ARTICLES Li and Truhlar Table 1.Freezing Temperature (Ti),Melting Temperature (Tm). 1600 Position of Sharp Peaks/Deep Valleys(Tp)in Unitiess Specific Heat T。ofc Capacity(c),Coefficient of Thermal Expansion(B),Natural Logarithm 1400 of Compressibility(In )and Temperature(TPso)at Which P(O)=50 T00 1200 Bulk melting temperature 1000 B 800 10 300717 NA NA 826 1240 320 708 NA 548 907 1300 600 560 1071 1225 840 NA NA 400 1 700 1188 1273 1026 NA NA 14* NA (347) 1353 1187 A 1480 200 NA 1394 A 1186 NA 16* 1446 220 1349 NA 0 17* 1438 NA 0 946 NA 50 100 150 200300 260 624 (311,(384),(456) NA 687 1580 n 600 894 937 26 1062 1420 20* 240 471 1025 542 1360 Figure 5.Peak position(Tp)of heat capacity and temperature at which 740 1127 A NA 1280 1180 P(0)=50(TPo-50)as a function of cluster size.The long dashed line is 0 1119 380 1220 759 66 785 the bulk melting temperature. 1100 520 819 NA 755 905 1100 3.1 936 (427) 543 851 1000 26 613 978 570 960 3.0 (a) 676 72889 617 711,971 (464) 492 544 1060 398 38 9 940 860 0 430 445 940 22 令 (416 (623) 31* (382) 365 1040 2 32* 0, (355) 599 6 800 864 NA 696 2 940 25 28 8 46 38 8 4.9 (b) * (305 36 829 35 38 940 4.8 * 38 6 9* 4 % 460.797 5 8 743 377 368 920 41* W源M M% 8 4.5 824 65 434 840 833 840 (c) 860 5.1 45* 双 品 161030 462 边箱达热00 860 760 5.0 800 4.9 920 9 740 e 820 51 0O1 8 47 820 200 400 600 8001000120014001600 460 蒸 600 582 820 T(K) 2345657 8 0 8 920 920 Figure 6.Three typical radius of gyration(Rg)curves:(a)change gradually 480 667 678 680 645 960 with temperature,(b)obvious jumps,(c)obvious drops 663 1060 1第W1000 608 561 1130 721 300 305. 648 230 1160 radius.We find that Rg is slightly larger than RcoM,and both (382) 686 429 1030 show similar trends with temperature;here we will focus on 60 732 360 345 402 1020 Rg.Figure 6 shows three typical plots of Rg vs T(the rest are in 0 889 (474) 481 1060 the Supporting Information).The majority of the particles 823 (363 388 1060 300 842 (335 360 345 studied in the present work have the first type of Rg curve,shown 1040 64* 240 311 804 (318) 320 NA 1000 in Figure 6a,where Rg increases gradually with temperature. 868 (343) 400 360 100 For some particles,for example,Alj3 and Al19,the curve shows 480 565 460 458 443 940 a semilocalized change of slope,whereas it is almost featureless 80* NA 532 (299).(446 484 NA 900 90* for other particles.The second type of R curve,shown in Figure 100* 8 051 (365).551 (380).524388 940 (327).575 (360).539 d 920 6b,exhibits a clear jump;this is common for large particles, 110 34 572 566 580 501 900 especially for those particles with a well-defined sharp peak in 00 594 8 560 900 heat capacity(AlsI-Als6 and Al7o-Al300).For the third type, 130 46 619 604 900 177 400 652 660 640 d 900 shown in Figure 6c,R drops suddenly at a certain temperature 200 300 657 662 660 d 900 and then increases gradually with temperature(Al27,Al30,Al3s, 300 580 709 717 700 880 Al58,Al59.Al61-Al65). Liquid nanodroplets generally have larger volumes and larger Temperatures are in Kelvin,and particles in slush state at room coefficients of thermal expansion (B)than solid particles with temperature are marked with an asterisk.Tp is the temperature at which the given quantity has a maximum or a minimum (in parentheses).For the same number of atoms.The volume has a similar depen- those In k without sharp peaks,Tp determined is the peak/valley position of dence on temperature as Rg,and all the plots are presented in d In k/dT.Intermediate configurations were not quenched. the Supporting Information.However,it is worth noting that 12704J.AM.CHEM.S0C.■VOL.130,NO.38,2008radius. We find that Rg is slightly larger than RCoM, and both show similar trends with temperature; here we will focus on Rg. Figure 6 shows three typical plots of Rg vs T (the rest are in the Supporting Information). The majority of the particles studied in the present work have the first type of Rg curve, shown in Figure 6a, where Rg increases gradually with temperature. For some particles, for example, Al13 and Al19, the curve shows a semilocalized change of slope, whereas it is almost featureless for other particles. The second type of Rg curve, shown in Figure 6b, exhibits a clear jump; this is common for large particles, especially for those particles with a well-defined sharp peak in heat capacity (Al51-Al56 and Al70-Al300). For the third type, shown in Figure 6c, Rg drops suddenly at a certain temperature and then increases gradually with temperature (Al27, Al30, Al35, Al58, Al59, Al61-Al65). Liquid nanodroplets generally have larger volumes and larger coefficients of thermal expansion (
) than solid particles with the same number of atoms. The volume has a similar depen￾dence on temperature as Rg, and all the plots are presented in the Supporting Information. However, it is worth noting that Table 1. Freezing Temperature (Tf), Melting Temperature (Tm), Position of Sharp Peaks/Deep Valleys (Tp) in Unitless Specific Heat Capacity (c), Coefficient of Thermal Expansion (
), Natural Logarithm of Compressibility (ln κ), and Temperature (TP50) at Which P(0) ) 50a Tp b n Tf c
ln κ c TP50 Tm 10 300 717 NA NA 826 1240 11 320 708 NA 548 907 1300 12 560 1071 1225 840 NA NA 13 700 1188 1273 1026 NA NA 14* NA (347), 1353 NA 1187 NA 1480 15* NA 1394 NA 1186 NA NA 16* NA 1446 NA 220 1349 NA 17* NA 1438 NA 260 946 NA 18* 260 624 (311), (384), (456) NA 687 1580 19 600 894 937 826 1062 1420 20* 240 471, 1025 NA 946 542 1360 21 740 1127 NA NA 1280 1180 22* 280 1119 326 317 380 1220 23 480 759 766 679 785 1100 24 520 819 NA 755 905 1100 25* 260 936 (427), 543 510, 851 543 1000 26 420 613, 978 570 519, 676 569 960 27 420 617, 711, 971 (464) 492 544 1060 28 400 750 NA 452 600 940 29 340 868 432 431 429 860 30 340 943 (416), (623) 430 445 940 31* NA 922 (382) 365 326 1040 32* NA 806 240, (355) 599 429 800 33* NA 864 NA 696 269 940 34* 260 878 346 507 364 960 35* 240 854 (305) 475 368 960 36* NA 829 325 NA 387 940 37* NA 834 248 320 270 940 38* 280 340, 460, 797 415 395 429 920 39* 280 743 377 368 390 920 40* NA 796 NA 405 367 860 41* 280 821 346 335 327 840 42 NA 824 284 434 261 840 43* 240 317, 833 (265) 302 322 840 44 300 835 NA 344 363 860 45* NA 789 NA NA 323 860 46* NA 615 (406) 564 323 760 47* NA 742 NA 486 407 800 48 340 510 541 462 503 920 49 320 580 507 435 389 740 50 380 723 460 447 470 820 51 360 547 517 540 506 820 52 460 597 599 600 582 820 53 440 643 654 660 644 920 54 460 666 674 700 668 920 55 480 667 678 680 645 960 56 480 663 676 680 664 1060 57* 240 608 NA 540 307 1130 58* NA 276, 721 300 305, 648 230 1160 59 300 773 (382) 686 429 1030 60 300 732 360 345 402 1020 61 400 730, 889 (474) 454 481 1060 62 300 823 (363) 310 388 1060 63 300 842 (335) 360 345 1040 64* 240 311, 804 (318) 320 NA 1000 65* 240 352, 868 (343) 400 360 1000 70* NA 420, 480, 565 460 458 443 940 80* NA 532 (299), (446) 484 NA 900 90* 240 340, 561 (365), 551 (380), 524 388 940 100* 240 340, 571 (327), 575 (360), 539 d 920 110 340 572 566 580 501 900 120 500 594 696 568 560 900 130 460 619 632 592 604 900 177 400 652 660 640 d 900 200 300 657 662 660 d 900 300 580 709 717 700 d 880 a Temperatures are in Kelvin, and particles in slush state at room temperature are marked with an asterisk. b Tp is the temperature at which the given quantity has a maximum or a minimum (in parentheses). c For those ln κ without sharp peaks, Tp determined is the peak/valley position of d ln κ/dT. d Intermediate configurations were not quenched. Figure 5. Peak position (Tp) of heat capacity and temperature at which P(0) ) 50 (TP(0))50) as a function of cluster size. The long dashed line is the bulk melting temperature. Figure 6. Three typical radius of gyration (Rg) curves: (a) change gradually with temperature, (b) obvious jumps, (c) obvious drops. 12704 J. AM. CHEM. SOC. 9 VOL. 130, NO. 38, 2008 ARTICLES Li and Truhlar