Home / Articles / Structure and properties of polymers in terms of the fractal approach

Structure and properties of polymers in terms of the fractal approach

Viktor Ustinovich Novikov 1
Viktor Ustinovich Novikov
, 
Georgii Vladimirovich Kozlov 2
Georgii Vladimirovich Kozlov
1 Moscow State Open University
2 Kabardino-Balkar State University, Nal'chik
Published 30 November 1999
Communication , Volume 69, Issue 6, 523-549
17
Share
Cite this
GOST
 | 
Cite this
GOST
Novikov V. U., Kozlov G. V. Structure and properties of polymers in terms of the fractal approach // Russian Chemical Reviews. 2000. Vol. 69. No. 6. pp. 523-549.
GOST all authors (up to 50)
Novikov V. U., Kozlov G. V. Structure and properties of polymers in terms of the fractal approach // Russian Chemical Reviews. 2000. Vol. 69. No. 6. pp. 523-549.
RIS
 | 
Cite this
RIS
TY - JOUR
DO - 10.1070/RC2000v069n06ABEH000592
UR - https://rcr.colab.ws/publications/10.1070/RC2000v069n06ABEH000592
TI - Structure and properties of polymers in terms of the fractal approach
T2 - Russian Chemical Reviews
AU - Novikov, Viktor Ustinovich
AU - Kozlov, Georgii Vladimirovich
PY - 2000
DA - 1999/11/30
PB - ANO Editorial Board of the journal Uspekhi Khimii
SP - 523-549
IS - 6
VL - 69
ER -
BibTex
 | 
Cite this
BibTex (up to 50 authors)
@article{2000_Novikov,
author = {Viktor Ustinovich Novikov and Georgii Vladimirovich Kozlov},
title = {Structure and properties of polymers in terms of the fractal approach},
journal = {Russian Chemical Reviews},
year = {2000},
volume = {69},
publisher = {ANO Editorial Board of the journal Uspekhi Khimii},
month = {Nov},
url = {https://rcr.colab.ws/publications/10.1070/RC2000v069n06ABEH000592},
number = {6},
pages = {523--549},
doi = {10.1070/RC2000v069n06ABEH000592}
}
MLA
Cite this
MLA
Novikov, Viktor Ustinovich, and Georgii Vladimirovich Kozlov. “Structure and properties of polymers in terms of the fractal approach.” Russian Chemical Reviews, vol. 69, no. 6, Nov. 2000, pp. 523-549. https://rcr.colab.ws/publications/10.1070/RC2000v069n06ABEH000592.
Views / Visits / Downloads
17 / 17 / 3

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
6.
Fractals in microstructure of metals
Hornbogen E.
International Materials Reviews , 1989
7.
7
E. Rabinowitch
"Photosynthesis" , 1956
8.
Stochastic and fractal analysis of fracture trajectories
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.
Random walks on fractal structures and percolation clusters
12.
12
V. B. Evstigneev
Dokl. Akad. Nauk SSSR , 1950
14.
14
V. B. Evstigneev
Zhur. Fiz. Khim. , 1958
15.
15
A. S. Holt
"Research in Photosynthesis" , 1957
16.
Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon
Witten T.A., Sander L.M.
Physical Review Letters , 1981
18.
Scaling of Kinetically Growing Clusters
Kolb M., Botet R., Jullien R.
Physical Review Letters , 1983
19.
19
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR , 1959
20.
Fractal dimension and grand Universality of critical phenomena
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
31.
31
A. A. Krasnovskii
Biokhimiya , 1960
32.
32
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR , 1952
33.
Structure of Amorphous Polymers
Lebedev V.P.
Russian Chemical Reviews , 1978
34.
35
Z. K. Maizus
Dokl. Akad. Nauk SSSR , 1960
35.
Computer simulation of chemically limited aggregation
Brown W.D., Ball R.C.
Journal of Physics A General Physics , 1985
36.
37
L. M. Kosobutskaya
Dokl. Akad. Nauk SSSR , 1950
38.
39
V. F. Gachkovskii
Biofizika , 1959
39.
Diffusion-limited aggregation at multiple growth sites
40.
41
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR , 1950
41.
Aggregation phenomena and fractal structures
Kolb M.
Physica A: Statistical Mechanics and its Applications , 1986
42.
43
N. Bunge
Ber. Deutsch. Chem. Ges. , 1870
43.
Dynamics of Diffusion-Limited Kinetic Aggregation
Weitz D.A., Huang J.S., Lin M.Y., Sung J.
Physical Review Letters , 1984
44.
Density of states on fractals : « fractons »
Alexander S., Orbach R.
Journal de Physique Lettres , 2007
45.
Flory theory of polymeric fractals - intersection, saturation and condensation
Vilgis T.A.
Physica A: Statistical Mechanics and its Applications , 1988
46.
47
G. Oster
"Research in Photosynthesis" , 1957
47.
Dynamical scaling and the growth of diffusion‐limited aggregates
Hentschel H.G., Deutch J.M., Meakin P.
Journal of Chemical Physics , 1984
48.
Dynamics of polymeric fractals
Muthukumar M.
Journal of Chemical Physics , 1985
50.
51
A. A. Krasnovskii
Dokl. Akad. Nauk SSSR , 1954
51.
The sol-gel transition modelled by irreversible aggregation of clusters
Kolb M., Herrmann H.J.
Journal of Physics A General Physics , 1985
54.
Dynamic Scaling for Aggregation of Clusters
Vicsek T., Family F.
Physical Review Letters , 1984
55.
56
T. Iasui
Bull. Chem. Soc. Japan. , 1935
56.
Size distribution of clusters in irreversible kinetic aggregation
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.
Chain structure and entanglement
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
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
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.
Flory exponents for generalized polymer problems
Isaacson J., Lubensky T.C.
Journal de Physique Lettres , 2007
82.
Polymer chain entanglements and brittle fracture
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
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.
Small‐angle x‐ray scattering study of the fractal morphology of porous silicas
Schmidt P.W., Höhr A., Neumann H., Kaiser H., Avnir D., Lin J.S.
Journal of Chemical Physics , 1989
98.
Strain hardening of thermoplastics
Haward R.N.
Macromolecules , 1993
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.
Conformations of macromolecules in condensed phases
116.
117
V. V. Levchenko
Zhur. Obshch. Khim. , 1948
117.
Structure of polymeric glasses and melts
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
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.
Towards a theory of viscosity for glass‐forming liquids
Sanchez I.C.
Journal of Applied Physics , 1974
127.
Fractal clusters
Smirnov B.M.
Uspekhi Fizicheskih Nauk , 2010
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
137.
Chemistry in noninteger dimensions between two and three. II: Fractal surfaces of adsorbents
138.
Temperature and time dependence of free volume in bisphenol A polycarbonate studied by positron lifetime spectroscopy
Kluin J.E., Yu Z., Vleeshouwers S., McGervey J.D., Jamieson A.M., Simha R.
Macromolecules , 1992
139.
Pressure dependence of free-volume hole properties in an epoxy polymer
Deng Q., Sundar C.S., Jean Y.C.
The Journal of Physical Chemistry , 1992
140.
Molecular weight-dependence of free volume in polystyrene studied by positron annihilation measurements
Yu Z., Yahsi U., McGervey J.D., Jamieson A.M., Simha R.
Journal of Polymer Science, Part B: Polymer Physics , 1994
142.
Positron annihilation in amine‐cured epoxy polymers—pressure dependence
Wang Y.Y., Nakanishi H., Jean Y.C., Sandreczki T.C.
Journal of Polymer Science, Part B: Polymer Physics , 1990
145.
146
V. V. Korshak
Dokl. Akad. Nauk SSSR , 1952
146.
Effects of deformation on the microstructure of PTFE polymer studied by positron annihilation
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.
Fractal dynamics of spin glasses
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.
Application of cluster model for the description of epoxy polymer structure and properties
158.
159
J. Tafel
Z. Elektrochem. , 1911
159.
160
1912
160.
161
Friedl.
161.
162
1917
162.
163
Friedl.
163.
Environmental crack and craze growth phenomena in polymers
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 1975
164.
165
Friedl.
165.
166
1917
167.
168
1918
169.
170
1918
170.
171
Friedl.
171.
172
1918
172.
Topological properties of diffusion limited aggregation and cluster-cluster aggregation
Meakin P., Majid I., Havlin S., Stanley H.E.
Journal of Physics A General Physics , 1984
174.
175
I. Mayer
1966
176.
Fractal character of crack propagation in epoxy and epoxy composites as revealed by photon emission during fracture
Zhenyi M., Langford S.C., Dickinson J.T., Engelhard M.H., Baer D.R.
Journal of Materials Research , 1991
177.
178
1946
179.
180
1946
180.
181
Chem. Abs. , 1947
181.
182
1947
183.
Fractal growth of copper electrodeposits
Brady R.M., Ball R.C.
Nature , 1984
184.
Diffusion-limited aggregation
Witten T.A., Sander L.M.
Physical Review B , 1983
185.
186
Chem. Abs. , 1956
186.
187
1954
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.
Cold flow of glassy polymers. III. Temperature dependence of yield elongation in BPA polycarbonate
Litt M.H., Koch P.J., Tobolsky A.V.
Journal of Macromolecular Science - Physics , 1967
192.
On chain entanglement in high-Tg amorphous polymers. II
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.
The brittle fracture of amorphous thermoplastic polymers
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.
Critical Properties of an Elastic Fractal
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
207.
208
O. A. Reutov
"Teoreticheskie Problemy Organicheskoi Khimii" (Theoretical Problems in Organic Chemistry) , 1956
208.
Fractal character of fracture surfaces of metals
Mandelbrot B.B., Passoja D.E., Paullay A.J.
Nature , 1984
209.
Fractal characterization of fractured surfaces
Pande C.S., Richards L.E., Louat N., Dempsey B.D., Schwoeble A.J.
Acta Metallurgica , 1987
213.
Fractals in fractography
Underwood E.E., Banerji K.
Materials Science and Engineering , 1986
214.
Fractals identified with fracture surface of high strength steel
Mu Z.Q., Lung C.W.
Theoretical and Applied Fracture Mechanics , 1992
216.
217
1925
217.
Quantitative Analysis of Brittle Fracture Surfaces Using Fractal Geometry
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
223.
224
Chem. Abs. , 1959
225.
The concept of multifractal elasticity
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.
Fractal Geometry of Colloidal Aggregates
Schaefer D.W., Martin J.E., Wiltzius P., Cannell D.S.
Physical Review Letters , 1984
230.
Molecular fractal surfaces
Avnir D., Farin D., Pfeifer P.
Nature , 1984
232.
A new approach to the determination of the surface fractal dimension of porous solids
233.
235
R. Peffen
1967
234.
Electrochemical determination of the fractal dimension of fractured surfaces
Imre A., Pajkossy T., Nyikos L.
Acta Metallurgica et Materialia , 1992
235.
237
P. Peshev
Rev. internat. hautes Temperat. et Réfract. , 1969
236.
Physics of fracture and mechanics of self-affine cracks
238.
Fractal geometry in branched epoxy polymer kinetics
Chu B., Wu C., Wu D.Q., Phillips J.C.
Macromolecules , 1987
240.
Configurational Statistics of Highly Branched Polymer Systems
Dobson G.R., Gordon M.
Journal of Chemical Physics , 1964
241.
243
G. A. Kudintseva
1958
243.
Fractal Geometry of Silica Condensation Polymers
Schaefer D.W., Keefer K.D.
Physical Review Letters , 1984
244.
The fractal nature of the surface of cement paste
Winslow D.N.
Cement and Concrete Research , 1985
247.
Fractal structure of the pore surface of hydrated portland cement pastes
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
252.
Hydrodynamic behavior of fractal aggregates
Wiltzius P.
Physical Review Letters , 1987