in [1], the stiffness of theoptical trap is periodically switched between two differ-ent values (k1 and k2) every 61 seconds by changing thelaser intensity. The position of the bead is recorded bya quadrant photodiode at the rate of 8192 Hz, then wecompute the variance of the position over the whole sig-nal,〈δx2〉=〈x2 − 〈x〉2〉, where the brackets stand foraverage over the time. To avoid transients, each recordis started 20 seconds after the laser switch. Assum-ing the equipartition principle still holds in this out-of-equilibrium system, the Teff is computed as in [1].Our results are shown on the Fig. 1a. We find that Teffis constant at the beginning and is very close to Tbath =294 K, then when the jamming occurs, it becomes noisywithout any clear increase with tw, contrary to Ref. [1].We now make three remarks. First, we point out thatthe uncertainty of their results are underestimated. Theerror bars in Fig. 1(a) are here evaluated from the stan-dard deviation of the variance using Eq. 2 in Ref [1] atthe time tw. Although they are small for short time tw,(∆Teff/Teff ≤ 10%), they increase for large tw. This isa consequence of the increase of variabilities of〈δx2i〉asthe colloidal glass forms. This point is not discussed inin Ref. [1] and we think that the measurement errors areof the same order or larger than the observed effect. Theresults depend on the length of the analysing time win-dow and the use of the principle of energy equipartitionbecomes questionable for the following reasons.First, these analysing windows cannot be made toolarge because the viscoelastic properties of Laponiteevolve as a function of time. Second, the corner frequencyof the global trap (optical trap and gel), the ratio of thetrap stiffness to viscosity, decreases continuously mainlybecause of the increase of viscosity. At the end of theexperiment, the power spectrum density of the displace-ment of the bead shows that the corner frequency is lowerthan 0.1 Hz. We thus observe long lived fluctuations,which could not be taken into account with short measur-ing times. This problem is shown on Fig. 1b. We split ourdata into equal time duration ∆τ , compute the varianceand average the results of all samples. The dotted linerepresents the duration 3.3 s chosen in [1]. At the begin-ning of the experiment, the variance of the displacementis constant for any reasonable durations of measurement.However, we clearly see that this method produces anunderestimate of〈∆x2〉for long aging times, speciallywhen the viscoelasticity of the gel becomes important.Long lived fluctuations are then ignored.0 1 2 3 4 51002003004005006000 2 4 60510x 10 2  10-1 100 10110 210 3Teff  (K)(a) (b)tw  (h)tw (h)<x2> (nm2)∆τ for analyses (s)<x2>∆τ  (nm2)twFIG. 1: a) Evolution of the effective temperature with agingtime for k1 = 6.34 pN/µm, k2 = 14.4 pN/µm, 2.3% wt ofLaponite and 1 µm glass bead. The error bars are computedfrom the statistical error of〈δx2i〉at the time tw. Inset: Evo-lution of〈δx2〉with tw for both stiffnesses (k1 ◦ and k2 ).b) Evolution of〈δx2〉∆τfor the low stiffness as a function ofthe duration ∆τ of the samples (see text) for different agingtimes : from top to bottom tw = 30, 57, 83, 110, 137, 163,190, 217, 243 and 270 minutes.Finally, a remark has to be made concerning the meanposition of the bead during aging. When the stiffness ofthe gel becomes comparable to the optical one, the beadstarts to move away from the center the optical trap. Weobserve a drift of the bead position at long time, whichcould lead to the escape of the bead. Moreover we haveperformed simultaneous measurements with a multipletrap using a fast camera showing that at very long twthe mean trajectories of beads separated by 7 µm are al-most identical. This proves that one must pay attentionwhen interpreting such measurements, specially on theduration of measurements. We also have seen that theway the sample is sealed can accelerate the formation ofthe gel and the drift of the bead by changing the chemicalproperties in the small sample. We have used differenttypes of cell, Laponite concentrations, bead sizes, stiff-2nesses of the optical trap. In each case we do not findany increase of the effective temperature.In conclusion, our results show no increase of Teff inLaponite and are in agreement with those of Jabbari-Farouji et al.[2], who measured fluctuations and re-sponses of the bead displacement in Laponite over a widerange of frequency and found that Teff is equal to thebath temperature.[1] N. Greinert et al., Phys. Rev. Lett. 97, 265702 (2006)[2] S. Jabbari-Farouji et al., Phys. Rev. Lett. 98, 108302(2007)

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