Abstract
The review considers various manifestations of fractality in the description of the synthesis of macromolecules and the formation of the quasi-equilibrium state in polymers, fluctuation free volume, macromolecular frameworks, order parameters, and dissipative structures, acting as centres of shear stress in clusters. The possibility of numerical modelling of the properties of network polymers within the framework of fractal formalism is demonstrated. The methods for determination of the fractal dimension are described. The bibliography includes 248 references.
References
1.
1
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1948
2.
2
A. A. Krasnovskii
Zhur. Fiz. Khim. ,
1956
3.
3
M. F. Shostakovskii
"Prostye Vinilovye Efiry" (Vinyl Ethers) ,
1952
4.
4
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1949
5.
Edwards S.F., Vilgis T.
Polymer ,
1987
6.
Hornbogen E.
International Materials Reviews ,
1989
7.
7
E. Rabinowitch
"Photosynthesis" ,
1956
8.
Bessendorf M.H.
International Journal of Engineering Science ,
1987
9.
9
V. H. Lynch
Carnegie Inst. Year Book ,
1954
10.
10
T. A. Kryukova
"Polyaro-graficheskii Analiz" (Polarographic Analysis) ,
1959
11.
Rammal R., Toulouse G.
Journal de Physique Lettres ,
2007
12.
12
V. B. Evstigneev
Dokl. Akad. Nauk SSSR ,
1950
13.
14.
14
V. B. Evstigneev
Zhur. Fiz. Khim. ,
1958
15.
15
A. S. Holt
"Research in Photosynthesis" ,
1957
16.
Witten T.A., Sander L.M.
Physical Review Letters ,
1981
17.
Meakin P.
Physical Review Letters ,
1983
18.
Kolb M., Botet R., Jullien R.
Physical Review Letters ,
1983
19.
19
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1959
20.
Family F.
Journal of Statistical Physics ,
1984
21.
21
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1958
23.
23
N. V. Vostrilova
Dokl. Akad. Nauk Uzbek. SSR ,
1958
24.
24
M. S. Ashkinazi
Dokl. Akad. Nauk SSSR ,
1951
25.
25
G. W. Robinson
J. Chem. Phys. ,
1955
26.
26
B. Ya. Dain
1957
27.
27
A. A. Krasnovskii
Biofizika ,
1956
28.
28
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1955
29.
29
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1951
30.
Pfeifer P., Avnir D., Farin D.
Journal of Statistical Physics ,
1984
31.
31
A. A. Krasnovskii
Biokhimiya ,
1960
32.
32
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1952
33.
Lebedev V.P.
Russian Chemical Reviews ,
1978
34.
35
Z. K. Maizus
Dokl. Akad. Nauk SSSR ,
1960
35.
Brown W.D., Ball R.C.
Journal of Physics A General Physics ,
1985
36.
37
L. M. Kosobutskaya
Dokl. Akad. Nauk SSSR ,
1950
37.
Kobayashi M., Yoshioka T., Imai M., Itoh Y.
Macromolecules ,
1995
38.
39
V. F. Gachkovskii
Biofizika ,
1959
39.
Witten T.A., Meakin P.
Physical Review B ,
1983
40.
41
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1950
41.
Kolb M.
Physica A: Statistical Mechanics and its Applications ,
1986
42.
43
N. Bunge
Ber. Deutsch. Chem. Ges. ,
1870
43.
Weitz D.A., Huang J.S., Lin M.Y., Sung J.
Physical Review Letters ,
1984
44.
Alexander S., Orbach R.
Journal de Physique Lettres ,
2007
45.
Vilgis T.A.
Physica A: Statistical Mechanics and its Applications ,
1988
46.
47
G. Oster
"Research in Photosynthesis" ,
1957
47.
Hentschel H.G., Deutch J.M., Meakin P.
Journal of Chemical Physics ,
1984
48.
49.
Aharoni S.M.
Macromolecules ,
1985
50.
51
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1954
51.
Kolb M., Herrmann H.J.
Journal of Physics A General Physics ,
1985
52.
Kolb M.
Physical Review Letters ,
1984
53.
Meakin P., Vicsek T., Family F.
Physical Review B ,
1985
54.
Vicsek T., Family F.
Physical Review Letters ,
1984
55.
56
T. Iasui
Bull. Chem. Soc. Japan. ,
1935
56.
Botet R., Jullien R.
Journal of Physics A General Physics ,
1984
57.
58
N. E. Khomutov
1953
58.
59
H. Linshitz
"Research in Photosynthesis" ,
1957
59.
60
A. N. Terenin
Optika i Spektrosk. ,
1956
60.
61
A. N. Terenin
1959
61.
62
A. A. Krasnovskii
"Sbornik, Voprosy Khimicheskoi Kinetiki" (Symposium, Problems of Chemical Kinetics) ,
1955
62.
63
1930
63.
Wu S.
Journal of Polymer Science, Part B: Polymer Physics ,
1989
64.
65
A. A. Krasnovskii
Biofizika ,
1959
65.
66
V. B. Evstigneev
Dokl. Akad. Nauk SSSR ,
1950
66.
Boyer R.F.
Macromolecules ,
1992
67.
Wu S.
Polymer Engineering and Science ,
1990
68.
Boyer R.F., Miller R.L.
Macromolecules ,
1977
69.
70
N. Bubnov
Biofizika ,
1960
70.
71
Yu. A. Shlyapnikov
Vysokomol. Soed. ,
1962
71.
72
A. F. Lukovnikov
"Starenie i Stabilizatsiya Polimerov" (Aging arid Stabilisation of Polymers) ,
1963
72.
73
T. Skwarski
Chem. Abs. ,
1957
73.
74
F. F. Litvin
Uspekhi Fiz. Nauk ,
1960
74.
75
V. B. Evstigneev
Dokl. Akad. Nauk SSSR ,
1950
75.
76
A. N. Terenin
"Fotokhimiya Krasitelei" (The Photochemistry of Dyes) ,
1947
76.
77
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1948
77.
Aharoni S.M.
Macromolecules ,
1983
78.
79
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1952
79.
80
N. N. Mel'nikov
Zhur. Obshch. Khim. ,
1937
80.
81
J. C. Ghosh
J. Indian Chem. Soc. ,
1934
81.
Isaacson J., Lubensky T.C.
Journal de Physique Lettres ,
2007
82.
Mikos A.G., Peppas N.A.
Journal of Chemical Physics ,
1988
83.
84
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1947
84.
85
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1947
85.
86
V. B. Evstigneev
Dokl. Akad. Nauk SSSR ,
1958
86.
87
J. F. Arens
"Advances in Organic Chemistry" ,
1960
87.
88
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1946
88.
Balankin A.S.
Physical Review B ,
1996
89.
90
V. B. Evstigneev
Dokl. Akad. Nauk SSSR ,
1951
90.
91
L. M. Vorob'eva
Biokhimiya ,
1956
91.
92
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR ,
1948
92.
93
V. B. Evstigneev
Dokl. Akad. Nauk SSSR ,
1956
93.
94
A. A. Krasnovskii
Fiziologiya Rastenii ,
1957
94.
95
A. A. Krasnovskii
Fiziologiya Rastenii ,
1957
95.
96
L. M. Vorob'eva
Biokhimiya ,
1958
96.
97
A. N. Terenin
Dokl. Akad. Nauk SSSR ,
1952
97.
Schmidt P.W., Höhr A., Neumann H., Kaiser H., Avnir D., Lin J.S.
Journal of Chemical Physics ,
1989
98.
99.
100
V. V. Zolotarev
Chem. Abs. ,
1941
100.
101
M. F. Shostakovskii
Izv. Akad. Nauk SSSR, Otd. Khim. Nauk ,
1960
101.
102
F. Fichter
Helv. Chim. Acta ,
1922
102.
103
L. N. Bell
Dokl. Akad. Nauk SSSR ,
1956
103.
104
O. P. Osipova
Dokl. Akad. Nauk SSSR ,
1950
104.
105
F. F. Litvin
Dokl. Akad. Nauk SSSR ,
1958
105.
106
F. Fichter
Helv. Chim. Acta ,
1927
106.
107
M. F. Shostakovskii
Zhur. Obshch. Khim. ,
1961
107.
108
F. Fichter
Helv. Chim. Acta ,
1924
108.
109
F. Ficher
Bull. Soc. chim. France (4) ,
1916
109.
110
M. F. Shostakovskii
Dokl. Akad. Nauk SSSR ,
1960
110.
111
M. Calvin
1956
111.
112
A. G. Pozdeeva
Zhur. Prikl. Khim. ,
1952
112.
113
H. Blum
"Photodynamic Action and Diseases caused Light" ,
1940
113.
114
L. Segal
"Chemical Reactions of Polymers" ,
1964
114.
Flory P.J.
Pure and Applied Chemistry ,
1984
115.
Petrie S.E.
Journal of Macromolecular Science - Physics ,
1976
116.
117
V. V. Levchenko
Zhur. Obshch. Khim. ,
1948
117.
Fischer E.W., Dettenmaier M.
Journal of Non-Crystalline Solids ,
1978
118.
119
V. V. Levchenko
Zhur. Obshch. Khim. ,
1947
119.
120
V. V. Levchenko
Zhur. Obshch. Khim. ,
1948
120.
Lipatov Y.S.
Russian Chemical Reviews ,
1978
121.
122
S. R. Rafikov
Izv. Akad. Nauk SSSR, Otd. Khim. Nauk ,
1953
122.
123
V. V. Levchenko
Zhur. Obshch. Khim. ,
1952
123.
124
V. V. Levchenko
Zhur. Obshch. Khim. ,
1952
124.
125
K. A. Andrianov
Vysokomol. Soed. ,
1960
125.
126
J. Wiemannand Ch. Clachet
Compt. rend. ,
1948
126.
Sanchez I.C.
Journal of Applied Physics ,
1974
127.
128.
129
J. Wiemann
Bull. Soc. chim. France ,
1955
129.
130
J. Wiemann
Bull. Soc. chim. France ,
1958
130.
131
N. Thooi
Compt. rend. ,
1958
131.
132
G. Shima
Kyoto Univ. ,
1929
132.
133
C. Wilson
Trans. Electrochem. Soc. ,
1941
133.
134
V. V. Korshak
Izv. Akad. Nauk SSSR, Otd. Khim. Nauk ,
1948
134.
135
V. V. Korshak
Dokl. Akad. Nauk SSSR ,
1945
135.
136
V. V. Korshak
Izv. Akad. Nauk SSSR, Otd. Khim. Nauk ,
1954
136.
Pfeifer P., Avnir D.
Journal of Chemical Physics ,
1983
137.
Avnir D., Farin D., Pfeifer P.
Journal of Chemical Physics ,
1983
138.
Kluin J.E., Yu Z., Vleeshouwers S., McGervey J.D., Jamieson A.M., Simha R.
Macromolecules ,
1992
139.
Deng Q., Sundar C.S., Jean Y.C.
The Journal of Physical Chemistry ,
1992
140.
Yu Z., Yahsi U., McGervey J.D., Jamieson A.M., Simha R.
Journal of Polymer Science, Part B: Polymer Physics ,
1994
141.
Deng Q., Zandiehnadem F., Jean Y.C.
Macromolecules ,
1992
142.
Wang Y.Y., Nakanishi H., Jean Y.C., Sandreczki T.C.
Journal of Polymer Science, Part B: Polymer Physics ,
1990
143.
Yu W.C., Sung C.S.
Macromolecules ,
1988
144.
Beloshenko V.A., Kozlov G.V., Varyukhin V.N., Slobodina V.G.
Acta Polymerica ,
1997
145.
146
V. V. Korshak
Dokl. Akad. Nauk SSSR ,
1952
146.
Wang C.L., Wang B., Li S.Q., Wang S.J.
Journal of Physics Condensed Matter ,
1993
147.
148
P. Kresse
Chem. Abs. ,
1960
148.
149
V. V. Korshak
Dokl. Akad. Nauk SSSR ,
1954
149.
Dotsenko V.S.
Journal of Physics C Solid State Physics ,
1985
150.
151
V. M. Rodionov
Zhur. Obshch. Khim. ,
1936
151.
152
W. Albert
Trans. Electrochem. Soc. ,
1943
152.
153
1899
153.
154
Friedl.
154.
155
M. V. Mal'tsev
Izv. Vys. Ucheb. Zaved., Tsvet. Met. ,
1960
155.
156
J. S. Fruton
J. Biol. Med. ,
1950
156.
157
1903
157.
Kozlov G.V., Beloshenko V.A., Varyukhin V.N., Lipatov Y.S.
Polymer ,
1999
158.
159
J. Tafel
Z. Elektrochem. ,
1911
159.
160
1912
160.
161
Friedl.
161.
162
1917
162.
163
Friedl.
163.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences ,
1975
164.
165
Friedl.
165.
166
1917
166.
Sokolov I.M.
Uspekhi Fizicheskih Nauk ,
2010
167.
168
1918
168.
Margolina A., Wu S.
Polymer ,
1988
169.
170
1918
170.
171
Friedl.
171.
172
1918
172.
Meakin P., Majid I., Havlin S., Stanley H.E.
Journal of Physics A General Physics ,
1984
173.
McCAULEY J.L.
International Journal of Modern Physics B ,
2004
174.
175
I. Mayer
1966
175.
Matsuoka S., Aloisio C.J., Bair H.E.
Journal of Applied Physics ,
1973
176.
Zhenyi M., Langford S.C., Dickinson J.T., Engelhard M.H., Baer D.R.
Journal of Materials Research ,
1991
177.
178
1946
178.
Vilgis T.A.
Journal de Physique ,
2007
179.
180
1946
180.
181
Chem. Abs. ,
1947
181.
182
1947
182.
Colvin J.T., Stapleton H.J.
Journal of Chemical Physics ,
1985
183.
184.
Witten T.A., Sander L.M.
Physical Review B ,
1983
185.
186
Chem. Abs. ,
1956
186.
187
1954
187.
Malinovsky V.K., Noviokov V.N.
Journal of Physics Condensed Matter ,
1992
188.
189
M. Godchot
Bull. Soc. chim. France (5) ,
1913
189.
190
H. Law
J. Chem. Soc. ,
1912
190.
191
M. Matsui
Mem. Coll. Sci., Kyoto Univ. ,
1920
191.
Litt M.H., Koch P.J., Tobolsky A.V.
Journal of Macromolecular Science - Physics ,
1967
192.
Prevorsek D.C., De Bona B.T.
Journal of Macromolecular Science - Physics ,
1981
193.
194
A. A. Vertman
"Svoistva Rasplavov Zheleza" (Properties of Iron Melts) ,
1969
194.
195
M. Allen
J. Chem. Soc. ,
1961
195.
196
E. Müller
Z. Elektrochem. ,
1910
196.
DiBenedetto A.T., Trachte K.L.
Journal of Applied Polymer Science ,
1970
197.
198
W. Cohen
Rec. Trav. chim. ,
1919
198.
199
Yu. K. Delimarskii
Byull. Izobr. ,
1970
199.
200
Ref. Zh. Khim. ,
1975
200.
201
A. Aladjem
1969
201.
202
G. Shiroa
Mem. Coll. Sci., Kyoto Univ. ,
1930
202.
Bergman D.J., Kantor Y.
Physical Review Letters ,
1984
203.
204
Cherkesov A I
Ref. Zh. Khim. ,
1968
204.
205
N. Bunge
Zhur. Russ. Fiz.-Khim. Obshch. ,
1889
205.
206
J. Petersen
Z. Phys. Chem. ,
1900
206.
COX B.L., WANG J.S.
Fractals ,
2003
207.
208
O. A. Reutov
"Teoreticheskie Problemy Organicheskoi Khimii" (Theoretical Problems in Organic Chemistry) ,
1956
208.
Mandelbrot B.B., Passoja D.E., Paullay A.J.
Nature ,
1984
209.
Pande C.S., Richards L.E., Louat N., Dempsey B.D., Schwoeble A.J.
Acta Metallurgica ,
1987
210.
Lung C.W., Mu Z.Q.
Physical Review B ,
1988
211.
A study of the slit island analysis as a method for measuring fractal dimension of fractured surface
Huang Z.H., Tian J.F., Wang Z.G.
Scripta Metallurgica et Materialia ,
1990
212.
Chen L.H.
Scripta Metallurgica et Materialia ,
1990
213.
Underwood E.E., Banerji K.
Materials Science and Engineering ,
1986
214.
Mu Z.Q., Lung C.W.
Theoretical and Applied Fracture Mechanics ,
1992
215.
Wright K., Karlsson B.
Journal of Microscopy ,
1983
216.
217
1925
217.
Mecholsky J.J., Passoja D.E., Feinberg-Ringel K.S.
Journal of the American Ceramic Society ,
1989
218.
219
G. I. Pustoshkin
Collected Papers "Biologicheskie Aktivnie Soedinenii" (Biologically Active Compounds) ,
1955
219.
220
K. Ziegler
Angew. Chem. ,
1955
220.
221
1960
221.
222
Chem. Abs. ,
1961
222.
Meakin P.
Physics Reports ,
1993
223.
224
Chem. Abs. ,
1959
224.
Balankin A.S.
International Journal of Fracture ,
1996
225.
Balankin A.S.
Physics Letters, Section A: General, Atomic and Solid State Physics ,
1996
226.
227
B. Roetheke
1958
227.
228
B. Roetheke
Chem. Abs. ,
1959
228.
229
1959
229.
Schaefer D.W., Martin J.E., Wiltzius P., Cannell D.S.
Physical Review Letters ,
1984
230.
231.
Pfeifer P., Avnir D., Farin D.
Surface Science ,
1983
232.
Neimark A.
Physica A: Statistical Mechanics and its Applications ,
1992
233.
235
R. Peffen
1967
234.
Imre A., Pajkossy T., Nyikos L.
Acta Metallurgica et Materialia ,
1992
235.
237
P. Peshev
Rev. internat. hautes Temperat. et Réfract. ,
1969
236.
Balankin A.S.
Engineering Fracture Mechanics ,
1997
237.
Xie R., Yang B., Jiang B.
Physical Review B ,
1994
238.
Chu B., Wu C., Wu D.Q., Phillips J.C.
Macromolecules ,
1987
239.
Meakin P., Stanley H.E.
Physical Review Letters ,
1983
240.
Dobson G.R., Gordon M.
Journal of Chemical Physics ,
1964
241.
243
G. A. Kudintseva
1958
242.
Bale H.D., Schmidt P.W.
Physical Review Letters ,
1984
243.
Schaefer D.W., Keefer K.D.
Physical Review Letters ,
1984
244.
Winslow D.N.
Cement and Concrete Research ,
1985
245.
Freltoft T., Kjems J.K., Sinha S.K.
Physical Review B ,
1986
246.
Spence C.A., Elliott S.R.
Solid State Communications ,
1989
247.
Casta�o V.M., Martinez G., Alem�n J.L., Jim�nez A.
Journal of Materials Science Letters ,
1990
248.
250
D. Goerrig
1955
249.
251
D. Goerrig
Chem. Abs. ,
1959
250.
252
D. Goerrig
1956
251.
Blumen A., Manz J.
Journal of Chemical Physics ,
1979
252.
Wiltzius P.
Physical Review Letters ,
1987