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SỞ KHOA HỌC VÀ CƠNG NGHỆ TP HỒ CHÍ MINH THÀNH ĐỒN TP HỒ CHÍ MINH CHƯƠNG TRÌNH VƯỜN ƯƠM SÁNG TẠO KHOA HỌC VÀ CÔNG NGHỆ TRẺ * BÁO CÁO NGHIỆM THU MƠ PHỎNG CẤU TRÚC VÀ CÁC TÍNH CHẤT NHIỆT ĐỘNG HỌC CỦA HẠT ALUMINOSILICATE VƠ ĐỊNH HÌNH CĨ KÍCH THƯỚC NANO Chủ nhiệm đề tài: NGUYỄN NGỌC LĨNH TRẦN THỊ THU HẠNH Cơ quan chủ trì: TRUNG TÂM PHÁT TRIỂN KHOA HỌC VÀ CÔNG NGHỆ TRẺ TP Hồ Chí Minh, tháng năm 2010 Lời cảm ơn Chúng chân thành cảm ơn Trung tâm Phát triển Khoa học Công nghệ trẻ tạo điều kiện quản lý chúng tơi hồn thành đề tài nghiên cứu Cảm ơn Sở Khoa học Công nghệ Thành phố Hồ Chí Minh, quan hỗ trợ kinh phí cho nhóm nghiên cứu Chúng tơi cảm ơn Trung tâm tính tốn trường Đại học Bách khoa thành phố Hồ Chí Minh cho chúng tơi th sử dụng hệ thống tính tốn Cảm ơn thành viên nhóm Vật lý tính tốn Khoa Khoa học Ứng dụng, Đại học Bách khoa Hồ Chi Minh giúp đỡ, trao đổi nỗ lực hoàn thành đề tài hạn Cảm ơn hội đồng xét duyệt đề tài, hội đồng nghiệm thu đề tài đọc nhận xét kết nghiên cứu Tóm tắt Nghiên cứu tính chất cấu trúc tính chất động học hạt aluminosilicate (A2S) kích thước nanomét tiến hành phương pháp Động lực học phân tử Các mơ hình với kích thước từ - nm xây dựng dựa điều kiện biên đóng tương tác nguyên tử mơ hình mơ tả có dạng BornMayer Từ mơ hình ban đầu trạng thái lỏng, hạt A2S có kích thước nanomét làm lạnh nhanh tốc độ làm lạnh khác đạt đến trạng thái vơ dịnh hình Các tính chất cấu trúc tính chất nhiệt động hạt kích thước nanomét khảo sát nhiệt độ khác Kết cho thấy phụ thuộc vào tốc độ làm lạnh tính chất nhiệt động số đại lượng đặc trưng cho cấu trúc hàm phân bố xuyên tâm, phân bố số phối vị lớn Những tính chất đặc trưng cấu trúc bề mặt lõi hạt nano trình làm lạnh nghiên cứu so sánh với vật liệu khối Ngoài ra, ảnh hưởng áp suất, cấu trúc động học hạt A2S nanomét lỏng nhiệt độ 4200 K khảo sát Dưói ảnh hưởng áp suất, giá trị áp suất cao so với giá trị áp suất vật liệu khối tương ứng, cấu trúc hạt A2S có kích thước nanomét biến đổi từ cấu trúc tứ diện sang cấu trúc ngũ diện, biến đổi đồng thời kéo theo biến đổi dị thường mặt động học liên quan đến hiệu ứng bề mặt xảy hạt nano Abstract The structural and dynamic properties of amorphous and liquid aluminosilicate nanoparticles have been intensively studied by Molecular Dynamics (MD) methods The models with dimensions ranging from to nm under non-periodic boundary conditions have been considered The empirical Born-Mayer potentials have been used to modify the interactions between ionic matters in nanoparticles The calculations start from the initial configurations at high temperature of 7000 K and cool downward room temperature with different cooling rates to approach the amorphous states of nanoparticles The studies show that the cooling rate dependence of thermodynamics and some structural quantities such as the radial distribution functions or average coordination distributions are significant as long as I comparing to the bulk counterpart Moreover, the structural properties of surface and core layer of nanoparticles have also calculated and referred to the bulk counterpart at the same computed conditions On the other hand, the pressure induced phase transitions in dynamics and structures also estimated The study shows a transition from slightly disorder tetrahedral units to pentalhedral units according to an anomalous dynamic transition in the nanoparticles, and the mechanism of atoms upon compression in the liquid nanoparticles is efficiently driven by the surface effects II MỤC LỤC Trang Tóm tắt đề tài/dự án (gồm tiếng Việt tiếng Anh) I Mục lục III Danh sách chữ viết tắt IV Danh sách bảng IV Danh sách hình IV Bảng toán V PHẦN MỞ ĐẦU CHƯƠNG I: TỔNG QUAN TÀI LIỆU CHƯƠNG II: NỘI DUNG-PH ƯƠNG PHÁP NGHIÊN CỨU CHƯƠNG III: KẾT QUẢ VÀ THẢO LUẬN 3.1 Khảo sát cấu trúc khuyết tật bề mặt hạt A2S kích thước nanomét lỏng vơ định hình 3.1 Khảo sát ảnh hưởng áp suất lên cấu trúc tính chất động học hạt A2S kích thước nanomét 3.2 Nguyên lý biến đổi tính chất nhiệt động cấu trúc hạt A2S nanomét phụ thuộc vào tốc độ làm lạnh CHƯƠNG IV: KẾT LUẬN VÀ ĐỀ NGHỊ 10 10 15 TÀI LIỆU THAM KHẢO 18 PHỤ LỤC 19 III DANH SÁCH CÁC CHỮ VIẾT TẮT VIẾT TẮT THUẬT NGỮ TIẾNG VIẾT A2S Aluminosilicate VĐH Vơ định hình DANH SÁCH BẢNG SỐ TÊN BẢNG SỐ LIỆU TRANG Các thơng số cấu trúc, khoảng cách trung bình ngun tử phân bố góc trung bình, hạt aluminosilicate VĐH kích thước nanomét 13 DANH SÁCH HÌNH SỐ TÊN HÌNH ẢNH TRANG Sự phụ thuộc tương tác hạt A2S kích thước nanomét theo tốc độ làm lạnh 11 Sự biến đổi khối lượng riêng theo nhiệt độ tốc độ làm lạnh hạt A2S kích thước nanomét 11 Sự phụ thuộc số phối vị trung bình cặp nguyên tử Al-O Si-O bề mặt lõi hạt A2S VĐH kích thước nanomét theo tốc độ làm lạnh 12 Hàm phân bố xuyên tâm cặp nguyên tử hạt A2S VĐH kích thước nanomét theo tốc độ làm lạnh 14 IV BÁO CÁO NGHIỆM THU Tên đề tài: MƠ PHỎNG CẤU TRÚC VÀ CÁC TÍNH CHẤT NHIỆT ĐỘNG HỌC CỦA HẠT ALUMINOSILICATE VƠ ĐỊNH HÌNH CĨ KÍCH THƢỚC NANO Chủ nhiệm đề tài: Thạc sĩ: Trần Thị Thu Hạnh Cử nhân: Nguyễn Ngọc Lĩnh Cơ quan chủ trì: TRUNG TÂM PHÁT TRIỂN KHOA HỌC VÀ CƠNG NGHỆ TRẺ Điện thoại: 8233 363 8230 780 - Fax: 8244 705 - E-mail: khoahoctre@gmail.com Địa chỉ: Số Phạm Ngọc Thạch, P Bến Nghé, Q1, Tp Hồ Chí Minh Số tài khoản: 946.90.01.00036 Kho bạc Nhà nước Q.1 – Tp Hồ Chí Minh Mã số thuế: 0301 744 926 Thời gian thực đề tài: 18 tháng (Từ tháng 10/2008 đến tháng 4/2010) Kinh phí đƣợc duyệt: 70 triệu đồng Kinh phí cấp: theo TB số : TB-SKHCN ngày / / Mục tiêu: (Theo đề cương duyệt) Nghiên cứu tồn diện cấu trúc vi mơ hạt A2S lỏng VĐH có kích thước nano (từ 2nm đến 5nm): - Khảo sát phân bố số phối vị ngun tử mơ hình có kích thước nanomét - Khảo sát khoảng cách ngun tử mơ hình có kích thước khác - Khảo sát hàm phân bố xuyên tâm, phân bố mật độ ngun tử mơ hình - So sánh tính chất cấu trúc mơ hình kích thước nano mơ hình khối - Chứng minh khảo sát ảnh hưởng cấu trúc bề mặt lên tính chất lý hố hạt A2S kích thước nano - Nghiên cứu tính chất nhiệt động học hạt A2S lỏng VĐH có kích thước nano - Khảo sát chuyển pha cấu trúc nhiệt động hạt A2S kích thước nanomét - Cơng bố kết đạt tạp chí khoa học quốc tế báo cáo Hội nghị nước Quốc tế chuyên ngành Nội dung: (Theo đề cương duyệt hợp đồng ký) Công việc dự kiến Nghiên cứu biến đổi cấu trúc trình làm lạnh với tốc độ làm lạnh khác Kết thực Hồn thành tính tốn mơ hình thời hạn Hồn thành xử lý số liệu thời hạn báo cáo kết Hội nghị Quốc tế “Mô vật liệu” Nghiên cứu tính chất cấu trúc, động học ảnh hưởng áp suất thay đổi hạt nano Hoàn thành thời hạn, kết nhận đăng tạp chí Physics and Chemistry of Liquid (2010) Dựng mơ hình Hoàn thành thời hạn, kết nhận đăng tạp chí tạp chí Advanced in Natural Science (2009) Physics and Chemistry of Liquid (2010) Tính tốn, xử lý số liệu, cơng bố kết Hồn thành thời hạn, kết định hướng nghiên cứu thực nghiệm đăng tạp chí: Advanced in Natural Sciences (2009) Physics and cho kết mô Chemistry of Liquid (2010) Khảo sát tượng động học chuyển pha, so sánh tính chất hạt nano với vật liệu khối Khảo sát tính chất bề mặt Sản phẩm đề tài 1) Nguyên lý biến đổi tính chất nhiệt động hạt A2S nano lỏng VĐH theo tốc độ làm lạnh áp suất mơ hình, bao gồm khảo sát thay đổi khối lượng riêng, hệ số khuếch tán, lượng bề mặt, tương tác hệ (Xem phần 3.2 3.3) 2) Các mơ hình cấu trúc hạt nano A2S lỏng VĐH, bao gồm: - Các bảng số liệu hình vẽ tính chất cấu trúc nhiệt động hạt A2S kích thước nanomét trình làm lạnh với tốc độ khác (Xem phần 3.3) - Các bảng số liệu hình vẽ mơ tả biến thiên tính chất cấu trúc bề mặt phụ thuộc theo kích thước, tốc độ làm lạnh, áp suất hạt nano (Xem phần 3.1, 3.2 3.3) - Mơ hình hạt aluminosilicate kích thước 3.2 4.0 nanomét mô tả phụ thuộc cấu trúc vào áp suất mơ hình (Xem phần 3.2) Những nguyên lý số liệu phản biện hội đồng phản biện tạp chí khoa học trước nhận đăng tạp chí chấp nhận báo cáo Hội nghị khoa học Quốc tế Bài báo đăng tạp chí quốc tế: đăng TT Tên tác giả, tên viết, tên tạp chí số tạp chí, trang đăng viết, năm xuất Nguyen Ngoc Linh, Vo Van Hoang, Surface structure and structural point defects of liquid and amorphous aluminosilicate nanoparticles, Advanced in Natural Sciences 10, 251 (2009) Nguyen Ngoc Linh, Ngo Huynh Buu Trong, Vo Van Hoang, Tran Thi Thu Hanh, Pressure induced structural and dynamic transitions in simulated liquid aluminosilicate nanoparticles, Physics and Chemistry of Liquid, proofreading, (2010) Tác giả/ đồng tác giả Số hiệu ISSN Điểm IF - - Tác giả 0.65 Tác giả I TỔNG QUAN 1.1 Tổng quan tình hình nghiên cứu thuộc lĩnh vực đề tài Ngồi nước: Nghiên cứu hạt có kích thước nano lĩnh vực quan tâm nhiều thời gian gần hạt nano thành phần trung gian nguyên tử-phân tử vật liệu khối Bên cạnh hạt nano có đặc tính cấu trúc, tính chất vật lý hố học khác nhiều so với vật liệu khối hứa hẹn có nhiều ứng dụng thực tế [1,2] Qua nhiều nghiên cứu thực nghiệm mô thời gian gần cho thấy, hạt A2S kích thước nano với thành phần hố học có dạng Al2O3-SiO2, có nhiều ứng dụng đời sống ngày vận chuyển thuốc y sinh, vật liệu dây dẫn quang điện tử, hạt aluminosilicate cịn có khả loại bỏ thành phần Arsenic nguồn nước nhiễm bẩn dùng bảo vệ mơi trường… [3-5] Đặc biệt, hạt A2S có kích thước nano cịn sử dụng để cracking dầu mỏ với khối lượng lớn cơng nghệ hố dầu [6] Trước ứng dụng rộng rãi vậy, hạt A2S có kích thước nano chế tạo nghiên cứu nhiều phương pháp khác như: nhiễu xạ tia X, cộng hưởng từ hạt nhân (NMR)…v.v [7-8] Những kết cho thấy: hạt A2S có kích thước nano có cấu trúc phân tử phức tạp, tính chất hoạt hố bề mặt cao Điều thể phân bố nguyên tử Al bề mặt [9] Tuy nhiên, việc khảo sát cách chi tiết hạt nano mức độ vi mơ tiến hành phương pháp mơ máy tính Theo hiểu biết chúng tôi, có nghiên cứu mơ hạt A2S nano công bố công bố lại chủ yếu dừng mức độ sơ khởi cấu trúc hạt A2S dạng cụm (cluster) [10] Một mặt khác, lại có nhiều cơng trình mơ tiến hành cách chi tiết hạt nano oxide tương tự SiO2, Al2O3, TiO2 [11-14] Chính vậy, việc tiến hành nghiên cứu cách toàn diện mặt cấu trúc tính chất 254 Nguyen Ngoc Linh and Vo Van Hoang shows the temperature dependence of of nm, nm and nm [1] O, [2] O, [3] O and [4] O distributions for three sizes Fig Number fraction of oxygen having one, two, three and four nearest T neighbors (T = Al, Si) in surface It is clear that the distributions decrease with decreasing temperature with an exception for [2] O Moreover, at high temperatures (i.e at about T ≥ 3500K) non-bridging oxygen (i.e [1] O) also appears and its number increases with increasing temperature like those observed in the Ref [10] Non-bridging oxygen has an important role in the diffusion of atomic species in the surface shell of nanoparticles due to their high mobility at high temperatures In contrast, the fraction of [4] O in the surface shell of AS2 nanoparticles has a tendency to decline with temperature and it is quite different from those observed in the bulk [10] This result is similar to those observed in sol-gel synthesis of a nanoparticulate aluminosilicate precursor for homogeneous mullite ceramics in which one found that these nanoparticles have significant amount of Al–O–Si bonds with Si atoms are mostly linked to three AlV I via oxygen bridges [11] Overall, one can see that the changes in [n] O concentration with temperature, although systematic, are quite different from those observed in the bulk aluminosilicates [12] In order to get more insights in to the microstructure of surface of AS2 nanoparticles, we also present the mean O–Al–O, Al–O–Al, O–Si–O and Si–O–Si bond-angles and their distributions One can see in Fig that the changes in bond-angles at the surface and in the core of nanoparticles upon cooling from the melt are not systematic Calculations show that the mean angles slightly increase with decreasing temperature and then decrease with an exception for Si–O–Si one We found that the mean O–Al–O angle in the surface thus is slightly smaller than that of an ideal tetrahedron due to the existence of AlO3 with large amount In contrast, larger O–Al–O angle in the core is related to the large Surface structure and structural defects of liquid and amorphous 255 amount of AlO5 existing in the core of AS2 nanoparticles [13] On the other hand, the distributions for O–Si–O and Si–O–Si angles in the surface shell are very close to those in the core, it indicates the similarities of Si–O subnetworks in both parts of nanoparticles Furthermore, the calculations show that the changes in angles at the surface and in the core upon cooling from the melt are not systematic indicating the complicated feature of the network structure in AS2 nanoparticles [12] Fig Bond-angle distributions in the surface of AS2 nanoparticles at three temperatures upon cooling compared with their averages at 350K 3.2 Surface energy of liquid and amorphous aluminosilicate nanoparticles Temperature dependence of the surface energy of nanoparticles is of great interest because from which one can infer important quantities related to the surface structure and thermodynamics of nanoparticles [1, 2] We found that Epot for nanoparticles is significantly higher than that for the bulk due to the surface energy of the formers [14, 15] We thus expect the relation: nano bulk Epot − Epot = Es /N Here Es is the surface energy and N is the total number of atoms in the system The most interesting observation is that the surface energy depends on the particle size over a large interval of temperature, which has a significant increase in surface energy with deceasing of nanoparticle sizes (Fig 4), like those observed for silica nanoclusters with BKS interatomic potential [14] This is, however, contrary to those observed for Lennard-Jones clusters or for silica nanoclusters [6, 16] 256 Nguyen Ngoc Linh and Vo Van Hoang One can see in Fig that surface energy of nanoparticles decreases with decreasing temperature, passes through a minimum in the temperature range between 4200K and 5600K and then it increases The phenomenon may be related to the occurrence of local sudden change in density of the system upon cooling from the melt like those found for the bulk silica by using NPT ensemble simulation [17] Es has the value of around 0.02 J/m2 to 0.14 J/m2 over the temperature range studied There is no experimental surface energy of AS2 nanoparticles to compare However, experimentally and computationally deduced value for the surface energy of amorphous silica in pure water is 0.340 J/m2 and in Al2 O3 thin films is 0.88 J/m2 [18, 19] This means that calculated Es in the present work is quite reasonable Fig Temperature dependence of surface energy for the nanoparticles with different sizes CONCLUSION Evolution of microstructure of the surface and core of liquid and amorphous AS2 nanoparticles upon cooling from the melts has been found It was found that the core of amorphous AS2 nanoparticles has a distorted tetrahedral network structure with the mean ZAl−O = 4.5 and ZSi−O = 4.2 like that of the bulk In contrast, surface of nanoparticles has significant amount of structural defects with the mean ZAl−O < 4.5 and ZSi−O ≈ 4.2 The temperature dependence of local environments of oxygen in AS2 nanoparticles was also found; it may affect thermodynamics of the system ACKNOWLEDGMENTS This work was supported by the Ho Chi Minh City Department of Science and Technology and the Youth Scientific and Technological Development Center through the program “The Support for Development of Young Engineers and Scientists” Surface structure and structural defects of liquid and amorphous 257 REFERENCES Y Kuroda, T Mori, and Y Yoshikawa, Chem Commun 11, 1006 (2001) V.L Parola, G Deganello, S Scir`e, and A.M Venezia, J Solid State Chem 482, 174 (2003) V.V Hoang, Phys Rev B 75, 174202 (2007) V.V Hoang, N.N Linh, and N.H Hung, Eur Phys J.: Appl Phys 37, 111 (2007) U Diebold, Surf Sci Rep 48, 53 (2003) I.V Schweigert, K.E.J Lehtinen, M.J Carrier, and M.R Zachariah, Phys Rev B 65, 235410 (2002) J F Stebbins and Z Xu, Nature 390, 60 (1997) N.A Morgan and F.J Spera, Am Mineralogist 83, 1220 (1998) P Pfleiderer, J Horbarch, and K Binder, Chem Geol 229, 186 (2006) 10 V.V Hoang, Phys Letters A 386, 499 (2007) 11 J Leivo, M Lind´en, C.V Teixeira, J Puputti, J Rosenholm, E Levăanen, and T.A Măantylăa, J Mat Research 21, 1279 (2006) 12 N.N Linh and V.V Hoang, Phys Scr 76, 165 (2007) 13 V.V Hoang, Phys Rev B 70, 134204 (2004) 14 A Roder, W Kob, and K Binder, J Chem Phys 114, 7602 (2001) 15 V.V Hoang, H Zung, and N.H.B Trong, Eur Phys J D 44, 515 (2007) 16 S.M Thompson, K.E Gubbins, J.P.R.B Walton, R.A.R Chantry, and J.S Rawlinson, J Chem Phys 81, 530 (1984) 17 K Vollmayr, W Kob, and K Binder, Phys Rev B 54, 15808 (1996) 18 S.P Adiga, P.Zapol, and L.A Curtiss, Phys Rev B 74, 064204 (2003) 19 J Mizele, J.L Dandurand, and J Schott, Surf Sci 162, 830 (1985) Corresponding author: Nguyen Ngoc Linh, Department of Physics, College of Technology, Vietnam National University, Ho Chi Minh City, 268 Ly Thuong Kiet Str., Distr 10, Ho Chi Minh City, Vietnam E-mail: ngoclinh84phys@yahoo.com AUTHOR QUERIES Journal id: GPCH_A_460117 Corresponding author: Nguyen Ngoc Linh Title: Pressured induced structural and dynamic transitions in stimulated liquid aluminosilicate nanoparticles Dear Author Please address all the numbered queries on this page which are clearly identified on the proof for your convenience Thank you for your cooperation Query number Query Please check the sentence “where the terms represent coulomb and repulsion energies, respectively” Please specify as to what terms represent the parameters mentioned here XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] Physics and Chemistry of Liquids Vol ??, No ?, Month?? 2010, 1–10 Pressured induced structural and dynamic transitions in stimulated liquid aluminosilicate nanoparticles Nguyen Ngoc Linh*, Ngo Huynh Buu Trong, Vo Van Hoang and Tran Thi Thu Hanh Department of Physics, Institute of Technology, National University of HoChiMinh, 268 Ly Thuong Kiet, District 10, HoChiMinh, Vietnam (Received 28 October 2009; final version received January 2010) 10 15 20 25 We have investigated the pressure-induced structural and dynamic transitions in liquid aluminosilicate (Al2O32SiO2) nanoparticles by a molecular dynamics (MD) method Simulations were done in spherical models under non-periodic boundary conditions containing 2596 ions with the Born–Mayer type pair potentials In order to study the structural and dynamic changes, the models of liquid aluminosilicate nanoparticles have been built at densities ranging from 2.60 g cm3 corresponding to the size of nm to the density of 4.2 g cm3 at a temperature of 4200 K The microstructure of the liquid nanoparticles has been analysed in detail through the coordination number distribution, bond-angle distribution and interatomic distances We found a clear evidence of transition from the low density state (LDS) to high density state (HDS) structure in the models upon compression, like that observed in the bulk counterparts This transition is accompanied by an anomalous diffusion of Al and Si atoms in the systems Moreover, we also show the surface distribution properties in order to highlight the surface effects on dynamics upon compression Keywords: aluminosilicate nanoparticles; molecular dynamics simulation pressure-induced transition; PACS: 61.20.Ja; 61.20.Lc; 78.55.Bq 30 35 Introduction Pressure-induced transition has been an important subject in condensed matter physics and material science for a long time In particular, the problems relating to liquid–liquid phase transitions, i.e occurrence of structural transition under high pressure, have been under intensive investigation by both experiments and computer simulations Through a variety of research on liquids with the bulk phase such as water, silica, carbon, GeO2, Al2O3 and silicon [1–8], it was found that the transition from low density state (LDS) to high density state (HDS) in network structure liquids with the bulk phase is often accompanied by an anomalous diffusion, i.e the diffusion constant increases with increasing density (or pressure) Analogously, the pressure-induced structure in nanosized substances has aroused great interest *Corresponding author Email: ngoclinh84phys@yahoo.com ISSN 0031–9104 print/ISSN 1029–0451 online ß 2010 Taylor & Francis DOI: 10.1080/00319101003596089 http://www.informaworld.com XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) 40 45 50 55 60 65 70 75 [1–10] [PREPRINTER stage] N.N Linh et al because the mechanism of structural transition in the finite size systems, compared with the bulk, can be different from their analogues in the bulk counterparts, i.e the finite size systems can have richer metastable structures due to the surface effects Recently, X-ray diffraction measurements for nanometre-sized silica particles have exhibited inelastic compression between and GPa, in which the anomalous compressive behaviour of fumed silica results from a decreased compressibility of nanoparticles [9] In addition, the liquid–liquid phase transitions were related to the soft-core interaction potential systems such as gallium confined droplets, which showed a clear change in the absorption in the liquid phase obtained between and 1.6 GPa, and it indicates that transformations involving microscopic structure and/or electronic states occur [10] Also, for the higher pressures, i.e between 2.7 and 5.8 GPa, the quantity of crystallised gallium droplets increases as a function of pressure [10] Furthermore, the pressure-induced phase transition from ice to water in the confined geometry was found by ab initio molecular dynamics (MD) simulation The study showed the breaks and then reforms of the H bonds corresponding to the changes of the self-diffusion coefficients during phase transition process that occurred in the simulated model [11] Since there is no general rule to determine the pressure induced on phase transition at nano-scaled materials, it is hard to avoid any artifact involved in the experiments and simulation Thus, it is really necessary to develop a study in this direction On the other hand, the study on property changes in liquid aluminosilicates under pressure is also of fundamental importance in both the earth and materials sciences, in which structure, evolution and dynamics of aluminosilicate systems at extremely high pressures are related to magma flows inside the Earth Therefore, the structure and diffusion in this system under high pressure have been investigated in detail by computer simulation and experiment Indeed, by using 27Al solid-state NMR spectrometry, pressure-induced transition from tetrahedral to octahedral unit structures for Al coordination has been evidenced in liquid aluminosilicates [12] Similarly, more details about the structural and dynamic transitions of this system have also been studied by computer simulation in our previous work A clear evidence of transition from a tetrahedral to an octahedral network structure was found in the model, accompanied by an anomalous diffusion of components in the system upon compression, similar to that observed in simple oxide systems [13] However, there is no study related to the same transition in liquid aluminosilicate nanoparticles It raises a question as to whether these behaviours still exist in the liquid phase of finite size systems in which a periodical boundary condition does not apply, i.e in the liquid aluminosilicate nanoparticles It motivates us to carry out the comprehensive study on the structural and dynamic transitions of liquid aluminosilicate spherical models under high pressure in order to highlight other features of liquid–liquid phase transitions in this nanoscaled material Calculation 80 MD simulations were carried out in initial spherical liquid aluminosilicate nanoparticles with a diameter of nm under non-periodic boundary conditions XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] Physics and Chemistry of Liquids The models contain 2596 atoms (including Al, Si and O) We use the empirical interatomic potentials of the Born–Mayer type, which have the form as given below: e2 r Uij ¼ zi zj ỵ Bij exp 1ị Rij r 85 90 95 100 105 110 where the terms represent Coulomb and repulsion energies, respectively Here, r denotes the distance between the centers of ith and jth ions; Zi and Zj the charges of ith and jth ions; Bij and Rij the parameters accounting for the repulsion of the ionic shells Values ZAl ẳ ỵ3, ZSiO ẳ ỵ4 and ZO ẳ 2 are the charges of Alỵ3 , Siỵ4 and O2 , respectively We use the values BAlAl ¼ eV, BAlO ¼ 1779:86 eV, ZAlO ¼ 4:10, BSiSi ¼ eV, BSiO ¼ 1729:50 eV, BOO ¼ 1500 eV and Rij ¼ 29 pm We found that interatomic potentials (Equation (1)) described well for both structure and dynamics of liquid and amorphous aluminosilicate nanoparticles compared with those obtained by experiment [14–15] The Coulomb interactions were taken into account by means of Ewald–Hansen method The equilibrated melt at 7000 K has been obtained by relaxing a random configuration for 50,000 MD steps We use the Verlet algorithm and MD time step is of 1.6 fs The system was cooling down from the melt at constant volume corresponding to the high density of 2.6 g cm3 The temperature of the system was decreased linearly in time as T ¼ To t with the cooling rate ¼ 4:375 1013 Ks1 to a temperature of 4200 K in order to obtain the properties of liquid nanoparticle models upon compression and compare them to that observed in the compression process of the bulk counterpart [13] The models have been built at different densities ranging from 2.6 g cm3 to 4.0 g cm3 at a constant temperature of 4200 K The volume of the spheres is reduced isotropically step-by-step corresponding to the density increment of 0.2 g cm3 The systems are thermalised for 100,000 MD steps (or 160 ps) to reach an equilibrium liquid state at each constant densities (e.g at constant volume) before calculating the static and dynamic properties Calculated data have been averaged over two independent runs for increasing statistics In order to calculate the coordination number and bond-angle distributions in the models, we adopt the fixed values RAlAl ¼ 3:80 A˚, RAlSi ¼ 3:70 A˚, RSiSi ¼ 3:50 A˚, RAlO ¼ 2:60 A˚, RSiO ¼ 2:50 A˚, ROO ¼ 3:70 A˚ Here, R is the cut-off radius, which was chosen as the position of the minimum after the first peak in gij(r) for the amorphous model at the ambient pressure like those used in Ref [14] These cut-off radii were chosen as the first minimum after the first peak in the corresponding partial radial distribution functions (PRDFs) Results and discussion 115 120 3.1 Structural evolution of liquid aluminosilicate nanoparticles upon compression In order to obtain an evolution of structure upon compression, we have studied the structural characteristics of well-relaxed models at different densities ranging from 2.6 to 4.0 g cm3 at a constant temperature of 4200 K Calculations, as presented in Tables 1–3, or Figures and 2, show that the structural evolution in the liquid nanoparticles shares a similar trend as that observed in the bulk counterpart upon compression Namely, the distance of Al–O and Si–O pairs increases, as found in the bulk [13], with increase of density while for other pairs it decreases, the decrease of Si–Si, Si–O and O–O pairs has been obtained identically in previous in situ XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] N.N Linh et al Table Mean interatomic distance, rij (in A˚) and bond-angle distributions, ijk , for different atomic pairs in liquid aluminosilicate nanoparticle models upon compression rij (A˚) ijk Density 3 (g cm ) P (GPa) Al–Al Al–Si Si–Si Al–O Si–O O–O O–Al–O Al—O–Al O–Si–O Si–O–Si 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 2.69 4.21 6.06 8.14 10.70 13.67 17.54 22.79 3.13 3.11 3.10 3.09 3.07 3.06 3.04 3.03 3.11 3.11 3.09 3.09 3.08 3.06 3.05 3.04 3.06 3.05 3.04 3.03 3.02 3.02 3.02 3.02 1.65 1.66 1.67 1.69 1.70 1.70 1.71 1.72 1.50 1.50 1.50 1.51 1.51 1.51 1.52 1.53 2.52 2.52 2.51 2.49 2.48 2.46 2.44 2.43 103.23 113.88 107.68 147.20 99.45 110.48 105.51 137.84 94.84 107.67 102.89 126.21 Table Mean coordination number, Zij, for different atomic pairs in liquid aluminosilicate nanoparticle models upon compression Zij Density (g cm3) Al–Al Al–Si Si–Al Si–Si Al–O O–Al Si–O O–Si O–O 3.44 3.66 3.85 3.99 3.88 3.98 4.19 4.40 2.67 2.94 3.03 3.22 3.55 3.78 3.95 4.29 2.81 3.03 3.09 3.27 3.63 3.82 4.01 4.30 2.28 3.29 2.51 2.64 2.66 2.88 3.08 3.25 4.01 4.27 4.35 4.49 4.67 4.79 5.03 5.21 1.58 1.63 1.69 1.70 1.70 1.72 1.78 1.79 4.08 4.18 4.27 4.35 4.50 4.68 4.78 4.95 1.37 1.39 1.41 1.46 1.46 1.51 1.54 1.57 8.47 9.06 9.55 10.04 10.57 11.11 11.52 12.05 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 Table Coordination number distribution for Al–O and Si–O pairs ZAl–O 125 ZSi–O Density (g cm3) 7 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 0 0 0 0 77 96 112 82 40 25 18 224 188 184 181 162 159 110 87 102 156 160 177 186 187 165 150 19 30 40 52 70 91 125 148 2 12 10 24 27 0 0 0 0 1 1 1 12 13 33 20 412 366 304 289 262 208 160 117 44 89 113 153 165 191 226 246 14 13 39 75 102 165 0 2 high-pressure diffraction experiments on the silica nanoparticles The experiment also states that within the range of pressure from to GPa, the configurations of the constituent of SiO4 tetrahedral units slightly change, which is similar to the mechanical transformation upon compression of the bulk counterpart [9] XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] Physics and Chemistry of Liquids (a) O–Al–O angle 0.02 Fraction (b) Al–O–Al angle 2.6 g.cm–3 3.2 g.cm–3 4.0 g.cm–3 3.2 g.cm–3 4.0 g.cm–3 0.01 0.01 0.00 0.00 0.03 2.6 g.cm–3 0.02 0.03 (c) O–Si–O angle (d) Si–O–Si angle 2.6 g.cm –3 Fraction 2.6 g.cm–3 3.2 g.cm–3 0.02 3.2 g.cm –3 0.02 4.0 g.cm–3 0.01 4.0 g.cm –3 0.01 0.00 0.00 40 80 120 160 40 80 Angle (degree) 120 160 Angle (degree) Figure Bond-angle distributions of aluminosilicate nanoparticles at 4200 K and at different densities 0.55 Fraction 0.50 0.45 Al Si O 0.40 2.8 3.2 3.6 Density (g.cm–3) 4.0 Figure The ratio of the number of each atomic species at the surface per total number ðsurf:Þ ðtotalÞ of atomic species, i.e NAl =NAl , NSiðsurf:Þ =NSiðtotalÞ and NOðsurf:Þ =NOðtotalÞ , upon compression 130 Analogously, in our calculation, the mean coordination number for all atomic pairs increases with increase in density, which indicates the formation of a more close-packing structure in the system In addition, the bond-angle distributions have been calculated for the most important angles such as O–Al–O, Al–O–Al, O–Si–O XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d 135 140 145 150 155 160 165 170 175 [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] N.N Linh et al and Si–O–Si, and compared to those of the bulk We see that upon compression the main peaks of the curves shifted towards smaller angles in accordance with the close-packing structure at high densities At a low density of 2.60 g cm3, the main peak of O–Al–O and O–Si–O angle distributions is centered at 103 and 108 , respectively, and at a high density of 4.00 g cm3 the values are at 94 and 103 , respectively Moreover, we find that at the LDS, 2.6 g cm3, the liquid aluminosilicate nanoparticles have a slightly distorted tetrahedral network structure with the mean coordination numbers ZAlO ¼ 4:10 and ZSiO ¼ 4:08, and these values are locally similar to the local structure of the liquid aluminosilicate observed in the bulk counterpart, but at higher density states, 4.00 g cm3, a new structure is formed with the mean coordination numbers ZAlO ¼ 5:21 and ZSiO ¼ 4:95, and these values correspond to those of a slightly distorted pentahedral network structure On the other hand, from Table 3, one can also find that upon compression the fraction of high-coordinated Al (or Si) atoms to oxygen, i.e ZAl, SiO ¼ and 6, increases while the fraction of low-coordinated Al (or Si) atoms to oxygen, i.e ZAl, SiO ¼ 4, decreases This trend is the same as that observed in the bulk counterpart However, in the nanoparticles the change of the fractions of low-coordinated atoms is gradual, and even at a high density such as 4.0 g cm3, the fractions of low-coordinated atoms are still high In contrast, compared with the pressure-induced phase transition in the liquid states of the bulk models, a structural transition from a tetrahedral to an octahedral network structure takes place completely at around 3.00 or 3.20 g cm3 [13] It means that the transition density (or transition pressure) in the liquid aluminosilicate nanoparticles is higher than that for the bulk counterpart It has been argued through the studies in crystal nanoparticles that as the crystallite size becomes smaller, the shape change at the phase transformation involves making higher index planes that are unstable As a consequence, the transition pressure increases [16] In contrast, in the liquid nanoparticles it should be pointed out that there may be other factors, such as defects and finite volume effects, that contribute to the elevation in transition pressure The result in our work is explained similarly to that found in pressure-induced structural transitions in the amorphous state of nanoparticles [17], in which the difference between phase transition in liquid nanoparticles and their bulk counterpart is estimated by the effects of the surface of nanoparticles, i.e breaking bonds at the surface reduces a large number of structural defects found in nanoparticles [18] Indeed, as presented in Table 3, we find that the fraction of low-coordinated atoms, i.e ZAl, SiO ¼ 3, is higher and changes more significant than that observed for the bulk This fraction increases with increasing density from 2.6 to 3.4 g cm3 and then it decreases at higher densities In addition, following our previous work, the fraction of low-coordinated atoms has a significant role in the formation of structure defects at the surface of the aluminosilicate nanoparticles [18] Thus, from Figure 2, it is essential to note that the change in the number of Al and Si atoms at the surface corresponds to the change in the mean coordination number of ZAl, SiO ¼ shown in Table Meanwhile, the number of oxygen atoms at the surface increases gradually In order to highlight this result, two snapshots of aluminosilicate nanoparticles at 3.2 and 4.00 g cm3 have been shown in Figure Overall, it is quite reasonable to conclude that upon compression from the melts the distribution of atoms in the nanoparticles is different for every different species of atom, i.e the number of Al and Si atoms in the surface shell of the liquid XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] Physics and Chemistry of Liquids Figure Snapshots of the aluminosilicate nanoparticle at densities of 3.2 (a) and 4.0 g cm3 (b) The biggest blue spheres are the oxygen atoms, the smaller red spheres are the silicon atoms and the smallest green spheres are aluminum atoms 180 185 190 195 200 aluminosilicate nanoparticles increases with density and then it decreases at the higher densities, while the number of oxygen atoms increases continuously with increasing density This phenomenon reflects the corresponding change not only in the mass density and in the concentration of defects in the surface of the nanoparticles but it also effects on the changes of dynamic properties of atoms upon compression, and more details will be shown in the next part of this article 3.2 Pressured induced dynamic transition in liquid aluminosilicate nanoparticles It is known that the liquid–liquid phase transition in network liquids is often accompanied by an anomalous diffusion of components in the bulk system However, this problem has not been investigated yet for the nano-scaled systems such as the liquid aluminosilicate nanoparticles In this work, the self-diffusion constant D of particles in nanoparticles was calculated via the Einstein relation r tị D ẳ lim t!1 6t where hr2 tịi is the mean-squared atomic displacement The time dependence of hr2 ðtÞi for Al, Si and O particles belonging to the core of the liquid aluminosilicate nanoparticles at a density of 4.0 g cm3 is shown in Figure 4(a) Moreover, the time dependence of hr2 ðtÞi for particles in the surface shell of nanoparticles is considered in Figure 4(b) One can see clearly that the pressure-induced dynamic transitions for oxygen atoms are quite different between in the core and in the surface shell of nanoparticles in that the mean-squared atomic displacement for oxygen at the surface shell are more pronounced at high pressures Furthermore, the density dependence of diffusion constant, D, in liquid aluminosilicate nanoparticles, presented in Figure 5, has been investigated with an anomalous behaviour of the diffusion constants of Al and Si particles, i.e they have a maximum at around the density of 3.20 g cm3, which is similar to those observed previously in liquid H2O, XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] N.N Linh et al Mean squared atomic displacement (Å2) 2000 Surface Al Si O Total Al Si O 1500 1000 500 0 40 80 120 Time steps 160 40 80 120 Time steps 160 Figure Mean-squared atomic displacement of atomic species in aluminosilicate nanoparticles obtained in averaged total and at surface nanoparticles Diffusion constant (10–6 cm2/s) 20 160 16 120 80 12 Al Si 2.8 3.2 3.6 Density (g/cm3) 40 4.0 O 2.8 3.2 3.6 4.0 Density (g.cm3) Figure Density dependence of diffusion constants of Al and Si atoms (left) and oxygen atoms (right) upon compression 205 210 SiO2 and in the bulk of aluminosilicate [13,19,20] This phenomenon has been considered that anomalous diffusion observed in water and Si results from the competition of the following two mechanisms [21]: (1) the breakdown of the tetrahedral network structure leading to the increase of atomic mobility, (2) the packing effects by densification leading to the decrease of atomic mobility However, the calculations show that the anomalous diffusivity for Al and Si atoms in the liquid aluminosilicate nanoparticles might be explained in a different XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] Physics and Chemistry of Liquids 215 220 225 230 way in which the behaviour of the change in the diffusivity of Al and Si atoms is dependent upon the change of the fraction of threefold coordinators with increasing density From Table 3, we can see that upon compression from 2.60 to 3.20 g cm3 the tetrahedral network structure of nanoparticles breaks down gradually (i.e the number of fourfold-coordinated Al or Si atoms to O decreases) and then the broken atoms have a trend towards moving to the outer surface of the nanoparticles It is very reasonable since the surface has more defects and the existence of these structural defects in the liquid and amorphous nanoparticles might enhance the diffusion of atomic species at the surface [22–24] It explains for the increase in the diffusivities for Al, Si and O atoms in the liquid aluminosilicate nanoparticles with increasing density from 2.60 to 3.20 g cm3 On the other hand, upon further compression, i.e when the density is larger than 3.2 g cm3, the system is completely transformed to a high density state in nanoparticles with the packing effect dominate for Al and Si atoms in the core in which the number of fivefold- and sixfold-coordinated Al and Si atoms to O forms and the domination of Oxygen atoms in the surface shell (Table and Figure 2) Therefore, the diffusion constant for Al and Si atoms strongly decreases with increasing density, and in contrast, the diffusion constant for oxygen atoms increases continuously Conclusions By using MD simulation, we have found the LDS ! HDS transition in liquid aluminosilicate nanoparticles in both structural and dynamic properties Several conclusions can be made as follows: (1) Upon compression, a clear evidence of transition from a tetrahedral to a pentahedral network structure in liquid aluminosilicate nanoparticles has been found (2) Such transition density (or transition pressure) in liquid aluminosilicate nanoparticles is higher than that for the bulk counterpart (3) Calculation has also shown that, upon compression, the number of Al and Si atoms in the surface changes corresponding to the change in anomalous diffusion of Al and Si atoms, in contrast, it is not found for oxygen atoms 235 240 Acknowledgements 245 This work was supported by the HoChiMinh City Department of Science and Technology and the Youth Scientific and Technological Development Centre, through the programme ‘the Support for Development of Young Engineers and Scientists’ References 250 [1] [2] [3] [4] [5] [6] J.R Rustad, D.A Yuen, and F.J Spera, Phys Rev A 42, 2081 (1990) S Tsuneyuki and Y Matsui, Phys Rev Lett 74, 3197 (1995) J.N Glosli and F.H Ree, Phys Rev Lett 82, 4659 (1999) J.R Errington and P.G Debenedetti, Nature (London) 409, 318 (2001) M.S Shell, P.G Debenedetti, and A.Z Panagiotopoulos, Phys Rev E 66, 011202 (2002) G Gutierrez and J Rogan, Phys Rev E 69, 031201 (2004) XML Template (2010) {TANDF_FPP}GPCH/GPCH_A_460117.3d 10 255 260 265 270 275 [25.1.2010–6:25pm] (GPCH) [1–10] [PREPRINTER stage] N.N Linh et al [7] V.V Hoang, Phys Lett A 335, 439 (2005) [8] T Morishita, Phys Rev E 72, 021201 (2005) [9] T Uchino, A Sakoh, M Azuma, S Kohara, M Takahashi, M Takano, and T Yoko, Phys Rev B 67, 092202 (2003) [10] S Meng, E.G Wang, and S Gao, J Phys.: Condens Matter 16, 8851 (2004) [11] R Poloni, S Panfilis, A.D Cicco, G Pratesi, E Pricipi, A Trapananti, and A Filipponi, Phys Rev B 71, 184111 (2005) [12] E Ohtani, F Taulelle, and C.A Angell, Nature 314, 78 (1985) [13] V.V Hoang, N.H Hung, and N.N Linh, Phys Scr 74, 697 (2006) [14] N.N Linh and V.V Hoang, Mol Simul 34, 29 (2008) [15] N.N Linh and V.V Hoang, NANO: Brief Reports and Reviews 2, 227 (2007) [16] S.B Qadri, J Yang, B.R Ratna, E.F Skelton, and J.Z Hu, Appl Phys Lett 69, 2205 (1996) [17] V.V Hoang, J Phys D Appl Phys 40, 754 (2007) [18] N.N Linh and V.V Hoang, J Phys Condens Matter 20, 265005 (2008) [19] J.R Errington and P.G Debenedetti, Nature (London) 409, 318 (2001) [20] S Tsuneyuki and Y Matsui, Phys Rev Lett 74, 3197 (1995) [21] T Morishita, Phys Rev E 72, 021201 (2005) [22] D.A Litton and S.H Garofalini, J Non-Cryst Solids 217, 250 (1997) [23] I.V Schweigert, K.E.J Lehtinen, M.J Carrier, and M.R Zachariah, Phys Rev B 65, 235410 (2002) [24] A Winkler, J Horbach, W Kob, and K Binder, J Chem Phys 120, 384 (2004)