• No results found

comparison between to versions of the SAFT EOS in the study of PVT and VLE phase behavior of pure polymer melts and binary polymer solutions

N/A
N/A
Protected

Academic year: 2020

Share "comparison between to versions of the SAFT EOS in the study of PVT and VLE phase behavior of pure polymer melts and binary polymer solutions"

Copied!
19
0
0

Loading.... (view fulltext now)

Full text

(1)

&RPSDULVRQ%HWZHHQ7ZR9HUVLRQVRIWKH6$)7(26LQWKH6WXG\

RI397DQG9/(3KDVH%HKDYLRURI3XUH3RO\PHU0HOWVDQG

%LQDU\3RO\PHU6ROXWLRQV

9$VDGL0DOHNVKDK97DJKLNKDQL $5DPD]DQL6$DQG0=DULQHMDG

'HSDUWPHQWRI&KHPLFDODQG3HWUROHXP(QJLQHHULQJ6KDULI8QLYHUVLW\RI7HFKQRORJ\7HKUDQ,UDQ 'HSDUWPHQWRI6FLHQFHDQG7HFKQRORJ\WKH%ULWLVK&RXQFLO7HKUDQ,UDQ

$EVWUDFW

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

.H\ZRUGV6$)7HTXDWLRQRIVWDWHSRO\PHUVROXWLRQ*966$)7

&RUUHVSRQGLQJDXWKRU (PDLOWDJKLNKDQL#VKDULIHGX ,QWURGXFWLRQ

.QRZOHGJH RI SKDVH EHKDYLRU LQ SRO\PHU VROXWLRQV LV FUXFLDO WR WKH SRO\PHU LQGXVWU\ (TXDWLRQV RI VWDWH SOD\ DQ LPSRUWDQW UROH LQ

(2)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R LPSURYH HTXDWLRQV RI VWDWH IRU FKDLQ

PROHFXOHV $V D PDWWHURI IDFW HTXDWLRQV RI VWDWH IRU SRO\PHU VROXWLRQV DUH HLWKHU EDVHG RQ WKH ODWWLFH WKHRU\ RU WKH SHUWXUEDWLRQ WKHRU\$PRQJ WKH ODWWLFHEDVHGPRGHOV WKH )ORU\±2UZROO±9ULM )29 (26 >@ DQG WKH 6DQFKH]/DFRPEH 6/ PRGHO >@ FDQ EH PHQWLRQHG9DULRXVPRGHOVVXFKDV3HUWXUEHG +DUG&KDLQ7KHRU\3+&7>@3HUWXUEHG 6RIW &KDLQ 7KHRU\ 36&7 >@ 3HUWXUEHG $QLVRWURSLF&KDLQ7KHRU\3$&7>@DQG 6WDWLVWLFDO $VVRFLDWLQJ )OXLG 7KHRU\ 6$)7 >@ KDYH EHHQ GHYHORSHG EDVHG RQ WKH SHUWXUEDWLRQWKHRU\6$)7ZDVGHYHORSHGE\ &KDSPDQHWDO>@EDVHGRQWKH:HUWKHLP ILUVWRUGHU SHUWXUEDWLRQ WKHRU\ >±@ IRU DVVRFLDWLQJDQGQRQDVVRFLDWLQJIOXLGV6$)7 (26LVDVXFFHVVIXOHTXDWLRQRIVWDWHDQGLWV GLIIHUHQW YHUVLRQV KDYH EHHQ HPSOR\HG E\ PDQ\UHVHDUFKHUVWRVWXG\WKHSKDVHEHKDYLRU RISRO\PHUVROXWLRQV1XPHURXVDSSOLFDWLRQV RIWKH6$)7HTXDWLRQRIVWDWHWRWKHSRO\PHU VROXWLRQV KDYH EHHQ PDGH VLQFH WKH HDUO\ ZRUN RI &KHQ DQG 5DGRV] >@ 0DQ\ DWWHPSWV KDYH EHHQ PDGH WR GHYHORS WKH 6$)7EDVHGHTXDWLRQRIVWDWHLQRUGHUWRZHOO GHVFULEH WKH SKDVH EHKDYLRU RI FRPSOH[ PL[WXUHV$PRQJWKHPWKH3&6$)7>@ 6$)795 >@ 6RIW6$)7 >@ &URVVRYHU 6$)7 >±@ 6$)7%$&. >@ 6$)7 :&$ >@ 6$)702= >@ DQG WKH &URVVRYHU6$)7%$&.>@FDQEHQDPHG 7KH PDLQ GLIIHUHQFHV EHWZHHQ GLIIHUHQW YHUVLRQV RI WKH 6$)7 PRGHO VWHP IURP WKH IDFW WKDW KRZ WKH VHJPHQW DQG WKH FKDLQ FRQWULEXWLRQV WR WKH UHVLGXDO +HOPKROW] IUHH HQHUJ\ FDQ EH HVWLPDWHG ,W VKRXOG EH VWDWHG WKDWWKHQXPEHURIVHJPHQWVSHUPROHFXOHP WKH VHJPHQW PRODU YROXPH ’ DQG WHPSHUDWXUHLQGHSHQGHQWGHSWKRIVTXDUHZHOO SRWHQWLDO ZKLFK FKDUDFWHUL]HV WKH VHJPHQW± VHJPHQW LQWHUDFWLRQV X DUH WKUHH HVVHQWLDO DGMXVWDEOH SDUDPHWHUV RI WKH 6$)7EDVHG HTXDWLRQV RI VWDWH IRU SXUH QRQDVVRFLDWLQJ IOXLGV >±@ )RU DVVRFLDWLQJ FRPSRXQGV WKHUH DUH WZR DGGLWLRQDO SDUDPHWHUV WKH DVVRFLDWLRQ HQHUJ\0$% DQG WKH DVVRFLDWLRQ

YROXPHN$%FKDUDFWHUL]LQJVSHFLILFLQWHUDFW WLRQ EHWZHHQ DVVRFLDWLRQ VLWHV RQ HDFK PROHFXOH>±@

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

7KHRU\

7KH6$)7EDVHGHTXDWLRQVRIVWDWHFRQVLGHU DW OHDVW IRXU PDMRU FRQWULEXWLRQV LQWR WKH UHVLGXDO+HOPKROW]IUHHHQHUJ\RIDV\VWHPDV IROORZV>@

DVVRF FKDLQ

GLVS KV

UHV D D D D

D

7KHWHUPVLQWURGXFHGLQHTXDWLRQIRUWKH VLPSOLILHG YHUVLRQ RI WKH 6$)7 66$)7 >@ DUH EULHIO\ H[SUHVVHG DFFRUGLQJ WR WKH IROORZLQJHTXDWLRQV

KV

P 57 D

K K K

ZKHUH LV WKH UHGXFHG GHQVLW\ DQG FDQ EH ZULWWHQDV

PG 1

$9U S

K

(3)

GHQVLW\ WHPSHUDWXUHGHSHQGHQW GLDPHWHU IRU WKHVHJPHQWVDQGWKH$YRJDGURQXPEHUUHV SHFWLYHO\ 7KH WHPSHUDWXUHGHSHQGHQW GLDP HWHU RI VHJPHQWV G FDQ EH H[SUHVVHG DFFRUGLQJWRWKHIROORZLQJUHODWLRQ>@ @@ N7 X H[S> & > 1 G $9 » » ¼ º « « ¬ ª Xf

7KH GLVSHUVLRQ FRQWULEXWLRQ WDNHV WKH IROORZLQJIRUP DV < /Q P= 57 D V V 0 GLVS Q Q Q ZLWK N7 X H[S < ZKHUHXLVWKHGHSWK RIVTXDUHZHOOSRWHQWLDO DQG FDQ EH FRQVLGHUHG WR EH WHPSHUDWXUH GHSHQGHQWDVIROORZV>@ @ N7 H > X X ,QHTXDWLRQHNLVVHWWREH±>@ 7KH FKDLQ DQG DVVRFLDWLRQFRQWULEXWLRQVLQWR WKH UHVLGXDO +HOPKROW] HQHUJ\ FDQ EH UHVSHFWLYHO\H[SUHVVHGDV G J /Q P 57

DFKDLQ KV

ZKHUH JKV G LV WKH UDGLDO GLVWULEXWLRQ

IXQFWLRQ5')DQGLVGHILQHGDVIROORZV K P KV ] G KV J

7KH DVVRFLDWLRQ WHUP LQ HTXDWLRQ FDQ EH ZULWWHQDFFRUGLQJWRWKHIROORZLQJHTXDWLRQ

¦

$ $ $ DVVRF 0 @ ; /Q; > 57 D

7KH 66$)7 HTXDWLRQ RI VWDWH FDQ EH H[WHQGHG WR WKH PL[WXUH RI KDUG VSKHUHV DFFRUGLQJWRWKHIROORZLQJUHODWLRQVIRUKDUG VSKHUH DQG GLVSHUVLRQ FRQWULEXWLRQV RI WKH UHVLGXDO+HOPKROW]IUHHHQHUJ\>@ $9 KV OQ @ > > 1 57 D K K K K K K K K K K K K K U S :KHUH

¦

U S K L N LL L L $9

N [ P G

1 N ZLWK G G

GLM L M

(4)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R

¦¦

' U M % % $ % M $9 $ M M L M

L > 1 [ ; @

; ZKHUH

¦

L L L

P [ P

¦¦

¦¦

Q

L M L M L M

L M LM

LM M L M L $9 P P [ [ @ N7 X >H[S G P P [ [ 1 < M L LM LM N X X

X

NLMLQ HTXDWLRQ LV WKH ELQDU\ LQWHUDFWLRQ SDUDPHWHU IRU HQHUJ\ SDUDPHWHU RI VTXDUH ZHOO SRWHQWLDO ,Q WKH VDPH ZD\ WKH ELQDU\ SDUDPHWHU OLM FDQ EH LQWURGXFHG LQWR WKH VHJPHQWQXPEHUDVIROORZV

¦¦

L M L M LM P [ [ P ZLWK O P P

P L M LM

LM

,W VKRXOG EH VWDWHG WKDW NLMDQG OLM DUH WZR DGMXVWDEOHSDUDPHWHUVDQGFDQEHREWDLQHGE\ ILWWLQJ WKH 6$)7EDVHG HTXDWLRQV RI VWDWH WR WKH9DSRU/LTXLG(TXLOLEULXP9/(GDWDIRU WKH SRO\PHU VROXWLRQV $OVR WKH FKDLQ DQG DVVRFLDWLRQ SDUWV RI WKH UHVLGXDO +HOPKROW] IUHH HQHUJ\ IRU WKH PL[WXUH RI KDUG VSKHUHV FDQEHZULWWHQDV

¦

L LL KV LL L L FKDLQ G J OQ P [ 57 D

ZKHUH JLLKVGLL LV WKH 5') DW FRQWDFW YDOXH EHWZHHQ WZR OLNH VHJPHQWV DQG LV JLYHQ EDVHGRQWKHIROORZLQJH[SUHVVLRQ MM LL MM LL MM LL MM LL LM KV

LM G G @

G G > G G G G G J K K K K K

7KH DVVRFLDWLRQ WHUP SURSRVHG E\ &KDSPDQ HWDO>@LVSUHVHQWHGDVIROORZV

¦ ¦

» ¼ º « ¬ ª » ¼ º « ¬ ª L $ L $ $ L DVVRF L L L 0 ; ; OQ [ 57 D

ZKHUH ;$L LV D PROH IUDFWLRQ RI HDFK DVVRFLDWLRQ VLWH RQ PROHFXOH L ZKLFK LV QRW ERQGHGDQGUHQGHUHGDVIROORZV

,Q HTXDWLRQ û$

L%M LV WKH DVVRFLDWLRQ VWUHQJWKEHWZHHQWZRVLWHVRI$DQG%DQGLV JLYHQDV M L M L M

L $%

LM % $ LM KV LM %

$ J G >H[SH N7@G N '

(5)

SRO\PHU EDFNERQH +RZHYHU LW LV DVVXPHG WKDW RQO\ WKH K\GUR[\ HQGJURXS LV FRQVLGHUHGDVDQDVVRFLDWLQJIDFWRURQD3(* PROHFXOH >@ 5HFHQWO\ DQRWKHU YHUVLRQ RI WKH 6$)7EDVHG HTXDWLRQ RI VWDWH WKH *9 66$)7 KDV EHHQ SURSRVHG E\ $VDGL HW DO >@,QWKH*966$)7HTXDWLRQRIVWDWHWKH KDUG VSKHUH FRPSUHVVLELOLW\ IDFWRU FDQ EH H[SUHVVHGDFFRUGLQJWRWKHIROORZLQJUHODWLRQ >@ P ] KV [ [ [ [ [ [ [ [ ZLWK W K [ DQG S W

ZKHUH DQG2 DUHWKHQRUPDOL]HGDQGFORVH SDFNHGUHGXFHGGHQVLWLHVUHVSHFWLYHO\

7KH KDUG VSKHUH +HOPKROW] IUHH HQHUJ\ FRUUHVSRQGLQJ WR ]KV FDQ EH REWDLQHG XVLQJ WKHIROORZLQJUHODWLRQ K K K U U U

³

³

U] G K] G 57 D KV KV KV 7KHUHIRUHXVLQJWKH*966$)7HTXDWLRQRI VWDWHWKHKDUGVSKHUH+HOPKROW]IUHHHQHUJ\ IRUPL[WXUHVFDQEHZULWWHQDVIROORZV >@ @ < < . < . > P

DKVPL[

ZKHUH< DQG < DUHGLPHQVLRQOHVVYROXPH LQGHSHQGHQW JURXSV JLYHQ E\ WKH IROORZLQJ UHODWLRQV < [ [ [ [ < [ [ [

,Q WKH DERYH HTXDWLRQVL LV WKH QRUPDOL]HG IRUPRILDQGSUHVHQWHGDV

W K

[ L

L

DQG .DQG . DUH JLYHQ E\ WKH IROORZLQJ UHODWLRQV OQ . [ [ [ [ [ [ [ [ OQ . [ [ [ [ [ [ [ [ [

(6)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R DQG WZR DGGLWLRQDO SDUDPHWHUV N$% DQG0$%

IRU DVVRFLDWLQJ IOXLGV 7KHVH SDUDPHWHUV FDQ EH REWDLQHG E\ ILWWLQJ WKH 6$)7EDVHG HTXDWLRQV RI VWDWH WR WKH 397 H[SHULPHQWDO GDWD RI SXUH SRO\PHU PHOWV VWXGLHG LQ WKLV ZRUN,QRUGHUWRILQGWKHUHJUHVVHGYDOXHVIRU WKHSDUDPHWHUVRIWKH6$)7EDVHGHTXDWLRQV RIVWDWHWKHIROORZLQJREMHFWLYHIXQFWLRQZDV XVHG>@ H[S FDO 3 3 ) 2

ZKHUH VXSHUVFULSWV FDO DQG H[S UHVSHFWLYHO\ VWDQG IRU WKH FDOFXODWHG DQG H[SHULPHQWDO YDSRU SUHVVXUH IRU WKH SRO\PHU V\VWHPV VWXGLHG LQ WKLV ZRUN ,W LV ZRUWK PHQWLRQLQJ WKDWWKHVDPHH[SHULPHQWDOGDWDDQGWKHVDPH PLQLPL]DWLRQ SURFHGXUH ZHUH XVHG IRU ERWK HTXDWLRQVRIVWDWHVWXGLHGLQWKLVZRUN

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

VROYHQW V\VWHP DQG VXEVFULSWV DQG UHVSHFWLYHO\ VWDQG IRU VROYHQW DQG SRO\PHU PROHFXOHVLQDSRO\PHU± VROYHQWPL[WXUH ,Q RUGHU WR FRQYHUW WKH SRO\PHU VHJPHQW IUDFWLRQ WR WKDW RI WKH PROH IUDFWLRQ WKH IROORZLQJUHODWLRQFDQEHXVHG Z P Z P P Z P [

f f f

f X X X X

ZKHUHPLVWKHVHJPHQWQXPEHUDQG’LVWKH

FORVHSDFNHG PRODU YROXPH RI HDFK FRPSRQHQW LQ D SRO\PHUVROYHQW PL[WXUH *RLQJWKURXJKHTXDWLRQLWFDQEHIRXQG RXW WKDW LQ RUGHU WR FRQYHUW WKH SRO\PHU VHJPHQWIUDFWLRQWRWKDWRIWKHPROHIUDFWLRQ WKH YDQ GHU :DDOV YROXPHV RI KDUG VSKHUHV IRU ERWK VROYHQW DQG SRO\PHU PROHFXOHV DUH UHTXLUHG 7KLV SDUDPHWHU FDQ EH REWDLQHG XVLQJ WKH GDWD UHSRUWHG E\ %RQGL >@ RU XVLQJ WKH SDUDPHWHUV REWDLQHG IURP WKH 6$)7EDVHGHTXDWLRQV RI VWDWH7KH YDQGHU :DDOV YROXPH IRU HDFK FRPSRQHQW LQ VROXWLRQ LV WR EH FRQVLGHUHG DV P’

7KHUHIRUHZLWKRXWFRQVLGHULQJDQ\DGGLWLRQDO SDUDPHWHU WKH VHJPHQW IUDFWLRQ LV VWUDLJKWIRUZDUGO\ FRQYHUWHG WR D ZHLJKW IUDFWLRQ XVLQJ WKH SDUDPHWHUV REWDLQHG IURP HDFKHTXDWLRQRIVWDWH

5HVXOWVDQGGLVFXVVLRQ

(7)

HTXDWLRQV RI VWDWH WKH VDPH H[SHULPHQWDO GDWD DQG PLQLPL]DWLRQSURFHGXUHZHUHXVHG $VFDQEHVHHQIURP7DEOHVDQGIRUQRQ DVVRFLDWLQJ SRO\PHU PHOWV WKH YDOXHV IRU WKUHHDGMXVWDEOHSDUDPHWHUVZHUHH[FOXVLYHO\ UHSRUWHG ZKLOH LQ FDVH RI DVVRFLDWLQJ SXUH

SRO\PHU PHOWV LH 3(* WKH QXPEHU RI DGMXVWDEOHSDUDPHWHUVUHSRUWHGZDVLQFUHDVHG WR ILYH $V PHQWLRQHG EHIRUH DVVRFLDWLRQ HQHUJ\ DQG DVVRFLDWLRQ YROXPH DUH WZR DGGLWLRQDOSDUDPHWHUVIRUWKHVHV\VWHPV

7DEOH7KHUHJUHVVHGYDOXHVRIWKHVHJPHQWSDUDPHWHUVRIWKH66$)7HTXDWLRQRIVWDWH REWDLQHGIRUDQXPEHURISXUHSRO\PHUPHOWV

SRO\PHU P ’ XN N$% 0$%N 0

Q

+'3(

+0'6

/'3(

3'06

3'06

3'06

3'06

3'06

3'06

3'06

3'06

36

37

39$&

3,%

33*

300$

39&

15

1\ORQ

3$5

3(*

3(*D

(8)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9YRO1R 7DEOH7KHUHJUHVVHGYDOXHVIRUWKHVHJPHQWSDUDPHWHUVRIWKH*966$)7HTXDWLRQRIVWDWH

REWDLQHGIRUDQXPEHURISXUHSRO\PHUPHOWV

SRO\PHU P ’ XN N$% 0$%N 0

Q

+'3(

+0'6

/'3(

3'06

3'06

3'06

3'06

3'06

3'06

3'06

3'06

36

37

39$&

3,%

33*

300$

39&

15

1\ORQ

3$5

3(*

3(*D

(9)

7DEOHJLYHVWKHUHVXOWVRIWKH6$)7EDVHG HTXDWLRQV RI VWDWH LH WKH *966$)7 DQG WKH 66$)7 (26 DORQJ ZLWK WKH SHUFHQW RI $EVROXWH $YHUDJH 5HODWLYH 'HYLDWLRQ $$5' IURP WKH H[SHULPHQWDO GDWD RI OLTXLG GHQVLW\ RYHU D ZLGH UDQJH RI

WHPSHUDWXUH IRU YDULRXV SXUH SRO\PHU PHOWV $V VKRZQ LQ 7DEOH ERWK WKH *966$)7 DQG WKH 66$)7 HTXDWLRQV RI VWDWH FDQ DFFXUDWHO\FRUUHODWHWKHH[SHULPHQWDOGDWDIRU OLTXLGGHQVLW\RISXUHSRO\PHUPHOWV

7DEOH7KHUHVXOWVIRUSRO\PHUGHQVLW\DORQJZLWKWKHSHUFHQWRI$$5'IURPH[SHULPHQWDO GDWDREWDLQHGXVLQJWKH66$)7DQG WKH*966$)7

D $VVRFLDWLRQLQWHUDFWLRQLVFRQVLGHUHGLQWKLVFDVH

¦

U U U 1

L H[S L H[S

FDO

(10)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R )LJXUHV DQG VKRZ WKH YDULDWLRQ RI WKH

VHJPHQW QXPEHU RI 3'06 YHUVXV QXPEHU DYHUDJHPROHFXODUZHLJKWRI3'06REWDLQHG IURP WKH 66$)7 DQG WKH *966$)7 UHVSHFWLYHO\$V FDQ EHREVHUYHGIURPWKHVH ILJXUHVWKHVHJPHQWQXPEHURIWKHSRO\PHU 3'06LVOLQHDUO\GHSHQGHQWXSRQPROHFXODU ZHLJKW 7KHUHIRUH WKH VHJPHQW QXPEHU IRU 3'06FDQEHIRXQGDWWKHKLJKHUPROHFXODU

ZHLJKW 7KH OLQHDU UHODWLRQVKLS EHWZHHQ VHJPHQW QXPEHU DQG PROHFXODU ZHLJKW REWDLQHG IURP WKH 66$)7 HTXDWLRQ RI VWDWH IRU3'06FDQEHJLYHQE\

P 0Q

)LJXUH 9DULDWLRQ RIWKHVHJPHQW QXPEHU ZLWK QXPEHU DYHUDJH PROHFXODU ZHLJKW IRU 3'06REWDLQHGIURP WKH 66$)7HTXDWLRQRIVWDWH

(11)

ZKHUH P DQG 0Q DUH VHJPHQW QXPEHU DQG

QXPEHU DYHUDJH PROHFXODU ZHLJKW UHV SHFWLYHO\ ,Q FDVH RI WKH *966$)7 WKH OLQHDUGHSHQGHQF\RIVHJPHQWQXPEHURQWKH QXPEHU DYHUDJH PROHFXODU ZHLJKW FDQ EH H[SUHVVHG DFFRUGLQJ WR WKH IROORZLQJ UHODWLRQ

P 0Q

)LJXUHV DQG UHSUHVHQW WKH YDULDWLRQ RI VSHFLILF YROXPH RI 3'06 ZLWK 0Q

YHUVXV WHPSHUDWXUH DW GLIIHUHQW SUHVVXUHV REWDLQHG XVLQJ WKH 66$)7 DQG WKH *9 66$)7 HTXDWLRQV RI VWDWH UHVSHFWLYHO\ *RLQJ WKURXJKWKHVH WZR ILJXUHV WKHUHVXOWV RI ERWK HTXDWLRQV RI VWDWH DUH LQ JRRG DJUHHPHQW ZLWK WKH FRUUHVSRQGLQJ H[SHULPHQWDOGDWD

)LJXUH9DULDWLRQRIWKHVSHFLILFYROXPHRI3'060Q YHUVXVWHPSHUDWXUHDWGLIIHUHQWSUHVVXUHREWDLQHG

IURPWKH66$)7HTXDWLRQRIVWDWH

7DEOHSUHVHQWVWKHUHVXOWVRIWKH9/(VWXG\ IRU D QXPEHU RI DVVRFLDWLQJ DQG QRQ DVVRFLDWLQJ SRO\PHUVROYHQW PL[WXUHV RYHU D ZLGH UDQJH RI WHPSHUDWXUH DORQJ ZLWK WKH SHUFHQW RI 5RRW 0HDQ 6TXDUH 'HYLDWLRQ 506' $V FDQ EH VHHQ IURP 7DEOH WKH ELQDU\ LQWHUDFWLRQ SDUDPHWHU NLM LV FRQ

VLGHUHG WR EH WHPSHUDWXUH GHSHQGHQW LQ WZR

6$)7EDVHGHTXDWLRQVRIVWDWHVWXGLHGLQWKLV ZRUN

7DEOHVKRZVWKHOLQHDUGHSHQGHQF\EHWZHHQ ELQDU\LQWHUDFWLRQSDUDPHWHUDQGWHPSHUDWXUH IRU WZR SRO\PHUVROYHQW PL[WXUHV XQGHU VWXG\DV

(12)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R

)LJXUH9DULDWLRQRIWKHVSHFLILFYROXPHRI3'060Q YHUVXVWHPSHUDWXUHDWGLIIHUHQWSUHVVXUHREWDLQHG IURPWKH*966$)7HTXDWLRQRIVWDWH

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

7DEOHJLYHVWKHVHJPHQWQXPEHUVHJPHQW PRODUYROXPHDQG WHPSHUDWXUHLQGHSHQGHQW GHSWKRIVTXDUHZHOOSRWHQWLDOIRUDQXPEHU RI VROYHQWV LQWKHSRO\PHUVROYHQWPL[WXUHV VWXGLHG XVLQJ ERWK WKH 66$)7 DQG *9 66$)7 HTXDWLRQV RI VWDWH DW WKH VSHFLILHG UDQJHRIWHPSHUDWXUHV,WVKRXOGEHVWUHVVHG WKDWWKHSDUDPHWHUVUHSRUWHGLQ7DEOHZHUH GLUHFWO\ XVHGLQ WKH 9/(VWXG\RISRO\PHU

VROYHQWPL[WXUHV

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

(13)

1 3 3 506'

1 L

FDO L H[S L ¦

7DEOH 7KHELQDU\LQWHUDFWLRQSDUDPHWHUVDORQJZLWKWKHSHUFHQWRI5RRW0HDQ6TXDUH'HYLDWLRQ506'IURP H[SHULPHQWDOGDWD>@REWDLQHGIURPWKH66$)7DQGWKH*966$)7HTXDWLRQVRIVWDWHIRUWKHSRO\PHUVROXWLRQV

33*KH[DQH

300$

WROXHQH 39&WROXHQH 15WROXHQH RYHUDOOHUURU

(14)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R

7DEOH5HJUHVVHGYDOXHVIRUWKHSDUDPHWHUVXVHGLQHTXDWLRQ IRUWKHV\VWHPVVWXGLHGLQWKLV ZRUNDQGREWDLQHGIURPERWKWKH66$)7DQGWKH*966$)7HTXDWLRQVRIVWDWH

PRGHO V\VWHP $ %

36EHQ]HQH

66$)7

33*F

36EHQ]HQH

*966$)7

33*F

7DEOH 3DUDPHWHUVRIWKH66$)7DQGWKH*966$)7HTXDWLRQVRIVWDWHIRUDQXPEHURIVROYHQWVVWXGLHGLQWKLV ZRUN>@

66$)7 *966$)7

&RPS

P ’ XN P ’ XN 7U

KH[DQH

QRQDQH

EHQ]HQH

WROXHQH

(15)

)LJXUH9DULDWLRQRIPROHIUDFWLRQRI3(*ERQGHGDWVLWH$ZLWKZHLJKWIUDFWLRQRI3(*DWGLIIHUHQWPROHFXODU ZHLJKWVRI3(*DQGDW.LQ3(*WROXHQHV\VWHPXVLQJWKH66$)7HTXDWLRQRIVWDWH

)LJXUH9DULDWLRQRIPROHIUDFWLRQRI3(*ERQGHGDWVLWH$ZLWKZHLJKWIUDFWLRQRI3(*DWGLIIHUHQWPROHFXODU

(16)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R PL[WXUHV RQH PRUH ELQDU\ LQWHUDFWLRQ

SDUDPHWHUZDVDGGHGWRWKHVHJPHQWQXPEHU RI SRO\PHU DQG VROYHQW PROHFXOHV 7KLV SDUDPHWHU LQ IDFW FRQVLGHUV D GHSHQGHQF\ IRUKDUGVSKHUHVHJPHQWQXPEHURQGLIIHUHQW W\SHVRIPROHFXODULQWHUDFWLRQVLQDSRO\PHU VROYHQWPL[WXUH7KHUHVXOWVDUHSUHVHQWHGLQ 7DEOH IRU D QXPEHU RI SRO\PHU VROYHQW PL[WXUHV$VFDQEHLQIHUUHGIURP7DEOHE\ DGGLQJ DQ DGMXVWDEOH ELQDU\ LQWHUDFWLRQ SDUDPHWHU WKH UHVXOWV REWDLQHG IURP WZR 6$)7 EDVHG HTXDWLRQV RI VWDWH DUH PXFK PRUHLPSURYHG

7DEOH UHSUHVHQWV WKH UHVXOWV RI VDWXUDWLRQ SUHVVXUH IRU WKH V\VWHP RI 3(* ZLWK GLIIHUHQW PROHFXODU ZHLJKW DQG WROXHQH DW . REWDLQHG IURP WZR 6$)7EDVHG HTXDWLRQV RI VWDWH VWXGLHG LQ WKLV ZRUN $ FDUHIXO VWXG\ RI 7DEOH LQGLFDWHV WKDW

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

7DEOH 7KH ELQDU\ LQWHUDFWLRQ SDUDPHWHUV DORQJ ZLWK WKH SHUFHQW RI 5RRW 0HDQ 6TXDUH

'HYLDWLRQ506'IURPH[SHULPHQWDOGDWD>@REWDLQHGIURPWKH66$)7DQGWKH*966$)7 HTXDWLRQVRIVWDWHIRUWKHSRO\PHUVROXWLRQV

1 3 3 506'

1

L

(17)

7DEOH7KH HIIHFWRIWKHDVVRFLDWLRQVLWHVLWHLQWHUDFWLRQIRU3(*PROHFXOHRQWKHYDSRUSUHVVXUHREWDLQHGIURP ERWKWKH66$)7DQGWKH*966$)7HTXDWLRQVRIVWDWH

&RQFOXVLRQ

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

RIVWDWHPRUHFRPSOLFDWHGWKHUHVXOWVFDQQRW EHPXFKLQIOXHQFHGE\VXFKFRPSOH[LW\7KH UHVXOWV VKRZHG WKDW WKH *966$)7 (26 VLPLODU WR WKH 66$)7 FDQ EH XVHG WR VWXG\ WKH SKDVH EHKDYLRU RI DVVRFLDWLQJ DQG QRQ DVVRFLDWLQJPL[WXUHV6LQFHWKHSHUIRUPDQFH RI WKH *96$)7LVRQO\DVJRRGDVWKDWRI WKH RULJLQDO 66$)7 WKH DGGHG YDOXH IRU SUDFWLFDO DSSOLFDWLRQV PD\ QRW EH VXIILFLHQW WR MXVWLI\ WKH JUHDWHU DOJHEUDLF DQG FRPSXWDWLRQDOFRPSOH[LW\

5HIHUHQFHV

)ORU\ 3 - 2UZROO 5 $ 9ULM $ 6WDWLVWLFDO 7KHUPRG\QDPLFV RI &KDLQ 0ROHFXOH /LTXLGV,$Q (TXDWLRQRI6WDWH

IRU 1RUPDO 3DUDIILQ +\GURFDUERQV - $P

&KHP6RF

6DQFKH],&/DFRPEH5+(OHPHQWDU\ 0ROHFXODU 7KHRU\ RI &ODVVLFDO )OXLGV 3XUH

)OXLGV-3K\V&KHP

%HUHW6 3UDXVQLW] -03HUWXUEHG+DUG &KDLQ 7KHRU\ $Q (TXDWLRQ RI 6WDWH IRU )OXLGV &RQWDLQLQJ 6PDOO RU /DUJH

0ROHFXOHV$,&K(-

'RQRKXH0' 3UDXVQLW] -0 3HUWXUEHG +DUG&KDLQ 7KHRU\ IRU )OXLG 0L[WXUHV 7KHUPRG\QDPLF 3URSHUWLHV IRU 0L[WXUHV LQ 1DWXUDO *DV DQG 3HWUROHXP 7HFKQRORJ\

(18)

,UDQLDQ-RXUQDORI&KHPLFDO(QJLQHHULQJ9RO1R 0RUULV : 2 9LPDOFKDQG 3 'RQRKXH

0 ' 7KH 3HUWXUEHG6RIW&KDLQ 7KHRU\ $Q (TXDWLRQ RI 6WDWH %DVHG RQ 7KH

/HQQDUG-RQHV 3RWHQWLDO )OXLG 3KDVH

(TXLOLE

9LPDOFKDQG 3 'RQRKXH 0 ' 7KHU PRG\QDPLFV RI 4XDGUXSRODU 0ROHFXOHV 7KH 3HUWXUEHG$QLVRWURSLF &KDLQ 7KHRU\

,QG (QJ &KHP )XQGDPHQWDOV

9LPDOFKDQG 3 &HOPLQV , 'RQRKXH 0 ' 9/( &DOFXODWLRQV IRU 0L[WXUHV &RQWDLQLQJ 0XOWLSRODU &RPSRXQGV 8VLQJ WKH 3HUWXUEHG $QLVRWURSLF &KDLQ 7KHRU\

$,&K(-

&KDSPDQ:*-DFNVRQ**XEELQV. ( 3KDVH (TXLOLEULD RI $VVRFLDWLQJ )OXLGV &KDLQ 0ROHFXOHV ZLWK 0XOWLSOH %RQGLQJ

6LWHV0RO3K\V

&KDSPDQ : * *XEELQV .( -DFNVRQ * 5DGRV] 0 6$)7 (TXDWLRQ RI 6WDWH 6ROXWLRQ 0RGHO IRU $VVRFLDWLQJ )OXLGV

)OXLG3KDVH(TXLOLE

&KDSPDQ : * *XEELQV .( -DFNVRQ *5DGRV]01HZ5HIHUHQFH(TXDWLRQRI

6WDWH IRU $VVRFLDWLQJ /LTXLGV ,QG (QJ

&KHP 5HV

:HUWKHLP 0 6 )OXLGV ZLWK +LJKO\ 'LU HFWLRQDO $WWUDFWLYH )RUFHV 6WDWLVWLFDO

7KHUPRG\QDPLFV - 6WDW 3K\V

:HUWKHLP 0 6 )OXLGV ZLWK +LJKO\ 'LUHFWLRQDO $WWUDFWLYH )RUFHV 7KHU

PRG\QDPLF 3HUWXUEDWLRQ 7KHRU\ DQG

,QWHJUDO (TXDWLRQV - 6WDW 3K\V

:HUWKHLP 0 6 )OXLGV ZLWK +LJKO\ 'LUHFWLRQDO $WWUDFWLYH )RUFHV 0XOWLSOH

$WWUDFWLRQ 6LWHV - 6WDW 3K\V

:HUWKHLP 0 6 )OXLGV ZLWK +LJKO\

'LUHFWLRQDO$WWUDFWLYH)RUFHV-6WDW3K\V

:HUWKHLP06)OXLGVRI'LPHUL]LQJ+DUG 6SKHUHV DQG )OXLG 0L[WXUHV RI +DUG 6SKHUHV DQG 'LVSKHUHV- &KHP 3K\V

:HUWKHLP 0 6 7KHUPRG\QDPLF 3HUWXU EDWLRQ 7KHRU\ RI 3RO\PHUL]DWLRQ- &KHP

3K\V

&KHQ 6- 5DGRV] 0 'HQVLW\7XQHG 3RO\ROHILQ 3KDVH (TXLOLEULD %LQDU\ 6ROXWLRQV RI $OWHUQDWLQJ 3RO\ HWK\OHQH SURS\OHQH LQ 6XEFULWLFDO DQG 6XSHUFULWLFDO 3URS\OHQH%XWHQHDQG+H[HQH([SHUL

PHQWDO DQG )ORU\3DWWHUVRQ 0RGHO0DFUR

PROHFXOHV

%RNLV & 3 2UEH\ + &KHQ && 3URSHUO\ 0RGHO 3RO\PHU 3URFHVVHV&KHP

(QJ3URJ

.LUE\ & ) 0F+XJK 0 $ 3KDVH %HKDYLRURI3RO\PHUVLQ6XSHUFULWLFDO)OXLG

6ROYHQWV&KHP5HY

/DPEHUW606RQJ<3UDXVQLW]-0 (TXDWLRQVRI6WDWHIRU3RO\PHU6\VWHPVLQ 6HQJHUV - 9 .D\VHU 5 ) 3HWHUV &-:KLWH-U(GV+-(TXDWLRQVRI6WDWHIRU

)OXLGV DQG )OXLG 0L[WXUHV (OVHYLHU

$PVWHUGDP

- *URVV * 6DGRZVNL 3HUWXUEHG&KDLQ 6$)7 $Q (TXDWLRQ RI 6WDWH %DVHG RQ D 3HUWXUEDWLRQ 7KHRU\ IRU &KDLQ 0ROHFXOHV

,QG(QJ&KHP5HV

$ *LOO9LOOHJDV $ *DOLQGR 3- :KLWH KHDG6- 0LOOV*-DFNVRQ$1%XUJHVV 6WDWLVWLFDO $VVRFLDWLQJ )OXLG 7KHRU\ IRU &KDLQ 0ROHFXOHV ZLWK $WWUDFWLYH 3RWHQWLDOV

RI 9DULDEOH 5DQJH- &KHP 3K\V

±

%ODV ) - 9HJD / ) 7KHUPRG\QDPLF %HKDYLRURI+RPRQXFOHDUDQG+HWURQXFOHDU /HQQDUG-RQHV &KDLQV ZLWK $VVRFLDWLRQ

6LWHV IURP VLPXODWLRQ DQG 7KHRU\ 0RO

3K\V

.LVHOHY 6% (O\ -) &URVVRYHU 6$)7 (TXDWLRQ RI 6WDWH $SSOLFDWLRQ IRU 1RUPDO

$ONDQHV ,QG (QJ &KHP 5HV

.LVHOHY 6% (O\ - ) 6LPSOLILHG &URVVRYHU 6$)7 (TXDWLRQ RI 6DWH )OXLG

3KDVH(TXLOLE

.LVHOHY 6 % (O\ - ) $GLGKDUPD + 5DGRV]0$&URVVRYHU(TXDWLRQRI6WDWH

(19)

.LVHOHY6%(O\-)$EGXODJDWRY,0 0DJJH -:&URVVRYHU 6$)7 (TXDWLRQRI 6WDWH DQG 7KHUPRG\QDPLF 3URSHUWLHV RI

3URSDQRO ,QW- 7KHUPRSK\V

=KDQJ =< <DQJ -& /L <* 7KH 8VHRI6WDWLVWLFDO$VVRFLDWLQJ)OXLG7KHRU\ WR ,PSURYH 7KH %$&. (TXDWLRQ RI 6WDWH

)OXLG3KDVH(TXLOLE

1GLD\H 3 0 'DULYD & 9ODGLPLU -2OLYHLUD ): ,PSURYLQJ 6$)7 (TXDWLRQ RI 6WDWH %\ 8VLQJ DQ (IIHFWLYH :&$

6HJPHQW 'LDPHWHU )OXLG 3KDVH (TXLOLE

0LQ 6XQ <HRP -DHHRQ &KDQJ +ZD\RQJ .LP (TXDWLRQ RI 6WDWH %DVHG RQ 7KH 7KHUPRG\QDPLF 3HUWXUEDWLRQ 7KHRU\ RI 6XSHUFULWLFDO3RO\PHUL]DWLRQIRU$VVRFLDWLQJ

0ROHFXOHV DQG 3RO\PHUV )OXLG 3KDVH

(TXLOLE

+X=4<DQJ-&/L<*&URVVRYHU 6$)7%$&. (TXDWLRQ RI 6WDWH IRU 3XUH

&2 DQG+2)OXLG3KDVH(TXLOLE

0DOHNVKDK 9 $ 7DJKLNKDQL 9 5DPD]DQL6$$*KRWEL&$SSOLFDWLRQ RID1HZ6LPSOLILHG6$)7WR9/(6WXG\RI $VVRFLDWLQJ DQG 1RQ$VVRFLDWLQJ )OXLGV

)OXLG3KDVH(TXLOLE

)X<+6DQGOHU6,$6LPSOLILHG6$)7 (TXDWLRQ RI 6WDWH IRU $VVRFLDWLQJ &RP SRXQGVDQG0L[WXUHV,QG(QJ&KHP5HV

+XDQJ6+5DGRV]0(TXDWLRQRI6WDWH IRU 6PDOO /DUJH 3RO\GLVSHUVH DQG $V VRFLDWLQJ 0ROHFXOHV,QG (QJ &KHP 5HV

+XDQJ65DGRV]0(TXDWLRQRI6WDWHIRU 6PDOO /DUJH 3RO\GLVSHUVH DQG $V VRFLDWLQJ 0ROHFXOHV([WHQVLRQ WR )OXLG

0L[WXUHV,QG (QJ &KHP 5HV

:LHVPHW 9 :HLGQHU ( %HKPH 6 6DGRZVNL * $UOW : 0HDVXUHPHQW DQG 0RGHOLQJ RI +LJK 3UHVVXUH 3KDVH (TXLOLEULD LQ 7KH 6\VWHPV 3RO\HWK\

OHQHJO\FRO 3(*3URSDQH 3(*1LWURJHQ DQG 3(*&DUERQ 'LR[LGH - 6XSHUFULWLFDO

)OXLGV

5RGJHUV 3 $ 3UHVVXUH9ROXPH7HPSHUD WXUH5HODWLRQVKLSVIRU3RO\PHULF/LTXLGV$ 5HYLHZ RI (TXDWLRQV RI 6WDWH DQG 7KHLU &KDUDFWHULVWLF 3DUDPHWHUV IRU 3RO\PHUV

-$SSO3RO\P6FL

:ROIDUWK & 9DSRU/LTXLG (TXLOLEULXP

'DWDRI%LQDU\3RO\PHU6ROXWLRQV(OVHYLHU 3XEOLVKLQJ&RPSDQ\

%RQGL-3K\VLFDO3URSHUWLHVRI0ROHFXODU

&U\VWDOV /LTXLGV DQG *ODVVHV - :LOH\ 6RQV1HZ<RUN

'DQQHU ,3 +LJK 06 +DQGERRN RI

3RO\PHU6ROXWLRQ7KHUPRG\QDPLFV 'HSDUW

PHQW RI &KHPLFDO (QJLQHHULQJ 7KH 3HQ QV\OYDQLD6WDWH8QLYHUVLW\8QLYHUVLW\3DUN 3$

=ROOHU 3 :DOVK '6WDQGDUG 3UHVVXUH

References

Related documents

FIA Masters Historic Sports Cars.

The drop in the technical change indicates that Saudi IPO firms are unable to produce more output (generate more net income) with a given vector of input quantities (total assets

The same model, but using WTI as the oil price series indicates the presence of cointegration for Brazil’s Real, the Euro, the Mexican Peso, the Nigerian Naira and the UK Pound..

Three overarching themes generated from the analysis of data are, “developing a mentor-student relationship,” “keeping your mentor sweet” and “the role of the mentor

as they try to complete their program and develop a sense of what the education system can provide them. This section has used elements of pastoral power to make sense of the

While listening to my JMM duo improvisation, I noted some polarities: Gypsy vs gadjé; caravans vs houses; nomadic vs sedentary; bands vs orchestras; playing by ear vs reading;

This study yielded 14 NT-EPAs and 52 required types of knowledge, skills and attitudes (KSAs) that nurses should possess when executing telehealth activities. Nurses can use

And finally, as in all business decisions, take every opportunity to reduce the risk – whether real or perceived - of moving to outsourced NOC and Service Desk: check out your