<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">radioelectronics</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений России. Радиоэлектроника</journal-title><trans-title-group xml:lang="en"><trans-title>Journal of the Russian Universities. Radioelectronics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1993-8985</issn><issn pub-type="epub">2658-4794</issn><publisher><publisher-name>Saint Petersburg Electrotechnical University</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">radioelectronics-195</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МИКРО- И НАНОЭЛЕКТРОНИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MICRO- AND NANOELECTRONICS</subject></subj-group></article-categories><title-group><article-title>Моделирование трехмерных пористых иерархических материалов, организованных посредством самосборки наносфер</article-title><trans-title-group xml:lang="en"><trans-title>Modeling of Three-Dimensional Hierarchical Porous Materials Organized by Means of Nanosphere Self-Assembly</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кононова</surname><given-names>И. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Kononova</surname><given-names>I. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>кандидат физико-математических наук (2009), доцент (2013) кафедры микро- и  наноэлектроники Санкт-Петербургского государственного электротехнического  университета "ЛЭТИ" им. В. И. Ульянова (Ленина). Автор более 150 научных  работ. Сфера научных интересов - синтез и диагностика наноматериалов</p></bio><bio xml:lang="en"><p>Ph.D. in Physics and Mathematics (2009), Associate Professor (2010) of the Micro- and Nanoelectronics Department of Saint  Petersburg Electrotechnical University "LETI". The author of  more than 150 scientific publications. Area of expertise: synthesis and diagnostics of nanomaterials</p></bio><email xlink:type="simple">iegrachova@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мошников</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Moshnikov</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>доктор физико-математических наук (1997), профессор (1999), зам. заведующего кафедрой микро- и наноэлектроники Санкт-Петербургского  государственного электротехнического университета "ЛЭТИ" им. В. И. Ульянова  (Ленина). Автор более 450 научных работ. Сфера научных интересов - нанотехнология и диагностика</p></bio><bio xml:lang="en"><p>D.Sc. in Physics and Mathematics (1997), Deputy Head of the Micro- and Nanoelectronics Department of Saint Petersburg  Electrotechnical University "LETI". The author of more than 450 scientific publications. Area of expertise: nanotechnology and diagnostics</p></bio><email xlink:type="simple">vamoshnikov@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кононов</surname><given-names>П. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kononov</surname><given-names>P. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>кандидат технических наук (2016), ассистент кафедры начертательной геометрии и графики Санкт-Петербургского горного университета . Автор более 30 научных  работ. Сфера научных интересов - компьютерное моделирование;  материаловедение функциональных и конструкционных материалов</p></bio><bio xml:lang="en"><p>Ph.D. in Engineering (2016), Assistant of the Department of Descriptive Geometry and Graphics at the Saint Petersburg  Mining University. The author of more than 30 scientific  publications. Area of expertise: computer simulation, material science of functional and structural materials</p></bio><email xlink:type="simple">kpv710@rambler.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В. И. Ульянова (Ленина)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Saint Petersburg Electrotechnical University "LETI"</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Санкт-Петербургский горный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Saint Petersburg Mining University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>28</day><month>10</month><year>2017</year></pub-date><volume>0</volume><issue>5</issue><fpage>54</fpage><lpage>63</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Кононова И.Е., Мошников В.А., Кононов П.В., 2017</copyright-statement><copyright-year>2017</copyright-year><copyright-holder xml:lang="ru">Кононова И.Е., Мошников В.А., Кононов П.В.</copyright-holder><copyright-holder xml:lang="en">Kononova I.E., Moshnikov V.A., Kononov P.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://re.eltech.ru/jour/article/view/195">https://re.eltech.ru/jour/article/view/195</self-uri><abstract><p>Рассмотрены возможности применения моделирования для развития двух перспективных направлений современного наноматериаловедения: материалов с иерархией пор, собранных посредством иерархической самосборки, а также иерархических структур из нанопористых  элементов. С использованием квазидвумерной проекции трехмерного детерминированного  фрактального агрегата Жюльена оценен размер пор в иерархических структурах. Трехмерное  моделирование иерархических структур, организованных посредством самосборки наносфер,  проведено в среде Autodesk 3ds Max. Проанализированы зависимости пористости, плотности,  удельной площади поверхности фрактальных структур от размеров агрегатов (при  возникновении новых уровней пор иерархических материалов), а также изменения пористости при замене первичных идентичных сферических частиц на пористые сферы.</p></abstract><trans-abstract xml:lang="en"><p>The article considers possibilities of using modeling fo r the development of two promising areas of modern nanomaterials, i. e.  materials with a hierarchy of pores organized hierarchical self- assembly and hierarchical structures with nanoporous elements. The  pore size of hierarchical structures was estimated by means of quasi- two-dimensional projection of three-dimensional deterministic fractal Julien aggregate. Three-dimensional modeling of hierarchical  structures organized by means of nanosphere self-assembly was conducted in the Autodesk 3ds Max environment. The article provides analysis of dependences of porosity, density, specific  surface area of fractal structures on the size of aggregates (with the  appearance of new pore levels of hierarchical materials),  dependences of the porosity change in the case of replacement of primary identical spherical particles on porous spheres.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Иерархические пористые материалы</kwd><kwd>иерархическая самосборка наносфер</kwd><kwd>фрактальные агрегаты</kwd><kwd>трехмерный детерминированный фрактальный агрегат Жюльена</kwd><kwd>пористость и плотность фрактала</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Hierarchical Porous Materials</kwd><kwd>Hierarchical Self-Assembly of Nanospheres</kwd><kwd>Fractal Aggregates</kwd><kwd>Three-Dimensional Deterministic Fractal Julien Aggregate</kwd><kwd>Porosity and Fractal Density</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Новые наноматериалы. Синтез. Диагностика. Моделирование: лабораторный практикум / под ред. В. А. Мошникова, О. А. Александровой. СПб.: Изд-во СПбГЭТУ "ЛЭТИ", 2015. 248 с.</mixed-citation><mixed-citation xml:lang="en">Novye nanomaterialy, sintez, diagnostika. Modelirovanie: Laboratornyi praktikum;  ed. by V. A. Moshnikov, O. A. Alexsandrova [New Nanomaterials, Synthesis,  Diagnostics. Modeling: Laboratory Practical Work]. SPb, Izd-vo SPbGETU "LETI", 2015, 248 p. (In Russian)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Gelatin-assisted Synthesis of ZnS Hollow Nanospheres: The Microstructure Tuning, Formation Mechanism and Application for Pt-free Photocatalytic Hydrogen Production / Q. Yan, A. Wu, H. Yan, Yu. Dong, Ch. Tian, B. Jiang, H. Fu // CrystEngComm. 2017. Vol. 19. P. 461- 468.</mixed-citation><mixed-citation xml:lang="en">Yan Q., Wu A., Yan H., Dong Yu., Tian Ch., Jiang B., Fu H. Gelatin-assisted  Synthesis of ZnS Hollow Nanospheres: The Microstructure Tuning, Formation Mechanism and Application for Pt-free Photocatalytic Hydrogen Production. CrystEngComm. 2017,  vol. 19, pp. 461-468.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Nanowire Networks and Hollow Nanospheres of Ag-Au Bimetallic Alloys at Room Temperature / R. Britto Hurtado, M. Cortez-Valadez, H. Arizpe-Chavez, N. S. Flores- Lopez, R. A. B. Alvarez, M. Flores-Acosta // Nanotechnology. 2017. Vol. 28, № 11. P. 115606.</mixed-citation><mixed-citation xml:lang="en">Britto Hurtado R., Cortez-Valadez M., Arizpe-Chavez H., Flores-Lopez N. S.,  Alvarez R. A. B., Flores-Acosta M. Nanowire Networks and Hollow Nanospheres of Ag-Au  Bimetallic Alloys at Room Temperature. Nanotechnology. 2017, vol. 28, no. 11, p. 115606.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Bioactive Mono-Dispersed Nanospheres with Long-Term Antibacterial Effects for Endodontic Sealing / X. Cheng, T. Qu, Ch. Ma, D. Xiang, Q. Yu, X. Liu // J. Mater. Chem. B. 2017. № 6. P. 1195-1204.</mixed-citation><mixed-citation xml:lang="en">Cheng X., Qu T., Ma Ch., Xiang D., Yu Q., Liu X. Bioactive Mono-Dispersed  Nanospheres with Long-Term Antibacterial Effects for Endodontic Sealing. Journal of Mater. Chem. B. 2017, no. 6, pp. 1195-1204.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Zeptonewton Force Sensing with Nanospheres in an Optical Lattice / G. Ranjit, M. Cunningham, K. Casey, A. A. Geraci // Phys. Rev. A. 2016. Vol. 93. P. 053801.</mixed-citation><mixed-citation xml:lang="en">Ranjit G., Cunningham M., Casey K., Geraci A. A. Zeptonewton Force Sensing with  Nanospheres in an Optical Lattice. Phys. Rev. A. 2016, vol. 93, p. 053801.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Targeted Photothermal Ablation of Murine Melanomas with Melanocyte-Stimulating Hormone Analog- Conjugated Hollow Gold Nanospheres / W. Lu, C. Xiong, G. Zhang, Q. Huang, R. Zhang, JZ. Zhang, C. Li // Clin Cancer Res. 2009. Vol. 15, № 3. Р. 876-886.</mixed-citation><mixed-citation xml:lang="en">Lu W., Xiong C., Zhang G., Huang Q., Zhang R., Zhang JZ., Li C. Targeted  Photothermal Ablation of Murine Melanomas with Melanocyte-Stimulating Hormone Analog-Conjugated Hollow Gold Nanospheres. Clin Cancer Res. 2009, vol. 15, no. 3, pp. 876-886.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Preparation of Core-Shell Nanospheres of Silica- Silver: SiO2@Ag / J. C. Flores, V. Torres, M. Popa, D. Crespo, J. M. Calderon-Moreno // J. of Non-Crystalline Solids. 2008. Vol. 354, № 52-54. P. 5435-5439.</mixed-citation><mixed-citation xml:lang="en">Flores J. C., Torres V., Popa M., Crespo D., Calderon-Moreno J. M. Preparation of  core-shell nanospheres of silica-silver: SiO2@Ag. Journal of Non-Crystalline Solids. 2008, vol. 354, no. 52-54, pp. 5435-5439.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Core-Shell Superparamagnetic Monodisperse Nanospheres Based on Amino- Functionalized CoFe2O4@SiO2 for Removal of Heavy Metals from Aqueous Solutions / Ch. Ren, X. Ding, H. Fu, W. Li, H. Wu, H. Yang // RSC Adv. 2017. № 7. P. 6911-6921.</mixed-citation><mixed-citation xml:lang="en">Ren Ch., Ding X., Fu H. et al. Core-shell superparamagnetic monodisperse  nanospheres based on aminofunctionalized CoFe2O4@SiO2 for removal of heavy metals from aqueous solutions. RSC Adv. 2017, no. 7, pp. 6911-6921.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Self-Assembled Nanospheres with Multiple Endohedral Binding Sites Pre-Organize Catalysts and Substrates for Highly Efficient Reactions // Qi-Q. Wang, S. Gonell, S. H. A. M. Leenders, M. DGrr, I. Ivanovic-Burmazovic, J. N. H. Reek // Nature Chemistry. 2016. Vol. 8, iss. 3. P. 225-230.</mixed-citation><mixed-citation xml:lang="en">Wang Qi-Q., Gonell S., Leenders S. H. A. M., DGrr M., Ivanovic-Burmazovic I.,  Reek J. N. H. Self-assembled nanospheres with multiple endohedral binding sites  preorganize catalysts and substrates for highly efficient reactions. Nature Chemistry. 2016, vol. 8, pp. 225-230.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Synthesis of Mesoporous Silica Hollow Nanospheres with Multiple Gold Cores and Catalytic Activity / J. Chen, Z. Xue, S. Feng, B. Tu, D. Zhao // J. of Colloid and Interface Science. 2014. Vol. 429, iss. 1. P. 62-67.</mixed-citation><mixed-citation xml:lang="en">Chen J., Xue Z., Feng S. Synthesis of mesoporous silica hollow nanospheres with  multiple gold cores and catalytic activity. Journal of Colloid and Interface  Science. 2014, vol. 429, pp. 62-67.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Mel A.-A. El, Nakamura R., Bittencourt C. The Kirkendall Effect and Nanoscience: Hollow Nanospheres And Nanotubes // Beilstein J. Nanotechnol. 2015. Vol. 6. P. 1348-1361.</mixed-citation><mixed-citation xml:lang="en">Mel A.-A. El, Nakamura R., Bittencourt C. The Kirkendall effect and nanoscience:  hollow nanospheres and nanotubes. Beilstein Journal of Nanotechnol. 2015, vol. 6, pp. 1348-1361.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Size-Dependent Nanoscale Kirkendall Effect During the Oxidation of Nickel Nanoparticles / J. G. Railsback, A. C. Johnston-Peck, Ju. Wang, Jo. B. Tracy // ACS Nano. 2010. Vol. 4, № 4. Р. 1913-1920.</mixed-citation><mixed-citation xml:lang="en">Railsback J. G., Johnston-Peck A. C., Wang Ju., Tracy Jo. B. Size-Dependent  Nanoscale Kirkendall Effect During the Oxidation of Nickel Nanoparticles. ACS Nano. 2010, vol. 4, no. 4, pp. 1913-1920.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Tu K. N., Gosele U. Hollow Nanostructures based on The Kirkendall Effect: Design and Stability Considerations // Appl. Phys. Lett. 2016. Vol. 86. P. 093111.</mixed-citation><mixed-citation xml:lang="en">Tu K. N., Gosele U. Hollow nanostructures based on the Kirkendall effect: Design  and stability considerations. Appl. Phys. Lett. 2016, vol. 86, p. 093111.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Synthesis of Layered Hierarchical Porous SnO2 For Enhancing Gas Sensing Performance / Y. Wang, X. Wang, G. Yi, Ya. Xu, Zhou L., Wei Y. // J. of Porous Materials. 2016. P. 1-8.</mixed-citation><mixed-citation xml:lang="en">Wang Y., Wang X., Yi G., Xu Ya., Zhou L., Wei Y. Synthesis of layered  hierarchical porous SnO2 for enhancing gas sensing performance. Journal of Porous Materials. 2016, pp. 1-8.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Synthesis and characterization of hierarchical porous SnO2 for enhancing ethanol sensing properties / Zh. Bowen, F. Wuyou, L. Huayang, F. Xinglin, W. Ying, B. Hari, W. Xiaodong, S. Guang, C. Jianliang, Zh. Zhanying // Appl. Surface Science. 2016. Vol. 363. P. 560-565.</mixed-citation><mixed-citation xml:lang="en">Bowen Zh., Wuyou F., Huayang L., Xinglin F., Ying W., Hari B., Xiaodong W.,  Guang S., Jianliang C., Zhanying Zh. Synthesis and characterization of hierarchical  porous SnO2 for enhancing ethanol sensing properties. Applied Surface Science. 2016,  vol. 363, pp. 560-565.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Hydrothermal Synthesis of Hierarchically Porous Rhdoped ZnO and its High Gas Sensing Performance to Acetone / Z. Chen, Z. Lin, H. Yu, N. Li, M. Xu // J. of Materials Science: Materials in Electronics. 2016. Vol. 27, № 3. P. 2633-2639.</mixed-citation><mixed-citation xml:lang="en">Chen Z., Lin Z., Yu H., Li N., Xu M. Hydrothermal synthesis of hierarchically  porous Rh-doped ZnO and its high gas sensing performance to acetone. Journal of Materials Science: Materials in Electronics. 2016, vol. 27, no. 3, pp. 2633-2639.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Abrashova E. V., Gracheva I. E., Moshnikov V. A. Functional Nanomaterials based on Metal Oxides with Hierarchical Structure // J. of Physics: Conference Series. 2013. Vol. 461, № 1. P. 012019.</mixed-citation><mixed-citation xml:lang="en">Abrashova E. V., Gracheva I. E., Moshnikov V. A. Functional nanomaterials based  on metal oxides with hierarchical structure. Journal of Physics: Conference Series.  2013, vol. 461, no. 1, p. 012019.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Nanostructured Materials Obtained under Conditions of Hierarchical Self-Assembly and Modified by Derivative Forms of Fullerenes / I. E. Gracheva, V. A. Moshnikov, E. V. Maraeva, S. S. Karpova, O. A. Alexsandrova, N. I. Alekseyev, V. V. Kuznetsov, G. Olchowik, K. N. Semenov, A. V. Startseva, A. V. Sitnikov, J. M. Olchowik // J. of Non-Crystalline Solids. 2012. Vol. 358. P. 433-439.</mixed-citation><mixed-citation xml:lang="en">Gracheva I. E., Moshnikov V. A., Maraeva E. V, Karpova S. S., Alexsandrova O.  A., Alekseyev N. I., Kuznetsov V. V., Olchowik G., Semenov K. N., Startseva A. V., Sitnikov A. V., Olchowik J. M. Nanostructured materials obtained under conditions of hierarchical self-assembly and modified by derivative forms of fullerenes. Journal of Non-Crystalline Solids. 2012, vol. 358, pp. 433-439.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Hierarchical Nanostructured Semiconductor Porous Materials for Gas Sensors / V. A. Moshnikov, I. E. Gracheva, V. V. Kuznezov, A. I. Maximov, S. S. Karpova, A. A. Ponomareva // J. of Non-Crystalline Solids. 2010. Vol. 356, № 37-40. P. 2020-2025.</mixed-citation><mixed-citation xml:lang="en">Moshnikov V. A., Gracheva I. E., Kuznezov V. V., Maximov A. I., Karpova S. S.,  Ponomareva A. A. Hierarchical nanostructured semiconductor porous materials for gas  sensors. Journal of Non-Crystalline Solids. 2010, vol. 356, no. 37-40, pp. 2020- 2025.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Грачева И. Е., Мошников В. А., Абрашова Е. В. Обобщение результатов анализа величины фрактальной размерности золь-гель пористых иерархических структур // Материаловедение. 2013. № 6. С. 13-22.</mixed-citation><mixed-citation xml:lang="en">Gracheva I. E., Moshnikov V. A., Abrashova E. V. Generalization of the results  of analysis of the fractal dimension of sol-gel porous hierarchical structures.  Materialovedenie [Materials Science]. 2013, no. 6, pp. 13-22. (In Russian)</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Грачева И. Е., Мошников В. А. Наноматериалы с иерархической структурой пор: учеб. пособие. СПб.: Изд-во СПбГЭТУ "ЛЭТИ", 2011. 107 с.</mixed-citation><mixed-citation xml:lang="en">Gracheva I. E., Moshnikov V. A. Nanomaterialy s ierarkhicheskoi strukturoi por:  ucheb. posobie [Nanomaterials with a hierarchical pore structure]. SPb, Izd-vo SPbGETU "LETI", 2011, 107 p. (In Russian)</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Self-assembly of Fractal Magnetite-Silica Aggregates in a Static Magnetic Field / I. E. Kononova, K. G. Gareev, V. A. Moshnikov, V. I. Al'myashev // Inorganic Materials. 2014. Vol. 50, № 1. P. 68-74.</mixed-citation><mixed-citation xml:lang="en">Kononova I. E., Gareev K. G., Moshnikov V. A. Al'myashev V. I. Self-assembly of  fractal magnetite-silica aggregates in a static magnetic field. Inorganic Materials. 2014, vol. 50, no. 1, pp. 68-74.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Основы золь-гель-технологии нанокомпозитов / А. И. Максимов, В. А. Мошников, Ю. М. Таиров, О. А. Шилова. СПб.: Элмор, 2007. 254 с.</mixed-citation><mixed-citation xml:lang="en">Maksimov A. I., Moshnikov V. A., Tairov Yu. M., Shilova O. A. Osnovy zol'-gel'- tekhnologii nanokompozitov [Fundamentals of sol-gel nanocomposite technology]. SPb,  Elmor, 2007, 254 p. (In Russian)</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Жюльен Р. Фрактальные агрегаты // Успехи физ. наук. 1989. Т. 157, № 2. С. 339-357.</mixed-citation><mixed-citation xml:lang="en">Jullien R. Fractal Aggregates. Comm. Cond. Mat. Phys. (Comm. Mod. Phys. Pt B).  1987, vol. 13, no. 4, pp. 177-205.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Мандельброт Б. Б. Фрактальная геометрия природы / Институт компьютерных исследований. М., 2002. 656 с.</mixed-citation><mixed-citation xml:lang="en">Mandelbrot B. B. The fractal geometry of nature. New York, W. H. Freeman and company, 1977, 468 p.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Everett D. H. Manual of Symbols and Terminology for Physicochemical Quantities and Units. Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry // Pure and Appl. Chem. 1972. Vol. 31, № 4. P. 577-638.</mixed-citation><mixed-citation xml:lang="en">Everett D. H. Manual of Symbols and Terminology for Physicochemical Quantities  and Units. Appendix II: Definitions, Terminology and Symbols in Colloid and Surface  Chemistry. Pure and Appl. Chem. 1972, vol. 31, no. 4, pp. 577-638.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
