Formation of a crystal nucleus from liquid - of a crystal nucleus from liquid ... and final ordered crystal phases as the only key players of nuclea- ... fitting by the Vogel–Fulcher–Tammann

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  • Corrections

    EVOLUTIONCorrection for Genome sequences of the human body louse andits primary endosymbiont provide insights into the permanentparasitic lifestyle, by Ewen F. Kirkness, Brian J. Haas, WeilinSun, Henk R. Braig, M. Alejandra Perotti, John M. Clark, SiHyeock Lee, Hugh M. Robertson, Ryan C. Kennedy, EranElhaik, Daniel Gerlach, Evgenia V. Kriventseva, ChristineG. Elsik, Dan Graur, Catherine A. Hill, Jan A. Veenstra, BrianWalenz, Jos Manuel C. Tubo, Jos M. C. Ribeiro, Julio Rozas,J. Spencer Johnston, Justin T. Reese, Aleksandar Popadic, MartaTojo, Didier Raoult, David L. Reed, Yoshinori Tomoyasu, EmilyKrause, Omprakash Mittapalli, Venu M. Margam, Hong-Mei Li,Jason M. Meyer, Reed M. Johnson, Jeanne Romero-Severson,Janice Pagel VanZee, David Alvarez-Ponce, Filipe G. Vieira,Montserrat Aguad, Sara Guirao-Rico, Juan M. Anzola, KyongS. Yoon, Joseph P. Strycharz, Maria F. Unger, Scott Christley,Neil F. Lobo, Manfredo J. Seufferheld, NaiKuan Wang, GregoryA. Dasch, Claudio J. Struchiner, Greg Madey, Linda I. Hannick,Shelby Bidwell, Vinita Joardar, Elisabet Caler, Renfu Shao,Stephen C. Barker, Stephen Cameron, Robert V. Bruggner,Allison Regier, Justin Johnson, Lakshmi Viswanathan, TerryR. Utterback, Granger G. Sutton, Daniel Lawson, Robert M.Waterhouse, J. Craig Venter, Robert L. Strausberg, May R.Berenbaum, Frank H. Collins, Evgeny M. Zdobnov, and BarryR. Pittendrigh, which appeared in issue 27, July 6, 2010, of ProcNatl Acad Sci USA (107:1216812173; first published June 21,2010; 10.1073/pnas.1003379107).The authors note that the author name Emily Krause should

    have appeared as Emily Kraus. The corrected author lineappears below. The online version has been corrected.

    Ewen F. Kirknessa,1, Brian J. Haasa,2, Weilin Sunb, Henk R.Braigc, M. Alejandra Perottid, John M. Clarke, Si Hyeock Leef,Hugh M. Robertsonb, Ryan C. Kennedyg,h, Eran Elhaiki,Daniel Gerlachj,k, Evgenia V. Kriventsevaj,k, Christine G.Elsikl,3, Dan Grauri, Catherine A. Hillm, Jan A. Veenstran,Brian Walenza, Jos Manuel C. Tuboo, Jos M. C. Ribeirop,Julio Rozasq, J. Spencer Johnstonr, Justin T. Reesel,Aleksandar Popadics, Marta Tojot, Didier Raoultu, David L.Reedv, Yoshinori Tomoyasuw,4, Emily Krausw, OmprakashMittapallix, Venu M. Margamm, Hong-Mei Lib, Jason M.Meyerm, Reed M. Johnsonb, Jeanne Romero-Seversong,y,Janice Pagel VanZeem, David Alvarez-Ponceq, Filipe G.Vieiraq, Montserrat Aguadq, Sara Guirao-Ricoq, Juan M.Anzolal, Kyong S. Yoone, Joseph P. Strycharze, Maria F.Ungerg,y, Scott Christleyg,h, Neil F. Lobog,y, Manfredo J.Seufferheldz, NaiKuanWangaa, Gregory A. Daschbb, Claudio J.Struchinercc, Greg Madeyg,h, Linda I. Hannicka, ShelbyBidwella, Vinita Joardara, Elisabet Calera, Renfu Shaodd,Stephen C. Barkerdd, Stephen Cameronee, Robert V.Bruggnerg,h, Allison Regierg,h, Justin Johnsona, LakshmiViswanathana, Terry R. Utterbacka, Granger G. Suttona,Daniel Lawsonff, Robert M. Waterhousej,k, J. CraigVentera, Robert L. Strausberga, May R. Berenbaumb,Frank H. Collinsg,y, Evgeny M. Zdobnovj,k,gg,1,and Barry R. Pittendrighb,1,5

    www.pnas.org/cgi/doi/10.1073/pnas.1103909108

    PHYSICSCorrection for Formation of a crystal nucleus from liquid, byTakeshi Kawasaki and Hajime Tanaka, which appeared in issue32, August 10, 2010, of Proc Natl Acad Sci USA (107:1403614041; first published July 27, 2010; 10.1073/pnas.1001040107).The authors note that Fig. 6 appeared incorrectly. The cor-

    rected figure and its legend appear below. This error does notaffect the conclusions of the article.

    www.pnas.org/cgi/doi/10.1073/pnas.1104042108

    Fig. 6. Crystal nucleation dynamics. (A) Temporal change of the number ofcrystal nuclei for a system of N = 4,096 (SI Text). From the rate of the increasein the number of crystal nuclei, we estimated the crystal nucleation fre-quency I. The numbers in the figure indicate the volume fraction . (B) Thevolume fraction dependence of the reduced crystal nucleation frequency Irfor our work, the numerical estimate by Auer and Frenkel (15), and theexperimental work by Sinn et al. (17). Curves are guides to the eye. We alsoshow the results for three different system sizes (N = 1,024, 4,096, and16,834), which indicate few finite size effects for N 4,096. Here we use thevolume fraction estimated with eff = 1.0953. Here BD stands for Brown-ian Dynamics simulations of the WCA system and HS stands for event-drivenMolecular Dynamics simulations of the hard sphere system.

    www.pnas.org PNAS | April 12, 2011 | vol. 108 | no. 15 | 63356336

    CORR

    ECTIONS

    www.pnas.org/cgi/doi/10.1073/pnas.1103909108www.pnas.org/cgi/doi/10.1073/pnas.1104042108

  • MEDICAL SCIENCES, CHEMISTRYCorrection for Multistage nanoparticle delivery system for deeppenetration into tumor tissue, by Cliff Wong, TriantafyllosStylianopoulos, Jian Cui, John Martin, Vikash P. Chauhan, WenJiang, Zoran Popovic, Rakesh K. Jain, Moungi G. Bawendi, andDai Fukumura, which appeared in issue 6, February 8, 2011 of

    Proc Natl Acad Sci USA (108:24262431; first published January18, 2011; 10.1073/pnas.1018382108).The authors note that Fig. 2 and its corresponding legend ap-

    peared incorrectly. This error does not affect the conclusions of thearticle. The correctedfigure and its corrected legend appearbelow.

    www.pnas.org/cgi/doi/10.1073/pnas.1104327108

    CA B D

    E F G H

    Incubation with230 ng (0.16 M)of MMP-2

    0 2 4 6 8 10 12

    0

    20

    40

    60

    80

    100

    Qu

    antu

    mD

    ots

    Rel

    ease

    d(%

    )

    Time (h)

    Incubation for 12 hours

    0 50 100 150 200 250

    0

    20

    40

    60

    80

    100

    Qu

    antu

    mD

    ots

    Rel

    ease

    d(%

    )

    MMP-2 (ng)

    Before MMP-2Incubation

    10-2 10-1 100 101 102 103 1040.0

    0.2

    0.4

    0.6

    0.8

    D = 6.1 x 10-8

    cm2/s

    G(

    )

    (ms)

    After 230 ngMMP-2 Incubation

    10-2 10-1 100 101 102 103 1040.0

    0.2

    0.4

    0.6

    G(

    )

    (ms)

    D = 4.4 x 10-7

    cm2/s

    0 50 100 150 2000

    25

    50

    Nu

    mb

    ero

    fP

    arti

    cles

    Diameter (nm)1 10 100 1000 10000

    0

    10

    20

    30

    %M

    ass

    Diameter (nm)

    Day 1Day 48

    540 570 600

    Flu

    ores

    cenc

    e(A

    U)

    (nm)

    Fig. 2. QDGelNP physical and in vitro characterization. (A) Epifluorescence image of QDGelNPs on a silicon substrate at 100magnification. (Scale bar: 5 m.)(B) DLS distribution of QDGelNP on day 1 and day 48 after synthesis and storage at 4 C. (C) SEM image of QDGelNPs at 15,000 magnification. (Scale bar: 1m.) (C Inset) SEM image of individual QDGelNP at 35,000 magnification. (Scale bar: 100 nm.) (D) Histogram of QDGelNPs size distribution from imageanalysis of SEM image. (E and F) Kinetics of MMP-2induced QD release from QDGelNPs. (E) QD-release curve from incubation of 0.1 mg of QDGelNPs with230 ng (0.16 M) of MMP-2. (F) QD release from incubation of 0.1 mg of QDGelNPs for 12 h with varying amounts of MMP-2. (G and H) FCS cross-correlogramsof QDGelNPs before (G) and after (H) incubation with MMP-2.

    6336 | www.pnas.org

    www.pnas.org/cgi/doi/10.1073/pnas.1104327108

  • Formation of a crystal nucleus from liquidTakeshi Kawasaki and Hajime Tanaka1

    Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

    Edited by Noel A. Clark, University of Colorado, Boulder, CO, and approved June 30, 2010 (received for review January 27, 2010)

    Crystallization is one of the most fundamental nonequilibriumphenomena universal to a variety of materials. It has so far beenassumed that a supercooled liquid is in a homogeneous disor-dered state before crystallization. Contrary to this common belief,we reveal that a supercooled colloidal liquid is actually not homo-geneous, but has transient medium-range structural order. We findthat nucleation preferentially takes place in regions of high struc-tural order via wetting effects, which reduce the crystalliquid in-terfacial energy significantly and thus promotes crystal nucleation.This novel scenario provides a clue to solving a long-standing mys-tery concerning a large discrepancy between the rigorous numer-ical estimation of the nucleation rate on the basis of the classicalnucleation theory and the experimentally observed ones. Our find-ingmay shed light not only on themechanism of crystal nucleation,but also on the fundamental nature of a supercooled liquid state.

    bond orientational order glass transition hard-sphere liquid metastable liquid

    Crystallization is a process in which an ordered phase emergesfrom a disordered state. It is important not only as a funda-mental problem of nonequilibrium statistical physics, but also asthat of materials science. The initial state is a disordered liquidand the final state is a stable crystal. The classical nucleation the-ory (13) considers these initial homogeneous disordered liquidand final ordered crystal phases as the only key players of nuclea-tion. In this theory, thus, crystal nucleation is controlled by thecompetition between the free-energy gain due to the liquidcrys-tal transformation and the free-energy loss associated with theformation of the liquidcrystal interface. The total free-energycost to form a spherical crystallite with radius R is

    G 43R3ns 4R2;

    where ns is the number density of particles in the solid, is thedifference between the liquid and solid chemical potentials, and is the liquidsolid interfacial tension. This G goes through amaximum at Rc 2ns (critical nucleus size) and the heightof the free-energy barrier is given by

    Gc 163

    3ns2:

    Then, the crystal nucleation frequency I per unit volume is ob-tained as

    I ktexpGckBT;

    where k is a constant, kB

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