Часова і просторова самоорганізація в електрохімічних системах: Автореф. дис… канд. хім. наук / М.М. Тураш, НАН України. Ін-т заг. та неорган. хімії

IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?inoeooo caaaeueii? oa iai?aai?/ii? o?i??

?i. A.?.Aa?iaaenueeiai

Oo?ao Ieeiea Ieeieaeiae/

OAeE 541.13: 541.12

*aniaa ? i?inoi?iaa naiii?aai?caoe?y

a aeaeo?io?i?/ieo nenoaiao

02.00.05 — Aeaeo?io?i?y

Aaoi?aoa?ao aeena?oaoe??

ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa o?i?/ieo iaoe

Ee?a — 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia ia eaoaae?? o?ce/ii? oa i?aai?/ii? o?i?? a
*a?i?aaoeueeiio aea?aeaaiiio oi?aa?neoao? ?i. TH. Oaaeueeiae/a

Iaoeiaee ea??aiee:

Aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Ia/eii?oe Aaneeue
Aaneeueiae/, eaoaae?a o?ce/ii? oa i?aai?/ii? o?i?? *a?i?aaoeueeiai
aea?aeoi?aa?neoaoo, i?ioani?

Io?oe?ei? iiiiaioe:

aeieoi? o?i?/ieo iaoe, Eieaania Aaiiaae?e sseiae/, ?inoeooo caaaeueii?
oa iai?aai?/ii? o?i?? ?i. A.?. Aa?iaaenueeiai IAI Oe?a?ie, caa?aeoth/ee
a?aeae?eii

aeieoi? o?i?/ieo iaoe, i?ioani? Eocueieinueeee ?aaai Aaneeueiae/, ?aaea
c ieoaiue iaoee oa iaoei-oaoi?/ii? iie?oeee i?e I?aceaeaioia? Oe?a?ie,
ea??aiee nae?aoa??aoo

I?ia?aeia onoaiiaa:

Oa?e?anueeee aea?aeaaiee oi?aa?neoao, Iaoeiai-aeine?aeiee ?inoeooo
o?i??, i. Oa?e?a

Caoeno a?aeaoaeaoueny “ 16 ” aa?aniy 1999 ?ieo i 12 aiaeei? ia
can?aeaii? niaoe?ae?ciaaiii? a/aii? ?aaee Ae 26.218.01 ?inoeoooo
caaaeueii? oa iai?aai?/ii? o?i?? ?i. A.?. Aa?iaaenueeiai IAI Oe?a?ie ca
aae?anith: 252680, Ee?a-142, i?iniaeo aeaaeai?ea Iaeeaae?ia, 32/34,
eiioa?aioe-cae.

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? ?inoeoooo caaaeueii?
oa iai?aai?/ii? o?i?? ?i. A.?. Aa?iaaenueeiai IAI Oe?a?ie.

Aaoi?aoa?ao ?ic?neaii “ 16 ” eeiiy 1999 ?ieo

A/aiee nae?aoa?

niaoe?ae?ciaaiii? ?aaee Iaiia A.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aeey ?ica’ycaiiy aaaaoueio oai?aoe/ieo ?
i?eeeaaeieo i?iaeai o?ce/ii? o?i?? aaeeea cia/aiiy ia? aea/aiiy
aaiethoe?? nenoai aeaeaei a?ae oa?iiaeeiai?/ii? ??aiiaaae. Oa?aeoa?iith
iniaeea?noth i?io?eaiiy i?ioean?a a iaeano? iae?i?eii? caeaaeiino?
iioie?a a?ae oa?iiaeeiai?/ieo nee ? oa, ui i?e e?eoe/ieo cia/aiiyo
oa?iiaeeiai?/ieo nee iiaea a?aeaooeny ??no oeoeooaoe?e ?ioaineaieo
aaee/ei, ui coiiaeth? no?eaeiiiae?aio ia?aaoaeiao ia??aiiaaaeii?
nenoaie, ??ceo ci?io aeeiai?/ieo oa?aeoa?enoee ? ooai?aiiy
aii?yaeeiaaieo aeeneiaoeaieo no?oeoo?.

Aeaeo?io?i?/i? nenoaie caaaeyee cia/iei iioaioe?aeueiei iiaeeeainoyi
aei naiii?aai?caoe?? (??ciiiai?oi?noue o?ce/ieo oa o?i?/ieo yaeu,
iia?euei?noue aei eaoae?oe/ieo ae?e, iayai?noue iaoai?ci?a ye
aeiaeaoi?o, oae ? a?ae’?iieo cai?ioi?o ca’yce?a) i?iyaeythoue aenieo
caeaoi?noue aei ooai?aiiy ??cieo oei?a aeeneiaoeaieo nenoai, ui
eeaneo?eothoueny ye /ania?, i?inoi?ia? oa i?inoi?iai-/ania?.

A iniia? no/anieo oyaeaiue i?i iiyao /aniaeo aeeneiaoeaieo no?oeoo?
(aaoieieeaaiiy) eaaeaoue aca?iica’ycee o?ainii?oieo i?ioean?a c
aeaeo?io?i?/ieie ia?aoai?aiiyie ia aeaeo?iae? oa oa?aeoa?enoeee
ciai?oiueiai eaioethaa, ye? aieeaathoue ia ?aaeei i?io?eaiiy i?ioeano.

Ui ae aei i?inoi?iai? naiii?aai?caoe??, oi iaea?eueoo oaaao i?eaa?oa?
ii?ooaiiy iaoai?/ii? ??aiiaaae oee?eoeyoe?eieie eii??eaie, ui
c’yaeythoueny, ia?ao?ae eai?ia?iiai ?ooo a oo?aoeaioiee oa aoaeo
Ia?aiaii? o aeiaaeeo aeaeo?io?i?/ii? nenoaie ??aeeee aeaeo?iae-??aeeee
aeaeo?ie?o. Inoaii?e coiiaeaiee aieeaii ia iiaa?oiaaee iaoya
iaiaeii??aeiino? aeaeo?e/iiai iioaioe?aeo oa eiioeaio?aoe?? ?aaaoth/eo
?a/iaei.

?ice?eooy caeiiii??iinoae naiii?aai?caoe?? ? iniiaith iaoeiaiai
i?aeoiaeo ia eeoa i?e ?ica’ycaii? i?eeeaaeieo i?iaeai ?ioaineo?eaoe?? oa
iioei?caoe?? oi?aae?iiy o?ceei-o?i?/ieie ia?aoai?aiiyie, aea e i?e
noai?aii? i?eioeeiiai iiaeo oaoiieia?/ieo ?ica’yce?a.

Iaoa ?iaioe: ciaeoe e?eoa??? oa oiiae /aniaiai ? i?inoi?iaiai
aeeneiaoeaiiai no?oeoo?oaaiiy a aeaeo?io?i?/ieo nenoaiao c ??aeeei
aeaeo?ie?oii oa iaeiei ??aeeei aeaeo?iaeii. Aeey aeinyaiaiiy iinoaaeaii?
iaoe iaiao?aeii aoei ae??oeoe oae? caaea/?:

— ?ic?iaeoe iiaeaeue aeaeo?ieaoae?oe/iiai a?aeiiaeaiiy iaoae?a i?e
iayaiino? aeaio oei?a aaeni?aiaaieo ?a/iaei;

— aecia/eoe e?eoe/i? /enea iiyae /aniaeo aeeneiaoeaieo no?oeoo? a
aeaeo?io?i?/ieo nenoaiao;

— ciaeoe oiiae aeeneiaoeaiiai no?oeoo?oaaiiy o nenoaiao c aoaeoii
Ia?aiaii?, aeine?aeeoe aieea aoaeoo ?aeay ia iano?ee?noue Ia?aiaii?,
?ic?aooaaoe e?eoe/i? /enea Ia?aiaii? c o?aooaaiiyi caeaaeiino?
iiaa?oiaaiai iaoyao a?ae iioaioe?aeo oa eiioeaio?aoe??;

— iaoiaeii e?ioeaaeo ??cieoeue c’ynoaaoe aieea /enae A?anaioa ia
eiioeaio?aoe?ei? i?io?e? oa oi?io eiiaaeoeaieo iioie?a a iaeano?
naiii?aai?caoe?? aeaeo?io?i?/ieo nenoai.

Iaoeiaa iiaecia io?eiaieo ?acoeueoao?a. Cai?iiiiiaaia iiaeaeue
aeaeo?ieaoae?oe/iiai a?aeiiaeaiiy iaoae?a i?e iayaiino? aeaio oei?a
aaeni?aiaaieo ?a/iaei ? aecia/ai? e?eoe/i? /enea iiyae /aniaeo
aeeneiaoeaieo no?oeoo?. Ciaeaeai? oiiae iiyae aeeneiaoeaieo no?oeoo? a
aeaeo?io?i?/ieo nenoaiao ??aeeee aeaeo?iae-??aeeee aeaeo?ie?o a
caeaaeiino? a?ae caeiiii??iinoae e?iaoeee i?ioeano, oiia eiai
i?iaaaeaiiy, a oaeiae ni?aa?aeiioaiiy oiauei oa??a aeaeo?iaeo oa
aeaeo?ie?oo. Ia/eneai? e?eoe/i? /enea Ia?aiaii? c o?aooaaiiyi
caeaaeiino? iiaa?oiaaiai iaoyao ia eeoa a?ae iioaioe?aeo, a e a?ae
eiioeaio?aoe??. Iaoiaeii e?ioeaaeo ??cieoeue aeine?aeaeaii aieea /enae
A?anaioa ia oi?io eiiaaeoeaieo iioie?a ? iieacaii iinooiiao ci?io
iaoai?cio ia?aiino a?ae aeeooc?eiiai aei eiiaaeoeaiiai.

I?aeoe/ia cia/aiiy io?eiaieo ?acoeueoao?a. ?icaeyioo? iiaeae?
aeeneiaoeaiiai no?oeoo?oaaiiy iinyoue ooiaeaiaioaeueiee oa?aeoa?. Ia
nueiaiaei? aeey io?eiaiiy ye?nieo ??aiii??ieo aaeueaai?/ieo iie?eoue
nooo?aei ? iayai?noue ia?ai?ooaaiiy. Canoinoaaiiy i?e?iaeiueiai
ia?ai?ooaaiiy (i?e?iaeii? eiiaaeoe??) iiaea cia/ii ciaioeoe aia?aaoe/i?
aeo?aoe ? i?enei?eoe (ii??aiyii c nenoaiith aac ia?ai?ooaaiiy)
o?ainii?oi? i?ioeane a aeaeo?io?i?/ieo ae?iaieoeoaao.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?eia
?iaioa aeeiiaia ia eaoaae?? o?ce/ii? oa i?aai?/ii? o?i?? *a?i?aaoeueeiai
aea?aeoi?aa?neoaoo ca?aeii ieaiiai? iaoeiai-aeine?aeii? athaeaeaoii?
oaie ? 0194U028036 “A?oo?eaoe?ei? yaeua, iiaa?oiaai-aeaeo?iaeia oa
a?ae?iaeeiai?/ia iano?ee?noue a aeaeo?io?i?/ieo nenoaiao”.

Iniaenoee aianie caeiaoaa/a iieyaa? a iinoaiiaoe? caaea/, ?o
?ica’ycaii? ? iiyniaii? io?eiaieo ?acoeueoao?a. Iniiai? iieiaeaiiy
aeena?oaoe?? iioae?eiaai? aaoi?ii ni?eueii c iaoeiaei ea??aieeii.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. ?acoeueoaoe aeine?aeaeaiue,
iaaaaeai? a ?iaio?, /anoeiai aoee ii?eethaeiai? o iaoa??aeao V
Oe?a?inueei? ?anioae?eainueei? eiioa?aioe?? ii aeaeo?io?i??, i.Oaeai?iae
(1990), a ?inoeooo? o?ce/ii? o?i?? Iieuenueei? Aeaaeai?? Iaoe , i.
Aa?oaaa (1993, 1994 ?.) oa aeiiia?aeaeenue ia ?? Oe?a?inueeiio
aeaeo?io?i?/iiio c’?cae?, i. Aei?i?iiao?ianuee (1999).

Ioae?eaoe??. Iaoa??aee, ye? eyaee a iniiao aeena?oaoe?eii? ?iaioe,
iioae?eiaai? o oanoe noaooyo iaoeiaeo aeo?iae?a oa iaeieo oacao iaoeiai?
eiioa?aioe??.

No?oeoo?a oa iac?i aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c anooio,
/ioe?ueio ?icae?e?a, aeniiae?a oa nieneo aeei?enoaieo aeaea?ae (102
iaeiaioaaiiy). ?iaioa aeeeaaeaia ia 109 noi??ieao iaoeiiieno ? i?noeoue
26 ?enoie?a ? 3 oaaeeoe?.

CI?NO ?IAIOE

Ia?oee ?icae?e aeena?oaoe?? i?enay/aiee e?oa?aoo?iiio iaeyaeo iiooeo
oiia iiyae oa ooieoe?thaaiiy /aniaeo ? i?inoi?iaeo aeeneiaoeaieo
no?oeoo? a aeaeo?io?i?/ieo nenoaiao.

A ??aeeiao ? aacao o iie? caiiiai oyae?iiy i?e iayaiino? i?inoi?iai?
iaiaeii??aeiino? i?e iaaieo oiiaao niinoa??aa?oueny iaoai?/ia ??aiiaaaa.
sseui iaiaeii??aei?noue aeineoue aaeeea, oi ??aiiaaaa noa? iano?eeith ?
a ?acoeueoao? c?inoaiiy cao?aiue ?ioaineaieo aaee/ei ci?ith?oueny
eiiaaeoeaiei ?ooii. A aeaeo?io?i?/ieo nenoaiao iiyaa
aeaeo?ia?ae?iaeeiai?/ii? iano?eeino? iiaeeeaa i?e aeinoaoiuei aenieeo
iai?oaao aai no?oiao, eiee aiie ia?aaeuothoue a?aie/i?. Aeaeo?i-o?i?/i?
nenoaie c ??aeeeie iaoae?/ieie aeaeo?iaeaie iiaeooue i?iyaeyoe
iano?ee?noue, coiiaeaio ii?ooaiiyi iaeii??aeiiai ?iciiae?eo iiaa?oiaaiai
iaoyao (aoaeo Ia?aiaii?).

Aenia?eiaioaeueii aoaeo Ia?aiaii? i?iyaey?oueny o iiya? iacae/aeieo
i?e?a aeaeo?e/iiai no?oio ia c?inoath/?e a?ooe? aieueo-aiia?ii? e?eai?.
A aeaeo?io?i?/i?e nenoai? ??aeeee aeaeo?iae-??aeeee aeaeo?ie?o ca
aeiiiiiaith iiaa?oiaaiai iaoyao anoaiiaeth?oueny iiceoeaiee cai?ioi?e
ca’ycie i?ae a?ae?iaeeiai?/iei ?ooii ?ic/eio oa ?ioaineai?noth
aeeooc?eiiai i?ioeano. Iaaaeeeee aeiaaeeiaee ?oo a ia’?i? ciaioo?
oiaueio aeeooc?eiiai oa?o, i?enei?thth/e aeeooc?eiee ia?aiin.
Iiaa?oiaaee aeaeo?io?i?/iee iioaioe?ae c?inoa?, a c iei ? iiaa?oiaaee
iaoya, ui i?eaiaeeoue aei ?ooo iiaa?oi?, yeee ia?aaea?oueny a ia’?i
aeaeo?ie?oo. Oeeee?/iee i?ioean naiii?enei?aiiy aoaeoeaiee, yeui i?e
oeueiio i?eai?/othoueny cao?aiiy, ye? aeeeeeai? iaiaeii??aei?noth
oaiia?aoo?e, aonoeie ?ic/eio ? ye? i?eaiaeyoue aei eiiaaeoe??. Oey
iniaeea?noue iaoai?cio naiii?enei?aiiy iiynith? ?aioiao iiyao ?
cieeiaiiy iiey?ia?ao?/ieo iaeneioi?a no?oio.

Iaeyae e?oa?aoo?ieo aeaieo ii /ania?e naiii?aai?caoe?? aeicaiey?
c?iaeoe ?yae ocaaaeueithth/eo aeniiae?a. A aaaaoueio aeaeo?io?i?/ieo
i?ioeanao, ye? i?iyaeythoue inoeeethth/o iiaaae?ieo, iano?ee?noue
c’yaey?oueny ye ?acoeueoao o?nii? aca?iiae?? o?ainii?oieo ? iiaa?oiaaeo
i?ioean?a, aaaeeeaith e?iaoe/iith oa?aeoa?enoeeith yeeo ? iayai?noue
iaeano? iaaaoeaiiai ?iiaaeaino. Ni?aaaaeeeaei ? oaa?aeaeaiiy, ui naia
e?iaoeea aeaeo?iaeieo aaoa?iaaiieo i?ioean?a iiaea i?eaiaeeoe aei
aeaeo?io?i?/ieo inoeeeyoe?e. Iaeiae nia?aiiy aeaeo?iaeieo i?ioean?a ?c
cae/aeii niia?eueiaieie aeeooc?eieie i?ioeanaie ?noioiuei iieaaoo? iiyao
inoeeeyoe?e oa ?o ianoaa?eueiinoae. Iioiaeaeaiiy iaaaoeaiiai
oa?aaea?anueeiai ?iiaaeaino iiaea aooe ??ciiiai?oiei ? ia aoei
anoaiiaeaii iaeiicia/ii aeey aaaaoueio nenoai. Iaei?ino?oa c oi/ee ci?o
iaoai?cio iiyniaiiy aoei cai?iiiiiaaii aeey eeano nenoai, iacaaiieo
Aieoiae/ai eaoiaeieie inoeeeyoi?aie. A oeeo nenoaiao iaaaoeaiee
?iiaaeain aoa i?eienaiee eoeii?anueeiio a?aeooiaooaaiith aai i?ae
aeaeo?iaeii ? eaoae?caoi?ii, aai i?ae aeaeo?iaeii ? naiith
aeaeo?iaeoeaiith ?a/iaeiith. A eaoiaeieo inoeeeyoi?ao c ?ia?a??oaaiiyi
aeaeo?iaeii? iiaa?oi? iiyaa iaaaoeaiiai ?iiaaeaino iia’ycaia c
aaeni?aoe??th ?ia?aoth/eo i?aai?/ieo ?a/iaei a Oa?aaea?anuee?e iaeano?.
A aiiaeieo i?ioeanao aeaeo?i?ic/eiaiiy iaoae?a oa?aeoa?enoeee
iaaaoeaiiai ?iiaaeaino cae/aeii iia’ycai? c iano?ee?noth ianeaoth/eo
ie?aie. O?ao?e eean ii eeaneo?eaoe?? Aieoiae/a — aiiaei? i?ioeane
ieeneaiiy aiaeith /e i?inoeo i?aai?/ieo niieoe ia ?ia?oieo aeaeo?iaeao.
Ooo aaaeeeaa cia/aiiy a aeanoaa?e?caoe?? nenoaie a?ae?a?a? ianeaaoe?y /e
no?aaeaiiy ?ioa?iaae?ao?a ?aaeoe?? ia aeaeo?iae?. E?oa?aoo?i?
aenia?eiaioaeuei? aeai? ii eieeaaiiyo no?oio oa iioaioe?aeo a ??cieo
aeaeo?io?i?/ieo nenoaiao nenoaiaoeciaaii o oaaeeoeth.

O ae?oaiio ?icae?e? iaaaaeai? ?acoeueoaoe aeine?aeaeaiue inoeeeyoe?e a
aeaeo?io?i?/ieo nenoaiao. Cai?iiiiiaaia iaie iiaeaeue aaco?oueny ia
?aaeueiiio i?eiouaii? i?i iayai?noue ii?yae c iacaeiyoith, aeaio ?ioeo
oei?a eaoiaeii? iiaa?oi?: iaei??? — qa, caeiyoi? aaeni?aiaaiiei
eaoae?caoi?ii A- (aaeiaai?aeii /e aaeiaaiiiae?aiei ?iiii) ? ae?oai? —
qe, ia ye?e eaoae?caoi? ca’ycaiee eiiieaenii c ?iiii a?aeiiaeaii?
?a/iaeie (iai?eeeaae Iaz+).

Aaaaeath/e, ui oaeaeeino? on?o aeaeo?io?i?/ieo ?aaeoe?e ci?iththoueny ca
caeiiii Oaoaey, ui ??aiiaaaa a ?aaeoe?? ooai?aiiy qa anoaiiaeth?oueny
oaeaeei ?, i?eeiath/e iaaeeaeaiiy aeeooc?eiiai oa?o iino?eii? oiaueie,
ie io?eiaee nenoaio c o?ueio ??aiyiue: ??aiyiiy aaeaino aeey iiaa?oi?,
caeiyoi? aaeni?aiaaiei ai?iiii; ??aiyiiy aaeaino ca?yaeo aeey i?ioeano
aeaeo?ie?co oa ??aiyiiy /aniai? aaiethoe?? aeey aeaeo?iaeoeaii? ?a/iaeie
ia iiaa?oi?.

Ie i?iaaee ii iiaeeeaino? aeaoaeueia aeine?aeaeaiiy iiaaae?iee
o?aaeoi??? nenoaie a ieieeoeyo noai?a ??aiiaaae a caeaaeiino? a?ae
cia/aiue ia?aiao??a nenoaie, aecia/eaoe oei noaoe?iia?iiai noaio ? ia
eiai iniia? iiaoaeoaaee ?yae a?oo?eaoe?eieo ae?aa?ai ia ieiuei?
aac?ici??ieo ci?iieo oaeaeeino? u oa iioaioe?aeo v.

Ia ae?aa?ai? (?en.1a)-1d)), yea i?aaenoaaey? ??ci? oeie noaoe?iia?ieo
noai?a ust ye ooieoe?? oaoaeaanueei? iino?eii? eiiieaeniooai?aiiy n
aeaeii, ui nenoaia ciaoiaeeoueny o no?eeiio noaoe?iia?iiio noai? aei
cia/aiiy c<1.4. I?e n=1.4 i?ioiaeeoue a?oo?eaoe?y n?aeei-aocie (SN). Oea icia/a?, ui iai?yiie iaei??? ?c o?aaeoi??e noaio ??aiiaaae ci?ith?oueny ia i?ioeeaaeiee ? no?eeee aocie noa? n?aeeii. No?eeee oieon (ieaeiy a?oea) caeeoa?oueny ? a nenoai? c'yaey?oueny iaeanoue a?noaa?eueiino? (?en.1n)). I?e iiaeaeueoiio ca?eueoai? ia?aiao?o n oey iaeanoue caoaeo?oueny ? cieea?, a i?e iaaiiio eiai cia/aii? c'yaey?oueny noaoe?iia?iee noai oeio n?aeei-oieon c iano?eeith naia?ao?eniith iiaa?oiath. O a?aeiia?aeiino? c oai???th, non?aenoai iaeanoae no?eeino? ? iano?eeino? aeaco? ia ?nioaaiiy a nenoai? ?ica'yceo, i?e yeiio ?aaeueia /anoeia eiiieaenieo cia/aiue noa? ??aiith ioeth, ui ? iaiao?aeiith ? aeinoaoiueith oiiaith iiyae ia??iaee/iiai ?ica'yceo (a?aie/iiai oeeeeo). Ia ?en.2a)-2d) i?aaenoaaeai? ??ci? a?oo?eaoe?ei? ae?aa?aie a caeaaeiino? a?ae eiao?oe??ioa ia?aiino b eaoiaeii? ?aaeoe??. Ca?eueoaiiy “b” aeanoaa?e?co? ?aeeiee no?eeee noaoe?iia?iee noai nenoaie, ?i?oe?thth/e noaoe/io a?oo?eaoe?th aei ??ciiiai?oieo noaoe?iia?ieo noai?a ? iiyae a?noaa?eueiino? a nenoai? (?en.2a)-2n)). Iiaeaeueoee ??no b i?eaiaeeoue aei a?oo?eaoe?? Oiioa (?en.2d)). Iaie i?iaaaeaii /eneiaa ?ioaa?oaaiiy nenoaie ??aiyiue c iaoith i?aeoaa?aeaeaiiy i?aaeeueiino? ?ic?aooie?a, a oaeiae /aniaeo i?io?e?a ci?ie iacaeaaeieo ia?aiao??a u, q ? aonoeie no?oio ?. I?e ?ioaa?oaaii? iaie aeei?enoiaoaaeanue FORTRAN aa?n?y aeai?eoio A??a /eneiaiai ?ioaa?oaaiiy “aei?noeeo” aeeoa?aioe?aeueieo ??aiyiue. Oa?aeoa? /aniai? ci?ie iacaeaaeieo ci?iieo cia?aaeaiee ia ?en.3. sse iaaaaeei cai?oeoe, eieeaaiiy ia aa?iii?/i?. Ia ?en.4a)-4d) iaaaaeai? a?ao?ee caeaaeiino? iniiaieo oa?aeoa?enoee eieeaiiai ?aaeeio a?ae a?aenoai? ia?aiao?a r aei oi/ee a?oo?eaoe?? ra?o. ?c ca?eueoaiiyi oe??? a?aenoai? ia??iae inoeeeyoe?? no?oio iaaea? (?en.4d)), a aiie?ooaea, aeinyaioaoe iaeneioio, a iiaeaeueoiio ciaioo?oueny (?en.4c)). Eiioeaioe?y iaoi? iiaeae? aeaeo?ieaoae?co, aaciaaia ia iayaiino? aeaio oei?a aaeni?aiaaieo ?a/iaei (? a?aeiia?aeii aeaio ??cieo oei?a eieaeueieo iie?eoue), i?eaeaoia aeey iiyniaiiy inoeeeyoe?e no?oio a oiae? aeaeo?ieaoae?oe/iiai a?aeiiaeaiiy ? iaiiaaii ocaiaeaeo?oueny c aenia?eiaioaeueieie aeaieie aeey inoeeeyoi?a (In/SCN), iaoe?ii i?aaenoaaeaieie ? iaaiai?aieie a ?iaio? Eoia?a. O o?aoueiio ?icae?e? iiaeaii aiae?c aeine?aeaeaiiy aieeao niaoeeo?ee aeaeo?iaeii? ?aaeoe?? ? oa?aeoa?enoee aieueoaiia?ii? e?eai? ia a?aieoeth a?ae?iaeeiai?/ii? no?eeino? a aeaeo?io?i?/i?e nenoai? c iaeiei ??aeeei aeaeo?iaeii. Caeiiii??iino? aieeao e?iaoeee oa ciai?oi?o oiia ia iiyao eiiaaeoeaieo no?oeoo? i?aaenoaaeai? ia iaeo?aeueieo e?eaeo (?en. 5). sseui aieueo-aiia?ia e?eaa ia i?noeoue iaaeath/i? ae?eyiee, oi aaee/eia picscalex100010009000003000200000300150000000000050000000b02000000000500 00000c029407be16030000001e000700000016049407be16000000000500000009020000 00000400000002010100050000000102ffffff00040000002e0118000500000031020100 0000050000000c02e006a014050000000b02000000000e00000026060f001200ffffffff 000008000000c0ffaaff60148a060b00000026060f000c004d6174685479706500007001 10000000fb0211fd4e01000000009001000000020002001053796d626f6c000204000000 2d01000008000000320ada05960301000000280010000000fb0213fd4d01000000009001 000000020002001053796d626f6c0002040000002d01010004000000f001000008000000 320ada05d80e01000000290009000000fa02000010000000000000002200040000002d01 00000500000014026b0394030500000013026b03a3120500000014025600d91205000000 13028006d91215000000fb0260fe0000000000009001010000000002001054696d657320 4e657720526f6d616e000082040000002d01020004000000f001010009000000320a0004 33000100000051002b0109000000320a47028a0a010000004900890009000000320a4702 6d0d010000006300b60009000000320aba05f806010000005200fd000a000000320a4a06 f707020000006f6dd0002b0109000000320aba05c70a010000004900890009000000320a ba05aa0d010000004500fd000c000000320aba05980f030000006e464400d000fd002b01 0a000000320a99061e13020000006374b600740010000000fb0260fe0000000000009001 000000020002001053796d626f6c0002040000002d01010004000000f001020009000000 320a00040102010000003d00e40009000000320aba057705010000002d00e40010000000 fb0260fe0000000000009001010000020002001053796d626f6c0002040000002d010200 04000000f001010009000000320a4702fd07010000006e00d80009000000320a4702bf09 01000000b600cb0009000000320a4702a20c01000000b600cb0009000000320aba05fc09 01000000b600cb0009000000320aba05df0c01000000b600cb0015000000fb0260fe0000 000000009001000000000002001054696d6573204e657720526f6d616e00000004000000 2d01010004000000f001020009000000320a2003ff08010000003100d00009000000320a ba054904010000003100d00009000000320a4702af0b010000002f00740009000000320a ba05ec0b010000002f0074000a00000026060f000a00ffffffff01000000000010000000 fb021000080000000000bc02000000cc0102022253797374656d0000040000002d010200 04000000f0010100040000002701ffff03000000000000000000, aea n-eiao?oe??io e?iaiaoe/ii? a'yceino?, ?-no?oi, N-eiioeaio?aoe?y, Rom-ciai?oi?e ii??, A-iai?oaa, n-eiao?oe??io ia?aiino, F-iino?eia Oa?aaeay, D-eiao?oe??aio aeeooc??; aeiaeaoiy ? aeey aeieeiaiiy no?oeoo? iaiao?aeii, uia iiaa?oiaaee iaoya c?inoaa c? ca?eueoaiiyi iioaioe?aeo. Aeey oi?ioaaiiy no?oeoo? ni?eyoeea?oei aeyaey?oueny i?iaaaeaiiy i?ioeano o aaeueaaiinoaoe/ieo oiiaao (Q = 0), ine?eueee ?c ca?eueoaiiyi Q e?eoe/ia /enei Ia?aiaii? c?inoa?. Ae?aiacii no?oi?a, i?e yeeo a nenoai? ?nio? iano?ee?noue, aecia/a?oueny aeaiia oaeoi?aie. Ii-ia?oa, i?e iaaeeaeaii? aei noaio ??aiiaaae ciaioo?oueny noaoe?iia?iee a?aae??io eiioeaio?aoe?? ? i?e aeayeiio e?eoe/iiio cia/aii? no?oio aaee/eia Ian noa? iaioith e?eoe/iiai cia/aiiy. Nenoaia noaa?e?co?oueny. I?e cia/aii? ca?yaeo aeaeo?iaea ~10 ieEe/ni2, oiaueie oa?o aeaeo?ie?oo 1 ni, eiioeaio?aoe?? aeaeo?iaeoeaiiai eiiiiiaioo 10-3 I ? a?aeiioaiiy oiaueie oa?o aeaeo?ie?oo aei oiaueie oa?o aeaeo?iaea h2/h1 a?eueoa 0.01, ciaoiaeeii, ui iano?ee?noue aeieea? oaea i?e aonoeiao no?oio ia ??ai? 10-10 iA/ni2. Ii-ae?oaa, i?e aeinyaiaii? noaio iioaioe?aeo ioeueiaiai ca?yaeo cia/aiiy /enea Ia?aiaii? ii/eia? ciaiooaaoeny. I?eeiath/e, ui oaeaee?noue eaoiaeii? ?aaeoe?? ?noioiuei ia?aaeuo? oaeaee?noue aiiaeii?, io?eio?ii i?e h=1 ni, n0=10-3 I ? no?oiao, aeecueeeo aei a?aie/iiai, ui noaa?e?caoe?y i?ioiaeeoue i?e ca?yaeao iiaa?oi? 10-5 ieEe/ni2. Oaeei /eiii, o aaeueaaiinoaoe/ieo oiiaao iano?ee?noue iiaea ?aae?coaaoeny i?e no?oiao a?ae ioey aei cia/aiue, ui a?aeiia?aeathoue iiey?ecaoe?? i?e iioaioe?ae? ioeueiaiai ca?yaeo. Ca?eueoaiiy eiioeaio?aoe?? oiiiaiai aeaeo?ie?oo a ?ic/ei? aaaea aei cieaeaiiy ii?/iiai iii?o ?, ye iane?aeie, aei ciaioaiiy aaee/eie /enea Ia?aiaii?. I?e iaai?e aeinoaoiuei aaeee?e eiioeaio?aoe?? oiiiaiai aeaeo?ie?oo no?oeoo?e cieeathoue. Ca?eueoaiiy oiaueie oa?o aeaeo?ie?oo oa eiioeaio?aoe?? aeaeo?iaeoeaiiai eiiiiiaioo aaaea aei ca?eueoaiiy ae?aiaciio iioaioe?ae?a no?oeoo?oaaiiy ? ?icoe?aiiy iaeano? oaeeueiaeo /enae, ye? oa?aeoa?ecothoue iano?ee? iiaee. sseui aieueo-aiia?ia oa?aeoa?enoeea ia i?noeoue iaaeath/i? ae?eyiee, oi no?oeoo?e aeieeathoue eeoa i?e aeiaeaoi?o cia/aiiyo /enea Ia?aiaii?. Ine?eueee aeey eaoiaeii? ?aaeoe?? aaee/eia dcco/dz>0, oi aeey Q>0
no?oeoo?e iiaeooue aeieeiooe o?eueee i?e ¶t/¶E<0 (t - iiaa?oiaaee iaoya), oiaoi i?e iioaioe?aeao aeiaeaoiuei? a?oee aeaeo?ieai?ey?ii? e?eai?. Ooai?aiiy no?oeoo? niinoa??aa?oueny i?e oeo i?ioeanao, ??aiiaaaeiee iioaioe?ae yeeo ? iiceoeai?oa iioaioe?aeo ioeueiaiai ca?yaeo, ui ocaiaeaeo?oueny c ?acoeueoaoii, io?eiaiei ?ai?oa aeey aeiaaeeo aaeeeeo aeeaei aeaeo?ie?oa ? ??aeeiai iaoae?/iiai aeaeo?iaea. ?icaeyiooi aeaeo?io?i?/io nenoaio c ??aeeei aeaeo?iaeii, eiee iiaa?oiaaee iaoya caeaaeeoue ia eeoa a?ae iioaioe?aeo, a ? a?ae eiioeaio?aoe??. ?c ciaioaiiyi oiaueie oa?o aeaeo?ie?oo a?aeaoaa?oueny noaa?e?caoe?y nenoaie ca ?aooiie acyceiai oa?oy (Oaae.1). A iaeano? /enoi aeeooc?eii? e?iaoeee nenoaia no?eea a?aeiinii aeanoaa?e?caoe?? aiane?aeie aoaeoo Ia?aiaii?. A iioaioe?inoaoe/iiio ?aaeei? iaiao?aeiith oiiaith iiyae iano?eeino? ? ciaioaiiy iiaa?oiaaiai iaoyao t i?e ca?eueoaii? eiioeaio?aoe?? aeaeo?iaeoeaiiai eiiiiiaioo N1, ui ?aae?co?oueny aeey a?eueoino? aiaeieo ?ic/ei?a nieae. Oaaeeoey 1. Caeaaei?noue e?eoe/ieo /enae Ia?aiaii? Makr a?ae ni?aa?aeiioaiiy i?ae oiaueiaie oa?o aeaeo?ie?oo h2 oa aeaeo?iaeo h1 h2h1kkrMakrAaeueaaiinoaoe/iee ?aaeei 0.1 1.0 5.0 10.02.5 2.0 1.7 1.7917 192 163 163Iioaioe?inoaoe/iee ?aaeei0.1 1.0 5.0 10.03.0 2.3 2.1 2.11447 334 304 304 A aaeueaaiinoaoe/iiio ?aaeei?, ia a?aei?io a?ae iioaioe?inoaoe/iiai. iano?ee?noue iiaea aooe oa?aoa?iith ? aeey ?ic/ei?a nieae c ¶t/¶C1>0.
Iaeiae, i?e oeueiio ??aiiaaaeiee iioaioe?ae iiaeiai aooe iiceoeai?oei ca
iioaioe?ae ioeueiaiai ca?yaeo ?, e??i oiai, ca?yae aeaeo?iaeo i?e
??aiiaaaeiiio iioaioe?ae? iiaeiai ia?aaeuoaaoe iaaia e?eoe/ia cia/aiiy.
Aeanoaa?e?caoe?y ianoa? a iiiaio aeinyaiaiiy ca?yaeii aeaeo?iaeo
e?eoe/iiai cia/aiiy, a ia a ?ioa?aae? aonoeie no?oio a?ae 0 aei ??
cia/aiiy i?e iioaioe?ae? ioeueiaiai ca?yaeo, ye aeacoaaeiny ?ai?oa.
Oaeei /eiii, a?aooaaiiy caeaaeiino? iiaa?oiaaiai iaoyao a?ae
eiioeaio?aoe?? aiineoue ye?ni? ci?ie o iiaaae?ieo aeaeo?io?i?/ii?
eii??ee ye a iioaioe?i- , oae ? a aaeueaaiinoaoe/iiio ?aaeeiao, a oaeiae
a iaeano? /enoi aeeooc?eii? e?iaoeee.

Aea/aii aieea aoaeoo ?aeay ia e?eoe/i? /enea Ia?aiaii? a
aeaeo?io?i?/i?e nenoai? c ??aeeei aeaeo?iaeii. Caeaaei?noue /enea
Ia?aiaii? a?ae /enea ?aeay cia?aaeaia ia ?en.6. Aeua e?eai?
ciaoiaeeoueny iaeanoue iano?eeino?. Ia?aoei e?eai? c a?nyie eii?aeeiao
oa?aeoa?eco? aeiaaeie, eiee a?aenooiy ae?y aeanoaa?e?coth/iai iaoai?cio
?aeay (Rakr=0) aai Ia?aiaii? (Makr=0). A ia?oiio aeiaaeeo e?eoe/ia /enei
Ia?aiaii? aei??aith? Makr=163, a ae?oaiio — e?eoe/ia /enei ?aeay
aei??aith? Rakr=915. O aeiaaeeo oiieeo oa??a aeaeo?ie?oo iaeo?aeueia
e?eaa ia?aoiaeeoue o i?yio, yea ia?aeaeueia in? i?aeeiao. Oiae? a?aieoey
no?eeino? iiacycaia eeoa c aoaeoii Ia?aiaii?.

O iioaioe?inoaoe/iiio ?aaeei? ?c ca?eueoaiiyi Q no?ee?noue
i?aeaeuo?oueny, oiaoi nenoaia a?eueo noaa?eueia, i?ae o
aaeueaaiinoaoe/iiio ?aaeei?. A iaeano? /enoi aeeooc?eii? e?iaoeee (Q®Y)
e?i?y no?eeino? i?ioiaeeoue ia?iaiaeeeoey?ii in? i?aeeiao, oiaoi aoaeo
Ia?aiaii? a?aenooi?e ? iano?ee?noue coiiaeaia eeoa a?aa?oaoe?eiei
iaoai?ciii. Oea iia’ycaii c oei, ui eiee aeeooc?y e?i?oo? aeaeo?iaeiee
i?ioean, ia i?aeoaci?e iiaa?oi? a?aenooi? oeoeooaoe?? eiioeaio?aoe??, a
ine?eueee t=t(c1(0),E), oi a?aenooi? ? cao?aiiy iiaa?oiaaiai iaoyao.
Aoaeo Ia?aiaii? a oeueiio aeiaaeeo a?aenooi?e.

O /aoaa?oiio ?icae?e? aea/aii no?ee?noue iaoai?/ii? ??aiiaaae
aeaeo?io?i?/ii? nenoaie c iino?eieie o?ceei-o?i?/ieie oa?aeoa?enoeeaie
ii a?aeiioaiith aei cao?aiue e?ioeaai? aiie?ooaee.

?icaeyiooi oa?i?/ii iaeii??aeio iaiaaeaio aeaeo?io?i?/io nenoaio
Me|Mez+,Xz-|Me a a?aa?oaoe?eiiio oa aeaeo?e/iiio iieyo, aaaaeath/e, ui
o?ce/i? aeanoeaino? aeaeo?ie?oo noae?, aeoeai? iaoae?/i? iiaa?oi?
aeaeo?iae?a ??aiiaeinooii? i?ae /an aeaeo?ie?co, aeaeo?ie?o iiai?noth
aeenioe?eiaaiee ia ?iie Mez+ i Xz-, iaeo?aeueiee ?ic/eiiee i?aeoe/ii ia
aeenioe?th?.

Ii?iaia? cia/aiiy /enae ?aeay ciaeaeaii eeane/iei aa??aoe?eiei
iaoiaeii. Io?eiaii oae? ?acoeueoaoe.

1. Ia?oa iaaeeaeaiiy:

a) aaeueaaiinoaoe/iee ?aaeei (Rkr)+=1445 ;

a) iioaioe?inoaoe/iee ?aaeei — (Rkr)+= 1555.

2. Ae?oaa iaaeeaeaiiy:

a) aaeueaaiinoaoe/iee ?aaeei — (Rkr)+= 1346.60;

a) iioaioe?inoaoe/iee ?aaeei — (Rkr)+=1496.64.

3. O?ao? iaaeeaeaiiy:

a) aaeueaaiinoaoe/iee ?aaeei — (Rkr)+= 1296.37;

a) iioaioe?inoaoe/iee ?aaeei -( Rkr)+= 1443.56.

4. *aoaa?oa iaaeeaeaiiy:

a) aaeueaaiinoaoe/iee ?aaeei — (Rkr)+= 1296.37;

a) iioaioe?inoaoe/iee ?aaeei — (Rkr)+= 1443.56.

sse aeaeii, ?acoeueoaoe o?aoueiai ? /aoaa?oiai iaaeeaeaiue i?aeoe/ii
ni?aiaaeathoue. Oe? ?acoeueoaoe aeineoue aeecuee? aei aenia?eiaioaeueieo
ye o aaeueaaiinoaoe/ieo — (Rkr)+=1351, oae ? a iioaioe?inoaoe/ieo —
(Rkr)+= 1540 oiiaao (? aeineoue a?ae??ciythoueny a?ae (Rkr)= 1708, yea
ne?aeo? c iiaeae? c eiioeaio?aoe?eieie a?aie/ieie oiiaaie ia?oiai
?iaeo). A?ae?iaeeiai?/i? aeeneiaoeai? no?oeoo?e aiane?aeie
a?aa?oaoe?eii? iano?eeino? aeieeathoue a aeaeo?io?i?/ieo nenoaiao
Me|Mez+,Xz-|Me c noaeeie o?ce/ieie oa?aeoa?enoeeaie i?e iioaioe?aeao ?
a?aeiia?aeieo no?oiao, i?e yeeo e?i?ooth/i? aeeooc?? ua ia
aeinyaa?oueny.

I?iaaaeaii aeine?aeaeaiiy ?icaeiooi? eiiaaeoe??, a oaeiae noaoe?iia?ieo
? ianoaoe?iia?ieo iaaee?eoe/ieo ?oo?a ia iniia? iaoiaeo e?ioeaaeo
??cieoeue. Oe? aeine?aeaeaiiy i?iaaaeai? aeey oe?ieeo ?ioa?aae?a /enae
A?anaioa c iaoith aea/aiiy ?o aieeao ia oae? ?ioaa?aeuei? oa?aeoa?enoeee
iioieo, ye ?iciiae?e aonoeie no?oio acaeiaae aeaeo?iae?a, eiioeaio?aoe??
i?io?e?a ? oi?ie eiiaaeoeaieo no?oeoo?.

?icaeyiooi aeaii??io iiaeaeueio aeaeo?ie?oe/io eii??eo, ui
neeaaea?oueny c ieineiia?aeaeueieo, ai?eciioaeueieo ? ?aeaaeueii
iaiiey?eciaaieo aeaeo?iae?a, ?ici?uaieo a ?ic/ei? a?ia?iiai aeaeo?ie?oo.
Nenoaia e?ioeaaa o aa?oeeaeueiiio (X) ? ai?eciioaeueiiio (Y) iai?yieao ?
iaiaiaaeaia o Z-iai?yieo. ?oo ??aeeie i?ioiaeeoue a XY-ieiuei? ? iio?e
??aeeie a z-iai?yieo a?aenooi?e.

Aeey ?ica’yceo iaoaiaoe/ii? iiaeae? cai?iiiiiaaii? caaea/?
aeei?enoiaoaaee iaoiae e?ioeaaeo ??cieoeue. Ia/eneaiiy i?iaiaeeeenue ii
?oa?aoe?eiiio iaoiaeo Aaonna-Caeaeaey c iiaeaeueoith ieaeiueith
?aeaenaoe??th. O a?aeiia?aeiino? c oeei iaoiaeii, /eneiaee ?ica’ycie ia
/aniaiio e?ioe? n+1 aoa io?eiaiee c ?ica’yceo ia iiia?aaeiueiio /aniaiio
e?ioe? n.

Ia ?en. 7-8 cia?aaeai? eiioeaio?aoe?ei? i?io?e? noaoe?iia?ieo noai?a ?
e?i?y no?oio aeey ??cieo /enae A?anaioa Gr. Aeey iaaaeeeeo cia/aiue Gr
iia?eueiee ?oo neaai aee?eaeth? ?iciiae?e eiioeaio?aoe?? ii aenio?
(?cieiioeaio?aoe ai?eciioaeuei?), ui aeaco? ia ia?aaaao aeeooc?eiiai
iaoai?cio ianiia?aiino.

?c ca?eueoaiiyi /enea Gr ?oo noa? ?ioaineai?oei, e?i?? no?oio
c?inoathoue ca aaee/eiith, ?o oi?ia aeaui ci?ith?oueny ? noa?
iaaeuei?oith. E?i?eiee ?iciiae?e eiioeaio?aoe?? i?ae aeaeo?iaeaie noa?
iae?i?eiei ? ?cie?i?? eiioeaio?aoe?e aee?eaeththoueny o aa?oeeaeueiiio
iai?yieo. Oe? ?acoeueoaoe iieacothoue, ui ?c ca?eueoaiiyi Gr
aeaeo?io?i?/iee i?ioean aaaea aei ci?ie aeeiai?/iiai ?aaeeio ?ic/eio.
?ie?aiaio a?aae??ioo aonoeie ?i?oe?th? ?oo aeaeo?ie?oo ? eiai
oee?eoeyoe?th i?ioe aiaeeiieeiai? no??eee. O oiae? aee?eaeaiiy
ai?eciioaeueiiai noaoe?iia?iiai ?iciiae?eo eiioeaio?aoe?? aeeaae
eiiaaeoeaiiai ia?aiino, o ii??aiyii? c aeeooc?eiei, c?inoa?.

?iciiae?e aonoeie eiioeaio?aoe?eiiai iioieo acaeiaae iiaa?oi?
aiiaea cia?aaeaii ia ?en. 9. Iaiaeiaeiaee ?iciiae?e iioieo (?,
a?aeiia?aeii aeaeo?e/iiai no?oio) ii iiaa?oi? ? ?acoeueoaoii c?inoath/i?
?ioaineaiino? e?oaiai? oee?eoeyoe?? aeaeo?ie?oo a eii??oe?. Ine?eueee
?oo i?ioiaeeoue i?ioe aiaeeiieeiai? no??eee, oi aei i?aai? /anoeie
aiiaeo i?aeoiaeyoue na?ae? ii?oe?? aeaeo?ie?oo c ia’?io, ui ? i?e/eiith
a?eueoi? aonoeie no?oio ii??aiyii c oeie iaeanoyie aeaeo?iaeii? iiaa?oi?
(?ici?uaieie ce?aa), aea a ia’?i ?ooathoueny ca?aei?e? ii?oe?? ?ic/eio.
Aeey nenoai c ??aeeei aeaeo?iaeii, ye a?aei?/aeinue ?ai?oa, oea aaaea
aei iiyae aoaeoo Ia?aiaii?.

AENIIAEE

1. Cai?iiiiiaaia aeeiai?/ia iiaeaeue aeaeo?ieaoae?oe/iiai a?aeiiaeaiiy
iaoae?a, o ye?e aeey a?aooaaiiy aaoa?iaaiieo i?ioean?a ia aeaeo?iae? a
yeino? ci?iieo nenoaie ?icaeyaeathoueny ae?eyiee iiaa?oi?, caeiyo?
aaeni?aiaaiei eaoae?caoi?ii, a oaeiae eiai i?ii?aeiiai eiiieaeno c
a?aeiiaethaaiei ?iiii iaoaeo. Iiaoaeiaaii ae?aa?aie e?i?eii? no?eeino?,
ia yeeo eieae?ciaai? a?oo?eaoe?? oeio n?aeei-aocie ? Oiioa ia ieiuei?
eiio?ieueiaaieo ia?aiao??a. Aecia/aii oi?io ? aiie?ooaeo inoeeeyoe?e o
caeaaeiino? a?ae a?aeaeaeaiiy a?ae e?eoe/ii? oi/ee.

2. Iiaeaeue aeaeo?ieaoae?oe/iiai a?aeiiaeaiiy iineoue caaaeueiee
oa?aeoa?, ine?eueee aiia ia i?ea’ycaia aei iaaiiai iieaeoey?iiai
iaoai?cio, ui eaaeeoue a eiai iniia? ? aeeth/a? aeaiaioa?i? i?ioeane,
oeiia? aeey aeaeo?io?i?/ieo nenoai — aaoa?iaaii? i?ioeane ia i?aeoaci?e
a?aieoe? a noeoiiino? c ianiia?aiinii c ia’?io ?ic/eio.

3. Io?eiaii oiiae iiyae eiiaaeoeaieo no?oeoo? a aeaeo?io?i?/ieo
nenoaiao, ye? i?iyaeythoue aoaeo Ia?aiaii?, o caeaaeiino? a?ae
caeiiii??iinoae e?iaoeee i?ioeano, oiia eiai i?iaaaeaiiy, a oaeiae
ni?aa?aeiioaiiy oiauei oa??a aeaeo?iaeo oa aeaeo?ie?oo. Eieae?ciaaii
iaeano? aeaeo?ieai?ey?ii? e?eai?, aea iiaeeeaa iiyaa eiiaaeoe??.
Iieacaii, ui ae?aiacii iano?eeino? noaoe?iia?ieo noai?a caoaeo?oueny c?
ciaioaiiyi eiioeaio?aoe?? aeaeo?iaeoeaiiai ?iio ? oiaueie oa?o
aeaeo?ie?oo.

4. Aecia/aii e?eoe/i? aaee/eie iiaeeo?eiaaieo /enae Ia?aiaii?, eiee
iaiaeii??aei?noue iiaa?oiaaiai iaoyao coiiaeaia ia o?eueee
iaiaeii??aei?noth aeaeo?iaeiiai iioaioe?aeo, aea e eiioeaio?aoe??.
Iieacaii, ui a?aooaaiiy oe??? caeaaeiino? aiineoue ye?ni? ci?ie o
aeeiai?/io iiaaae?ieo nenoaie ? ii?iaia? cia/aiiy ia?aiao??a iano?eeino?
ii??aiyii ?c aeiaaeeii caeaaeiino? iiaa?oiaaiai iaoyao eeoa a?ae
iioaioe?aeo. Aeine?aeaeaia caeaaei?noue no?eeino? nenoaie ii
a?aeiioaiith aei niaeo?o cao?aiue ??cii? aeiaaeeie oaee? aeey ??cieo
ni?aa?aeiioaiue oiaueie oa??a aeaeo?ie?oo ? ??aeeiai aeaeo?iaeo.

5. Noi?ioeueiaaia caaea/a ? aea/aia ieoaiiy no?eeino? ??aiiaaae ieineiai
ai?eciioaeueiiai oa?o nenoaie ??aeeee aeaeo?iae-??aeeee aeaeo?ie?o c
o?aooaaiiyi ye nee iiaa?oiaaiai iaoyao, oae ? a?aa?oaoe?eieo nee. A
i?eiouaii? iiiioiiiino? cao?aiue aeey noaio iaeo?aeueii? no?eeino?
i?iaaaeaii e?euee?niee aiae?c aeeaaeo aoaeoo ?aeay a iano?ee?noue
Ia?aiaii?. Aecia/ai? aac?ici??i? e?eoe/i? /enea Ia?aiaii? ? ?aeay
aeicaieythoue anoaiiaeoe e?eoe/iee a?aae??io eiioeaio?aoe??, ui
i?eaiaeeoue aei iiyae eiiaaeoe??.

6. A ?aieao eeane/iiai aa??aoe?eiiai i?aeoiaeo aeine?aeaeaii
a?aa?oaoe?eio ianoaa?euei?noue iaoai?/ii? ??aiiaaae a ?cioa?i?/ieo
aeaeo?io?i?/ieo nenoaiao Me|Mez+,Xz-|Me, eiee eiioeaio?aoe?y aeaeo?ie?oo
ia eaoiae? caaeia?eueiy? a?aie/iei oiiaai ia?oiai ?iaeo. ?ic?aoiaaii
e?eoe/i? /enea ?aeay aeey iioaioe?i- oa aaeueaaiinoaoe/iiai ?aaeei?a
aeaeo?ie?co ? iieacaii, ui a iaaeao /aoaa?oiai iaaeeaeaiiy ?o cia/aiiy
iaeaea ia ci?iththoueny ? iaei a?ae??ciythoueny a?ae aenia?eiaioaeueieo.

7. Iaoiaeii e?ioeaaeo ??cieoeue i?iaaaeaii /eneiaa aea/aiiy
noaoe?iia?ieo ? ia?ao?aeieo eiiaaeoeaieo ?oo?a aeaeo?io?i?/ii? nenoaie c
a?aa?oaoe?eiith iano?ee?noth. Aeine?aeaeaii aieea /enae A?anaioa ia
oi?io eiiaaeoeaieo iioie?a, eiioeaio?aoe?eieo i?io?e?a oa aeaye?
?ioaa?aeuei? oa?aeoa?enoeee iioieo (/enei Ionnaeueoa) a?ey iiaa?oi?
aiiaeo. Iieacaii iinooiiao ci?io iaoai?cio ianiia?aiino a?ae
aeeooc?eiiai aei eiiaaeoeaiiai, ?ioaineai?noue yeiai c?inoa? ?c
ca?eueoaiiyi iaaee?eoe/iino?.

INIIAI? ?ACOEUeOAOE ?IAIOE AEEEAAeAII O IOAE?EAOe?ssO

1. Ia/eii?oe A.A., Oo?ao I.I., Yeueao?o E.E. Aeeyiea eeiaoeee e oneiaee
i?iaaaeaiey yeaeo?ioeie/aneie ?aaeoeee ia yooaeo Ia?aiaiie a nenoaia n
aeeaeeei yeaeo?iaeii// Yeaeo?ioeiey.- 1991.- o.27.- N.124-127.

2. Ia/eii?oe A.A., Oo?ao I.I., Yeueao?o E.E. Aiaeec yooaeoa Ia?aiaiie a
nenoaia aeeaeeee yeaeo?iae — ?anoai? yeaeo?ieeoa// V Oe?aeineay
?anioaeeeaineay eiioa?aioeey ii yeaeo?ioeiee. Oacenu aeieeaaeia,
Oaeai?iae, 18-20 naioya?y 1990 a., N.62-63.

3. Aaa’the Ae.I., Ia/eii?oe A.A., Iao?aiei I.?., Oo?ao I.I. Aoaeo
Ia?aiaii? a aeaeo?io?i?/ieo nenoaiao aiane?aeie cao?aiue iioaioe?aeo
aeaeo?iaeo oa eiioeaio?aoe?? aeaeo?ie?oo ia i?aeoaci?e iiaa?oi?// Oe?.
o?i. aeo?iae.- 1997.- o.63.- ?1.- N.28-31.

4. A.I. Eai?aiia, A.A. Ia/eii?oe, O.I. Ie?eiee, I.I. Oo?ao. Aieea
oa?iiaeeooc?? ia a?ae?iaeeiai?/ia aeeneiaoeaia no?oeoo?oaaiiy//
?ioaa?aeuei? ia?aoai?aiiy oa ?o canoinoaaiiy aei e?aeiaeo caaea/.- IAI
Oe?a?ie: ?inoeooo iaoaiaoeee.- 1997.- Aei. 16.- N.127-133.

5. Eai?aiia A.I., Eiiooainueea I.?., Ia/eii?oe A.A., Ie?eiee O.I., Oo?ao
I.I. A?aa?oaoe?eia iano?ee?noue a oa?i?/ii iaeii??aeieo nenoaiao c
eiioeaio?aoe?eiith iiey?ecaoe??th.// ?ioaa?aeuei? ia?aoai?aiiy oa ?o
canoinoaaiiy aei e?aeiaeo caaea/.- IAI Oe?a?ie: ?inoeooo iaoaiaoeee.-
1997.- Aei. 14.- N.115-123.

6. Nechiporuk V.V., Petrenko O.Ye., Korzhik V.P.,Babiuk D.P.,Turash N.N.
Numerical Study of Steady-State Convective Motions and Concentration
Profiles in an Electrochemical Cell with the Benard Type Instability//
Polish J. Chem.- 1997.- V.71.- P.213-220.

7. I.I. Oo?ao, A.A. Ia/eii?oe. Iaonoie/eainoue e inoeeeeyoeee a iiaeaee
yeaeo?ieaoaeeoe/aneiai ainnoaiiaeaiey n o/aoii aiaoiaai nii?ioeaeaiey
oeaie e ianniia?aiina// Aii?inu oeiee e oeie/aneie oaoiieiaee, Niaoe.
auione. Yeaeo?ioeiey.- 1999, ?1.- N.340-342.

AIIOAOe?ss

Oo?ao I.I. *aniaa oa i?inoi?iaa naiii?aai?caoe?y a aeaeo?io?i?/ieo
nenoaiao. ?oeiien. Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy
eaiaeeaeaoa o?i?/ieo iaoe. Niaoe?aeuei?noue 00.02.05 — aeaeo?io?i?y.
?inoeooo caaaeueii? oa iai?aai?/ii? o?i?? ?i. A.?. Aa?iaaenueeiai IAI
Oe?a?ie, Ee?a, 1999.

Cai?iiiiiaaia aeeiai?/ia iiaeaeue aeaeo?ieaoae?oe/iiai a?aeiiaeaiiy
iaoae?a. A oe?e iiaeae? ca ?aooiie aaoa?iaaiieo i?ioean?a ia aeaeo?iae?,
/anoeie iiaa?oi?, iie?eo? aaeni?aiaaiei eaoae?caoi?ii, a oaeiae eiai
eiiieaeno c a?aeiiaeaiei ?iiii iaoaeo, ?icaeyaeathoueny, ye ci?ii?
nenoaie. Iiaoaeiaaia ae?aa?aia no?eeino?. Aecia/ai? oi?ia ? aiie?ooaea
eieeaaiue a caeaaeiino? a?ae a?aenoai? aei e?eoe/ii? oi/ee. Io?eiaii
oiiae ooai?aiiy aeeneiaoeaieo no?oeoo? a aeaeo?io?i?/ieo nenoaiao, ye?
i?iyaeythoue aoaeo Ia?aiaii?. Aea/aii aieea /enea A?anaioa ia oi?io
eiiaaeoeaieo iioie?a, eiioeaio?aoe?ei? i?io?e? oa /enei Ionnaeueoa a?ey
iiaa?oi? aiiaea.

Eeth/ia? neiaa. aeaeo?iae, eieeaaiiy, /aniaa naiii?aai?caoe?y,
aeaeo?io?i?/ia nenoaia, aeeneiaoeai? no?oeoo?e, eiiaaeoe?y, aoaeo
Ia?aiaii?, /enei A?anaioa.

Oo?ao I.I. A?aiaiiay e i?ino?ainoaaiiay naiii?aaiecaoeey a
yeaeo?ioeie/aneeo nenoaiao. ?oeiienue. Aeenna?oaoeey ia nieneaiea o/aiie
noaiaie eaiaeeaeaoa oeie/aneeo iaoe. Niaoeeaeueiinoue 00.02.05 —
yeaeo?ioeiey. Einoeooo iauae e iai?aaie/aneie oeiee ei. A.E.
Aa?iaaeneiai IAI Oe?aeiu, Eeaa, 1999.

I?aaeeiaeaia aeeiaie/aneay iiaeaeue yeaeo?ieaoaeeoe/aneiai
ainnoaiiaeaiey iaoaeia ia aeeaeeii yeaeo?iaea. A yoie iiaeaee ca n/ao
aaoa?iaaiiuo i?ioeannia ia yeaeo?iaea, /anoe iiaa?oiinoe, iie?uoua
aaeni?ae?iaaiiui eaoaeecaoi?ii, a oaeaea aai eiiieaenii n ainnoaiiaeaiui
eiiii iaoaeea, ?anniao?eaathony, eae ia?aiaiiua nenoaiu. Iino?iaiu
aeeaa?aiiu eeiaeiie onoie/eainoe, ia eioi?uo eieaeeciaaiu aeoo?eaoeee
oeia naaeei-ocae e Oiioa. Ii?aaeaeaiu oi?ia e aiieeooaea inoeeeeyoeee a
caaeneiinoe io oaeaeaiey aei e?eoe/aneie oi/ee. Iiaeaeue
yeaeo?ieaoaeeoe/aneiai ainnoaiiaeaiey iineo iauee oa?aeoa?, iineieueeo
iia ia i?eaycaia e ii?aaeaeaiiiio iieaeoey?iiio iaoaiecio, eaaeauaio a
aai iniiaa e aeeth/aao yeaiaioa?iua i?ioeannu, oeie/iua aeey
yeaeo?ioeie/aneeo nenoai — aaoa?iaaiiua i?ioeannu ia iaaeoaciie a?aieoea
a ni/aoaiee n ianniia?aiinii ec iauaia ?anoai?a.

?anniio?aia yeaeo?ioeie/aneay nenoaia, niaea?aeauay iaeei aeeaeeee
yeaeo?iae. Oaeay nenoaia niiniaia i?iyaeyoue iaonoie/eainoue Ia?aiaiie.
Ii?aaeaeaiu oneiaey iiyaeaiey eiiaaeoeaiuo no?oeoo? a caaeneiinoe io
caeiiiia?iinoae eeiaoeee i?ioeanna, oneiaee aai i?iaaaeaiey, a oaeaea
niioiioaiey neiaa yeaeo?iaea e yeaeo?ieeoa. Eieaeeciaaiu iaeanoe
yeaeo?ieaieeey?iie e?eaie, aaea aiciiaeii iiyaeaiea eiiaaeoeee. N
oiaiueoaieai eiioeaio?aoeee yeaeo?iaeoeaiiai eiiiiiaioa e oieueiu neiy
yeaeo?ieeoa iaeanoue iaonoie/eainoe noaoeeiia?iuo ninoiyiee noaeaaony.
Oaaee/aiea eiioeaio?aoeee oiiiaiai yeaeo?ieeoa aaaeao e oiaiueoaieth
aiaoiaai nii?ioeaeaiey e i?e ii?aaeaeaiiie aeinoaoi/ii aieueoie aai
eiioeaio?aoeee no?oeoo?u en/acatho. Ii?aaeaeaiu e?eoe/aneea
iiaeeoeoee?iaaiiua /enea Ia?aiaiie, eiaaea iaiaeii?iaeiinoue
iiaa?oiinoiiai iaoyaeaiey iaoneiaeaia iaiaeii?iaeiinoueth yeaeo?iaeiiai
iioaioeeaea e eiioeaio?aoeee. Iieo/aiiua ?acoeueoaou iicaieytho
caeeth/eoue, /oi o/ao yoie caaeneiinoe aiineo ea/anoaaiiua eciaiaiey a
aeeiaie/aneia iiaaaeaiea nenoaiu e ii?iaiaua cia/aiey ia?aiao?ia
iaonoie/eainoe ii n?aaiaieth ni neo/aai caaeneiinoe iiaa?oiinoiiai
iaoyaeaiey oieueei io iioaioeeaea. Noi?ioee?iaaia caaea/a e eco/aia
onoie/eainoue ?aaiiaaney ieineiai ai?eciioaeueiiai neiy nenoaiu aeeaeeee
yeaeo?iae-aeeaeeee yeaeo?ieeo, iaoneiaeaiiay a?aaeoaoeeiiiui iaoaieciii
?aeay e yooaeoii Ia?aiaiie. Iieo/aiu caaeneiinoe e?eoe/aneeo /enae
Ia?aiaiie io e?eoe/aneeo /enae ?aeay aeey aaeueaaii- e
iioaioeeinoaoe/aneiai ?aaeeiia. A iioaioeeinoaoe/aneii ?aaeeia nenoaia
aieaa onoie/eaa, /ai a aaeueaaiinoaoe/aneii; a iaeanoe /enoi
aeeoooceiiiie eeiaoeee iaonoie/eainoue aiciiaeia oieueei aneaaenoaea
iaoaiecia ?aeay.

Enneaaeiaaii a?aaeoaoeeiiioth ianoaaeeueiinoue iaoaie/aneiai ?aaiiaaney
a ecioa?ie/aneeo yeaeo?ioeie/aneeo nenoaiao Me|Mez+,Xz-|Me, eiaaea
eiioeaio?aoeey yeaeo?ieeoa ia eaoiaea oaeiaeaoai?yao a?aie/iua oneiaey
ia?aiai ?iaea. Eeanne/aneei aa?eaoeeiiiui iaoiaeii ii?aaeaeaiu
e?eoe/aneea /enea ?aeay aeey iioaioeei- e aaeueaaii-noaoe/aneiai
?aaeeiia yeaeo?ieeca e iieacaii, ui i?e /aoaa?oii i?eaeeaeaiee eo
cia/aiey ii/oe ia eciaiythony e iaei ioee/athony io yenia?eiaioaeueiuo.

I?iaaaeaii /eneaiiia eco/aiea noaoeeiia?iuo e ia?aoiaeiuo eiiaaeoeaiuo
aeaeaeaiee yeaeo?ioeie/aneie nenoaiu n a?aaeoaoeeiiiie iaonoie/eainoueth
iaoiaeii eiia/iuo ?aciinoae. Enneaaeiaaii aeeyiea /enae A?anaiooa ia
oi?io eiiaaeoeaiuo iioieia, eiioeaio?aoeeiiiuo i?ioeeae /enei Ionnaeueoa
o iiaa?onoiinoe aiiaea. I?e oaaee/aiea /enae A?anaiooa ianniia?aiin
iinoaiaiii ia?aoiaeeo io aeeoooceiiiiai aei eiiaaeoeaiiai,
eioaineaiinoue eioi?iai ?anoao n oaaee/aieai iaaee?eoe/iinoe.

Eeth/aaua neiaa: yeaeo?iae, eieaaaiey, a?aiaiiay naiii?aaiecaoeey,
yeaeo?ioeie/aneay nenoaia, aeenneiaoeaiua no?oeoo?u, eiiaaeoeey, yooaeo
Ia?aiaiie, /enei A?anaiooa.

Turash N.N. Temporary and Spatial Selforganization in Electrochemical
Systems. Manuscript. Thesis for a scientific degree of Candidate of
Chemical Sciencies. Speciality 00.02.05- electrochemistry.
V.I.Vernadskii Institute of General and Inorganic Chemistry ofUkrainian
National Academy of Science, Kyiv, 1999.

The dymanic model of electrocatalytic reduction of metals is suggested.
In this model for account of heterogeneous processes on the elctrode,
the surface parts covered with adsorbed catalyst and also with its
complex with a reduced metal ion are considered as replaced systems.
The resistance diagram is constructed. The form and the amplitude of
oscillation in relation to the distance of the critical point are
determined. The conditions of advent of spatial dissipative structures
in electrochemical systems are obtained, which display the Marangoni
effect. The influence of the Gragoff number on the form of convectional
flows, concentrational profiles and the Nusselt number near the anode’s
surface have been investigated.

Key words: electrode, oscillation, temporal selforganization,
electrochemical system, dissipative structures, convection, the
Marangoni effect, the Grasgoff number.

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